feat: deprecate Array.mkArray in favour of Array.replicate

This PR fixes a bug introduced in #7589, causing pretty printed
structure instances to not be hoverable in the Infoview.

This was caused by a choice node being introduced, since `{ $fields,* }`
is ambiguous syntax.

.github/workflows/awaiting-mathlib.yml

@@ -0,0 +1,20 @@
+name: Check awaiting-mathlib label
+
+on:
+  merge_group:
+  pull_request:
+    types: [opened, synchronize, reopened, labeled, unlabeled]
+
+jobs:
+  check-awaiting-mathlib:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Check awaiting-mathlib label
+        if: github.event_name == 'pull_request'
+        uses: actions/github-script@v7
+        with:
+          script: |
+            const { labels } = context.payload.pull_request;
+            if (labels.some(label => label.name == "awaiting-mathlib") && !labels.some(label => label.name == "builds-mathlib")) {
+              core.setFailed('PR is marked "awaiting-mathlib" but "builds-mathlib" label has not been applied yet by the bot');
+            }

.github/workflows/build-template.yml

@@ -0,0 +1,246 @@
+name: build-template
+on:
+  workflow_call:
+    inputs:
+      check-level:
+        type: string
+        required: true
+      config:
+        type: string
+        required: true
+      nightly:
+        type: string
+        required: true
+      LEAN_VERSION_MAJOR:
+        type: string
+        required: true
+      LEAN_VERSION_MINOR:
+        type: string
+        required: true
+      LEAN_VERSION_PATCH:
+        type: string
+        required: true
+      LEAN_SPECIAL_VERSION_DESC:
+        type: string
+        required: true
+      RELEASE_TAG:
+        type: string
+        required: true
+
+jobs:
+  build:
+    if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
+    strategy:
+      matrix:
+        include: ${{fromJson(inputs.config)}}
+      # complete all jobs
+      fail-fast: false
+    runs-on: ${{ matrix.os }}
+    defaults:
+      run:
+        shell: ${{ matrix.shell || 'nix develop -c bash -euxo pipefail {0}' }}
+    name: ${{ matrix.name }}
+    env:
+      # must be inside workspace
+      CCACHE_DIR: ${{ github.workspace }}/.ccache
+      CCACHE_COMPRESS: true
+      # current cache limit
+      CCACHE_MAXSIZE: 200M
+      # squelch error message about missing nixpkgs channel
+      NIX_BUILD_SHELL: bash
+      LSAN_OPTIONS: max_leaks=10
+      # somehow MinGW clang64 (or cmake?) defaults to `g++` even though it doesn't exist
+      CXX: c++
+      MACOSX_DEPLOYMENT_TARGET: 10.15
+    steps:
+      - name: Install Nix
+        uses: DeterminateSystems/nix-installer-action@main
+        if: runner.os == 'Linux' && !matrix.cmultilib
+      - name: Install MSYS2
+        uses: msys2/setup-msys2@v2
+        with:
+          msystem: clang64
+          # `:` means do not prefix with msystem
+          pacboy: "make: python: cmake clang ccache gmp libuv git: zip: unzip: diffutils: binutils: tree: zstd tar:"
+        if: runner.os == 'Windows'
+      - name: Install Brew Packages
+        run: |
+          brew install ccache tree zstd coreutils gmp libuv
+        if: runner.os == 'macOS'
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          # the default is to use a virtual merge commit between the PR and master: just use the PR
+          ref: ${{ github.event.pull_request.head.sha }}
+      - name: Open Nix shell once
+        run: true
+        if: runner.os == 'Linux'
+      # Do check out some CI-relevant files from virtual merge commit to accommodate CI changes on
+      # master (as the workflow files themselves are always taken from the merge)
+      # (needs to be after "Install *" to use the right shell)
+      - name: CI Merge Checkout
+        run: |
+          git fetch --depth=1 origin ${{ github.sha }}
+          git checkout FETCH_HEAD flake.nix flake.lock
+        if: github.event_name == 'pull_request'
+      # (needs to be after "Checkout" so files don't get overridden)
+      - name: Setup emsdk
+        uses: mymindstorm/setup-emsdk@v14
+        with:
+          version: 3.1.44
+          actions-cache-folder: emsdk
+        if: matrix.wasm
+      - name: Install 32bit c libs
+        run: |
+          sudo dpkg --add-architecture i386
+          sudo apt-get update
+          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386 pkgconf:i386
+        if: matrix.cmultilib
+      - name: Cache
+        if: matrix.name != 'Linux Lake'
+        uses: actions/cache@v4
+        with:
+          path: |
+            .ccache
+          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
+          # fall back to (latest) previous cache
+          restore-keys: |
+            ${{ matrix.name }}-build-v3
+          save-always: true
+      - name: Cache
+        if: matrix.name == 'Linux Lake'
+        uses: actions/cache@v4
+        with:
+          path: |
+            .ccache
+            build/stage1/**/*.trace
+            build/stage1/**/*.olean
+            build/stage1/**/*.ilean
+            build/stage1/**/*.c
+            build/stage1/**/*.c.o*
+          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
+          # fall back to (latest) previous cache
+          restore-keys: |
+            ${{ matrix.name }}-build-v3
+          save-always: true
+      # open nix-shell once for initial setup
+      - name: Setup
+        run: |
+          ccache --zero-stats
+        if: runner.os == 'Linux'
+      - name: Set up NPROC
+        run: |
+          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
+      - name: Build
+        run: |
+          ulimit -c unlimited  # coredumps
+          [ -d build ] || mkdir build
+          cd build
+          # arguments passed to `cmake`
+          # this also enables githash embedding into stage 1 library
+          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
+          OPTIONS+=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
+          if [[ -n '${{ matrix.cross_target }}' ]]; then
+            # used by `prepare-llvm`
+            export EXTRA_FLAGS=--target=${{ matrix.cross_target }}
+            OPTIONS+=(-DLEAN_PLATFORM_TARGET=${{ matrix.cross_target }})
+          fi
+          if [[ -n '${{ matrix.prepare-llvm }}' ]]; then
+            wget -q ${{ matrix.llvm-url }}
+            PREPARE="$(${{ matrix.prepare-llvm }})"
+            eval "OPTIONS+=($PREPARE)"
+          fi
+          if [[ -n '${{ matrix.release }}' && -n '${{ inputs.nightly }}' ]]; then
+            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ inputs.nightly }})
+          fi
+          if [[ -n '${{ matrix.release }}' && -n '${{ inputs.RELEASE_TAG }}' ]]; then
+            OPTIONS+=(-DLEAN_VERSION_MAJOR=${{ inputs.LEAN_VERSION_MAJOR }})
+            OPTIONS+=(-DLEAN_VERSION_MINOR=${{ inputs.LEAN_VERSION_MINOR }})
+            OPTIONS+=(-DLEAN_VERSION_PATCH=${{ inputs.LEAN_VERSION_PATCH }})
+            OPTIONS+=(-DLEAN_VERSION_IS_RELEASE=1)
+            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ inputs.LEAN_SPECIAL_VERSION_DESC }})
+          fi
+          # contortion to support empty OPTIONS with old macOS bash
+          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
+          time make -j$NPROC
+      - name: Install
+        run: |
+          make -C build install
+      - name: Check Binaries
+        run: ${{ matrix.binary-check }} lean-*/bin/* || true
+      - name: Count binary symbols
+        run: |
+          for f in lean-*/bin/*; do
+            echo "$f: $(nm $f | grep " T " | wc -l) exported symbols"
+          done
+        if: matrix.name == 'Windows'
+      - name: List Install Tree
+        run: |
+          # omit contents of Init/, ...
+          tree --du -h lean-*-* | grep -E ' (Init|Lean|Lake|LICENSE|[a-z])'
+      - name: Pack
+        run: |
+          dir=$(echo lean-*-*)
+          mkdir pack
+          # high-compression tar.zst + zip for release, fast tar.zst otherwise
+          if [[ '${{ startsWith(github.ref, 'refs/tags/') && matrix.release }}' == true || -n '${{ inputs.nightly }}' || -n '${{ inputs.RELEASE_TAG }}' ]]; then
+            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -19 -o pack/$dir.tar.zst
+            zip -rq pack/$dir.zip $dir
+          else
+            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
+          fi
+      - uses: actions/upload-artifact@v4
+        if: matrix.release
+        with:
+          name: build-${{ matrix.name }}
+          path: pack/*
+      - name: Lean stats
+        run: |
+          build/stage1/bin/lean --stats src/Lean.lean
+        if: ${{ !matrix.cross }}
+      - name: Test
+        id: test
+        run: |
+          ulimit -c unlimited  # coredumps
+          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
+        if: (matrix.wasm || !matrix.cross) && inputs.check-level >= 1
+      - name: Test Summary
+        uses: test-summary/action@v2
+        with:
+          paths: build/stage1/test-results.xml
+        # prefix `if` above with `always` so it's run even if tests failed
+        if: always() && steps.test.conclusion != 'skipped'
+      - name: Check Test Binary
+        run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
+        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
+      - name: Build Stage 2
+        run: |
+          make -C build -j$NPROC stage2
+        if: matrix.test-speedcenter
+      - name: Check Stage 3
+        run: |
+          make -C build -j$NPROC check-stage3
+        if: matrix.test-speedcenter
+      - name: Test Speedcenter Benchmarks
+        run: |
+          # Necessary for some timing metrics but does not work on Namespace runners
+          # and we just want to test that the benchmarks run at all here
+          #echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
+          export BUILD=$PWD/build PATH=$PWD/build/stage1/bin:$PATH
+          cd tests/bench
+          nix shell .#temci -c temci exec --config speedcenter.yaml --included_blocks fast --runs 1
+        if: matrix.test-speedcenter
+      - name: Check rebootstrap
+        run: |
+          # clean rebuild in case of Makefile changes
+          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
+        if: matrix.name == 'Linux' && inputs.check-level >= 1
+      - name: CCache stats
+        run: ccache -s
+      - name: Show stacktrace for coredumps
+        if: failure() && runner.os == 'Linux'
+        run: |
+          for c in $(find . -name core); do
+            progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
+            echo bt | $GDB/bin/gdb -q $progbin $c || true
+          done

.github/workflows/check-stage0.yml

@@ -20,9 +20,7 @@ jobs:
 
     - name: Identify stage0 changes
       run: |
-        git diff "${BASE:-HEAD^}..HEAD" --name-only -- stage0 |
-          grep -v -x -F $'stage0/src/stdlib_flags.h\nstage0/src/lean.mk.in' \
-          > "$RUNNER_TEMP/stage0" || true
+        git diff "${BASE:-HEAD^}..HEAD" --name-only -- stage0/stdlib > "$RUNNER_TEMP/stage0" || true
         if test -s "$RUNNER_TEMP/stage0"
         then
           echo "CHANGES=yes" >> "$GITHUB_ENV"

.github/workflows/ci.yml

@@ -36,7 +36,9 @@ jobs:
       # 2: PRs with `release-ci` label, releases (incl. nightlies)
       check-level: ${{ steps.set-level.outputs.check-level }}
       # The build matrix, dynamically generated here
-      matrix: ${{ steps.set-matrix.outputs.result }}
+      matrix: ${{ steps.set-matrix.outputs.matrix }}
+      # secondary build jobs that should not block the CI success/merge queue
+      matrix-secondary: ${{ steps.set-matrix.outputs.matrix-secondary }}
       # Should we make a nightly release? If so, this output contains the lean version string, else it is empty
       nightly: ${{ steps.set-nightly.outputs.nightly }}
       # Should this be the CI for a tagged release?
@@ -135,9 +137,9 @@ jobs:
             console.log(`level: ${level}`);
             // use large runners where available (original repo)
             let large = ${{ github.repository == 'leanprover/lean4' }};
+            const isPr = "${{ github.event_name }}" == "pull_request";
             let matrix = [
               {
-                // portable release build: use channel with older glibc (2.27)
                 "name": "Linux LLVM",
                 "os": "ubuntu-latest",
                 "release": false,
@@ -152,6 +154,7 @@ jobs:
                 "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
               },
               {
+                // portable release build: use channel with older glibc (2.26)
                 "name": "Linux release",
                 "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
                 "release": true,
@@ -163,6 +166,14 @@ jobs:
                 // foreign code may be linked against more recent glibc
                 "CTEST_OPTIONS": "-E 'foreign'"
               },
+              {
+                "name": "Linux Lake",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
+                // just a secondary PR build job for now
+                "check-level": isPr ? 0 : 3,
+                "secondary": true,
+                "CMAKE_OPTIONS": "-DUSE_LAKE=ON"
+              },
               {
                 "name": "Linux",
                 "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
@@ -175,8 +186,8 @@ jobs:
                 "os": "ubuntu-latest",
                 "check-level": 2,
                 "CMAKE_PRESET": "debug",
-                // exclude seriously slow tests
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest|bv_bitblast_stress'"
+                // exclude seriously slow/stackoverflowing tests
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest|bv_bitblast_stress|3807'"
               },
               // TODO: suddenly started failing in CI
               /*{
@@ -204,12 +215,18 @@ jobs:
                 "os": "macos-14",
                 "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
                 "release": true,
-                "check-level": 0,
                 "shell": "bash -euxo pipefail {0}",
                 "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst",
                 "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
                 "binary-check": "otool -L",
-                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
+                "tar": "gtar", // https://github.com/actions/runner-images/issues/2619
+                // Special handling for MacOS aarch64, we want:
+                // 1. To run it in PRs so Mac devs get PR toolchains (so secondary is sufficient)
+                // 2. To skip it in merge queues as it takes longer than the Linux build and adds
+                //    little value in the merge queue
+                // 3. To run it in release (obviously)
+                "check-level": isPr ? 0 : 2,
+                "secondary": isPr,
               },
               {
                 "name": "Windows",
@@ -238,7 +255,7 @@ jobs:
                 "name": "Linux 32bit",
                 "os": "ubuntu-latest",
                 // Use 32bit on stage0 and stage1 to keep oleans compatible
-                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/",
+                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DPKG_CONFIG_EXECUTABLE=/usr/bin/i386-linux-gnu-pkg-config",
                 "cmultilib": true,
                 "release": true,
                 "check-level": 2,
@@ -260,196 +277,41 @@ jobs:
               //   "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean|leanruntest_tempfile.lean\\.|leanruntest_libuv\\.lean\""
               // }
             ];
-            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
-            return matrix.filter((job) => level >= job["check-level"])
+            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
+            matrix = matrix.filter((job) => level >= job["check-level"]);
+            core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));
+            core.setOutput('matrix-secondary', matrix.filter((job) => job["secondary"]));
 
   build:
-    needs: [configure]
     if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
-    strategy:
-      matrix:
-        include: ${{fromJson(needs.configure.outputs.matrix)}}
-      # complete all jobs
-      fail-fast: false
-    runs-on: ${{ matrix.os }}
-    defaults:
-      run:
-        shell: ${{ matrix.shell || 'nix develop -c bash -euxo pipefail {0}' }}
-    name: ${{ matrix.name }}
-    env:
-      # must be inside workspace
-      CCACHE_DIR: ${{ github.workspace }}/.ccache
-      CCACHE_COMPRESS: true
-      # current cache limit
-      CCACHE_MAXSIZE: 200M
-      # squelch error message about missing nixpkgs channel
-      NIX_BUILD_SHELL: bash
-      LSAN_OPTIONS: max_leaks=10
-      # somehow MinGW clang64 (or cmake?) defaults to `g++` even though it doesn't exist
-      CXX: c++
-      MACOSX_DEPLOYMENT_TARGET: 10.15
-    steps:
-      - name: Install Nix
-        uses: DeterminateSystems/nix-installer-action@main
-        if: runner.os == 'Linux' && !matrix.cmultilib
-      - name: Install MSYS2
-        uses: msys2/setup-msys2@v2
-        with:
-          msystem: clang64
-          # `:` means do not prefix with msystem
-          pacboy: "make: python: cmake clang ccache gmp libuv git: zip: unzip: diffutils: binutils: tree: zstd tar:"
-        if: runner.os == 'Windows'
-      - name: Install Brew Packages
-        run: |
-          brew install ccache tree zstd coreutils gmp libuv
-        if: runner.os == 'macOS'
-      - name: Checkout
-        uses: actions/checkout@v4
-        with:
-          # the default is to use a virtual merge commit between the PR and master: just use the PR
-          ref: ${{ github.event.pull_request.head.sha }}
-      # Do check out some CI-relevant files from virtual merge commit to accommodate CI changes on
-      # master (as the workflow files themselves are always taken from the merge)
-      # (needs to be after "Install *" to use the right shell)
-      - name: CI Merge Checkout
-        run: |
-          git fetch --depth=1 origin ${{ github.sha }}
-          git checkout FETCH_HEAD flake.nix flake.lock
-        if: github.event_name == 'pull_request'
-      # (needs to be after "Checkout" so files don't get overridden)
-      - name: Setup emsdk
-        uses: mymindstorm/setup-emsdk@v14
-        with:
-          version: 3.1.44
-          actions-cache-folder: emsdk
-        if: matrix.wasm
-      - name: Install 32bit c libs
-        run: |
-          sudo dpkg --add-architecture i386
-          sudo apt-get update
-          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386
-        if: matrix.cmultilib
-      - name: Cache
-        uses: actions/cache@v4
-        with:
-          path: .ccache
-          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
-          # fall back to (latest) previous cache
-          restore-keys: |
-            ${{ matrix.name }}-build-v3
-          save-always: true
-      # open nix-shell once for initial setup
-      - name: Setup
-        run: |
-          ccache --zero-stats
-        if: runner.os == 'Linux'
-      - name: Set up NPROC
-        run: |
-          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
-      - name: Build
-        run: |
-          mkdir build
-          cd build
-          # arguments passed to `cmake`
-          # this also enables githash embedding into stage 1 library
-          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
-          OPTIONS+=(-DLEAN_EXTRA_MAKE_OPTS=-DwarningAsError=true)
-          if [[ -n '${{ matrix.cross_target }}' ]]; then
-            # used by `prepare-llvm`
-            export EXTRA_FLAGS=--target=${{ matrix.cross_target }}
-            OPTIONS+=(-DLEAN_PLATFORM_TARGET=${{ matrix.cross_target }})
-          fi
-          if [[ -n '${{ matrix.prepare-llvm }}' ]]; then
-            wget -q ${{ matrix.llvm-url }}
-            PREPARE="$(${{ matrix.prepare-llvm }})"
-            eval "OPTIONS+=($PREPARE)"
-          fi
-          if [[ -n '${{ matrix.release }}' && -n '${{ needs.configure.outputs.nightly }}' ]]; then
-            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.nightly }})
-          fi
-          if [[ -n '${{ matrix.release }}' && -n '${{ needs.configure.outputs.RELEASE_TAG }}' ]]; then
-            OPTIONS+=(-DLEAN_VERSION_MAJOR=${{ needs.configure.outputs.LEAN_VERSION_MAJOR }})
-            OPTIONS+=(-DLEAN_VERSION_MINOR=${{ needs.configure.outputs.LEAN_VERSION_MINOR }})
-            OPTIONS+=(-DLEAN_VERSION_PATCH=${{ needs.configure.outputs.LEAN_VERSION_PATCH }})
-            OPTIONS+=(-DLEAN_VERSION_IS_RELEASE=1)
-            OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }})
-          fi
-          # contortion to support empty OPTIONS with old macOS bash
-          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
-          time make -j$NPROC
-      - name: Install
-        run: |
-          make -C build install
-      - name: Check Binaries
-        run: ${{ matrix.binary-check }} lean-*/bin/* || true
-      - name: Count binary symbols
-        run: |
-          for f in lean-*/bin/*; do
-            echo "$f: $(nm $f | grep " T " | wc -l) exported symbols"
-          done
-        if: matrix.name == 'Windows'
-      - name: List Install Tree
-        run: |
-          # omit contents of Init/, ...
-          tree --du -h lean-*-* | grep -E ' (Init|Lean|Lake|LICENSE|[a-z])'
-      - name: Pack
-        run: |
-          dir=$(echo lean-*-*)
-          mkdir pack
-          # high-compression tar.zst + zip for release, fast tar.zst otherwise
-          if [[ '${{ startsWith(github.ref, 'refs/tags/') && matrix.release }}' == true || -n '${{ needs.configure.outputs.nightly }}' || -n '${{ needs.configure.outputs.RELEASE_TAG }}' ]]; then
-            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -19 -o pack/$dir.tar.zst
-            zip -rq pack/$dir.zip $dir
-          else
-            ${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
-          fi
-      - uses: actions/upload-artifact@v4
-        if: matrix.release
-        with:
-          name: build-${{ matrix.name }}
-          path: pack/*
-      - name: Lean stats
-        run: |
-          build/stage1/bin/lean --stats src/Lean.lean
-        if: ${{ !matrix.cross }}
-      - name: Test
-        id: test
-        run: |
-          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
-        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.check-level >= 1
-      - name: Test Summary
-        uses: test-summary/action@v2
-        with:
-          paths: build/stage1/test-results.xml
-        # prefix `if` above with `always` so it's run even if tests failed
-        if: always() && steps.test.conclusion != 'skipped'
-      - name: Check Test Binary
-        run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
-        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
-      - name: Build Stage 2
-        run: |
-          make -C build -j$NPROC stage2
-        if: matrix.test-speedcenter
-      - name: Check Stage 3
-        run: |
-          make -C build -j$NPROC check-stage3
-        if: matrix.test-speedcenter
-      - name: Test Speedcenter Benchmarks
-        run: |
-          # Necessary for some timing metrics but does not work on Namespace runners
-          # and we just want to test that the benchmarks run at all here
-          #echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
-          export BUILD=$PWD/build PATH=$PWD/build/stage1/bin:$PATH
-          cd tests/bench
-          nix shell .#temci -c temci exec --config speedcenter.yaml --included_blocks fast --runs 1
-        if: matrix.test-speedcenter
-      - name: Check rebootstrap
-        run: |
-          # clean rebuild in case of Makefile changes
-          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
-        if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
-      - name: CCache stats
-        run: ccache -s
+    needs: [configure]
+    uses: ./.github/workflows/build-template.yml
+    with:
+      config: ${{needs.configure.outputs.matrix}}
+      check-level: ${{ needs.configure.outputs.check-level }}
+      nightly: ${{ needs.configure.outputs.nightly }}
+      LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
+      LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
+      LEAN_VERSION_PATCH: ${{ needs.configure.outputs.LEAN_VERSION_PATCH }}
+      LEAN_SPECIAL_VERSION_DESC: ${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }}
+      RELEASE_TAG: ${{ needs.configure.outputs.RELEASE_TAG }}
+    secrets: inherit
+
+  # build jobs that should not be considered by `all-done` below
+  build-secondary:
+    needs: [configure]
+    if: needs.configure.outputs.matrix-secondary != '[]'
+    uses: ./.github/workflows/build-template.yml
+    with:
+      config: ${{needs.configure.outputs.matrix-secondary}}
+      check-level: ${{ needs.configure.outputs.check-level }}
+      nightly: ${{ needs.configure.outputs.nightly }}
+      LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
+      LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
+      LEAN_VERSION_PATCH: ${{ needs.configure.outputs.LEAN_VERSION_PATCH }}
+      LEAN_SPECIAL_VERSION_DESC: ${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }}
+      RELEASE_TAG: ${{ needs.configure.outputs.RELEASE_TAG }}
+    secrets: inherit
 
   # This job collects results from all the matrix jobs
   # This can be made the "required" job, instead of listing each

.github/workflows/pr-release.yml

@@ -34,7 +34,7 @@ jobs:
       - name: Download artifact from the previous workflow.
         if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
         id: download-artifact
-        uses: dawidd6/action-download-artifact@v7 # https://github.com/marketplace/actions/download-workflow-artifact
+        uses: dawidd6/action-download-artifact@v9 # https://github.com/marketplace/actions/download-workflow-artifact
         with:
           run_id: ${{ github.event.workflow_run.id }}
           path: artifacts
@@ -155,6 +155,20 @@ jobs:
           fi
 
           if [[ -n "$MESSAGE" ]]; then
+            # Check if force-mathlib-ci label is present
+            LABELS="$(curl --retry 3 --location --silent \
+                          -H "Authorization: token ${{ secrets.MATHLIB4_COMMENT_BOT }}" \
+                          -H "Accept: application/vnd.github.v3+json" \
+                          "https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
+                          | jq -r '.[].name')"
+            
+            if echo "$LABELS" | grep -q "^force-mathlib-ci$"; then
+              echo "force-mathlib-ci label detected, forcing CI despite issues"
+              MESSAGE="Forcing Mathlib CI because the \`force-mathlib-ci\` label is present, despite problem: $MESSAGE"
+              FORCE_CI=true
+            else
+              MESSAGE="$MESSAGE You can force Mathlib CI using the \`force-mathlib-ci\` label."
+            fi
 
             echo "Checking existing messages"
 
@@ -201,7 +215,12 @@ jobs:
             else
               echo "The message already exists in the comment body."
             fi
-            echo "mathlib_ready=false" >> "$GITHUB_OUTPUT"
+
+            if [[ "$FORCE_CI" == "true" ]]; then
+              echo "mathlib_ready=true" >> "$GITHUB_OUTPUT"
+            else
+              echo "mathlib_ready=false" >> "$GITHUB_OUTPUT"
+            fi
           else
             echo "mathlib_ready=true" >> "$GITHUB_OUTPUT"
           fi
@@ -252,7 +271,7 @@ jobs:
           if git ls-remote --heads --tags --exit-code origin "nightly-testing-${MOST_RECENT_NIGHTLY}" >/dev/null; then
             BASE="nightly-testing-${MOST_RECENT_NIGHTLY}"
           else
-            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
+            echo "Couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
             BASE=nightly-testing
           fi
 
@@ -316,7 +335,7 @@ jobs:
           if git ls-remote --heads --tags --exit-code origin "nightly-testing-${MOST_RECENT_NIGHTLY}" >/dev/null; then
             BASE="nightly-testing-${MOST_RECENT_NIGHTLY}"
           else
-            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' branch at Mathlib. Falling back to 'nightly-testing'."
+            echo "Couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' branch at Mathlib. Falling back to 'nightly-testing'."
             BASE=nightly-testing
           fi
 

CMakeLists.txt

@@ -15,7 +15,7 @@ foreach(var ${vars})
       # must forward options that generate incompatible .olean format
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
     endif()
-    if("${var}" MATCHES "LLVM*")
+    if("${var}" MATCHES "LLVM*|PKG_CONFIG|USE_LAKE")
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
     endif()
   elseif(("${var}" MATCHES "CMAKE_.*") AND NOT ("${var}" MATCHES "CMAKE_BUILD_TYPE") AND NOT ("${var}" MATCHES "CMAKE_HOME_DIRECTORY"))
@@ -44,10 +44,11 @@ if (NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
     if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
       string(APPEND CADICAL_CXXFLAGS " -DNUNLOCKED")
     endif()
+    string(APPEND CADICAL_CXXFLAGS " -DNCLOSEFROM")
     ExternalProject_add(cadical
       PREFIX cadical
       GIT_REPOSITORY https://github.com/arminbiere/cadical
-      GIT_TAG rel-1.9.5
+      GIT_TAG rel-2.1.2
       CONFIGURE_COMMAND ""
       # https://github.com/arminbiere/cadical/blob/master/BUILD.md#manual-build
       BUILD_COMMAND $(MAKE) -f ${CMAKE_SOURCE_DIR}/src/cadical.mk CMAKE_EXECUTABLE_SUFFIX=${CMAKE_EXECUTABLE_SUFFIX} CXX=${CADICAL_CXX} CXXFLAGS=${CADICAL_CXXFLAGS}
@@ -64,8 +65,8 @@ ExternalProject_add(stage0
   SOURCE_SUBDIR src
   BINARY_DIR stage0
   # do not rebuild stage0 when git hash changes; it's not from this commit anyway
-  # (however, `CHECK_OLEAN_VERSION=ON` in CI will override this as we need to
-  # embed the githash into the stage 1 library built by stage 0)
+  # (however, CI will override this as we need to embed the githash into the stage 1 library built
+  # by stage 0)
   CMAKE_ARGS -DSTAGE=0 -DUSE_GITHASH=OFF ${PLATFORM_ARGS} ${STAGE0_ARGS}
   BUILD_ALWAYS ON  # cmake doesn't auto-detect changes without a download method
   INSTALL_COMMAND ""  # skip install
@@ -79,6 +80,7 @@ ExternalProject_add(stage1
   BUILD_ALWAYS ON
   INSTALL_COMMAND ""
   DEPENDS stage0
+  STEP_TARGETS configure
 )
 ExternalProject_add(stage2
   SOURCE_DIR "${LEAN_SOURCE_DIR}"

CMakePresets.json

@@ -26,7 +26,7 @@
       "displayName": "Sanitize build config",
       "cacheVariables": {
         "LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined",
-        "LEANC_EXTRA_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
+        "LEANC_EXTRA_CC_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
         "SMALL_ALLOCATOR": "OFF",
         "BSYMBOLIC": "OFF"
       },

doc/declarations.md

@@ -590,9 +590,9 @@ This table should be read as follows:
  * No other proofs were attempted, either because the parameter has a type without a non-trivial ``WellFounded`` instance (parameter 3), or because it is already clear that no decreasing measure can be found.
 
 
-Lean will print the termination argument it found if ``set_option showInferredTerminationBy true`` is set.
+Lean will print the termination measure it found if ``set_option showInferredTerminationBy true`` is set.
 
-If Lean does not find the termination argument, or if you want to be explicit, you can append a `termination_by` clause to the function definition, after the function's body, but before the `where` clause if present. It is of the form
+If Lean does not find the termination measure, or if you want to be explicit, you can append a `termination_by` clause to the function definition, after the function's body, but before the `where` clause if present. It is of the form
 ```
 termination_by e
 ```
@@ -672,7 +672,7 @@ def num_consts_lst : List Term → Nat
 end
 ```
 
-In a set of mutually recursive function, either all or no functions must have an explicit termination argument (``termination_by``). A change of the default termination tactic (``decreasing_by``) only affects the proofs about the recursive calls of that function, not the other functions in the group.
+In a set of mutually recursive function, either all or no functions must have an explicit termination measure (``termination_by``). A change of the default termination tactic (``decreasing_by``) only affects the proofs about the recursive calls of that function, not the other functions in the group.
 
 ```
 mutual
@@ -764,11 +764,12 @@ Structures and Records
 The ``structure`` command in Lean is used to define an inductive data type with a single constructor and to define its projections at the same time. The syntax is as follows:
 
 ```
-structure Foo (a : α) extends Bar, Baz : Sort u :=
+structure Foo (a : α) : Sort u extends Bar, Baz :=
 constructor :: (field₁ : β₁) ... (fieldₙ : βₙ)
 ```
 
-Here ``(a : α)`` is a telescope, that is, the parameters to the inductive definition. The name ``constructor`` followed by the double colon is optional; if it is not present, the name ``mk`` is used by default. The keyword ``extends`` followed by a list of previously defined structures is also optional; if it is present, an instance of each of these structures is included among the fields to ``Foo``, and the types ``βᵢ`` can refer to their fields as well. The output type, ``Sort u``, can be omitted, in which case Lean infers to smallest non-``Prop`` sort possible. Finally, ``(field₁ : β₁) ... (fieldₙ : βₙ)`` is a telescope relative to ``(a : α)`` and the fields in ``bar`` and ``baz``.
+Here ``(a : α)`` is a telescope, that is, the parameters to the inductive definition. The name ``constructor`` followed by the double colon is optional; if it is not present, the name ``mk`` is used by default. The keyword ``extends`` followed by a list of previously defined structures is also optional; if it is present, an instance of each of these structures is included among the fields to ``Foo``, and the types ``βᵢ`` can refer to their fields as well. The output type, ``Sort u``, can be omitted, in which case Lean infers to smallest non-``Prop`` sort possible (unless all the fields are ``Prop``, in which case it infers ``Prop``).
+Finally, ``(field₁ : β₁) ... (fieldₙ : βₙ)`` is a telescope relative to ``(a : α)`` and the fields in ``bar`` and ``baz``.
 
 The declaration above is syntactic sugar for an inductive type declaration, and so results in the addition of the following constants to the environment:
 

doc/dev/commit_convention.md

@@ -33,6 +33,9 @@ Format of the commit message
  - chore (maintain, ex: travis-ci)
  - perf (performance improvement, optimization, ...)
 
+Every `feat` or `fix` commit must have a `changelog-*` label, and a commit message
+beginning with "This PR " that will be included in the changelog.
+
 ``<subject>`` has the following constraints:
 
  - use imperative, present tense: "change" not "changed" nor "changes"
@@ -44,6 +47,7 @@ Format of the commit message
  - just as in ``<subject>``, use imperative, present tense
  - includes motivation for the change and contrasts with previous
    behavior
+ - If a `changelog-*` label is present, the body must begin with "This PR ".
 
 ``<footer>`` is optional and may contain two items:
 
@@ -60,17 +64,21 @@ Examples
 
 fix: add declarations for operator<<(std::ostream&, expr const&) and operator<<(std::ostream&, context const&) in the kernel
 
+This PR adds declarations `operator<<` for raw printing.
 The actual implementation of these two operators is outside of the
-kernel. They are implemented in the file 'library/printer.cpp'. We
-declare them in the kernel to prevent the following problem. Suppose
-there is a file 'foo.cpp' that does not include 'library/printer.h',
-but contains
+kernel. They are implemented in the file 'library/printer.cpp'.
 
-    expr a;
-    ...
-    std::cout << a << "\n";
-    ...
+We declare them in the kernel to prevent the following problem.
+Suppose there is a file 'foo.cpp' that does not include 'library/printer.h',
+but contains
+```cpp
+expr a;
+...
+std::cout << a << "\n";
+...
+```
 
 The compiler does not generate an error message. It silently uses the
 operator bool() to coerce the expression into a Boolean. This produces
 counter-intuitive behavior, and may confuse developers.
+

doc/dev/ffi.md

@@ -49,8 +49,9 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
   is represented by the representation of that parameter's type.
 
   For example, `{ x : α // p }`, the `Subtype` structure of a value of type `α` and an irrelevant proof, is represented by the representation of `α`.
-* `Nat` is represented by `lean_object *`.
-  Its runtime value is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number (`lean_box`/`lean_unbox`).
+  Similarly, the signed integer types `Int8`, ..., `Int64`, `ISize` are also represented by the unsigned C types `uint8_t`, ..., `uint64_t`, `size_t`, respectively, because they have a trivial structure.
+* `Nat` and `Int` are represented by `lean_object *`.
+  Their runtime values is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number or integer (`lean_box`/`lean_unbox`).
 * A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
 * Any other type is represented by `lean_object *`.
   Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
@@ -139,7 +140,7 @@ lean_object * initialize_C(uint8_t builtin, lean_object *);
 ...
 
 lean_initialize_runtime_module();
-//lean_initialize();  // necessary if you (indirectly) access the `Lean` package
+//lean_initialize();  // necessary (and replaces `lean_initialize_runtime_module`) if you (indirectly) access the `Lean` package
 
 lean_object * res;
 // use same default as for Lean executables

doc/dev/index.md

@@ -80,3 +80,10 @@ Unlike most Lean projects, all submodules of the `Lean` module begin with the
 `prelude` keyword. This disables the automated import of `Init`, meaning that
 developers need to figure out their own subset of `Init` to import. This is done
 such that changing files in `Init` doesn't force a full rebuild of `Lean`.
+
+### Testing against Mathlib/Batteries
+You can test a Lean PR against Mathlib and Batteries by rebasing your PR
+on to `nightly-with-mathlib` branch. (It is fine to force push after rebasing.)
+CI will generate a branch of Mathlib and Batteries called `lean-pr-testing-NNNN`
+that uses the toolchain for your PR, and will report back to the Lean PR with results from Mathlib CI.
+See https://leanprover-community.github.io/contribute/tags_and_branches.html for more details.

doc/dev/release_checklist.md

@@ -5,11 +5,8 @@ See below for the checklist for release candidates.
 
 We'll use `v4.6.0` as the intended release version as a running example.
 
-- One week before the planned release, ensure that
-  (1) someone has written the release notes and
-  (2) someone has written the first draft of the release blog post.
-  If there is any material in `./releases_drafts/` on the `releases/v4.6.0` branch, then the release notes are not done.
-  (See the section "Writing the release notes".)
+- Run `scripts/release_checklist.py v4.6.0` to check the status of the release.
+  This script is purely informational, idempotent, and safe to run at any stage of the release process.
 - `git checkout releases/v4.6.0`
   (This branch should already exist, from the release candidates.)
 - `git pull`
@@ -25,14 +22,28 @@ We'll use `v4.6.0` as the intended release version as a running example.
   - This step can take up to an hour.
   - If you are intending to cut the next release candidate on the same day,
     you may want to start on the release candidate checklist now.
+- Next we need to prepare the release notes.
+  - If the stable release is identical to the last release candidate (this should usually be the case),
+    you can reuse the release notes from `RELEASES.md`.
+  - If you want to regenerate the release notes,
+    use `script/release_notes.py --since v4.5.0`, run on the `releases/v4.6.0` branch,
+    and see the section "Writing the release notes" below for more information.
+  - Release notes should go in `RELEASES.md` on the `releases/v4.6.0` branch,
+    and should also be PR'd to `master` (suggested title: "chore: update release notes for v4.6.0").
 - Go to https://github.com/leanprover/lean4/releases and verify that the `v4.6.0` release appears.
-  - Edit the release notes on Github to select the "Set as the latest release".
-  - Follow the instructions in creating a release candidate for the "GitHub release notes" step,
-    now that we have a written `RELEASES.md` section.
-    Do a quick sanity check.
+  - Verify on Github that "Set as the latest release" is checked.
+  - Copy the generated release note into the text box, adding the header
+    ```
+    v4.6.0
+    ----------
+    ```
 - Next, we will move a curated list of downstream repos to the latest stable release.
+  - In order to have the access rights to push to these repositories and merge PRs,
+    you will need to be a member of the `lean-release-managers` team at both `leanprover-community` and `leanprover`.
+    Contact Kim Morrison (@kim-em) to arrange access.
   - For each of the repositories listed below:
     - Make a PR to `master`/`main` changing the toolchain to `v4.6.0`
+      - The usual branch name would be `bump_to_v4.6.0`.
       - Update the toolchain file
       - In the Lakefile, if there are dependencies on specific version tags of dependencies that you've already pushed as part of this process, update them to the new tag.
         If they depend on `main` or `master`, don't change this; you've just updated the dependency, so it will work and be saved in the manifest
@@ -42,16 +53,38 @@ We'll use `v4.6.0` as the intended release version as a running example.
     - Create the tag `v4.6.0` from `master`/`main` and push it.
     - Merge the tag `v4.6.0` into the `stable` branch and push it.
   - We do this for the repositories:
-    - [lean4checker](https://github.com/leanprover/lean4checker)
-      - No dependencies
-      - Toolchain bump PR
-      - Create and push the tag
-      - Merge the tag into `stable`
     - [Batteries](https://github.com/leanprover-community/batteries)
       - No dependencies
       - Toolchain bump PR
       - Create and push the tag
       - Merge the tag into `stable`
+    - [lean4checker](https://github.com/leanprover/lean4checker)
+      - No dependencies
+      - Toolchain bump PR
+      - Create and push the tag
+      - Merge the tag into `stable`
+    - [quote4](https://github.com/leanprover-community/quote4)
+      - No dependencies
+      - Toolchain bump PR
+      - Create and push the tag
+      - Merge the tag into `stable`
+    - [doc-gen4](https://github.com/leanprover/doc-gen4)
+      - Dependencies: exist, but they're not part of the release workflow
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
+    - [Verso](https://github.com/leanprover/verso)
+      - Dependencies: exist, but they're not part of the release workflow
+      - The `SubVerso` dependency should be compatible with _every_ Lean release simultaneously, rather than following this workflow
+      - Warnings during `lake update` and `lake build` are expected.
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
+    - [Cli](https://github.com/leanprover/lean4-cli)
+      - No dependencies
+      - Toolchain bump PR
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
     - [ProofWidgets4](https://github.com/leanprover-community/ProofWidgets4)
       - Dependencies: `Batteries`
       - Note on versions and branches:
@@ -66,27 +99,19 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - Merge the tag into `stable`
-    - [doc-gen4](https://github.com/leanprover/doc-gen4)
-      - Dependencies: exist, but they're not part of the release workflow
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - There is no `stable` branch; skip this step
-    - [Verso](https://github.com/leanprover/verso)
-      - Dependencies: exist, but they're not part of the release workflow
-      - The `SubVerso` dependency should be compatible with _every_ Lean release simultaneously, rather than following this workflow
-      - Toolchain bump PR including updated Lake manifest
-      - Create and push the tag
-      - There is no `stable` branch; skip this step
     - [import-graph](https://github.com/leanprover-community/import-graph)
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - There is no `stable` branch; skip this step
+    - [plausible](https://github.com/leanprover-community/plausible)
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
     - [Mathlib](https://github.com/leanprover-community/mathlib4)
-      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Batteries`, `doc-gen4`, `import-graph`
+      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Batteries`, `doc-gen4`, `quote4`, `import-graph`
       - Toolchain bump PR notes:
-        - In addition to updating the `lean-toolchain` and `lakefile.lean`,
-          in `.github/workflows/lean4checker.yml` update the line
-          `git checkout v4.6.0` to the appropriate tag. 
+        - Upstream dependencies should use their `main` or `master` branch, not toolchain tags.
+          (Unlike for other repos.)
         - Push the PR branch to the main Mathlib repository rather than a fork, or CI may not work reliably
         - Create and push the tag
         - Create a new branch from the tag, push it, and open a pull request against `stable`.
@@ -98,16 +123,12 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - Merge the tag into `stable`
-- The `v4.6.0` section of `RELEASES.md` is out of sync between
-  `releases/v4.6.0` and `master`. This should be reconciled:
-  - Replace the `v4.6.0` section on `master` with the `v4.6.0` section on `releases/v4.6.0`
-    and commit this to `master`.
-- Merge the release announcement PR for the Lean website - it will be deployed automatically
+- Run `script/release_checklist.py v4.6.0` again to check that everything is in order.
 - Finally, make an announcement!
   This should go in https://leanprover.zulipchat.com/#narrow/stream/113486-announce, with topic `v4.6.0`.
   Please see previous announcements for suggested language.
   You will want a few bullet points for main topics from the release notes.
-  Link to the blog post from the Zulip announcement.
+  If there is a blog post, link to that from the zulip announcement.
 - Make sure that whoever is handling social media knows the release is out.
 
 ## Optimistic(?) time estimates:
@@ -127,6 +148,8 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
 
 - Decide which nightly release you want to turn into a release candidate.
   We will use `nightly-2024-02-29` in this example.
+- It is essential to choose the nightly that will become the release candidate as early as possible, to avoid confusion.
+- Throughout this process you can use `script/release_checklist.py v4.7.0-rc1` to track progress.
 - It is essential that Batteries and Mathlib already have reviewed branches compatible with this nightly.
   - Check that both Batteries and Mathlib's `bump/v4.7.0` branch contain `nightly-2024-02-29`
     in their `lean-toolchain`.
@@ -139,24 +162,19 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
     git checkout -b releases/v4.7.0
     ```
 - In `RELEASES.md` replace `Development in progress` in the `v4.7.0` section with `Release notes to be written.`
-- We will rely on automatically generated release notes for release candidates,
-  and the written release notes will be used for stable versions only.
-  It is essential to choose the nightly that will become the release candidate as early as possible, to avoid confusion.
 - In `src/CMakeLists.txt`,
   - verify that you see `set(LEAN_VERSION_MINOR 7)` (for whichever `7` is appropriate); this should already have been updated when the development cycle began.
-  - `set(LEAN_VERSION_IS_RELEASE 1)` (this should be a change; on `master` and nightly releases it is always `0`).
+  - change the `LEAN_VERSION_IS_RELEASE` line to `set(LEAN_VERSION_IS_RELEASE 1)` (this should be a change; on `master` and nightly releases it is always `0`).
   - Commit your changes to `src/CMakeLists.txt`, and push.
 - `git tag v4.7.0-rc1`
 - `git push origin v4.7.0-rc1`
-- Ping the FRO Zulip that release notes need to be written. The release notes do not block completing the rest of this checklist.
 - Now wait, while CI runs.
   - You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`, looking for the `v4.7.0-rc1` tag.
   - This step can take up to an hour.
 - (GitHub release notes) Once the release appears at https://github.com/leanprover/lean4/releases/
   - Verify that the release is marked as a prerelease (this should have been done automatically by the CI release job).
-  - In the "previous tag" dropdown, select `v4.6.0`, and click "Generate release notes".
-    This will add a list of all the commits since the last stable version.
-    - Delete "update stage0" commits, and anything with a completely inscrutable commit message.
+  - Generate release notes by running `script/release_notes.py --since v4.6.0` on the `releases/v4.7.0` branch.
+    See the section "Writing the release notes" below for more information.
 - Next, we will move a curated list of downstream repos to the release candidate.
   - This assumes that for each repository either:
     * There is already a *reviewed* branch `bump/v4.7.0` containing the required adaptations.
@@ -181,10 +199,11 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
   - We do this for the same list of repositories as for stable releases, see above.
     As above, there are dependencies between these, and so the process above is iterative.
     It greatly helps if you can merge the `bump/v4.7.0` PRs yourself!
-    It is essential for Mathlib CI that you then create the next `bump/v4.8.0` branch
+  - It is essential for Mathlib and Batteries CI that you then create the next `bump/v4.8.0` branch
     for the next development cycle.
     Set the `lean-toolchain` file on this branch to same `nightly` you used for this release.
-  - For Batteries/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
+  - (Note: we're currently uncertain if we really want to do this step. Check with Kim Morrison if you're unsure.)
+    For Batteries/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
     `nightly-testing-2024-02-29` with date corresponding to the nightly used for the release
     (create it if not), and then on the `nightly-testing` branch `git reset --hard master`, and force push.
 - Make an announcement!
@@ -248,15 +267,26 @@ Please read https://leanprover-community.github.io/contribute/tags_and_branches.
 
 # Writing the release notes
 
-We are currently trying a system where release notes are compiled all at once from someone looking through the commit history.
-The exact steps are a work in progress.
-Here is the general idea:
+Release notes are automatically generated from the commit history, using `script/release_notes.py`.
 
-* The work is done right on the `releases/v4.6.0` branch sometime after it is created but before the stable release is made.
-  The release notes for `v4.6.0` will later be copied to `master` when we begin a new development cycle.
-* There can be material for release notes entries in commit messages.
-* There can also be pre-written entries in `./releases_drafts`, which should be all incorporated in the release notes and then deleted from the branch.
+Run this as `script/release_notes.py --since v4.6.0`, where `v4.6.0` is the *previous* release version.
+This script should be run on the `releases/v4.7.0` branch.
+This will generate output for all commits since that tag.
+Note that there is output on both stderr, which should be manually reviewed,
+and on stdout, which should be manually copied to `RELEASES.md`.
+
+The output on stderr should mostly be about commits for which the script could not find an associated PR,
+usually because a PR was rebase-merged because it contained an update to stage0.
+Some judgement is required here: ignore commits which look minor,
+but manually add items to the release notes for significant PRs that were rebase-merged.
+
+There can also be pre-written entries in `./releases_drafts`, which should be all incorporated in the release notes and then deleted from the branch.
   See `./releases_drafts/README.md` for more information.
-* The release notes should be written from a downstream expert user's point of view.
 
-This section will be updated when the next release notes are written (for `v4.10.0`).
+# `release_checklist.py`
+
+The script `script/release_checklist.py` attempts to automate checking the status of the release.
+
+Future improvements:
+* We check the release notes have been posted on Github,
+  but do not check that they are present in `RELEASES.md` on the release branch or on `master`.

doc/examples/bintree.lean

@@ -179,7 +179,7 @@ local macro "have_eq " lhs:term:max rhs:term:max : tactic =>
   `(tactic|
     (have h : $lhs = $rhs :=
        -- TODO: replace with linarith
-       by simp_arith at *; apply Nat.le_antisymm <;> assumption
+       by simp +arith at *; apply Nat.le_antisymm <;> assumption
      try subst $lhs))
 
 /-!

doc/lexical_structure.md

@@ -61,7 +61,7 @@ Parts of atomic names can be escaped by enclosing them in pairs of French double
    letterlike_symbols: [℀-⅏]
    escaped_ident_part: "«" [^«»\r\n\t]* "»"
    atomic_ident_rest: atomic_ident_start | [0-9'ⁿ] | subscript
-   subscript: [₀-₉ₐ-ₜᵢ-ᵪ]
+   subscript: [₀-₉ₐ-ₜᵢ-ᵪⱼ]
 ```
 
 String Literals

doc/make/osx-10.9.md

@@ -32,12 +32,13 @@ following to use `g++`.
 cmake -DCMAKE_CXX_COMPILER=g++ ...
 ```
 
-## Required Packages: CMake, GMP, libuv
+## Required Packages: CMake, GMP, libuv, pkgconf
 
 ```bash
 brew install cmake
 brew install gmp
 brew install libuv
+brew install pkgconf
 ```
 
 ## Recommended Packages: CCache

doc/make/ubuntu.md

@@ -8,5 +8,5 @@ follow the [generic build instructions](index.md).
 ## Basic packages
 
 ```bash
-sudo apt-get install git libgmp-dev libuv1-dev cmake ccache clang
+sudo apt-get install git libgmp-dev libuv1-dev cmake ccache clang pkgconf
 ```

doc/setup.md

@@ -4,7 +4,7 @@
 
 Platforms built & tested by our CI, available as binary releases via elan (see below)
 
-* x86-64 Linux with glibc 2.27+
+* x86-64 Linux with glibc 2.26+
 * x86-64 macOS 10.15+
 * aarch64 (Apple Silicon) macOS 10.15+
 * x86-64 Windows 11 (any version), Windows 10 (version 1903 or higher), Windows Server 2022

doc/std/README.md

@@ -0,0 +1,9 @@
+# The Lean standard library
+
+This directory contains development information about the Lean standard library. The user-facing documentation of the standard library
+is part of the [Lean Language Reference](https://lean-lang.org/doc/reference/latest/).
+
+Here you will find
+* the [standard library vision document](./vision.md), including the call for contributions,
+* the [standard library style guide](./style.md), and
+* the [standard library naming conventions](./naming.md).

doc/std/naming.md

@@ -0,0 +1,260 @@
+# Standard library naming conventions
+
+The easiest way to access a result in the standard library is to correctly guess the name of the declaration (possibly with the help of identifier autocompletion). This is faster and has lower friction than more sophisticated search tools, so easily guessable names (which are still reasonably short) make Lean users more productive.
+
+The guide that follows contains very few hard rules, many heuristics and a selection of examples. It cannot and does not present a deterministic algorithm for choosing good names in all situations. It is intended as a living document that gets clarified and expanded as situations arise during code reviews for the standard library. If applying one of the suggestions in this guide leads to nonsensical results in a certain situation, it is
+probably safe to ignore the suggestion (or even better, suggest a way to improve the suggestion).
+
+## Prelude
+
+Identifiers use a mix of `UpperCamelCase`, `lowerCamelCase` and `snake_case`, used for types, data, and theorems, respectively.
+
+Structure fields should be named such that the projections have the correct names.
+
+## Naming convention for types
+
+When defining a type, i.e., a (possibly 0-ary) function whose codomain is Sort u for some u, it should be named in UpperCamelCase. Examples include `List`, and `List.IsPrefix`.
+
+When defining a predicate, prefix the name by `Is`, like in `List.IsPrefix`. The `Is` prefix may be omitted if
+* the resulting name would be ungrammatical, or
+* the predicate depends on additional data in a way where the `Is` prefix would be confusing (like `List.Pairwise`), or
+* the name is an adjective (like `Std.Time.Month.Ordinal.Valid`)
+
+## Namespaces and generalized projection notation
+
+Almost always, definitions and theorems relating to a type should be placed in a namespace with the same name as the type. For example, operations and theorems about lists should be placed in the `List` namespace, and operations and theorems about `Std.Time.PlainDate` should be placed in the `Std.Time.PlainDate` namespace.
+
+Declarations in the root namespace will be relatively rare. The most common type of declaration in the root namespace are declarations about data and properties exported by notation type classes, as long as they are not about a specific type implementing that type class. For example, we have
+
+```lean
+theorem beq_iff_eq [BEq α] [LawfulBEq α] {a b : α} : a == b ↔ a = b := sorry
+```
+
+in the root namespace, but
+
+```lean
+theorem List.cons_beq_cons [BEq α] {a b : α} {l₁ l₂ : List α} :
+    (a :: l₁ == b :: l₂) = (a == b && l₁ == l₂) := rfl
+```
+
+belongs in the `List` namespace.
+
+Subtleties arise when multiple namespaces are in play. Generally, place your theorem in the most specific namespace that appears in one of the hypotheses of the theorem. The following names are both correct according to this convention:
+
+```lean
+theorem List.Sublist.reverse : l₁ <+ l₂ → l₁.reverse <+ l₂.reverse := sorry
+theorem List.reverse_sublist : l₁.reverse <+ l₂.reverse ↔ l₁ <+ l₂ := sorry
+```
+
+Notice that the second theorem does not have a hypothesis of type `List.Sublist l` for some `l`, so the name `List.Sublist.reverse_iff` would be incorrect.
+
+The advantage of placing results in a namespace like `List.Sublist` is that it enables generalized projection notation, i.e., given `h : l₁ <+ l₂`,
+one can write `h.reverse` to obtain a proof of `l₁.reverse <+ l₂.reverse`. Thinking about which dot notations are convenient can act as a guideline
+for deciding where to place a theorem, and is, on occasion, a good reason to duplicate a theorem into multiple namespaces.
+
+### The `Std` namespace
+
+New types that are added will usually be placed in the `Std` namespace and in the `Std/` source directory, unless there are good reasons to place
+them elsewhere.
+
+Inside the `Std` namespace, all internal declarations should be `private` or else have a name component that clearly marks them as internal, preferably
+`Internal`.
+
+
+## Naming convention for data
+
+When defining data, i.e., a (possibly 0-ary) function whose codomain is not Sort u, but has type Type u for some u, it should be named in lowerCamelCase. Examples include `List.append` and `List.isPrefixOf`.
+If your data is morally fully specified by its type, then use the naming procedure for theorems described below and convert the result to lower camel case.
+
+If your function returns an `Option`, consider adding `?` as a suffix. If your function may panic, consider adding `!` as a suffix. In many cases, there will be multiple variants of a function; one returning an option, one that may panic and possibly one that takes a proof argument.
+
+## Naming algorithm for theorems and some definitions
+
+There is, in principle, a general algorithm for naming a theorem. The problem with this algorithm is that it produces very long and unwieldy names which need to be shortened. So choosing a name for a declaration can be thought of as consisting of a mechanical part and a creative part.
+
+Usually the first part is to decide which namespace the result should live in, according to the guidelines described above.
+
+Next, consider the type of your declaration as a tree. Inner nodes of this tree are function types or function applications. Leaves of the tree are 0-ary functions or bound variables.
+
+As an example, consider the following result from the standard library:
+
+```lean
+example {α : Type u} {β : Type v} [BEq α] [Hashable α] [EquivBEq α] [LawfulHashable α]
+    [Inhabited β] {m : Std.HashMap α β} {a : α} {h' : a ∈ m} : m[a]? = some (m[a]'h') :=
+  sorry
+```
+
+The correct namespace is clearly `Std.HashMap`. The corresponding tree looks like this:
+
+![](naming-tree.svg)
+
+The preferred spelling of a notation can be looked up by hovering over the notation.
+
+Now traverse the tree and build a name according to the following rules:
+
+* When encountering a function type, first turn the result type into a name, then all of the argument types from left to right, and join the names using `_of_`.
+* When encountering a function that is neither an infix notation nor a structure projection, first put the function name and then the arguments, joined by an underscore.
+* When encountering an infix notation, join the arguments using the name of the notation, separated by underscores.
+* When encountering a structure projection, proceed as for normal functions, but put the name of the projection last.
+* When encountering a name, put it in lower camel case.
+* Skip bound variables and proofs.
+* Type class arguments are also generally skipped.
+
+When encountering namespaces names, concatenate them in lower camel case.
+
+Applying this algorithm to our example yields the name `Std.HashMap.getElem?_eq_optionSome_getElem_of_mem`.
+
+From there, the name should be shortened, using the following heuristics:
+
+* The namespace of functions can be omitted if it is clear from context or if the namespace is the current one. This is almost always the case.
+* For infix operators, it is possible to leave out the RHS or the name of the notation and the RHS if they are clear from context.
+* Hypotheses can be left out if it is clear that they are required or if they appear in the conclusion.
+
+Based on this, here are some possible names for our example:
+
+1. `Std.HashMap.getElem?_eq`
+2. `Std.HashMap.getElem?_eq_of_mem`
+3. `Std.HashMap.getElem?_eq_some`
+4. `Std.HashMap.getElem?_eq_some_of_mem`
+5. `Std.HashMap.getElem?_eq_some_getElem`
+6. `Std.Hashmap.getElem?_eq_some_getElem_of_mem`
+
+Choosing a good name among these then requires considering the context of the lemma. In this case it turns out that the first four options are underspecified as there is also a lemma relating `m[a]?` and `m[a]!` which could have the same name. This leaves the last two options, the first of which is shorter, and this is how the lemma is called in the Lean standard library.
+
+Here are some additional examples:
+
+```lean
+example {x y : List α} (h : x <+: y) (hx : x ≠ []) :
+  x.head hx = y.head (h.ne_nil hx) := sorry
+```
+
+Since we have an `IsPrefix` parameter, this should live in the `List.IsPrefix` namespace, and the algorithm suggests `List.IsPrefix.head_eq_head_of_ne_nil`, which is shortened to `List.IsPrefix.head`. Note here the difference between the namespace name (`IsPrefix`) and the recommended spelling of the corresponding notation (`prefix`).
+
+```lean
+example : l₁ <+: l₂ → reverse l₁ <:+ reverse l₂ := sorry
+```
+
+Again, this result should be in the `List.IsPrefix` namespace; the algorithm suggests `List.IsPrefix.reverse_prefix_reverse`, which becomes `List.IsPrefix.reverse`.
+
+The following examples show how the traversal order often matters.
+
+```lean
+theorem Nat.mul_zero (n : Nat) : n * 0 = 0 := sorry
+theorem Nat.zero_mul (n : Nat) : 0 * n = 0 := sorry
+```
+
+Here we see that one name may be a prefix of another name:
+
+```lean
+theorem Int.mul_ne_zero {a b : Int} (a0 : a ≠ 0) (b0 : b ≠ 0) : a * b ≠ 0 := sorry
+theorem Int.mul_ne_zero_iff {a b : Int} : a * b ≠ 0 ↔ a ≠ 0 ∧ b ≠ 0 := sorry
+```
+
+It is usually a good idea to include the `iff` in a theorem name even if the name would still be unique without the name. For example,
+
+```lean
+theorem List.head?_eq_none_iff : l.head? = none ↔ l = [] := sorry
+```
+
+is a good name: if the lemma was simply called `List.head?_eq_none`, users might try to `apply` it when the goal is `l.head? = none`, leading
+to confusion.
+
+The more common you expect (or want) a theorem to be, the shorter you should try to make the name. For example, we have both
+
+```lean
+theorem Std.HashMap.getElem?_eq_none_of_contains_eq_false {a : α} : m.contains a = false → m[a]? = none := sorry
+theorem Std.HashMap.getElem?_eq_none {a : α} : ¬a ∈ m → m[a]? = none := sorry
+```
+
+As users of the hash map are encouraged to use ∈ rather than contains, the second lemma gets the shorter name.
+
+## Special cases
+
+There are certain special “keywords” that may appear in identifiers.
+
+| Keyword | Meaning | Example |
+| :---- | :---- | :---- |
+| `def` | Unfold a definition. Avoid this for public APIs. | `Nat.max_def` |
+| `refl` | Theorems of the form `a R a`, where R is a reflexive relation and `a` is an explicit parameter | `Nat.le_refl` |
+| `rfl` | Like `refl`, but with `a` implicit | `Nat.le_rfl` |
+| `irrefl` | Theorems of the form `¬a R a`, where R is an irreflexive relation | `Nat.lt_irrefl` |
+| `symm` | Theorems of the form `a R b → b R a`, where R is a symmetric relation (compare `comm` below) | `Eq.symm` |
+| `trans` | Theorems of the form `a R b → b R c → a R c`, where R is a transitive relation (R may carry data) | `Eq.trans` |
+| `antisymmm` | Theorems of the form `a R b → b R a → a = b`, where R is an antisymmetric relation | `Nat.le_antisymm` |
+| `congr` | Theorems of the form `a R b → f a S f b`, where R and S are usually equivalence relations | `Std.HashMap.mem_congr` |
+| `comm` | Theorems of the form `f a b = f b a` (compare `symm` above) | `Eq.comm`, `Nat.add_comm` |
+| `assoc` | Theorems of the form `g (f a b) c = f a (g b c)` (note the order! In most cases, we have f = g) | `Nat.add_sub_assoc` |
+| `distrib` | Theorems of the form `f (g a b) = g (f a) (f b)` | `Nat.add_left_distrib` |
+| `self` | May be used if a variable appears multiple times in the conclusion | `List.mem_cons_self` |
+| `inj` | Theorems of the form `f a = f b ↔ a = b`. | `Int.neg_inj`, `Nat.add_left_inj` |
+| `cancel` | Theorems which have one of the forms `f a = f b → a = b` or `g (f a) = a`, where `f` and `g` usually involve a binary operator | `Nat.add_sub_cancel` |
+| `cancel_iff` | Same as `inj`, but with different conventions for left and right (see below) | `Nat.add_right_cancel_iff` |
+| `ext` | Theorems of the form `f a = f b → a = b`, where `f` usually involves some kind of projection | `List.ext_getElem`
+| `mono` | Theorems of the form `a R b → f a R f b`, where `R` is a transitive relation | `List.countP_mono_left`
+
+### Left and right
+
+The keywords left and right are useful to disambiguate symmetric variants of theorems.
+
+```lean
+theorem imp_congr_left (h : a ↔ b) : (a → c) ↔ (b → c) := sorry
+theorem imp_congr_right (h : a → (b ↔ c)) : (a → b) ↔ (a → c) := sorry
+```
+
+It is not always obvious which version of a theorem should be “left” and which should be “right”.
+Heuristically, the theorem should name the side which is “more variable”, but there are exceptions. For some of the special keywords discussed in this section, there are conventions which should be followed, as laid out in the following examples:
+
+```lean
+theorem Nat.left_distrib (n m k : Nat) : n * (m + k) = n * m + n * k := sorry
+theorem Nat.right_distrib (n m k : Nat) : (n + m) * k = n * k + m * k := sorry
+theorem Nat.add_left_cancel {n m k : Nat} : n + m = n + k → m = k := sorry
+theorem Nat.add_right_cancel {n m k : Nat} : n + m = k + m → n = k := sorry
+theorem Nat.add_left_cancel_iff {m k n : Nat} : n + m = n + k ↔ m = k := sorry
+theorem Nat.add_right_cancel_iff {m k n : Nat} : m + n = k + n ↔ m = k := sorry
+theorem Nat.add_left_inj {m k n : Nat} : m + n = k + n ↔ m = k := sorry
+theorem Nat.add_right_inj {m k n : Nat} : n + m = n + k ↔ m = k := sorry
+```
+
+Note in particular that the convention is opposite for `cancel_iff` and `inj`.
+
+```lean
+theorem Nat.add_sub_self_left (a b : Nat) : (a + b) - a = b := sorry
+theorem Nat.add_sub_self_right (a b : Nat) : (a + b) - b = a := sorry
+theorem Nat.add_sub_cancel (n m : Nat) : (n + m) - m = n := sorry
+```
+
+## Primed names
+
+Avoid disambiguating variants of a concept by appending the `'` character (e.g., introducing both `BitVec.sshiftRight` and `BitVec.sshiftRight'`), as it is impossible to tell the difference without looking at the type signature, the documentation or even the code, and even if you know what the two variants are there is no way to tell which is which. Prefer descriptive pairs `BitVec.sshiftRightNat`/`BitVec.sshiftRight`.
+
+## Acronyms
+
+For acronyms which are three letters or shorter, all letters should use the same case as dictated by the convention. For example, `IO` is a correct name for a type and the name `IO.Ref` may become `IORef` when used as part of a definition name and `ioRef` when used as part of a theorem name.
+
+For acronyms which are at least four letters long, switch to lower case starting from the second letter. For example, `Json` is a correct name for a type, as is `JsonRPC`.
+
+If an acronym is typically spelled using mixed case, this mixed spelling may be used in identifiers (for example `Std.Net.IPv4Addr`).
+
+## Simp sets
+
+Simp sets centered around a conversion function should be called `source_to_target`. For example, a simp set for the `BitVec.toNat` function, which goes from `BitVec` to
+`Nat`, should be called `bitvec_to_nat`.
+
+## Variable names
+
+We make the following recommendations for variable names, but without insisting on them:
+* Simple hypotheses should be named `h`, `h'`, or using a numerical sequence `h₁`, `h₂`, etc.
+* Another common name for a simple hypothesis is `w` (for "witness").
+* `List`s should be named `l`, `l'`, `l₁`, etc, or `as`, `bs`, etc.
+  (Use of `as`, `bs` is encouraged when the lists are of different types, e.g. `as : List α` and `bs : List β`.)
+  `xs`, `ys`, `zs` are allowed, but it is better if these are reserved for `Array` and `Vector`.
+  A list of lists may be named `L`.
+* `Array`s should be named `xs`, `ys`, `zs`, although `as`, `bs` are encouraged when the arrays are of different types, e.g. `as : Array α` and `bs : Array β`.
+  An array of arrays may be named `xss`.
+* `Vector`s should be named `xs`, `ys`, `zs`, although `as`, `bs` are encouraged when the vectors are of different types, e.g. `as : Vector α n` and `bs : Vector β n`.
+  A vector of vectors may be named `xss`.
+* A common exception for `List` / `Array` / `Vector` is to use `acc` for an accumulator in a recursive function.
+* `i`, `j`, `k` are preferred for numerical indices.
+  Descriptive names such as `start`, `stop`, `lo`, and `hi` are encouraged when they increase readability.
+* `n`, `m` are preferred for sizes, e.g. in `Vector α n` or `xs.size = n`.
+* `w` is preferred for the width of a `BitVec`.

doc/std/style.md

@@ -0,0 +1,522 @@
+# Standard library style
+
+Please take some time to familiarize yourself with the stylistic conventions of
+the project and the specific part of the library you are planning to contribute
+to. While the Lean compiler may not enforce strict formatting rules,
+consistently formatted code is much easier for others to read and maintain.
+Attention to formatting is more than a cosmetic concern—it reflects the same
+level of precision and care required to meet the deeper standards of the Lean 4
+standard library.
+
+Below we will give specific formatting prescriptions for various language constructs. Note that this style guide only applies to the Lean standard library, even though some examples in the guide are taken from other parts of the Lean code base.
+
+## Basic whitespace rules
+
+Syntactic elements (like `:`, `:=`, `|`, `::`) are surrounded by single spaces, with the exception of `,` and `;`, which are followed by a space but not preceded by one. Delimiters (like `()`, `{}`) do not have spaces on the inside, with the exceptions of subtype notation and structure instance notation.
+
+Examples of correctly formatted function parameters:
+
+* `{α : Type u}`
+* `[BEq α]`
+* `(cmp : α → α → Ordering)`
+* `(hab : a = b)`
+* `{d : { l : List ((n : Nat) × Vector Nat n) // l.length % 2 = 0 }}`
+
+Examples of correctly formatted terms:
+
+* `1 :: [2, 3]`
+* `letI : Ord α := ⟨cmp⟩; True`
+* `(⟨2, 3⟩ : Nat × Nat)`
+* `((2, 3) : Nat × Nat)`
+* `{ x with fst := f (4 + f 0), snd := 4, .. }`
+* `match 1 with | 0 => 0 | _ => 0`
+* `fun ⟨a, b⟩ _ _ => by cases hab <;> apply id; rw [hbc]`
+
+Configure your editor to remove trailing whitespace. If you have set up Visual Studio Code for Lean development in the recommended way then the correct setting is applied automatically.
+
+## Splitting terms across multiple lines
+
+When splitting a term across multiple lines, increase indentation by two spaces starting from the second line. When splitting a function application, try to split at argument boundaries. If an argument itself needs to be split, increase indentation further as appropriate.
+
+When splitting at an infix operator, the operator goes at the end of the first line, not at the beginning of the second line. When splitting at an infix operator, you may or may not increase indentation depth, depending on what is more readable.
+
+When splitting an `if`-`then`-`else` expression, the `then` keyword wants to stay with the condition and the `else` keyword wants to stay with the alternative term. Otherwise, indent as if the `if` and `else` keywords were arguments to the same function.
+
+When splitting a comma-separated bracketed sequence (i.e., anonymous constructor application, list/array/vector literal, tuple) it is allowed to indent subsequent lines for alignment, but indenting by two spaces is also allowed.
+
+Do not orphan parentheses.
+
+Correct:
+```lean
+def MacroScopesView.isPrefixOf (v₁ v₂ : MacroScopesView) : Bool :=
+  v₁.name.isPrefixOf v₂.name &&
+  v₁.scopes == v₂.scopes &&
+  v₁.mainModule == v₂.mainModule &&
+  v₁.imported == v₂.imported
+```
+
+Correct:
+```lean
+theorem eraseP_eq_iff {p} {l : List α} :
+    l.eraseP p = l' ↔
+      ((∀ a ∈ l, ¬ p a) ∧ l = l') ∨
+        ∃ a l₁ l₂, (∀ b ∈ l₁, ¬ p b) ∧ p a ∧
+          l = l₁ ++ a :: l₂ ∧ l' = l₁ ++ l₂ :=
+  sorry
+```
+
+Correct:
+```lean
+example : Nat :=
+  functionWithAVeryLongNameSoThatSomeArgumentsWillNotFit firstArgument secondArgument
+    (firstArgumentWithAnEquallyLongNameAndThatFunctionDoesHaveMoreArguments firstArgument
+      secondArgument)
+    secondArgument
+```
+
+Correct:
+```lean
+theorem size_alter [LawfulBEq α] {k : α} {f : Option (β k) → Option (β k)} (h : m.WF) :
+    (m.alter k f).size =
+      if m.contains k && (f (m.get? k)).isNone then
+        m.size - 1
+      else if !m.contains k && (f (m.get? k)).isSome then
+        m.size + 1
+      else
+        m.size := by
+ simp_to_raw using Raw₀.size_alter
+```
+
+Correct:
+```lean
+theorem get?_alter [LawfulBEq α] {k k' : α} {f : Option (β k) → Option (β k)} (h : m.WF) :
+    (m.alter k f).get? k' =
+      if h : k == k' then
+        cast (congrArg (Option ∘ β) (eq_of_beq h)) (f (m.get? k))
+      else m.get? k' := by
+ simp_to_raw using Raw₀.get?_alter
+```
+
+Correct:
+```lean
+example : Nat × Nat :=
+  ⟨imagineThisWasALongTerm,
+   imagineThisWasAnotherLongTerm⟩
+```
+
+Correct:
+```lean
+example : Nat × Nat :=
+  ⟨imagineThisWasALongTerm,
+    imagineThisWasAnotherLongTerm⟩
+```
+
+Correct:
+```lean
+example : Vector Nat :=
+  #v[imagineThisWasALongTerm,
+     imagineThisWasAnotherLongTerm]
+```
+
+## Basic file structure
+
+Every file should start with a copyright header, imports (in the standard library, this always includes a `prelude` declaration) and a module documentation string. There should not be a blank line between the copyright header and the imports. There should be a blank line between the imports and the module documentation string.
+
+If you explicitly declare universe variables, do so at the top of the file, after the module documentation.
+
+Correct:
+```lean
+/-
+Copyright (c) 2014 Parikshit Khanna. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro,
+  Yury Kudryashov
+-/
+prelude
+import Init.Data.List.Pairwise
+import Init.Data.List.Find
+
+/-!
+**# Lemmas about `List.eraseP` and `List.erase`.**
+-/
+
+universe u u'
+```
+
+Syntax that is not supposed to be user-facing must be scoped. New public syntax must always be discussed explicitly in an RFC.
+
+## Top-level commands and declarations
+
+All top-level commands are unindented. Sectioning commands like `section` and `namespace` do not increase the indentation level.
+
+Attributes may be placed on the same line as the rest of the command or on a separate line.
+
+Multi-line declaration headers are indented by four spaces starting from the second line. The colon that indicates the type of a declaration may not be placed at the start of a line or on its own line.
+
+Declaration bodies are indented by two spaces. Short declaration bodies may be placed on the same line as the declaration type.
+
+Correct:
+```lean
+theorem eraseP_eq_iff {p} {l : List α} :
+    l.eraseP p = l' ↔
+      ((∀ a ∈ l, ¬ p a) ∧ l = l') ∨
+        ∃ a l₁ l₂, (∀ b ∈ l₁, ¬ p b) ∧ p a ∧
+          l = l₁ ++ a :: l₂ ∧ l' = l₁ ++ l₂ :=
+  sorry
+```
+
+Correct:
+```lean
+@[simp] theorem eraseP_nil : [].eraseP p = [] := rfl
+```
+
+Correct:
+```lean
+@[simp]
+theorem eraseP_nil : [].eraseP p = [] := rfl
+```
+
+### Documentation comments
+
+Note to external contributors: this is a section where the Lean style and the mathlib style are different.
+
+Declarations should be documented as required by the `docBlame` linter, which may be activated in a file using
+`set_option linter.missingDocs true` (we allow these to stay in the file).
+
+Single-line documentation comments should go on the same line as `/--`/`-/`, while multi-line documentation strings
+should have these delimiters on their own line, with the documentation comment itself unindented.
+
+Documentation comments must be written in the indicative mood. Use American orthography.
+
+Correct:
+```lean
+/-- Carries out a monadic action on each mapping in the hash map in some order. -/
+@[inline] def forM (f : (a : α) → β a → m PUnit) (b : Raw α β) : m PUnit :=
+  b.buckets.forM (AssocList.forM f)
+```
+
+Correct:
+```lean
+/--
+Monadically computes a value by folding the given function over the mappings in the hash
+map in some order.
+-/
+@[inline] def foldM (f : δ → (a : α) → β a → m δ) (init : δ) (b : Raw α β) : m δ :=
+  b.buckets.foldlM (fun acc l => l.foldlM f acc) init
+```
+
+### Where clauses
+
+The `where` keyword should be unindented, and all declarations bound by it should be indented with two spaces.
+
+Blank lines before and after `where` and between declarations bound by `where` are optional and should be chosen
+to maximize readability.
+
+Correct:
+```lean
+@[simp] theorem partition_eq_filter_filter (p : α → Bool) (l : List α) :
+    partition p l = (filter p l, filter (not ∘ p) l) := by
+  simp [partition, aux]
+where
+  aux (l) {as bs} : partition.loop p l (as, bs) =
+      (as.reverse ++ filter p l, bs.reverse ++ filter (not ∘ p) l) :=
+    match l with
+    | [] => by simp [partition.loop, filter]
+    | a :: l => by cases pa : p a <;> simp [partition.loop, pa, aux, filter, append_assoc]
+```
+
+### Termination arguments
+
+The `termination_by`, `decreasing_by`, `partial_fixpoint` keywords should be unindented. The associated terms should be indented like declaration bodies.
+
+Correct:
+```lean
+@[inline] def multiShortOption (handle : Char → m PUnit) (opt : String) : m PUnit := do
+  let rec loop (p : String.Pos) := do
+    if h : opt.atEnd p then
+      return
+    else
+      handle (opt.get' p h)
+      loop (opt.next' p h)
+  termination_by opt.utf8ByteSize - p.byteIdx
+  decreasing_by
+    simp [String.atEnd] at h
+    apply Nat.sub_lt_sub_left h
+    simp [String.lt_next opt p]
+  loop ⟨1⟩
+```
+
+Correct:
+```lean
+def substrEq (s1 : String) (off1 : String.Pos) (s2 : String) (off2 : String.Pos) (sz : Nat) : Bool :=
+  off1.byteIdx + sz ≤ s1.endPos.byteIdx && off2.byteIdx + sz ≤ s2.endPos.byteIdx && loop off1 off2 { byteIdx := off1.byteIdx + sz }
+where
+  loop (off1 off2 stop1 : Pos) :=
+    if _h : off1.byteIdx < stop1.byteIdx then
+      let c₁ := s1.get off1
+      let c₂ := s2.get off2
+      c₁ == c₂ && loop (off1 + c₁) (off2 + c₂) stop1
+    else true
+  termination_by stop1.1 - off1.1
+  decreasing_by
+    have := Nat.sub_lt_sub_left _h (Nat.add_lt_add_left c₁.utf8Size_pos off1.1)
+    decreasing_tactic
+```
+
+Correct:
+```lean
+theorem div_add_mod (m n : Nat) : n * (m / n) + m % n = m := by
+  rw [div_eq, mod_eq]
+  have h : Decidable (0 < n ∧ n ≤ m) := inferInstance
+  cases h with
+  | isFalse h => simp [h]
+  | isTrue h =>
+    simp [h]
+    have ih := div_add_mod (m - n) n
+    rw [Nat.left_distrib, Nat.mul_one, Nat.add_assoc, Nat.add_left_comm, ih, Nat.add_comm, Nat.sub_add_cancel h.2]
+decreasing_by apply div_rec_lemma; assumption
+```
+
+### Deriving
+
+The `deriving` clause should be unindented.
+
+Correct:
+```lean
+structure Iterator where
+  array : ByteArray
+  idx : Nat
+deriving Inhabited
+```
+
+## Notation and Unicode
+
+We generally prefer to use notation as available. We usually prefer the Unicode versions of notations over non-Unicode alternatives.
+
+There are some rules and exceptions regarding specific notations which are listed below:
+
+* Sigma types: use `(a : α) × β a` instead of `Σ a, β a` or `Sigma β`.
+* Function arrows: use `fun a => f x` instead of `fun x ↦ f x` or `λ x => f x` or any other variant.
+
+## Language constructs
+
+### Pattern matching, induction etc.
+
+Match arms are indented at the indentation level that the match statement would have if it was on its own line. If the match is implicit, then the arms should be indented as if the match was explicitly given. The content of match arms is indented two spaces, so that it appears on the same level as the match pattern.
+
+Correct:
+```lean
+def alter [BEq α] {β : Type v} (a : α) (f : Option β → Option β) :
+    AssocList α (fun _ => β) → AssocList α (fun _ => β)
+  | nil => match f none with
+    | none => nil
+    | some b => AssocList.cons a b nil
+  | cons k v l =>
+    if k == a then
+      match f v with
+      | none => l
+      | some b => cons a b l
+    else
+      cons k v (alter a f l)
+```
+
+Correct:
+```lean
+theorem eq_append_cons_of_mem {a : α} {xs : List α} (h : a ∈ xs) :
+    ∃ as bs, xs = as ++ a :: bs ∧ a ∉ as := by
+  induction xs with
+  | nil => cases h
+  | cons x xs ih =>
+    simp at h
+    cases h with
+    | inl h => exact ⟨[], xs, by simp_all⟩
+    | inr h =>
+      by_cases h' : a = x
+      · subst h'
+        exact ⟨[], xs, by simp⟩
+      · obtain ⟨as, bs, rfl, h⟩ := ih h
+        exact ⟨x :: as, bs, rfl, by simp_all⟩
+```
+
+Aligning match arms is allowed, but not required.
+
+Correct:
+```lean
+def mkEqTrans? (h₁? h₂? : Option Expr) : MetaM (Option Expr) :=
+  match h₁?, h₂? with
+  | none, none       => return none
+  | none, some h     => return h
+  | some h, none     => return h
+  | some h₁, some h₂ => mkEqTrans h₁ h₂
+```
+
+Correct:
+```lean
+def mkEqTrans? (h₁? h₂? : Option Expr) : MetaM (Option Expr) :=
+  match h₁?, h₂? with
+  | none, none => return none
+  | none, some h => return h
+  | some h, none => return h
+  | some h₁, some h₂ => mkEqTrans h₁ h₂
+```
+
+Correct:
+```lean
+def mkEqTrans? (h₁? h₂? : Option Expr) : MetaM (Option Expr) :=
+  match h₁?, h₂? with
+  | none,    none    => return none
+  | none,    some h  => return h
+  | some h,  none    => return h
+  | some h₁, some h₂ => mkEqTrans h₁ h₂
+```
+
+### Structures
+
+Note to external contributors: this is a section where the Lean style and the mathlib style are different.
+
+When using structure instance syntax over multiple lines, the opening brace should go on the preceding line, while the closing brace should go on its own line. The rest of the syntax should be indented by one level. During structure updates, the `with` clause goes on the same line as the opening brace. Aligning at the assignment symbol is allowed but not required.
+
+Correct:
+```lean
+def addConstAsync (env : Environment) (constName : Name) (kind : ConstantKind) (reportExts := true) :
+    IO AddConstAsyncResult := do
+  let sigPromise ← IO.Promise.new
+  let infoPromise ← IO.Promise.new
+  let extensionsPromise ← IO.Promise.new
+  let checkedEnvPromise ← IO.Promise.new
+  let asyncConst := {
+    constInfo := {
+      name := constName
+      kind
+      sig := sigPromise.result
+      constInfo := infoPromise.result
+    }
+    exts? := guard reportExts *> some extensionsPromise.result
+  }
+  return {
+    constName, kind
+    mainEnv := { env with
+      asyncConsts := env.asyncConsts.add asyncConst
+      checked := checkedEnvPromise.result }
+    asyncEnv := { env with
+      asyncCtx? := some { declPrefix := privateToUserName constName.eraseMacroScopes }
+    }
+    sigPromise, infoPromise, extensionsPromise, checkedEnvPromise
+  }
+```
+
+Correct:
+```lean
+instance [Inhabited α] : Inhabited (Descr α β σ) where
+  default := {
+    name         := default
+    mkInitial    := default
+    ofOLeanEntry := default
+    toOLeanEntry := default
+    addEntry     := fun s _ => s
+  }
+```
+
+### Declaring structures
+
+When defining structure types, do not parenthesize structure fields.
+
+When declaring a structure type with a custom constructor name, put the custom name on its own line, indented like the
+structure fields, and add a documentation comment.
+
+Correct:
+
+```lean
+/--
+A bitvector of the specified width.
+
+This is represented as the underlying `Nat` number in both the runtime
+and the kernel, inheriting all the special support for `Nat`.
+-/
+structure BitVec (w : Nat) where
+  /--
+  Constructs a `BitVec w` from a number less than `2^w`.
+  O(1), because we use `Fin` as the internal representation of a bitvector.
+  -/
+  ofFin ::
+  /--
+  Interprets a bitvector as a number less than `2^w`.
+  O(1), because we use `Fin` as the internal representation of a bitvector.
+  -/
+  toFin : Fin (2 ^ w)
+```
+
+## Tactic proofs
+
+Tactic proofs are the most common thing to break during any kind of upgrade, so it is important to write them in a way that minimizes the likelihood of proofs breaking and that makes it easy to debug breakages if they do occur.
+
+If there are multiple goals, either use a tactic combinator (like `all_goals`) to operate on all of them or a clearly specified subset, or use focus dots to work on goals one at a time. Using structured proofs (e.g., `induction … with`) is encouraged but not mandatory.
+
+Squeeze non-terminal `simp`s (i.e., calls to `simp` which do not close the goal). Squeezing terminal `simp`s is generally discouraged, although there are exceptions (for example if squeezing yields a noticeable performance improvement).
+
+Do not over-golf proofs in ways that are likely to lead to hard-to-debug breakage. Examples of things to avoid include complex multi-goal manipulation using lots of tactic combinators, complex uses of the substitution operator (`▸`) and clever point-free expressions (possibly involving anonymous function notation for multiple arguments).
+
+Do not under-golf proofs: for routine tasks, use the most powerful tactics available.
+
+Do not use `erw`. Avoid using `rfl` after `simp` or `rw`, as this usually indicates a missing lemma that should be used instead of `rfl`.
+
+Use `(d)simp` or `rw` instead of `delta` or `unfold`. Use `refine` instead of `refine’`. Use `haveI` and `letI` only if they are actually required.
+
+Prefer highly automated tactics (like `grind` and `omega`) over low-level proofs, unless the automated tactic requires unacceptable additional imports or has bad performance. If you decide against using a highly automated tactic, leave a comment explaining the decision.
+
+## `do` notation
+
+The `do` keyword goes on the same line as the corresponding `:=` (or `=>`, or similar). `Id.run do` should be treated as if it was a bare `do`.
+
+Use early `return` statements to reduce nesting depth and make the non-exceptional control flow of a function easier to see.
+
+Alternatives for `let` matches may be placed in the same line or in the next line, indented by two spaces. If the term that is
+being matched on is itself more than one line and there is an alternative present, consider breaking immediately after `←` and indent
+as far as necessary to ensure readability.
+
+Correct:
+```lean
+def getFunDecl (fvarId : FVarId) : CompilerM FunDecl := do
+  let some decl ← findFunDecl? fvarId | throwError "unknown local function {fvarId.name}"
+  return decl
+```
+
+Correct:
+```lean
+def getFunDecl (fvarId : FVarId) : CompilerM FunDecl := do
+  let some decl ←
+        findFunDecl? fvarId
+    | throwError "unknown local function {fvarId.name}"
+  return decl
+```
+
+Correct:
+```lean
+def getFunDecl (fvarId : FVarId) : CompilerM FunDecl := do
+  let some decl ← findFunDecl?
+      fvarId
+    | throwError "unknown local function {fvarId.name}"
+  return decl
+```
+
+Correct:
+```lean
+def tagUntaggedGoals (parentTag : Name) (newSuffix : Name) (newGoals : List MVarId) : TacticM Unit := do
+  let mctx ← getMCtx
+  let mut numAnonymous := 0
+  for g in newGoals do
+    if mctx.isAnonymousMVar g then
+      numAnonymous := numAnonymous + 1
+  modifyMCtx fun mctx => Id.run do
+    let mut mctx := mctx
+    let mut idx  := 1
+    for g in newGoals do
+      if mctx.isAnonymousMVar g then
+        if numAnonymous == 1 then
+          mctx := mctx.setMVarUserName g parentTag
+        else
+          mctx := mctx.setMVarUserName g (parentTag ++ newSuffix.appendIndexAfter idx)
+        idx := idx + 1
+    pure mctx
+```
+

doc/std/vision.md

@@ -0,0 +1,98 @@
+# The Lean 4 standard library
+
+Maintainer team (in alphabetical order): Henrik Böving, Markus Himmel
+(community contact & external contribution coordinator), Kim Morrison, Paul
+Reichert, Sofia Rodrigues.
+
+The Lean 4 standard library is a core part of the Lean distribution, providing
+essential building blocks for functional programming, verified software
+development, and software verification. Unlike the standard libraries of most
+other languages, many of its components are formally verified and can be used
+as part of verified applications.
+
+The standard library is a public API that contains the components listed in the
+standard library outline below. Not all public APIs in the Lean distribution
+are part of the standard library, and the standard library does not correspond
+to a certain directory within the Lean source repository (like `Std`). For
+example, the metaprogramming framework is not part of the standard library, but
+basic types like `True` and `Nat` are.
+
+The standard library is under active development. Our guiding principles are:
+
+* Provide comprehensive, verified building blocks for real-world software.
+* Build a public API of the highest quality with excellent internal consistency.
+* Carefully optimize components that may be used in performance-critical software.
+* Ensure smooth adoption and maintenance for users.
+* Offer excellent documentation, example projects, and guides.
+* Provide a reliable and extensible basis that libraries for software
+  development, software verification and mathematics can build on.
+
+The standard library is principally developed by the Lean FRO. Community
+contributions are welcome. If you would like to contribute, please refer to the
+call for contributions below.
+
+### Standard library outline
+
+1. Core types and operations
+   1. Basic types
+   2. Numeric types, including floating point numbers
+   3. Containers
+   4. Strings and formatting
+2. Language constructs
+   1. Ranges and iterators
+   2. Comparison, ordering, hashing and related type classes
+   3. Basic monad infrastructure
+3. Libraries
+   1. Random numbers
+   2. Dates and times
+4. Operating system abstractions
+   1. Concurrency and parallelism primitives
+   2. Asynchronous I/O
+   3. FFI helpers
+   4. Environment, file system, processes
+   5. Locales
+
+The material covered in the first three sections (core types and operations,
+language constructs and libraries) will be verified, with the exception of
+floating point numbers and the parts of the libraries that interface with the
+operating system (e.g., sources of operating system randomness or time zone
+database access).
+
+### Call for contributions
+
+Thank you for taking interest in contributing to the Lean standard library\!
+There are two main ways for community members to contribute to the Lean
+standard library: by contributing experience reports or by contributing code
+and lemmas.
+
+**If you are using Lean for software verification or verified software
+development:** hearing about your experiences using Lean and its standard
+library for software verification is extremely valuable to us. We are committed
+to building a standard library suitable for real-world applications and your
+input will directly influence the continued evolution of the Lean standard
+library. Please reach out to the standard library maintainer team via Zulip
+(either in a public thread in the \#lean4 channel or via direct message). Even
+just a link to your code helps. Thanks\!
+
+**If you have code that you believe could enhance the Lean 4 standard
+library:** we encourage you to initiate a discussion in the \#lean4 channel on
+Zulip. This is the most effective way to receive preliminary feedback on your
+contribution. The Lean standard library has a very precise scope and it has
+very high quality standards, so at the moment we are mostly interested in
+contributions that expand upon existing material rather than introducing novel
+concepts.
+
+**If you would like to contribute code to the standard library but don’t know
+what to work on:** we are always excited to meet motivated community members
+who would like to contribute, and there is always impactful work that is
+suitable for new contributors. Please reach out to Markus Himmel on Zulip to
+discuss possible contributions.
+
+As laid out in the [project-wide External Contribution
+Guidelines](../../CONTRIBUTING.md),
+PRs are much more likely to be merged if they are preceded by an RFC or if you
+discussed your planned contribution with a member of the standard library
+maintainer team. When in doubt, introducing yourself is always a good idea.
+
+All code in the standard library is expected to strictly adhere to the
+[standard library coding conventions](./style.md).

flake.lock

@@ -36,17 +36,17 @@
     },
     "nixpkgs-cadical": {
       "locked": {
-        "lastModified": 1722221733,
-        "narHash": "sha256-sga9SrrPb+pQJxG1ttJfMPheZvDOxApFfwXCFO0H9xw=",
+        "lastModified": 1740791350,
+        "narHash": "sha256-igS2Z4tVw5W/x3lCZeeadt0vcU9fxtetZ/RyrqsCRQ0=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "12bf09802d77264e441f48e25459c10c93eada2e",
+        "rev": "199169a2135e6b864a888e89a2ace345703c025d",
         "type": "github"
       },
       "original": {
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "12bf09802d77264e441f48e25459c10c93eada2e",
+        "rev": "199169a2135e6b864a888e89a2ace345703c025d",
         "type": "github"
       }
     },
@@ -67,12 +67,30 @@
         "type": "github"
       }
     },
+    "nixpkgs-older": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1523316493,
+        "narHash": "sha256-5qJS+i5ECICPAKA6FhPLIWkhPKDnOZsZbh2PHYF1Kbs=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "0b307aa73804bbd7a7172899e59ae0b8c347a62d",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "0b307aa73804bbd7a7172899e59ae0b8c347a62d",
+        "type": "github"
+      }
+    },
     "root": {
       "inputs": {
         "flake-utils": "flake-utils",
         "nixpkgs": "nixpkgs",
         "nixpkgs-cadical": "nixpkgs-cadical",
-        "nixpkgs-old": "nixpkgs-old"
+        "nixpkgs-old": "nixpkgs-old",
+        "nixpkgs-older": "nixpkgs-older"
       }
     },
     "systems": {

flake.nix

@@ -5,17 +5,20 @@
   # old nixpkgs used for portable release with older glibc (2.27)
   inputs.nixpkgs-old.url = "github:NixOS/nixpkgs/nixos-19.03";
   inputs.nixpkgs-old.flake = false;
-  # for cadical 1.9.5; sync with CMakeLists.txt
-  inputs.nixpkgs-cadical.url = "github:NixOS/nixpkgs/12bf09802d77264e441f48e25459c10c93eada2e";
+  # old nixpkgs used for portable release with older glibc (2.26)
+  inputs.nixpkgs-older.url = "github:NixOS/nixpkgs/0b307aa73804bbd7a7172899e59ae0b8c347a62d";
+  inputs.nixpkgs-older.flake = false;
+  # for cadical 2.1.2; sync with CMakeLists.txt by taking commit from https://www.nixhub.io/packages/cadical
+  inputs.nixpkgs-cadical.url = "github:NixOS/nixpkgs/199169a2135e6b864a888e89a2ace345703c025d";
   inputs.flake-utils.url = "github:numtide/flake-utils";
 
-  outputs = { self, nixpkgs, nixpkgs-old, flake-utils, ... }@inputs: flake-utils.lib.eachDefaultSystem (system:
+  outputs = inputs: inputs.flake-utils.lib.eachDefaultSystem (system:
     let
-      pkgs = import nixpkgs { inherit system; };
+      pkgs = import inputs.nixpkgs { inherit system; };
       # An old nixpkgs for creating releases with an old glibc
-      pkgsDist-old = import nixpkgs-old { inherit system; };
+      pkgsDist-old = import inputs.nixpkgs-older { inherit system; };
       # An old nixpkgs for creating releases with an old glibc
-      pkgsDist-old-aarch = import nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
+      pkgsDist-old-aarch = import inputs.nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
       pkgsCadical = import inputs.nixpkgs-cadical { inherit system; };
       cadical = if pkgs.stdenv.isLinux then
         # use statically-linked cadical on Linux to avoid glibc versioning troubles
@@ -28,7 +31,7 @@
           stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
         } ({
           buildInputs = with pkgs; [
-            cmake gmp libuv ccache cadical
+            cmake gmp libuv ccache cadical pkg-config
             lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
             gdb
             tree  # for CI
@@ -60,6 +63,7 @@
           GLIBC_DEV = pkgsDist.glibc.dev;
           GCC_LIB = pkgsDist.gcc.cc.lib;
           ZLIB = pkgsDist.zlib;
+          # for CI coredumps
           GDB = pkgsDist.gdb;
         });
     in {

nix/bootstrap.nix

@@ -1,12 +1,12 @@
 { src, debug ? false, stage0debug ? false, extraCMakeFlags ? [],
-  stdenv, lib, cmake, gmp, libuv, cadical, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
+  stdenv, lib, cmake, pkg-config, gmp, libuv, cadical, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
   ... } @ args:
 with builtins;
 lib.warn "The Nix-based build is deprecated" rec {
   inherit stdenv;
   sourceByRegex = p: rs: lib.sourceByRegex p (map (r: "(/src/)?${r}") rs);
   buildCMake = args: stdenv.mkDerivation ({
-    nativeBuildInputs = [ cmake ];
+    nativeBuildInputs = [ cmake pkg-config ];
     buildInputs = [ gmp libuv llvmPackages.llvm ];
     # https://github.com/NixOS/nixpkgs/issues/60919
     hardeningDisable = [ "all" ];

releases/v4.0.0-m4.md

@@ -0,0 +1,292 @@
+v4.0.0-m4 (23 March 2022)
+---------
+
+* `simp` now takes user-defined simp-attributes. You can define a new `simp` attribute by creating a file (e.g., `MySimp.lean`) containing
+  ```lean
+  import Lean
+  open Lean.Meta
+
+  initialize my_ext : SimpExtension ← registerSimpAttr `my_simp "my own simp attribute"
+  ```
+  If you don't need to access `my_ext`, you can also use the macro
+  ```lean
+  import Lean
+
+  register_simp_attr my_simp "my own simp attribute"
+  ```
+  Recall that the new `simp` attribute is not active in the Lean file where it was defined.
+  Here is a small example using the new feature.
+  ```lean
+  import MySimp
+
+  def f (x : Nat) := x + 2
+  def g (x : Nat) := x + 1
+
+  @[my_simp] theorem f_eq : f x = x + 2 := rfl
+  @[my_simp] theorem g_eq : g x = x + 1 := rfl
+
+  example : f x + g x = 2*x + 3 := by
+    simp_arith [my_simp]
+  ```
+
+* Extend `match` syntax: multiple left-hand-sides in a single alternative. Example:
+  ```lean
+  def fib : Nat → Nat
+  | 0 | 1 => 1
+  | n+2 => fib n + fib (n+1)
+  ```
+  This feature was discussed at [issue 371](https://github.com/leanprover/lean4/issues/371). It was implemented as a macro expansion. Thus, the following is accepted.
+  ```lean
+  inductive StrOrNum where
+    | S (s : String)
+    | I (i : Int)
+
+  def StrOrNum.asString (x : StrOrNum) :=
+    match x with
+    | I a | S a => toString a
+  ```
+
+
+* Improve `#eval` command. Now, when it fails to synthesize a `Lean.MetaEval` instance for the result type, it reduces the type and tries again. The following example now works without additional annotations
+  ```lean
+  def Foo := List Nat
+
+  def test (x : Nat) : Foo :=
+    [x, x+1, x+2]
+
+  #eval test 4
+  ```
+
+* `rw` tactic can now apply auto-generated equation theorems for a given definition. Example:
+  ```lean
+  example (a : Nat) (h : n = 1) : [a].length = n := by
+    rw [List.length]
+    trace_state -- .. |- [].length + 1 = n
+    rw [List.length]
+    trace_state -- .. |- 0 + 1 = n
+    rw [h]
+  ```
+
+* [Fuzzy matching for auto completion](https://github.com/leanprover/lean4/pull/1023)
+
+* Extend dot-notation `x.field` for arrow types. If type of `x` is an arrow, we look up for `Function.field`.
+For example, given `f : Nat → Nat` and `g : Nat → Nat`, `f.comp g` is now notation for `Function.comp f g`.
+
+* The new `.<identifier>` notation is now also accepted where a function type is expected.
+  ```lean
+  example (xs : List Nat) : List Nat := .map .succ xs
+  example (xs : List α) : Std.RBTree α ord := xs.foldl .insert ∅
+  ```
+
+* [Add code folding support to the language server](https://github.com/leanprover/lean4/pull/1014).
+
+* Support notation `let <pattern> := <expr> | <else-case>` in `do` blocks.
+
+* Remove support for "auto" `pure`. In the [Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/for.2C.20unexpected.20need.20for.20type.20ascription/near/269083574), the consensus seemed to be that "auto" `pure` is more confusing than it's worth.
+
+* Remove restriction in `congr` theorems that all function arguments on the left-hand-side must be free variables. For example, the following theorem is now a valid `congr` theorem.
+  ```lean
+  @[congr]
+  theorem dep_congr [DecidableEq ι] {p : ι → Set α} [∀ i, Inhabited (p i)] :
+                    ∀ {i j} (h : i = j) (x : p i) (y : α) (hx : x = y), Pi.single (f := (p ·)) i x = Pi.single (f := (p ·)) j ⟨y, hx ▸ h ▸ x.2⟩ :=
+  ```
+
+* [Partially applied congruence theorems.](https://github.com/leanprover/lean4/issues/988)
+
+* Improve elaboration postponement heuristic when expected type is a metavariable. Lean now reduces the expected type before performing the test.
+
+* [Remove deprecated leanpkg](https://github.com/leanprover/lean4/pull/985) in favor of [Lake](https://github.com/leanprover/lake) now bundled with Lean.
+
+* Various improvements to go-to-definition & find-all-references accuracy.
+
+* Auto generated congruence lemmas with support for casts on proofs and `Decidable` instances (see [wishlist](https://github.com/leanprover/lean4/issues/988)).
+
+* Rename option `autoBoundImplicitLocal` => `autoImplicit`.
+
+* [Relax auto-implicit restrictions](https://github.com/leanprover/lean4/pull/1011). The command `set_option relaxedAutoImplicit false` disables the relaxations.
+
+* `contradiction` tactic now closes the goal if there is a `False.elim` application in the target.
+
+* Renamed tatic `byCases` => `by_cases` (motivation: enforcing naming convention).
+
+* Local instances occurring in patterns are now considered by the type class resolution procedure. Example:
+  ```lean
+  def concat : List ((α : Type) × ToString α × α) → String
+    | [] => ""
+    | ⟨_, _, a⟩ :: as => toString a ++ concat as
+  ```
+
+* Notation for providing the motive for `match` expressions has changed.
+  before:
+  ```lean
+  match x, rfl : (y : Nat) → x = y → Nat with
+  | 0,   h => ...
+  | x+1, h => ...
+  ```
+  now:
+  ```lean
+  match (motive := (y : Nat) → x = y → Nat) x, rfl with
+  | 0,   h => ...
+  | x+1, h => ...
+  ```
+  With this change, the notation for giving names to equality proofs in `match`-expressions is not whitespace sensitive anymore. That is,
+  we can now write
+  ```lean
+  match h : sort.swap a b with
+  | (r₁, r₂) => ... -- `h : sort.swap a b = (r₁, r₂)`
+  ```
+
+* `(generalizing := true)` is the default behavior for `match` expressions even if the expected type is not a proposition. In the following example, we used to have to include `(generalizing := true)` manually.
+  ```lean
+  inductive Fam : Type → Type 1 where
+    | any : Fam α
+    | nat : Nat → Fam Nat
+
+  example (a : α) (x : Fam α) : α :=
+    match x with
+    | Fam.any   => a
+    | Fam.nat n => n
+  ```
+
+* We now use `PSum` (instead of `Sum`) when compiling mutually recursive definitions using well-founded recursion.
+
+* Better support for parametric well-founded relations. See [issue #1017](https://github.com/leanprover/lean4/issues/1017). This change affects the low-level `termination_by'` hint because the fixed prefix of the function parameters in not "packed" anymore when constructing the well-founded relation type. For example, in the following definition, `as` is part of the fixed prefix, and is not packed anymore. In previous versions, the `termination_by'` term would be written as `measure fun ⟨as, i, _⟩ => as.size - i`
+  ```lean
+  def sum (as : Array Nat) (i : Nat) (s : Nat) : Nat :=
+    if h : i < as.size then
+      sum as (i+1) (s + as.get ⟨i, h⟩)
+    else
+      s
+  termination_by' measure fun ⟨i, _⟩ => as.size - i
+  ```
+
+* Add `while <cond> do <do-block>`, `repeat <do-block>`, and `repeat <do-block> until <cond>` macros for `do`-block. These macros are based on `partial` definitions, and consequently are useful only for writing programs we don't want to prove anything about.
+
+* Add `arith` option to `Simp.Config`, the macro `simp_arith` expands to `simp (config := { arith := true })`. Only `Nat` and linear arithmetic is currently supported. Example:
+  ```lean
+  example : 0 < 1 + x ∧ x + y + 2 ≥ y + 1 := by
+    simp_arith
+  ```
+
+* Add `fail <string>?` tactic that always fail.
+
+* Add support for acyclicity at dependent elimination. See [issue #1022](https://github.com/leanprover/lean4/issues/1022).
+
+* Add `trace <string>` tactic for debugging purposes.
+
+* Add nontrivial `SizeOf` instance for types `Unit → α`, and add support for them in the auto-generated `SizeOf` instances for user-defined inductive types. For example, given the inductive datatype
+  ```lean
+  inductive LazyList (α : Type u) where
+    | nil                               : LazyList α
+    | cons (hd : α) (tl : LazyList α)   : LazyList α
+    | delayed (t : Thunk (LazyList α))  : LazyList α
+  ```
+  we now have `sizeOf (LazyList.delayed t) = 1 + sizeOf t` instead of `sizeOf (LazyList.delayed t) = 2`.
+
+* Add support for guessing (very) simple well-founded relations when proving termination. For example, the following function does not require a `termination_by` annotation anymore.
+  ```lean
+  def Array.insertAtAux (i : Nat) (as : Array α) (j : Nat) : Array α :=
+    if h : i < j then
+      let as := as.swap! (j-1) j;
+      insertAtAux i as (j-1)
+    else
+      as
+  ```
+
+* Add support for `for h : x in xs do ...` notation where `h : x ∈ xs`. This is mainly useful for showing termination.
+
+* Auto implicit behavior changed for inductive families. An auto implicit argument occurring in inductive family index is also treated as an index (IF it is not fixed, see next item). For example
+  ```lean
+  inductive HasType : Index n → Vector Ty n → Ty → Type where
+  ```
+  is now interpreted as
+  ```lean
+  inductive HasType : {n : Nat} → Index n → Vector Ty n → Ty → Type where
+  ```
+
+* To make the previous feature more convenient to use, we promote a fixed prefix of inductive family indices to parameters. For example, the following declaration is now accepted by Lean
+  ```lean
+  inductive Lst : Type u → Type u
+    | nil  : Lst α
+    | cons : α → Lst α → Lst α
+  ```
+  and `α` in `Lst α` is a parameter. The actual number of parameters can be inspected using the command `#print Lst`. This feature also makes sure we still accept the declaration
+  ```lean
+  inductive Sublist : List α → List α → Prop
+    | slnil : Sublist [] []
+    | cons l₁ l₂ a : Sublist l₁ l₂ → Sublist l₁ (a :: l₂)
+    | cons2 l₁ l₂ a : Sublist l₁ l₂ → Sublist (a :: l₁) (a :: l₂)
+  ```
+
+* Added auto implicit "chaining". Unassigned metavariables occurring in the auto implicit types now become new auto implicit locals. Consider the following example:
+  ```lean
+  inductive HasType : Fin n → Vector Ty n → Ty → Type where
+    | stop : HasType 0 (ty :: ctx) ty
+    | pop  : HasType k ctx ty → HasType k.succ (u :: ctx) ty
+  ```
+  `ctx` is an auto implicit local in the two constructors, and it has type `ctx : Vector Ty ?m`. Without auto implicit "chaining", the metavariable `?m` will remain unassigned. The new feature creates yet another implicit local `n : Nat` and assigns `n` to `?m`. So, the declaration above is shorthand for
+  ```lean
+  inductive HasType : {n : Nat} → Fin n → Vector Ty n → Ty → Type where
+    | stop : {ty : Ty} → {n : Nat} → {ctx : Vector Ty n} → HasType 0 (ty :: ctx) ty
+    | pop  : {n : Nat} → {k : Fin n} → {ctx : Vector Ty n} → {ty : Ty} → HasType k ctx ty → HasType k.succ (u :: ctx) ty
+  ```
+
+* Eliminate auxiliary type annotations (e.g, `autoParam` and `optParam`) from recursor minor premises and projection declarations. Consider the following example
+  ```lean
+  structure A :=
+    x : Nat
+    h : x = 1 := by trivial
+
+  example (a : A) : a.x = 1 := by
+    have aux := a.h
+    -- `aux` has now type `a.x = 1` instead of `autoParam (a.x = 1) auto✝`
+    exact aux
+
+  example (a : A) : a.x = 1 := by
+    cases a with
+    | mk x h =>
+      -- `h` has now type `x = 1` instead of `autoParam (x = 1) auto✝`
+      assumption
+  ```
+
+* We now accept overloaded notation in patterns, but we require the set of pattern variables in each alternative to be the same. Example:
+  ```lean
+  inductive Vector (α : Type u) : Nat → Type u
+    | nil : Vector α 0
+    | cons : α → Vector α n → Vector α (n+1)
+
+  infix:67 " :: " => Vector.cons -- Overloading the `::` notation
+
+  def head1 (x : List α) (h : x ≠ []) : α :=
+    match x with
+    | a :: as => a -- `::` is `List.cons` here
+
+  def head2 (x : Vector α (n+1)) : α :=
+    match x with
+    | a :: as => a -- `::` is `Vector.cons` here
+  ```
+
+* New notation `.<identifier>` based on Swift. The namespace is inferred from the expected type. See [issue #944](https://github.com/leanprover/lean4/issues/944). Examples:
+  ```lean
+  def f (x : Nat) : Except String Nat :=
+    if x > 0 then
+      .ok x
+    else
+      .error "x is zero"
+
+  namespace Lean.Elab
+  open Lsp
+
+  def identOf : Info → Option (RefIdent × Bool)
+    | .ofTermInfo ti => match ti.expr with
+      | .const n .. => some (.const n, ti.isBinder)
+      | .fvar id .. => some (.fvar id, ti.isBinder)
+      | _ => none
+    | .ofFieldInfo fi => some (.const fi.projName, false)
+    | _ => none
+
+  def isImplicit (bi : BinderInfo) : Bool :=
+    bi matches .implicit
+
+  end Lean.Elab
+  ```

releases/v4.0.0-m5.md

@@ -0,0 +1,715 @@
+v4.0.0-m5 (07 August 2022)
+---------
+
+* Update Lake to v4.0.0. See the [v4.0.0 release notes](https://github.com/leanprover/lake/releases/tag/v4.0.0) for detailed changes.
+
+* Mutual declarations in different namespaces are now supported. Example:
+  ```lean
+  mutual
+    def Foo.boo (x : Nat) :=
+      match x with
+      | 0 => 1
+      | x + 1 => 2*Boo.bla x
+
+    def Boo.bla (x : Nat) :=
+      match x with
+      | 0 => 2
+      | x+1 => 3*Foo.boo x
+  end
+  ```
+  A `namespace` is automatically created for the common prefix. Example:
+  ```lean
+  mutual
+    def Tst.Foo.boo (x : Nat) := ...
+    def Tst.Boo.bla (x : Nat) := ...
+  end
+  ```
+  expands to
+  ```lean
+  namespace Tst
+  mutual
+    def Foo.boo (x : Nat) := ...
+    def Boo.bla (x : Nat) := ...
+  end
+  end Tst
+  ```
+
+* Allow users to install their own `deriving` handlers for existing type classes.
+  See example at [Simple.lean](https://github.com/leanprover/lean4/blob/master/tests/pkg/deriving/UserDeriving/Simple.lean).
+
+* Add tactic `congr (num)?`. See doc string for additional details.
+
+* [Missing doc linter](https://github.com/leanprover/lean4/pull/1390)
+
+* `match`-syntax notation now checks for unused alternatives. See issue [#1371](https://github.com/leanprover/lean4/issues/1371).
+
+* Auto-completion for structure instance fields. Example:
+  ```lean
+  example : Nat × Nat := {
+    f -- HERE
+  }
+  ```
+  `fst` now appears in the list of auto-completion suggestions.
+
+* Auto-completion for dotted identifier notation. Example:
+  ```lean
+  example : Nat :=
+    .su -- HERE
+  ```
+  `succ` now appears in the list of auto-completion suggestions.
+
+* `nat_lit` is not needed anymore when declaring `OfNat` instances. See issues [#1389](https://github.com/leanprover/lean4/issues/1389) and [#875](https://github.com/leanprover/lean4/issues/875). Example:
+  ```lean
+  inductive Bit where
+    | zero
+    | one
+
+  instance inst0 : OfNat Bit 0 where
+    ofNat := Bit.zero
+
+  instance : OfNat Bit 1 where
+    ofNat := Bit.one
+
+  example : Bit := 0
+  example : Bit := 1
+  ```
+
+* Add `[elabAsElim]` attribute (it is called `elab_as_eliminator` in Lean 3). Motivation: simplify the Mathlib port to Lean 4.
+
+* `Trans` type class now accepts relations in `Type u`. See this [Zulip issue](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Calc.20mode/near/291214574).
+
+* Accept unescaped keywords as inductive constructor names. Escaping can often be avoided at use sites via dot notation.
+  ```lean
+  inductive MyExpr
+    | let : ...
+
+  def f : MyExpr → MyExpr
+    | .let ... => .let ...
+  ```
+
+* Throw an error message at parametric local instances such as `[Nat -> Decidable p]`. The type class resolution procedure
+  cannot use this kind of local instance because the parameter does not have a forward dependency.
+  This check can be disabled using `set_option checkBinderAnnotations false`.
+
+* Add option `pp.showLetValues`. When set to `false`, the info view hides the value of `let`-variables in a goal.
+  By default, it is `true` when visualizing tactic goals, and `false` otherwise.
+  See [issue #1345](https://github.com/leanprover/lean4/issues/1345) for additional details.
+
+* Add option `warningAsError`. When set to true, warning messages are treated as errors.
+
+* Support dotted notation and named arguments in patterns. Example:
+  ```lean
+  def getForallBinderType (e : Expr) : Expr :=
+    match e with
+    | .forallE (binderType := type) .. => type
+    | _ => panic! "forall expected"
+  ```
+
+* "jump-to-definition" now works for function names embedded in the following attributes
+  `@[implementedBy funName]`, `@[tactic parserName]`, `@[termElab parserName]`, `@[commandElab parserName]`,
+  `@[builtinTactic parserName]`, `@[builtinTermElab parserName]`, and `@[builtinCommandElab parserName]`.
+   See [issue #1350](https://github.com/leanprover/lean4/issues/1350).
+
+* Improve `MVarId` methods discoverability. See [issue #1346](https://github.com/leanprover/lean4/issues/1346).
+  We still have to add similar methods for `FVarId`, `LVarId`, `Expr`, and other objects.
+  Many existing methods have been marked as deprecated.
+
+* Add attribute `[deprecated]` for marking deprecated declarations. Examples:
+  ```lean
+  def g (x : Nat) := x + 1
+
+  -- Whenever `f` is used, a warning message is generated suggesting to use `g` instead.
+  @[deprecated g]
+  def f (x : Nat) := x + 1
+
+  #check f 0 -- warning: `f` has been deprecated, use `g` instead
+
+  -- Whenever `h` is used, a warning message is generated.
+  @[deprecated]
+  def h (x : Nat) := x + 1
+
+  #check h 0 -- warning: `h` has been deprecated
+  ```
+
+* Add type `LevelMVarId` (and abbreviation `LMVarId`) for universe level metavariable ids.
+  Motivation: prevent meta-programmers from mixing up universe and expression metavariable ids.
+
+* Improve `calc` term and tactic. See [issue #1342](https://github.com/leanprover/lean4/issues/1342).
+
+* [Relaxed antiquotation parsing](https://github.com/leanprover/lean4/pull/1272) further reduces the need for explicit `$x:p` antiquotation kind annotations.
+
+* Add support for computed fields in inductives. Example:
+  ```lean
+  inductive Exp
+    | var (i : Nat)
+    | app (a b : Exp)
+  with
+    @[computedField] hash : Exp → Nat
+      | .var i => i
+      | .app a b => a.hash * b.hash + 1
+  ```
+  The result of the `Exp.hash` function is then stored as an extra "computed" field in the `.var` and `.app` constructors;
+  `Exp.hash` accesses this field and thus runs in constant time (even on dag-like values).
+
+* Update `a[i]` notation. It is now based on the typeclass
+  ```lean
+  class GetElem (cont : Type u) (idx : Type v) (elem : outParam (Type w)) (dom : outParam (cont → idx → Prop)) where
+    getElem (xs : cont) (i : idx) (h : dom xs i) : Elem
+  ```
+  The notation `a[i]` is now defined as follows
+  ```lean
+  macro:max x:term noWs "[" i:term "]" : term => `(getElem $x $i (by get_elem_tactic))
+  ```
+  The proof that `i` is a valid index is synthesized using the tactic `get_elem_tactic`.
+  For example, the type `Array α` has the following instances
+  ```lean
+  instance : GetElem (Array α) Nat α fun xs i => LT.lt i xs.size where ...
+  instance : GetElem (Array α) USize α fun xs i => LT.lt i.toNat xs.size where ...
+  ```
+  You can use the notation `a[i]'h` to provide the proof manually.
+  Two other notations were introduced: `a[i]!` and `a[i]?`, For `a[i]!`, a panic error message is produced at
+  runtime if `i` is not a valid index. `a[i]?` has type `Option α`, and `a[i]?` evaluates to `none` if the
+  index `i` is not valid.
+  The three new notations are defined as follows:
+  ```lean
+  @[inline] def getElem' [GetElem cont idx elem dom] (xs : cont) (i : idx) (h : dom xs i) : elem :=
+  getElem xs i h
+
+  @[inline] def getElem! [GetElem cont idx elem dom] [Inhabited elem] (xs : cont) (i : idx) [Decidable (dom xs i)] : elem :=
+    if h : _ then getElem xs i h else panic! "index out of bounds"
+
+  @[inline] def getElem? [GetElem cont idx elem dom] (xs : cont) (i : idx) [Decidable (dom xs i)] : Option elem :=
+    if h : _ then some (getElem xs i h) else none
+
+  macro:max x:term noWs "[" i:term "]" noWs "?" : term => `(getElem? $x $i)
+  macro:max x:term noWs "[" i:term "]" noWs "!" : term => `(getElem! $x $i)
+  macro x:term noWs "[" i:term "]'" h:term:max : term => `(getElem' $x $i $h)
+  ```
+  See discussion on [Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/String.2EgetOp/near/287855425).
+  Examples:
+  ```lean
+  example (a : Array Int) (i : Nat) : Int :=
+    a[i] -- Error: failed to prove index is valid ...
+
+  example (a : Array Int) (i : Nat) (h : i < a.size) : Int :=
+    a[i] -- Ok
+
+  example (a : Array Int) (i : Nat) : Int :=
+    a[i]! -- Ok
+
+  example (a : Array Int) (i : Nat) : Option Int :=
+    a[i]? -- Ok
+
+  example (a : Array Int) (h : a.size = 2) : Int :=
+    a[0]'(by rw [h]; decide) -- Ok
+
+  example (a : Array Int) (h : a.size = 2) : Int :=
+    have : 0 < a.size := by rw [h]; decide
+    have : 1 < a.size := by rw [h]; decide
+    a[0] + a[1] -- Ok
+
+  example (a : Array Int) (i : USize) (h : i.toNat < a.size) : Int :=
+    a[i] -- Ok
+  ```
+  The `get_elem_tactic` is defined as
+  ```lean
+  macro "get_elem_tactic" : tactic =>
+    `(first
+      | get_elem_tactic_trivial
+      | fail "failed to prove index is valid, ..."
+     )
+  ```
+  The `get_elem_tactic_trivial` auxiliary tactic can be extended using `macro_rules`. By default, it tries `trivial`, `simp_arith`, and a special case for `Fin`. In the future, it will also try `linarith`.
+  You can extend `get_elem_tactic_trivial` using `my_tactic` as follows
+  ```lean
+  macro_rules
+  | `(tactic| get_elem_tactic_trivial) => `(tactic| my_tactic)
+  ```
+  Note that `Idx`'s type in `GetElem` does not depend on `Cont`. So, you cannot write the instance `instance : GetElem (Array α) (Fin ??) α fun xs i => ...`, but the Lean library comes equipped with the following auxiliary instance:
+  ```lean
+  instance [GetElem cont Nat elem dom] : GetElem cont (Fin n) elem fun xs i => dom xs i where
+    getElem xs i h := getElem xs i.1 h
+  ```
+  and helper tactic
+  ```lean
+  macro_rules
+  | `(tactic| get_elem_tactic_trivial) => `(tactic| apply Fin.val_lt_of_le; get_elem_tactic_trivial; done)
+  ```
+  Example:
+  ```lean
+  example (a : Array Nat) (i : Fin a.size) :=
+    a[i] -- Ok
+
+  example (a : Array Nat) (h : n ≤ a.size) (i : Fin n) :=
+    a[i] -- Ok
+  ```
+
+* Better support for qualified names in recursive declarations. The following is now supported:
+  ```lean
+  namespace Nat
+    def fact : Nat → Nat
+    | 0 => 1
+    | n+1 => (n+1) * Nat.fact n
+  end Nat
+  ```
+
+* Add support for `CommandElabM` monad at `#eval`. Example:
+  ```lean
+  import Lean
+
+  open Lean Elab Command
+
+  #eval do
+    let id := mkIdent `foo
+    elabCommand (← `(def $id := 10))
+
+  #eval foo -- 10
+  ```
+
+* Try to elaborate `do` notation even if the expected type is not available. We still delay elaboration when the expected type
+  is not available. This change is particularly useful when writing examples such as
+  ```lean
+  #eval do
+    IO.println "hello"
+    IO.println "world"
+  ```
+  That is, we don't have to use the idiom `#eval show IO _ from do ...` anymore.
+  Note that auto monadic lifting is less effective when the expected type is not available.
+  Monadic polymorphic functions (e.g., `ST.Ref.get`) also require the expected type.
+
+* On Linux, panics now print a backtrace by default, which can be disabled by setting the environment variable `LEAN_BACKTRACE` to `0`.
+  Other platforms are TBD.
+
+* The `group(·)` `syntax` combinator is now introduced automatically where necessary, such as when using multiple parsers inside `(...)+`.
+
+* Add ["Typed Macros"](https://github.com/leanprover/lean4/pull/1251): syntax trees produced and accepted by syntax antiquotations now remember their syntax kinds, preventing accidental production of ill-formed syntax trees and reducing the need for explicit `:kind` antiquotation annotations. See PR for details.
+
+* Aliases of protected definitions are protected too. Example:
+  ```lean
+  protected def Nat.double (x : Nat) := 2*x
+
+  namespace Ex
+  export Nat (double) -- Add alias Ex.double for Nat.double
+  end Ex
+
+  open Ex
+  #check Ex.double -- Ok
+  #check double -- Error, `Ex.double` is alias for `Nat.double` which is protected
+  ```
+
+* Use `IO.getRandomBytes` to initialize random seed for `IO.rand`. See discussion at [this PR](https://github.com/leanprover/lean4-samples/pull/2).
+
+* Improve dot notation and aliases interaction. See discussion on [Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Namespace-based.20overloading.20does.20not.20find.20exports/near/282946185) for additional details.
+  Example:
+  ```lean
+  def Set (α : Type) := α → Prop
+  def Set.union (s₁ s₂ : Set α) : Set α := fun a => s₁ a ∨ s₂ a
+  def FinSet (n : Nat) := Fin n → Prop
+
+  namespace FinSet
+    export Set (union) -- FinSet.union is now an alias for `Set.union`
+  end FinSet
+
+  example (x y : FinSet 10) : FinSet 10 :=
+    x.union y -- Works
+  ```
+
+* `ext` and `enter` conv tactics can now go inside let-declarations. Example:
+  ```lean
+  example (g : Nat → Nat) (y : Nat) (h : let x := y + 1; g (0+x) = x) : g (y + 1) = y + 1 := by
+    conv at h => enter [x, 1, 1]; rw [Nat.zero_add]
+    /-
+      g : Nat → Nat
+      y : Nat
+      h : let x := y + 1;
+          g x = x
+      ⊢ g (y + 1) = y + 1
+    -/
+    exact h
+  ```
+
+* Add `zeta` conv tactic to expand let-declarations. Example:
+  ```lean
+  example (h : let x := y + 1; 0 + x = y) : False := by
+    conv at h => zeta; rw [Nat.zero_add]
+    /-
+      y : Nat
+      h : y + 1 = y
+      ⊢ False
+    -/
+    simp_arith at h
+  ```
+
+* Improve namespace resolution. See issue [#1224](https://github.com/leanprover/lean4/issues/1224). Example:
+  ```lean
+  import Lean
+  open Lean Parser Elab
+  open Tactic -- now opens both `Lean.Parser.Tactic` and `Lean.Elab.Tactic`
+  ```
+
+* Rename `constant` command to `opaque`. See discussion at [Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/What.20is.20.60opaque.60.3F/near/284926171).
+
+* Extend `induction` and `cases` syntax: multiple left-hand-sides in a single alternative. This extension is very similar to the one implemented for `match` expressions. Examples:
+  ```lean
+  inductive Foo where
+    | mk1 (x : Nat) | mk2 (x : Nat) | mk3
+
+  def f (v : Foo) :=
+    match v with
+    | .mk1 x => x + 1
+    | .mk2 x => 2*x + 1
+    | .mk3   => 1
+
+  theorem f_gt_zero : f v > 0 := by
+    cases v with
+    | mk1 x | mk2 x => simp_arith!  -- New feature used here!
+    | mk3 => decide
+  ```
+
+* [`let/if` indentation in `do` blocks in now supported.](https://github.com/leanprover/lean4/issues/1120)
+
+* Add unnamed antiquotation `$_` for use in syntax quotation patterns.
+
+* [Add unused variables linter](https://github.com/leanprover/lean4/pull/1159). Feedback welcome!
+
+* Lean now generates an error if the body of a declaration body contains a universe parameter that does not occur in the declaration type, nor is an explicit parameter.
+  Examples:
+  ```lean
+  /-
+  The following declaration now produces an error because `PUnit` is universe polymorphic,
+  but the universe parameter does not occur in the function type `Nat → Nat`
+  -/
+  def f (n : Nat) : Nat :=
+    let aux (_ : PUnit) : Nat := n + 1
+    aux ⟨⟩
+
+  /-
+  The following declaration is accepted because the universe parameter was explicitly provided in the
+  function signature.
+  -/
+  def g.{u} (n : Nat) : Nat :=
+    let aux (_ : PUnit.{u}) : Nat := n + 1
+    aux ⟨⟩
+  ```
+
+* Add `subst_vars` tactic.
+
+* [Fix `autoParam` in structure fields lost in multiple inheritance.](https://github.com/leanprover/lean4/issues/1158).
+
+* Add `[eliminator]` attribute. It allows users to specify default recursor/eliminators for the `induction` and `cases` tactics.
+  It is an alternative for the `using` notation. Example:
+  ```lean
+  @[eliminator] protected def recDiag {motive : Nat → Nat → Sort u}
+      (zero_zero : motive 0 0)
+      (succ_zero : (x : Nat) → motive x 0 → motive (x + 1) 0)
+      (zero_succ : (y : Nat) → motive 0 y → motive 0 (y + 1))
+      (succ_succ : (x y : Nat) → motive x y → motive (x + 1) (y + 1))
+      (x y : Nat) :  motive x y :=
+    let rec go : (x y : Nat) → motive x y
+      | 0,     0 => zero_zero
+      | x+1, 0   => succ_zero x (go x 0)
+      | 0,   y+1 => zero_succ y (go 0 y)
+      | x+1, y+1 => succ_succ x y (go x y)
+    go x y
+  termination_by go x y => (x, y)
+
+  def f (x y : Nat) :=
+    match x, y with
+    | 0,   0   => 1
+    | x+1, 0   => f x 0
+    | 0,   y+1 => f 0 y
+    | x+1, y+1 => f x y
+  termination_by f x y => (x, y)
+
+  example (x y : Nat) : f x y > 0 := by
+    induction x, y <;> simp [f, *]
+  ```
+
+* Add support for `casesOn` applications to structural and well-founded recursion modules.
+  This feature is useful when writing definitions using tactics. Example:
+  ```lean
+  inductive Foo where
+    | a | b | c
+    | pair: Foo × Foo → Foo
+
+  def Foo.deq (a b : Foo) : Decidable (a = b) := by
+    cases a <;> cases b
+    any_goals apply isFalse Foo.noConfusion
+    any_goals apply isTrue rfl
+    case pair a b =>
+      let (a₁, a₂) := a
+      let (b₁, b₂) := b
+      exact match deq a₁ b₁, deq a₂ b₂ with
+      | isTrue h₁, isTrue h₂ => isTrue (by rw [h₁,h₂])
+      | isFalse h₁, _ => isFalse (fun h => by cases h; cases (h₁ rfl))
+      | _, isFalse h₂ => isFalse (fun h => by cases h; cases (h₂ rfl))
+  ```
+
+* `Option` is again a monad. The auxiliary type `OptionM` has been removed. See [Zulip thread](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Do.20we.20still.20need.20OptionM.3F/near/279761084).
+
+* Improve `split` tactic. It used to fail on `match` expressions of the form `match h : e with ...` where `e` is not a free variable.
+  The failure used to occur during generalization.
+
+
+* New encoding for `match`-expressions that use the `h :` notation for discriminants. The information is not lost during delaboration,
+  and it is the foundation for a better `split` tactic. at delaboration time. Example:
+  ```lean
+  #print Nat.decEq
+  /-
+  protected def Nat.decEq : (n m : Nat) → Decidable (n = m) :=
+  fun n m =>
+    match h : Nat.beq n m with
+    | true => isTrue (_ : n = m)
+    | false => isFalse (_ : ¬n = m)
+  -/
+  ```
+
+* `exists` tactic is now takes a comma separated list of terms.
+
+* Add `dsimp` and `dsimp!` tactics. They guarantee the result term is definitionally equal, and only apply
+  `rfl`-theorems.
+
+* Fix binder information for `match` patterns that use definitions tagged with `[matchPattern]` (e.g., `Nat.add`).
+  We now have proper binder information for the variable `y` in the following example.
+  ```lean
+  def f (x : Nat) : Nat :=
+    match x with
+    | 0 => 1
+    | y + 1 => y
+  ```
+
+* (Fix) the default value for structure fields may now depend on the structure parameters. Example:
+  ```lean
+  structure Something (i: Nat) where
+  n1: Nat := 1
+  n2: Nat := 1 + i
+
+  def s : Something 10 := {}
+  example : s.n2 = 11 := rfl
+  ```
+
+* Apply `rfl` theorems at the `dsimp` auxiliary method used by `simp`. `dsimp` can be used anywhere in an expression
+  because it preserves definitional equality.
+
+* Refine auto bound implicit feature. It does not consider anymore unbound variables that have the same
+  name of a declaration being defined. Example:
+  ```lean
+  def f : f → Bool := -- Error at second `f`
+    fun _ => true
+
+  inductive Foo : List Foo → Type -- Error at second `Foo`
+    | x : Foo []
+  ```
+  Before this refinement, the declarations above would be accepted and the
+  second `f` and `Foo` would be treated as auto implicit variables. That is,
+  `f : {f : Sort u} → f → Bool`, and
+  `Foo : {Foo : Type u} → List Foo → Type`.
+
+
+* Fix syntax highlighting for recursive declarations. Example
+  ```lean
+  inductive List (α : Type u) where
+    | nil : List α  -- `List` is not highlighted as a variable anymore
+    | cons (head : α) (tail : List α) : List α
+
+  def List.map (f : α → β) : List α → List β
+    | []    => []
+    | a::as => f a :: map f as -- `map` is not highlighted as a variable anymore
+  ```
+* Add `autoUnfold` option to `Lean.Meta.Simp.Config`, and the following macros
+  - `simp!` for `simp (config := { autoUnfold := true })`
+  - `simp_arith!` for `simp (config := { autoUnfold := true, arith := true })`
+  - `simp_all!` for `simp_all (config := { autoUnfold := true })`
+  - `simp_all_arith!` for `simp_all (config := { autoUnfold := true, arith := true })`
+
+  When the `autoUnfold` is set to true, `simp` tries to unfold the following kinds of definition
+  - Recursive definitions defined by structural recursion.
+  - Non-recursive definitions where the body is a `match`-expression. This
+    kind of definition is only unfolded if the `match` can be reduced.
+  Example:
+  ```lean
+  def append (as bs : List α) : List α :=
+    match as with
+    | [] => bs
+    | a :: as => a :: append as bs
+
+  theorem append_nil (as : List α) : append as [] = as := by
+    induction as <;> simp_all!
+
+  theorem append_assoc (as bs cs : List α) : append (append as bs) cs = append as (append bs cs) := by
+    induction as <;> simp_all!
+  ```
+
+* Add `save` tactic for creating checkpoints more conveniently. Example:
+  ```lean
+  example : <some-proposition> := by
+    tac_1
+    tac_2
+    save
+    tac_3
+    ...
+  ```
+  is equivalent to
+  ```lean
+  example : <some-proposition> := by
+    checkpoint
+      tac_1
+      tac_2
+    tac_3
+    ...
+  ```
+
+* Remove support for `{}` annotation from inductive datatype constructors. This annotation was barely used, and we can control the binder information for parameter bindings using the new inductive family indices to parameter promotion. Example: the following declaration using `{}`
+  ```lean
+  inductive LE' (n : Nat) : Nat → Prop where
+    | refl {} : LE' n n -- Want `n` to be explicit
+    | succ  : LE' n m → LE' n (m+1)
+  ```
+  can now be written as
+  ```lean
+  inductive LE' : Nat → Nat → Prop where
+    | refl (n : Nat) : LE' n n
+    | succ : LE' n m → LE' n (m+1)
+  ```
+  In both cases, the inductive family has one parameter and one index.
+  Recall that the actual number of parameters can be retrieved using the command `#print`.
+
+* Remove support for `{}` annotation in the `structure` command.
+
+* Several improvements to LSP server. Examples: "jump to definition" in mutually recursive sections, fixed incorrect hover information in "match"-expression patterns, "jump to definition" for pattern variables, fixed auto-completion in function headers, etc.
+
+* In `macro ... xs:p* ...` and similar macro bindings of combinators, `xs` now has the correct type `Array Syntax`
+
+* Identifiers in syntax patterns now ignore macro scopes during matching.
+
+* Improve binder names for constructor auto implicit parameters. Example, given the inductive datatype
+  ```lean
+  inductive Member : α → List α → Type u
+    | head : Member a (a::as)
+    | tail : Member a bs → Member a (b::bs)
+  ```
+  before:
+  ```lean
+  #check @Member.head
+  -- @Member.head : {x : Type u_1} → {a : x} → {as : List x} → Member a (a :: as)
+  ```
+  now:
+  ```lean
+  #check @Member.head
+  -- @Member.head : {α : Type u_1} → {a : α} → {as : List α} → Member a (a :: as)
+  ```
+
+* Improve error message when constructor parameter universe level is too big.
+
+* Add support for `for h : i in [start:stop] do .. ` where `h : i ∈ [start:stop]`. This feature is useful for proving
+  termination of functions such as:
+  ```lean
+  inductive Expr where
+    | app (f : String) (args : Array Expr)
+
+  def Expr.size (e : Expr) : Nat := Id.run do
+    match e with
+    | app f args =>
+      let mut sz := 1
+      for h : i in [: args.size] do
+        -- h.upper : i < args.size
+        sz := sz + size (args.get ⟨i, h.upper⟩)
+      return sz
+  ```
+
+* Add tactic `case'`. It is similar to `case`, but does not admit the goal on failure.
+  For example, the new tactic is useful when writing tactic scripts where we need to use `case'`
+  at `first | ... | ...`, and we want to take the next alternative when `case'` fails.
+
+* Add tactic macro
+  ```lean
+  macro "stop" s:tacticSeq : tactic => `(repeat sorry)
+  ```
+  See discussion on [Zulip](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Partial.20evaluation.20of.20a.20file).
+
+* When displaying goals, we do not display inaccessible proposition names
+if they do not have forward dependencies. We still display their types.
+For example, the goal
+  ```lean
+  case node.inl.node
+  β : Type u_1
+  b : BinTree β
+  k : Nat
+  v : β
+  left : Tree β
+  key : Nat
+  value : β
+  right : Tree β
+  ihl : BST left → Tree.find? (Tree.insert left k v) k = some v
+  ihr : BST right → Tree.find? (Tree.insert right k v) k = some v
+  h✝ : k < key
+  a✝³ : BST left
+  a✝² : ForallTree (fun k v => k < key) left
+  a✝¹ : BST right
+  a✝ : ForallTree (fun k v => key < k) right
+  ⊢ BST left
+  ```
+  is now displayed as
+  ```lean
+  case node.inl.node
+  β : Type u_1
+  b : BinTree β
+  k : Nat
+  v : β
+  left : Tree β
+  key : Nat
+  value : β
+  right : Tree β
+  ihl : BST left → Tree.find? (Tree.insert left k v) k = some v
+  ihr : BST right → Tree.find? (Tree.insert right k v) k = some v
+   : k < key
+   : BST left
+   : ForallTree (fun k v => k < key) left
+   : BST right
+   : ForallTree (fun k v => key < k) right
+  ⊢ BST left
+  ```
+
+* The hypothesis name is now optional in the `by_cases` tactic.
+
+* [Fix inconsistency between `syntax` and kind names](https://github.com/leanprover/lean4/issues/1090).
+  The node kinds `numLit`, `charLit`, `nameLit`, `strLit`, and `scientificLit` are now called
+  `num`, `char`, `name`, `str`, and `scientific` respectively. Example: we now write
+  ```lean
+  macro_rules | `($n:num) => `("hello")
+  ```
+  instead of
+  ```lean
+  macro_rules | `($n:numLit) => `("hello")
+  ```
+
+* (Experimental) New `checkpoint <tactic-seq>` tactic for big interactive proofs.
+
+* Rename tactic `nativeDecide` => `native_decide`.
+
+* Antiquotations are now accepted in any syntax. The `incQuotDepth` `syntax` parser is therefore obsolete and has been removed.
+
+* Renamed tactic `nativeDecide` => `native_decide`.
+
+* "Cleanup" local context before elaborating a `match` alternative right-hand-side. Examples:
+  ```lean
+  example (x : Nat) : Nat :=
+    match g x with
+    | (a, b) => _ -- Local context does not contain the auxiliary `_discr := g x` anymore
+
+  example (x : Nat × Nat) (h : x.1 > 0) : f x > 0 := by
+    match x with
+    | (a, b) => _ -- Local context does not contain the `h✝ : x.fst > 0` anymore
+  ```
+
+* Improve `let`-pattern (and `have`-pattern) macro expansion. In the following example,
+  ```lean
+  example (x : Nat × Nat) : f x > 0 := by
+    let (a, b) := x
+    done
+  ```
+  The resulting goal is now `... |- f (a, b) > 0` instead of `... |- f x > 0`.
+
+* Add cross-compiled [aarch64 Linux](https://github.com/leanprover/lean4/pull/1066) and [aarch64 macOS](https://github.com/leanprover/lean4/pull/1076) releases.
+
+* [Add tutorial-like examples to our documentation](https://github.com/leanprover/lean4/tree/master/doc/examples), rendered using LeanInk+Alectryon.

releases/v4.0.0.md

@@ -0,0 +1,120 @@
+v4.0.0
+---------
+
+* [`Lean.Meta.getConst?` has been renamed](https://github.com/leanprover/lean4/pull/2454).
+  We have renamed `getConst?` to `getUnfoldableConst?` (and `getConstNoEx?` to `getUnfoldableConstNoEx?`).
+  These were not intended to be part of the public API, but downstream projects had been using them
+  (sometimes expecting different behaviour) incorrectly instead of `Lean.getConstInfo`.
+
+* [`dsimp` / `simp` / `simp_all` now fail by default if they make no progress](https://github.com/leanprover/lean4/pull/2336).
+
+  This can be overridden with the `(config := { failIfUnchanged := false })` option.
+  This change was made to ease manual use of `simp` (with complicated goals it can be hard to tell if it was effective)
+  and to allow easier flow control in tactics internally using `simp`.
+  See the [summary discussion](https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/simp.20fails.20if.20no.20progress/near/380153295)
+  on zulip for more details.
+
+* [`simp_all` now preserves order of hypotheses](https://github.com/leanprover/lean4/pull/2334).
+
+  In order to support the `failIfUnchanged` configuration option for `dsimp` / `simp` / `simp_all`
+  the way `simp_all` replaces hypotheses has changed.
+  In particular it is now more likely to preserve the order of hypotheses.
+  See [`simp_all` reorders hypotheses unnecessarily](https://github.com/leanprover/lean4/pull/2334).
+  (Previously all non-dependent propositional hypotheses were reverted and reintroduced.
+  Now only such hypotheses which were changed, or which come after a changed hypothesis,
+  are reverted and reintroduced.
+  This has the effect of preserving the ordering amongst the non-dependent propositional hypotheses,
+  but now any dependent or non-propositional hypotheses retain their position amongst the unchanged
+  non-dependent propositional hypotheses.)
+  This may affect proofs that use `rename_i`, `case ... =>`, or `next ... =>`.
+
+* [New `have this` implementation](https://github.com/leanprover/lean4/pull/2247).
+
+  `this` is now a regular identifier again that is implicitly introduced by anonymous `have :=` for the remainder of the tactic block. It used to be a keyword that was visible in all scopes and led to unexpected behavior when explicitly used as a binder name.
+
+* [Show typeclass and tactic names in profile output](https://github.com/leanprover/lean4/pull/2170).
+
+* [Make `calc` require the sequence of relation/proof-s to have the same indentation](https://github.com/leanprover/lean4/pull/1844),
+  and [add `calc` alternative syntax allowing underscores `_` in the first relation](https://github.com/leanprover/lean4/pull/1844).
+
+  The flexible indentation in `calc` was often used to align the relation symbols:
+  ```lean
+  example (x y : Nat) : (x + y) * (x + y) = x * x + y * x + x * y + y * y :=
+    calc
+        (x + y) * (x + y) = (x + y) * x + (x + y) * y       := by rw [Nat.mul_add]
+                        -- improper indentation
+                        _ = x * x + y * x + (x + y) * y     := by rw [Nat.add_mul]
+                        _ = x * x + y * x + (x * y + y * y) := by rw [Nat.add_mul]
+                        _ = x * x + y * x + x * y + y * y   := by rw [←Nat.add_assoc]
+  ```
+
+  This is no longer legal.  The new syntax puts the first term right after the `calc` and each step has the same indentation:
+  ```lean
+  example (x y : Nat) : (x + y) * (x + y) = x * x + y * x + x * y + y * y :=
+    calc (x + y) * (x + y)
+      _ = (x + y) * x + (x + y) * y       := by rw [Nat.mul_add]
+      _ = x * x + y * x + (x + y) * y     := by rw [Nat.add_mul]
+      _ = x * x + y * x + (x * y + y * y) := by rw [Nat.add_mul]
+      _ = x * x + y * x + x * y + y * y   := by rw [←Nat.add_assoc]
+  ```
+
+
+* Update Lake to latest prerelease.
+
+* [Make go-to-definition on a typeclass projection application go to the instance(s)](https://github.com/leanprover/lean4/pull/1767).
+
+* [Include timings in trace messages when `profiler` is true](https://github.com/leanprover/lean4/pull/1995).
+
+* [Pretty-print signatures in hover and `#check <ident>`](https://github.com/leanprover/lean4/pull/1943).
+
+* [Introduce parser memoization to avoid exponential behavior](https://github.com/leanprover/lean4/pull/1799).
+
+* [feat: allow `doSeq` in `let x <- e | seq`](https://github.com/leanprover/lean4/pull/1809).
+
+* [Add hover/go-to-def/refs for options](https://github.com/leanprover/lean4/pull/1783).
+
+* [Add empty type ascription syntax `(e :)`](https://github.com/leanprover/lean4/pull/1797).
+
+* [Make tokens in `<|>` relevant to syntax match](https://github.com/leanprover/lean4/pull/1744).
+
+* [Add `linter.deprecated` option to silence deprecation warnings](https://github.com/leanprover/lean4/pull/1768).
+
+* [Improve fuzzy-matching heuristics](https://github.com/leanprover/lean4/pull/1710).
+
+* [Implementation-detail hypotheses](https://github.com/leanprover/lean4/pull/1692).
+
+* [Hover information for `cases`/`induction` case names](https://github.com/leanprover/lean4/pull/1660).
+
+* [Prefer longer parse even if unsuccessful](https://github.com/leanprover/lean4/pull/1658).
+
+* [Show declaration module in hover](https://github.com/leanprover/lean4/pull/1638).
+
+* [New `conv` mode structuring tactics](https://github.com/leanprover/lean4/pull/1636).
+
+* `simp` can track information and can print an equivalent `simp only`. [PR #1626](https://github.com/leanprover/lean4/pull/1626).
+
+* Enforce uniform indentation in tactic blocks / do blocks. See issue [#1606](https://github.com/leanprover/lean4/issues/1606).
+
+* Moved `AssocList`, `HashMap`, `HashSet`, `RBMap`, `RBSet`, `PersistentArray`, `PersistentHashMap`, `PersistentHashSet` to the Lean package. The [standard library](https://github.com/leanprover/std4) contains versions that will evolve independently to simplify bootstrapping process.
+
+* Standard library moved to the [std4 GitHub repository](https://github.com/leanprover/std4).
+
+* `InteractiveGoals` now has information that a client infoview can use to show what parts of the goal have changed after applying a tactic. [PR #1610](https://github.com/leanprover/lean4/pull/1610).
+
+* Add `[inheritDoc]` attribute. [PR #1480](https://github.com/leanprover/lean4/pull/1480).
+
+* Expose that `panic = default`. [PR #1614](https://github.com/leanprover/lean4/pull/1614).
+
+* New [code generator](https://github.com/leanprover/lean4/tree/master/src/Lean/Compiler/LCNF) project has started.
+
+* Remove description argument from `register_simp_attr`. [PR #1566](https://github.com/leanprover/lean4/pull/1566).
+
+* [Additional concurrency primitives](https://github.com/leanprover/lean4/pull/1555).
+
+* [Collapsible traces with messages](https://github.com/leanprover/lean4/pull/1448).
+
+* [Hygienic resolution of namespaces](https://github.com/leanprover/lean4/pull/1442).
+
+* [New `Float` functions](https://github.com/leanprover/lean4/pull/1460).
+
+* Many new doc strings have been added to declarations at `Init`.

releases/v4.1.0.md

@@ -0,0 +1,21 @@
+v4.1.0
+---------
+
+* The error positioning on missing tokens has been [improved](https://github.com/leanprover/lean4/pull/2393). In particular, this should make it easier to spot errors in incomplete tactic proofs.
+
+* After elaborating a configuration file, Lake will now cache the configuration to a `lakefile.olean`. Subsequent runs of Lake will import this OLean instead of elaborating the configuration file. This provides a significant performance improvement (benchmarks indicate that using the OLean cuts Lake's startup time in half), but there are some important details to keep in mind:
+  + Lake will regenerate this OLean after each modification to the `lakefile.lean` or `lean-toolchain`. You can also force a reconfigure by passing the new `--reconfigure` / `-R` option to `lake`.
+  + Lake configuration options (i.e., `-K`) will be fixed at the moment of elaboration. Setting these options when `lake` is using the cached configuration will have no effect. To change options, run `lake` with `-R` / `--reconfigure`.
+  + **The `lakefile.olean` is a local configuration and should not be committed to Git. Therefore, existing Lake packages need to add it to their `.gitignore`.**
+
+* The signature of `Lake.buildO` has changed, `args` has been split into `weakArgs` and `traceArgs`. `traceArgs` are included in the input trace and `weakArgs` are not. See Lake's [FFI example](src/lake/examples/ffi/lib/lakefile.lean) for a demonstration of how to adapt to this change.
+
+* The signatures of `Lean.importModules`, `Lean.Elab.headerToImports`, and `Lean.Elab.parseImports`
+  have [changed](https://github.com/leanprover/lean4/pull/2480) from taking `List Import` to `Array Import`.
+
+* There is now [an `occs` field](https://github.com/leanprover/lean4/pull/2470)
+  in the configuration object for the `rewrite` tactic,
+  allowing control of which occurrences of a pattern should be rewritten.
+  This was previously a separate argument for `Lean.MVarId.rewrite`,
+  and this has been removed in favour of an additional field of `Rewrite.Config`.
+  It was not previously accessible from user tactics.

releases/v4.10.0.md

@@ -0,0 +1,281 @@
+v4.10.0
+----------
+
+### Language features, tactics, and metaprograms
+
+* `split` tactic:
+  * [#4401](https://github.com/leanprover/lean4/pull/4401) improves the strategy `split` uses to generalize discriminants of matches and adds `trace.split.failure` trace class for diagnosing issues.
+
+* `rw` tactic:
+  * [#4385](https://github.com/leanprover/lean4/pull/4385) prevents the tactic from claiming pre-existing goals are new subgoals.
+  * [dac1da](https://github.com/leanprover/lean4/commit/dac1dacc5b39911827af68247d575569d9c399b5) adds configuration for ordering new goals, like for `apply`.
+
+* `simp` tactic:
+  * [#4430](https://github.com/leanprover/lean4/pull/4430) adds `dsimproc`s for `if` expressions (`ite` and `dite`).
+  * [#4434](https://github.com/leanprover/lean4/pull/4434) improves heuristics for unfolding. Equational lemmas now have priorities where more-specific equationals lemmas are tried first before a possible catch-all.
+  * [#4481](https://github.com/leanprover/lean4/pull/4481) fixes an issue where function-valued `OfNat` numeric literals would become denormalized.
+  * [#4467](https://github.com/leanprover/lean4/pull/4467) fixes an issue where dsimp theorems might not apply to literals.
+  * [#4484](https://github.com/leanprover/lean4/pull/4484) fixes the source position for the warning for deprecated simp arguments.
+  * [#4258](https://github.com/leanprover/lean4/pull/4258) adds docstrings for `dsimp` configuration.
+  * [#4567](https://github.com/leanprover/lean4/pull/4567) improves the accuracy of used simp lemmas reported by `simp?`.
+  * [fb9727](https://github.com/leanprover/lean4/commit/fb97275dcbb683efe6da87ed10a3f0cd064b88fd) adds (but does not implement) the simp configuration option `implicitDefEqProofs`, which will enable including `rfl`-theorems in proof terms.
+* `omega` tactic:
+  * [#4360](https://github.com/leanprover/lean4/pull/4360) makes the tactic generate error messages lazily, improving its performance when used in tactic combinators.
+* `bv_omega` tactic:
+  * [#4579](https://github.com/leanprover/lean4/pull/4579) works around changes to the definition of `Fin.sub` in this release.
+* [#4490](https://github.com/leanprover/lean4/pull/4490) sets up groundwork for a tactic index in generated documentation, as there was in Lean 3. See PR description for details.
+
+* **Commands**
+  * [#4370](https://github.com/leanprover/lean4/pull/4370) makes the `variable` command fully elaborate binders during validation, fixing an issue where some errors would be reported only at the next declaration.
+  * [#4408](https://github.com/leanprover/lean4/pull/4408) fixes a discrepancy in universe parameter order between `theorem` and `def` declarations.
+  * [#4493](https://github.com/leanprover/lean4/pull/4493) and
+    [#4482](https://github.com/leanprover/lean4/pull/4482) fix a discrepancy in the elaborators for `theorem`, `def`, and `example`,
+    making `Prop`-valued `example`s and other definition commands elaborate like `theorem`s.
+  * [8f023b](https://github.com/leanprover/lean4/commit/8f023b85c554186ae562774b8122322d856c674e), [3c4d6b](https://github.com/leanprover/lean4/commit/3c4d6ba8648eb04d90371eb3fdbd114d16949501) and [0783d0](https://github.com/leanprover/lean4/commit/0783d0fcbe31b626fbd3ed2f29d838e717f09101) change the `#reduce` command to be able to control what gets reduced.
+    For example, `#reduce (proofs := true) (types := false) e` reduces both proofs and types in the expression `e`.
+    By default, neither proofs or types are reduced.
+  * [#4489](https://github.com/leanprover/lean4/pull/4489) fixes an elaboration bug in `#check_tactic`.
+  * [#4505](https://github.com/leanprover/lean4/pull/4505) adds support for `open _root_.<namespace>`.
+
+* **Options**
+  * [#4576](https://github.com/leanprover/lean4/pull/4576) adds the `debug.byAsSorry` option. Setting `set_option debug.byAsSorry true` causes all `by ...` terms to elaborate as `sorry`.
+  * [7b56eb](https://github.com/leanprover/lean4/commit/7b56eb20a03250472f4b145118ae885274d1f8f7) and [d8e719](https://github.com/leanprover/lean4/commit/d8e719f9ab7d049e423473dfc7a32867d32c856f) add the `debug.skipKernelTC` option. Setting `set_option debug.skipKernelTC true` turns off kernel typechecking. This is meant for temporarily working around kernel performance issues, and it compromises soundness since buggy tactics may produce invalid proofs, which will not be caught if this option is set to true.
+
+* [#4301](https://github.com/leanprover/lean4/pull/4301)
+  adds a linter to flag situations where a local variable's name is one of
+  the argumentless constructors of its type. This can arise when a user either
+  doesn't open a namespace or doesn't add a dot or leading qualifier, as
+  in the following:
+
+  ```lean
+  inductive Tree (α : Type) where
+    | leaf
+    | branch (left : Tree α) (val : α) (right : Tree α)
+
+  def depth : Tree α → Nat
+    | leaf => 0
+  ```
+
+  With this linter, the `leaf` pattern is highlighted as a local
+  variable whose name overlaps with the constructor `Tree.leaf`.
+
+  The linter can be disabled with `set_option linter.constructorNameAsVariable false`.
+
+  Additionally, the error message that occurs when a name in a pattern that takes arguments isn't valid now suggests similar names that would be valid. This means that the following definition:
+
+  ```lean
+  def length (list : List α) : Nat :=
+    match list with
+    | nil => 0
+    | cons x xs => length xs + 1
+  ```
+
+  now results in the following warning:
+
+  ```
+  warning: Local variable 'nil' resembles constructor 'List.nil' - write '.nil' (with a dot) or 'List.nil' to use the constructor.
+  note: this linter can be disabled with `set_option linter.constructorNameAsVariable false`
+  ```
+
+  and error:
+
+  ```
+  invalid pattern, constructor or constant marked with '[match_pattern]' expected
+
+  Suggestion: 'List.cons' is similar
+  ```
+
+* **Metaprogramming**
+  * [#4454](https://github.com/leanprover/lean4/pull/4454) adds public `Name.isInternalDetail` function for filtering declarations using naming conventions for internal names.
+
+* **Other fixes or improvements**
+  * [#4416](https://github.com/leanprover/lean4/pull/4416) sorts the output of `#print axioms` for determinism.
+  * [#4528](https://github.com/leanprover/lean4/pull/4528) fixes error message range for the cdot focusing tactic.
+
+### Language server, widgets, and IDE extensions
+
+* [#4443](https://github.com/leanprover/lean4/pull/4443) makes the watchdog be more resilient against badly behaving clients.
+
+### Pretty printing
+
+* [#4433](https://github.com/leanprover/lean4/pull/4433) restores fallback pretty printers when context is not available, and documents `addMessageContext`.
+* [#4556](https://github.com/leanprover/lean4/pull/4556) introduces `pp.maxSteps` option and sets the default value of `pp.deepTerms` to `false`. Together, these keep excessively large or deep terms from overwhelming the Infoview.
+
+### Library
+* [#4560](https://github.com/leanprover/lean4/pull/4560) splits `GetElem` class into `GetElem` and `GetElem?`.
+  This enables removing `Decidable` instance arguments from `GetElem.getElem?` and `GetElem.getElem!`, improving their rewritability.
+  See the docstrings for these classes for more information.
+* `Array`
+  * [#4389](https://github.com/leanprover/lean4/pull/4389) makes `Array.toArrayAux_eq` be a `simp` lemma.
+  * [#4399](https://github.com/leanprover/lean4/pull/4399) improves robustness of the proof for `Array.reverse_data`.
+* `List`
+  * [#4469](https://github.com/leanprover/lean4/pull/4469) and [#4475](https://github.com/leanprover/lean4/pull/4475) improve the organization of the `List` API.
+  * [#4470](https://github.com/leanprover/lean4/pull/4470) improves the `List.set` and `List.concat` API.
+  * [#4472](https://github.com/leanprover/lean4/pull/4472) upstreams lemmas about `List.filter` from Batteries.
+  * [#4473](https://github.com/leanprover/lean4/pull/4473) adjusts `@[simp]` attributes.
+  * [#4488](https://github.com/leanprover/lean4/pull/4488) makes `List.getElem?_eq_getElem` be a simp lemma.
+  * [#4487](https://github.com/leanprover/lean4/pull/4487) adds missing `List.replicate` API.
+  * [#4521](https://github.com/leanprover/lean4/pull/4521) adds lemmas about `List.map`.
+  * [#4500](https://github.com/leanprover/lean4/pull/4500) changes `List.length_cons` to use `as.length + 1` instead of `as.length.succ`.
+  * [#4524](https://github.com/leanprover/lean4/pull/4524) fixes the statement of `List.filter_congr`.
+  * [#4525](https://github.com/leanprover/lean4/pull/4525) changes binder explicitness in `List.bind_map`.
+  * [#4550](https://github.com/leanprover/lean4/pull/4550) adds `maximum?_eq_some_iff'` and `minimum?_eq_some_iff?`.
+* [#4400](https://github.com/leanprover/lean4/pull/4400) switches the normal forms for indexing `List` and `Array` to `xs[n]` and `xs[n]?`.
+* `HashMap`
+  * [#4372](https://github.com/leanprover/lean4/pull/4372) fixes linearity in `HashMap.insert` and `HashMap.erase`, leading to a 40% speedup in a replace-heavy workload.
+* `Option`
+  * [#4403](https://github.com/leanprover/lean4/pull/4403) generalizes type of `Option.forM` from `Unit` to `PUnit`.
+  * [#4504](https://github.com/leanprover/lean4/pull/4504) remove simp attribute from `Option.elim` and instead adds it to individual reduction lemmas, making unfolding less aggressive.
+* `Nat`
+  * [#4242](https://github.com/leanprover/lean4/pull/4242) adds missing theorems for `n + 1` and `n - 1` normal forms.
+  * [#4486](https://github.com/leanprover/lean4/pull/4486) makes `Nat.min_assoc` be a simp lemma.
+  * [#4522](https://github.com/leanprover/lean4/pull/4522) moves `@[simp]` from `Nat.pred_le` to `Nat.sub_one_le`.
+  * [#4532](https://github.com/leanprover/lean4/pull/4532) changes various `Nat.succ n` to `n + 1`.
+* `Int`
+  * [#3850](https://github.com/leanprover/lean4/pull/3850) adds complete div/mod simprocs for `Int`.
+* `String`/`Char`
+  * [#4357](https://github.com/leanprover/lean4/pull/4357) make the byte size interface be `Nat`-valued with functions `Char.utf8Size` and `String.utf8ByteSize`.
+  * [#4438](https://github.com/leanprover/lean4/pull/4438) upstreams `Char.ext` from Batteries and adds some `Char` documentation to the manual.
+* `Fin`
+  * [#4421](https://github.com/leanprover/lean4/pull/4421) adjusts `Fin.sub` to be more performant in definitional equality checks.
+* `Prod`
+  * [#4526](https://github.com/leanprover/lean4/pull/4526) adds missing `Prod.map` lemmas.
+  * [#4533](https://github.com/leanprover/lean4/pull/4533) fixes binder explicitness in lemmas.
+* `BitVec`
+  * [#4428](https://github.com/leanprover/lean4/pull/4428) adds missing `simproc` for `BitVec` equality.
+  * [#4417](https://github.com/leanprover/lean4/pull/4417) adds `BitVec.twoPow` and lemmas, toward bitblasting multiplication for LeanSAT.
+* `Std` library
+  * [#4499](https://github.com/leanprover/lean4/pull/4499) introduces `Std`, a library situated between `Init` and `Lean`, providing functionality not in the prelude both to Lean's implementation and to external users.
+* **Other fixes or improvements**
+  * [#3056](https://github.com/leanprover/lean4/pull/3056) standardizes on using `(· == a)` over `(a == ·)`.
+  * [#4502](https://github.com/leanprover/lean4/pull/4502) fixes errors reported by running the library through the the Batteries linters.
+
+### Lean internals
+
+* [#4391](https://github.com/leanprover/lean4/pull/4391) makes `getBitVecValue?` recognize `BitVec.ofNatLt`.
+* [#4410](https://github.com/leanprover/lean4/pull/4410) adjusts `instantiateMVars` algorithm to zeta reduce `let` expressions while beta reducing instantiated metavariables.
+* [#4420](https://github.com/leanprover/lean4/pull/4420) fixes occurs check for metavariable assignments to also take metavariable types into account.
+* [#4425](https://github.com/leanprover/lean4/pull/4425) fixes `forEachModuleInDir` to iterate over each Lean file exactly once.
+* [#3886](https://github.com/leanprover/lean4/pull/3886) adds support to build Lean core oleans using Lake.
+* **Defeq and WHNF algorithms**
+  * [#4387](https://github.com/leanprover/lean4/pull/4387) improves performance of `isDefEq` by eta reducing lambda-abstracted terms during metavariable assignments, since these are beta reduced during metavariable instantiation anyway.
+  * [#4388](https://github.com/leanprover/lean4/pull/4388) removes redundant code in `isDefEqQuickOther`.
+* **Typeclass inference**
+  * [#4530](https://github.com/leanprover/lean4/pull/4530) fixes handling of metavariables when caching results at `synthInstance?`.
+* **Elaboration**
+  * [#4426](https://github.com/leanprover/lean4/pull/4426) makes feature where the "don't know how to synthesize implicit argument" error reports the name of the argument more reliable.
+  * [#4497](https://github.com/leanprover/lean4/pull/4497) fixes a name resolution bug for generalized field notation (dot notation).
+  * [#4536](https://github.com/leanprover/lean4/pull/4536) blocks the implicit lambda feature for `(e :)` notation.
+  * [#4562](https://github.com/leanprover/lean4/pull/4562) makes it be an error for there to be two functions with the same name in a `where`/`let rec` block.
+* Recursion principles
+  * [#4549](https://github.com/leanprover/lean4/pull/4549) refactors `findRecArg`, extracting `withRecArgInfo`.
+    Errors are now reported in parameter order rather than the order they are tried (non-indices are tried first).
+    For every argument, it will say why it wasn't tried, even if the reason is obvious (e.g. a fixed prefix or is `Prop`-typed, etc.).
+* Porting core C++ to Lean
+  * [#4474](https://github.com/leanprover/lean4/pull/4474) takes a step to refactor `constructions` toward a future port to Lean.
+  * [#4498](https://github.com/leanprover/lean4/pull/4498) ports `mk_definition_inferring_unsafe` to Lean.
+  * [#4516](https://github.com/leanprover/lean4/pull/4516) ports `recOn` construction to Lean.
+  * [#4517](https://github.com/leanprover/lean4/pull/4517), [#4653](https://github.com/leanprover/lean4/pull/4653), and [#4651](https://github.com/leanprover/lean4/pull/4651) port `below` and `brecOn` construction to Lean.
+* Documentation
+  * [#4501](https://github.com/leanprover/lean4/pull/4501) adds a more-detailed docstring for `PersistentEnvExtension`.
+* **Other fixes or improvements**
+  * [#4382](https://github.com/leanprover/lean4/pull/4382) removes `@[inline]` attribute from `NameMap.find?`, which caused respecialization at each call site.
+  * [5f9ded](https://github.com/leanprover/lean4/commit/5f9dedfe5ee9972acdebd669f228f487844a6156) improves output of `trace.Elab.snapshotTree`.
+  * [#4424](https://github.com/leanprover/lean4/pull/4424) removes "you might need to open '{dir}' in your editor" message that is now handled by Lake and the VS Code extension.
+  * [#4451](https://github.com/leanprover/lean4/pull/4451) improves the performance of `CollectMVars` and `FindMVar`.
+  * [#4479](https://github.com/leanprover/lean4/pull/4479) adds missing `DecidableEq` and `Repr` instances for intermediate structures used by the `BitVec` and `Fin` simprocs.
+  * [#4492](https://github.com/leanprover/lean4/pull/4492) adds tests for a previous `isDefEq` issue.
+  * [9096d6](https://github.com/leanprover/lean4/commit/9096d6fc7180fe533c504f662bcb61550e4a2492) removes `PersistentHashMap.size`.
+  * [#4508](https://github.com/leanprover/lean4/pull/4508) fixes `@[implemented_by]` for functions defined by well-founded recursion.
+  * [#4509](https://github.com/leanprover/lean4/pull/4509) adds additional tests for `apply?` tactic.
+  * [d6eab3](https://github.com/leanprover/lean4/commit/d6eab393f4df9d473b5736d636b178eb26d197e6) fixes a benchmark.
+  * [#4563](https://github.com/leanprover/lean4/pull/4563) adds a workaround for a bug in `IndPredBelow.mkBelowMatcher`.
+* **Cleanup:** [#4380](https://github.com/leanprover/lean4/pull/4380), [#4431](https://github.com/leanprover/lean4/pull/4431), [#4494](https://github.com/leanprover/lean4/pull/4494), [e8f768](https://github.com/leanprover/lean4/commit/e8f768f9fd8cefc758533bc76e3a12b398ed4a39), [de2690](https://github.com/leanprover/lean4/commit/de269060d17a581ed87f40378dbec74032633b27), [d3a756](https://github.com/leanprover/lean4/commit/d3a7569c97123d022828106468d54e9224ed8207), [#4404](https://github.com/leanprover/lean4/pull/4404), [#4537](https://github.com/leanprover/lean4/pull/4537).
+
+### Compiler, runtime, and FFI
+
+* [d85d3d](https://github.com/leanprover/lean4/commit/d85d3d5f3a09ff95b2ee47c6f89ef50b7e339126) fixes criterion for tail-calls in ownership calculation.
+* [#3963](https://github.com/leanprover/lean4/pull/3963) adds validation of UTF-8 at the C++-to-Lean boundary in the runtime.
+* [#4512](https://github.com/leanprover/lean4/pull/4512) fixes missing unboxing in interpreter when loading initialized value.
+* [#4477](https://github.com/leanprover/lean4/pull/4477) exposes the compiler flags for the bundled C compiler (clang).
+
+### Lake
+
+* [#4384](https://github.com/leanprover/lean4/pull/4384) deprecates `inputFile` and replaces it with `inputBinFile` and `inputTextFile`. Unlike `inputBinFile` (and `inputFile`), `inputTextFile` normalizes line endings, which helps ensure text file traces are platform-independent.
+* [#4371](https://github.com/leanprover/lean4/pull/4371) simplifies dependency resolution code.
+* [#4439](https://github.com/leanprover/lean4/pull/4439) touches up the Lake configuration DSL and makes other improvements:
+  string literals can now be used instead of identifiers for names,
+  avoids using French quotes in `lake new` and `lake init` templates,
+  changes the `exe` template to use `Main` for the main module,
+  improves the `math` template error if `lean-toolchain` fails to download,
+  and downgrades unknown configuration fields from an error to a warning to improve cross-version compatibility.
+* [#4496](https://github.com/leanprover/lean4/pull/4496) tweaks `require` syntax and updates docs. Now `require` in TOML for a package name such as `doc-gen4` does not need French quotes.
+* [#4485](https://github.com/leanprover/lean4/pull/4485) fixes a bug where package versions in indirect dependencies would take precedence over direct dependencies.
+* [#4478](https://github.com/leanprover/lean4/pull/4478) fixes a bug where Lake incorrectly included the module dynamic library in a platform-independent trace.
+* [#4529](https://github.com/leanprover/lean4/pull/4529) fixes some issues with bad import errors.
+  A bad import in an executable no longer prevents the executable's root
+  module from being built. This also fixes a problem where the location
+  of a transitive bad import would not been shown.
+  The root module of the executable now respects `nativeFacets`.
+* [#4564](https://github.com/leanprover/lean4/pull/4564) fixes a bug where non-identifier script names could not be entered on the CLI without French quotes.
+* [#4566](https://github.com/leanprover/lean4/pull/4566) addresses a few issues with precompiled libraries.
+  * Fixes a bug where Lake would always precompile the package of a module.
+  * If a module is precompiled, it now precompiles its imports. Previously, it would only do this if imported.
+* [#4495](https://github.com/leanprover/lean4/pull/4495), [#4692](https://github.com/leanprover/lean4/pull/4692), [#4849](https://github.com/leanprover/lean4/pull/4849)
+  add a new type of `require` that fetches package metadata from a
+  registry API endpoint (e.g. Reservoir) and then clones a Git package
+  using the information provided. To require such a dependency, the new
+  syntax is:
+
+  ```lean
+  require <scope> / <pkg-name> [@ git <rev>]
+  -- Examples:
+  require "leanprover" / "doc-gen4"
+  require "leanprover-community" / "proofwidgets" @ git "v0.0.39"
+  ```
+
+  Or in TOML:
+  ```toml
+  [[require]]
+  name = "<pkg-name>"
+  scope = "<scope>"
+  rev = "<rev>"
+  ```
+
+  Unlike with Git dependencies, Lake can make use of the richer
+  information provided by the registry to determine the default branch of
+  the package. This means for repositories of packages like `doc-gen4`
+  which have a default branch that is not `master`, Lake will now use said
+  default branch (e.g., in `doc-gen4`'s case, `main`).
+
+  Lake also supports configuring the registry endpoint via an environment
+  variable: `RESERVIOR_API_URL`. Thus, any server providing a similar
+  interface to Reservoir can be used as the registry. Further
+  configuration options paralleling those of Cargo's [Alternative Registries](https://doc.rust-lang.org/cargo/reference/registries.html)
+  and [Source Replacement](https://doc.rust-lang.org/cargo/reference/source-replacement.html)
+  will come in the future.
+
+### DevOps/CI
+* [#4427](https://github.com/leanprover/lean4/pull/4427) uses Namespace runners for CI for `leanprover/lean4`.
+* [#4440](https://github.com/leanprover/lean4/pull/4440) fixes speedcenter tests in CI.
+* [#4441](https://github.com/leanprover/lean4/pull/4441) fixes that workflow change would break CI for unrebased PRs.
+* [#4442](https://github.com/leanprover/lean4/pull/4442) fixes Wasm release-ci.
+* [6d265b](https://github.com/leanprover/lean4/commit/6d265b42b117eef78089f479790587a399da7690) fixes for `github.event.pull_request.merge_commit_sha` sometimes not being available.
+* [16cad2](https://github.com/leanprover/lean4/commit/16cad2b45c6a77efe4dce850dcdbaafaa7c91fc3) adds optimization for CI to not fetch complete history.
+* [#4544](https://github.com/leanprover/lean4/pull/4544) causes releases to be marked as prerelease on GitHub.
+* [#4446](https://github.com/leanprover/lean4/pull/4446) switches Lake to using `src/lake/lakefile.toml` to avoid needing to load a version of Lake to build Lake.
+* Nix
+  * [5eb5fa](https://github.com/leanprover/lean4/commit/5eb5fa49cf9862e99a5bccff8d4ca1a062f81900) fixes `update-stage0-commit` for Nix.
+  * [#4476](https://github.com/leanprover/lean4/pull/4476) adds gdb to Nix shell.
+  * [e665a0](https://github.com/leanprover/lean4/commit/e665a0d716dc42ba79b339b95e01eb99fe932cb3) fixes `update-stage0` for Nix.
+  * [4808eb](https://github.com/leanprover/lean4/commit/4808eb7c4bfb98f212b865f06a97d46c44978a61) fixes `cacheRoots` for Nix.
+  * [#3811](https://github.com/leanprover/lean4/pull/3811) adds platform-dependent flag to lib target.
+  * [#4587](https://github.com/leanprover/lean4/pull/4587) adds linking of `-lStd` back into nix build flags on darwin.
+
+### Breaking changes
+
+* `Char.csize` is replaced by `Char.utf8Size` ([#4357](https://github.com/leanprover/lean4/pull/4357)).
+* Library lemmas now are in terms of `(· == a)` over `(a == ·)` ([#3056](https://github.com/leanprover/lean4/pull/3056)).
+* Now the normal forms for indexing into `List` and `Array` is `xs[n]` and `xs[n]?` rather than using functions like `List.get` ([#4400](https://github.com/leanprover/lean4/pull/4400)).
+* Sometimes terms created via a sequence of unifications will be more eta reduced than before and proofs will require adaptation ([#4387](https://github.com/leanprover/lean4/pull/4387)).
+* The `GetElem` class has been split into two; see the docstrings for `GetElem` and `GetElem?` for more information ([#4560](https://github.com/leanprover/lean4/pull/4560)).

releases/v4.11.0.md

@@ -0,0 +1,337 @@
+v4.11.0
+----------
+
+### Language features, tactics, and metaprograms
+
+* The variable inclusion mechanism has been changed. Like before, when a definition mentions a variable, Lean will add it as an argument of the definition, but now in theorem bodies, variables are not included based on usage in order to ensure that changes to the proof cannot change the statement of the overall theorem. Instead, variables are only available to the proof if they have been mentioned in the theorem header or in an **`include` command** or are instance implicit and depend only on such variables. The **`omit` command** can be used to omit included variables.
+
+  See breaking changes below.
+
+  PRs: [#4883](https://github.com/leanprover/lean4/pull/4883), [#4814](https://github.com/leanprover/lean4/pull/4814), [#5000](https://github.com/leanprover/lean4/pull/5000), [#5036](https://github.com/leanprover/lean4/pull/5036), [#5138](https://github.com/leanprover/lean4/pull/5138), [0edf1b](https://github.com/leanprover/lean4/commit/0edf1bac392f7e2fe0266b28b51c498306363a84).
+
+* **Recursive definitions**
+  * Structural recursion can now be explicitly requested using
+    ```
+    termination_by structural x
+    ```
+    in analogy to the existing `termination_by x` syntax that causes well-founded recursion to be used.
+    [#4542](https://github.com/leanprover/lean4/pull/4542)
+  * [#4672](https://github.com/leanprover/lean4/pull/4672) fixes a bug that could lead to ill-typed terms.
+  * The `termination_by?` syntax no longer forces the use of well-founded recursion, and when structural
+    recursion is inferred, it will print the result using the `termination_by structural` syntax.
+  * **Mutual structural recursion** is now supported. This feature supports both mutual recursion over a non-mutual
+    data type, as well as recursion over mutual or nested data types:
+
+    ```lean
+    mutual
+    def Even : Nat → Prop
+      | 0 => True
+      | n+1 => Odd n
+
+    def Odd : Nat → Prop
+      | 0 => False
+      | n+1 => Even n
+    end
+
+    mutual
+    inductive A
+    | other : B → A
+    | empty
+    inductive B
+    | other : A → B
+    | empty
+    end
+
+    mutual
+    def A.size : A → Nat
+    | .other b => b.size + 1
+    | .empty => 0
+
+    def B.size : B → Nat
+    | .other a => a.size + 1
+    | .empty => 0
+    end
+
+    inductive Tree where | node : List Tree → Tree
+
+    mutual
+    def Tree.size : Tree → Nat
+    | node ts => Tree.list_size ts
+
+    def Tree.list_size : List Tree → Nat
+    | [] => 0
+    | t::ts => Tree.size t + Tree.list_size ts
+    end
+    ```
+
+    Functional induction principles are generated for these functions as well (`A.size.induct`, `A.size.mutual_induct`).
+
+    Nested structural recursion is still not supported.
+
+    PRs: [#4639](https://github.com/leanprover/lean4/pull/4639), [#4715](https://github.com/leanprover/lean4/pull/4715), [#4642](https://github.com/leanprover/lean4/pull/4642), [#4656](https://github.com/leanprover/lean4/pull/4656), [#4684](https://github.com/leanprover/lean4/pull/4684), [#4715](https://github.com/leanprover/lean4/pull/4715), [#4728](https://github.com/leanprover/lean4/pull/4728), [#4575](https://github.com/leanprover/lean4/pull/4575), [#4731](https://github.com/leanprover/lean4/pull/4731), [#4658](https://github.com/leanprover/lean4/pull/4658), [#4734](https://github.com/leanprover/lean4/pull/4734), [#4738](https://github.com/leanprover/lean4/pull/4738), [#4718](https://github.com/leanprover/lean4/pull/4718), [#4733](https://github.com/leanprover/lean4/pull/4733), [#4787](https://github.com/leanprover/lean4/pull/4787), [#4788](https://github.com/leanprover/lean4/pull/4788), [#4789](https://github.com/leanprover/lean4/pull/4789), [#4807](https://github.com/leanprover/lean4/pull/4807), [#4772](https://github.com/leanprover/lean4/pull/4772)
+  * [#4809](https://github.com/leanprover/lean4/pull/4809) makes unnecessary `termination_by` clauses cause warnings, not errors.
+  * [#4831](https://github.com/leanprover/lean4/pull/4831) improves handling of nested structural recursion through non-recursive types.
+  * [#4839](https://github.com/leanprover/lean4/pull/4839) improves support for structural recursive over inductive predicates when there are reflexive arguments.
+* `simp` tactic
+  * [#4784](https://github.com/leanprover/lean4/pull/4784) sets configuration `Simp.Config.implicitDefEqProofs` to `true` by default.
+
+* `omega` tactic
+  * [#4612](https://github.com/leanprover/lean4/pull/4612) normalizes the order that constraints appear in error messages.
+  * [#4695](https://github.com/leanprover/lean4/pull/4695) prevents pushing casts into multiplications unless it produces a non-trivial linear combination.
+  * [#4989](https://github.com/leanprover/lean4/pull/4989) fixes a regression.
+
+* `decide` tactic
+  * [#4711](https://github.com/leanprover/lean4/pull/4711) switches from using default transparency to *at least* default transparency when reducing the `Decidable` instance.
+  * [#4674](https://github.com/leanprover/lean4/pull/4674) adds detailed feedback on `decide` tactic failure. It tells you which `Decidable` instances it unfolded, if it get stuck on `Eq.rec` it gives a hint about avoiding tactics when defining `Decidable` instances, and if it gets stuck on `Classical.choice` it gives hints about classical instances being in scope. During this process, it processes `Decidable.rec`s and matches to pin blame on a non-reducing instance.
+
+* `@[ext]` attribute
+  * [#4543](https://github.com/leanprover/lean4/pull/4543) and [#4762](https://github.com/leanprover/lean4/pull/4762) make `@[ext]` realize `ext_iff` theorems from user `ext` theorems. Fixes the attribute so that `@[local ext]` and `@[scoped ext]` are usable. The `@[ext (iff := false)]` option can be used to turn off `ext_iff` realization.
+  * [#4694](https://github.com/leanprover/lean4/pull/4694) makes "go to definition" work for the generated lemmas. Also adjusts the core library to make use of `ext_iff` generation.
+  * [#4710](https://github.com/leanprover/lean4/pull/4710) makes `ext_iff` theorem preserve inst implicit binder types, rather than making all binder types implicit.
+
+* `#eval` command
+  * [#4810](https://github.com/leanprover/lean4/pull/4810) introduces a safer `#eval` command that prevents evaluation of terms that contain `sorry`. The motivation is that failing tactics, in conjunction with operations such as array accesses, can lead to the Lean process crashing. Users can use the new `#eval!` command to use the previous unsafe behavior. ([#4829](https://github.com/leanprover/lean4/pull/4829) adjusts a test.)
+
+* [#4447](https://github.com/leanprover/lean4/pull/4447) adds `#discr_tree_key` and `#discr_tree_simp_key` commands, for helping debug discrimination tree failures. The `#discr_tree_key t` command prints the discrimination tree keys for a term `t` (or, if it is a single identifier, the type of that constant). It uses the default configuration for generating keys. The `#discr_tree_simp_key` command is similar to `#discr_tree_key`, but treats the underlying type as one of a simp lemma, that is it transforms it into an equality and produces the key of the left-hand side.
+
+  For example,
+  ```
+  #discr_tree_key (∀ {a n : Nat}, bar a (OfNat.ofNat n))
+  -- bar _ (@OfNat.ofNat Nat _ _)
+
+  #discr_tree_simp_key Nat.add_assoc
+  -- @HAdd.hAdd Nat Nat Nat _ (@HAdd.hAdd Nat Nat Nat _ _ _) _
+  ```
+
+* [#4741](https://github.com/leanprover/lean4/pull/4741) changes option parsing to allow user-defined options from the command line. Initial options are now re-parsed and validated after importing. Command line option assignments prefixed with `weak.` are silently discarded if the option name without the prefix does not exist.
+
+* **Deriving handlers**
+  * [7253ef](https://github.com/leanprover/lean4/commit/7253ef8751f76bcbe0e6f46dcfa8069699a2bac7) and [a04f3c](https://github.com/leanprover/lean4/commit/a04f3cab5a9fe2870825af6544ca13c5bb766706) improve the construction of the `BEq` deriving handler.
+  * [86af04](https://github.com/leanprover/lean4/commit/86af04cc08c0dbbe0e735ea13d16edea3465f850) makes `BEq` deriving handler work when there are dependently typed fields.
+  * [#4826](https://github.com/leanprover/lean4/pull/4826) refactors the `DecidableEq` deriving handle to use `termination_by structural`.
+
+* **Metaprogramming**
+  * [#4593](https://github.com/leanprover/lean4/pull/4593) adds `unresolveNameGlobalAvoidingLocals`.
+  * [#4618](https://github.com/leanprover/lean4/pull/4618) deletes deprecated functions from 2022.
+  * [#4642](https://github.com/leanprover/lean4/pull/4642) adds `Meta.lambdaBoundedTelescope`.
+  * [#4731](https://github.com/leanprover/lean4/pull/4731) adds `Meta.withErasedFVars`, to enter a context with some fvars erased from the local context.
+  * [#4777](https://github.com/leanprover/lean4/pull/4777) adds assignment validation at `closeMainGoal`, preventing users from circumventing the occurs check for tactics such as `exact`.
+  * [#4807](https://github.com/leanprover/lean4/pull/4807) introduces `Lean.Meta.PProdN` module for packing and projecting nested `PProd`s.
+  * [#5170](https://github.com/leanprover/lean4/pull/5170) fixes `Syntax.unsetTrailing`. A consequence of this is that "go to definition" now works on the last module name in an `import` block (issue [#4958](https://github.com/leanprover/lean4/issues/4958)).
+
+
+### Language server, widgets, and IDE extensions
+
+* [#4727](https://github.com/leanprover/lean4/pull/4727) makes it so that responses to info view requests come as soon as the relevant tactic has finished execution.
+* [#4580](https://github.com/leanprover/lean4/pull/4580) makes it so that whitespace changes do not invalidate imports, and so starting to type the first declaration after imports should no longer cause them to reload.
+* [#4780](https://github.com/leanprover/lean4/pull/4780) fixes an issue where hovering over unimported builtin names could result in a panic.
+
+### Pretty printing
+
+* [#4558](https://github.com/leanprover/lean4/pull/4558) fixes the `pp.instantiateMVars` setting and changes the default value to `true`.
+* [#4631](https://github.com/leanprover/lean4/pull/4631) makes sure syntax nodes always run their formatters. Fixes an issue where if `ppSpace` appears in a `macro` or `elab` command then it does not format with a space.
+* [#4665](https://github.com/leanprover/lean4/pull/4665) fixes a bug where pretty printed signatures (for example in `#check`) were overly hoverable due to `pp.tagAppFns` being set.
+* [#4724](https://github.com/leanprover/lean4/pull/4724) makes `match` pretty printer be sensitive to `pp.explicit`, which makes hovering over a `match` in the Infoview show the underlying term.
+* [#4764](https://github.com/leanprover/lean4/pull/4764) documents why anonymous constructor notation isn't pretty printed with flattening.
+* [#4786](https://github.com/leanprover/lean4/pull/4786) adjusts the parenthesizer so that only the parentheses are hoverable, implemented by having the parentheses "steal" the term info from the parenthesized expression.
+* [#4854](https://github.com/leanprover/lean4/pull/4854) allows arbitrarily long sequences of optional arguments to be omitted from the end of applications, versus the previous conservative behavior of omitting up to one optional argument.
+
+### Library
+
+* `Nat`
+  * [#4597](https://github.com/leanprover/lean4/pull/4597) adds bitwise lemmas `Nat.and_le_(left|right)`.
+  * [#4874](https://github.com/leanprover/lean4/pull/4874) adds simprocs for simplifying bit expressions.
+* `Int`
+  * [#4903](https://github.com/leanprover/lean4/pull/4903) fixes performance of `HPow Int Nat Int` synthesis by rewriting it as a `NatPow Int` instance.
+* `UInt*` and `Fin`
+  * [#4605](https://github.com/leanprover/lean4/pull/4605) adds lemmas.
+  * [#4629](https://github.com/leanprover/lean4/pull/4629) adds `*.and_toNat`.
+* `Option`
+  * [#4599](https://github.com/leanprover/lean4/pull/4599) adds `get` lemmas.
+  * [#4600](https://github.com/leanprover/lean4/pull/4600) adds `Option.or`, a version of `Option.orElse` that is strict in the second argument.
+* `GetElem`
+  * [#4603](https://github.com/leanprover/lean4/pull/4603) adds `getElem_congr` to help with rewriting indices.
+* `List` and `Array`
+  * Upstreamed from Batteries: [#4586](https://github.com/leanprover/lean4/pull/4586) upstreams `List.attach` and `Array.attach`, [#4697](https://github.com/leanprover/lean4/pull/4697) upstreams `List.Subset` and `List.Sublist` and API, [#4706](https://github.com/leanprover/lean4/pull/4706) upstreams basic material on `List.Pairwise` and `List.Nodup`, [#4720](https://github.com/leanprover/lean4/pull/4720) upstreams more `List.erase` API, [#4836](https://github.com/leanprover/lean4/pull/4836) and [#4837](https://github.com/leanprover/lean4/pull/4837) upstream `List.IsPrefix`/`List.IsSuffix`/`List.IsInfix` and add `Decidable` instances, [#4855](https://github.com/leanprover/lean4/pull/4855) upstreams `List.tail`, `List.findIdx`, `List.indexOf`, `List.countP`, `List.count`, and `List.range'`, [#4856](https://github.com/leanprover/lean4/pull/4856) upstreams more List lemmas, [#4866](https://github.com/leanprover/lean4/pull/4866) upstreams `List.pairwise_iff_getElem`, [#4865](https://github.com/leanprover/lean4/pull/4865) upstreams `List.eraseIdx` lemmas.
+  * [#4687](https://github.com/leanprover/lean4/pull/4687) adjusts `List.replicate` simp lemmas and simprocs.
+  * [#4704](https://github.com/leanprover/lean4/pull/4704) adds characterizations of `List.Sublist`.
+  * [#4707](https://github.com/leanprover/lean4/pull/4707) adds simp normal form tests for `List.Pairwise` and `List.Nodup`.
+  * [#4708](https://github.com/leanprover/lean4/pull/4708) and [#4815](https://github.com/leanprover/lean4/pull/4815) reorganize lemmas on list getters.
+  * [#4765](https://github.com/leanprover/lean4/pull/4765) adds simprocs for literal array accesses such as `#[1,2,3,4,5][2]`.
+  * [#4790](https://github.com/leanprover/lean4/pull/4790) removes typeclass assumptions for `List.Nodup.eraseP`.
+  * [#4801](https://github.com/leanprover/lean4/pull/4801) adds efficient `usize` functions for array types.
+  * [#4820](https://github.com/leanprover/lean4/pull/4820) changes `List.filterMapM` to run left-to-right.
+  * [#4835](https://github.com/leanprover/lean4/pull/4835) fills in and cleans up gaps in List API.
+  * [#4843](https://github.com/leanprover/lean4/pull/4843), [#4868](https://github.com/leanprover/lean4/pull/4868), and [#4877](https://github.com/leanprover/lean4/pull/4877) correct `List.Subset` lemmas.
+  * [#4863](https://github.com/leanprover/lean4/pull/4863) splits `Init.Data.List.Lemmas` into function-specific files.
+  * [#4875](https://github.com/leanprover/lean4/pull/4875) fixes statement of `List.take_takeWhile`.
+  * Lemmas: [#4602](https://github.com/leanprover/lean4/pull/4602), [#4627](https://github.com/leanprover/lean4/pull/4627), [#4678](https://github.com/leanprover/lean4/pull/4678) for `List.head` and `list.getLast`, [#4723](https://github.com/leanprover/lean4/pull/4723) for `List.erase`, [#4742](https://github.com/leanprover/lean4/pull/4742)
+* `ByteArray`
+  * [#4582](https://github.com/leanprover/lean4/pull/4582) eliminates `partial` from `ByteArray.toList` and `ByteArray.findIdx?`.
+* `BitVec`
+  * [#4568](https://github.com/leanprover/lean4/pull/4568) adds recurrence theorems for bitblasting multiplication.
+  * [#4571](https://github.com/leanprover/lean4/pull/4571) adds `shiftLeftRec` lemmas.
+  * [#4872](https://github.com/leanprover/lean4/pull/4872) adds `ushiftRightRec` and lemmas.
+  * [#4873](https://github.com/leanprover/lean4/pull/4873) adds `getLsb_replicate`.
+* `Std.HashMap` added:
+  * [#4583](https://github.com/leanprover/lean4/pull/4583) **adds `Std.HashMap`** as a verified replacement for `Lean.HashMap`. See the PR for naming differences, but [#4725](https://github.com/leanprover/lean4/pull/4725) renames `HashMap.remove` to `HashMap.erase`.
+  * [#4682](https://github.com/leanprover/lean4/pull/4682) adds `Inhabited` instances.
+  * [#4732](https://github.com/leanprover/lean4/pull/4732) improves `BEq` argument order in hash map lemmas.
+  * [#4759](https://github.com/leanprover/lean4/pull/4759) makes lemmas resolve instances via unification.
+  * [#4771](https://github.com/leanprover/lean4/pull/4771) documents that hash maps should be used linearly to avoid expensive copies.
+  * [#4791](https://github.com/leanprover/lean4/pull/4791) removes `bif` from hash map lemmas, which is inconvenient to work with in practice.
+  * [#4803](https://github.com/leanprover/lean4/pull/4803) adds more lemmas.
+* `SMap`
+  * [#4690](https://github.com/leanprover/lean4/pull/4690) upstreams `SMap.foldM`.
+* `BEq`
+  * [#4607](https://github.com/leanprover/lean4/pull/4607) adds `PartialEquivBEq`, `ReflBEq`, `EquivBEq`, and `LawfulHashable` classes.
+* `IO`
+  * [#4660](https://github.com/leanprover/lean4/pull/4660) adds `IO.Process.Child.tryWait`.
+* [#4747](https://github.com/leanprover/lean4/pull/4747), [#4730](https://github.com/leanprover/lean4/pull/4730), and [#4756](https://github.com/leanprover/lean4/pull/4756) add `×'` syntax for `PProd`. Adds a delaborator for `PProd` and `MProd` values to pretty print as flattened angle bracket tuples.
+* **Other fixes or improvements**
+  * [#4604](https://github.com/leanprover/lean4/pull/4604) adds lemmas for cond.
+  * [#4619](https://github.com/leanprover/lean4/pull/4619) changes some definitions into theorems.
+  * [#4616](https://github.com/leanprover/lean4/pull/4616) fixes some names with duplicated namespaces.
+  * [#4620](https://github.com/leanprover/lean4/pull/4620) fixes simp lemmas flagged by the simpNF linter.
+  * [#4666](https://github.com/leanprover/lean4/pull/4666) makes the `Antisymm` class be a `Prop`.
+  * [#4621](https://github.com/leanprover/lean4/pull/4621) cleans up unused arguments flagged by linter.
+  * [#4680](https://github.com/leanprover/lean4/pull/4680) adds imports for orphaned `Init` modules.
+  * [#4679](https://github.com/leanprover/lean4/pull/4679) adds imports for orphaned `Std.Data` modules.
+  * [#4688](https://github.com/leanprover/lean4/pull/4688) adds forward and backward directions of `not_exists`.
+  * [#4689](https://github.com/leanprover/lean4/pull/4689) upstreams `eq_iff_true_of_subsingleton`.
+  * [#4709](https://github.com/leanprover/lean4/pull/4709) fixes precedence handling for `Repr` instances for negative numbers for `Int` and `Float`.
+  * [#4760](https://github.com/leanprover/lean4/pull/4760) renames `TC` ("transitive closure") to `Relation.TransGen`.
+  * [#4842](https://github.com/leanprover/lean4/pull/4842) fixes `List` deprecations.
+  * [#4852](https://github.com/leanprover/lean4/pull/4852) upstreams some Mathlib attributes applied to lemmas.
+  * [93ac63](https://github.com/leanprover/lean4/commit/93ac635a89daa5a8e8ef33ec96b0bcbb5d7ec1ea) improves proof.
+  * [#4862](https://github.com/leanprover/lean4/pull/4862) and [#4878](https://github.com/leanprover/lean4/pull/4878) generalize the universe for `PSigma.exists` and rename it to `Exists.of_psigma_prop`.
+  * Typos: [#4737](https://github.com/leanprover/lean4/pull/4737), [7d2155](https://github.com/leanprover/lean4/commit/7d2155943c67c743409420b4546d47fadf73af1c)
+  * Docs: [#4782](https://github.com/leanprover/lean4/pull/4782), [#4869](https://github.com/leanprover/lean4/pull/4869), [#4648](https://github.com/leanprover/lean4/pull/4648)
+
+### Lean internals
+* **Elaboration**
+  * [#4596](https://github.com/leanprover/lean4/pull/4596) enforces `isDefEqStuckEx` at `unstuckMVar` procedure, causing isDefEq to throw a stuck defeq exception if the metavariable was created in a previous level. This results in some better error messages, and it helps `rw` succeed in synthesizing instances (see issue [#2736](https://github.com/leanprover/lean4/issues/2736)).
+  * [#4713](https://github.com/leanprover/lean4/pull/4713) fixes deprecation warnings when there are overloaded symbols.
+  * `elab_as_elim` algorithm:
+    * [#4722](https://github.com/leanprover/lean4/pull/4722) adds check that inferred motive is type-correct.
+    * [#4800](https://github.com/leanprover/lean4/pull/4800) elaborates arguments for parameters appearing in the types of targets.
+    * [#4817](https://github.com/leanprover/lean4/pull/4817) makes the algorithm correctly handle eliminators with explicit motive arguments.
+  * [#4792](https://github.com/leanprover/lean4/pull/4792) adds term elaborator for `Lean.Parser.Term.namedPattern` (e.g. `n@(n' + 1)`) to report errors when used in non-pattern-matching contexts.
+  * [#4818](https://github.com/leanprover/lean4/pull/4818) makes anonymous dot notation work when the expected type is a pi-type-valued type synonym.
+* **Typeclass inference**
+  * [#4646](https://github.com/leanprover/lean4/pull/4646) improves `synthAppInstances`, the function responsible for synthesizing instances for the `rw` and `apply` tactics. Adds a synthesis loop to handle functions whose instances need to be synthesized in a complex order.
+* **Inductive types**
+  * [#4684](https://github.com/leanprover/lean4/pull/4684) (backported as [98ee78](https://github.com/leanprover/lean4/commit/98ee789990f91ff5935627787b537911ef8773c4)) refactors `InductiveVal` to have a `numNested : Nat` field instead of `isNested : Bool`. This modifies the kernel.
+* **Definitions**
+  * [#4776](https://github.com/leanprover/lean4/pull/4776) improves performance of `Replacement.apply`.
+  * [#4712](https://github.com/leanprover/lean4/pull/4712) fixes `.eq_def` theorem generation with messy universes.
+  * [#4841](https://github.com/leanprover/lean4/pull/4841) improves success of finding `T.below x` hypothesis when transforming `match` statements for `IndPredBelow`.
+* **Diagnostics and profiling**
+  * [#4611](https://github.com/leanprover/lean4/pull/4611) makes kernel diagnostics appear when `diagnostics` is enabled even if it is the only section.
+  * [#4753](https://github.com/leanprover/lean4/pull/4753) adds missing `profileitM` functions.
+  * [#4754](https://github.com/leanprover/lean4/pull/4754) adds `Lean.Expr.numObjs` to compute the number of allocated sub-expressions in a given expression, primarily for diagnosing performance issues.
+  * [#4769](https://github.com/leanprover/lean4/pull/4769) adds missing `withTraceNode`s to improve `trace.profiler` output.
+  * [#4781](https://github.com/leanprover/lean4/pull/4781) and [#4882](https://github.com/leanprover/lean4/pull/4882) make the "use `set_option diagnostics true`" message be conditional on current setting of `diagnostics`.
+* **Performance**
+  * [#4767](https://github.com/leanprover/lean4/pull/4767), [#4775](https://github.com/leanprover/lean4/pull/4775), and [#4887](https://github.com/leanprover/lean4/pull/4887) add `ShareCommon.shareCommon'` for sharing common terms. In an example with 16 million subterms, it is 20 times faster than the old `shareCommon` procedure.
+  * [#4779](https://github.com/leanprover/lean4/pull/4779) ensures `Expr.replaceExpr` preserves DAG structure in `Expr`s.
+  * [#4783](https://github.com/leanprover/lean4/pull/4783) documents performance issue in `Expr.replaceExpr`.
+  * [#4794](https://github.com/leanprover/lean4/pull/4794), [#4797](https://github.com/leanprover/lean4/pull/4797), [#4798](https://github.com/leanprover/lean4/pull/4798) make `for_each` use precise cache.
+  * [#4795](https://github.com/leanprover/lean4/pull/4795) makes `Expr.find?` and `Expr.findExt?` use the kernel implementations.
+  * [#4799](https://github.com/leanprover/lean4/pull/4799) makes `Expr.replace` use the kernel implementation.
+  * [#4871](https://github.com/leanprover/lean4/pull/4871) makes `Expr.foldConsts` use a precise cache.
+  * [#4890](https://github.com/leanprover/lean4/pull/4890) makes `expr_eq_fn` use a precise cache.
+* **Utilities**
+  * [#4453](https://github.com/leanprover/lean4/pull/4453) upstreams `ToExpr FilePath` and `compile_time_search_path%`.
+* **Module system**
+  * [#4652](https://github.com/leanprover/lean4/pull/4652) fixes handling of `const2ModIdx` in `finalizeImport`, making it prefer the original module for a declaration when a declaration is re-declared.
+* **Kernel**
+  * [#4637](https://github.com/leanprover/lean4/pull/4637) adds a check to prevent large `Nat` exponentiations from evaluating. Elaborator reduction is controlled by the option `exponentiation.threshold`.
+  * [#4683](https://github.com/leanprover/lean4/pull/4683) updates comments in `kernel/declaration.h`, making sure they reflect the current Lean 4 types.
+  * [#4796](https://github.com/leanprover/lean4/pull/4796) improves performance by using `replace` with a precise cache.
+  * [#4700](https://github.com/leanprover/lean4/pull/4700) improves performance by fixing the implementation of move constructors and move assignment operators. Expression copying was taking 10% of total runtime in some workloads. See issue [#4698](https://github.com/leanprover/lean4/issues/4698).
+  * [#4702](https://github.com/leanprover/lean4/pull/4702) improves performance in `replace_rec_fn::apply` by avoiding expression copies. These copies represented about 13% of time spent in `save_result` in some workloads. See the same issue.
+* **Other fixes or improvements**
+  * [#4590](https://github.com/leanprover/lean4/pull/4590) fixes a typo in some constants and `trace.profiler.useHeartbeats`.
+  * [#4617](https://github.com/leanprover/lean4/pull/4617) add 'since' dates to `deprecated` attributes.
+  * [#4625](https://github.com/leanprover/lean4/pull/4625) improves the robustness of the constructor-as-variable test.
+  * [#4740](https://github.com/leanprover/lean4/pull/4740) extends test with nice example reported on Zulip.
+  * [#4766](https://github.com/leanprover/lean4/pull/4766) moves `Syntax.hasIdent` to be available earlier and shakes dependencies.
+  * [#4881](https://github.com/leanprover/lean4/pull/4881) splits out `Lean.Language.Lean.Types`.
+  * [#4893](https://github.com/leanprover/lean4/pull/4893) adds `LEAN_EXPORT` for `sharecommon` functions.
+  * Typos: [#4635](https://github.com/leanprover/lean4/pull/4635), [#4719](https://github.com/leanprover/lean4/pull/4719), [af40e6](https://github.com/leanprover/lean4/commit/af40e618111581c82fc44de922368a02208b499f)
+  * Docs: [#4748](https://github.com/leanprover/lean4/pull/4748) (`Command.Scope`)
+
+### Compiler, runtime, and FFI
+* [#4661](https://github.com/leanprover/lean4/pull/4661) moves `Std` from `libleanshared` to much smaller `libInit_shared`. This fixes the Windows build.
+* [#4668](https://github.com/leanprover/lean4/pull/4668) fixes initialization, explicitly initializing `Std` in `lean_initialize`.
+* [#4746](https://github.com/leanprover/lean4/pull/4746) adjusts `shouldExport` to exclude more symbols to get below Windows symbol limit. Some exceptions are added by [#4884](https://github.com/leanprover/lean4/pull/4884) and [#4956](https://github.com/leanprover/lean4/pull/4956) to support Verso.
+* [#4778](https://github.com/leanprover/lean4/pull/4778) adds `lean_is_exclusive_obj` (`Lean.isExclusiveUnsafe`) and `lean_set_external_data`.
+* [#4515](https://github.com/leanprover/lean4/pull/4515) fixes calling programs with spaces on Windows.
+
+### Lake
+
+* [#4735](https://github.com/leanprover/lean4/pull/4735) improves a number of elements related to Git checkouts, cloud releases,
+and related error handling.
+
+  * On error, Lake now prints all top-level logs. Top-level logs are those produced by Lake outside of the job monitor (e.g., when cloning dependencies).
+  * When fetching a remote for a dependency, Lake now forcibly fetches tags. This prevents potential errors caused by a repository recreating tags already fetched.
+  * Git error handling is now more informative.
+  * The builtin package facets `release`, `optRelease`, `extraDep` are now captions in the same manner as other facets.
+  * `afterReleaseSync` and `afterReleaseAsync` now fetch `optRelease` rather than `release`.
+  * Added support for optional jobs, whose failure does not cause the whole build to failure. Now `optRelease` is such a job.
+
+* [#4608](https://github.com/leanprover/lean4/pull/4608) adds draft CI workflow when creating new projects.
+* [#4847](https://github.com/leanprover/lean4/pull/4847) adds CLI options to control log levels. The `--log-level=<lv>` controls the minimum log level Lake should output. For instance, `--log-level=error` will only print errors (not warnings or info). Also, adds an analogous `--fail-level` option to control the minimum log level for build failures. The existing `--iofail` and `--wfail` options are respectively equivalent to `--fail-level=info` and `--fail-level=warning`.
+
+* Docs: [#4853](https://github.com/leanprover/lean4/pull/4853)
+
+
+### DevOps/CI
+
+* **Workflows**
+  * [#4531](https://github.com/leanprover/lean4/pull/4531) makes release trigger an update of `release.lean-lang.org`.
+  * [#4598](https://github.com/leanprover/lean4/pull/4598) adjusts `pr-release` to the new `lakefile.lean` syntax.
+  * [#4632](https://github.com/leanprover/lean4/pull/4632) makes `pr-release` use the correct tag name.
+  * [#4638](https://github.com/leanprover/lean4/pull/4638) adds ability to manually trigger nightly release.
+  * [#4640](https://github.com/leanprover/lean4/pull/4640) adds more debugging output for `restart-on-label` CI.
+  * [#4663](https://github.com/leanprover/lean4/pull/4663) bumps up waiting for 10s to 30s for `restart-on-label`.
+  * [#4664](https://github.com/leanprover/lean4/pull/4664) bumps versions for `actions/checkout` and `actions/upload-artifacts`.
+  * [582d6e](https://github.com/leanprover/lean4/commit/582d6e7f7168e0dc0819099edaace27d913b893e) bumps version for `actions/download-artifact`.
+  * [6d9718](https://github.com/leanprover/lean4/commit/6d971827e253a4dc08cda3cf6524d7f37819eb47) adds back dropped `check-stage3`.
+  * [0768ad](https://github.com/leanprover/lean4/commit/0768ad4eb9020af0777587a25a692d181e857c14) adds Jira sync (for FRO).
+  * [#4830](https://github.com/leanprover/lean4/pull/4830) adds support to report CI errors on FRO Zulip.
+  * [#4838](https://github.com/leanprover/lean4/pull/4838) adds trigger for `nightly_bump_toolchain` on mathlib4 upon nightly release.
+  * [abf420](https://github.com/leanprover/lean4/commit/abf4206e9c0fcadf17b6f7933434fd1580175015) fixes msys2.
+  * [#4895](https://github.com/leanprover/lean4/pull/4895) deprecates Nix-based builds and removes interactive components. Users who prefer the flake build should maintain it externally.
+* [#4693](https://github.com/leanprover/lean4/pull/4693), [#4458](https://github.com/leanprover/lean4/pull/4458), and [#4876](https://github.com/leanprover/lean4/pull/4876) update the **release checklist**.
+* [#4669](https://github.com/leanprover/lean4/pull/4669) fixes the "max dynamic symbols" metric per static library.
+* [#4691](https://github.com/leanprover/lean4/pull/4691) improves compatibility of `tests/list_simp` for retesting simp normal forms with Mathlib.
+* [#4806](https://github.com/leanprover/lean4/pull/4806) updates the quickstart guide.
+* [c02aa9](https://github.com/leanprover/lean4/commit/c02aa98c6a08c3a9b05f68039c071085a4ef70d7) documents the **triage team** in the contribution guide.
+
+
+### Breaking changes
+
+* For `@[ext]`-generated `ext` and `ext_iff` lemmas, the `x` and `y` term arguments are now implicit. Furthermore these two lemmas are now protected ([#4543](https://github.com/leanprover/lean4/pull/4543)).
+
+* Now `trace.profiler.useHearbeats` is `trace.profiler.useHeartbeats` ([#4590](https://github.com/leanprover/lean4/pull/4590)).
+
+* A bugfix in the structural recursion code may in some cases break existing code, when a parameter of the type of the recursive argument is bound behind indices of that type. This can usually be fixed by reordering the parameters of the function ([#4672](https://github.com/leanprover/lean4/pull/4672)).
+
+* Now `List.filterMapM` sequences monadic actions left-to-right ([#4820](https://github.com/leanprover/lean4/pull/4820)).
+
+* The effect of the `variable` command on proofs of `theorem`s has been changed. Whether such section variables are accessible in the proof now depends only on the theorem signature and other top-level commands, not on the proof itself. This change ensures that
+  * the statement of a theorem is independent of its proof. In other words, changes in the proof cannot change the theorem statement.
+  * tactics such as `induction` cannot accidentally include a section variable.
+  * the proof can be elaborated in parallel to subsequent declarations in a future version of Lean.
+
+  The effect of `variable`s on the theorem header as well as on other kinds of declarations is unchanged.
+
+  Specifically, section variables are included if they
+  * are directly referenced by the theorem header,
+  * are included via the new `include` command in the current section and not subsequently mentioned in an `omit` statement,
+  * are directly referenced by any variable included by these rules, OR
+  * are instance-implicit variables that reference only variables included by these rules.
+
+  For porting, a new option `deprecated.oldSectionVars` is included to locally switch back to the old behavior.

releases/v4.12.0.md

@@ -0,0 +1,312 @@
+v4.12.0
+----------
+
+### Language features, tactics, and metaprograms
+
+* `bv_decide` tactic. This release introduces a new tactic for proving goals involving `BitVec` and `Bool`. It reduces the goal to a SAT instance that is refuted by an external solver, and the resulting LRAT proof is checked in Lean. This is used to synthesize a proof of the goal by reflection. As this process uses verified algorithms, proofs generated by this tactic use `Lean.ofReduceBool`, so this tactic includes the Lean compiler as part of the trusted code base. The external solver CaDiCaL is included with Lean and does not need to be installed separately to make use of `bv_decide`.
+
+  For example, we can use `bv_decide` to verify that a bit twiddling formula leaves at most one bit set:
+  ```lean
+  def popcount (x : BitVec 64) : BitVec 64 :=
+    let rec go (x pop : BitVec 64) : Nat → BitVec 64
+      | 0 => pop
+      | n + 1 => go (x >>> 2) (pop + (x &&& 1)) n
+    go x 0 64
+
+  example (x : BitVec 64) : popcount ((x &&& (x - 1)) ^^^ x) ≤ 1 := by
+    simp only [popcount, popcount.go]
+    bv_decide
+  ```
+  When the external solver fails to refute the SAT instance generated by `bv_decide`, it can report a counterexample:
+  ```lean
+  /--
+  error: The prover found a counterexample, consider the following assignment:
+  x = 0xffffffffffffffff#64
+  -/
+  #guard_msgs in
+  example (x : BitVec 64) : x < x + 1 := by
+    bv_decide
+  ```
+
+  See `Lean.Elab.Tactic.BVDecide` for a more detailed overview, and look in `tests/lean/run/bv_*` for examples.
+
+  [#5013](https://github.com/leanprover/lean4/pull/5013), [#5074](https://github.com/leanprover/lean4/pull/5074), [#5100](https://github.com/leanprover/lean4/pull/5100), [#5113](https://github.com/leanprover/lean4/pull/5113), [#5137](https://github.com/leanprover/lean4/pull/5137), [#5203](https://github.com/leanprover/lean4/pull/5203), [#5212](https://github.com/leanprover/lean4/pull/5212), [#5220](https://github.com/leanprover/lean4/pull/5220).
+
+* `simp` tactic
+  * [#4988](https://github.com/leanprover/lean4/pull/4988) fixes a panic in the `reducePow` simproc.
+  * [#5071](https://github.com/leanprover/lean4/pull/5071) exposes the `index` option to the `dsimp` tactic, introduced to `simp` in [#4202](https://github.com/leanprover/lean4/pull/4202).
+  * [#5159](https://github.com/leanprover/lean4/pull/5159) fixes a panic at `Fin.isValue` simproc.
+  * [#5167](https://github.com/leanprover/lean4/pull/5167) and [#5175](https://github.com/leanprover/lean4/pull/5175) rename the `simpCtorEq` simproc to `reduceCtorEq` and makes it optional. (See breaking changes.)
+  * [#5187](https://github.com/leanprover/lean4/pull/5187) ensures `reduceCtorEq` is enabled in the `norm_cast` tactic.
+  * [#5073](https://github.com/leanprover/lean4/pull/5073) modifies the simp debug trace messages to tag with "dpre" and "dpost" instead of "pre" and "post" when in definitional rewrite mode. [#5054](https://github.com/leanprover/lean4/pull/5054) explains the `reduce` steps for `trace.Debug.Meta.Tactic.simp` trace messages.
+* `ext` tactic
+  * [#4996](https://github.com/leanprover/lean4/pull/4996) reduces default maximum iteration depth from 1000000 to 100.
+* `induction` tactic
+  * [#5117](https://github.com/leanprover/lean4/pull/5117) fixes a bug where `let` bindings in minor premises wouldn't be counted correctly.
+
+* `omega` tactic
+  * [#5157](https://github.com/leanprover/lean4/pull/5157) fixes a panic.
+
+* `conv` tactic
+  * [#5149](https://github.com/leanprover/lean4/pull/5149) improves `arg n` to handle subsingleton instance arguments.
+
+* [#5044](https://github.com/leanprover/lean4/pull/5044) upstreams the `#time` command.
+* [#5079](https://github.com/leanprover/lean4/pull/5079) makes `#check` and `#reduce` typecheck the elaborated terms.
+
+* **Incrementality**
+  * [#4974](https://github.com/leanprover/lean4/pull/4974) fixes regression where we would not interrupt elaboration of previous document versions.
+  * [#5004](https://github.com/leanprover/lean4/pull/5004) fixes a performance regression.
+  * [#5001](https://github.com/leanprover/lean4/pull/5001) disables incremental body elaboration in presence of `where` clauses in declarations.
+  * [#5018](https://github.com/leanprover/lean4/pull/5018) enables infotrees on the command line for ilean generation.
+  * [#5040](https://github.com/leanprover/lean4/pull/5040) and [#5056](https://github.com/leanprover/lean4/pull/5056) improve performance of info trees.
+  * [#5090](https://github.com/leanprover/lean4/pull/5090) disables incrementality in the `case .. | ..` tactic.
+  * [#5312](https://github.com/leanprover/lean4/pull/5312) fixes a bug where changing whitespace after the module header could break subsequent commands.
+
+* **Definitions**
+  * [#5016](https://github.com/leanprover/lean4/pull/5016) and [#5066](https://github.com/leanprover/lean4/pull/5066) add `clean_wf` tactic to clean up tactic state in `decreasing_by`. This can be disabled with `set_option debug.rawDecreasingByGoal false`.
+  * [#5055](https://github.com/leanprover/lean4/pull/5055) unifies equational theorems between structural and well-founded recursion.
+  * [#5041](https://github.com/leanprover/lean4/pull/5041) allows mutually recursive functions to use different parameter names among the “fixed parameter prefix”
+  * [#4154](https://github.com/leanprover/lean4/pull/4154) and [#5109](https://github.com/leanprover/lean4/pull/5109) add fine-grained equational lemmas for non-recursive functions. See breaking changes.
+  * [#5129](https://github.com/leanprover/lean4/pull/5129) unifies equation lemmas for recursive and non-recursive definitions. The `backward.eqns.deepRecursiveSplit` option can be set to `false` to get the old behavior. See breaking changes.
+  * [#5141](https://github.com/leanprover/lean4/pull/5141) adds `f.eq_unfold` lemmas. Now Lean produces the following zoo of rewrite rules:
+    ```
+    Option.map.eq_1      : Option.map f none = none
+    Option.map.eq_2      : Option.map f (some x) = some (f x)
+    Option.map.eq_def    : Option.map f p = match o with | none => none | (some x) => some (f x)
+    Option.map.eq_unfold : Option.map = fun f p => match o with | none => none | (some x) => some (f x)
+    ```
+    The `f.eq_unfold` variant is especially useful to rewrite with `rw` under binders.
+  * [#5136](https://github.com/leanprover/lean4/pull/5136) fixes bugs in recursion over predicates.
+
+* **Variable inclusion**
+  * [#5206](https://github.com/leanprover/lean4/pull/5206) documents that `include` currently only applies to theorems.
+
+* **Elaboration**
+  * [#4926](https://github.com/leanprover/lean4/pull/4926) fixes a bug where autoparam errors were associated to an incorrect source position.
+  * [#4833](https://github.com/leanprover/lean4/pull/4833) fixes an issue where cdot anonymous functions (e.g. `(· + ·)`) would not handle ambiguous notation correctly. Numbers the parameters, making this example expand as `fun x1 x2 => x1 + x2` rather than `fun x x_1 => x + x_1`.
+  * [#5037](https://github.com/leanprover/lean4/pull/5037) improves strength of the tactic that proves array indexing is in bounds.
+  * [#5119](https://github.com/leanprover/lean4/pull/5119) fixes a bug in the tactic that proves indexing is in bounds where it could loop in the presence of mvars.
+  * [#5072](https://github.com/leanprover/lean4/pull/5072) makes the structure type clickable in "not a field of structure" errors for structure instance notation.
+  * [#4717](https://github.com/leanprover/lean4/pull/4717) fixes a bug where mutual `inductive` commands could create terms that the kernel rejects.
+  * [#5142](https://github.com/leanprover/lean4/pull/5142) fixes a bug where `variable` could fail when mixing binder updates and declarations.
+
+* **Other fixes or improvements**
+  * [#5118](https://github.com/leanprover/lean4/pull/5118) changes the definition of the `syntheticHole` parser so that hovering over `_` in `?_` gives the docstring for synthetic holes.
+  * [#5173](https://github.com/leanprover/lean4/pull/5173) uses the emoji variant selector for ✅️,❌️,💥️ in messages, improving fonts selection.
+  * [#5183](https://github.com/leanprover/lean4/pull/5183) fixes a bug in `rename_i` where implementation detail hypotheses could be renamed.
+
+### Language server, widgets, and IDE extensions
+
+* [#4821](https://github.com/leanprover/lean4/pull/4821) resolves two language server bugs that especially affect Windows users. (1) Editing the header could result in the watchdog not correctly restarting the file worker, which would lead to the file seemingly being processed forever. (2) On an especially slow Windows machine, we found that starting the language server would sometimes not succeed at all. This PR also resolves an issue where we would not correctly emit messages that we received while the file worker is being restarted to the corresponding file worker after the restart.
+* [#5006](https://github.com/leanprover/lean4/pull/5006) updates the user widget manual.
+* [#5193](https://github.com/leanprover/lean4/pull/5193) updates the quickstart guide with the new display name for the Lean 4 extension ("Lean 4").
+* [#5185](https://github.com/leanprover/lean4/pull/5185) fixes a bug where over time "import out of date" messages would accumulate.
+* [#4900](https://github.com/leanprover/lean4/pull/4900) improves ilean loading performance by about a factor of two. Optimizes the JSON parser and the conversion from JSON to Lean data structures; see PR description for details.
+* **Other fixes or improvements**
+  * [#5031](https://github.com/leanprover/lean4/pull/5031) localizes an instance in `Lsp.Diagnostics`.
+
+### Pretty printing
+
+* [#4976](https://github.com/leanprover/lean4/pull/4976) introduces `@[app_delab]`, a macro for creating delaborators for particular constants. The `@[app_delab ident]` syntax resolves `ident` to its constant name `name` and then expands to `@[delab app.name]`.
+* [#4982](https://github.com/leanprover/lean4/pull/4982) fixes a bug where the pretty printer assumed structure projections were type correct (such terms can appear in type mismatch errors). Improves hoverability of `#print` output for structures.
+* [#5218](https://github.com/leanprover/lean4/pull/5218) and [#5239](https://github.com/leanprover/lean4/pull/5239) add `pp.exprSizes` debugging option. When true, each pretty printed expression is prefixed with `[size a/b/c]`, where `a` is the size without sharing, `b` is the actual size, and `c` is the size with the maximum possible sharing.
+
+### Library
+
+* [#5020](https://github.com/leanprover/lean4/pull/5020) swaps the parameters to `Membership.mem`. A purpose of this change is to make set-like `CoeSort` coercions to refer to the eta-expanded function `fun x => Membership.mem s x`, which can reduce in many computations. Another is that having the `s` argument first leads to better discrimination tree keys. (See breaking changes.)
+* `Array`
+  * [#4970](https://github.com/leanprover/lean4/pull/4970) adds `@[ext]` attribute to `Array.ext`.
+  * [#4957](https://github.com/leanprover/lean4/pull/4957) deprecates `Array.get_modify`.
+* `List`
+  * [#4995](https://github.com/leanprover/lean4/pull/4995) upstreams `List.findIdx` lemmas.
+  * [#5029](https://github.com/leanprover/lean4/pull/5029), [#5048](https://github.com/leanprover/lean4/pull/5048) and [#5132](https://github.com/leanprover/lean4/pull/5132) add `List.Sublist` lemmas, some upstreamed. [#5077](https://github.com/leanprover/lean4/pull/5077) fixes implicitness in refl/rfl lemma binders.  add `List.Sublist` theorems.
+  * [#5047](https://github.com/leanprover/lean4/pull/5047) upstreams `List.Pairwise` lemmas.
+  * [#5053](https://github.com/leanprover/lean4/pull/5053), [#5124](https://github.com/leanprover/lean4/pull/5124), and [#5161](https://github.com/leanprover/lean4/pull/5161) add `List.find?/findSome?/findIdx?` theorems.
+  * [#5039](https://github.com/leanprover/lean4/pull/5039) adds `List.foldlRecOn` and `List.foldrRecOn` recursion principles to prove things about `List.foldl` and `List.foldr`.
+  * [#5069](https://github.com/leanprover/lean4/pull/5069) upstreams `List.Perm`.
+  * [#5092](https://github.com/leanprover/lean4/pull/5092) and [#5107](https://github.com/leanprover/lean4/pull/5107) add `List.mergeSort` and a fast `@[csimp]` implementation.
+  * [#5103](https://github.com/leanprover/lean4/pull/5103) makes the simp lemmas for `List.subset` more aggressive.
+  * [#5106](https://github.com/leanprover/lean4/pull/5106) changes the statement of `List.getLast?_cons`.
+  * [#5123](https://github.com/leanprover/lean4/pull/5123) and [#5158](https://github.com/leanprover/lean4/pull/5158) add `List.range` and `List.iota` lemmas.
+  * [#5130](https://github.com/leanprover/lean4/pull/5130) adds `List.join` lemmas.
+  * [#5131](https://github.com/leanprover/lean4/pull/5131) adds `List.append` lemmas.
+  * [#5152](https://github.com/leanprover/lean4/pull/5152) adds `List.erase(|P|Idx)` lemmas.
+  * [#5127](https://github.com/leanprover/lean4/pull/5127) makes miscellaneous lemma updates.
+  * [#5153](https://github.com/leanprover/lean4/pull/5153) and [#5160](https://github.com/leanprover/lean4/pull/5160) add lemmas about `List.attach` and `List.pmap`.
+  * [#5164](https://github.com/leanprover/lean4/pull/5164), [#5177](https://github.com/leanprover/lean4/pull/5177), and [#5215](https://github.com/leanprover/lean4/pull/5215) add `List.find?` and `List.range'/range/iota` lemmas.
+  * [#5196](https://github.com/leanprover/lean4/pull/5196) adds `List.Pairwise_erase` and related lemmas.
+  * [#5151](https://github.com/leanprover/lean4/pull/5151) and [#5163](https://github.com/leanprover/lean4/pull/5163) improve confluence of `List` simp lemmas. [#5105](https://github.com/leanprover/lean4/pull/5105) and [#5102](https://github.com/leanprover/lean4/pull/5102) adjust `List` simp lemmas.
+  * [#5178](https://github.com/leanprover/lean4/pull/5178) removes `List.getLast_eq_iff_getLast_eq_some` as a simp lemma.
+  * [#5210](https://github.com/leanprover/lean4/pull/5210) reverses the meaning of `List.getElem_drop` and `List.getElem_drop'`.
+  * [#5214](https://github.com/leanprover/lean4/pull/5214) moves `@[csimp]` lemmas earlier where possible.
+* `Nat` and `Int`
+  * [#5104](https://github.com/leanprover/lean4/pull/5104) adds `Nat.add_left_eq_self` and relatives.
+  * [#5146](https://github.com/leanprover/lean4/pull/5146) adds missing `Nat.and_xor_distrib_(left|right)`.
+  * [#5148](https://github.com/leanprover/lean4/pull/5148) and [#5190](https://github.com/leanprover/lean4/pull/5190) improve `Nat` and `Int` simp lemma confluence.
+  * [#5165](https://github.com/leanprover/lean4/pull/5165) adjusts `Int` simp lemmas.
+  * [#5166](https://github.com/leanprover/lean4/pull/5166) adds `Int` lemmas relating `neg` and `emod`/`mod`.
+  * [#5208](https://github.com/leanprover/lean4/pull/5208) reverses the direction of the `Int.toNat_sub` simp lemma.
+  * [#5209](https://github.com/leanprover/lean4/pull/5209) adds `Nat.bitwise` lemmas.
+  * [#5230](https://github.com/leanprover/lean4/pull/5230) corrects the docstrings for integer division and modulus.
+* `Option`
+  * [#5128](https://github.com/leanprover/lean4/pull/5128) and [#5154](https://github.com/leanprover/lean4/pull/5154) add `Option` lemmas.
+* `BitVec`
+  * [#4889](https://github.com/leanprover/lean4/pull/4889) adds `sshiftRight` bitblasting.
+  * [#4981](https://github.com/leanprover/lean4/pull/4981) adds `Std.Associative` and `Std.Commutative` instances for `BitVec.[and|or|xor]`.
+  * [#4913](https://github.com/leanprover/lean4/pull/4913) enables `missingDocs` error for `BitVec` modules.
+  * [#4930](https://github.com/leanprover/lean4/pull/4930) makes parameter names for `BitVec` more consistent.
+  * [#5098](https://github.com/leanprover/lean4/pull/5098) adds `BitVec.intMin`. Introduces `boolToPropSimps` simp set for converting from boolean to propositional expressions.
+  * [#5200](https://github.com/leanprover/lean4/pull/5200) and [#5217](https://github.com/leanprover/lean4/pull/5217) rename `BitVec.getLsb` to `BitVec.getLsbD`, etc., to bring naming in line with `List`/`Array`/etc.
+  * **Theorems:** [#4977](https://github.com/leanprover/lean4/pull/4977), [#4951](https://github.com/leanprover/lean4/pull/4951), [#4667](https://github.com/leanprover/lean4/pull/4667), [#5007](https://github.com/leanprover/lean4/pull/5007), [#4997](https://github.com/leanprover/lean4/pull/4997), [#5083](https://github.com/leanprover/lean4/pull/5083), [#5081](https://github.com/leanprover/lean4/pull/5081), [#4392](https://github.com/leanprover/lean4/pull/4392)
+* `UInt`
+  * [#4514](https://github.com/leanprover/lean4/pull/4514) fixes naming convention for `UInt` lemmas.
+* `Std.HashMap` and `Std.HashSet`
+  * [#4943](https://github.com/leanprover/lean4/pull/4943) deprecates variants of hash map query methods. (See breaking changes.)
+  * [#4917](https://github.com/leanprover/lean4/pull/4917) switches the library and Lean to `Std.HashMap` and `Std.HashSet` almost everywhere.
+  * [#4954](https://github.com/leanprover/lean4/pull/4954) deprecates `Lean.HashMap` and `Lean.HashSet`.
+  * [#5023](https://github.com/leanprover/lean4/pull/5023) cleans up lemma parameters.
+
+* `Std.Sat` (for `bv_decide`)
+  * [#4933](https://github.com/leanprover/lean4/pull/4933) adds definitions of SAT and CNF.
+  * [#4953](https://github.com/leanprover/lean4/pull/4953) defines "and-inverter graphs" (AIGs) as described in section 3 of [Davis-Swords 2013](https://arxiv.org/pdf/1304.7861.pdf).
+
+* **Parsec**
+  * [#4774](https://github.com/leanprover/lean4/pull/4774) generalizes the `Parsec` library, allowing parsing of iterable data beyond `String` such as `ByteArray`. (See breaking changes.)
+  * [#5115](https://github.com/leanprover/lean4/pull/5115) moves `Lean.Data.Parsec` to `Std.Internal.Parsec` for bootstrappng reasons.
+
+* `Thunk`
+  * [#4969](https://github.com/leanprover/lean4/pull/4969) upstreams `Thunk.ext`.
+
+* **IO**
+  * [#4973](https://github.com/leanprover/lean4/pull/4973) modifies `IO.FS.lines` to handle `\r\n` on all operating systems instead of just on Windows.
+  * [#5125](https://github.com/leanprover/lean4/pull/5125) adds `createTempFile` and `withTempFile` for creating temporary files that can only be read and written by the current user.
+
+* **Other fixes or improvements**
+  * [#4945](https://github.com/leanprover/lean4/pull/4945) adds `Array`, `Bool` and `Prod` utilities from LeanSAT.
+  * [#4960](https://github.com/leanprover/lean4/pull/4960) adds `Relation.TransGen.trans`.
+  * [#5012](https://github.com/leanprover/lean4/pull/5012) states `WellFoundedRelation Nat` using `<`, not `Nat.lt`.
+  * [#5011](https://github.com/leanprover/lean4/pull/5011) uses `≠` instead of `Not (Eq ...)` in `Fin.ne_of_val_ne`.
+  * [#5197](https://github.com/leanprover/lean4/pull/5197) upstreams `Fin.le_antisymm`.
+  * [#5042](https://github.com/leanprover/lean4/pull/5042) reduces usage of `refine'`.
+  * [#5101](https://github.com/leanprover/lean4/pull/5101) adds about `if-then-else` and `Option`.
+  * [#5112](https://github.com/leanprover/lean4/pull/5112) adds basic instances for `ULift` and `PLift`.
+  * [#5133](https://github.com/leanprover/lean4/pull/5133) and [#5168](https://github.com/leanprover/lean4/pull/5168) make fixes from running the simpNF linter over Lean.
+  * [#5156](https://github.com/leanprover/lean4/pull/5156) removes a bad simp lemma in `omega` theory.
+  * [#5155](https://github.com/leanprover/lean4/pull/5155) improves confluence of `Bool` simp lemmas.
+  * [#5162](https://github.com/leanprover/lean4/pull/5162) improves confluence of `Function.comp` simp lemmas.
+  * [#5191](https://github.com/leanprover/lean4/pull/5191) improves confluence of `if-then-else` simp lemmas.
+  * [#5147](https://github.com/leanprover/lean4/pull/5147) adds `@[elab_as_elim]` to `Quot.rec`, `Nat.strongInductionOn` and `Nat.casesStrongInductionOn`, and also renames the latter two to `Nat.strongRecOn` and `Nat.casesStrongRecOn` (deprecated in [#5179](https://github.com/leanprover/lean4/pull/5179)).
+  * [#5180](https://github.com/leanprover/lean4/pull/5180) disables some simp lemmas with bad discrimination tree keys.
+  * [#5189](https://github.com/leanprover/lean4/pull/5189) cleans up internal simp lemmas that had leaked.
+  * [#5198](https://github.com/leanprover/lean4/pull/5198) cleans up `allowUnsafeReducibility`.
+  * [#5229](https://github.com/leanprover/lean4/pull/5229) removes unused lemmas from some `simp` tactics.
+  * [#5199](https://github.com/leanprover/lean4/pull/5199) removes >6 month deprecations.
+
+### Lean internals
+
+* **Performance**
+  * Some core algorithms have been rewritten in C++ for performance.
+    * [#4910](https://github.com/leanprover/lean4/pull/4910) and [#4912](https://github.com/leanprover/lean4/pull/4912) reimplement `instantiateLevelMVars`.
+    * [#4915](https://github.com/leanprover/lean4/pull/4915), [#4922](https://github.com/leanprover/lean4/pull/4922), and [#4931](https://github.com/leanprover/lean4/pull/4931) reimplement `instantiateExprMVars`, 30% faster on a benchmark.
+  * [#4934](https://github.com/leanprover/lean4/pull/4934) has optimizations for the kernel's `Expr` equality test.
+  * [#4990](https://github.com/leanprover/lean4/pull/4990) fixes bug in hashing for the kernel's `Expr` equality test.
+  * [#4935](https://github.com/leanprover/lean4/pull/4935) and [#4936](https://github.com/leanprover/lean4/pull/4936) skip some `PreDefinition` transformations if they are not needed.
+  * [#5225](https://github.com/leanprover/lean4/pull/5225) adds caching for visited exprs at `CheckAssignmentQuick` in `ExprDefEq`.
+  * [#5226](https://github.com/leanprover/lean4/pull/5226) maximizes term sharing at `instantiateMVarDeclMVars`, used by `runTactic`.
+* **Diagnostics and profiling**
+  * [#4923](https://github.com/leanprover/lean4/pull/4923) adds profiling for `instantiateMVars` in `Lean.Elab.MutualDef`, which can be a bottleneck there.
+  * [#4924](https://github.com/leanprover/lean4/pull/4924) adds diagnostics for large theorems, controlled by the `diagnostics.threshold.proofSize` option.
+  * [#4897](https://github.com/leanprover/lean4/pull/4897) improves display of diagnostic results.
+* **Other fixes or improvements**
+  * [#4921](https://github.com/leanprover/lean4/pull/4921) cleans up `Expr.betaRev`.
+  * [#4940](https://github.com/leanprover/lean4/pull/4940) fixes tests by not writing directly to stdout, which is unreliable now that elaboration and reporting are executed in separate threads.
+  * [#4955](https://github.com/leanprover/lean4/pull/4955) documents that `stderrAsMessages` is now the default on the command line as well.
+  * [#4647](https://github.com/leanprover/lean4/pull/4647) adjusts documentation for building on macOS.
+  * [#4987](https://github.com/leanprover/lean4/pull/4987) makes regular mvar assignments take precedence over delayed ones in `instantiateMVars`. Normally delayed assignment metavariables are never directly assigned, but on errors Lean assigns `sorry` to unassigned metavariables.
+  * [#4967](https://github.com/leanprover/lean4/pull/4967) adds linter name to errors when a linter crashes.
+  * [#5043](https://github.com/leanprover/lean4/pull/5043) cleans up command line snapshots logic.
+  * [#5067](https://github.com/leanprover/lean4/pull/5067) minimizes some imports.
+  * [#5068](https://github.com/leanprover/lean4/pull/5068) generalizes the monad for `addMatcherInfo`.
+  * [f71a1f](https://github.com/leanprover/lean4/commit/f71a1fb4ae958fccb3ad4d48786a8f47ced05c15) adds missing test for [#5126](https://github.com/leanprover/lean4/issues/5126).
+  * [#5201](https://github.com/leanprover/lean4/pull/5201) restores a test.
+  * [#3698](https://github.com/leanprover/lean4/pull/3698) fixes a bug where label attributes did not pass on the attribute kind.
+  * Typos: [#5080](https://github.com/leanprover/lean4/pull/5080), [#5150](https://github.com/leanprover/lean4/pull/5150), [#5202](https://github.com/leanprover/lean4/pull/5202)
+
+### Compiler, runtime, and FFI
+
+* [#3106](https://github.com/leanprover/lean4/pull/3106) moves frontend to new snapshot architecture. Note that `Frontend.processCommand` and `FrontendM` are no longer used by Lean core, but they will be preserved.
+* [#4919](https://github.com/leanprover/lean4/pull/4919) adds missing include in runtime for `AUTO_THREAD_FINALIZATION` feature on Windows.
+* [#4941](https://github.com/leanprover/lean4/pull/4941) adds more `LEAN_EXPORT`s for Windows.
+* [#4911](https://github.com/leanprover/lean4/pull/4911) improves formatting of CLI help text for the frontend.
+* [#4950](https://github.com/leanprover/lean4/pull/4950) improves file reading and writing.
+  * `readBinFile` and `readFile` now only require two system calls (`stat` + `read`) instead of one `read` per 1024 byte chunk.
+  * `Handle.getLine` and `Handle.putStr` no longer get tripped up by NUL characters.
+* [#4971](https://github.com/leanprover/lean4/pull/4971) handles the SIGBUS signal when detecting stack overflows.
+* [#5062](https://github.com/leanprover/lean4/pull/5062) avoids overwriting existing signal handlers, like in [rust-lang/rust#69685](https://github.com/rust-lang/rust/pull/69685).
+* [#4860](https://github.com/leanprover/lean4/pull/4860) improves workarounds for building on Windows. Splits `libleanshared` on Windows to avoid symbol limit, removes the `LEAN_EXPORT` denylist workaround, adds missing `LEAN_EXPORT`s.
+* [#4952](https://github.com/leanprover/lean4/pull/4952) output panics into Lean's redirected stderr, ensuring panics ARE visible as regular messages in the language server and properly ordered in relation to other messages on the command line.
+* [#4963](https://github.com/leanprover/lean4/pull/4963) links LibUV.
+
+### Lake
+
+* [#5030](https://github.com/leanprover/lean4/pull/5030) removes dead code.
+* [#4770](https://github.com/leanprover/lean4/pull/4770) adds additional fields to the package configuration which will be used by Reservoir. See the PR description for details.
+
+
+### DevOps/CI
+* [#4914](https://github.com/leanprover/lean4/pull/4914) and [#4937](https://github.com/leanprover/lean4/pull/4937) improve the release checklist.
+* [#4925](https://github.com/leanprover/lean4/pull/4925) ignores stale leanpkg tests.
+* [#5003](https://github.com/leanprover/lean4/pull/5003) upgrades `actions/cache` in CI.
+* [#5010](https://github.com/leanprover/lean4/pull/5010) sets `save-always` in cache actions in CI.
+* [#5008](https://github.com/leanprover/lean4/pull/5008) adds more libuv search patterns for the speedcenter.
+* [#5009](https://github.com/leanprover/lean4/pull/5009) reduce number of runs in the speedcenter for "fast" benchmarks from 10 to 3.
+* [#5014](https://github.com/leanprover/lean4/pull/5014) adjusts lakefile editing to use new `git` syntax in `pr-release` workflow.
+* [#5025](https://github.com/leanprover/lean4/pull/5025) has `pr-release` workflow pass `--retry` to `curl`.
+* [#5022](https://github.com/leanprover/lean4/pull/5022) builds MacOS Aarch64 release for PRs by default.
+* [#5045](https://github.com/leanprover/lean4/pull/5045) adds libuv to the required packages heading in macos docs.
+* [#5034](https://github.com/leanprover/lean4/pull/5034) fixes the install name of `libleanshared_1` on macOS.
+* [#5051](https://github.com/leanprover/lean4/pull/5051) fixes Windows stage 0.
+* [#5052](https://github.com/leanprover/lean4/pull/5052) fixes 32bit stage 0 builds in CI.
+* [#5057](https://github.com/leanprover/lean4/pull/5057) avoids rebuilding `leanmanifest` in each build.
+* [#5099](https://github.com/leanprover/lean4/pull/5099) makes `restart-on-label` workflow also filter by commit SHA.
+* [#4325](https://github.com/leanprover/lean4/pull/4325) adds CaDiCaL.
+
+### Breaking changes
+
+* [LibUV](https://libuv.org/) is now required to build Lean. This change only affects developers who compile Lean themselves instead of obtaining toolchains via `elan`. We have updated the official build instructions with information on how to obtain LibUV on our supported platforms. ([#4963](https://github.com/leanprover/lean4/pull/4963))
+
+* Recursive definitions with a `decreasing_by` clause that begins with `simp_wf` may break. Try removing `simp_wf` or replacing it with `simp`. ([#5016](https://github.com/leanprover/lean4/pull/5016))
+
+* The behavior of `rw [f]` where `f` is a non-recursive function defined by pattern matching changed.
+
+  For example, preciously, `rw [Option.map]` would rewrite `Option.map f o` to `match o with … `. Now this rewrite fails because it will use the equational lemmas, and these require constructors – just like for `List.map`.
+
+  Remedies:
+  * Split on `o` before rewriting.
+  * Use `rw [Option.map.eq_def]`, which rewrites any (saturated) application of `Option.map`.
+  * Use `set_option backward.eqns.nonrecursive false` when *defining* the function in question.
+  ([#4154](https://github.com/leanprover/lean4/pull/4154))
+
+* The unified handling of equation lemmas for recursive and non-recursive functions can break existing code, as there now can be extra equational lemmas:
+
+  * Explicit uses of `f.eq_2` might have to be adjusted if the numbering changed.
+
+  * Uses of `rw [f]` or `simp [f]` may no longer apply if they previously matched (and introduced a `match` statement), when the equational lemmas got more fine-grained.
+
+    In this case either case analysis on the parameters before rewriting helps, or setting the option `backward.eqns.deepRecursiveSplit false` while *defining* the function.
+
+  ([#5129](https://github.com/leanprover/lean4/pull/5129), [#5207](https://github.com/leanprover/lean4/pull/5207))
+
+* The `reduceCtorEq` simproc is now optional, and it might need to be included in lists of simp lemmas, like `simp only [reduceCtorEq]`. This simproc is responsible for reducing equalities of constructors. ([#5167](https://github.com/leanprover/lean4/pull/5167))
+
+* `Nat.strongInductionOn` is now `Nat.strongRecOn` and `Nat.caseStrongInductionOn` to `Nat.caseStrongRecOn`. ([#5147](https://github.com/leanprover/lean4/pull/5147))
+
+* The parameters to `Membership.mem` have been swapped, which affects all `Membership` instances. ([#5020](https://github.com/leanprover/lean4/pull/5020))
+
+* The meanings of `List.getElem_drop` and `List.getElem_drop'` have been reversed and the first is now a simp lemma. ([#5210](https://github.com/leanprover/lean4/pull/5210))
+
+* The `Parsec` library has moved from `Lean.Data.Parsec` to `Std.Internal.Parsec`. The `Parsec` type is now more general with a parameter for an iterable. Users parsing strings can migrate to `Parser` in the `Std.Internal.Parsec.String` namespace, which also includes string-focused parsing combinators. ([#4774](https://github.com/leanprover/lean4/pull/4774))
+
+* The `Lean` module has switched from `Lean.HashMap` and `Lean.HashSet` to `Std.HashMap` and `Std.HashSet` ([#4943](https://github.com/leanprover/lean4/pull/4943)). `Lean.HashMap` and `Lean.HashSet` are now deprecated ([#4954](https://github.com/leanprover/lean4/pull/4954)) and will be removed in a future release. Users of `Lean` APIs that interact with hash maps, for example `Lean.Environment.const2ModIdx`, might encounter minor breakage due to the following changes from `Lean.HashMap` to `Std.HashMap`:
+  * query functions use the term `get` instead of `find`, ([#4943](https://github.com/leanprover/lean4/pull/4943))
+  * the notation `map[key]` no longer returns an optional value but instead expects a proof that the key is present in the map. The previous behavior is available via the `map[key]?` notation.

releases/v4.13.0.md

@@ -0,0 +1,312 @@
+v4.13.0
+----------
+
+**Full Changelog**: https://github.com/leanprover/lean4/compare/v4.12.0...v4.13.0
+
+### Language features, tactics, and metaprograms
+
+* `structure` command
+  * [#5511](https://github.com/leanprover/lean4/pull/5511) allows structure parents to be type synonyms.
+  * [#5531](https://github.com/leanprover/lean4/pull/5531) allows default values for structure fields to be noncomputable.
+
+* `rfl` and `apply_rfl` tactics
+  * [#3714](https://github.com/leanprover/lean4/pull/3714), [#3718](https://github.com/leanprover/lean4/pull/3718) improve the `rfl` tactic and give better error messages.
+  * [#3772](https://github.com/leanprover/lean4/pull/3772) makes `rfl` no longer use kernel defeq for ground terms.
+  * [#5329](https://github.com/leanprover/lean4/pull/5329) tags `Iff.refl` with `@[refl]` (@Parcly-Taxel)
+  * [#5359](https://github.com/leanprover/lean4/pull/5359) ensures that the `rfl` tactic tries `Iff.rfl` (@Parcly-Taxel)
+
+* `unfold` tactic
+  * [#4834](https://github.com/leanprover/lean4/pull/4834) let `unfold` do zeta-delta reduction of local definitions, incorporating functionality of the Mathlib `unfold_let` tactic.
+
+* `omega` tactic
+  * [#5382](https://github.com/leanprover/lean4/pull/5382) fixes spurious error in [#5315](https://github.com/leanprover/lean4/issues/5315)
+  * [#5523](https://github.com/leanprover/lean4/pull/5523) supports `Int.toNat`
+
+* `simp` tactic
+  * [#5479](https://github.com/leanprover/lean4/pull/5479) lets `simp` apply rules with higher-order patterns.
+
+* `induction` tactic
+  * [#5494](https://github.com/leanprover/lean4/pull/5494) fixes `induction`’s "pre-tactic" block to always be indented, avoiding unintended uses of it.
+
+* `ac_nf` tactic
+  * [#5524](https://github.com/leanprover/lean4/pull/5524) adds `ac_nf`, a counterpart to `ac_rfl`, for normalizing expressions with respect to associativity and commutativity. Tests it with `BitVec` expressions.
+
+* `bv_decide`
+  * [#5211](https://github.com/leanprover/lean4/pull/5211) makes `extractLsb'` the primitive `bv_decide` understands, rather than `extractLsb` (@alexkeizer)
+  * [#5365](https://github.com/leanprover/lean4/pull/5365) adds `bv_decide` diagnoses.
+  * [#5375](https://github.com/leanprover/lean4/pull/5375) adds `bv_decide` normalization rules for `ofBool (a.getLsbD i)` and `ofBool a[i]` (@alexkeizer)
+  * [#5423](https://github.com/leanprover/lean4/pull/5423) enhances the rewriting rules of `bv_decide`
+  * [#5433](https://github.com/leanprover/lean4/pull/5433) presents the `bv_decide` counterexample at the API
+  * [#5484](https://github.com/leanprover/lean4/pull/5484) handles `BitVec.ofNat` with `Nat` fvars in `bv_decide`
+  * [#5506](https://github.com/leanprover/lean4/pull/5506), [#5507](https://github.com/leanprover/lean4/pull/5507) add `bv_normalize` rules.
+  * [#5568](https://github.com/leanprover/lean4/pull/5568) generalize the `bv_normalize` pipeline to support more general preprocessing passes
+  * [#5573](https://github.com/leanprover/lean4/pull/5573) gets `bv_normalize` up-to-date with the current `BitVec` rewrites
+  * Cleanups: [#5408](https://github.com/leanprover/lean4/pull/5408), [#5493](https://github.com/leanprover/lean4/pull/5493), [#5578](https://github.com/leanprover/lean4/pull/5578)
+
+
+* Elaboration improvements
+  * [#5266](https://github.com/leanprover/lean4/pull/5266) preserve order of overapplied arguments in `elab_as_elim` procedure.
+  * [#5510](https://github.com/leanprover/lean4/pull/5510) generalizes `elab_as_elim` to allow arbitrary motive applications.
+  * [#5283](https://github.com/leanprover/lean4/pull/5283), [#5512](https://github.com/leanprover/lean4/pull/5512) refine how named arguments suppress explicit arguments. Breaking change: some previously omitted explicit arguments may need explicit `_` arguments now.
+  * [#5376](https://github.com/leanprover/lean4/pull/5376) modifies projection instance binder info for instances, making parameters that are instance implicit in the type be implicit.
+  * [#5402](https://github.com/leanprover/lean4/pull/5402) localizes universe metavariable errors to `let` bindings and `fun` binders if possible. Makes "cannot synthesize metavariable" errors take precedence over unsolved universe level errors.
+  * [#5419](https://github.com/leanprover/lean4/pull/5419) must not reduce `ite` in the discriminant of `match`-expression when reducibility setting is `.reducible`
+  * [#5474](https://github.com/leanprover/lean4/pull/5474) have autoparams report parameter/field on failure
+  * [#5530](https://github.com/leanprover/lean4/pull/5530) makes automatic instance names about types with hygienic names be hygienic.
+
+* Deriving handlers
+  * [#5432](https://github.com/leanprover/lean4/pull/5432) makes `Repr` deriving instance handle explicit type parameters
+
+* Functional induction
+  * [#5364](https://github.com/leanprover/lean4/pull/5364) adds more equalities in context, more careful cleanup.
+
+* Linters
+  * [#5335](https://github.com/leanprover/lean4/pull/5335) fixes the unused variables linter complaining about match/tactic combinations
+  * [#5337](https://github.com/leanprover/lean4/pull/5337) fixes the unused variables linter complaining about some wildcard patterns
+
+* Other fixes
+  * [#4768](https://github.com/leanprover/lean4/pull/4768) fixes a parse error when `..` appears with a `.` on the next line
+
+* Metaprogramming
+  * [#3090](https://github.com/leanprover/lean4/pull/3090) handles level parameters in `Meta.evalExpr` (@eric-wieser)
+  * [#5401](https://github.com/leanprover/lean4/pull/5401) instance for `Inhabited (TacticM α)` (@alexkeizer)
+  * [#5412](https://github.com/leanprover/lean4/pull/5412) expose Kernel.check for debugging purposes
+  * [#5556](https://github.com/leanprover/lean4/pull/5556) improves the "invalid projection" type inference error in `inferType`.
+  * [#5587](https://github.com/leanprover/lean4/pull/5587) allows `MVarId.assertHypotheses` to set `BinderInfo` and `LocalDeclKind`.
+  * [#5588](https://github.com/leanprover/lean4/pull/5588) adds `MVarId.tryClearMany'`, a variant of `MVarId.tryClearMany`.
+
+
+
+### Language server, widgets, and IDE extensions
+
+* [#5205](https://github.com/leanprover/lean4/pull/5205) decreases the latency of auto-completion in tactic blocks.
+* [#5237](https://github.com/leanprover/lean4/pull/5237) fixes symbol occurrence highlighting in VS Code not highlighting occurrences when moving the text cursor into the identifier from the right.
+* [#5257](https://github.com/leanprover/lean4/pull/5257) fixes several instances of incorrect auto-completions being reported.
+* [#5299](https://github.com/leanprover/lean4/pull/5299) allows auto-completion to report completions for global identifiers when the elaborator fails to provide context-specific auto-completions.
+* [#5312](https://github.com/leanprover/lean4/pull/5312) fixes the server breaking when changing whitespace after the module header.
+* [#5322](https://github.com/leanprover/lean4/pull/5322) fixes several instances of auto-completion reporting non-existent namespaces.
+* [#5428](https://github.com/leanprover/lean4/pull/5428) makes sure to always report some recent file range as progress when waiting for elaboration.
+
+
+### Pretty printing
+
+* [#4979](https://github.com/leanprover/lean4/pull/4979) make pretty printer escape identifiers that are tokens.
+* [#5389](https://github.com/leanprover/lean4/pull/5389) makes formatter use the current token table.
+* [#5513](https://github.com/leanprover/lean4/pull/5513) use breakable instead of unbreakable whitespace when formatting tokens.
+
+
+### Library
+
+* [#5222](https://github.com/leanprover/lean4/pull/5222) reduces allocations in `Json.compress`.
+* [#5231](https://github.com/leanprover/lean4/pull/5231) upstreams `Zero` and `NeZero`
+* [#5292](https://github.com/leanprover/lean4/pull/5292) refactors `Lean.Elab.Deriving.FromToJson` (@arthur-adjedj)
+* [#5415](https://github.com/leanprover/lean4/pull/5415) implements `Repr Empty` (@TomasPuverle)
+* [#5421](https://github.com/leanprover/lean4/pull/5421) implements `To/FromJSON Empty` (@TomasPuverle)
+
+* Logic
+  * [#5263](https://github.com/leanprover/lean4/pull/5263) allows simplifying `dite_not`/`decide_not` with only `Decidable (¬p)`.
+  * [#5268](https://github.com/leanprover/lean4/pull/5268) fixes binders on `ite_eq_left_iff`
+  * [#5284](https://github.com/leanprover/lean4/pull/5284) turns off `Inhabited (Sum α β)` instances
+  * [#5355](https://github.com/leanprover/lean4/pull/5355) adds simp lemmas for `LawfulBEq`
+  * [#5374](https://github.com/leanprover/lean4/pull/5374) add `Nonempty` instances for products, allowing more `partial` functions to elaborate successfully
+  * [#5447](https://github.com/leanprover/lean4/pull/5447) updates Pi instance names
+  * [#5454](https://github.com/leanprover/lean4/pull/5454) makes some instance arguments implicit
+  * [#5456](https://github.com/leanprover/lean4/pull/5456) adds `heq_comm`
+  * [#5529](https://github.com/leanprover/lean4/pull/5529) moves `@[simp]` from `exists_prop'` to `exists_prop`
+
+* `Bool`
+  * [#5228](https://github.com/leanprover/lean4/pull/5228) fills gaps in Bool lemmas
+  * [#5332](https://github.com/leanprover/lean4/pull/5332) adds notation `^^` for Bool.xor
+  * [#5351](https://github.com/leanprover/lean4/pull/5351) removes `_root_.and` (and or/not/xor) and instead exports/uses `Bool.and` (etc.).
+
+* `BitVec`
+  * [#5240](https://github.com/leanprover/lean4/pull/5240) removes BitVec simps with complicated RHS
+  * [#5247](https://github.com/leanprover/lean4/pull/5247) `BitVec.getElem_zeroExtend`
+  * [#5248](https://github.com/leanprover/lean4/pull/5248) simp lemmas for BitVec, improving confluence
+  * [#5249](https://github.com/leanprover/lean4/pull/5249) removes `@[simp]` from some BitVec lemmas
+  * [#5252](https://github.com/leanprover/lean4/pull/5252) changes `BitVec.intMin/Max` from abbrev to def
+  * [#5278](https://github.com/leanprover/lean4/pull/5278) adds `BitVec.getElem_truncate` (@tobiasgrosser)
+  * [#5281](https://github.com/leanprover/lean4/pull/5281) adds udiv/umod bitblasting for `bv_decide` (@bollu)
+  * [#5297](https://github.com/leanprover/lean4/pull/5297) `BitVec` unsigned order theoretic results
+  * [#5313](https://github.com/leanprover/lean4/pull/5313) adds more basic BitVec ordering theory for UInt
+  * [#5314](https://github.com/leanprover/lean4/pull/5314) adds `toNat_sub_of_le` (@bollu)
+  * [#5357](https://github.com/leanprover/lean4/pull/5357) adds `BitVec.truncate` lemmas
+  * [#5358](https://github.com/leanprover/lean4/pull/5358) introduces `BitVec.setWidth` to unify zeroExtend and truncate (@tobiasgrosser)
+  * [#5361](https://github.com/leanprover/lean4/pull/5361) some BitVec GetElem lemmas
+  * [#5385](https://github.com/leanprover/lean4/pull/5385) adds `BitVec.ofBool_[and|or|xor]_ofBool` theorems (@tobiasgrosser)
+  * [#5404](https://github.com/leanprover/lean4/pull/5404) more of `BitVec.getElem_*` (@tobiasgrosser)
+  * [#5410](https://github.com/leanprover/lean4/pull/5410) BitVec analogues of `Nat.{mul_two, two_mul, mul_succ, succ_mul}` (@bollu)
+  * [#5411](https://github.com/leanprover/lean4/pull/5411) `BitVec.toNat_{add,sub,mul_of_lt}` for BitVector non-overflow reasoning (@bollu)
+  * [#5413](https://github.com/leanprover/lean4/pull/5413) adds `_self`, `_zero`, and `_allOnes` for `BitVec.[and|or|xor]` (@tobiasgrosser)
+  * [#5416](https://github.com/leanprover/lean4/pull/5416) adds LawCommIdentity + IdempotentOp for `BitVec.[and|or|xor]` (@tobiasgrosser)
+  * [#5418](https://github.com/leanprover/lean4/pull/5418) decidable quantifers for BitVec
+  * [#5450](https://github.com/leanprover/lean4/pull/5450) adds `BitVec.toInt_[intMin|neg|neg_of_ne_intMin]` (@tobiasgrosser)
+  * [#5459](https://github.com/leanprover/lean4/pull/5459) missing BitVec lemmas
+  * [#5469](https://github.com/leanprover/lean4/pull/5469) adds `BitVec.[not_not, allOnes_shiftLeft_or_shiftLeft, allOnes_shiftLeft_and_shiftLeft]` (@luisacicolini)
+  * [#5478](https://github.com/leanprover/lean4/pull/5478) adds `BitVec.(shiftLeft_add_distrib, shiftLeft_ushiftRight)` (@luisacicolini)
+  * [#5487](https://github.com/leanprover/lean4/pull/5487) adds `sdiv_eq`, `smod_eq` to allow `sdiv`/`smod` bitblasting (@bollu)
+  * [#5491](https://github.com/leanprover/lean4/pull/5491) adds `BitVec.toNat_[abs|sdiv|smod]` (@tobiasgrosser)
+  * [#5492](https://github.com/leanprover/lean4/pull/5492) `BitVec.(not_sshiftRight, not_sshiftRight_not, getMsb_not, msb_not)` (@luisacicolini)
+  * [#5499](https://github.com/leanprover/lean4/pull/5499) `BitVec.Lemmas` - drop non-terminal simps (@tobiasgrosser)
+  * [#5505](https://github.com/leanprover/lean4/pull/5505) unsimps `BitVec.divRec_succ'`
+  * [#5508](https://github.com/leanprover/lean4/pull/5508) adds `BitVec.getElem_[add|add_add_bool|mul|rotateLeft|rotateRight…` (@tobiasgrosser)
+  * [#5554](https://github.com/leanprover/lean4/pull/5554) adds `Bitvec.[add, sub, mul]_eq_xor` and `width_one_cases` (@luisacicolini)
+
+* `List`
+  * [#5242](https://github.com/leanprover/lean4/pull/5242) improve naming for `List.mergeSort` lemmas
+  * [#5302](https://github.com/leanprover/lean4/pull/5302) provide `mergeSort` comparator autoParam
+  * [#5373](https://github.com/leanprover/lean4/pull/5373) fix name of `List.length_mergeSort`
+  * [#5377](https://github.com/leanprover/lean4/pull/5377) upstream `map_mergeSort`
+  * [#5378](https://github.com/leanprover/lean4/pull/5378) modify signature of lemmas about `mergeSort`
+  * [#5245](https://github.com/leanprover/lean4/pull/5245) avoid importing `List.Basic` without List.Impl
+  * [#5260](https://github.com/leanprover/lean4/pull/5260) review of List API
+  * [#5264](https://github.com/leanprover/lean4/pull/5264) review of List API
+  * [#5269](https://github.com/leanprover/lean4/pull/5269) remove HashMap's duplicated Pairwise and Sublist
+  * [#5271](https://github.com/leanprover/lean4/pull/5271) remove @[simp] from `List.head_mem` and similar
+  * [#5273](https://github.com/leanprover/lean4/pull/5273) lemmas about `List.attach`
+  * [#5275](https://github.com/leanprover/lean4/pull/5275) reverse direction of `List.tail_map`
+  * [#5277](https://github.com/leanprover/lean4/pull/5277) more `List.attach` lemmas
+  * [#5285](https://github.com/leanprover/lean4/pull/5285) `List.count` lemmas
+  * [#5287](https://github.com/leanprover/lean4/pull/5287) use boolean predicates in `List.filter`
+  * [#5289](https://github.com/leanprover/lean4/pull/5289) `List.mem_ite_nil_left` and analogues
+  * [#5293](https://github.com/leanprover/lean4/pull/5293) cleanup of `List.findIdx` / `List.take` lemmas
+  * [#5294](https://github.com/leanprover/lean4/pull/5294) switch primes on `List.getElem_take`
+  * [#5300](https://github.com/leanprover/lean4/pull/5300) more `List.findIdx` theorems
+  * [#5310](https://github.com/leanprover/lean4/pull/5310) fix `List.all/any` lemmas
+  * [#5311](https://github.com/leanprover/lean4/pull/5311) fix `List.countP` lemmas
+  * [#5316](https://github.com/leanprover/lean4/pull/5316) `List.tail` lemma
+  * [#5331](https://github.com/leanprover/lean4/pull/5331) fix implicitness of `List.getElem_mem`
+  * [#5350](https://github.com/leanprover/lean4/pull/5350) `List.replicate` lemmas
+  * [#5352](https://github.com/leanprover/lean4/pull/5352) `List.attachWith` lemmas
+  * [#5353](https://github.com/leanprover/lean4/pull/5353) `List.head_mem_head?`
+  * [#5360](https://github.com/leanprover/lean4/pull/5360) lemmas about `List.tail`
+  * [#5391](https://github.com/leanprover/lean4/pull/5391) review of `List.erase` / `List.find` lemmas
+  * [#5392](https://github.com/leanprover/lean4/pull/5392) `List.fold` / `attach` lemmas
+  * [#5393](https://github.com/leanprover/lean4/pull/5393) `List.fold` relators
+  * [#5394](https://github.com/leanprover/lean4/pull/5394) lemmas about `List.maximum?`
+  * [#5403](https://github.com/leanprover/lean4/pull/5403) theorems about `List.toArray`
+  * [#5405](https://github.com/leanprover/lean4/pull/5405) reverse direction of `List.set_map`
+  * [#5448](https://github.com/leanprover/lean4/pull/5448) add lemmas about `List.IsPrefix` (@Command-Master)
+  * [#5460](https://github.com/leanprover/lean4/pull/5460) missing `List.set_replicate_self`
+  * [#5518](https://github.com/leanprover/lean4/pull/5518) rename `List.maximum?` to `max?`
+  * [#5519](https://github.com/leanprover/lean4/pull/5519) upstream `List.fold` lemmas
+  * [#5520](https://github.com/leanprover/lean4/pull/5520) restore `@[simp]` on `List.getElem_mem` etc.
+  * [#5521](https://github.com/leanprover/lean4/pull/5521) List simp fixes
+  * [#5550](https://github.com/leanprover/lean4/pull/5550) `List.unattach` and simp lemmas
+  * [#5594](https://github.com/leanprover/lean4/pull/5594) induction-friendly `List.min?_cons`
+
+* `Array`
+  * [#5246](https://github.com/leanprover/lean4/pull/5246) cleanup imports of Array.Lemmas
+  * [#5255](https://github.com/leanprover/lean4/pull/5255) split Init.Data.Array.Lemmas for better bootstrapping
+  * [#5288](https://github.com/leanprover/lean4/pull/5288) rename `Array.data` to `Array.toList`
+  * [#5303](https://github.com/leanprover/lean4/pull/5303) cleanup of `List.getElem_append` variants
+  * [#5304](https://github.com/leanprover/lean4/pull/5304) `Array.not_mem_empty`
+  * [#5400](https://github.com/leanprover/lean4/pull/5400) reorganization in Array/Basic
+  * [#5420](https://github.com/leanprover/lean4/pull/5420) make `Array` functions either semireducible or use structural recursion
+  * [#5422](https://github.com/leanprover/lean4/pull/5422) refactor `DecidableEq (Array α)`
+  * [#5452](https://github.com/leanprover/lean4/pull/5452) refactor of Array
+  * [#5458](https://github.com/leanprover/lean4/pull/5458) cleanup of Array docstrings after refactor
+  * [#5461](https://github.com/leanprover/lean4/pull/5461) restore `@[simp]` on `Array.swapAt!_def`
+  * [#5465](https://github.com/leanprover/lean4/pull/5465) improve Array GetElem lemmas
+  * [#5466](https://github.com/leanprover/lean4/pull/5466) `Array.foldX` lemmas
+  * [#5472](https://github.com/leanprover/lean4/pull/5472) @[simp] lemmas about `List.toArray`
+  * [#5485](https://github.com/leanprover/lean4/pull/5485) reverse simp direction for `toArray_concat`
+  * [#5514](https://github.com/leanprover/lean4/pull/5514) `Array.eraseReps`
+  * [#5515](https://github.com/leanprover/lean4/pull/5515) upstream `Array.qsortOrd`
+  * [#5516](https://github.com/leanprover/lean4/pull/5516) upstream `Subarray.empty`
+  * [#5526](https://github.com/leanprover/lean4/pull/5526) fix name of `Array.length_toList`
+  * [#5527](https://github.com/leanprover/lean4/pull/5527) reduce use of deprecated lemmas in Array
+  * [#5534](https://github.com/leanprover/lean4/pull/5534) cleanup of Array GetElem lemmas
+  * [#5536](https://github.com/leanprover/lean4/pull/5536) fix `Array.modify` lemmas
+  * [#5551](https://github.com/leanprover/lean4/pull/5551) upstream `Array.flatten` lemmas
+  * [#5552](https://github.com/leanprover/lean4/pull/5552) switch obvious cases of array "bang"`[]!` indexing to rely on hypothesis (@TomasPuverle)
+  * [#5577](https://github.com/leanprover/lean4/pull/5577) add missing simp to `Array.size_feraseIdx`
+  * [#5586](https://github.com/leanprover/lean4/pull/5586) `Array/Option.unattach`
+
+* `Option`
+  * [#5272](https://github.com/leanprover/lean4/pull/5272) remove @[simp] from `Option.pmap/pbind` and add simp lemmas
+  * [#5307](https://github.com/leanprover/lean4/pull/5307) restoring Option simp confluence
+  * [#5354](https://github.com/leanprover/lean4/pull/5354) remove @[simp] from `Option.bind_map`
+  * [#5532](https://github.com/leanprover/lean4/pull/5532) `Option.attach`
+  * [#5539](https://github.com/leanprover/lean4/pull/5539) fix explicitness of `Option.mem_toList`
+
+* `Nat`
+  * [#5241](https://github.com/leanprover/lean4/pull/5241) add @[simp] to `Nat.add_eq_zero_iff`
+  * [#5261](https://github.com/leanprover/lean4/pull/5261) Nat bitwise lemmas
+  * [#5262](https://github.com/leanprover/lean4/pull/5262) `Nat.testBit_add_one` should not be a global simp lemma
+  * [#5267](https://github.com/leanprover/lean4/pull/5267) protect some Nat bitwise theorems
+  * [#5305](https://github.com/leanprover/lean4/pull/5305) rename Nat bitwise lemmas
+  * [#5306](https://github.com/leanprover/lean4/pull/5306) add `Nat.self_sub_mod` lemma
+  * [#5503](https://github.com/leanprover/lean4/pull/5503) restore @[simp] to upstreamed `Nat.lt_off_iff`
+
+* `Int`
+  * [#5301](https://github.com/leanprover/lean4/pull/5301) rename `Int.div/mod` to `Int.tdiv/tmod`
+  * [#5320](https://github.com/leanprover/lean4/pull/5320) add `ediv_nonneg_of_nonpos_of_nonpos` to DivModLemmas (@sakehl)
+
+* `Fin`
+  * [#5250](https://github.com/leanprover/lean4/pull/5250) missing lemma about `Fin.ofNat'`
+  * [#5356](https://github.com/leanprover/lean4/pull/5356) `Fin.ofNat'` uses `NeZero`
+  * [#5379](https://github.com/leanprover/lean4/pull/5379) remove some @[simp]s from Fin lemmas
+  * [#5380](https://github.com/leanprover/lean4/pull/5380) missing Fin @[simp] lemmas
+
+* `HashMap`
+  * [#5244](https://github.com/leanprover/lean4/pull/5244) (`DHashMap`|`HashMap`|`HashSet`).(`getKey?`|`getKey`|`getKey!`|`getKeyD`)
+  * [#5362](https://github.com/leanprover/lean4/pull/5362) remove the last use of `Lean.(HashSet|HashMap)`
+  * [#5369](https://github.com/leanprover/lean4/pull/5369) `HashSet.ofArray`
+  * [#5370](https://github.com/leanprover/lean4/pull/5370) `HashSet.partition`
+  * [#5581](https://github.com/leanprover/lean4/pull/5581) `Singleton`/`Insert`/`Union` instances for `HashMap`/`Set`
+  * [#5582](https://github.com/leanprover/lean4/pull/5582) `HashSet.all`/`any`
+  * [#5590](https://github.com/leanprover/lean4/pull/5590) adding `Insert`/`Singleton`/`Union` instances for `HashMap`/`Set.Raw`
+  * [#5591](https://github.com/leanprover/lean4/pull/5591) `HashSet.Raw.all/any`
+
+* `Monads`
+  * [#5463](https://github.com/leanprover/lean4/pull/5463) upstream some monad lemmas
+  * [#5464](https://github.com/leanprover/lean4/pull/5464) adjust simp attributes on monad lemmas
+  * [#5522](https://github.com/leanprover/lean4/pull/5522) more monadic simp lemmas
+
+* Simp lemma cleanup
+  * [#5251](https://github.com/leanprover/lean4/pull/5251) remove redundant simp annotations
+  * [#5253](https://github.com/leanprover/lean4/pull/5253) remove Int simp lemmas that can't fire
+  * [#5254](https://github.com/leanprover/lean4/pull/5254) variables appearing on both sides of an iff should be implicit
+  * [#5381](https://github.com/leanprover/lean4/pull/5381) cleaning up redundant simp lemmas
+
+
+### Compiler, runtime, and FFI
+
+* [#4685](https://github.com/leanprover/lean4/pull/4685) fixes a typo in the C `run_new_frontend` signature
+* [#4729](https://github.com/leanprover/lean4/pull/4729) has IR checker suggest using `noncomputable`
+* [#5143](https://github.com/leanprover/lean4/pull/5143) adds a shared library for Lake
+* [#5437](https://github.com/leanprover/lean4/pull/5437) removes (syntactically) duplicate imports (@euprunin)
+* [#5462](https://github.com/leanprover/lean4/pull/5462) updates `src/lake/lakefile.toml` to the adjusted Lake build process
+* [#5541](https://github.com/leanprover/lean4/pull/5541) removes new shared libs before build to better support Windows
+* [#5558](https://github.com/leanprover/lean4/pull/5558) make `lean.h` compile with MSVC (@kant2002)
+* [#5564](https://github.com/leanprover/lean4/pull/5564) removes non-conforming size-0 arrays (@eric-wieser)
+
+
+### Lake
+  * Reservoir build cache. Lake will now attempt to fetch a pre-built copy of the package from Reservoir before building it. This is only enabled for packages in the leanprover or leanprover-community organizations on versions indexed by Reservoir. Users can force Lake to build packages from the source by passing --no-cache on the CLI or by setting the  LAKE_NO_CACHE environment variable to true. [#5486](https://github.com/leanprover/lean4/pull/5486), [#5572](https://github.com/leanprover/lean4/pull/5572), [#5583](https://github.com/leanprover/lean4/pull/5583), [#5600](https://github.com/leanprover/lean4/pull/5600), [#5641](https://github.com/leanprover/lean4/pull/5641), [#5642](https://github.com/leanprover/lean4/pull/5642).
+  * [#5504](https://github.com/leanprover/lean4/pull/5504) lake new and lake init now produce TOML configurations by default.
+  * [#5878](https://github.com/leanprover/lean4/pull/5878) fixes a serious issue where Lake would delete path dependencies when attempting to cleanup a dependency required with an incorrect name.
+
+  * **Breaking changes**
+    * [#5641](https://github.com/leanprover/lean4/pull/5641) A Lake build of target within a package will no longer build a package's dependencies package-level extra target dependencies. At the technical level, a package's extraDep facet no longer transitively builds its dependencies’ extraDep facets (which include their extraDepTargets).
+
+### Documentation fixes
+
+* [#3918](https://github.com/leanprover/lean4/pull/3918) `@[builtin_doc]` attribute (@digama0)
+* [#4305](https://github.com/leanprover/lean4/pull/4305) explains the borrow syntax (@eric-wieser)
+* [#5349](https://github.com/leanprover/lean4/pull/5349) adds documentation for `groupBy.loop` (@vihdzp)
+* [#5473](https://github.com/leanprover/lean4/pull/5473) fixes typo in `BitVec.mul` docstring (@llllvvuu)
+* [#5476](https://github.com/leanprover/lean4/pull/5476) fixes typos in `Lean.MetavarContext`
+* [#5481](https://github.com/leanprover/lean4/pull/5481) removes mention of `Lean.withSeconds` (@alexkeizer)
+* [#5497](https://github.com/leanprover/lean4/pull/5497) updates documentation and tests for `toUIntX` functions (@TomasPuverle)
+* [#5087](https://github.com/leanprover/lean4/pull/5087) mentions that `inferType` does not ensure type correctness
+* Many fixes to spelling across the doc-strings, (@euprunin): [#5425](https://github.com/leanprover/lean4/pull/5425) [#5426](https://github.com/leanprover/lean4/pull/5426) [#5427](https://github.com/leanprover/lean4/pull/5427) [#5430](https://github.com/leanprover/lean4/pull/5430)  [#5431](https://github.com/leanprover/lean4/pull/5431) [#5434](https://github.com/leanprover/lean4/pull/5434) [#5435](https://github.com/leanprover/lean4/pull/5435) [#5436](https://github.com/leanprover/lean4/pull/5436) [#5438](https://github.com/leanprover/lean4/pull/5438) [#5439](https://github.com/leanprover/lean4/pull/5439) [#5440](https://github.com/leanprover/lean4/pull/5440) [#5599](https://github.com/leanprover/lean4/pull/5599)
+
+### Changes to CI
+
+* [#5343](https://github.com/leanprover/lean4/pull/5343) allows addition of `release-ci` label via comment (@thorimur)
+* [#5344](https://github.com/leanprover/lean4/pull/5344) sets check level correctly during workflow (@thorimur)
+* [#5444](https://github.com/leanprover/lean4/pull/5444) Mathlib's `lean-pr-testing-NNNN` branches should use Batteries' `lean-pr-testing-NNNN` branches
+* [#5489](https://github.com/leanprover/lean4/pull/5489) commit `lake-manifest.json` when updating `lean-pr-testing` branches
+* [#5490](https://github.com/leanprover/lean4/pull/5490) use separate secrets for commenting and branching in `pr-release.yml`

releases/v4.14.0.md

@@ -0,0 +1,282 @@
+v4.14.0
+----------
+
+**Full Changelog**: https://github.com/leanprover/lean4/compare/v4.13.0...v4.14.0
+
+### Language features, tactics, and metaprograms
+
+* `structure` and `inductive` commands
+  * [#5517](https://github.com/leanprover/lean4/pull/5517) improves universe level inference for the resulting type of an `inductive` or `structure.` Recall that a `Prop`-valued inductive type is a syntactic subsingleton if it has at most one constructor and all the arguments to the constructor are in `Prop`. Such types have large elimination, so they could be defined in `Type` or `Prop` without any trouble. The way inference has changed is that if a type is a syntactic subsingleton with exactly one constructor, and the constructor has at least one parameter/field, then the `inductive`/`structure` command will prefer creating a `Prop` instead of a `Type`. The upshot is that the `: Prop` in `structure S : Prop` is often no longer needed. (With @arthur-adjedj).
+  * [#5842](https://github.com/leanprover/lean4/pull/5842) and [#5783](https://github.com/leanprover/lean4/pull/5783) implement a feature where the `structure` command can now define recursive inductive types:
+    ```lean
+    structure Tree where
+      n : Nat
+      children : Fin n → Tree
+
+    def Tree.size : Tree → Nat
+      | {n, children} => Id.run do
+        let mut s := 0
+        for h : i in [0 : n] do
+          s := s + (children ⟨i, h.2⟩).size
+        pure s
+    ```
+  * [#5814](https://github.com/leanprover/lean4/pull/5814) fixes a bug where Mathlib's `Type*` elaborator could lead to incorrect universe parameters with the `inductive` command.
+  * [#3152](https://github.com/leanprover/lean4/pull/3152) and [#5844](https://github.com/leanprover/lean4/pull/5844) fix bugs in default value processing for structure instance notation (with @arthur-adjedj).
+  * [#5399](https://github.com/leanprover/lean4/pull/5399) promotes instance synthesis order calculation failure from a soft error to a hard error.
+  * [#5542](https://github.com/leanprover/lean4/pull/5542) deprecates `:=` variants of `inductive` and `structure` (see breaking changes).
+
+* **Application elaboration improvements**
+  * [#5671](https://github.com/leanprover/lean4/pull/5671) makes `@[elab_as_elim]` require at least one discriminant, since otherwise there is no advantage to this alternative elaborator.
+  * [#5528](https://github.com/leanprover/lean4/pull/5528) enables field notation in explicit mode. The syntax `@x.f` elaborates as `@S.f` with `x` supplied to the appropriate parameter.
+  * [#5692](https://github.com/leanprover/lean4/pull/5692) modifies the dot notation resolution algorithm so that it can apply `CoeFun` instances. For example, Mathlib has `Multiset.card : Multiset α →+ Nat`, and now with `m : Multiset α`, the notation `m.card` resolves to `⇑Multiset.card m`.
+  * [#5658](https://github.com/leanprover/lean4/pull/5658) fixes a bug where 'don't know how to synthesize implicit argument' errors might have the incorrect local context when the eta arguments feature is activated.
+  * [#5933](https://github.com/leanprover/lean4/pull/5933) fixes a bug where `..` ellipses in patterns made use of optparams and autoparams.
+  * [#5770](https://github.com/leanprover/lean4/pull/5770) makes dot notation for structures resolve using *all* ancestors. Adds a *resolution order* for generalized field notation. This is the order of namespaces visited during resolution when trying to resolve names. The algorithm to compute a resolution order is the commonly used C3 linearization (used for example by Python), which when successful ensures that immediate parents' namespaces are considered before more distant ancestors' namespaces. By default we use a relaxed version of the algorithm that tolerates inconsistencies, but using `set_option structure.strictResolutionOrder true` makes inconsistent parent orderings into warnings.
+
+* **Recursion and induction principles**
+  * [#5619](https://github.com/leanprover/lean4/pull/5619) fixes functional induction principle generation to avoid over-eta-expanding in the preprocessing step.
+  * [#5766](https://github.com/leanprover/lean4/pull/5766) fixes structural nested recursion so that it is not confused when a nested type appears first.
+  * [#5803](https://github.com/leanprover/lean4/pull/5803) fixes a bug in functional induction principle generation when there are `let` bindings.
+  * [#5904](https://github.com/leanprover/lean4/pull/5904) improves functional induction principle generation to unfold aux definitions more carefully.
+  * [#5850](https://github.com/leanprover/lean4/pull/5850) refactors code for `Predefinition.Structural`.
+
+* **Error messages**
+  * [#5276](https://github.com/leanprover/lean4/pull/5276) fixes a bug in "type mismatch" errors that would structurally assign metavariables during the algorithm to expose differences.
+  * [#5919](https://github.com/leanprover/lean4/pull/5919) makes "type mismatch" errors add type ascriptions to expose differences for numeric literals.
+  * [#5922](https://github.com/leanprover/lean4/pull/5922) makes "type mismatch" errors expose differences in the bodies of functions and pi types.
+  * [#5888](https://github.com/leanprover/lean4/pull/5888) improves the error message for invalid induction alternative names in `match` expressions (@josojo).
+  * [#5719](https://github.com/leanprover/lean4/pull/5719) improves `calc` error messages.
+
+* [#5627](https://github.com/leanprover/lean4/pull/5627) and [#5663](https://github.com/leanprover/lean4/pull/5663) improve the **`#eval` command** and introduce some new features.
+  * Now results can be pretty printed if there is a `ToExpr` instance, which means **hoverable output**. If `ToExpr` fails, it then tries looking for a `Repr` or `ToString` instance like before. Setting `set_option eval.pp false` disables making use of `ToExpr` instances.
+  * There is now **auto-derivation** of `Repr` instances, enabled with the `pp.derive.repr` option (default to **true**). For example:
+    ```lean
+    inductive Baz
+    | a | b
+
+    #eval Baz.a
+    -- Baz.a
+    ```
+    It simply does `deriving instance Repr for Baz` when there's no way to represent `Baz`.
+  * The option `eval.type` controls whether or not to include the type in the output. For now the default is false.
+  * Now expressions such as `#eval do return 2`, where monad is unknown, work. It tries unifying the monad with `CommandElabM`, `TermElabM`, or `IO`.
+  * The classes `Lean.Eval` and `Lean.MetaEval` have been removed. These each used to be responsible for adapting monads and printing results. Now the `MonadEval` class is responsible for adapting monads for evaluation (it is similar to `MonadLift`, but instances are allowed to use default data when initializing state), and representing results is handled through a separate process.
+  * Error messages about failed instance synthesis are now more precise. Once it detects that a `MonadEval` class applies, then the error message will be specific about missing `ToExpr`/`Repr`/`ToString` instances.
+  * Fixes bugs where evaluating `MetaM` and `CoreM` wouldn't collect log messages.
+  * Fixes a bug where `let rec` could not be used in `#eval`.
+
+* `partial` definitions
+  * [#5780](https://github.com/leanprover/lean4/pull/5780) improves the error message when `partial` fails to prove a type is inhabited. Add delta deriving.
+  * [#5821](https://github.com/leanprover/lean4/pull/5821) gives `partial` inhabitation the ability to create local `Inhabited` instances from parameters.
+
+* **New tactic configuration syntax.** The configuration syntax for all core tactics has been given an upgrade. Rather than `simp (config := { contextual := true, maxSteps := 22})`, one can now write `simp +contextual (maxSteps := 22)`. Tactic authors can migrate by switching from `(config)?` to `optConfig` in tactic syntaxes and potentially deleting `mkOptionalNode` in elaborators. [#5883](https://github.com/leanprover/lean4/pull/5883), [#5898](https://github.com/leanprover/lean4/pull/5898),  [#5928](https://github.com/leanprover/lean4/pull/5928), and [#5932](https://github.com/leanprover/lean4/pull/5932). (Tactic authors, see breaking changes.)
+
+* `simp` tactic
+  * [#5632](https://github.com/leanprover/lean4/pull/5632) fixes the simpproc for `Fin` literals to reduce more consistently.
+  * [#5648](https://github.com/leanprover/lean4/pull/5648) fixes a bug in `simpa ... using t` where metavariables in `t` were not properly accounted for, and also improves the type mismatch error.
+  * [#5838](https://github.com/leanprover/lean4/pull/5838) fixes the docstring of `simp!` to actually talk about `simp!`.
+  * [#5870](https://github.com/leanprover/lean4/pull/5870) adds support for `attribute [simp ←]` (note the reverse direction). This adds the reverse of a theorem as a global simp theorem.
+
+* `decide` tactic
+  * [#5665](https://github.com/leanprover/lean4/pull/5665) adds `decide!` tactic for using kernel reduction (warning: this is renamed to `decide +kernel` in a future release).
+
+* `bv_decide` tactic
+  * [#5714](https://github.com/leanprover/lean4/pull/5714) adds inequality regression tests (@alexkeizer).
+  * [#5608](https://github.com/leanprover/lean4/pull/5608) adds `bv_toNat` tag for `toNat_ofInt` (@bollu).
+  * [#5618](https://github.com/leanprover/lean4/pull/5618) adds support for `at` in `ac_nf` and uses it in `bv_normalize` (@tobiasgrosser).
+  * [#5628](https://github.com/leanprover/lean4/pull/5628) adds udiv support.
+  * [#5635](https://github.com/leanprover/lean4/pull/5635) adds auxiliary bitblasters for negation and subtraction.
+  * [#5637](https://github.com/leanprover/lean4/pull/5637) adds more `getLsbD` bitblaster theory.
+  * [#5652](https://github.com/leanprover/lean4/pull/5652) adds umod support.
+  * [#5653](https://github.com/leanprover/lean4/pull/5653) adds performance benchmark for modulo.
+  * [#5655](https://github.com/leanprover/lean4/pull/5655) reduces error on `bv_check` to warning.
+  * [#5670](https://github.com/leanprover/lean4/pull/5670) adds `~~~(-x)` support.
+  * [#5673](https://github.com/leanprover/lean4/pull/5673) disables `ac_nf` by default.
+  * [#5675](https://github.com/leanprover/lean4/pull/5675) fixes context tracking in `bv_decide` counter example.
+  * [#5676](https://github.com/leanprover/lean4/pull/5676) adds an error when the LRAT proof is invalid.
+  * [#5781](https://github.com/leanprover/lean4/pull/5781) introduces uninterpreted symbols everywhere.
+  * [#5823](https://github.com/leanprover/lean4/pull/5823) adds `BitVec.sdiv` support.
+  * [#5852](https://github.com/leanprover/lean4/pull/5852) adds `BitVec.ofBool` support.
+  * [#5855](https://github.com/leanprover/lean4/pull/5855) adds `if` support.
+  * [#5869](https://github.com/leanprover/lean4/pull/5869) adds support for all the SMTLIB BitVec divison/remainder operations.
+  * [#5886](https://github.com/leanprover/lean4/pull/5886) adds embedded constraint substitution.
+  * [#5918](https://github.com/leanprover/lean4/pull/5918) fixes loose mvars bug in `bv_normalize`.
+  * Documentation:
+    * [#5636](https://github.com/leanprover/lean4/pull/5636) adds remarks about multiplication.
+
+* `conv` mode
+  * [#5861](https://github.com/leanprover/lean4/pull/5861) improves the `congr` conv tactic to handle "over-applied" functions.
+  * [#5894](https://github.com/leanprover/lean4/pull/5894) improves the `arg` conv tactic so that it can access more arguments and so that it can handle "over-applied" functions (it generates a specialized congruence lemma for the specific argument in question). Makes `arg 1` and `arg 2` apply to pi types in more situations. Adds negative indexing, for example `arg -2` is equivalent to the `lhs` tactic. Makes the `enter [...]` tactic show intermediate states like `rw`.
+
+* **Other tactics**
+  * [#4846](https://github.com/leanprover/lean4/pull/4846) fixes a bug where `generalize ... at *` would apply to implementation details (@ymherklotz).
+  * [#5730](https://github.com/leanprover/lean4/pull/5730) upstreams the `classical` tactic combinator.
+  * [#5815](https://github.com/leanprover/lean4/pull/5815) improves the error message when trying to unfold a local hypothesis that is not a local definition.
+  * [#5862](https://github.com/leanprover/lean4/pull/5862) and [#5863](https://github.com/leanprover/lean4/pull/5863) change how `apply` and `simp` elaborate, making them not disable error recovery. This improves hovers and completions when the term has elaboration errors.
+
+* `deriving` clauses
+  * [#5899](https://github.com/leanprover/lean4/pull/5899) adds declaration ranges for delta-derived instances.
+  * [#5265](https://github.com/leanprover/lean4/pull/5265) removes unused syntax in `deriving` clauses for providing arguments to deriving handlers (see breaking changes).
+
+* [#5065](https://github.com/leanprover/lean4/pull/5065) upstreams and updates `#where`, a command that reports the current scope information.
+
+* **Linters**
+  * [#5338](https://github.com/leanprover/lean4/pull/5338) makes the unused variables linter ignore variables defined in tactics by default now, avoiding performance bottlenecks.
+  * [#5644](https://github.com/leanprover/lean4/pull/5644) ensures that linters in general do not run on `#guard_msgs` itself.
+
+* **Metaprogramming interface**
+  * [#5720](https://github.com/leanprover/lean4/pull/5720) adds `pushGoal`/`pushGoals` and `popGoal` for manipulating the goal state. These are an alternative to `replaceMainGoal` and `getMainGoal`, and with them you don't need to worry about making sure nothing clears assigned metavariables from the goal list between assigning the main goal and using `replaceMainGoal`. Modifies `closeMainGoalUsing`, which is like a `TacticM` version of `liftMetaTactic`. Now the callback is run in a context where the main goal is removed from the goal list, and the callback is free to modify the goal list. Furthermore, the `checkUnassigned` argument has been replaced with `checkNewUnassigned`, which checks whether the value assigned to the goal has any *new* metavariables, relative to the start of execution of the callback. Modifies `withCollectingNewGoalsFrom` to take the `parentTag` argument explicitly rather than indirectly via `getMainTag`. Modifies `elabTermWithHoles` to optionally take `parentTag?`.
+  * [#5563](https://github.com/leanprover/lean4/pull/5563) fixes `getFunInfo` and `inferType` to use `withAtLeastTransparency` rather than `withTransparency`.
+  * [#5679](https://github.com/leanprover/lean4/pull/5679) fixes `RecursorVal.getInduct` to return the name of major argument’s type. This makes "structure eta" work for nested inductives.
+  * [#5681](https://github.com/leanprover/lean4/pull/5681) removes unused `mkRecursorInfoForKernelRec`.
+  * [#5686](https://github.com/leanprover/lean4/pull/5686) makes discrimination trees index the domains of foralls, for better performance of the simplify and type class search.
+  * [#5760](https://github.com/leanprover/lean4/pull/5760) adds `Lean.Expr.name?` recognizer for `Name` expressions.
+  * [#5800](https://github.com/leanprover/lean4/pull/5800) modifies `liftCommandElabM` to preserve more state, fixing an issue where using it would drop messages.
+  * [#5857](https://github.com/leanprover/lean4/pull/5857) makes it possible to use dot notation in `m!` strings, for example `m!"{.ofConstName n}"`.
+  * [#5841](https://github.com/leanprover/lean4/pull/5841) and [#5853](https://github.com/leanprover/lean4/pull/5853) record the complete list of `structure` parents in the `StructureInfo` environment extension.
+
+* **Other fixes or improvements**
+  * [#5566](https://github.com/leanprover/lean4/pull/5566) fixes a bug introduced in [#4781](https://github.com/leanprover/lean4/pull/4781) where heartbeat exceptions were no longer being handled properly. Now such exceptions are tagged with `runtime.maxHeartbeats` (@eric-wieser).
+  * [#5708](https://github.com/leanprover/lean4/pull/5708) modifies the proof objects produced by the proof-by-reflection tactics `ac_nf0` and `simp_arith` so that the kernel is less prone to reducing expensive atoms.
+  * [#5768](https://github.com/leanprover/lean4/pull/5768) adds a `#version` command that prints Lean's version information.
+  * [#5822](https://github.com/leanprover/lean4/pull/5822) fixes elaborator algorithms to match kernel algorithms for primitive projections (`Expr.proj`).
+  * [#5811](https://github.com/leanprover/lean4/pull/5811) improves the docstring for the `rwa` tactic.
+
+
+### Language server, widgets, and IDE extensions
+
+* [#5224](https://github.com/leanprover/lean4/pull/5224) fixes `WorkspaceClientCapabilities` to make `applyEdit` optional, in accordance with the LSP specification (@pzread).
+* [#5340](https://github.com/leanprover/lean4/pull/5340) fixes a server deadlock when shutting down the language server and a desync between client and language server after a file worker crash.
+* [#5560](https://github.com/leanprover/lean4/pull/5560) makes `initialize` and `builtin_initialize` participate in the call hierarchy and other requests.
+* [#5650](https://github.com/leanprover/lean4/pull/5650) makes references in attributes participate in the call hierarchy and other requests.
+* [#5666](https://github.com/leanprover/lean4/pull/5666) add auto-completion in tactic blocks without having to type the first character of the tactic, and adds tactic completion docs to tactic auto-completion items.
+* [#5677](https://github.com/leanprover/lean4/pull/5677) fixes several cases where goal states were not displayed in certain text cursor positions.
+* [#5707](https://github.com/leanprover/lean4/pull/5707) indicates deprecations in auto-completion items.
+* [#5736](https://github.com/leanprover/lean4/pull/5736), [#5752](https://github.com/leanprover/lean4/pull/5752), [#5763](https://github.com/leanprover/lean4/pull/5763), [#5802](https://github.com/leanprover/lean4/pull/5802), and [#5805](https://github.com/leanprover/lean4/pull/5805) fix various performance issues in the language server.
+* [#5801](https://github.com/leanprover/lean4/pull/5801) distinguishes theorem auto-completions from non-theorem auto-completions.
+
+### Pretty printing
+
+* [#5640](https://github.com/leanprover/lean4/pull/5640) fixes a bug where goal states in messages might print newlines as spaces.
+* [#5643](https://github.com/leanprover/lean4/pull/5643) adds option `pp.mvars.delayed` (default false), which when false causes delayed assignment metavariables to pretty print with what they are assigned to. Now `fun x : Nat => ?a` pretty prints as `fun x : Nat => ?a` rather than `fun x ↦ ?m.7 x`.
+* [#5711](https://github.com/leanprover/lean4/pull/5711) adds options `pp.mvars.anonymous` and `pp.mvars.levels`, which when false respectively cause expression metavariables and level metavariables to pretty print as `?_`.
+* [#5710](https://github.com/leanprover/lean4/pull/5710) adjusts the `⋯` elaboration warning to mention `pp.maxSteps`.
+
+* [#5759](https://github.com/leanprover/lean4/pull/5759) fixes the app unexpander for `sorryAx`.
+* [#5827](https://github.com/leanprover/lean4/pull/5827) improves accuracy of binder names in the signature pretty printer (like in output of `#check`). Also fixes the issue where consecutive hygienic names pretty print without a space separating them, so we now have `(x✝ y✝ : Nat)` rather than `(x✝y✝ : Nat)`.
+* [#5830](https://github.com/leanprover/lean4/pull/5830) makes sure all the core delaborators respond to `pp.explicit` when appropriate.
+* [#5639](https://github.com/leanprover/lean4/pull/5639) makes sure name literals use escaping when pretty printing.
+* [#5854](https://github.com/leanprover/lean4/pull/5854) adds delaborators for `<|>`, `<*>`, `>>`, `<*`, and `*>`.
+
+### Library
+
+* `Array`
+  * [#5687](https://github.com/leanprover/lean4/pull/5687) deprecates `Array.data`.
+  * [#5705](https://github.com/leanprover/lean4/pull/5705) uses a better default value for `Array.swapAt!`.
+  * [#5748](https://github.com/leanprover/lean4/pull/5748) moves `Array.mapIdx` lemmas to a new file.
+  * [#5749](https://github.com/leanprover/lean4/pull/5749) simplifies signature of `Array.mapIdx`.
+  * [#5758](https://github.com/leanprover/lean4/pull/5758) upstreams `Array.reduceOption`.
+  * [#5786](https://github.com/leanprover/lean4/pull/5786) adds simp lemmas for `Array.isEqv` and `BEq`.
+  * [#5796](https://github.com/leanprover/lean4/pull/5796) renames `Array.shrink` to `Array.take`, and relates it to `List.take`.
+  * [#5798](https://github.com/leanprover/lean4/pull/5798) upstreams `List.modify`, adds lemmas, relates to `Array.modify`.
+  * [#5799](https://github.com/leanprover/lean4/pull/5799) relates `Array.forIn` and `List.forIn`.
+  * [#5833](https://github.com/leanprover/lean4/pull/5833) adds `Array.forIn'`, and relates to `List`.
+  * [#5848](https://github.com/leanprover/lean4/pull/5848) fixes deprecations in `Init.Data.Array.Basic` to not recommend the deprecated constant.
+  * [#5895](https://github.com/leanprover/lean4/pull/5895) adds `LawfulBEq (Array α) ↔ LawfulBEq α`.
+  * [#5896](https://github.com/leanprover/lean4/pull/5896) moves `@[simp]` from `back_eq_back?` to `back_push`.
+  * [#5897](https://github.com/leanprover/lean4/pull/5897) renames `Array.back` to `back!`.
+
+* `List`
+  * [#5605](https://github.com/leanprover/lean4/pull/5605) removes `List.redLength`.
+  * [#5696](https://github.com/leanprover/lean4/pull/5696) upstreams `List.mapIdx` and adds lemmas.
+  * [#5697](https://github.com/leanprover/lean4/pull/5697) upstreams `List.foldxM_map`.
+  * [#5701](https://github.com/leanprover/lean4/pull/5701) renames `List.join` to `List.flatten`.
+  * [#5703](https://github.com/leanprover/lean4/pull/5703) upstreams `List.sum`.
+  * [#5706](https://github.com/leanprover/lean4/pull/5706) marks `prefix_append_right_inj` as a simp lemma.
+  * [#5716](https://github.com/leanprover/lean4/pull/5716) fixes `List.drop_drop` addition order.
+  * [#5731](https://github.com/leanprover/lean4/pull/5731) renames `List.bind` and `Array.concatMap` to `flatMap`.
+  * [#5732](https://github.com/leanprover/lean4/pull/5732) renames `List.pure` to `List.singleton`.
+  * [#5742](https://github.com/leanprover/lean4/pull/5742) upstreams `ne_of_mem_of_not_mem`.
+  * [#5743](https://github.com/leanprover/lean4/pull/5743) upstreams `ne_of_apply_ne`.
+  * [#5816](https://github.com/leanprover/lean4/pull/5816) adds more `List.modify` lemmas.
+  * [#5879](https://github.com/leanprover/lean4/pull/5879) renames `List.groupBy` to `splitBy`.
+  * [#5913](https://github.com/leanprover/lean4/pull/5913) relates `for` loops over `List` with `foldlM`.
+
+* `Nat`
+  * [#5694](https://github.com/leanprover/lean4/pull/5694) removes `instBEqNat`, which is redundant with `instBEqOfDecidableEq` but not defeq.
+  * [#5746](https://github.com/leanprover/lean4/pull/5746) deprecates `Nat.sum`.
+  * [#5785](https://github.com/leanprover/lean4/pull/5785) adds `Nat.forall_lt_succ` and variants.
+
+* Fixed width integers
+  * [#5323](https://github.com/leanprover/lean4/pull/5323) redefine unsigned fixed width integers in terms of `BitVec`.
+  * [#5735](https://github.com/leanprover/lean4/pull/5735) adds `UIntX.[val_ofNat, toBitVec_ofNat]`.
+  * [#5790](https://github.com/leanprover/lean4/pull/5790) defines `Int8`.
+  * [#5901](https://github.com/leanprover/lean4/pull/5901) removes native code for `UInt8.modn`.
+
+* `BitVec`
+  * [#5604](https://github.com/leanprover/lean4/pull/5604) completes `BitVec.[getMsbD|getLsbD|msb]` for shifts (@luisacicolini).
+  * [#5609](https://github.com/leanprover/lean4/pull/5609) adds lemmas for division when denominator is zero (@bollu).
+  * [#5620](https://github.com/leanprover/lean4/pull/5620) documents Bitblasting (@bollu)
+  * [#5623](https://github.com/leanprover/lean4/pull/5623) moves `BitVec.udiv/umod/sdiv/smod` after `add/sub/mul/lt` (@tobiasgrosser).
+  * [#5645](https://github.com/leanprover/lean4/pull/5645) defines `udiv` normal form to be `/`, resp. `umod` and `%` (@bollu).
+  * [#5646](https://github.com/leanprover/lean4/pull/5646) adds lemmas about arithmetic inequalities (@bollu).
+  * [#5680](https://github.com/leanprover/lean4/pull/5680) expands relationship with `toFin` (@tobiasgrosser).
+  * [#5691](https://github.com/leanprover/lean4/pull/5691) adds `BitVec.(getMSbD, msb)_(add, sub)` and `BitVec.getLsbD_sub` (@luisacicolini).
+  * [#5712](https://github.com/leanprover/lean4/pull/5712) adds `BitVec.[udiv|umod]_[zero|one|self]` (@tobiasgrosser).
+  * [#5718](https://github.com/leanprover/lean4/pull/5718) adds `BitVec.sdiv_[zero|one|self]` (@tobiasgrosser).
+  * [#5721](https://github.com/leanprover/lean4/pull/5721) adds `BitVec.(msb, getMsbD, getLsbD)_(neg, abs)` (@luisacicolini).
+  * [#5772](https://github.com/leanprover/lean4/pull/5772) adds `BitVec.toInt_sub`, simplifies `BitVec.toInt_neg` (@tobiasgrosser).
+  * [#5778](https://github.com/leanprover/lean4/pull/5778) prove that `intMin` the smallest signed bitvector (@alexkeizer).
+  * [#5851](https://github.com/leanprover/lean4/pull/5851) adds `(msb, getMsbD)_twoPow` (@luisacicolini).
+  * [#5858](https://github.com/leanprover/lean4/pull/5858) adds `BitVec.[zero_ushiftRight|zero_sshiftRight|zero_mul]` and cleans up BVDecide (@tobiasgrosser).
+  * [#5865](https://github.com/leanprover/lean4/pull/5865) adds `BitVec.(msb, getMsbD)_concat` (@luisacicolini).
+  * [#5881](https://github.com/leanprover/lean4/pull/5881) adds `Hashable (BitVec n)`
+
+* `String`/`Char`
+  * [#5728](https://github.com/leanprover/lean4/pull/5728) upstreams `String.dropPrefix?`.
+  * [#5745](https://github.com/leanprover/lean4/pull/5745) changes `String.dropPrefix?` signature.
+  * [#5747](https://github.com/leanprover/lean4/pull/5747) adds `Hashable Char` instance
+
+* `HashMap`
+  * [#5880](https://github.com/leanprover/lean4/pull/5880) adds interim implementation of `HashMap.modify`/`alter`
+
+* **Other**
+  * [#5704](https://github.com/leanprover/lean4/pull/5704) removes `@[simp]` from `Option.isSome_eq_isSome`.
+  * [#5739](https://github.com/leanprover/lean4/pull/5739) upstreams material on `Prod`.
+  * [#5740](https://github.com/leanprover/lean4/pull/5740) moves `Antisymm` to `Std.Antisymm`.
+  * [#5741](https://github.com/leanprover/lean4/pull/5741) upstreams basic material on `Sum`.
+  * [#5756](https://github.com/leanprover/lean4/pull/5756) adds `Nat.log2_two_pow` (@spinylobster).
+  * [#5892](https://github.com/leanprover/lean4/pull/5892) removes duplicated `ForIn` instances.
+  * [#5900](https://github.com/leanprover/lean4/pull/5900) removes `@[simp]` from `Sum.forall` and `Sum.exists`.
+  * [#5812](https://github.com/leanprover/lean4/pull/5812) removes redundant `Decidable` assumptions (@FR-vdash-bot).
+
+### Compiler, runtime, and FFI
+
+* [#5685](https://github.com/leanprover/lean4/pull/5685) fixes help message flags, removes the `-f` flag and adds the `-g` flag (@James-Oswald).
+* [#5930](https://github.com/leanprover/lean4/pull/5930) adds `--short-version` (`-V`) option to display short version (@juhp).
+* [#5144](https://github.com/leanprover/lean4/pull/5144) switches all 64-bit platforms over to consistently using GMP for bignum arithmetic.
+* [#5753](https://github.com/leanprover/lean4/pull/5753) raises the minimum supported Windows version to Windows 10 1903 (released May 2019).
+
+### Lake
+
+* [#5715](https://github.com/leanprover/lean4/pull/5715) changes `lake new math` to use `autoImplicit false` (@eric-wieser).
+* [#5688](https://github.com/leanprover/lean4/pull/5688) makes `Lake` not create core aliases in the `Lake` namespace.
+* [#5924](https://github.com/leanprover/lean4/pull/5924) adds a `text` option for `buildFile*` utilities.
+* [#5789](https://github.com/leanprover/lean4/pull/5789) makes `lake init` not `git init` when inside git work tree (@haoxins).
+* [#5684](https://github.com/leanprover/lean4/pull/5684) has Lake update a package's `lean-toolchain` file on `lake update` if it finds the package's direct dependencies use a newer compatible toolchain. To skip this step, use the `--keep-toolchain` CLI option. (See breaking changes.)
+* [#6218](https://github.com/leanprover/lean4/pull/6218) makes Lake no longer automatically fetch GitHub cloud releases if the package build directory is already present (mirroring the behavior of the Reservoir cache). This prevents the cache from clobbering existing prebuilt artifacts. Users can still manually fetch the cache and clobber the build directory by running `lake build <pkg>:release`.
+* [#6231](https://github.com/leanprover/lean4/pull/6231) improves the errors Lake produces when it fails to fetch a dependency from Reservoir. If the package is not indexed, it will produce a suggestion about how to require it from GitHub.
+
+### Documentation
+
+* [#5617](https://github.com/leanprover/lean4/pull/5617) fixes MSYS2 build instructions.
+* [#5725](https://github.com/leanprover/lean4/pull/5725) points out that `OfScientific` is called with raw literals (@eric-wieser).
+* [#5794](https://github.com/leanprover/lean4/pull/5794) adds a stub for application ellipsis notation (@eric-wieser).
+
+### Breaking changes
+
+* The syntax for providing arguments to deriving handlers has been removed, which was not used by any major Lean projects in the ecosystem. As a result, the  `applyDerivingHandlers` now takes one fewer argument, `registerDerivingHandlerWithArgs` is now simply `registerDerivingHandler`, `DerivingHandler` no longer includes the unused parameter, and `DerivingHandlerNoArgs` has been deprecated. To migrate code, delete the unused `none` argument and use `registerDerivingHandler` and `DerivingHandler`. ([#5265](https://github.com/leanprover/lean4/pull/5265))
+* The minimum supported Windows version has been raised to Windows 10 1903, released May 2019. ([#5753](https://github.com/leanprover/lean4/pull/5753))
+* The `--lean` CLI option for `lake` was removed. Use the `LEAN` environment variable instead. ([#5684](https://github.com/leanprover/lean4/pull/5684))
+* The `inductive ... :=`, `structure ... :=`, and `class ... :=` syntaxes have been deprecated in favor of the `... where` variants. The old syntax produces a warning, controlled by the `linter.deprecated` option. ([#5542](https://github.com/leanprover/lean4/pull/5542))
+* The generated tactic configuration elaborators now land in `TacticM` to make use of the current recovery state. Commands that wish to elaborate configurations should now use `declare_command_config_elab` instead of `declare_config_elab` to get an elaborator landing in `CommandElabM`. Syntaxes should migrate to `optConfig` instead of `(config)?`, but the elaborators are reverse compatible. ([#5883](https://github.com/leanprover/lean4/pull/5883))

releases/v4.15.0.md

@@ -0,0 +1,645 @@
+v4.15.0
+----------
+
+## Language
+
+- [#4595](https://github.com/leanprover/lean4/pull/4595) implements `Simp.Config.implicitDefEqsProofs`. When `true`
+(default: `true`), `simp` will **not** create a proof term for a
+rewriting rule associated with an `rfl`-theorem. Rewriting rules are
+provided by users by annotating theorems with the attribute `@[simp]`.
+If the proof of the theorem is just `rfl` (reflexivity), and
+`implicitDefEqProofs := true`, `simp` will **not** create a proof term
+which is an application of the annotated theorem.
+
+- [#5429](https://github.com/leanprover/lean4/pull/5429) avoid negative environment lookup
+
+- [#5501](https://github.com/leanprover/lean4/pull/5501) ensure `instantiateMVarsProfiling` adds a trace node
+
+- [#5856](https://github.com/leanprover/lean4/pull/5856) adds a feature to the the mutual def elaborator where the
+`instance` command yields theorems instead of definitions when the class
+is a `Prop`.
+
+- [#5907](https://github.com/leanprover/lean4/pull/5907) unset trailing for `simpa?` "try this" suggestion
+
+- [#5920](https://github.com/leanprover/lean4/pull/5920) changes the rule for which projections become instances. Before,
+all parents along with all indirect ancestors that were represented as
+subobject fields would have their projections become instances. Now only
+projections for direct parents become instances.
+
+- [#5934](https://github.com/leanprover/lean4/pull/5934) make `all_goals` admit goals on failure
+
+- [#5942](https://github.com/leanprover/lean4/pull/5942) introduce synthetic atoms in bv_decide
+
+- [#5945](https://github.com/leanprover/lean4/pull/5945) adds a new definition `Message.kind` which returns the top-level
+tag of a message. This is serialized as the new field `kind` in
+`SerialMessaege` so that i can be used by external consumers (e.g.,
+Lake) to identify messages via `lean --json`.
+
+- [#5968](https://github.com/leanprover/lean4/pull/5968) `arg` conv tactic misreported number of arguments on error
+
+- [#5979](https://github.com/leanprover/lean4/pull/5979) BitVec.twoPow in bv_decide
+
+- [#5991](https://github.com/leanprover/lean4/pull/5991) simplifies the implementation of `omega`.
+
+- [#5992](https://github.com/leanprover/lean4/pull/5992) fix style in bv_decide normalizer
+
+- [#5999](https://github.com/leanprover/lean4/pull/5999) adds configuration options for
+`decide`/`decide!`/`native_decide` and refactors the tactics to be
+frontends to the same backend. Adds a `+revert` option that cleans up
+the local context and reverts all local variables the goal depends on,
+along with indirect propositional hypotheses. Makes `native_decide` fail
+at elaboration time on failure without sacrificing performance (the
+decision procedure is still evaluated just once). Now `native_decide`
+supports universe polymorphism.
+
+- [#6010](https://github.com/leanprover/lean4/pull/6010) changes `bv_decide`'s configuration from lots of `set_option` to
+an elaborated config like `simp` or `omega`. The notable exception is
+`sat.solver` which is still a `set_option` such that users can configure
+a custom SAT solver globally for an entire project or file. Additionally
+it introduces the ability to set `maxSteps` for the simp preprocessing
+run through the new config.
+
+- [#6012](https://github.com/leanprover/lean4/pull/6012) improves the validation of new syntactic tokens. Previously, the
+validation code had inconsistencies: some atoms would be accepted only
+if they had a leading space as a pretty printer hint. Additionally,
+atoms with internal whitespace are no longer allowed.
+
+- [#6016](https://github.com/leanprover/lean4/pull/6016) removes the `decide!` tactic in favor of `decide +kernel`
+(breaking change).
+
+- [#6019](https://github.com/leanprover/lean4/pull/6019) removes @[specilize] from `MkBinding.mkBinding`, which is a
+function that cannot be specialized (as none of its arguments are
+functions). As a result, the specializable function `Nat.foldRevM.loop`
+doesn't get specialized, which leads to worse performing code.
+
+- [#6022](https://github.com/leanprover/lean4/pull/6022) makes the `change` tactic and conv tactic use the same
+elaboration strategy. It works uniformly for both the target and local
+hypotheses. Now `change` can assign metavariables, for example:
+```lean
+example (x y z : Nat) : x + y = z := by
+  change ?a = _
+  let w := ?a
+  -- now `w : Nat := x + y`
+```
+
+- [#6024](https://github.com/leanprover/lean4/pull/6024) fixes a bug where the monad lift coercion elaborator would
+partially unify expressions even if they were not monads. This could be
+taken advantage of to propagate information that could help elaboration
+make progress, for example the first `change` worked because the monad
+lift coercion elaborator was unifying `@Eq _ _` with `@Eq (Nat × Nat)
+p`:
+```lean
+example (p : Nat × Nat) : p = p := by
+  change _ = ⟨_, _⟩ -- used to work (yielding `p = (p.fst, p.snd)`), now it doesn't
+  change ⟨_, _⟩ = _ -- never worked
+```
+As such, this is a breaking change; you may need to adjust expressions
+to include additional implicit arguments.
+
+- [#6029](https://github.com/leanprover/lean4/pull/6029) adds a normalization rule to `bv_normalize` (which is used by
+`bv_decide`) that converts `x / 2^k` into `x >>> k` under suitable
+conditions. This allows us to simplify the expensive division circuits
+that are used for bitblasting into much cheaper shifting circuits.
+Concretely, it allows for the following canonicalization:
+
+- [#6030](https://github.com/leanprover/lean4/pull/6030) fixes `simp only [· ∈ ·]` after #5020.
+
+- [#6035](https://github.com/leanprover/lean4/pull/6035) introduces the and flattening pre processing pass from Bitwuzla
+to `bv_decide`. It splits hypotheses of the form `(a && b) = true` into
+`a = true` and `b = true` which has synergy potential with the already
+existing embedded constraint substitution pass.
+
+- [#6037](https://github.com/leanprover/lean4/pull/6037) fixes `bv_decide`'s embedded constraint substitution to generate
+correct counter examples in the corner case where duplicate theorems are
+in the local context.
+
+- [#6045](https://github.com/leanprover/lean4/pull/6045) add `LEAN_ALWAYS_INLINE` to some functions
+
+- [#6048](https://github.com/leanprover/lean4/pull/6048) fixes `simp?` suggesting output with invalid indentation
+
+- [#6051](https://github.com/leanprover/lean4/pull/6051) mark `Meta.Context.config` as private
+
+- [#6053](https://github.com/leanprover/lean4/pull/6053) fixes the caching infrastructure for `whnf` and `isDefEq`,
+ensuring the cache accounts for all relevant configuration flags. It
+also cleans up the `WHNF.lean` module and improves the configuration of
+`whnf`.
+
+- [#6061](https://github.com/leanprover/lean4/pull/6061) adds a simp_arith benchmark.
+
+- [#6062](https://github.com/leanprover/lean4/pull/6062) optimize Nat.Linear.Expr.toPoly
+
+- [#6064](https://github.com/leanprover/lean4/pull/6064) optimize Nat.Linear.Poly.norm
+
+- [#6068](https://github.com/leanprover/lean4/pull/6068) improves the asymptotic performance of `simp_arith` when there are many variables to consider.
+
+- [#6077](https://github.com/leanprover/lean4/pull/6077) adds options to `bv_decide`'s configuration structure such that
+all non mandatory preprocessing passes can be disabled.
+
+- [#6082](https://github.com/leanprover/lean4/pull/6082) changes how the canonicalizer handles `forall` and `lambda`,
+replacing bvars with temporary fvars. Fixes a bug reported by @hrmacbeth
+on
+[zulip](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Quantifiers.20in.20CanonM/near/482483448).
+
+- [#6093](https://github.com/leanprover/lean4/pull/6093) use mkFreshUserName in ArgsPacker
+
+- [#6096](https://github.com/leanprover/lean4/pull/6096) improves the `#print` command for structures to show all fields
+and which parents the fields were inherited from, hiding internal
+details such as which parents are represented as subobjects. This
+information is still present in the constructor if needed. The pretty
+printer for private constants is also improved, and it now handles
+private names from the current module like any other name; private names
+from other modules are made hygienic.
+
+- [#6098](https://github.com/leanprover/lean4/pull/6098) modifies `Lean.MVarId.replaceTargetDefEq` and
+`Lean.MVarId.replaceLocalDeclDefEq` to use `Expr.equal` instead of
+`Expr.eqv` when determining whether the expression has changed. This is
+justified on the grounds that binder names and binder infos are
+user-visible and affect elaboration.
+
+- [#6105](https://github.com/leanprover/lean4/pull/6105) fixes a stack overflow caused by a cyclic assignment in the
+metavariable context. The cycle is unintentionally introduced by the
+structure instance elaborator.
+
+- [#6108](https://github.com/leanprover/lean4/pull/6108) turn off pp.mvars in apply? results
+
+- [#6109](https://github.com/leanprover/lean4/pull/6109) fixes an issue in the `injection` tactic. This tactic may
+execute multiple sub-tactics. If any of them fail, we must backtrack the
+partial assignment. This issue was causing the error: "`mvarId` is
+already assigned" in issue #6066. The issue is not yet resolved, as the
+equation generator for the match expressions is failing in the example
+provided in this issue.
+
+- [#6112](https://github.com/leanprover/lean4/pull/6112) makes stricter requirements for the `@[deprecated]` attribute,
+requiring either a replacement identifier as `@[deprecated bar]` or
+suggestion text `@[deprecated "Past its use by date"]`, and also
+requires a `since := "..."` field.
+
+- [#6114](https://github.com/leanprover/lean4/pull/6114) liberalizes atom rules by allowing `''` to be a prefix of an
+atom, after #6012 only added an exception for `''` alone, and also adds
+some unit tests for atom validation.
+
+- [#6116](https://github.com/leanprover/lean4/pull/6116) fixes a bug where structural recursion did not work when indices
+of the recursive argument appeared as function parameters in a different
+order than in the argument's type's definition.
+
+- [#6125](https://github.com/leanprover/lean4/pull/6125) adds support for `structure` in `mutual` blocks, allowing
+inductive types defined by `inductive` and `structure` to be mutually
+recursive. The limitations are (1) that the parents in the `extends`
+clause must be defined before the `mutual` block and (2) mutually
+recursive classes are not allowed (a limitation shared by `class
+inductive`). There are also improvements to universe level inference for
+inductive types and structures. Breaking change: structure parents now
+elaborate with the structure in scope (fix: use qualified names or
+rename the structure to avoid shadowing), and structure parents no
+longer elaborate with autoimplicits enabled.
+
+- [#6128](https://github.com/leanprover/lean4/pull/6128) does the same fix as #6104, but such that it doesn't break the
+test/the file in `Plausible`. This is done by not creating unused let
+binders in metavariable types that are made by `elimMVar`. (This is also
+a positive thing for users looking at metavariable types, for example in
+error messages)
+
+- [#6129](https://github.com/leanprover/lean4/pull/6129) fixes a bug at `isDefEq` when `zetaDelta := false`. See new test
+for a small example that exposes the issue.
+
+- [#6131](https://github.com/leanprover/lean4/pull/6131) fixes a bug at the definitional equality test (`isDefEq`). At
+unification constraints of the form `c.{u} =?= c.{v}`, it was not trying
+to unfold `c`. This bug did not affect the kernel.
+
+- [#6141](https://github.com/leanprover/lean4/pull/6141) make use of recursive structures in snapshot types
+
+- [#6145](https://github.com/leanprover/lean4/pull/6145) fixes the `revert` tactic so that it creates a `syntheticOpaque`
+metavariable as the new goal, instead of a `natural` metavariable
+
+- [#6146](https://github.com/leanprover/lean4/pull/6146) fixes a non-termination bug that occurred when generating the
+match-expression splitter theorem. The bug was triggered when the proof
+automation for the splitter theorem repeatedly applied `injection` to
+the same local declaration, as it could not be removed due to forward
+dependencies. See issue #6065 for an example that reproduces this issue.
+
+- [#6165](https://github.com/leanprover/lean4/pull/6165) modifies structure instance notation and `where` notation to use
+the same notation for fields. Structure instance notation now admits
+binders, type ascriptions, and equations, and `where` notation admits
+full structure lvals. Examples of these for structure instance notation:
+```lean
+structure PosFun where
+  f : Nat → Nat
+  pos : ∀ n, 0 < f n
+```
+
+- [#6168](https://github.com/leanprover/lean4/pull/6168) extends the "motive is not type correct" error message for the
+rewrite tactic to explain what it means. It also pretty prints the
+type-incorrect motive and reports the type error.
+
+- [#6170](https://github.com/leanprover/lean4/pull/6170) adds core metaprogramming functions for forking off background
+tasks from elaboration such that their results are visible to reporting
+and the language server
+
+- [#6175](https://github.com/leanprover/lean4/pull/6175) fixes a bug with the `structure`/`class` command where if there
+are parents that are not represented as subobjects but which used other
+parents as instances, then there would be a kernel error. Closes #2611.
+
+- [#6180](https://github.com/leanprover/lean4/pull/6180) fixes a non-termination bug that occurred when generating the
+match-expression equation theorems. The bug was triggered when the proof
+automation for the equation theorem repeatedly applied `injection(` to
+the same local declaration, as it could not be removed due to forward
+dependencies. See issue #6067 for an example that reproduces this issue.
+
+- [#6189](https://github.com/leanprover/lean4/pull/6189) changes how generalized field notation ("dot notation") resolves
+the function. The new resolution rule is that if `x : S`, then `x.f`
+resolves the name `S.f` relative to the root namespace (hence it now
+affected by `export` and `open`). Breaking change: aliases now resolve
+differently. Before, if `x : S`, and if `S.f` is an alias for `S'.f`,
+then `x.f` would use `S'.f` and look for an argument of type `S'`. Now,
+it looks for an argument of type `S`, which is more generally useful
+behavior. Code making use of the old behavior should consider defining
+`S` or `S'` in terms of the other, since dot notation can unfold
+definitions during resolution.
+
+- [#6206](https://github.com/leanprover/lean4/pull/6206) makes it possible to write `rw (occs := [1,2]) ...` instead of
+`rw (occs := .pos [1,2]) ...` by adding a coercion from `List.Nat` to
+`Lean.Meta.Occurrences`.
+
+- [#6220](https://github.com/leanprover/lean4/pull/6220) adds proper support for `let_fun` in `simp`.
+
+- [#6236](https://github.com/leanprover/lean4/pull/6236) fixes an issue where edits to a command containing a nested
+docstring fail to reparse the entire command.
+
+## Library
+
+- [#4904](https://github.com/leanprover/lean4/pull/4904) introduces date and time functionality to the Lean 4 Std.
+
+- [#5616](https://github.com/leanprover/lean4/pull/5616) is a follow-up to https://github.com/leanprover/lean4/pull/5609,
+where we add lemmas characterizing `smtUDiv` and `smtSDiv`'s behavior
+when the denominator is zero.
+
+- [#5866](https://github.com/leanprover/lean4/pull/5866) verifies the `keys` function on `Std.HashMap`.
+
+- [#5885](https://github.com/leanprover/lean4/pull/5885) add Int16/Int32/Int64
+
+- [#5926](https://github.com/leanprover/lean4/pull/5926) add `Option.or_some'`
+
+- [#5927](https://github.com/leanprover/lean4/pull/5927) `List.pmap_eq_self`
+
+- [#5937](https://github.com/leanprover/lean4/pull/5937) upstream lemmas about Fin.foldX
+
+- [#5938](https://github.com/leanprover/lean4/pull/5938) upstream List.ofFn and relate to Array.ofFn
+
+- [#5941](https://github.com/leanprover/lean4/pull/5941) List.mapFinIdx, lemmas, relate to Array version
+
+- [#5949](https://github.com/leanprover/lean4/pull/5949) consolidate `decide_True` and `decide_true_eq_true`
+
+- [#5950](https://github.com/leanprover/lean4/pull/5950) relate Array.takeWhile with List.takeWhile
+
+- [#5951](https://github.com/leanprover/lean4/pull/5951) remove @[simp] from BitVec.ofFin_sub and sub_ofFin
+
+- [#5952](https://github.com/leanprover/lean4/pull/5952) relate Array.eraseIdx with List.eraseIdx
+
+- [#5961](https://github.com/leanprover/lean4/pull/5961) define ISize and basic operations on it
+
+- [#5969](https://github.com/leanprover/lean4/pull/5969) upstream List.insertIdx from Batteries, lemmas from Mathlib, and revise lemmas
+
+- [#5970](https://github.com/leanprover/lean4/pull/5970) deprecate Array.split in favour of identical Array.partition
+
+- [#5971](https://github.com/leanprover/lean4/pull/5971) relate Array.isPrefixOf with List.isPrefixOf
+
+- [#5972](https://github.com/leanprover/lean4/pull/5972) relate Array.zipWith/zip/unzip with List versions
+
+- [#5974](https://github.com/leanprover/lean4/pull/5974) add another List.find?_eq_some lemma
+
+- [#5981](https://github.com/leanprover/lean4/pull/5981) names the default SizeOf instance `instSizeOfDefault`
+
+- [#5982](https://github.com/leanprover/lean4/pull/5982) minor lemmas about List.ofFn
+
+- [#5984](https://github.com/leanprover/lean4/pull/5984) adds lemmas for `List` for the interactions between {`foldl`,
+`foldr`, `foldlM`, `foldlrM`} and {`filter`, `filterMap`}.
+
+- [#5985](https://github.com/leanprover/lean4/pull/5985) relates the operations `findSomeM?`, `findM?`, `findSome?`, and
+`find?` on `Array` with the corresponding operations on `List`, and also
+provides simp lemmas for the `Array` operations `findSomeRevM?`,
+`findRevM?`, `findSomeRev?`, `findRev?` (in terms of `reverse` and the
+usual forward find operations).
+
+- [#5987](https://github.com/leanprover/lean4/pull/5987) BitVec.getMsbD in bv_decide
+
+- [#5988](https://github.com/leanprover/lean4/pull/5988) changes the signature of `Array.set` to take a `Nat`, and a
+tactic-provided bound, rather than a `Fin`.
+
+- [#5995](https://github.com/leanprover/lean4/pull/5995) BitVec.sshiftRight' in bv_decide
+
+- [#6007](https://github.com/leanprover/lean4/pull/6007) List.modifyTailIdx naming fix
+
+- [#6008](https://github.com/leanprover/lean4/pull/6008) missing @[ext] attribute on monad transformer ext lemmas
+
+- [#6023](https://github.com/leanprover/lean4/pull/6023) variants of List.forIn_eq_foldlM
+
+- [#6025](https://github.com/leanprover/lean4/pull/6025) deprecate duplicated Fin.size_pos
+
+- [#6032](https://github.com/leanprover/lean4/pull/6032) changes the signature of `Array.get` to take a Nat and a proof,
+rather than a `Fin`, for consistency with the rest of the (planned)
+Array API. Note that because of bootstrapping issues we can't provide
+`get_elem_tactic` as an autoparameter for the proof. As users will
+mostly use the `xs[i]` notation provided by `GetElem`, this hopefully
+isn't a problem.
+
+- [#6041](https://github.com/leanprover/lean4/pull/6041) modifies the order of arguments for higher-order `Array`
+functions, preferring to put the `Array` last (besides positional
+arguments with defaults). This is more consistent with the `List` API,
+and is more flexible, as dot notation allows two different partially
+applied versions.
+
+- [#6049](https://github.com/leanprover/lean4/pull/6049) adds a primitive for accessing the current thread ID
+
+- [#6052](https://github.com/leanprover/lean4/pull/6052) adds `Array.pmap`, as well as a `@[csimp]` lemma in terms of the
+no-copy `Array.attachWith`.
+
+- [#6055](https://github.com/leanprover/lean4/pull/6055) adds lemmas about for loops over `Array`, following the existing
+lemmas for `List`.
+
+- [#6056](https://github.com/leanprover/lean4/pull/6056) upstream some NameMap functions
+
+- [#6060](https://github.com/leanprover/lean4/pull/6060) implements conversion functions from `Bool` to all `UIntX` and
+`IntX` types.
+
+- [#6070](https://github.com/leanprover/lean4/pull/6070) adds the Lean.RArray data structure.
+
+- [#6074](https://github.com/leanprover/lean4/pull/6074) allow `Sort u` in `Squash`
+
+- [#6094](https://github.com/leanprover/lean4/pull/6094) adds raw transmutation of floating-point numbers to and from
+`UInt64`. Floats and UInts share the same endianness across all
+supported platforms. The IEEE 754 standard precisely specifies the bit
+layout of floats. Note that `Float.toBits` is distinct from
+`Float.toUInt64`, which attempts to preserve the numeric value rather
+than the bitwise value.
+
+- [#6095](https://github.com/leanprover/lean4/pull/6095) generalize `List.get_mem`
+
+- [#6097](https://github.com/leanprover/lean4/pull/6097) naming convention and `NaN` normalization
+
+- [#6102](https://github.com/leanprover/lean4/pull/6102) moves `IO.rand` and `IO.setRandSeed` to be in the `BaseIO`
+monad.
+
+- [#6106](https://github.com/leanprover/lean4/pull/6106) fix naming of left/right injectivity lemmas
+
+- [#6111](https://github.com/leanprover/lean4/pull/6111) fills in the API for `Array.findSome?` and `Array.find?`,
+transferring proofs from the corresponding List statements.
+
+- [#6120](https://github.com/leanprover/lean4/pull/6120) adds theorems `BitVec.(getMsbD, msb)_(rotateLeft, rotateRight)`.
+
+- [#6126](https://github.com/leanprover/lean4/pull/6126) adds lemmas for extracting a given bit of a `BitVec` obtained
+via `sub`/`neg`/`sshiftRight'`/`abs`.
+
+- [#6130](https://github.com/leanprover/lean4/pull/6130) adds `Lean.loadPlugin` which exposes functionality similar to
+the `lean` executable's `--plugin` option to Lean code.
+
+- [#6132](https://github.com/leanprover/lean4/pull/6132) duplicates the verification API for
+`List.attach`/`attachWith`/`pmap` over to `Array`.
+
+- [#6133](https://github.com/leanprover/lean4/pull/6133) replaces `Array.feraseIdx` and `Array.insertAt` with
+`Array.eraseIdx` and `Array.insertIdx`, both of which take a `Nat`
+argument and a tactic-provided proof that it is in bounds. We also have
+`eraseIdxIfInBounds` and `insertIdxIfInBounds` which are noops if the
+index is out of bounds. We also provide a `Fin` valued version of
+`Array.findIdx?`. Together, these quite ergonomically improve the array
+indexing safety at a number of places in the compiler/elaborator.
+
+- [#6136](https://github.com/leanprover/lean4/pull/6136) fixes the run-time evaluation of `(default : Float)`.
+
+- [#6139](https://github.com/leanprover/lean4/pull/6139) modifies the signature of the functions `Nat.fold`,
+`Nat.foldRev`, `Nat.any`, `Nat.all`, so that the function is passed the
+upper bound. This allows us to change runtime array bounds checks to
+compile time checks in many places.
+
+- [#6148](https://github.com/leanprover/lean4/pull/6148) adds a primitive for creating temporary directories, akin to the
+existing functionality for creating temporary files.
+
+- [#6149](https://github.com/leanprover/lean4/pull/6149) completes the elementwise accessors for `ofNatLt`, `allOnes`,
+and `not` by adding their implementations of `getMsbD`.
+
+- [#6151](https://github.com/leanprover/lean4/pull/6151) completes the `toInt` interface for `BitVec` bitwise operations.
+
+- [#6154](https://github.com/leanprover/lean4/pull/6154) implements `BitVec.toInt_abs`.
+
+- [#6155](https://github.com/leanprover/lean4/pull/6155) adds `toNat` theorems for `BitVec.signExtend.`
+
+- [#6157](https://github.com/leanprover/lean4/pull/6157) adds toInt theorems for BitVec.signExtend.
+
+- [#6160](https://github.com/leanprover/lean4/pull/6160) adds theorem `mod_eq_sub`, makes theorem
+`sub_mul_eq_mod_of_lt_of_le` not private anymore and moves its location
+within the `rotate*` section to use it in other proofs.
+
+- [#6184](https://github.com/leanprover/lean4/pull/6184) uses `Array.findFinIdx?` in preference to `Array.findIdx?` where
+it allows converting a runtime bounds check to a compile time bounds
+check.
+
+- [#6188](https://github.com/leanprover/lean4/pull/6188) completes the `toNat` theorems for the bitwise operations
+(`and`, `or`, `xor`, `shiftLeft`, `shiftRight`) of the UInt types and
+adds `toBitVec` theorems as well. It also renames `and_toNat` to
+`toNat_and` to fit with the current naming convention.
+
+- [#6190](https://github.com/leanprover/lean4/pull/6190) adds the builtin simproc `USize.reduceToNat` which reduces the
+`USize.toNat` operation on literals less than `UInt32.size` (i.e.,
+`4294967296`).
+
+- [#6191](https://github.com/leanprover/lean4/pull/6191) adds `Array.zipWithAll`, and the basic lemmas relating it to
+`List.zipWithAll`.
+
+- [#6192](https://github.com/leanprover/lean4/pull/6192) adds deprecations for `Lean.HashMap` functions which did not
+receive deprecation attributes initially.
+
+- [#6193](https://github.com/leanprover/lean4/pull/6193) completes the TODO in `Init.Data.Array.BinSearch`, removing the
+`partial` keyword and converting runtime bounds checks to compile time
+bounds checks.
+
+- [#6194](https://github.com/leanprover/lean4/pull/6194) changes the signature of `Array.swap`, so it takes `Nat`
+arguments with tactic provided bounds checking. It also renames
+`Array.swap!` to `Array.swapIfInBounds`.
+
+- [#6195](https://github.com/leanprover/lean4/pull/6195) renames `Array.setD` to `Array.setIfInBounds`.
+
+- [#6197](https://github.com/leanprover/lean4/pull/6197) upstreams the definition of `Vector` from Batteries, along with
+the basic functions.
+
+- [#6200](https://github.com/leanprover/lean4/pull/6200) upstreams `Nat.lt_pow_self` and `Nat.lt_two_pow` from Mathlib
+and uses them to prove the simp theorem `Nat.mod_two_pow`.
+
+- [#6202](https://github.com/leanprover/lean4/pull/6202) makes `USize.toUInt64` a regular non-opaque definition.
+
+- [#6203](https://github.com/leanprover/lean4/pull/6203) adds the theorems `le_usize_size` and `usize_size_le`, which
+make proving inequalities about `USize.size` easier.
+
+- [#6205](https://github.com/leanprover/lean4/pull/6205) upstreams some UInt theorems from Batteries and adds more
+`toNat`-related theorems. It also adds the missing `UInt8` and `UInt16`
+to/from `USize` conversions so that the the interface is uniform across
+the UInt types.
+
+- [#6207](https://github.com/leanprover/lean4/pull/6207) ensures the `Fin.foldl` and `Fin.foldr` are semireducible.
+Without this the defeq `example (f : Fin 3 → ℕ) : List.ofFn f = [f 0, f
+1, f 2] := rfl` was failing.
+
+- [#6208](https://github.com/leanprover/lean4/pull/6208) fix Vector.indexOf?
+
+- [#6217](https://github.com/leanprover/lean4/pull/6217) adds `simp` lemmas about `List`'s `==` operation.
+
+- [#6221](https://github.com/leanprover/lean4/pull/6221) fixes:
+- Problems in other linux distributions that the default `tzdata`
+directory is not the same as previously defined by ensuring it with a
+fallback behavior when directory is missing.
+- Trim unnecessary characters from local time identifier.
+
+- [#6222](https://github.com/leanprover/lean4/pull/6222) changes the definition of `HashSet.insertMany` and
+`HashSet.Raw.insertMany` so that it is equivalent to repeatedly calling
+`HashSet.insert`/`HashSet.Raw.insert`. It also clarifies the docstrings
+of all the `insert` and `insertMany` functions.
+
+- [#6230](https://github.com/leanprover/lean4/pull/6230) copies some lemmas about `List.foldX` to `Array`.
+
+- [#6233](https://github.com/leanprover/lean4/pull/6233) upstreams lemmas about `Vector` from Batteries.
+
+- [#6234](https://github.com/leanprover/lean4/pull/6234) upstreams the definition and basic lemmas about `List.finRange`
+from Batteries.
+
+- [#6235](https://github.com/leanprover/lean4/pull/6235) relates that operations `Nat.fold`/`foldRev`/`any`/`all` to the
+corresponding List operations over `List.finRange`.
+
+- [#6241](https://github.com/leanprover/lean4/pull/6241) refactors `Array.qsort` to remove runtime array bounds checks,
+and avoids the use of `partial`. We use the `Vector` API, along with
+auto_params, to avoid having to write any proofs. The new code
+benchmarks indistinguishably from the old.
+
+- [#6242](https://github.com/leanprover/lean4/pull/6242) deprecates `Fin.ofNat` in favour of `Fin.ofNat'` (which takes an
+`[NeZero]` instance, rather than returning an element of `Fin (n+1)`).
+
+- [#6247](https://github.com/leanprover/lean4/pull/6247) adds the theorems `numBits_pos`, `le_numBits`, `numBits_le` ,
+which make proving inequalities about `System.Platform.numBits` easier.
+
+## Compiler
+
+- [#5840](https://github.com/leanprover/lean4/pull/5840) changes `lean_sharecommon_{eq,hash}` to only consider the
+salient bytes of an object, and not any bytes of any
+unspecified/uninitialized unused capacity.
+
+- [#6087](https://github.com/leanprover/lean4/pull/6087) fixes a bug in the constant folding for the `Nat.ble` and
+`Nat.blt` function in the old code generator, leading to a
+miscompilation.
+
+- [#6143](https://github.com/leanprover/lean4/pull/6143) should make lean better-behaved around sanitizers, per
+https://github.com/google/sanitizers/issues/1688.
+As far as I can tell,
+https://github.com/google/sanitizers/wiki/AddressSanitizerUseAfterReturn#algorithm
+replaces local variables with heap allocations, and so taking the
+address of a local is not effective at producing a monotonic measure of
+stack usage.
+
+- [#6209](https://github.com/leanprover/lean4/pull/6209) documents under which conditions `Runtime.markPersistent` is
+unsafe and adjusts the elaborator accordingly
+
+- [#6257](https://github.com/leanprover/lean4/pull/6257) harden `markPersistent` uses
+
+## Pretty Printing
+
+- [#2934](https://github.com/leanprover/lean4/pull/2934) adds the option `pp.parens` (default: false) that causes the
+pretty printer to eagerly insert parentheses, which can be useful for
+teaching and for understanding the structure of expressions. For
+example, it causes `p → q → r` to pretty print as `p → (q → r)`.
+
+- [#6014](https://github.com/leanprover/lean4/pull/6014) prevents `Nat.succ ?_` from pretty printing as `?_.succ`, which
+should make `apply?` be more usable.
+
+- [#6085](https://github.com/leanprover/lean4/pull/6085) improves the term info for coercions marked with
+`CoeFnType.coeFun` (such as `DFunLike.coe` in Mathlib), making "go to
+definition" on the function name work. Hovering over such a coerced
+function will show the coercee rather than the coercion expression. The
+coercion expression can still be seen by hovering over the whitespace in
+the function application.
+
+- [#6096](https://github.com/leanprover/lean4/pull/6096) improves the `#print` command for structures to show all fields
+and which parents the fields were inherited from, hiding internal
+details such as which parents are represented as subobjects. This
+information is still present in the constructor if needed. The pretty
+printer for private constants is also improved, and it now handles
+private names from the current module like any other name; private names
+from other modules are made hygienic.
+
+- [#6119](https://github.com/leanprover/lean4/pull/6119) adds a new delab option `pp.coercions.types` which, when
+enabled, will display all coercions with an explicit type ascription.
+
+- [#6161](https://github.com/leanprover/lean4/pull/6161) ensures whitespace is printed before `+opt` and `-opt`
+configuration options when pretty printing, improving the experience of
+tactics such as `simp?`.
+
+- [#6181](https://github.com/leanprover/lean4/pull/6181) fixes a bug where the signature pretty printer would ignore the
+current setting of `pp.raw`. This fixes an issue where `#check ident`
+would not heed `pp.raw`. Closes #6090.
+
+- [#6213](https://github.com/leanprover/lean4/pull/6213) exposes the difference in "synthesized type class instance is
+not definitionally equal" errors.
+
+## Documentation
+
+- [#6009](https://github.com/leanprover/lean4/pull/6009) fixes a typo in the docstring for prec and makes the text
+slightly more precise.
+
+- [#6040](https://github.com/leanprover/lean4/pull/6040) join → flatten in docstring
+
+- [#6110](https://github.com/leanprover/lean4/pull/6110) does some mild refactoring of the `Lean.Elab.StructInst` module
+while adding documentation.
+
+- [#6144](https://github.com/leanprover/lean4/pull/6144) converts 3 doc-string to module docs since it seems that this is
+what they were intended to be!
+
+- [#6150](https://github.com/leanprover/lean4/pull/6150) refine kernel code comments
+
+- [#6158](https://github.com/leanprover/lean4/pull/6158) adjust file reference in Data.Sum
+
+- [#6239](https://github.com/leanprover/lean4/pull/6239) explains the order in which `Expr.abstract` introduces de Bruijn
+indices.
+
+## Server
+
+- [#5835](https://github.com/leanprover/lean4/pull/5835) adds auto-completion for the fields of structure instance notation. Specifically, querying the completions via `Ctrl+Space` in the whitespace of a structure instance notation will now bring up the full list of fields. Whitespace structure completion can be enabled for custom syntax by wrapping the parser for the list of fields in a `structInstFields` parser.
+
+- [#5837](https://github.com/leanprover/lean4/pull/5837) fixes an old auto-completion bug where `x.` would issue
+nonsensical completions when `x.` could not be elaborated as a dot
+completion.
+
+- [#5996](https://github.com/leanprover/lean4/pull/5996) avoid max heartbeat error in completion
+
+- [#6031](https://github.com/leanprover/lean4/pull/6031) fixes a regression with go-to-definition and document highlight
+misbehaving on tactic blocks.
+
+- [#6246](https://github.com/leanprover/lean4/pull/6246) fixes a performance issue where the Lean language server would
+walk the full project file tree every time a file was saved, blocking
+the processing of all other requests and notifications and significantly
+increasing overall language server latency after saving.
+
+## Lake
+
+- [#5684](https://github.com/leanprover/lean4/pull/5684) update toolchain on `lake update`
+
+- [#6026](https://github.com/leanprover/lean4/pull/6026) adds a newline at end of each Lean file generated by `lake new`
+templates.
+
+- [#6218](https://github.com/leanprover/lean4/pull/6218) makes Lake no longer automatically fetch GitHub cloud releases
+if the package build directory is already present (mirroring the
+behavior of the Reservoir cache). This prevents the cache from
+clobbering existing prebuilt artifacts. Users can still manually fetch
+the cache and clobber the build directory by running `lake build
+<pkg>:release`.
+
+- [#6225](https://github.com/leanprover/lean4/pull/6225) makes `lake build` also eagerly print package materialization
+log lines. Previously, only a `lake update` performed eager logging.
+
+- [#6231](https://github.com/leanprover/lean4/pull/6231) improves the errors Lake produces when it fails to fetch a
+dependency from Reservoir. If the package is not indexed, it will
+produce a suggestion about how to require it from GitHub.
+
+## Other
+
+- [#6137](https://github.com/leanprover/lean4/pull/6137) adds support for displaying multiple threads in the trace
+profiler output.
+
+- [#6138](https://github.com/leanprover/lean4/pull/6138) fixes `trace.profiler.pp` not using the term pretty printer.
+
+- [#6259](https://github.com/leanprover/lean4/pull/6259) ensures that nesting trace nodes are annotated with timing
+information iff `trace.profiler` is active.

releases/v4.16.0.md

@@ -0,0 +1,565 @@
+v4.16.0
+----------
+## Highlights
+
+### Unique `sorry`s
+
+[#5757](https://github.com/leanprover/lean4/pull/5757) makes it harder to create "fake" theorems about definitions that
+are stubbed-out with `sorry` by ensuring that each `sorry` is not
+definitionally equal to any other. For example, this now fails:
+```lean
+example : (sorry : Nat) = sorry := rfl -- fails
+```
+However, this still succeeds, since the `sorry` is a single
+indeterminate `Nat`:
+```lean
+def f (n : Nat) : Nat := sorry
+example : f 0 = f 1 := rfl -- succeeds
+```
+One can be more careful by putting parameters to the right of the colon:
+```lean
+def f : (n : Nat) → Nat := sorry
+example : f 0 = f 1 := rfl -- fails
+```
+Most sources of synthetic sorries (recall: a sorry that originates from
+the elaborator) are now unique, except for elaboration errors, since
+making these unique tends to cause a confusing cascade of errors. In
+general, however, such sorries are labeled. This enables "go to
+definition" on `sorry` in the Infoview, which brings you to its origin.
+The option `set_option pp.sorrySource true` causes the pretty printer to
+show source position information on sorries.
+
+### Separators in numeric literals
+
+[#6204](https://github.com/leanprover/lean4/pull/6204) lets `_` be used in numeric literals as a separator. For
+example, `1_000_000`, `0xff_ff` or `0b_10_11_01_00`. New lexical syntax:
+```text
+numeral10 : [0-9]+ ("_"+ [0-9]+)*
+numeral2  : "0" [bB] ("_"* [0-1]+)+
+numeral8  : "0" [oO] ("_"* [0-7]+)+
+numeral16 : "0" [xX] ("_"* hex_char+)+
+float     : numeral10 "." numeral10? [eE[+-]numeral10]
+```
+
+### Additional new featues
+
+* [#6300](https://github.com/leanprover/lean4/pull/6300) adds the `debug.proofAsSorry` option. When enabled, the proofs
+of theorems are ignored and replaced with `sorry`.
+
+* [#6362](https://github.com/leanprover/lean4/pull/6362) adds the `--error=kind` option (shorthand: `-Ekind`) to the
+`lean` CLI. When set, messages of `kind` (e.g.,
+`linter.unusedVariables`) will be reported as errors. This setting does
+nothing in interactive contexts (e.g., the server).
+
+* [#6366](https://github.com/leanprover/lean4/pull/6366) adds support for `Float32` and fixes a bug in the runtime.
+
+### Library updates
+
+The Lean 4 library saw many changes that improve arithmetic reasoning, enhance data structure APIs,
+and refine library organization. Key changes include better support for bitwise operations, shifts,
+and conversions, expanded lemmas for `Array`, `Vector`, and `List`, and improved ordering definitions.
+Some modules have been reorganized for clarity, and internal refinements ensure greater consistency and correctness.
+
+### Breaking changes
+
+[#6330](https://github.com/leanprover/lean4/pull/6330) removes unnecessary parameters from the functional induction
+principles. This is a breaking change; broken code can typically be adjusted
+simply by passing fewer parameters.
+
+_This highlights section was contributed by Violetta Sim._
+
+For this release, 201 changes landed. In addition to the 74 feature additions and 44 fixes listed below there were 7 refactoring changes, 5 documentation improvements and 62 chores.
+
+## Language
+
+* [#3696](https://github.com/leanprover/lean4/pull/3696) makes all message constructors handle pretty printer errors.
+
+* [#4460](https://github.com/leanprover/lean4/pull/4460) runs all linters for a single command (together) on a separate
+thread from further elaboration, making a first step towards
+parallelizing the elaborator.
+
+* [#5757](https://github.com/leanprover/lean4/pull/5757), see the highlights section above for details.
+
+* [#6123](https://github.com/leanprover/lean4/pull/6123) ensures that the configuration in `Simp.Config` is used when
+reducing terms and checking definitional equality in `simp`.
+
+* [#6204](https://github.com/leanprover/lean4/pull/6204), see the highlights section above for details.
+
+* [#6270](https://github.com/leanprover/lean4/pull/6270) fixes a bug that could cause the `injectivity` tactic to fail in
+reducible mode, which could cause unfolding lemma generation to fail
+(used by tactics such as `unfold`). In particular,
+`Lean.Meta.isConstructorApp'?` was not aware that `n + 1` is equivalent
+to `Nat.succ n`.
+
+* [#6273](https://github.com/leanprover/lean4/pull/6273) modifies the "foo has been deprecated: use betterFoo instead"
+warning so that foo and betterFoo are hoverable.
+
+* [#6278](https://github.com/leanprover/lean4/pull/6278) enables simp configuration options to be passed to `norm_cast`.
+
+* [#6286](https://github.com/leanprover/lean4/pull/6286) ensure `bv_decide` uses definitional equality in its reflection
+procedure as much as possible. Previously it would build up explicit
+congruence proofs for the kernel to check. This reduces the size of
+proof terms passed to kernel speeds up checking of large reflection
+proofs.
+
+* [#6288](https://github.com/leanprover/lean4/pull/6288) uses Lean.RArray in bv_decide's reflection proofs. Giving
+speedups on problems with lots of variables.
+
+* [#6295](https://github.com/leanprover/lean4/pull/6295) sets up simprocs for all the remaining operations defined in
+`Init.Data.Fin.Basic`
+
+* [#6300](https://github.com/leanprover/lean4/pull/6300), see the highlights section above for details.
+
+* [#6330](https://github.com/leanprover/lean4/pull/6330), see the highlights section above for details.
+
+* [#6362](https://github.com/leanprover/lean4/pull/6362), see the highlights section above for details.
+
+* [#6366](https://github.com/leanprover/lean4/pull/6366), see the highlights section above for details.
+
+* [#6375](https://github.com/leanprover/lean4/pull/6375) fixes a bug in the simplifier. It was producing terms with loose
+bound variables when eliminating unused `let_fun` expressions.
+
+* [#6378](https://github.com/leanprover/lean4/pull/6378) adds an explanation to the error message when `cases` and
+`induction` are applied to a term whose type is not an inductive type.
+For `Prop`, these tactics now suggest the `by_cases` tactic. Example:
+```
+tactic 'cases' failed, major premise type is not an inductive type
+  Prop
+```
+
+* [#6381](https://github.com/leanprover/lean4/pull/6381) fixes a bug in `withTrackingZetaDelta` and
+`withTrackingZetaDeltaSet`. The `MetaM` caches need to be reset. See new
+test.
+
+* [#6385](https://github.com/leanprover/lean4/pull/6385) fixes a bug in `simp_all?` that caused some local declarations
+to be omitted from the `Try this:` suggestions.
+
+* [#6386](https://github.com/leanprover/lean4/pull/6386) ensures that `revertAll` clears auxiliary declarations when
+invoked directly by users.
+
+* [#6387](https://github.com/leanprover/lean4/pull/6387) fixes a type error in the proof generated by the `contradiction`
+tactic.
+
+* [#6397](https://github.com/leanprover/lean4/pull/6397) ensures that `simp` and `dsimp` do not unfold definitions that
+are not intended to be unfolded by the user. See issue #5755 for an
+example affected by this issue.
+
+* [#6398](https://github.com/leanprover/lean4/pull/6398) ensures `Meta.check` check projections.
+
+* [#6412](https://github.com/leanprover/lean4/pull/6412) adds reserved names for congruence theorems used in the
+simplifier and `grind` tactics. The idea is prevent the same congruence
+theorems to be generated over and over again.
+
+* [#6413](https://github.com/leanprover/lean4/pull/6413) introduces the following features to the WIP `grind` tactic:
+- `Expr` internalization.
+- Congruence theorem cache.
+- Procedure for adding new facts
+- New tracing options
+- New preprocessing steps: fold projections and eliminate dangling
+`Expr.mdata`
+
+* [#6414](https://github.com/leanprover/lean4/pull/6414) fixes a bug in `Lean.Meta.Closure` that would introduce
+under-applied delayed assignment metavariables, which would keep them
+from ever getting instantiated. This bug affected `match` elaboration
+when the expected type contained postponed elaboration problems, for
+example tactic blocks.
+
+* [#6419](https://github.com/leanprover/lean4/pull/6419) fixes multiple bugs in the WIP `grind` tactic. It also adds
+support for printing the `grind` internal state.
+
+* [#6428](https://github.com/leanprover/lean4/pull/6428) adds a new preprocessing step to the `grind` tactic:
+universe-level normalization. The goal is to avoid missing equalities in
+the congruence closure module.
+
+* [#6430](https://github.com/leanprover/lean4/pull/6430) adds the predicate `Expr.fvarsSet a b`, which returns `true` if
+and only if the free variables in `a` are a subset of the free variables
+in `b`.
+
+* [#6433](https://github.com/leanprover/lean4/pull/6433) adds a custom type and instance canonicalizer for the (WIP)
+`grind` tactic. The `grind` tactic uses congruence closure but
+disregards types, type formers, instances, and proofs. Proofs are
+ignored due to proof irrelevance. Types, type formers, and instances are
+considered supporting elements and are not factored into congruence
+detection. Instead, `grind` only checks whether elements are
+structurally equal, which, in the context of the `grind` tactic, is
+equivalent to pointer equality. See new tests for examples where the
+canonicalizer is important.
+
+* [#6435](https://github.com/leanprover/lean4/pull/6435) implements the congruence table for the (WIP) `grind` tactic. It
+also fixes several bugs, and adds a new preprocessing step.
+
+* [#6437](https://github.com/leanprover/lean4/pull/6437) adds support for detecting congruent terms in the (WIP) `grind`
+tactic. It also introduces the `grind.debug` option, which, when set to
+`true`, checks many invariants after each equivalence class is merged.
+This option is intended solely for debugging purposes.
+
+* [#6438](https://github.com/leanprover/lean4/pull/6438) ensures `norm_cast` doesn't fail to act in the presence of
+`no_index` annotations
+
+* [#6441](https://github.com/leanprover/lean4/pull/6441) adds basic truth value propagation rules to the (WIP) `grind`
+tactic.
+
+* [#6442](https://github.com/leanprover/lean4/pull/6442) fixes the `checkParents` sanity check in `grind`.
+
+* [#6443](https://github.com/leanprover/lean4/pull/6443) adds support for propagating the truth value of equalities in
+the (WIP) `grind` tactic.
+
+* [#6447](https://github.com/leanprover/lean4/pull/6447) refactors `grind` and adds support for invoking the simplifier
+using the `GrindM` monad.
+
+* [#6448](https://github.com/leanprover/lean4/pull/6448) declares the command `builtin_grind_propagator` for registering
+equation propagator for `grind`. It also declares the auxiliary the
+attribute.
+
+* [#6449](https://github.com/leanprover/lean4/pull/6449) completes the implementation of the command
+`builtin_grind_propagator`.
+
+* [#6452](https://github.com/leanprover/lean4/pull/6452) adds support for generating (small) proofs for any two
+expressions that belong to the same equivalence class in the `grind`
+tactic state.
+
+* [#6453](https://github.com/leanprover/lean4/pull/6453) improves bv_decide's performance in the presence of large
+literals.
+
+* [#6455](https://github.com/leanprover/lean4/pull/6455) fixes a bug in the equality proof generator in the (WIP) `grind`
+tactic.
+
+* [#6456](https://github.com/leanprover/lean4/pull/6456) fixes another bug in the equality proof generator in the (WIP)
+`grind` tactic.
+
+* [#6457](https://github.com/leanprover/lean4/pull/6457) adds support for generating congruence proofs for congruences
+detected by the `grind` tactic.
+
+* [#6458](https://github.com/leanprover/lean4/pull/6458) adds support for compact congruence proofs in the (WIP) `grind`
+tactic. The `mkCongrProof` function now verifies whether the congruence
+proof can be constructed using only `congr`, `congrFun`, and `congrArg`,
+avoiding the need to generate the more complex `hcongr` auxiliary
+theorems.
+
+* [#6459](https://github.com/leanprover/lean4/pull/6459) adds the (WIP) `grind` tactic. It currently generates a warning
+message to make it clear that the tactic is not ready for production.
+
+* [#6461](https://github.com/leanprover/lean4/pull/6461) adds a new propagation rule for negation to the (WIP) `grind`
+tactic.
+
+* [#6463](https://github.com/leanprover/lean4/pull/6463) adds support for constructors to the (WIP) `grind` tactic. When
+merging equivalence classes, `grind` checks for equalities between
+constructors. If they are distinct, it closes the goal; if they are the
+same, it applies injectivity.
+
+* [#6464](https://github.com/leanprover/lean4/pull/6464) completes support for literal values in the (WIP) `grind`
+tactic. `grind` now closes the goal whenever it merges two equivalence
+classes with distinct literal values.
+
+* [#6465](https://github.com/leanprover/lean4/pull/6465) adds support for projection functions to the (WIP) `grind`
+tactic.
+
+* [#6466](https://github.com/leanprover/lean4/pull/6466) completes the implementation of `addCongrTable` in the (WIP)
+`grind` tactic. It also adds a new test to demonstrate why the extra
+check is needed. It also updates the field `cgRoot` (congruence root).
+
+* [#6468](https://github.com/leanprover/lean4/pull/6468) fixes issue #6467
+
+* [#6469](https://github.com/leanprover/lean4/pull/6469) adds support code for implementing e-match in the (WIP) `grind`
+tactic.
+
+* [#6470](https://github.com/leanprover/lean4/pull/6470) introduces a command for specifying patterns used in the
+heuristic instantiation of global theorems in the `grind` tactic. Note
+that this PR only adds the parser.
+
+* [#6472](https://github.com/leanprover/lean4/pull/6472) implements the command `grind_pattern`. The new command allows
+users to associate patterns with theorems. These patterns are used for
+performing heuristic instantiation with e-matching. In the future, we
+will add the attributes `@[grind_eq]`, `@[grind_fwd]`, and
+`@[grind_bwd]` to compute the patterns automatically for theorems.
+
+* [#6473](https://github.com/leanprover/lean4/pull/6473) adds a deriving handler for the `ToExpr` class. It can handle
+mutual and nested inductive types, however it falls back to creating
+`partial` instances in such cases. This is upstreamed from the Mathlib
+deriving handler written by @kmill, but has fixes to handle autoimplicit
+universe level variables.
+
+* [#6474](https://github.com/leanprover/lean4/pull/6474) adds pattern validation to the `grind_pattern` command. The new
+`checkCoverage` function will also be used to implement the attributes
+`@[grind_eq]`, `@[grind_fwd]`, and `@[grind_bwd]`.
+
+* [#6475](https://github.com/leanprover/lean4/pull/6475) adds support for activating relevant theorems for the (WIP)
+`grind` tactic. We say a theorem is relevant to a `grind` goal if the
+symbols occurring in its patterns also occur in the goal.
+
+* [#6478](https://github.com/leanprover/lean4/pull/6478) internalize nested ground patterns when activating ematch
+theorems in the (WIP) `grind` tactic.
+
+* [#6481](https://github.com/leanprover/lean4/pull/6481) implements E-matching for the (WIP) `grind` tactic. We still
+need to finalize and internalize the new instances.
+
+* [#6484](https://github.com/leanprover/lean4/pull/6484) addresses a few error messages where diffs weren't being
+exposed.
+
+* [#6485](https://github.com/leanprover/lean4/pull/6485) implements `Grind.EMatch.instantiateTheorem` in the (WIP)
+`grind` tactic.
+
+* [#6487](https://github.com/leanprover/lean4/pull/6487) adds source position information for `structure` parent
+projections, supporting "go to definition". Closes #3063.
+
+* [#6488](https://github.com/leanprover/lean4/pull/6488) fixes and refactors the E-matching module for the (WIP) `grind`
+tactic.
+
+* [#6490](https://github.com/leanprover/lean4/pull/6490) adds basic configuration options for the `grind` tactic.
+
+* [#6492](https://github.com/leanprover/lean4/pull/6492) fixes a bug in the theorem instantiation procedure in the (WIP)
+`grind` tactic. 
+
+* [#6497](https://github.com/leanprover/lean4/pull/6497) fixes another theorem instantiation bug in the `grind` tactic.
+It also moves new instances to be processed to `Goal`.
+
+* [#6498](https://github.com/leanprover/lean4/pull/6498) adds support in the `grind` tactic for propagating dependent
+forall terms `forall (h : p), q[h]` where `p` is a proposition.
+
+* [#6499](https://github.com/leanprover/lean4/pull/6499) fixes the proof canonicalizer for `grind`.
+
+* [#6500](https://github.com/leanprover/lean4/pull/6500) fixes a bug in the `markNestedProofs` used in `grind`. See new
+test.
+
+* [#6502](https://github.com/leanprover/lean4/pull/6502) fixes a bug in the proof assembly procedure utilized by the
+`grind` tactic.
+
+* [#6503](https://github.com/leanprover/lean4/pull/6503) adds a simple strategy to the (WIP) `grind` tactic. It just
+keeps internalizing new theorem instances found by E-matching. 
+
+* [#6506](https://github.com/leanprover/lean4/pull/6506) adds the `monotonicity` tactic, intended to be used inside the
+`partial_fixpoint` feature.
+
+* [#6508](https://github.com/leanprover/lean4/pull/6508) fixes a bug in the sanity checkers for the `grind` tactic. See
+the new test for an example of a case where it was panicking.
+
+* [#6509](https://github.com/leanprover/lean4/pull/6509) fixes a bug in the congruence closure data structure used in the
+`grind` tactic. The new test includes an example that previously caused
+a panic. A similar panic was also occurring in the test
+`grind_nested_proofs.lean`.
+
+* [#6510](https://github.com/leanprover/lean4/pull/6510) adds a custom congruence rule for equality in `grind`. The new
+rule takes into account that `Eq` is a symmetric relation. In the
+future, we will add support for arbitrary symmetric relations. The
+current rule is important for propagating disequalities effectively in
+`grind`.
+
+* [#6512](https://github.com/leanprover/lean4/pull/6512) introduces support for user-defined fallback code in the `grind`
+tactic. The fallback code can be utilized to inspect the state of
+failing `grind` subgoals and/or invoke user-defined automation. Users
+can now write `grind on_failure <code>`, where `<code>` should have the
+type `GoalM Unit`. See the modified tests in this PR for examples.
+
+* [#6513](https://github.com/leanprover/lean4/pull/6513) adds support for (dependent) if-then-else terms (i.e., `ite` and
+`dite` applications) in the `grind` tactic.
+
+* [#6514](https://github.com/leanprover/lean4/pull/6514) enhances the assertion of new facts in `grind` by avoiding the
+creation of unnecessary metavariables.
+
+## Library
+
+* [#6182](https://github.com/leanprover/lean4/pull/6182) adds `BitVec.[toInt|toFin]_concat` and moves a couple of
+theorems into the concat section, as `BitVec.msb_concat` is needed for
+the `toInt_concat` proof.
+
+* [#6188](https://github.com/leanprover/lean4/pull/6188) completes the `toNat` theorems for the bitwise operations
+(`and`, `or`, `xor`, `shiftLeft`, `shiftRight`) of the UInt types and
+adds `toBitVec` theorems as well. It also renames `and_toNat` to
+`toNat_and` to fit with the current naming convention.
+
+* [#6238](https://github.com/leanprover/lean4/pull/6238) adds theorems characterizing the value of the unsigned shift
+right of a bitvector in terms of its 2s complement interpretation as an
+integer.
+Unsigned shift right by at least one bit makes the value of the
+bitvector less than or equal to `2^(w-1)`,
+makes the interpretation of the bitvector `Int` and `Nat` agree.
+In the case when `n = 0`, then the shift right value equals the integer
+interpretation.
+
+* [#6244](https://github.com/leanprover/lean4/pull/6244) changes the implementation of `HashMap.toList`, so the ordering
+agrees with `HashMap.toArray`.
+
+* [#6272](https://github.com/leanprover/lean4/pull/6272) introduces the basic theory of permutations of `Array`s and
+proves `Array.swap_perm`.
+
+* [#6282](https://github.com/leanprover/lean4/pull/6282) moves `IO.Channel` and `IO.Mutex` from `Init` to `Std.Sync` and
+renames them to `Std.Channel` and `Std.Mutex`.
+
+* [#6294](https://github.com/leanprover/lean4/pull/6294) upstreams `List.length_flatMap`, `countP_flatMap` and
+`count_flatMap` from Mathlib. These were not possible to state before we
+upstreamed `List.sum`.
+
+* [#6315](https://github.com/leanprover/lean4/pull/6315) adds `protected` to `Fin.cast` and `BitVec.cast`, to avoid
+confusion with `_root_.cast`. These should mostly be used via
+dot-notation in any case.
+
+* [#6316](https://github.com/leanprover/lean4/pull/6316) adds lemmas simplifying `for` loops over `Option` into
+`Option.pelim`, giving parity with lemmas simplifying `for` loops of
+`List` into `List.fold`.
+
+* [#6317](https://github.com/leanprover/lean4/pull/6317) completes the basic API for BitVec.ofBool.
+
+* [#6318](https://github.com/leanprover/lean4/pull/6318) generalizes the universe level for `Array.find?`, by giving it a
+separate implementation from `Array.findM?`.
+
+* [#6324](https://github.com/leanprover/lean4/pull/6324) adds `GetElem` lemmas for the basic `Vector` operations.
+
+* [#6333](https://github.com/leanprover/lean4/pull/6333) generalizes the panic functions to a type of `Sort u` rather
+than `Type u`. This better supports universe polymorphic types and
+avoids confusing errors.
+
+* [#6334](https://github.com/leanprover/lean4/pull/6334) adds `Nat` theorems for distributing `>>>` over bitwise
+operations, paralleling those of `BitVec`.
+
+* [#6338](https://github.com/leanprover/lean4/pull/6338) adds `BitVec.[toFin|getMsbD]_setWidth` and
+`[getMsb|msb]_signExtend` as well as `ofInt_toInt`.
+
+* [#6341](https://github.com/leanprover/lean4/pull/6341) generalizes `DecidableRel` to allow a heterogeneous relation.
+
+* [#6353](https://github.com/leanprover/lean4/pull/6353) reproduces the API around `List.any/all` for `Array.any/all`.
+
+* [#6364](https://github.com/leanprover/lean4/pull/6364) makes fixes suggested by the Batteries environment linters,
+particularly `simpNF`, and `unusedHavesSuffices`.
+
+* [#6365](https://github.com/leanprover/lean4/pull/6365) expands the `Array.set` and `Array.setIfInBounds` lemmas to
+match existing lemmas for `List.set`.
+
+* [#6367](https://github.com/leanprover/lean4/pull/6367) brings Vector lemmas about membership and indexing to parity
+with List and Array.
+
+* [#6369](https://github.com/leanprover/lean4/pull/6369) adds lemmas about `Vector.set`, `anyM`, `any`, `allM`, and
+`all`.
+
+* [#6376](https://github.com/leanprover/lean4/pull/6376) adds theorems about `==` on `Vector`, reproducing those already
+on `List` and `Array`.
+
+* [#6379](https://github.com/leanprover/lean4/pull/6379) replaces the inductive predicate `List.lt` with an upstreamed version of `List.Lex` from Mathlib.
+(Previously `Lex.lt` was defined in terms of `<`; now it is generalized to take an arbitrary relation.)
+This subtly changes the notion of ordering on `List α`.
+
+  `List.lt` was a weaker relation: in particular if `l₁ < l₂`, then `a :: l₁ < b :: l₂` may hold according to `List.lt` even if `a` and `b` are merely incomparable (either neither `a < b` nor `b < a`), whereas according to `List.Lex` this would require `a = b`.
+
+  When `<` is total, in the sense that `¬ · < ·` is antisymmetric, then the two relations coincide.
+
+  Mathlib was already overriding the order instances for `List α`, so this change should not be noticed by anyone already using Mathlib.
+
+  We simultaneously add the boolean valued `List.lex` function, parameterised by a `BEq` typeclass and an arbitrary `lt` function. This will support the flexibility previously provided for `List.lt`, via a `==` function which is weaker than strict equality.
+
+* [#6390](https://github.com/leanprover/lean4/pull/6390) redefines `Range.forIn'` and `Range.forM`, in preparation for
+writing lemmas about them.
+
+* [#6391](https://github.com/leanprover/lean4/pull/6391) requires that the step size in `Std.Range` is positive, to avoid
+ill-specified behaviour.
+
+* [#6396](https://github.com/leanprover/lean4/pull/6396) adds lemmas reducing for loops over `Std.Range` to for loops
+over `List.range'`.
+
+* [#6399](https://github.com/leanprover/lean4/pull/6399) adds basic lemmas about lexicographic order on Array and Vector,
+achieving parity with List.
+
+* [#6423](https://github.com/leanprover/lean4/pull/6423) adds missing lemmas about lexicographic order on
+List/Array/Vector.
+
+* [#6477](https://github.com/leanprover/lean4/pull/6477) adds the necessary domain theory that backs the
+`partial_fixpoint` feature.
+
+## Compiler
+
+* [#6311](https://github.com/leanprover/lean4/pull/6311) adds support for `HEq` to the new code generator.
+
+* [#6348](https://github.com/leanprover/lean4/pull/6348) adds support for `Float32` to the Lean runtime.
+
+* [#6350](https://github.com/leanprover/lean4/pull/6350) adds missing features and fixes bugs in the `Float32` support
+
+* [#6383](https://github.com/leanprover/lean4/pull/6383) ensures the new code generator produces code for `opaque`
+definitions that are not tagged as `@[extern]`.
+Remark: This is the behavior of the old code generator.
+
+* [#6405](https://github.com/leanprover/lean4/pull/6405) adds support for erasure of `Decidable.decide` to the new code
+generator. It also adds a new `Probe.runOnDeclsNamed` function, which is
+helpful for writing targeted single-file tests of compiler internals.
+
+* [#6415](https://github.com/leanprover/lean4/pull/6415) fixes a bug in the `sharecommon` module, which was returning
+incorrect results for objects that had already been processed by
+`sharecommon`. See the new test for an example that triggered the bug.
+
+* [#6429](https://github.com/leanprover/lean4/pull/6429) adds support for extern LCNF decls, which is required for parity
+with the existing code generator.
+
+* [#6535](https://github.com/leanprover/lean4/pull/6535) avoids a linker warning on Windows.
+
+* [#6547](https://github.com/leanprover/lean4/pull/6547) should prevent Lake from accidentally picking up other linkers
+installed on the machine.
+
+* [#6574](https://github.com/leanprover/lean4/pull/6574) actually prevents Lake from accidentally picking up other
+toolchains installed on the machine.
+
+## Pretty Printing
+
+* [#5689](https://github.com/leanprover/lean4/pull/5689) adjusts the way the pretty printer unresolves names. It used to
+make use of all `export`s when pretty printing, but now it only uses
+`export`s that put names into parent namespaces (heuristic: these are
+"API exports" that are intended by the library author), rather than
+"horizontal exports" that put the names into an unrelated namespace,
+which the dot notation feature in #6189 now incentivizes.
+
+* [#5757](https://github.com/leanprover/lean4/pull/5757), aside from introducing labeled sorries, fixes the bug that the metadata attached to the pretty-printed representation of arguments with a borrow annotation (for example, the second argument of `String.append`), is inconsistent with the metadata attached to the regular arguments.
+
+## Documentation
+
+* [#6450](https://github.com/leanprover/lean4/pull/6450) adds a docstring to the `@[app_delab]` attribute.
+
+## Server
+
+* [#6279](https://github.com/leanprover/lean4/pull/6279) fixes a bug in structure instance field completion that caused
+it to not function correctly for bracketed structure instances written
+in Mathlib style.
+
+* [#6408](https://github.com/leanprover/lean4/pull/6408) fixes a regression where goals that don't exist were being
+displayed. The regression was triggered by #5835 and originally caused
+by #4926.
+
+## Lake
+
+* [#6176](https://github.com/leanprover/lean4/pull/6176) changes Lake's build process to no longer use `leanc` for
+compiling C files or linking shared libraries and executables. Instead,
+it directly invokes the bundled compiler (or the native compiler if
+none) using the necessary flags.
+
+* [#6289](https://github.com/leanprover/lean4/pull/6289) adapts Lake modules to use `prelude` and includes them in the
+`check-prelude` CI.
+
+* [#6291](https://github.com/leanprover/lean4/pull/6291) ensures the the log error position is properly preserved when
+prepending stray log entries to the job log. It also adds comparison
+support for `Log.Pos`.
+
+* [#6388](https://github.com/leanprover/lean4/pull/6388) merges `BuildJob` and `Job`, deprecating the former. `Job` now
+contains a trace as part of its state which can be interacted with
+monadically. also simplifies the implementation of `OpaqueJob`.
+
+* [#6411](https://github.com/leanprover/lean4/pull/6411) adds the ability to override package entries in a Lake manifest
+via a separate JSON file. This file can be specified on the command line
+with `--packages` or applied persistently by placing it at
+`.lake/package-overrides.json`.
+
+* [#6422](https://github.com/leanprover/lean4/pull/6422) fixes a bug in #6388 where the `Package.afterBuildCahe*`
+functions would produce different traces depending on whether the cache
+was fetched.
+
+* [#6627](https://github.com/leanprover/lean4/pull/6627) aims to fix the trace issues reported by Mathlib that are
+breaking `lake exe cache` in downstream projects.
+
+* [#6631](https://github.com/leanprover/lean4/pull/6631) sets `MACOSX_DEPLOYMENT_TARGET` for shared libraries (it was
+previously only set for executables).
+
+## Other
+
+* [#6285](https://github.com/leanprover/lean4/pull/6285) upstreams the `ToLevel` typeclass from mathlib and uses it to
+fix the existing `ToExpr` instances so that they are truly universe
+polymorphic (previously it generated malformed expressions when the
+universe level was nonzero). We improve on the mathlib definition of
+`ToLevel` to ensure the class always lives in `Type`, irrespective of
+the universe parameter.
+
+* [#6363](https://github.com/leanprover/lean4/pull/6363) fixes errors at load time in the comparison mode of the Firefox
+profiler.

releases/v4.2.0.md

@@ -0,0 +1,16 @@
+v4.2.0
+---------
+
+* [isDefEq cache for terms not containing metavariables.](https://github.com/leanprover/lean4/pull/2644).
+* Make [`Environment.mk`](https://github.com/leanprover/lean4/pull/2604) and [`Environment.add`](https://github.com/leanprover/lean4/pull/2642) private, and add [`replay`](https://github.com/leanprover/lean4/pull/2617) as a safer alternative.
+* `IO.Process.output` no longer inherits the standard input of the caller.
+* [Do not inhibit caching](https://github.com/leanprover/lean4/pull/2612) of default-level `match` reduction.
+* [List the valid case tags](https://github.com/leanprover/lean4/pull/2629) when the user writes an invalid one.
+* The derive handler for `DecidableEq` [now handles](https://github.com/leanprover/lean4/pull/2591) mutual inductive types.
+* [Show path of failed import in Lake](https://github.com/leanprover/lean4/pull/2616).
+* [Fix linker warnings on macOS](https://github.com/leanprover/lean4/pull/2598).
+* **Lake:** Add `postUpdate?` package configuration option. Used by a package to specify some code which should be run after a successful `lake update` of the package or one of its downstream dependencies. ([lake#185](https://github.com/leanprover/lake/issues/185))
+* Improvements to Lake startup time ([#2572](https://github.com/leanprover/lean4/pull/2572), [#2573](https://github.com/leanprover/lean4/pull/2573))
+* `refine e` now replaces the main goal with metavariables which were created during elaboration of `e` and no longer captures pre-existing metavariables that occur in `e` ([#2502](https://github.com/leanprover/lean4/pull/2502)).
+  * This is accomplished via changes to `withCollectingNewGoalsFrom`, which also affects `elabTermWithHoles`, `refine'`, `calc` (tactic), and `specialize`. Likewise, all of these now only include newly-created metavariables in their output.
+  * Previously, both newly-created and pre-existing metavariables occurring in `e` were returned inconsistently in different edge cases, causing duplicated goals in the infoview (issue [#2495](https://github.com/leanprover/lean4/issues/2495)), erroneously closed goals (issue [#2434](https://github.com/leanprover/lean4/issues/2434)), and unintuitive behavior due to `refine e` capturing previously-created goals appearing unexpectedly in `e` (no issue; see PR).

releases/v4.3.0.md

@@ -0,0 +1,37 @@
+v4.3.0
+---------
+
+* `simp [f]` does not unfold partial applications of `f` anymore. See issue [#2042](https://github.com/leanprover/lean4/issues/2042).
+  To fix proofs affected by this change, use `unfold f` or `simp (config := { unfoldPartialApp := true }) [f]`.
+* By default, `simp` will no longer try to use Decidable instances to rewrite terms. In particular, not all decidable goals will be closed by `simp`, and the `decide` tactic may be useful in such cases. The `decide` simp configuration option can be used to locally restore the old `simp` behavior, as in `simp (config := {decide := true})`; this includes using Decidable instances to verify side goals such as numeric inequalities.
+
+* Many bug fixes:
+  * [Add left/right actions to term tree coercion elaborator and make `^`` a right action](https://github.com/leanprover/lean4/pull/2778)
+  * [Fix for #2775, don't catch max recursion depth errors](https://github.com/leanprover/lean4/pull/2790)
+  * [Reduction of `Decidable` instances very slow when using `cases` tactic](https://github.com/leanprover/lean4/issues/2552)
+  * [`simp` not rewriting in binder](https://github.com/leanprover/lean4/issues/1926)
+  * [`simp` unfolding `let` even with `zeta := false` option](https://github.com/leanprover/lean4/issues/2669)
+  * [`simp` (with beta/zeta disabled) and discrimination trees](https://github.com/leanprover/lean4/issues/2281)
+  * [unknown free variable introduced by `rw ... at h`](https://github.com/leanprover/lean4/issues/2711)
+  * [`dsimp` doesn't use `rfl` theorems which consist of an unapplied constant](https://github.com/leanprover/lean4/issues/2685)
+  * [`dsimp` does not close reflexive equality goals if they are wrapped in metadata](https://github.com/leanprover/lean4/issues/2514)
+  * [`rw [h]` uses `h` from the environment in preference to `h` from the local context](https://github.com/leanprover/lean4/issues/2729)
+  * [missing `withAssignableSyntheticOpaque` for `assumption` tactic](https://github.com/leanprover/lean4/issues/2361)
+  * [ignoring default value for field warning](https://github.com/leanprover/lean4/issues/2178)
+* [Cancel outstanding tasks on document edit in the language server](https://github.com/leanprover/lean4/pull/2648).
+* [Remove unnecessary `%` operations in `Fin.mod` and `Fin.div`](https://github.com/leanprover/lean4/pull/2688)
+* [Avoid `DecidableEq` in `Array.mem`](https://github.com/leanprover/lean4/pull/2774)
+* [Ensure `USize.size` unifies with `?m + 1`](https://github.com/leanprover/lean4/issues/1926)
+* [Improve compatibility with emacs eglot client](https://github.com/leanprover/lean4/pull/2721)
+
+**Lake:**
+
+* [Sensible defaults for `lake new MyProject math`](https://github.com/leanprover/lean4/pull/2770)
+* Changed `postUpdate?` configuration option to a `post_update` declaration. See the `post_update` syntax docstring for more information on the new syntax.
+* [A manifest is automatically created on workspace load if one does not exists.](https://github.com/leanprover/lean4/pull/2680).
+* The `:=` syntax for configuration declarations (i.e., `package`, `lean_lib`, and `lean_exe`) has been deprecated. For example, `package foo := {...}` is deprecated.
+* [support for overriding package URLs via `LAKE_PKG_URL_MAP`](https://github.com/leanprover/lean4/pull/2709)
+* Moved the default build directory (e.g., `build`), default packages directory (e.g., `lake-packages`), and the compiled configuration (e.g., `lakefile.olean`) into a new dedicated directory for Lake outputs, `.lake`. The cloud release build archives are also stored here, fixing [#2713](https://github.com/leanprover/lean4/issues/2713).
+* Update manifest format to version 7 (see [lean4#2801](https://github.com/leanprover/lean4/pull/2801) for details on the changes).
+* Deprecate the `manifestFile` field of a package configuration.
+* There is now a more rigorous check on `lakefile.olean` compatibility (see [#2842](https://github.com/leanprover/lean4/pull/2842) for more details).

releases/v4.4.0.md

@@ -0,0 +1,45 @@
+v4.4.0
+---------
+
+* Lake and the language server now support per-package server options using the `moreServerOptions` config field, as well as options that apply to both the language server and `lean` using the `leanOptions` config field. Setting either of these fields instead of `moreServerArgs` ensures that viewing files from a dependency uses the options for that dependency. Additionally, `moreServerArgs` is being deprecated in favor of the `moreGlobalServerArgs` field. See PR [#2858](https://github.com/leanprover/lean4/pull/2858).
+
+  A Lakefile with the following deprecated package declaration:
+  ```lean
+  def moreServerArgs := #[
+    "-Dpp.unicode.fun=true"
+  ]
+  def moreLeanArgs := moreServerArgs
+
+  package SomePackage where
+    moreServerArgs := moreServerArgs
+    moreLeanArgs := moreLeanArgs
+  ```
+
+  ... can be updated to the following package declaration to use per-package options:
+  ```lean
+  package SomePackage where
+    leanOptions := #[⟨`pp.unicode.fun, true⟩]
+  ```
+* [Rename request handler](https://github.com/leanprover/lean4/pull/2462).
+* [Import auto-completion](https://github.com/leanprover/lean4/pull/2904).
+* [`pp.beta`` to apply beta reduction when pretty printing](https://github.com/leanprover/lean4/pull/2864).
+* [Embed and check githash in .olean](https://github.com/leanprover/lean4/pull/2766).
+* [Guess lexicographic order for well-founded recursion](https://github.com/leanprover/lean4/pull/2874).
+* [Allow trailing comma in tuples, lists, and tactics](https://github.com/leanprover/lean4/pull/2643).
+
+Bug fixes for [#2628](https://github.com/leanprover/lean4/issues/2628), [#2883](https://github.com/leanprover/lean4/issues/2883),
+[#2810](https://github.com/leanprover/lean4/issues/2810), [#2925](https://github.com/leanprover/lean4/issues/2925), and [#2914](https://github.com/leanprover/lean4/issues/2914).
+
+**Lake:**
+
+* `lake init .` and a bare `lake init` and will now use the current directory as the package name. [#2890](https://github.com/leanprover/lean4/pull/2890)
+* `lake new` and `lake init` will now produce errors on invalid package names such as `..`, `foo/bar`, `Init`, `Lean`, `Lake`, and `Main`. See issue [#2637](https://github.com/leanprover/lean4/issues/2637) and PR [#2890](https://github.com/leanprover/lean4/pull/2890).
+* `lean_lib` no longer converts its name to upper camel case (e.g., `lean_lib bar` will include modules named `bar.*` rather than `Bar.*`). See issue [#2567](https://github.com/leanprover/lean4/issues/2567) and PR [#2889](https://github.com/leanprover/lean4/pull/2889).
+* Lean and Lake now properly support non-identifier library names (e.g., `lake new 123-hello` and `import «123Hello»` now work correctly). See issue [#2865](https://github.com/leanprover/lean4/issues/2865) and PR [#2889](https://github.com/leanprover/lean4/pull/2888).
+* Lake now filters the environment extensions loaded from a compiled configuration (`lakefile.olean`) to include only those relevant to Lake's workspace loading process. This resolves segmentation faults caused by environment extension type mismatches (e.g., when defining custom elaborators via `elab` in configurations). See issue [#2632](https://github.com/leanprover/lean4/issues/2632) and PR [#2896](https://github.com/leanprover/lean4/pull/2896).
+* Cloud releases will now properly be re-unpacked if the build directory is removed. See PR [#2928](https://github.com/leanprover/lean4/pull/2928).
+* Lake's `math` template has been simplified. See PR [#2930](https://github.com/leanprover/lean4/pull/2930).
+* `lake exe <target>` now parses `target` like a build target (as the help text states it should) rather than as a basic name. For example, `lake exe @mathlib/runLinter` should now work. See PR [#2932](https://github.com/leanprover/lean4/pull/2932).
+* `lake new foo.bar [std]` now generates executables named `foo-bar` and `lake new foo.bar exe` properly creates `foo/bar.lean`. See PR [#2932](https://github.com/leanprover/lean4/pull/2932).
+* Later packages and libraries in the dependency tree are now preferred over earlier ones. That is, the later ones "shadow" the earlier ones. Such an ordering is more consistent with how declarations generally work in programming languages. This will break any package that relied on the previous ordering. See issue [#2548](https://github.com/leanprover/lean4/issues/2548) and PR [#2937](https://github.com/leanprover/lean4/pull/2937).
+* Executable roots are no longer mistakenly treated as importable. They will no longer be picked up by `findModule?`. See PR [#2937](https://github.com/leanprover/lean4/pull/2937).

releases/v4.5.0.md

@@ -0,0 +1,77 @@
+v4.5.0
+---------
+
+* Modify the lexical syntax of string literals to have string gaps, which are escape sequences of the form `"\" newline whitespace*`.
+  These have the interpretation of an empty string and allow a string to flow across multiple lines without introducing additional whitespace.
+  The following is equivalent to `"this is a string"`.
+  ```lean
+  "this is \
+     a string"
+  ```
+  [PR #2821](https://github.com/leanprover/lean4/pull/2821) and [RFC #2838](https://github.com/leanprover/lean4/issues/2838).
+
+* Add raw string literal syntax. For example, `r"\n"` is equivalent to `"\\n"`, with no escape processing.
+  To include double quote characters in a raw string one can add sufficiently many `#` characters before and after
+  the bounding `"`s, as in `r#"the "the" is in quotes"#` for `"the \"the\" is in quotes"`.
+  [PR #2929](https://github.com/leanprover/lean4/pull/2929) and [issue #1422](https://github.com/leanprover/lean4/issues/1422).
+
+* The low-level `termination_by'` clause is no longer supported.
+
+  Migration guide: Use `termination_by` instead, e.g.:
+  ```diff
+  -termination_by' measure (fun ⟨i, _⟩ => as.size - i)
+  +termination_by i _ => as.size - i
+  ```
+
+  If the well-founded relation you want to use is not the one that the
+  `WellFoundedRelation` type class would infer for your termination argument,
+  you can use `WellFounded.wrap` from the std library to explicitly give one:
+  ```diff
+  -termination_by' ⟨r, hwf⟩
+  +termination_by x => hwf.wrap x
+  ```
+
+* Support snippet edits in LSP `TextEdit`s. See `Lean.Lsp.SnippetString` for more details.
+
+* Deprecations and changes in the widget API.
+  - `Widget.UserWidgetDefinition` is deprecated in favour of `Widget.Module`. The annotation `@[widget]` is deprecated in favour of `@[widget_module]`. To migrate a definition of type `UserWidgetDefinition`, remove the `name` field and replace the type with `Widget.Module`. Removing the `name` results in a title bar no longer being drawn above your panel widget. To add it back, draw it as part of the component using `<details open=true><summary class='mv2 pointer'>{name}</summary>{rest_of_widget}</details>`. See an example migration [here](https://github.com/leanprover/std4/pull/475/files#diff-857376079661a0c28a53b7ff84701afabbdf529836a6944d106c5294f0e68109R43-R83).
+  - The new command `show_panel_widgets` allows displaying always-on and locally-on panel widgets.
+  - `RpcEncodable` widget props can now be stored in the infotree.
+  - See [RFC 2963](https://github.com/leanprover/lean4/issues/2963) for more details and motivation.
+
+* If no usable lexicographic order can be found automatically for a termination proof, explain why.
+  See [feat: GuessLex: if no measure is found, explain why](https://github.com/leanprover/lean4/pull/2960).
+
+* Option to print [inferred termination argument](https://github.com/leanprover/lean4/pull/3012).
+  With `set_option showInferredTerminationBy true` you will get messages like
+  ```
+  Inferred termination argument:
+  termination_by
+  ackermann n m => (sizeOf n, sizeOf m)
+  ```
+  for automatically generated `termination_by` clauses.
+
+* More detailed error messages for [invalid mutual blocks](https://github.com/leanprover/lean4/pull/2949).
+
+* [Multiple](https://github.com/leanprover/lean4/pull/2923) [improvements](https://github.com/leanprover/lean4/pull/2969) to the output of `simp?` and `simp_all?`.
+
+* Tactics with `withLocation *` [no longer fail](https://github.com/leanprover/lean4/pull/2917) if they close the main goal.
+
+* Implementation of a `test_extern` command for writing tests for `@[extern]` and `@[implemented_by]` functions.
+  Usage is
+  ```
+  import Lean.Util.TestExtern
+
+  test_extern Nat.add 17 37
+  ```
+  The head symbol must be the constant with the `@[extern]` or `@[implemented_by]` attribute. The return type must have a `DecidableEq` instance.
+
+Bug fixes for
+[#2853](https://github.com/leanprover/lean4/issues/2853), [#2953](https://github.com/leanprover/lean4/issues/2953), [#2966](https://github.com/leanprover/lean4/issues/2966),
+[#2971](https://github.com/leanprover/lean4/issues/2971), [#2990](https://github.com/leanprover/lean4/issues/2990), [#3094](https://github.com/leanprover/lean4/issues/3094).
+
+Bug fix for [eager evaluation of default value](https://github.com/leanprover/lean4/pull/3043) in `Option.getD`.
+Avoid [panic in `leanPosToLspPos`](https://github.com/leanprover/lean4/pull/3071) when file source is unavailable.
+Improve [short-circuiting behavior](https://github.com/leanprover/lean4/pull/2972) for `List.all` and `List.any`.
+
+Several Lake bug fixes: [#3036](https://github.com/leanprover/lean4/issues/3036), [#3064](https://github.com/leanprover/lean4/issues/3064), [#3069](https://github.com/leanprover/lean4/issues/3069).

releases/v4.6.0.md

@@ -0,0 +1,230 @@
+v4.6.0
+---------
+
+* Add custom simplification procedures (aka `simproc`s) to `simp`. Simprocs can be triggered by the simplifier on a specified term-pattern. Here is an small example:
+  ```lean
+  import Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat
+
+  def foo (x : Nat) : Nat :=
+    x + 10
+
+  /--
+  The `simproc` `reduceFoo` is invoked on terms that match the pattern `foo _`.
+  -/
+  simproc reduceFoo (foo _) :=
+    /- A term of type `Expr → SimpM Step -/
+    fun e => do
+      /-
+      The `Step` type has three constructors: `.done`, `.visit`, `.continue`.
+      * The constructor `.done` instructs `simp` that the result does
+        not need to be simplified further.
+      * The constructor `.visit` instructs `simp` to visit the resulting expression.
+      * The constructor `.continue` instructs `simp` to try other simplification procedures.
+
+      All three constructors take a `Result`. The `.continue` constructor may also take `none`.
+      `Result` has two fields `expr` (the new expression), and `proof?` (an optional proof).
+       If the new expression is definitionally equal to the input one, then `proof?` can be omitted or set to `none`.
+      -/
+      /- `simp` uses matching modulo reducibility. So, we ensure the term is a `foo`-application. -/
+      unless e.isAppOfArity ``foo 1 do
+        return .continue
+      /- `Nat.fromExpr?` tries to convert an expression into a `Nat` value -/
+      let some n ← Nat.fromExpr? e.appArg!
+        | return .continue
+      return .done { expr := Lean.mkNatLit (n+10) }
+  ```
+  We disable simprocs support by using the command `set_option simprocs false`. This command is particularly useful when porting files to v4.6.0.
+  Simprocs can be scoped, manually added to `simp` commands, and suppressed using `-`. They are also supported by `simp?`. `simp only` does not execute any `simproc`. Here are some examples for the `simproc` defined above.
+  ```lean
+  example : x + foo 2 = 12 + x := by
+    set_option simprocs false in
+      /- This `simp` command does not make progress since `simproc`s are disabled. -/
+      fail_if_success simp
+    simp_arith
+
+  example : x + foo 2 = 12 + x := by
+    /- `simp only` must not use the default simproc set. -/
+    fail_if_success simp only
+    simp_arith
+
+  example : x + foo 2 = 12 + x := by
+    /-
+    `simp only` does not use the default simproc set,
+    but we can provide simprocs as arguments. -/
+    simp only [reduceFoo]
+    simp_arith
+
+  example : x + foo 2 = 12 + x := by
+    /- We can use `-` to disable `simproc`s. -/
+    fail_if_success simp [-reduceFoo]
+    simp_arith
+  ```
+  The command `register_simp_attr <id>` now creates a `simp` **and** a `simproc` set with the name `<id>`. The following command instructs Lean to insert the `reduceFoo` simplification procedure into the set `my_simp`. If no set is specified, Lean uses the default `simp` set.
+  ```lean
+  simproc [my_simp] reduceFoo (foo _) := ...
+  ```
+
+* The syntax of the `termination_by` and `decreasing_by` termination hints is overhauled:
+
+  * They are now placed directly after the function they apply to, instead of
+    after the whole `mutual` block.
+  * Therefore, the function name no longer has to be mentioned in the hint.
+  * If the function has a `where` clause, the `termination_by` and
+    `decreasing_by` for that function come before the `where`. The
+    functions in the `where` clause can have their own termination hints, each
+    following the corresponding definition.
+  * The `termination_by` clause can only bind “extra parameters”, that are not
+    already bound by the function header, but are bound in a lambda (`:= fun x
+    y z =>`) or in patterns (`| x, n + 1 => …`). These extra parameters used to
+    be understood as a suffix of the function parameters; now it is a prefix.
+
+  Migration guide: In simple cases just remove the function name, and any
+  variables already bound at the header.
+  ```diff
+   def foo : Nat → Nat → Nat := …
+  -termination_by foo a b => a - b
+  +termination_by a b => a - b
+  ```
+  or
+  ```diff
+   def foo : Nat → Nat → Nat := …
+  -termination_by _ a b => a - b
+  +termination_by a b => a - b
+  ```
+
+  If the parameters are bound in the function header (before the `:`), remove them as well:
+  ```diff
+   def foo (a b : Nat) : Nat := …
+  -termination_by foo a b => a - b
+  +termination_by a - b
+  ```
+
+  Else, if there are multiple extra parameters, make sure to refer to the right
+  ones; the bound variables are interpreted from left to right, no longer from
+  right to left:
+  ```diff
+   def foo : Nat → Nat → Nat → Nat
+     | a, b, c => …
+  -termination_by foo b c => b
+  +termination_by a b => b
+  ```
+
+  In the case of a `mutual` block, place the termination arguments (without the
+  function name) next to the function definition:
+  ```diff
+  -mutual
+  -def foo : Nat → Nat → Nat := …
+  -def bar : Nat → Nat := …
+  -end
+  -termination_by
+  -  foo a b => a - b
+  -  bar a => a
+  +mutual
+  +def foo : Nat → Nat → Nat := …
+  +termination_by a b => a - b
+  +def bar : Nat → Nat := …
+  +termination_by a => a
+  +end
+  ```
+
+  Similarly, if you have (mutual) recursion through `where` or `let rec`, the
+  termination hints are now placed directly after the function they apply to:
+  ```diff
+  -def foo (a b : Nat) : Nat := …
+  -  where bar (x : Nat) : Nat := …
+  -termination_by
+  -  foo a b => a - b
+  -  bar x => x
+  +def foo (a b : Nat) : Nat := …
+  +termination_by a - b
+  +  where
+  +    bar (x : Nat) : Nat := …
+  +    termination_by x
+
+  -def foo (a b : Nat) : Nat :=
+  -  let rec bar (x : Nat) :  Nat := …
+  -  …
+  -termination_by
+  -  foo a b => a - b
+  -  bar x => x
+  +def foo (a b : Nat) : Nat :=
+  +  let rec bar (x : Nat) : Nat := …
+  +    termination_by x
+  +  …
+  +termination_by a - b
+  ```
+
+  In cases where a single `decreasing_by` clause applied to multiple mutually
+  recursive functions before, the tactic now has to be duplicated.
+
+* The semantics of `decreasing_by` changed; the tactic is applied to all
+  termination proof goals together, not individually.
+
+  This helps when writing termination proofs interactively, as one can focus
+  each subgoal individually, for example using `·`. Previously, the given
+  tactic script had to work for _all_ goals, and one had to resort to tactic
+  combinators like `first`:
+
+  ```diff
+   def foo (n : Nat) := … foo e1 … foo e2 …
+  -decreasing_by
+  -simp_wf
+  -first | apply something_about_e1; …
+  -      | apply something_about_e2; …
+  +decreasing_by
+  +all_goals simp_wf
+  +· apply something_about_e1; …
+  +· apply something_about_e2; …
+  ```
+
+  To obtain the old behaviour of applying a tactic to each goal individually,
+  use `all_goals`:
+  ```diff
+   def foo (n : Nat) := …
+  -decreasing_by some_tactic
+  +decreasing_by all_goals some_tactic
+  ```
+
+  In the case of mutual recursion each `decreasing_by` now applies to just its
+  function. If some functions in a recursive group do not have their own
+  `decreasing_by`, the default `decreasing_tactic` is used. If the same tactic
+  ought to be applied to multiple functions, the `decreasing_by` clause has to
+  be repeated at each of these functions.
+
+* Modify `InfoTree.context` to facilitate augmenting it with partial contexts while elaborating a command. This breaks backwards compatibility with all downstream projects that traverse the `InfoTree` manually instead of going through the functions in `InfoUtils.lean`, as well as those manually creating and saving `InfoTree`s. See [PR #3159](https://github.com/leanprover/lean4/pull/3159) for how to migrate your code.
+
+* Add language server support for [call hierarchy requests](https://www.youtube.com/watch?v=r5LA7ivUb2c) ([PR #3082](https://github.com/leanprover/lean4/pull/3082)). The change to the .ilean format in this PR means that projects must be fully rebuilt once in order to generate .ilean files with the new format before features like "find references" work correctly again.
+
+* Structure instances with multiple sources (for example `{a, b, c with x := 0}`) now have their fields filled from these sources
+  in strict left-to-right order. Furthermore, the structure instance elaborator now aggressively use sources to fill in subobject
+  fields, which prevents unnecessary eta expansion of the sources,
+  and hence greatly reduces the reliance on costly structure eta reduction. This has a large impact on mathlib,
+  reducing total CPU instructions by 3% and enabling impactful refactors like leanprover-community/mathlib4#8386
+  which reduces the build time by almost 20%.
+  See [PR #2478](https://github.com/leanprover/lean4/pull/2478) and [RFC #2451](https://github.com/leanprover/lean4/issues/2451).
+
+* Add pretty printer settings to omit deeply nested terms (`pp.deepTerms false` and `pp.deepTerms.threshold`) ([PR #3201](https://github.com/leanprover/lean4/pull/3201))
+
+* Add pretty printer options `pp.numeralTypes` and `pp.natLit`.
+  When `pp.numeralTypes` is true, then natural number literals, integer literals, and rational number literals
+  are pretty printed with type ascriptions, such as `(2 : Rat)`, `(-2 : Rat)`, and `(-2 / 3 : Rat)`.
+  When `pp.natLit` is true, then raw natural number literals are pretty printed as `nat_lit 2`.
+  [PR #2933](https://github.com/leanprover/lean4/pull/2933) and [RFC #3021](https://github.com/leanprover/lean4/issues/3021).
+
+Lake updates:
+* improved platform information & control [#3226](https://github.com/leanprover/lean4/pull/3226)
+* `lake update` from unsupported manifest versions [#3149](https://github.com/leanprover/lean4/pull/3149)
+
+Other improvements:
+* make `intro` be aware of `let_fun` [#3115](https://github.com/leanprover/lean4/pull/3115)
+* produce simpler proof terms in `rw` [#3121](https://github.com/leanprover/lean4/pull/3121)
+* fuse nested `mkCongrArg` calls in proofs generated by `simp` [#3203](https://github.com/leanprover/lean4/pull/3203)
+* `induction using` followed by a general term [#3188](https://github.com/leanprover/lean4/pull/3188)
+* allow generalization in `let` [#3060](https://github.com/leanprover/lean4/pull/3060), fixing [#3065](https://github.com/leanprover/lean4/issues/3065)
+* reducing out-of-bounds `swap!` should return `a`, not `default`` [#3197](https://github.com/leanprover/lean4/pull/3197), fixing [#3196](https://github.com/leanprover/lean4/issues/3196)
+* derive `BEq` on structure with `Prop`-fields [#3191](https://github.com/leanprover/lean4/pull/3191), fixing [#3140](https://github.com/leanprover/lean4/issues/3140)
+* refine through more `casesOnApp`/`matcherApp` [#3176](https://github.com/leanprover/lean4/pull/3176), fixing [#3175](https://github.com/leanprover/lean4/pull/3175)
+* do not strip dotted components from lean module names [#2994](https://github.com/leanprover/lean4/pull/2994), fixing [#2999](https://github.com/leanprover/lean4/issues/2999)
+* fix `deriving` only deriving the first declaration for some handlers [#3058](https://github.com/leanprover/lean4/pull/3058), fixing [#3057](https://github.com/leanprover/lean4/issues/3057)
+* do not instantiate metavariables in kabstract/rw for disallowed occurrences [#2539](https://github.com/leanprover/lean4/pull/2539), fixing [#2538](https://github.com/leanprover/lean4/issues/2538)
+* hover info for `cases h : ...` [#3084](https://github.com/leanprover/lean4/pull/3084)

releases/v4.6.1.md

@@ -0,0 +1,4 @@
+v4.6.1
+---------
+* Backport of [#3552](https://github.com/leanprover/lean4/pull/3552) fixing a performance regression
+  in server startup.

releases/v4.7.0.md

@@ -0,0 +1,186 @@
+v4.7.0
+---------
+
+* `simp` and `rw` now use instance arguments found by unification,
+  rather than always resynthesizing. For backwards compatibility, the original behaviour is
+  available via `set_option tactic.skipAssignedInstances false`.
+  [#3507](https://github.com/leanprover/lean4/pull/3507) and
+  [#3509](https://github.com/leanprover/lean4/pull/3509).
+
+* When the `pp.proofs` is false, now omitted proofs use `⋯` rather than `_`,
+  which gives a more helpful error message when copied from the Infoview.
+  The `pp.proofs.threshold` option lets small proofs always be pretty printed.
+  [#3241](https://github.com/leanprover/lean4/pull/3241).
+
+* `pp.proofs.withType` is now set to false by default to reduce noise in the info view.
+
+* The pretty printer for applications now handles the case of over-application itself when applying app unexpanders.
+  In particular, the ``| `($_ $a $b $xs*) => `(($a + $b) $xs*)`` case of an `app_unexpander` is no longer necessary.
+  [#3495](https://github.com/leanprover/lean4/pull/3495).
+
+* New `simp` (and `dsimp`) configuration option: `zetaDelta`. It is `false` by default.
+  The `zeta` option is still `true` by default, but their meaning has changed.
+  - When `zeta := true`, `simp` and `dsimp` reduce terms of the form
+    `let x := val; e[x]` into `e[val]`.
+  - When `zetaDelta := true`, `simp` and `dsimp` will expand let-variables in
+    the context. For example, suppose the context contains `x := val`. Then,
+    any occurrence of `x` is replaced with `val`.
+
+  See [issue #2682](https://github.com/leanprover/lean4/pull/2682) for additional details. Here are some examples:
+  ```
+  example (h : z = 9) : let x := 5; let y := 4; x + y = z := by
+    intro x
+    simp
+    /-
+    New goal:
+    h : z = 9; x := 5 |- x + 4 = z
+    -/
+    rw [h]
+
+  example (h : z = 9) : let x := 5; let y := 4; x + y = z := by
+    intro x
+    -- Using both `zeta` and `zetaDelta`.
+    simp (config := { zetaDelta := true })
+    /-
+    New goal:
+    h : z = 9; x := 5 |- 9 = z
+    -/
+    rw [h]
+
+  example (h : z = 9) : let x := 5; let y := 4; x + y = z := by
+    intro x
+    simp [x] -- asks `simp` to unfold `x`
+    /-
+    New goal:
+    h : z = 9; x := 5 |- 9 = z
+    -/
+    rw [h]
+
+  example (h : z = 9) : let x := 5; let y := 4; x + y = z := by
+    intro x
+    simp (config := { zetaDelta := true, zeta := false })
+    /-
+    New goal:
+    h : z = 9; x := 5 |- let y := 4; 5 + y = z
+    -/
+    rw [h]
+  ```
+
+* When adding new local theorems to `simp`, the system assumes that the function application arguments
+  have been annotated with `no_index`. This modification, which addresses [issue #2670](https://github.com/leanprover/lean4/issues/2670),
+  restores the Lean 3 behavior that users expect. With this modification, the following examples are now operational:
+  ```
+  example {α β : Type} {f : α × β → β → β} (h : ∀ p : α × β, f p p.2 = p.2)
+    (a : α) (b : β) : f (a, b) b = b := by
+    simp [h]
+
+  example {α β : Type} {f : α × β → β → β}
+    (a : α) (b : β) (h : f (a,b) (a,b).2 = (a,b).2) : f (a, b) b = b := by
+    simp [h]
+  ```
+  In both cases, `h` is applicable because `simp` does not index f-arguments anymore when adding `h` to the `simp`-set.
+  It's important to note, however, that global theorems continue to be indexed in the usual manner.
+
+* Improved the error messages produced by the `decide` tactic. [#3422](https://github.com/leanprover/lean4/pull/3422)
+
+* Improved auto-completion performance. [#3460](https://github.com/leanprover/lean4/pull/3460)
+
+* Improved initial language server startup performance. [#3552](https://github.com/leanprover/lean4/pull/3552)
+
+* Changed call hierarchy to sort entries and strip private header from names displayed in the call hierarchy. [#3482](https://github.com/leanprover/lean4/pull/3482)
+
+* There is now a low-level error recovery combinator in the parsing framework, primarily intended for DSLs. [#3413](https://github.com/leanprover/lean4/pull/3413)
+
+* You can now write `termination_by?` after a declaration to see the automatically inferred
+  termination argument, and turn it into a `termination_by …` clause using the “Try this” widget or a code action. [#3514](https://github.com/leanprover/lean4/pull/3514)
+
+* A large fraction of `Std` has been moved into the Lean repository.
+  This was motivated by:
+  1. Making universally useful tactics such as `ext`, `by_cases`, `change at`,
+    `norm_cast`, `rcases`, `simpa`, `simp?`, `omega`, and `exact?`
+    available to all users of Lean, without imports.
+  2. Minimizing the syntactic changes between plain Lean and Lean with `import Std`.
+  3. Simplifying the development process for the basic data types
+     `Nat`, `Int`, `Fin` (and variants such as `UInt64`), `List`, `Array`,
+     and `BitVec` as we begin making the APIs and simp normal forms for these types
+     more complete and consistent.
+  4. Laying the groundwork for the Std roadmap, as a library focused on
+     essential datatypes not provided by the core language (e.g. `RBMap`)
+     and utilities such as basic IO.
+  While we have achieved most of our initial aims in `v4.7.0-rc1`,
+  some upstreaming will continue over the coming months.
+
+* The `/` and `%` notations in `Int` now use `Int.ediv` and `Int.emod`
+  (i.e. the rounding conventions have changed).
+  Previously `Std` overrode these notations, so this is no change for users of `Std`.
+  There is now kernel support for these functions.
+  [#3376](https://github.com/leanprover/lean4/pull/3376).
+
+* `omega`, our integer linear arithmetic tactic, is now available in the core language.
+  * It is supplemented by a preprocessing tactic `bv_omega` which can solve goals about `BitVec`
+    which naturally translate into linear arithmetic problems.
+    [#3435](https://github.com/leanprover/lean4/pull/3435).
+  * `omega` now has support for `Fin` [#3427](https://github.com/leanprover/lean4/pull/3427),
+    the `<<<` operator [#3433](https://github.com/leanprover/lean4/pull/3433).
+  * During the port `omega` was modified to no longer identify atoms up to definitional equality
+    (so in particular it can no longer prove `id x ≤ x`). [#3525](https://github.com/leanprover/lean4/pull/3525).
+    This may cause some regressions.
+    We plan to provide a general purpose preprocessing tactic later, or an `omega!` mode.
+  * `omega` is now invoked in Lean's automation for termination proofs
+    [#3503](https://github.com/leanprover/lean4/pull/3503) as well as in
+    array indexing proofs [#3515](https://github.com/leanprover/lean4/pull/3515).
+    This automation will be substantially revised in the medium term,
+    and while `omega` does help automate some proofs, we plan to make this much more robust.
+
+* The library search tactics `exact?` and `apply?` that were originally in
+  Mathlib are now available in Lean itself.  These use the implementation using
+  lazy discrimination trees from `Std`, and thus do not require a disk cache but
+  have a slightly longer startup time.  The order used for selection lemmas has
+  changed as well to favor goals purely based on how many terms in the head
+  pattern match the current goal.
+
+* The `solve_by_elim` tactic has been ported from `Std` to Lean so that library
+  search can use it.
+
+* New `#check_tactic` and `#check_simp` commands have been added.  These are
+  useful for checking tactics (particularly `simp`) behave as expected in test
+  suites.
+
+* Previously, app unexpanders would only be applied to entire applications. However, some notations produce
+  functions, and these functions can be given additional arguments. The solution so far has been to write app unexpanders so that they can take an arbitrary number of additional arguments. However this leads to misleading hover information in the Infoview. For example, while `HAdd.hAdd f g 1` pretty prints as `(f + g) 1`, hovering over `f + g` shows `f`. There is no way to fix the situation from within an app unexpander; the expression position for `HAdd.hAdd f g` is absent, and app unexpanders cannot register TermInfo.
+
+  This commit changes the app delaborator to try running app unexpanders on every prefix of an application, from longest to shortest prefix. For efficiency, it is careful to only try this when app delaborators do in fact exist for the head constant, and it also ensures arguments are only delaborated once. Then, in `(f + g) 1`, the `f + g` gets TermInfo registered for that subexpression, making it properly hoverable.
+
+  [#3375](https://github.com/leanprover/lean4/pull/3375)
+
+Breaking changes:
+* `Lean.withTraceNode` and variants got a stronger `MonadAlwaysExcept` assumption to
+  fix trace trees not being built on elaboration runtime exceptions. Instances for most elaboration
+  monads built on `EIO Exception` should be synthesized automatically.
+* The `match ... with.` and `fun.` notations previously in Std have been replaced by
+  `nomatch ...` and `nofun`. [#3279](https://github.com/leanprover/lean4/pull/3279) and [#3286](https://github.com/leanprover/lean4/pull/3286)
+
+
+Other improvements:
+* several bug fixes for `simp`:
+  * we should not crash when `simp` loops [#3269](https://github.com/leanprover/lean4/pull/3269)
+  * `simp` gets stuck on `autoParam` [#3315](https://github.com/leanprover/lean4/pull/3315)
+  * `simp` fails when custom discharger makes no progress [#3317](https://github.com/leanprover/lean4/pull/3317)
+  * `simp` fails to discharge `autoParam` premises even when it can reduce them to `True` [#3314](https://github.com/leanprover/lean4/pull/3314)
+  * `simp?` suggests generated equations lemma names, fixes [#3547](https://github.com/leanprover/lean4/pull/3547) [#3573](https://github.com/leanprover/lean4/pull/3573)
+* fixes for `match` expressions:
+  * fix regression with builtin literals [#3521](https://github.com/leanprover/lean4/pull/3521)
+  * accept `match` when patterns cover all cases of a `BitVec` finite type [#3538](https://github.com/leanprover/lean4/pull/3538)
+  * fix matching `Int` literals [#3504](https://github.com/leanprover/lean4/pull/3504)
+  * patterns containing int values and constructors [#3496](https://github.com/leanprover/lean4/pull/3496)
+* improve `termination_by` error messages [#3255](https://github.com/leanprover/lean4/pull/3255)
+* fix `rename_i` in macros, fixes [#3553](https://github.com/leanprover/lean4/pull/3553) [#3581](https://github.com/leanprover/lean4/pull/3581)
+* fix excessive resource usage in `generalize`, fixes [#3524](https://github.com/leanprover/lean4/pull/3524) [#3575](https://github.com/leanprover/lean4/pull/3575)
+* an equation lemma with autoParam arguments fails to rewrite, fixing [#2243](https://github.com/leanprover/lean4/pull/2243) [#3316](https://github.com/leanprover/lean4/pull/3316)
+* `add_decl_doc` should check that declarations are local [#3311](https://github.com/leanprover/lean4/pull/3311)
+* instantiate the types of inductives with the right parameters, closing [#3242](https://github.com/leanprover/lean4/pull/3242) [#3246](https://github.com/leanprover/lean4/pull/3246)
+* New simprocs for many basic types. [#3407](https://github.com/leanprover/lean4/pull/3407)
+
+Lake fixes:
+* Warn on fetch cloud release failure [#3401](https://github.com/leanprover/lean4/pull/3401)
+* Cloud release trace & `lake build :release` errors [#3248](https://github.com/leanprover/lean4/pull/3248)

releases/v4.8.0.md

@@ -0,0 +1,494 @@
+v4.8.0
+---------
+
+### Language features, tactics, and metaprograms
+
+* **Functional induction principles.**
+  [#3432](https://github.com/leanprover/lean4/pull/3432), [#3620](https://github.com/leanprover/lean4/pull/3620),
+  [#3754](https://github.com/leanprover/lean4/pull/3754), [#3762](https://github.com/leanprover/lean4/pull/3762),
+  [#3738](https://github.com/leanprover/lean4/pull/3738), [#3776](https://github.com/leanprover/lean4/pull/3776),
+  [#3898](https://github.com/leanprover/lean4/pull/3898).
+
+  Derived from the definition of a (possibly mutually) recursive function,
+  a **functional induction principle** is created that is tailored to proofs about that function.
+
+  For example from:
+  ```
+  def ackermann : Nat → Nat → Nat
+    | 0, m => m + 1
+    | n+1, 0 => ackermann n 1
+    | n+1, m+1 => ackermann n (ackermann (n + 1) m)
+  ```
+  we get
+  ```
+  ackermann.induct (motive : Nat → Nat → Prop) (case1 : ∀ (m : Nat), motive 0 m)
+    (case2 : ∀ (n : Nat), motive n 1 → motive (Nat.succ n) 0)
+    (case3 : ∀ (n m : Nat), motive (n + 1) m → motive n (ackermann (n + 1) m) → motive (Nat.succ n) (Nat.succ m))
+    (x x : Nat) : motive x x
+  ```
+
+  It can be used in the `induction` tactic using the `using` syntax:
+  ```
+  induction n, m using ackermann.induct
+  ```
+* The termination checker now recognizes more recursion patterns without an
+  explicit `termination_by`. In particular the idiom of counting up to an upper
+  bound, as in
+  ```
+  def Array.sum (arr : Array Nat) (i acc : Nat) : Nat :=
+    if _ : i < arr.size then
+      Array.sum arr (i+1) (acc + arr[i])
+    else
+      acc
+  ```
+  is recognized without having to say `termination_by arr.size - i`.
+  * [#3630](https://github.com/leanprover/lean4/pull/3630) makes `termination_by?` not use `sizeOf` when not needed
+  * [#3652](https://github.com/leanprover/lean4/pull/3652) improves the `termination_by` syntax.
+  * [#3658](https://github.com/leanprover/lean4/pull/3658) changes how termination arguments are elaborated.
+  * [#3665](https://github.com/leanprover/lean4/pull/3665) refactors GuessLex to allow inferring more complex termination arguments
+  * [#3666](https://github.com/leanprover/lean4/pull/3666) infers termination arguments such as `xs.size - i`
+* [#3629](https://github.com/leanprover/lean4/pull/3629),
+  [#3655](https://github.com/leanprover/lean4/pull/3655),
+  [#3747](https://github.com/leanprover/lean4/pull/3747):
+  Adds `@[induction_eliminator]` and `@[cases_eliminator]` attributes to be able to define custom eliminators
+  for the `induction` and `cases` tactics, replacing the `@[eliminator]` attribute.
+  Gives custom eliminators for `Nat` so that `induction` and `cases` put goal states into terms of `0` and `n + 1`
+  rather than `Nat.zero` and `Nat.succ n`.
+  Added option `tactic.customEliminators` to control whether to use custom eliminators.
+  Added a hack for `rcases`/`rintro`/`obtain` to use the custom eliminator for `Nat`.
+* **Shorter instances names.** There is a new algorithm for generating names for anonymous instances.
+  Across Std and Mathlib, the median ratio between lengths of new names and of old names is about 72%.
+  With the old algorithm, the longest name was 1660 characters, and now the longest name is 202 characters.
+  The new algorithm's 95th percentile name length is 67 characters, versus 278 for the old algorithm.
+  While the new algorithm produces names that are 1.2% less unique,
+  it avoids cross-project collisions by adding a module-based suffix
+  when it does not refer to declarations from the same "project" (modules that share the same root).
+  [#3089](https://github.com/leanprover/lean4/pull/3089)
+  and [#3934](https://github.com/leanprover/lean4/pull/3934).
+* [8d2adf](https://github.com/leanprover/lean4/commit/8d2adf521d2b7636347a5b01bfe473bf0fcfaf31)
+  Importing two different files containing proofs of the same theorem is no longer considered an error.
+  This feature is particularly useful for theorems that are automatically generated on demand (e.g., equational theorems).
+* [84b091](https://github.com/leanprover/lean4/commit/84b0919a116e9be12f933e764474f45d964ce85c)
+  Lean now generates an error if the type of a theorem is **not** a proposition.
+* **Definition transparency.** [47a343](https://github.com/leanprover/lean4/commit/47a34316fc03ce936fddd2d3dce44784c5bcdfa9). `@[reducible]`, `@[semireducible]`, and `@[irreducible]` are now scoped and able to be set for imported declarations.
+* `simp`/`dsimp`
+  * [#3607](https://github.com/leanprover/lean4/pull/3607) enables kernel projection reduction in `dsimp`
+  * [b24fbf](https://github.com/leanprover/lean4/commit/b24fbf44f3aaa112f5d799ef2a341772d1eb222d)
+    and [acdb00](https://github.com/leanprover/lean4/commit/acdb0054d5a0efa724cff596ac26852fad5724c4):
+    `dsimproc` command
+    to define defeq-preserving simplification procedures.
+  * [#3624](https://github.com/leanprover/lean4/pull/3624) makes `dsimp` normalize raw nat literals as `OfNat.ofNat` applications.
+  * [#3628](https://github.com/leanprover/lean4/pull/3628) makes `simp` correctly handle `OfScientific.ofScientific` literals.
+  * [#3654](https://github.com/leanprover/lean4/pull/3654) makes `dsimp?` report used simprocs.
+  * [dee074](https://github.com/leanprover/lean4/commit/dee074dcde03a37b7895a4901df2e4fa490c73c7) fixes equation theorem
+    handling in `simp` for non-recursive definitions.
+  * [#3819](https://github.com/leanprover/lean4/pull/3819) improved performance when simp encounters a loop.
+  * [#3821](https://github.com/leanprover/lean4/pull/3821) fixes discharger/cache interaction.
+  * [#3824](https://github.com/leanprover/lean4/pull/3824) keeps `simp` from breaking `Char` literals.
+  * [#3838](https://github.com/leanprover/lean4/pull/3838) allows `Nat` instances matching to be more lenient.
+  * [#3870](https://github.com/leanprover/lean4/pull/3870) documentation for `simp` configuration options.
+  * [#3972](https://github.com/leanprover/lean4/pull/3972) fixes simp caching.
+  * [#4044](https://github.com/leanprover/lean4/pull/4044) improves cache behavior for "well-behaved" dischargers.
+* `omega`
+  * [#3639](https://github.com/leanprover/lean4/pull/3639), [#3766](https://github.com/leanprover/lean4/pull/3766),
+    [#3853](https://github.com/leanprover/lean4/pull/3853), [#3875](https://github.com/leanprover/lean4/pull/3875):
+    introduces a term canonicalizer.
+  * [#3736](https://github.com/leanprover/lean4/pull/3736) improves handling of positivity for the modulo operator for `Int`.
+  * [#3828](https://github.com/leanprover/lean4/pull/3828) makes it work as a `simp` discharger.
+  * [#3847](https://github.com/leanprover/lean4/pull/3847) adds helpful error messages.
+* `rfl`
+  * [#3671](https://github.com/leanprover/lean4/pull/3671), [#3708](https://github.com/leanprover/lean4/pull/3708): upstreams the `@[refl]` attribute and the `rfl` tactic.
+  * [#3751](https://github.com/leanprover/lean4/pull/3751) makes `apply_rfl` not operate on `Eq` itself.
+  * [#4067](https://github.com/leanprover/lean4/pull/4067) improves error message when there are no goals.
+* [#3719](https://github.com/leanprover/lean4/pull/3719) upstreams the `rw?` tactic, with fixes and improvements in
+  [#3783](https://github.com/leanprover/lean4/pull/3783), [#3794](https://github.com/leanprover/lean4/pull/3794),
+  [#3911](https://github.com/leanprover/lean4/pull/3911).
+* `conv`
+  * [#3659](https://github.com/leanprover/lean4/pull/3659) adds a `conv` version of the `calc` tactic.
+  * [#3763](https://github.com/leanprover/lean4/pull/3763) makes `conv` clean up using `try with_reducible rfl` instead of `try rfl`.
+* `#guard_msgs`
+  * [#3617](https://github.com/leanprover/lean4/pull/3617) introduces whitespace protection using the `⏎` character.
+  * [#3883](https://github.com/leanprover/lean4/pull/3883):
+    The `#guard_msgs` command now has options to change whitespace normalization and sensitivity to message ordering.
+    For example, `#guard_msgs (whitespace := lax) in cmd` collapses whitespace before checking messages,
+    and `#guard_msgs (ordering := sorted) in cmd` sorts the messages in lexicographic order before checking.
+  * [#3931](https://github.com/leanprover/lean4/pull/3931) adds an unused variables ignore function for `#guard_msgs`.
+  * [#3912](https://github.com/leanprover/lean4/pull/3912) adds a diff between the expected and actual outputs. This feature is currently
+    disabled by default, but can be enabled with `set_option guard_msgs.diff true`.
+    Depending on user feedback, this option may default to `true` in a future version of Lean.
+* `do` **notation**
+  * [#3820](https://github.com/leanprover/lean4/pull/3820) makes it an error to lift `(<- ...)` out of a pure `if ... then ... else ...`
+* **Lazy discrimination trees**
+  * [#3610](https://github.com/leanprover/lean4/pull/3610) fixes a name collision for `LazyDiscrTree` that could lead to cache poisoning.
+  * [#3677](https://github.com/leanprover/lean4/pull/3677) simplifies and fixes `LazyDiscrTree` handling for `exact?`/`apply?`.
+  * [#3685](https://github.com/leanprover/lean4/pull/3685) moves general `exact?`/`apply?` functionality into `LazyDiscrTree`.
+  * [#3769](https://github.com/leanprover/lean4/pull/3769) has lemma selection improvements for `rw?` and `LazyDiscrTree`.
+  * [#3818](https://github.com/leanprover/lean4/pull/3818) improves ordering of matches.
+* [#3590](https://github.com/leanprover/lean4/pull/3590) adds `inductive.autoPromoteIndices` option to be able to disable auto promotion of indices in the `inductive` command.
+* **Miscellaneous bug fixes and improvements**
+  * [#3606](https://github.com/leanprover/lean4/pull/3606) preserves `cache` and `dischargeDepth` fields in `Lean.Meta.Simp.Result.mkEqSymm`.
+  * [#3633](https://github.com/leanprover/lean4/pull/3633) makes `elabTermEnsuringType` respect `errToSorry`, improving error recovery of the `have` tactic.
+  * [#3647](https://github.com/leanprover/lean4/pull/3647) enables `noncomputable unsafe` definitions, for deferring implementations until later.
+  * [#3672](https://github.com/leanprover/lean4/pull/3672) adjust namespaces of tactics.
+  * [#3725](https://github.com/leanprover/lean4/pull/3725) fixes `Ord` derive handler for indexed inductive types with unused alternatives.
+  * [#3893](https://github.com/leanprover/lean4/pull/3893) improves performance of derived `Ord` instances.
+  * [#3771](https://github.com/leanprover/lean4/pull/3771) changes error reporting for failing tactic macros. Improves `rfl` error message.
+  * [#3745](https://github.com/leanprover/lean4/pull/3745) fixes elaboration of generalized field notation if the object of the notation is an optional parameter.
+  * [#3799](https://github.com/leanprover/lean4/pull/3799) makes commands such as `universe`, `variable`, `namespace`, etc. require that their argument appear in a later column.
+    Commands that can optionally parse an `ident` or parse any number of `ident`s generally should require
+    that the `ident` use `colGt`. This keeps typos in commands from being interpreted as identifiers.
+  * [#3815](https://github.com/leanprover/lean4/pull/3815) lets the `split` tactic be used for writing code.
+  * [#3822](https://github.com/leanprover/lean4/pull/3822) adds missing info in `induction` tactic for `with` clauses of the form `| cstr a b c => ?_`.
+  * [#3806](https://github.com/leanprover/lean4/pull/3806) fixes `withSetOptionIn` combinator.
+  * [#3844](https://github.com/leanprover/lean4/pull/3844) removes unused `trace.Elab.syntax` option.
+  * [#3896](https://github.com/leanprover/lean4/pull/3896) improves hover and go-to-def for `attribute` command.
+  * [#3989](https://github.com/leanprover/lean4/pull/3989) makes linter options more discoverable.
+  * [#3916](https://github.com/leanprover/lean4/pull/3916) fixes go-to-def for syntax defined with `@[builtin_term_parser]`.
+  * [#3962](https://github.com/leanprover/lean4/pull/3962) fixes how `solveByElim` handles `symm` lemmas, making `exact?`/`apply?` usable again.
+  * [#3968](https://github.com/leanprover/lean4/pull/3968) improves the `@[deprecated]` attribute, adding `(since := "<date>")` field.
+  * [#3768](https://github.com/leanprover/lean4/pull/3768) makes `#print` command show structure fields.
+  * [#3974](https://github.com/leanprover/lean4/pull/3974) makes `exact?%` behave like `by exact?` rather than `by apply?`.
+  * [#3994](https://github.com/leanprover/lean4/pull/3994) makes elaboration of `he ▸ h` notation more predictable.
+  * [#3991](https://github.com/leanprover/lean4/pull/3991) adjusts transparency for `decreasing_trivial` macros.
+  * [#4092](https://github.com/leanprover/lean4/pull/4092) improves performance of `binop%` and `binrel%` expression tree elaborators.
+* **Docs:** [#3748](https://github.com/leanprover/lean4/pull/3748), [#3796](https://github.com/leanprover/lean4/pull/3796),
+[#3800](https://github.com/leanprover/lean4/pull/3800), [#3874](https://github.com/leanprover/lean4/pull/3874),
+[#3863](https://github.com/leanprover/lean4/pull/3863), [#3862](https://github.com/leanprover/lean4/pull/3862),
+[#3891](https://github.com/leanprover/lean4/pull/3891), [#3873](https://github.com/leanprover/lean4/pull/3873),
+[#3908](https://github.com/leanprover/lean4/pull/3908), [#3872](https://github.com/leanprover/lean4/pull/3872).
+
+### Language server and IDE extensions
+
+* [#3602](https://github.com/leanprover/lean4/pull/3602) enables `import` auto-completions.
+* [#3608](https://github.com/leanprover/lean4/pull/3608) fixes issue [leanprover/vscode-lean4#392](https://github.com/leanprover/vscode-lean4/issues/392).
+  Diagnostic ranges had an off-by-one error that would misplace goal states for example.
+* [#3014](https://github.com/leanprover/lean4/pull/3014) introduces snapshot trees, foundational work for incremental tactics and parallelism.
+  [#3849](https://github.com/leanprover/lean4/pull/3849) adds basic incrementality API.
+* [#3271](https://github.com/leanprover/lean4/pull/3271) adds support for server-to-client requests.
+* [#3656](https://github.com/leanprover/lean4/pull/3656) fixes jump to definition when there are conflicting names from different files.
+  Fixes issue [#1170](https://github.com/leanprover/lean4/issues/1170).
+* [#3691](https://github.com/leanprover/lean4/pull/3691), [#3925](https://github.com/leanprover/lean4/pull/3925),
+  [#3932](https://github.com/leanprover/lean4/pull/3932) keep semantic tokens synchronized (used for semantic highlighting), with performance improvements.
+* [#3247](https://github.com/leanprover/lean4/pull/3247) and [#3730](https://github.com/leanprover/lean4/pull/3730)
+  add diagnostics to run "Restart File" when a file dependency is saved.
+* [#3722](https://github.com/leanprover/lean4/pull/3722) uses the correct module names when displaying references.
+* [#3728](https://github.com/leanprover/lean4/pull/3728) makes errors in header reliably appear and makes the "Import out of date" warning be at "hint" severity.
+  [#3739](https://github.com/leanprover/lean4/pull/3739) simplifies the text of this warning.
+* [#3778](https://github.com/leanprover/lean4/pull/3778) fixes [#3462](https://github.com/leanprover/lean4/issues/3462),
+  where info nodes from before the cursor would be used for computing completions.
+* [#3985](https://github.com/leanprover/lean4/pull/3985) makes trace timings appear in Infoview.
+
+### Pretty printing
+
+* [#3797](https://github.com/leanprover/lean4/pull/3797) fixes the hovers over binders so that they show their types.
+* [#3640](https://github.com/leanprover/lean4/pull/3640) and [#3735](https://github.com/leanprover/lean4/pull/3735): Adds attribute `@[pp_using_anonymous_constructor]` to make structures pretty print as `⟨x, y, z⟩`
+  rather than as `{a := x, b := y, c := z}`.
+  This attribute is applied to `Sigma`, `PSigma`, `PProd`, `Subtype`, `And`, and `Fin`.
+* [#3749](https://github.com/leanprover/lean4/pull/3749)
+  Now structure instances pretty print with parent structures' fields inlined.
+  That is, if `B` extends `A`, then `{ toA := { x := 1 }, y := 2 }` now pretty prints as `{ x := 1, y := 2 }`.
+  Setting option `pp.structureInstances.flatten` to false turns this off.
+* [#3737](https://github.com/leanprover/lean4/pull/3737), [#3744](https://github.com/leanprover/lean4/pull/3744)
+  and [#3750](https://github.com/leanprover/lean4/pull/3750):
+  Option `pp.structureProjections` is renamed to `pp.fieldNotation`, and there is now a suboption `pp.fieldNotation.generalized`
+  to enable pretty printing function applications using generalized field notation (defaults to true).
+  Field notation can be disabled on a function-by-function basis using the `@[pp_nodot]` attribute.
+  The notation is not used for theorems.
+* [#4071](https://github.com/leanprover/lean4/pull/4071) fixes interaction between app unexpanders and `pp.fieldNotation.generalized`
+* [#3625](https://github.com/leanprover/lean4/pull/3625) makes `delabConstWithSignature` (used by `#check`) have the ability to put arguments "after the colon"
+  to avoid printing inaccessible names.
+* [#3798](https://github.com/leanprover/lean4/pull/3798),
+  [#3978](https://github.com/leanprover/lean4/pull/3978),
+  [#3798](https://github.com/leanprover/lean4/pull/3980):
+  Adds options `pp.mvars` (default: true) and `pp.mvars.withType` (default: false).
+  When `pp.mvars` is false, expression metavariables pretty print as `?_` and universe metavariables pretty print as `_`.
+  When `pp.mvars.withType` is true, expression metavariables pretty print with a type ascription.
+  These can be set when using `#guard_msgs` to make tests not depend on the particular names of metavariables.
+* [#3917](https://github.com/leanprover/lean4/pull/3917) makes binders hoverable and gives them docstrings.
+* [#4034](https://github.com/leanprover/lean4/pull/4034) makes hovers for RHS terms in `match` expressions in the Infoview reliably show the correct term.
+
+### Library
+
+* `Bool`/`Prop`
+  * [#3508](https://github.com/leanprover/lean4/pull/3508) improves `simp` confluence for `Bool` and `Prop` terms.
+  * Theorems: [#3604](https://github.com/leanprover/lean4/pull/3604)
+* `Nat`
+  * [#3579](https://github.com/leanprover/lean4/pull/3579) makes `Nat.succ_eq_add_one` be a simp lemma, now that `induction`/`cases` uses `n + 1` instead of `Nat.succ n`.
+  * [#3808](https://github.com/leanprover/lean4/pull/3808) replaces `Nat.succ` simp rules with simprocs.
+  * [#3876](https://github.com/leanprover/lean4/pull/3876) adds faster `Nat.repr` implementation in C.
+* `Int`
+  * Theorems: [#3890](https://github.com/leanprover/lean4/pull/3890)
+* `UInt`s
+  * [#3960](https://github.com/leanprover/lean4/pull/3960) improves performance of upcasting.
+* `Array` and `Subarray`
+  * [#3676](https://github.com/leanprover/lean4/pull/3676) removes `Array.eraseIdxAux`, `Array.eraseIdxSzAux`, and `Array.eraseIdx'`.
+  * [#3648](https://github.com/leanprover/lean4/pull/3648) simplifies `Array.findIdx?`.
+  * [#3851](https://github.com/leanprover/lean4/pull/3851) renames fields of `Subarray`.
+* `List`
+  * [#3785](https://github.com/leanprover/lean4/pull/3785) upstreams tail-recursive List operations and `@[csimp]` lemmas.
+* `BitVec`
+  * Theorems: [#3593](https://github.com/leanprover/lean4/pull/3593),
+  [#3593](https://github.com/leanprover/lean4/pull/3593), [#3597](https://github.com/leanprover/lean4/pull/3597),
+  [#3598](https://github.com/leanprover/lean4/pull/3598), [#3721](https://github.com/leanprover/lean4/pull/3721),
+  [#3729](https://github.com/leanprover/lean4/pull/3729), [#3880](https://github.com/leanprover/lean4/pull/3880),
+  [#4039](https://github.com/leanprover/lean4/pull/4039).
+  * [#3884](https://github.com/leanprover/lean4/pull/3884) protects `Std.BitVec`.
+* `String`
+  * [#3832](https://github.com/leanprover/lean4/pull/3832) fixes `String.splitOn`.
+  * [#3959](https://github.com/leanprover/lean4/pull/3959) adds `String.Pos.isValid`.
+  * [#3959](https://github.com/leanprover/lean4/pull/3959) UTF-8 string validation.
+  * [#3961](https://github.com/leanprover/lean4/pull/3961) adds a model implementation for UTF-8 encoding and decoding.
+* `IO`
+  * [#4097](https://github.com/leanprover/lean4/pull/4097) adds `IO.getTaskState` which returns whether a task is finished, actively running, or waiting on other Tasks to finish.
+
+* **Refactors**
+  * [#3605](https://github.com/leanprover/lean4/pull/3605) reduces imports for `Init.Data.Nat` and `Init.Data.Int`.
+  * [#3613](https://github.com/leanprover/lean4/pull/3613) reduces imports for `Init.Omega.Int`.
+  * [#3634](https://github.com/leanprover/lean4/pull/3634) upstreams `Std.Data.Nat`
+    and [#3635](https://github.com/leanprover/lean4/pull/3635) upstreams `Std.Data.Int`.
+  * [#3790](https://github.com/leanprover/lean4/pull/3790) reduces more imports for `omega`.
+  * [#3694](https://github.com/leanprover/lean4/pull/3694) extends `GetElem` interface with `getElem!` and `getElem?` to simplify containers like `RBMap`.
+  * [#3865](https://github.com/leanprover/lean4/pull/3865) renames `Option.toMonad` (see breaking changes below).
+  * [#3882](https://github.com/leanprover/lean4/pull/3882) unifies `lexOrd` with `compareLex`.
+* **Other fixes or improvements**
+  * [#3765](https://github.com/leanprover/lean4/pull/3765) makes `Quotient.sound` be a `theorem`.
+  * [#3645](https://github.com/leanprover/lean4/pull/3645) fixes `System.FilePath.parent` in the case of absolute paths.
+  * [#3660](https://github.com/leanprover/lean4/pull/3660) `ByteArray.toUInt64LE!` and `ByteArray.toUInt64BE!` were swapped.
+  * [#3881](https://github.com/leanprover/lean4/pull/3881), [#3887](https://github.com/leanprover/lean4/pull/3887) fix linearity issues in `HashMap.insertIfNew`, `HashSet.erase`, and `HashMap.erase`.
+    The `HashMap.insertIfNew` fix improves `import` performance.
+  * [#3830](https://github.com/leanprover/lean4/pull/3830) ensures linearity in `Parsec.many*Core`.
+  * [#3930](https://github.com/leanprover/lean4/pull/3930) adds `FS.Stream.isTty` field.
+  * [#3866](https://github.com/leanprover/lean4/pull/3866) deprecates `Option.toBool` in favor of `Option.isSome`.
+  * [#3975](https://github.com/leanprover/lean4/pull/3975) upstreams `Data.List.Init` and `Data.Array.Init` material from Std.
+  * [#3942](https://github.com/leanprover/lean4/pull/3942) adds instances that make `ac_rfl` work without Mathlib.
+  * [#4010](https://github.com/leanprover/lean4/pull/4010) changes `Fin.induction` to use structural induction.
+  * [02753f](https://github.com/leanprover/lean4/commit/02753f6e4c510c385efcbf71fa9a6bec50fce9ab)
+    fixes bug in `reduceLeDiff` simproc.
+  * [#4097](https://github.com/leanprover/lean4/pull/4097)
+    adds `IO.TaskState` and `IO.getTaskState` to get the task from the Lean runtime's task manager.
+* **Docs:** [#3615](https://github.com/leanprover/lean4/pull/3615), [#3664](https://github.com/leanprover/lean4/pull/3664),
+  [#3707](https://github.com/leanprover/lean4/pull/3707), [#3734](https://github.com/leanprover/lean4/pull/3734),
+  [#3868](https://github.com/leanprover/lean4/pull/3868), [#3861](https://github.com/leanprover/lean4/pull/3861),
+  [#3869](https://github.com/leanprover/lean4/pull/3869), [#3858](https://github.com/leanprover/lean4/pull/3858),
+  [#3856](https://github.com/leanprover/lean4/pull/3856), [#3857](https://github.com/leanprover/lean4/pull/3857),
+  [#3867](https://github.com/leanprover/lean4/pull/3867), [#3864](https://github.com/leanprover/lean4/pull/3864),
+  [#3860](https://github.com/leanprover/lean4/pull/3860), [#3859](https://github.com/leanprover/lean4/pull/3859),
+  [#3871](https://github.com/leanprover/lean4/pull/3871), [#3919](https://github.com/leanprover/lean4/pull/3919).
+
+### Lean internals
+
+* **Defeq and WHNF algorithms**
+  * [#3616](https://github.com/leanprover/lean4/pull/3616) gives better support for reducing `Nat.rec` expressions.
+  * [#3774](https://github.com/leanprover/lean4/pull/3774) add tracing for "non-easy" WHNF cases.
+  * [#3807](https://github.com/leanprover/lean4/pull/3807) fixes an `isDefEq` performance issue, now trying structure eta *after* lazy delta reduction.
+  * [#3816](https://github.com/leanprover/lean4/pull/3816) fixes `.yesWithDeltaI` behavior to prevent increasing transparency level when reducing projections.
+  * [#3837](https://github.com/leanprover/lean4/pull/3837) improves heuristic at `isDefEq`.
+  * [#3965](https://github.com/leanprover/lean4/pull/3965) improves `isDefEq` for constraints of the form `t.i =?= s.i`.
+  * [#3977](https://github.com/leanprover/lean4/pull/3977) improves `isDefEqProj`.
+  * [#3981](https://github.com/leanprover/lean4/pull/3981) adds universe constraint approximations to be able to solve `u =?= max u ?v` using `?v = u`.
+    These approximations are only applied when universe constraints cannot be postponed anymore.
+  * [#4004](https://github.com/leanprover/lean4/pull/4004) improves `isDefEqProj` during typeclass resolution.
+  * [#4012](https://github.com/leanprover/lean4/pull/4012) adds `backward.isDefEq.lazyProjDelta` and `backward.isDefEq.lazyWhnfCore` backwards compatibility flags.
+* **Kernel**
+  * [#3966](https://github.com/leanprover/lean4/pull/3966) removes dead code.
+  * [#4035](https://github.com/leanprover/lean4/pull/4035) fixes mismatch for `TheoremVal` between Lean and C++.
+* **Discrimination trees**
+  * [423fed](https://github.com/leanprover/lean4/commit/423fed79a9de75705f34b3e8648db7e076c688d7)
+    and [3218b2](https://github.com/leanprover/lean4/commit/3218b25974d33e92807af3ce42198911c256ff1d):
+    simplify handling of dependent/non-dependent pi types.
+* **Typeclass instance synthesis**
+  * [#3638](https://github.com/leanprover/lean4/pull/3638) eta-reduces synthesized instances
+  * [ce350f](https://github.com/leanprover/lean4/commit/ce350f348161e63fccde6c4a5fe1fd2070e7ce0f) fixes a linearity issue
+  * [917a31](https://github.com/leanprover/lean4/commit/917a31f694f0db44d6907cc2b1485459afe74d49)
+    improves performance by considering at most one answer for subgoals not containing metavariables.
+    [#4008](https://github.com/leanprover/lean4/pull/4008) adds `backward.synthInstance.canonInstances` backward compatibility flag.
+* **Definition processing**
+  * [#3661](https://github.com/leanprover/lean4/pull/3661), [#3767](https://github.com/leanprover/lean4/pull/3767) changes automatically generated equational theorems to be named
+    using suffix `.eq_<idx>` instead of `._eq_<idx>`, and `.eq_def` instead of `._unfold`. (See breaking changes below.)
+    [#3675](https://github.com/leanprover/lean4/pull/3675) adds a mechanism to reserve names.
+    [#3803](https://github.com/leanprover/lean4/pull/3803) fixes reserved name resolution inside namespaces and fixes handling of `match`er declarations and equation lemmas.
+  * [#3662](https://github.com/leanprover/lean4/pull/3662) causes auxiliary definitions nested inside theorems to become `def`s if they are not proofs.
+  * [#4006](https://github.com/leanprover/lean4/pull/4006) makes proposition fields of `structure`s be theorems.
+  * [#4018](https://github.com/leanprover/lean4/pull/4018) makes it an error for a theorem to be `extern`.
+  * [#4047](https://github.com/leanprover/lean4/pull/4047) improves performance making equations for well-founded recursive definitions.
+* **Refactors**
+  * [#3614](https://github.com/leanprover/lean4/pull/3614) avoids unfolding in `Lean.Meta.evalNat`.
+  * [#3621](https://github.com/leanprover/lean4/pull/3621) centralizes functionality for `Fix`/`GuessLex`/`FunInd` in the `ArgsPacker` module.
+  * [#3186](https://github.com/leanprover/lean4/pull/3186) rewrites the UnusedVariable linter to be more performant.
+  * [#3589](https://github.com/leanprover/lean4/pull/3589) removes coercion from `String` to `Name` (see breaking changes below).
+  * [#3237](https://github.com/leanprover/lean4/pull/3237) removes the `lines` field from `FileMap`.
+  * [#3951](https://github.com/leanprover/lean4/pull/3951) makes msg parameter to `throwTacticEx` optional.
+* **Diagnostics**
+  * [#4016](https://github.com/leanprover/lean4/pull/4016), [#4019](https://github.com/leanprover/lean4/pull/4019),
+    [#4020](https://github.com/leanprover/lean4/pull/4020), [#4030](https://github.com/leanprover/lean4/pull/4030),
+    [#4031](https://github.com/leanprover/lean4/pull/4031),
+    [c3714b](https://github.com/leanprover/lean4/commit/c3714bdc6d46845c0428735b283c5b48b23cbcf7),
+    [#4049](https://github.com/leanprover/lean4/pull/4049) adds `set_option diagnostics true` for diagnostic counters.
+    Tracks number of unfolded declarations, instances, reducible declarations, used instances, recursor reductions,
+    `isDefEq` heuristic applications, among others.
+    This option is suggested in exceptional situations, such as at deterministic timeout and maximum recursion depth.
+  * [283587](https://github.com/leanprover/lean4/commit/283587987ab2eb3b56fbc3a19d5f33ab9e04a2ef)
+    adds diagnostic information for `simp`.
+  * [#4043](https://github.com/leanprover/lean4/pull/4043) adds diagnostic information for congruence theorems.
+  * [#4048](https://github.com/leanprover/lean4/pull/4048) display diagnostic information
+    for `set_option diagnostics true in <tactic>` and `set_option diagnostics true in <term>`.
+* **Other features**
+  * [#3800](https://github.com/leanprover/lean4/pull/3800) adds environment extension to record which definitions use structural or well-founded recursion.
+  * [#3801](https://github.com/leanprover/lean4/pull/3801) `trace.profiler` can now export to Firefox Profiler.
+  * [#3918](https://github.com/leanprover/lean4/pull/3918), [#3953](https://github.com/leanprover/lean4/pull/3953) adds `@[builtin_doc]` attribute to make docs and location of a declaration available as a builtin.
+  * [#3939](https://github.com/leanprover/lean4/pull/3939) adds the `lean --json` CLI option to print messages as JSON.
+  * [#3075](https://github.com/leanprover/lean4/pull/3075) improves `test_extern` command.
+  * [#3970](https://github.com/leanprover/lean4/pull/3970) gives monadic generalization of `FindExpr`.
+* **Docs:** [#3743](https://github.com/leanprover/lean4/pull/3743), [#3921](https://github.com/leanprover/lean4/pull/3921),
+  [#3954](https://github.com/leanprover/lean4/pull/3954).
+* **Other fixes:** [#3622](https://github.com/leanprover/lean4/pull/3622),
+  [#3726](https://github.com/leanprover/lean4/pull/3726), [#3823](https://github.com/leanprover/lean4/pull/3823),
+  [#3897](https://github.com/leanprover/lean4/pull/3897), [#3964](https://github.com/leanprover/lean4/pull/3964),
+  [#3946](https://github.com/leanprover/lean4/pull/3946), [#4007](https://github.com/leanprover/lean4/pull/4007),
+  [#4026](https://github.com/leanprover/lean4/pull/4026).
+
+### Compiler, runtime, and FFI
+
+* [#3632](https://github.com/leanprover/lean4/pull/3632) makes it possible to allocate and free thread-local runtime resources for threads not started by Lean itself.
+* [#3627](https://github.com/leanprover/lean4/pull/3627) improves error message about compacting closures.
+* [#3692](https://github.com/leanprover/lean4/pull/3692) fixes deadlock in `IO.Promise.resolve`.
+* [#3753](https://github.com/leanprover/lean4/pull/3753) catches error code from `MoveFileEx` on Windows.
+* [#4028](https://github.com/leanprover/lean4/pull/4028) fixes a double `reset` bug in `ResetReuse` transformation.
+* [6e731b](https://github.com/leanprover/lean4/commit/6e731b4370000a8e7a5cfb675a7f3d7635d21f58)
+  removes `interpreter` copy constructor to avoid potential memory safety issues.
+
+### Lake
+
+* **TOML Lake configurations**. [#3298](https://github.com/leanprover/lean4/pull/3298), [#4104](https://github.com/leanprover/lean4/pull/4104).
+
+  Lake packages can now use TOML as a alternative configuration file format instead of Lean. If the default `lakefile.lean` is missing, Lake will also look for a `lakefile.toml`. The TOML version of the configuration supports a restricted set of the Lake configuration options, only including those which can easily mapped to a TOML data structure. The TOML syntax itself fully compiles with the TOML v1.0.0 specification.
+
+  As part of the introduction of this new feature, we have been helping maintainers of some major packages within the ecosystem switch to this format. For example, the following is Aesop's new `lakefile.toml`:
+
+
+  **[leanprover-community/aesop/lakefile.toml](https://raw.githubusercontent.com/leanprover-community/aesop/de11e0ecf372976e6d627c210573146153090d2d/lakefile.toml)**
+  ```toml
+  name = "aesop"
+  defaultTargets = ["Aesop"]
+  testRunner = "test"
+  precompileModules = false
+
+  [[require]]
+  name = "batteries"
+  git = "https://github.com/leanprover-community/batteries"
+  rev = "main"
+
+  [[lean_lib]]
+  name = "Aesop"
+
+  [[lean_lib]]
+  name = "AesopTest"
+  globs = ["AesopTest.+"]
+  leanOptions = {linter.unusedVariables = false}
+
+  [[lean_exe]]
+  name = "test"
+  srcDir = "scripts"
+  ```
+
+  To assist users who wish to transition their packages between configuration file formats, there is also a new `lake translate-config` command for migrating to/from TOML.
+
+  Running `lake translate-config toml` will produce a `lakefile.toml` version of a package's `lakefile.lean`. Any configuration options unsupported by the TOML format will be discarded during translation, but the original `lakefile.lean` will remain so that you can verify the translation looks good before deleting it.
+
+* **Build progress overhaul.** [#3835](https://github.com/leanprover/lean4/pull/3835), [#4115](https://github.com/leanprover/lean4/pull/4115), [#4127](https://github.com/leanprover/lean4/pull/4127), [#4220](https://github.com/leanprover/lean4/pull/4220), [#4232](https://github.com/leanprover/lean4/pull/4232), [#4236](https://github.com/leanprover/lean4/pull/4236).
+
+  Builds are now managed by a top-level Lake build monitor, this makes the output of Lake builds more standardized and enables producing prettier and more configurable progress reports.
+
+  As part of this change, job isolation has improved. Stray I/O and other build related errors in custom targets are now properly isolated and caught as part of their job. Import errors no longer cause Lake to abort the entire build and are instead localized to the build jobs of the modules in question.
+
+  Lake also now uses ANSI escape sequences to add color and produce progress lines that update in-place; this can be toggled on and off using `--ansi` / `--no-ansi`.
+
+
+  `--wfail` and `--iofail` options have been added that causes a build to fail if any of the jobs log a warning (`--wfail`) or produce any output or log information messages (`--iofail`). Unlike some other build systems, these options do **NOT** convert these logs into errors, and Lake does not abort jobs on such a log (i.e., dependent jobs will still continue unimpeded).
+
+* `lake test`. [#3779](https://github.com/leanprover/lean4/pull/3779).
+
+  Lake now has a built-in `test` command which will run a script or executable labelled `@[test_runner]` (in Lean) or defined as the `testRunner` (in TOML) in the root package.
+
+  Lake also provides a `lake check-test` command which will exit with code `0` if the package has a properly configured test runner or error with `1` otherwise.
+
+* `lake lean`. [#3793](https://github.com/leanprover/lean4/pull/3793).
+
+  The new command `lake lean <file> [-- <args...>]` functions like `lake env lean <file> <args...>`, except that it builds the imports of `file` before running `lean`. This makes it very useful for running test or example code that imports modules that are not guaranteed to have been built beforehand.
+
+* **Miscellaneous bug fixes and improvements**
+  * [#3609](https://github.com/leanprover/lean4/pull/3609) `LEAN_GITHASH` environment variable to override the detected Git hash for Lean when computing traces, useful for testing custom builds of Lean.
+  * [#3795](https://github.com/leanprover/lean4/pull/3795) improves relative package directory path normalization in the pre-rename check.
+  * [#3957](https://github.com/leanprover/lean4/pull/3957) fixes handling of packages that appear multiple times in a dependency tree.
+  * [#3999](https://github.com/leanprover/lean4/pull/3999) makes it an error for there to be a mismatch between a package name and what it is required as. Also adds a special message for the `std`-to-`batteries` rename.
+  * [#4033](https://github.com/leanprover/lean4/pull/4033) fixes quiet mode.
+* **Docs:** [#3704](https://github.com/leanprover/lean4/pull/3704).
+
+### DevOps
+
+* [#3536](https://github.com/leanprover/lean4/pull/3536) and [#3833](https://github.com/leanprover/lean4/pull/3833)
+  add a checklist for the release process.
+* [#3600](https://github.com/leanprover/lean4/pull/3600) runs nix-ci more uniformly.
+* [#3612](https://github.com/leanprover/lean4/pull/3612) avoids argument limits when building on Windows.
+* [#3682](https://github.com/leanprover/lean4/pull/3682) builds Lean's `.o` files in parallel to rest of core.
+* [#3601](https://github.com/leanprover/lean4/pull/3601)
+  changes the way Lean is built on Windows (see breaking changes below).
+  As a result, Lake now dynamically links executables with `supportInterpreter := true` on Windows
+  to `libleanshared.dll` and `libInit_shared.dll`. Therefore, such executables will not run
+  unless those shared libraries are co-located with the executables or part of `PATH`.
+  Running the executable via `lake exe` will ensure these libraries are part of `PATH`.
+
+  In a related change, the signature of the `nativeFacets` Lake configuration options has changed
+  from a static `Array` to a function `(shouldExport : Bool) → Array`.
+  See its docstring or Lake's [README](src/lake/README.md) for further details on the changed option.
+* [#3690](https://github.com/leanprover/lean4/pull/3690) marks "Build matrix complete" as canceled if the build is canceled.
+* [#3700](https://github.com/leanprover/lean4/pull/3700), [#3702](https://github.com/leanprover/lean4/pull/3702),
+  [#3701](https://github.com/leanprover/lean4/pull/3701), [#3834](https://github.com/leanprover/lean4/pull/3834),
+  [#3923](https://github.com/leanprover/lean4/pull/3923): fixes and improvements for std and mathlib CI.
+* [#3712](https://github.com/leanprover/lean4/pull/3712) fixes `nix build .` on macOS.
+* [#3717](https://github.com/leanprover/lean4/pull/3717) replaces `shell.nix` in devShell with `flake.nix`.
+* [#3715](https://github.com/leanprover/lean4/pull/3715) and [#3790](https://github.com/leanprover/lean4/pull/3790) add test result summaries.
+* [#3971](https://github.com/leanprover/lean4/pull/3971) prevents stage0 changes via the merge queue.
+* [#3979](https://github.com/leanprover/lean4/pull/3979) adds handling for `changes-stage0` label.
+* [#3952](https://github.com/leanprover/lean4/pull/3952) adds a script to summarize GitHub issues.
+* [18a699](https://github.com/leanprover/lean4/commit/18a69914da53dbe37c91bc2b9ce65e1dc01752b6)
+  fixes asan linking
+
+### Breaking changes
+
+* Due to the major Lake build refactor, code using the affected parts of the Lake API or relying on the previous output format of Lake builds is likely to have been broken. We have tried to minimize the breakages and, where possible, old definitions have been marked `@[deprecated]` with a reference to the new alternative.
+
+* Executables configured with `supportInterpreter := true` on Windows should now be run via `lake exe` to function properly.
+
+* Automatically generated equational theorems are now named using suffix `.eq_<idx>` instead of `._eq_<idx>`, and `.eq_def` instead of `._unfold`. Example:
+```
+def fact : Nat → Nat
+  | 0 => 1
+  | n+1 => (n+1) * fact n
+
+theorem ex : fact 0 = 1 := by unfold fact; decide
+
+#check fact.eq_1
+-- fact.eq_1 : fact 0 = 1
+
+#check fact.eq_2
+-- fact.eq_2 (n : Nat) : fact (Nat.succ n) = (n + 1) * fact n
+
+#check fact.eq_def
+/-
+fact.eq_def :
+  ∀ (x : Nat),
+    fact x =
+      match x with
+      | 0 => 1
+      | Nat.succ n => (n + 1) * fact n
+-/
+```
+
+* The coercion from `String` to `Name` was removed. Previously, it was `Name.mkSimple`, which does not separate strings at dots, but experience showed that this is not always the desired coercion. For the previous behavior, manually insert a call to `Name.mkSimple`.
+
+* The `Subarray` fields `as`, `h₁` and `h₂` have been renamed to `array`, `start_le_stop`, and `stop_le_array_size`, respectively. This more closely follows standard Lean conventions. Deprecated aliases for the field projections were added; these will be removed in a future release.
+
+* The change to the instance name algorithm (described above) can break projects that made use of the auto-generated names.
+
+* `Option.toMonad` has been renamed to `Option.getM` and the unneeded `[Monad m]` instance argument has been removed.

releases/v4.9.0.md

@@ -0,0 +1,321 @@
+v4.9.0
+----------
+
+### Language features, tactics, and metaprograms
+
+* **Definition transparency**
+  * [#4053](https://github.com/leanprover/lean4/pull/4053) adds the `seal` and `unseal` commands, which make definitions locally be irreducible or semireducible.
+  * [#4061](https://github.com/leanprover/lean4/pull/4061) marks functions defined by well-founded recursion with `@[irreducible]` by default,
+    which should prevent the expensive and often unfruitful unfolding of such definitions (see breaking changes below).
+* **Incrementality**
+  * [#3940](https://github.com/leanprover/lean4/pull/3940) extends incremental elaboration into various steps inside of declarations:
+    definition headers, bodies, and tactics.
+    ![Recording 2024-05-10](https://github.com/leanprover/lean4/assets/109126/c9d67b6f-c131-4bc3-a0de-7d63eaf1bfc9).
+  * [250994](https://github.com/leanprover/lean4/commit/250994166ce036ab8644e459129f51ea79c1c2d2)
+    and [67338b](https://github.com/leanprover/lean4/commit/67338bac2333fa39a8656e8f90574784e4c23d3d)
+    add `@[incremental]` attribute to mark an elaborator as supporting incremental elaboration.
+  * [#4259](https://github.com/leanprover/lean4/pull/4259) improves resilience by ensuring incremental commands and tactics are reached only in supported ways.
+  * [#4268](https://github.com/leanprover/lean4/pull/4268) adds special handling for `:= by` so that stray tokens in tactic blocks do not inhibit incrementality.
+  * [#4308](https://github.com/leanprover/lean4/pull/4308) adds incremental `have` tactic.
+  * [#4340](https://github.com/leanprover/lean4/pull/4340) fixes incorrect info tree reuse.
+  * [#4364](https://github.com/leanprover/lean4/pull/4364) adds incrementality for careful command macros such as `set_option in theorem`, `theorem foo.bar`, and `lemma`.
+  * [#4395](https://github.com/leanprover/lean4/pull/4395) adds conservative fix for whitespace handling to avoid incremental reuse leading to goals in front of the text cursor being shown.
+  * [#4407](https://github.com/leanprover/lean4/pull/4407) fixes non-incremental commands in macros blocking further incremental reporting.
+  * [#4436](https://github.com/leanprover/lean4/pull/4436) fixes incremental reporting when there are nested tactics in terms.
+  * [#4459](https://github.com/leanprover/lean4/pull/4459) adds incrementality support for `next` and `if` tactics.
+  * [#4554](https://github.com/leanprover/lean4/pull/4554) disables incrementality for tactics in terms in tactics.
+* **Functional induction**
+  * [#4135](https://github.com/leanprover/lean4/pull/4135) ensures that the names used for functional induction are reserved.
+  * [#4327](https://github.com/leanprover/lean4/pull/4327) adds support for structural recursion on reflexive types.
+    For example,
+    ```lean4
+    inductive Many (α : Type u) where
+      | none : Many α
+      | more : α → (Unit → Many α) → Many α
+
+    def Many.map {α β : Type u} (f : α → β) : Many α → Many β
+      | .none => .none
+      | .more x xs => .more (f x) (fun _ => (xs ()).map f)
+
+    #check Many.map.induct
+    /-
+    Many.map.induct {α β : Type u} (f : α → β) (motive : Many α → Prop)
+      (case1 : motive Many.none)
+      (case2 : ∀ (x : α) (xs : Unit → Many α), motive (xs ()) → motive (Many.more x xs)) :
+      ∀ (a : Many α), motive a
+    -/
+    ```
+* [#3903](https://github.com/leanprover/lean4/pull/3903) makes the Lean frontend normalize all line endings to LF before processing.
+  This lets Lean be insensitive to CRLF vs LF line endings, improving the cross-platform experience and making Lake hashes be faithful to what Lean processes.
+* [#4130](https://github.com/leanprover/lean4/pull/4130) makes the tactic framework be able to recover from runtime errors (for example, deterministic timeouts or maximum recursion depth errors).
+* `split` tactic
+  * [#4211](https://github.com/leanprover/lean4/pull/4211) fixes `split at h` when `h` has forward dependencies.
+  * [#4349](https://github.com/leanprover/lean4/pull/4349) allows `split` for `if`-expressions to work on non-propositional goals.
+* `apply` tactic
+  * [#3929](https://github.com/leanprover/lean4/pull/3929) makes error message for `apply` show implicit arguments in unification errors as needed.
+    Modifies `MessageData` type (see breaking changes below).
+* `cases` tactic
+  * [#4224](https://github.com/leanprover/lean4/pull/4224) adds support for unification of offsets such as `x + 20000 = 20001` in `cases` tactic.
+* `omega` tactic
+  * [#4073](https://github.com/leanprover/lean4/pull/4073) lets `omega` fall back to using classical `Decidable` instances when setting up contradiction proofs.
+  * [#4141](https://github.com/leanprover/lean4/pull/4141) and [#4184](https://github.com/leanprover/lean4/pull/4184) fix bugs.
+  * [#4264](https://github.com/leanprover/lean4/pull/4264) improves `omega` error message if no facts found in local context.
+  * [#4358](https://github.com/leanprover/lean4/pull/4358) improves expression matching in `omega` by using `match_expr`.
+* `simp` tactic
+  * [#4176](https://github.com/leanprover/lean4/pull/4176) makes names of erased lemmas clickable.
+  * [#4208](https://github.com/leanprover/lean4/pull/4208) adds a pretty printer for discrimination tree keys.
+  * [#4202](https://github.com/leanprover/lean4/pull/4202) adds `Simp.Config.index` configuration option,
+    which controls whether to use the full discrimination tree when selecting candidate simp lemmas.
+    When `index := false`, only the head function is taken into account, like in Lean 3.
+    This feature can help users diagnose tricky simp failures or issues in code from libraries
+    developed using Lean 3 and then ported to Lean 4.
+
+    In the following example, it will report that `foo` is a problematic theorem.
+    ```lean
+    opaque f : Nat → Nat → Nat
+
+    @[simp] theorem foo : f x (x, y).2 = y := by sorry
+
+    example : f a b ≤ b := by
+      set_option diagnostics true in
+      simp (config := { index := false })
+    /-
+    [simp] theorems with bad keys
+      foo, key: f _ (@Prod.mk ℕ ℕ _ _).2
+    -/
+    ```
+    With the information above, users can annotate theorems such as `foo` using `no_index` for problematic subterms. Example:
+    ```lean
+    opaque f : Nat → Nat → Nat
+
+    @[simp] theorem foo : f x (no_index (x, y).2) = y := by sorry
+
+    example : f a b ≤ b := by
+      simp -- `foo` is still applied with `index := true`
+    ```
+  * [#4274](https://github.com/leanprover/lean4/pull/4274) prevents internal `match` equational theorems from appearing in simp trace.
+  * [#4177](https://github.com/leanprover/lean4/pull/4177) and [#4359](https://github.com/leanprover/lean4/pull/4359) make `simp` continue even if a simp lemma does not elaborate, if the tactic state is in recovery mode.
+  * [#4341](https://github.com/leanprover/lean4/pull/4341) fixes panic when applying `@[simp]` to malformed theorem syntax.
+  * [#4345](https://github.com/leanprover/lean4/pull/4345) fixes `simp` so that it does not use the forward version of a user-specified backward theorem.
+  * [#4352](https://github.com/leanprover/lean4/pull/4352) adds missing `dsimp` simplifications for fixed parameters of generated congruence theorems.
+  * [#4362](https://github.com/leanprover/lean4/pull/4362) improves trace messages for `simp` so that constants are hoverable.
+* **Elaboration**
+  * [#4046](https://github.com/leanprover/lean4/pull/4046) makes subst notation (`he ▸ h`) try rewriting in both directions even when there is no expected type available.
+  * [#3328](https://github.com/leanprover/lean4/pull/3328) adds support for identifiers in autoparams (for example, `rfl` in `(h : x = y := by exact rfl)`).
+  * [#4096](https://github.com/leanprover/lean4/pull/4096) changes how the type in `let` and `have` is elaborated, requiring that any tactics in the type be evaluated before proceeding, improving performance.
+  * [#4215](https://github.com/leanprover/lean4/pull/4215) ensures the expression tree elaborator commits to the computed "max type" for the entire arithmetic expression.
+  * [#4267](https://github.com/leanprover/lean4/pull/4267) cases signature elaboration errors to show even if there are parse errors in the body.
+  * [#4368](https://github.com/leanprover/lean4/pull/4368) improves error messages when numeric literals fail to synthesize an `OfNat` instance,
+    including special messages warning when the expected type of the numeral can be a proposition.
+  * [#4643](https://github.com/leanprover/lean4/pull/4643) fixes issue leading to nested error messages and info trees vanishing, where snapshot subtrees were not restored on reuse.
+  * [#4657](https://github.com/leanprover/lean4/pull/4657) calculates error suppression per snapshot, letting elaboration errors appear even when there are later parse errors ([RFC #3556](https://github.com/leanprover/lean4/issues/3556)).
+* **Metaprogramming**
+  * [#4167](https://github.com/leanprover/lean4/pull/4167) adds `Lean.MVarId.revertAll` to revert all free variables.
+  * [#4169](https://github.com/leanprover/lean4/pull/4169) adds `Lean.MVarId.ensureNoMVar` to ensure the goal's target contains no expression metavariables.
+  * [#4180](https://github.com/leanprover/lean4/pull/4180) adds `cleanupAnnotations` parameter to `forallTelescope` methods.
+  * [#4307](https://github.com/leanprover/lean4/pull/4307) adds support for parser aliases in syntax quotations.
+* Work toward implementing `grind` tactic
+  * [0a515e](https://github.com/leanprover/lean4/commit/0a515e2ec939519dafb4b99daa81d6bf3c411404)
+    and [#4164](https://github.com/leanprover/lean4/pull/4164)
+    add `grind_norm` and `grind_norm_proc` attributes and `@[grind_norm]` theorems.
+  * [#4170](https://github.com/leanprover/lean4/pull/4170), [#4221](https://github.com/leanprover/lean4/pull/4221),
+    and [#4249](https://github.com/leanprover/lean4/pull/4249) create `grind` preprocessor and core module.
+  * [#4235](https://github.com/leanprover/lean4/pull/4235) and [d6709e](https://github.com/leanprover/lean4/commit/d6709eb1576c5d40fc80462637dc041f970e4d9f)
+    add special `cases` tactic to `grind` along with `@[grind_cases]` attribute to mark types that this `cases` tactic should automatically apply to.
+  * [#4243](https://github.com/leanprover/lean4/pull/4243) adds special `injection?` tactic to `grind`.
+* **Other fixes or improvements**
+  * [#4065](https://github.com/leanprover/lean4/pull/4065) fixes a bug in the `Nat.reduceLeDiff` simproc.
+  * [#3969](https://github.com/leanprover/lean4/pull/3969) makes deprecation warnings activate even for generalized field notation ("dot notation").
+  * [#4132](https://github.com/leanprover/lean4/pull/4132) fixes the `sorry` term so that it does not activate the implicit lambda feature
+  * [9803c5](https://github.com/leanprover/lean4/commit/9803c5dd63dc993628287d5f998525e74af03839)
+    and [47c8e3](https://github.com/leanprover/lean4/commit/47c8e340d65b01f4d9f011686e3dda0d4bb30a20)
+    move `cdot` and `calc` parsers to `Lean` namespace.
+  * [#4252](https://github.com/leanprover/lean4/pull/4252) fixes the `case` tactic so that it is usable in macros by having it erase macro scopes from the tag.
+  * [26b671](https://github.com/leanprover/lean4/commit/26b67184222e75529e1b166db050aaebee323d2d)
+    and [cc33c3](https://github.com/leanprover/lean4/commit/cc33c39cb022d8a3166b1e89677c78835ead1fc7)
+    extract `haveId` syntax.
+  * [#4335](https://github.com/leanprover/lean4/pull/4335) fixes bugs in partial `calc` tactic when there is mdata or metavariables.
+  * [#4329](https://github.com/leanprover/lean4/pull/4329) makes `termination_by?` report unused each unused parameter as `_`.
+* **Docs:** [#4238](https://github.com/leanprover/lean4/pull/4238), [#4294](https://github.com/leanprover/lean4/pull/4294),
+  [#4338](https://github.com/leanprover/lean4/pull/4338).
+
+### Language server, widgets, and IDE extensions
+* [#4066](https://github.com/leanprover/lean4/pull/4066) fixes features like "Find References" when browsing core Lean sources.
+* [#4254](https://github.com/leanprover/lean4/pull/4254) allows embedding user widgets in structured messages.
+  Companion PR is [vscode-lean4#449](https://github.com/leanprover/vscode-lean4/pull/449).
+* [#4445](https://github.com/leanprover/lean4/pull/4445) makes watchdog more resilient against badly behaving clients.
+
+### Library
+* [#4059](https://github.com/leanprover/lean4/pull/4059) upstreams many `List` and `Array` operations and theorems from Batteries.
+* [#4055](https://github.com/leanprover/lean4/pull/4055) removes the unused `Inhabited` instance for `Subtype`.
+* [#3967](https://github.com/leanprover/lean4/pull/3967) adds dates in existing `@[deprecated]` attributes.
+* [#4231](https://github.com/leanprover/lean4/pull/4231) adds boilerplate `Char`, `UInt`, and `Fin` theorems.
+* [#4205](https://github.com/leanprover/lean4/pull/4205) fixes the `MonadStore` type classes to use `semiOutParam`.
+* [#4350](https://github.com/leanprover/lean4/pull/4350) renames `IsLawfulSingleton` to `LawfulSingleton`.
+* `Nat`
+  * [#4094](https://github.com/leanprover/lean4/pull/4094) swaps `Nat.zero_or` and `Nat.or_zero`.
+  * [#4098](https://github.com/leanprover/lean4/pull/4098) and [#4145](https://github.com/leanprover/lean4/pull/4145)
+    change the definition of `Nat.mod` so that `n % (m + n)` reduces when `n` is literal without relying on well-founded recursion,
+    which becomes irreducible by default in [#4061](https://github.com/leanprover/lean4/pull/4061).
+  * [#4188](https://github.com/leanprover/lean4/pull/4188) redefines `Nat.testBit` to be more performant.
+  * Theorems: [#4199](https://github.com/leanprover/lean4/pull/4199).
+* `Array`
+  * [#4074](https://github.com/leanprover/lean4/pull/4074) improves the functional induction principle `Array.feraseIdx.induct`.
+* `List`
+  * [#4172](https://github.com/leanprover/lean4/pull/4172) removes `@[simp]` from `List.length_pos`.
+* `Option`
+  * [#4037](https://github.com/leanprover/lean4/pull/4037) adds theorems to simplify `Option`-valued dependent if-then-else.
+  * [#4314](https://github.com/leanprover/lean4/pull/4314) removes `@[simp]` from `Option.bind_eq_some`.
+* `BitVec`
+  * Theorems: [#3920](https://github.com/leanprover/lean4/pull/3920), [#4095](https://github.com/leanprover/lean4/pull/4095),
+    [#4075](https://github.com/leanprover/lean4/pull/4075), [#4148](https://github.com/leanprover/lean4/pull/4148),
+    [#4165](https://github.com/leanprover/lean4/pull/4165), [#4178](https://github.com/leanprover/lean4/pull/4178),
+    [#4200](https://github.com/leanprover/lean4/pull/4200), [#4201](https://github.com/leanprover/lean4/pull/4201),
+    [#4298](https://github.com/leanprover/lean4/pull/4298), [#4299](https://github.com/leanprover/lean4/pull/4299),
+    [#4257](https://github.com/leanprover/lean4/pull/4257), [#4179](https://github.com/leanprover/lean4/pull/4179),
+    [#4321](https://github.com/leanprover/lean4/pull/4321), [#4187](https://github.com/leanprover/lean4/pull/4187).
+  * [#4193](https://github.com/leanprover/lean4/pull/4193) adds simprocs for reducing `x >>> i` and `x <<< i` where `i` is a bitvector literal.
+  * [#4194](https://github.com/leanprover/lean4/pull/4194) adds simprocs for reducing `(x <<< i) <<< j` and `(x >>> i) >>> j` where `i` and `j` are natural number literals.
+  * [#4229](https://github.com/leanprover/lean4/pull/4229) redefines `rotateLeft`/`rotateRight` to use modulo reduction of shift offset.
+  * [0d3051](https://github.com/leanprover/lean4/commit/0d30517dca094a07bcb462252f718e713b93ffba) makes `<num>#<term>` bitvector literal notation global.
+* `Char`/`String`
+  * [#4143](https://github.com/leanprover/lean4/pull/4143) modifies `String.substrEq` to avoid linter warnings in downstream code.
+  * [#4233](https://github.com/leanprover/lean4/pull/4233) adds simprocs for `Char` and `String` inequalities.
+  * [#4348](https://github.com/leanprover/lean4/pull/4348) upstreams Mathlib lemmas.
+  * [#4354](https://github.com/leanprover/lean4/pull/4354) upstreams basic `String` lemmas.
+* `HashMap`
+  * [#4248](https://github.com/leanprover/lean4/pull/4248) fixes implicitness of typeclass arguments in `HashMap.ofList`.
+* `IO`
+  * [#4036](https://github.com/leanprover/lean4/pull/4036) adds `IO.Process.getCurrentDir` and `IO.Process.setCurrentDir` for adjusting the current process's working directory.
+* **Cleanup:** [#4077](https://github.com/leanprover/lean4/pull/4077), [#4189](https://github.com/leanprover/lean4/pull/4189),
+  [#4304](https://github.com/leanprover/lean4/pull/4304).
+* **Docs:** [#4001](https://github.com/leanprover/lean4/pull/4001), [#4166](https://github.com/leanprover/lean4/pull/4166),
+  [#4332](https://github.com/leanprover/lean4/pull/4332).
+
+### Lean internals
+* **Defeq and WHNF algorithms**
+  * [#4029](https://github.com/leanprover/lean4/pull/4029) remove unnecessary `checkpointDefEq`
+  * [#4206](https://github.com/leanprover/lean4/pull/4206) fixes `isReadOnlyOrSyntheticOpaque` to respect metavariable depth.
+  * [#4217](https://github.com/leanprover/lean4/pull/4217) fixes missing occurs check for delayed assignments.
+* **Definition transparency**
+  * [#4052](https://github.com/leanprover/lean4/pull/4052) adds validation to application of `@[reducible]`/`@[semireducible]`/`@[irreducible]` attributes (with `local`/`scoped` modifiers as well).
+    Setting `set_option allowUnsafeReductibility true` turns this validation off.
+* **Inductive types**
+  * [#3591](https://github.com/leanprover/lean4/pull/3591) fixes a bug where indices could be incorrectly promoted to parameters.
+  * [#3398](https://github.com/leanprover/lean4/pull/3398) fixes a bug in the injectivity theorem generator.
+  * [#4342](https://github.com/leanprover/lean4/pull/4342) fixes elaboration of mutual inductives with instance parameters.
+* **Diagnostics and profiling**
+  * [#3986](https://github.com/leanprover/lean4/pull/3986) adds option `trace.profiler.useHeartbeats` to switch `trace.profiler.threshold` to being in terms of heartbeats instead of milliseconds.
+  * [#4082](https://github.com/leanprover/lean4/pull/4082) makes `set_option diagnostics true` report kernel diagnostic information.
+* **Typeclass resolution**
+  * [#4119](https://github.com/leanprover/lean4/pull/4119) fixes multiple issues with TC caching interacting with `synthPendingDepth`, adds `maxSynthPendingDepth` option with default value `1`.
+  * [#4210](https://github.com/leanprover/lean4/pull/4210) ensures local instance cache does not contain multiple copies of the same instance.
+  * [#4216](https://github.com/leanprover/lean4/pull/4216) fix handling of metavariables, to avoid needing to set the option `backward.synthInstance.canonInstances` to `false`.
+* **Other fixes or improvements**
+  * [#4080](https://github.com/leanprover/lean4/pull/4080) fixes propagation of state for `Lean.Elab.Command.liftCoreM` and `Lean.Elab.Command.liftTermElabM`.
+  * [#3944](https://github.com/leanprover/lean4/pull/3944) makes the `Repr` deriving handler be consistent between `structure` and `inductive` for how types and proofs are erased.
+  * [#4113](https://github.com/leanprover/lean4/pull/4113) propagates `maxHeartbeats` to kernel to control "(kernel) deterministic timeout" error.
+  * [#4125](https://github.com/leanprover/lean4/pull/4125) reverts [#3970](https://github.com/leanprover/lean4/pull/3970) (monadic generalization of `FindExpr`).
+  * [#4128](https://github.com/leanprover/lean4/pull/4128) catches stack overflow in auto-bound implicits feature.
+  * [#4129](https://github.com/leanprover/lean4/pull/4129) adds `tryCatchRuntimeEx` combinator to replace `catchRuntimeEx` reader state.
+  * [#4155](https://github.com/leanprover/lean4/pull/4155) simplifies the expression canonicalizer.
+  * [#4151](https://github.com/leanprover/lean4/pull/4151) and [#4369](https://github.com/leanprover/lean4/pull/4369)
+    add many missing trace classes.
+  * [#4185](https://github.com/leanprover/lean4/pull/4185) makes congruence theorem generators clean up type annotations of argument types.
+  * [#4192](https://github.com/leanprover/lean4/pull/4192) fixes restoration of infotrees when auto-bound implicit feature is activated,
+    fixing a pretty printing error in hovers and strengthening the unused variable linter.
+  * [dfb496](https://github.com/leanprover/lean4/commit/dfb496a27123c3864571aec72f6278e2dad1cecf) fixes `declareBuiltin` to allow it to be called multiple times per declaration.
+  * [#4569](https://github.com/leanprover/lean4/pull/4569) fixes an issue introduced in a merge conflict, where the interrupt exception was swallowed by some `tryCatchRuntimeEx` uses.
+  * [#4584](https://github.com/leanprover/lean4/pull/4584) (backported as [b056a0](https://github.com/leanprover/lean4/commit/b056a0b395bb728512a3f3e83bf9a093059d4301)) adapts kernel interruption to the new cancellation system.
+  * Cleanup: [#4112](https://github.com/leanprover/lean4/pull/4112), [#4126](https://github.com/leanprover/lean4/pull/4126), [#4091](https://github.com/leanprover/lean4/pull/4091), [#4139](https://github.com/leanprover/lean4/pull/4139), [#4153](https://github.com/leanprover/lean4/pull/4153).
+  * Tests: [030406](https://github.com/leanprover/lean4/commit/03040618b8f9b35b7b757858483e57340900cdc4), [#4133](https://github.com/leanprover/lean4/pull/4133).
+
+### Compiler, runtime, and FFI
+* [#4100](https://github.com/leanprover/lean4/pull/4100) improves reset/reuse algorithm; it now runs a second pass relaxing the constraint that reused memory cells must only be for the exact same constructor.
+* [#2903](https://github.com/leanprover/lean4/pull/2903) fixes segfault in old compiler from mishandling `noConfusion` applications.
+* [#4311](https://github.com/leanprover/lean4/pull/4311) fixes bug in constant folding.
+* [#3915](https://github.com/leanprover/lean4/pull/3915) documents the runtime memory layout for inductive types.
+
+### Lake
+* [#4518](https://github.com/leanprover/lean4/pull/4518) makes trace reading more robust. Lake now rebuilds if trace files are invalid or unreadable and is backwards compatible with previous pure numeric traces.
+* [#4057](https://github.com/leanprover/lean4/pull/4057) adds support for docstrings on `require` commands.
+* [#4088](https://github.com/leanprover/lean4/pull/4088) improves hovers for `family_def` and `library_data` commands.
+* [#4147](https://github.com/leanprover/lean4/pull/4147) adds default `README.md` to package templates
+* [#4261](https://github.com/leanprover/lean4/pull/4261) extends `lake test` help page, adds help page for `lake check-test`,
+  adds `lake lint` and tag `@[lint_driver]`, adds support for specifying test and lint drivers from dependencies,
+  adds `testDriverArgs` and `lintDriverArgs` options, adds support for library test drivers,
+  makes `lake check-test` and `lake check-lint` only load the package without dependencies.
+* [#4270](https://github.com/leanprover/lean4/pull/4270) adds `lake pack` and `lake unpack` for packing and unpacking Lake build artifacts from an archive.
+* [#4083](https://github.com/leanprover/lean4/pull/4083)
+  Switches the manifest format to use `major.minor.patch` semantic
+  versions. Major version increments indicate breaking changes (e.g., new
+  required fields and semantic changes to existing fields). Minor version
+  increments (after `0.x`) indicate backwards-compatible extensions (e.g.,
+  adding optional fields, removing fields). This change is backwards
+  compatible. Lake will still successfully read old manifests with numeric
+  versions. It will treat the numeric version `N` as semantic version
+  `0.N.0`. Lake will also accept manifest versions with `-` suffixes
+  (e.g., `x.y.z-foo`) and then ignore the suffix.
+* [#4273](https://github.com/leanprover/lean4/pull/4273) adds a lift from `JobM` to `FetchM` for backwards compatibility reasons.
+* [#4351](https://github.com/leanprover/lean4/pull/4351) fixes `LogIO`-to-`CliM`-lifting performance issues.
+* [#4343](https://github.com/leanprover/lean4/pull/4343) make Lake store the dependency trace for a build in
+  the cached build long and then verifies that it matches the trace of the current build before replaying the log.
+* [#4402](https://github.com/leanprover/lean4/pull/4402) moves the cached log into the trace file (no more `.log.json`).
+  This means logs are no longer cached on fatal errors and this ensures that an out-of-date log is not associated with an up-to-date trace.
+  Separately, `.hash` file generation was changed to be more reliable as well.
+  The `.hash` files are deleted as part of the build and always regenerate with `--rehash`.
+* **Other fixes or improvements**
+  * [#4056](https://github.com/leanprover/lean4/pull/4056) cleans up tests
+  * [#4244](https://github.com/leanprover/lean4/pull/4244) fixes `noRelease` test when Lean repo is tagged
+  * [#4346](https://github.com/leanprover/lean4/pull/4346) improves `tests/serve`
+  * [#4356](https://github.com/leanprover/lean4/pull/4356) adds build log path to the warning for a missing or invalid build log.
+
+### DevOps
+* [#3984](https://github.com/leanprover/lean4/pull/3984) adds a script (`script/rebase-stage0.sh`) for `git rebase -i` that automatically updates each stage0.
+* [#4108](https://github.com/leanprover/lean4/pull/4108) finishes renamings from transition to Std to Batteries.
+* [#4109](https://github.com/leanprover/lean4/pull/4109) adjusts the Github bug template to mention testing using [live.lean-lang.org](https://live.lean-lang.org).
+* [#4136](https://github.com/leanprover/lean4/pull/4136) makes CI rerun only when `full-ci` label is added or removed.
+* [#4175](https://github.com/leanprover/lean4/pull/4175) and [72b345](https://github.com/leanprover/lean4/commit/72b345c621a9a06d3a5a656da2b793a5eea5f168)
+  switch to using `#guard_msgs` to run tests as much as possible.
+* [#3125](https://github.com/leanprover/lean4/pull/3125) explains the Lean4 `pygments` lexer.
+* [#4247](https://github.com/leanprover/lean4/pull/4247) sets up a procedure for preparing release notes.
+* [#4032](https://github.com/leanprover/lean4/pull/4032) modernizes build instructions and workflows.
+* [#4255](https://github.com/leanprover/lean4/pull/4255) moves some expensive checks from merge queue to releases.
+* [#4265](https://github.com/leanprover/lean4/pull/4265) adds aarch64 macOS as native compilation target for CI.
+* [f05a82](https://github.com/leanprover/lean4/commit/f05a82799a01569edeb5e2594cd7d56282320f9e) restores macOS aarch64 install suffix in CI
+* [#4317](https://github.com/leanprover/lean4/pull/4317) updates build instructions for macOS.
+* [#4333](https://github.com/leanprover/lean4/pull/4333) adjusts workflow to update Batteries in manifest when creating `lean-pr-testing-NNNN` Mathlib branches.
+* [#4355](https://github.com/leanprover/lean4/pull/4355) simplifies `lean4checker` step of release checklist.
+* [#4361](https://github.com/leanprover/lean4/pull/4361) adds installing elan to `pr-release` CI step.
+* [#4628](https://github.com/leanprover/lean4/pull/4628) fixes the Windows build, which was missing an exported symbol.
+
+### Breaking changes
+While most changes could be considered to be a breaking change, this section makes special note of API changes.
+
+* `Nat.zero_or` and `Nat.or_zero` have been swapped ([#4094](https://github.com/leanprover/lean4/pull/4094)).
+* `IsLawfulSingleton` is now `LawfulSingleton` ([#4350](https://github.com/leanprover/lean4/pull/4350)).
+* The `BitVec` literal notation is now `<num>#<term>` rather than `<term>#<term>`, and it is global rather than scoped. Use `BitVec.ofNat w x` rather than `x#w` when `x` is a not a numeric literal ([0d3051](https://github.com/leanprover/lean4/commit/0d30517dca094a07bcb462252f718e713b93ffba)).
+* `BitVec.rotateLeft` and `BitVec.rotateRight` now take the shift modulo the bitwidth ([#4229](https://github.com/leanprover/lean4/pull/4229)).
+* These are no longer simp lemmas:
+  `List.length_pos` ([#4172](https://github.com/leanprover/lean4/pull/4172)),
+  `Option.bind_eq_some` ([#4314](https://github.com/leanprover/lean4/pull/4314)).
+* Types in `let` and `have` (both the expressions and tactics) may fail to elaborate due to new restrictions on what sorts of elaboration problems may be postponed ([#4096](https://github.com/leanprover/lean4/pull/4096)).
+  In particular, tactics embedded in the type will no longer make use of the type of `value` in expressions such as `let x : type := value; body`.
+* Now functions defined by well-founded recursion are marked with `@[irreducible]` by default ([#4061](https://github.com/leanprover/lean4/pull/4061)).
+  Existing proofs that hold by definitional equality (e.g. `rfl`) can be
+  rewritten to explicitly unfold the function definition (using `simp`,
+  `unfold`, `rw`), or the recursive function can be temporarily made
+  semireducible (using `unseal f in` before the command), or the function
+  definition itself can be marked as `@[semireducible]` to get the previous
+  behavior.
+* Due to [#3929](https://github.com/leanprover/lean4/pull/3929):
+  * The `MessageData.ofPPFormat` constructor has been removed.
+    Its functionality has been split into two:
+
+    - for lazy structured messages, please use `MessageData.lazy`;
+    - for embedding `Format` or `FormatWithInfos`, use `MessageData.ofFormatWithInfos`.
+
+    An example migration can be found in [#3929](https://github.com/leanprover/lean4/pull/3929/files#diff-5910592ab7452a0e1b2616c62d22202d2291a9ebb463145f198685aed6299867L109).
+
+  * The `MessageData.ofFormat` constructor has been turned into a function.
+    If you need to inspect `MessageData`, you can pattern-match on `MessageData.ofFormatWithInfos`.

releases_drafts/list_lex.md

@@ -1,16 +0,0 @@
-We replace the inductive predicate `List.lt` with an upstreamed version of `List.Lex` from Mathlib.
-(Previously `Lex.lt` was defined in terms of `<`; now it is generalized to take an arbitrary relation.)
-This subtely changes the notion of ordering on `List α`.
-
-`List.lt` was a weaker relation: in particular if `l₁ < l₂`, then
-`a :: l₁ < b :: l₂` may hold according to `List.lt` even if `a` and `b` are merely incomparable
-(either neither `a < b` nor `b < a`), whereas according to `List.Lex` this would require `a = b`.
-
-When `<` is total, in the sense that `¬ · < ·` is antisymmetric, then the two relations coincide.
-
-Mathlib was already overriding the order instances for `List α`,
-so this change should not be noticed by anyone already using Mathlib.
-
-We simultaneously add the boolean valued `List.lex` function, parameterised by a `BEq` typeclass
-and an arbitrary `lt` function. This will support the flexibility previously provided for `List.lt`,
-via a `==` function which is weaker than strict equality.

script/prepare-llvm-linux.sh

@@ -63,8 +63,8 @@ else
 fi
 # use `-nostdinc` to make sure headers are not visible by default (in particular, not to `#include_next` in the clang headers),
 # but do not change sysroot so users can still link against system libs
-echo -n " -DLEANC_INTERNAL_FLAGS='-nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-Wl,--as-needed -lgmp -luv -lpthread -ldl -lrt -Wl,--no-as-needed'"
 # do not set `LEAN_CC` for tests

script/prepare-llvm-macos.sh

@@ -48,12 +48,11 @@ if [[ -L llvm-host ]]; then
   echo -n " -DCMAKE_C_COMPILER=$PWD/stage1/bin/clang"
   gcp $GMP/lib/libgmp.a stage1/lib/
   gcp $LIBUV/lib/libuv.a stage1/lib/
-  echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/libc -fuse-ld=lld'"
   echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp -luv'"
 else
   echo -n " -DCMAKE_C_COMPILER=$PWD/llvm-host/bin/clang -DLEANC_OPTS='--sysroot $PWD/stage1 -resource-dir $PWD/stage1/lib/clang/15.0.1 ${EXTRA_FLAGS:-}'"
-  echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/libc -fuse-ld=lld'"
 fi
-echo -n " -DLEANC_INTERNAL_FLAGS='-nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
+echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -L ROOT/lib/libc -fuse-ld=lld'"
 # do not set `LEAN_CC` for tests
 echo -n " -DLEAN_TEST_VARS=''"

script/prepare-llvm-mingw.sh

@@ -25,7 +25,10 @@ cp llvm/lib/clang/*/include/{std*,__std*,limits}.h stage1/include/clang
 echo '
 // https://docs.microsoft.com/en-us/windows/win32/api/errhandlingapi/nf-errhandlingapi-seterrormode
 #define SEM_FAILCRITICALERRORS 0x0001
-__declspec(dllimport) __stdcall unsigned int SetErrorMode(unsigned int uMode);' > stage1/include/clang/windows.h
+__declspec(dllimport) __stdcall unsigned int SetErrorMode(unsigned int uMode);
+// https://docs.microsoft.com/en-us/windows/console/setconsoleoutputcp
+#define CP_UTF8 65001
+__declspec(dllimport) __stdcall int SetConsoleOutputCP(unsigned int wCodePageID);' > stage1/include/clang/windows.h
 # COFF dependencies
 cp /clang64/lib/{crtbegin,crtend,crt2,dllcrt2}.o stage1/lib/
 # runtime
@@ -43,7 +46,7 @@ echo -n " -DCMAKE_C_COMPILER=$PWD/stage1/bin/clang.exe -DCMAKE_C_COMPILER_WORKS=
 echo -n " -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_CXX_COMPILER=clang++"
 echo -n " -DLEAN_EXTRA_CXX_FLAGS='--sysroot $PWD/llvm -idirafter /clang64/include/'"
 echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang.exe"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -static-libgcc -Wl,-Bstatic -lgmp $(pkg-config --static --libs libuv) -lunwind -Wl,-Bdynamic -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='--sysroot ROOT -L ROOT/lib -Wl,-Bstatic -lgmp $(pkg-config --static --libs libuv) -lunwind -Wl,-Bdynamic -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual. Always link ICU dynamically.
 echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp $(pkg-config --libs libuv) -lucrtbase'"
 # do not set `LEAN_CC` for tests

script/push_repo_release_tag.py

@@ -0,0 +1,69 @@
+#!/usr/bin/env python3
+import sys
+import subprocess
+import requests
+
+def main():
+    if len(sys.argv) != 4:
+        print("Usage: ./push_repo_release_tag.py <repo> <branch> <version_tag>")
+        sys.exit(1)
+
+    repo, branch, version_tag = sys.argv[1], sys.argv[2], sys.argv[3]
+
+    if branch not in {"master", "main"}:
+        print(f"Error: Branch '{branch}' is not 'master' or 'main'.")
+        sys.exit(1)
+
+    # Get the `lean-toolchain` file content
+    lean_toolchain_url = f"https://raw.githubusercontent.com/{repo}/{branch}/lean-toolchain"
+    try:
+        response = requests.get(lean_toolchain_url)
+        response.raise_for_status()
+    except requests.exceptions.RequestException as e:
+        print(f"Error fetching 'lean-toolchain' file: {e}")
+        sys.exit(1)
+
+    lean_toolchain_content = response.text.strip()
+    expected_prefix = "leanprover/lean4:"
+    if not lean_toolchain_content.startswith(expected_prefix) or lean_toolchain_content != f"{expected_prefix}{version_tag}":
+        print(f"Error: 'lean-toolchain' content does not match '{expected_prefix}{version_tag}'.")
+        sys.exit(1)
+
+    # Create and push the tag using `gh`
+    try:
+        # Check if the tag already exists
+        list_tags_cmd = ["gh", "api", f"repos/{repo}/git/matching-refs/tags/v4", "--jq", ".[].ref"]
+        list_tags_output = subprocess.run(list_tags_cmd, capture_output=True, text=True)
+
+        if list_tags_output.returncode == 0:
+            existing_tags = list_tags_output.stdout.strip().splitlines()
+            if f"refs/tags/{version_tag}" in existing_tags:
+                print(f"Error: Tag '{version_tag}' already exists.")
+                print("Existing tags starting with 'v4':")
+                for tag in existing_tags:
+                    print(tag.replace("refs/tags/", ""))
+                sys.exit(1)
+
+        # Get the SHA of the branch
+        get_sha_cmd = [
+            "gh", "api", f"repos/{repo}/git/ref/heads/{branch}", "--jq", ".object.sha"
+        ]
+        sha_result = subprocess.run(get_sha_cmd, capture_output=True, text=True, check=True)
+        sha = sha_result.stdout.strip()
+
+        # Create the tag
+        create_tag_cmd = [
+            "gh", "api", f"repos/{repo}/git/refs",
+            "-X", "POST",
+            "-F", f"ref=refs/tags/{version_tag}",
+            "-F", f"sha={sha}"
+        ]
+        subprocess.run(create_tag_cmd, capture_output=True, text=True, check=True)
+
+        print(f"Successfully created and pushed tag '{version_tag}' to {repo}.")
+    except subprocess.CalledProcessError as e:
+        print(f"Error while creating/pushing tag: {e.stderr.strip() if e.stderr else e}")
+        sys.exit(1)
+
+if __name__ == "__main__":
+    main()

script/release_checklist.py

@@ -0,0 +1,309 @@
+#!/usr/bin/env python3
+
+import argparse
+import yaml
+import requests
+import base64
+import subprocess
+import sys
+import os
+
+def parse_repos_config(file_path):
+    with open(file_path, "r") as f:
+        return yaml.safe_load(f)["repositories"]
+
+def get_github_token():
+    try:
+        import subprocess
+        result = subprocess.run(['gh', 'auth', 'token'], capture_output=True, text=True)
+        if result.returncode == 0:
+            return result.stdout.strip()
+    except FileNotFoundError:
+        print("Warning: 'gh' CLI not found. Some API calls may be rate-limited.")
+    return None
+
+def strip_rc_suffix(toolchain):
+    """Remove -rcX suffix from the toolchain."""
+    return toolchain.split("-")[0]
+
+def branch_exists(repo_url, branch, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/branches/{branch}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    return response.status_code == 200
+
+def tag_exists(repo_url, tag_name, github_token):
+    # Use /git/matching-refs/tags/ to get all matching tags
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/git/matching-refs/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+
+    if response.status_code != 200:
+        return False
+
+    # Check if any of the returned refs exactly match our tag
+    matching_tags = response.json()
+    return any(tag["ref"] == f"refs/tags/{tag_name}" for tag in matching_tags)
+
+def release_page_exists(repo_url, tag_name, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    return response.status_code == 200
+
+def get_release_notes(repo_url, tag_name, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    if response.status_code == 200:
+        return response.json().get("body", "").strip()
+    return None
+
+def get_branch_content(repo_url, branch, file_path, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/contents/{file_path}?ref={branch}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    if response.status_code == 200:
+        content = response.json().get("content", "")
+        content = content.replace("\n", "")
+        try:
+            return base64.b64decode(content).decode('utf-8').strip()
+        except Exception:
+            return None
+    return None
+
+def parse_version(version_str):
+    # Remove 'v' prefix and extract version and release candidate suffix
+    if ':' in version_str:
+        version_str = version_str.split(':')[1]
+    version = version_str.lstrip('v')
+    parts = version.split('-')
+    base_version = tuple(map(int, parts[0].split('.')))
+    rc_part = parts[1] if len(parts) > 1 and parts[1].startswith('rc') else None
+    rc_number = int(rc_part[2:]) if rc_part else float('inf')  # Treat non-rc as higher than rc
+    return base_version + (rc_number,)
+
+def is_version_gte(version1, version2):
+    """Check if version1 >= version2, including proper handling of release candidates."""
+    return parse_version(version1) >= parse_version(version2)
+
+def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token):
+    # First get the commit SHA for the tag
+    api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+
+    # Get tag's commit SHA
+    tag_response = requests.get(f"{api_base}/git/refs/tags/{tag_name}", headers=headers)
+    if tag_response.status_code != 200:
+        return False
+    
+    # Handle both single object and array responses
+    tag_data = tag_response.json()
+    if isinstance(tag_data, list):
+        # Find the exact matching tag in the list
+        matching_tags = [tag for tag in tag_data if tag['ref'] == f'refs/tags/{tag_name}']
+        if not matching_tags:
+            return False
+        tag_sha = matching_tags[0]['object']['sha']
+    else:
+        tag_sha = tag_data['object']['sha']
+
+    # Get commits on stable branch containing this SHA
+    commits_response = requests.get(
+        f"{api_base}/commits?sha={stable_branch}&per_page=100",
+        headers=headers
+    )
+    if commits_response.status_code != 200:
+        return False
+
+    # Check if any commit in stable's history matches our tag's SHA
+    stable_commits = [commit['sha'] for commit in commits_response.json()]
+    return tag_sha in stable_commits
+
+def is_release_candidate(version):
+    return "-rc" in version
+
+def check_cmake_version(repo_url, branch, version_major, version_minor, github_token):
+    """Verify the CMake version settings in src/CMakeLists.txt."""
+    cmake_file_path = "src/CMakeLists.txt"
+    content = get_branch_content(repo_url, branch, cmake_file_path, github_token)
+    if content is None:
+        print(f"  ❌ Could not retrieve {cmake_file_path} from {branch}")
+        return False
+
+    expected_lines = [
+        f"set(LEAN_VERSION_MAJOR {version_major})",
+        f"set(LEAN_VERSION_MINOR {version_minor})",
+        f"set(LEAN_VERSION_PATCH 0)",
+        f"set(LEAN_VERSION_IS_RELEASE 1)"
+    ]
+
+    for line in expected_lines:
+        if not any(l.strip().startswith(line) for l in content.splitlines()):
+            print(f"  ❌ Missing or incorrect line in {cmake_file_path}: {line}")
+            return False
+
+    print(f"  ✅ CMake version settings are correct in {cmake_file_path}")
+    return True
+
+def extract_org_repo_from_url(repo_url):
+    """Extract the 'org/repo' part from a GitHub URL."""
+    if repo_url.startswith("https://github.com/"):
+        return repo_url.replace("https://github.com/", "").rstrip("/")
+    return repo_url
+
+def get_next_version(version):
+    """Calculate the next version number, ignoring RC suffix."""
+    # Strip v prefix and RC suffix if present
+    base_version = strip_rc_suffix(version.lstrip('v'))
+    major, minor, patch = map(int, base_version.split('.'))
+    # Next version is always .0
+    return f"v{major}.{minor + 1}.0"
+
+def check_bump_branch_toolchain(url, bump_branch, github_token):
+    """Check if the lean-toolchain file in bump branch starts with either 'leanprover/lean4:nightly-' or the next version."""
+    content = get_branch_content(url, bump_branch, "lean-toolchain", github_token)
+    if content is None:
+        print(f"  ❌ No lean-toolchain file found in {bump_branch} branch")
+        return False
+    
+    # Extract the next version from the bump branch name (bump/v4.X.0)
+    next_version = bump_branch.split('/')[1]
+    
+    if not (content.startswith("leanprover/lean4:nightly-") or 
+            content.startswith(f"leanprover/lean4:{next_version}")):
+        print(f"  ❌ Bump branch toolchain should use either nightly or {next_version}, but found: {content}")
+        return False
+    
+    print(f"  ✅ Bump branch correctly uses toolchain: {content}")
+    return True
+
+def main():
+    github_token = get_github_token()
+
+    if len(sys.argv) != 2:
+        print("Usage: python3 release_checklist.py <toolchain>")
+        sys.exit(1)
+
+    toolchain = sys.argv[1]
+    stripped_toolchain = strip_rc_suffix(toolchain)
+    lean_repo_url = "https://github.com/leanprover/lean4"
+
+    # Preliminary checks
+    print("\nPerforming preliminary checks...")
+
+    # Check for branch releases/v4.Y.0
+    version_major, version_minor, _ = map(int, stripped_toolchain.lstrip('v').split('.'))
+    branch_name = f"releases/v{version_major}.{version_minor}.0"
+    if branch_exists(lean_repo_url, branch_name, github_token):
+        print(f"  ✅ Branch {branch_name} exists")
+
+        # Check CMake version settings
+        check_cmake_version(lean_repo_url, branch_name, version_major, version_minor, github_token)
+    else:
+        print(f"  ❌ Branch {branch_name} does not exist")
+
+    # Check for tag v4.X.Y(-rcZ)
+    if tag_exists(lean_repo_url, toolchain, github_token):
+        print(f"  ✅ Tag {toolchain} exists")
+    else:
+        print(f"  ❌ Tag {toolchain} does not exist.")
+
+    # Check for release page
+    if release_page_exists(lean_repo_url, toolchain, github_token):
+        print(f"  ✅ Release page for {toolchain} exists")
+
+        # Check the first line of the release notes
+        release_notes = get_release_notes(lean_repo_url, toolchain, github_token)
+        if release_notes and toolchain in release_notes.splitlines()[0].strip():
+            print(f"  ✅ Release notes look good.")
+        else:
+            previous_minor_version = version_minor - 1
+            previous_release = f"v{version_major}.{previous_minor_version}.0"
+            print(f"  ❌ Release notes not published. Please run `script/release_notes.py --since {previous_release}` on branch `{branch_name}`.")
+    else:
+        print(f"  ❌ Release page for {toolchain} does not exist")
+
+    # Load repositories and perform further checks
+    print("\nChecking repositories...")
+
+    with open(os.path.join(os.path.dirname(__file__), "release_repos.yml")) as f:
+        repos = yaml.safe_load(f)["repositories"]
+
+    for repo in repos:
+        name = repo["name"]
+        url = repo["url"]
+        branch = repo["branch"]
+        check_stable = repo["stable-branch"]
+        check_tag = repo.get("toolchain-tag", True)
+        check_bump = repo.get("bump-branch", False)
+
+        print(f"\nRepository: {name}")
+
+        # Check if branch is on at least the target toolchain
+        lean_toolchain_content = get_branch_content(url, branch, "lean-toolchain", github_token)
+        if lean_toolchain_content is None:
+            print(f"  ❌ No lean-toolchain file found in {branch} branch")
+            continue
+
+        on_target_toolchain = is_version_gte(lean_toolchain_content.strip(), toolchain)
+        if not on_target_toolchain:
+            print(f"  ❌ Not on target toolchain (needs ≥ {toolchain}, but {branch} is on {lean_toolchain_content.strip()})")
+            continue
+        print(f"  ✅ On compatible toolchain (>= {toolchain})")
+
+        # Only check for tag if toolchain-tag is true
+        if check_tag:
+            if not tag_exists(url, toolchain, github_token):
+                print(f"  ❌ Tag {toolchain} does not exist. Run `script/push_repo_release_tag.py {extract_org_repo_from_url(url)} {branch} {toolchain}`.")
+            else:
+                print(f"  ✅ Tag {toolchain} exists")
+
+        # Only check merging into stable if stable-branch is true and not a release candidate
+        if check_stable and not is_release_candidate(toolchain):
+            if not is_merged_into_stable(url, toolchain, "stable", github_token):
+                print(f"  ❌ Tag {toolchain} is not merged into stable")
+            else:
+                print(f"  ✅ Tag {toolchain} is merged into stable")
+
+        # Check for bump branch if configured
+        if check_bump:
+            next_version = get_next_version(toolchain)
+            bump_branch = f"bump/{next_version}"
+            if branch_exists(url, bump_branch, github_token):
+                print(f"  ✅ Bump branch {bump_branch} exists")
+                check_bump_branch_toolchain(url, bump_branch, github_token)
+            else:
+                print(f"  ❌ Bump branch {bump_branch} does not exist")
+
+    # Check lean4 master branch for next development cycle
+    print("\nChecking lean4 master branch configuration...")
+    next_version = get_next_version(toolchain)
+    next_minor = int(next_version.split('.')[1])
+    
+    cmake_content = get_branch_content(lean_repo_url, "master", "src/CMakeLists.txt", github_token)
+    if cmake_content is None:
+        print("  ❌ Could not retrieve CMakeLists.txt from master")
+    else:
+        cmake_lines = cmake_content.splitlines()
+        # Find the actual minor version in CMakeLists.txt
+        for line in cmake_lines:
+            if line.strip().startswith("set(LEAN_VERSION_MINOR "):
+                actual_minor = int(line.split()[-1].rstrip(")"))
+                version_minor_correct = actual_minor >= next_minor
+                break
+        else:
+            version_minor_correct = False
+            
+        is_release_correct = any(
+            l.strip().startswith("set(LEAN_VERSION_IS_RELEASE 0)") 
+            for l in cmake_lines
+        )
+        
+        if not (version_minor_correct and is_release_correct):
+            print("  ❌ lean4 needs a \"begin dev cycle\" PR")
+        else:
+            print("  ✅ lean4 master branch is configured for next development cycle")
+
+if __name__ == "__main__":
+    main()

script/release_notes.py

@@ -0,0 +1,181 @@
+#!/usr/bin/env python3
+
+import sys
+import re
+import json
+import requests
+import subprocess
+import argparse
+from collections import defaultdict
+from git import Repo
+
+def get_commits_since_tag(repo, tag):
+    try:
+        tag_commit = repo.commit(tag)
+        commits = list(repo.iter_commits(f"{tag_commit.hexsha}..HEAD"))
+        return [
+            (commit.hexsha, commit.message.splitlines()[0], commit.message)
+            for commit in commits
+        ]
+    except Exception as e:
+        sys.stderr.write(f"Error retrieving commits: {e}\n")
+        sys.exit(1)
+
+def check_pr_number(first_line):
+    match = re.search(r"\(\#(\d+)\)$", first_line)
+    if match:
+        return int(match.group(1))
+    return None
+
+def fetch_pr_labels(pr_number):
+    try:
+        # Use gh CLI to fetch PR details
+        result = subprocess.run([
+            "gh", "api", f"repos/leanprover/lean4/pulls/{pr_number}"
+        ], capture_output=True, text=True, check=True)
+        pr_data = result.stdout
+        pr_json = json.loads(pr_data)
+        return [label["name"] for label in pr_json.get("labels", [])]
+    except subprocess.CalledProcessError as e:
+        sys.stderr.write(f"Failed to fetch PR #{pr_number} using gh: {e.stderr}\n")
+        return []
+
+def format_section_title(label):
+    title = label.replace("changelog-", "").capitalize()
+    if title == "Doc":
+        return "Documentation"
+    elif title == "Pp":
+        return "Pretty Printing"
+    return title
+
+def sort_sections_order():
+    return [
+        "Language",
+        "Library",
+        "Compiler",
+        "Pretty Printing",
+        "Documentation",
+        "Server",
+        "Lake",
+        "Other",
+        "Uncategorised"
+    ]
+
+def format_markdown_description(pr_number, description):
+    link = f"[#{pr_number}](https://github.com/leanprover/lean4/pull/{pr_number})"
+    return f"{link} {description}"
+
+def commit_types():
+    # see doc/dev/commit_convention.md
+    return ['feat', 'fix', 'doc', 'style', 'refactor', 'test', 'chore', 'perf']
+
+def count_commit_types(commits):
+    counts = {
+        'total': len(commits),
+    }
+    for commit_type in commit_types():
+        counts[commit_type] = 0
+    
+    for _, first_line, _ in commits:
+        for commit_type in commit_types():
+            if first_line.startswith(f'{commit_type}:'):
+                counts[commit_type] += 1
+                break
+    
+    return counts
+
+def main():
+    parser = argparse.ArgumentParser(description='Generate release notes from Git commits')
+    parser.add_argument('--since', required=True, help='Git tag to generate release notes since')
+    args = parser.parse_args()
+
+    try:
+        repo = Repo(".")
+    except Exception as e:
+        sys.stderr.write(f"Error opening Git repository: {e}\n")
+        sys.exit(1)
+
+    commits = get_commits_since_tag(repo, args.since)
+
+    sys.stderr.write(f"Found {len(commits)} commits since tag {args.since}:\n")
+    for commit_hash, first_line, _ in commits:
+        sys.stderr.write(f"- {commit_hash}: {first_line}\n")
+
+    changelog = defaultdict(list)
+
+    for commit_hash, first_line, full_message in commits:
+        # Skip commits with the specific first lines
+        if first_line == "chore: update stage0" or first_line.startswith("chore: CI: bump "):
+            continue
+
+        pr_number = check_pr_number(first_line)
+
+        if not pr_number:
+            sys.stderr.write(f"No PR number found in commit:\n{commit_hash}\n{first_line}\n")
+            continue
+
+        # Remove the first line from the full_message for further processing
+        body = full_message[len(first_line):].strip()
+
+        paragraphs = body.split('\n\n')
+        description = paragraphs[0] if len(paragraphs) > 0 else ""
+        
+        # If there's a third paragraph and second ends with colon, include it
+        if len(paragraphs) > 1 and description.endswith(':'):
+            description = description + '\n\n' + paragraphs[1]
+
+        labels = fetch_pr_labels(pr_number)
+
+        # Skip entries with the "changelog-no" label
+        if "changelog-no" in labels:
+            continue
+
+        report_errors = first_line.startswith("feat:") or first_line.startswith("fix:")
+
+        if not description.startswith("This PR "):
+            if report_errors:
+                sys.stderr.write(f"No PR description found in commit:\n{commit_hash}\n{first_line}\n{body}\n\n")
+                fallback_description = re.sub(r":$", "", first_line.split(" ", 1)[1]).rsplit(" (#", 1)[0]
+                markdown_description = format_markdown_description(pr_number, fallback_description)
+            else:
+                continue
+        else:
+            markdown_description = format_markdown_description(pr_number, description.replace("This PR ", ""))
+
+        changelog_labels = [label for label in labels if label.startswith("changelog-")]
+        if len(changelog_labels) > 1:
+            sys.stderr.write(f"Warning: Multiple changelog-* labels found for PR #{pr_number}: {changelog_labels}\n")
+
+        if not changelog_labels:
+            if report_errors:
+                sys.stderr.write(f"Warning: No changelog-* label found for PR #{pr_number}\n")
+            else:
+                continue
+
+        for label in changelog_labels:
+            changelog[label].append((pr_number, markdown_description))
+
+    # Add commit type counting
+    counts = count_commit_types(commits)
+    print(f"For this release, {counts['total']} changes landed. "
+          f"In addition to the {counts['feat']} feature additions and {counts['fix']} fixes listed below "
+          f"there were {counts['refactor']} refactoring changes, {counts['doc']} documentation improvements, "
+          f"{counts['perf']} performance improvements, {counts['test']} improvements to the test suite "
+          f"and {counts['style'] + counts['chore']} other changes.\n")
+
+    section_order = sort_sections_order()
+    sorted_changelog = sorted(changelog.items(), key=lambda item: section_order.index(format_section_title(item[0])) if format_section_title(item[0]) in section_order else len(section_order))
+
+    for label, entries in sorted_changelog:
+        section_title = format_section_title(label) if label != "Uncategorised" else "Uncategorised"
+        print(f"## {section_title}\n")
+        for _, entry in sorted(entries, key=lambda x: x[0]):
+            # Split entry into lines and indent all lines after the first
+            lines = entry.splitlines()
+            print(f"* {lines[0]}")
+            for line in lines[1:]:
+                print(f"  {line}")
+            print()  # Empty line after each entry
+
+if __name__ == "__main__":
+    main()

script/release_repos.yml

@@ -0,0 +1,95 @@
+repositories:
+  - name: Batteries
+    url: https://github.com/leanprover-community/batteries
+    toolchain-tag: true
+    stable-branch: true
+    branch: main
+    bump-branch: true
+    dependencies: []
+
+  - name: lean4checker
+    url: https://github.com/leanprover/lean4checker
+    toolchain-tag: true
+    stable-branch: true
+    branch: master
+    dependencies: []
+
+  - name: quote4
+    url: https://github.com/leanprover-community/quote4
+    toolchain-tag: true
+    stable-branch: true
+    branch: master
+    dependencies: []
+
+  - name: doc-gen4
+    url: https://github.com/leanprover/doc-gen4
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
+  - name: Verso
+    url: https://github.com/leanprover/verso
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
+  - name: Cli
+    url: https://github.com/leanprover/lean4-cli
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
+  - name: ProofWidgets4
+    url: https://github.com/leanprover-community/ProofWidgets4
+    toolchain-tag: false
+    stable-branch: false
+    branch: main
+    dependencies:
+      - Batteries
+
+  - name: Aesop
+    url: https://github.com/leanprover-community/aesop
+    toolchain-tag: true
+    stable-branch: true
+    branch: master
+    dependencies:
+      - Batteries
+
+  - name: import-graph
+    url: https://github.com/leanprover-community/import-graph
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
+  - name: plausible
+    url: https://github.com/leanprover-community/plausible
+    toolchain-tag: true
+    stable-branch: false
+    branch: main
+    dependencies: []
+
+  - name: Mathlib
+    url: https://github.com/leanprover-community/mathlib4
+    toolchain-tag: true
+    stable-branch: true
+    branch: master
+    bump-branch: true
+    dependencies:
+      - Aesop
+      - ProofWidgets4
+      - lean4checker
+      - Batteries
+      - doc-gen4
+      - import-graph
+
+  - name: REPL
+    url: https://github.com/leanprover-community/repl
+    toolchain-tag: true
+    stable-branch: true
+    branch: master
+    dependencies:
+      - Mathlib

src/CMakeLists.txt

@@ -10,7 +10,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 16)
+set(LEAN_VERSION_MINOR 19)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -144,11 +144,12 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
   # do not import the world from windows.h using appropriately named flag
   string(APPEND LEAN_EXTRA_CXX_FLAGS " -D WIN32_LEAN_AND_MEAN")
   # DLLs must go next to executables on Windows
-  set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/bin")
+  set(CMAKE_RELATIVE_LIBRARY_OUTPUT_DIRECTORY "bin")
 else()
-  set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib/lean")
+  set(CMAKE_RELATIVE_LIBRARY_OUTPUT_DIRECTORY "lib/lean")
 endif()
 
+set(CMAKE_LIBRARY_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/${CMAKE_RELATIVE_LIBRARY_OUTPUT_DIRECTORY}")
 set(CMAKE_ARCHIVE_OUTPUT_DIRECTORY "${CMAKE_BINARY_DIR}/lib/lean")
 
 # OSX default thread stack size is very small. Moreover, in Debug mode, each new stack frame consumes a lot of extra memory.
@@ -295,14 +296,15 @@ index 5e8e0166..f3b29134 100644
 	  PATCH_COMMAND git reset --hard HEAD && printf "${LIBUV_PATCH}" > patch.diff && git apply patch.diff
     BUILD_IN_SOURCE ON
     INSTALL_COMMAND "")
-  set(LIBUV_INCLUDE_DIR "${CMAKE_BINARY_DIR}/libuv/src/libuv/include")
-  set(LIBUV_LIBRARIES "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
+  set(LIBUV_INCLUDE_DIRS "${CMAKE_BINARY_DIR}/libuv/src/libuv/include")
+  set(LIBUV_LDFLAGS "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
 else()
   find_package(LibUV 1.0.0 REQUIRED)
 endif()
-include_directories(${LIBUV_INCLUDE_DIR})
+include_directories(${LIBUV_INCLUDE_DIRS})
 if(NOT LEAN_STANDALONE)
-  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LIBRARIES}")
+  string(JOIN " " LIBUV_LDFLAGS ${LIBUV_LDFLAGS})
+  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LDFLAGS}")
 endif()
 
 # Windows SDK (for ICU)
@@ -453,20 +455,20 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC -ftls-model=initial-exec")
   string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
   string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " -Wl,-rpath=\\$$ORIGIN/..:\\$$ORIGIN")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
-  string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=\\\$ORIGIN/../lib:\\\$ORIGIN/../lib/lean")
+  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -Wl,--no-whole-archive")
+  string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath=$ORIGIN/../lib:$ORIGIN/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
   string(APPEND CMAKE_CXX_FLAGS " -ftls-model=initial-exec")
   string(APPEND INIT_SHARED_LINKER_FLAGS " -install_name @rpath/libInit_shared.dylib")
   string(APPEND LEANSHARED_1_LINKER_FLAGS " -install_name @rpath/libleanshared_1.dylib")
   string(APPEND LEANSHARED_LINKER_FLAGS " -install_name @rpath/libleanshared.dylib")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -install_name @rpath/libLake_shared.dylib")
+  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -install_name @rpath/libLake_shared.dylib")
   string(APPEND CMAKE_EXE_LINKER_FLAGS " -Wl,-rpath,@executable_path/../lib -Wl,-rpath,@executable_path/../lib/lean")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   string(APPEND CMAKE_CXX_FLAGS " -fPIC")
   string(APPEND LEANC_EXTRA_CC_FLAGS " -fPIC")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
-  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libLake_shared.dll.a -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLake.a.export -Wl,--no-whole-archive")
+  string(APPEND LAKESHARED_LINKER_FLAGS " -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libLake_shared.dll.a -Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/lean/libLake.a.export -Wl,--no-whole-archive")
 endif()
 
 if(${CMAKE_SYSTEM_NAME} MATCHES "Linux")
@@ -513,7 +515,16 @@ if(USE_GITHASH)
     message(STATUS "git commit sha1: ${GIT_SHA1}")
   endif()
 else()
-  set(GIT_SHA1 "")
+  if(USE_LAKE AND ${STAGE} EQUAL 0)
+    # we need to embed *some* hash for Lake to invalidate stage 1 on stage 0 changes
+    execute_process(
+        COMMAND git ls-tree HEAD "${CMAKE_CURRENT_SOURCE_DIR}/../../stage0" --object-only
+        OUTPUT_VARIABLE GIT_SHA1
+        OUTPUT_STRIP_TRAILING_WHITESPACE)
+    message(STATUS "stage0 sha1: ${GIT_SHA1}")
+  else()
+    set(GIT_SHA1 "")
+  endif()
 endif()
 configure_file("${LEAN_SOURCE_DIR}/githash.h.in" "${LEAN_BINARY_DIR}/githash.h")
 
@@ -540,6 +551,9 @@ include_directories(${LEAN_SOURCE_DIR})
 include_directories(${CMAKE_BINARY_DIR})  # version.h etc., "private" headers
 include_directories(${CMAKE_BINARY_DIR}/include)  # config.h etc., "public" headers
 
+# Lean code only needs this one include
+string(APPEND LEANC_OPTS " -I${CMAKE_BINARY_DIR}/include")
+
 # Use CMake profile C++ flags for building Lean libraries, but do not embed in `leanc`
 string(TOUPPER "${CMAKE_BUILD_TYPE}" uppercase_CMAKE_BUILD_TYPE)
 string(APPEND LEANC_OPTS " ${CMAKE_CXX_FLAGS_${uppercase_CMAKE_BUILD_TYPE}}")
@@ -698,12 +712,12 @@ else()
 endif()
 
 if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  add_custom_target(lake_lib ALL
+  add_custom_target(lake_lib
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS leanshared
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Lake
     VERBATIM)
-  add_custom_target(lake_shared ALL
+  add_custom_target(lake_shared
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS lake_lib
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make libLake_shared
@@ -752,7 +766,12 @@ add_custom_target(clean-olean
   DEPENDS clean-stdlib)
 
 install(DIRECTORY "${CMAKE_BINARY_DIR}/lib/" DESTINATION lib
-  PATTERN temp EXCLUDE)
+  PATTERN temp
+  PATTERN "*.export"
+  PATTERN "*.hash"
+  PATTERN "*.trace"
+  PATTERN "*.rsp"
+  EXCLUDE)
 
 # symlink source into expected installation location for go-to-definition, if file system allows it
 file(MAKE_DIRECTORY ${CMAKE_BINARY_DIR}/src)
@@ -783,10 +802,32 @@ if(LEAN_INSTALL_PREFIX)
 endif()
 
 # Escape for `make`. Yes, twice.
-string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE "${CMAKE_EXE_LINKER_FLAGS}")
+string(REPLACE "$" "\\\$$" CMAKE_EXE_LINKER_FLAGS_MAKE "${CMAKE_EXE_LINKER_FLAGS}")
 string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE_MAKE "${CMAKE_EXE_LINKER_FLAGS_MAKE}")
 configure_file(${LEAN_SOURCE_DIR}/stdlib.make.in ${CMAKE_BINARY_DIR}/stdlib.make)
 
+# hacky
+function(toml_escape IN OUTVAR)
+  if(IN)
+    string(STRIP "${IN}" OUT)
+    string(REPLACE " " "\", \"" OUT "${OUT}")
+    set(${OUTVAR} "\"${OUT}\"" PARENT_SCOPE)
+  endif()
+endfunction()
+string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_CC "${LEANC_CC}")
+string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_FLAGS "${LEANC_INTERNAL_FLAGS}")
+string(REPLACE "ROOT" "${CMAKE_BINARY_DIR}" LEANC_INTERNAL_LINKER_FLAGS "${LEANC_INTERNAL_LINKER_FLAGS}")
+set(LEANC_OPTS_TOML "${LEANC_OPTS} ${LEANC_EXTRA_CC_FLAGS} ${LEANC_INTERNAL_FLAGS}")
+set(LINK_OPTS_TOML "${LEANC_INTERNAL_LINKER_FLAGS} -L${CMAKE_BINARY_DIR}/lib/lean ${LEAN_EXTRA_LINKER_FLAGS}")
+
+toml_escape("${LEAN_EXTRA_MAKE_OPTS}" LEAN_EXTRA_OPTS_TOML)
+toml_escape("${LEANC_OPTS_TOML}" LEANC_OPTS_TOML)
+toml_escape("${LINK_OPTS_TOML}" LINK_OPTS_TOML)
+
+if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
+  set(LAKE_LIB_PREFIX "lib")
+endif()
+
 if(USE_LAKE AND STAGE EQUAL 1)
   configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/lakefile.toml)
   configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../tests/lakefile.toml)

src/Init.lean

@@ -37,3 +37,7 @@ import Init.MacroTrace
 import Init.Grind
 import Init.While
 import Init.Syntax
+import Init.Internal
+import Init.Try
+import Init.BinderNameHint
+import Init.Task

src/Init/BinderNameHint.lean

@@ -0,0 +1,42 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joachim Breitner
+-/
+
+prelude
+import Init.Prelude
+import Init.Tactics
+
+set_option linter.unusedVariables false in
+/--
+The expression `binderNameHint v binder e` defined to be `e`.
+
+If it is used on the right-hand side of an equation that is used for rewriting by `rw` or `simp`,
+and `v` is a local variable, and `binder` is an expression that (after beta-reduction) is a binder
+(`fun w => …` or `∀ w, …`), then it will rename `v` to the name used in that binder, and remove
+the `binderNameHint`.
+
+A typical use of this gadget would be as follows; the gadget ensures that after rewriting, the local
+variable is still `name`, and not `x`:
+```
+theorem all_eq_not_any_not (l : List α) (p : α → Bool) :
+    l.all p = !l.any fun x => binderNameHint x p (!p x) := sorry
+
+example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name) = true := by
+  rw [all_eq_not_any_not]
+  -- ⊢ (!names.any fun name => !"Waldo".isPrefixOf name) = true
+```
+
+If `binder` is not a binder, then the name of `v` attains a macro scope. This only matters when the
+resulting term is used in a non-hygienic way, e.g. in termination proofs for well-founded recursion.
+
+This gadget is supported by
+* `simp`, `dsimp` and `rw` in the right-hand-side of an equation
+* `simp` in the assumptions of congruence rules
+
+It is ineffective in other positions (hyptheses of rewrite rules) or when used by other tactics
+(e.g. `apply`).
+-/
+@[simp ↓]
+def binderNameHint {α : Sort u} {β : Sort v} {γ : Sort w} (v : α) (binder : β) (e : γ) : γ := e

src/Init/ByCases.lean

@@ -38,7 +38,8 @@ theorem apply_ite (f : α → β) (P : Prop) [Decidable P] (x y : α) :
   apply_dite f P (fun _ => x) (fun _ => y)
 
 /-- A `dite` whose results do not actually depend on the condition may be reduced to an `ite`. -/
-@[simp] theorem dite_eq_ite [Decidable P] : (dite P (fun _ => a) fun _ => b) = ite P a b := rfl
+@[simp] theorem dite_eq_ite [Decidable P] :
+  (dite P (fun _ => a) (fun _ => b)) = ite P a b := rfl
 
 @[deprecated "Use `ite_eq_right_iff`" (since := "2024-09-18")]
 theorem ite_some_none_eq_none [Decidable P] :

src/Init/Classical.lean

@@ -175,7 +175,10 @@ theorem or_iff_not_imp_right : a ∨ b ↔ (¬b → a) := Decidable.or_iff_not_i
 
 theorem not_imp_iff_and_not : ¬(a → b) ↔ a ∧ ¬b := Decidable.not_imp_iff_and_not
 
-theorem not_and_iff_or_not_not : ¬(a ∧ b) ↔ ¬a ∨ ¬b := Decidable.not_and_iff_or_not_not
+theorem not_and_iff_not_or_not : ¬(a ∧ b) ↔ ¬a ∨ ¬b := Decidable.not_and_iff_not_or_not
+
+@[deprecated not_and_iff_not_or_not (since := "2025-03-18")]
+abbrev not_and_iff_or_not_not := @not_and_iff_not_or_not
 
 theorem not_iff : ¬(a ↔ b) ↔ (¬a ↔ b) := Decidable.not_iff
 
@@ -195,7 +198,7 @@ end Classical
 /- Export for Mathlib compat. -/
 export Classical (imp_iff_right_iff imp_and_neg_imp_iff and_or_imp not_imp)
 
-/-- Extract an element from a existential statement, using `Classical.choose`. -/
+/-- Extract an element from an existential statement, using `Classical.choose`. -/
 -- This enables projection notation.
 @[reducible] noncomputable def Exists.choose {p : α → Prop} (P : ∃ a, p a) : α := Classical.choose P
 

src/Init/Control/Basic.lean

@@ -5,6 +5,7 @@ Author: Leonardo de Moura, Sebastian Ullrich
 -/
 prelude
 import Init.Core
+import Init.BinderNameHint
 
 universe u v w
 
@@ -35,6 +36,12 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
   simp [h]
   rfl
 
+@[wf_preprocess] theorem forIn_eq_forin' [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m]
+    (x : ρ) (b : β) (f : (a : α) → β → m (ForInStep β)) :
+    forIn x b f = forIn' x b (fun x h => binderNameHint x f <| binderNameHint h () <| f x) := by
+  simp [binderNameHint]
+  rfl -- very strange why `simp` did not close it
+
 /-- Extract the value from a `ForInStep`, ignoring whether it is `done` or `yield`. -/
 def ForInStep.value (x : ForInStep α) : α :=
   match x with
@@ -44,12 +51,28 @@ def ForInStep.value (x : ForInStep α) : α :=
 @[simp] theorem ForInStep.value_done (b : β) : (ForInStep.done b).value = b := rfl
 @[simp] theorem ForInStep.value_yield (b : β) : (ForInStep.yield b).value = b := rfl
 
+/--
+Maps a function over a functor, with parameters swapped so that the function comes last.
+
+This function is `Functor.map` with the parameters reversed, typically used via the `<&>` operator.
+-/
 @[reducible]
 def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β) → f β :=
   fun a f => f <$> a
 
+@[inherit_doc Functor.mapRev]
 infixr:100 " <&> " => Functor.mapRev
 
+recommended_spelling "mapRev" for "<&>" in [Functor.mapRev, «term_<&>_»]
+
+/--
+Discards the value in a functor, retaining the functor's structure.
+
+Discarding values is especially useful when using `Applicative` functors or `Monad`s to implement
+effects, and some operation should be carried out only for its effects. In `do`-notation, statements
+whose values are discarded must return `Unit`, and `discard` can be used to explicitly discard their
+values.
+-/
 @[always_inline, inline]
 def Functor.discard {f : Type u → Type v} {α : Type u} [Functor f] (x : f α) : f PUnit :=
   Functor.mapConst PUnit.unit x
@@ -69,7 +92,7 @@ Error recovery and state can interact subtly. For example, the implementation of
 -/
 -- NB: List instance is in mathlib. Once upstreamed, add
 -- * `List`, where `failure` is the empty list and `<|>` concatenates.
-class Alternative (f : Type u → Type v) extends Applicative f : Type (max (u+1) v) where
+class Alternative (f : Type u → Type v) : Type (max (u+1) v) extends Applicative f where
   /--
   Produces an empty collection or recoverable failure.  The `<|>` operator collects values or recovers
   from failures. See `Alternative` for more details.
@@ -112,6 +135,13 @@ instance : ToBool Bool where
   | true  => t
   | false => f
 
+/--
+Converts the result of the monadic action `x` to a `Bool`. If it is `true`, returns it and ignores
+`y`; otherwise, runs `y` and returns its result.
+
+This a monadic counterpart to the short-circuiting `||` operator, usually accessed via the `<||>`
+operator.
+-/
 @[macro_inline] def orM {m : Type u → Type v} {β : Type u} [Monad m] [ToBool β] (x y : m β) : m β := do
   let b ← x
   match toBool b with
@@ -120,6 +150,15 @@ instance : ToBool Bool where
 
 infixr:30 " <||> " => orM
 
+recommended_spelling "orM" for "<||>" in [orM, «term_<||>_»]
+
+/--
+Converts the result of the monadic action `x` to a `Bool`. If it is `true`, returns `y`; otherwise,
+returns the original result of `x`.
+
+This a monadic counterpart to the short-circuiting `&&` operator, usually accessed via the `<&&>`
+operator.
+-/
 @[macro_inline] def andM {m : Type u → Type v} {β : Type u} [Monad m] [ToBool β] (x y : m β) : m β := do
   let b ← x
   match toBool b with
@@ -128,6 +167,11 @@ infixr:30 " <||> " => orM
 
 infixr:35 " <&&> " => andM
 
+recommended_spelling "andM" for "<&&>" in [andM, «term_<&&>_»]
+
+/--
+Runs a monadic action and returns the negation of its result.
+-/
 @[macro_inline] def notM {m : Type → Type v} [Applicative m] (x : m Bool) : m Bool :=
   not <$> x
 
@@ -243,21 +287,61 @@ Using `control` means that `runInBase` can be used multiple times.
 -/
 
 
-/-- MonadControl is a way of stating that the monad `m` can be 'run inside' the monad `n`.
-
-This is the same as [`MonadBaseControl`](https://hackage.haskell.org/package/monad-control-1.0.3.1/docs/Control-Monad-Trans-Control.html#t:MonadBaseControl) in Haskell.
-To learn about `MonadControl`, see the comment above this docstring.
+/--
+A way to lift a computation from one monad to another while providing the lifted computation with a
+means of interpreting computations from the outer monad. This provides a means of lifting
+higher-order operations automatically.
 
+Clients should typically use `control` or `controlAt`, which request an instance of `MonadControlT`:
+the reflexive, transitive closure of `MonadControl`. New instances should be defined for
+`MonadControl` itself.
 -/
+-- This is the same as
+-- [`MonadBaseControl`](https://hackage.haskell.org/package/monad-control-1.0.3.1/docs/Control-Monad-Trans-Control.html#t:MonadBaseControl)
+-- in Haskell.
 class MonadControl (m : semiOutParam (Type u → Type v)) (n : Type u → Type w) where
+  /--
+  A type that can be used to reconstruct both a returned value and any state used by the outer
+  monad.
+  -/
   stM      : Type u → Type u
+  /--
+  Lifts an action from the inner monad `m` to the outer monad `n`. The inner monad has access to a
+  reverse lifting operator that can run an `n` action, returning a value and state together.
+  -/
   liftWith : {α : Type u} → (({β : Type u} → n β → m (stM β)) → m α) → n α
+  /--
+  Lifts a monadic action that returns a state and a value in the inner monad to an action in the
+  outer monad. The extra state information is used to restore the results of effects from the
+  reverse lift passed to `liftWith`'s parameter.
+  -/
   restoreM : {α : Type u} → m (stM α) → n α
 
-/-- Transitive closure of MonadControl. -/
+/--
+A way to lift a computation from one monad to another while providing the lifted computation with a
+means of interpreting computations from the outer monad. This provides a means of lifting
+higher-order operations automatically.
+
+Clients should typically use `control` or `controlAt`, which request an instance of `MonadControlT`:
+the reflexive, transitive closure of `MonadControl`. New instances should be defined for
+`MonadControl` itself.
+-/
 class MonadControlT (m : Type u → Type v) (n : Type u → Type w) where
+  /--
+  A type that can be used to reconstruct both a returned value and any state used by the outer
+  monad.
+  -/
   stM      : Type u → Type u
+  /--
+  Lifts an action from the inner monad `m` to the outer monad `n`. The inner monad has access to a
+  reverse lifting operator that can run an `n` action, returning a value and state together.
+  -/
   liftWith : {α : Type u} → (({β : Type u} → n β → m (stM β)) → m α) → n α
+  /--
+  Lifts a monadic action that returns a state and a value in the inner monad to an action in the
+  outer monad. The extra state information is used to restore the results of effects from the
+  reverse lift passed to `liftWith`'s parameter.
+  -/
   restoreM {α : Type u} : stM α → n α
 
 export MonadControlT (stM liftWith restoreM)
@@ -273,11 +357,28 @@ instance (m : Type u → Type v) [Pure m] : MonadControlT m m where
   liftWith f := f fun x => x
   restoreM x := pure x
 
+/--
+Lifts an operation from an inner monad to an outer monad, providing it with a reverse lifting
+operator that allows outer monad computations to be run in the inner monad. The lifted operation is
+required to return extra information that is required in order to reconstruct the reverse lift's
+effects in the outer monad; this extra information is determined by `stM`.
+
+This function takes the inner monad as an explicit parameter. Use `control` to infer the monad.
+-/
 @[always_inline, inline]
 def controlAt (m : Type u → Type v) {n : Type u → Type w} [MonadControlT m n] [Bind n] {α : Type u}
     (f : ({β : Type u} → n β → m (stM m n β)) → m (stM m n α)) : n α :=
   liftWith f >>= restoreM
 
+/--
+Lifts an operation from an inner monad to an outer monad, providing it with a reverse lifting
+operator that allows outer monad computations to be run in the inner monad. The lifted operation is
+required to return extra information that is required in order to reconstruct the reverse lift's
+effects in the outer monad; this extra information is determined by `stM`.
+
+This function takes the inner monad as an implicit parameter. Use `controlAt` to specify it
+explicitly.
+-/
 @[always_inline, inline]
 def control {m : Type u → Type v} {n : Type u → Type w} [MonadControlT m n] [Bind n] {α : Type u}
     (f : ({β : Type u} → n β → m (stM m n β)) → m (stM m n α)) : n α :=
@@ -315,3 +416,7 @@ def Bind.bindLeft [Bind m] (f : α → m β) (ma : m α) : m β :=
 @[inherit_doc] infixr:55 " >=> " => Bind.kleisliRight
 @[inherit_doc] infixr:55 " <=< " => Bind.kleisliLeft
 @[inherit_doc] infixr:55 " =<< " => Bind.bindLeft
+
+recommended_spelling "kleisliRight" for ">=>" in [Bind.kleisliRight, «term_>=>_»]
+recommended_spelling "kleisliLeft" for "<=<" in [Bind.kleisliLeft, «term_<=<_»]
+recommended_spelling "bindLeft" for "=<<" in [Bind.bindLeft, «term_=<<_»]

src/Init/Control/Except.lean

@@ -13,10 +13,20 @@ import Init.Coe
 namespace Except
 variable {ε : Type u}
 
+/--
+A successful computation in the `Except ε` monad: `a` is returned, and no exception is thrown.
+-/
 @[always_inline, inline]
 protected def pure (a : α) : Except ε α :=
   Except.ok a
 
+/--
+Transforms a successful result with a function, doing nothing when an exception is thrown.
+
+Examples:
+ * `(pure 2 : Except String Nat).map toString = pure 2`
+ * `(throw "Error" : Except String Nat).map toString = throw "Error"`
+-/
 @[always_inline, inline]
 protected def map (f : α → β) : Except ε α → Except ε β
   | Except.error err => Except.error err
@@ -27,36 +37,78 @@ protected def map (f : α → β) : Except ε α → Except ε β
   intro e
   simp [Except.map]; cases e <;> rfl
 
+/--
+Transforms exceptions with a function, doing nothing on successful results.
+
+Examples:
+ * `(pure 2 : Except String Nat).mapError (·.length) = pure 2`
+ * `(throw "Error" : Except String Nat).mapError (·.length) = throw 5`
+-/
 @[always_inline, inline]
 protected def mapError (f : ε → ε') : Except ε α → Except ε' α
   | Except.error err => Except.error <| f err
   | Except.ok v      => Except.ok v
 
+/--
+Sequences two operations that may throw exceptions, allowing the second to depend on the value
+returned by the first.
+
+If the first operation throws an exception, then it is the result of the computation. If the first
+succeeds but the second throws an exception, then that exception is the result. If both succeed,
+then the result is the result of the second computation.
+
+This is the implementation of the `>>=` operator for `Except ε`.
+-/
 @[always_inline, inline]
 protected def bind (ma : Except ε α) (f : α → Except ε β) : Except ε β :=
   match ma with
   | Except.error err => Except.error err
   | Except.ok v      => f v
 
-/-- Returns true if the value is `Except.ok`, false otherwise. -/
+/-- Returns `true` if the value is `Except.ok`, `false` otherwise. -/
 @[always_inline, inline]
 protected def toBool : Except ε α → Bool
   | Except.ok _    => true
   | Except.error _ => false
 
+@[inherit_doc Except.toBool]
 abbrev isOk : Except ε α → Bool := Except.toBool
 
+/--
+Returns `none` if an exception was thrown, or `some` around the value on success.
+
+Examples:
+ * `(pure 10 : Except String Nat).toOption = some 10`
+ * `(throw "Failure" : Except String Nat).toOption = none`
+-/
 @[always_inline, inline]
 protected def toOption : Except ε α → Option α
   | Except.ok a    => some a
   | Except.error _ => none
 
+/--
+Handles exceptions thrown in the `Except ε` monad.
+
+If `ma` is successful, its result is returned. If it throws an exception, then `handle` is invoked
+on the exception's value.
+
+Examples:
+ * `(pure 2 : Except String Nat).tryCatch (pure ·.length) = pure 2`
+ * `(throw "Error" : Except String Nat).tryCatch (pure ·.length) = pure 5`
+ * `(throw "Error" : Except String Nat).tryCatch (fun x => throw ("E: " ++ x)) = throw "E: Error"`
+-/
 @[always_inline, inline]
 protected def tryCatch (ma : Except ε α) (handle : ε → Except ε α) : Except ε α :=
   match ma with
   | Except.ok a    => Except.ok a
   | Except.error e => handle e
 
+/--
+Recovers from exceptions thrown in the `Except ε` monad. Typically used via the `<|>` operator.
+
+`Except.tryCatch` is a related operator that allows the recovery procedure to depend on _which_
+exception was thrown.
+-/
 def orElseLazy (x : Except ε α) (y : Unit → Except ε α) : Except ε α :=
   match x with
   | Except.ok a    => Except.ok a
@@ -70,12 +122,26 @@ instance : Monad (Except ε) where
 
 end Except
 
+/--
+Adds exceptions of type `ε` to a monad `m`.
+-/
 def ExceptT (ε : Type u) (m : Type u → Type v) (α : Type u) : Type v :=
   m (Except ε α)
 
+/--
+Use a monadic action that may return an exception's value as an action in the transformed monad that
+may throw the corresponding exception.
+
+This is the inverse of `ExceptT.run`.
+-/
 @[always_inline, inline]
 def ExceptT.mk {ε : Type u} {m : Type u → Type v} {α : Type u} (x : m (Except ε α)) : ExceptT ε m α := x
 
+/--
+Use a monadic action that may throw an exception as an action that may return an exception's value.
+
+This is the inverse of `ExceptT.mk`.
+-/
 @[always_inline, inline]
 def ExceptT.run {ε : Type u} {m : Type u → Type v} {α : Type u} (x : ExceptT ε m α) : m (Except ε α) := x
 
@@ -83,25 +149,41 @@ namespace ExceptT
 
 variable {ε : Type u} {m : Type u → Type v} [Monad m]
 
+/--
+Returns the value `a` without throwing exceptions or having any other effect.
+-/
 @[always_inline, inline]
 protected def pure {α : Type u} (a : α) : ExceptT ε m α :=
   ExceptT.mk <| pure (Except.ok a)
 
+/--
+Handles exceptions thrown by an action that can have no effects _other_ than throwing exceptions.
+-/
 @[always_inline, inline]
 protected def bindCont {α β : Type u} (f : α → ExceptT ε m β) : Except ε α → m (Except ε β)
   | Except.ok a    => f a
   | Except.error e => pure (Except.error e)
 
+/--
+Sequences two actions that may throw exceptions. Typically used via `do`-notation or the `>>=`
+operator.
+-/
 @[always_inline, inline]
 protected def bind {α β : Type u} (ma : ExceptT ε m α) (f : α → ExceptT ε m β) : ExceptT ε m β :=
   ExceptT.mk <| ma >>= ExceptT.bindCont f
 
+/--
+Transforms a successful computation's value using `f`. Typically used via the `<$>` operator.
+-/
 @[always_inline, inline]
 protected def map {α β : Type u} (f : α → β) (x : ExceptT ε m α) : ExceptT ε m β :=
   ExceptT.mk <| x >>= fun a => match a with
     | (Except.ok a)    => pure <| Except.ok (f a)
     | (Except.error e) => pure <| Except.error e
 
+/--
+Runs a computation from an underlying monad in the transformed monad with exceptions.
+-/
 @[always_inline, inline]
 protected def lift {α : Type u} (t : m α) : ExceptT ε m α :=
   ExceptT.mk <| Except.ok <$> t
@@ -110,6 +192,9 @@ protected def lift {α : Type u} (t : m α) : ExceptT ε m α :=
 instance : MonadLift (Except ε) (ExceptT ε m) := ⟨fun e => ExceptT.mk <| pure e⟩
 instance : MonadLift m (ExceptT ε m) := ⟨ExceptT.lift⟩
 
+/--
+Handles exceptions produced in the `ExceptT ε` transformer.
+-/
 @[always_inline, inline]
 protected def tryCatch {α : Type u} (ma : ExceptT ε m α) (handle : ε → ExceptT ε m α) : ExceptT ε m α :=
   ExceptT.mk <| ma >>= fun res => match res with
@@ -124,6 +209,11 @@ instance : Monad (ExceptT ε m) where
   bind := ExceptT.bind
   map  := ExceptT.map
 
+/--
+Transforms exceptions using the function `f`.
+
+This is the `ExceptT` version of `Except.mapError`.
+-/
 @[always_inline, inline]
 protected def adapt {ε' α : Type u} (f : ε → ε') : ExceptT ε m α → ExceptT ε' m α := fun x =>
   ExceptT.mk <| Except.mapError f <$> x
@@ -150,8 +240,12 @@ instance (ε) : MonadExceptOf ε (Except ε) where
 namespace MonadExcept
 variable {ε : Type u} {m : Type v → Type w}
 
-/-- Alternative orelse operator that allows to select which exception should be used.
-    The default is to use the first exception since the standard `orelse` uses the second. -/
+/--
+An alternative unconditional error recovery operator that allows callers to specify which exception
+to throw in cases where both operations throw exceptions.
+
+By default, the first is thrown, because the `<|>` operator throws the second.
+-/
 @[always_inline, inline]
 def orelse' [MonadExcept ε m] {α : Type v} (t₁ t₂ : m α) (useFirstEx := true) : m α :=
   tryCatch t₁ fun e₁ => tryCatch t₂ fun e₂ => throw (if useFirstEx then e₁ else e₂)
@@ -171,13 +265,24 @@ instance (ε : Type u) (m : Type u → Type v) [Monad m] : MonadControl m (Excep
   liftWith f := liftM <| f fun x => x.run
   restoreM x := x
 
+/--
+Monads that provide the ability to ensure an action happens, regardless of exceptions or other
+failures.
+
+`MonadFinally.tryFinally'` is used to desugar `try ... finally ...` syntax.
+-/
 class MonadFinally (m : Type u → Type v) where
-  /-- `tryFinally' x f` runs `x` and then the "finally" computation `f`.
-  When `x` succeeds with `a : α`, `f (some a)` is returned. If `x` fails
-  for `m`'s definition of failure, `f none` is returned. Hence `tryFinally'`
-  can be thought of as performing the same role as a `finally` block in
-  an imperative programming language. -/
-  tryFinally' {α β} : m α → (Option α → m β) → m (α × β)
+  /--
+  Runs an action, ensuring that some other action always happens afterward.
+
+  More specifically, `tryFinally' x f` runs `x` and then the “finally” computation `f`. If `x`
+  succeeds with some value `a : α`, `f (some a)` is returned. If `x` fails for `m`'s definition of
+  failure, `f none` is returned.
+
+  `tryFinally'` can be thought of as performing the same role as a `finally` block in an imperative
+  programming language.
+  -/
+  tryFinally' {α β} : (x : m α) → (f : Option α → m β) → m (α × β)
 
 export MonadFinally (tryFinally')
 

src/Init/Control/ExceptCps.lean

@@ -10,19 +10,37 @@ import Init.Control.Lawful.Basic
 The Exception monad transformer using CPS style.
 -/
 
+/--
+Adds exceptions of type `ε` to a monad `m`.
+
+Instead of using `Except ε` to model exceptions, this implementation uses continuation passing
+style. This has different performance characteristics from `ExceptT ε`.
+-/
 def ExceptCpsT (ε : Type u) (m : Type u → Type v) (α : Type u) := (β : Type u) → (α → m β) → (ε → m β) → m β
 
 namespace ExceptCpsT
 
+/--
+Use a monadic action that may throw an exception as an action that may return an exception's value.
+-/
 @[always_inline, inline]
 def run {ε α : Type u} [Monad m] (x : ExceptCpsT ε m α) : m (Except ε α) :=
   x _ (fun a => pure (Except.ok a)) (fun e => pure (Except.error e))
 
 set_option linter.unusedVariables false in  -- `s` unused
+/--
+Use a monadic action that may throw an exception by providing explicit success and failure
+continuations.
+-/
 @[always_inline, inline]
 def runK {ε α : Type u} (x : ExceptCpsT ε m α) (s : ε) (ok : α → m β) (error : ε → m β) : m β :=
   x _ ok error
 
+/--
+Returns the value of a computation, forgetting whether it was an exception or a success.
+
+This corresponds to early return.
+-/
 @[always_inline, inline]
 def runCatch [Monad m] (x : ExceptCpsT α m α) : m α :=
   x α pure pure
@@ -40,6 +58,9 @@ instance : MonadExceptOf ε (ExceptCpsT ε m) where
   throw e  := fun _ _ k => k e
   tryCatch x handle := fun _ k₁ k₂ => x _ k₁ (fun e => handle e _ k₁ k₂)
 
+/--
+Run an action from the transformed monad in the exception monad.
+-/
 @[always_inline, inline]
 def lift [Monad m] (x : m α) : ExceptCpsT ε m α :=
   fun _ k _ => x >>= k

src/Init/Control/Id.lean

@@ -10,6 +10,28 @@ import Init.Core
 
 universe u
 
+/--
+The identity function on types, used primarily for its `Monad` instance.
+
+The identity monad is useful together with monad transformers to construct monads for particular
+purposes. Additionally, it can be used with `do`-notation in order to use control structures such as
+local mutability, `for`-loops, and early returns in code that does not otherwise use monads.
+
+Examples:
+```lean example
+def containsFive (xs : List Nat) : Bool := Id.run do
+  for x in xs do
+    if x == 5 then return true
+  return false
+```
+
+```lean example
+#eval containsFive [1, 3, 5, 7]
+```
+```output
+true
+```
+-/
 def Id (type : Type u) : Type u := type
 
 namespace Id
@@ -20,9 +42,18 @@ instance : Monad Id where
   bind x f := f x
   map f x := f x
 
+/--
+The identity monad has a `bind` operator.
+-/
 def hasBind : Bind Id :=
   inferInstance
 
+/--
+Runs a computation in the identity monad.
+
+This function is the identity function. Because its parameter has type `Id α`, it causes
+`do`-notation in its arguments to use the `Monad Id` instance.
+-/
 @[always_inline, inline]
 protected def run (x : Id α) : α := x
 

src/Init/Control/Lawful.lean

@@ -6,3 +6,4 @@ Authors: Sebastian Ullrich, Leonardo de Moura, Mario Carneiro
 prelude
 import Init.Control.Lawful.Basic
 import Init.Control.Lawful.Instances
+import Init.Control.Lawful.Lemmas

src/Init/Control/Lawful/Basic.lean

@@ -13,17 +13,26 @@ open Function
   rfl
 
 /--
-The `Functor` typeclass only contains the operations of a functor.
-`LawfulFunctor` further asserts that these operations satisfy the laws of a functor,
-including the preservation of the identity and composition laws:
-```
-id <$> x = x
-(h ∘ g) <$> x = h <$> g <$> x
-```
+A functor satisfies the functor laws.
+
+The `Functor` class contains the operations of a functor, but does not require that instances
+prove they satisfy the laws of a functor. A `LawfulFunctor` instance includes proofs that the laws
+are satisfied. Because `Functor` instances may provide optimized implementations of `mapConst`,
+`LawfulFunctor` instances must also prove that the optimized implementation is equivalent to the
+standard implementation.
 -/
 class LawfulFunctor (f : Type u → Type v) [Functor f] : Prop where
+  /--
+  The `mapConst` implementation is equivalent to the default implementation.
+  -/
   map_const          : (Functor.mapConst : α → f β → f α) = Functor.map ∘ const β
+  /--
+  The `map` implementation preserves identity.
+  -/
   id_map   (x : f α) : id <$> x = x
+  /--
+  The `map` implementation preserves function composition.
+  -/
   comp_map (g : α → β) (h : β → γ) (x : f α) : (h ∘ g) <$> x = h <$> g <$> x
 
 export LawfulFunctor (map_const id_map comp_map)
@@ -38,21 +47,48 @@ attribute [simp] id_map
   (comp_map _ _ _).symm
 
 /--
-The `Applicative` typeclass only contains the operations of an applicative functor.
-`LawfulApplicative` further asserts that these operations satisfy the laws of an applicative functor:
-```
-pure id <*> v = v
-pure (·∘·) <*> u <*> v <*> w = u <*> (v <*> w)
-pure f <*> pure x = pure (f x)
-u <*> pure y = pure (· y) <*> u
-```
+An applicative functor satisfies the laws of an applicative functor.
+
+The `Applicative` class contains the operations of an applicative functor, but does not require that
+instances prove they satisfy the laws of an applicative functor. A `LawfulApplicative` instance
+includes proofs that the laws are satisfied.
+
+Because `Applicative` instances may provide optimized implementations of `seqLeft` and `seqRight`,
+`LawfulApplicative` instances must also prove that the optimized implementation is equivalent to the
+standard implementation.
 -/
-class LawfulApplicative (f : Type u → Type v) [Applicative f] extends LawfulFunctor f : Prop where
+class LawfulApplicative (f : Type u → Type v) [Applicative f] : Prop extends LawfulFunctor f where
+  /-- `seqLeft` is equivalent to the default implementation. -/
   seqLeft_eq  (x : f α) (y : f β)     : x <* y = const β <$> x <*> y
+  /-- `seqRight` is equivalent to the default implementation. -/
   seqRight_eq (x : f α) (y : f β)     : x *> y = const α id <$> x <*> y
+  /--
+  `pure` before `seq` is equivalent to `Functor.map`.
+
+  This means that `pure` really is pure when occurring immediately prior to `seq`.
+   -/
   pure_seq    (g : α → β) (x : f α)   : pure g <*> x = g <$> x
+
+  /--
+  Mapping a function over the result of `pure` is equivalent to applying the function under `pure`.
+
+  This means that `pure` really is pure with respect to `Functor.map`.
+  -/
   map_pure    (g : α → β) (x : α)     : g <$> (pure x : f α) = pure (g x)
+
+  /--
+  `pure` after `seq` is equivalent to `Functor.map`.
+
+  This means that `pure` really is pure when occurring just after `seq`.
+  -/
   seq_pure    {α β : Type u} (g : f (α → β)) (x : α) : g <*> pure x = (fun h => h x) <$> g
+
+  /--
+  `seq` is associative.
+
+  Changing the nesting of `seq` calls while maintaining the order of computations results in an
+  equivalent computation. This means that `seq` is not doing any more than sequencing.
+  -/
   seq_assoc   {α β γ : Type u} (x : f α) (g : f (α → β)) (h : f (β → γ)) : h <*> (g <*> x) = ((@comp α β γ) <$> h) <*> g <*> x
   comp_map g h x := (by
     repeat rw [← pure_seq]
@@ -66,21 +102,36 @@ attribute [simp] map_pure seq_pure
   simp [pure_seq]
 
 /--
-The `Monad` typeclass only contains the operations of a monad.
-`LawfulMonad` further asserts that these operations satisfy the laws of a monad,
-including associativity and identity laws for `bind`:
-```
-pure x >>= f = f x
-x >>= pure = x
-x >>= f >>= g = x >>= (fun x => f x >>= g)
-```
+Lawful monads are those that satisfy a certain behavioral specification. While all instances of
+`Monad` should satisfy these laws, not all implementations are required to prove this.
 
-`LawfulMonad.mk'` is an alternative constructor containing useful defaults for many fields.
+`LawfulMonad.mk'` is an alternative constructor that contains useful defaults for many fields.
 -/
-class LawfulMonad (m : Type u → Type v) [Monad m] extends LawfulApplicative m : Prop where
+class LawfulMonad (m : Type u → Type v) [Monad m] : Prop extends LawfulApplicative m where
+  /--
+  A `bind` followed by `pure` composed with a function is equivalent to a functorial map.
+
+  This means that `pure` really is pure after a `bind` and has no effects.
+  -/
   bind_pure_comp (f : α → β) (x : m α) : x >>= (fun a => pure (f a)) = f <$> x
+  /--
+  A `bind` followed by a functorial map is equivalent to `Applicative` sequencing.
+
+  This means that the effect sequencing from `Monad` and `Applicative` are the same.
+  -/
   bind_map       {α β : Type u} (f : m (α → β)) (x : m α) : f >>= (. <$> x) = f <*> x
+  /--
+  `pure` followed by `bind` is equivalent to function application.
+
+  This means that `pure` really is pure before a `bind` and has no effects.
+  -/
   pure_bind      (x : α) (f : α → m β) : pure x >>= f = f x
+  /--
+  `bind` is associative.
+
+  Changing the nesting of `bind` calls while maintaining the order of computations results in an
+  equivalent computation. This means that `bind` is not doing more than data-dependent sequencing.
+  -/
   bind_assoc     (x : m α) (f : α → m β) (g : β → m γ) : x >>= f >>= g = x >>= fun x => f x >>= g
   map_pure g x    := (by rw [← bind_pure_comp, pure_bind])
   seq_pure g x    := (by rw [← bind_map]; simp [map_pure, bind_pure_comp])
@@ -136,6 +187,23 @@ theorem seqLeft_eq_bind [Monad m] [LawfulMonad m] (x : m α) (y : m β) : x <* y
 theorem Functor.map_unit [Monad m] [LawfulMonad m] {a : m PUnit} : (fun _ => PUnit.unit) <$> a = a := by
   simp [map]
 
+/--
+This is just a duplicate of `LawfulApplicative.map_pure`,
+but sometimes applies when that doesn't.
+
+It is named with a prime to avoid conflict with the inherited field `LawfulMonad.map_pure`.
+-/
+@[simp] theorem LawfulMonad.map_pure' [Monad m] [LawfulMonad m] {a : α} :
+    (f <$> pure a : m β) = pure (f a) := by
+  simp only [map_pure]
+
+/--
+This is just a duplicate of `Functor.map_map`, but sometimes applies when that doesn't.
+-/
+@[simp] theorem LawfulMonad.map_map {m} [Monad m] [LawfulMonad m] {x : m α} :
+    g <$> f <$> x = (fun a => g (f a)) <$> x := by
+  simp only [Functor.map_map]
+
 /--
 An alternative constructor for `LawfulMonad` which has more
 defaultable fields in the common case.

src/Init/Control/Lawful/Lemmas.lean

@@ -0,0 +1,57 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Control.Lawful.Basic
+import Init.RCases
+import Init.ByCases
+
+-- Mapping by a function with a left inverse is injective.
+theorem map_inj_of_left_inverse [Functor m] [LawfulFunctor m] {f : α → β}
+    (w : ∃ g : β → α, ∀ x, g (f x) = x) {x y : m α} :
+    f <$> x = f <$> y ↔ x = y := by
+  constructor
+  · intro h
+    rcases w with ⟨g, w⟩
+    replace h := congrArg (g <$> ·) h
+    simpa [w] using h
+  · rintro rfl
+    rfl
+
+-- Mapping by an injective function is injective, as long as the domain is nonempty.
+@[simp] theorem map_inj_right_of_nonempty [Functor m] [LawfulFunctor m] [Nonempty α] {f : α → β}
+    (w : ∀ {x y}, f x = f y → x = y) {x y : m α} :
+    f <$> x = f <$> y ↔ x = y := by
+  constructor
+  · intro h
+    apply (map_inj_of_left_inverse ?_).mp h
+    let ⟨a⟩ := ‹Nonempty α›
+    refine ⟨?_, ?_⟩
+    · intro b
+      by_cases p : ∃ a, f a = b
+      · exact Exists.choose p
+      · exact a
+    · intro b
+      simp only [exists_apply_eq_apply, ↓reduceDIte]
+      apply w
+      apply Exists.choose_spec (p := fun a => f a = f b)
+  · rintro rfl
+    rfl
+
+@[simp] theorem map_inj_right [Monad m] [LawfulMonad m]
+    {f : α → β} (h : ∀ {x y : α}, f x = f y → x = y) {x y : m α} :
+    f <$> x = f <$> y ↔ x = y := by
+  by_cases hempty : Nonempty α
+  · exact map_inj_right_of_nonempty h
+  · constructor
+    · intro h'
+      have (z : m α) : z = (do let a ← z; let b ← pure (f a); x) := by
+        conv => lhs; rw [← bind_pure z]
+        congr; funext a
+        exact (hempty ⟨a⟩).elim
+      rw [this x, this y]
+      rw [← bind_assoc, ← map_eq_pure_bind, h', map_eq_pure_bind, bind_assoc]
+    · intro h'
+      rw [h']

src/Init/Control/Option.lean

@@ -8,13 +8,22 @@ import Init.Data.Option.Basic
 import Init.Control.Basic
 import Init.Control.Except
 
+set_option linter.missingDocs true
+
 universe u v
 
 instance : ToBool (Option α) := ⟨Option.isSome⟩
 
+/--
+Adds the ability to fail to a monad. Unlike ordinary exceptions, there is no way to signal why a
+failure occurred.
+-/
 def OptionT (m : Type u → Type v) (α : Type u) : Type v :=
   m (Option α)
 
+/--
+Executes an action that might fail in the underlying monad `m`, returning `none` in case of failure.
+-/
 @[always_inline, inline]
 def OptionT.run {m : Type u → Type v} {α : Type u} (x : OptionT m α) : m (Option α) :=
   x
@@ -22,15 +31,25 @@ def OptionT.run {m : Type u → Type v} {α : Type u} (x : OptionT m α) : m (Op
 namespace OptionT
 variable {m : Type u → Type v} [Monad m] {α β : Type u}
 
+/--
+Converts an action that returns an `Option` into one that might fail, with `none` indicating
+failure.
+-/
 protected def mk (x : m (Option α)) : OptionT m α :=
   x
 
+/--
+Sequences two potentially-failing actions. The second action is run only if the first succeeds.
+-/
 @[always_inline, inline]
 protected def bind (x : OptionT m α) (f : α → OptionT m β) : OptionT m β := OptionT.mk do
   match (← x) with
   | some a => f a
   | none   => pure none
 
+/--
+Succeeds with the provided value.
+-/
 @[always_inline, inline]
 protected def pure (a : α) : OptionT m α := OptionT.mk do
   pure (some a)
@@ -40,11 +59,17 @@ instance : Monad (OptionT m) where
   pure := OptionT.pure
   bind := OptionT.bind
 
+/--
+Recovers from failures. Typically used via the `<|>` operator.
+-/
 @[always_inline, inline] protected def orElse (x : OptionT m α) (y : Unit → OptionT m α) : OptionT m α := OptionT.mk do
   match (← x) with
   | some a => pure (some a)
   | _      => y ()
 
+/--
+A recoverable failure.
+-/
 @[always_inline, inline] protected def fail : OptionT m α := OptionT.mk do
   pure none
 
@@ -52,6 +77,12 @@ instance : Alternative (OptionT m) where
   failure := OptionT.fail
   orElse  := OptionT.orElse
 
+/--
+Converts a computation from the underlying monad into one that could fail, even though it does not.
+
+This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
+lifting](lean-manual://section/monad-lifting).
+-/
 @[always_inline, inline] protected def lift (x : m α) : OptionT m α := OptionT.mk do
   return some (← x)
 
@@ -59,6 +90,9 @@ instance : MonadLift m (OptionT m) := ⟨OptionT.lift⟩
 
 instance : MonadFunctor m (OptionT m) := ⟨fun f x => f x⟩
 
+/--
+Handles failures by treating them as exceptions of type `Unit`.
+-/
 @[always_inline, inline] protected def tryCatch (x : OptionT m α) (handle : Unit → OptionT m α) : OptionT m α := OptionT.mk do
   let some a ← x | handle ()
   pure a

src/Init/Control/Reader.lean

@@ -10,12 +10,21 @@ import Init.Control.Basic
 import Init.Control.Id
 import Init.Control.Except
 
+set_option linter.missingDocs true
+
 namespace ReaderT
 
+/--
+Recovers from errors. The same local value is provided to both branches. Typically used via the
+`<|>` operator.
+-/
 @[always_inline, inline]
 protected def orElse [Alternative m] (x₁ : ReaderT ρ m α) (x₂ : Unit → ReaderT ρ m α) : ReaderT ρ m α :=
   fun s => x₁ s <|> x₂ () s
 
+/--
+Fails with a recoverable error.
+-/
 @[always_inline, inline]
 protected def failure [Alternative m] : ReaderT ρ m α :=
   fun _ => failure
@@ -35,4 +44,8 @@ instance : MonadControl m (ReaderT ρ m) where
 instance ReaderT.tryFinally [MonadFinally m] : MonadFinally (ReaderT ρ m) where
   tryFinally' x h ctx := tryFinally' (x ctx) (fun a? => h a? ctx)
 
+/--
+A monad with access to a read-only value of type `ρ`. The value can be locally overridden by
+`withReader`, but it cannot be mutated.
+-/
 @[reducible] def ReaderM (ρ : Type u) := ReaderT ρ Id

src/Init/Control/State.lean

@@ -9,19 +9,42 @@ prelude
 import Init.Control.Basic
 import Init.Control.Id
 import Init.Control.Except
+
+set_option linter.missingDocs true
+
 universe u v w
 
+/--
+Adds a mutable state of type `σ` to a monad.
+
+Actions in the resulting monad are functions that take an initial state and return, in `m`, a tuple
+of a value and a state.
+-/
 def StateT (σ : Type u) (m : Type u → Type v) (α : Type u) : Type (max u v) :=
   σ → m (α × σ)
 
+/--
+Executes an action from a monad with added state in the underlying monad `m`. Given an initial
+state, it returns a value paired with the final state.
+-/
 @[always_inline, inline]
 def StateT.run {σ : Type u} {m : Type u → Type v} {α : Type u} (x : StateT σ m α) (s : σ) : m (α × σ) :=
   x s
 
+/--
+Executes an action from a monad with added state in the underlying monad `m`. Given an initial
+state, it returns a value, discarding the final state.
+-/
 @[always_inline, inline]
 def StateT.run' {σ : Type u} {m : Type u → Type v} [Functor m] {α : Type u} (x : StateT σ m α) (s : σ) : m α :=
   (·.1) <$> x s
 
+/--
+A tuple-based state monad.
+
+Actions in `StateM σ` are functions that take an initial state and return a value paired with a
+final state.
+-/
 @[reducible]
 def StateM (σ α : Type u) : Type u := StateT σ Id α
 
@@ -38,14 +61,23 @@ section
 variable {σ : Type u} {m : Type u → Type v}
 variable [Monad m] {α β : Type u}
 
+/--
+Returns the given value without modifying the state. Typically used via `Pure.pure`.
+-/
 @[always_inline, inline]
 protected def pure (a : α) : StateT σ m α :=
   fun s => pure (a, s)
 
+/--
+Sequences two actions. Typically used via the `>>=` operator.
+-/
 @[always_inline, inline]
 protected def bind (x : StateT σ m α) (f : α → StateT σ m β) : StateT σ m β :=
   fun s => do let (a, s) ← x s; f a s
 
+/--
+Modifies the value returned by a computation. Typically used via the `<$>` operator.
+-/
 @[always_inline, inline]
 protected def map (f : α → β) (x : StateT σ m α) : StateT σ m β :=
   fun s => do let (a, s) ← x s; pure (f a, s)
@@ -56,10 +88,17 @@ instance : Monad (StateT σ m) where
   bind := StateT.bind
   map  := StateT.map
 
+/--
+Recovers from errors. The state is rolled back on error recovery. Typically used via the `<|>`
+operator.
+-/
 @[always_inline, inline]
 protected def orElse [Alternative m] {α : Type u} (x₁ : StateT σ m α) (x₂ : Unit → StateT σ m α) : StateT σ m α :=
   fun s => x₁ s <|> x₂ () s
 
+/--
+Fails with a recoverable error. The state is rolled back on error recovery.
+-/
 @[always_inline, inline]
 protected def failure [Alternative m] {α : Type u} : StateT σ m α :=
   fun _ => failure
@@ -68,18 +107,40 @@ instance [Alternative m] : Alternative (StateT σ m) where
   failure := StateT.failure
   orElse  := StateT.orElse
 
+/--
+Retrieves the current value of the monad's mutable state.
+
+This increments the reference count of the state, which may inhibit in-place updates.
+-/
 @[always_inline, inline]
 protected def get : StateT σ m σ :=
   fun s => pure (s, s)
 
+/--
+Replaces the mutable state with a new value.
+-/
 @[always_inline, inline]
 protected def set : σ → StateT σ m PUnit :=
   fun s' _ => pure (⟨⟩, s')
 
+/--
+Applies a function to the current state that both computes a new state and a value. The new state
+replaces the current state, and the value is returned.
+
+It is equivalent to `do let (a, s) := f (← StateT.get); StateT.set s; pure a`. However, using
+`StateT.modifyGet` may lead to better performance because it doesn't add a new reference to the
+state value, and additional references can inhibit in-place updates of data.
+-/
 @[always_inline, inline]
 protected def modifyGet (f : σ → α × σ) : StateT σ m α :=
   fun s => pure (f s)
 
+/--
+Runs an action from the underlying monad in the monad with state. The state is not modified.
+
+This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
+lifting](lean-manual://section/monad-lifting).
+-/
 @[always_inline, inline]
 protected def lift {α : Type u} (t : m α) : StateT σ m α :=
   fun s => do let a ← t; pure (a, s)

src/Init/Control/StateCps.lean

@@ -6,24 +6,45 @@ Authors: Leonardo de Moura
 prelude
 import Init.Control.Lawful.Basic
 
+set_option linter.missingDocs true
+
 /-!
 The State monad transformer using CPS style.
 -/
 
+/--
+An alternative implementation of a state monad transformer that internally uses continuation passing
+style instead of tuples.
+-/
 def StateCpsT (σ : Type u) (m : Type u → Type v) (α : Type u) := (δ : Type u) → σ → (α → σ → m δ) → m δ
 
 namespace StateCpsT
 
 variable {α σ : Type u} {m : Type u → Type v}
 
+/--
+Runs a stateful computation that's represented using continuation passing style by providing it with
+an initial state and a continuation.
+-/
 @[always_inline, inline]
 def runK (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
   x _ s k
 
+/--
+Executes an action from a monad with added state in the underlying monad `m`. Given an initial
+state, it returns a value paired with the final state.
+
+While the state is internally represented in continuation passing style, the resulting value is the
+same as for a non-CPS state monad.
+-/
 @[always_inline, inline]
 def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
   runK x s (fun a s => pure (a, s))
 
+/--
+Executes an action from a monad with added state in the underlying monad `m`. Given an initial
+state, it returns a value, discarding the final state.
+-/
 @[always_inline, inline]
 def run' [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
   runK x s (fun a _ => pure a)
@@ -43,6 +64,12 @@ instance : MonadStateOf σ (StateCpsT σ m) where
   set s := fun _ _ k => k ⟨⟩ s
   modifyGet f := fun _ s k => let (a, s) := f s; k a s
 
+/--
+Runs an action from the underlying monad in the monad with state. The state is not modified.
+
+This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
+lifting](lean-manual://section/monad-lifting).
+-/
 @[always_inline, inline]
 protected def lift [Monad m] (x : m α) : StateCpsT σ m α :=
   fun _ s k => x >>= (k . s)

src/Init/Control/StateRef.lean

@@ -8,10 +8,23 @@ The State monad transformer using IO references.
 prelude
 import Init.System.ST
 
+set_option linter.missingDocs true
+
+/--
+A state monad that uses an actual mutable reference cell (i.e. an `ST.Ref ω σ`).
+
+The macro `StateRefT σ m α` infers `ω` from `m`. It should normally be used instead.
+-/
 def StateRefT' (ω : Type) (σ : Type) (m : Type → Type) (α : Type) : Type := ReaderT (ST.Ref ω σ) m α
 
 /-! Recall that `StateRefT` is a macro that infers `ω` from the `m`. -/
 
+/--
+Executes an action from a monad with added state in the underlying monad `m`. Given an initial
+state, it returns a value paired with the final state.
+
+The monad `m` must support `ST` effects in order to create and mutate reference cells.
+-/
 @[always_inline, inline]
 def StateRefT'.run {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST ω) m] {α : Type} (x : StateRefT' ω σ m α) (s : σ) : m (α × σ) := do
   let ref ← ST.mkRef s
@@ -19,6 +32,12 @@ def StateRefT'.run {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST
   let s ← ref.get
   pure (a, s)
 
+/--
+Executes an action from a monad with added state in the underlying monad `m`. Given an initial
+state, it returns a value, discarding the final state.
+
+The monad `m` must support `ST` effects in order to create and mutate reference cells.
+-/
 @[always_inline, inline]
 def StateRefT'.run' {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST ω) m] {α : Type} (x : StateRefT' ω σ m α) (s : σ) : m α := do
   let (a, _) ← x.run s
@@ -27,6 +46,12 @@ def StateRefT'.run' {ω σ : Type} {m : Type → Type} [Monad m] [MonadLiftT (ST
 namespace StateRefT'
 variable {ω σ : Type} {m : Type → Type} {α : Type}
 
+/--
+Runs an action from the underlying monad in the monad with state. The state is not modified.
+
+This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
+lifting](lean-manual://section/monad-lifting).
+-/
 @[always_inline, inline]
 protected def lift (x : m α) : StateRefT' ω σ m α :=
   fun _ => x
@@ -36,14 +61,30 @@ instance : MonadLift m (StateRefT' ω σ m) := ⟨StateRefT'.lift⟩
 instance (σ m) : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
 instance [Alternative m] [Monad m] : Alternative (StateRefT' ω σ m) := inferInstanceAs (Alternative (ReaderT _ _))
 
+/--
+Retrieves the current value of the monad's mutable state.
+
+This increments the reference count of the state, which may inhibit in-place updates.
+-/
 @[inline]
 protected def get [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
   fun ref => ref.get
 
+/--
+Replaces the mutable state with a new value.
+-/
 @[inline]
 protected def set [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
   fun ref => ref.set s
 
+/--
+Applies a function to the current state that both computes a new state and a value. The new state
+replaces the current state, and the value is returned.
+
+It is equivalent to a `get` followed by a `set`. However, using `modifyGet` may lead to higher
+performance because it doesn't add a new reference to the state value. Additional references can
+inhibit in-place updates of data.
+-/
 @[inline]
 protected def modifyGet [MonadLiftT (ST ω) m] (f : σ → α × σ) : StateRefT' ω σ m α :=
   fun ref => ref.modifyGet f

src/Init/Conv.lean

@@ -150,6 +150,10 @@ See the `simp` tactic for more information. -/
 syntax (name := simp) "simp" optConfig (discharger)? (&" only")?
   (" [" withoutPosition((simpStar <|> simpErase <|> simpLemma),*) "]")? : conv
 
+/-- `simp?` takes the same arguments as `simp`, but reports an equivalent call to `simp only`
+that would be sufficient to close the goal. See the `simp?` tactic for more information. -/
+syntax (name := simpTrace) "simp?" optConfig (discharger)? (&" only")? (simpArgs)? : conv
+
 /--
 `dsimp` is the definitional simplifier in `conv`-mode. It differs from `simp` in that it only
 applies theorems that hold by reflexivity.
@@ -167,6 +171,9 @@ example (a : Nat): (0 + 0) = a - a := by
 syntax (name := dsimp) "dsimp" optConfig (discharger)? (&" only")?
   (" [" withoutPosition((simpErase <|> simpLemma),*) "]")? : conv
 
+@[inherit_doc simpTrace]
+syntax (name := dsimpTrace) "dsimp?" optConfig (&" only")? (dsimpArgs)? : conv
+
 /-- `simp_match` simplifies match expressions. For example,
 ```
 match [a, b] with

src/Init/Data/AC.lean

@@ -39,7 +39,7 @@ class EvalInformation (α : Sort u) (β : Sort v) where
   evalVar : α → Nat → β
 
 def Context.var (ctx : Context α) (idx : Nat) : Variable ctx.op :=
-  ctx.vars.getD idx ⟨ctx.arbitrary, none⟩
+  ctx.vars[idx]?.getD ⟨ctx.arbitrary, none⟩
 
 instance : ContextInformation (Context α) where
   isNeutral ctx x := ctx.var x |>.neutral.isSome

src/Init/Data/Array.lean

@@ -23,3 +23,8 @@ import Init.Data.Array.FinRange
 import Init.Data.Array.Perm
 import Init.Data.Array.Find
 import Init.Data.Array.Lex
+import Init.Data.Array.Range
+import Init.Data.Array.Erase
+import Init.Data.Array.Zip
+import Init.Data.Array.InsertIdx
+import Init.Data.Array.Extract

src/Init/Data/Array/Attach.lean

@@ -6,20 +6,23 @@ Authors: Joachim Breitner, Mario Carneiro
 prelude
 import Init.Data.Array.Mem
 import Init.Data.Array.Lemmas
+import Init.Data.Array.Count
 import Init.Data.List.Attach
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 /--
-`O(n)`. Partial map. If `f : Π a, P a → β` is a partial function defined on
-`a : α` satisfying `P`, then `pmap f l h` is essentially the same as `map f l`
-but is defined only when all members of `l` satisfy `P`, using the proof
-to apply `f`.
+Maps a partially defined function (defined on those terms of `α` that satisfy a predicate `P`) over
+an array `xs : Array α`, given a proof that every element of `xs` in fact satisfies `P`.
 
-We replace this at runtime with a more efficient version via the `csimp` lemma `pmap_eq_pmapImpl`.
+`Array.pmap`, named for “partial map,” is the equivalent of `Array.map` for such partial functions.
 -/
-def pmap {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) : Array β :=
-  (l.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
+
+def pmap {P : α → Prop} (f : ∀ a, P a → β) (xs : Array α) (H : ∀ a ∈ xs, P a) : Array β :=
+  (xs.toList.pmap f (fun a m => H a (mem_def.mpr m))).toArray
 
 /--
 Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
@@ -28,14 +31,27 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
 @[inline] private unsafe def attachWithImpl
     (xs : Array α) (P : α → Prop) (_ : ∀ x ∈ xs, P x) : Array {x // P x} := unsafeCast xs
 
-/-- `O(1)`. "Attach" a proof `P x` that holds for all the elements of `xs` to produce a new array
-  with the same elements but in the type `{x // P x}`. -/
+/--
+“Attaches” individual proofs to an array of values that satisfy a predicate `P`, returning an array
+of elements in the corresponding subtype `{ x // P x }`.
+
+`O(1)`.
+-/
 @[implemented_by attachWithImpl] def attachWith
     (xs : Array α) (P : α → Prop) (H : ∀ x ∈ xs, P x) : Array {x // P x} :=
   ⟨xs.toList.attachWith P fun x h => H x (Array.Mem.mk h)⟩
 
-/-- `O(1)`. "Attach" the proof that the elements of `xs` are in `xs` to produce a new array
-  with the same elements but in the type `{x // x ∈ xs}`. -/
+/--
+“Attaches” the proof that the elements of `xs` are in fact elements of `xs`, producing a new array with
+the same elements but in the subtype `{ x // x ∈ xs }`.
+
+`O(1)`.
+
+This function is primarily used to allow definitions by [well-founded
+recursion](lean-manual://section/well-founded-recursion) that use higher-order functions (such as
+`Array.map`) to prove that an value taken from a list is smaller than the list. This allows the
+well-founded recursion mechanism to prove that the function terminates.
+-/
 @[inline] def attach (xs : Array α) : Array {x // x ∈ xs} := xs.attachWith _ fun _ => id
 
 @[simp] theorem _root_.List.attachWith_toArray {l : List α} {P : α → Prop} {H : ∀ x ∈ l.toArray, P x} :
@@ -50,35 +66,35 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
     l.toArray.pmap f H = (l.pmap f (by simpa using H)).toArray := by
   simp [pmap]
 
-@[simp] theorem toList_attachWith {l : Array α} {P : α → Prop} {H : ∀ x ∈ l, P x} :
-   (l.attachWith P H).toList = l.toList.attachWith P (by simpa [mem_toList] using H) := by
+@[simp] theorem toList_attachWith {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs, P x} :
+   (xs.attachWith P H).toList = xs.toList.attachWith P (by simpa [mem_toList] using H) := by
   simp [attachWith]
 
-@[simp] theorem toList_attach {α : Type _} {l : Array α} :
-    l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
+@[simp] theorem toList_attach {xs : Array α} :
+    xs.attach.toList = xs.toList.attachWith (· ∈ xs) (by simp [mem_toList]) := by
   simp [attach]
 
-@[simp] theorem toList_pmap {l : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ l, P a} :
-    (l.pmap f H).toList = l.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
+@[simp] theorem toList_pmap {xs : Array α} {P : α → Prop} {f : ∀ a, P a → β} {H : ∀ a ∈ xs, P a} :
+    (xs.pmap f H).toList = xs.toList.pmap f (fun a m => H a (mem_def.mpr m)) := by
   simp [pmap]
 
 /-- Implementation of `pmap` using the zero-copy version of `attach`. -/
-@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (l : Array α) (H : ∀ a ∈ l, P a) :
-    Array β := (l.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
+@[inline] private def pmapImpl {P : α → Prop} (f : ∀ a, P a → β) (xs : Array α) (H : ∀ a ∈ xs, P a) :
+    Array β := (xs.attachWith _ H).map fun ⟨x, h'⟩ => f x h'
 
 @[csimp] private theorem pmap_eq_pmapImpl : @pmap = @pmapImpl := by
-  funext α β p f L h'
-  cases L
-  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith]
+  funext α β p f xs H
+  cases xs
+  simp only [pmap, pmapImpl, List.attachWith_toArray, List.map_toArray, mk.injEq, List.map_attachWith_eq_pmap]
   apply List.pmap_congr_left
   intro a m h₁ h₂
   congr
 
 @[simp] theorem pmap_empty {P : α → Prop} (f : ∀ a, P a → β) : pmap f #[] (by simp) = #[] := rfl
 
-@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (l : Array α) (h : ∀ b ∈ l.push a, P b) :
-    pmap f (l.push a) h =
-      (pmap f l (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
+@[simp] theorem pmap_push {P : α → Prop} (f : ∀ a, P a → β) (a : α) (xs : Array α) (h : ∀ b ∈ xs.push a, P b) :
+    pmap f (xs.push a) h =
+      (pmap f xs (fun a m => by simp at h; exact h a (.inl m))).push (f a (h a (by simp))) := by
   simp [pmap]
 
 @[simp] theorem attach_empty : (#[] : Array α).attach = #[] := rfl
@@ -93,147 +109,158 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   simp
 
 @[simp]
-theorem pmap_eq_map (p : α → Prop) (f : α → β) (l : Array α) (H) :
-    @pmap _ _ p (fun a _ => f a) l H = map f l := by
-  cases l; simp
+theorem pmap_eq_map (p : α → Prop) (f : α → β) (xs : Array α) (H) :
+    @pmap _ _ p (fun a _ => f a) xs H = map f xs := by
+  cases xs; simp
 
-theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (l : Array α) {H₁ H₂}
-    (h : ∀ a ∈ l, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f l H₁ = pmap g l H₂ := by
-  cases l
+theorem pmap_congr_left {p q : α → Prop} {f : ∀ a, p a → β} {g : ∀ a, q a → β} (xs : Array α) {H₁ H₂}
+    (h : ∀ a ∈ xs, ∀ (h₁ h₂), f a h₁ = g a h₂) : pmap f xs H₁ = pmap g xs H₂ := by
+  cases xs
   simp only [mem_toArray] at h
   simp only [List.pmap_toArray, mk.injEq]
   rw [List.pmap_congr_left _ h]
 
-theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (l H) :
-    map g (pmap f l H) = pmap (fun a h => g (f a h)) l H := by
-  cases l
+theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (xs H) :
+    map g (pmap f xs H) = pmap (fun a h => g (f a h)) xs H := by
+  cases xs
   simp [List.map_pmap]
 
-theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (l H) :
-    pmap g (map f l) H = pmap (fun a h => g (f a) h) l fun _ h => H _ (mem_map_of_mem _ h) := by
-  cases l
+theorem pmap_map {p : β → Prop} (g : ∀ b, p b → γ) (f : α → β) (xs H) :
+    pmap g (map f xs) H = pmap (fun a h => g (f a) h) xs fun _ h => H _ (mem_map_of_mem _ h) := by
+  cases xs
   simp [List.pmap_map]
 
-theorem attach_congr {l₁ l₂ : Array α} (h : l₁ = l₂) :
-    l₁.attach = l₂.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
+theorem attach_congr {xs ys : Array α} (h : xs = ys) :
+    xs.attach = ys.attach.map (fun x => ⟨x.1, h ▸ x.2⟩) := by
   subst h
   simp
 
-theorem attachWith_congr {l₁ l₂ : Array α} (w : l₁ = l₂) {P : α → Prop} {H : ∀ x ∈ l₁, P x} :
-    l₁.attachWith P H = l₂.attachWith P fun _ h => H _ (w ▸ h) := by
+theorem attachWith_congr {xs ys : Array α} (w : xs = ys) {P : α → Prop} {H : ∀ x ∈ xs, P x} :
+    xs.attachWith P H = ys.attachWith P fun _ h => H _ (w ▸ h) := by
   subst w
   simp
 
-@[simp] theorem attach_push {a : α} {l : Array α} :
-    (l.push a).attach =
-      (l.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
-  cases l
+@[simp] theorem attach_push {a : α} {xs : Array α} :
+    (xs.push a).attach =
+      (xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_push_of_mem a h⟩)).push ⟨a, by simp⟩ := by
+  cases xs
   rw [attach_congr (List.push_toArray _ _)]
   simp [Function.comp_def]
 
-@[simp] theorem attachWith_push {a : α} {l : Array α} {P : α → Prop} {H : ∀ x ∈ l.push a, P x} :
-    (l.push a).attachWith P H =
-      (l.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
-  cases l
+@[simp] theorem attachWith_push {a : α} {xs : Array α} {P : α → Prop} {H : ∀ x ∈ xs.push a, P x} :
+    (xs.push a).attachWith P H =
+      (xs.attachWith P (fun x h => by simp at H; exact H x (.inl h))).push ⟨a, H a (by simp)⟩ := by
+  cases xs
   simp [attachWith_congr (List.push_toArray _ _)]
 
-theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (l H) :
-    pmap f l H = l.attach.map fun x => f x.1 (H _ x.2) := by
-  cases l
+theorem pmap_eq_map_attach {p : α → Prop} (f : ∀ a, p a → β) (xs H) :
+    pmap f xs H = xs.attach.map fun x => f x.1 (H _ x.2) := by
+  cases xs
   simp [List.pmap_eq_map_attach]
 
-theorem attach_map_coe (l : Array α) (f : α → β) :
-    (l.attach.map fun (i : {i // i ∈ l}) => f i) = l.map f := by
-  cases l
-  simp [List.attach_map_coe]
+@[simp]
+theorem pmap_eq_attachWith {p q : α → Prop} (f : ∀ a, p a → q a) (xs H) :
+    pmap (fun a h => ⟨a, f a h⟩) xs H = xs.attachWith q (fun x h => f x (H x h)) := by
+  cases xs
+  simp [List.pmap_eq_attachWith]
 
-theorem attach_map_val (l : Array α) (f : α → β) : (l.attach.map fun i => f i.val) = l.map f :=
-  attach_map_coe _ _
+theorem attach_map_val (xs : Array α) (f : α → β) :
+    (xs.attach.map fun (i : {i // i ∈ xs}) => f i) = xs.map f := by
+  cases xs
+  simp
 
-theorem attach_map_subtype_val (l : Array α) : l.attach.map Subtype.val = l := by
-  cases l; simp
+@[deprecated attach_map_val (since := "2025-02-17")]
+abbrev attach_map_coe := @attach_map_val
 
-theorem attachWith_map_coe {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
-    ((l.attachWith p H).map fun (i : { i // p i}) => f i) = l.map f := by
-  cases l; simp
+theorem attach_map_subtype_val (xs : Array α) : xs.attach.map Subtype.val = xs := by
+  cases xs; simp
 
-theorem attachWith_map_val {p : α → Prop} (f : α → β) (l : Array α) (H : ∀ a ∈ l, p a) :
-    ((l.attachWith p H).map fun i => f i.val) = l.map f :=
-  attachWith_map_coe _ _ _
+theorem attachWith_map_val {p : α → Prop} (f : α → β) (xs : Array α) (H : ∀ a ∈ xs, p a) :
+    ((xs.attachWith p H).map fun (i : { i // p i}) => f i) = xs.map f := by
+  cases xs; simp
 
-theorem attachWith_map_subtype_val {p : α → Prop} (l : Array α) (H : ∀ a ∈ l, p a) :
-    (l.attachWith p H).map Subtype.val = l := by
-  cases l; simp
+@[deprecated attachWith_map_val (since := "2025-02-17")]
+abbrev attachWith_map_coe := @attachWith_map_val
+
+theorem attachWith_map_subtype_val {p : α → Prop} (xs : Array α) (H : ∀ a ∈ xs, p a) :
+    (xs.attachWith p H).map Subtype.val = xs := by
+  cases xs; simp
 
 @[simp]
-theorem mem_attach (l : Array α) : ∀ x, x ∈ l.attach
+theorem mem_attach (xs : Array α) : ∀ x, x ∈ xs.attach
   | ⟨a, h⟩ => by
     have := mem_map.1 (by rw [attach_map_subtype_val] <;> exact h)
     rcases this with ⟨⟨_, _⟩, m, rfl⟩
     exact m
 
 @[simp]
-theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H b} :
-    b ∈ pmap f l H ↔ ∃ (a : _) (h : a ∈ l), f a (H a h) = b := by
+theorem mem_attachWith (xs : Array α) {q : α → Prop} (H) (x : {x // q x}) :
+    x ∈ xs.attachWith q H ↔ x.1 ∈ xs := by
+  cases xs
+  simp
+
+@[simp]
+theorem mem_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H b} :
+    b ∈ pmap f xs H ↔ ∃ (a : _) (h : a ∈ xs), f a (H a h) = b := by
   simp only [pmap_eq_map_attach, mem_map, mem_attach, true_and, Subtype.exists, eq_comm]
 
-theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {l H} {a} (h : a ∈ l) :
-    f a (H a h) ∈ pmap f l H := by
+theorem mem_pmap_of_mem {p : α → Prop} {f : ∀ a, p a → β} {xs H} {a} (h : a ∈ xs) :
+    f a (H a h) ∈ pmap f xs H := by
   rw [mem_pmap]
   exact ⟨a, h, rfl⟩
 
 @[simp]
-theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {l H} : (pmap f l H).size = l.size := by
-  cases l; simp
+theorem size_pmap {p : α → Prop} {f : ∀ a, p a → β} {xs H} : (pmap f xs H).size = xs.size := by
+  cases xs; simp
 
 @[simp]
-theorem size_attach {L : Array α} : L.attach.size = L.size := by
-  cases L; simp
+theorem size_attach {xs : Array α} : xs.attach.size = xs.size := by
+  cases xs; simp
 
 @[simp]
-theorem size_attachWith {p : α → Prop} {l : Array α} {H} : (l.attachWith p H).size = l.size := by
-  cases l; simp
+theorem size_attachWith {p : α → Prop} {xs : Array α} {H} : (xs.attachWith p H).size = xs.size := by
+  cases xs; simp
 
 @[simp]
-theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {l H} : pmap f l H = #[] ↔ l = #[] := by
-  cases l; simp
+theorem pmap_eq_empty_iff {p : α → Prop} {f : ∀ a, p a → β} {xs H} : pmap f xs H = #[] ↔ xs = #[] := by
+  cases xs; simp
 
 theorem pmap_ne_empty_iff {P : α → Prop} (f : (a : α) → P a → β) {xs : Array α}
     (H : ∀ (a : α), a ∈ xs → P a) : xs.pmap f H ≠ #[] ↔ xs ≠ #[] := by
   cases xs; simp
 
-theorem pmap_eq_self {l : Array α} {p : α → Prop} {hp : ∀ (a : α), a ∈ l → p a}
-    {f : (a : α) → p a → α} : l.pmap f hp = l ↔ ∀ a (h : a ∈ l), f a (hp a h) = a := by
-  cases l; simp [List.pmap_eq_self]
+theorem pmap_eq_self {xs : Array α} {p : α → Prop} {hp : ∀ (a : α), a ∈ xs → p a}
+    {f : (a : α) → p a → α} : xs.pmap f hp = xs ↔ ∀ a (h : a ∈ xs), f a (hp a h) = a := by
+  cases xs; simp [List.pmap_eq_self]
 
 @[simp]
-theorem attach_eq_empty_iff {l : Array α} : l.attach = #[] ↔ l = #[] := by
-  cases l; simp
+theorem attach_eq_empty_iff {xs : Array α} : xs.attach = #[] ↔ xs = #[] := by
+  cases xs; simp
 
-theorem attach_ne_empty_iff {l : Array α} : l.attach ≠ #[] ↔ l ≠ #[] := by
-  cases l; simp
+theorem attach_ne_empty_iff {xs : Array α} : xs.attach ≠ #[] ↔ xs ≠ #[] := by
+  cases xs; simp
 
 @[simp]
-theorem attachWith_eq_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
-    l.attachWith P H = #[] ↔ l = #[] := by
-  cases l; simp
+theorem attachWith_eq_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
+    xs.attachWith P H = #[] ↔ xs = #[] := by
+  cases xs; simp
 
-theorem attachWith_ne_empty_iff {l : Array α} {P : α → Prop} {H : ∀ a ∈ l, P a} :
-    l.attachWith P H ≠ #[] ↔ l ≠ #[] := by
-  cases l; simp
+theorem attachWith_ne_empty_iff {xs : Array α} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
+    xs.attachWith P H ≠ #[] ↔ xs ≠ #[] := by
+  cases xs; simp
 
 @[simp]
-theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) (n : Nat) :
-    (pmap f l h)[n]? = Option.pmap f l[n]? fun x H => h x (mem_of_getElem? H) := by
-  cases l; simp
+theorem getElem?_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (h : ∀ a ∈ xs, p a) (i : Nat) :
+    (pmap f xs h)[i]? = Option.pmap f xs[i]? fun x H => h x (mem_of_getElem? H) := by
+  cases xs; simp
 
 @[simp]
-theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {l : Array α} (h : ∀ a ∈ l, p a) {n : Nat}
-    (hn : n < (pmap f l h).size) :
-    (pmap f l h)[n] =
-      f (l[n]'(@size_pmap _ _ p f l h ▸ hn))
-        (h _ (getElem_mem (@size_pmap _ _ p f l h ▸ hn))) := by
-  cases l; simp
+theorem getElem_pmap {p : α → Prop} (f : ∀ a, p a → β) {xs : Array α} (h : ∀ a ∈ xs, p a) {i : Nat}
+    (hi : i < (pmap f xs h).size) :
+    (pmap f xs h)[i] =
+      f (xs[i]'(@size_pmap _ _ p f xs h ▸ hi))
+        (h _ (getElem_mem (@size_pmap _ _ p f xs h ▸ hi))) := by
+  cases xs; simp
 
 @[simp]
 theorem getElem?_attachWith {xs : Array α} {i : Nat} {P : α → Prop} {H : ∀ a ∈ xs, P a} :
@@ -256,16 +283,42 @@ theorem getElem_attach {xs : Array α} {i : Nat} (h : i < xs.attach.size) :
     xs.attach[i] = ⟨xs[i]'(by simpa using h), getElem_mem (by simpa using h)⟩ :=
   getElem_attachWith h
 
-theorem foldl_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
-  (H : ∀ (a : α), a ∈ l → P a) (g : γ → β → γ) (x : γ) :
-    (l.pmap f H).foldl g x = l.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
+@[simp] theorem pmap_attach (xs : Array α) {p : {x // x ∈ xs} → Prop} (f : ∀ a, p a → β) (H) :
+    pmap f xs.attach H =
+      xs.pmap (P := fun a => ∃ h : a ∈ xs, p ⟨a, h⟩)
+        (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨h, H ⟨a, h⟩ (by simp)⟩) := by
+  ext <;> simp
+
+@[simp] theorem pmap_attachWith (xs : Array α) {p : {x // q x} → Prop} (f : ∀ a, p a → β) (H₁ H₂) :
+    pmap f (xs.attachWith q H₁) H₂ =
+      xs.pmap (P := fun a => ∃ h : q a, p ⟨a, h⟩)
+        (fun a h => f ⟨a, h.1⟩ h.2) (fun a h => ⟨H₁ _ h, H₂ ⟨a, H₁ _ h⟩ (by simpa)⟩) := by
+  ext <;> simp
+
+theorem foldl_pmap (xs : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ xs → P a) (g : γ → β → γ) (x : γ) :
+    (xs.pmap f H).foldl g x = xs.attach.foldl (fun acc a => g acc (f a.1 (H _ a.2))) x := by
   rw [pmap_eq_map_attach, foldl_map]
 
-theorem foldr_pmap (l : Array α) {P : α → Prop} (f : (a : α) → P a → β)
-  (H : ∀ (a : α), a ∈ l → P a) (g : β → γ → γ) (x : γ) :
-    (l.pmap f H).foldr g x = l.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
+theorem foldr_pmap (xs : Array α) {P : α → Prop} (f : (a : α) → P a → β)
+  (H : ∀ (a : α), a ∈ xs → P a) (g : β → γ → γ) (x : γ) :
+    (xs.pmap f H).foldr g x = xs.attach.foldr (fun a acc => g (f a.1 (H _ a.2)) acc) x := by
   rw [pmap_eq_map_attach, foldr_map]
 
+@[simp] theorem foldl_attachWith
+    (xs : Array α) {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : β → { x // q x} → β} {b} (w : stop = xs.size) :
+    (xs.attachWith q H).foldl f b 0 stop = xs.attach.foldl (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp [List.foldl_attachWith, List.foldl_map]
+
+@[simp] theorem foldr_attachWith
+    (xs : Array α) {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : { x // q x} → β → β} {b} (w : start = xs.size) :
+    (xs.attachWith q H).foldr f b start 0 = xs.attach.foldr (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp [List.foldr_attachWith, List.foldr_map]
+
 /--
 If we fold over `l.attach` with a function that ignores the membership predicate,
 we get the same results as folding over `l` directly.
@@ -276,10 +329,10 @@ Unfortunately this can't be applied by `simp` because of the higher order unific
 and even when rewriting we need to specify the function explicitly.
 See however `foldl_subtype` below.
 -/
-theorem foldl_attach (l : Array α) (f : β → α → β) (b : β) :
-    l.attach.foldl (fun acc t => f acc t.1) b = l.foldl f b := by
-  rcases l with ⟨l⟩
-  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
+theorem foldl_attach (xs : Array α) (f : β → α → β) (b : β) :
+    xs.attach.foldl (fun acc t => f acc t.1) b = xs.foldl f b := by
+  rcases xs with ⟨xs⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
     List.length_pmap, List.foldl_toArray', mem_toArray, List.foldl_subtype]
   congr
   ext
@@ -295,81 +348,101 @@ Unfortunately this can't be applied by `simp` because of the higher order unific
 and even when rewriting we need to specify the function explicitly.
 See however `foldr_subtype` below.
 -/
-theorem foldr_attach (l : Array α) (f : α → β → β) (b : β) :
-    l.attach.foldr (fun t acc => f t.1 acc) b = l.foldr f b := by
-  rcases l with ⟨l⟩
-  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.map_attach, size_toArray,
+theorem foldr_attach (xs : Array α) (f : α → β → β) (b : β) :
+    xs.attach.foldr (fun t acc => f t.1 acc) b = xs.foldr f b := by
+  rcases xs with ⟨xs⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.size_toArray,
     List.length_pmap, List.foldr_toArray', mem_toArray, List.foldr_subtype]
   congr
   ext
   simpa using fun a => List.mem_of_getElem? a
 
-theorem attach_map {l : Array α} (f : α → β) :
-    (l.map f).attach = l.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
-  cases l
+theorem attach_map {xs : Array α} (f : α → β) :
+    (xs.map f).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨f x, mem_map_of_mem f h⟩) := by
+  cases xs
   ext <;> simp
 
-theorem attachWith_map {l : Array α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ l.map f → P b} :
-    (l.map f).attachWith P H = (l.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
+theorem attachWith_map {xs : Array α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ xs.map f → P b} :
+    (xs.map f).attachWith P H = (xs.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
-  cases l
-  ext
-  · simp
-  · simp only [List.map_toArray, List.attachWith_toArray, List.getElem_toArray,
-      List.getElem_attachWith, List.getElem_map, Function.comp_apply]
-    erw [List.getElem_attachWith] -- Why is `erw` needed here?
+  cases xs
+  simp [List.attachWith_map]
 
-theorem map_attachWith {l : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ l → P a}
+@[simp] theorem map_attachWith {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
     (f : { x // P x } → β) :
-    (l.attachWith P H).map f =
-      l.pmap (fun a (h : a ∈ l ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
-  cases l
+    (xs.attachWith P H).map f = xs.attach.map fun ⟨x, h⟩ => f ⟨x, H _ h⟩ := by
+  cases xs <;> simp_all
+
+theorem map_attachWith_eq_pmap {xs : Array α} {P : α → Prop} {H : ∀ (a : α), a ∈ xs → P a}
+    (f : { x // P x } → β) :
+    (xs.attachWith P H).map f =
+      xs.pmap (fun a (h : a ∈ xs ∧ P a) => f ⟨a, H _ h.1⟩) (fun a h => ⟨h, H a h⟩) := by
+  cases xs
   ext <;> simp
 
 /-- See also `pmap_eq_map_attach` for writing `pmap` in terms of `map` and `attach`. -/
-theorem map_attach {l : Array α} (f : { x // x ∈ l } → β) :
-    l.attach.map f = l.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
-  cases l
+theorem map_attach_eq_pmap {xs : Array α} (f : { x // x ∈ xs } → β) :
+    xs.attach.map f = xs.pmap (fun a h => f ⟨a, h⟩) (fun _ => id) := by
+  cases xs
   ext <;> simp
 
-theorem attach_filterMap {l : Array α} {f : α → Option β} :
-    (l.filterMap f).attach = l.attach.filterMap
+@[deprecated map_attach_eq_pmap (since := "2025-02-09")]
+abbrev map_attach := @map_attach_eq_pmap
+
+theorem attach_filterMap {xs : Array α} {f : α → Option β} :
+    (xs.filterMap f).attach = xs.attach.filterMap
       fun ⟨x, h⟩ => (f x).pbind (fun b m => some ⟨b, mem_filterMap.mpr ⟨x, h, m⟩⟩) := by
-  cases l
+  cases xs
   rw [attach_congr (List.filterMap_toArray f _)]
   simp [List.attach_filterMap, List.map_filterMap, Function.comp_def]
 
-theorem attach_filter {l : Array α} (p : α → Bool) :
-    (l.filter p).attach = l.attach.filterMap
+theorem attach_filter {xs : Array α} (p : α → Bool) :
+    (xs.filter p).attach = xs.attach.filterMap
       fun x => if w : p x.1 then some ⟨x.1, mem_filter.mpr ⟨x.2, w⟩⟩ else none := by
-  cases l
+  cases xs
   rw [attach_congr (List.filter_toArray p _)]
   simp [List.attach_filter, List.map_filterMap, Function.comp_def]
 
 -- We are still missing here `attachWith_filterMap` and `attachWith_filter`.
--- Also missing are `filterMap_attach`, `filter_attach`, `filterMap_attachWith` and `filter_attachWith`.
 
-theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (l H₁ H₂) :
-    pmap f (pmap g l H₁) H₂ =
-      pmap (α := { x // x ∈ l }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) l.attach
+@[simp]
+theorem filterMap_attachWith {q : α → Prop} {xs : Array α} {f : {x // q x} → Option β} (H)
+    (w : stop = (xs.attachWith q H).size) :
+    (xs.attachWith q H).filterMap f 0 stop = xs.attach.filterMap (fun ⟨x, h⟩ => f ⟨x, H _ h⟩) := by
+  subst w
+  cases xs
+  simp [Function.comp_def]
+
+@[simp]
+theorem filter_attachWith {q : α → Prop} {xs : Array α} {p : {x // q x} → Bool} (H)
+    (w : stop = (xs.attachWith q H).size) :
+    (xs.attachWith q H).filter p 0 stop =
+      (xs.attach.filter (fun ⟨x, h⟩ => p ⟨x, H _ h⟩)).map (fun ⟨x, h⟩ => ⟨x, H _ h⟩) := by
+  subst w
+  cases xs
+  simp [Function.comp_def, List.filter_map]
+
+theorem pmap_pmap {p : α → Prop} {q : β → Prop} (g : ∀ a, p a → β) (f : ∀ b, q b → γ) (xs H₁ H₂) :
+    pmap f (pmap g xs H₁) H₂ =
+      pmap (α := { x // x ∈ xs }) (fun a h => f (g a h) (H₂ (g a h) (mem_pmap_of_mem a.2))) xs.attach
         (fun a _ => H₁ a a.2) := by
-  cases l
+  cases xs
   simp [List.pmap_pmap, List.pmap_map]
 
-@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (l₁ l₂ : Array ι)
-    (h : ∀ a ∈ l₁ ++ l₂, p a) :
-    (l₁ ++ l₂).pmap f h =
-      (l₁.pmap f fun a ha => h a (mem_append_left l₂ ha)) ++
-        l₂.pmap f fun a ha => h a (mem_append_right l₁ ha) := by
-  cases l₁
-  cases l₂
+@[simp] theorem pmap_append {p : ι → Prop} (f : ∀ a : ι, p a → α) (xs ys : Array ι)
+    (h : ∀ a ∈ xs ++ ys, p a) :
+    (xs ++ ys).pmap f h =
+      (xs.pmap f fun a ha => h a (mem_append_left ys ha)) ++
+        ys.pmap f fun a ha => h a (mem_append_right xs ha) := by
+  cases xs
+  cases ys
   simp
 
-theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (l₁ l₂ : Array α)
-    (h₁ : ∀ a ∈ l₁, p a) (h₂ : ∀ a ∈ l₂, p a) :
-    ((l₁ ++ l₂).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
-      l₁.pmap f h₁ ++ l₂.pmap f h₂ :=
-  pmap_append f l₁ l₂ _
+theorem pmap_append' {p : α → Prop} (f : ∀ a : α, p a → β) (xs ys : Array α)
+    (h₁ : ∀ a ∈ xs, p a) (h₂ : ∀ a ∈ ys, p a) :
+    ((xs ++ ys).pmap f fun a ha => (mem_append.1 ha).elim (h₁ a) (h₂ a)) =
+      xs.pmap f h₁ ++ ys.pmap f h₂ :=
+  pmap_append f xs ys _
 
 @[simp] theorem attach_append (xs ys : Array α) :
     (xs ++ ys).attach = xs.attach.map (fun ⟨x, h⟩ => ⟨x, mem_append_left ys h⟩) ++
@@ -427,16 +500,48 @@ theorem reverse_attach (xs : Array α) :
 
 @[simp] theorem back?_attachWith {P : α → Prop} {xs : Array α}
     {H : ∀ (a : α), a ∈ xs → P a} :
-    (xs.attachWith P H).back? = xs.back?.pbind (fun a h => some ⟨a, H _ (mem_of_back?_eq_some h)⟩) := by
+    (xs.attachWith P H).back? = xs.back?.pbind (fun a h => some ⟨a, H _ (mem_of_back? h)⟩) := by
   cases xs
   simp
 
 @[simp]
 theorem back?_attach {xs : Array α} :
-    xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back?_eq_some h⟩ := by
+    xs.attach.back? = xs.back?.pbind fun a h => some ⟨a, mem_of_back? h⟩ := by
   cases xs
   simp
 
+@[simp]
+theorem countP_attach (xs : Array α) (p : α → Bool) :
+    xs.attach.countP (fun a : {x // x ∈ xs} => p a) = xs.countP p := by
+  cases xs
+  simp [Function.comp_def]
+
+@[simp]
+theorem countP_attachWith {p : α → Prop} (xs : Array α) (H : ∀ a ∈ xs, p a) (q : α → Bool) :
+    (xs.attachWith p H).countP (fun a : {x // p x} => q a) = xs.countP q := by
+  cases xs
+  simp
+
+@[simp]
+theorem count_attach [DecidableEq α] (xs : Array α) (a : {x // x ∈ xs}) :
+    xs.attach.count a = xs.count ↑a := by
+  rcases xs with ⟨xs⟩
+  simp only [List.attach_toArray, List.attachWith_mem_toArray, List.count_toArray]
+  rw [List.map_attach_eq_pmap, List.count_eq_countP]
+  simp only [Subtype.beq_iff]
+  rw [List.countP_pmap, List.countP_attach (p := (fun x => x == a.1)), List.count]
+
+@[simp]
+theorem count_attachWith [DecidableEq α] {p : α → Prop} (xs : Array α) (H : ∀ a ∈ xs, p a) (a : {x // p x}) :
+    (xs.attachWith p H).count a = xs.count ↑a := by
+  cases xs
+  simp
+
+@[simp] theorem countP_pmap {p : α → Prop} (g : ∀ a, p a → β) (f : β → Bool) (xs : Array α) (H₁) :
+    (xs.pmap g H₁).countP f =
+      xs.attach.countP (fun ⟨a, m⟩ => f (g a (H₁ a m))) := by
+  simp [pmap_eq_map_attach, countP_map, Function.comp_def]
+
 /-! ## unattach
 
 `Array.unattach` is the (one-sided) inverse of `Array.attach`. It is a synonym for `Array.map Subtype.val`.
@@ -449,49 +554,63 @@ Further, we provide simp lemmas that push `unattach` inwards.
 -/
 
 /--
-A synonym for `l.map (·.val)`. Mostly this should not be needed by users.
-It is introduced as in intermediate step by lemmas such as `map_subtype`,
-and is ideally subsequently simplified away by `unattach_attach`.
+Maps an array of terms in a subtype to the corresponding terms in the type by forgetting that they
+satisfy the predicate.
 
-If not, usually the right approach is `simp [Array.unattach, -Array.map_subtype]` to unfold.
+This is the inverse of `Array.attachWith` and a synonym for `xs.map (·.val)`.
+
+Mostly this should not be needed by users. It is introduced as an intermediate step by lemmas such
+as `map_subtype`, and is ideally subsequently simplified away by `unattach_attach`.
+
+This function is usually inserted automatically by Lean as an intermediate step while proving
+termination. It is rarely used explicitly in code. It is introduced as an intermediate step during
+the elaboration of definitions by [well-founded
+recursion](lean-manual://section/well-founded-recursion). If this function is encountered in a proof
+state, the right approach is usually the tactic `simp [Array.unattach, -Array.map_subtype]`.
 -/
-def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (·.val)
+def unattach {α : Type _} {p : α → Prop} (xs : Array { x // p x }) : Array α := xs.map (·.val)
 
-@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := rfl
-@[simp] theorem unattach_push {p : α → Prop} {a : { x // p x }} {l : Array { x // p x }} :
-    (l.push a).unattach = l.unattach.push a.1 := by
+@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := by
+  simp [unattach]
+
+@[simp] theorem unattach_push {p : α → Prop} {a : { x // p x }} {xs : Array { x // p x }} :
+    (xs.push a).unattach = xs.unattach.push a.1 := by
   simp only [unattach, Array.map_push]
 
-@[simp] theorem size_unattach {p : α → Prop} {l : Array { x // p x }} :
-    l.unattach.size = l.size := by
+@[simp] theorem mem_unattach {p : α → Prop} {xs : Array { x // p x }} {a} :
+    a ∈ xs.unattach ↔ ∃ h : p a, ⟨a, h⟩ ∈ xs := by
+  simp only [unattach, mem_map, Subtype.exists, exists_and_right, exists_eq_right]
+
+@[simp] theorem size_unattach {p : α → Prop} {xs : Array { x // p x }} :
+    xs.unattach.size = xs.size := by
   unfold unattach
   simp
 
-@[simp] theorem _root_.List.unattach_toArray {p : α → Prop} {l : List { x // p x }} :
-    l.toArray.unattach = l.unattach.toArray := by
+@[simp] theorem _root_.List.unattach_toArray {p : α → Prop} {xs : List { x // p x }} :
+    xs.toArray.unattach = xs.unattach.toArray := by
   simp only [unattach, List.map_toArray, List.unattach]
 
-@[simp] theorem toList_unattach {p : α → Prop} {l : Array { x // p x }} :
-    l.unattach.toList = l.toList.unattach := by
+@[simp] theorem toList_unattach {p : α → Prop} {xs : Array { x // p x }} :
+    xs.unattach.toList = xs.toList.unattach := by
   simp only [unattach, toList_map, List.unattach]
 
-@[simp] theorem unattach_attach {l : Array α} : l.attach.unattach = l := by
-  cases l
+@[simp] theorem unattach_attach {xs : Array α} : xs.attach.unattach = xs := by
+  cases xs
   simp only [List.attach_toArray, List.unattach_toArray, List.unattach_attachWith]
 
-@[simp] theorem unattach_attachWith {p : α → Prop} {l : Array α}
-    {H : ∀ a ∈ l, p a} :
-    (l.attachWith p H).unattach = l := by
-  cases l
+@[simp] theorem unattach_attachWith {p : α → Prop} {xs : Array α}
+    {H : ∀ a ∈ xs, p a} :
+    (xs.attachWith p H).unattach = xs := by
+  cases xs
   simp
 
-@[simp] theorem getElem?_unattach {p : α → Prop} {l : Array { x // p x }} (i : Nat) :
-    l.unattach[i]? = l[i]?.map Subtype.val := by
+@[simp] theorem getElem?_unattach {p : α → Prop} {xs : Array { x // p x }} (i : Nat) :
+    xs.unattach[i]? = xs[i]?.map Subtype.val := by
   simp [unattach]
 
 @[simp] theorem getElem_unattach
-    {p : α → Prop} {l : Array { x // p x }} (i : Nat) (h : i < l.unattach.size) :
-    l.unattach[i] = (l[i]'(by simpa using h)).1 := by
+    {p : α → Prop} {xs : Array { x // p x }} (i : Nat) (h : i < xs.unattach.size) :
+    xs.unattach[i] = (xs[i]'(by simpa using h)).1 := by
   simp [unattach]
 
 /-! ### Recognizing higher order functions using a function that only depends on the value. -/
@@ -500,20 +619,20 @@ def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (
 This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-theorem foldl_subtype {p : α → Prop} {l : Array { x // p x }}
+theorem foldl_subtype {p : α → Prop} {xs : Array { x // p x }}
     {f : β → { x // p x } → β} {g : β → α → β} {x : β}
-    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} :
-    l.foldl f x = l.unattach.foldl g x := by
-  cases l
+    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) :
+    xs.foldl f x = xs.unattach.foldl g x := by
+  cases xs
   simp only [List.foldl_toArray', List.unattach_toArray]
   rw [List.foldl_subtype] -- Why can't simp do this?
   simp [hf]
 
 /-- Variant of `foldl_subtype` with side condition to check `stop = l.size`. -/
-@[simp] theorem foldl_subtype' {p : α → Prop} {l : Array { x // p x }}
+@[simp] theorem foldl_subtype' {p : α → Prop} {xs : Array { x // p x }}
     {f : β → { x // p x } → β} {g : β → α → β} {x : β}
-    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} (h : stop = l.size) :
-    l.foldl f x 0 stop = l.unattach.foldl g x := by
+    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) (h : stop = xs.size) :
+    xs.foldl f x 0 stop = xs.unattach.foldl g x := by
   subst h
   rwa [foldl_subtype]
 
@@ -521,20 +640,20 @@ theorem foldl_subtype {p : α → Prop} {l : Array { x // p x }}
 This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-theorem foldr_subtype {p : α → Prop} {l : Array { x // p x }}
+theorem foldr_subtype {p : α → Prop} {xs : Array { x // p x }}
     {f : { x // p x } → β → β} {g : α → β → β} {x : β}
-    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} :
-    l.foldr f x = l.unattach.foldr g x := by
-  cases l
+    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) :
+    xs.foldr f x = xs.unattach.foldr g x := by
+  cases xs
   simp only [List.foldr_toArray', List.unattach_toArray]
   rw [List.foldr_subtype]
   simp [hf]
 
 /-- Variant of `foldr_subtype` with side condition to check `stop = l.size`. -/
-@[simp] theorem foldr_subtype' {p : α → Prop} {l : Array { x // p x }}
+@[simp] theorem foldr_subtype' {p : α → Prop} {xs : Array { x // p x }}
     {f : { x // p x } → β → β} {g : α → β → β} {x : β}
-    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} (h : start = l.size) :
-    l.foldr f x start 0 = l.unattach.foldr g x := by
+    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) (h : start = xs.size) :
+    xs.foldr f x start 0 = xs.unattach.foldr g x := by
   subst h
   rwa [foldr_subtype]
 
@@ -542,40 +661,156 @@ theorem foldr_subtype {p : α → Prop} {l : Array { x // p x }}
 This lemma identifies maps over arrays of subtypes, where the function only depends on the value, not the proposition,
 and simplifies these to the function directly taking the value.
 -/
-@[simp] theorem map_subtype {p : α → Prop} {l : Array { x // p x }}
-    {f : { x // p x } → β} {g : α → β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
-    l.map f = l.unattach.map g := by
-  cases l
+@[simp] theorem map_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → β} {g : α → β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.map f = xs.unattach.map g := by
+  cases xs
   simp only [List.map_toArray, List.unattach_toArray]
   rw [List.map_subtype]
   simp [hf]
 
-@[simp] theorem filterMap_subtype {p : α → Prop} {l : Array { x // p x }}
-    {f : { x // p x } → Option β} {g : α → Option β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
-    l.filterMap f = l.unattach.filterMap g := by
-  cases l
-  simp only [size_toArray, List.filterMap_toArray', List.unattach_toArray, List.length_unattach,
+@[simp] theorem filterMap_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Option β} {g : α → Option β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.filterMap f = xs.unattach.filterMap g := by
+  cases xs
+  simp only [List.size_toArray, List.filterMap_toArray', List.unattach_toArray, List.length_unattach,
     mk.injEq]
   rw [List.filterMap_subtype]
   simp [hf]
 
-@[simp] theorem unattach_filter {p : α → Prop} {l : Array { x // p x }}
-    {f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
-    (l.filter f).unattach = l.unattach.filter g := by
-  cases l
+
+@[simp] theorem flatMap_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Array β} {g : α → Array β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    (xs.flatMap f) = xs.unattach.flatMap g := by
+  cases xs
+  simp only [List.size_toArray, List.flatMap_toArray, List.unattach_toArray, List.length_unattach,
+    mk.injEq]
+  rw [List.flatMap_subtype]
+  simp [hf]
+
+@[simp] theorem findSome?_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Option β} {g : α → Option β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.findSome? f = xs.unattach.findSome? g := by
+  cases xs
+  simp
+  rw [List.findSome?_subtype hf]
+
+@[simp] theorem find?_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    (xs.find? f).map Subtype.val = xs.unattach.find? g := by
+  cases xs
+  simp
+  rw [List.find?_subtype hf]
+
+@[simp] theorem all_subtype {p : α → Prop} {xs : Array { x // p x }} {f : { x // p x } → Bool} {g : α → Bool}
+    (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = xs.size) :
+    xs.all f 0 stop = xs.unattach.all g := by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp [hf]
+
+@[simp] theorem any_subtype {p : α → Prop} {xs : Array { x // p x }} {f : { x // p x } → Bool} {g : α → Bool}
+    (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = xs.size) :
+    xs.any f 0 stop = xs.unattach.any g := by
+  subst w
+  rcases xs with ⟨xs⟩
   simp [hf]
 
 /-! ### Simp lemmas pushing `unattach` inwards. -/
 
-@[simp] theorem unattach_reverse {p : α → Prop} {l : Array { x // p x }} :
-    l.reverse.unattach = l.unattach.reverse := by
-  cases l
+@[simp] theorem unattach_filter {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    (xs.filter f).unattach = xs.unattach.filter g := by
+  cases xs
+  simp [hf]
+
+@[simp] theorem unattach_reverse {p : α → Prop} {xs : Array { x // p x }} :
+    xs.reverse.unattach = xs.unattach.reverse := by
+  cases xs
   simp
 
-@[simp] theorem unattach_append {p : α → Prop} {l₁ l₂ : Array { x // p x }} :
-    (l₁ ++ l₂).unattach = l₁.unattach ++ l₂.unattach := by
-  cases l₁
-  cases l₂
+@[simp] theorem unattach_append {p : α → Prop} {xs₁ xs₂ : Array { x // p x }} :
+    (xs₁ ++ xs₂).unattach = xs₁.unattach ++ xs₂.unattach := by
+  cases xs₁
+  cases xs₂
   simp
 
+@[simp] theorem unattach_flatten {p : α → Prop} {xs : Array (Array { x // p x })} :
+    xs.flatten.unattach = (xs.map unattach).flatten := by
+  unfold unattach
+  cases xs using array₂_induction
+  simp only [flatten_toArray, List.map_map, Function.comp_def, List.map_id_fun', id_eq,
+    List.map_toArray, List.map_flatten, map_subtype, map_id_fun', List.unattach_toArray, mk.injEq]
+  simp only [List.unattach]
+
+@[simp] theorem unattach_replicate {p : α → Prop} {n : Nat} {x : { x // p x }} :
+    (Array.replicate n x).unattach = Array.replicate n x.1 := by
+  simp [unattach]
+
+@[deprecated unattach_replicate (since := "2025-03-18")]
+abbrev unattach_mkArray := @unattach_replicate
+
+/-! ### Well-founded recursion preprocessing setup -/
+
+@[wf_preprocess] theorem Array.map_wfParam (xs : Array α) (f : α → β) :
+    (wfParam xs).map f = xs.attach.unattach.map f := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem Array.map_unattach (P : α → Prop) (xs : Array (Subtype P)) (f : α → β) :
+    xs.unattach.map f = xs.map fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem foldl_wfParam (xs : Array α) (f : β → α → β) (x : β) :
+    (wfParam xs).foldl f x = xs.attach.unattach.foldl f x := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem foldl_unattach (P : α → Prop) (xs : Array (Subtype P)) (f : β → α → β) (x : β):
+    xs.unattach.foldl f x = xs.foldl (fun s ⟨x, h⟩ =>
+      binderNameHint s f <| binderNameHint x (f s) <| binderNameHint h () <| f s (wfParam x)) x := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem foldr_wfParam (xs : Array α) (f : α → β → β) (x : β) :
+    (wfParam xs).foldr f x = xs.attach.unattach.foldr f x := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem foldr_unattach (P : α → Prop) (xs : Array (Subtype P)) (f : α → β → β) (x : β):
+    xs.unattach.foldr f x = xs.foldr (fun ⟨x, h⟩ s =>
+      binderNameHint x f <| binderNameHint s (f x) <| binderNameHint h () <| f (wfParam x) s) x := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem filter_wfParam (xs : Array α) (f : α → Bool) :
+    (wfParam xs).filter f = xs.attach.unattach.filter f:= by
+  simp [wfParam]
+
+@[wf_preprocess] theorem filter_unattach (P : α → Prop) (xs : Array (Subtype P)) (f : α → Bool) :
+    xs.unattach.filter f = (xs.filter (fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x))).unattach := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem reverse_wfParam (xs : Array α) :
+    (wfParam xs).reverse = xs.attach.unattach.reverse := by simp [wfParam]
+
+@[wf_preprocess] theorem reverse_unattach (P : α → Prop) (xs : Array (Subtype P)) :
+    xs.unattach.reverse = xs.reverse.unattach := by simp
+
+@[wf_preprocess] theorem filterMap_wfParam (xs : Array α) (f : α → Option β) :
+    (wfParam xs).filterMap f = xs.attach.unattach.filterMap f := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem filterMap_unattach (P : α → Prop) (xs : Array (Subtype P)) (f : α → Option β) :
+    xs.unattach.filterMap f = xs.filterMap fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem flatMap_wfParam (xs : Array α) (f : α → Array β) :
+    (wfParam xs).flatMap f = xs.attach.unattach.flatMap f := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem flatMap_unattach (P : α → Prop) (xs : Array (Subtype P)) (f : α → Array β) :
+    xs.unattach.flatMap f = xs.flatMap fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
+  simp [wfParam]
+
+
 end Array

src/Init/Data/Array/BasicAux.lean

@@ -8,6 +8,9 @@ import Init.Data.Array.Basic
 import Init.Data.Nat.Linear
 import Init.NotationExtra
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : as = bs ∧ a = b := by
   simp only [push, mk.injEq] at h
   have ⟨h₁, h₂⟩ := List.of_concat_eq_concat h
@@ -17,13 +20,13 @@ theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : a
 private theorem List.size_toArrayAux (as : List α) (bs : Array α) : (as.toArrayAux bs).size = as.length + bs.size := by
   induction as generalizing bs with
   | nil => simp [toArrayAux]
-  | cons a as ih => simp_arith [toArrayAux, *]
+  | cons a as ih => simp +arith [toArrayAux, *]
 
 private theorem List.of_toArrayAux_eq_toArrayAux {as bs : List α} {cs ds : Array α} (h : as.toArrayAux cs = bs.toArrayAux ds) (hlen : cs.size = ds.size) : as = bs ∧ cs = ds := by
   match as, bs with
   | [], []    => simp [toArrayAux] at h; simp [h]
-  | a::as, [] => simp [toArrayAux] at h; rw [← h] at hlen; simp_arith [size_toArrayAux] at hlen
-  | [], b::bs => simp [toArrayAux] at h; rw [h] at hlen; simp_arith [size_toArrayAux] at hlen
+  | a::as, [] => simp [toArrayAux] at h; rw [← h] at hlen; simp +arith [size_toArrayAux] at hlen
+  | [], b::bs => simp [toArrayAux] at h; rw [h] at hlen; simp +arith [size_toArrayAux] at hlen
   | a::as, b::bs =>
     simp [toArrayAux] at h
     have : (cs.push a).size = (ds.push b).size := by simp [*]
@@ -35,6 +38,11 @@ private theorem List.of_toArrayAux_eq_toArrayAux {as bs : List α} {cs ds : Arra
 theorem List.toArray_eq_toArray_eq (as bs : List α) : (as.toArray = bs.toArray) = (as = bs) := by
   simp
 
+/--
+Applies the monadic action `f` to every element in the array, left-to-right, and returns the array
+of results. Furthermore, the resulting array's type guarantees that it contains the same number of
+elements as the input array.
+-/
 def Array.mapM' [Monad m] (f : α → m β) (as : Array α) : m { bs : Array β // bs.size = as.size } :=
   go 0 ⟨mkEmpty as.size, rfl⟩ (by simp)
 where
@@ -63,11 +71,19 @@ where
       return as
 
 /--
-Monomorphic `Array.mapM`. The internal implementation uses pointer equality, and does not allocate a new array
-if the result of each `f a` is a pointer equal value `a`.
+Applies a monadic function to each element of an array, returning the array of results. The function is
+monomorphic: it is required to return a value of the same type. The internal implementation uses
+pointer equality, and does not allocate a new array if the result of each function call is
+pointer-equal to its argument.
 -/
 @[implemented_by mapMonoMImp] def Array.mapMonoM [Monad m] (as : Array α) (f : α → m α) : m (Array α) :=
   as.mapM f
 
+/--
+Applies a function to each element of an array, returning the array of results. The function is
+monomorphic: it is required to return a value of the same type. The internal implementation uses
+pointer equality, and does not allocate a new array if the result of each function call is
+pointer-equal to its argument.
+-/
 @[inline] def Array.mapMono (as : Array α) (f : α → α) : Array α :=
   Id.run <| as.mapMonoM f

src/Init/Data/Array/BinSearch.lean

@@ -5,9 +5,13 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.Basic
+import Init.Data.Int.DivMod.Lemmas
 import Init.Omega
 universe u v
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+-- We do not use `linter.indexVariables` here as it is helpful to name the index variables as `lo`, `mid`, and `hi`.
+
 namespace Array
 
 @[specialize] def binSearchAux {α : Type u} {β : Type v} (lt : α → α → Bool) (found : Option α → β) (as : Array α) (k : α) :
@@ -25,6 +29,16 @@ namespace Array
     else found (some a)
 termination_by lo hi => hi.1 - lo.1
 
+/--
+Binary search for an element equivalent to `k` in the sorted array `as`. Returns the element from
+the array, if it is found, or `none` otherwise.
+
+The array `as` must be sorted according to the comparison operator `lt`, which should be a total
+order.
+
+The optional parameters `lo` and `hi` determine the region of the array indices to be searched. Both
+are inclusive, and default to searching the entire array.
+-/
 @[inline] def binSearch {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Option α :=
   if h : lo < as.size then
     let hi := if hi < as.size then hi else as.size - 1
@@ -35,6 +49,16 @@ termination_by lo hi => hi.1 - lo.1
   else
     none
 
+/--
+Binary search for an element equivalent to `k` in the sorted array `as`. Returns `true` if the
+element is found, or `false` otherwise.
+
+The array `as` must be sorted according to the comparison operator `lt`, which should be a total
+order.
+
+The optional parameters `lo` and `hi` determine the region of the array indices to be searched. Both
+are inclusive, and default to searching the entire array.
+-/
 @[inline] def binSearchContains {α : Type} (as : Array α) (k : α) (lt : α → α → Bool) (lo := 0) (hi := as.size - 1) : Bool :=
   if h : lo < as.size then
     let hi := if hi < as.size then hi else as.size - 1
@@ -64,6 +88,16 @@ termination_by lo hi => hi.1 - lo.1
       as.modifyM mid <| fun v => merge v
 termination_by lo hi => hi.1 - lo.1
 
+/--
+Inserts an element `k` into a sorted array `as` such that the resulting array is sorted.
+
+The ordering predicate `lt` should be a total order on elements, and the array `as` should be sorted
+with respect to `lt`.
+
+If an element that `lt` equates to `k` is already present in `as`, then `merge` is applied to the
+existing element to determine the value of that position in the resulting array. If no element equal
+to `k` is present, then `add` is used to determine the value to be inserted.
+-/
 @[specialize] def binInsertM {α : Type u} {m : Type u → Type v} [Monad m]
     (lt : α → α → Bool)
     (merge : α → m α)
@@ -77,6 +111,21 @@ termination_by lo hi => hi.1 - lo.1
   else if !lt k as[as.size - 1] then as.modifyM (as.size - 1) <| merge
   else binInsertAux lt merge add as k ⟨0, by omega⟩ ⟨as.size - 1, by omega⟩ (by simp) (by simpa using h')
 
+/--
+Inserts an element into a sorted array such that the resulting array is sorted. If the element is
+already present in the array, it is not inserted.
+
+The ordering predicate `lt` should be a total order on elements, and the array `as` should be sorted
+with respect to `lt`.
+
+`Array.binInsertM` is a more general operator that provides greater control over the handling of
+duplicate elements in addition to running in a monad.
+
+Examples:
+* `#[0, 1, 3, 5].binInsert (· < ·) 2 = #[0, 1, 2, 3, 5]`
+* `#[0, 1, 3, 5].binInsert (· < ·) 1 = #[0, 1, 3, 5]`
+* `#[].binInsert (· < ·) 1 = #[1]`
+-/
 @[inline] def binInsert {α : Type u} (lt : α → α → Bool) (as : Array α) (k : α) : Array α :=
   Id.run <| binInsertM lt (fun _ => k) (fun _ => k) as k
 

src/Init/Data/Array/Bootstrap.lean

@@ -13,116 +13,151 @@ import Init.Data.List.TakeDrop
 This file contains some theorems about `Array` and `List` needed for `Init.Data.List.Impl`.
 -/
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
+/--
+Use the indexing notation `a[i]` instead.
+
+Access an element from an array without needing a runtime bounds checks,
+using a `Nat` index and a proof that it is in bounds.
+
+This function does not use `get_elem_tactic` to automatically find the proof that
+the index is in bounds. This is because the tactic itself needs to look up values in
+arrays.
+-/
+@[deprecated "Use indexing notation `as[i]` instead" (since := "2025-02-17")]
+def get {α : Type u} (a : @& Array α) (i : @& Nat) (h : LT.lt i a.size) : α :=
+  a.toList.get ⟨i, h⟩
+
+/--
+Use the indexing notation `a[i]!` instead.
+
+Access an element from an array, or panic if the index is out of bounds.
+-/
+@[deprecated "Use indexing notation `as[i]!` instead" (since := "2025-02-17")]
+def get! {α : Type u} [Inhabited α] (a : @& Array α) (i : @& Nat) : α :=
+  Array.getD a i default
+
 theorem foldlM_toList.aux [Monad m]
-    (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
-    foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.toList.drop j).foldlM f b := by
+    (f : β → α → m β) (xs : Array α) (i j) (H : xs.size ≤ i + j) (b) :
+    foldlM.loop f xs xs.size (Nat.le_refl _) i j b = (xs.toList.drop j).foldlM f b := by
   unfold foldlM.loop
   split; split
   · cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
   · rename_i i; rw [Nat.succ_add] at H
-    simp [foldlM_toList.aux f arr i (j+1) H]
+    simp [foldlM_toList.aux f xs i (j+1) H]
     rw (occs := [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
     rfl
   · rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
 
 @[simp] theorem foldlM_toList [Monad m]
-    (f : β → α → m β) (init : β) (arr : Array α) :
-    arr.toList.foldlM f init = arr.foldlM f init := by
+    (f : β → α → m β) (init : β) (xs : Array α) :
+    xs.toList.foldlM f init = xs.foldlM f init := by
   simp [foldlM, foldlM_toList.aux]
 
-@[simp] theorem foldl_toList (f : β → α → β) (init : β) (arr : Array α) :
-    arr.toList.foldl f init = arr.foldl f init :=
+@[simp] theorem foldl_toList (f : β → α → β) (init : β) (xs : Array α) :
+    xs.toList.foldl f init = xs.foldl f init :=
   List.foldl_eq_foldlM .. ▸ foldlM_toList ..
 
 theorem foldrM_eq_reverse_foldlM_toList.aux [Monad m]
-    (f : α → β → m β) (arr : Array α) (init : β) (i h) :
-    (arr.toList.take i).reverse.foldlM (fun x y => f y x) init = foldrM.fold f arr 0 i h init := by
+    (f : α → β → m β) (xs : Array α) (init : β) (i h) :
+    (xs.toList.take i).reverse.foldlM (fun x y => f y x) init = foldrM.fold f xs 0 i h init := by
   unfold foldrM.fold
   match i with
   | 0 => simp [List.foldlM, List.take]
-  | i+1 => rw [← List.take_concat_get _ _ h]; simp [← (aux f arr · i)]
+  | i+1 => rw [← List.take_concat_get _ _ h]; simp [← (aux f xs · i)]
 
-theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.foldrM f init = arr.toList.reverse.foldlM (fun x y => f y x) init := by
-  have : arr = #[] ∨ 0 < arr.size :=
-    match arr with | ⟨[]⟩ => .inl rfl | ⟨a::l⟩ => .inr (Nat.zero_lt_succ _)
-  match arr, this with | _, .inl rfl => rfl | arr, .inr h => ?_
+theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init : β) (xs : Array α) :
+    xs.foldrM f init = xs.toList.reverse.foldlM (fun x y => f y x) init := by
+  have : xs = #[] ∨ 0 < xs.size :=
+    match xs with | ⟨[]⟩ => .inl rfl | ⟨a::l⟩ => .inr (Nat.zero_lt_succ _)
+  match xs, this with | _, .inl rfl => rfl | xs, .inr h => ?_
   simp [foldrM, h, ← foldrM_eq_reverse_foldlM_toList.aux, List.take_length]
 
 @[simp] theorem foldrM_toList [Monad m]
-    (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.toList.foldrM f init = arr.foldrM f init := by
+    (f : α → β → m β) (init : β) (xs : Array α) :
+    xs.toList.foldrM f init = xs.foldrM f init := by
   rw [foldrM_eq_reverse_foldlM_toList, List.foldlM_reverse]
 
-@[simp] theorem foldr_toList (f : α → β → β) (init : β) (arr : Array α) :
-    arr.toList.foldr f init = arr.foldr f init :=
+@[simp] theorem foldr_toList (f : α → β → β) (init : β) (xs : Array α) :
+    xs.toList.foldr f init = xs.foldr f init :=
   List.foldr_eq_foldrM .. ▸ foldrM_toList ..
 
-@[simp] theorem push_toList (arr : Array α) (a : α) : (arr.push a).toList = arr.toList ++ [a] := by
+@[simp] theorem push_toList (xs : Array α) (a : α) : (xs.push a).toList = xs.toList ++ [a] := by
   simp [push, List.concat_eq_append]
 
-@[simp] theorem toListAppend_eq (arr : Array α) (l) : arr.toListAppend l = arr.toList ++ l := by
+@[simp] theorem toListAppend_eq (xs : Array α) (l : List α) : xs.toListAppend l = xs.toList ++ l := by
   simp [toListAppend, ← foldr_toList]
 
-@[simp] theorem toListImpl_eq (arr : Array α) : arr.toListImpl = arr.toList := by
+@[simp] theorem toListImpl_eq (xs : Array α) : xs.toListImpl = xs.toList := by
   simp [toListImpl, ← foldr_toList]
 
-@[simp] theorem pop_toList (arr : Array α) : arr.pop.toList = arr.toList.dropLast := rfl
+@[simp] theorem toList_pop (xs : Array α) : xs.pop.toList = xs.toList.dropLast := rfl
 
-@[simp] theorem append_eq_append (arr arr' : Array α) : arr.append arr' = arr ++ arr' := rfl
+@[deprecated toList_pop (since := "2025-02-17")]
+abbrev pop_toList := @Array.toList_pop
 
-@[simp] theorem toList_append (arr arr' : Array α) :
-    (arr ++ arr').toList = arr.toList ++ arr'.toList := by
+@[simp] theorem append_eq_append (xs ys : Array α) : xs.append ys = xs ++ ys := rfl
+
+@[simp] theorem toList_append (xs ys : Array α) :
+    (xs ++ ys).toList = xs.toList ++ ys.toList := by
   rw [← append_eq_append]; unfold Array.append
   rw [← foldl_toList]
-  induction arr'.toList generalizing arr <;> simp [*]
+  induction ys.toList generalizing xs <;> simp [*]
 
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
-@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
+@[simp] theorem append_empty (xs : Array α) : xs ++ #[] = xs := by
   apply ext'; simp only [toList_append, toList_empty, List.append_nil]
 
-@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
+@[deprecated append_empty (since := "2025-01-13")]
+abbrev append_nil := @append_empty
+
+@[simp] theorem empty_append (xs : Array α) : #[] ++ xs = xs := by
   apply ext'; simp only [toList_append, toList_empty, List.nil_append]
 
-@[simp] theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
+@[deprecated empty_append (since := "2025-01-13")]
+abbrev nil_append := @empty_append
+
+@[simp] theorem append_assoc (xs ys zs : Array α) : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
   apply ext'; simp only [toList_append, List.append_assoc]
 
 @[simp] theorem appendList_eq_append
-    (arr : Array α) (l : List α) : arr.appendList l = arr ++ l := rfl
+    (xs : Array α) (l : List α) : xs.appendList l = xs ++ l := rfl
 
-@[simp] theorem toList_appendList (arr : Array α) (l : List α) :
-    (arr ++ l).toList = arr.toList ++ l := by
+@[simp] theorem toList_appendList (xs : Array α) (l : List α) :
+    (xs ++ l).toList = xs.toList ++ l := by
   rw [← appendList_eq_append]; unfold Array.appendList
-  induction l generalizing arr <;> simp [*]
+  induction l generalizing xs <;> simp [*]
 
 @[deprecated toList_appendList (since := "2024-12-11")]
 abbrev appendList_toList := @toList_appendList
 
 @[deprecated "Use the reverse direction of `foldrM_toList`." (since := "2024-11-13")]
 theorem foldrM_eq_foldrM_toList [Monad m]
-    (f : α → β → m β) (init : β) (arr : Array α) :
-    arr.foldrM f init = arr.toList.foldrM f init := by
+    (f : α → β → m β) (init : β) (xs : Array α) :
+    xs.foldrM f init = xs.toList.foldrM f init := by
   simp
 
 @[deprecated "Use the reverse direction of `foldlM_toList`." (since := "2024-11-13")]
 theorem foldlM_eq_foldlM_toList [Monad m]
-    (f : β → α → m β) (init : β) (arr : Array α) :
-    arr.foldlM f init = arr.toList.foldlM f init:= by
+    (f : β → α → m β) (init : β) (xs : Array α) :
+    xs.foldlM f init = xs.toList.foldlM f init:= by
   simp
 
 @[deprecated "Use the reverse direction of `foldr_toList`." (since := "2024-11-13")]
 theorem foldr_eq_foldr_toList
-    (f : α → β → β) (init : β) (arr : Array α) :
-    arr.foldr f init = arr.toList.foldr f init := by
+    (f : α → β → β) (init : β) (xs : Array α) :
+    xs.foldr f init = xs.toList.foldr f init := by
   simp
 
 @[deprecated "Use the reverse direction of `foldl_toList`." (since := "2024-11-13")]
 theorem foldl_eq_foldl_toList
-    (f : β → α → β) (init : β) (arr : Array α) :
-    arr.foldl f init = arr.toList.foldl f init:= by
+    (f : β → α → β) (init : β) (xs : Array α) :
+    xs.foldl f init = xs.toList.foldl f init:= by
   simp
 
 @[deprecated foldlM_toList (since := "2024-09-09")]
@@ -147,7 +182,7 @@ abbrev push_data := @push_toList
 abbrev toList_eq := @toListImpl_eq
 
 @[deprecated pop_toList (since := "2024-09-09")]
-abbrev pop_data := @pop_toList
+abbrev pop_data := @toList_pop
 
 @[deprecated toList_append (since := "2024-09-09")]
 abbrev append_data := @toList_append

src/Init/Data/Array/Count.lean

@@ -0,0 +1,305 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.Nat.Count
+
+/-!
+# Lemmas about `Array.countP` and `Array.count`.
+-/
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+namespace Array
+
+open Nat
+
+/-! ### countP -/
+section countP
+
+variable (p q : α → Bool)
+
+@[simp] theorem _root_.List.countP_toArray (l : List α) : countP p l.toArray = l.countP p := by
+  simp [countP]
+  induction l with
+  | nil => rfl
+  | cons hd tl ih =>
+    simp only [List.foldr_cons, ih, List.countP_cons]
+    split <;> simp_all
+
+@[simp] theorem countP_toList (xs : Array α) : xs.toList.countP p = countP p xs := by
+  cases xs
+  simp
+
+@[simp] theorem countP_empty : countP p #[] = 0 := rfl
+
+@[simp] theorem countP_push_of_pos (xs) (pa : p a) : countP p (xs.push a) = countP p xs + 1 := by
+  rcases xs with ⟨xs⟩
+  simp_all
+
+@[simp] theorem countP_push_of_neg (xs) (pa : ¬p a) : countP p (xs.push a) = countP p xs := by
+  rcases xs with ⟨xs⟩
+  simp_all
+
+theorem countP_push (a : α) (xs) : countP p (xs.push a) = countP p xs + if p a then 1 else 0 := by
+  rcases xs with ⟨xs⟩
+  simp_all
+
+@[simp] theorem countP_singleton (a : α) : countP p #[a] = if p a then 1 else 0 := by
+  simp [countP_push]
+
+theorem size_eq_countP_add_countP (xs) : xs.size = countP p xs + countP (fun a => ¬p a) xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.length_eq_countP_add_countP (p := p)]
+
+theorem countP_eq_size_filter (xs) : countP p xs = (filter p xs).size := by
+  rcases xs with ⟨xs⟩
+  simp [List.countP_eq_length_filter]
+
+theorem countP_eq_size_filter' : countP p = size ∘ filter p := by
+  funext xs
+  apply countP_eq_size_filter
+
+theorem countP_le_size : countP p xs ≤ xs.size := by
+  simp only [countP_eq_size_filter]
+  apply size_filter_le
+
+@[simp] theorem countP_append (xs ys) : countP p (xs ++ ys) = countP p xs + countP p ys := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp
+
+@[simp] theorem countP_pos_iff {p} : 0 < countP p xs ↔ ∃ a ∈ xs, p a := by
+  rcases xs with ⟨xs⟩
+  simp
+
+@[simp] theorem one_le_countP_iff {p} : 1 ≤ countP p xs ↔ ∃ a ∈ xs, p a :=
+  countP_pos_iff
+
+@[simp] theorem countP_eq_zero {p} : countP p xs = 0 ↔ ∀ a ∈ xs, ¬p a := by
+  rcases xs with ⟨xs⟩
+  simp
+
+@[simp] theorem countP_eq_size {p} : countP p xs = xs.size ↔ ∀ a ∈ xs, p a := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem countP_replicate (p : α → Bool) (a : α) (n : Nat) :
+    countP p (replicate n a) = if p a then n else 0 := by
+  simp [← List.toArray_replicate, List.countP_replicate]
+
+@[deprecated countP_replicate (since := "2025-03-18")]
+abbrev countP_mkArray := @countP_replicate
+
+theorem boole_getElem_le_countP (p : α → Bool) (xs : Array α) (i : Nat) (h : i < xs.size) :
+    (if p xs[i] then 1 else 0) ≤ xs.countP p := by
+  rcases xs with ⟨xs⟩
+  simp [List.boole_getElem_le_countP]
+
+theorem countP_set (p : α → Bool) (xs : Array α) (i : Nat) (a : α) (h : i < xs.size) :
+    (xs.set i a).countP p = xs.countP p - (if p xs[i] then 1 else 0) + (if p a then 1 else 0) := by
+  rcases xs with ⟨xs⟩
+  simp [List.countP_set, h]
+
+theorem countP_filter (xs : Array α) :
+    countP p (filter q xs) = countP (fun a => p a && q a) xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.countP_filter]
+
+@[simp] theorem countP_true : (countP fun (_ : α) => true) = size := by
+  funext xs
+  simp
+
+@[simp] theorem countP_false : (countP fun (_ : α) => false) = Function.const _ 0 := by
+  funext xs
+  simp
+
+@[simp] theorem countP_map (p : β → Bool) (f : α → β) (xs : Array α) :
+    countP p (map f xs) = countP (p ∘ f) xs := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem size_filterMap_eq_countP (f : α → Option β) (xs : Array α) :
+    (filterMap f xs).size = countP (fun a => (f a).isSome) xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.length_filterMap_eq_countP]
+
+theorem countP_filterMap (p : β → Bool) (f : α → Option β) (xs : Array α) :
+    countP p (filterMap f xs) = countP (fun a => ((f a).map p).getD false) xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.countP_filterMap]
+
+@[simp] theorem countP_flatten (xss : Array (Array α)) :
+    countP p xss.flatten = (xss.map (countP p)).sum := by
+  cases xss using array₂_induction
+  simp [List.countP_flatten, Function.comp_def]
+
+theorem countP_flatMap (p : β → Bool) (xs : Array α) (f : α → Array β) :
+    countP p (xs.flatMap f) = sum (map (countP p ∘ f) xs) := by
+  rcases xs with ⟨xs⟩
+  simp [List.countP_flatMap, Function.comp_def]
+
+@[simp] theorem countP_reverse (xs : Array α) : countP p xs.reverse = countP p xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.countP_reverse]
+
+variable {p q}
+
+theorem countP_mono_left (h : ∀ x ∈ xs, p x → q x) : countP p xs ≤ countP q xs := by
+  rcases xs with ⟨xs⟩
+  simpa using List.countP_mono_left (by simpa using h)
+
+theorem countP_congr (h : ∀ x ∈ xs, p x ↔ q x) : countP p xs = countP q xs :=
+  Nat.le_antisymm
+    (countP_mono_left fun x hx => (h x hx).1)
+    (countP_mono_left fun x hx => (h x hx).2)
+
+end countP
+
+/-! ### count -/
+section count
+
+variable [BEq α]
+
+@[simp] theorem _root_.List.count_toArray (l : List α) (a : α) : count a l.toArray = l.count a := by
+  simp [count, List.count_eq_countP]
+
+@[simp] theorem count_toList (xs : Array α) (a : α) : xs.toList.count a = xs.count a := by
+  cases xs
+  simp
+
+@[simp] theorem count_empty (a : α) : count a #[] = 0 := rfl
+
+theorem count_push (a b : α) (xs : Array α) :
+    count a (xs.push b) = count a xs + if b == a then 1 else 0 := by
+  simp [count, countP_push]
+
+theorem count_eq_countP (a : α) (xs : Array α) : count a xs = countP (· == a) xs := rfl
+theorem count_eq_countP' {a : α} : count a = countP (· == a) := by
+  funext xs
+  apply count_eq_countP
+
+theorem count_le_size (a : α) (xs : Array α) : count a xs ≤ xs.size := countP_le_size _
+
+theorem count_le_count_push (a b : α) (xs : Array α) : count a xs ≤ count a (xs.push b) := by
+  simp [count_push]
+
+theorem count_singleton (a b : α) : count a #[b] = if b == a then 1 else 0 := by
+  simp [count_eq_countP]
+
+@[simp] theorem count_append (a : α) : ∀ xs ys, count a (xs ++ ys) = count a xs + count a ys :=
+  countP_append _
+
+@[simp] theorem count_flatten (a : α) (xss : Array (Array α)) :
+    count a xss.flatten = (xss.map (count a)).sum := by
+  cases xss using array₂_induction
+  simp [List.count_flatten, Function.comp_def]
+
+@[simp] theorem count_reverse (a : α) (xs : Array α) : count a xs.reverse = count a xs := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem boole_getElem_le_count (a : α) (xs : Array α) (i : Nat) (h : i < xs.size) :
+    (if xs[i] == a then 1 else 0) ≤ xs.count a := by
+  rw [count_eq_countP]
+  apply boole_getElem_le_countP (· == a)
+
+theorem count_set (a b : α) (xs : Array α) (i : Nat) (h : i < xs.size) :
+    (xs.set i a).count b = xs.count b - (if xs[i] == b then 1 else 0) + (if a == b then 1 else 0) := by
+  simp [count_eq_countP, countP_set, h]
+
+variable [LawfulBEq α]
+
+@[simp] theorem count_push_self (a : α) (xs : Array α) : count a (xs.push a) = count a xs + 1 := by
+  simp [count_push]
+
+@[simp] theorem count_push_of_ne (h : b ≠ a) (xs : Array α) : count a (xs.push b) = count a xs := by
+  simp_all [count_push, h]
+
+theorem count_singleton_self (a : α) : count a #[a] = 1 := by simp
+
+@[simp]
+theorem count_pos_iff {a : α} {xs : Array α} : 0 < count a xs ↔ a ∈ xs := by
+  simp only [count, countP_pos_iff, beq_iff_eq, exists_eq_right]
+
+@[simp] theorem one_le_count_iff {a : α} {xs : Array α} : 1 ≤ count a xs ↔ a ∈ xs :=
+  count_pos_iff
+
+theorem count_eq_zero_of_not_mem {a : α} {xs : Array α} (h : a ∉ xs) : count a xs = 0 :=
+  Decidable.byContradiction fun h' => h <| count_pos_iff.1 (Nat.pos_of_ne_zero h')
+
+theorem not_mem_of_count_eq_zero {a : α} {xs : Array α} (h : count a xs = 0) : a ∉ xs :=
+  fun h' => Nat.ne_of_lt (count_pos_iff.2 h') h.symm
+
+theorem count_eq_zero {xs : Array α} : count a xs = 0 ↔ a ∉ xs :=
+  ⟨not_mem_of_count_eq_zero, count_eq_zero_of_not_mem⟩
+
+theorem count_eq_size {xs : Array α} : count a xs = xs.size ↔ ∀ b ∈ xs, a = b := by
+  rw [count, countP_eq_size]
+  refine ⟨fun h b hb => Eq.symm ?_, fun h b hb => ?_⟩
+  · simpa using h b hb
+  · rw [h b hb, beq_self_eq_true]
+
+@[simp] theorem count_replicate_self (a : α) (n : Nat) : count a (replicate n a) = n := by
+  simp [← List.toArray_replicate]
+
+@[deprecated count_replicate_self (since := "2025-03-18")]
+abbrev count_mkArray_self := @count_replicate_self
+
+theorem count_replicate (a b : α) (n : Nat) : count a (replicate n b) = if b == a then n else 0 := by
+  simp [← List.toArray_replicate, List.count_replicate]
+
+@[deprecated count_replicate (since := "2025-03-18")]
+abbrev count_mkArray := @count_replicate
+
+theorem filter_beq (xs : Array α) (a : α) : xs.filter (· == a) = replicate (count a xs) a := by
+  rcases xs with ⟨xs⟩
+  simp [List.filter_beq]
+
+theorem filter_eq {α} [DecidableEq α] (xs : Array α) (a : α) : xs.filter (· = a) = replicate (count a xs) a :=
+  filter_beq xs a
+
+theorem replicate_count_eq_of_count_eq_size {xs : Array α} (h : count a xs = xs.size) :
+    replicate (count a xs) a = xs := by
+  rcases xs with ⟨xs⟩
+  rw [← toList_inj]
+  simp [List.replicate_count_eq_of_count_eq_length (by simpa using h)]
+
+@[deprecated replicate_count_eq_of_count_eq_size (since := "2025-03-18")]
+abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
+
+@[simp] theorem count_filter {xs : Array α} (h : p a) : count a (filter p xs) = count a xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.count_filter, h]
+
+theorem count_le_count_map [DecidableEq β] (xs : Array α) (f : α → β) (x : α) :
+    count x xs ≤ count (f x) (map f xs) := by
+  rcases xs with ⟨xs⟩
+  simp [List.count_le_count_map, countP_map]
+
+theorem count_filterMap {α} [BEq β] (b : β) (f : α → Option β) (xs : Array α) :
+    count b (filterMap f xs) = countP (fun a => f a == some b) xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.count_filterMap, countP_filterMap]
+
+theorem count_flatMap {α} [BEq β] (xs : Array α) (f : α → Array β) (x : β) :
+    count x (xs.flatMap f) = sum (map (count x ∘ f) xs) := by
+  rcases xs with ⟨xs⟩
+  simp [List.count_flatMap, countP_flatMap, Function.comp_def]
+
+-- FIXME these theorems can be restored once `List.erase` and `Array.erase` have been related.
+
+-- theorem count_erase (a b : α) (l : Array α) : count a (l.erase b) = count a l - if b == a then 1 else 0 := by
+--   sorry
+
+-- @[simp] theorem count_erase_self (a : α) (l : Array α) :
+--     count a (l.erase a) = count a l - 1 := by rw [count_erase, if_pos (by simp)]
+
+-- @[simp] theorem count_erase_of_ne (ab : a ≠ b) (l : Array α) : count a (l.erase b) = count a l := by
+--   rw [count_erase, if_neg (by simpa using ab.symm), Nat.sub_zero]
+
+end count

src/Init/Data/Array/DecidableEq.lean

@@ -9,12 +9,15 @@ import Init.Data.BEq
 import Init.Data.List.Nat.BEq
 import Init.ByCases
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
-theorem rel_of_isEqvAux
-    {r : α → α → Bool} {a b : Array α} (hsz : a.size = b.size) {i : Nat} (hi : i ≤ a.size)
-    (heqv : Array.isEqvAux a b hsz r i hi)
-    {j : Nat} (hj : j < i) : r (a[j]'(Nat.lt_of_lt_of_le hj hi)) (b[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi))) := by
+private theorem rel_of_isEqvAux
+    {r : α → α → Bool} {xs ys : Array α} (hsz : xs.size = ys.size) {i : Nat} (hi : i ≤ xs.size)
+    (heqv : Array.isEqvAux xs ys hsz r i hi)
+    {j : Nat} (hj : j < i) : r (xs[j]'(Nat.lt_of_lt_of_le hj hi)) (ys[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi))) := by
   induction i with
   | zero => contradiction
   | succ i ih =>
@@ -27,31 +30,32 @@ theorem rel_of_isEqvAux
       subst hj'
       exact heqv.left
 
-theorem isEqvAux_of_rel {r : α → α → Bool} {a b : Array α} (hsz : a.size = b.size) {i : Nat} (hi : i ≤ a.size)
-    (w : ∀ j, (hj : j < i) → r (a[j]'(Nat.lt_of_lt_of_le hj hi)) (b[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi)))) : Array.isEqvAux a b hsz r i hi := by
+private theorem isEqvAux_of_rel {r : α → α → Bool} {xs ys : Array α} (hsz : xs.size = ys.size) {i : Nat} (hi : i ≤ xs.size)
+    (w : ∀ j, (hj : j < i) → r (xs[j]'(Nat.lt_of_lt_of_le hj hi)) (ys[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi)))) : Array.isEqvAux xs ys hsz r i hi := by
   induction i with
   | zero => simp [Array.isEqvAux]
   | succ i ih =>
     simp only [isEqvAux, Bool.and_eq_true]
     exact ⟨w i (Nat.lt_add_one i), ih _ fun j hj => w j (Nat.lt_add_right 1 hj)⟩
 
-theorem rel_of_isEqv {r : α → α → Bool} {a b : Array α} :
-    Array.isEqv a b r → ∃ h : a.size = b.size, ∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h')) := by
+-- This is private as the forward direction of `isEqv_iff_rel` may be used.
+private theorem rel_of_isEqv {r : α → α → Bool} {xs ys : Array α} :
+    Array.isEqv xs ys r → ∃ h : xs.size = ys.size, ∀ (i : Nat) (h' : i < xs.size), r (xs[i]) (ys[i]'(h ▸ h')) := by
   simp only [isEqv]
   split <;> rename_i h
   · exact fun h' => ⟨h, fun i => rel_of_isEqvAux h (Nat.le_refl ..) h'⟩
   · intro; contradiction
 
-theorem isEqv_iff_rel {a b : Array α} {r} :
-    Array.isEqv a b r ↔ ∃ h : a.size = b.size, ∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h')) :=
+theorem isEqv_iff_rel {xs ys : Array α} {r} :
+    Array.isEqv xs ys r ↔ ∃ h : xs.size = ys.size, ∀ (i : Nat) (h' : i < xs.size), r (xs[i]) (ys[i]'(h ▸ h')) :=
   ⟨rel_of_isEqv, fun ⟨h, w⟩ => by
     simp only [isEqv, ← h, ↓reduceDIte]
     exact isEqvAux_of_rel h (by simp [h]) w⟩
 
-theorem isEqv_eq_decide (a b : Array α) (r) :
-    Array.isEqv a b r =
-      if h : a.size = b.size then decide (∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h'))) else false := by
-  by_cases h : Array.isEqv a b r
+theorem isEqv_eq_decide (xs ys : Array α) (r) :
+    Array.isEqv xs ys r =
+      if h : xs.size = ys.size then decide (∀ (i : Nat) (h' : i < xs.size), r (xs[i]) (ys[i]'(h ▸ h'))) else false := by
+  by_cases h : Array.isEqv xs ys r
   · simp only [h, Bool.true_eq]
     simp only [isEqv_iff_rel] at h
     obtain ⟨h, w⟩ := h
@@ -62,48 +66,58 @@ theorem isEqv_eq_decide (a b : Array α) (r) :
       Bool.not_eq_true]
     simpa [isEqv_iff_rel] using h'
 
-@[simp] theorem isEqv_toList [BEq α] (a b : Array α) : (a.toList.isEqv b.toList r) = (a.isEqv b r) := by
+@[simp] theorem isEqv_toList [BEq α] (xs ys : Array α) : (xs.toList.isEqv ys.toList r) = (xs.isEqv ys r) := by
   simp [isEqv_eq_decide, List.isEqv_eq_decide]
 
-theorem eq_of_isEqv [DecidableEq α] (a b : Array α) (h : Array.isEqv a b (fun x y => x = y)) : a = b := by
+theorem eq_of_isEqv [DecidableEq α] (xs ys : Array α) (h : Array.isEqv xs ys (fun x y => x = y)) : xs = ys := by
   have ⟨h, h'⟩ := rel_of_isEqv h
   exact ext _ _ h (fun i lt _ => by simpa using h' i lt)
 
-theorem isEqvAux_self (r : α → α → Bool) (hr : ∀ a, r a a) (a : Array α) (i : Nat) (h : i ≤ a.size) :
-    Array.isEqvAux a a rfl r i h = true := by
+private theorem isEqvAux_self (r : α → α → Bool) (hr : ∀ a, r a a) (xs : Array α) (i : Nat) (h : i ≤ xs.size) :
+    Array.isEqvAux xs xs rfl r i h = true := by
   induction i with
   | zero => simp [Array.isEqvAux]
   | succ i ih =>
     simp_all only [isEqvAux, Bool.and_self]
 
-theorem isEqv_self_beq [BEq α] [ReflBEq α] (a : Array α) : Array.isEqv a a (· == ·) = true := by
+theorem isEqv_self_beq [BEq α] [ReflBEq α] (xs : Array α) : Array.isEqv xs xs (· == ·) = true := by
   simp [isEqv, isEqvAux_self]
 
-theorem isEqv_self [DecidableEq α] (a : Array α) : Array.isEqv a a (· = ·) = true := by
+theorem isEqv_self [DecidableEq α] (xs : Array α) : Array.isEqv xs xs (· = ·) = true := by
   simp [isEqv, isEqvAux_self]
 
 instance [DecidableEq α] : DecidableEq (Array α) :=
-  fun a b =>
-    match h:isEqv a b (fun a b => a = b) with
-    | true  => isTrue (eq_of_isEqv a b h)
+  fun xs ys =>
+    match h:isEqv xs ys (fun a b => a = b) with
+    | true  => isTrue (eq_of_isEqv xs ys h)
     | false => isFalse fun h' => by subst h'; rw [isEqv_self] at h; contradiction
 
-theorem beq_eq_decide [BEq α] (a b : Array α) :
-    (a == b) = if h : a.size = b.size then
-      decide (∀ (i : Nat) (h' : i < a.size), a[i] == b[i]'(h ▸ h')) else false := by
+theorem beq_eq_decide [BEq α] (xs ys : Array α) :
+    (xs == ys) = if h : xs.size = ys.size then
+      decide (∀ (i : Nat) (h' : i < xs.size), xs[i] == ys[i]'(h ▸ h')) else false := by
   simp [BEq.beq, isEqv_eq_decide]
 
-@[simp] theorem beq_toList [BEq α] (a b : Array α) : (a.toList == b.toList) = (a == b) := by
+@[simp] theorem beq_toList [BEq α] (xs ys : Array α) : (xs.toList == ys.toList) = (xs == ys) := by
   simp [beq_eq_decide, List.beq_eq_decide]
 
 end Array
 
 namespace List
 
-@[simp] theorem isEqv_toArray [BEq α] (a b : List α) : (a.toArray.isEqv b.toArray r) = (a.isEqv b r) := by
+@[simp] theorem isEqv_toArray [BEq α] (as bs : List α) : (as.toArray.isEqv bs.toArray r) = (as.isEqv bs r) := by
   simp [isEqv_eq_decide, Array.isEqv_eq_decide]
 
-@[simp] theorem beq_toArray [BEq α] (a b : List α) : (a.toArray == b.toArray) = (a == b) := by
+@[simp] theorem beq_toArray [BEq α] (as bs : List α) : (as.toArray == bs.toArray) = (as == bs) := by
   simp [beq_eq_decide, Array.beq_eq_decide]
 
 end List
+
+namespace Array
+
+instance [BEq α] [LawfulBEq α] : LawfulBEq (Array α) where
+  rfl := by simp [BEq.beq, isEqv_self_beq]
+  eq_of_beq := by
+    rintro ⟨_⟩ ⟨_⟩ h
+    simpa using h
+
+end Array

src/Init/Data/Array/Erase.lean

@@ -0,0 +1,428 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.Nat.Erase
+import Init.Data.List.Nat.Basic
+
+/-!
+# Lemmas about `Array.eraseP`, `Array.erase`, and `Array.eraseIdx`.
+-/
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+namespace Array
+
+open Nat
+
+/-! ### eraseP -/
+
+@[simp] theorem eraseP_empty : #[].eraseP p = #[] := by simp
+
+theorem eraseP_of_forall_mem_not {xs : Array α} (h : ∀ a, a ∈ xs → ¬p a) : xs.eraseP p = xs := by
+  rcases xs with ⟨xs⟩
+  simp_all [List.eraseP_of_forall_not]
+
+theorem eraseP_of_forall_getElem_not {xs : Array α} (h : ∀ i, (h : i < xs.size) → ¬p xs[i]) : xs.eraseP p = xs :=
+  eraseP_of_forall_mem_not fun a m => by
+    rw [mem_iff_getElem] at m
+    obtain ⟨i, w, rfl⟩ := m
+    exact h i w
+
+@[simp] theorem eraseP_eq_empty_iff {xs : Array α} {p : α → Bool} : xs.eraseP p = #[] ↔ xs = #[] ∨ ∃ x, p x ∧ xs = #[x] := by
+  cases xs
+  simp
+
+theorem eraseP_ne_empty_iff {xs : Array α} {p : α → Bool} : xs.eraseP p ≠ #[] ↔ xs ≠ #[] ∧ ∀ x, p x → xs ≠ #[x] := by
+  simp
+
+theorem exists_of_eraseP {xs : Array α} {a} (hm : a ∈ xs) (hp : p a) :
+    ∃ a ys zs, (∀ b ∈ ys, ¬p b) ∧ p a ∧ xs = ys.push a ++ zs ∧ xs.eraseP p = ys ++ zs := by
+  rcases xs with ⟨xs⟩
+  obtain ⟨a, l₁, l₂, h₁, h₂, rfl, h₃⟩ := List.exists_of_eraseP (by simpa using hm) (hp)
+  refine ⟨a, ⟨l₁⟩, ⟨l₂⟩, by simpa using h₁, h₂, by simp, by simpa using h₃⟩
+
+theorem exists_or_eq_self_of_eraseP (p) (xs : Array α) :
+    xs.eraseP p = xs ∨
+    ∃ a ys zs, (∀ b ∈ ys, ¬p b) ∧ p a ∧ xs = ys.push a ++ zs ∧ xs.eraseP p = ys ++ zs :=
+  if h : ∃ a ∈ xs, p a then
+    let ⟨_, ha, pa⟩ := h
+    .inr (exists_of_eraseP ha pa)
+  else
+    .inl (eraseP_of_forall_mem_not (h ⟨·, ·, ·⟩))
+
+@[simp] theorem size_eraseP_of_mem {xs : Array α} (al : a ∈ xs) (pa : p a) :
+    (xs.eraseP p).size = xs.size - 1 := by
+  let ⟨_, ys, zs, _, _, e₁, e₂⟩ := exists_of_eraseP al pa
+  rw [e₂]; simp [size_append, e₁]; omega
+
+theorem size_eraseP {xs : Array α} : (xs.eraseP p).size = if xs.any p then xs.size - 1 else xs.size := by
+  split <;> rename_i h
+  · simp only [any_eq_true] at h
+    obtain ⟨i, h, w⟩ := h
+    simp [size_eraseP_of_mem (xs := xs) (by simp) w]
+  · simp only [any_eq_true] at h
+    rw [eraseP_of_forall_getElem_not]
+    simp_all
+
+theorem size_eraseP_le (xs : Array α) : (xs.eraseP p).size ≤ xs.size := by
+  rcases xs with ⟨xs⟩
+  simpa using List.length_eraseP_le xs
+
+theorem le_size_eraseP (xs : Array α) : xs.size - 1 ≤ (xs.eraseP p).size := by
+  rcases xs with ⟨xs⟩
+  simpa using List.le_length_eraseP xs
+
+theorem mem_of_mem_eraseP {xs : Array α} : a ∈ xs.eraseP p → a ∈ xs := by
+  rcases xs with ⟨xs⟩
+  simpa using List.mem_of_mem_eraseP
+
+@[simp] theorem mem_eraseP_of_neg {xs : Array α} (pa : ¬p a) : a ∈ xs.eraseP p ↔ a ∈ xs := by
+  rcases xs with ⟨xs⟩
+  simpa using List.mem_eraseP_of_neg pa
+
+@[simp] theorem eraseP_eq_self_iff {xs : Array α} : xs.eraseP p = xs ↔ ∀ a ∈ xs, ¬ p a := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem eraseP_map (f : β → α) (xs : Array β) : (xs.map f).eraseP p = (xs.eraseP (p ∘ f)).map f := by
+  rcases xs with ⟨xs⟩
+  simpa using List.eraseP_map f xs
+
+theorem eraseP_filterMap (f : α → Option β) (xs : Array α) :
+    (filterMap f xs).eraseP p = filterMap f (xs.eraseP (fun x => match f x with | some y => p y | none => false)) := by
+  rcases xs with ⟨xs⟩
+  simpa using List.eraseP_filterMap f xs
+
+theorem eraseP_filter (f : α → Bool) (xs : Array α) :
+    (filter f xs).eraseP p = filter f (xs.eraseP (fun x => p x && f x)) := by
+  rcases xs with ⟨xs⟩
+  simpa using List.eraseP_filter f xs
+
+theorem eraseP_append_left {a : α} (pa : p a) {xs : Array α} {ys : Array α} (h : a ∈ xs) :
+    (xs ++ ys).eraseP p = xs.eraseP p ++ ys := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simpa using List.eraseP_append_left pa ys (by simpa using h)
+
+theorem eraseP_append_right {xs : Array α} ys (h : ∀ b ∈ xs, ¬p b) :
+    (xs ++ ys).eraseP p = xs ++ ys.eraseP p := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simpa using List.eraseP_append_right ys (by simpa using h)
+
+theorem eraseP_append {xs : Array α} {ys : Array α} :
+    (xs ++ ys).eraseP p = if xs.any p then xs.eraseP p ++ ys else xs ++ ys.eraseP p := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp only [List.append_toArray, List.eraseP_toArray, List.eraseP_append, List.any_toArray]
+  split <;> simp
+
+theorem eraseP_replicate (n : Nat) (a : α) (p : α → Bool) :
+    (replicate n a).eraseP p = if p a then replicate (n - 1) a else replicate n a := by
+  simp only [← List.toArray_replicate, List.eraseP_toArray, List.eraseP_replicate]
+  split <;> simp
+
+@[deprecated eraseP_replicate (since := "2025-03-18")]
+abbrev eraseP_mkArray := @eraseP_replicate
+
+@[simp] theorem eraseP_replicate_of_pos {n : Nat} {a : α} (h : p a) :
+    (replicate n a).eraseP p = replicate (n - 1) a := by
+  simp only [← List.toArray_replicate, List.eraseP_toArray]
+  simp [h]
+
+@[deprecated eraseP_replicate_of_pos (since := "2025-03-18")]
+abbrev eraseP_mkArray_of_pos := @eraseP_replicate_of_pos
+
+@[simp] theorem eraseP_replicate_of_neg {n : Nat} {a : α} (h : ¬p a) :
+    (replicate n a).eraseP p = replicate n a := by
+  simp only [← List.toArray_replicate, List.eraseP_toArray]
+  simp [h]
+
+@[deprecated eraseP_replicate_of_neg (since := "2025-03-18")]
+abbrev eraseP_mkArray_of_neg := @eraseP_replicate_of_neg
+
+theorem eraseP_eq_iff {p} {xs : Array α} :
+    xs.eraseP p = ys ↔
+      ((∀ a ∈ xs, ¬ p a) ∧ xs = ys) ∨
+        ∃ a as bs, (∀ b ∈ as, ¬ p b) ∧ p a ∧ xs = as.push a ++ bs ∧ ys = as ++ bs := by
+  rcases xs with ⟨l⟩
+  rcases ys with ⟨ys⟩
+  simp [List.eraseP_eq_iff]
+  constructor
+  · rintro (h | ⟨a, l₁, h₁, h₂, ⟨l, rfl, rfl⟩⟩)
+    · exact Or.inl h
+    · exact Or.inr ⟨a, ⟨l₁⟩, by simpa using h₁, h₂, ⟨⟨l⟩, by simp⟩⟩
+  · rintro (h | ⟨a, ⟨l₁⟩, h₁, h₂, ⟨⟨l⟩, rfl, rfl⟩⟩)
+    · exact Or.inl h
+    · exact Or.inr ⟨a, l₁, by simpa using h₁, h₂, ⟨l, by simp⟩⟩
+
+theorem eraseP_comm {xs : Array α} (h : ∀ a ∈ xs, ¬ p a ∨ ¬ q a) :
+    (xs.eraseP p).eraseP q = (xs.eraseP q).eraseP p := by
+  rcases xs with ⟨xs⟩
+  simpa using List.eraseP_comm (by simpa using h)
+
+/-! ### erase -/
+
+section erase
+variable [BEq α]
+
+theorem erase_of_not_mem [LawfulBEq α] {a : α} {xs : Array α} (h : a ∉ xs) : xs.erase a = xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.erase_of_not_mem (by simpa using h)]
+
+theorem erase_eq_eraseP' (a : α) (xs : Array α) : xs.erase a = xs.eraseP (· == a) := by
+  rcases xs with ⟨xs⟩
+  simp [List.erase_eq_eraseP']
+
+theorem erase_eq_eraseP [LawfulBEq α] (a : α) (xs : Array α) : xs.erase a = xs.eraseP (a == ·) := by
+  rcases xs with ⟨xs⟩
+  simp [List.erase_eq_eraseP]
+
+@[simp] theorem erase_eq_empty_iff [LawfulBEq α] {xs : Array α} {a : α} :
+    xs.erase a = #[] ↔ xs = #[] ∨ xs = #[a] := by
+  rcases xs with ⟨xs⟩
+  simp [List.erase_eq_nil_iff]
+
+theorem erase_ne_empty_iff [LawfulBEq α] {xs : Array α} {a : α} :
+    xs.erase a ≠ #[] ↔ xs ≠ #[] ∧ xs ≠ #[a] := by
+  rcases xs with ⟨xs⟩
+  simp [List.erase_ne_nil_iff]
+
+theorem exists_erase_eq [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
+    ∃ ys zs, a ∉ ys ∧ xs = ys.push a ++ zs ∧ xs.erase a = ys ++ zs := by
+  let ⟨_, ys, zs, h₁, e, h₂, h₃⟩ := exists_of_eraseP h (beq_self_eq_true _)
+  rw [erase_eq_eraseP]; exact ⟨ys, zs, fun h => h₁ _ h (beq_self_eq_true _), eq_of_beq e ▸ h₂, h₃⟩
+
+@[simp] theorem size_erase_of_mem [LawfulBEq α] {a : α} {xs : Array α} (h : a ∈ xs) :
+    (xs.erase a).size = xs.size - 1 := by
+  rw [erase_eq_eraseP]; exact size_eraseP_of_mem h (beq_self_eq_true a)
+
+theorem size_erase [LawfulBEq α] (a : α) (xs : Array α) :
+    (xs.erase a).size = if a ∈ xs then xs.size - 1 else xs.size := by
+  rw [erase_eq_eraseP, size_eraseP]
+  congr
+  simp [mem_iff_getElem, eq_comm (a := a)]
+
+theorem size_erase_le (a : α) (xs : Array α) : (xs.erase a).size ≤ xs.size := by
+  rcases xs with ⟨xs⟩
+  simpa using List.length_erase_le a xs
+
+theorem le_size_erase [LawfulBEq α] (a : α) (xs : Array α) : xs.size - 1 ≤ (xs.erase a).size := by
+  rcases xs with ⟨xs⟩
+  simpa using List.le_length_erase a xs
+
+theorem mem_of_mem_erase {a b : α} {xs : Array α} (h : a ∈ xs.erase b) : a ∈ xs := by
+  rcases xs with ⟨xs⟩
+  simpa using List.mem_of_mem_erase (by simpa using h)
+
+@[simp] theorem mem_erase_of_ne [LawfulBEq α] {a b : α} {xs : Array α} (ab : a ≠ b) :
+    a ∈ xs.erase b ↔ a ∈ xs :=
+  erase_eq_eraseP b xs ▸ mem_eraseP_of_neg (mt eq_of_beq ab.symm)
+
+@[simp] theorem erase_eq_self_iff [LawfulBEq α] {xs : Array α} : xs.erase a = xs ↔ a ∉ xs := by
+  rw [erase_eq_eraseP', eraseP_eq_self_iff]
+  simp [forall_mem_ne']
+
+theorem erase_filter [LawfulBEq α] (f : α → Bool) (xs : Array α) :
+    (filter f xs).erase a = filter f (xs.erase a) := by
+  rcases xs with ⟨xs⟩
+  simpa using List.erase_filter f xs
+
+theorem erase_append_left [LawfulBEq α] {xs : Array α} (ys) (h : a ∈ xs) :
+    (xs ++ ys).erase a = xs.erase a ++ ys := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simpa using List.erase_append_left ys (by simpa using h)
+
+theorem erase_append_right [LawfulBEq α] {a : α} {xs : Array α} (ys : Array α) (h : a ∉ xs) :
+    (xs ++ ys).erase a = (xs ++ ys.erase a) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simpa using List.erase_append_right ys (by simpa using h)
+
+theorem erase_append [LawfulBEq α] {a : α} {xs ys : Array α} :
+    (xs ++ ys).erase a = if a ∈ xs then xs.erase a ++ ys else xs ++ ys.erase a := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp only [List.append_toArray, List.erase_toArray, List.erase_append, mem_toArray]
+  split <;> simp
+
+theorem erase_replicate [LawfulBEq α] (n : Nat) (a b : α) :
+    (replicate n a).erase b = if b == a then replicate (n - 1) a else replicate n a := by
+  simp only [← List.toArray_replicate, List.erase_toArray]
+  simp only [List.erase_replicate, beq_iff_eq, List.toArray_replicate]
+  split <;> simp
+
+@[deprecated erase_replicate (since := "2025-03-18")]
+abbrev erase_mkArray := @erase_replicate
+
+theorem erase_comm [LawfulBEq α] (a b : α) (xs : Array α) :
+    (xs.erase a).erase b = (xs.erase b).erase a := by
+  rcases xs with ⟨xs⟩
+  simpa using List.erase_comm a b xs
+
+theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
+    xs.erase a = ys ↔
+      (a ∉ xs ∧ xs = ys) ∨
+        ∃ as bs, a ∉ as ∧ xs = as.push a ++ bs ∧ ys = as ++ bs := by
+  rw [erase_eq_eraseP', eraseP_eq_iff]
+  simp only [beq_iff_eq, forall_mem_ne', exists_and_left]
+  constructor
+  · rintro (⟨h, rfl⟩ | ⟨a', as, h, rfl, bs, rfl, rfl⟩)
+    · left; simp_all
+    · right; refine ⟨as, h, bs, by simp⟩
+  · rintro (⟨h, rfl⟩ | ⟨as, h, bs, rfl, rfl⟩)
+    · left; simp_all
+    · right; refine ⟨a, as, h, rfl, bs, by simp⟩
+
+@[simp] theorem erase_replicate_self [LawfulBEq α] {a : α} :
+    (replicate n a).erase a = replicate (n - 1) a := by
+  simp only [← List.toArray_replicate, List.erase_toArray]
+  simp [List.erase_replicate]
+
+@[deprecated erase_replicate_self (since := "2025-03-18")]
+abbrev erase_mkArray_self := @erase_replicate_self
+
+@[simp] theorem erase_replicate_ne [LawfulBEq α] {a b : α} (h : !b == a) :
+    (replicate n a).erase b = replicate n a := by
+  rw [erase_of_not_mem]
+  simp_all
+
+@[deprecated erase_replicate_ne (since := "2025-03-18")]
+abbrev erase_mkArray_ne := @erase_replicate_ne
+
+end erase
+
+/-! ### eraseIdx -/
+
+theorem eraseIdx_eq_eraseIdxIfInBounds {xs : Array α} {i : Nat} (h : i < xs.size) :
+    xs.eraseIdx i h = xs.eraseIdxIfInBounds i := by
+  simp [eraseIdxIfInBounds, h]
+
+theorem eraseIdx_eq_take_drop_succ (xs : Array α) (i : Nat) (h) : xs.eraseIdx i = xs.take i ++ xs.drop (i + 1) := by
+  rcases xs with ⟨xs⟩
+  simp only [List.size_toArray] at h
+  simp only [List.eraseIdx_toArray, List.eraseIdx_eq_take_drop_succ, take_eq_extract,
+    List.extract_toArray, List.extract_eq_drop_take, Nat.sub_zero, List.drop_zero, drop_eq_extract,
+    List.size_toArray, List.append_toArray, mk.injEq, List.append_cancel_left_eq]
+  rw [List.take_of_length_le]
+  simp
+
+theorem getElem?_eraseIdx (xs : Array α) (i : Nat) (h : i < xs.size) (j : Nat) :
+    (xs.eraseIdx i)[j]? = if j < i then xs[j]? else xs[j + 1]? := by
+  rcases xs with ⟨xs⟩
+  simp [List.getElem?_eraseIdx]
+
+theorem getElem?_eraseIdx_of_lt (xs : Array α) (i : Nat) (h : i < xs.size) (j : Nat) (h' : j < i) :
+    (xs.eraseIdx i)[j]? = xs[j]? := by
+  rw [getElem?_eraseIdx]
+  simp [h']
+
+theorem getElem?_eraseIdx_of_ge (xs : Array α) (i : Nat) (h : i < xs.size) (j : Nat) (h' : i ≤ j) :
+    (xs.eraseIdx i)[j]? = xs[j + 1]? := by
+  rw [getElem?_eraseIdx]
+  simp only [dite_eq_ite, ite_eq_right_iff]
+  intro h'
+  omega
+
+theorem getElem_eraseIdx (xs : Array α) (i : Nat) (h : i < xs.size) (j : Nat) (h' : j < (xs.eraseIdx i).size) :
+    (xs.eraseIdx i)[j] = if h'' : j < i then
+        xs[j]
+      else
+        xs[j + 1]'(by rw [size_eraseIdx] at h'; omega) := by
+  apply Option.some.inj
+  rw [← getElem?_eq_getElem, getElem?_eraseIdx]
+  split <;> simp
+
+@[simp] theorem eraseIdx_eq_empty_iff {xs : Array α} {i : Nat} {h} : xs.eraseIdx i = #[] ↔ xs.size = 1 ∧ i = 0 := by
+  rcases xs with ⟨xs⟩
+  simp only [List.eraseIdx_toArray, mk.injEq, List.eraseIdx_eq_nil_iff, List.size_toArray,
+    or_iff_right_iff_imp]
+  rintro rfl
+  simp_all
+
+theorem eraseIdx_ne_empty_iff {xs : Array α} {i : Nat} {h} : xs.eraseIdx i ≠ #[] ↔ 2 ≤ xs.size := by
+  rcases xs with ⟨_ | ⟨a, (_ | ⟨b, l⟩)⟩⟩
+  · simp
+  · simp at h
+    simp [h]
+  · simp
+
+theorem mem_of_mem_eraseIdx {xs : Array α} {i : Nat} {h} {a : α} (h : a ∈ xs.eraseIdx i) : a ∈ xs := by
+  rcases xs with ⟨xs⟩
+  simpa using List.mem_of_mem_eraseIdx (by simpa using h)
+
+theorem eraseIdx_append_of_lt_size {xs : Array α} {k : Nat} (hk : k < xs.size) (ys : Array α) (h) :
+    eraseIdx (xs ++ ys) k = eraseIdx xs k ++ ys := by
+  rcases xs with ⟨l⟩
+  rcases ys with ⟨l'⟩
+  simp at hk
+  simp [List.eraseIdx_append_of_lt_length, *]
+
+theorem eraseIdx_append_of_length_le {xs : Array α} {k : Nat} (hk : xs.size ≤ k) (ys : Array α) (h) :
+    eraseIdx (xs ++ ys) k = xs ++ eraseIdx ys (k - xs.size) (by simp at h; omega) := by
+  rcases xs with ⟨l⟩
+  rcases ys with ⟨l'⟩
+  simp at hk
+  simp [List.eraseIdx_append_of_length_le, *]
+
+theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} {h} :
+    (replicate n a).eraseIdx k = replicate (n - 1) a := by
+  simp at h
+  simp only [← List.toArray_replicate, List.eraseIdx_toArray]
+  simp [List.eraseIdx_replicate, h]
+
+@[deprecated eraseIdx_replicate (since := "2025-03-18")]
+abbrev eraseIdx_mkArray := @eraseIdx_replicate
+
+theorem mem_eraseIdx_iff_getElem {x : α} {xs : Array α} {k} {h} : x ∈ xs.eraseIdx k h ↔ ∃ i w, i ≠ k ∧ xs[i]'w = x := by
+  rcases xs with ⟨xs⟩
+  simp [List.mem_eraseIdx_iff_getElem, *]
+
+theorem mem_eraseIdx_iff_getElem? {x : α} {xs : Array α} {k} {h} : x ∈ xs.eraseIdx k h ↔ ∃ i ≠ k, xs[i]? = some x := by
+  rcases xs with ⟨xs⟩
+  simp [List.mem_eraseIdx_iff_getElem?, *]
+
+theorem erase_eq_eraseIdx_of_idxOf [BEq α] [LawfulBEq α] (xs : Array α) (a : α) (i : Nat) (w : xs.idxOf a = i) (h : i < xs.size) :
+    xs.erase a = xs.eraseIdx i := by
+  rcases xs with ⟨xs⟩
+  simp at w
+  simp [List.erase_eq_eraseIdx_of_idxOf, *]
+
+theorem getElem_eraseIdx_of_lt (xs : Array α) (i : Nat) (w : i < xs.size) (j : Nat) (h : j < (xs.eraseIdx i).size) (h' : j < i) :
+    (xs.eraseIdx i)[j] = xs[j] := by
+  rcases xs with ⟨xs⟩
+  simp [List.getElem_eraseIdx_of_lt, *]
+
+theorem getElem_eraseIdx_of_ge (xs : Array α) (i : Nat) (w : i < xs.size) (j : Nat) (h : j < (xs.eraseIdx i).size) (h' : i ≤ j) :
+    (xs.eraseIdx i)[j] = xs[j + 1]'(by simp at h; omega) := by
+  rcases xs with ⟨xs⟩
+  simp [List.getElem_eraseIdx_of_ge, *]
+
+theorem eraseIdx_set_eq {xs : Array α} {i : Nat} {a : α} {h : i < xs.size} :
+    (xs.set i a).eraseIdx i (by simp; omega) = xs.eraseIdx i := by
+  rcases xs with ⟨xs⟩
+  simp [List.eraseIdx_set_eq, *]
+
+theorem eraseIdx_set_lt {xs : Array α} {i : Nat} {w : i < xs.size} {j : Nat} {a : α} (h : j < i) :
+    (xs.set i a).eraseIdx j (by simp; omega) = (xs.eraseIdx j).set (i - 1) a (by simp; omega) := by
+  rcases xs with ⟨xs⟩
+  simp [List.eraseIdx_set_lt, *]
+
+theorem eraseIdx_set_gt {xs : Array α} {i : Nat} {j : Nat} {a : α} (h : i < j) {w : j < xs.size} :
+    (xs.set i a).eraseIdx j (by simp; omega) = (xs.eraseIdx j).set i a (by simp; omega) := by
+  rcases xs with ⟨xs⟩
+  simp [List.eraseIdx_set_gt, *]
+
+@[simp] theorem set_getElem_succ_eraseIdx_succ
+    {xs : Array α} {i : Nat} (h : i + 1 < xs.size) :
+    (xs.eraseIdx (i + 1)).set i xs[i + 1] (by simp; omega) = xs.eraseIdx i := by
+  rcases xs with ⟨xs⟩
+  simp [List.set_getElem_succ_eraseIdx_succ, *]
+
+end Array

src/Init/Data/Array/Extract.lean

@@ -0,0 +1,445 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.Nat.TakeDrop
+
+/-!
+# Lemmas about `Array.extract`
+
+This file follows the contents of `Init.Data.List.TakeDrop` and `Init.Data.List.Nat.TakeDrop`.
+-/
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+open Nat
+namespace Array
+
+/-! ### extract -/
+
+@[simp] theorem extract_of_size_lt {as : Array α} {i j : Nat} (h : as.size < j) :
+    as.extract i j = as.extract i as.size := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract] at h₁ h₂
+    simp [h]
+
+theorem size_extract_le {as : Array α} {i j : Nat} :
+    (as.extract i j).size ≤ j - i := by
+  simp
+  omega
+
+theorem size_extract_le' {as : Array α} {i j : Nat} :
+    (as.extract i j).size ≤ as.size - i := by
+  simp
+  omega
+
+theorem size_extract_of_le {as : Array α} {i j : Nat} (h : j ≤ as.size) :
+    (as.extract i j).size = j - i := by
+  simp
+  omega
+
+@[simp]
+theorem extract_push {as : Array α} {b : α} {start stop : Nat} (h : stop ≤ as.size) :
+    (as.push b).extract start stop = as.extract start stop := by
+  ext i h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract, size_push] at h₁ h₂
+    simp only [getElem_extract, getElem_push]
+    rw [dif_pos (by omega)]
+
+@[simp]
+theorem extract_eq_pop {as : Array α} {stop : Nat} (h : stop = as.size - 1) :
+    as.extract 0 stop = as.pop := by
+  ext i h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract, size_pop] at h₁ h₂
+    simp [getElem_extract, getElem_pop]
+
+@[simp]
+theorem extract_append_extract {as : Array α} {i j k : Nat} :
+    as.extract i j ++ as.extract j k = as.extract (min i j) (max j k) := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_append, size_extract] at h₁ h₂
+    simp only [getElem_append, size_extract, getElem_extract]
+    split <;>
+    · congr 1
+      omega
+
+@[simp]
+theorem extract_eq_empty_iff {as : Array α} :
+    as.extract i j = #[] ↔ min j as.size ≤ i := by
+  constructor
+  · intro h
+    replace h := congrArg Array.size h
+    simp at h
+    omega
+  · intro h
+    exact eq_empty_of_size_eq_zero (by simp; omega)
+
+theorem extract_eq_empty_of_le {as : Array α} (h : min j as.size ≤ i) :
+    as.extract i j = #[] :=
+  extract_eq_empty_iff.2 h
+
+theorem lt_of_extract_ne_empty {as : Array α} (h : as.extract i j ≠ #[]) :
+    i < min j as.size :=
+  gt_of_not_le (mt extract_eq_empty_of_le h)
+
+@[simp]
+theorem extract_eq_self_iff {as : Array α} :
+    as.extract i j = as ↔ as.size = 0 ∨ i = 0 ∧ as.size ≤ j := by
+  constructor
+  · intro h
+    replace h := congrArg Array.size h
+    simp at h
+    omega
+  · intro h
+    ext l h₁ h₂
+    · simp
+      omega
+    · simp only [size_extract] at h₁
+      simp only [getElem_extract]
+      congr 1
+      omega
+
+theorem extract_eq_self_of_le {as : Array α} (h : as.size ≤ j) :
+    as.extract 0 j = as :=
+  extract_eq_self_iff.2 (.inr ⟨rfl, h⟩)
+
+theorem le_of_extract_eq_self {as : Array α} (h : as.extract i j = as) :
+    as.size ≤ j := by
+  replace h := congrArg Array.size h
+  simp at h
+  omega
+
+@[simp]
+theorem extract_size_left {as : Array α} :
+    as.extract as.size j = #[] := by
+  simp
+  omega
+
+@[simp]
+theorem push_extract_getElem {as : Array α} {i j : Nat} (h : j < as.size) :
+    (as.extract i j).push as[j] = as.extract (min i j) (j + 1) := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_push, size_extract] at h₁ h₂
+    simp only [getElem_push, size_extract, getElem_extract]
+    split <;>
+    · congr
+      omega
+
+theorem extract_succ_right {as : Array α} {i j : Nat} (w : i < j + 1) (h : j < as.size) :
+    as.extract i (j + 1) = (as.extract i j).push as[j] := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract, push_extract_getElem] at h₁ h₂
+    simp only [getElem_extract, push_extract_getElem]
+    congr
+    omega
+
+theorem extract_sub_one {as : Array α} {i j : Nat} (h : j < as.size) :
+    as.extract i (j - 1) = (as.extract i j).pop := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract, size_pop] at h₁ h₂
+    simp only [getElem_extract, getElem_pop]
+
+@[simp]
+theorem getElem?_extract_of_lt {as : Array α} {i j k : Nat} (h : k < min j as.size - i) :
+    (as.extract i j)[k]? = some (as[i + k]'(by omega)) := by
+  simp [getElem?_extract, h]
+
+theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
+    (as.extract 0 (j + 1))[j]? = as[j]? := by
+  simp [getElem?_extract]
+  omega
+
+@[simp] theorem extract_extract {as : Array α} {i j k l : Nat} :
+    (as.extract i j).extract k l = as.extract (i + k) (min (i + l) j) := by
+  ext m h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract] at h₁ h₂
+    simp [Nat.add_assoc]
+
+theorem extract_eq_empty_of_eq_empty {as : Array α} {i j : Nat} (h : as = #[]) :
+    as.extract i j = #[] := by
+  simp [h]
+
+theorem ne_empty_of_extract_ne_empty {as : Array α} {i j : Nat} (h : as.extract i j ≠ #[]) :
+    as ≠ #[] :=
+  mt extract_eq_empty_of_eq_empty h
+
+theorem extract_set {as : Array α} {i j k : Nat} (h : k < as.size) {a : α} :
+    (as.set k a).extract i j =
+      if _ : k < i then
+        as.extract i j
+      else if _ : k < min j as.size then
+        (as.extract i j).set (k - i) a (by simp; omega)
+      else as.extract i j := by
+  split
+  · ext l h₁ h₂
+    · simp
+    · simp at h₁ h₂
+      simp [getElem_set]
+      omega
+  · split
+    · ext l h₁ h₂
+      · simp
+      · simp only [getElem_extract, getElem_set]
+        split
+        · rw [if_pos]; omega
+        · rw [if_neg]; omega
+    · ext l h₁ h₂
+      · simp
+      · simp at h₁ h₂
+        simp [getElem_set]
+        omega
+
+theorem set_extract {as : Array α} {i j k : Nat} (h : k < (as.extract i j).size) {a : α} :
+    (as.extract i j).set k a = (as.set (i + k) a (by simp at h; omega)).extract i j := by
+  ext l h₁ h₂
+  · simp
+  · simp_all [getElem_set]
+
+@[simp]
+theorem extract_append {as bs : Array α} {i j : Nat} :
+    (as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract, size_append] at h₁ h₂
+    simp only [getElem_extract, getElem_append, size_extract]
+    split
+    · split
+      · rfl
+      · omega
+    · split
+      · omega
+      · congr 1
+        omega
+
+theorem extract_append_left {as bs : Array α} :
+    (as ++ bs).extract 0 as.size = as.extract 0 as.size := by
+  simp
+
+@[simp] theorem extract_append_right {as bs : Array α} :
+    (as ++ bs).extract as.size (as.size + i) = bs.extract 0 i := by
+  simp only [extract_append, extract_size_left, Nat.sub_self, empty_append]
+  congr 1
+  omega
+
+@[simp] theorem map_extract {as : Array α} {i j : Nat} :
+    (as.extract i j).map f = (as.map f).extract i j := by
+  ext l h₁ h₂
+  · simp
+  · simp only [size_map, size_extract] at h₁ h₂
+    simp only [getElem_map, getElem_extract]
+
+@[simp] theorem extract_replicate {a : α} {n i j : Nat} :
+    (replicate n a).extract i j = replicate (min j n - i) a := by
+  ext l h₁ h₂
+  · simp
+  · simp only [size_extract, size_replicate] at h₁ h₂
+    simp only [getElem_extract, getElem_replicate]
+
+@[deprecated extract_replicate (since := "2025-03-18")]
+abbrev extract_mkArray := @extract_replicate
+
+theorem extract_eq_extract_right {as : Array α} {i j j' : Nat} :
+    as.extract i j = as.extract i j' ↔ min (j - i) (as.size - i) = min (j' - i) (as.size - i) := by
+  rcases as with ⟨as⟩
+  simp
+
+theorem extract_eq_extract_left {as : Array α} {i i' j : Nat} :
+    as.extract i j = as.extract i' j ↔ min j as.size - i = min j as.size - i' := by
+  constructor
+  · intro h
+    replace h := congrArg Array.size h
+    simpa using h
+  · intro h
+    ext l h₁ h₂
+    · simpa
+    · simp only [size_extract] at h₁ h₂
+      simp only [getElem_extract]
+      congr 1
+      omega
+
+theorem extract_add_left {as : Array α} {i j k : Nat} :
+    as.extract (i + j) k = (as.extract i k).extract j (k - i) := by
+  simp [extract_eq_extract_right]
+  omega
+
+theorem mem_extract_iff_getElem {as : Array α} {a : α} {i j : Nat} :
+    a ∈ as.extract i j ↔ ∃ (k : Nat) (hm : k < min j as.size - i), as[i + k] = a := by
+  rcases as with ⟨as⟩
+  simp [List.mem_take_iff_getElem]
+  constructor <;>
+  · rintro ⟨k, h, rfl⟩
+    exact ⟨k, by omega, rfl⟩
+
+theorem set_eq_push_extract_append_extract {as : Array α} {i : Nat} (h : i < as.size) {a : α} :
+    as.set i a = (as.extract 0 i).push a ++ (as.extract (i + 1) as.size) := by
+  rcases as with ⟨as⟩
+  simp at h
+  simp [List.set_eq_take_append_cons_drop, h, List.take_of_length_le]
+
+theorem extract_reverse {as : Array α} {i j : Nat} :
+    as.reverse.extract i j = (as.extract (as.size - j) (as.size - i)).reverse := by
+  ext l h₁ h₂
+  · simp
+    omega
+  · simp only [size_extract, size_reverse] at h₁ h₂
+    simp only [getElem_extract, getElem_reverse, size_extract]
+    congr 1
+    omega
+
+theorem reverse_extract {as : Array α} {i j : Nat} :
+    (as.extract i j).reverse = as.reverse.extract (as.size - j) (as.size - i) := by
+  rw [extract_reverse]
+  simp
+  by_cases h : j ≤ as.size
+  · have : as.size - (as.size - j) = j := by omega
+    simp [this, extract_eq_extract_left]
+    omega
+  · have : as.size - (as.size - j) = as.size := by omega
+    simp only [Nat.not_le] at h
+    simp [h, this, extract_eq_extract_left]
+    omega
+
+/-! ### takeWhile -/
+
+theorem takeWhile_map (f : α → β) (p : β → Bool) (as : Array α) :
+    (as.map f).takeWhile p = (as.takeWhile (p ∘ f)).map f := by
+  rcases as with ⟨as⟩
+  simp [List.takeWhile_map]
+
+theorem popWhile_map (f : α → β) (p : β → Bool) (as : Array α) :
+    (as.map f).popWhile p = (as.popWhile (p ∘ f)).map f := by
+  rcases as with ⟨as⟩
+  simp [List.dropWhile_map, ← List.map_reverse]
+
+theorem takeWhile_filterMap (f : α → Option β) (p : β → Bool) (as : Array α) :
+    (as.filterMap f).takeWhile p = (as.takeWhile fun a => (f a).all p).filterMap f := by
+  rcases as with ⟨as⟩
+  simp [List.takeWhile_filterMap]
+
+theorem popWhile_filterMap (f : α → Option β) (p : β → Bool) (as : Array α) :
+    (as.filterMap f).popWhile p = (as.popWhile fun a => (f a).all p).filterMap f := by
+  rcases as with ⟨as⟩
+  simp [List.dropWhile_filterMap, ← List.filterMap_reverse]
+
+theorem takeWhile_filter (p q : α → Bool) (as : Array α) :
+    (as.filter p).takeWhile q = (as.takeWhile fun a => !p a || q a).filter p := by
+  rcases as with ⟨as⟩
+  simp [List.takeWhile_filter]
+
+theorem popWhile_filter (p q : α → Bool) (as : Array α) :
+    (as.filter p).popWhile q = (as.popWhile fun a => !p a || q a).filter p := by
+  rcases as with ⟨as⟩
+  simp [List.dropWhile_filter, ← List.filter_reverse]
+
+theorem takeWhile_append {xs ys : Array α} :
+    (xs ++ ys).takeWhile p =
+      if (xs.takeWhile p).size = xs.size then xs ++ ys.takeWhile p else xs.takeWhile p := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp only [List.append_toArray, List.takeWhile_toArray, List.takeWhile_append, List.size_toArray]
+  split <;> rfl
+
+@[simp] theorem takeWhile_append_of_pos {p : α → Bool} {xs ys : Array α} (h : ∀ a ∈ xs, p a) :
+    (xs ++ ys).takeWhile p = xs ++ ys.takeWhile p := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp at h
+  simp [List.takeWhile_append_of_pos h]
+
+theorem popWhile_append {xs ys : Array α} :
+    (xs ++ ys).popWhile p =
+      if (ys.popWhile p).isEmpty then xs.popWhile p else xs ++ ys.popWhile p := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp only [List.append_toArray, List.popWhile_toArray, List.reverse_append, List.dropWhile_append,
+    List.isEmpty_iff, List.isEmpty_toArray, List.isEmpty_reverse]
+  -- Why do these not fire with `simp`?
+  rw [List.popWhile_toArray, List.isEmpty_toArray, List.isEmpty_reverse]
+  split
+  · rfl
+  · simp
+
+@[simp] theorem popWhile_append_of_pos {p : α → Bool} {xs ys : Array α} (h : ∀ a ∈ ys, p a) :
+    (xs ++ ys).popWhile p = xs.popWhile p := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp at h
+  simp only [List.append_toArray, List.popWhile_toArray, List.reverse_append, mk.injEq,
+    List.reverse_inj]
+  rw [List.dropWhile_append_of_pos]
+  simpa
+
+@[simp] theorem takeWhile_replicate_eq_filter (p : α → Bool) :
+    (replicate n a).takeWhile p = (replicate n a).filter p := by
+  simp [← List.toArray_replicate]
+
+@[deprecated takeWhile_replicate_eq_filter (since := "2025-03-18")]
+abbrev takeWhile_mkArray_eq_filter := @takeWhile_replicate_eq_filter
+
+theorem takeWhile_replicate (p : α → Bool) :
+    (replicate n a).takeWhile p = if p a then replicate n a else #[] := by
+  simp [takeWhile_replicate_eq_filter, filter_replicate]
+
+@[deprecated takeWhile_replicate (since := "2025-03-18")]
+abbrev takeWhile_mkArray := @takeWhile_replicate
+
+@[simp] theorem popWhile_replicate_eq_filter_not (p : α → Bool) :
+    (replicate n a).popWhile p = (replicate n a).filter (fun a => !p a) := by
+  simp [← List.toArray_replicate, ← List.filter_reverse]
+
+@[deprecated popWhile_replicate_eq_filter_not (since := "2025-03-18")]
+abbrev popWhile_mkArray_eq_filter_not := @popWhile_replicate_eq_filter_not
+
+theorem popWhile_replicate (p : α → Bool) :
+    (replicate n a).popWhile p = if p a then #[] else replicate n a := by
+  simp only [popWhile_replicate_eq_filter_not, size_replicate, filter_replicate, Bool.not_eq_eq_eq_not,
+    Bool.not_true]
+  split <;> simp_all
+
+@[deprecated popWhile_replicate (since := "2025-03-18")]
+abbrev popWhile_mkArray := @popWhile_replicate
+
+theorem extract_takeWhile {as : Array α} {i : Nat} :
+    (as.takeWhile p).extract 0 i = (as.extract 0 i).takeWhile p := by
+  rcases as with ⟨as⟩
+  simp [List.take_takeWhile]
+
+@[simp] theorem all_takeWhile {as : Array α} :
+    (as.takeWhile p).all p = true := by
+  rcases as with ⟨as⟩
+  rw [List.takeWhile_toArray] -- Not sure why this doesn't fire with `simp`.
+  simp
+
+@[simp] theorem any_popWhile {as : Array α} :
+    (as.popWhile p).any (fun a => !p a) = !as.all p := by
+  rcases as with ⟨as⟩
+  rw [List.popWhile_toArray] -- Not sure why this doesn't fire with `simp`.
+  simp
+
+theorem takeWhile_eq_extract_findIdx_not {xs : Array α} {p : α → Bool} :
+    takeWhile p xs = xs.extract 0 (xs.findIdx (fun a => !p a)) := by
+  rcases xs with ⟨xs⟩
+  simp [List.takeWhile_eq_take_findIdx_not]
+
+end Array

src/Init/Data/Array/FinRange.lean

@@ -5,10 +5,52 @@ Authors: François G. Dorais
 -/
 prelude
 import Init.Data.List.FinRange
+import Init.Data.Array.OfFn
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 
 namespace Array
 
-/-- `finRange n` is the array of all elements of `Fin n` in order. -/
+/--
+Returns an array of all elements of `Fin n` in order, starting at `0`.
+
+Examples:
+ * `Array.finRange 0 = (#[] : Array (Fin 0))`
+ * `Array.finRange 2 = (#[0, 1] : Array (Fin 2))`
+-/
 protected def finRange (n : Nat) : Array (Fin n) := ofFn fun i => i
 
+@[simp] theorem size_finRange (n) : (Array.finRange n).size = n := by
+  simp [Array.finRange]
+
+@[simp] theorem getElem_finRange (i : Nat) (h : i < (Array.finRange n).size) :
+    (Array.finRange n)[i] = Fin.cast (size_finRange n) ⟨i, h⟩ := by
+  simp [Array.finRange]
+
+@[simp] theorem finRange_zero : Array.finRange 0 = #[] := by simp [Array.finRange]
+
+theorem finRange_succ (n) : Array.finRange (n+1) = #[0] ++ (Array.finRange n).map Fin.succ := by
+  ext
+  · simp [Nat.add_comm]
+  · simp [getElem_append]
+    split <;>
+    · simp; omega
+
+theorem finRange_succ_last (n) :
+    Array.finRange (n+1) = (Array.finRange n).map Fin.castSucc ++ #[Fin.last n] := by
+  ext
+  · simp
+  · simp [getElem_push]
+    split
+    · simp
+    · simp_all
+      omega
+
+theorem finRange_reverse (n) : (Array.finRange n).reverse = (Array.finRange n).map Fin.rev := by
+  ext i h
+  · simp
+  · simp
+    omega
+
 end Array

src/Init/Data/Array/Find.lean

@@ -4,115 +4,128 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kim Morrison
 -/
 prelude
-import Init.Data.List.Find
+import Init.Data.List.Nat.Find
 import Init.Data.Array.Lemmas
 import Init.Data.Array.Attach
+import Init.Data.Array.Range
 
 /-!
-# Lemmas about `Array.findSome?`, `Array.find?`.
+# Lemmas about `Array.findSome?`, `Array.find?, `Array.findIdx`, `Array.findIdx?`, `Array.idxOf`.
 -/
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
 namespace Array
 
 open Nat
 
 /-! ### findSome? -/
 
-@[simp] theorem findSomeRev?_push_of_isSome (l : Array α) (h : (f a).isSome) : (l.push a).findSomeRev? f = f a := by
-  cases l; simp_all
+@[simp] theorem findSomeRev?_push_of_isSome (xs : Array α) (h : (f a).isSome) : (xs.push a).findSomeRev? f = f a := by
+  cases xs; simp_all
 
-@[simp] theorem findSomeRev?_push_of_isNone (l : Array α) (h : (f a).isNone) : (l.push a).findSomeRev? f = l.findSomeRev? f := by
-  cases l; simp_all
+@[simp] theorem findSomeRev?_push_of_isNone (xs : Array α) (h : (f a).isNone) : (xs.push a).findSomeRev? f = xs.findSomeRev? f := by
+  cases xs; simp_all
 
-theorem exists_of_findSome?_eq_some {f : α → Option β} {l : Array α} (w : l.findSome? f = some b) :
-    ∃ a, a ∈ l ∧ f a = b := by
-  cases l; simp_all [List.exists_of_findSome?_eq_some]
+theorem exists_of_findSome?_eq_some {f : α → Option β} {xs : Array α} (w : xs.findSome? f = some b) :
+    ∃ a, a ∈ xs ∧ f a = b := by
+  cases xs; simp_all [List.exists_of_findSome?_eq_some]
 
-@[simp] theorem findSome?_eq_none_iff : findSome? p l = none ↔ ∀ x ∈ l, p x = none := by
-  cases l; simp
+@[simp] theorem findSome?_eq_none_iff : findSome? p xs = none ↔ ∀ x ∈ xs, p x = none := by
+  cases xs; simp
 
-@[simp] theorem findSome?_isSome_iff {f : α → Option β} {l : Array α} :
-    (l.findSome? f).isSome ↔ ∃ x, x ∈ l ∧ (f x).isSome := by
-  cases l; simp
+@[simp] theorem findSome?_isSome_iff {f : α → Option β} {xs : Array α} :
+    (xs.findSome? f).isSome ↔ ∃ x, x ∈ xs ∧ (f x).isSome := by
+  cases xs; simp
 
-theorem findSome?_eq_some_iff {f : α → Option β} {l : Array α} {b : β} :
-    l.findSome? f = some b ↔ ∃ (l₁ : Array α) (a : α) (l₂ : Array α), l = l₁.push a ++ l₂ ∧ f a = some b ∧ ∀ x ∈ l₁, f x = none := by
-  cases l
+theorem findSome?_eq_some_iff {f : α → Option β} {xs : Array α} {b : β} :
+    xs.findSome? f = some b ↔ ∃ (ys : Array α) (a : α) (zs : Array α), xs = ys.push a ++ zs ∧ f a = some b ∧ ∀ x ∈ ys, f x = none := by
+  cases xs
   simp only [List.findSome?_toArray, List.findSome?_eq_some_iff]
   constructor
   · rintro ⟨l₁, a, l₂, rfl, h₁, h₂⟩
     exact ⟨l₁.toArray, a, l₂.toArray, by simp_all⟩
-  · rintro ⟨l₁, a, l₂, h₀, h₁, h₂⟩
-    exact ⟨l₁.toList, a, l₂.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
+  · rintro ⟨xs, a, ys, h₀, h₁, h₂⟩
+    exact ⟨xs.toList, a, ys.toList, by simpa using congrArg toList h₀, h₁, by simpa⟩
 
-@[simp] theorem findSome?_guard (l : Array α) : findSome? (Option.guard fun x => p x) l = find? p l := by
-  cases l; simp
+@[simp] theorem findSome?_guard (xs : Array α) : findSome? (Option.guard fun x => p x) xs = find? p xs := by
+  cases xs; simp
 
-@[simp] theorem getElem?_zero_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f)[0]? = l.findSome? f := by
-  cases l; simp [← List.head?_eq_getElem?]
+theorem find?_eq_findSome?_guard (xs : Array α) : find? p xs = findSome? (Option.guard fun x => p x) xs :=
+  (findSome?_guard xs).symm
 
-@[simp] theorem getElem_zero_filterMap (f : α → Option β) (l : Array α) (h) :
-    (l.filterMap f)[0] = (l.findSome? f).get (by cases l; simpa [List.length_filterMap_eq_countP] using h) := by
-  cases l; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
+@[simp] theorem getElem?_zero_filterMap (f : α → Option β) (xs : Array α) : (xs.filterMap f)[0]? = xs.findSome? f := by
+  cases xs; simp [← List.head?_eq_getElem?]
 
-@[simp] theorem back?_filterMap (f : α → Option β) (l : Array α) : (l.filterMap f).back? = l.findSomeRev? f := by
-  cases l; simp
+@[simp] theorem getElem_zero_filterMap (f : α → Option β) (xs : Array α) (h) :
+    (xs.filterMap f)[0] = (xs.findSome? f).get (by cases xs; simpa [List.length_filterMap_eq_countP] using h) := by
+  cases xs; simp [← List.head_eq_getElem, ← getElem?_zero_filterMap]
 
-@[simp] theorem back!_filterMap [Inhabited β] (f : α → Option β) (l : Array α) :
-    (l.filterMap f).back! = (l.findSomeRev? f).getD default := by
-  cases l; simp
+@[simp] theorem back?_filterMap (f : α → Option β) (xs : Array α) : (xs.filterMap f).back? = xs.findSomeRev? f := by
+  cases xs; simp
 
-@[simp] theorem map_findSome? (f : α → Option β) (g : β → γ) (l : Array α) :
-    (l.findSome? f).map g = l.findSome? (Option.map g ∘ f) := by
-  cases l; simp
+@[simp] theorem back!_filterMap [Inhabited β] (f : α → Option β) (xs : Array α) :
+    (xs.filterMap f).back! = (xs.findSomeRev? f).getD default := by
+  cases xs; simp
 
-theorem findSome?_map (f : β → γ) (l : Array β) : findSome? p (l.map f) = l.findSome? (p ∘ f) := by
-  cases l; simp [List.findSome?_map]
+@[simp] theorem map_findSome? (f : α → Option β) (g : β → γ) (xs : Array α) :
+    (xs.findSome? f).map g = xs.findSome? (Option.map g ∘ f) := by
+  cases xs; simp
 
-theorem findSome?_append {l₁ l₂ : Array α} : (l₁ ++ l₂).findSome? f = (l₁.findSome? f).or (l₂.findSome? f) := by
-  cases l₁; cases l₂; simp [List.findSome?_append]
+theorem findSome?_map (f : β → γ) (xs : Array β) : findSome? p (xs.map f) = xs.findSome? (p ∘ f) := by
+  cases xs; simp [List.findSome?_map]
 
-theorem getElem?_zero_flatten (L : Array (Array α)) :
-    (flatten L)[0]? = L.findSome? fun l => l[0]? := by
-  cases L using array_array_induction
+theorem findSome?_append {xs ys : Array α} : (xs ++ ys).findSome? f = (xs.findSome? f).or (ys.findSome? f) := by
+  cases xs; cases ys; simp [List.findSome?_append]
+
+theorem getElem?_zero_flatten (xss : Array (Array α)) :
+    (flatten xss)[0]? = xss.findSome? fun xs => xs[0]? := by
+  cases xss using array₂_induction
   simp [← List.head?_eq_getElem?, List.head?_flatten, List.findSome?_map, Function.comp_def]
 
-theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.size) :
-    (L.findSome? fun l => l[0]?).isSome := by
-  cases L using array_array_induction
+theorem getElem_zero_flatten.proof {xss : Array (Array α)} (h : 0 < xss.flatten.size) :
+    (xss.findSome? fun xs => xs[0]?).isSome := by
+  cases xss using array₂_induction
   simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
     List.findSome?_isSome_iff, isSome_getElem?]
-  simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
+  simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
     Nat.sum_pos_iff_exists_pos, List.mem_map] at h
   obtain ⟨_, ⟨xs, m, rfl⟩, h⟩ := h
   exact ⟨xs, m, by simpa using h⟩
 
-theorem getElem_zero_flatten {L : Array (Array α)} (h) :
-    (flatten L)[0] = (L.findSome? fun l => l[0]?).get (getElem_zero_flatten.proof h) := by
-  have t := getElem?_zero_flatten L
+theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
+    (flatten xss)[0] = (xss.findSome? fun xs => xs[0]?).get (getElem_zero_flatten.proof h) := by
+  have t := getElem?_zero_flatten xss
   simp [getElem?_eq_getElem, h] at t
   simp [← t]
 
-theorem back?_flatten {L : Array (Array α)} :
-    (flatten L).back? = (L.findSomeRev? fun l => l.back?) := by
-  cases L using array_array_induction
-  simp [List.getLast?_flatten, ← List.map_reverse, List.findSome?_map, Function.comp_def]
-
-theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else f a := by
+theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
   simp [← List.toArray_replicate, List.findSome?_replicate]
 
-@[simp] theorem findSome?_mkArray_of_pos (h : 0 < n) : findSome? f (mkArray n a) = f a := by
-  simp [findSome?_mkArray, Nat.ne_of_gt h]
+@[deprecated findSome?_replicate (since := "2025-03-18")]
+abbrev findSome?_mkArray := @findSome?_replicate
+
+@[simp] theorem findSome?_replicate_of_pos (h : 0 < n) : findSome? f (replicate n a) = f a := by
+  simp [findSome?_replicate, Nat.ne_of_gt h]
+
+@[deprecated findSome?_replicate_of_pos (since := "2025-03-18")]
+abbrev findSome?_mkArray_of_pos := @findSome?_replicate_of_pos
 
 -- Argument is unused, but used to decide whether `simp` should unfold.
-@[simp] theorem findSome?_mkArray_of_isSome (_ : (f a).isSome) :
-   findSome? f (mkArray n a) = if n = 0 then none else f a := by
-  simp [findSome?_mkArray]
+@[simp] theorem findSome?_replicate_of_isSome (_ : (f a).isSome) :
+   findSome? f (replicate n a) = if n = 0 then none else f a := by
+  simp [findSome?_replicate]
 
-@[simp] theorem findSome?_mkArray_of_isNone (h : (f a).isNone) :
-    findSome? f (mkArray n a) = none := by
+@[deprecated findSome?_replicate_of_isSome (since := "2025-03-18")]
+abbrev findSome?_mkArray_of_isSome := @findSome?_replicate_of_isSome
+
+@[simp] theorem findSome?_replicate_of_isNone (h : (f a).isNone) :
+    findSome? f (replicate n a) = none := by
   rw [Option.isNone_iff_eq_none] at h
-  simp [findSome?_mkArray, h]
+  simp [findSome?_replicate, h]
+
+@[deprecated findSome?_replicate_of_isNone (since := "2025-03-18")]
+abbrev findSome?_mkArray_of_isNone := @findSome?_replicate_of_isNone
 
 /-! ### find? -/
 
@@ -120,16 +133,16 @@ theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else
     #[a].find? p = if p a then some a else none := by
   simp [singleton_eq_toArray_singleton]
 
-@[simp] theorem findRev?_push_of_pos (l : Array α) (h : p a) :
-    findRev? p (l.push a) = some a := by
-  cases l; simp [h]
+@[simp] theorem findRev?_push_of_pos (xs : Array α) (h : p a) :
+    findRev? p (xs.push a) = some a := by
+  cases xs; simp [h]
 
-@[simp] theorem findRev?_cons_of_neg (l : Array α) (h : ¬p a) :
-    findRev? p (l.push a) = findRev? p l := by
-  cases l; simp [h]
+@[simp] theorem findRev?_cons_of_neg (xs : Array α) (h : ¬p a) :
+    findRev? p (xs.push a) = findRev? p xs := by
+  cases xs; simp [h]
 
-@[simp] theorem find?_eq_none : find? p l = none ↔ ∀ x ∈ l, ¬ p x := by
-  cases l; simp
+@[simp] theorem find?_eq_none : find? p xs = none ↔ ∀ x ∈ xs, ¬ p x := by
+  cases xs; simp
 
 theorem find?_eq_some_iff_append {xs : Array α} :
     xs.find? p = some b ↔ p b ∧ ∃ (as bs : Array α), xs = as.push b ++ bs ∧ ∀ a ∈ as, !p a := by
@@ -138,10 +151,10 @@ theorem find?_eq_some_iff_append {xs : Array α} :
     Bool.not_true, exists_and_right, and_congr_right_iff]
   intro w
   constructor
-  · rintro ⟨as, ⟨⟨x, rfl⟩, h⟩⟩
-    exact ⟨as.toArray, ⟨x.toArray, by simp⟩ , by simpa using h⟩
-  · rintro ⟨as, ⟨⟨x, h'⟩, h⟩⟩
-    exact ⟨as.toList, ⟨x.toList, by simpa using congrArg Array.toList h'⟩,
+  · rintro ⟨as, ⟨⟨xs, rfl⟩, h⟩⟩
+    exact ⟨as.toArray, ⟨xs.toArray, by simp⟩ , by simpa using h⟩
+  · rintro ⟨as, ⟨⟨⟨l⟩, h'⟩, h⟩⟩
+    exact ⟨as.toList, ⟨l, by simpa using congrArg Array.toList h'⟩,
       by simpa using h⟩
 
 @[simp]
@@ -170,22 +183,22 @@ theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
     (xs.filter p).find? q = xs.find? (fun a => p a ∧ q a) := by
   cases xs; simp
 
-@[simp] theorem getElem?_zero_filter (p : α → Bool) (l : Array α) :
-    (l.filter p)[0]? = l.find? p := by
-  cases l; simp [← List.head?_eq_getElem?]
+@[simp] theorem getElem?_zero_filter (p : α → Bool) (xs : Array α) :
+    (xs.filter p)[0]? = xs.find? p := by
+  cases xs; simp [← List.head?_eq_getElem?]
 
-@[simp] theorem getElem_zero_filter (p : α → Bool) (l : Array α) (h) :
-    (l.filter p)[0] =
-      (l.find? p).get (by cases l; simpa [← List.countP_eq_length_filter] using h) := by
-  cases l
+@[simp] theorem getElem_zero_filter (p : α → Bool) (xs : Array α) (h) :
+    (xs.filter p)[0] =
+      (xs.find? p).get (by cases xs; simpa [← List.countP_eq_length_filter] using h) := by
+  cases xs
   simp [List.getElem_zero_eq_head]
 
-@[simp] theorem back?_filter (p : α → Bool) (l : Array α) : (l.filter p).back? = l.findRev? p := by
-  cases l; simp
+@[simp] theorem back?_filter (p : α → Bool) (xs : Array α) : (xs.filter p).back? = xs.findRev? p := by
+  cases xs; simp
 
-@[simp] theorem back!_filter [Inhabited α] (p : α → Bool) (l : Array α) :
-    (l.filter p).back! = (l.findRev? p).get! := by
-  cases l; simp [Option.get!_eq_getD]
+@[simp] theorem back!_filter [Inhabited α] (p : α → Bool) (xs : Array α) :
+    (xs.filter p).back! = (xs.findRev? p).get! := by
+  cases xs; simp [Option.get!_eq_getD]
 
 @[simp] theorem find?_filterMap (xs : Array α) (f : α → Option β) (p : β → Bool) :
     (xs.filterMap f).find? p = (xs.find? (fun a => (f a).any p)).bind f := by
@@ -195,33 +208,36 @@ theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
     find? p (xs.map f) = (xs.find? (p ∘ f)).map f := by
   cases xs; simp
 
-@[simp] theorem find?_append {l₁ l₂ : Array α} :
-    (l₁ ++ l₂).find? p = (l₁.find? p).or (l₂.find? p) := by
-  cases l₁
-  cases l₂
+@[simp] theorem find?_append {xs ys : Array α} :
+    (xs ++ ys).find? p = (xs.find? p).or (ys.find? p) := by
+  cases xs
+  cases ys
   simp
 
-@[simp] theorem find?_flatten (xs : Array (Array α)) (p : α → Bool) :
-    xs.flatten.find? p = xs.findSome? (·.find? p) := by
-  cases xs using array_array_induction
+@[simp] theorem find?_flatten (xss : Array (Array α)) (p : α → Bool) :
+    xss.flatten.find? p = xss.findSome? (·.find? p) := by
+  cases xss using array₂_induction
   simp [List.findSome?_map, Function.comp_def]
 
-theorem find?_flatten_eq_none {xs : Array (Array α)} {p : α → Bool} :
-    xs.flatten.find? p = none ↔ ∀ ys ∈ xs, ∀ x ∈ ys, !p x := by
+theorem find?_flatten_eq_none_iff {xss : Array (Array α)} {p : α → Bool} :
+    xss.flatten.find? p = none ↔ ∀ ys ∈ xss, ∀ x ∈ ys, !p x := by
   simp
 
+@[deprecated find?_flatten_eq_none_iff (since := "2025-02-03")]
+abbrev find?_flatten_eq_none := @find?_flatten_eq_none_iff
+
 /--
 If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
 some array in `xs` contains `a`, and no earlier element of that array satisfies `p`.
 Moreover, no earlier array in `xs` has an element satisfying `p`.
 -/
-theorem find?_flatten_eq_some {xs : Array (Array α)} {p : α → Bool} {a : α} :
-    xs.flatten.find? p = some a ↔
+theorem find?_flatten_eq_some_iff {xss : Array (Array α)} {p : α → Bool} {a : α} :
+    xss.flatten.find? p = some a ↔
       p a ∧ ∃ (as : Array (Array α)) (ys zs : Array α) (bs : Array (Array α)),
-        xs = as.push (ys.push a ++ zs) ++ bs ∧
-        (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
-  cases xs using array_array_induction
-  simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some]
+        xss = as.push (ys.push a ++ zs) ++ bs ∧
+        (∀ ws ∈ as, ∀ x ∈ ws, !p x) ∧ (∀ x ∈ ys, !p x) := by
+  cases xss using array₂_induction
+  simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some_iff]
   simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
   intro w
   constructor
@@ -235,47 +251,410 @@ theorem find?_flatten_eq_some {xs : Array (Array α)} {p : α → Bool} {a : α}
       ⟨zs.toList, bs.toList.map Array.toList, by simpa using h⟩,
         by simpa using h₁, by simpa using h₂⟩
 
+@[deprecated find?_flatten_eq_some_iff (since := "2025-02-03")]
+abbrev find?_flatten_eq_some := @find?_flatten_eq_some_iff
+
 @[simp] theorem find?_flatMap (xs : Array α) (f : α → Array β) (p : β → Bool) :
     (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
   cases xs
   simp [List.find?_flatMap, Array.flatMap_toArray]
 
-theorem find?_flatMap_eq_none {xs : Array α} {f : α → Array β} {p : β → Bool} :
+theorem find?_flatMap_eq_none_iff {xs : Array α} {f : α → Array β} {p : β → Bool} :
     (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
   simp
 
-theorem find?_mkArray :
-    find? p (mkArray n a) = if n = 0 then none else if p a then some a else none := by
+@[deprecated find?_flatMap_eq_none_iff (since := "2025-02-03")]
+abbrev find?_flatMap_eq_none := @find?_flatMap_eq_none_iff
+
+theorem find?_replicate :
+    find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
   simp [← List.toArray_replicate, List.find?_replicate]
 
-@[simp] theorem find?_mkArray_of_length_pos (h : 0 < n) :
-    find? p (mkArray n a) = if p a then some a else none := by
-  simp [find?_mkArray, Nat.ne_of_gt h]
+@[deprecated find?_replicate (since := "2025-03-18")]
+abbrev find?_mkArray := @find?_replicate
 
-@[simp] theorem find?_mkArray_of_pos (h : p a) :
-    find? p (mkArray n a) = if n = 0 then none else some a := by
-  simp [find?_mkArray, h]
+@[simp] theorem find?_replicate_of_size_pos (h : 0 < n) :
+    find? p (replicate n a) = if p a then some a else none := by
+  simp [find?_replicate, Nat.ne_of_gt h]
 
-@[simp] theorem find?_mkArray_of_neg (h : ¬ p a) : find? p (mkArray n a) = none := by
-  simp [find?_mkArray, h]
+@[deprecated find?_replicate_of_size_pos (since := "2025-03-18")]
+abbrev find?_mkArray_of_length_pos := @find?_replicate_of_size_pos
+
+@[simp] theorem find?_replicate_of_pos (h : p a) :
+    find? p (replicate n a) = if n = 0 then none else some a := by
+  simp [find?_replicate, h]
+
+@[deprecated find?_replicate_of_pos (since := "2025-03-18")]
+abbrev find?_mkArray_of_pos := @find?_replicate_of_pos
+
+@[simp] theorem find?_replicate_of_neg (h : ¬ p a) : find? p (replicate n a) = none := by
+  simp [find?_replicate, h]
+
+@[deprecated find?_replicate_of_neg (since := "2025-03-18")]
+abbrev find?_mkArray_of_neg := @find?_replicate_of_neg
 
 -- This isn't a `@[simp]` lemma since there is already a lemma for `l.find? p = none` for any `l`.
-theorem find?_mkArray_eq_none {n : Nat} {a : α} {p : α → Bool} :
-    (mkArray n a).find? p = none ↔ n = 0 ∨ !p a := by
-  simp [← List.toArray_replicate, List.find?_replicate_eq_none, Classical.or_iff_not_imp_left]
+theorem find?_replicate_eq_none_iff {n : Nat} {a : α} {p : α → Bool} :
+    (replicate n a).find? p = none ↔ n = 0 ∨ !p a := by
+  simp [← List.toArray_replicate, List.find?_replicate_eq_none_iff, Classical.or_iff_not_imp_left]
 
-@[simp] theorem find?_mkArray_eq_some {n : Nat} {a b : α} {p : α → Bool} :
-    (mkArray n a).find? p = some b ↔ n ≠ 0 ∧ p a ∧ a = b := by
+@[deprecated find?_replicate_eq_none_iff (since := "2025-03-18")]
+abbrev find?_mkArray_eq_none_iff := @find?_replicate_eq_none_iff
+
+@[simp] theorem find?_replicate_eq_some_iff {n : Nat} {a b : α} {p : α → Bool} :
+    (replicate n a).find? p = some b ↔ n ≠ 0 ∧ p a ∧ a = b := by
   simp [← List.toArray_replicate]
 
-@[simp] theorem get_find?_mkArray (n : Nat) (a : α) (p : α → Bool) (h) :
-    ((mkArray n a).find? p).get h = a := by
+@[deprecated find?_replicate_eq_some_iff (since := "2025-03-18")]
+abbrev find?_mkArray_eq_some_iff := @find?_replicate_eq_some_iff
+
+@[deprecated find?_replicate_eq_some_iff (since := "2025-02-03")]
+abbrev find?_mkArray_eq_some := @find?_replicate_eq_some_iff
+
+@[simp] theorem get_find?_replicate (n : Nat) (a : α) (p : α → Bool) (h) :
+    ((replicate n a).find? p).get h = a := by
   simp [← List.toArray_replicate]
 
+@[deprecated get_find?_replicate (since := "2025-03-18")]
+abbrev get_find?_mkArray := @get_find?_replicate
+
 theorem find?_pmap {P : α → Prop} (f : (a : α) → P a → β) (xs : Array α)
     (H : ∀ (a : α), a ∈ xs → P a) (p : β → Bool) :
     (xs.pmap f H).find? p = (xs.attach.find? (fun ⟨a, m⟩ => p (f a (H a m)))).map fun ⟨a, m⟩ => f a (H a m) := by
   simp only [pmap_eq_map_attach, find?_map]
   rfl
 
+theorem find?_eq_some_iff_getElem {xs : Array α} {p : α → Bool} {b : α} :
+    xs.find? p = some b ↔ p b ∧ ∃ i h, xs[i] = b ∧ ∀ j : Nat, (hj : j < i) → !p xs[j] := by
+  rcases xs with ⟨xs⟩
+  simp [List.find?_eq_some_iff_getElem]
+
+/-! ### findIdx -/
+
+theorem findIdx_of_getElem?_eq_some {xs : Array α} (w : xs[xs.findIdx p]? = some y) : p y := by
+  rcases xs with ⟨xs⟩
+  exact List.findIdx_of_getElem?_eq_some (by simpa using w)
+
+theorem findIdx_getElem {xs : Array α} {w : xs.findIdx p < xs.size} :
+    p xs[xs.findIdx p] :=
+  xs.findIdx_of_getElem?_eq_some (getElem?_eq_getElem w)
+
+theorem findIdx_lt_size_of_exists {xs : Array α} (h : ∃ x ∈ xs, p x) :
+    xs.findIdx p < xs.size := by
+  rcases xs with ⟨xs⟩
+  simpa using List.findIdx_lt_length_of_exists (by simpa using h)
+
+theorem findIdx_getElem?_eq_getElem_of_exists {xs : Array α} (h : ∃ x ∈ xs, p x) :
+    xs[xs.findIdx p]? = some (xs[xs.findIdx p]'(xs.findIdx_lt_size_of_exists h)) :=
+  getElem?_eq_getElem (findIdx_lt_size_of_exists h)
+
+@[simp]
+theorem findIdx_eq_size {p : α → Bool} {xs : Array α} :
+    xs.findIdx p = xs.size ↔ ∀ x ∈ xs, p x = false := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem findIdx_eq_size_of_false {p : α → Bool} {xs : Array α} (h : ∀ x ∈ xs, p x = false) :
+    xs.findIdx p = xs.size := by
+  rcases xs with ⟨xs⟩
+  simp_all
+
+theorem findIdx_le_size (p : α → Bool) {xs : Array α} : xs.findIdx p ≤ xs.size := by
+  by_cases e : ∃ x ∈ xs, p x
+  · exact Nat.le_of_lt (findIdx_lt_size_of_exists e)
+  · simp at e
+    exact Nat.le_of_eq (findIdx_eq_size.mpr e)
+
+@[simp]
+theorem findIdx_lt_size {p : α → Bool} {xs : Array α} :
+    xs.findIdx p < xs.size ↔ ∃ x ∈ xs, p x := by
+  rcases xs with ⟨xs⟩
+  simp
+
+/-- `p` does not hold for elements with indices less than `xs.findIdx p`. -/
+theorem not_of_lt_findIdx {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.findIdx p) :
+    p (xs[i]'(Nat.le_trans h (findIdx_le_size p))) = false := by
+  rcases xs with ⟨xs⟩
+  simpa using List.not_of_lt_findIdx (by simpa using h)
+
+/-- If `¬ p xs[j]` for all `j < i`, then `i ≤ xs.findIdx p`. -/
+theorem le_findIdx_of_not {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.size)
+    (h2 : ∀ j (hji : j < i), p (xs[j]'(Nat.lt_trans hji h)) = false) : i ≤ xs.findIdx p := by
+  apply Decidable.byContradiction
+  intro f
+  simp only [Nat.not_le] at f
+  exact absurd (@findIdx_getElem _ p xs (Nat.lt_trans f h)) (by simpa using h2 (xs.findIdx p) f)
+
+/-- If `¬ p xs[j]` for all `j ≤ i`, then `i < xs.findIdx p`. -/
+theorem lt_findIdx_of_not {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.size)
+    (h2 : ∀ j (hji : j ≤ i), ¬p (xs[j]'(Nat.lt_of_le_of_lt hji h))) : i < xs.findIdx p := by
+  apply Decidable.byContradiction
+  intro f
+  simp only [Nat.not_lt] at f
+  exact absurd (@findIdx_getElem _ p xs (Nat.lt_of_le_of_lt f h)) (h2 (xs.findIdx p) f)
+
+/-- `xs.findIdx p = i` iff `p xs[i]` and `¬ p xs [j]` for all `j < i`. -/
+theorem findIdx_eq {p : α → Bool} {xs : Array α} {i : Nat} (h : i < xs.size) :
+    xs.findIdx p = i ↔ p xs[i] ∧ ∀ j (hji : j < i), p (xs[j]'(Nat.lt_trans hji h)) = false := by
+  refine ⟨fun f ↦ ⟨f ▸ (@findIdx_getElem _ p xs (f ▸ h)), fun _ hji ↦ not_of_lt_findIdx (f ▸ hji)⟩,
+    fun ⟨_, h2⟩ ↦ ?_⟩
+  apply Nat.le_antisymm _ (le_findIdx_of_not h h2)
+  apply Decidable.byContradiction
+  intro h3
+  simp at h3
+  simp_all [not_of_lt_findIdx h3]
+
+theorem findIdx_append (p : α → Bool) (xs ys : Array α) :
+    (xs ++ ys).findIdx p =
+      if xs.findIdx p < xs.size then xs.findIdx p else ys.findIdx p + xs.size := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp [List.findIdx_append]
+
+theorem findIdx_le_findIdx {xs : Array α} {p q : α → Bool} (h : ∀ x ∈ xs, p x → q x) : xs.findIdx q ≤ xs.findIdx p := by
+  rcases xs with ⟨xs⟩
+  simp_all [List.findIdx_le_findIdx]
+
+@[simp] theorem findIdx_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.findIdx f = xs.unattach.findIdx g := by
+  cases xs
+  simp [hf]
+
+theorem false_of_mem_extract_findIdx {xs : Array α} {p : α → Bool} (h : x ∈ xs.extract 0 (xs.findIdx p)) :
+    p x = false := by
+  rcases xs with ⟨xs⟩
+  exact List.false_of_mem_take_findIdx (by simpa using h)
+
+@[simp] theorem findIdx_extract {xs : Array α} {i : Nat} {p : α → Bool} :
+    (xs.extract 0 i).findIdx p = min i (xs.findIdx p) := by
+  cases xs
+  simp
+
+@[simp] theorem min_findIdx_findIdx {xs : Array α} {p q : α → Bool} :
+    min (xs.findIdx p) (xs.findIdx q) = xs.findIdx (fun a => p a || q a) := by
+  cases xs
+  simp
+
+/-! ### findIdx? -/
+
+@[simp] theorem findIdx?_empty : (#[] : Array α).findIdx? p = none := by simp
+
+@[simp]
+theorem findIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
+    xs.findIdx? p = none ↔ ∀ x, x ∈ xs → p x = false := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem findIdx?_isSome {xs : Array α} {p : α → Bool} :
+    (xs.findIdx? p).isSome = xs.any p := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_isSome]
+
+theorem findIdx?_isNone {xs : Array α} {p : α → Bool} :
+    (xs.findIdx? p).isNone = xs.all (¬p ·) := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_isNone]
+
+theorem findIdx?_eq_some_iff_findIdx_eq {xs : Array α} {p : α → Bool} {i : Nat} :
+    xs.findIdx? p = some i ↔ i < xs.size ∧ xs.findIdx p = i := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_some_iff_findIdx_eq]
+
+theorem findIdx?_eq_some_of_exists {xs : Array α} {p : α → Bool} (h : ∃ x, x ∈ xs ∧ p x) :
+    xs.findIdx? p = some (xs.findIdx p) := by
+  rw [findIdx?_eq_some_iff_findIdx_eq]
+  exact ⟨findIdx_lt_size_of_exists h, rfl⟩
+
+theorem findIdx?_eq_none_iff_findIdx_eq {xs : Array α} {p : α → Bool} :
+    xs.findIdx? p = none ↔ xs.findIdx p = xs.size := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_none_iff_findIdx_eq]
+
+theorem findIdx?_eq_guard_findIdx_lt {xs : Array α} {p : α → Bool} :
+    xs.findIdx? p = Option.guard (fun i => i < xs.size) (xs.findIdx p) := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_guard_findIdx_lt]
+
+theorem findIdx?_eq_some_iff_getElem {xs : Array α} {p : α → Bool} {i : Nat} :
+    xs.findIdx? p = some i ↔
+      ∃ h : i < xs.size, p xs[i] ∧ ∀ j (hji : j < i), ¬p (xs[j]'(Nat.lt_trans hji h)) := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_some_iff_getElem]
+
+theorem of_findIdx?_eq_some {xs : Array α} {p : α → Bool} (w : xs.findIdx? p = some i) :
+    match xs[i]? with | some a => p a | none => false := by
+  rcases xs with ⟨xs⟩
+  simpa using List.of_findIdx?_eq_some (by simpa using w)
+
+theorem of_findIdx?_eq_none {xs : Array α} {p : α → Bool} (w : xs.findIdx? p = none) :
+    ∀ i : Nat, match xs[i]? with | some a => ¬ p a | none => true := by
+  rcases xs with ⟨xs⟩
+  simpa using List.of_findIdx?_eq_none (by simpa using w)
+
+@[simp] theorem findIdx?_map (f : β → α) (xs : Array β) : findIdx? p (xs.map f) = xs.findIdx? (p ∘ f) := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_map]
+
+@[simp] theorem findIdx?_append :
+    (xs ++ ys : Array α).findIdx? p =
+      (xs.findIdx? p).or ((ys.findIdx? p).map fun i => i + xs.size) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp [List.findIdx?_append]
+
+theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
+    xss.flatten.findIdx? p =
+      (xss.findIdx? (·.any p)).map
+        fun i => ((xss.take i).map Array.size).sum +
+          (xss[i]?.map fun xs => xs.findIdx p).getD 0 := by
+  cases xss using array₂_induction
+  simp [List.findIdx?_flatten, Function.comp_def]
+
+@[simp] theorem findIdx?_replicate :
+    (replicate n a).findIdx? p = if 0 < n ∧ p a then some 0 else none := by
+  rw [← List.toArray_replicate]
+  simp only [List.findIdx?_toArray]
+  simp
+
+@[deprecated findIdx?_replicate (since := "2025-03-18")]
+abbrev findIdx?_mkArray := @findIdx?_replicate
+
+theorem findIdx?_eq_findSome?_zipIdx {xs : Array α} {p : α → Bool} :
+    xs.findIdx? p = xs.zipIdx.findSome? fun ⟨a, i⟩ => if p a then some i else none := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_findSome?_zipIdx]
+
+theorem findIdx?_eq_fst_find?_zipIdx {xs : Array α} {p : α → Bool} :
+    xs.findIdx? p = (xs.zipIdx.find? fun ⟨x, _⟩ => p x).map (·.2) := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_fst_find?_zipIdx]
+
+-- See also `findIdx_le_findIdx`.
+theorem findIdx?_eq_none_of_findIdx?_eq_none {xs : Array α} {p q : α → Bool} (w : ∀ x ∈ xs, p x → q x) :
+    xs.findIdx? q = none → xs.findIdx? p = none := by
+  rcases xs with ⟨xs⟩
+  simpa using List.findIdx?_eq_none_of_findIdx?_eq_none (by simpa using w)
+
+theorem findIdx_eq_getD_findIdx? {xs : Array α} {p : α → Bool} :
+    xs.findIdx p = (xs.findIdx? p).getD xs.size := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx_eq_getD_findIdx?]
+
+theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : Array α} {p q : α → Bool} (w : ∀ x ∈ xs, p x → q x) {i : Nat}
+    (h : xs.findIdx? p = some i) : ∃ j, j ≤ i ∧ xs.findIdx? q = some j := by
+  rcases xs with ⟨xs⟩
+  simp [List.findIdx?_eq_some_le_of_findIdx?_eq_some (by simpa using w) (by simpa using h)]
+
+@[simp] theorem findIdx?_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.findIdx? f = xs.unattach.findIdx? g := by
+  cases xs
+  simp [hf]
+
+@[simp] theorem findIdx?_take {xs : Array α} {i : Nat} {p : α → Bool} :
+    (xs.take i).findIdx? p = (xs.findIdx? p).bind (Option.guard (fun j => j < i)) := by
+  cases xs
+  simp
+
+/-! ### findFinIdx? -/
+
+@[simp] theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := by simp
+
+-- We can't mark this as a `@[congr]` lemma since the head of the RHS is not `findFinIdx?`.
+theorem findFinIdx?_congr {p : α → Bool} {xs ys : Array α} (w : xs = ys) :
+    findFinIdx? p xs = (findFinIdx? p ys).map (fun i => i.cast (by simp [w])) := by
+  subst w
+  simp
+
+theorem findFinIdx?_eq_pmap_findIdx? {xs : Array α} {p : α → Bool} :
+    xs.findFinIdx? p =
+      (xs.findIdx? p).pmap
+        (fun i m => by simp [findIdx?_eq_some_iff_getElem] at m; exact ⟨i, m.choose⟩)
+        (fun i h => h) := by
+  simp [findIdx?_eq_map_findFinIdx?_val, Option.pmap_map]
+
+@[simp] theorem findFinIdx?_eq_none_iff {xs : Array α} {p : α → Bool} :
+    xs.findFinIdx? p = none ↔ ∀ x, x ∈ xs → ¬ p x := by
+  simp [findFinIdx?_eq_pmap_findIdx?]
+
+@[simp]
+theorem findFinIdx?_eq_some_iff {xs : Array α} {p : α → Bool} {i : Fin xs.size} :
+    xs.findFinIdx? p = some i ↔
+      p xs[i] ∧ ∀ j (hji : j < i), ¬p (xs[j]'(Nat.lt_trans hji i.2)) := by
+  simp only [findFinIdx?_eq_pmap_findIdx?, Option.pmap_eq_some_iff, findIdx?_eq_some_iff_getElem,
+    Bool.not_eq_true, Option.mem_def, exists_and_left, and_exists_self, Fin.getElem_fin]
+  constructor
+  · rintro ⟨a, ⟨h, w₁, w₂⟩, rfl⟩
+    exact ⟨w₁, fun j hji => by simpa using w₂ j hji⟩
+  · rintro ⟨h, w⟩
+    exact ⟨i, ⟨i.2, h, fun j hji => w ⟨j, by omega⟩ hji⟩, rfl⟩
+
+@[simp] theorem findFinIdx?_subtype {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.findFinIdx? f = (xs.unattach.findFinIdx? g).map (fun i => i.cast (by simp)) := by
+  cases xs
+  simp only [List.findFinIdx?_toArray, hf, List.findFinIdx?_subtype]
+  rw [findFinIdx?_congr List.unattach_toArray]
+  simp [Function.comp_def]
+
+/-! ### idxOf
+
+The verification API for `idxOf` is still incomplete.
+The lemmas below should be made consistent with those for `findIdx` (and proved using them).
+-/
+
+theorem idxOf_append [BEq α] [LawfulBEq α] {xs ys : Array α} {a : α} :
+    (xs ++ ys).idxOf a = if a ∈ xs then xs.idxOf a else ys.idxOf a + xs.size := by
+  rw [idxOf, findIdx_append]
+  split <;> rename_i h
+  · rw [if_pos]
+    simpa using h
+  · rw [if_neg]
+    simpa using h
+
+theorem idxOf_eq_size [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∉ xs) : xs.idxOf a = xs.size := by
+  rcases xs with ⟨xs⟩
+  simp [List.idxOf_eq_length (by simpa using h)]
+
+theorem idxOf_lt_length [BEq α] [LawfulBEq α] {xs : Array α} (h : a ∈ xs) : xs.idxOf a < xs.size := by
+  rcases xs with ⟨xs⟩
+  simp [List.idxOf_lt_length (by simpa using h)]
+
+
+/-! ### idxOf?
+
+The verification API for `idxOf?` is still incomplete.
+The lemmas below should be made consistent with those for `findIdx?` (and proved using them).
+-/
+
+@[simp] theorem idxOf?_empty [BEq α] : (#[] : Array α).idxOf? a = none := by simp
+
+@[simp] theorem idxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
+    xs.idxOf? a = none ↔ a ∉ xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.idxOf?_eq_none_iff]
+
+/-! ### finIdxOf?
+
+The verification API for `finIdxOf?` is still incomplete.
+The lemmas below should be made consistent with those for `findFinIdx?` (and proved using them).
+-/
+
+theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : Array α} {a : α} :
+    xs.idxOf? a = (xs.finIdxOf? a).map (·.val) := by
+  simp [idxOf?, finIdxOf?, findIdx?_eq_map_findFinIdx?_val]
+
+@[simp] theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp
+
+@[simp] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
+    xs.finIdxOf? a = none ↔ a ∉ xs := by
+  rcases xs with ⟨xs⟩
+  simp [List.finIdxOf?_eq_none_iff]
+
+@[simp] theorem finIdxOf?_eq_some_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} {i : Fin xs.size} :
+    xs.finIdxOf? a = some i ↔ xs[i] = a ∧ ∀ j (_ : j < i), ¬xs[j] = a := by
+  rcases xs with ⟨xs⟩
+  simp [List.finIdxOf?_eq_some_iff]
+
 end Array

src/Init/Data/Array/GetLit.lean

@@ -7,40 +7,43 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 /-! ### getLit -/
 
 -- auxiliary declaration used in the equation compiler when pattern matching array literals.
-abbrev getLit {α : Type u} {n : Nat} (a : Array α) (i : Nat) (h₁ : a.size = n) (h₂ : i < n) : α :=
+abbrev getLit {α : Type u} {n : Nat} (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : α :=
   have := h₁.symm ▸ h₂
-  a[i]
+  xs[i]
 
 theorem extLit {n : Nat}
-    (a b : Array α)
-    (hsz₁ : a.size = n) (hsz₂ : b.size = n)
-    (h : (i : Nat) → (hi : i < n) → a.getLit i hsz₁ hi = b.getLit i hsz₂ hi) : a = b :=
-  Array.ext a b (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
+    (xs ys : Array α)
+    (hsz₁ : xs.size = n) (hsz₂ : ys.size = n)
+    (h : (i : Nat) → (hi : i < n) → xs.getLit i hsz₁ hi = ys.getLit i hsz₂ hi) : xs = ys :=
+  Array.ext xs ys (hsz₁.trans hsz₂.symm) fun i hi₁ _ => h i (hsz₁ ▸ hi₁)
 
-def toListLitAux (a : Array α) (n : Nat) (hsz : a.size = n) : ∀ (i : Nat), i ≤ a.size → List α → List α
+def toListLitAux (xs : Array α) (n : Nat) (hsz : xs.size = n) : ∀ (i : Nat), i ≤ xs.size → List α → List α
   | 0,     _,  acc => acc
-  | (i+1), hi, acc => toListLitAux a n hsz i (Nat.le_of_succ_le hi) (a.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
+  | (i+1), hi, acc => toListLitAux xs n hsz i (Nat.le_of_succ_le hi) (xs.getLit i hsz (Nat.lt_of_lt_of_eq (Nat.lt_of_lt_of_le (Nat.lt_succ_self i) hi) hsz) :: acc)
 
-def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
-  List.toArray <| toListLitAux a n hsz n (hsz ▸ Nat.le_refl _) []
+def toArrayLit (xs : Array α) (n : Nat) (hsz : xs.size = n) : Array α :=
+  List.toArray <| toListLitAux xs n hsz n (hsz ▸ Nat.le_refl _) []
 
-theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
+theorem toArrayLit_eq (xs : Array α) (n : Nat) (hsz : xs.size = n) : xs = toArrayLit xs n hsz := by
   apply ext'
-  simp [toArrayLit, toList_toArray]
-  have hle : n ≤ as.size := hsz ▸ Nat.le_refl _
-  have hge : as.size ≤ n := hsz ▸ Nat.le_refl _
+  simp [toArrayLit, List.toList_toArray]
+  have hle : n ≤ xs.size := hsz ▸ Nat.le_refl _
+  have hge : xs.size ≤ n := hsz ▸ Nat.le_refl _
   have := go n hle
   rw [List.drop_eq_nil_of_le hge] at this
   rw [this]
 where
-  getLit_eq (as : Array α) (i : Nat) (h₁ : as.size = n) (h₂ : i < n) : as.getLit i h₁ h₂ = getElem as.toList i ((id (α := as.toList.length = n) h₁) ▸ h₂) :=
+  getLit_eq (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : xs.getLit i h₁ h₂ = getElem xs.toList i ((id (α := xs.toList.length = n) h₁) ▸ h₂) :=
     rfl
-  go (i : Nat) (hi : i ≤ as.size) : toListLitAux as n hsz i hi (as.toList.drop i) = as.toList := by
+  go (i : Nat) (hi : i ≤ xs.size) : toListLitAux xs n hsz i hi (xs.toList.drop i) = xs.toList := by
     induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop_succ_eq_drop, *]
 
 end Array

src/Init/Data/Array/InsertIdx.lean

@@ -0,0 +1,132 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.Nat.InsertIdx
+
+/-!
+# insertIdx
+
+Proves various lemmas about `Array.insertIdx`.
+-/
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+open Function
+
+open Nat
+
+namespace Array
+
+universe u
+
+variable {α : Type u}
+
+section InsertIdx
+
+variable {a : α}
+
+@[simp] theorem toList_insertIdx (xs : Array α) (i x) (h) :
+    (xs.insertIdx i x h).toList = xs.toList.insertIdx i x := by
+  rcases xs with ⟨xs⟩
+  simp
+
+@[simp]
+theorem insertIdx_zero (xs : Array α) (x : α) : xs.insertIdx 0 x = #[x] ++ xs := by
+  rcases xs with ⟨xs⟩
+  simp
+
+@[simp] theorem size_insertIdx {xs : Array α} (h : i ≤ xs.size) : (xs.insertIdx i a).size = xs.size + 1 := by
+  rcases xs with ⟨xs⟩
+  simp [List.length_insertIdx, h]
+
+theorem eraseIdx_insertIdx (i : Nat) (xs : Array α) (h : i ≤ xs.size) :
+    (xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
+  rcases xs with ⟨xs⟩
+  simp_all
+
+theorem insertIdx_eraseIdx_of_ge {as : Array α}
+    (w₁ : i < as.size) (w₂ : j ≤ (as.eraseIdx i).size) (h : i ≤ j) :
+    (as.eraseIdx i).insertIdx j a =
+      (as.insertIdx (j + 1) a (by simp at w₂; omega)).eraseIdx i (by simp_all; omega) := by
+  cases as
+  simpa using List.insertIdx_eraseIdx_of_ge _ _ _ (by simpa) (by simpa)
+
+theorem insertIdx_eraseIdx_of_le {as : Array α}
+    (w₁ : i < as.size) (w₂ : j ≤ (as.eraseIdx i).size) (h : j ≤ i) :
+    (as.eraseIdx i).insertIdx j a =
+      (as.insertIdx j a (by simp at w₂; omega)).eraseIdx (i + 1) (by simp_all) := by
+  cases as
+  simpa using List.insertIdx_eraseIdx_of_le _ _ _ (by simpa) (by simpa)
+
+theorem insertIdx_comm (a b : α) (i j : Nat) (xs : Array α) (_ : i ≤ j) (_ : j ≤ xs.size) :
+    (xs.insertIdx i a).insertIdx (j + 1) b (by simpa) =
+      (xs.insertIdx j b).insertIdx i a (by simp; omega) := by
+  rcases xs with ⟨xs⟩
+  simpa using List.insertIdx_comm a b i j _ (by simpa) (by simpa)
+
+theorem mem_insertIdx {xs : Array α} {h : i ≤ xs.size} : a ∈ xs.insertIdx i b h ↔ a = b ∨ a ∈ xs := by
+  rcases xs with ⟨xs⟩
+  simpa using List.mem_insertIdx (by simpa)
+
+@[simp]
+theorem insertIdx_size_self (xs : Array α) (x : α) : xs.insertIdx xs.size x = xs.push x := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem getElem_insertIdx {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < (xs.insertIdx i x).size) :
+    (xs.insertIdx i x)[k] =
+      if h₁ : k < i then
+        xs[k]'(by simp [size_insertIdx] at h; omega)
+      else
+        if h₂ : k = i then
+          x
+        else
+          xs[k-1]'(by simp [size_insertIdx] at h; omega) := by
+  cases xs
+  simp [List.getElem_insertIdx, w]
+
+theorem getElem_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
+    (xs.insertIdx i x)[k]'(by simp; omega) = xs[k] := by
+  simp [getElem_insertIdx, w, h]
+
+theorem getElem_insertIdx_self {xs : Array α} {x : α} {i : Nat} (w : i ≤ xs.size) :
+    (xs.insertIdx i x)[i]'(by simp; omega) = x := by
+  simp [getElem_insertIdx, w]
+
+theorem getElem_insertIdx_of_gt {xs : Array α} {x : α} {i k : Nat} (w : k ≤ xs.size) (h : k > i) :
+    (xs.insertIdx i x)[k]'(by simp; omega) = xs[k - 1]'(by omega) := by
+  simp [getElem_insertIdx, w, h]
+  rw [dif_neg (by omega), dif_neg (by omega)]
+
+theorem getElem?_insertIdx {xs : Array α} {x : α} {i k : Nat} (h : i ≤ xs.size) :
+    (xs.insertIdx i x)[k]? =
+      if k < i then
+        xs[k]?
+      else
+        if k = i then
+          if k ≤ xs.size then some x else none
+        else
+          xs[k-1]? := by
+  cases xs
+  simp [List.getElem?_insertIdx, h]
+
+theorem getElem?_insertIdx_of_lt {xs : Array α} {x : α} {i k : Nat} (w : i ≤ xs.size) (h : k < i) :
+    (xs.insertIdx i x)[k]? = xs[k]? := by
+  rw [getElem?_insertIdx, if_pos h]
+
+theorem getElem?_insertIdx_self {xs : Array α} {x : α} {i : Nat} (w : i ≤ xs.size) :
+    (xs.insertIdx i x)[i]? = some x := by
+  rw [getElem?_insertIdx, if_neg (by omega), if_pos rfl, if_pos w]
+
+theorem getElem?_insertIdx_of_ge {xs : Array α} {x : α} {i k : Nat} (w : i < k) (h : k ≤ xs.size) :
+    (xs.insertIdx i x)[k]? = xs[k - 1]? := by
+  rw [getElem?_insertIdx, if_neg (by omega), if_neg (by omega)]
+
+end InsertIdx
+
+end Array

src/Init/Data/Array/InsertionSort.lean

@@ -6,23 +6,32 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 
-@[inline] def Array.insertionSort (a : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
-  traverse a 0 a.size
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+/--
+Sorts an array using insertion sort.
+
+The optional parameter `lt` specifies an ordering predicate. It defaults to `LT.lt`, which must be
+decidable to be used for sorting.
+-/
+@[inline] def Array.insertionSort (xs : Array α) (lt : α → α → Bool := by exact (· < ·)) : Array α :=
+  traverse xs 0 xs.size
 where
-  @[specialize] traverse (a : Array α) (i : Nat) (fuel : Nat) : Array α :=
+  @[specialize] traverse (xs : Array α) (i : Nat) (fuel : Nat) : Array α :=
     match fuel with
-    | 0      => a
+    | 0      => xs
     | fuel+1 =>
-      if h : i < a.size then
-        traverse (swapLoop a i h) (i+1) fuel
+      if h : i < xs.size then
+        traverse (swapLoop xs i h) (i+1) fuel
       else
-        a
-  @[specialize] swapLoop (a : Array α) (j : Nat) (h : j < a.size) : Array α :=
+        xs
+  @[specialize] swapLoop (xs : Array α) (j : Nat) (h : j < xs.size) : Array α :=
     match (generalizing := false) he:j with -- using `generalizing` because we don't want to refine the type of `h`
-    | 0    => a
+    | 0    => xs
     | j'+1 =>
-      have h' : j' < a.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
-      if lt a[j] a[j'] then
-        swapLoop (a.swap j j') j' (by rw [size_swap]; assumption; done)
+      have h' : j' < xs.size := by subst j; exact Nat.lt_trans (Nat.lt_succ_self _) h
+      if lt xs[j] xs[j'] then
+        swapLoop (xs.swap j j') j' (by rw [size_swap]; assumption; done)
       else
-        a
+        xs

src/Init/Data/Array/Lex/Basic.lean

@@ -8,14 +8,18 @@ import Init.Data.Array.Basic
 import Init.Data.Nat.Lemmas
 import Init.Data.Range
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 /--
-Lexicographic comparator for arrays.
+Compares arrays lexicographically with respect to a comparison `lt` on their elements.
 
-`lex as bs lt` is true if
-- `bs` is larger than `as` and `as` is pairwise equivalent via `==` to the initial segment of `bs`, or
-- there is an index `i` such that `lt as[i] bs[i]`, and for all `j < i`, `as[j] == bs[j]`.
+Specifically, `Array.lex as bs lt` is true if
+* `bs` is larger than `as` and `as` is pairwise equivalent via `==` to the initial segment of `bs`,
+  or
+* there is an index `i` such that `lt as[i] bs[i]`, and for all `j < i`, `as[j] == bs[j]`.
 -/
 def lex [BEq α] (as bs : Array α) (lt : α → α → Bool := by exact (· < ·)) : Bool := Id.run do
   for h : i in [0 : min as.size bs.size] do

src/Init/Data/Array/Lex/Lemmas.lean

@@ -7,6 +7,9 @@ prelude
 import Init.Data.Array.Lemmas
 import Init.Data.List.Lex
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 /-! ### Lexicographic ordering -/
@@ -14,15 +17,15 @@ namespace Array
 @[simp] theorem _root_.List.lt_toArray [LT α] (l₁ l₂ : List α) : l₁.toArray < l₂.toArray ↔ l₁ < l₂ := Iff.rfl
 @[simp] theorem _root_.List.le_toArray [LT α] (l₁ l₂ : List α) : l₁.toArray ≤ l₂.toArray ↔ l₁ ≤ l₂ := Iff.rfl
 
-@[simp] theorem lt_toList [LT α] (l₁ l₂ : Array α) : l₁.toList < l₂.toList ↔ l₁ < l₂ := Iff.rfl
-@[simp] theorem le_toList [LT α] (l₁ l₂ : Array α) : l₁.toList ≤ l₂.toList ↔ l₁ ≤ l₂ := Iff.rfl
+@[simp] theorem lt_toList [LT α] (xs ys : Array α) : xs.toList < ys.toList ↔ xs < ys := Iff.rfl
+@[simp] theorem le_toList [LT α] (xs ys : Array α) : xs.toList ≤ ys.toList ↔ xs ≤ ys := Iff.rfl
 
 protected theorem not_lt_iff_ge [LT α] (l₁ l₂ : List α) : ¬ l₁ < l₂ ↔ l₂ ≤ l₁ := Iff.rfl
 protected theorem not_le_iff_gt [DecidableEq α] [LT α] [DecidableLT α] (l₁ l₂ : List α) :
     ¬ l₁ ≤ l₂ ↔ l₂ < l₁ :=
   Decidable.not_not
 
-@[simp] theorem lex_empty [BEq α] {lt : α → α → Bool} (l : Array α) : l.lex #[] lt = false := by
+@[simp] theorem lex_empty [BEq α] {lt : α → α → Bool} (xs : Array α) : xs.lex #[] lt = false := by
   simp [lex, Id.run]
 
 @[simp] theorem singleton_lex_singleton [BEq α] {lt : α → α → Bool} : #[a].lex #[b] lt = lt a b := by
@@ -33,7 +36,7 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
      (#[a] ++ xs).lex (#[b] ++ ys) lt =
        (lt a b || a == b && xs.lex ys lt) := by
   simp only [lex, Id.run]
-  simp only [Std.Range.forIn'_eq_forIn'_range', size_append, size_toArray, List.length_singleton,
+  simp only [Std.Range.forIn'_eq_forIn'_range', size_append, List.size_toArray, List.length_singleton,
     Nat.add_comm 1]
   simp [Nat.add_min_add_right, List.range'_succ, getElem_append_left, List.range'_succ_left,
     getElem_append_right]
@@ -52,35 +55,35 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
     | cons y l₂ =>
       rw [List.toArray_cons, List.toArray_cons y, cons_lex_cons, List.lex, ih]
 
-@[simp] theorem lex_toList [BEq α] (lt : α → α → Bool) (l₁ l₂ : Array α) :
-    l₁.toList.lex l₂.toList lt = l₁.lex l₂ lt := by
-  cases l₁ <;> cases l₂ <;> simp
+@[simp] theorem lex_toList [BEq α] (lt : α → α → Bool) (xs ys : Array α) :
+    xs.toList.lex ys.toList lt = xs.lex ys lt := by
+  cases xs <;> cases ys <;> simp
 
-protected theorem lt_irrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] (l : Array α) : ¬ l < l :=
-  List.lt_irrefl l.toList
+protected theorem lt_irrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] (xs : Array α) : ¬ xs < xs :=
+  List.lt_irrefl xs.toList
 
 instance ltIrrefl [LT α] [Std.Irrefl (· < · : α → α → Prop)] : Std.Irrefl (α := Array α) (· < ·) where
   irrefl := Array.lt_irrefl
 
-@[simp] theorem not_lt_empty [LT α] (l : Array α) : ¬ l < #[] := List.not_lt_nil l.toList
-@[simp] theorem empty_le [LT α] (l : Array α) : #[] ≤ l := List.nil_le l.toList
+@[simp] theorem not_lt_empty [LT α] (xs : Array α) : ¬ xs < #[] := List.not_lt_nil xs.toList
+@[simp] theorem empty_le [LT α] (xs : Array α) : #[] ≤ xs := List.nil_le xs.toList
 
-@[simp] theorem le_empty [LT α] (l : Array α) : l ≤ #[] ↔ l = #[] := by
-  cases l
+@[simp] theorem le_empty [LT α] (xs : Array α) : xs ≤ #[] ↔ xs = #[] := by
+  cases xs
   simp
 
-@[simp] theorem empty_lt_push [LT α] (l : Array α) (a : α) : #[] < l.push a := by
-  rcases l with (_ | ⟨x, l⟩) <;> simp
+@[simp] theorem empty_lt_push [LT α] (xs : Array α) (a : α) : #[] < xs.push a := by
+  rcases xs with (_ | ⟨x, xs⟩) <;> simp
 
-protected theorem le_refl [LT α] [i₀ : Std.Irrefl (· < · : α → α → Prop)] (l : Array α) : l ≤ l :=
-  List.le_refl l.toList
+protected theorem le_refl [LT α] [i₀ : Std.Irrefl (· < · : α → α → Prop)] (xs : Array α) : xs ≤ xs :=
+  List.le_refl xs.toList
 
 instance [LT α] [Std.Irrefl (· < · : α → α → Prop)] : Std.Refl (· ≤ · : Array α → Array α → Prop) where
   refl := Array.le_refl
 
 protected theorem lt_trans [LT α]
     [i₁ : Trans (· < · : α → α → Prop) (· < ·) (· < ·)]
-    {l₁ l₂ l₃ : Array α} (h₁ : l₁ < l₂) (h₂ : l₂ < l₃) : l₁ < l₃ :=
+    {xs ys zs : Array α} (h₁ : xs < ys) (h₂ : ys < zs) : xs < zs :=
   List.lt_trans h₁ h₂
 
 instance [LT α] [Trans (· < · : α → α → Prop) (· < ·) (· < ·)] :
@@ -92,7 +95,7 @@ protected theorem lt_of_le_of_lt [DecidableEq α] [LT α] [DecidableLT α]
     [i₁ : Std.Asymm (· < · : α → α → Prop)]
     [i₂ : Std.Antisymm (¬ · < · : α → α → Prop)]
     [i₃ : Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
-    {l₁ l₂ l₃ : Array α} (h₁ : l₁ ≤ l₂) (h₂ : l₂ < l₃) : l₁ < l₃ :=
+    {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys < zs) : xs < zs :=
   List.lt_of_le_of_lt h₁ h₂
 
 protected theorem le_trans [DecidableEq α] [LT α] [DecidableLT α]
@@ -100,7 +103,7 @@ protected theorem le_trans [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
     [Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
-    {l₁ l₂ l₃ : Array α} (h₁ : l₁ ≤ l₂) (h₂ : l₂ ≤ l₃) : l₁ ≤ l₃ :=
+    {xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys ≤ zs) : xs ≤ zs :=
   fun h₃ => h₁ (Array.lt_of_le_of_lt h₂ h₃)
 
 instance [DecidableEq α] [LT α] [DecidableLT α]
@@ -113,7 +116,7 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
 
 protected theorem lt_asymm [LT α]
     [i : Std.Asymm (· < · : α → α → Prop)]
-    {l₁ l₂ : Array α} (h : l₁ < l₂) : ¬ l₂ < l₁ := List.lt_asymm h
+    {xs ys : Array α} (h : xs < ys) : ¬ ys < xs := List.lt_asymm h
 
 instance [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Asymm (· < · : α → α → Prop)] :
@@ -121,26 +124,26 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
   asymm _ _ := Array.lt_asymm
 
 protected theorem le_total [DecidableEq α] [LT α] [DecidableLT α]
-    [i : Std.Total (¬ · < · : α → α → Prop)] (l₁ l₂ : Array α) : l₁ ≤ l₂ ∨ l₂ ≤ l₁ :=
-  List.le_total _ _
+    [i : Std.Total (¬ · < · : α → α → Prop)] (xs ys : Array α) : xs ≤ ys ∨ ys ≤ xs :=
+  List.le_total xs.toList ys.toList
 
 @[simp] protected theorem not_lt [LT α]
-    {l₁ l₂ : Array α} : ¬ l₁ < l₂ ↔ l₂ ≤ l₁ := Iff.rfl
+    {xs ys : Array α} : ¬ xs < ys ↔ ys ≤ xs := Iff.rfl
 
 @[simp] protected theorem not_le [DecidableEq α] [LT α] [DecidableLT α]
-    {l₁ l₂ : Array α} : ¬ l₂ ≤ l₁ ↔ l₁ < l₂ := Decidable.not_not
+    {xs ys : Array α} : ¬ ys ≤ xs ↔ xs < ys := Decidable.not_not
 
 protected theorem le_of_lt [DecidableEq α] [LT α] [DecidableLT α]
     [i : Std.Total (¬ · < · : α → α → Prop)]
-    {l₁ l₂ : Array α} (h : l₁ < l₂) : l₁ ≤ l₂ :=
+    {xs ys : Array α} (h : xs < ys) : xs ≤ ys :=
   List.le_of_lt h
 
 protected theorem le_iff_lt_or_eq [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
     [Std.Total (¬ · < · : α → α → Prop)]
-    {l₁ l₂ : Array α} : l₁ ≤ l₂ ↔ l₁ < l₂ ∨ l₁ = l₂ := by
-  simpa using List.le_iff_lt_or_eq (l₁ := l₁.toList) (l₂ := l₂.toList)
+    {xs ys : Array α} : xs ≤ ys ↔ xs < ys ∨ xs = ys := by
+  simpa using List.le_iff_lt_or_eq (l₁ := xs.toList) (l₂ := ys.toList)
 
 instance [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Total (¬ · < · : α → α → Prop)] :
@@ -148,22 +151,22 @@ instance [DecidableEq α] [LT α] [DecidableLT α]
   total := Array.le_total
 
 @[simp] theorem lex_eq_true_iff_lt [DecidableEq α] [LT α] [DecidableLT α]
-    {l₁ l₂ : Array α} : lex l₁ l₂ = true ↔ l₁ < l₂ := by
-  cases l₁
-  cases l₂
+    {xs ys : Array α} : lex xs ys = true ↔ xs < ys := by
+  cases xs
+  cases ys
   simp
 
 @[simp] theorem lex_eq_false_iff_ge [DecidableEq α] [LT α] [DecidableLT α]
-    {l₁ l₂ : Array α} : lex l₁ l₂ = false ↔ l₂ ≤ l₁ := by
-  cases l₁
-  cases l₂
+    {xs ys : Array α} : lex xs ys = false ↔ ys ≤ xs := by
+  cases xs
+  cases ys
   simp [List.not_lt_iff_ge]
 
 instance [DecidableEq α] [LT α] [DecidableLT α] : DecidableLT (Array α) :=
-  fun l₁ l₂ => decidable_of_iff (lex l₁ l₂ = true) lex_eq_true_iff_lt
+  fun xs ys => decidable_of_iff (lex xs ys = true) lex_eq_true_iff_lt
 
 instance [DecidableEq α] [LT α] [DecidableLT α] : DecidableLE (Array α) :=
-  fun l₁ l₂ => decidable_of_iff (lex l₂ l₁ = false) lex_eq_false_iff_ge
+  fun xs ys => decidable_of_iff (lex ys xs = false) lex_eq_false_iff_ge
 
 /--
 `l₁` is lexicographically less than `l₂` if either
@@ -211,58 +214,58 @@ theorem lex_eq_false_iff_exists [BEq α] [PartialEquivBEq α] (lt : α → α
   cases l₂
   simp_all [List.lex_eq_false_iff_exists]
 
-protected theorem lt_iff_exists [DecidableEq α] [LT α] [DecidableLT α] {l₁ l₂ : Array α} :
-    l₁ < l₂ ↔
-      (l₁ = l₂.take l₁.size ∧ l₁.size < l₂.size) ∨
-        (∃ (i : Nat) (h₁ : i < l₁.size) (h₂ : i < l₂.size),
+protected theorem lt_iff_exists [DecidableEq α] [LT α] [DecidableLT α] {xs ys : Array α} :
+    xs < ys ↔
+      (xs = ys.take xs.size ∧ xs.size < ys.size) ∨
+        (∃ (i : Nat) (h₁ : i < xs.size) (h₂ : i < ys.size),
           (∀ j, (hj : j < i) →
-            l₁[j]'(Nat.lt_trans hj h₁) = l₂[j]'(Nat.lt_trans hj h₂)) ∧ l₁[i] < l₂[i]) := by
-  cases l₁
-  cases l₂
+            xs[j]'(Nat.lt_trans hj h₁) = ys[j]'(Nat.lt_trans hj h₂)) ∧ xs[i] < ys[i]) := by
+  cases xs
+  cases ys
   simp [List.lt_iff_exists]
 
 protected theorem le_iff_exists [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
-    [Std.Antisymm (¬ · < · : α → α → Prop)] {l₁ l₂ : Array α} :
-    l₁ ≤ l₂ ↔
-      (l₁ = l₂.take l₁.size) ∨
-        (∃ (i : Nat) (h₁ : i < l₁.size) (h₂ : i < l₂.size),
+    [Std.Antisymm (¬ · < · : α → α → Prop)] {xs ys : Array α} :
+    xs ≤ ys ↔
+      (xs = ys.take xs.size) ∨
+        (∃ (i : Nat) (h₁ : i < xs.size) (h₂ : i < ys.size),
           (∀ j, (hj : j < i) →
-            l₁[j]'(Nat.lt_trans hj h₁) = l₂[j]'(Nat.lt_trans hj h₂)) ∧ l₁[i] < l₂[i]) := by
-  cases l₁
-  cases l₂
+            xs[j]'(Nat.lt_trans hj h₁) = ys[j]'(Nat.lt_trans hj h₂)) ∧ xs[i] < ys[i]) := by
+  cases xs
+  cases ys
   simp [List.le_iff_exists]
 
-theorem append_left_lt [LT α] {l₁ l₂ l₃ : Array α} (h : l₂ < l₃) :
-    l₁ ++ l₂ < l₁ ++ l₃ := by
-  cases l₁
-  cases l₂
-  cases l₃
+theorem append_left_lt [LT α] {xs ys zs : Array α} (h : ys < zs) :
+    xs ++ ys < xs ++ zs := by
+  cases xs
+  cases ys
+  cases zs
   simpa using List.append_left_lt h
 
 theorem append_left_le [DecidableEq α] [LT α] [DecidableLT α]
     [Std.Irrefl (· < · : α → α → Prop)]
     [Std.Asymm (· < · : α → α → Prop)]
     [Std.Antisymm (¬ · < · : α → α → Prop)]
-    {l₁ l₂ l₃ : Array α} (h : l₂ ≤ l₃) :
-    l₁ ++ l₂ ≤ l₁ ++ l₃ := by
-  cases l₁
-  cases l₂
-  cases l₃
+    {xs ys zs : Array α} (h : ys ≤ zs) :
+    xs ++ ys ≤ xs ++ zs := by
+  cases xs
+  cases ys
+  cases zs
   simpa using List.append_left_le h
 
 theorem le_append_left [LT α] [Std.Irrefl (· < · : α → α → Prop)]
-    {l₁ l₂ : Array α} : l₁ ≤ l₁ ++ l₂ := by
-  cases l₁
-  cases l₂
+    {xs ys : Array α} : xs ≤ xs ++ ys := by
+  cases xs
+  cases ys
   simpa using List.le_append_left
 
 protected theorem map_lt [LT α] [LT β]
-    {l₁ l₂ : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : l₁ < l₂) :
-    map f l₁ < map f l₂ := by
-  cases l₁
-  cases l₂
+    {xs ys : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : xs < ys) :
+    map f xs < map f ys := by
+  cases xs
+  cases ys
   simpa using List.map_lt w h
 
 protected theorem map_le [DecidableEq α] [LT α] [DecidableLT α] [DecidableEq β] [LT β] [DecidableLT β]
@@ -272,10 +275,10 @@ protected theorem map_le [DecidableEq α] [LT α] [DecidableLT α] [DecidableEq
     [Std.Irrefl (· < · : β → β → Prop)]
     [Std.Asymm (· < · : β → β → Prop)]
     [Std.Antisymm (¬ · < · : β → β → Prop)]
-    {l₁ l₂ : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : l₁ ≤ l₂) :
-    map f l₁ ≤ map f l₂ := by
-  cases l₁
-  cases l₂
+    {xs ys : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : xs ≤ ys) :
+    map f xs ≤ map f ys := by
+  cases xs
+  cases ys
   simpa using List.map_le w h
 
 end Array

src/Init/Data/Array/MapIdx.lean

@@ -5,103 +5,111 @@ Authors: Mario Carneiro, Kim Morrison
 -/
 prelude
 import Init.Data.Array.Lemmas
+import Init.Data.Array.Attach
+import Init.Data.Array.OfFn
 import Init.Data.List.MapIdx
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 /-! ### mapFinIdx -/
 
 -- This could also be proved from `SatisfiesM_mapIdxM` in Batteries.
-theorem mapFinIdx_induction (as : Array α) (f : Fin as.size → α → β)
+theorem mapFinIdx_induction (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β)
     (motive : Nat → Prop) (h0 : motive 0)
-    (p : Fin as.size → β → Prop)
-    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
-    motive as.size ∧ ∃ eq : (Array.mapFinIdx as f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((Array.mapFinIdx as f)[i]) := by
-  let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : ∀ i h h', p ⟨i, h⟩ bs[i]) (hm : motive j) :
-    let arr : Array β := Array.mapFinIdxM.map (m := Id) as f i j h bs
-    motive as.size ∧ ∃ eq : arr.size = as.size, ∀ i h, p ⟨i, h⟩ arr[i] := by
+    (p : (i : Nat) → β → (h : i < xs.size) → Prop)
+    (hs : ∀ i h, motive i → p i (f i xs[i] h) h ∧ motive (i + 1)) :
+    motive xs.size ∧ ∃ eq : (Array.mapFinIdx xs f).size = xs.size,
+      ∀ i h, p i ((Array.mapFinIdx xs f)[i]) h := by
+  let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : ∀ i h h', p i bs[i] h) (hm : motive j) :
+    let as : Array β := Array.mapFinIdxM.map (m := Id) xs f i j h bs
+    motive xs.size ∧ ∃ eq : as.size = xs.size, ∀ i h, p i as[i] h := by
     induction i generalizing j bs with simp [mapFinIdxM.map]
     | zero =>
       have := (Nat.zero_add _).symm.trans h
       exact ⟨this ▸ hm, h₁ ▸ this, fun _ _ => h₂ ..⟩
     | succ i ih =>
-      apply @ih (bs.push (f ⟨j, by omega⟩ as[j])) (j + 1) (by omega) (by simp; omega)
+      apply @ih (bs.push (f j xs[j] (by omega))) (j + 1) (by omega) (by simp; omega)
       · intro i i_lt h'
         rw [getElem_push]
         split
         · apply h₂
         · simp only [size_push] at h'
           obtain rfl : i = j := by omega
-          apply (hs ⟨i, by omega⟩ hm).1
-      · exact (hs ⟨j, by omega⟩ hm).2
+          apply (hs i (by omega) hm).1
+      · exact (hs j (by omega) hm).2
   simp [mapFinIdx, mapFinIdxM]; exact go rfl nofun h0
 
-theorem mapFinIdx_spec (as : Array α) (f : Fin as.size → α → β)
-    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
-    ∃ eq : (Array.mapFinIdx as f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((Array.mapFinIdx as f)[i]) :=
-  (mapFinIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+theorem mapFinIdx_spec (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β)
+    (p : (i : Nat) → β → (h : i < xs.size) → Prop) (hs : ∀ i h, p i (f i xs[i] h) h) :
+    ∃ eq : (Array.mapFinIdx xs f).size = xs.size,
+      ∀ i h, p i ((Array.mapFinIdx xs f)[i]) h :=
+  (mapFinIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapFinIdx (a : Array α) (f : Fin a.size → α → β) : (a.mapFinIdx f).size = a.size :=
-  (mapFinIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+@[simp] theorem size_mapFinIdx (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β) :
+    (xs.mapFinIdx f).size = xs.size :=
+  (mapFinIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem size_zipWithIndex (as : Array α) : as.zipWithIndex.size = as.size :=
+@[simp] theorem size_zipIdx (xs : Array α) (k : Nat) : (xs.zipIdx k).size = xs.size :=
   Array.size_mapFinIdx _ _
 
-@[simp] theorem getElem_mapFinIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat)
-    (h : i < (mapFinIdx a f).size) :
-    (a.mapFinIdx f)[i] = f ⟨i, by simp_all⟩ (a[i]'(by simp_all)) :=
-  (mapFinIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
+@[deprecated size_zipIdx (since := "2025-01-21")] abbrev size_zipWithIndex := @size_zipIdx
 
-@[simp] theorem getElem?_mapFinIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat) :
-    (a.mapFinIdx f)[i]? =
-      a[i]?.pbind fun b h => f ⟨i, (getElem?_eq_some_iff.1 h).1⟩ b := by
+@[simp] theorem getElem_mapFinIdx (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β) (i : Nat)
+    (h : i < (xs.mapFinIdx f).size) :
+    (xs.mapFinIdx f)[i] = f i (xs[i]'(by simp_all)) (by simp_all) :=
+  (mapFinIdx_spec _ _ (fun i b h => b = f i xs[i] h) fun _ _ => rfl).2 i _
+
+@[simp] theorem getElem?_mapFinIdx (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β) (i : Nat) :
+    (xs.mapFinIdx f)[i]? =
+      xs[i]?.pbind fun b h => f i b (getElem?_eq_some_iff.1 h).1 := by
   simp only [getElem?_def, size_mapFinIdx, getElem_mapFinIdx]
   split <;> simp_all
 
-@[simp] theorem toList_mapFinIdx (a : Array α) (f : Fin a.size → α → β) :
-    (a.mapFinIdx f).toList = a.toList.mapFinIdx (fun i a => f ⟨i, by simp⟩ a) := by
+@[simp] theorem toList_mapFinIdx (xs : Array α) (f : (i : Nat) → α → (h : i < xs.size) → β) :
+    (xs.mapFinIdx f).toList = xs.toList.mapFinIdx (fun i a h => f i a (by simpa)) := by
   apply List.ext_getElem <;> simp
 
 /-! ### mapIdx -/
 
-theorem mapIdx_induction (f : Nat → α → β) (as : Array α)
+theorem mapIdx_induction (f : Nat → α → β) (xs : Array α)
     (motive : Nat → Prop) (h0 : motive 0)
-    (p : Fin as.size → β → Prop)
-    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
-    motive as.size ∧ ∃ eq : (as.mapIdx f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((as.mapIdx f)[i]) :=
-  mapFinIdx_induction as (fun i a => f i a) motive h0 p hs
+    (p : (i : Nat) → β → (h : i < xs.size) → Prop)
+    (hs : ∀ i h, motive i → p i (f i xs[i]) h ∧ motive (i + 1)) :
+    motive xs.size ∧ ∃ eq : (xs.mapIdx f).size = xs.size,
+      ∀ i h, p i ((xs.mapIdx f)[i]) h :=
+  mapFinIdx_induction xs (fun i a _ => f i a) motive h0 p hs
 
-theorem mapIdx_spec (f : Nat → α → β) (as : Array α)
-    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
-    ∃ eq : (as.mapIdx f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((as.mapIdx f)[i]) :=
-  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+theorem mapIdx_spec (f : Nat → α → β) (xs : Array α)
+    (p : (i : Nat) → β → (h : i < xs.size) → Prop) (hs : ∀ i h, p i (f i xs[i]) h) :
+    ∃ eq : (xs.mapIdx f).size = xs.size,
+      ∀ i h, p i ((xs.mapIdx f)[i]) h :=
+  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapIdx (f : Nat → α → β) (as : Array α) : (as.mapIdx f).size = as.size :=
-  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+@[simp] theorem size_mapIdx (f : Nat → α → β) (xs : Array α) : (xs.mapIdx f).size = xs.size :=
+  (mapIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
-@[simp] theorem getElem_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat)
-    (h : i < (as.mapIdx f).size) :
-    (as.mapIdx f)[i] = f i (as[i]'(by simp_all)) :=
-  (mapIdx_spec _ _ (fun i b => b = f i as[i]) fun _ => rfl).2 i (by simp_all)
+@[simp] theorem getElem_mapIdx (f : Nat → α → β) (xs : Array α) (i : Nat)
+    (h : i < (xs.mapIdx f).size) :
+    (xs.mapIdx f)[i] = f i (xs[i]'(by simp_all)) :=
+  (mapIdx_spec _ _ (fun i b h => b = f i xs[i]) fun _ _ => rfl).2 i (by simp_all)
 
-@[simp] theorem getElem?_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat) :
-    (as.mapIdx f)[i]? =
-      as[i]?.map (f i) := by
+@[simp] theorem getElem?_mapIdx (f : Nat → α → β) (xs : Array α) (i : Nat) :
+    (xs.mapIdx f)[i]? =
+      xs[i]?.map (f i) := by
   simp [getElem?_def, size_mapIdx, getElem_mapIdx]
 
-@[simp] theorem toList_mapIdx (f : Nat → α → β) (as : Array α) :
-    (as.mapIdx f).toList = as.toList.mapIdx (fun i a => f i a) := by
+@[simp] theorem toList_mapIdx (f : Nat → α → β) (xs : Array α) :
+    (xs.mapIdx f).toList = xs.toList.mapIdx (fun i a => f i a) := by
   apply List.ext_getElem <;> simp
 
 end Array
 
 namespace List
 
-@[simp] theorem mapFinIdx_toArray (l : List α) (f : Fin l.length → α → β) :
+@[simp] theorem mapFinIdx_toArray (l : List α) (f : (i : Nat) → α → (h : i < l.length) → β) :
     l.toArray.mapFinIdx f = (l.mapFinIdx f).toArray := by
   ext <;> simp
 
@@ -110,3 +118,388 @@ namespace List
   ext <;> simp
 
 end List
+
+namespace Array
+
+/-! ### zipIdx -/
+
+@[simp] theorem getElem_zipIdx (xs : Array α) (k : Nat) (i : Nat) (h : i < (xs.zipIdx k).size) :
+    (xs.zipIdx k)[i] = (xs[i]'(by simp_all), k + i) := by
+  simp [zipIdx]
+
+@[deprecated getElem_zipIdx (since := "2025-01-21")]
+abbrev getElem_zipWithIndex := @getElem_zipIdx
+
+@[simp] theorem zipIdx_toArray {l : List α} {k : Nat} :
+    l.toArray.zipIdx k = (l.zipIdx k).toArray := by
+  ext i hi₁ hi₂ <;> simp [Nat.add_comm]
+
+@[deprecated zipIdx_toArray (since := "2025-01-21")]
+abbrev zipWithIndex_toArray := @zipIdx_toArray
+
+@[simp] theorem toList_zipIdx (xs : Array α) (k : Nat) :
+    (xs.zipIdx k).toList = xs.toList.zipIdx k := by
+  rcases xs with ⟨xs⟩
+  simp
+
+@[deprecated toList_zipIdx (since := "2025-01-21")]
+abbrev toList_zipWithIndex := @toList_zipIdx
+
+theorem mk_mem_zipIdx_iff_le_and_getElem?_sub {k i : Nat} {x : α} {xs : Array α} :
+    (x, i) ∈ xs.zipIdx k ↔ k ≤ i ∧ xs[i - k]? = some x := by
+  rcases xs with ⟨xs⟩
+  simp [List.mk_mem_zipIdx_iff_le_and_getElem?_sub]
+
+/-- Variant of `mk_mem_zipIdx_iff_le_and_getElem?_sub` specialized at `k = 0`,
+to avoid the inequality and the subtraction. -/
+theorem mk_mem_zipIdx_iff_getElem? {x : α} {i : Nat} {xs : Array α} :
+    (x, i) ∈ xs.zipIdx ↔ xs[i]? = x := by
+  rw [mk_mem_zipIdx_iff_le_and_getElem?_sub]
+  simp
+
+theorem mem_zipIdx_iff_le_and_getElem?_sub {x : α × Nat} {xs : Array α} {k : Nat} :
+    x ∈ xs.zipIdx k ↔ k ≤ x.2 ∧ xs[x.2 - k]? = some x.1 := by
+  cases x
+  simp [mk_mem_zipIdx_iff_le_and_getElem?_sub]
+
+/-- Variant of `mem_zipIdx_iff_le_and_getElem?_sub` specialized at `k = 0`,
+to avoid the inequality and the subtraction. -/
+theorem mem_zipIdx_iff_getElem? {x : α × Nat} {xs : Array α} :
+    x ∈ xs.zipIdx ↔ xs[x.2]? = some x.1 := by
+  rw [mk_mem_zipIdx_iff_getElem?]
+
+@[deprecated mk_mem_zipIdx_iff_getElem? (since := "2025-01-21")]
+abbrev mk_mem_zipWithIndex_iff_getElem? := @mk_mem_zipIdx_iff_getElem?
+
+@[deprecated mem_zipIdx_iff_getElem? (since := "2025-01-21")]
+abbrev mem_zipWithIndex_iff_getElem? := @mem_zipIdx_iff_getElem?
+
+/-! ### mapFinIdx -/
+
+@[congr] theorem mapFinIdx_congr {xs ys : Array α} (w : xs = ys)
+    (f : (i : Nat) → α → (h : i < xs.size) → β) :
+    mapFinIdx xs f = mapFinIdx ys (fun i a h => f i a (by simp [w]; omega)) := by
+  subst w
+  rfl
+
+@[simp]
+theorem mapFinIdx_empty {f : (i : Nat) → α → (h : i < 0) → β} : mapFinIdx #[] f = #[] :=
+  rfl
+
+theorem mapFinIdx_eq_ofFn {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+    xs.mapFinIdx f = Array.ofFn fun i : Fin xs.size => f i xs[i] i.2 := by
+  cases xs
+  simp [List.mapFinIdx_eq_ofFn]
+
+theorem mapFinIdx_append {xs ys : Array α} {f : (i : Nat) → α → (h : i < (xs ++ ys).size) → β} :
+    (xs ++ ys).mapFinIdx f =
+      xs.mapFinIdx (fun i a h => f i a (by simp; omega)) ++
+        ys.mapFinIdx (fun i a h => f (i + xs.size) a (by simp; omega)) := by
+  cases xs
+  cases ys
+  simp [List.mapFinIdx_append]
+
+@[simp]
+theorem mapFinIdx_push {xs : Array α} {a : α} {f : (i : Nat) → α → (h : i < (xs.push a).size) → β} :
+    mapFinIdx (xs.push a) f =
+      (mapFinIdx xs (fun i a h => f i a (by simp; omega))).push (f xs.size a (by simp)) := by
+  simp [← append_singleton, mapFinIdx_append]
+
+theorem mapFinIdx_singleton {a : α} {f : (i : Nat) → α → (h : i < 1) → β} :
+    #[a].mapFinIdx f = #[f 0 a (by simp)] := by
+  simp
+
+theorem mapFinIdx_eq_zipIdx_map {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+    xs.mapFinIdx f = xs.zipIdx.attach.map
+      fun ⟨⟨x, i⟩, m⟩ =>
+        f i x (by simp [mk_mem_zipIdx_iff_getElem?, getElem?_eq_some_iff] at m; exact m.1) := by
+  ext <;> simp
+
+@[deprecated mapFinIdx_eq_zipIdx_map (since := "2025-01-21")]
+abbrev mapFinIdx_eq_zipWithIndex_map := @mapFinIdx_eq_zipIdx_map
+
+@[simp]
+theorem mapFinIdx_eq_empty_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+    xs.mapFinIdx f = #[] ↔ xs = #[] := by
+  cases xs
+  simp
+
+theorem mapFinIdx_ne_empty_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+    xs.mapFinIdx f ≠ #[] ↔ xs ≠ #[] := by
+  simp
+
+theorem exists_of_mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β}
+    (h : b ∈ xs.mapFinIdx f) : ∃ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
+  rcases xs with ⟨xs⟩
+  exact List.exists_of_mem_mapFinIdx (by simpa using h)
+
+@[simp] theorem mem_mapFinIdx {b : β} {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+    b ∈ xs.mapFinIdx f ↔ ∃ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem mapFinIdx_eq_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {ys : Array β} :
+    xs.mapFinIdx f = ys ↔ ∃ h : ys.size = xs.size, ∀ (i : Nat) (h : i < xs.size), ys[i] = f i xs[i] h := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simpa using List.mapFinIdx_eq_iff
+
+@[simp] theorem mapFinIdx_eq_singleton_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {b : β} :
+    xs.mapFinIdx f = #[b] ↔ ∃ (a : α) (w : xs = #[a]), f 0 a (by simp [w]) = b := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem mapFinIdx_eq_append_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {ys zs : Array β} :
+    xs.mapFinIdx f = ys ++ zs ↔
+      ∃ (ys' : Array α) (zs' : Array α) (w : xs = ys' ++ zs'),
+        ys'.mapFinIdx (fun i a h => f i a (by simp [w]; omega)) = ys ∧
+        zs'.mapFinIdx (fun i a h => f (i + ys'.size) a (by simp [w]; omega)) = zs := by
+  rcases xs with ⟨l⟩
+  rcases ys with ⟨l₁⟩
+  rcases zs with ⟨l₂⟩
+  simp only [List.mapFinIdx_toArray, List.append_toArray, mk.injEq, List.mapFinIdx_eq_append_iff,
+    toArray_eq_append_iff]
+  constructor
+  · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
+    refine ⟨l₁.toArray, l₂.toArray, by simp_all⟩
+  · rintro ⟨⟨l₁⟩, ⟨l₂⟩, rfl, h₁, h₂⟩
+    simp [← toList_inj] at h₁ h₂
+    obtain rfl := h₁
+    obtain rfl := h₂
+    refine ⟨l₁, l₂, by simp_all⟩
+
+theorem mapFinIdx_eq_push_iff {xs : Array α} {b : β} {f : (i : Nat) → α → (h : i < xs.size) → β} :
+    xs.mapFinIdx f = ys.push b ↔
+      ∃ (zs : Array α) (a : α) (w : xs = zs.push a),
+        zs.mapFinIdx (fun i a h => f i a (by simp [w]; omega)) = ys ∧ b = f (xs.size - 1) a (by simp [w]) := by
+  rw [push_eq_append, mapFinIdx_eq_append_iff]
+  constructor
+  · rintro ⟨ys', zs', rfl, rfl, h₂⟩
+    simp only [mapFinIdx_eq_singleton_iff, Nat.zero_add] at h₂
+    obtain ⟨a, rfl, rfl⟩ := h₂
+    exact ⟨ys', a, by simp⟩
+  · rintro ⟨zs, a, rfl, rfl, rfl⟩
+    exact ⟨zs, #[a], by simp⟩
+
+theorem mapFinIdx_eq_mapFinIdx_iff {xs : Array α} {f g : (i : Nat) → α → (h : i < xs.size) → β} :
+    xs.mapFinIdx f = xs.mapFinIdx g ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = g i xs[i] h := by
+  rw [eq_comm, mapFinIdx_eq_iff]
+  simp
+
+@[simp] theorem mapFinIdx_mapFinIdx {xs : Array α}
+    {f : (i : Nat) → α → (h : i < xs.size) → β}
+    {g : (i : Nat) → β → (h : i < (xs.mapFinIdx f).size) → γ} :
+    (xs.mapFinIdx f).mapFinIdx g = xs.mapFinIdx (fun i a h => g i (f i a h) (by simpa using h)) := by
+  simp [mapFinIdx_eq_iff]
+
+theorem mapFinIdx_eq_replicate_iff {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {b : β} :
+    xs.mapFinIdx f = replicate xs.size b ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = b := by
+  rcases xs with ⟨l⟩
+  rw [← toList_inj]
+  simp [List.mapFinIdx_eq_replicate_iff]
+
+@[deprecated mapFinIdx_eq_replicate_iff (since := "2025-03-18")]
+abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
+
+@[simp] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) → α → (h : i < xs.reverse.size) → β} :
+    xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
+  rcases xs with ⟨l⟩
+  simp [List.mapFinIdx_reverse]
+
+/-! ### mapIdx -/
+
+@[simp]
+theorem mapIdx_empty {f : Nat → α → β} : mapIdx f #[] = #[] :=
+  rfl
+
+@[simp] theorem mapFinIdx_eq_mapIdx {xs : Array α} {f : (i : Nat) → α → (h : i < xs.size) → β} {g : Nat → α → β}
+    (h : ∀ (i : Nat) (h : i < xs.size), f i xs[i] h = g i xs[i]) :
+    xs.mapFinIdx f = xs.mapIdx g := by
+  simp_all [mapFinIdx_eq_iff]
+
+theorem mapIdx_eq_mapFinIdx {xs : Array α} {f : Nat → α → β} :
+    xs.mapIdx f = xs.mapFinIdx (fun i a _ => f i a) := by
+  simp [mapFinIdx_eq_mapIdx]
+
+theorem mapIdx_eq_zipIdx_map {xs : Array α} {f : Nat → α → β} :
+    xs.mapIdx f = xs.zipIdx.map fun ⟨a, i⟩ => f i a := by
+  ext <;> simp
+
+@[deprecated mapIdx_eq_zipIdx_map (since := "2025-01-21")]
+abbrev mapIdx_eq_zipWithIndex_map := @mapIdx_eq_zipIdx_map
+
+theorem mapIdx_append {xs ys : Array α} :
+    (xs ++ ys).mapIdx f = xs.mapIdx f ++ ys.mapIdx (fun i => f (i + xs.size)) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp [List.mapIdx_append]
+
+@[simp]
+theorem mapIdx_push {xs : Array α} {a : α} :
+    mapIdx f (xs.push a) = (mapIdx f xs).push (f xs.size a) := by
+  simp [← append_singleton, mapIdx_append]
+
+theorem mapIdx_singleton {a : α} : mapIdx f #[a] = #[f 0 a] := by
+  simp
+
+@[simp]
+theorem mapIdx_eq_empty_iff {xs : Array α} : mapIdx f xs = #[] ↔ xs = #[] := by
+  rcases xs with ⟨xs⟩
+  simp
+
+theorem mapIdx_ne_empty_iff {xs : Array α} :
+    mapIdx f xs ≠ #[] ↔ xs ≠ #[] := by
+  simp
+
+theorem exists_of_mem_mapIdx {b : β} {xs : Array α}
+    (h : b ∈ mapIdx f xs) : ∃ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
+  rw [mapIdx_eq_mapFinIdx] at h
+  simpa [Fin.exists_iff] using exists_of_mem_mapFinIdx h
+
+@[simp] theorem mem_mapIdx {b : β} {xs : Array α} :
+    b ∈ mapIdx f xs ↔ ∃ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
+  constructor
+  · intro h
+    exact exists_of_mem_mapIdx h
+  · rintro ⟨i, h, rfl⟩
+    rw [mem_iff_getElem]
+    exact ⟨i, by simpa using h, by simp⟩
+
+theorem mapIdx_eq_push_iff {xs : Array α} {b : β} :
+    mapIdx f xs = ys.push b ↔
+      ∃ (a : α) (zs : Array α), xs = zs.push a ∧ mapIdx f zs = ys ∧ f zs.size a = b := by
+  rw [mapIdx_eq_mapFinIdx, mapFinIdx_eq_push_iff]
+  simp only [mapFinIdx_eq_mapIdx, exists_and_left, exists_prop]
+  constructor
+  · rintro ⟨zs, rfl, a, rfl, rfl⟩
+    exact ⟨a, zs, by simp⟩
+  · rintro ⟨a, zs, rfl, rfl, rfl⟩
+    exact ⟨zs, rfl, a, by simp⟩
+
+@[simp] theorem mapIdx_eq_singleton_iff {xs : Array α} {f : Nat → α → β} {b : β} :
+    mapIdx f xs = #[b] ↔ ∃ (a : α), xs = #[a] ∧ f 0 a = b := by
+  rcases xs with ⟨xs⟩
+  simp [List.mapIdx_eq_singleton_iff]
+
+theorem mapIdx_eq_append_iff {xs : Array α} {f : Nat → α → β} {ys zs : Array β} :
+    mapIdx f xs = ys ++ zs ↔
+      ∃ (xs' : Array α) (zs' : Array α), xs = xs' ++ zs' ∧
+        xs'.mapIdx f = ys ∧
+        zs'.mapIdx (fun i => f (i + xs'.size)) = zs := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  rcases zs with ⟨zs⟩
+  simp only [List.mapIdx_toArray, List.append_toArray, mk.injEq, List.mapIdx_eq_append_iff,
+    toArray_eq_append_iff]
+  constructor
+  · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
+    exact ⟨l₁.toArray, l₂.toArray, by simp⟩
+  · rintro ⟨⟨l₁⟩, ⟨l₂⟩, rfl, h₁, h₂⟩
+    simp only [List.mapIdx_toArray, mk.injEq, List.size_toArray] at h₁ h₂
+    obtain rfl := h₁
+    obtain rfl := h₂
+    exact ⟨l₁, l₂, by simp⟩
+
+theorem mapIdx_eq_iff {xs : Array α} : mapIdx f xs = ys ↔ ∀ i : Nat, ys[i]? = xs[i]?.map (f i) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp [List.mapIdx_eq_iff]
+
+theorem mapIdx_eq_mapIdx_iff {xs : Array α} :
+    mapIdx f xs = mapIdx g xs ↔ ∀ i : Nat, (h : i < xs.size) → f i xs[i] = g i xs[i] := by
+  rcases xs with ⟨xs⟩
+  simp [List.mapIdx_eq_mapIdx_iff]
+
+@[simp] theorem mapIdx_set {xs : Array α} {i : Nat} {h : i < xs.size} {a : α} :
+    (xs.set i a).mapIdx f = (xs.mapIdx f).set i (f i a) (by simpa) := by
+  rcases xs with ⟨xs⟩
+  simp [List.mapIdx_set]
+
+@[simp] theorem mapIdx_setIfInBounds {xs : Array α} {i : Nat} {a : α} :
+    (xs.setIfInBounds i a).mapIdx f = (xs.mapIdx f).setIfInBounds i (f i a) := by
+  rcases xs with ⟨xs⟩
+  simp [List.mapIdx_set]
+
+@[simp] theorem back?_mapIdx {xs : Array α} {f : Nat → α → β} :
+    (mapIdx f xs).back? = (xs.back?).map (f (xs.size - 1)) := by
+  rcases xs with ⟨xs⟩
+  simp [List.getLast?_mapIdx]
+
+@[simp] theorem back_mapIdx {xs : Array α} {f : Nat → α → β} (h) :
+    (xs.mapIdx f).back h = f (xs.size - 1) (xs.back (by simpa using h)) := by
+  rcases xs with ⟨xs⟩
+  simp [List.getLast_mapIdx]
+
+@[simp] theorem mapIdx_mapIdx {xs : Array α} {f : Nat → α → β} {g : Nat → β → γ} :
+    (xs.mapIdx f).mapIdx g = xs.mapIdx (fun i => g i ∘ f i) := by
+  simp [mapIdx_eq_iff]
+
+theorem mapIdx_eq_replicate_iff {xs : Array α} {f : Nat → α → β} {b : β} :
+    mapIdx f xs = replicate xs.size b ↔ ∀ (i : Nat) (h : i < xs.size), f i xs[i] = b := by
+  rcases xs with ⟨xs⟩
+  rw [← toList_inj]
+  simp [List.mapIdx_eq_replicate_iff]
+
+@[deprecated mapIdx_eq_replicate_iff (since := "2025-03-18")]
+abbrev mapIdx_eq_mkArray_iff := @mapIdx_eq_replicate_iff
+
+@[simp] theorem mapIdx_reverse {xs : Array α} {f : Nat → α → β} :
+    xs.reverse.mapIdx f = (mapIdx (fun i => f (xs.size - 1 - i)) xs).reverse := by
+  rcases xs with ⟨xs⟩
+  simp [List.mapIdx_reverse]
+
+end Array
+
+namespace List
+
+theorem mapFinIdxM_toArray [Monad m] [LawfulMonad m] (l : List α)
+    (f : (i : Nat) → α → (h : i < l.length) → m β) :
+    l.toArray.mapFinIdxM f = toArray <$> l.mapFinIdxM f := by
+  let rec go (i : Nat) (acc : Array β) (inv : i + acc.size = l.length) :
+      Array.mapFinIdxM.map l.toArray f i acc.size inv acc
+      = toArray <$> mapFinIdxM.go l f (l.drop acc.size) acc
+        (by simp [Nat.sub_add_cancel (Nat.le.intro (Nat.add_comm _ _ ▸ inv))]) := by
+    match i with
+    | 0 =>
+      rw [Nat.zero_add] at inv
+      simp only [Array.mapFinIdxM.map, inv, drop_length, mapFinIdxM.go, map_pure]
+    | k + 1 =>
+      conv => enter [2, 2, 3]; rw [← getElem_cons_drop l acc.size (by omega)]
+      simp only [Array.mapFinIdxM.map, mapFinIdxM.go, _root_.map_bind]
+      congr; funext x
+      conv => enter [1, 4]; rw [← Array.size_push _ x]
+      conv => enter [2, 2, 3]; rw [← Array.size_push _ x]
+      refine go k (acc.push x) _
+  simp only [Array.mapFinIdxM, mapFinIdxM]
+  exact go _ #[] _
+
+theorem mapIdxM_toArray [Monad m] [LawfulMonad m] (l : List α)
+    (f : Nat → α → m β) :
+    l.toArray.mapIdxM f = toArray <$> l.mapIdxM f := by
+  let rec go (bs : List α) (acc : Array β) (inv : bs.length + acc.size = l.length) :
+      mapFinIdxM.go l (fun i a h => f i a) bs acc inv = mapIdxM.go f bs acc := by
+    match bs with
+    | [] => simp only [mapFinIdxM.go, mapIdxM.go]
+    | x :: xs => simp only [mapFinIdxM.go, mapIdxM.go, go]
+  unfold Array.mapIdxM
+  rw [mapFinIdxM_toArray]
+  simp only [mapFinIdxM, mapIdxM]
+  rw [go]
+
+end List
+
+namespace Array
+
+theorem toList_mapFinIdxM [Monad m] [LawfulMonad m] (xs : Array α)
+    (f : (i : Nat) → α → (h : i < xs.size) → m β) :
+    toList <$> xs.mapFinIdxM f = xs.toList.mapFinIdxM f := by
+  rw [List.mapFinIdxM_toArray]
+  simp only [Functor.map_map, id_map']
+
+theorem toList_mapIdxM [Monad m] [LawfulMonad m] (xs : Array α)
+    (f : Nat → α → m β) :
+    toList <$> xs.mapIdxM f = xs.toList.mapIdxM f := by
+  rw [List.mapIdxM_toArray]
+  simp only [Functor.map_map, id_map']
+
+end Array

src/Init/Data/Array/Mem.lean

@@ -8,15 +8,18 @@ import Init.Data.Array.Basic
 import Init.Data.Nat.Linear
 import Init.Data.List.BasicAux
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 theorem sizeOf_lt_of_mem [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a < sizeOf as := by
   cases as with | _ as =>
-  exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp_arith)
+  exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp +arith)
 
-theorem sizeOf_get [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf (as.get i h) < sizeOf as := by
+theorem sizeOf_get [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) : sizeOf as[i] < sizeOf as := by
   cases as with | _ as =>
-  simpa using Nat.lt_trans (List.sizeOf_get _ ⟨i, h⟩) (by simp_arith)
+  simpa using Nat.lt_trans (List.sizeOf_get _ ⟨i, h⟩) (by simp +arith)
 
 @[simp] theorem sizeOf_getElem [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) :
   sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _ h
@@ -29,8 +32,8 @@ macro "array_get_dec" : tactic =>
     -- subsumed by simp
     -- | with_reducible apply sizeOf_get
     -- | with_reducible apply sizeOf_getElem
-    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_get ..)); simp_arith
-    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_getElem ..)); simp_arith
+    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_get ..)); simp +arith
+    | (with_reducible apply Nat.lt_of_lt_of_le (sizeOf_getElem ..)); simp +arith
     )
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_get_dec)
@@ -45,7 +48,7 @@ macro "array_mem_dec" : tactic =>
     | with_reducible
         apply Nat.lt_of_lt_of_le (Array.sizeOf_lt_of_mem ?h)
         case' h => assumption
-      simp_arith)
+      simp +arith)
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_mem_dec)
 

src/Init/Data/Array/Monadic.lean

@@ -12,6 +12,9 @@ import Init.Data.List.Monadic
 # Lemmas about `Array.forIn'` and `Array.forIn`.
 -/
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 open Nat
@@ -20,76 +23,116 @@ open Nat
 
 /-! ### mapM -/
 
-theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] (f : α → m β) (l : Array α) :
-    mapM f l = l.foldlM (fun acc a => return (acc.push (← f a))) #[] := by
-  rcases l with ⟨l⟩
-  simp only [List.mapM_toArray, bind_pure_comp, size_toArray, List.foldlM_toArray']
+@[simp] theorem mapM_pure [Monad m] [LawfulMonad m] (xs : Array α) (f : α → β) :
+    xs.mapM (m := m) (pure <| f ·) = pure (xs.map f) := by
+  induction xs; simp_all
+
+@[simp] theorem mapM_id {xs : Array α} {f : α → Id β} : xs.mapM f = xs.map f :=
+  mapM_pure _ _
+
+@[simp] theorem mapM_append [Monad m] [LawfulMonad m] (f : α → m β) {xs ys : Array α} :
+    (xs ++ ys).mapM f = (return (← xs.mapM f) ++ (← ys.mapM f)) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp
+
+theorem mapM_eq_foldlM_push [Monad m] [LawfulMonad m] (f : α → m β) (xs : Array α) :
+    mapM f xs = xs.foldlM (fun acc a => return (acc.push (← f a))) #[] := by
+  rcases xs with ⟨xs⟩
+  simp only [List.mapM_toArray, bind_pure_comp, List.size_toArray, List.foldlM_toArray']
   rw [List.mapM_eq_reverse_foldlM_cons]
   simp only [bind_pure_comp, Functor.map_map]
-  suffices ∀ (k), (fun a => a.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) k l =
-      List.foldlM (fun acc a => acc.push <$> f a) k.reverse.toArray l by
+  suffices ∀ (l), (fun l' => l'.reverse.toArray) <$> List.foldlM (fun acc a => (fun a => a :: acc) <$> f a) l xs =
+      List.foldlM (fun acc a => acc.push <$> f a) l.reverse.toArray xs by
     exact this []
-  intro k
-  induction l generalizing k with
+  intro l
+  induction xs generalizing l with
   | nil => simp
   | cons a as ih =>
     simp [ih, List.foldlM_cons]
 
 /-! ### foldlM and foldrM -/
 
-theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : Array β₁) (init : α) :
-    (l.map f).foldlM g init = l.foldlM (fun x y => g x (f y)) init := by
-  cases l
-  rw [List.map_toArray] -- Why doesn't this fire via `simp`?
+theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (xs : Array β₁) (init : α) (w : stop = xs.size) :
+    (xs.map f).foldlM g init 0 stop = xs.foldlM (fun x y => g x (f y)) init 0 stop := by
+  subst w
+  cases xs
   simp [List.foldlM_map]
 
-theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : Array β₁)
-    (init : α) : (l.map f).foldrM g init = l.foldrM (fun x y => g (f x) y) init := by
-  cases l
-  rw [List.map_toArray] -- Why doesn't this fire via `simp`?
+theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (xs : Array β₁)
+    (init : α) (w : start = xs.size) :
+    (xs.map f).foldrM g init start 0 = xs.foldrM (fun x y => g (f x) y) init start 0 := by
+  subst w
+  cases xs
   simp [List.foldrM_map]
 
-theorem foldlM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : γ → β → m γ) (l : Array α) (init : γ) :
-    (l.filterMap f).foldlM g init =
-      l.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
-  cases l
-  rw [List.filterMap_toArray] -- Why doesn't this fire via `simp`?
+theorem foldlM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : γ → β → m γ)
+    (xs : Array α) (init : γ) (w : stop = (xs.filterMap f).size) :
+    (xs.filterMap f).foldlM g init 0 stop =
+      xs.foldlM (fun x y => match f y with | some b => g x b | none => pure x) init := by
+  subst w
+  cases xs
   simp [List.foldlM_filterMap]
   rfl
 
-theorem foldrM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : β → γ → m γ) (l : Array α) (init : γ) :
-    (l.filterMap f).foldrM g init =
-      l.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
-  cases l
-  rw [List.filterMap_toArray] -- Why doesn't this fire via `simp`?
+theorem foldrM_filterMap [Monad m] [LawfulMonad m] (f : α → Option β) (g : β → γ → m γ)
+    (xs : Array α) (init : γ) (w : start = (xs.filterMap f).size) :
+    (xs.filterMap f).foldrM g init start 0 =
+      xs.foldrM (fun x y => match f x with | some b => g b y | none => pure y) init := by
+  subst w
+  cases xs
   simp [List.foldrM_filterMap]
   rfl
 
-theorem foldlM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : β → α → m β) (l : Array α) (init : β) :
-    (l.filter p).foldlM g init =
-      l.foldlM (fun x y => if p y then g x y else pure x) init := by
-  cases l
-  rw [List.filter_toArray] -- Why doesn't this fire via `simp`?
+theorem foldlM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : β → α → m β)
+    (xs : Array α) (init : β) (w : stop = (xs.filter p).size) :
+    (xs.filter p).foldlM g init 0 stop =
+      xs.foldlM (fun x y => if p y then g x y else pure x) init := by
+  subst w
+  cases xs
   simp [List.foldlM_filter]
 
-theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β → m β) (l : Array α) (init : β) :
-    (l.filter p).foldrM g init =
-      l.foldrM (fun x y => if p x then g x y else pure y) init := by
-  cases l
-  rw [List.filter_toArray] -- Why doesn't this fire via `simp`?
+theorem foldrM_filter [Monad m] [LawfulMonad m] (p : α → Bool) (g : α → β → m β)
+    (xs : Array α) (init : β) (w : start = (xs.filter p).size) :
+    (xs.filter p).foldrM g init start 0 =
+      xs.foldrM (fun x y => if p x then g x y else pure y) init := by
+  subst w
+  cases xs
   simp [List.foldrM_filter]
 
+@[simp] theorem foldlM_attachWith [Monad m]
+    (xs : Array α) {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : β → { x // q x} → m β} {b} (w : stop = xs.size):
+    (xs.attachWith q H).foldlM f b 0 stop =
+      xs.attach.foldlM (fun b ⟨a, h⟩ => f b ⟨a, H _ h⟩) b := by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp [List.foldlM_map]
+
+@[simp] theorem foldrM_attachWith [Monad m] [LawfulMonad m]
+    (xs : Array α) {q : α → Prop} (H : ∀ a, a ∈ xs → q a) {f : { x // q x} → β → m β} {b} (w : start = xs.size):
+    (xs.attachWith q H).foldrM f b start 0 =
+      xs.attach.foldrM (fun a acc => f ⟨a.1, H _ a.2⟩ acc) b := by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp [List.foldrM_map]
+
 /-! ### forM -/
 
 @[congr] theorem forM_congr [Monad m] {as bs : Array α} (w : as = bs)
     {f : α → m PUnit} :
-    forM f as = forM f bs := by
+    forM as f = forM bs f := by
   cases as <;> cases bs
   simp_all
 
-@[simp] theorem forM_map [Monad m] [LawfulMonad m] (l : Array α) (g : α → β) (f : β → m PUnit) :
-    (l.map g).forM f = l.forM (fun a => f (g a)) := by
-  cases l
+@[simp] theorem forM_append [Monad m] [LawfulMonad m] (xs ys : Array α) (f : α → m PUnit) :
+    forM (xs ++ ys) f = (do forM xs f; forM ys f) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp
+
+@[simp] theorem forM_map [Monad m] [LawfulMonad m] (xs : Array α) (g : α → β) (f : β → m PUnit) :
+    forM (xs.map g) f = forM xs (fun a => f (g a)) := by
+  rcases xs with ⟨xs⟩
   simp
 
 /-! ### forIn' -/
@@ -109,44 +152,41 @@ We can express a for loop over an array as a fold,
 in which whenever we reach `.done b` we keep that value through the rest of the fold.
 -/
 theorem forIn'_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : Array α) (f : (a : α) → a ∈ l → β → m (ForInStep β)) (init : β) :
-    forIn' l init f = ForInStep.value <$>
-      l.attach.foldlM (fun b ⟨a, m⟩ => match b with
+    (xs : Array α) (f : (a : α) → a ∈ xs → β → m (ForInStep β)) (init : β) :
+    forIn' xs init f = ForInStep.value <$>
+      xs.attach.foldlM (fun b ⟨a, m⟩ => match b with
         | .yield b => f a m b
         | .done b => pure (.done b)) (ForInStep.yield init) := by
-  cases l
-  rw [List.attach_toArray] -- Why doesn't this fire via `simp`?
-  simp only [List.forIn'_toArray, List.forIn'_eq_foldlM, List.attachWith_mem_toArray, size_toArray,
-    List.length_map, List.length_attach, List.foldlM_toArray', List.foldlM_map]
+  rcases xs with ⟨xs⟩
+  simp [List.forIn'_eq_foldlM, List.foldlM_map]
   congr
 
 /-- We can express a for loop over an array which always yields as a fold. -/
 @[simp] theorem forIn'_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : Array α) (f : (a : α) → a ∈ l → β → m γ) (g : (a : α) → a ∈ l → β → γ → β) (init : β) :
-    forIn' l init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
-      l.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
-  cases l
-  rw [List.attach_toArray] -- Why doesn't this fire via `simp`?
+    (xs : Array α) (f : (a : α) → a ∈ xs → β → m γ) (g : (a : α) → a ∈ xs → β → γ → β) (init : β) :
+    forIn' xs init (fun a m b => (fun c => .yield (g a m b c)) <$> f a m b) =
+      xs.attach.foldlM (fun b ⟨a, m⟩ => g a m b <$> f a m b) init := by
+  rcases xs with ⟨xs⟩
   simp [List.foldlM_map]
 
-theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
-    forIn' l init (fun a m b => pure (.yield (f a m b))) =
-      pure (f := m) (l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
-  cases l
+@[simp] theorem forIn'_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
+    (xs : Array α) (f : (a : α) → a ∈ xs → β → β) (init : β) :
+    forIn' xs init (fun a m b => pure (.yield (f a m b))) =
+      pure (f := m) (xs.attach.foldl (fun b ⟨a, h⟩ => f a h b) init) := by
+  rcases xs with ⟨xs⟩
   simp [List.forIn'_pure_yield_eq_foldl, List.foldl_map]
 
 @[simp] theorem forIn'_yield_eq_foldl
-    (l : Array α) (f : (a : α) → a ∈ l → β → β) (init : β) :
-    forIn' (m := Id) l init (fun a m b => .yield (f a m b)) =
-      l.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
-  cases l
+    (xs : Array α) (f : (a : α) → a ∈ xs → β → β) (init : β) :
+    forIn' (m := Id) xs init (fun a m b => .yield (f a m b)) =
+      xs.attach.foldl (fun b ⟨a, h⟩ => f a h b) init := by
+  rcases xs with ⟨xs⟩
   simp [List.foldl_map]
 
 @[simp] theorem forIn'_map [Monad m] [LawfulMonad m]
-    (l : Array α) (g : α → β) (f : (b : β) → b ∈ l.map g → γ → m (ForInStep γ)) :
-    forIn' (l.map g) init f = forIn' l init fun a h y => f (g a) (mem_map_of_mem g h) y := by
-  cases l
+    (xs : Array α) (g : α → β) (f : (b : β) → b ∈ xs.map g → γ → m (ForInStep γ)) :
+    forIn' (xs.map g) init f = forIn' xs init fun a h y => f (g a) (mem_map_of_mem g h) y := by
+  rcases xs with ⟨xs⟩
   simp
 
 /--
@@ -154,41 +194,290 @@ We can express a for loop over an array as a fold,
 in which whenever we reach `.done b` we keep that value through the rest of the fold.
 -/
 theorem forIn_eq_foldlM [Monad m] [LawfulMonad m]
-    (f : α → β → m (ForInStep β)) (init : β) (l : Array α) :
-    forIn l init f = ForInStep.value <$>
-      l.foldlM (fun b a => match b with
+    (f : α → β → m (ForInStep β)) (init : β) (xs : Array α) :
+    forIn xs init f = ForInStep.value <$>
+      xs.foldlM (fun b a => match b with
         | .yield b => f a b
         | .done b => pure (.done b)) (ForInStep.yield init) := by
-  cases l
-  simp only [List.forIn_toArray, List.forIn_eq_foldlM, size_toArray, List.foldlM_toArray']
+  rcases xs with ⟨xs⟩
+  simp only [List.forIn_toArray, List.forIn_eq_foldlM, List.size_toArray, List.foldlM_toArray']
   congr
 
 /-- We can express a for loop over an array which always yields as a fold. -/
 @[simp] theorem forIn_yield_eq_foldlM [Monad m] [LawfulMonad m]
-    (l : Array α) (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
-    forIn l init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
-      l.foldlM (fun b a => g a b <$> f a b) init := by
-  cases l
+    (xs : Array α) (f : α → β → m γ) (g : α → β → γ → β) (init : β) :
+    forIn xs init (fun a b => (fun c => .yield (g a b c)) <$> f a b) =
+      xs.foldlM (fun b a => g a b <$> f a b) init := by
+  rcases xs with ⟨xs⟩
   simp [List.foldlM_map]
 
-theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
-    (l : Array α) (f : α → β → β) (init : β) :
-    forIn l init (fun a b => pure (.yield (f a b))) =
-      pure (f := m) (l.foldl (fun b a => f a b) init) := by
-  cases l
+@[simp] theorem forIn_pure_yield_eq_foldl [Monad m] [LawfulMonad m]
+    (xs : Array α) (f : α → β → β) (init : β) :
+    forIn xs init (fun a b => pure (.yield (f a b))) =
+      pure (f := m) (xs.foldl (fun b a => f a b) init) := by
+  rcases xs with ⟨xs⟩
   simp [List.forIn_pure_yield_eq_foldl, List.foldl_map]
 
 @[simp] theorem forIn_yield_eq_foldl
-    (l : Array α) (f : α → β → β) (init : β) :
-    forIn (m := Id) l init (fun a b => .yield (f a b)) =
-      l.foldl (fun b a => f a b) init := by
-  cases l
+    (xs : Array α) (f : α → β → β) (init : β) :
+    forIn (m := Id) xs init (fun a b => .yield (f a b)) =
+      xs.foldl (fun b a => f a b) init := by
+  rcases xs with ⟨xs⟩
   simp [List.foldl_map]
 
 @[simp] theorem forIn_map [Monad m] [LawfulMonad m]
-    (l : Array α) (g : α → β) (f : β → γ → m (ForInStep γ)) :
-    forIn (l.map g) init f = forIn l init fun a y => f (g a) y := by
-  cases l
+    (xs : Array α) (g : α → β) (f : β → γ → m (ForInStep γ)) :
+    forIn (xs.map g) init f = forIn xs init fun a y => f (g a) y := by
+  rcases xs with ⟨xs⟩
+  simp
+
+/-! ### allM and anyM -/
+
+@[simp] theorem anyM_pure [Monad m] [LawfulMonad m] (p : α → Bool) (xs : Array α) :
+    xs.anyM (m := m) (pure <| p ·) = pure (xs.any p) := by
+  cases xs
+  simp
+
+@[simp] theorem allM_pure [Monad m] [LawfulMonad m] (p : α → Bool) (xs : Array α) :
+    xs.allM (m := m) (pure <| p ·) = pure (xs.all p) := by
+  cases xs
+  simp
+
+/-! ### findM? and findSomeM? -/
+
+@[simp]
+theorem findM?_pure {m} [Monad m] [LawfulMonad m] (p : α → Bool) (xs : Array α) :
+    findM? (m := m) (pure <| p ·) xs = pure (xs.find? p) := by
+  cases xs
+  simp
+
+@[simp]
+theorem findSomeM?_pure [Monad m] [LawfulMonad m] (f : α → Option β) (xs : Array α) :
+    findSomeM? (m := m) (pure <| f ·) xs = pure (xs.findSome? f) := by
+  cases xs
   simp
 
 end Array
+
+namespace List
+
+theorem filterM_toArray [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) :
+    l.toArray.filterM p = toArray <$> l.filterM p := by
+  simp only [Array.filterM, filterM, foldlM_toArray, bind_pure_comp, Functor.map_map]
+  conv => lhs; rw [← reverse_nil]
+  generalize [] = acc
+  induction l generalizing acc with simp
+  | cons x xs ih =>
+    congr; funext b
+    cases b
+    · simp only [Bool.false_eq_true, ↓reduceIte, pure_bind, cond_false]
+      exact ih acc
+    · simp only [↓reduceIte, ← reverse_cons, pure_bind, cond_true]
+      exact ih (x :: acc)
+
+/-- Variant of `filterM_toArray` with a side condition for the stop position. -/
+@[simp] theorem filterM_toArray' [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) (w : stop = l.length) :
+    l.toArray.filterM p 0 stop = toArray <$> l.filterM p := by
+  subst w
+  rw [filterM_toArray]
+
+theorem filterRevM_toArray [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) :
+    l.toArray.filterRevM p = toArray <$> l.filterRevM p := by
+  simp [Array.filterRevM, filterRevM]
+  rw [← foldlM_reverse, ← foldlM_toArray, ← Array.filterM, filterM_toArray]
+  simp only [filterM, bind_pure_comp, Functor.map_map, reverse_toArray, reverse_reverse]
+
+/-- Variant of `filterRevM_toArray` with a side condition for the start position. -/
+@[simp] theorem filterRevM_toArray' [Monad m] [LawfulMonad m] (l : List α) (p : α → m Bool) (w : start = l.length) :
+    l.toArray.filterRevM p start 0 = toArray <$> l.filterRevM p := by
+  subst w
+  rw [filterRevM_toArray]
+
+theorem filterMapM_toArray [Monad m] [LawfulMonad m] (l : List α) (f : α → m (Option β)) :
+    l.toArray.filterMapM f = toArray <$> l.filterMapM f := by
+  simp [Array.filterMapM, filterMapM]
+  conv => lhs; rw [← reverse_nil]
+  generalize [] = acc
+  induction l generalizing acc with simp [filterMapM.loop]
+  | cons x xs ih =>
+    congr; funext o
+    cases o
+    · simp only [pure_bind]; exact ih acc
+    · simp only [pure_bind]; rw [← List.reverse_cons]; exact ih _
+
+/-- Variant of `filterMapM_toArray` with a side condition for the stop position. -/
+@[simp] theorem filterMapM_toArray' [Monad m] [LawfulMonad m] (l : List α) (f : α → m (Option β)) (w : stop = l.length) :
+    l.toArray.filterMapM f 0 stop = toArray <$> l.filterMapM f := by
+  subst w
+  rw [filterMapM_toArray]
+
+@[simp] theorem flatMapM_toArray [Monad m] [LawfulMonad m] (l : List α) (f : α → m (Array β)) :
+    l.toArray.flatMapM f = toArray <$> l.flatMapM (fun a => Array.toList <$> f a) := by
+  simp only [Array.flatMapM, bind_pure_comp, foldlM_toArray, flatMapM]
+  conv => lhs; arg 2; change [].reverse.flatten.toArray
+  generalize [] = acc
+  induction l generalizing acc with
+  | nil => simp only [foldlM_nil, flatMapM.loop, map_pure]
+  | cons x xs ih =>
+    simp only [foldlM_cons, bind_map_left, flatMapM.loop, _root_.map_bind]
+    congr; funext xs
+    conv => lhs; rw [Array.toArray_append, ← flatten_concat, ← reverse_cons]
+    exact ih _
+
+end List
+
+namespace Array
+
+@[congr] theorem filterM_congr [Monad m] {as bs : Array α} (w : as = bs)
+    {p : α → m Bool} {q : α → m Bool} (h : ∀ a, p a = q a) :
+    as.filterM p = bs.filterM q := by
+  subst w
+  simp [filterM, h]
+
+@[congr] theorem filterRevM_congr [Monad m] {as bs : Array α} (w : as = bs)
+    {p : α → m Bool} {q : α → m Bool} (h : ∀ a, p a = q a) :
+    as.filterRevM p = bs.filterRevM q := by
+  subst w
+  simp [filterRevM, h]
+
+@[congr] theorem filterMapM_congr [Monad m] {as bs : Array α} (w : as = bs)
+    {f : α → m (Option β)} {g : α → m (Option β)} (h : ∀ a, f a = g a) :
+    as.filterMapM f = bs.filterMapM g := by
+  subst w
+  simp [filterMapM, h]
+
+@[congr] theorem flatMapM_congr [Monad m] {as bs : Array α} (w : as = bs)
+    {f : α → m (Array β)} {g : α → m (Array β)} (h : ∀ a, f a = g a) :
+    as.flatMapM f = bs.flatMapM g := by
+  subst w
+  simp [flatMapM, h]
+
+theorem toList_filterM [Monad m] [LawfulMonad m] (xs : Array α) (p : α → m Bool) :
+    toList <$> xs.filterM p = xs.toList.filterM p := by
+  rw [List.filterM_toArray]
+  simp only [Functor.map_map, id_map']
+
+theorem toList_filterRevM [Monad m] [LawfulMonad m] (xs : Array α) (p : α → m Bool) :
+    toList <$> xs.filterRevM p = xs.toList.filterRevM p := by
+  rw [List.filterRevM_toArray]
+  simp only [Functor.map_map, id_map']
+
+theorem toList_filterMapM [Monad m] [LawfulMonad m] (xs : Array α) (f : α → m (Option β)) :
+    toList <$> xs.filterMapM f = xs.toList.filterMapM f := by
+  rw [List.filterMapM_toArray]
+  simp only [Functor.map_map, id_map']
+
+theorem toList_flatMapM [Monad m] [LawfulMonad m] (xs : Array α) (f : α → m (Array β)) :
+    toList <$> xs.flatMapM f = xs.toList.flatMapM (fun a => toList <$> f a) := by
+  rw [List.flatMapM_toArray]
+  simp only [Functor.map_map, id_map']
+
+/-! ### Recognizing higher order functions using a function that only depends on the value. -/
+
+/--
+This lemma identifies monadic folds over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem foldlM_subtype [Monad m] {p : α → Prop} {xs : Array { x // p x }}
+    {f : β → { x // p x } → m β} {g : β → α → m β} {x : β}
+    (hf : ∀ b x h, f b ⟨x, h⟩ = g b x) (w : stop = xs.size) :
+    xs.foldlM f x 0 stop = xs.unattach.foldlM g x 0 stop := by
+  subst w
+  rcases xs with ⟨l⟩
+  simp
+  rw [List.foldlM_subtype hf]
+
+@[wf_preprocess] theorem foldlM_wfParam [Monad m] (xs : Array α) (f : β → α → m β) (init : β) :
+    (wfParam xs).foldlM f init = xs.attach.unattach.foldlM f init := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem foldlM_unattach [Monad m] (P : α → Prop) (xs : Array (Subtype P)) (f : β → α → m β) (init : β) :
+    xs.unattach.foldlM f init = xs.foldlM (init := init) fun b ⟨x, h⟩ =>
+      binderNameHint b f <| binderNameHint x (f b) <| binderNameHint h () <|
+      f b (wfParam x) := by
+  simp [wfParam]
+
+/--
+This lemma identifies monadic folds over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem foldrM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → β → m β} {g : α → β → m β} {x : β}
+    (hf : ∀ x h b, f ⟨x, h⟩ b = g x b) (w : start = xs.size) :
+    xs.foldrM f x start 0 = xs.unattach.foldrM g x start 0:= by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp
+  rw [List.foldrM_subtype hf]
+
+
+@[wf_preprocess] theorem foldrM_wfParam [Monad m] [LawfulMonad m] (xs : Array α) (f : α → β → m β) (init : β) :
+    (wfParam xs).foldrM f init = xs.attach.unattach.foldrM f init := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem foldrM_unattach [Monad m] [LawfulMonad m] (P : α → Prop) (xs : Array (Subtype P)) (f : α → β → m β) (init : β):
+    xs.unattach.foldrM f init = xs.foldrM (init := init) fun ⟨x, h⟩ b =>
+      binderNameHint x f <| binderNameHint h () <| binderNameHint b (f x) <|
+      f (wfParam x) b := by
+  simp [wfParam]
+
+/--
+This lemma identifies monadic maps over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem mapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → m β} {g : α → m β} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    xs.mapM f = xs.unattach.mapM g := by
+  rcases xs with ⟨xs⟩
+  simp
+  rw [List.mapM_subtype hf]
+
+@[wf_preprocess] theorem mapM_wfParam [Monad m] [LawfulMonad m] (xs : Array α) (f : α → m β) :
+    (wfParam xs).mapM f = xs.attach.unattach.mapM f := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem mapM_unattach [Monad m] [LawfulMonad m] (P : α → Prop) (xs : Array (Subtype P)) (f : α → m β) :
+    xs.unattach.mapM f = xs.mapM fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
+  simp [wfParam]
+
+@[simp] theorem filterMapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → m (Option β)} {g : α → m (Option β)} (hf : ∀ x h, f ⟨x, h⟩ = g x) (w : stop = xs.size) :
+    xs.filterMapM f 0 stop = xs.unattach.filterMapM g := by
+  subst w
+  rcases xs with ⟨xs⟩
+  simp
+  rw [List.filterMapM_subtype hf]
+
+
+@[wf_preprocess] theorem filterMapM_wfParam [Monad m] [LawfulMonad m]
+    (xs : Array α) (f : α → m (Option β)) :
+    (wfParam xs).filterMapM f = xs.attach.unattach.filterMapM f := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem filterMapM_unattach [Monad m] [LawfulMonad m]
+    (P : α → Prop) (xs : Array (Subtype P)) (f : α → m (Option β)) :
+    xs.unattach.filterMapM f = xs.filterMapM fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
+  simp [wfParam]
+
+@[simp] theorem flatMapM_subtype [Monad m] [LawfulMonad m] {p : α → Prop} {xs : Array { x // p x }}
+    {f : { x // p x } → m (Array β)} {g : α → m (Array β)} (hf : ∀ x h, f ⟨x, h⟩ = g x) :
+    (xs.flatMapM f) = xs.unattach.flatMapM g := by
+  rcases xs with ⟨xs⟩
+  simp
+  rw [List.flatMapM_subtype]
+  simp [hf]
+
+@[wf_preprocess] theorem flatMapM_wfParam [Monad m] [LawfulMonad m]
+    (xs : Array α) (f : α → m (Array β)) :
+    (wfParam xs).flatMapM f = xs.attach.unattach.flatMapM f := by
+  simp [wfParam]
+
+@[wf_preprocess] theorem flatMapM_unattach [Monad m] [LawfulMonad m]
+    (P : α → Prop) (xs : Array (Subtype P)) (f : α → m (Array β)) :
+    xs.unattach.flatMapM f = xs.flatMapM fun ⟨x, h⟩ =>
+      binderNameHint x f <| binderNameHint h () <| f (wfParam x) := by
+  simp [wfParam]
+
+end Array

src/Init/Data/Array/OfFn.lean

@@ -0,0 +1,53 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.OfFn
+
+/-!
+# Theorems about `Array.ofFn`
+-/
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+namespace Array
+
+@[simp] theorem ofFn_zero (f : Fin 0 → α) : ofFn f = #[] := by
+  simp [ofFn, ofFn.go]
+
+theorem ofFn_succ (f : Fin (n+1) → α) :
+    ofFn f = (ofFn (fun (i : Fin n) => f i.castSucc)).push (f ⟨n, by omega⟩) := by
+  ext i h₁ h₂
+  · simp
+  · simp [getElem_push]
+    split <;> rename_i h₃
+    · rfl
+    · congr
+      simp at h₁ h₂
+      omega
+
+@[simp] theorem _rooy_.List.toArray_ofFn (f : Fin n → α) : (List.ofFn f).toArray = Array.ofFn f := by
+  ext <;> simp
+
+@[simp] theorem toList_ofFn (f : Fin n → α) : (Array.ofFn f).toList = List.ofFn f := by
+  apply List.ext_getElem <;> simp
+
+@[simp]
+theorem ofFn_eq_empty_iff {f : Fin n → α} : ofFn f = #[] ↔ n = 0 := by
+  rw [← Array.toList_inj]
+  simp
+
+@[simp 500]
+theorem mem_ofFn {n} (f : Fin n → α) (a : α) : a ∈ ofFn f ↔ ∃ i, f i = a := by
+  constructor
+  · intro w
+    obtain ⟨i, h, rfl⟩ := getElem_of_mem w
+    exact ⟨⟨i, by simpa using h⟩, by simp⟩
+  · rintro ⟨i, rfl⟩
+    apply mem_of_getElem (i := i) <;> simp
+
+end Array

src/Init/Data/Array/Perm.lean

@@ -7,6 +7,9 @@ prelude
 import Init.Data.List.Nat.Perm
 import Init.Data.Array.Lemmas
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
 namespace Array
 
 open List
@@ -27,38 +30,38 @@ theorem perm_iff_toList_perm {as bs : Array α} : as ~ bs ↔ as.toList ~ bs.toL
 @[simp] theorem perm_toArray (as bs : List α) : as.toArray ~ bs.toArray ↔ as ~ bs := by
   simp [perm_iff_toList_perm]
 
-@[simp, refl] protected theorem Perm.refl (l : Array α) : l ~ l := by
-  cases l
+@[simp, refl] protected theorem Perm.refl (xs : Array α) : xs ~ xs := by
+  cases xs
   simp
 
-protected theorem Perm.rfl {l : List α} : l ~ l := .refl _
+protected theorem Perm.rfl {xs : List α} : xs ~ xs := .refl _
 
-theorem Perm.of_eq {l₁ l₂ : Array α} (h : l₁ = l₂) : l₁ ~ l₂ := h ▸ .rfl
+theorem Perm.of_eq {xs ys : Array α} (h : xs = ys) : xs ~ ys := h ▸ .rfl
 
-protected theorem Perm.symm {l₁ l₂ : Array α} (h : l₁ ~ l₂) : l₂ ~ l₁ := by
-  cases l₁; cases l₂
+protected theorem Perm.symm {xs ys : Array α} (h : xs ~ ys) : ys ~ xs := by
+  cases xs; cases ys
   simp only [perm_toArray] at h
   simpa using h.symm
 
-protected theorem Perm.trans {l₁ l₂ l₃ : Array α} (h₁ : l₁ ~ l₂) (h₂ : l₂ ~ l₃) : l₁ ~ l₃ := by
-  cases l₁; cases l₂; cases l₃
+protected theorem Perm.trans {xs ys zs : Array α} (h₁ : xs ~ ys) (h₂ : ys ~ zs) : xs ~ zs := by
+  cases xs; cases ys; cases zs
   simp only [perm_toArray] at h₁ h₂
   simpa using h₁.trans h₂
 
 instance : Trans (Perm (α := α)) (Perm (α := α)) (Perm (α := α)) where
   trans h₁ h₂ := Perm.trans h₁ h₂
 
-theorem perm_comm {l₁ l₂ : Array α} : l₁ ~ l₂ ↔ l₂ ~ l₁ := ⟨Perm.symm, Perm.symm⟩
+theorem perm_comm {xs ys : Array α} : xs ~ ys ↔ ys ~ xs := ⟨Perm.symm, Perm.symm⟩
 
-theorem Perm.push (x y : α) {l₁ l₂ : Array α} (p : l₁ ~ l₂) :
-    (l₁.push x).push y ~ (l₂.push y).push x := by
-  cases l₁; cases l₂
+theorem Perm.push (x y : α) {xs ys : Array α} (p : xs ~ ys) :
+    (xs.push x).push y ~ (ys.push y).push x := by
+  cases xs; cases ys
   simp only [perm_toArray] at p
   simp only [push_toArray, List.append_assoc, singleton_append, perm_toArray]
   exact p.append (Perm.swap' _ _ Perm.nil)
 
-theorem swap_perm {as : Array α} {i j : Nat} (h₁ : i < as.size) (h₂ : j < as.size) :
-    as.swap i j ~ as := by
+theorem swap_perm {xs : Array α} {i j : Nat} (h₁ : i < xs.size) (h₂ : j < xs.size) :
+    xs.swap i j ~ xs := by
   simp only [swap, perm_iff_toList_perm, toList_set]
   apply set_set_perm
 

src/Init/Data/Array/QSort.lean

@@ -7,6 +7,9 @@ prelude
 import Init.Data.Vector.Basic
 import Init.Data.Ord
 
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+-- We do not enable `linter.indexVariables` because it is helpful to name index variables `lo`, `mid`, `hi`, etc.
+
 namespace Array
 
 private def qpartition {n} (as : Vector α n) (lt : α → α → Bool) (lo hi : Nat)
@@ -27,6 +30,16 @@ private def qpartition {n} (as : Vector α n) (lt : α → α → Bool) (lo hi :
       (⟨i, ilo⟩, as.swap i hi)
   loop as lo lo
 
+/--
+Sorts an array using the Quicksort algorithm.
+
+The optional parameter `lt` specifies an ordering predicate. It defaults to `LT.lt`, which must be
+decidable to be used for sorting. Use `Array.qsortOrd` to sort the array according to the `Ord α`
+instance.
+
+The optional parameters `low` and `high` delimit the region of the array that is sorted. Both are
+inclusive, and default to sorting the entire array.
+-/
 @[inline] def qsort (as : Array α) (lt : α → α → Bool := by exact (· < ·))
     (low := 0) (high := as.size - 1) : Array α :=
   let rec @[specialize] sort {n} (as : Vector α n) (lo hi : Nat)
@@ -47,7 +60,7 @@ private def qpartition {n} (as : Vector α n) (lt : α → α → Bool) (lo hi :
 
 set_option linter.unusedVariables.funArgs false in
 /--
-Sort an array using `compare` to compare elements.
+Sorts an array using the Quicksort algorithm, using `Ord.compare` to compare elements.
 -/
 def qsortOrd [ord : Ord α] (xs : Array α) : Array α :=
   xs.qsort fun x y => compare x y |>.isLT

src/Init/Data/Array/Range.lean

@@ -0,0 +1,301 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.Array.OfFn
+import Init.Data.Array.MapIdx
+import Init.Data.Array.Zip
+import Init.Data.List.Nat.Range
+
+/-!
+# Lemmas about `Array.range'`, `Array.range`, and `Array.zipIdx`
+
+-/
+
+set_option linter.listVariables true -- Enforce naming conventions for `List`/`Array`/`Vector` variables.
+set_option linter.indexVariables true -- Enforce naming conventions for index variables.
+
+namespace Array
+
+open Nat
+
+/-! ## Ranges and enumeration -/
+
+/-! ### range' -/
+
+theorem range'_succ (s n step) : range' s (n + 1) step = #[s] ++ range' (s + step) n step := by
+  rw [← toList_inj]
+  simp [List.range'_succ]
+
+@[simp] theorem range'_eq_empty_iff : range' s n step = #[] ↔ n = 0 := by
+  rw [← size_eq_zero_iff, size_range']
+
+theorem range'_ne_empty_iff (s : Nat) {n step : Nat} : range' s n step ≠ #[] ↔ n ≠ 0 := by
+  cases n <;> simp
+
+@[simp] theorem range'_zero : range' s 0 step = #[] := by
+  simp
+
+@[simp] theorem range'_one {s step : Nat} : range' s 1 step = #[s] := by
+  simp [range', ofFn, ofFn.go]
+
+@[simp] theorem range'_inj : range' s n = range' s' n' ↔ n = n' ∧ (n = 0 ∨ s = s') := by
+  rw [← toList_inj]
+  simp [List.range'_inj]
+
+theorem mem_range' {n} : m ∈ range' s n step ↔ ∃ i < n, m = s + step * i := by
+  simp [range']
+  constructor
+  · rintro ⟨⟨i, w⟩, h, h'⟩
+    exact ⟨i, w, by simp_all⟩
+  · rintro ⟨i, w, h'⟩
+    exact ⟨⟨i, w⟩, by simp_all⟩
+
+theorem pop_range' : (range' s n step).pop = range' s (n - 1) step := by
+  ext <;> simp
+
+theorem map_add_range' (a) (s n step) : map (a + ·) (range' s n step) = range' (a + s) n step := by
+  ext <;> simp <;> omega
+
+theorem range'_succ_left : range' (s + 1) n step = (range' s n step).map (· + 1) := by
+  ext <;> simp <;> omega
+
+theorem range'_append (s m n step : Nat) :
+    range' s m step ++ range' (s + step * m) n step = range' s (m + n) step := by
+  ext i h₁ h₂
+  · simp
+  · simp only [size_append, size_range'] at h₁ h₂
+    simp only [getElem_append, size_range', getElem_range', Nat.mul_sub_left_distrib, dite_eq_ite,
+      ite_eq_left_iff, Nat.not_lt]
+    intro h
+    have : step * m ≤ step * i := by exact mul_le_mul_left step h
+    omega
+
+@[simp] theorem range'_append_1 (s m n : Nat) :
+    range' s m ++ range' (s + m) n = range' s (m + n) := by simpa using range'_append s m n 1
+
+theorem range'_concat (s n : Nat) : range' s (n + 1) step = range' s n step ++ #[s + step * n] := by
+  simpa using (range'_append s n 1 step).symm
+
+theorem range'_1_concat (s n : Nat) : range' s (n + 1) = range' s n ++ #[s + n] := by
+  simp [range'_concat]
+
+@[simp] theorem mem_range'_1 : m ∈ range' s n ↔ s ≤ m ∧ m < s + n := by
+  simp [mem_range']; exact ⟨
+    fun ⟨i, h, e⟩ => e ▸ ⟨Nat.le_add_right .., Nat.add_lt_add_left h _⟩,
+    fun ⟨h₁, h₂⟩ => ⟨m - s, Nat.sub_lt_left_of_lt_add h₁ h₂, (Nat.add_sub_cancel' h₁).symm⟩⟩
+
+theorem map_sub_range' (a s n : Nat) (h : a ≤ s) :
+    map (· - a) (range' s n step) = range' (s - a) n step := by
+  conv => lhs; rw [← Nat.add_sub_cancel' h]
+  rw [← map_add_range', map_map, (?_ : _∘_ = _), map_id]
+  funext x; apply Nat.add_sub_cancel_left
+
+@[simp] theorem range'_eq_singleton_iff {s n a : Nat} : range' s n = #[a] ↔ s = a ∧ n = 1 := by
+  rw [← toList_inj]
+  simp
+
+theorem range'_eq_append_iff : range' s n = xs ++ ys ↔ ∃ k, k ≤ n ∧ xs = range' s k ∧ ys = range' (s + k) (n - k) := by
+  simp [← toList_inj, List.range'_eq_append_iff]
+
+@[simp] theorem find?_range'_eq_some {s n : Nat} {i : Nat} {p : Nat → Bool} :
+    (range' s n).find? p = some i ↔ p i ∧ i ∈ range' s n ∧ ∀ j, s ≤ j → j < i → !p j := by
+  rw [← List.toArray_range']
+  simp only [List.find?_toArray, mem_toArray]
+  simp [List.find?_range'_eq_some]
+
+@[simp] theorem find?_range'_eq_none {s n : Nat} {p : Nat → Bool} :
+    (range' s n).find? p = none ↔ ∀ i, s ≤ i → i < s + n → !p i := by
+  rw [← List.toArray_range']
+  simp only [List.find?_toArray]
+  simp
+
+theorem erase_range' :
+    (range' s n).erase i =
+      range' s (min n (i - s)) ++ range' (max s (i + 1)) (min s (i + 1) + n - (i + 1)) := by
+  simp only [← List.toArray_range', List.erase_toArray]
+  simp [List.erase_range']
+
+/-! ### range -/
+
+theorem range_eq_range' (n : Nat) : range n = range' 0 n := by
+  simp [range, range']
+
+theorem range_succ_eq_map (n : Nat) : range (n + 1) = #[0] ++ map succ (range n) := by
+  ext i h₁ h₂
+  · simp
+    omega
+  · simp only [getElem_range, getElem_append, List.size_toArray, List.length_cons, List.length_nil,
+      Nat.zero_add, lt_one_iff, List.getElem_toArray, List.getElem_singleton, getElem_map,
+      succ_eq_add_one, dite_eq_ite]
+    split <;> omega
+
+theorem range'_eq_map_range (s n : Nat) : range' s n = map (s + ·) (range n) := by
+  rw [range_eq_range', map_add_range']; rfl
+
+@[simp] theorem range_eq_empty_iff {n : Nat} : range n = #[] ↔ n = 0 := by
+  rw [← size_eq_zero_iff, size_range]
+
+theorem range_ne_empty_iff {n : Nat} : range n ≠ #[] ↔ n ≠ 0 := by
+  cases n <;> simp
+
+theorem range_succ (n : Nat) : range (succ n) = range n ++ #[n] := by
+  ext i h₁ h₂
+  · simp
+  · simp only [succ_eq_add_one, size_range] at h₁
+    simp only [succ_eq_add_one, getElem_range, append_singleton, getElem_push, size_range,
+      dite_eq_ite]
+    split <;> omega
+
+theorem range_add (n m : Nat) : range (n + m) = range n ++ (range m).map (n + ·) := by
+  rw [← range'_eq_map_range]
+  simpa [range_eq_range', Nat.add_comm] using (range'_append_1 0 n m).symm
+
+theorem reverse_range' (s n : Nat) : reverse (range' s n) = map (s + n - 1 - ·) (range n) := by
+  simp [← toList_inj, List.reverse_range']
+
+@[simp]
+theorem mem_range {m n : Nat} : m ∈ range n ↔ m < n := by
+  simp only [range_eq_range', mem_range'_1, Nat.zero_le, true_and, Nat.zero_add]
+
+theorem not_mem_range_self {n : Nat} : n ∉ range n := by simp
+
+theorem self_mem_range_succ (n : Nat) : n ∈ range (n + 1) := by simp
+
+@[simp] theorem take_range (i n : Nat) : take (range n) i = range (min i n) := by
+  ext <;> simp
+
+@[simp] theorem find?_range_eq_some {n : Nat} {i : Nat} {p : Nat → Bool} :
+    (range n).find? p = some i ↔ p i ∧ i ∈ range n ∧ ∀ j, j < i → !p j := by
+  simp [range_eq_range']
+
+@[simp] theorem find?_range_eq_none {n : Nat} {p : Nat → Bool} :
+    (range n).find? p = none ↔ ∀ i, i < n → !p i := by
+  simp only [← List.toArray_range, List.find?_toArray, List.find?_range_eq_none]
+
+theorem erase_range : (range n).erase i = range (min n i) ++ range' (i + 1) (n - (i + 1)) := by
+  simp [range_eq_range', erase_range']
+
+
+/-! ### zipIdx -/
+
+@[simp]
+theorem zipIdx_eq_empty_iff {xs : Array α} {i : Nat} : xs.zipIdx i = #[] ↔ xs = #[] := by
+  cases xs
+  simp
+
+@[simp]
+theorem getElem?_zipIdx (xs : Array α) (i j) : (zipIdx xs i)[j]? = xs[j]?.map fun a => (a, i + j) := by
+  simp [getElem?_def]
+
+theorem map_snd_add_zipIdx_eq_zipIdx (xs : Array α) (n k : Nat) :
+    map (Prod.map id (· + n)) (zipIdx xs k) = zipIdx xs (n + k) :=
+  ext_getElem? fun i ↦ by simp [(· ∘ ·), Nat.add_comm, Nat.add_left_comm]; rfl
+
+@[simp]
+theorem zipIdx_map_snd (i) (xs : Array α) : map Prod.snd (zipIdx xs i) = range' i xs.size := by
+  cases xs
+  simp
+
+@[simp]
+theorem zipIdx_map_fst (i) (xs : Array α) : map Prod.fst (zipIdx xs i) = xs := by
+  cases xs
+  simp
+
+theorem zipIdx_eq_zip_range' (xs : Array α) {i : Nat} : xs.zipIdx i = xs.zip (range' i xs.size) := by
+  simp [zip_of_prod (zipIdx_map_fst _ _) (zipIdx_map_snd _ _)]
+
+@[simp]
+theorem unzip_zipIdx_eq_prod (xs : Array α) {i : Nat} :
+    (xs.zipIdx i).unzip = (xs, range' i xs.size) := by
+  simp only [zipIdx_eq_zip_range', unzip_zip, size_range']
+
+/-- Replace `zipIdx` with a starting index `n+1` with `zipIdx` starting from `n`,
+followed by a `map` increasing the indices by one. -/
+theorem zipIdx_succ (xs : Array α) (i : Nat) :
+    xs.zipIdx (i + 1) = (xs.zipIdx i).map (fun ⟨a, j⟩ => (a, j + 1)) := by
+  cases xs
+  simp [List.zipIdx_succ]
+
+/-- Replace `zipIdx` with a starting index with `zipIdx` starting from 0,
+followed by a `map` increasing the indices. -/
+theorem zipIdx_eq_map_add (xs : Array α) (i : Nat) :
+    xs.zipIdx i = (xs.zipIdx 0).map (fun ⟨a, j⟩ => (a, i + j)) := by
+  cases xs
+  simp only [zipIdx_toArray, List.map_toArray, mk.injEq]
+  rw [List.zipIdx_eq_map_add]
+
+@[simp]
+theorem zipIdx_singleton (x : α) (k : Nat) : zipIdx #[x] k = #[(x, k)] :=
+  rfl
+
+theorem mk_add_mem_zipIdx_iff_getElem? {k i : Nat} {x : α} {xs : Array α} :
+    (x, k + i) ∈ zipIdx xs k ↔ xs[i]? = some x := by
+  simp [mem_iff_getElem?, and_left_comm]
+
+theorem le_snd_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (h : x ∈ zipIdx xs k) :
+    k ≤ x.2 :=
+  (mk_mem_zipIdx_iff_le_and_getElem?_sub.1 h).1
+
+theorem snd_lt_add_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (h : x ∈ zipIdx xs k) :
+    x.2 < k + xs.size := by
+  rcases mem_iff_getElem.1 h with ⟨i, h', rfl⟩
+  simpa using h'
+
+theorem snd_lt_of_mem_zipIdx {x : α × Nat} {k : Nat} {xs : Array α} (h : x ∈ zipIdx xs k) : x.2 < xs.size + k := by
+  simpa [Nat.add_comm] using snd_lt_add_of_mem_zipIdx h
+
+theorem map_zipIdx (f : α → β) (xs : Array α) (k : Nat) :
+    map (Prod.map f id) (zipIdx xs k) = zipIdx (xs.map f) k := by
+  cases xs
+  simp [List.map_zipIdx]
+
+theorem fst_mem_of_mem_zipIdx {x : α × Nat} {xs : Array α} {k : Nat} (h : x ∈ zipIdx xs k) : x.1 ∈ xs :=
+  zipIdx_map_fst k xs ▸ mem_map_of_mem _ h
+
+theorem fst_eq_of_mem_zipIdx {x : α × Nat} {xs : Array α} {k : Nat} (h : x ∈ zipIdx xs k) :
+    x.1 = xs[x.2 - k]'(by have := le_snd_of_mem_zipIdx h; have := snd_lt_add_of_mem_zipIdx h; omega) := by
+  cases xs
+  exact List.fst_eq_of_mem_zipIdx (by simpa using h)
+
+theorem mem_zipIdx {x : α} {i : Nat} {xs : Array α} {k : Nat} (h : (x, i) ∈ xs.zipIdx k) :
+    k ≤ i ∧ i < k + xs.size ∧
+      x = xs[i - k]'(by have := le_snd_of_mem_zipIdx h; have := snd_lt_add_of_mem_zipIdx h; omega) :=
+  ⟨le_snd_of_mem_zipIdx h, snd_lt_add_of_mem_zipIdx h, fst_eq_of_mem_zipIdx h⟩
+
+/-- Variant of `mem_zipIdx` specialized at `k = 0`. -/
+theorem mem_zipIdx' {x : α} {i : Nat} {xs : Array α} (h : (x, i) ∈ xs.zipIdx) :
+    i < xs.size ∧ x = xs[i]'(by have := le_snd_of_mem_zipIdx h; have := snd_lt_add_of_mem_zipIdx h; omega) :=
+  ⟨by simpa using snd_lt_add_of_mem_zipIdx h, fst_eq_of_mem_zipIdx h⟩
+
+theorem zipIdx_map (xs : Array α) (k : Nat) (f : α → β) :
+    zipIdx (xs.map f) k = (zipIdx xs k).map (Prod.map f id) := by
+  cases xs
+  simp [List.zipIdx_map]
+
+theorem zipIdx_append (xs ys : Array α) (k : Nat) :
+    zipIdx (xs ++ ys) k = zipIdx xs k ++ zipIdx ys (k + xs.size) := by
+  cases xs
+  cases ys
+  simp [List.zipIdx_append]
+
+theorem zipIdx_eq_append_iff {xs : Array α} {k : Nat} :
+    zipIdx xs k = ys ++ zs ↔
+      ∃ ys' zs', xs = ys' ++ zs' ∧ ys = zipIdx ys' k ∧ zs = zipIdx zs' (k + ys'.size) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  rcases zs with ⟨zs⟩
+  simp only [zipIdx_toArray, List.append_toArray, mk.injEq, List.zipIdx_eq_append_iff,
+    toArray_eq_append_iff]
+  constructor
+  · rintro ⟨l₁', l₂', rfl, rfl, rfl⟩
+    exact ⟨⟨l₁'⟩, ⟨l₂'⟩, by simp⟩
+  · rintro ⟨⟨l₁'⟩, ⟨l₂'⟩, rfl, h⟩
+    simp only [zipIdx_toArray, mk.injEq, List.size_toArray] at h
+    obtain ⟨rfl, rfl⟩ := h
+    exact ⟨l₁', l₂', by simp⟩
+
+end Array