update scripts

Fixes #3556

---------

Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

.github/ISSUE_TEMPLATE/bug_report.md

@@ -9,9 +9,15 @@ assignees: ''
 
 ### Prerequisites
 
-* [ ] Put an X between the brackets on this line if you have done all of the following:
-    * Check that your issue is not already [filed](https://github.com/leanprover/lean4/issues).
-    * Reduce the issue to a minimal, self-contained, reproducible test case. Avoid dependencies to mathlib4 or std4.
+Please put an X between the brackets as you perform the following steps:
+
+* [ ] Check that your issue is not already filed:
+      https://github.com/leanprover/lean4/issues
+* [ ] Reduce the issue to a minimal, self-contained, reproducible test case.
+      Avoid dependencies to Mathlib or Batteries.
+* [ ] Test your test case against the latest nightly release, for example on
+      https://live.lean-lang.org/#project=lean-nightly
+      (You can also use the settings there to switch to “Lean nightly”)
 
 ### Description
 
@@ -33,8 +39,8 @@ assignees: ''
 
 ### Versions
 
-[Output of `#eval Lean.versionString` or of `lean --version` in the folder that the issue occured in]
-[OS version]
+[Output of `#eval Lean.versionString`]
+[OS version, if not using live.lean-lang.org.]
 
 ### Additional Information
 

.github/workflows/ci.yml

@@ -6,7 +6,6 @@ on:
     tags:
       - '*'
   pull_request:
-    types: [opened, synchronize, reopened, labeled]
   merge_group:
   schedule:
     - cron: '0 7 * * *'  # 8AM CET/11PM PT
@@ -21,8 +20,10 @@ jobs:
   configure:
     runs-on: ubuntu-latest
     outputs:
-      # Should we run only a quick CI? Yes on a pull request without the full-ci label
-      quick: ${{ steps.set-quick.outputs.quick }}
+      # 0: PRs without special label
+      # 1: PRs with `merge-ci` label, merge queue checks, master commits
+      # 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 }}
       # Should we make a nightly release? If so, this output contains the lean version string, else it is empty
@@ -39,161 +40,6 @@ jobs:
       RELEASE_TAG: ${{ steps.set-release.outputs.RELEASE_TAG }}
 
     steps:
-      - name: Run quick CI?
-        id: set-quick
-        env:
-          quick: ${{
-            github.event_name == 'pull_request' && !contains( github.event.pull_request.labels.*.name, 'full-ci')
-           }}
-        run: |
-          echo "quick=${{env.quick}}" >> "$GITHUB_OUTPUT"
-
-      - name: Configure build matrix
-        id: set-matrix
-        uses: actions/github-script@v7
-        with:
-          script: |
-            const quick = ${{ steps.set-quick.outputs.quick }};
-            console.log(`quick: ${quick}`);
-            // use large runners outside PRs where available (original repo)
-            // for now Windows only, which is the slowest non-debug job
-            let large = ${{ github.event_name != 'pull_request' && github.repository == 'leanprover/lean4' }} ? "-large" : "";
-            let matrix = [
-              {
-                // portable release build: use channel with older glibc (2.27)
-                "name": "Linux LLVM",
-                "os": "ubuntu-latest",
-                "release": false,
-                "quick": false,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                // reverse-ffi needs to be updated to link to LLVM libraries
-                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
-                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
-              },
-              {
-                "name": "Linux release",
-                "os": "ubuntu-latest",
-                "release": true,
-                "quick": true,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                "CTEST_OPTIONS": "-E 'foreign'"
-              },
-              {
-                "name": "Linux",
-                "os": "ubuntu-latest",
-                "check-stage3": true,
-                "test-speedcenter": true,
-                "quick": false,
-              },
-              {
-                "name": "Linux Debug",
-                "os": "ubuntu-latest",
-                "quick": false,
-                "CMAKE_OPTIONS": "-DCMAKE_BUILD_TYPE=Debug",
-                // exclude seriously slow tests
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
-              },
-              // TODO: suddenly started failing in CI
-              /*{
-                "name": "Linux fsanitize",
-                "os": "ubuntu-latest",
-                "quick": false,
-                // turn off custom allocator & symbolic functions to make LSAN do its magic
-                "CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-fsanitize=address,undefined -DLEANC_EXTRA_FLAGS='-fsanitize=address,undefined -fsanitize-link-c++-runtime' -DSMALL_ALLOCATOR=OFF -DBSYMBOLIC=OFF",
-                // exclude seriously slow/problematic tests (laketests crash)
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
-              },*/
-              {
-                "name": "macOS",
-                "os": "macos-13",
-                "release": true,
-                "quick": false,
-                "shell": "bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-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
-              },
-              {
-                "name": "macOS aarch64",
-                "os": "macos-13",
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "cross_target": "aarch64-apple-darwin",
-                "shell": "bash -euxo pipefail {0}",
-                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm-aarch64-* lean-llvm-x86_64-*",
-                "binary-check": "otool -L",
-                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
-              },
-              {
-                "name": "Windows",
-                "os": `windows-2022${large}`,
-                "release": true,
-                "quick": false,
-                "shell": "msys2 {0}",
-                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
-                // for reasons unknown, interactivetests are flaky on Windows
-                "CTEST_OPTIONS": "--repeat until-pass:2",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
-                "binary-check": "ldd"
-              },
-              {
-                "name": "Linux aarch64",
-                "os": "ubuntu-latest",
-                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "cross_target": "aarch64-unknown-linux-gnu",
-                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
-              },
-              {
-                "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",
-                "cmultilib": true,
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "shell": "bash -euxo pipefail {0}"
-              },
-              {
-                "name": "Web Assembly",
-                "os": "ubuntu-latest",
-                // Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
-                "CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
-                "wasm": true,
-                "cmultilib": true,
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "shell": "bash -euxo pipefail {0}",
-                // Just a few selected tests because wasm is slow
-                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean\""
-              }
-            ];
-            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
-            if (quick) {
-              return matrix.filter((job) => job.quick)
-            } else {
-              return matrix
-            }
-
       - name: Checkout
         uses: actions/checkout@v3
         # don't schedule nightlies on forks
@@ -244,6 +90,170 @@ jobs:
             echo "Tag ${TAG_NAME} did not match SemVer regex."
           fi
 
+      - name: Set check level
+        id: set-level
+        # We do not use github.event.pull_request.labels.*.name here because
+        # re-running a run does not update that list, and we do want to be able to
+        # rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
+        run: |
+          check_level=0
+
+          if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" ]]; then
+            check_level=2
+          elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
+            check_level=1
+          else
+            labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }}) --jq '.labels'"
+            if echo "$labels" | grep -q "release-ci"; then
+              check_level=2
+            elif echo "$labels" | grep -q "merge-ci"; then
+              check_level=1
+            fi
+          fi
+
+          echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
+        env:
+          GH_TOKEN: ${{ github.token }}
+
+      - name: Configure build matrix
+        id: set-matrix
+        uses: actions/github-script@v7
+        with:
+          script: |
+            const level = ${{ steps.set-level.outputs.check-level }};
+            console.log(`level: ${level}`);
+            // use large runners outside PRs where available (original repo)
+            // disabled for now as this mostly just speeds up the test suite which is not a bottleneck
+            // let large = ${{ github.event_name != 'pull_request' && github.repository == 'leanprover/lean4' }} ? "-large" : "";
+            let matrix = [
+              {
+                // portable release build: use channel with older glibc (2.27)
+                "name": "Linux LLVM",
+                "os": "ubuntu-latest",
+                "release": false,
+                "check-level": 2,
+                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "binary-check": "ldd -v",
+                // foreign code may be linked against more recent glibc
+                // reverse-ffi needs to be updated to link to LLVM libraries
+                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
+                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
+              },
+              {
+                "name": "Linux release",
+                "os": "ubuntu-latest",
+                "release": true,
+                "check-level": 0,
+                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "binary-check": "ldd -v",
+                // foreign code may be linked against more recent glibc
+                "CTEST_OPTIONS": "-E 'foreign'"
+              },
+              {
+                "name": "Linux",
+                "os": "ubuntu-latest",
+                "check-stage3": level >= 2,
+                "test-speedcenter": level >= 2,
+                "check-level": 1,
+              },
+              {
+                "name": "Linux Debug",
+                "os": "ubuntu-latest",
+                "check-level": 2,
+                "CMAKE_PRESET": "debug",
+                // exclude seriously slow tests
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
+              },
+              // TODO: suddenly started failing in CI
+              /*{
+                "name": "Linux fsanitize",
+                "os": "ubuntu-latest",
+                "check-level": 2,
+                // turn off custom allocator & symbolic functions to make LSAN do its magic
+                "CMAKE_PRESET": "sanitize",
+                // exclude seriously slow/problematic tests (laketests crash)
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
+              },*/
+              {
+                "name": "macOS",
+                "os": "macos-13",
+                "release": true,
+                "check-level": 2,
+                "shell": "bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-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
+              },
+              {
+                "name": "macOS aarch64",
+                "os": "macos-14",
+                "release": true,
+                "check-level": 1,
+                "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
+              },
+              {
+                "name": "Windows",
+                "os": "windows-2022",
+                "release": true,
+                "check-level": 2,
+                "shell": "msys2 {0}",
+                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
+                // for reasons unknown, interactivetests are flaky on Windows
+                "CTEST_OPTIONS": "--repeat until-pass:2",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
+                "binary-check": "ldd"
+              },
+              {
+                "name": "Linux aarch64",
+                "os": "ubuntu-latest",
+                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
+                "release": true,
+                "check-level": 2,
+                "cross": true,
+                "cross_target": "aarch64-unknown-linux-gnu",
+                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
+              },
+              {
+                "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",
+                "cmultilib": true,
+                "release": true,
+                "check-level": 2,
+                "cross": true,
+                "shell": "bash -euxo pipefail {0}"
+              },
+              {
+                "name": "Web Assembly",
+                "os": "ubuntu-latest",
+                // Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
+                "CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
+                "wasm": true,
+                "cmultilib": true,
+                "release": true,
+                "check-level": 2,
+                "cross": true,
+                "shell": "bash -euxo pipefail {0}",
+                // Just a few selected tests because wasm is slow
+                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean\""
+              }
+            ];
+            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
+            return matrix.filter((job) => level >= job["check-level"])
+
   build:
     needs: [configure]
     if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
@@ -322,6 +332,9 @@ jobs:
           # store in current directory, for easy uploading together with binary
           echo $PWD/coredumps/%e.%p.%t | sudo tee /proc/sys/kernel/core_pattern
         if: runner.os == 'Linux'
+      - name: Set up NPROC
+        run: |
+          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
       - name: Build
         run: |
           mkdir build
@@ -352,8 +365,8 @@ jobs:
             OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }})
           fi
           # contortion to support empty OPTIONS with old macOS bash
-          cmake .. ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
-          make -j4
+          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
+          make -j$NPROC
           make install
       - name: Check Binaries
         run: ${{ matrix.binary-check }} lean-*/bin/* || true
@@ -382,32 +395,29 @@ jobs:
           build/stage1/bin/lean --stats src/Lean.lean
         if: ${{ !matrix.cross }}
       - name: Test
+        id: test
         run: |
-          cd build/stage1
           ulimit -c unlimited # coredumps
-          # exclude nonreproducible test
-          ctest -j4 --progress --output-junit test-results.xml --output-on-failure ${{ matrix.CTEST_OPTIONS }} < /dev/null
-        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
+          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() && (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
+        if: always() && steps.test.conclusion != 'skipped'
       - name: Check Test Binary
         run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
-        if: ${{ !matrix.cross && needs.configure.outputs.quick == 'false' }}
+        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
       - name: Build Stage 2
         run: |
-          cd build
           ulimit -c unlimited # coredumps
-          make -j4 stage2
+          make -C build -j$NPROC stage2
         if: matrix.test-speedcenter
       - name: Check Stage 3
         run: |
-          cd build
           ulimit -c unlimited # coredumps
-          make -j4 check-stage3
+          make -C build -j$NPROC stage3
         if: matrix.test-speedcenter
       - name: Test Speedcenter Benchmarks
         run: |
@@ -418,11 +428,10 @@ jobs:
         if: matrix.test-speedcenter
       - name: Check rebootstrap
         run: |
-          cd build
           ulimit -c unlimited # coredumps
           # clean rebuild in case of Makefile changes
-          make update-stage0 && rm -rf ./stage* && make -j4
-        if: matrix.name == 'Linux' && needs.configure.outputs.quick == 'false'
+          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
+        if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
       - name: CCache stats
         run: ccache -s
       - name: Show stacktrace for coredumps

.github/workflows/nix-ci.yml

@@ -6,7 +6,6 @@ on:
     tags:
       - '*'
   pull_request:
-    types: [opened, synchronize, reopened, labeled]
   merge_group:
 
 concurrency:

.github/workflows/pr-release.yml

@@ -126,11 +126,11 @@ jobs:
           if [ "$NIGHTLY_SHA" = "$MERGE_BASE_SHA" ]; then
             echo "The merge base of this PR coincides with the nightly release"
 
-            STD_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover/std4.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
+            BATTERIES_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/batteries.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
             MATHLIB_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/mathlib4.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
 
-            if [[ -n "$STD_REMOTE_TAGS" ]]; then
-              echo "... and Std has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
+            if [[ -n "$BATTERIES_REMOTE_TAGS" ]]; then
+              echo "... and Batteries has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
               MESSAGE=""
 
               if [[ -n "$MATHLIB_REMOTE_TAGS" ]]; then
@@ -140,8 +140,8 @@ jobs:
                 MESSAGE="- ❗ Mathlib CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Mathlib CI should run now."
               fi
             else
-              echo "... but Std does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
-              MESSAGE="- ❗ Std CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Std CI should run now."
+              echo "... but Batteries does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
+              MESSAGE="- ❗ Batteries CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Batteries CI should run now."
             fi
 
           else
@@ -151,7 +151,7 @@ jobs:
 
             git -C lean4.git fetch origin nightly-with-mathlib 
             NIGHTLY_WITH_MATHLIB_SHA="$(git -C lean4.git rev-parse "origin/nightly-with-mathlib")"
-            MESSAGE="- ❗ Std/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MATHLIB_SHA\`."
+            MESSAGE="- ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MATHLIB_SHA\`."
           fi
 
           if [[ -n "$MESSAGE" ]]; then
@@ -223,27 +223,27 @@ jobs:
               description: description,
             });
 
-      # We next automatically create a Std branch using this toolchain.
-      # Std doesn't itself have a mechanism to report results of CI from this branch back to Lean
-      # Instead this is taken care of by Mathlib CI, which will fail if Std fails.
+      # We next automatically create a Batteries branch using this toolchain.
+      # Batteries doesn't itself have a mechanism to report results of CI from this branch back to Lean
+      # Instead this is taken care of by Mathlib CI, which will fail if Batteries fails.
       - name: Cleanup workspace
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
         run: |
           sudo rm -rf ./*
 
-      # Checkout the Std repository with all branches
-      - name: Checkout Std repository
+      # Checkout the Batteries repository with all branches
+      - name: Checkout Batteries repository
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
         uses: actions/checkout@v3
         with:
-          repository: leanprover/std4
+          repository: leanprover-community/batteries
           token: ${{ secrets.MATHLIB4_BOT }}
           ref: nightly-testing
           fetch-depth: 0 # This ensures we check out all tags and branches.
 
       - name: Check if tag exists
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
-        id: check_std_tag
+        id: check_batteries_tag
         run: |
           git config user.name "leanprover-community-mathlib4-bot"
           git config user.email "leanprover-community-mathlib4-bot@users.noreply.github.com"
@@ -251,7 +251,7 @@ 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-${MOST_RECENT_NIGHTLY}' tag at Std. Falling back to 'nightly-testing'."
+            echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
             BASE=nightly-testing
           fi
 
@@ -268,7 +268,7 @@ jobs:
           else
             echo "Branch already exists, pushing an empty commit."
             git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
-            # The Std `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
+            # The Batteries `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
             # (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
             git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
             git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
@@ -321,7 +321,7 @@ jobs:
             git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
             echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
             git add lean-toolchain
-            sed -i "s/require std from git \"https:\/\/github.com\/leanprover\/std4\" @ \".\+\"/require std from git \"https:\/\/github.com\/leanprover\/std4\" @ \"nightly-testing-${MOST_RECENT_NIGHTLY}\"/" lakefile.lean
+            sed -i "s/require batteries from git \"https:\/\/github.com\/leanprover-community\/batteries\" @ \".\+\"/require batteries from git \"https:\/\/github.com\/leanprover-community\/batteries\" @ \"nightly-testing-${MOST_RECENT_NIGHTLY}\"/" lakefile.lean
             git add lakefile.lean
             git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           else

.github/workflows/restart-on-label.yml

@@ -0,0 +1,31 @@
+name: Restart by label
+on:
+  pull_request_target:
+    types:
+      - unlabeled
+      - labeled
+jobs:
+  restart-on-label:
+    runs-on: ubuntu-latest
+    if: contains(github.event.label.name, 'merge-ci') || contains(github.event.label.name, 'release-ci')
+    steps:
+    - run: |
+        # Finding latest CI workflow run on current pull request
+        # (unfortunately cannot search by PR number, only base branch,
+        # and that is't even unique given PRs from forks, but the risk
+        # of confusion is low and the danger is mild)
+        run_id=$(gh run list -e pull_request -b "$head_ref" --workflow 'CI' --limit 1 \
+          --limit 1 --json databaseId --jq '.[0].databaseId')
+        echo "Run id: ${run_id}"
+        gh run view "$run_id"
+        echo "Cancelling (just in case)"
+        gh run cancel "$run_id" || echo "(failed)"
+        echo "Waiting for 10s"
+        sleep 10
+        echo "Rerunning"
+        gh run rerun "$run_id"
+      shell: bash
+      env:
+        head_ref: ${{ github.head_ref }}
+        GH_TOKEN: ${{ github.token }}
+        GH_REPO: ${{ github.repository }}

CMakePresets.json

@@ -0,0 +1,83 @@
+{
+  "version": 2,
+  "cmakeMinimumRequired": {
+    "major": 3,
+    "minor": 10,
+    "patch": 0
+  },
+  "configurePresets": [
+    {
+      "name": "release",
+      "displayName": "Default development optimized build config",
+      "generator": "Unix Makefiles",
+      "binaryDir": "${sourceDir}/build/release"
+    },
+    {
+      "name": "debug",
+      "displayName": "Debug build config",
+      "cacheVariables": {
+        "CMAKE_BUILD_TYPE": "Debug"
+      },
+      "generator": "Unix Makefiles",
+      "binaryDir": "${sourceDir}/build/debug"
+    },
+    {
+      "name": "sanitize",
+      "displayName": "Sanitize build config",
+      "cacheVariables": {
+        "LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined",
+        "LEANC_EXTRA_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
+        "SMALL_ALLOCATOR": "OFF",
+        "BSYMBOLIC": "OFF"
+      },
+      "generator": "Unix Makefiles",
+      "binaryDir": "${sourceDir}/build/sanitize"
+    },
+    {
+      "name": "sandebug",
+      "inherits": ["debug", "sanitize"],
+      "displayName": "Sanitize+debug build config",
+      "binaryDir": "${sourceDir}/build/sandebug"
+    }
+  ],
+  "buildPresets": [
+    {
+      "name": "release",
+      "configurePreset": "release"
+    },
+    {
+      "name": "debug",
+      "configurePreset": "debug"
+    },
+    {
+      "name": "sanitize",
+      "configurePreset": "sanitize"
+    },
+    {
+      "name": "sandebug",
+      "configurePreset": "sandebug"
+    }
+  ],
+  "testPresets": [
+    {
+      "name": "release",
+      "configurePreset": "release",
+      "output": {"outputOnFailure": true, "shortProgress": true}
+    },
+    {
+      "name": "debug",
+      "configurePreset": "debug",
+      "inherits": "release"
+    },
+    {
+      "name": "sanitize",
+      "configurePreset": "sanitize",
+      "inherits": "release"
+    },
+    {
+      "name": "sandebug",
+      "configurePreset": "sandebug",
+      "inherits": "release"
+    }
+  ]
+}

RELEASES.md

@@ -1,145 +1,23 @@
 # Lean 4 releases
 
+This file contains release notes for each stable release.
+Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
+of each version.
+During development, drafts of future release notes appear in [`releases_drafts`](https://github.com/leanprover/lean4/tree/master/script).
+
 We intend to provide regular "minor version" releases of the Lean language at approximately monthly intervals.
 There is not yet a strong guarantee of backwards compatibility between versions,
 only an expectation that breaking changes will be documented in this file.
 
-This file contains work-in-progress notes for the upcoming release, as well as previous stable releases.
-Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
-of each version.
-
-v4.8.0 (development in progress)
+v4.9.0
 ---------
 
-* **Executables configured with `supportInterpreter := true` on Windows should now be run via `lake exe` to function properly.**
+Development in progress.
 
-  The way Lean is built on Windows has changed (see PR [#3601](https://github.com/leanprover/lean4/pull/3601)). 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`.
+v4.8.0
+---------
 
-  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.
-
-* Lean now generates an error if the type of a theorem is **not** a proposition.
-
-* 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).
-
-* Functional induction principles.
-
-  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`.
-
-* 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).
-  PR [#3089](https://github.com/leanprover/lean4/pull/3089).
-
-* Attribute `@[pp_using_anonymous_constructor]` to make structures pretty print like `⟨x, y, z⟩`
-  rather than `{a := x, b := y, c := z}`.
-  This attribute is applied to `Sigma`, `PSigma`, `PProd`, `Subtype`, `And`, and `Fin`.
-
-* 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.
-
-* 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.
-
-* Added 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.
-  [#3798](https://github.com/leanprover/lean4/pull/3798) and
-  [#3978](https://github.com/leanprover/lean4/pull/3978).
-
-* Hovers for terms in `match` expressions in the Infoview now reliably show the correct term.
-
-* Added `@[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`.
-  [#3629](https://github.com/leanprover/lean4/pull/3629),
-  [#3655](https://github.com/leanprover/lean4/pull/3655), and
-  [#3747](https://github.com/leanprover/lean4/pull/3747).
-
-* 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.
-  PR [#3883](https://github.com/leanprover/lean4/pull/3883).
-
-* The `#guard_msgs` command now supports showing 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.
-
-Breaking changes:
-
-* Automatically generated equational theorems are now named using suffix `.eq_<idx>` instead of `._eq_<idx>`, and `.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.def
-/-
-fact.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.
+Release candidate, release notes will be copied from branch `releases/v4.8.0` once completed.
 
 v4.7.0
 ---------

doc/BoolExpr.lean

@@ -1,4 +1,4 @@
-open Std
+open Batteries
 open Lean
 
 inductive BoolExpr where

doc/dev/bootstrap.md

@@ -84,10 +84,12 @@ gh workflow run update-stage0.yml
 Leaving stage0 updates to the CI automation is preferable, but should you need
 to do it locally, you can use `make update-stage0-commit` in `build/release` to
 update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to
-update from another stage.
+update from another stage. This command will automatically stage the updated files
+and introduce a commit,so make sure to commit your work before that.
 
-This command will automatically stage the updated files and introduce a commit,
-so make sure to commit your work before that.
+If you rebased the branch (either onto a newer version of `master`, or fixing
+up some commits prior to the stage0 update, recreate the stage0 update commits.
+The script `script/rebase-stage0.sh` can be used for that.
 
 The CI should prevent PRs with changes to stage0 (besides `stdlib_flags.h`)
 from entering `master` through the (squashing!) merge queue, and label such PRs
@@ -95,6 +97,7 @@ with the `changes-stage0` label. Such PRs should have a cleaned up history,
 with separate stage0 update commits; then coordinate with the admins to merge
 your PR using rebase merge, bypassing the merge queue.
 
+
 ## Further Bootstrapping Complications
 
 As written above, changes in meta code in the current stage usually will only

doc/dev/ffi.md

@@ -53,10 +53,59 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
   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`).
 * 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 respective declarations in `lean.h`) 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.
+  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.
 
   Example: the runtime value of `u : Unit` is always `lean_box(0)`.
 
+#### Inductive types
+
+For inductive types which are in the fallback `lean_object *` case above and not trivial constructors, the type is stored as a `lean_ctor_object`, and `lean_is_ctor` will return true. A `lean_ctor_object` stores the constructor index in the header, and the fields are stored in the `m_objs` portion of the object.
+
+The memory order of the fields is derived from the types and order of the fields in the declaration. They are ordered as follows:
+
+* Non-scalar fields stored as `lean_object *`
+* Fields of type `USize`
+* Other scalar fields, in decreasing order by size
+
+Within each group the fields are ordered in declaration order. **Warning**: Trivial wrapper types still count toward a field being treated as non-scalar for this purpose.
+
+* To access fields of the first kind, use `lean_ctor_get(val, i)` to get the `i`th non-scalar field.
+* To access `USize` fields, use `lean_ctor_get_usize(val, n+i)` to get the `i`th usize field and `n` is the total number of fields of the first kind.
+* To access other scalar fields, use `lean_ctor_get_uintN(val, off)` or `lean_ctor_get_usize(val, off)` as appropriate. Here `off` is the byte offset of the field in the structure, starting at `n*sizeof(void*)` where `n` is the number of fields of the first two kinds.
+
+For example, a structure such as
+```lean
+structure S where
+  ptr_1 : Array Nat
+  usize_1 : USize
+  sc64_1 : UInt64
+  ptr_2 : { x : UInt64 // x > 0 } -- wrappers don't count as scalars
+  sc64_2 : Float -- `Float` is 64 bit
+  sc8_1 : Bool
+  sc16_1 : UInt16
+  sc8_2 : UInt8
+  sc64_3 : UInt64
+  usize_2 : USize
+  ptr_3 : Char -- trivial wrapper around `UInt32`
+  sc32_1 : UInt32
+  sc16_2 : UInt16
+```
+would get re-sorted into the following memory order:
+
+* `S.ptr_1` - `lean_ctor_get(val, 0)`
+* `S.ptr_2` - `lean_ctor_get(val, 1)`
+* `S.ptr_3` - `lean_ctor_get(val, 2)`
+* `S.usize_1` - `lean_ctor_get_usize(val, 3)`
+* `S.usize_2` - `lean_ctor_get_usize(val, 4)`
+* `S.sc64_1` - `lean_ctor_get_uint64(val, sizeof(void*)*5)`
+* `S.sc64_2` - `lean_ctor_get_float(val, sizeof(void*)*5 + 8)`
+* `S.sc64_3` - `lean_ctor_get_uint64(val, sizeof(void*)*5 + 16)`
+* `S.sc32_1` - `lean_ctor_get_uint32(val, sizeof(void*)*5 + 24)`
+* `S.sc16_1` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 28)`
+* `S.sc16_2` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 30)`
+* `S.sc8_1` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 32)`
+* `S.sc8_2` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 33)`
+
 ### Borrowing
 
 By default, all `lean_object *` parameters of an `@[extern]` function are considered *owned*, i.e. the external code is passed a "virtual RC token" and is responsible for passing this token along to another consuming function (exactly once) or freeing it via `lean_dec`.

doc/dev/release_checklist.md

@@ -50,13 +50,13 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR
       - Create and push the tag
       - Merge the tag into `stable`
-    - [Std](https://github.com/leanprover-community/std4)
+    - [Batteries](https://github.com/leanprover-community/batteries)
       - No dependencies
       - Toolchain bump PR
       - Create and push the tag
       - Merge the tag into `stable`
     - [ProofWidgets4](https://github.com/leanprover-community/ProofWidgets4)
-      - Dependencies: `Std`
+      - Dependencies: `Batteries`
       - Note on versions and branches:
         - `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
           which does not refer to the toolchain being used.
@@ -65,7 +65,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Toolchain bump PR
       - Create and push the tag, following the version convention of the repository
     - [Aesop](https://github.com/leanprover-community/aesop)
-      - Dependencies: `Std`
+      - Dependencies: `Batteries`
       - Toolchain bump PR including updated Lake manifest
       - Create and push the tag
       - Merge the tag into `stable`
@@ -79,7 +79,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - Create and push the tag
       - There is no `stable` branch; skip this step
     - [Mathlib](https://github.com/leanprover-community/mathlib4)
-      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Std`, `doc-gen4`, `import-graph`
+      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Batteries`, `doc-gen4`, `import-graph`
       - Toolchain bump PR notes:
         - In addition to updating the `lean-toolchain` and `lakefile.lean`,
           in `.github/workflows/build.yml.in` in the `lean4checker` section update the line
@@ -123,8 +123,8 @@ 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 that Std and Mathlib already have reviewed branches compatible with this nightly.
-  - Check that both Std and Mathlib's `bump/v4.7.0` branch contain `nightly-2024-02-29`
+- 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`.
   - The steps required to reach that state are beyond the scope of this checklist, but see below!
 - Create the release branch from this nightly tag:
@@ -182,7 +182,7 @@ 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!
-  - For Std/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
+  - 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!
@@ -204,7 +204,7 @@ In particular, updating the downstream repositories is significantly more work
 # Preparing `bump/v4.7.0` branches
 
 While not part of the release process per se,
-this is a brief summary of the work that goes into updating Std/Aesop/Mathlib to new versions.
+this is a brief summary of the work that goes into updating Batteries/Aesop/Mathlib to new versions.
 
 Please read https://leanprover-community.github.io/contribute/tags_and_branches.html
 

doc/examples/test_single.sh

@@ -1,4 +1,4 @@
 #!/usr/bin/env bash
 source ../../tests/common.sh
 
-exec_check lean -j 0 -Dlinter.all=false "$f"
+exec_check lean -Dlinter.all=false "$f"

doc/latex/lean4.py

@@ -1,100 +0,0 @@
-# -*- coding: utf-8 -*-
-"""
-    pygments.lexers.theorem
-    ~~~~~~~~~~~~~~~~~~~~~~~
-
-    Lexers for theorem-proving languages.
-
-    :copyright: Copyright 2006-2017 by the Pygments team, see AUTHORS.
-    :license: BSD, see LICENSE for details.
-"""
-
-import re
-
-from pygments.lexer import RegexLexer, default, words
-from pygments.token import Text, Comment, Operator, Keyword, Name, String, \
-    Number, Punctuation, Generic
-
-__all__ = ['Lean4Lexer']
-
-class Lean4Lexer(RegexLexer):
-    """
-    For the `Lean 4 <https://github.com/leanprover/lean4>`_
-    theorem prover.
-
-    .. versionadded:: 2.0
-    """
-    name = 'Lean4'
-    aliases = ['lean4']
-    filenames = ['*.lean']
-    mimetypes = ['text/x-lean']
-
-    flags = re.MULTILINE | re.UNICODE
-
-    keywords1 = (
-        'import', 'abbreviation', 'opaque_hint', 'tactic_hint', 'definition',
-        'renaming', 'inline', 'hiding', 'parameter', 'lemma', 'variable',
-        'theorem', 'axiom', 'inductive', 'structure', 'universe', 'alias',
-        'help', 'options', 'precedence', 'postfix', 'prefix',
-        'infix', 'infixl', 'infixr', 'notation', '#eval',
-        '#check', '#reduce', '#exit', 'coercion', 'end', 'private', 'using', 'namespace',
-        'including', 'instance', 'section', 'context', 'protected', 'expose',
-        'export', 'set_option', 'extends', 'open', 'example',
-        'constant', 'constants', 'print', 'opaque', 'reducible', 'irreducible',
-        'def', 'macro', 'elab', 'syntax', 'macro_rules', 'reduce', 'where',
-        'abbrev', 'noncomputable', 'class', 'attribute', 'synth', 'mutual',
-    )
-
-    keywords2 = (
-        'forall', 'fun', 'Pi', 'obtain', 'from', 'have', 'show', 'assume',
-        'take', 'let', 'if', 'else', 'then', 'by', 'in', 'with', 'begin',
-        'proof', 'qed', 'calc', 'match', 'nomatch', 'do', 'at',
-    )
-
-    keywords3 = (
-        # Sorts
-        'Type', 'Prop', 'Sort',
-    )
-
-    operators = (
-        u'!=', u'#', u'&', u'&&', u'*', u'+', u'-', u'/', u'@', u'!', u'`',
-        u'-.', u'->', u'.', u'..', u'...', u'::', u':>', u';', u';;', u'<',
-        u'<-', u'=', u'==', u'>', u'_', u'|', u'||', u'~', u'=>', u'<=', u'>=',
-        u'/\\', u'\\/', u'∀', u'Π', u'λ', u'↔', u'∧', u'∨', u'≠', u'≤', u'≥',
-        u'¬', u'⁻¹', u'⬝', u'▸', u'→', u'∃', u'ℕ', u'ℤ', u'≈', u'×', u'⌞',
-        u'⌟', u'≡', u'⟨', u'⟩',
-    )
-
-    punctuation = (u'(', u')', u':', u'{', u'}', u'[', u']', u'⦃', u'⦄',
-                   u':=', u',')
-
-    tokens = {
-        'root': [
-            (r'\s+', Text),
-            (r'/-', Comment, 'comment'),
-            (r'--.*?$', Comment.Single),
-            (words(keywords1, prefix=r'\b', suffix=r'\b'), Keyword.Namespace),
-            (words(keywords2, prefix=r'\b', suffix=r'\b'), Keyword),
-            (words(keywords3, prefix=r'\b', suffix=r'\b'), Keyword.Type),
-            (words(operators), Name.Builtin.Pseudo),
-            (words(punctuation), Operator),
-            (u"[A-Za-z_\u03b1-\u03ba\u03bc-\u03fb\u1f00-\u1ffe\u2100-\u214f]"
-             u"[A-Za-z_'\u03b1-\u03ba\u03bc-\u03fb\u1f00-\u1ffe\u2070-\u2079"
-             u"\u207f-\u2089\u2090-\u209c\u2100-\u214f0-9]*", Name),
-            (r'\d+', Number.Integer),
-            (r'"', String.Double, 'string'),
-            (r'[~?][a-z][\w\']*:', Name.Variable)
-        ],
-        'comment': [
-            # Multiline Comments
-            (r'[^/-]', Comment.Multiline),
-            (r'/-', Comment.Multiline, '#push'),
-            (r'-/', Comment.Multiline, '#pop'),
-            (r'[/-]', Comment.Multiline)
-        ],
-        'string': [
-            (r'[^\\"]+', String.Double),
-            (r'\\[n"\\]', String.Escape),
-            ('"', String.Double, '#pop'),
-        ],
-    }

doc/make/index.md

@@ -1,3 +1,7 @@
+These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](doc/dev/index.md).
+
+We strongly suggest that new users instead follow the [Quickstart](doc/quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
+
 Requirements
 ------------
 
@@ -17,39 +21,27 @@ Platform-Specific Setup
 Generic Build Instructions
 --------------------------
 
-Setting up a basic release build:
+Setting up a basic parallelized release build:
 
 ```bash
-git clone https://github.com/leanprover/lean4 --recurse-submodules
+git clone https://github.com/leanprover/lean4
 cd lean4
-mkdir -p build/release
-cd build/release
-cmake ../..
-make
+cmake --preset release
+make -C build/release -j$(nproc)  # see below for macOS
 ```
-
-For regular development, we recommend running
-```bash
-git config submodule.recurse true
-```
-in the checkout so that `--recurse-submodules` doesn't have to be
-specified with `git pull/checkout/...`.
+You can replace `$(nproc)`, which is not available on macOS and some alternative shells, with the desired parallelism amount.
 
 The above commands will compile the Lean library and binaries into the
-`stage1` subfolder; see below for details. Add `-j N` for an
-appropriate `N` to `make` for a parallel build.
+`stage1` subfolder; see below for details.
 
-For example, on an AMD Ryzen 9 `make` takes 00:04:55, whereas `make -j 10`
-takes 00:01:38.  Your results may vary depending on the speed of your hard
-drive.
-
-You should not usually run `make install` after a successful build.
+You should not usually run `cmake --install` after a successful build.
 See [Dev setup using elan](../dev/index.md#dev-setup-using-elan) on how to properly set up your editor to use the correct stage depending on the source directory.
 
 Useful CMake Configuration Settings
 -----------------------------------
 
-Pass these along with the `cmake ../..` command.
+Pass these along with the `cmake --preset release` command.
+There are also two alternative presets that combine some of these options you can use instead of `release`: `debug` and `sandebug` (sanitize + debug).
 
 * `-D CMAKE_BUILD_TYPE=`\
   Select the build type. Valid values are `RELEASE` (default), `DEBUG`,

doc/make/msvc.md

@@ -1,39 +0,0 @@
-# Compiling Lean with Visual Studio
-
-WARNING: Compiling Lean with Visual Studio doesn't currently work.
-There's an ongoing effort to port Lean to Visual Studio.
-The instructions below are for VS 2017.
-
-In the meantime you can use [MSYS2](msys2.md) or [WSL](wsl.md).
-
-## Installing dependencies
-
-First, install `vcpkg` from https://github.com/Microsoft/vcpkg if you haven't
-done so already.
-Then, open a console in the directory you cloned `vcpkg` to, and type:
-`vcpkg install mpir` for the 32-bit library or
-`vcpkg install mpir:x64-windows` for the x64 one.
-
-In Visual Studio, use the "open folder" feature and open the Lean directory.
-Go to the `CMake->Change CMake Settings` menu. File `CMakeSettings.json` opens.
-In each of the targets, add the following snippet (i.e., after every
-`ctestCommandArgs`):
-
-```json
-    "variables": [
-      {
-        "name": "CMAKE_TOOLCHAIN_FILE",
-        "value": "C:\\path\\to\\vcpkg\\scripts\\buildsystems\\vcpkg.cmake"
-      }
-    ]
-```
-
-## Enable Intellisense
-
-In Visual Studio, press Ctrl+Q and type `CppProperties.json` and press Enter.
-Ensure `includePath` variables include `"${workspaceRoot}\\src"`.
-
-
-## Build Lean
-
-Press F7.

doc/make/msys2.md

@@ -38,10 +38,9 @@ cmake --version
 Then follow the [generic build instructions](index.md) in the MSYS2
 MinGW shell, using:
 ```
-cmake ../.. -G "Unix Makefiles"  -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
+cmake --preset release -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
 ```
-instead of `cmake ../..`. This ensures that cmake will call `sh` instead of `cmd.exe`
-for script tasks and it will use the clang compiler instead of gcc, which is required.
+instead of `cmake --preset release`. This will use the clang compiler instead of gcc, which is required with msys2.
 
 ## Install lean
 

doc/monads/states.lean

@@ -15,7 +15,7 @@ data type containing several important pieces of information. First and foremost
 current player, and it has a random generator.
 -/
 
-open Std (HashMap)
+open Batteries (HashMap)
 abbrev TileIndex := Nat × Nat -- a 2D index
 
 inductive TileState where

doc/setup.md

@@ -6,6 +6,7 @@ Platforms built & tested by our CI, available as binary releases via elan (see b
 
 * x86-64 Linux with glibc 2.27+
 * x86-64 macOS 10.15+
+* aarch64 (Apple Silicon) macOS 10.15+
 * x86-64 Windows 10+
 
 ### Tier 2
@@ -16,7 +17,6 @@ Releases may be silently broken due to the lack of automated testing.
 Issue reports and fixes are welcome.
 
 * aarch64 Linux with glibc 2.27+
-* aarch64 (Apple Silicon) macOS
 * x86 (32-bit) Linux
 * Emscripten Web Assembly
 

doc/syntax_highlight_in_latex.md

@@ -43,7 +43,8 @@ $ pdflatex test.tex
 
 ## Example with `minted`
 
-First [install Pygments](https://pygments.org/download/). Then save [`lean4.py`](https://raw.githubusercontent.com/leanprover/lean4/master/doc/latex/lean4.py), which contains an version of the Lean highlighter updated for Lean 4, and the following sample LaTeX file `test.tex` into the same directory:
+First [install Pygments](https://pygments.org/download/) (version 2.18 or newer).
+Then save the following sample LaTeX file `test.tex` into the same directory:
 
 ```latex
 \documentclass{article}
@@ -51,9 +52,8 @@ First [install Pygments](https://pygments.org/download/). Then save [`lean4.py`]
 % switch to a monospace font supporting more Unicode characters
 \setmonofont{FreeMono}
 \usepackage{minted}
-% instruct minted to use our local theorem.py
-\newmintinline[lean]{lean4.py:Lean4Lexer -x}{bgcolor=white}
-\newminted[leancode]{lean4.py:Lean4Lexer -x}{fontsize=\footnotesize}
+\newmintinline[lean]{lean4}{bgcolor=white}
+\newminted[leancode]{lean4}{fontsize=\footnotesize}
 \usemintedstyle{tango}  % a nice, colorful theme
 
 \begin{document}
@@ -67,9 +67,6 @@ theorem funext {f₁ f₂ : ∀ (x : α), β x} (h : ∀ x, f₁ x = f₂ x) : f
 \end{document}
 ```
 
-If your version of `minted` is v2.7 or newer, but before v3.0,
-you will additionally need to follow the workaround described in https://github.com/gpoore/minted/issues/360.
-
 You can then compile `test.tex` by executing the following command:
 
 ```bash
@@ -81,11 +78,14 @@ Some remarks:
  - either `xelatex` or `lualatex` is required to handle Unicode characters in the code.
  - `--shell-escape` is needed to allow `xelatex` to execute `pygmentize` in a shell.
  - If the chosen monospace font is missing some Unicode symbols, you can direct them to be displayed using a fallback font or other replacement LaTeX code.
-``` latex
-\usepackage{newunicodechar}
-\newfontfamily{\freeserif}{DejaVu Sans}
-\newunicodechar{✝}{\freeserif{✝}}
-\newunicodechar{𝓞}{\ensuremath{\mathcal{O}}}
-```
- - minted has a "helpful" feature that draws red boxes around characters the chosen lexer doesn't recognize.
- Since the Lean lexer cannot encompass all user-defined syntax, it is advisable to [work around](https://tex.stackexchange.com/a/343506/14563) this feature.
+   ``` latex
+   \usepackage{newunicodechar}
+   \newfontfamily{\freeserif}{DejaVu Sans}
+   \newunicodechar{✝}{\freeserif{✝}}
+   \newunicodechar{𝓞}{\ensuremath{\mathcal{O}}}
+   ```
+ - If you are using an old version of Pygments, you can copy 
+   [`lean.py`](https://raw.githubusercontent.com/pygments/pygments/master/pygments/lexers/lean.py) into your working directory,
+   and use `lean4.py:Lean4Lexer -x` instead of `lean4` above.
+   If your version of `minted` is v2.7 or newer, but before v3.0,
+   you will additionally need to follow the workaround described in https://github.com/gpoore/minted/issues/360.

nix/bootstrap.nix

@@ -170,7 +170,7 @@ rec {
           ln -sf ${lean-all}/* .
         '';
         buildPhase = ''
-          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)' -j$NIX_BUILD_CORES
+          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_init' -j$NIX_BUILD_CORES
         '';
         installPhase = ''
           mkdir $out
@@ -180,7 +180,7 @@ rec {
       update-stage0 =
         let cTree = symlinkJoin { name = "cs"; paths = [ Init.cTree Lean.cTree ]; }; in
         writeShellScriptBin "update-stage0" ''
-          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/update-stage0"}
+          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
         '';
       update-stage0-commit = writeShellScriptBin "update-stage0-commit" ''
         set -euo pipefail

releases_drafts/README.md

@@ -0,0 +1,22 @@
+Draft release notes
+-------------------
+
+This folder contains drafts of release notes for inclusion in `RELEASES.md`.
+During the process to create a release candidate, we look through all the commits that make up the release
+to prepare the release notes, and in that process we take these drafts into account.
+
+Guidelines:
+- You should prefer adding release notes to commit messages over adding anything to this folder.
+  A release note should briefly explain the impact of a change from a user's point of view.
+  Please mark these parts out with words such as **release notes** and/or **breaking changes**.
+- It is not necessary to add anything to this folder. It is meant for larger features that span multiple PRs,
+  or for anything that would be helpful when preparing the release notes that might be missed
+  by someone reading through the change log.
+- If the PR that adds a feature simultaneously adds a draft release note, including the PR number is not required
+  since it can be obtained from the git history for the file.
+
+When release notes are prepared, all the draft release notes are deleted from this folder.
+For release candidates beyond the first one, you can either update `RELEASE.md` directly
+or continue to add drafts.
+
+When a release is finalized, we will copy the completed release notes from `RELEASE.md` to the `master` branch.

releases_drafts/messagedata.md

@@ -0,0 +1,13 @@
+* 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`.
+
+part of #3929

releases_drafts/wf.md

@@ -0,0 +1,12 @@
+Functions defined by well-founded recursion are now marked as
+`@[irreducible]`, which should prevent expensive and often unfruitful
+unfolding of such definitions.
+
+Existing proofs that hold by definitional equality (e.g. `rfl`) can be
+rewritten to explictly unfold the function definition (using `simp`,
+`unfold`, `rw`), or the recursive function can be temporariliy made
+semireducible (using `unseal f in` before the command) or the function
+definition itself can be marked as `@[semireducible]` to get the previous
+behavor.
+
+#4061

script/github-issues-fro.py

@@ -0,0 +1,180 @@
+#!/usr/bin/env python3
+
+import subprocess
+import sys
+import json
+from datetime import datetime, timedelta
+from urllib.parse import urlencode
+import argparse
+import calendar
+import time
+import statistics
+
+# Reminder: Ensure you have `gh` CLI installed and authorized before running this script.
+# Follow instructions from https://cli.github.com/ to set up `gh` and ensure it is authorized.
+
+LABELS = ["bug", "feature", "RFC", "new-user-papercuts", "Lake"]
+
+def get_items(query):
+    items = []
+    page = 1
+    base_url = 'https://api.github.com/search/issues'
+    retries = 0
+    max_retries = 5
+    while True:
+        params = {'q': query, 'per_page': 100, 'page': page}
+        url = f"{base_url}?{urlencode(params)}"
+        # print(f"Fetching page {page} from URL: {url}")
+        try:
+            result = subprocess.run(['gh', 'api', url], capture_output=True, text=True)
+            data = json.loads(result.stdout)
+            if 'items' in data:
+                items.extend(data['items'])
+            elif 'message' in data and 'rate limit' in data['message'].lower():
+                if retries < max_retries:
+                    wait_time = (2 ** retries) * 60  # Exponential backoff
+                    time.sleep(wait_time)
+                    retries += 1
+                    continue
+                else:
+                    print("Max retries exceeded. Exiting.")
+                    break
+            else:
+                print(f"Error fetching data: {data}")
+                break
+            if len(data['items']) < 100:
+                break
+            page += 1
+        except Exception as e:
+            print(f"Error fetching data: {e}")
+            print(result.stdout)  # Print the JSON output for debugging
+            break
+    return items
+
+def get_fro_team_members():
+    try:
+        result = subprocess.run(['gh', 'api', '-H', 'Accept: application/vnd.github.v3+json', '/orgs/leanprover/teams/fro/members'], capture_output=True, text=True)
+        members = json.loads(result.stdout)
+        return [member['login'] for member in members]
+    except Exception as e:
+        print(f"Error fetching team members: {e}")
+        return []
+
+def calculate_average_time_to_close(closed_items):
+    times_to_close = [(datetime.strptime(item['closed_at'], '%Y-%m-%dT%H:%M:%SZ') - datetime.strptime(item['created_at'], '%Y-%m-%dT%H:%M:%SZ')).days for item in closed_items]
+    average_time_to_close = sum(times_to_close) / len(times_to_close) if times_to_close else 0
+    return average_time_to_close
+
+def parse_dates(date_args):
+    if len(date_args) == 2:
+        start_date = date_args[0]
+        end_date = date_args[1]
+    elif len(date_args) == 1:
+        if len(date_args[0]) == 7:  # YYYY-MM format
+            year, month = map(int, date_args[0].split('-'))
+            start_date = f"{year}-{month:02d}-01"
+            end_date = f"{year}-{month:02d}-{calendar.monthrange(year, month)[1]}"
+        elif len(date_args[0]) == 4:  # YYYY format
+            year = int(date_args[0])
+            start_date = f"{year}-07-01"
+            end_date = f"{year+1}-06-30"
+        elif len(date_args[0]) == 6 and date_args[0][4] == 'Q':  # YYYYQn format
+            year = int(date_args[0][:4])
+            quarter = int(date_args[0][5])
+            if quarter == 1:
+                start_date = f"{year}-01-01"
+                end_date = f"{year}-03-31"
+            elif quarter == 2:
+                start_date = f"{year}-04-01"
+                end_date = f"{year}-06-30"
+            elif quarter == 3:
+                start_date = f"{year}-07-01"
+                end_date = f"{year}-09-30"
+            elif quarter == 4:
+                start_date = f"{year}-10-01"
+                end_date = f"{year}-12-31"
+            else:
+                raise ValueError("Invalid quarter format")
+        else:
+            raise ValueError("Invalid date format")
+    else:
+        raise ValueError("Invalid number of date arguments")
+
+    return start_date, end_date
+
+def split_date_range(start_date, end_date):
+    start = datetime.strptime(start_date, '%Y-%m-%d')
+    end = datetime.strptime(end_date, '%Y-%m-%d')
+    date_ranges = []
+
+    # Splitting into month-long windows to work around the GitHub search 1000 result limit.
+    while start <= end:
+        month_end = start + timedelta(days=calendar.monthrange(start.year, start.month)[1] - start.day)
+        month_end = min(month_end, end)
+        date_ranges.append((start.strftime('%Y-%m-%d'), month_end.strftime('%Y-%m-%d')))
+        start = month_end + timedelta(days=1)
+
+    return date_ranges
+
+def main():
+    parser = argparse.ArgumentParser(description="Fetch and count GitHub issues assigned to fro team members between two dates.")
+    parser.add_argument("dates", type=str, nargs='+', help="Start and end dates in YYYY-MM-DD, YYYY-MM, YYYY-Qn, or YYYY format")
+
+    args = parser.parse_args()
+    start_date, end_date = parse_dates(args.dates)
+
+    repo = "leanprover/lean4"
+
+    date_ranges = split_date_range(start_date, end_date)
+
+    fro_members = get_fro_team_members()
+    fro_members.append("unassigned")  # Add "unassigned" for issues with no assignee
+
+    label_headers = ", ".join([f"MTTR ({label})" for label in LABELS])
+    print(f"# username, open issues, new issues, closed issues, MTTR (all), {label_headers}")
+
+    for member in fro_members:
+        open_issues_count = 0
+        new_issues_count = 0
+        closed_issues_count = 0
+        total_time_to_close_issues = 0
+        closed_issues = []
+        label_times = {label: [] for label in LABELS}
+
+        for start, end in date_ranges:
+            if member == "unassigned":
+                open_issues_query1 = f'repo:{repo} is:issue no:assignee state:open created:<={end}'
+                open_issues_query2 = f'repo:{repo} is:issue no:assignee state:closed created:<={end} closed:>{end}'
+                new_issues_query = f'repo:{repo} is:issue no:assignee created:{start}..{end}'
+                closed_issues_query = f'repo:{repo} is:issue no:assignee closed:{start}..{end}'
+            else:
+                open_issues_query1 = f'repo:{repo} is:issue assignee:{member} state:open created:<={end}'
+                open_issues_query2 = f'repo:{repo} is:issue assignee:{member} state:closed created:<={end} closed:>{end}'
+                new_issues_query = f'repo:{repo} is:issue assignee:{member} created:{start}..{end}'
+                closed_issues_query = f'repo:{repo} is:issue assignee:{member} closed:{start}..{end}'
+
+            open_issues1 = get_items(open_issues_query1)
+            open_issues2 = get_items(open_issues_query2)
+            new_issues = get_items(new_issues_query)
+            closed_issues_period = get_items(closed_issues_query)
+
+            open_issues_count = len(open_issues1) + len(open_issues2)
+            new_issues_count += len(new_issues)
+            closed_issues_count += len(closed_issues_period)
+            closed_issues.extend(closed_issues_period)
+
+            for issue in closed_issues_period:
+                time_to_close = (datetime.strptime(issue['closed_at'], '%Y-%m-%dT%H:%M:%SZ') - datetime.strptime(issue['created_at'], '%Y-%m-%dT%H:%M:%SZ')).days
+                total_time_to_close_issues += time_to_close
+                for label in LABELS:
+                    if label in [l['name'] for l in issue['labels']]:
+                        label_times[label].append(time_to_close)
+
+        average_time_to_close_issues = total_time_to_close_issues / closed_issues_count if closed_issues_count else 0
+        label_averages = {label: (sum(times) / len(times)) if times else 0 for label, times in label_times.items()}
+
+        label_averages_str = ", ".join([f"{label_averages[label]:.2f}" for label in LABELS])
+        print(f"{member},{open_issues_count},{new_issues_count},{closed_issues_count},{average_time_to_close_issues:.2f},{label_averages_str}")
+
+if __name__ == "__main__":
+    main()

script/github-metrics.py

@@ -0,0 +1,163 @@
+#!/usr/bin/env python3
+
+import subprocess
+import sys
+import json
+from datetime import datetime, timedelta
+from urllib.parse import urlencode
+import argparse
+import calendar
+import time
+
+# Reminder: Ensure you have `gh` CLI installed and authorized before running this script.
+# Follow instructions from https://cli.github.com/ to set up `gh` and ensure it is authorized.
+
+def get_items(query):
+    items = []
+    page = 1
+    base_url = 'https://api.github.com/search/issues'
+    retries = 0
+    max_retries = 5
+    while True:
+        params = {'q': query, 'per_page': 100, 'page': page}
+        url = f"{base_url}?{urlencode(params)}"
+        # print(f"Fetching page {page} from URL: {url}")
+        try:
+            result = subprocess.run(['gh', 'api', url], capture_output=True, text=True)
+            data = json.loads(result.stdout)
+            if 'items' in data:
+                items.extend(data['items'])
+            elif 'message' in data and 'rate limit' in data['message'].lower():
+                if retries < max_retries:
+                    wait_time = (2 ** retries) * 60  # Exponential backoff
+                    print(f"Rate limit exceeded. Retrying in {wait_time} seconds...")
+                    time.sleep(wait_time)
+                    retries += 1
+                    continue
+                else:
+                    print("Max retries exceeded. Exiting.")
+                    break
+            else:
+                print(f"Error fetching data: {data}")
+                break
+            if len(data['items']) < 100:
+                break
+            page += 1
+        except Exception as e:
+            print(f"Error fetching data: {e}")
+            print(result.stdout)  # Print the JSON output for debugging
+            break
+    return items
+
+def calculate_average_time_to_close(closed_items):
+    times_to_close = [(datetime.strptime(item['closed_at'], '%Y-%m-%dT%H:%M:%SZ') - datetime.strptime(item['created_at'], '%Y-%m-%dT%H:%M:%SZ')).days for item in closed_items]
+    average_time_to_close = sum(times_to_close) / len(times_to_close) if times_to_close else 0
+    return average_time_to_close
+
+def parse_dates(date_args):
+    if len(date_args) == 2:
+        start_date = date_args[0]
+        end_date = date_args[1]
+    elif len(date_args) == 1:
+        if len(date_args[0]) == 7:  # YYYY-MM format
+            year, month = map(int, date_args[0].split('-'))
+            start_date = f"{year}-{month:02d}-01"
+            end_date = f"{year}-{month:02d}-{calendar.monthrange(year, month)[1]}"
+        elif len(date_args[0]) == 4:  # YYYY format
+            year = int(date_args[0])
+            start_date = f"{year}-07-01"
+            end_date = f"{year+1}-06-30"
+        elif len(date_args[0]) == 6 and date_args[0][4] == 'Q':  # YYYYQn format
+            year = int(date_args[0][:4])
+            quarter = int(date_args[0][5])
+            if quarter == 1:
+                start_date = f"{year}-01-01"
+                end_date = f"{year}-03-31"
+            elif quarter == 2:
+                start_date = f"{year}-04-01"
+                end_date = f"{year}-06-30"
+            elif quarter == 3:
+                start_date = f"{year}-07-01"
+                end_date = f"{year}-09-30"
+            elif quarter == 4:
+                start_date = f"{year}-10-01"
+                end_date = f"{year}-12-31"
+            else:
+                raise ValueError("Invalid quarter format")
+        else:
+            raise ValueError("Invalid date format")
+    else:
+        raise ValueError("Invalid number of date arguments")
+
+    return start_date, end_date
+
+def split_date_range(start_date, end_date):
+    start = datetime.strptime(start_date, '%Y-%m-%d')
+    end = datetime.strptime(end_date, '%Y-%m-%d')
+    date_ranges = []
+
+    # Splitting into month-long windows to work around the GitHub search 1000 result limit.
+    while start <= end:
+        month_end = start + timedelta(days=calendar.monthrange(start.year, start.month)[1] - start.day)
+        month_end = min(month_end, end)
+        date_ranges.append((start.strftime('%Y-%m-%d'), month_end.strftime('%Y-%m-%d')))
+        start = month_end + timedelta(days=1)
+
+    return date_ranges
+
+def main():
+    parser = argparse.ArgumentParser(description="Fetch and count GitHub issues and pull requests between two dates.")
+    parser.add_argument("dates", type=str, nargs='+', help="Start and end dates in YYYY-MM-DD, YYYY-MM, YYYY-Qn, or YYYY format")
+
+    args = parser.parse_args()
+    start_date, end_date = parse_dates(args.dates)
+
+    repo = "leanprover/lean4"
+
+    date_ranges = split_date_range(start_date, end_date)
+
+    open_issues_count = 0
+    opened_issues_count = 0
+    closed_issues_count = 0
+    total_time_to_close_issues = 0
+    open_prs_count = 0
+    closed_but_not_merged_prs_count = 0
+    merged_prs_count = 0
+
+    for start, end in date_ranges:
+        open_issues_query1 = f'repo:{repo} is:issue state:open created:<={end}'
+        open_issues_query2 = f'repo:{repo} is:issue state:closed created:<={end} closed:>{end}'
+        opened_issues_query = f'repo:{repo} is:issue created:{start}..{end}'
+        closed_issues_query = f'repo:{repo} is:issue closed:{start}..{end}'
+
+        open_prs_query1 = f'repo:{repo} is:pr state:open created:<={end}'
+        open_prs_query2 = f'repo:{repo} is:pr state:closed created:<={end} closed:>{end}'
+        closed_but_not_merged_prs_query = f'repo:{repo} is:pr state:closed is:unmerged closed:{start}..{end}'
+        merged_prs_query = f'repo:{repo} is:pr is:merged closed:{start}..{end}'
+
+        open_issues1 = get_items(open_issues_query1)
+        open_issues2 = get_items(open_issues_query2)
+        opened_issues = get_items(opened_issues_query)
+        closed_issues = get_items(closed_issues_query)
+
+        open_prs1 = get_items(open_prs_query1)
+        open_prs2 = get_items(open_prs_query2)
+        closed_but_not_merged_prs = get_items(closed_but_not_merged_prs_query)
+        merged_prs = get_items(merged_prs_query)
+
+        open_issues_count = len(open_issues1) + len(open_issues2)
+        opened_issues_count += len(opened_issues)
+        closed_issues_count += len(closed_issues)
+        total_time_to_close_issues += sum((datetime.strptime(item['closed_at'], '%Y-%m-%dT%H:%M:%SZ') - datetime.strptime(item['created_at'], '%Y-%m-%dT%H:%M:%SZ')).days for item in closed_issues)
+
+        open_prs_count = len(open_prs1) + len(open_prs2)
+        closed_but_not_merged_prs_count += len(closed_but_not_merged_prs)
+        merged_prs_count += len(merged_prs)
+
+    average_time_to_close_issues = total_time_to_close_issues / closed_issues_count if closed_issues_count else 0
+
+    print("# open issues, opened issues, closed issues, average age of closed issues, open PRs, closed PRs, merged PRs")
+    print(f"{open_issues_count},{opened_issues_count},{closed_issues_count},{average_time_to_close_issues:.2f},{open_prs_count},{closed_but_not_merged_prs_count},{merged_prs_count}")
+
+if __name__ == "__main__":
+    main()

script/lib/README.md

@@ -0,0 +1,2 @@
+This directory contains various scripts that are *not* meant to be called
+directly, but through other scripts or makefiles.

script/lib/rebase-editor.sh

@@ -0,0 +1,19 @@
+#!/usr/bin/env bash
+
+
+# Script internal to `./script/rebase-stage0.sh`
+
+# Determine OS type for sed in-place editing
+SED_CMD=("sed" "-i")
+if [[ "$OSTYPE" == "darwin"* ]]
+then
+    # macOS requires an empty string argument with -i for in-place editing
+    SED_CMD=("sed" "-i" "")
+fi
+
+if [ "$STAGE0_WITH_NIX" = true ]
+then
+  "${SED_CMD[@]}" '/chore: update stage0/ s,.*,x nix run .#update-stage0-commit,' "$1"
+else
+  "${SED_CMD[@]}" '/chore: update stage0/ s,.*,x make -j32 -C build/release update-stage0 \&\& git commit -m "chore: update stage0",' "$1"
+fi

script/rebase-stage0.sh

@@ -0,0 +1,24 @@
+#!/usr/bin/env bash
+
+# This script rebases onto the given branch/commit, and updates
+# all `chore: update stage0` commits along the way.
+
+# Whether to use nix or make to update stage0
+if [ "$1" = "-nix" ]
+then
+   export STAGE0_WITH_NIX=true
+   shift
+fi
+
+# Check if an argument is provided
+if [ "$#" -eq 0 ]; then
+    echo "Usage: $0 [-nix] <options to git rebase -i>"
+    exit 1
+fi
+
+REPO_ROOT=$(git rev-parse --show-toplevel)
+
+# Run git rebase in interactive mode, but automatically edit the todo list
+# using the defined GIT_SEQUENCE_EDITOR command
+GIT_SEQUENCE_EDITOR="$REPO_ROOT/script/lib/rebase-editor.sh" git rebase -i "$@"
+

src/CMakeLists.txt

@@ -9,7 +9,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 8)
+set(LEAN_VERSION_MINOR 9)
 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'")
@@ -591,7 +591,7 @@ endif()
 
 if(PREV_STAGE)
   add_custom_target(update-stage0
-    COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/update-stage0'
+    COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/lib/update-stage0'
     DEPENDS make_stdlib
     WORKING_DIRECTORY "${LEAN_SOURCE_DIR}/..")
 

src/Init.lean

@@ -34,3 +34,4 @@ import Init.BinderPredicates
 import Init.Ext
 import Init.Omega
 import Init.MacroTrace
+import Init.Grind

src/Init/ByCases.lean

@@ -63,3 +63,16 @@ theorem ite_some_none_eq_none [Decidable P] :
 @[simp] theorem ite_some_none_eq_some [Decidable P] :
     (if P then some x else none) = some y ↔ P ∧ x = y := by
   split <;> simp_all
+
+-- This is not marked as `simp` as it is already handled by `dite_eq_right_iff`.
+theorem dite_some_none_eq_none [Decidable P] {x : P → α} :
+    (if h : P then some (x h) else none) = none ↔ ¬P := by
+  simp only [dite_eq_right_iff]
+  rfl
+
+@[simp] theorem dite_some_none_eq_some [Decidable P] {x : P → α} {y : α} :
+    (if h : P then some (x h) else none) = some y ↔ ∃ h : P, x h = y := by
+  by_cases h : P <;> simp only [h, dite_cond_eq_true, dite_cond_eq_false, Option.some.injEq,
+    false_iff, not_exists]
+  case pos => exact ⟨fun h_eq ↦ Exists.intro h h_eq, fun h_exists => h_exists.2⟩
+  case neg => exact fun h_false _ ↦ h_false

src/Init/Core.lean

@@ -1114,9 +1114,6 @@ theorem eta (a : {x // p x}) (h : p (val a)) : mk (val a) h = a := by
   cases a
   exact rfl
 
-instance {α : Type u} {p : α → Prop} {a : α} (h : p a) : Inhabited {x // p x} where
-  default := ⟨a, h⟩
-
 instance {α : Type u} {p : α → Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
   fun ⟨a, h₁⟩ ⟨b, h₂⟩ =>
     if h : a = b then isTrue (by subst h; exact rfl)

src/Init/Data/Array/Basic.lean

@@ -44,7 +44,7 @@ instance : EmptyCollection (Array α) := ⟨Array.empty⟩
 instance : Inhabited (Array α) where
   default := Array.empty
 
-def isEmpty (a : Array α) : Bool :=
+@[simp] def isEmpty (a : Array α) : Bool :=
   a.size = 0
 
 def singleton (v : α) : Array α :=
@@ -53,7 +53,7 @@ def singleton (v : α) : Array α :=
 /-- Low-level version of `fget` which is as fast as a C array read.
    `Fin` values are represented as tag pointers in the Lean runtime. Thus,
    `fget` may be slightly slower than `uget`. -/
-@[extern "lean_array_uget"]
+@[extern "lean_array_uget", simp]
 def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
   a[i.toNat]
 
@@ -733,17 +733,15 @@ def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
   if h : i.val + 1 < a.size then
     let a' := a.swap ⟨i.val + 1, h⟩ i
     let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
-    have : a'.size - i' < a.size - i := by
-      simp [a', Nat.sub_succ_lt_self _ _ i.isLt]
     a'.feraseIdx i'
   else
     a.pop
 termination_by a.size - i.val
-decreasing_by simp_wf; decreasing_trivial_pre_omega
+decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
 
 theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
   induction a, i using Array.feraseIdx.induct with
-  | @case1 a i h a' _ _ ih =>
+  | @case1 a i h a' _ ih =>
     unfold feraseIdx
     simp [h, a', ih]
   | case2 a i h =>

src/Init/Data/Array/Lemmas.lean

@@ -21,6 +21,13 @@ namespace Array
 
 attribute [simp] data_toArray uset
 
+@[simp] theorem singleton_def (v : α) : singleton v = #[v] := rfl
+
+@[simp] theorem toArray_data : (a : Array α) → a.data.toArray = a
+  | ⟨l⟩ => ext' (data_toArray l)
+
+@[simp] theorem data_length {l : Array α} : l.data.length = l.size := rfl
+
 @[simp] theorem mkEmpty_eq (α n) : @mkEmpty α n = #[] := rfl
 
 @[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
@@ -141,7 +148,8 @@ where
   simp [H]
 
 @[simp] theorem size_map (f : α → β) (arr : Array α) : (arr.map f).size = arr.size := by
-  simp [size]
+  simp only [← data_length]
+  simp
 
 @[simp] theorem pop_data (arr : Array α) : arr.pop.data = arr.data.dropLast := rfl
 
@@ -308,5 +316,749 @@ termination_by n - i
     (ofFn f)[i] = f ⟨i, size_ofFn f ▸ h⟩ :=
   getElem_ofFn_go _ _ _ (by simp) (by simp) nofun
 
+/-- # mkArray -/
+
+@[simp] theorem mkArray_data (n : Nat) (v : α) : (mkArray n v).data = List.replicate n v := rfl
+
+@[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
+    (mkArray n v)[i] = v := by simp [Array.getElem_eq_data_get]
+
+/-- # mem -/
+
+theorem mem_data {a : α} {l : Array α} : a ∈ l.data ↔ a ∈ l := (mem_def _ _).symm
+
+theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
+
+/-- # get lemmas -/
+
+theorem getElem?_mem {l : Array α} {i : Fin l.size} : l[i] ∈ l := by
+  erw [Array.mem_def, getElem_eq_data_get]
+  apply List.get_mem
+
+theorem getElem_fin_eq_data_get (a : Array α) (i : Fin _) : a[i] = a.data.get i := rfl
+
+@[simp] theorem ugetElem_eq_getElem (a : Array α) {i : USize} (h : i.toNat < a.size) :
+  a[i] = a[i.toNat] := rfl
+
+theorem getElem?_eq_getElem (a : Array α) (i : Nat) (h : i < a.size) : a[i]? = a[i] :=
+  getElem?_pos ..
+
+theorem get?_len_le (a : Array α) (i : Nat) (h : a.size ≤ i) : a[i]? = none := by
+  simp [getElem?_neg, h]
+
+theorem getElem_mem_data (a : Array α) (h : i < a.size) : a[i] ∈ a.data := by
+  simp only [getElem_eq_data_get, List.get_mem]
+
+theorem getElem?_eq_data_get? (a : Array α) (i : Nat) : a[i]? = a.data.get? i := by
+  by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]; rfl
+
+theorem get?_eq_data_get? (a : Array α) (i : Nat) : a.get? i = a.data.get? i :=
+  getElem?_eq_data_get? ..
+
+theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
+  simp [get!_eq_getD]
+
+@[simp] theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
+  simp [back, back?]
+
+@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
+  simp [back?, getElem?_eq_data_get?]
+
+theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
+
+theorem get?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
+    (a.push x)[i]? = some a[i] := by
+  rw [getElem?_pos, get_push_lt]
+
+theorem get?_push_eq (a : Array α) (x : α) : (a.push x)[a.size]? = some x := by
+  rw [getElem?_pos, get_push_eq]
+
+theorem get?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x else a[i]? := by
+  match Nat.lt_trichotomy i a.size with
+  | Or.inl g =>
+    have h1 : i < a.size + 1 := by omega
+    have h2 : i ≠ a.size := by omega
+    simp [getElem?, size_push, g, h1, h2, get_push_lt]
+  | Or.inr (Or.inl heq) =>
+    simp [heq, getElem?_pos, get_push_eq]
+  | Or.inr (Or.inr g) =>
+    simp only [getElem?, size_push]
+    have h1 : ¬ (i < a.size) := by omega
+    have h2 : ¬ (i < a.size + 1) := by omega
+    have h3 : i ≠ a.size := by omega
+    simp [h1, h2, h3]
+
+@[simp] theorem get?_size {a : Array α} : a[a.size]? = none := by
+  simp only [getElem?, Nat.lt_irrefl, dite_false]
+
+@[simp] theorem data_set (a : Array α) (i v) : (a.set i v).data = a.data.set i.1 v := rfl
+
+theorem get_set_eq (a : Array α) (i : Fin a.size) (v : α) :
+    (a.set i v)[i.1] = v := by
+  simp only [set, getElem_eq_data_get, List.get_set_eq]
+
+theorem get?_set_eq (a : Array α) (i : Fin a.size) (v : α) :
+    (a.set i v)[i.1]? = v := by simp [getElem?_pos, i.2]
+
+@[simp] theorem get?_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α)
+    (h : i.1 ≠ j) : (a.set i v)[j]? = a[j]? := by
+  by_cases j < a.size <;> simp [getElem?_pos, getElem?_neg, *]
+
+theorem get?_set (a : Array α) (i : Fin a.size) (j : Nat) (v : α) :
+    (a.set i v)[j]? = if i.1 = j then some v else a[j]? := by
+  if h : i.1 = j then subst j; simp [*] else simp [*]
+
+theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v : α) :
+    (a.set i v)[j]'(by simp [*]) = if i = j then v else a[j] := by
+  if h : i.1 = j then subst j; simp [*] else simp [*]
+
+@[simp] theorem get_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α) (hj : j < a.size)
+    (h : i.1 ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
+  simp only [set, getElem_eq_data_get, List.get_set_ne _ h]
+
+theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
+  (setD a i v)[i] = v := by
+  simp at h
+  simp only [setD, h, dite_true, get_set, ite_true]
+
+theorem set_set (a : Array α) (i : Fin a.size) (v v' : α) :
+    (a.set i v).set ⟨i, by simp [i.2]⟩ v' = a.set i v' := by simp [set, List.set_set]
+
+private theorem fin_cast_val (e : n = n') (i : Fin n) : e ▸ i = ⟨i.1, e ▸ i.2⟩ := by cases e; rfl
+
+theorem swap_def (a : Array α) (i j : Fin a.size) :
+    a.swap i j = (a.set i (a.get j)).set ⟨j.1, by simp [j.2]⟩ (a.get i) := by
+  simp [swap, fin_cast_val]
+
+theorem data_swap (a : Array α) (i j : Fin a.size) :
+    (a.swap i j).data = (a.data.set i (a.get j)).set j (a.get i) := by simp [swap_def]
+
+theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
+    if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
+  simp [swap_def, get?_set, ← getElem_fin_eq_data_get]
+
+@[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
+    a.swapAt i v = (a[i.1], a.set i v) := rfl
+
+-- @[simp] -- FIXME: gives a weird linter error
+theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
+    a.swapAt! i v = (a[i], a.set ⟨i, h⟩ v) := by simp [swapAt!, h]
+
+@[simp] theorem data_pop (a : Array α) : a.pop.data = a.data.dropLast := by simp [pop]
+
+@[simp] theorem pop_empty : (#[] : Array α).pop = #[] := rfl
+
+@[simp] theorem pop_push (a : Array α) : (a.push x).pop = a := by simp [pop]
+
+@[simp] theorem getElem_pop (a : Array α) (i : Nat) (hi : i < a.pop.size) :
+    a.pop[i] = a[i]'(Nat.lt_of_lt_of_le (a.size_pop ▸ hi) (Nat.sub_le _ _)) :=
+  List.get_dropLast ..
+
+theorem eq_empty_of_size_eq_zero {as : Array α} (h : as.size = 0) : as = #[] := by
+  apply ext
+  · simp [h]
+  · intros; contradiction
+
+theorem eq_push_pop_back_of_size_ne_zero [Inhabited α] {as : Array α} (h : as.size ≠ 0) :
+    as = as.pop.push as.back := by
+  apply ext
+  · simp [Nat.sub_add_cancel (Nat.zero_lt_of_ne_zero h)]
+  · intros i h h'
+    if hlt : i < as.pop.size then
+      rw [get_push_lt (h:=hlt), getElem_pop]
+    else
+      have heq : i = as.pop.size :=
+        Nat.le_antisymm (size_pop .. ▸ Nat.le_pred_of_lt h) (Nat.le_of_not_gt hlt)
+      cases heq; rw [get_push_eq, back, ←size_pop, get!_eq_getD, getD, dif_pos h]; rfl
+
+theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size ≠ 0) :
+    ∃ (bs : Array α) (c : α), as = bs.push c :=
+  let _ : Inhabited α := ⟨as[0]⟩
+  ⟨as.pop, as.back, eq_push_pop_back_of_size_ne_zero h⟩
+
+theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
+
+@[simp] theorem size_swap! (a : Array α) (i j) :
+    (a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
+
+@[simp] theorem size_reverse (a : Array α) : a.reverse.size = a.size := by
+  let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
+    rw [reverse.loop]
+    if h : i < j then
+      have := reverse.termination h
+      simp [(go · (i+1) ⟨j-1, ·⟩), h]
+    else simp [h]
+    termination_by j - i
+  simp only [reverse]; split <;> simp [go]
+
+@[simp] theorem size_range {n : Nat} : (range n).size = n := by
+  unfold range
+  induction n with
+  | zero      => simp [Nat.fold]
+  | succ k ih =>
+    rw [Nat.fold, flip]
+    simp only [mkEmpty_eq, size_push] at *
+    omega
+
+@[simp] theorem reverse_data (a : Array α) : a.reverse.data = a.data.reverse := by
+  let rec go (as : Array α) (i j hj)
+      (h : i + j + 1 = a.size) (h₂ : as.size = a.size)
+      (H : ∀ k, as.data.get? k = if i ≤ k ∧ k ≤ j then a.data.get? k else a.data.reverse.get? k)
+      (k) : (reverse.loop as i ⟨j, hj⟩).data.get? k = a.data.reverse.get? k := by
+    rw [reverse.loop]; dsimp; split <;> rename_i h₁
+    · have := reverse.termination h₁
+      match j with | j+1 => ?_
+      simp at *
+      rw [(go · (i+1) j)]
+      · rwa [Nat.add_right_comm i]
+      · simp [size_swap, h₂]
+      · intro k
+        rw [← getElem?_eq_data_get?, get?_swap]
+        simp [getElem?_eq_data_get?, getElem_eq_data_get, ← List.get?_eq_get, H, Nat.le_of_lt h₁]
+        split <;> rename_i h₂
+        · simp [← h₂, Nat.not_le.2 (Nat.lt_succ_self _)]
+          exact (List.get?_reverse' _ _ (Eq.trans (by simp_arith) h)).symm
+        split <;> rename_i h₃
+        · simp [← h₃, Nat.not_le.2 (Nat.lt_succ_self _)]
+          exact (List.get?_reverse' _ _ (Eq.trans (by simp_arith) h)).symm
+        simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
+          Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
+    · rw [H]; split <;> rename_i h₂
+      · cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
+        cases Nat.le_antisymm h₂.1 h₂.2
+        exact (List.get?_reverse' _ _ h).symm
+      · rfl
+    termination_by j - i
+  simp only [reverse]; split
+  · match a with | ⟨[]⟩ | ⟨[_]⟩ => rfl
+  · have := Nat.sub_add_cancel (Nat.le_of_not_le ‹_›)
+    refine List.ext <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
+    split; {rfl}; rename_i h
+    simp [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this] at h
+    rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.data.length_reverse ▸ ‹_›)]
+
+/-! ### foldl / foldr -/
+
+-- This proof is the pure version of `Array.SatisfiesM_foldlM`,
+-- reproduced to avoid a dependency on `SatisfiesM`.
+theorem foldl_induction
+    {as : Array α} (motive : Nat → β → Prop) {init : β} (h0 : motive 0 init) {f : β → α → β}
+    (hf : ∀ i : Fin as.size, ∀ b, motive i.1 b → motive (i.1 + 1) (f b as[i])) :
+    motive as.size (as.foldl f init) := by
+  let rec go {i j b} (h₁ : j ≤ as.size) (h₂ : as.size ≤ i + j) (H : motive j b) :
+    (motive as.size) (foldlM.loop (m := Id) f as as.size (Nat.le_refl _) i j b) := by
+    unfold foldlM.loop; split
+    · next hj =>
+      split
+      · cases Nat.not_le_of_gt (by simp [hj]) h₂
+      · exact go hj (by rwa [Nat.succ_add] at h₂) (hf ⟨j, hj⟩ b H)
+    · next hj => exact Nat.le_antisymm h₁ (Nat.ge_of_not_lt hj) ▸ H
+  simpa [foldl, foldlM] using go (Nat.zero_le _) (Nat.le_refl _) h0
+
+-- This proof is the pure version of `Array.SatisfiesM_foldrM`,
+-- reproduced to avoid a dependency on `SatisfiesM`.
+theorem foldr_induction
+    {as : Array α} (motive : Nat → β → Prop) {init : β} (h0 : motive as.size init) {f : α → β → β}
+    (hf : ∀ i : Fin as.size, ∀ b, motive (i.1 + 1) b → motive i.1 (f as[i] b)) :
+    motive 0 (as.foldr f init) := by
+  let rec go {i b} (hi : i ≤ as.size) (H : motive i b) :
+    (motive 0) (foldrM.fold (m := Id) f as 0 i hi b) := by
+    unfold foldrM.fold; simp; split
+    · next hi => exact (hi ▸ H)
+    · next hi =>
+      split; {simp at hi}
+      · next i hi' =>
+        exact go _ (hf ⟨i, hi'⟩ b H)
+  simp [foldr, foldrM]; split; {exact go _ h0}
+  · next h => exact (Nat.eq_zero_of_not_pos h ▸ h0)
+
+/-! ### map -/
+
+@[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
+  simp only [mem_def, map_data, List.mem_map]
+
+theorem mapM_eq_mapM_data [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
+    arr.mapM f = return mk (← arr.data.mapM f) := by
+  rw [mapM_eq_foldlM, foldlM_eq_foldlM_data, ← List.foldrM_reverse]
+  conv => rhs; rw [← List.reverse_reverse arr.data]
+  induction arr.data.reverse with
+  | nil => simp; rfl
+  | cons a l ih => simp [ih]; simp [map_eq_pure_bind, push]
+
+theorem mapM_map_eq_foldl (as : Array α) (f : α → β) (i) :
+    mapM.map (m := Id) f as i b = as.foldl (start := i) (fun r a => r.push (f a)) b := by
+  unfold mapM.map
+  split <;> rename_i h
+  · simp only [Id.bind_eq]
+    dsimp [foldl, Id.run, foldlM]
+    rw [mapM_map_eq_foldl, dif_pos (by omega), foldlM.loop, dif_pos h]
+    -- Calling `split` here gives a bad goal.
+    have : size as - i = Nat.succ (size as - i - 1) := by omega
+    rw [this]
+    simp [foldl, foldlM, Id.run, Nat.sub_add_eq]
+  · dsimp [foldl, Id.run, foldlM]
+    rw [dif_pos (by omega), foldlM.loop, dif_neg h]
+    rfl
+termination_by as.size - i
+
+theorem map_eq_foldl (as : Array α) (f : α → β) :
+    as.map f = as.foldl (fun r a => r.push (f a)) #[] :=
+  mapM_map_eq_foldl _ _ _
+
+theorem map_induction (as : Array α) (f : α → β) (motive : Nat → Prop) (h0 : motive 0)
+    (p : Fin as.size → β → Prop) (hs : ∀ i, motive i.1 → p i (f as[i]) ∧ motive (i+1)) :
+    motive as.size ∧
+      ∃ eq : (as.map f).size = as.size, ∀ i h, p ⟨i, h⟩ ((as.map f)[i]) := by
+  have t := foldl_induction (as := as) (β := Array β)
+    (motive := fun i arr => motive i ∧ arr.size = i ∧ ∀ i h2, p i arr[i.1])
+    (init := #[]) (f := fun r a => r.push (f a)) ?_ ?_
+  obtain ⟨m, eq, w⟩ := t
+  · refine ⟨m, by simpa [map_eq_foldl] using eq, ?_⟩
+    intro i h
+    simp [eq] at w
+    specialize w ⟨i, h⟩ h
+    simpa [map_eq_foldl] using w
+  · exact ⟨h0, rfl, nofun⟩
+  · intro i b ⟨m, ⟨eq, w⟩⟩
+    refine ⟨?_, ?_, ?_⟩
+    · exact (hs _ m).2
+    · simp_all
+    · intro j h
+      simp at h ⊢
+      by_cases h' : j < size b
+      · rw [get_push]
+        simp_all
+      · rw [get_push, dif_neg h']
+        simp only [show j = i by omega]
+        exact (hs _ m).1
+
+theorem map_spec (as : Array α) (f : α → β) (p : Fin as.size → β → Prop)
+    (hs : ∀ i, p i (f as[i])) :
+    ∃ eq : (as.map f).size = as.size, ∀ i h, p ⟨i, h⟩ ((as.map f)[i]) := by
+  simpa using map_induction as f (fun _ => True) trivial p (by simp_all)
+
+@[simp] theorem getElem_map (f : α → β) (as : Array α) (i : Nat) (h) :
+    ((as.map f)[i]) = f (as[i]'(size_map .. ▸ h)) := by
+  have := map_spec as f (fun i b => b = f (as[i]))
+  simp only [implies_true, true_implies] at this
+  obtain ⟨eq, w⟩ := this
+  apply w
+  simp_all
+
+/-! ### mapIdx -/
+
+-- This could also be prove from `SatisfiesM_mapIdxM`.
+theorem mapIdx_induction (as : Array α) (f : Fin as.size → α → 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.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx 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.mapIdxM.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
+    induction i generalizing j bs with simp [mapIdxM.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)
+      · intro i i_lt h'
+        rw [get_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
+  simp [mapIdx, mapIdxM]; exact go rfl nofun h0
+
+theorem mapIdx_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.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
+  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+
+@[simp] theorem size_mapIdx (a : Array α) (f : Fin a.size → α → β) : (a.mapIdx f).size = a.size :=
+  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+
+@[simp] theorem size_zipWithIndex (as : Array α) : as.zipWithIndex.size = as.size :=
+  Array.size_mapIdx _ _
+
+@[simp] theorem getElem_mapIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat)
+    (h : i < (mapIdx a f).size) :
+    haveI : i < a.size := by simp_all
+    (a.mapIdx f)[i] = f ⟨i, this⟩ a[i] :=
+  (mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
+
+/-! ### modify -/
+
+@[simp] theorem size_modify (a : Array α) (i : Nat) (f : α → α) : (a.modify i f).size = a.size := by
+  unfold modify modifyM Id.run
+  split <;> simp
+
+theorem get_modify {arr : Array α} {x i} (h : i < arr.size) :
+    (arr.modify x f).get ⟨i, by simp [h]⟩ =
+    if x = i then f (arr.get ⟨i, h⟩) else arr.get ⟨i, h⟩ := by
+  simp [modify, modifyM, Id.run]; split
+  · simp [get_set _ _ _ h]; split <;> simp [*]
+  · rw [if_neg (mt (by rintro rfl; exact h) ‹_›)]
+
+/-! ### filter -/
+
+@[simp] theorem filter_data (p : α → Bool) (l : Array α) :
+    (l.filter p).data = l.data.filter p := by
+  dsimp only [filter]
+  rw [foldl_eq_foldl_data]
+  generalize l.data = l
+  suffices ∀ a, (List.foldl (fun r a => if p a = true then push r a else r) a l).data =
+      a.data ++ List.filter p l by
+    simpa using this #[]
+  induction l with simp
+  | cons => split <;> simp [*]
+
+@[simp] theorem filter_filter (q) (l : Array α) :
+    filter p (filter q l) = filter (fun a => p a ∧ q a) l := by
+  apply ext'
+  simp only [filter_data, List.filter_filter]
+
+@[simp] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
+  simp only [mem_def, filter_data, List.mem_filter]
+
+theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
+  (mem_filter.mp h).1
+
+/-! ### filterMap -/
+
+@[simp] theorem filterMap_data (f : α → Option β) (l : Array α) :
+    (l.filterMap f).data = l.data.filterMap f := by
+  dsimp only [filterMap, filterMapM]
+  rw [foldlM_eq_foldlM_data]
+  generalize l.data = l
+  have this : ∀ a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).data =
+    a.data ++ List.filterMap f l := ?_
+  exact this #[]
+  induction l
+  · simp_all [Id.run]
+  · simp_all [Id.run]
+    split <;> simp_all
+
+@[simp] theorem mem_filterMap (f : α → Option β) (l : Array α) {b : β} :
+    b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
+  simp only [mem_def, filterMap_data, List.mem_filterMap]
+
+/-! ### empty -/
+
+theorem size_empty : (#[] : Array α).size = 0 := rfl
+
+theorem empty_data : (#[] : Array α).data = [] := rfl
+
+/-! ### append -/
+
+theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] := rfl
+
+@[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
+  simp only [mem_def, append_data, List.mem_append]
+
+theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
+  simp only [size, append_data, List.length_append]
+
+theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
+    (as ++ bs)[i] = as[i] := by
+  simp only [getElem_eq_data_get]
+  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
+  conv => rhs; rw [← List.get_append_left (bs:=bs.data) (h':=h')]
+  apply List.get_of_eq; rw [append_data]
+
+theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
+    (hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
+    (as ++ bs)[i] = bs[i - as.size] := by
+  simp only [getElem_eq_data_get]
+  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
+  conv => rhs; rw [← List.get_append_right (h':=h') (h:=Nat.not_lt_of_ge hle)]
+  apply List.get_of_eq; rw [append_data]
+
+@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
+  apply ext'; simp only [append_data, empty_data, List.append_nil]
+
+@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
+  apply ext'; simp only [append_data, empty_data, List.nil_append]
+
+theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
+  apply ext'; simp only [append_data, List.append_assoc]
+
+/-! ### extract -/
+
+theorem extract_loop_zero (as bs : Array α) (start : Nat) : extract.loop as 0 start bs = bs := by
+  rw [extract.loop]; split <;> rfl
+
+theorem extract_loop_succ (as bs : Array α) (size start : Nat) (h : start < as.size) :
+    extract.loop as (size+1) start bs = extract.loop as size (start+1) (bs.push as[start]) := by
+  rw [extract.loop, dif_pos h]; rfl
+
+theorem extract_loop_of_ge (as bs : Array α) (size start : Nat) (h : start ≥ as.size) :
+    extract.loop as size start bs = bs := by
+  rw [extract.loop, dif_neg (Nat.not_lt_of_ge h)]
+
+theorem extract_loop_eq_aux (as bs : Array α) (size start : Nat) :
+    extract.loop as size start bs = bs ++ extract.loop as size start #[] := by
+  induction size using Nat.recAux generalizing start bs with
+  | zero => rw [extract_loop_zero, extract_loop_zero, append_nil]
+  | succ size ih =>
+    if h : start < as.size then
+      rw [extract_loop_succ (h:=h), ih (bs.push _), push_eq_append_singleton]
+      rw [extract_loop_succ (h:=h), ih (#[].push _), push_eq_append_singleton, nil_append]
+      rw [append_assoc]
+    else
+      rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
+      rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
+      rw [append_nil]
+
+theorem extract_loop_eq (as bs : Array α) (size start : Nat) (h : start + size ≤ as.size) :
+  extract.loop as size start bs = bs ++ as.extract start (start + size) := by
+  simp [extract]; rw [extract_loop_eq_aux, Nat.min_eq_left h, Nat.add_sub_cancel_left]
+
+theorem size_extract_loop (as bs : Array α) (size start : Nat) :
+    (extract.loop as size start bs).size = bs.size + min size (as.size - start) := by
+  induction size using Nat.recAux generalizing start bs with
+  | zero => rw [extract_loop_zero, Nat.zero_min, Nat.add_zero]
+  | succ size ih =>
+    if h : start < as.size then
+      rw [extract_loop_succ (h:=h), ih, size_push, Nat.add_assoc, ←Nat.add_min_add_left,
+        Nat.sub_succ, Nat.one_add, Nat.one_add, Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt h)]
+    else
+      have h := Nat.le_of_not_gt h
+      rw [extract_loop_of_ge (h:=h), Nat.sub_eq_zero_of_le h, Nat.min_zero, Nat.add_zero]
+
+@[simp] theorem size_extract (as : Array α) (start stop : Nat) :
+    (as.extract start stop).size = min stop as.size - start := by
+  simp [extract]; rw [size_extract_loop, size_empty, Nat.zero_add, Nat.sub_min_sub_right,
+    Nat.min_assoc, Nat.min_self]
+
+theorem get_extract_loop_lt_aux (as bs : Array α) (size start : Nat) (hlt : i < bs.size) :
+    i < (extract.loop as size start bs).size := by
+  rw [size_extract_loop]
+  apply Nat.lt_of_lt_of_le hlt
+  exact Nat.le_add_right ..
+
+theorem get_extract_loop_lt (as bs : Array α) (size start : Nat) (hlt : i < bs.size)
+    (h := get_extract_loop_lt_aux as bs size start hlt) :
+    (extract.loop as size start bs)[i] = bs[i] := by
+  apply Eq.trans _ (get_append_left (bs:=extract.loop as size start #[]) hlt)
+  · rw [size_append]; exact Nat.lt_of_lt_of_le hlt (Nat.le_add_right ..)
+  · congr; rw [extract_loop_eq_aux]
+
+theorem get_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
+    (h : i < (extract.loop as size start bs).size) : start + i - bs.size < as.size := by
+  have h : i < bs.size + (as.size - start) := by
+      apply Nat.lt_of_lt_of_le h
+      rw [size_extract_loop]
+      apply Nat.add_le_add_left
+      exact Nat.min_le_right ..
+  rw [Nat.add_sub_assoc hge]
+  apply Nat.add_lt_of_lt_sub'
+  exact Nat.sub_lt_left_of_lt_add hge h
+
+theorem get_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
+    (h : i < (extract.loop as size start bs).size)
+    (h' := get_extract_loop_ge_aux as bs size start hge h) :
+    (extract.loop as size start bs)[i] = as[start + i - bs.size] := by
+  induction size using Nat.recAux generalizing start bs with
+  | zero =>
+    rw [size_extract_loop, Nat.zero_min, Nat.add_zero] at h
+    omega
+  | succ size ih =>
+    have : start < as.size := by
+      apply Nat.lt_of_le_of_lt (Nat.le_add_right start (i - bs.size))
+      rwa [← Nat.add_sub_assoc hge]
+    have : i < (extract.loop as size (start+1) (bs.push as[start])).size := by
+      rwa [← extract_loop_succ]
+    have heq : (extract.loop as (size+1) start bs)[i] =
+        (extract.loop as size (start+1) (bs.push as[start]))[i] := by
+      congr 1; rw [extract_loop_succ]
+    rw [heq]
+    if hi : bs.size = i then
+      cases hi
+      have h₁ : bs.size < (bs.push as[start]).size := by rw [size_push]; exact Nat.lt_succ_self ..
+      have h₂ : bs.size < (extract.loop as size (start+1) (bs.push as[start])).size := by
+        rw [size_extract_loop]; apply Nat.lt_of_lt_of_le h₁; exact Nat.le_add_right ..
+      have h : (extract.loop as size (start + 1) (push bs as[start]))[bs.size] = as[start] := by
+        rw [get_extract_loop_lt as (bs.push as[start]) size (start+1) h₁ h₂, get_push_eq]
+      rw [h]; congr; rw [Nat.add_sub_cancel]
+    else
+      have hge : bs.size + 1 ≤ i := Nat.lt_of_le_of_ne hge hi
+      rw [ih (bs.push as[start]) (start+1) ((size_push ..).symm ▸ hge)]
+      congr 1; rw [size_push, Nat.add_right_comm, Nat.add_sub_add_right]
+
+theorem get_extract_aux {as : Array α} {start stop : Nat} (h : i < (as.extract start stop).size) :
+    start + i < as.size := by
+  rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
+  apply Nat.sub_le_sub_right; apply Nat.min_le_right
+
+@[simp] theorem get_extract {as : Array α} {start stop : Nat}
+    (h : i < (as.extract start stop).size) :
+    (as.extract start stop)[i] = as[start + i]'(get_extract_aux h) :=
+  show (extract.loop as (min stop as.size - start) start #[])[i]
+    = as[start + i]'(get_extract_aux h) by rw [get_extract_loop_ge]; rfl; exact Nat.zero_le _
+
+@[simp] theorem extract_all (as : Array α) : as.extract 0 as.size = as := by
+  apply ext
+  · rw [size_extract, Nat.min_self, Nat.sub_zero]
+  · intros; rw [get_extract]; congr; rw [Nat.zero_add]
+
+theorem extract_empty_of_stop_le_start (as : Array α) {start stop : Nat} (h : stop ≤ start) :
+    as.extract start stop = #[] := by
+  simp [extract]; rw [←Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.zero_min,
+    extract_loop_zero]
+
+theorem extract_empty_of_size_le_start (as : Array α) {start stop : Nat} (h : as.size ≤ start) :
+    as.extract start stop = #[] := by
+  simp [extract]; rw [←Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.min_zero,
+    extract_loop_zero]
+
+@[simp] theorem extract_empty (start stop : Nat) : (#[] : Array α).extract start stop = #[] :=
+  extract_empty_of_size_le_start _ (Nat.zero_le _)
+
+/-! ### any -/
+
+-- Auxiliary for `any_iff_exists`.
+theorem anyM_loop_iff_exists (p : α → Bool) (as : Array α) (start stop) (h : stop ≤ as.size) :
+    anyM.loop (m := Id) p as stop h start = true ↔
+      ∃ i : Fin as.size, start ≤ ↑i ∧ ↑i < stop ∧ p as[i] = true := by
+  unfold anyM.loop
+  split <;> rename_i h₁
+  · dsimp
+    split <;> rename_i h₂
+    · simp only [true_iff]
+      refine ⟨⟨start, by omega⟩, by dsimp; omega, by dsimp; omega, h₂⟩
+    · rw [anyM_loop_iff_exists]
+      constructor
+      · rintro ⟨i, ge, lt, h⟩
+        have : start ≠ i := by rintro rfl; omega
+        exact ⟨i, by omega, lt, h⟩
+      · rintro ⟨i, ge, lt, h⟩
+        have : start ≠ i := by rintro rfl; erw [h] at h₂; simp_all
+        exact ⟨i, by omega, lt, h⟩
+  · simp
+    omega
+termination_by stop - start
+
+-- This could also be proved from `SatisfiesM_anyM_iff_exists` in `Batteries.Data.Array.Init.Monadic`
+theorem any_iff_exists (p : α → Bool) (as : Array α) (start stop) :
+    any as p start stop ↔ ∃ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop ∧ p as[i] := by
+  dsimp [any, anyM, Id.run]
+  split
+  · rw [anyM_loop_iff_exists]; rfl
+  · rw [anyM_loop_iff_exists]
+    constructor
+    · rintro ⟨i, ge, _, h⟩
+      exact ⟨i, by omega, by omega, h⟩
+    · rintro ⟨i, ge, _, h⟩
+      exact ⟨i, by omega, by omega, h⟩
+
+theorem any_eq_true (p : α → Bool) (as : Array α) :
+    any as p ↔ ∃ i : Fin as.size, p as[i] := by simp [any_iff_exists, Fin.isLt]
+
+theorem any_def {p : α → Bool} (as : Array α) : as.any p = as.data.any p := by
+  rw [Bool.eq_iff_iff, any_eq_true, List.any_eq_true]; simp only [List.mem_iff_get]
+  exact ⟨fun ⟨i, h⟩ => ⟨_, ⟨i, rfl⟩, h⟩, fun ⟨_, ⟨i, rfl⟩, h⟩ => ⟨i, h⟩⟩
+
+/-! ### all -/
+
+theorem all_eq_not_any_not (p : α → Bool) (as : Array α) (start stop) :
+    all as p start stop = !(any as (!p ·) start stop) := by
+  dsimp [all, allM]
+  rfl
+
+theorem all_iff_forall (p : α → Bool) (as : Array α) (start stop) :
+    all as p start stop ↔ ∀ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop → p as[i] := by
+  rw [all_eq_not_any_not]
+  suffices ¬(any as (!p ·) start stop = true) ↔
+      ∀ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop → p as[i] by
+    simp_all
+  rw [any_iff_exists]
+  simp
+
+theorem all_eq_true (p : α → Bool) (as : Array α) : all as p ↔ ∀ i : Fin as.size, p as[i] := by
+  simp [all_iff_forall, Fin.isLt]
+
+theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.data.all p := by
+  rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_get]
+  constructor
+  · rintro w x ⟨r, rfl⟩
+    rw [← getElem_eq_data_get]
+    apply w
+  · intro w i
+    exact w as[i] ⟨i, (getElem_eq_data_get as i.2).symm⟩
+
+theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
+  simp only [all_def, List.all_eq_true, mem_def]
+
+/-! ### contains -/
+
+theorem contains_def [DecidableEq α] {a : α} {as : Array α} : as.contains a ↔ a ∈ as := by
+  rw [mem_def, contains, any_def, List.any_eq_true]; simp [and_comm]
+
+instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
+  decidable_of_iff _ contains_def
+
+/-! ### swap -/
+
+open Fin
+
+@[simp] theorem get_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.val] = a[i] :=
+  by simp only [swap, fin_cast_val, get_eq_getElem, getElem_set_eq, getElem_fin]
+
+@[simp] theorem get_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.val] = a[j] :=
+  if he : ((Array.size_set _ _ _).symm ▸ j).val = i.val then by
+    simp only [←he, fin_cast_val, get_swap_right, getElem_fin]
+  else by
+    apply Eq.trans
+    · apply Array.get_set_ne
+      · simp only [size_set, Fin.isLt]
+      · assumption
+    · simp [get_set_ne]
+
+@[simp] theorem get_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
+    (hi : p ≠ i) (hj : p ≠ j) : (a.swap i j)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
+  apply Eq.trans
+  · have : ((a.size_set i (a.get j)).symm ▸ j).val = j.val := by simp only [fin_cast_val]
+    apply Array.get_set_ne
+    · simp only [this]
+      apply Ne.symm
+      · assumption
+  · apply Array.get_set_ne
+    · apply Ne.symm
+      · assumption
+
+theorem get_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk: k < a.size) :
+    (a.swap i j)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i]  else a[k] := by
+  split
+  · simp_all only [get_swap_left]
+  · split <;> simp_all
+
+theorem get_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk' : k < (a.swap i j).size) :
+    (a.swap i j)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
+  apply get_swap
+
+@[simp] theorem swap_swap (a : Array α) {i j : Fin a.size} :
+    (a.swap i j).swap ⟨i.1, (a.size_swap ..).symm ▸i.2⟩ ⟨j.1, (a.size_swap ..).symm ▸j.2⟩ = a := by
+  apply ext
+  · simp only [size_swap]
+  · intros
+    simp only [get_swap']
+    split
+    · simp_all
+    · split <;> simp_all
+
+theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i := by
+  apply ext
+  · simp only [size_swap]
+  · intros
+    simp only [get_swap']
+    split
+    · split <;> simp_all
+    · split <;> simp_all
+
 
 end Array

src/Init/Data/Array/Subarray.lean

@@ -15,14 +15,14 @@ structure Subarray (α : Type u)  where
   start_le_stop : start ≤ stop
   stop_le_array_size : stop ≤ array.size
 
-@[deprecated Subarray.array]
+@[deprecated Subarray.array (since := "2024-04-13")]
 abbrev Subarray.as (s : Subarray α) : Array α := s.array
 
-@[deprecated Subarray.start_le_stop]
+@[deprecated Subarray.start_le_stop (since := "2024-04-13")]
 theorem Subarray.h₁ (s : Subarray α) : s.start ≤ s.stop := s.start_le_stop
 
-@[deprecated Subarray.stop_le_array_size]
-theorem Subarray.h₂ (s : Subarray α) : s.stop ≤ s.as.size := s.stop_le_array_size
+@[deprecated Subarray.stop_le_array_size (since := "2024-04-13")]
+theorem Subarray.h₂ (s : Subarray α) : s.stop ≤ s.array.size := s.stop_le_array_size
 
 namespace Subarray
 

src/Init/Data/BitVec/Basic.lean

@@ -34,7 +34,8 @@ structure BitVec (w : Nat) where
   O(1), because we use `Fin` as the internal representation of a bitvector. -/
   toFin : Fin (2^w)
 
-@[deprecated] protected abbrev Std.BitVec := _root_.BitVec
+@[deprecated (since := "2024-04-12")]
+protected abbrev Std.BitVec := _root_.BitVec
 
 -- We manually derive the `DecidableEq` instances for `BitVec` because
 -- we want to have builtin support for bit-vector literals, and we
@@ -73,7 +74,7 @@ protected def toNat (a : BitVec n) : Nat := a.toFin.val
 /-- Return the bound in terms of toNat. -/
 theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
 
-@[deprecated isLt]
+@[deprecated isLt (since := "2024-03-12")]
 theorem toNat_lt (x : BitVec n) : x.toNat < 2^n := x.isLt
 
 /-- Theorem for normalizing the bit vector literal representation. -/
@@ -533,6 +534,11 @@ def sshiftRight (a : BitVec n) (s : Nat) : BitVec n := .ofInt n (a.toInt >>> s)
 instance {n} : HShiftLeft  (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x <<< y.toNat⟩
 instance {n} : HShiftRight (BitVec m) (BitVec n) (BitVec m) := ⟨fun x y => x >>> y.toNat⟩
 
+/-- Auxiliary function for `rotateLeft`, which does not take into account the case where
+the rotation amount is greater than the bitvector width. -/
+def rotateLeftAux (x : BitVec w) (n : Nat) : BitVec w :=
+  x <<< n ||| x >>> (w - n)
+
 /--
 Rotate left for bit vectors. All the bits of `x` are shifted to higher positions, with the top `n`
 bits wrapping around to fill the low bits.
@@ -542,7 +548,15 @@ rotateLeft  0b0011#4 3 = 0b1001
 ```
 SMT-Lib name: `rotate_left` except this operator uses a `Nat` shift amount.
 -/
-def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := x <<< n ||| x >>> (w - n)
+def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := rotateLeftAux x (n % w)
+
+
+/--
+Auxiliary function for `rotateRight`, which does not take into account the case where
+the rotation amount is greater than the bitvector width.
+-/
+def rotateRightAux (x : BitVec w) (n : Nat) : BitVec w :=
+  x >>> n ||| x <<< (w - n)
 
 /--
 Rotate right for bit vectors. All the bits of `x` are shifted to lower positions, with the
@@ -553,7 +567,7 @@ rotateRight 0b01001#5 1 = 0b10100
 ```
 SMT-Lib name: `rotate_right` except this operator uses a `Nat` shift amount.
 -/
-def rotateRight (x : BitVec w) (n : Nat) : BitVec w := x >>> n ||| x <<< (w - n)
+def rotateRight (x : BitVec w) (n : Nat) : BitVec w := rotateRightAux x (n % w)
 
 /--
 Concatenation of bitvectors. This uses the "big endian" convention that the more significant

src/Init/Data/BitVec/Bitblast.lean

@@ -159,4 +159,80 @@ theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := b
 theorem allOnes_sub_eq_not (x : BitVec w) : allOnes w - x = ~~~x := by
   rw [← add_not_self x, BitVec.add_comm, add_sub_cancel]
 
+/-! ### Negation -/
+
+theorem bit_not_testBit (x : BitVec w) (i : Fin w) :
+  getLsb (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) i.val = !(getLsb x i.val) := by
+  apply iunfoldr_getLsb (fun _ => ()) i (by simp)
+
+theorem bit_not_add_self (x : BitVec w) :
+  ((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd + x  = -1 := by
+  simp only [add_eq_adc]
+  apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
+  intro i; simp only [ BitVec.not, adcb, testBit_toNat]
+  rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd)]
+  <;> simp [bit_not_testBit, negOne_eq_allOnes, getLsb_allOnes]
+
+theorem bit_not_eq_not (x : BitVec w) :
+  ((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd = ~~~ x := by
+  simp [←allOnes_sub_eq_not, BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), ←negOne_eq_allOnes]
+
+theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) (BitVec.ofNat w 1) false).snd:= by
+  simp only [← add_eq_adc]
+  rw [iunfoldr_replace_snd ((fun _ => ())) (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) _ rfl]
+  · rw [BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), sub_toAdd, BitVec.add_comm _ (-x)]
+    simp [← sub_toAdd, BitVec.sub_add_cancel]
+  · simp [bit_not_testBit x _]
+
+/-! ### Inequalities (le / lt) -/
+
+theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true := by
+  simp only [BitVec.ult, carry, toNat_mod_cancel, toNat_not, toNat_true, ge_iff_le, ← decide_not,
+    Nat.not_le, decide_eq_decide]
+  rw [Nat.mod_eq_of_lt (by omega)]
+  omega
+
+theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
+  simp [BitVec.ule, BitVec.ult, ← decide_not]
+
+theorem ule_eq_carry (x y : BitVec w) : x.ule y = carry w y (~~~x) true := by
+  simp [ule_eq_not_ult, ult_eq_not_carry]
+
+/-- If two bitvectors have the same `msb`, then signed and unsigned comparisons coincide -/
+theorem slt_eq_ult_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) :
+    x.slt y = x.ult y := by
+  simp only [BitVec.slt, toInt_eq_msb_cond, BitVec.ult, decide_eq_decide, h]
+  cases y.msb <;> simp
+
+/-- If two bitvectors have different `msb`s, then unsigned comparison is determined by this bit -/
+theorem ult_eq_msb_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
+    x.ult y = y.msb := by
+  simp only [BitVec.ult, msb_eq_decide, ne_eq, decide_eq_decide] at *
+  omega
+
+/-- If two bitvectors have different `msb`s, then signed and unsigned comparisons are opposites -/
+theorem slt_eq_not_ult_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
+    x.slt y = !x.ult y := by
+  simp only [BitVec.slt, toInt_eq_msb_cond, Bool.eq_not_of_ne h, ult_eq_msb_of_msb_neq h]
+  cases y.msb <;> (simp; omega)
+
+theorem slt_eq_ult (x y : BitVec w) :
+    x.slt y = (x.msb != y.msb).xor (x.ult y) := by
+  by_cases h : x.msb = y.msb
+  · simp [h, slt_eq_ult_of_msb_eq]
+  · have h' : x.msb != y.msb := by simp_all
+    simp [slt_eq_not_ult_of_msb_neq h, h']
+
+theorem slt_eq_not_carry (x y : BitVec w) :
+    x.slt y = (x.msb == y.msb).xor (carry w x (~~~y) true) := by
+  simp only [slt_eq_ult, bne, ult_eq_not_carry]
+  cases x.msb == y.msb <;> simp
+
+theorem sle_eq_not_slt (x y : BitVec w) : x.sle y = !y.slt x := by
+  simp only [BitVec.sle, BitVec.slt, ← decide_not, decide_eq_decide]; omega
+
+theorem sle_eq_carry (x y : BitVec w) :
+    x.sle y = !((x.msb == y.msb).xor (carry w y (~~~x) true)) := by
+  rw [sle_eq_not_slt, slt_eq_not_carry, beq_comm]
+
 end BitVec

src/Init/Data/BitVec/Folds.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix
+Authors: Joe Hendrix, Harun Khan
 -/
 prelude
 import Init.Data.BitVec.Lemmas
@@ -48,6 +48,51 @@ private theorem iunfoldr.eq_test
     intro i
     simp_all [truncate_succ]
 
+theorem iunfoldr_getLsb' {f : Fin w → α → α × Bool} (state : Nat → α)
+    (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :
+  (∀ i : Fin w, getLsb (iunfoldr f (state 0)).snd i.val = (f i (state i.val)).snd)
+  ∧ (iunfoldr f (state 0)).fst = state w := by
+  unfold iunfoldr
+  simp
+  apply Fin.hIterate_elim
+        (fun j (p : α × BitVec j) => (hj : j ≤ w) →
+         (∀ i : Fin j,  getLsb p.snd i.val = (f ⟨i.val, Nat.lt_of_lt_of_le i.isLt hj⟩ (state i.val)).snd)
+          ∧ p.fst = state j)
+  case hj => simp
+  case init =>
+    intro
+    apply And.intro
+    · intro i
+      have := Fin.size_pos i
+      contradiction
+    · rfl
+  case step =>
+    intro j ⟨s, v⟩ ih hj
+    apply And.intro
+    case left =>
+      intro i
+      simp only [getLsb_cons]
+      have hj2 : j.val ≤ w := by simp
+      cases (Nat.lt_or_eq_of_le (Nat.lt_succ.mp i.isLt)) with
+      | inl h3 => simp [if_neg, (Nat.ne_of_lt h3)]
+                  exact (ih hj2).1 ⟨i.val, h3⟩
+      | inr h3 => simp [h3, if_pos]
+                  cases (Nat.eq_zero_or_pos j.val) with
+                  | inl hj3 => congr
+                               rw [← (ih hj2).2]
+                  | inr hj3 => congr
+                               exact (ih hj2).2
+    case right =>
+      simp
+      have hj2 : j.val ≤ w := by simp
+      rw [← ind j, ← (ih hj2).2]
+
+
+theorem iunfoldr_getLsb {f : Fin w → α → α × Bool} (state : Nat → α) (i : Fin w)
+    (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :
+  getLsb (iunfoldr f (state 0)).snd i.val = (f i (state i.val)).snd := by
+  exact (iunfoldr_getLsb' state ind).1 i
+
 /--
 Correctness theorem for `iunfoldr`.
 -/
@@ -58,4 +103,11 @@ theorem iunfoldr_replace
     iunfoldr f a = (state w, value) := by
   simp [iunfoldr.eq_test state value a init step]
 
+theorem iunfoldr_replace_snd
+  {f : Fin w → α → α × Bool} (state : Nat → α) (value : BitVec w) (a : α)
+    (init : state 0 = a)
+    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value.getLsb i.val)) :
+    (iunfoldr f a).snd = value := by
+  simp [iunfoldr.eq_test state value a init step]
+
 end BitVec

src/Init/Data/BitVec/Lemmas.lean

@@ -2,12 +2,14 @@
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed,
+
 -/
 prelude
 import Init.Data.Bool
 import Init.Data.BitVec.Basic
 import Init.Data.Fin.Lemmas
 import Init.Data.Nat.Lemmas
+import Init.Data.Nat.Mod
 
 namespace BitVec
 
@@ -145,7 +147,8 @@ theorem getLsb_ofNat (n : Nat) (x : Nat) (i : Nat) :
   getLsb (x#n) i = (i < n && x.testBit i) := by
   simp [getLsb, BitVec.ofNat, Fin.val_ofNat']
 
-@[simp, deprecated toNat_ofNat] theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
+@[simp, deprecated toNat_ofNat (since := "2024-02-22")]
+theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
 
 @[simp] theorem getLsb_zero : (0#w).getLsb i = false := by simp [getLsb]
 
@@ -172,8 +175,7 @@ theorem msb_eq_getLsb_last (x : BitVec w) :
     x.getLsb (w-1) = decide (2 ^ (w-1) ≤ x.toNat) := by
   rcases w with rfl | w
   · simp
-  · simp only [Nat.zero_lt_succ, decide_True, getLsb, Nat.testBit, Nat.succ_sub_succ_eq_sub,
-    Nat.sub_zero, Nat.and_one_is_mod, Bool.true_and, Nat.shiftRight_eq_div_pow]
+  · simp only [getLsb, Nat.testBit_to_div_mod, Nat.succ_sub_succ_eq_sub, Nat.sub_zero]
     rcases (Nat.lt_or_ge (BitVec.toNat x) (2 ^ w)) with h | h
     · simp [Nat.div_eq_of_lt h, h]
     · simp only [h]
@@ -220,9 +222,21 @@ theorem toInt_eq_toNat_cond (i : BitVec n) :
       if 2*i.toNat < 2^n then
         (i.toNat : Int)
       else
-        (i.toNat : Int) - (2^n : Nat) := by
-  unfold BitVec.toInt
-  split <;> omega
+        (i.toNat : Int) - (2^n : Nat) :=
+  rfl
+
+theorem msb_eq_false_iff_two_mul_lt (x : BitVec w) : x.msb = false ↔ 2 * x.toNat < 2^w := by
+  cases w <;> simp [Nat.pow_succ, Nat.mul_comm _ 2, msb_eq_decide]
+
+theorem msb_eq_true_iff_two_mul_ge (x : BitVec w) : x.msb = true ↔ 2 * x.toNat ≥ 2^w := by
+  simp [← Bool.ne_false_iff, msb_eq_false_iff_two_mul_lt]
+
+/-- Characterize `x.toInt` in terms of `x.msb`. -/
+theorem toInt_eq_msb_cond (x : BitVec w) :
+    x.toInt = if x.msb then (x.toNat : Int) - (2^w : Nat) else (x.toNat : Int) := by
+  simp only [BitVec.toInt, ← msb_eq_false_iff_two_mul_lt]
+  cases x.msb <;> rfl
+
 
 theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) := by
   simp only [toInt_eq_toNat_cond]
@@ -244,6 +258,12 @@ theorem eq_of_toInt_eq {i j : BitVec n} : i.toInt = j.toInt → i = j := by
   have _jlt := j.isLt
   split <;> split <;> omega
 
+theorem toInt_inj (x y : BitVec n) : x.toInt = y.toInt ↔ x = y :=
+  Iff.intro eq_of_toInt_eq (congrArg BitVec.toInt)
+
+theorem toInt_ne (x y : BitVec n) : x.toInt ≠ y.toInt ↔ x ≠ y  := by
+  rw [Ne, toInt_inj]
+
 @[simp] theorem toNat_ofInt {n : Nat} (i : Int) :
   (BitVec.ofInt n i).toNat = (i % (2^n : Nat)).toNat := by
   unfold BitVec.ofInt
@@ -601,6 +621,17 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
     (shiftLeftZeroExtend x i).msb = x.msb := by
   simp [shiftLeftZeroExtend_eq, BitVec.msb]
 
+theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x <<< n) <<< m = x <<< (n + m) := by
+  ext i
+  simp only [getLsb_shiftLeft, Fin.is_lt, decide_True, Bool.true_and]
+  rw [show i - (n + m) = (i - m - n) by omega]
+  cases h₂ : decide (i < m) <;>
+  cases h₃ : decide (i - m < w) <;>
+  cases h₄ : decide (i - m < n) <;>
+  cases h₅ : decide (i < n + m) <;>
+    simp at * <;> omega
+
 /-! ### ushiftRight -/
 
 @[simp, bv_toNat] theorem toNat_ushiftRight (x : BitVec n) (i : Nat) :
@@ -686,6 +717,11 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
   simp only [getLsb_append, cond_eq_if]
   split <;> simp [*]
 
+theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x >>> n) >>> m = x >>> (n + m) := by
+  ext i
+  simp [Nat.add_assoc n m i]
+
 /-! ### rev -/
 
 theorem getLsb_rev (x : BitVec w) (i : Fin w) :
@@ -896,10 +932,19 @@ theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
 
 theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
   apply eq_of_toNat_eq
-  have y_toNat_le := Nat.le_of_lt y.toNat_lt
+  have y_toNat_le := Nat.le_of_lt y.isLt
   rw [toNat_sub, toNat_add, Nat.mod_add_mod, Nat.add_assoc, ← Nat.add_sub_assoc y_toNat_le,
     Nat.add_sub_cancel_left, Nat.add_mod_right, toNat_mod_cancel]
 
+theorem sub_add_cancel (x y : BitVec w) : x - y + y = x := by
+  rw [sub_toAdd, BitVec.add_assoc, BitVec.add_comm _ y,
+      ← BitVec.add_assoc, ← sub_toAdd, add_sub_cancel]
+
+theorem eq_sub_iff_add_eq {x y z : BitVec w} : x = z - y ↔ x + y = z := by
+  apply Iff.intro <;> intro h
+  · simp [h, sub_add_cancel]
+  · simp [←h, add_sub_cancel]
+
 theorem negOne_eq_allOnes : -1#w = allOnes w := by
   apply eq_of_toNat_eq
   if g : w = 0 then
@@ -909,6 +954,13 @@ theorem negOne_eq_allOnes : -1#w = allOnes w := by
     have r : (2^w - 1) < 2^w := by omega
     simp [Nat.mod_eq_of_lt q, Nat.mod_eq_of_lt r]
 
+theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1 := by
+  apply eq_of_toNat_eq
+  simp only [toNat_neg, ofNat_eq_ofNat, toNat_add, toNat_not, toNat_ofNat, Nat.add_mod_mod]
+  congr
+  have hx : x.toNat < 2^w := x.isLt
+  rw [Nat.sub_sub, Nat.add_comm 1 x.toNat, ← Nat.sub_sub, Nat.sub_add_cancel (by omega)]
+
 /-! ### mul -/
 
 theorem mul_def {n} {x y : BitVec n} : x * y = (ofFin <| x.toFin * y.toFin) := by rfl
@@ -1003,4 +1055,32 @@ theorem toNat_intMax_eq : (intMax w).toNat = 2^w - 1 := by
     (ofBoolListLE bs).getMsb i = (decide (i < bs.length) && bs.getD (bs.length - 1 - i) false) := by
   simp [getMsb_eq_getLsb]
 
+/-! # Rotate Left -/
+
+/-- rotateLeft is invariant under `mod` by the bitwidth. -/
+@[simp]
+theorem rotateLeft_mod_eq_rotateLeft {x : BitVec w} {r : Nat} :
+    x.rotateLeft (r % w) = x.rotateLeft r := by
+  simp only [rotateLeft, Nat.mod_mod]
+
+/-- `rotateLeft` equals the bit fiddling definition of `rotateLeftAux` when the rotation amount is
+smaller than the bitwidth. -/
+theorem rotateLeft_eq_rotateLeftAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :
+    x.rotateLeft r = x.rotateLeftAux r := by
+  simp only [rotateLeft, Nat.mod_eq_of_lt hr]
+
+/-! ## Rotate Right -/
+
+/-- `rotateRight` equals the bit fiddling definition of `rotateRightAux` when the rotation amount is
+smaller than the bitwidth. -/
+theorem rotateRight_eq_rotateRightAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :
+    x.rotateRight r = x.rotateRightAux r := by
+  simp only [rotateRight, Nat.mod_eq_of_lt hr]
+
+/-- rotateRight is invariant under `mod` by the bitwidth. -/
+@[simp]
+theorem rotateRight_mod_eq_rotateRight {x : BitVec w} {r : Nat} :
+    x.rotateRight (r % w) = x.rotateRight r := by
+  simp only [rotateRight, Nat.mod_mod]
+
 end BitVec

src/Init/Data/Bool.lean

@@ -227,6 +227,8 @@ instance : Std.Associative (· != ·) := ⟨bne_assoc⟩
 @[simp] theorem bne_left_inj  : ∀ (x y z : Bool), (x != y) = (x != z) ↔ y = z := by decide
 @[simp] theorem bne_right_inj : ∀ (x y z : Bool), (x != z) = (y != z) ↔ x = y := by decide
 
+theorem eq_not_of_ne : ∀ {x y : Bool}, x ≠ y → x = !y := by decide
+
 /-! ### coercision related normal forms -/
 
 theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
@@ -360,7 +362,8 @@ def toNat (b:Bool) : Nat := cond b 1 0
 theorem toNat_le (c : Bool) : c.toNat ≤ 1 := by
   cases c <;> trivial
 
-@[deprecated toNat_le] abbrev toNat_le_one := toNat_le
+@[deprecated toNat_le (since := "2024-02-23")]
+abbrev toNat_le_one := toNat_le
 
 theorem toNat_lt (b : Bool) : b.toNat < 2 :=
   Nat.lt_succ_of_le (toNat_le _)

src/Init/Data/Char.lean

@@ -5,3 +5,4 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Char.Basic
+import Init.Data.Char.Lemmas

src/Init/Data/Char/Lemmas.lean

@@ -0,0 +1,25 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Data.Char.Basic
+import Init.Data.UInt.Lemmas
+
+namespace Char
+
+theorem le_def {a b : Char} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
+theorem lt_def {a b : Char} : a < b ↔ a.1 < b.1 := .rfl
+theorem lt_iff_val_lt_val {a b : Char} : a < b ↔ a.val < b.val := Iff.rfl
+@[simp] protected theorem not_le {a b : Char} : ¬ a ≤ b ↔ b < a := UInt32.not_le
+@[simp] protected theorem not_lt {a b : Char} : ¬ a < b ↔ b ≤ a := UInt32.not_lt
+@[simp] protected theorem le_refl (a : Char) : a ≤ a := by simp [le_def]
+@[simp] protected theorem lt_irrefl (a : Char) : ¬ a < a := by simp
+protected theorem le_trans {a b c : Char} : a ≤ b → b ≤ c → a ≤ c := UInt32.le_trans
+protected theorem lt_trans {a b c : Char} : a < b → b < c → a < c := UInt32.lt_trans
+protected theorem le_total (a b : Char) : a ≤ b ∨ b ≤ a := UInt32.le_total a.1 b.1
+protected theorem lt_asymm {a b : Char} (h : a < b) : ¬ b < a := UInt32.lt_asymm h
+protected theorem ne_of_lt {a b : Char} (h : a < b) : a ≠ b := Char.ne_of_val_ne (UInt32.ne_of_lt h)
+
+end Char

src/Init/Data/Fin/Lemmas.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2022 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Mario Carneiro
+Authors: Mario Carneiro, Leonardo de Moura
 -/
 prelude
 import Init.Data.Fin.Basic
@@ -11,6 +11,9 @@ import Init.ByCases
 import Init.Conv
 import Init.Omega
 
+-- Remove after the next stage0 update
+set_option allowUnsafeReducibility true
+
 namespace Fin
 
 /-- If you actually have an element of `Fin n`, then the `n` is always positive -/
@@ -59,7 +62,8 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
 @[simp] theorem val_ofNat' (a : Nat) (is_pos : n > 0) :
   (Fin.ofNat' a is_pos).val = a % n := rfl
 
-@[deprecated ofNat'_zero_val] theorem ofNat'_zero_val : (Fin.ofNat' 0 h).val = 0 := Nat.zero_mod _
+@[deprecated ofNat'_zero_val (since := "2024-02-22")]
+theorem ofNat'_zero_val : (Fin.ofNat' 0 h).val = 0 := Nat.zero_mod _
 
 @[simp] theorem mod_val (a b : Fin n) : (a % b).val = a.val % b.val :=
   rfl
@@ -90,6 +94,18 @@ theorem lt_iff_val_lt_val {a b : Fin n} : a < b ↔ a.val < b.val := Iff.rfl
 
 @[simp] protected theorem not_lt {a b : Fin n} : ¬ a < b ↔ b ≤ a := Nat.not_lt
 
+@[simp] protected theorem le_refl (a : Fin n) : a ≤ a := by simp [le_def]
+
+@[simp] protected theorem lt_irrefl (a : Fin n) : ¬ a < a := by simp
+
+protected theorem le_trans {a b c : Fin n} : a ≤ b → b ≤ c → a ≤ c := Nat.le_trans
+
+protected theorem lt_trans {a b c : Fin n} : a < b → b < c → a < c := Nat.lt_trans
+
+protected theorem le_total (a b : Fin n) : a ≤ b ∨ b ≤ a := Nat.le_total a b
+
+protected theorem lt_asymm {a b : Fin n} (h : a < b) : ¬ b < a := Nat.lt_asymm h
+
 protected theorem ne_of_lt {a b : Fin n} (h : a < b) : a ≠ b := Fin.ne_of_val_ne (Nat.ne_of_lt h)
 
 protected theorem ne_of_gt {a b : Fin n} (h : a < b) : b ≠ a := Fin.ne_of_val_ne (Nat.ne_of_gt h)
@@ -819,27 +835,3 @@ protected theorem zero_mul (k : Fin (n + 1)) : (0 : Fin (n + 1)) * k = 0 := by
   simp [ext_iff, mul_def]
 
 end Fin
-
-namespace USize
-
-@[simp] theorem lt_def {a b : USize} : a < b ↔ a.toNat < b.toNat := .rfl
-
-@[simp] theorem le_def {a b : USize} : a ≤ b ↔ a.toNat ≤ b.toNat := .rfl
-
-@[simp] theorem zero_toNat : (0 : USize).toNat = 0 := Nat.zero_mod _
-
-@[simp] theorem mod_toNat (a b : USize) : (a % b).toNat = a.toNat % b.toNat :=
-  Fin.mod_val ..
-
-@[simp] theorem div_toNat (a b : USize) : (a / b).toNat = a.toNat / b.toNat :=
-  Fin.div_val ..
-
-@[simp] theorem modn_toNat (a : USize) (b : Nat) : (a.modn b).toNat = a.toNat % b :=
-  Fin.modn_val ..
-
-theorem mod_lt (a b : USize) (h : 0 < b) : a % b < b := USize.modn_lt _ (by simp at h; exact h)
-
-theorem toNat.inj : ∀ {a b : USize}, a.toNat = b.toNat → a = b
-  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
-
-end USize

src/Init/Data/Int/DivModLemmas.lean

@@ -14,6 +14,8 @@ import Init.RCases
 # Lemmas about integer division needed to bootstrap `omega`.
 -/
 
+-- Remove after the next stage0 update
+set_option allowUnsafeReducibility true
 
 open Nat (succ)
 
@@ -142,12 +144,14 @@ theorem eq_one_of_mul_eq_one_left {a b : Int} (H : 0 ≤ b) (H' : a * b = 1) : b
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => show -ofNat _ = _ by simp
 
+unseal Nat.div in
 @[simp] protected theorem div_zero : ∀ a : Int, div a 0 = 0
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => rfl
 
 @[simp] theorem zero_fdiv (b : Int) : fdiv 0 b = 0 := by cases b <;> rfl
 
+unseal Nat.div in
 @[simp] protected theorem fdiv_zero : ∀ a : Int, fdiv a 0 = 0
   | 0      => rfl
   | succ _ => rfl
@@ -178,7 +182,7 @@ theorem fdiv_eq_div {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fdiv a b = div a
 
 @[simp] theorem mod_zero : ∀ a : Int, mod a 0 = a
   | ofNat _ => congrArg ofNat <| Nat.mod_zero _
-  | -[_+1] => rfl
+  | -[_+1] => congrArg (fun n => -ofNat n) <| Nat.mod_zero _
 
 @[simp] theorem zero_fmod (b : Int) : fmod 0 b = 0 := by cases b <;> rfl
 
@@ -225,7 +229,9 @@ theorem mod_add_div : ∀ a b : Int, mod a b + b * (a.div b) = a
   | ofNat m, -[n+1] => by
     show (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
     rw [Int.neg_mul_neg]; exact congrArg ofNat (Nat.mod_add_div ..)
-  | -[_+1], 0 => rfl
+  | -[m+1], 0 => by
+    show -(↑((succ m) % 0) : Int) + 0 * -↑(succ m / 0) = -↑(succ m)
+    rw [Nat.mod_zero, Int.zero_mul, Int.add_zero]
   | -[m+1], ofNat n => by
     show -(↑((succ m) % n) : Int) + ↑n * -↑(succ m / n) = -↑(succ m)
     rw [Int.mul_neg, ← Int.neg_add]
@@ -763,11 +769,13 @@ theorem ediv_eq_ediv_of_mul_eq_mul {a b c d : Int}
   | (n:Nat) => congrArg ofNat (Nat.div_one _)
   | -[n+1] => by simp [Int.div, neg_ofNat_succ]; rfl
 
+unseal Nat.div in
 @[simp] protected theorem div_neg : ∀ a b : Int, a.div (-b) = -(a.div b)
   | ofNat m, 0 => show ofNat (m / 0) = -↑(m / 0) by rw [Nat.div_zero]; rfl
   | ofNat m, -[n+1] | -[m+1], succ n => (Int.neg_neg _).symm
   | ofNat m, succ n | -[m+1], 0 | -[m+1], -[n+1] => rfl
 
+unseal Nat.div in
 @[simp] protected theorem neg_div : ∀ a b : Int, (-a).div b = -(a.div b)
   | 0, n => by simp [Int.neg_zero]
   | succ m, (n:Nat) | -[m+1], 0 | -[m+1], -[n+1] => rfl
@@ -936,6 +944,7 @@ theorem fdiv_nonneg {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : 0 ≤ a.fdiv b :
   match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
   | _, _, ⟨_, rfl⟩, ⟨_, rfl⟩ => ofNat_fdiv .. ▸ ofNat_zero_le _
 
+unseal Nat.div in
 theorem fdiv_nonpos : ∀ {a b : Int}, 0 ≤ a → b ≤ 0 → a.fdiv b ≤ 0
   | 0, 0, _, _ | 0, -[_+1], _, _ | succ _, 0, _, _ | succ _, -[_+1], _, _ => ⟨_⟩
 

src/Init/Data/Int/Order.lean

@@ -96,7 +96,7 @@ protected theorem le_antisymm {a b : Int} (h₁ : a ≤ b) (h₂ : b ≤ a) : a
   have := Int.ofNat.inj <| Int.add_left_cancel <| this.trans (Int.add_zero _).symm
   rw [← hn, Nat.eq_zero_of_add_eq_zero_left this, ofNat_zero, Int.add_zero a]
 
-protected theorem lt_irrefl (a : Int) : ¬a < a := fun H =>
+@[simp] protected theorem lt_irrefl (a : Int) : ¬a < a := fun H =>
   let ⟨n, hn⟩ := lt.dest H
   have : (a+Nat.succ n) = a+0 := by
     rw [hn, Int.add_zero]
@@ -813,6 +813,20 @@ protected theorem sub_lt_sub_right {a b : Int} (h : a < b) (c : Int) : a - c < b
 protected theorem sub_lt_sub {a b c d : Int} (hab : a < b) (hcd : c < d) : a - d < b - c :=
   Int.add_lt_add hab (Int.neg_lt_neg hcd)
 
+protected theorem lt_of_sub_lt_sub_left {a b c : Int} (h : c - a < c - b) : b < a :=
+  Int.lt_of_neg_lt_neg <| Int.lt_of_add_lt_add_left h
+
+protected theorem lt_of_sub_lt_sub_right {a b c : Int} (h : a - c < b - c) : a < b :=
+  Int.lt_of_add_lt_add_right h
+
+@[simp] protected theorem sub_lt_sub_left_iff (a b c : Int) :
+    c - a < c - b ↔ b < a :=
+  ⟨Int.lt_of_sub_lt_sub_left, (Int.sub_lt_sub_left · c)⟩
+
+@[simp] protected theorem sub_lt_sub_right_iff (a b c : Int) :
+    a - c < b - c ↔ a < b :=
+  ⟨Int.lt_of_sub_lt_sub_right, (Int.sub_lt_sub_right · c)⟩
+
 protected theorem sub_lt_sub_of_le_of_lt {a b c d : Int}
   (hab : a ≤ b) (hcd : c < d) : a - d < b - c :=
   Int.add_lt_add_of_le_of_lt hab (Int.neg_lt_neg hcd)

src/Init/Data/List.lean

@@ -9,3 +9,4 @@ import Init.Data.List.BasicAux
 import Init.Data.List.Control
 import Init.Data.List.Lemmas
 import Init.Data.List.Impl
+import Init.Data.List.TakeDrop

src/Init/Data/List/TakeDrop.lean

@@ -0,0 +1,360 @@
+/-
+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
+-/
+prelude
+import Init.Data.List.Lemmas
+import Init.Data.Nat.Lemmas
+
+/-!
+# Lemmas about `List.take`, `List.drop`, `List.zip` and `List.zipWith`.
+
+These are in a separate file from most of the list lemmas
+as they required importing more lemmas about natural numbers.
+-/
+
+namespace List
+
+open Nat
+
+/-! ### take -/
+
+abbrev take_succ_cons := @take_cons_succ
+
+@[simp] theorem length_take : ∀ (i : Nat) (l : List α), length (take i l) = min i (length l)
+  | 0, l => by simp [Nat.zero_min]
+  | succ n, [] => by simp [Nat.min_zero]
+  | succ n, _ :: l => by simp [Nat.succ_min_succ, length_take]
+
+theorem length_take_le (n) (l : List α) : length (take n l) ≤ n := by simp [Nat.min_le_left]
+
+theorem length_take_le' (n) (l : List α) : length (take n l) ≤ l.length :=
+  by simp [Nat.min_le_right]
+
+theorem length_take_of_le (h : n ≤ length l) : length (take n l) = n := by simp [Nat.min_eq_left h]
+
+theorem take_all_of_le {n} {l : List α} (h : length l ≤ n) : take n l = l :=
+  take_length_le h
+
+@[simp]
+theorem take_left : ∀ l₁ l₂ : List α, take (length l₁) (l₁ ++ l₂) = l₁
+  | [], _ => rfl
+  | a :: l₁, l₂ => congrArg (cons a) (take_left l₁ l₂)
+
+theorem take_left' {l₁ l₂ : List α} {n} (h : length l₁ = n) : take n (l₁ ++ l₂) = l₁ := by
+  rw [← h]; apply take_left
+
+theorem take_take : ∀ (n m) (l : List α), take n (take m l) = take (min n m) l
+  | n, 0, l => by rw [Nat.min_zero, take_zero, take_nil]
+  | 0, m, l => by rw [Nat.zero_min, take_zero, take_zero]
+  | succ n, succ m, nil => by simp only [take_nil]
+  | succ n, succ m, a :: l => by
+    simp only [take, succ_min_succ, take_take n m l]
+
+theorem take_replicate (a : α) : ∀ n m : Nat, take n (replicate m a) = replicate (min n m) a
+  | n, 0 => by simp [Nat.min_zero]
+  | 0, m => by simp [Nat.zero_min]
+  | succ n, succ m => by simp [succ_min_succ, take_replicate]
+
+theorem map_take (f : α → β) :
+    ∀ (L : List α) (i : Nat), (L.take i).map f = (L.map f).take i
+  | [], i => by simp
+  | _, 0 => by simp
+  | h :: t, n + 1 => by dsimp; rw [map_take f t n]
+
+/-- Taking the first `n` elements in `l₁ ++ l₂` is the same as appending the first `n` elements
+of `l₁` to the first `n - l₁.length` elements of `l₂`. -/
+theorem take_append_eq_append_take {l₁ l₂ : List α} {n : Nat} :
+    take n (l₁ ++ l₂) = take n l₁ ++ take (n - l₁.length) l₂ := by
+  induction l₁ generalizing n
+  · simp
+  · cases n
+    · simp [*]
+    · simp only [cons_append, take_cons_succ, length_cons, succ_eq_add_one, cons.injEq,
+        append_cancel_left_eq, true_and, *]
+      congr 1
+      omega
+
+theorem take_append_of_le_length {l₁ l₂ : List α} {n : Nat} (h : n ≤ l₁.length) :
+    (l₁ ++ l₂).take n = l₁.take n := by
+  simp [take_append_eq_append_take, Nat.sub_eq_zero_of_le h]
+
+/-- Taking the first `l₁.length + i` elements in `l₁ ++ l₂` is the same as appending the first
+`i` elements of `l₂` to `l₁`. -/
+theorem take_append {l₁ l₂ : List α} (i : Nat) :
+    take (l₁.length + i) (l₁ ++ l₂) = l₁ ++ take i l₂ := by
+  rw [take_append_eq_append_take, take_all_of_le (Nat.le_add_right _ _), Nat.add_sub_cancel_left]
+
+/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
+length `> i`. Version designed to rewrite from the big list to the small list. -/
+theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
+    get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ :=
+  get_of_eq (take_append_drop j L).symm _ ▸ get_append ..
+
+/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
+length `> i`. Version designed to rewrite from the small list to the big list. -/
+theorem get_take' (L : List α) {j i} :
+    get (L.take j) i =
+    get L ⟨i.1, Nat.lt_of_lt_of_le i.2 (length_take_le' _ _)⟩ := by
+  let ⟨i, hi⟩ := i; rw [length_take, Nat.lt_min] at hi; rw [get_take L _ hi.1]
+
+theorem get?_take {l : List α} {n m : Nat} (h : m < n) : (l.take n).get? m = l.get? m := by
+  induction n generalizing l m with
+  | zero =>
+    exact absurd h (Nat.not_lt_of_le m.zero_le)
+  | succ _ hn =>
+    cases l with
+    | nil => simp only [take_nil]
+    | cons hd tl =>
+      cases m
+      · simp only [get?, take]
+      · simpa only using hn (Nat.lt_of_succ_lt_succ h)
+
+theorem get?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
+    (l.take n).get? m = none :=
+  get?_eq_none.mpr <| Nat.le_trans (length_take_le _ _) h
+
+theorem get?_take_eq_if {l : List α} {n m : Nat} :
+    (l.take n).get? m = if m < n then l.get? m else none := by
+  split
+  · next h => exact get?_take h
+  · next h => exact get?_take_eq_none (Nat.le_of_not_lt h)
+
+@[simp]
+theorem nth_take_of_succ {l : List α} {n : Nat} : (l.take (n + 1)).get? n = l.get? n :=
+  get?_take (Nat.lt_succ_self n)
+
+theorem take_succ {l : List α} {n : Nat} : l.take (n + 1) = l.take n ++ (l.get? n).toList := by
+  induction l generalizing n with
+  | nil =>
+    simp only [Option.toList, get?, take_nil, append_nil]
+  | cons hd tl hl =>
+    cases n
+    · simp only [Option.toList, get?, eq_self_iff_true, take, nil_append]
+    · simp only [hl, cons_append, get?, eq_self_iff_true, take]
+
+@[simp]
+theorem take_eq_nil_iff {l : List α} {k : Nat} : l.take k = [] ↔ l = [] ∨ k = 0 := by
+  cases l <;> cases k <;> simp [Nat.succ_ne_zero]
+
+@[simp]
+theorem take_eq_take :
+    ∀ {l : List α} {m n : Nat}, l.take m = l.take n ↔ min m l.length = min n l.length
+  | [], m, n => by simp [Nat.min_zero]
+  | _ :: xs, 0, 0 => by simp
+  | x :: xs, m + 1, 0 => by simp [Nat.zero_min, succ_min_succ]
+  | x :: xs, 0, n + 1 => by simp [Nat.zero_min, succ_min_succ]
+  | x :: xs, m + 1, n + 1 => by simp [succ_min_succ, take_eq_take]; omega
+
+theorem take_add (l : List α) (m n : Nat) : l.take (m + n) = l.take m ++ (l.drop m).take n := by
+  suffices take (m + n) (take m l ++ drop m l) = take m l ++ take n (drop m l) by
+    rw [take_append_drop] at this
+    assumption
+  rw [take_append_eq_append_take, take_all_of_le, append_right_inj]
+  · simp only [take_eq_take, length_take, length_drop]
+    omega
+  apply Nat.le_trans (m := m)
+  · apply length_take_le
+  · apply Nat.le_add_right
+
+theorem take_eq_nil_of_eq_nil : ∀ {as : List α} {i}, as = [] → as.take i = []
+  | _, _, rfl => take_nil
+
+theorem ne_nil_of_take_ne_nil {as : List α} {i : Nat} (h: as.take i ≠ []) : as ≠ [] :=
+  mt take_eq_nil_of_eq_nil h
+
+theorem dropLast_eq_take (l : List α) : l.dropLast = l.take l.length.pred := by
+  cases l with
+  | nil => simp [dropLast]
+  | cons x l =>
+    induction l generalizing x with
+    | nil => simp [dropLast]
+    | cons hd tl hl => simp [dropLast, hl]
+
+theorem dropLast_take {n : Nat} {l : List α} (h : n < l.length) :
+    (l.take n).dropLast = l.take n.pred := by
+  simp only [dropLast_eq_take, length_take, Nat.le_of_lt h, take_take, pred_le, Nat.min_eq_left]
+
+theorem map_eq_append_split {f : α → β} {l : List α} {s₁ s₂ : List β}
+    (h : map f l = s₁ ++ s₂) : ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = s₁ ∧ map f l₂ = s₂ := by
+  have := h
+  rw [← take_append_drop (length s₁) l] at this ⊢
+  rw [map_append] at this
+  refine ⟨_, _, rfl, append_inj this ?_⟩
+  rw [length_map, length_take, Nat.min_eq_left]
+  rw [← length_map l f, h, length_append]
+  apply Nat.le_add_right
+
+/-! ### drop -/
+
+@[simp]
+theorem drop_eq_nil_iff_le {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by
+  refine' ⟨fun h => _, drop_eq_nil_of_le⟩
+  induction k generalizing l with
+  | zero =>
+    simp only [drop] at h
+    simp [h]
+  | succ k hk =>
+    cases l
+    · simp
+    · simp only [drop] at h
+      simpa [Nat.succ_le_succ_iff] using hk h
+
+theorem drop_length_cons {l : List α} (h : l ≠ []) (a : α) :
+    (a :: l).drop l.length = [l.getLast h] := by
+  induction l generalizing a with
+  | nil =>
+    cases h rfl
+  | cons y l ih =>
+    simp only [drop, length]
+    by_cases h₁ : l = []
+    · simp [h₁]
+    rw [getLast_cons' _ h₁]
+    exact ih h₁ y
+
+/-- Dropping the elements up to `n` in `l₁ ++ l₂` is the same as dropping the elements up to `n`
+in `l₁`, dropping the elements up to `n - l₁.length` in `l₂`, and appending them. -/
+theorem drop_append_eq_append_drop {l₁ l₂ : List α} {n : Nat} :
+    drop n (l₁ ++ l₂) = drop n l₁ ++ drop (n - l₁.length) l₂ := by
+  induction l₁ generalizing n
+  · simp
+  · cases n
+    · simp [*]
+    · simp only [cons_append, drop_succ_cons, length_cons, succ_eq_add_one, append_cancel_left_eq, *]
+      congr 1
+      omega
+
+theorem drop_append_of_le_length {l₁ l₂ : List α} {n : Nat} (h : n ≤ l₁.length) :
+    (l₁ ++ l₂).drop n = l₁.drop n ++ l₂ := by
+  simp [drop_append_eq_append_drop, Nat.sub_eq_zero_of_le h]
+
+
+/-- Dropping the elements up to `l₁.length + i` in `l₁ + l₂` is the same as dropping the elements
+up to `i` in `l₂`. -/
+@[simp]
+theorem drop_append {l₁ l₂ : List α} (i : Nat) : drop (l₁.length + i) (l₁ ++ l₂) = drop i l₂ := by
+  rw [drop_append_eq_append_drop, drop_eq_nil_of_le] <;>
+    simp [Nat.add_sub_cancel_left, Nat.le_add_right]
+
+theorem drop_sizeOf_le [SizeOf α] (l : List α) (n : Nat) : sizeOf (l.drop n) ≤ sizeOf l := by
+  induction l generalizing n with
+  | nil => rw [drop_nil]; apply Nat.le_refl
+  | cons _ _ lih =>
+    induction n with
+    | zero => apply Nat.le_refl
+    | succ n =>
+      exact Trans.trans (lih _) (Nat.le_add_left _ _)
+
+theorem lt_length_drop (L : List α) {i j : Nat} (h : i + j < L.length) : j < (L.drop i).length := by
+  have A : i < L.length := Nat.lt_of_le_of_lt (Nat.le.intro rfl) h
+  rw [(take_append_drop i L).symm] at h
+  simpa only [Nat.le_of_lt A, Nat.min_eq_left, Nat.add_lt_add_iff_left, length_take,
+    length_append] using h
+
+/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
+dropping the first `i` elements. Version designed to rewrite from the big list to the small list. -/
+theorem get_drop (L : List α) {i j : Nat} (h : i + j < L.length) :
+    get L ⟨i + j, h⟩ = get (L.drop i) ⟨j, lt_length_drop L h⟩ := by
+  have : i ≤ L.length := Nat.le_trans (Nat.le_add_right _ _) (Nat.le_of_lt h)
+  rw [get_of_eq (take_append_drop i L).symm ⟨i + j, h⟩, get_append_right'] <;>
+    simp [Nat.min_eq_left this, Nat.add_sub_cancel_left, Nat.le_add_right]
+
+/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
+dropping the first `i` elements. Version designed to rewrite from the small list to the big list. -/
+theorem get_drop' (L : List α) {i j} :
+    get (L.drop i) j = get L ⟨i + j, by
+      rw [Nat.add_comm]
+      exact Nat.add_lt_of_lt_sub (length_drop i L ▸ j.2)⟩ := by
+  rw [get_drop]
+
+@[simp]
+theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j) := by
+  ext
+  simp only [get?_eq_some, get_drop', Option.mem_def]
+  constructor <;> intro ⟨h, ha⟩
+  · exact ⟨_, ha⟩
+  · refine ⟨?_, ha⟩
+    rw [length_drop]
+    rw [Nat.add_comm] at h
+    apply Nat.lt_sub_of_add_lt h
+
+@[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (n + m) l
+  | m, [] => by simp
+  | 0, l => by simp
+  | m + 1, a :: l =>
+    calc
+      drop n (drop (m + 1) (a :: l)) = drop n (drop m l) := rfl
+      _ = drop (n + m) l := drop_drop n m l
+      _ = drop (n + (m + 1)) (a :: l) := rfl
+
+theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (take (m + n) l)
+  | 0, _, _ => by simp
+  | _, _, [] => by simp
+  | _+1, _, _ :: _ => by simpa [Nat.succ_add, take_succ_cons, drop_succ_cons] using take_drop ..
+
+theorem drop_take : ∀ (m n : Nat) (l : List α), drop n (take m l) = take (m - n) (drop n l)
+  | 0, _, _ => by simp
+  | _, 0, _ => by simp
+  | _, _, [] => by simp
+  | m+1, n+1, h :: t => by
+    simp [take_succ_cons, drop_succ_cons, drop_take m n t]
+    congr 1
+    omega
+
+theorem map_drop (f : α → β) :
+    ∀ (L : List α) (i : Nat), (L.drop i).map f = (L.map f).drop i
+  | [], i => by simp
+  | L, 0 => by simp
+  | h :: t, n + 1 => by
+    dsimp
+    rw [map_drop f t]
+
+theorem reverse_take {α} {xs : List α} (n : Nat) (h : n ≤ xs.length) :
+    xs.reverse.take n = (xs.drop (xs.length - n)).reverse := by
+  induction xs generalizing n <;>
+    simp only [reverse_cons, drop, reverse_nil, Nat.zero_sub, length, take_nil]
+  next xs_hd xs_tl xs_ih =>
+  cases Nat.lt_or_eq_of_le h with
+  | inl h' =>
+    have h' := Nat.le_of_succ_le_succ h'
+    rw [take_append_of_le_length, xs_ih _ h']
+    rw [show xs_tl.length + 1 - n = succ (xs_tl.length - n) from _, drop]
+    · rwa [succ_eq_add_one, Nat.sub_add_comm]
+    · rwa [length_reverse]
+  | inr h' =>
+    subst h'
+    rw [length, Nat.sub_self, drop]
+    suffices xs_tl.length + 1 = (xs_tl.reverse ++ [xs_hd]).length by
+      rw [this, take_length, reverse_cons]
+    rw [length_append, length_reverse]
+    rfl
+
+@[simp]
+theorem get_cons_drop : ∀ (l : List α) i, get l i :: drop (i + 1) l = drop i l
+  | _::_, ⟨0, _⟩ => rfl
+  | _::_, ⟨i+1, _⟩ => get_cons_drop _ ⟨i, _⟩
+
+theorem drop_eq_get_cons {n} {l : List α} (h) : drop n l = get l ⟨n, h⟩ :: drop (n + 1) l :=
+  (get_cons_drop _ ⟨n, h⟩).symm
+
+theorem drop_eq_nil_of_eq_nil : ∀ {as : List α} {i}, as = [] → as.drop i = []
+  | _, _, rfl => drop_nil
+
+theorem ne_nil_of_drop_ne_nil {as : List α} {i : Nat} (h: as.drop i ≠ []) : as ≠ [] :=
+  mt drop_eq_nil_of_eq_nil h
+
+/-! ### zipWith -/
+
+@[simp] theorem length_zipWith (f : α → β → γ) (l₁ l₂) :
+    length (zipWith f l₁ l₂) = min (length l₁) (length l₂) := by
+  induction l₁ generalizing l₂ <;> cases l₂ <;>
+    simp_all [succ_min_succ, Nat.zero_min, Nat.min_zero]
+
+/-! ### zip -/
+
+@[simp] theorem length_zip (l₁ : List α) (l₂ : List β) :
+    length (zip l₁ l₂) = min (length l₁) (length l₂) := by
+  simp [zip]
+
+end List

src/Init/Data/Nat/Bitwise/Basic.lean

@@ -78,6 +78,8 @@ of a number.
 -/
 
 /-- `testBit m n` returns whether the `(n+1)` least significant bit is `1` or `0`-/
-def testBit (m n : Nat) : Bool := (m >>> n) &&& 1 != 0
+def testBit (m n : Nat) : Bool :=
+  -- `1 &&& n` is faster than `n &&& 1` for big `n`.
+  1 &&& (m >>> n) != 0
 
 end Nat

src/Init/Data/Nat/Bitwise/Lemmas.lean

@@ -50,13 +50,23 @@ noncomputable def div2Induction {motive : Nat → Sort u}
       apply hyp
       exact Nat.div_lt_self n_pos (Nat.le_refl _)
 
-@[simp] theorem zero_and (x : Nat) : 0 &&& x = 0 := by rfl
+@[simp] theorem zero_and (x : Nat) : 0 &&& x = 0 := by
+  simp only [HAnd.hAnd, AndOp.and, land]
+  unfold bitwise
+  simp
 
 @[simp] theorem and_zero (x : Nat) : x &&& 0 = 0 := by
   simp only [HAnd.hAnd, AndOp.and, land]
   unfold bitwise
   simp
 
+@[simp] theorem one_and_eq_mod_two (n : Nat) : 1 &&& n = n % 2 := by
+  if n0 : n = 0 then
+    subst n0; decide
+  else
+    simp only [HAnd.hAnd, AndOp.and, land]
+    cases mod_two_eq_zero_or_one n with | _ h => simp [bitwise, n0, h]
+
 @[simp] theorem and_one_is_mod (x : Nat) : x &&& 1 = x % 2 := by
   if xz : x = 0 then
     simp [xz, zero_and]
@@ -71,7 +81,7 @@ noncomputable def div2Induction {motive : Nat → Sort u}
 /-! ### testBit -/
 
 @[simp] theorem zero_testBit (i : Nat) : testBit 0 i = false := by
-  simp only [testBit, zero_shiftRight, zero_and, bne_self_eq_false]
+  simp only [testBit, zero_shiftRight, and_zero, bne_self_eq_false]
 
 @[simp] theorem testBit_zero (x : Nat) : testBit x 0 = decide (x % 2 = 1) := by
   cases mod_two_eq_zero_or_one x with | _ p => simp [testBit, p]
@@ -188,8 +198,6 @@ theorem lt_pow_two_of_testBit (x : Nat) (p : ∀i, i ≥ n → testBit x i = fal
   have test_false := p _ i_ge_n
   simp only [test_true] at test_false
 
-/-! ### testBit -/
-
 private theorem succ_mod_two : succ x % 2 = 1 - x % 2 := by
   induction x with
   | zero =>
@@ -233,7 +241,7 @@ theorem testBit_two_pow_add_gt {i j : Nat} (j_lt_i : j < i) (x : Nat) :
     rw [Nat.sub_eq_zero_iff_le] at i_sub_j_eq
     exact Nat.not_le_of_gt j_lt_i i_sub_j_eq
   | d+1 =>
-    simp [Nat.pow_succ, Nat.mul_comm _ 2,  Nat.mul_add_mod]
+    simp [Nat.pow_succ, Nat.mul_comm _ 2, Nat.mul_add_mod]
 
 @[simp] theorem testBit_mod_two_pow (x j i : Nat) :
     testBit (x % 2^j) i = (decide (i < j) && testBit x i) := by
@@ -257,7 +265,7 @@ theorem testBit_two_pow_add_gt {i j : Nat} (j_lt_i : j < i) (x : Nat) :
             exact Nat.lt_add_of_pos_right (Nat.two_pow_pos j)
       simp only [hyp y y_lt_x]
       if i_lt_j : i < j then
-        rw [ Nat.add_comm _ (2^_), testBit_two_pow_add_gt i_lt_j]
+        rw [Nat.add_comm _ (2^_), testBit_two_pow_add_gt i_lt_j]
       else
         simp [i_lt_j]
 
@@ -402,12 +410,12 @@ theorem and_pow_two_identity {x : Nat} (lt : x < 2^n) : x &&& 2^n-1 = x := by
 
 /-! ### lor -/
 
-@[simp] theorem or_zero (x : Nat) : 0 ||| x = x := by
+@[simp] theorem zero_or (x : Nat) : 0 ||| x = x := by
   simp only [HOr.hOr, OrOp.or, lor]
   unfold bitwise
   simp [@eq_comm _ 0]
 
-@[simp] theorem zero_or (x : Nat) : x ||| 0 = x := by
+@[simp] theorem or_zero (x : Nat) : x ||| 0 = x := by
   simp only [HOr.hOr, OrOp.or, lor]
   unfold bitwise
   simp [@eq_comm _ 0]

src/Init/Data/Nat/Div.lean

@@ -82,22 +82,34 @@ decreasing_by apply div_rec_lemma; assumption
 
 @[extern "lean_nat_mod"]
 protected def mod : @& Nat → @& Nat → Nat
-  /- This case is not needed mathematically as the case below is equal to it; however, it makes
-  `0 % n = 0` true definitionally rather than just propositionally.
-  This property is desirable for `Fin n`, as it means `(ofNat 0 : Fin n).val = 0` by definition.
-  Primarily, this is valuable because mathlib in Lean3 assumed this was true definitionally, and so
-  keeping this definitional equality makes mathlib easier to port to mathlib4. -/
+  /-
+  Nat.modCore is defined by well-founded recursion and thus irreducible. Nevertheless it is
+  desireable if trivial `Nat.mod` calculations, namely
+  * `Nat.mod 0 m` for all `m`
+  * `Nat.mod n (m+n)` for concrete literals `n`
+  reduce definitionally.
+  This property is desirable for `Fin n` literals, as it means `(ofNat 0 : Fin n).val = 0` by
+  definition.
+   -/
   | 0, _ => 0
-  | x@(_ + 1), y => Nat.modCore x y
+  | n@(_ + 1), m =>
+    if m ≤ n -- NB: if n < m does not reduce as well as `m ≤ n`!
+    then Nat.modCore n m
+    else n
 
 instance instMod : Mod Nat := ⟨Nat.mod⟩
 
-protected theorem modCore_eq_mod (x y : Nat) : Nat.modCore x y = x % y := by
-  cases x with
-  | zero =>
+protected theorem modCore_eq_mod (n m : Nat) : Nat.modCore n m = n % m := by
+  show Nat.modCore n m = Nat.mod n m
+  match n, m with
+  | 0, _ =>
     rw [Nat.modCore]
     exact if_neg fun ⟨hlt, hle⟩ => Nat.lt_irrefl _ (Nat.lt_of_lt_of_le hlt hle)
-  | succ x => rfl
+  | (_ + 1), _ =>
+    rw [Nat.mod]; dsimp
+    refine iteInduction (fun _ => rfl) (fun h => ?false) -- cannot use `split` this early yet
+    rw [Nat.modCore]
+    exact if_neg fun ⟨_hlt, hle⟩ => h hle
 
 theorem mod_eq (x y : Nat) : x % y = if 0 < y ∧ y ≤ x then (x - y) % y else x := by
   rw [←Nat.modCore_eq_mod, ←Nat.modCore_eq_mod, Nat.modCore]

src/Init/Data/Nat/Gcd.lean

@@ -37,11 +37,11 @@ def gcd (m n : @& Nat) : Nat :=
   termination_by m
   decreasing_by simp_wf; apply mod_lt _ (zero_lt_of_ne_zero _); assumption
 
-@[simp] theorem gcd_zero_left (y : Nat) : gcd 0 y = y :=
-  rfl
+@[simp] theorem gcd_zero_left (y : Nat) : gcd 0 y = y := by
+  rw [gcd]; rfl
 
-theorem gcd_succ (x y : Nat) : gcd (succ x) y = gcd (y % succ x) (succ x) :=
-  rfl
+theorem gcd_succ (x y : Nat) : gcd (succ x) y = gcd (y % succ x) (succ x) := by
+  rw [gcd]; rfl
 
 @[simp] theorem gcd_one_left (n : Nat) : gcd 1 n = 1 := by
   rw [gcd_succ, mod_one]
@@ -64,7 +64,7 @@ instance : Std.IdempotentOp gcd := ⟨gcd_self⟩
 
 theorem gcd_rec (m n : Nat) : gcd m n = gcd (n % m) m :=
   match m with
-  | 0 => by have := (mod_zero n).symm; rwa [gcd_zero_right]
+  | 0 => by have := (mod_zero n).symm; rwa [gcd, gcd_zero_right]
   | _ + 1 => by simp [gcd_succ]
 
 @[elab_as_elim] theorem gcd.induction {P : Nat → Nat → Prop} (m n : Nat)

src/Init/Data/Nat/Lemmas.lean

@@ -137,14 +137,14 @@ protected theorem sub_le_iff_le_add' {a b c : Nat} : a - b ≤ c ↔ a ≤ b + c
 protected theorem le_sub_iff_add_le {n : Nat} (h : k ≤ m) : n ≤ m - k ↔ n + k ≤ m :=
   ⟨Nat.add_le_of_le_sub h, Nat.le_sub_of_add_le⟩
 
-@[deprecated Nat.le_sub_iff_add_le]
+@[deprecated Nat.le_sub_iff_add_le (since := "2024-02-19")]
 protected theorem add_le_to_le_sub (n : Nat) (h : m ≤ k) : n + m ≤ k ↔ n ≤ k - m :=
   (Nat.le_sub_iff_add_le h).symm
 
 protected theorem add_le_of_le_sub' {n k m : Nat} (h : m ≤ k) : n ≤ k - m → m + n ≤ k :=
   Nat.add_comm .. ▸ Nat.add_le_of_le_sub h
 
-@[deprecated Nat.add_le_of_le_sub']
+@[deprecated Nat.add_le_of_le_sub' (since := "2024-02-19")]
 protected theorem add_le_of_le_sub_left {n k m : Nat} (h : m ≤ k) : n ≤ k - m → m + n ≤ k :=
   Nat.add_le_of_le_sub' h
 
@@ -401,11 +401,11 @@ protected theorem mul_min_mul_left (a b c : Nat) : min (a * b) (a * c) = a * min
 
 /-! ### mul -/
 
-@[deprecated Nat.mul_le_mul_left]
+@[deprecated Nat.mul_le_mul_left (since := "2024-02-19")]
 protected theorem mul_le_mul_of_nonneg_left {a b c : Nat} : a ≤ b → c * a ≤ c * b :=
   Nat.mul_le_mul_left c
 
-@[deprecated Nat.mul_le_mul_right]
+@[deprecated Nat.mul_le_mul_right (since := "2024-02-19")]
 protected theorem mul_le_mul_of_nonneg_right {a b c : Nat} : a ≤ b → a * c ≤ b * c :=
   Nat.mul_le_mul_right c
 
@@ -478,6 +478,7 @@ protected theorem mul_lt_mul_of_lt_of_lt {a b c d : Nat} (hac : a < c) (hbd : b
 
 theorem succ_mul_succ (a b) : succ a * succ b = a * b + a + b + 1 := by
   rw [succ_mul, mul_succ]; rfl
+
 theorem mul_le_add_right (m k n : Nat) : k * m ≤ m + n ↔ (k-1) * m ≤ n := by
   match k with
   | 0 =>
@@ -677,6 +678,10 @@ protected theorem pow_lt_pow_iff_right {a n m : Nat} (h : 1 < a) :
 
 /-! ### log2 -/
 
+@[simp]
+theorem log2_zero : Nat.log2 0 = 0 := by
+  simp [Nat.log2]
+
 theorem le_log2 (h : n ≠ 0) : k ≤ n.log2 ↔ 2 ^ k ≤ n := by
   match k with
   | 0 => simp [show 1 ≤ n from Nat.pos_of_ne_zero h]
@@ -697,7 +702,7 @@ theorem log2_self_le (h : n ≠ 0) : 2 ^ n.log2 ≤ n := (le_log2 h).1 (Nat.le_r
 
 theorem lt_log2_self : n < 2 ^ (n.log2 + 1) :=
   match n with
-  | 0 => Nat.zero_lt_two
+  | 0 => by simp
   | n+1 => (log2_lt n.succ_ne_zero).1 (Nat.le_refl _)
 
 /-! ### dvd -/
@@ -789,6 +794,9 @@ theorem shiftLeft_shiftLeft (m n : Nat) : ∀ k, (m <<< n) <<< k = m <<< (n + k)
   | 0 => rfl
   | k + 1 => by simp [← Nat.add_assoc, shiftLeft_shiftLeft _ _ k, shiftLeft_succ]
 
+@[simp] theorem shiftLeft_shiftRight (x n : Nat) : x <<< n >>> n = x := by
+  rw [Nat.shiftLeft_eq, Nat.shiftRight_eq_div_pow, Nat.mul_div_cancel _ (Nat.two_pow_pos _)]
+
 theorem mul_add_div {m : Nat} (m_pos : m > 0) (x y : Nat) : (m * x + y) / m = x + y / m := by
   match x with
   | 0 => simp

src/Init/Data/Nat/Linear.lean

@@ -714,4 +714,10 @@ theorem Expr.eq_of_toNormPoly_eq (ctx : Context) (e e' : Expr) (h : e.toNormPoly
   simp [Expr.toNormPoly, Poly.norm] at h
   assumption
 
-end Nat.Linear
+end Linear
+
+def elimOffset {α : Sort u} (a b k : Nat) (h₁ : a + k = b + k) (h₂ : a = b → α) : α := by
+  simp_arith at h₁
+  exact h₂ h₁
+
+end Nat

src/Init/Data/Option/Basic.lean

@@ -18,8 +18,8 @@ def getM [Alternative m] : Option α → m α
   | none     => failure
   | some a   => pure a
 
-@[deprecated getM] def toMonad [Monad m] [Alternative m] : Option α → m α :=
-  getM
+@[deprecated getM (since := "2024-04-17")]
+def toMonad [Monad m] [Alternative m] : Option α → m α := getM
 
 /-- Returns `true` on `some x` and `false` on `none`. -/
 @[inline] def isSome : Option α → Bool

src/Init/Data/Stream.lean

@@ -94,7 +94,7 @@ instance : Stream (Subarray α) α where
   next? s :=
     if h : s.start < s.stop then
       have : s.start + 1 ≤ s.stop := Nat.succ_le_of_lt h
-      some (s.as.get ⟨s.start, Nat.lt_of_lt_of_le h s.stop_le_array_size⟩,
+      some (s.array.get ⟨s.start, Nat.lt_of_lt_of_le h s.stop_le_array_size⟩,
         { s with start := s.start + 1, start_le_stop := this })
     else
       none

src/Init/Data/String.lean

@@ -6,3 +6,4 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.String.Basic
 import Init.Data.String.Extra
+import Init.Data.String.Lemmas

src/Init/Data/String/Basic.lean

@@ -24,23 +24,59 @@ instance : LT String :=
 instance decLt (s₁ s₂ : @& String) : Decidable (s₁ < s₂) :=
   List.hasDecidableLt s₁.data s₂.data
 
+@[reducible] protected def le (a b : String) : Prop := ¬ b < a
+
+instance : LE String :=
+  ⟨String.le⟩
+
+instance decLE (s₁ s₂ : String) : Decidable (s₁ ≤ s₂) :=
+  inferInstanceAs (Decidable (Not _))
+
+/--
+Returns the length of a string in Unicode code points.
+
+Examples:
+* `"".length = 0`
+* `"abc".length = 3`
+* `"L∃∀N".length = 4`
+-/
 @[extern "lean_string_length"]
 def length : (@& String) → Nat
   | ⟨s⟩ => s.length
 
-/-- The internal implementation uses dynamic arrays and will perform destructive updates
-   if the String is not shared. -/
+/--
+Pushes a character onto the end of a string.
+
+The internal implementation uses dynamic arrays and will perform destructive updates
+if the string is not shared.
+
+Example: `"abc".push 'd' = "abcd"`
+-/
 @[extern "lean_string_push"]
 def push : String → Char → String
   | ⟨s⟩, c => ⟨s ++ [c]⟩
 
-/-- The internal implementation uses dynamic arrays and will perform destructive updates
-   if the String is not shared. -/
+/--
+Appends two strings.
+
+The internal implementation uses dynamic arrays and will perform destructive updates
+if the string is not shared.
+
+Example: `"abc".append "def" = "abcdef"`
+-/
 @[extern "lean_string_append"]
 def append : String → (@& String) → String
   | ⟨a⟩, ⟨b⟩ => ⟨a ++ b⟩
 
-/-- O(n) in the runtime, where n is the length of the String -/
+/--
+Converts a string to a list of characters.
+
+Even though the logical model of strings is as a structure that wraps a list of characters,
+this operation takes time and space linear in the length of the string, because the compiler
+uses an optimized representation as dynamic arrays.
+
+Example: `"abc".toList = ['a', 'b', 'c']`
+-/
 def toList (s : String) : List Char :=
   s.data
 
@@ -59,9 +95,17 @@ def utf8GetAux : List Char → Pos → Pos → Char
   | c::cs, i, p => if i = p then c else utf8GetAux cs (i + c) p
 
 /--
-  Return character at position `p`. If `p` is not a valid position
-  returns `(default : Char)`.
-  See `utf8GetAux` for the reference implementation.
+Returns the character at position `p` of a string. If `p` is not a valid position,
+returns `(default : Char)`.
+
+See `utf8GetAux` for the reference implementation.
+
+Examples:
+* `"abc".get ⟨1⟩ = 'b'`
+* `"abc".get ⟨3⟩ = (default : Char) = 'A'`
+
+Positions can also be invalid if a byte index points into the middle of a multi-byte UTF-8
+character. For example,`"L∃∀N".get ⟨2⟩ = (default : Char) = 'A'`.
 -/
 @[extern "lean_string_utf8_get"]
 def get (s : @& String) (p : @& Pos) : Char :=
@@ -72,12 +116,30 @@ def utf8GetAux? : List Char → Pos → Pos → Option Char
   | [],    _, _ => none
   | c::cs, i, p => if i = p then c else utf8GetAux? cs (i + c) p
 
+/--
+Returns the character at position `p`. If `p` is not a valid position, returns `none`.
+
+Examples:
+* `"abc".get? ⟨1⟩ = some 'b'`
+* `"abc".get? ⟨3⟩ = none`
+
+Positions can also be invalid if a byte index points into the middle of a multi-byte UTF-8
+character. For example, `"L∃∀N".get? ⟨2⟩ = none`
+-/
 @[extern "lean_string_utf8_get_opt"]
 def get? : (@& String) → (@& Pos) → Option Char
   | ⟨s⟩, p => utf8GetAux? s 0 p
 
 /--
-  Similar to `get`, but produces a panic error message if `p` is not a valid `String.Pos`.
+Returns the character at position `p` of a string. If `p` is not a valid position,
+returns `(default : Char)` and produces a panic error message.
+
+Examples:
+* `"abc".get! ⟨1⟩ = 'b'`
+* `"abc".get! ⟨3⟩` panics
+
+Positions can also be invalid if a byte index points into the middle of a multi-byte UTF-8 character. For example,
+`"L∃∀N".get! ⟨2⟩` panics.
 -/
 @[extern "lean_string_utf8_get_bang"]
 def get! (s : @& String) (p : @& Pos) : Char :=
@@ -89,13 +151,49 @@ def utf8SetAux (c' : Char) : List Char → Pos → Pos → List Char
   | c::cs, i, p =>
     if i = p then (c'::cs) else c::(utf8SetAux c' cs (i + c) p)
 
+/--
+Replaces the character at a specified position in a string with a new character. If the position
+is invalid, the string is returned unchanged.
+
+If both the replacement character and the replaced character are ASCII characters and the string
+is not shared, destructive updates are used.
+
+Examples:
+* `"abc".set ⟨1⟩ 'B' = "aBc"`
+* `"abc".set ⟨3⟩ 'D' = "abc"`
+* `"L∃∀N".set ⟨4⟩ 'X' = "L∃XN"`
+
+Because `'∃'` is a multi-byte character, the byte index `2` in `L∃∀N` is an invalid position,
+so `"L∃∀N".set ⟨2⟩ 'X' = "L∃∀N"`.
+-/
 @[extern "lean_string_utf8_set"]
 def set : String → (@& Pos) → Char → String
   | ⟨s⟩, i, c => ⟨utf8SetAux c s 0 i⟩
 
+/--
+Replaces the character at position `p` in the string `s` with the result of applying `f` to that character.
+If `p` is an invalid position, the string is returned unchanged.
+
+Examples:
+* `abc.modify ⟨1⟩ Char.toUpper = "aBc"`
+* `abc.modify ⟨3⟩ Char.toUpper = "abc"`
+-/
 def modify (s : String) (i : Pos) (f : Char → Char) : String :=
   s.set i <| f <| s.get i
 
+/--
+Returns the next position in a string after position `p`. If `p` is not a valid position or `p = s.endPos`,
+the result is unspecified.
+
+Examples:
+Given `def abc := "abc"` and `def lean := "L∃∀N"`,
+* `abc.get (0 |> abc.next) = 'b'`
+* `lean.get (0 |> lean.next |> lean.next) = '∀'`
+
+Cases where the result is unspecified:
+* `"abc".next ⟨3⟩`, since `3 = s.endPos`
+* `"L∃∀N".next ⟨2⟩`, since `2` points into the middle of a multi-byte UTF-8 character
+-/
 @[extern "lean_string_utf8_next"]
 def next (s : @& String) (p : @& Pos) : Pos :=
   let c := get s p
@@ -107,16 +205,52 @@ def utf8PrevAux : List Char → Pos → Pos → Pos
     let i' := i + c
     if i' = p then i else utf8PrevAux cs i' p
 
+/--
+Returns the position in a string before a specified position, `p`. If `p = ⟨0⟩`, returns `0`.
+If `p` is not a valid position, the result is unspecified.
+
+Examples:
+Given `def abc := "abc"` and `def lean := "L∃∀N"`,
+* `abc.get (abc.endPos |> abc.prev) = 'c'`
+* `lean.get (lean.endPos |> lean.prev |> lean.prev |> lean.prev) = '∃'`
+* `"L∃∀N".prev ⟨3⟩` is unspecified, since byte 3 occurs in the middle of the multi-byte character `'∃'`.
+-/
 @[extern "lean_string_utf8_prev"]
 def prev : (@& String) → (@& Pos) → Pos
   | ⟨s⟩, p => if p = 0 then 0 else utf8PrevAux s 0 p
 
+/--
+Returns the first character in `s`. If `s = ""`, returns `(default : Char)`.
+
+Examples:
+* `"abc".front = 'a'`
+* `"".front = (default : Char)`
+-/
 def front (s : String) : Char :=
   get s 0
 
+/--
+Returns the last character in `s`. If `s = ""`, returns `(default : Char)`.
+
+Examples:
+* `"abc".back = 'c'`
+* `"".back = (default : Char)`
+-/
 def back (s : String) : Char :=
   get s (prev s s.endPos)
 
+/--
+Returns `true` if a specified position is greater than or equal to the position which
+points to the end of a string. Otherwise, returns `false`.
+
+Examples:
+Given `def abc := "abc"` and `def lean := "L∃∀N"`,
+* `(0 |> abc.next |> abc.next |> abc.atEnd) = false`
+* `(0 |> abc.next |> abc.next |> abc.next |> abc.next |> abc.atEnd) = true`
+* `(0 |> lean.next |> lean.next |> lean.next |> lean.next |> lean.atEnd) = true`
+
+Because `"L∃∀N"` contains multi-byte characters, `lean.next (lean.next 0)` is not equal to `abc.next (abc.next 0)`.
+-/
 @[extern "lean_string_utf8_at_end"]
 def atEnd : (@& String) → (@& Pos) → Bool
   | s, p => p.byteIdx ≥ utf8ByteSize s
@@ -594,13 +728,15 @@ def substrEq (s1 : String) (off1 : String.Pos) (s2 : String) (off2 : String.Pos)
   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
+    if _h : off1.byteIdx < stop1.byteIdx then
       let c₁ := s1.get off1
       let c₂ := s2.get off2
-      have := Nat.sub_lt_sub_left h (Nat.add_lt_add_left (one_le_csize c₁) off1.1)
       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 (one_le_csize c₁) off1.1)
+    decreasing_tactic
 
 /-- Return true iff `p` is a prefix of `s` -/
 def isPrefixOf (p : String) (s : String) : Bool :=
@@ -815,6 +951,10 @@ def beq (ss1 ss2 : Substring) : Bool :=
 
 instance hasBeq : BEq Substring := ⟨beq⟩
 
+/-- Checks whether two substrings have the same position and content. -/
+def sameAs (ss1 ss2 : Substring) : Bool :=
+  ss1.startPos == ss2.startPos && ss1 == ss2
+
 end Substring
 
 namespace String

src/Init/Data/String/Extra.lean

@@ -198,4 +198,35 @@ def removeLeadingSpaces (s : String) : String :=
   let n := findLeadingSpacesSize s
   if n == 0 then s else removeNumLeadingSpaces n s
 
+/--
+Replaces each `\r\n` with `\n` to normalize line endings,
+but does not validate that there are no isolated `\r` characters.
+It is an optimized version of `String.replace text "\r\n" "\n"`.
+-/
+def crlfToLf (text : String) : String :=
+  go "" 0 0
+where
+  go (acc : String) (accStop pos : String.Pos) : String :=
+    if h : text.atEnd pos then
+      -- note: if accStop = 0 then acc is empty
+      if accStop = 0 then text else acc ++ text.extract accStop pos
+    else
+      let c := text.get' pos h
+      let pos' := text.next' pos h
+      if h' : ¬ text.atEnd pos' ∧ c == '\r' ∧ text.get pos' == '\n' then
+        let acc := acc ++ text.extract accStop pos
+        go acc pos' (text.next' pos' h'.1)
+      else
+        go acc accStop pos'
+  termination_by text.utf8ByteSize - pos.byteIdx
+  decreasing_by
+    decreasing_with
+      show text.utf8ByteSize - (text.next' (text.next' pos _) _).byteIdx < text.utf8ByteSize - pos.byteIdx
+      have k := Nat.gt_of_not_le <| mt decide_eq_true h
+      exact Nat.sub_lt_sub_left k (Nat.lt_trans (String.lt_next text pos) (String.lt_next _ _))
+    decreasing_with
+      show text.utf8ByteSize - (text.next' pos _).byteIdx < text.utf8ByteSize - pos.byteIdx
+      have k := Nat.gt_of_not_le <| mt decide_eq_true h
+      exact Nat.sub_lt_sub_left k (String.lt_next _ _)
+
 end String

src/Init/Data/String/Lemmas.lean

@@ -0,0 +1,21 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Data.Char.Lemmas
+
+namespace String
+
+protected theorem data_eq_of_eq {a b : String} (h : a = b) : a.data = b.data :=
+  h ▸ rfl
+protected theorem ne_of_data_ne {a b : String} (h : a.data ≠ b.data) : a ≠ b :=
+  fun h' => absurd (String.data_eq_of_eq h') h
+@[simp] protected theorem lt_irrefl (s : String) : ¬ s < s :=
+  List.lt_irrefl' Char.lt_irrefl s.data
+protected theorem ne_of_lt {a b : String} (h : a < b) : a ≠ b := by
+  have := String.lt_irrefl a
+  intro h; subst h; contradiction
+
+end String

src/Init/Data/UInt.lean

@@ -6,3 +6,4 @@ Authors: Henrik Böving
 prelude
 import Init.Data.UInt.Basic
 import Init.Data.UInt.Log2
+import Init.Data.UInt.Lemmas

src/Init/Data/UInt/Basic.lean

@@ -364,6 +364,3 @@ instance (a b : USize) : Decidable (a < b) := USize.decLt a b
 instance (a b : USize) : Decidable (a ≤ b) := USize.decLe a b
 instance : Max USize := maxOfLe
 instance : Min USize := minOfLe
-
-theorem USize.modn_lt {m : Nat} : ∀ (u : USize), m > 0 → USize.toNat (u % m) < m
-  | ⟨u⟩, h => Fin.modn_lt u h

src/Init/Data/UInt/Lemmas.lean

@@ -0,0 +1,66 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Data.UInt.Basic
+import Init.Data.Fin.Lemmas
+
+set_option hygiene false in
+macro "declare_uint_theorems" typeName:ident : command =>
+`(
+namespace $typeName
+
+instance : Inhabited $typeName where
+  default := 0
+
+theorem zero_def : (0 : $typeName) = ⟨0⟩ := rfl
+theorem one_def : (1 : $typeName) = ⟨1⟩ := rfl
+theorem sub_def (a b : $typeName) : a - b = ⟨a.val - b.val⟩ := rfl
+theorem mul_def (a b : $typeName) : a * b = ⟨a.val * b.val⟩ := rfl
+theorem mod_def (a b : $typeName) : a % b = ⟨a.val % b.val⟩ := rfl
+theorem add_def (a b : $typeName) : a + b = ⟨a.val + b.val⟩ := rfl
+
+@[simp] theorem mk_val_eq : ∀ (a : $typeName), mk a.val = a
+  | ⟨_, _⟩ => rfl
+theorem val_eq_of_lt {a : Nat} : a < size → ((ofNat a).val : Nat) = a :=
+  Nat.mod_eq_of_lt
+
+theorem le_def {a b : $typeName} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
+theorem lt_def {a b : $typeName} : a < b ↔ a.1 < b.1 := .rfl
+theorem lt_iff_val_lt_val {a b : $typeName} : a < b ↔ a.val < b.val := .rfl
+@[simp] protected theorem not_le {a b : $typeName} : ¬ a ≤ b ↔ b < a := Fin.not_le
+@[simp] protected theorem not_lt {a b : $typeName} : ¬ a < b ↔ b ≤ a := Fin.not_lt
+@[simp] protected theorem le_refl (a : $typeName) : a ≤ a := by simp [le_def]
+@[simp] protected theorem lt_irrefl (a : $typeName) : ¬ a < a := by simp
+protected theorem le_trans {a b c : $typeName} : a ≤ b → b ≤ c → a ≤ c := Fin.le_trans
+protected theorem lt_trans {a b c : $typeName} : a < b → b < c → a < c := Fin.lt_trans
+protected theorem le_total (a b : $typeName) : a ≤ b ∨ b ≤ a := Fin.le_total a.1 b.1
+protected theorem lt_asymm {a b : $typeName} (h : a < b) : ¬ b < a := Fin.lt_asymm h
+protected theorem val_eq_of_eq {a b : $typeName} (h : a = b) : a.val = b.val := h ▸ rfl
+protected theorem eq_of_val_eq {a b : $typeName} (h : a.val = b.val) : a = b := by cases a; cases b; simp at h; simp [h]
+open $typeName (val_eq_of_eq) in
+protected theorem ne_of_val_ne {a b : $typeName} (h : a.val ≠ b.val) : a ≠ b := fun h' => absurd (val_eq_of_eq h') h
+open $typeName (ne_of_val_ne) in
+protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := ne_of_val_ne (Fin.ne_of_lt h)
+
+@[simp] protected theorem zero_toNat : (0 : $typeName).toNat = 0 := Nat.zero_mod _
+@[simp] protected theorem mod_toNat (a b : $typeName) : (a % b).toNat = a.toNat % b.toNat := Fin.mod_val ..
+@[simp] protected theorem div_toNat (a b : $typeName) : (a / b).toNat = a.toNat / b.toNat := Fin.div_val ..
+@[simp] protected theorem modn_toNat (a : $typeName) (b : Nat) : (a.modn b).toNat = a.toNat % b := Fin.modn_val ..
+protected theorem modn_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % m) < m
+  | ⟨u⟩, h => Fin.modn_lt u h
+open $typeName (modn_lt) in
+protected theorem mod_lt (a b : $typeName) (h : 0 < b) : a % b < b := modn_lt _ (by simp [lt_def] at h; exact h)
+protected theorem toNat.inj : ∀ {a b : $typeName}, a.toNat = b.toNat → a = b
+  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
+
+end $typeName
+)
+
+declare_uint_theorems UInt8
+declare_uint_theorems UInt16
+declare_uint_theorems UInt32
+declare_uint_theorems UInt64
+declare_uint_theorems USize

src/Init/Grind.lean

@@ -0,0 +1,10 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Grind.Norm
+import Init.Grind.Tactics
+import Init.Grind.Lemmas
+import Init.Grind.Cases

src/Init/Grind/Cases.lean

@@ -0,0 +1,15 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Core
+
+attribute [grind_cases] And Prod False Empty True Unit Exists
+
+namespace Lean.Grind.Eager
+
+attribute [scoped grind_cases] Or
+
+end Lean.Grind.Eager

src/Init/Grind/Lemmas.lean

@@ -0,0 +1,14 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Core
+
+namespace Lean.Grind
+
+theorem intro_with_eq (p p' q : Prop) (he : p = p') (h : p' → q) : p → q :=
+  fun hp => h (he.mp hp)
+
+end Lean.Grind

src/Init/Grind/Norm.lean

@@ -0,0 +1,110 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.SimpLemmas
+import Init.Classical
+import Init.ByCases
+
+namespace Lean.Grind
+/-!
+Normalization theorems for the `grind` tactic.
+
+We are also going to use simproc's in the future.
+-/
+
+-- Not
+attribute [grind_norm] Classical.not_not
+
+-- Ne
+attribute [grind_norm] ne_eq
+
+-- Iff
+@[grind_norm] theorem iff_eq (p q : Prop) : (p ↔ q) = (p = q) := by
+  by_cases p <;> by_cases q <;> simp [*]
+
+-- Eq
+attribute [grind_norm] eq_self heq_eq_eq
+
+-- Prop equality
+@[grind_norm] theorem eq_true_eq (p : Prop) : (p = True) = p := by simp
+@[grind_norm] theorem eq_false_eq (p : Prop) : (p = False) = ¬p := by simp
+@[grind_norm] theorem not_eq_prop (p q : Prop) : (¬(p = q)) = (p = ¬q) := by
+  by_cases p <;> by_cases q <;> simp [*]
+
+-- True
+attribute [grind_norm] not_true
+
+-- False
+attribute [grind_norm] not_false_eq_true
+
+-- Implication as a clause
+@[grind_norm] theorem imp_eq (p q : Prop) : (p → q) = (¬ p ∨ q) := by
+  by_cases p <;> by_cases q <;> simp [*]
+
+-- And
+@[grind_norm↓] theorem not_and (p q : Prop) : (¬(p ∧ q)) = (¬p ∨ ¬q) := by
+  by_cases p <;> by_cases q <;> simp [*]
+attribute [grind_norm] and_true true_and and_false false_and and_assoc
+
+-- Or
+attribute [grind_norm↓] not_or
+attribute [grind_norm] or_true true_or or_false false_or or_assoc
+
+-- ite
+attribute [grind_norm] ite_true ite_false
+@[grind_norm↓] theorem not_ite {_ : Decidable p} (q r : Prop) : (¬ite p q r) = ite p (¬q) (¬r) := by
+  by_cases p <;> simp [*]
+
+-- Forall
+@[grind_norm↓] theorem not_forall (p : α → Prop) : (¬∀ x, p x) = ∃ x, ¬p x := by simp
+attribute [grind_norm] forall_and
+
+-- Exists
+@[grind_norm↓] theorem not_exists (p : α → Prop) : (¬∃ x, p x) = ∀ x, ¬p x := by simp
+attribute [grind_norm] exists_const exists_or
+
+-- Bool cond
+@[grind_norm] theorem cond_eq_ite (c : Bool) (a b : α) : cond c a b = ite c a b := by
+  cases c <;> simp [*]
+
+-- Bool or
+attribute [grind_norm]
+  Bool.or_false Bool.or_true Bool.false_or Bool.true_or Bool.or_eq_true Bool.or_assoc
+
+-- Bool and
+attribute [grind_norm]
+  Bool.and_false Bool.and_true Bool.false_and Bool.true_and Bool.and_eq_true Bool.and_assoc
+
+-- Bool not
+attribute [grind_norm]
+  Bool.not_not
+
+-- beq
+attribute [grind_norm] beq_iff_eq
+
+-- bne
+attribute [grind_norm] bne_iff_ne
+
+-- Bool not eq true/false
+attribute [grind_norm] Bool.not_eq_true Bool.not_eq_false
+
+-- decide
+attribute [grind_norm] decide_eq_true_eq decide_not not_decide_eq_true
+
+-- Nat LE
+attribute [grind_norm] Nat.le_zero_eq
+
+-- Nat/Int LT
+@[grind_norm] theorem Nat.lt_eq (a b : Nat) : (a < b) = (a + 1 ≤ b) := by
+  simp [Nat.lt, LT.lt]
+
+@[grind_norm] theorem Int.lt_eq (a b : Int) : (a < b) = (a + 1 ≤ b) := by
+  simp [Int.lt, LT.lt]
+
+-- GT GE
+attribute [grind_norm] GT.gt GE.ge
+
+end Lean.Grind

src/Init/Grind/Tactics.lean

@@ -0,0 +1,25 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Tactics
+
+namespace Lean.Grind
+/--
+The configuration for `grind`.
+Passed to `grind` using, for example, the `grind (config := { eager := true })` syntax.
+-/
+structure Config where
+  /--
+  When `eager` is true (default: `false`), `grind` eagerly splits `if-then-else` and `match`
+  expressions.
+  -/
+  eager : Bool := false
+  deriving Inhabited, BEq
+
+/-!
+`grind` tactic and related tactics.
+-/
+end Lean.Grind

src/Init/MetaTypes.lean

@@ -169,6 +169,11 @@ structure Config where
   That is, given a local context containing entry `x : t := e`, the free variable `x` reduces to `e`.
   -/
   zetaDelta         : Bool := false
+  /--
+  When `index` (default : `true`) is `false`, `simp` will only use the root symbol
+  to find candidate `simp` theorems. It approximates Lean 3 `simp` behavior.
+  -/
+  index             : Bool := true
   deriving Inhabited, BEq
 
 -- Configuration object for `simp_all`

src/Init/Notation.lean

@@ -687,4 +687,27 @@ syntax (name := checkSimp) "#check_simp " term "~>" term : command
 -/
 syntax (name := checkSimpFailure) "#check_simp " term "!~>" : command
 
+/--
+The `seal foo` command ensures that the definition of `foo` is sealed, meaning it is marked as `[irreducible]`.
+This command is particularly useful in contexts where you want to prevent the reduction of `foo` in proofs.
+
+In terms of functionality, `seal foo` is equivalent to `attribute [local irreducible] foo`.
+This attribute specifies that `foo` should be treated as irreducible only within the local scope,
+which helps in maintaining the desired abstraction level without affecting global settings.
+-/
+syntax "seal " (ppSpace ident)+ : command
+
+/--
+The `unseal foo` command ensures that the definition of `foo` is unsealed, meaning it is marked as `[semireducible]`, the
+default reducibility setting. This command is useful when you need to allow some level of reduction of `foo` in proofs.
+
+Functionally, `unseal foo` is equivalent to `attribute [local semireducible] foo`.
+Applying this attribute makes `foo` semireducible only within the local scope.
+-/
+syntax "unseal " (ppSpace ident)+ : command
+
+macro_rules
+  | `(seal $fs:ident*) => `(attribute [local irreducible] $fs:ident*)
+  | `(unseal $fs:ident*) => `(attribute [local semireducible] $fs:ident*)
+
 end Parser

src/Init/NotationExtra.lean

@@ -87,6 +87,7 @@ macro:35 xs:bracketedExplicitBinders " × " b:term:35  : term => expandBrackedBi
 macro:35 xs:bracketedExplicitBinders " ×' " b:term:35 : term => expandBrackedBinders ``PSigma xs b
 end
 
+namespace Lean
 -- first step of a `calc` block
 syntax calcFirstStep := ppIndent(colGe term (" := " term)?)
 -- enforce indentation of calc steps so we know when to stop parsing them
@@ -136,6 +137,7 @@ syntax (name := calcTactic) "calc" calcSteps : tactic
 @[inherit_doc «calc»]
 macro tk:"calc" steps:calcSteps : conv =>
   `(conv| tactic => calc%$tk $steps)
+end Lean
 
 @[app_unexpander Unit.unit] def unexpandUnit : Lean.PrettyPrinter.Unexpander
   | `($(_)) => `(())
@@ -361,6 +363,7 @@ macro_rules
   | `(letI $_:ident $_* : $_ := $_; $_) => Lean.Macro.throwUnsupported -- handled by elab
 
 
+namespace Lean
 syntax cdotTk := patternIgnore("· " <|> ". ")
 /-- `· tac` focuses on the main goal and tries to solve it using `tac`, or else fails. -/
 syntax (name := cdot) cdotTk tacticSeqIndentGt : tactic
@@ -368,12 +371,11 @@ syntax (name := cdot) cdotTk tacticSeqIndentGt : tactic
 /--
   Similar to `first`, but succeeds only if one the given tactics solves the current goal.
 -/
-syntax (name := solve) "solve" withPosition((ppDedent(ppLine) colGe "| " tacticSeq)+) : tactic
+syntax (name := solveTactic) "solve" withPosition((ppDedent(ppLine) colGe "| " tacticSeq)+) : tactic
 
 macro_rules
   | `(tactic| solve $[| $ts]* ) => `(tactic| focus first $[| ($ts); done]*)
 
-namespace Lean
 /-! # `repeat` and `while` notation -/
 
 inductive Loop where

src/Init/Omega/Coeffs.lean

@@ -68,7 +68,7 @@ abbrev map (f : Int → Int) (xs : Coeffs) : Coeffs := List.map f xs
 /-- Shim for `.enum.find?`. -/
 abbrev findIdx? (f : Int → Bool) (xs : Coeffs) : Option Nat :=
   -- List.findIdx? f xs
-  -- We could avoid `Std.Data.List.Basic` by using the less efficient:
+  -- We could avoid `Batteries.Data.List.Basic` by using the less efficient:
   xs.enum.find? (f ·.2) |>.map (·.1)
 /-- Shim for `IntList.bmod`. -/
 abbrev bmod (x : Coeffs) (m : Nat) : Coeffs := IntList.bmod x m

src/Init/Prelude.lean

@@ -3644,6 +3644,17 @@ def getPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos :=
   | synthetic (pos := pos) .., false => some pos
   | _,                         _     => none
 
+/--
+Gets the end position information from a `SourceInfo`, if available.
+If `originalOnly` is true, then `.synthetic` syntax will also return `none`.
+-/
+def getTailPos? (info : SourceInfo) (canonicalOnly := false) : Option String.Pos :=
+  match info, canonicalOnly with
+  | original (endPos := endPos) ..,  _
+  | synthetic (endPos := endPos) (canonical := true) .., _
+  | synthetic (endPos := endPos) .., false => some endPos
+  | _,                               _     => none
+
 end SourceInfo
 
 /--

src/Init/System/IO.lean

@@ -210,8 +210,44 @@ def sleep (ms : UInt32) : BaseIO Unit :=
 /-- Request cooperative cancellation of the task. The task must explicitly call `IO.checkCanceled` to react to the cancellation. -/
 @[extern "lean_io_cancel"] opaque cancel : @& Task α → BaseIO Unit
 
+/-- The current state of a `Task` in the Lean runtime's task manager. -/
+inductive TaskState
+  /--
+  The `Task` is waiting to be run.
+  It can be waiting for dependencies to complete or
+  sitting in the task manager queue waiting for a thread to run on.
+  -/
+  | waiting
+  /--
+  The `Task` is actively running on a thread or,
+  in the case of a `Promise`, waiting for a call to `IO.Promise.resolve`.
+  -/
+  | running
+  /--
+  The `Task` has finished running and its result is available.
+  Calling `Task.get` or `IO.wait` on the task will not block.
+  -/
+  | finished
+  deriving Inhabited, Repr, DecidableEq, Ord
+
+instance : LT TaskState := ltOfOrd
+instance : LE TaskState := leOfOrd
+instance : Min TaskState := minOfLe
+instance : Max TaskState := maxOfLe
+
+protected def TaskState.toString : TaskState → String
+  | .waiting => "waiting"
+  | .running => "running"
+  | .finished => "finished"
+
+instance : ToString TaskState := ⟨TaskState.toString⟩
+
+/-- Returns current state of the `Task` in the Lean runtime's task manager. -/
+@[extern "lean_io_get_task_state"] opaque getTaskState : @& Task α → BaseIO TaskState
+
 /-- Check if the task has finished execution, at which point calling `Task.get` will return immediately. -/
-@[extern "lean_io_has_finished"] opaque hasFinished : @& Task α → BaseIO Bool
+@[inline] def hasFinished (task : Task α) : BaseIO Bool := do
+  return (← getTaskState task) matches .finished
 
 /-- Wait for the task to finish, then return its result. -/
 @[extern "lean_io_wait"] opaque wait (t : Task α) : BaseIO α :=
@@ -228,6 +264,13 @@ local macro "nonempty_list" : tactic =>
 /-- Helper method for implementing "deterministic" timeouts. It is the number of "small" memory allocations performed by the current execution thread. -/
 @[extern "lean_io_get_num_heartbeats"] opaque getNumHeartbeats : BaseIO Nat
 
+/--
+Adjusts the heartbeat counter of the current thread by the given amount. This can be useful to give
+allocation-avoiding code additional "weight" and is also used to adjust the counter after resuming
+from a snapshot.
+-/
+@[extern "lean_io_add_heartbeats"] opaque addHeartbeats (count : UInt64) : BaseIO Unit
+
 /--
 The mode of a file handle (i.e., a set of `open` flags and an `fdopen` mode).
 
@@ -625,7 +668,13 @@ partial def FS.removeDirAll (p : FilePath) : IO Unit := do
 
 namespace Process
 
-/-- Returns the process ID of the current process. -/
+/-- Returns the current working directory of the calling process. -/
+@[extern "lean_io_process_get_current_dir"] opaque getCurrentDir : IO FilePath
+
+/-- Sets the current working directory of the calling process. -/
+@[extern "lean_io_process_set_current_dir"] opaque setCurrentDir (path : @& FilePath) : IO Unit
+
+/-- Returns the process ID of the calling process. -/
 @[extern "lean_io_process_get_pid"] opaque getPID : BaseIO UInt32
 
 inductive Stdio where
@@ -744,6 +793,32 @@ instance : MonadLift (ST IO.RealWorld) BaseIO := ⟨id⟩
 def mkRef (a : α) : BaseIO (IO.Ref α) :=
   ST.mkRef a
 
+/--
+Mutable cell that can be passed around for purposes of cooperative task cancellation: request
+cancellation with `CancelToken.set` and check for it with `CancelToken.isSet`.
+
+This is a more flexible alternative to `Task.cancel` as the token can be shared between multiple
+tasks.
+-/
+structure CancelToken where
+  private ref : IO.Ref Bool
+
+namespace CancelToken
+
+/-- Creates a new cancellation token. -/
+def new : BaseIO CancelToken :=
+  CancelToken.mk <$> IO.mkRef false
+
+/-- Activates a cancellation token. Idempotent. -/
+def set (tk : CancelToken) : BaseIO Unit :=
+  tk.ref.set true
+
+/-- Checks whether the cancellation token has been activated. -/
+def isSet (tk : CancelToken) : BaseIO Bool :=
+  tk.ref.get
+
+end CancelToken
+
 namespace FS
 namespace Stream
 

src/Init/Tactics.lean

@@ -368,7 +368,7 @@ for new reflexive relations.
 Remark: `rfl` is an extensible tactic. We later add `macro_rules` to try different
 reflexivity theorems (e.g., `Iff.rfl`).
 -/
-macro "rfl" : tactic => `(tactic| fail "The rfl tactic failed. Possible reasons:
+macro "rfl" : tactic => `(tactic| case' _ => fail "The rfl tactic failed. Possible reasons:
 - The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma).
 - The arguments of the relation are not equal.
 Try using the reflexivitiy lemma for your relation explicitly, e.g. `exact Eq.rfl`.")
@@ -835,7 +835,7 @@ syntax (name := renameI) "rename_i" (ppSpace colGt binderIdent)+ : tactic
 /--
 `repeat tac` repeatedly applies `tac` to the main goal until it fails.
 That is, if `tac` produces multiple subgoals, only subgoals up to the first failure will be visited.
-The `Std` library provides `repeat'` which repeats separately in each subgoal.
+The `Batteries` library provides `repeat'` which repeats separately in each subgoal.
 -/
 syntax "repeat " tacticSeq : tactic
 macro_rules
@@ -1266,7 +1266,7 @@ Optional arguments passed via a configuration argument as `solve_by_elim (config
   but it is often useful to change to `.reducible`,
   so semireducible definitions will not be unfolded when trying to apply a lemma.
 
-See also the doc-comment for `Std.Tactic.BacktrackConfig` for the options
+See also the doc-comment for `Lean.Meta.Tactic.Backtrack.BacktrackConfig` for the options
 `proc`, `suspend`, and `discharge` which allow further customization of `solve_by_elim`.
 Both `apply_assumption` and `apply_rules` are implemented via these hooks.
 -/
@@ -1425,6 +1425,16 @@ If there are several with the same priority, it is uses the "most recent one". E
 -/
 syntax (name := simp) "simp" (Tactic.simpPre <|> Tactic.simpPost)? (ppSpace prio)? : attr
 
+/--
+Theorems tagged with the `grind_norm` attribute are used by the `grind` tactic normalizer/pre-processor.
+-/
+syntax (name := grind_norm) "grind_norm" (Tactic.simpPre <|> Tactic.simpPost)? (ppSpace prio)? : attr
+
+/--
+Simplification procedures tagged with the `grind_norm_proc` attribute are used by the `grind` tactic normalizer/pre-processor.
+-/
+syntax (name := grind_norm_proc) "grind_norm_proc" (Tactic.simpPre <|> Tactic.simpPost)? : attr
+
 
 /-- The possible `norm_cast` kinds: `elim`, `move`, or `squash`. -/
 syntax normCastLabel := &"elim" <|> &"move" <|> &"squash"

src/Lean.lean

@@ -37,3 +37,4 @@ import Lean.Log
 import Lean.Linter
 import Lean.SubExpr
 import Lean.LabelAttribute
+import Lean.AddDecl

src/Lean/AddDecl.lean

@@ -0,0 +1,31 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.CoreM
+
+namespace Lean
+
+def Environment.addDecl (env : Environment) (opts : Options) (decl : Declaration) : Except KernelException Environment :=
+  addDeclCore env (Core.getMaxHeartbeats opts).toUSize decl
+
+def Environment.addAndCompile (env : Environment) (opts : Options) (decl : Declaration) : Except KernelException Environment := do
+  let env ← addDecl env opts decl
+  compileDecl env opts decl
+
+def addDecl (decl : Declaration) : CoreM Unit := do
+  profileitM Exception "type checking" (← getOptions) do
+    withTraceNode `Kernel (fun _ => return m!"typechecking declaration") do
+      if !(← MonadLog.hasErrors) && decl.hasSorry then
+        logWarning "declaration uses 'sorry'"
+      match (← getEnv).addDecl (← getOptions) decl with
+      | .ok    env => setEnv env
+      | .error ex  => throwKernelException ex
+
+def addAndCompile (decl : Declaration) : CoreM Unit := do
+  addDecl decl
+  compileDecl decl
+
+end Lean

src/Lean/Attributes.lean

@@ -67,13 +67,11 @@ def registerBuiltinAttribute (attr : AttributeImpl) : IO Unit := do
   Helper methods for decoding the parameters of builtin attributes that are defined before `Lean.Parser`.
   We have the following ones:
   ```
-  @[builtin_attr_parser] def simple     := leading_parser ident >> optional ident >> optional priorityParser
-  /- We can't use `simple` for `class`, `instance`, `export` and `macro` because they are  keywords. -/
-  @[builtin_attr_parser] def «class»    := leading_parser "class"
-  @[builtin_attr_parser] def «instance» := leading_parser "instance" >> optional priorityParser
+  @[builtin_attr_parser] def simple     := leading_parser ident >> optional (ppSpace >> (priorityParser <|> ident))
   @[builtin_attr_parser] def «macro»    := leading_parser "macro " >> ident
+  @[builtin_attr_parser] def «export»   := leading_parser "export " >> ident
   ```
-  Note that we need the parsers for `class`, `instance`, and `macros` because they are keywords.
+  Note that we need the parsers for `class`, `instance`, `export` and `macros` because they are keywords.
 -/
 
 def Attribute.Builtin.ensureNoArgs (stx : Syntax) : AttrM Unit := do

src/Lean/Compiler/IR/ResetReuse.lean

@@ -29,43 +29,50 @@ Here are the main differences:
   does not occur in a function body. See example at `livevars.lean`.
 -/
 
-private def mayReuse (c₁ c₂ : CtorInfo) : Bool :=
+private def mayReuse (c₁ c₂ : CtorInfo) (relaxedReuse : Bool) : Bool :=
   c₁.size == c₂.size && c₁.usize == c₂.usize && c₁.ssize == c₂.ssize &&
   /- The following condition is a heuristic.
-     We don't want to reuse cells from different types even when they are compatible
+     If `relaxedReuse := false`, then we don't want to reuse cells from
+     different constructors even when they are compatible
      because it produces counterintuitive behavior. -/
-  c₁.name.getPrefix == c₂.name.getPrefix
+  (relaxedReuse || c₁.name.getPrefix == c₂.name.getPrefix)
 
 /--
 Replace `ctor` applications with `reuse` applications if compatible.
 `w` contains the "memory cell" being reused.
 -/
-private partial def S (w : VarId) (c : CtorInfo) : FnBody → FnBody
+private partial def S (w : VarId) (c : CtorInfo) (relaxedReuse : Bool) (b : FnBody) : FnBody :=
+  go b
+where
+  go : FnBody → FnBody
   | .vdecl x t v@(.ctor c' ys) b   =>
-    if mayReuse c c' then
+    if mayReuse c c' relaxedReuse then
       let updtCidx := c.cidx != c'.cidx
       .vdecl x t (.reuse w c' updtCidx ys) b
     else
-      .vdecl x t v (S w c b)
+      .vdecl x t v (go b)
   | .jdecl j ys v b   =>
-    let v' := S w c v
+    let v' := go v
     if v == v' then
-      .jdecl j ys v (S w c b)
+      .jdecl j ys v (go b)
     else
       .jdecl j ys v' b
   | .case tid x xType alts =>
-    .case tid x xType <| alts.map fun alt => alt.modifyBody (S w c)
+    .case tid x xType <| alts.map fun alt => alt.modifyBody go
   | b =>
     if b.isTerminal then
       b
-    else let
-      (instr, b) := b.split
-      instr.setBody (S w c b)
+    else
+      let (instr, b) := b.split
+      instr.setBody (go b)
 
 structure Context where
   lctx      : LocalContext := {}
   /--
-  Contains all variables in `cases` statements in the current path.
+  Contains all variables in `cases` statements in the current path
+  and variables that are already in `reset` statements when we
+  invoke `R`.
+
   We use this information to prevent double-reset in code such as
   ```
   case x_i : obj of
@@ -74,8 +81,18 @@ structure Context where
     Prod.mk →
     ...
   ```
+
+  A variable can already be in a `reset` statement when we
+  invoke `R` because we execute it with and without `relaxedReuse`.
   -/
-  casesVars : PHashSet VarId := {}
+  alreadyFound : PHashSet VarId := {}
+  /--
+  If `relaxedReuse := true`, then allow memory cells from different
+  constructors to be reused. For example, we can reuse a `PSigma.mk`
+  to allocate a `Prod.mk`. To avoid counterintuitive behavior,
+  we first try `relaxedReuse := false`, and then `relaxedReuse := true`.
+  -/
+  relaxedReuse : Bool := false
 
 /-- We use `Context` to track join points in scope. -/
 abbrev M := ReaderT Context (StateT Index Id)
@@ -90,7 +107,7 @@ to replace a `ctor` withe `reuse` in `b`.
 -/
 private def tryS (x : VarId) (c : CtorInfo) (b : FnBody) : M FnBody := do
   let w ← mkFresh
-  let b' := S w c b
+  let b' := S w c (← read).relaxedReuse b
   if b == b' then
     return b
   else
@@ -102,8 +119,8 @@ private def Dfinalize (x : VarId) (c : CtorInfo) : FnBody × Bool → M FnBody
 
 private def argsContainsVar (ys : Array Arg) (x : VarId) : Bool :=
   ys.any fun arg => match arg with
-    | Arg.var y => x == y
-    | _         => false
+    | .var y => x == y
+    | _      => false
 
 private def isCtorUsing (b : FnBody) (x : VarId) : Bool :=
   match b with
@@ -161,8 +178,8 @@ private def D (x : VarId) (c : CtorInfo) (b : FnBody) : M FnBody :=
 partial def R (e : FnBody) : M FnBody := do
   match e with
   | .case tid x xType alts =>
-    let alreadyFound := (← read).casesVars.contains x
-    withReader (fun ctx => { ctx with casesVars := ctx.casesVars.insert x }) do
+    let alreadyFound := (← read).alreadyFound.contains x
+    withReader (fun ctx => { ctx with alreadyFound := ctx.alreadyFound.insert x }) do
       let alts ← alts.mapM fun alt => do
         let alt ← alt.mmodifyBody R
         match alt with
@@ -187,16 +204,43 @@ partial def R (e : FnBody) : M FnBody := do
       let b ← R b
       return instr.setBody b
 
-end ResetReuse
+abbrev N := StateT (PHashSet VarId) Id
 
+partial def collectResets (e : FnBody) : N Unit := do
+  match e with
+  | .case _ _ _ alts => alts.forM fun alt => collectResets alt.body
+  | .jdecl _ _ v b => collectResets v; collectResets b
+  | .vdecl _ _ (.reset _ x) b => modify fun s => s.insert x; collectResets b
+  | e => unless e.isTerminal do
+    let (_, b) := e.split
+    collectResets b
+
+end ResetReuse
 open ResetReuse
 
-def Decl.insertResetReuse (d : Decl) : Decl :=
+
+def Decl.insertResetReuseCore (d : Decl) (relaxedReuse : Bool) : Decl :=
   match d with
   | .fdecl (body := b) .. =>
     let nextIndex := d.maxIndex + 1
-    let bNew      := (R b {}).run' nextIndex
+    -- First time we execute `insertResetReuseCore`, `relaxedReuse := false`.
+    let alreadyFound : PHashSet VarId := if relaxedReuse then (collectResets b *> get).run' {} else {}
+    let bNew := R b { relaxedReuse, alreadyFound } |>.run' nextIndex
     d.updateBody! bNew
   | other => other
 
+def Decl.insertResetReuse (d : Decl) : Decl :=
+  /-
+  We execute the reset/reuse algorithm twice. The first time, we only reuse memory cells
+  between identical constructor memory cells. That is, we do not reuse a `PSigma.mk` memory cell
+  when allocating a `Prod.mk` memory cell, even though they have the same layout. Recall
+  that the reset/reuse placement algorithm is a heuristic, and the first pass prevents reuses
+  that are unlikely to be useful at runtime. Then, we run the procedure again,
+  relaxing this restriction. If there are still opportunities for reuse, we will take advantage of them.
+
+  The second pass addresses issue #4089.
+  -/
+  d.insertResetReuseCore (relaxedReuse := false)
+  |>.insertResetReuseCore (relaxedReuse := true)
+
 end Lean.IR

src/Lean/Compiler/InitAttr.lean

@@ -4,6 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
+import Lean.AddDecl
+import Lean.MonadEnv
 import Lean.Elab.InfoTree.Main
 
 namespace Lean
@@ -138,7 +140,7 @@ def setBuiltinInitAttr (env : Environment) (declName : Name) (initFnName : Name
   builtinInitAttr.setParam env declName initFnName
 
 def declareBuiltin (forDecl : Name) (value : Expr) : CoreM Unit := do
-  let name := `_regBuiltin ++ forDecl
+  let name ← mkAuxName (`_regBuiltin ++ forDecl) 1
   let type := mkApp (mkConst `IO) (mkConst `Unit)
   let decl := Declaration.defnDecl { name, levelParams := [], type, value, hints := ReducibilityHints.opaque,
                                      safety := DefinitionSafety.safe }

src/Lean/Compiler/Old.lean

@@ -67,9 +67,4 @@ opaque compileDecls (env : Environment) (opt : @& Options) (decls : @& List Name
 def compileDecl (env : Environment) (opt : @& Options) (decl : @& Declaration) : Except KernelException Environment :=
   compileDecls env opt (Compiler.getDeclNamesForCodeGen decl)
 
-
-def addAndCompile (env : Environment) (opt : Options) (decl : Declaration) : Except KernelException Environment := do
-  let env ← addDecl env decl
-  compileDecl env opt decl
-
 end Environment

src/Lean/CoreM.lean

@@ -11,6 +11,7 @@ import Lean.Eval
 import Lean.ResolveName
 import Lean.Elab.InfoTree.Types
 import Lean.MonadEnv
+import Lean.Elab.Exception
 
 namespace Lean
 register_builtin_option diagnostics : Bool := {
@@ -30,6 +31,8 @@ register_builtin_option maxHeartbeats : Nat := {
   descr := "maximum amount of heartbeats per command. A heartbeat is number of (small) memory allocations (in thousands), 0 means no limit"
 }
 
+def useDiagnosticMsg := s!"use `set_option {diagnostics.name} true` to get diagnostic information"
+
 namespace Core
 
 builtin_initialize registerTraceClass `Kernel
@@ -79,16 +82,17 @@ structure Context where
   maxHeartbeats  : Nat := getMaxHeartbeats options
   currMacroScope : MacroScope := firstFrontendMacroScope
   /--
-  If `catchRuntimeEx = false`, then given `try x catch ex => h ex`,
-  an runtime exception occurring in `x` is not handled by `h`.
-  Recall that runtime exceptions are `maxRecDepth` or `maxHeartbeats`.
-  -/
-  catchRuntimeEx : Bool := false
-  /--
   If `diag := true`, different parts of the system collect diagnostics.
   Use the `set_option diag true` to set it to true.
   -/
   diag           : Bool := false
+  /-- If set, used to cancel elaboration from outside when results are not needed anymore. -/
+  cancelTk?      : Option IO.CancelToken := none
+  /--
+  If set (when `showPartialSyntaxErrors` is not set and parsing failed), suppresses most elaboration
+  errors; see also `logMessage` below.
+  -/
+  suppressElabErrors : Bool := false
   deriving Nonempty
 
 /-- CoreM is a monad for manipulating the Lean environment.
@@ -121,16 +125,23 @@ instance : MonadOptions CoreM where
   getOptions := return (← read).options
 
 instance : MonadWithOptions CoreM where
-  withOptions f x :=
+  withOptions f x := do
+    let options := f (← read).options
+    let diag := diagnostics.get options
+    if Kernel.isDiagnosticsEnabled (← getEnv) != diag then
+      modifyEnv fun env => Kernel.enableDiag env diag
     withReader
       (fun ctx =>
-        let options := f ctx.options
         { ctx with
           options
-          diag := diagnostics.get options
+          diag
           maxRecDepth := maxRecDepth.get options })
       x
 
+-- Helper function for ensuring fields that depend on `options` have the correct value.
+@[inline] private def withConsistentCtx (x : CoreM α) : CoreM α := do
+  withOptions id x
+
 instance : AddMessageContext CoreM where
   addMessageContext := addMessageContextPartial
 
@@ -198,16 +209,45 @@ instance : MonadTrace CoreM where
   getTraceState := return (← get).traceState
   modifyTraceState f := modify fun s => { s with traceState := f s.traceState }
 
-/-- Restore backtrackable parts of the state. -/
-def restore (b : State) : CoreM Unit :=
-  modify fun s => { s with env := b.env, messages := b.messages, infoState := b.infoState }
+structure SavedState extends State where
+  /-- Number of heartbeats passed inside `withRestoreOrSaveFull`, not used otherwise. -/
+  passedHearbeats : Nat
+deriving Nonempty
+
+def saveState : CoreM SavedState := do
+  let s ← get
+  return { toState := s, passedHearbeats := 0 }
 
 /--
-Restores full state including sources for unique identifiers. Only intended for incremental reuse
-between elaboration runs, not for backtracking within a single run.
+Incremental reuse primitive: if `reusableResult?` is `none`, runs `cont` with an action `save` that
+on execution returns the saved monadic state at this point including the heartbeats used by `cont`
+so far. If `reusableResult?` on the other hand is `some (a, state)`, restores full `state` including
+heartbeats used and returns `a`.
+
+The intention is for steps that support incremental reuse to initially pass `none` as
+`reusableResult?` and call `save` as late as possible in `cont`. In a further run, if reuse is
+possible, `reusableResult?` should be set to the previous state and result, ensuring that the state
+after running `withRestoreOrSaveFull` is identical in both runs. Note however that necessarily this
+is only an approximation in the case of heartbeats as heartbeats used by `withRestoreOrSaveFull`, by
+the remainder of `cont` after calling `save`, as well as by reuse-handling code such as the one
+supplying `reusableResult?` are not accounted for.
 -/
-def restoreFull (b : State) : CoreM Unit :=
-  set b
+@[specialize] def withRestoreOrSaveFull (reusableResult? : Option (α × SavedState))
+    (cont : (save : CoreM SavedState) → CoreM α) : CoreM α := do
+  if let some (val, state) := reusableResult? then
+    set state.toState
+    IO.addHeartbeats state.passedHearbeats.toUInt64
+    return val
+
+  let startHeartbeats ← IO.getNumHeartbeats
+  cont (do
+    let s ← get
+    let stopHeartbeats ← IO.getNumHeartbeats
+    return { toState := s, passedHearbeats := stopHeartbeats - startHeartbeats })
+
+/-- Restore backtrackable parts of the state. -/
+def SavedState.restore (b : SavedState) : CoreM Unit :=
+  modify fun s => { s with env := b.env, messages := b.messages, infoState := b.infoState }
 
 private def mkFreshNameImp (n : Name) : CoreM Name := do
   let fresh ← modifyGet fun s => (s.nextMacroScope, { s with nextMacroScope := s.nextMacroScope + 1 })
@@ -217,7 +257,7 @@ def mkFreshUserName (n : Name) : CoreM Name :=
   mkFreshNameImp n
 
 @[inline] def CoreM.run (x : CoreM α) (ctx : Context) (s : State) : EIO Exception (α × State) :=
-  (x ctx).run s
+  ((withConsistentCtx x) ctx).run s
 
 @[inline] def CoreM.run' (x : CoreM α) (ctx : Context) (s : State) : EIO Exception α :=
   Prod.fst <$> x.run ctx s
@@ -231,20 +271,36 @@ def mkFreshUserName (n : Name) : CoreM Name :=
 instance [MetaEval α] : MetaEval (CoreM α) where
   eval env opts x _ := do
     let x : CoreM α := do try x finally printTraces
-    let (a, s) ← (withOptions (fun _ => opts) x).toIO { fileName := "<CoreM>", fileMap := default } { env := env }
+    let (a, s) ← (withConsistentCtx x).toIO { fileName := "<CoreM>", fileMap := default, options := opts } { env := env }
     MetaEval.eval s.env opts a (hideUnit := true)
 
 -- withIncRecDepth for a monad `m` such that `[MonadControlT CoreM n]`
 protected def withIncRecDepth [Monad m] [MonadControlT CoreM m] (x : m α) : m α :=
   controlAt CoreM fun runInBase => withIncRecDepth (runInBase x)
 
+builtin_initialize interruptExceptionId : InternalExceptionId ← registerInternalExceptionId `interrupt
+
+/--
+Throws an internal interrupt exception if cancellation has been requested. The exception is not
+caught by `try catch` but is intended to be caught by `Command.withLoggingExceptions` at the top
+level of elaboration. In particular, we want to skip producing further incremental snapshots after
+the exception has been thrown.
+ -/
 @[inline] def checkInterrupted : CoreM Unit := do
-  if (← IO.checkCanceled) then
-    -- should never be visible to users!
-    throw <| Exception.error .missing "elaboration interrupted"
+  if let some tk := (← read).cancelTk? then
+    if (← tk.isSet) then
+      throw <| .internal interruptExceptionId
+
+register_builtin_option debug.moduleNameAtTimeout : Bool := {
+  defValue := true
+  group    := "debug"
+  descr    := "include module name in deterministic timeout error messages.\nRemark: we set this option to false to increase the stability of our test suite"
+}
 
 def throwMaxHeartbeat (moduleName : Name) (optionName : Name) (max : Nat) : CoreM Unit := do
-  let msg := s!"(deterministic) timeout at `{moduleName}`, maximum number of heartbeats ({max/1000}) has been reached\nuse `set_option {optionName} <num>` to set the limit\nuse `set_option {diagnostics.name} true` to get diagnostic information"
+  let includeModuleName := debug.moduleNameAtTimeout.get (← getOptions)
+  let atModuleName := if includeModuleName then s!" at `{moduleName}`" else ""
+  let msg := s!"(deterministic) timeout{atModuleName}, maximum number of heartbeats ({max/1000}) has been reached\nuse `set_option {optionName} <num>` to set the limit\n{useDiagnosticMsg}"
   throw <| Exception.error (← getRef) (MessageData.ofFormat (Std.Format.text msg))
 
 def checkMaxHeartbeatsCore (moduleName : String) (optionName : Name) (max : Nat) : CoreM Unit := do
@@ -278,11 +334,13 @@ def getMessageLog : CoreM MessageLog :=
   return (← get).messages
 
 /--
-Returns the current log and then resets its messages but does NOT reset `MessageLog.hadErrors`. Used
+Returns the current log and then resets its messages while adjusting `MessageLog.hadErrors`. Used
 for incremental reporting during elaboration of a single command.
 -/
 def getAndEmptyMessageLog : CoreM MessageLog :=
-  modifyGet fun log => ({ log with msgs := {} }, log)
+  modifyGet fun s => (s.messages, { s with
+    messages.unreported := {}
+    messages.hadErrors  := s.messages.hasErrors })
 
 instance : MonadLog CoreM where
   getRef      := getRef
@@ -290,6 +348,12 @@ instance : MonadLog CoreM where
   getFileName := return (← read).fileName
   hasErrors   := return (← get).messages.hasErrors
   logMessage msg := do
+    if (← read).suppressElabErrors then
+      -- discard elaboration errors, except for a few important and unlikely misleading ones, on
+      -- parse error
+      unless msg.data.hasTag (· matches `Elab.synthPlaceholder | `Tactic.unsolvedGoals) do
+        return
+
     let ctx ← read
     let msg := { msg with data := MessageData.withNamingContext { currNamespace := ctx.currNamespace, openDecls := ctx.openDecls } msg.data };
     modify fun s => { s with messages := s.messages.add msg }
@@ -321,7 +385,8 @@ export Core (CoreM mkFreshUserName checkSystem withCurrHeartbeats)
   We used a similar hack at `Exception.isMaxRecDepth` -/
 def Exception.isMaxHeartbeat (ex : Exception) : Bool :=
   match ex with
-  | Exception.error _ (MessageData.ofFormat (Std.Format.text msg)) => "(deterministic) timeout".isPrefixOf msg
+  | Exception.error _ (MessageData.ofFormatWithInfos ⟨Std.Format.text msg, _⟩) =>
+    "(deterministic) timeout".isPrefixOf msg
   | _ => false
 
 /-- Creates the expression `d → b` -/
@@ -331,15 +396,6 @@ def mkArrow (d b : Expr) : CoreM Expr :=
 /-- Iterated `mkArrow`, creates the expression `a₁ → a₂ → … → aₙ → b`. Also see `arrowDomainsN`. -/
 def mkArrowN (ds : Array Expr) (e : Expr) : CoreM Expr := ds.foldrM mkArrow e
 
-def addDecl (decl : Declaration) : CoreM Unit := do
-  profileitM Exception "type checking" (← getOptions) do
-    withTraceNode `Kernel (fun _ => return m!"typechecking declaration") do
-      if !(← MonadLog.hasErrors) && decl.hasSorry then
-        logWarning "declaration uses 'sorry'"
-      match (← getEnv).addDecl decl with
-      | Except.ok    env => setEnv env
-      | Except.error ex  => throwKernelException ex
-
 private def supportedRecursors :=
   #[``Empty.rec, ``False.rec, ``Eq.ndrec, ``Eq.rec, ``Eq.recOn, ``Eq.casesOn, ``False.casesOn, ``Empty.casesOn, ``And.rec, ``And.casesOn]
 
@@ -393,10 +449,6 @@ def compileDecls (decls : List Name) : CoreM Unit := do
   | Except.error ex =>
     throwKernelException ex
 
-def addAndCompile (decl : Declaration) : CoreM Unit := do
-  addDecl decl;
-  compileDecl decl
-
 def getDiag (opts : Options) : Bool :=
   diagnostics.get opts
 
@@ -409,42 +461,55 @@ def ImportM.runCoreM (x : CoreM α) : ImportM α := do
   let (a, _) ← (withOptions (fun _ => ctx.opts) x).toIO { fileName := "<ImportM>", fileMap := default } { env := ctx.env }
   return a
 
-/-- Return `true` if the exception was generated by one our resource limits. -/
+/-- Return `true` if the exception was generated by one of our resource limits. -/
 def Exception.isRuntime (ex : Exception) : Bool :=
   ex.isMaxHeartbeat || ex.isMaxRecDepth
 
+/-- Returns `true` if the exception is an interrupt generated by `checkInterrupted`. -/
+def Exception.isInterrupt : Exception → Bool
+  | Exception.internal id _ => id == Core.interruptExceptionId
+  | _ => false
+
 /--
-Custom `try-catch` for all monads based on `CoreM`. We don't want to catch "runtime exceptions"
-in these monads, but on `CommandElabM`. See issues #2775 and #2744 as well as `MonadAlwayExcept`.
+Custom `try-catch` for all monads based on `CoreM`. We usually don't want to catch "runtime
+exceptions" these monads, but on `CommandElabM`. See issues #2775 and #2744 as well as
+`MonadAlwaysExcept`. Also, we never want to catch interrupt exceptions inside the elaborator.
 -/
 @[inline] protected def Core.tryCatch (x : CoreM α) (h : Exception → CoreM α) : CoreM α := do
   try
     x
   catch ex =>
-    if ex.isRuntime && !(← read).catchRuntimeEx then
-      throw ex
+    if ex.isInterrupt || ex.isRuntime then
+
+      throw ex -- We should use `tryCatchRuntimeEx` for catching runtime exceptions
     else
       h ex
 
+@[inline] protected def Core.tryCatchRuntimeEx (x : CoreM α) (h : Exception → CoreM α) : CoreM α := do
+  try
+    x
+  catch ex =>
+    h ex
+
 instance : MonadExceptOf Exception CoreM where
   throw    := throw
   tryCatch := Core.tryCatch
 
-@[inline] def Core.withCatchingRuntimeEx (flag : Bool) (x : CoreM α) : CoreM α :=
-  withReader (fun ctx => { ctx with catchRuntimeEx := flag }) x
+class MonadRuntimeException (m : Type → Type) where
+  tryCatchRuntimeEx (body : m α) (handler : Exception → m α) : m α
+
+export MonadRuntimeException (tryCatchRuntimeEx)
+
+instance : MonadRuntimeException CoreM where
+  tryCatchRuntimeEx := Core.tryCatchRuntimeEx
+
+@[inline] instance [MonadRuntimeException m] : MonadRuntimeException (ReaderT ρ m) where
+  tryCatchRuntimeEx := fun x c r => tryCatchRuntimeEx (x r) (fun e => (c e) r)
+
+@[inline] instance [MonadRuntimeException m] : MonadRuntimeException (StateRefT' ω σ m) where
+  tryCatchRuntimeEx := fun x c s => tryCatchRuntimeEx (x s) (fun e => c e s)
 
 @[inline] def mapCoreM [MonadControlT CoreM m] [Monad m] (f : forall {α}, CoreM α → CoreM α) {α} (x : m α) : m α :=
   controlAt CoreM fun runInBase => f <| runInBase x
 
-/--
-Execute `x` with `catchRuntimeEx = flag`. That is, given `try x catch ex => h ex`,
-if `x` throws a runtime exception, the handler `h` will be invoked if `flag = true`
-Recall that
--/
-@[inline] def withCatchingRuntimeEx [MonadControlT CoreM m] [Monad m] (x : m α) : m α :=
-  mapCoreM (Core.withCatchingRuntimeEx true) x
-
-@[inline] def withoutCatchingRuntimeEx [MonadControlT CoreM m] [Monad m] (x : m α) : m α :=
-  mapCoreM (Core.withCatchingRuntimeEx false) x
-
 end Lean

src/Lean/Data/HashMap.lean

@@ -249,6 +249,8 @@ def toArray (m : HashMap α β) : Array (α × β) :=
 def numBuckets (m : HashMap α β) : Nat :=
   m.val.buckets.val.size
 
+variable [BEq α] [Hashable α]
+
 /-- Builds a `HashMap` from a list of key-value pairs. Values of duplicated keys are replaced by their respective last occurrences. -/
 def ofList (l : List (α × β)) : HashMap α β :=
   l.foldl (init := HashMap.empty) (fun m p => m.insert p.fst p.snd)
@@ -260,6 +262,7 @@ def ofListWith (l : List (α × β)) (f : β → β → β) : HashMap α β :=
       match m.find? p.fst with
         | none   => m.insert p.fst p.snd
         | some v => m.insert p.fst $ f v p.snd)
+
 end Lean.HashMap
 
 /--

src/Lean/Data/Position.lean

@@ -106,7 +106,7 @@ def ofPosition (text : FileMap) (pos : Position) : String.Pos :=
 
 /--
 Returns the position of the start of (1-based) line `line`.
-This gives the stame result as `map.ofPosition ⟨line, 0⟩`, but is more efficient.
+This gives the same result as `map.ofPosition ⟨line, 0⟩`, but is more efficient.
 -/
 def lineStart (map : FileMap) (line : Nat) : String.Pos :=
   if h : line - 1 < map.positions.size then

src/Lean/Data/RBTree.lean

@@ -100,7 +100,7 @@ def fromArray (l : Array α) (cmp : α → α → Ordering) : RBTree α cmp :=
   RBMap.any t (fun a _ => p a)
 
 def subset (t₁ t₂ : RBTree α cmp) : Bool :=
-  t₁.all fun a => (t₂.find? a).toBool
+  t₁.all fun a => (t₂.find? a).isSome
 
 def seteq (t₁ t₂ : RBTree α cmp) : Bool :=
   subset t₁ t₂ && subset t₂ t₁

src/Lean/Elab/Binders.lean

@@ -7,6 +7,7 @@ prelude
 import Lean.Elab.Quotation.Precheck
 import Lean.Elab.Term
 import Lean.Elab.BindersUtil
+import Lean.Elab.SyntheticMVars
 import Lean.Elab.PreDefinition.WF.TerminationHint
 
 namespace Lean.Elab.Term
@@ -70,30 +71,34 @@ def kindOfBinderName (binderName : Name) : LocalDeclKind :=
   else
     .default
 
-partial def quoteAutoTactic : Syntax → TermElabM Syntax
-  | stx@(.ident ..) => throwErrorAt stx "invalid auto tactic, identifier is not allowed"
+partial def quoteAutoTactic : Syntax → CoreM Expr
+  | .ident _ _ val preresolved =>
+    return mkApp4 (.const ``Syntax.ident [])
+      (.const ``SourceInfo.none [])
+      (.app (.const ``String.toSubstring []) (mkStrLit (toString val)))
+      (toExpr val)
+      (toExpr preresolved)
   | stx@(.node _ k args) => do
     if stx.isAntiquot then
       throwErrorAt stx "invalid auto tactic, antiquotation is not allowed"
     else
-      let mut quotedArgs ← `(Array.empty)
+      let ty := .const ``Syntax []
+      let mut quotedArgs := mkApp (.const ``Array.empty [.zero]) ty
       for arg in args do
         if k == nullKind && (arg.isAntiquotSuffixSplice || arg.isAntiquotSplice) then
           throwErrorAt arg "invalid auto tactic, antiquotation is not allowed"
         else
           let quotedArg ← quoteAutoTactic arg
-          quotedArgs ← `(Array.push $quotedArgs $quotedArg)
-      `(Syntax.node SourceInfo.none $(quote k) $quotedArgs)
-  | .atom _ val => `(mkAtom $(quote val))
+          quotedArgs := mkApp3 (.const ``Array.push [.zero]) ty quotedArgs quotedArg
+      return mkApp3 (.const ``Syntax.node []) (.const ``SourceInfo.none []) (toExpr k) quotedArgs
+  | .atom _ val => return .app (.const ``mkAtom []) (toExpr val)
   | .missing    => throwError "invalid auto tactic, tactic is missing"
 
 def declareTacticSyntax (tactic : Syntax) : TermElabM Name :=
   withFreshMacroScope do
     let name ← MonadQuotation.addMacroScope `_auto
     let type := Lean.mkConst `Lean.Syntax
-    let tactic ← quoteAutoTactic tactic
-    let value ← elabTerm tactic type
-    let value ← instantiateMVars value
+    let value ← quoteAutoTactic tactic
     trace[Elab.autoParam] value
     let decl := Declaration.defnDecl { name, levelParams := [], type, value, hints := .opaque,
                                        safety := DefinitionSafety.safe }
@@ -642,7 +647,29 @@ def elabLetDeclAux (id : Syntax) (binders : Array Syntax) (typeStx : Syntax) (va
     (expectedType? : Option Expr) (useLetExpr : Bool) (elabBodyFirst : Bool) (usedLetOnly : Bool) : TermElabM Expr := do
   let (type, val, binders) ← elabBindersEx binders fun xs => do
     let (binders, fvars) := xs.unzip
-    let type ← elabType typeStx
+    /-
+    We use `withSynthesize` to ensure that any postponed elaboration problem
+    and nested tactics in `type` are resolved before elaborating `val`.
+    Resolved: we want to avoid synthethic opaque metavariables in `type`.
+    Recall that this kind of metavariable is non-assignable, and `isDefEq`
+    may waste a lot of time unfolding declarations before failing.
+    See issue #4051 for an example.
+
+    Here is the analysis for issue #4051.
+    - Given `have x : type := value; body`, we were previously elaborating `value` even
+      if `type` contained postponed elaboration problems.
+    - Moreover, the metavariables in `type` corresponding to postponed elaboration
+      problems cannot be assigned by `isDefEq` since the elaborator is supposed to assign them.
+    - Then, when checking whether type of `value` is definitionally equal to `type`,
+      a very long-time was spent unfolding a bunch of declarations before it failed.
+      In #4051, it was unfolding `Array.swaps` which is defined by well-founded recursion.
+      After the failure, the elaborator inserted a postponed coercion
+      that would be resolved later as soon as the types don't have unassigned metavariables.
+
+    We use `postpone := .partial` to allow type class (TC) resolution problems to be postponed
+    Recall that TC resolution does **not** produce synthetic opaque metavariables.
+    -/
+    let type ← withSynthesize (postpone := .partial) <| elabType typeStx
     registerCustomErrorIfMVar type typeStx "failed to infer 'let' declaration type"
     if elabBodyFirst then
       let type ← mkForallFVars fvars type

src/Lean/Elab/BuiltinCommand.lean

@@ -123,7 +123,7 @@ private partial def elabChoiceAux (cmds : Array Syntax) (i : Nat) : CommandElabM
   n[1].forArgsM addUnivLevel
 
 @[builtin_command_elab «init_quot»] def elabInitQuot : CommandElab := fun _ => do
-  match (← getEnv).addDecl Declaration.quotDecl with
+  match (← getEnv).addDecl (← getOptions) Declaration.quotDecl with
   | Except.ok env   => setEnv env
   | Except.error ex => throwError (ex.toMessageData (← getOptions))
 

src/Lean/Elab/BuiltinNotation.lean

@@ -98,7 +98,7 @@ open Meta
       show Nat from 0
     ```
     -/
-    let type ← withSynthesize (mayPostpone := true) do
+    let type ← withSynthesize (postpone := .yes) do
       let type ← elabType type
       if let some expectedType := expectedType? then
         -- Recall that a similar approach is used when elaborating applications
@@ -205,7 +205,7 @@ private def elabTParserMacroAux (prec lhsPrec e : Term) : TermElabM Syntax := do
   | _                                        => Macro.throwUnsupported
 
 @[builtin_term_elab «sorry»] def elabSorry : TermElab := fun stx expectedType? => do
-  let stxNew ← `(sorryAx _ false)
+  let stxNew ← `(@sorryAx _ false) -- Remark: we use `@` to ensure `sorryAx` will not consume auot params
   withMacroExpansion stx stxNew <| elabTerm stxNew expectedType?
 
 /-- Return syntax `Prod.mk elems[0] (Prod.mk elems[1] ... (Prod.mk elems[elems.size - 2] elems[elems.size - 1])))` -/
@@ -314,11 +314,11 @@ where
 
 @[builtin_term_elab typeAscription] def elabTypeAscription : TermElab
   | `(($e : $type)), _ => do
-    let type ← withSynthesize (mayPostpone := true) <| elabType type
+    let type ← withSynthesize (postpone := .yes) <| elabType type
     let e ← elabTerm e type
     ensureHasType type e
   | `(($e :)), expectedType? => do
-    let e ← withSynthesize (mayPostpone := false) <| elabTerm e none
+    let e ← withSynthesize (postpone := .no) <| elabTerm e none
     ensureHasType expectedType? e
   | _, _ => throwUnsupportedSyntax
 

src/Lean/Elab/Calc.lean

@@ -42,7 +42,7 @@ def mkCalcTrans (result resultType step stepType : Expr) : MetaM (Expr × Expr)
     unless (← getCalcRelation? resultType).isSome do
       throwError "invalid 'calc' step, step result is not a relation{indentExpr resultType}"
     return (result, resultType)
-  | _ => throwError "invalid 'calc' step, failed to synthesize `Trans` instance{indentExpr selfType}"
+  | _ => throwError "invalid 'calc' step, failed to synthesize `Trans` instance{indentExpr selfType}\n{useDiagnosticMsg}"
 
 /--
 Adds a type annotation to a hole that occurs immediately at the beginning of the term.
@@ -112,10 +112,12 @@ def elabCalcSteps (steps : TSyntax ``calcSteps) : TermElabM Expr := do
   return result?.get!.1
 
 /-- Elaborator for the `calc` term mode variant. -/
-@[builtin_term_elab «calc»]
+@[builtin_term_elab Lean.calc]
 def elabCalc : TermElab := fun stx expectedType? => do
   let steps : TSyntax ``calcSteps := ⟨stx[1]⟩
   let result ← elabCalcSteps steps
   synthesizeSyntheticMVarsUsingDefault
   let result ← ensureHasType expectedType? result
   return result
+
+end Lean.Elab.Term

src/Lean/Elab/Command.lean

@@ -47,8 +47,9 @@ structure Context where
   ref            : Syntax := Syntax.missing
   tacticCache?   : Option (IO.Ref Tactic.Cache)
   /--
-  Snapshot for incremental reuse and reporting of command elaboration. Currently unused in Lean
-  itself.
+  Snapshot for incremental reuse and reporting of command elaboration. Currently only used for
+  (mutual) defs and contained tactics, in which case the `DynamicSnapshot` is a
+  `HeadersParsedSnapshot`.
 
   Definitely resolved in `Language.Lean.process.doElab`.
 
@@ -56,6 +57,13 @@ structure Context where
   old elaboration are identical.
   -/
   snap?          : Option (Language.SnapshotBundle Language.DynamicSnapshot)
+  /-- Cancellation token forwarded to `Core.cancelTk?`. -/
+  cancelTk?      : Option IO.CancelToken
+  /--
+  If set (when `showPartialSyntaxErrors` is not set and parsing failed), suppresses most elaboration
+  errors; see also `logMessage` below.
+  -/
+  suppressElabErrors : Bool := false
 
 abbrev CommandElabCoreM (ε) := ReaderT Context $ StateRefT State $ EIO ε
 abbrev CommandElabM := CommandElabCoreM Exception
@@ -73,6 +81,21 @@ Remark: see comment at TermElabM
 @[always_inline]
 instance : Monad CommandElabM := let i := inferInstanceAs (Monad CommandElabM); { pure := i.pure, bind := i.bind }
 
+/-- Like `Core.tryCatch` but do catch runtime exceptions. -/
+@[inline] protected def tryCatch (x : CommandElabM α) (h : Exception → CommandElabM α) :
+    CommandElabM α := do
+  try
+    x
+  catch ex =>
+    if ex.isInterrupt then
+      throw ex
+    else
+      h ex
+
+instance : MonadExceptOf Exception CommandElabM where
+  throw    := throw
+  tryCatch := Command.tryCatch
+
 def mkState (env : Environment) (messages : MessageLog := {}) (opts : Options := {}) : State := {
   env         := env
   messages    := messages
@@ -128,20 +151,6 @@ def mkMessageAux (ctx : Context) (ref : Syntax) (msgData : MessageData) (severit
   let endPos := ref.getTailPos?.getD pos
   mkMessageCore ctx.fileName ctx.fileMap msgData severity pos endPos
 
-private def mkCoreContext (ctx : Context) (s : State) (heartbeats : Nat) : Core.Context :=
-  let scope        := s.scopes.head!
-  { fileName       := ctx.fileName
-    fileMap        := ctx.fileMap
-    options        := scope.opts
-    currRecDepth   := ctx.currRecDepth
-    maxRecDepth    := s.maxRecDepth
-    ref            := ctx.ref
-    currNamespace  := scope.currNamespace
-    openDecls      := scope.openDecls
-    initHeartbeats := heartbeats
-    currMacroScope := ctx.currMacroScope
-    diag           := getDiag scope.opts }
-
 private def addTraceAsMessagesCore (ctx : Context) (log : MessageLog) (traceState : TraceState) : MessageLog := Id.run do
   if traceState.traces.isEmpty then return log
   let mut traces : HashMap (String.Pos × String.Pos) (Array MessageData) := ∅
@@ -167,31 +176,50 @@ private def addTraceAsMessages : CommandElabM Unit := do
       traceState.traces := {}
     }
 
-def liftCoreM (x : CoreM α) : CommandElabM α := do
+private def runCore (x : CoreM α) : CommandElabM α := do
   let s ← get
   let ctx ← read
   let heartbeats ← IO.getNumHeartbeats
-  let Eα := Except Exception α
-  let x : CoreM Eα := try let a ← x; pure <| Except.ok a catch ex => pure <| Except.error ex
-  let x : EIO Exception (Eα × Core.State) := (ReaderT.run x (mkCoreContext ctx s heartbeats)).run { env := s.env, ngen := s.ngen, traceState := s.traceState, messages := {}, infoState.enabled := s.infoState.enabled }
+  let env := Kernel.resetDiag s.env
+  let scope := s.scopes.head!
+  let coreCtx : Core.Context := {
+    fileName           := ctx.fileName
+    fileMap            := ctx.fileMap
+    currRecDepth       := ctx.currRecDepth
+    maxRecDepth        := s.maxRecDepth
+    ref                := ctx.ref
+    currNamespace      := scope.currNamespace
+    openDecls          := scope.openDecls
+    initHeartbeats     := heartbeats
+    currMacroScope     := ctx.currMacroScope
+    options            := scope.opts
+    cancelTk?          := ctx.cancelTk?
+    suppressElabErrors := ctx.suppressElabErrors }
+  let x : EIO _ _ := x.run coreCtx {
+    env
+    ngen := s.ngen
+    nextMacroScope := s.nextMacroScope
+    infoState.enabled := s.infoState.enabled
+    traceState := s.traceState
+  }
   let (ea, coreS) ← liftM x
   modify fun s => { s with
-    env := coreS.env
-    ngen := coreS.ngen
-    messages := s.messages ++ coreS.messages
+    env               := coreS.env
+    nextMacroScope    := coreS.nextMacroScope
+    ngen              := coreS.ngen
+    infoState.trees   := s.infoState.trees.append coreS.infoState.trees
     traceState.traces := coreS.traceState.traces.map fun t => { t with ref := replaceRef t.ref ctx.ref }
-    infoState.trees := s.infoState.trees.append coreS.infoState.trees
+    messages          := s.messages ++ coreS.messages
   }
-  match ea with
-  | Except.ok a    => pure a
-  | Except.error e => throw e
+  return ea
+
+def liftCoreM (x : CoreM α) : CommandElabM α := do
+  MonadExcept.ofExcept (← runCore (observing x))
 
 private def ioErrorToMessage (ctx : Context) (ref : Syntax) (err : IO.Error) : Message :=
   let ref := getBetterRef ref ctx.macroStack
   mkMessageAux ctx ref (toString err) MessageSeverity.error
 
-@[inline] def liftEIO {α} (x : EIO Exception α) : CommandElabM α := liftM x
-
 @[inline] def liftIO {α} (x : IO α) : CommandElabM α := do
   let ctx ← read
   IO.toEIO (fun (ex : IO.Error) => Exception.error ctx.ref ex.toString) x
@@ -211,6 +239,11 @@ instance : MonadLog CommandElabM where
   getFileName := return (← read).fileName
   hasErrors   := return (← get).messages.hasErrors
   logMessage msg := do
+    if (← read).suppressElabErrors then
+      -- discard elaboration errors on parse error
+      -- NOTE: unlike `CoreM`'s `logMessage`, we do not currently have any command-level errors that
+      -- we want to allowlist
+      return
     let currNamespace ← getCurrNamespace
     let openDecls ← getOpenDecls
     let msg := { msg with data := MessageData.withNamingContext { currNamespace := currNamespace, openDecls := openDecls } msg.data }
@@ -263,15 +296,33 @@ private def mkInfoTree (elaborator : Name) (stx : Syntax) (trees : PersistentArr
   }
   return InfoTree.context ctx tree
 
+/--
+Disables incremental command reuse *and* reporting for `act` if `cond` is true by setting
+`Context.snap?` to `none`.
+-/
+def withoutCommandIncrementality (cond : Bool) (act : CommandElabM α) : CommandElabM α := do
+  let opts ← getOptions
+  withReader (fun ctx => { ctx with snap? := ctx.snap?.filter fun snap => Id.run do
+    if let some old := snap.old? then
+      if cond && opts.getBool `trace.Elab.reuse then
+        dbg_trace "reuse stopped: guard failed at {old.stx}"
+    return !cond
+  }) act
+
 private def elabCommandUsing (s : State) (stx : Syntax) : List (KeyedDeclsAttribute.AttributeEntry CommandElab) → CommandElabM Unit
   | []                => withInfoTreeContext (mkInfoTree := mkInfoTree `no_elab stx) <| throwError "unexpected syntax{indentD stx}"
   | (elabFn::elabFns) =>
     catchInternalId unsupportedSyntaxExceptionId
-      (withInfoTreeContext (mkInfoTree := mkInfoTree elabFn.declName stx) <| elabFn.value stx)
+      (do
+        -- prevent unsupported commands from accidentally accessing `Context.snap?` (e.g. by nested
+        -- supported commands)
+        withoutCommandIncrementality (!(← isIncrementalElab elabFn.declName)) do
+        withInfoTreeContext (mkInfoTree := mkInfoTree elabFn.declName stx) do
+         elabFn.value stx)
       (fun _ => do set s; elabCommandUsing s stx elabFns)
 
 /-- Elaborate `x` with `stx` on the macro stack -/
-def withMacroExpansion {α} (beforeStx afterStx : Syntax) (x : CommandElabM α) : CommandElabM α :=
+def withMacroExpansion (beforeStx afterStx : Syntax) (x : CommandElabM α) : CommandElabM α :=
   withInfoContext (mkInfo := pure <| .ofMacroExpansionInfo { stx := beforeStx, output := afterStx, lctx := .empty }) do
     withReader (fun ctx => { ctx with macroStack := { before := beforeStx, after := afterStx } :: ctx.macroStack }) x
 
@@ -294,7 +345,10 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
       if k == nullKind then
         -- list of commands => elaborate in order
         -- The parser will only ever return a single command at a time, but syntax quotations can return multiple ones
-        args.forM elabCommand
+        -- TODO: support incrementality at least for some cases such as expansions of
+        -- `set_option in` or `def a.b`
+        withoutCommandIncrementality true do
+          args.forM elabCommand
       else withTraceNode `Elab.command (fun _ => return stx) (tag :=
         -- special case: show actual declaration kind for `declaration` commands
         (if stx.isOfKind ``Parser.Command.declaration then stx[1] else stx).getKind.toString) do
@@ -317,11 +371,19 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
 
 builtin_initialize registerTraceClass `Elab.input
 
+/-- Option for showing elaboration errors from partial syntax errors. -/
+register_builtin_option showPartialSyntaxErrors : Bool := {
+  defValue := false
+  descr    := "show elaboration errors from partial syntax trees (i.e. after parser recovery)"
+}
+
 /--
 `elabCommand` wrapper that should be used for the initial invocation, not for recursive calls after
 macro expansion etc.
 -/
 def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do profileitM Exception "elaboration" (← getOptions) do
+  withReader ({ · with suppressElabErrors :=
+    stx.hasMissing && !showPartialSyntaxErrors.get (← getOptions) }) do
   let initMsgs ← modifyGet fun st => (st.messages, { st with messages := {} })
   let initInfoTrees ← getResetInfoTrees
   try
@@ -404,7 +466,6 @@ def printExpr (e : Expr) : MetaM Unit := do
 def liftTermElabM (x : TermElabM α) : CommandElabM α := do
   let ctx ← read
   let s   ← get
-  let heartbeats ← IO.getNumHeartbeats
   -- dbg_trace "heartbeats: {heartbeats}"
   let scope := s.scopes.head!
   -- We execute `x` with an empty message log. Thus, `x` cannot modify/view messages produced by previous commands.
@@ -413,18 +474,9 @@ def liftTermElabM (x : TermElabM α) : CommandElabM α := do
   -- make sure `observing` below also catches runtime exceptions (like we do by default in
   -- `CommandElabM`)
   let _ := MonadAlwaysExcept.except (m := TermElabM)
-  let x : MetaM _      := (observing (try x finally Meta.reportDiag)).run (mkTermContext ctx s) { levelNames := scope.levelNames }
-  let x : CoreM _      := x.run mkMetaContext {}
-  let x : EIO _ _      := x.run (mkCoreContext ctx s heartbeats) { env := s.env, ngen := s.ngen, nextMacroScope := s.nextMacroScope, infoState.enabled := s.infoState.enabled, traceState := s.traceState }
-  let (((ea, _), _), coreS) ← liftEIO x
-  modify fun s => { s with
-    env               := coreS.env
-    nextMacroScope    := coreS.nextMacroScope
-    ngen              := coreS.ngen
-    infoState.trees   := s.infoState.trees.append coreS.infoState.trees
-    traceState.traces := coreS.traceState.traces.map fun t => { t with ref := replaceRef t.ref ctx.ref }
-    messages          := s.messages ++ coreS.messages
-  }
+  let x : MetaM _ := (observing (try x finally Meta.reportDiag)).run (mkTermContext ctx s) { levelNames := scope.levelNames }
+  let x : CoreM _ := x.run mkMetaContext {}
+  let ((ea, _), _) ← runCore x
   MonadExcept.ofExcept ea
 
 /--
@@ -468,7 +520,12 @@ def runTermElabM (elabFn : Array Expr → TermElabM α) : CommandElabM α := do
           Term.addAutoBoundImplicits' xs someType fun xs _ =>
             Term.withoutAutoBoundImplicit <| elabFn xs
 
-@[inline] def catchExceptions (x : CommandElabM Unit) : CommandElabCoreM Empty Unit := fun ctx ref =>
+/--
+Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
+catches interrupt exceptions as well and thus is intended for use at the top level of elaboration.
+Interrupt and abort exceptions are caught but not logged.
+-/
+@[inline] def withLoggingExceptions (x : CommandElabM Unit) : CommandElabCoreM Empty Unit := fun ctx ref =>
   EIO.catchExceptions (withLogging x ctx ref) (fun _ => pure ())
 
 private def liftAttrM {α} (x : AttrM α) : CommandElabM α := do
@@ -534,6 +591,7 @@ def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
       ref := ← getRef
       tacticCache? := none
       snap? := none
+      cancelTk? := (← read).cancelTk?
     } |>.run {
       env := ← getEnv
       maxRecDepth := ← getMaxRecDepth
@@ -543,7 +601,7 @@ def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
     traceState.traces := coreState.traceState.traces ++ commandState.traceState.traces
     env := commandState.env
   }
-  if let some err := commandState.messages.msgs.toArray.find? (·.severity matches .error) then
+  if let some err := commandState.messages.toArray.find? (·.severity matches .error) then
     throwError err.data
   pure a
 

src/Lean/Elab/Declaration.lean

@@ -188,7 +188,7 @@ def elabClassInductive (modifiers : Modifiers) (stx : Syntax) : CommandElabM Uni
   let v ← classInductiveSyntaxToView modifiers stx
   elabInductiveViews #[v]
 
-@[builtin_command_elab declaration]
+@[builtin_command_elab declaration, builtin_incremental]
 def elabDeclaration : CommandElab := fun stx => do
   match (← liftMacroM <| expandDeclNamespace? stx) with
   | some (ns, newStx) => do
@@ -198,22 +198,24 @@ def elabDeclaration : CommandElab := fun stx => do
   | none => do
     let decl     := stx[1]
     let declKind := decl.getKind
-    if declKind == ``Lean.Parser.Command.«axiom» then
-      let modifiers ← elabModifiers stx[0]
-      elabAxiom modifiers decl
-    else if declKind == ``Lean.Parser.Command.«inductive» then
-      let modifiers ← elabModifiers stx[0]
-      elabInductive modifiers decl
-    else if declKind == ``Lean.Parser.Command.classInductive then
-      let modifiers ← elabModifiers stx[0]
-      elabClassInductive modifiers decl
-    else if declKind == ``Lean.Parser.Command.«structure» then
-      let modifiers ← elabModifiers stx[0]
-      elabStructure modifiers decl
-    else if isDefLike decl then
+    if isDefLike decl then
+      -- only case implementing incrementality currently
       elabMutualDef #[stx]
-    else
-      throwError "unexpected declaration"
+    else withoutCommandIncrementality true do
+      if declKind == ``Lean.Parser.Command.«axiom» then
+        let modifiers ← elabModifiers stx[0]
+        elabAxiom modifiers decl
+      else if declKind == ``Lean.Parser.Command.«inductive» then
+        let modifiers ← elabModifiers stx[0]
+        elabInductive modifiers decl
+      else if declKind == ``Lean.Parser.Command.classInductive then
+        let modifiers ← elabModifiers stx[0]
+        elabClassInductive modifiers decl
+      else if declKind == ``Lean.Parser.Command.«structure» then
+        let modifiers ← elabModifiers stx[0]
+        elabStructure modifiers decl
+      else
+        throwError "unexpected declaration"
 
 /-- Return true if all elements of the mutual-block are inductive declarations. -/
 private def isMutualInductive (stx : Syntax) : Bool :=
@@ -322,14 +324,16 @@ def expandMutualPreamble : Macro := fun stx =>
     let endCmd    ← `(end)
     return mkNullNode (#[secCmd] ++ preamble ++ #[newMutual] ++ #[endCmd])
 
-@[builtin_command_elab «mutual»]
+@[builtin_command_elab «mutual», builtin_incremental]
 def elabMutual : CommandElab := fun stx => do
-  if isMutualInductive stx then
-    elabMutualInductive stx[1].getArgs
-  else if isMutualDef stx then
+  if isMutualDef stx then
+    -- only case implementing incrementality currently
     elabMutualDef stx[1].getArgs
-  else
-    throwError "invalid mutual block: either all elements of the block must be inductive declarations, or they must all be definitions/theorems/abbrevs"
+  else withoutCommandIncrementality true do
+    if isMutualInductive stx then
+      elabMutualInductive stx[1].getArgs
+    else
+      throwError "invalid mutual block: either all elements of the block must be inductive declarations, or they must all be definitions/theorems/abbrevs"
 
 /- leading_parser "attribute " >> "[" >> sepBy1 (eraseAttr <|> Term.attrInstance) ", " >> "]" >> many1 ident -/
 @[builtin_command_elab «attribute»] def elabAttr : CommandElab := fun stx => do

src/Lean/Elab/DefView.lean

@@ -28,14 +28,101 @@ def DefKind.isExample : DefKind → Bool
   | .example => true
   | _        => false
 
+/-- Header elaboration data of a `DefView`. -/
+structure DefViewElabHeaderData where
+  /--
+    Short name. Recall that all declarations in Lean 4 are potentially recursive. We use `shortDeclName` to refer
+    to them at `valueStx`, and other declarations in the same mutual block. -/
+  shortDeclName : Name
+  /-- Full name for this declaration. This is the name that will be added to the `Environment`. -/
+  declName      : Name
+  /-- Universe level parameter names explicitly provided by the user. -/
+  levelNames    : List Name
+  /-- Syntax objects for the binders occurring before `:`, we use them to populate the `InfoTree` when elaborating `valueStx`. -/
+  binderIds     : Array Syntax
+  /-- Number of parameters before `:`, it also includes auto-implicit parameters automatically added by Lean. -/
+  numParams     : Nat
+  /-- Type including parameters. -/
+  type          : Expr
+deriving Inhabited
+
+section Snapshots
+open Language
+
+/-- Snapshot after processing of a definition body.  -/
+structure BodyProcessedSnapshot extends Language.Snapshot where
+  /-- State after elaboration. -/
+  state : Term.SavedState
+  /-- Elaboration result. -/
+  value : Expr
+deriving Nonempty
+instance : Language.ToSnapshotTree BodyProcessedSnapshot where
+  toSnapshotTree s := ⟨s.toSnapshot, #[]⟩
+
+/-- Snapshot after elaboration of a definition header. -/
+structure HeaderProcessedSnapshot extends Language.Snapshot where
+  /-- Elaboration results. -/
+  view : DefViewElabHeaderData
+  /-- Resulting elaboration state, including any environment additions. -/
+  state : Term.SavedState
+  /-- Syntax of top-level tactic block if any, for checking reuse of `tacSnap?`. -/
+  tacStx? : Option Syntax
+  /-- Incremental execution of main tactic block, if any. -/
+  tacSnap? : Option (SnapshotTask Tactic.TacticParsedSnapshot)
+  /-- Syntax of definition body, for checking reuse of `bodySnap`. -/
+  bodyStx : Syntax
+  /-- Result of body elaboration. -/
+  bodySnap : SnapshotTask (Option BodyProcessedSnapshot)
+deriving Nonempty
+instance : Language.ToSnapshotTree HeaderProcessedSnapshot where
+  toSnapshotTree s := ⟨s.toSnapshot,
+    (match s.tacSnap? with
+      | some tac => #[tac.map (sync := true) toSnapshotTree]
+      | none     => #[]) ++
+    #[s.bodySnap.map (sync := true) toSnapshotTree]⟩
+
+/-- State before elaboration of a mutual definition. -/
+structure DefParsed where
+  /--
+  Unstructured syntax object comprising the full "header" of the definition from the modifiers
+  (incl. docstring) up to the value, used for determining header elaboration reuse.
+  -/
+  fullHeaderRef : Syntax
+  /-- Elaboration result, unless fatal exception occurred. -/
+  headerProcessedSnap : SnapshotTask (Option HeaderProcessedSnapshot)
+deriving Nonempty
+
+/-- Snapshot after syntax tree has been split into separate mutual def headers. -/
+structure DefsParsedSnapshot extends Language.Snapshot where
+  /-- Definitions of this mutual block. -/
+  defs : Array DefParsed
+deriving Nonempty, TypeName
+instance : Language.ToSnapshotTree DefsParsedSnapshot where
+  toSnapshotTree s := ⟨s.toSnapshot,
+    s.defs.map (·.headerProcessedSnap.map (sync := true) toSnapshotTree)⟩
+
+end Snapshots
+
 structure DefView where
   kind          : DefKind
   ref           : Syntax
+  /--
+  An unstructured syntax object that comprises the "header" of the definition, i.e. everything up
+  to the value. Used as a more specific ref for header elaboration.
+  -/
+  headerRef     : Syntax
   modifiers     : Modifiers
   declId        : Syntax
   binders       : Syntax
   type?         : Option Syntax
   value         : Syntax
+  /--
+  Snapshot for incremental processing of this definition.
+
+  Invariant: If the bundle's `old?` is set, then elaboration of the header is guaranteed to result
+  in the same elaboration result and state, i.e. reuse is possible.
+  -/
+  headerSnap?   : Option (Language.SnapshotBundle (Option HeaderProcessedSnapshot)) := none
   deriving?     : Option (Array Syntax) := none
   deriving Inhabited
 
@@ -50,20 +137,20 @@ def mkDefViewOfAbbrev (modifiers : Modifiers) (stx : Syntax) : DefView :=
   let (binders, type) := expandOptDeclSig stx[2]
   let modifiers       := modifiers.addAttribute { name := `inline }
   let modifiers       := modifiers.addAttribute { name := `reducible }
-  { ref := stx, kind := DefKind.abbrev, modifiers,
+  { ref := stx, headerRef := mkNullNode stx.getArgs[:3], kind := DefKind.abbrev, modifiers,
     declId := stx[1], binders, type? := type, value := stx[3] }
 
 def mkDefViewOfDef (modifiers : Modifiers) (stx : Syntax) : DefView :=
   -- leading_parser "def " >> declId >> optDeclSig >> declVal >> optDefDeriving
   let (binders, type) := expandOptDeclSig stx[2]
   let deriving? := if stx[4].isNone then none else some stx[4][1].getSepArgs
-  { ref := stx, kind := DefKind.def, modifiers,
+  { ref := stx, headerRef := mkNullNode stx.getArgs[:3], kind := DefKind.def, modifiers,
     declId := stx[1], binders, type? := type, value := stx[3], deriving? }
 
 def mkDefViewOfTheorem (modifiers : Modifiers) (stx : Syntax) : DefView :=
   -- leading_parser "theorem " >> declId >> declSig >> declVal
   let (binders, type) := expandDeclSig stx[2]
-  { ref := stx, kind := DefKind.theorem, modifiers,
+  { ref := stx, headerRef := mkNullNode stx.getArgs[:3], kind := DefKind.theorem, modifiers,
     declId := stx[1], binders, type? := some type, value := stx[3] }
 
 def mkDefViewOfInstance (modifiers : Modifiers) (stx : Syntax) : CommandElabM DefView := do
@@ -84,7 +171,7 @@ def mkDefViewOfInstance (modifiers : Modifiers) (stx : Syntax) : CommandElabM De
       trace[Elab.instance.mkInstanceName] "generated {(← getCurrNamespace) ++ id}"
       pure <| mkNode ``Parser.Command.declId #[mkIdentFrom stx id, mkNullNode]
   return {
-    ref := stx, kind := DefKind.def, modifiers := modifiers,
+    ref := stx, headerRef := mkNullNode stx.getArgs[:5], kind := DefKind.def, modifiers := modifiers,
     declId := declId, binders := binders, type? := type, value := stx[5]
   }
 
@@ -97,7 +184,7 @@ def mkDefViewOfOpaque (modifiers : Modifiers) (stx : Syntax) : CommandElabM DefV
       let val ← if modifiers.isUnsafe then `(default_or_ofNonempty% unsafe) else `(default_or_ofNonempty%)
       `(Parser.Command.declValSimple| := $val)
   return {
-    ref := stx, kind := DefKind.opaque, modifiers := modifiers,
+    ref := stx, headerRef := mkNullNode stx.getArgs[:3], kind := DefKind.opaque, modifiers := modifiers,
     declId := stx[1], binders := binders, type? := some type, value := val
   }
 
@@ -106,7 +193,7 @@ def mkDefViewOfExample (modifiers : Modifiers) (stx : Syntax) : DefView :=
   let (binders, type) := expandOptDeclSig stx[1]
   let id              := mkIdentFrom stx `_example
   let declId          := mkNode ``Parser.Command.declId #[id, mkNullNode]
-  { ref := stx, kind := DefKind.example, modifiers := modifiers,
+  { ref := stx, headerRef := mkNullNode stx.getArgs[:2], kind := DefKind.example, modifiers := modifiers,
     declId := declId, binders := binders, type? := type, value := stx[2] }
 
 def isDefLike (stx : Syntax) : Bool :=

src/Lean/Elab/Deriving/Repr.lean

@@ -70,6 +70,8 @@ where
           if localDecl.binderInfo.isExplicit then
             if (← inferType x).isAppOf indVal.name then
               rhs ← `($rhs ++ Format.line ++ $(mkIdent auxFunName):ident $a:ident max_prec)
+            else if (← isType x <||> isProof x) then
+              rhs ← `($rhs ++ Format.line ++ "_")
             else
               rhs ← `($rhs ++ Format.line ++ reprArg $a)
         patterns := patterns.push (← `(@$(mkIdent ctorName):ident $ctorArgs:term*))

src/Lean/Elab/Exception.lean

@@ -5,7 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Lean.InternalExceptionId
-import Lean.Meta.Basic
+import Lean.Exception
 
 namespace Lean.Elab
 

src/Lean/Elab/Extra.lean

@@ -188,7 +188,7 @@ private partial def toTree (s : Syntax) : TermElabM Tree := do
   the macro declaration names in the `op` nodes.
   -/
   let result ← go s
-  synthesizeSyntheticMVars (mayPostpone := true)
+  synthesizeSyntheticMVars (postpone := .yes)
   return result
 where
   go (s : Syntax) := do
@@ -241,7 +241,10 @@ private def hasCoe (fromType toType : Expr) : TermElabM Bool := do
 
 private structure AnalyzeResult where
   max?            : Option Expr := none
-  hasUncomparable : Bool := false -- `true` if there are two types `α` and `β` where we don't have coercions in any direction.
+  /-- `true` if there are two types `α` and `β` where we don't have coercions in any direction. -/
+  hasUncomparable : Bool := false
+  /-- `true` if there are any leaf terms with an unknown type (according to `isUnknown`). -/
+  hasUnknown      : Bool := false
 
 private def isUnknown : Expr → Bool
   | .mvar ..        => true
@@ -255,7 +258,7 @@ private def analyze (t : Tree) (expectedType? : Option Expr) : TermElabM Analyze
     match expectedType? with
     | none => pure none
     | some expectedType =>
-      let expectedType ← instantiateMVars expectedType
+      let expectedType := (← instantiateMVars expectedType).cleanupAnnotations
       if isUnknown expectedType then pure none else pure (some expectedType)
   (go t *> get).run' { max? }
 where
@@ -268,12 +271,40 @@ where
        | .binop _ _ _ lhs rhs => go lhs; go rhs
        | .unop _ _ arg => go arg
        | .term _ _ val =>
-         let type ← instantiateMVars (← inferType val)
-         unless isUnknown type do
+         let type := (← instantiateMVars (← inferType val)).cleanupAnnotations
+         if isUnknown type then
+           modify fun s => { s with hasUnknown := true }
+         else
            match (← get).max? with
            | none     => modify fun s => { s with max? := type }
            | some max =>
-             unless (← withNewMCtxDepth <| isDefEqGuarded max type) do
+             /-
+              Remark: Previously, we used `withNewMCtxDepth` to prevent metavariables in `max` and `type` from being assigned.
+
+              Reason: This is a heuristic procedure for introducing coercions in scenarios such as:
+              - Given `(n : Nat) (i : Int)`, elaborate `n = i`. The coercion must be inserted at `n`.
+                Consider the elaboration problem `(n + 0) + i`, where the type of term `0` is a metavariable.
+                We do not want it to be elaborated as `(Int.ofNat n + Int.ofNat (0 : Nat)) + i`; instead, we prefer the result to be `(Int.ofNat n + (0 : Int)) + i`.
+                Here is another example where we avoid assigning metavariables: `max := BitVec n` and `type := BitVec ?m`.
+
+              However, the combination `withNewMCtxDepth <| isDefEqGuarded max type` introduced performance issues in several
+              Mathlib files because `isDefEq` was spending a lot of time unfolding definitions in `max` and `type` before failing.
+
+              To address this issue, we allowed only reducible definitions to be unfolded during this check, using
+              `withNewMCtxDepth <| withReducible <| isDefEqGuarded max type`. This change fixed some performance issues but created new ones.
+              Lean was now spending time trying to use `hasCoe`, likely occurring in places where `withNewMCtxDepth <| isDefEqGuarded max type`
+              used to succeed but was now failing after we introduced `withReducible`.
+
+              We then considered using just `isDefEqGuarded max type` and changing the definition of `isUnknown`. In the new definition,
+              the else-case would be `| e => e.hasExprMVar` instead of `| _ => false`. However, we could not even compile this repo using
+              this configuration. The problem arises because some files require coercions even when `max` contains metavariables,
+              for example: `max := Option ?m` and `type := Name`.
+
+              As a result, rather than restricting reducibility, we decided to set `Meta.Config.isDefEqStuckEx := true`.
+              This means that if `isDefEq` encounters a subproblem `?m =?= a` where `?m` is non-assignable, it aborts the test
+              instead of unfolding definitions.
+             -/
+             unless (← withNewMCtxDepth <| withConfig (fun config => { config with isDefEqStuckEx := true }) <| isDefEqGuarded max type) do
                if (← hasCoe type max) then
                  return ()
                else if (← hasCoe max type) then
@@ -404,7 +435,7 @@ mutual
       | .unop ref f arg =>
         return .unop ref f (← go arg none false false)
       | .term ref trees e =>
-        let type ← instantiateMVars (← inferType e)
+        let type := (← instantiateMVars (← inferType e)).cleanupAnnotations
         trace[Elab.binop] "visiting {e} : {type} =?= {maxType}"
         if isUnknown type then
           if let some f := f? then
@@ -422,12 +453,17 @@ mutual
 
   private partial def toExpr (tree : Tree) (expectedType? : Option Expr) : TermElabM Expr := do
     let r ← analyze tree expectedType?
-    trace[Elab.binop] "hasUncomparable: {r.hasUncomparable}, maxType: {r.max?}"
+    trace[Elab.binop] "hasUncomparable: {r.hasUncomparable}, hasUnknown: {r.hasUnknown}, maxType: {r.max?}"
     if r.hasUncomparable || r.max?.isNone then
       let result ← toExprCore tree
       ensureHasType expectedType? result
     else
       let result ← toExprCore (← applyCoe tree r.max?.get! (isPred := false))
+      unless r.hasUnknown do
+        -- Record the resulting maxType calculation.
+        -- We can do this when all the types are known, since in this case `hasUncomparable` is valid.
+        -- If they're not known, recording maxType like this can lead to heterogeneous operations failing to elaborate.
+        discard <| isDefEqGuarded (← inferType result) r.max?.get!
       trace[Elab.binop] "result: {result}"
       ensureHasType expectedType? result
 
@@ -460,7 +496,6 @@ def elabBinRelCore (noProp : Bool) (stx : Syntax) (expectedType? : Option Expr)
   | some f => withSynthesizeLight do
     /-
     We used to use `withSynthesize (mayPostpone := true)` here instead of `withSynthesizeLight` here.
-    Recall that `withSynthesizeLight` is equivalent to `withSynthesize (mayPostpone := true) (synthesizeDefault := false)`.
     It seems too much to apply default instances at binary relations. For example, we cannot elaborate
     ```
     def as : List Int := [-1, 2, 0, -3, 4]
@@ -494,7 +529,7 @@ def elabBinRelCore (noProp : Bool) (stx : Syntax) (expectedType? : Option Expr)
     let rhs ← withRef rhsStx <| toTree rhsStx
     let tree := .binop stx .regular f lhs rhs
     let r ← analyze tree none
-    trace[Elab.binrel] "hasUncomparable: {r.hasUncomparable}, maxType: {r.max?}"
+    trace[Elab.binrel] "hasUncomparable: {r.hasUncomparable}, hasUnknown: {r.hasUnknown}, maxType: {r.max?}"
     if r.hasUncomparable || r.max?.isNone then
       -- Use default elaboration strategy + `toBoolIfNecessary`
       let lhs ← toExprCore lhs

src/Lean/Elab/Frontend.lean

@@ -16,6 +16,7 @@ structure State where
   parserState  : Parser.ModuleParserState
   cmdPos       : String.Pos
   commands     : Array Syntax := #[]
+deriving Nonempty
 
 structure Context where
   inputCtx : Parser.InputContext
@@ -34,6 +35,7 @@ def setCommandState (commandState : Command.State) : FrontendM Unit :=
     fileMap      := ctx.inputCtx.fileMap
     tacticCache? := none
     snap?        := none
+    cancelTk?    := none
   }
   match (← liftM <| EIO.toIO' <| (x cmdCtx).run s.commandState) with
   | Except.error e      => throw <| IO.Error.userError s!"unexpected internal error: {← e.toMessageData.toString}"
@@ -44,15 +46,6 @@ def elabCommandAtFrontend (stx : Syntax) : FrontendM Unit := do
     let initMsgs ← modifyGet fun st => (st.messages, { st with messages := {} })
     Command.elabCommandTopLevel stx
     let mut msgs := (← get).messages
-    -- `stx.hasMissing` should imply `initMsgs.hasErrors`, but the latter should be cheaper to check
-    -- in general
-    if !Language.Lean.showPartialSyntaxErrors.get (← getOptions) && initMsgs.hasErrors &&
-        stx.hasMissing then
-      -- discard elaboration errors, except for a few important and unlikely misleading ones, on
-      -- parse error
-      msgs := ⟨msgs.msgs.filter fun msg =>
-        msg.data.hasTag (fun tag => tag == `Elab.synthPlaceholder ||
-          tag == `Tactic.unsolvedGoals || (`_traceMsg).isSuffixOf tag)⟩
     modify ({ · with messages := initMsgs ++ msgs })
 
 def updateCmdPos : FrontendM Unit := do
@@ -92,6 +85,47 @@ def IO.processCommands (inputCtx : Parser.InputContext) (parserState : Parser.Mo
   let (_, s) ← (Frontend.processCommands.run { inputCtx := inputCtx }).run { commandState := commandState, parserState := parserState, cmdPos := parserState.pos }
   pure s
 
+structure IncrementalState extends State where
+  inputCtx    : Parser.InputContext
+  initialSnap : Language.Lean.CommandParsedSnapshot
+deriving Nonempty
+
+open Language in
+/--
+Variant of `IO.processCommands` that uses the new Lean language processor implementation for
+potential incremental reuse. Pass in result of a previous invocation done with the same state
+(but usually different input context) to allow for reuse.
+-/
+-- `IO.processCommands` can be reimplemented on top of this as soon as the additional tasks speed up
+-- things instead of slowing them down
+partial def IO.processCommandsIncrementally (inputCtx : Parser.InputContext)
+    (parserState : Parser.ModuleParserState) (commandState : Command.State)
+    (old? : Option IncrementalState) :
+    BaseIO IncrementalState := do
+  let task ← Language.Lean.processCommands inputCtx parserState commandState
+    (old?.map fun old => (old.inputCtx, old.initialSnap))
+  go task.get task #[]
+where
+  go initialSnap t commands :=
+    let snap := t.get
+    let commands := commands.push snap.data.stx
+    if let some next := snap.nextCmdSnap? then
+      go initialSnap next commands
+    else
+      -- Opting into reuse also enables incremental reporting, so make sure to collect messages from
+      -- all snapshots
+      let messages := toSnapshotTree initialSnap
+        |>.getAll.map (·.diagnostics.msgLog)
+        |>.foldl (· ++ ·) {}
+      let trees := toSnapshotTree initialSnap
+        |>.getAll.map (·.infoTree?) |>.filterMap id |>.toPArray'
+      return {
+        commandState := { snap.data.finishedSnap.get.cmdState with messages, infoState.trees := trees }
+        parserState := snap.data.parserState
+        cmdPos := snap.data.parserState.pos
+        inputCtx, initialSnap, commands
+      }
+
 def process (input : String) (env : Environment) (opts : Options) (fileName : Option String := none) : IO (Environment × MessageLog) := do
   let fileName   := fileName.getD "<input>"
   let inputCtx   := Parser.mkInputContext input fileName
@@ -113,8 +147,7 @@ def runFrontend
     : IO (Environment × Bool) := do
   let startTime := (← IO.monoNanosNow).toFloat / 1000000000
   let inputCtx := Parser.mkInputContext input fileName
-  -- TODO: replace with `#lang` processing
-  if /- Lean #lang? -/ true then
+  if true then
     -- Temporarily keep alive old cmdline driver for the Lean language so that we don't pay the
     -- overhead of passing the environment between snapshots until we actually make good use of it
     -- outside the server
@@ -154,9 +187,9 @@ def runFrontend
 
     return (s.commandState.env, !s.commandState.messages.hasErrors)
 
-  let ctx := { inputCtx with mainModuleName, opts, trustLevel }
+  let ctx := { inputCtx with }
   let processor := Language.Lean.process
-  let snap ← processor none ctx
+  let snap ← processor (fun _ => pure <| .ok { mainModuleName, opts, trustLevel }) none ctx
   let snaps := Language.toSnapshotTree snap
   snaps.runAndReport opts jsonOutput
   if let some ileanFileName := ileanFileName? then

src/Lean/Elab/Inductive.lean

@@ -324,7 +324,7 @@ private def elabCtors (indFVars : Array Expr) (indFVar : Expr) (params : Array E
           | some ctorType =>
             let type ← Term.elabType ctorType
             trace[Elab.inductive] "elabType {ctorView.declName} : {type} "
-            Term.synthesizeSyntheticMVars (mayPostpone := true)
+            Term.synthesizeSyntheticMVars (postpone := .yes)
             let type ← instantiateMVars type
             let type ← checkParamOccs type
             forallTelescopeReducing type fun _ resultingType => do
@@ -686,8 +686,8 @@ private def computeFixedIndexBitMask (numParams : Nat) (indType : InductiveType)
               maskRef.modify fun mask => mask.set! i false
           for x in xs[numParams:] do
             let xType ← inferType x
-            let cond (e : Expr) := indFVars.any (fun indFVar => e.getAppFn == indFVar) && e.getAppNumArgs > numParams
-            xType.forEachWhere cond fun e => do
+            let cond (e : Expr) := indFVars.any (fun indFVar => e.getAppFn == indFVar)
+            xType.forEachWhere (stopWhenVisited := true) cond fun e => do
               let eArgs := e.getAppArgs
               for i in [numParams:eArgs.size] do
                 if i >= typeArgs.size then
@@ -695,6 +695,19 @@ private def computeFixedIndexBitMask (numParams : Nat) (indType : InductiveType)
                 else
                   unless eArgs[i]! == typeArgs[i]! do
                     maskRef.modify (resetMaskAt · i)
+              /-If an index is missing in the arguments of the inductive type, then it must be non-fixed.
+                Consider the following example:
+                ```lean
+                inductive All {I : Type u} (P : I → Type v) : List I → Type (max u v) where
+                  | cons : P x → All P xs → All P (x :: xs)
+
+                inductive Iμ {I : Type u}  : I → Type (max u v) where
+                  | mk : (i : I)  → All Iμ [] → Iμ i
+                ```
+                because `i` doesn't appear in `All Iμ []`, the index shouldn't be fixed.
+              -/
+              for i in [eArgs.size:arity] do
+                maskRef.modify (resetMaskAt · i)
         go ctors
     go indType.ctors
 

src/Lean/Elab/MutualDef.lean

@@ -20,28 +20,24 @@ import Lean.Elab.DeclarationRange
 namespace Lean.Elab
 open Lean.Parser.Term
 
-/-- `DefView` after elaborating the header. -/
-structure DefViewElabHeader where
-  ref           : Syntax
-  modifiers     : Modifiers
-  /-- Stores whether this is the header of a definition, theorem, ... -/
-  kind          : DefKind
+open Language
+
+/-- `DefView` plus header elaboration data and snapshot. -/
+structure DefViewElabHeader extends DefView, DefViewElabHeaderData where
   /--
-    Short name. Recall that all declarations in Lean 4 are potentially recursive. We use `shortDeclName` to refer
-    to them at `valueStx`, and other declarations in the same mutual block. -/
-  shortDeclName : Name
-  /-- Full name for this declaration. This is the name that will be added to the `Environment`. -/
-  declName      : Name
-  /-- Universe level parameter names explicitly provided by the user. -/
-  levelNames    : List Name
-  /-- Syntax objects for the binders occurring before `:`, we use them to populate the `InfoTree` when elaborating `valueStx`. -/
-  binderIds     : Array Syntax
-  /-- Number of parameters before `:`, it also includes auto-implicit parameters automatically added by Lean. -/
-  numParams     : Nat
-  /-- Type including parameters. -/
-  type          : Expr
-  /-- `Syntax` object the body/value of the definition. -/
-  valueStx      : Syntax
+  Snapshot for incremental processing of top-level tactic block, if any.
+
+  Invariant: if the bundle's `old?` is set, then the state *up to the start* of the tactic block is
+  unchanged, i.e. reuse is possible.
+  -/
+  tacSnap? : Option (Language.SnapshotBundle Tactic.TacticParsedSnapshot)
+  /--
+  Snapshot for incremental processing of definition body.
+
+  Invariant: if the bundle's `old?` is set, then elaboration of the body is guaranteed to result in
+  the same elaboration result and state, i.e. reuse is possible.
+  -/
+  bodySnap? : Option (Language.SnapshotBundle (Option BodyProcessedSnapshot))
   deriving Inhabited
 
 namespace Term
@@ -127,16 +123,71 @@ private def cleanupOfNat (type : Expr) : MetaM Expr := do
     let eNew := mkApp e.appFn! argArgs[1]!
     return .done eNew
 
-/-- Elaborate only the declaration headers. We have to elaborate the headers first because we support mutually recursive declarations in Lean 4. -/
-private def elabHeaders (views : Array DefView) : TermElabM (Array DefViewElabHeader) := do
-  let expandedDeclIds ← views.mapM fun view => withRef view.ref do
+/--
+Elaborates only the declaration view headers. We have to elaborate the headers first because we
+support mutually recursive declarations in Lean 4.
+-/
+private def elabHeaders (views : Array DefView)
+    (bodyPromises : Array (IO.Promise (Option BodyProcessedSnapshot)))
+    (tacPromises : Array (IO.Promise Tactic.TacticParsedSnapshot)) :
+    TermElabM (Array DefViewElabHeader) := do
+  let expandedDeclIds ← views.mapM fun view => withRef view.headerRef do
     Term.expandDeclId (← getCurrNamespace) (← getLevelNames) view.declId view.modifiers
   withAutoBoundImplicitForbiddenPred (fun n => expandedDeclIds.any (·.shortName == n)) do
     let mut headers := #[]
-    for view in views, ⟨shortDeclName, declName, levelNames⟩ in expandedDeclIds do
-      let newHeader ← withRef view.ref do
-        addDeclarationRanges declName view.ref
+    -- Can we reuse the result for a body? For starters, all headers (even those below the body)
+    -- must be reusable
+    let mut reuseBody := views.all (·.headerSnap?.any (·.old?.isSome))
+    for view in views, ⟨shortDeclName, declName, levelNames⟩ in expandedDeclIds,
+        tacPromise in tacPromises, bodyPromise in bodyPromises do
+      let mut reusableResult? := none
+      if let some snap := view.headerSnap? then
+        -- by the `DefView.headerSnap?` invariant, safe to reuse results at this point, so let's
+        -- wait for them!
+        if let some old := snap.old?.bind (·.val.get) then
+          let (tacStx?, newTacTask?) ← mkTacTask view.value tacPromise
+          snap.new.resolve <| some { old with
+            tacStx?
+            tacSnap? := newTacTask?
+            bodyStx := view.value
+            bodySnap := mkBodyTask view.value bodyPromise
+          }
+          -- Transition from `DefView.snap?` to `DefViewElabHeader.tacSnap?` invariant: if all
+          -- headers and all previous bodies could be reused, then the state at the *start* of the
+          -- top-level tactic block (if any) is unchanged
+          let reuseTac := reuseBody
+          -- Transition from `DefView.snap?` to `DefViewElabHeader.bodySnap?` invariant: if all
+          -- headers and all previous bodies could be reused and this body syntax is unchanged, then
+          -- we can reuse the result
+          reuseBody := reuseBody &&
+            view.value.structRangeEqWithTraceReuse (← getOptions) old.bodyStx
+          let header := { old.view, view with
+            -- We should only forward the promise if we are actually waiting on the corresponding
+            -- task; otherwise, diagnostics assigned to it will be lost
+            tacSnap? := guard newTacTask?.isSome *> some {
+              old? := do
+                guard reuseTac
+                some ⟨(← old.tacStx?), (← old.tacSnap?)⟩
+              new := tacPromise
+            }
+            bodySnap? := some {
+              -- no syntax guard to store, we already did the necessary checks
+              old? := guard reuseBody *> pure ⟨.missing, old.bodySnap⟩
+              new := bodyPromise
+            }
+          }
+          reusableResult? := some (header, old.state)
+        else
+          reuseBody := false
+
+      let header ← withRestoreOrSaveFull reusableResult? fun save => do
+        withRef view.headerRef do
+        addDeclarationRanges declName view.ref  -- NOTE: this should be the full `ref`
         applyAttributesAt declName view.modifiers.attrs .beforeElaboration
+        -- do not hide header errors on partial body syntax as these two elaboration parts are
+        -- sufficiently independent
+        withTheReader Core.Context ({ · with suppressElabErrors :=
+          view.headerRef.hasMissing && !Command.showPartialSyntaxErrors.get (← getOptions) }) do
         withDeclName declName <| withAutoBoundImplicit <| withLevelNames levelNames <|
           elabBindersEx view.binders.getArgs fun xs => do
             let refForElabFunType := view.value
@@ -164,21 +215,62 @@ private def elabHeaders (views : Array DefView) : TermElabM (Array DefViewElabHe
               let pendingMVarIds ← getMVars type
               discard <| logUnassignedUsingErrorInfos pendingMVarIds <|
                 getPendindMVarErrorMessage views
-            let newHeader := {
-              ref           := view.ref
-              modifiers     := view.modifiers
-              kind          := view.kind
-              shortDeclName := shortDeclName
-              declName, type, levelNames, binderIds
-              numParams     := xs.size
-              valueStx      := view.value : DefViewElabHeader }
+            let newHeader : DefViewElabHeaderData := {
+              declName, shortDeclName, type, levelNames, binderIds
+              numParams := xs.size
+            }
+            let mut newHeader : DefViewElabHeader := { view, newHeader with
+              bodySnap? := none, tacSnap? := none }
+            if let some snap := view.headerSnap? then
+              let (tacStx?, newTacTask?) ← mkTacTask view.value tacPromise
+              snap.new.resolve <| some {
+                diagnostics :=
+                  (← Language.Snapshot.Diagnostics.ofMessageLog (← Core.getAndEmptyMessageLog))
+                view := newHeader.toDefViewElabHeaderData
+                state := (← save)
+                tacStx?
+                tacSnap? := newTacTask?
+                bodyStx := view.value
+                bodySnap := mkBodyTask view.value bodyPromise
+              }
+              newHeader := { newHeader with
+                -- We should only forward the promise if we are actually waiting on the
+                -- corresponding task; otherwise, diagnostics assigned to it will be lost
+                tacSnap? := guard newTacTask?.isSome *> some { old? := none, new := tacPromise }
+                bodySnap? := some { old? := none, new := bodyPromise }
+              }
             check headers newHeader
             return newHeader
-      headers := headers.push newHeader
+      headers := headers.push header
     return headers
+where
+  getBodyTerm? (stx : Syntax) : Option Syntax :=
+    -- TODO: does not work with partial syntax
+    --| `(Parser.Command.declVal| := $body $_suffix:suffix $[$_where]?) => body
+    guard (stx.isOfKind ``Parser.Command.declValSimple) *> some stx[1]
+
+  /-- Creates snapshot task with appropriate range from body syntax and promise. -/
+  mkBodyTask (body : Syntax) (new : IO.Promise (Option BodyProcessedSnapshot)) :
+      Language.SnapshotTask (Option BodyProcessedSnapshot) :=
+    let rangeStx := getBodyTerm? body |>.getD body
+    { range? := rangeStx.getRange?, task := new.result }
+
+  /--
+  If `body` allows for incremental tactic reporting and reuse, creates a snapshot task out of the
+  passed promise with appropriate range, otherwise immediately resolves the promise to a dummy
+  value.
+  -/
+  mkTacTask (body : Syntax) (tacPromise : IO.Promise Tactic.TacticParsedSnapshot) :
+      TermElabM (Option Syntax × Option (Language.SnapshotTask Tactic.TacticParsedSnapshot))
+   := do
+    if let some e := getBodyTerm? body then
+      if let `(by $tacs*) := e then
+        return (e, some { range? := mkNullNode tacs |>.getRange?, task := tacPromise.result })
+    tacPromise.resolve default
+    return (none, none)
 
 /--
-  Create auxiliary local declarations `fs` for the given hearders using their `shortDeclName` and `type`, given hearders, and execute `k fs`.
+  Create auxiliary local declarations `fs` for the given headers using their `shortDeclName` and `type`, given headers, and execute `k fs`.
   The new free variables are tagged as `auxDecl`.
   Remark: `fs.size = headers.size`.
 -/
@@ -250,15 +342,44 @@ private def declValToTerminationHint (declVal : Syntax) : TermElabM WF.Terminati
     return .none
 
 private def elabFunValues (headers : Array DefViewElabHeader) : TermElabM (Array Expr) :=
-  headers.mapM fun header => withDeclName header.declName <| withLevelNames header.levelNames do
-    let valStx ← liftMacroM <| declValToTerm header.valueStx
-    forallBoundedTelescope header.type header.numParams fun xs type => do
-      -- Add new info nodes for new fvars. The server will detect all fvars of a binder by the binder's source location.
-      for i in [0:header.binderIds.size] do
-        -- skip auto-bound prefix in `xs`
-        addLocalVarInfo header.binderIds[i]! xs[header.numParams - header.binderIds.size + i]!
-      let val ← elabTermEnsuringType valStx type
-      mkLambdaFVars xs val
+  headers.mapM fun header => do
+    let mut reusableResult? := none
+    if let some snap := header.bodySnap? then
+      if let some old := snap.old? then
+        -- guaranteed reusable as by the `bodySnap?` invariant, so let's wait on the previous
+        -- elaboration
+        if let some old := old.val.get then
+          snap.new.resolve <| some old
+          -- also make sure to reuse tactic snapshots if present so that body reuse does not lead to
+          -- missed tactic reuse on further changes
+          if let some tacSnap := header.tacSnap? then
+            if let some oldTacSnap := tacSnap.old? then
+              tacSnap.new.resolve oldTacSnap.val.get
+          reusableResult? := some (old.value, old.state)
+
+    withRestoreOrSaveFull reusableResult? fun save => do
+      withDeclName header.declName <| withLevelNames header.levelNames do
+      let valStx ← liftMacroM <| declValToTerm header.value
+      forallBoundedTelescope header.type header.numParams fun xs type => do
+        -- Add new info nodes for new fvars. The server will detect all fvars of a binder by the binder's source location.
+        for i in [0:header.binderIds.size] do
+          -- skip auto-bound prefix in `xs`
+          addLocalVarInfo header.binderIds[i]! xs[header.numParams - header.binderIds.size + i]!
+        let val ← withReader ({ · with tacSnap? := header.tacSnap? }) do
+          -- synthesize mvars here to force the top-level tactic block (if any) to run
+          elabTermEnsuringType valStx type <* synthesizeSyntheticMVarsNoPostponing
+        -- NOTE: without this `instantiatedMVars`, `mkLambdaFVars` may leave around a redex that
+        -- leads to more section variables being included than necessary
+        let val ← instantiateMVars val
+        let val ← mkLambdaFVars xs val
+        if let some snap := header.bodySnap? then
+          snap.new.resolve <| some {
+            diagnostics :=
+              (← Language.Snapshot.Diagnostics.ofMessageLog (← Core.getAndEmptyMessageLog))
+            state := (← save)
+            value := val
+          }
+        return val
 
 private def collectUsed (headers : Array DefViewElabHeader) (values : Array Expr) (toLift : List LetRecToLift)
     : StateRefT CollectFVars.State MetaM Unit := do
@@ -640,7 +761,7 @@ def pushMain (preDefs : Array PreDefinition) (sectionVars : Array Expr) (mainHea
     : TermElabM (Array PreDefinition) :=
   mainHeaders.size.foldM (init := preDefs) fun i preDefs => do
     let header := mainHeaders[i]!
-    let termination ← declValToTerminationHint header.valueStx
+    let termination ← declValToTerminationHint header.value
     let termination := termination.rememberExtraParams header.numParams mainVals[i]!
     let value ← mkLambdaFVars sectionVars mainVals[i]!
     let type ← mkForallFVars sectionVars header.type
@@ -796,38 +917,40 @@ def elabMutualDef (vars : Array Expr) (views : Array DefView) : TermElabM Unit :
   else
     go
 where
-  go := do
-    let scopeLevelNames ← getLevelNames
-    let headers ← elabHeaders views
-    let headers ← levelMVarToParamHeaders views headers
-    let allUserLevelNames := getAllUserLevelNames headers
-    withFunLocalDecls headers fun funFVars => do
-      for view in views, funFVar in funFVars do
-        addLocalVarInfo view.declId funFVar
-      let values ←
-        try
-          let values ← elabFunValues headers
-          Term.synthesizeSyntheticMVarsNoPostponing
-          values.mapM (instantiateMVars ·)
-        catch ex =>
-          logException ex
-          headers.mapM fun header => mkSorry header.type (synthetic := true)
-      let headers ← headers.mapM instantiateMVarsAtHeader
-      let letRecsToLift ← getLetRecsToLift
-      let letRecsToLift ← letRecsToLift.mapM instantiateMVarsAtLetRecToLift
-      checkLetRecsToLiftTypes funFVars letRecsToLift
-      withUsed vars headers values letRecsToLift fun vars => do
-        let preDefs ← MutualClosure.main vars headers funFVars values letRecsToLift
-        for preDef in preDefs do
-          trace[Elab.definition] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
-        let preDefs ← withLevelNames allUserLevelNames <| levelMVarToParamPreDecls preDefs
-        let preDefs ← instantiateMVarsAtPreDecls preDefs
-        let preDefs ← fixLevelParams preDefs scopeLevelNames allUserLevelNames
-        for preDef in preDefs do
-          trace[Elab.definition] "after eraseAuxDiscr, {preDef.declName} : {preDef.type} :=\n{preDef.value}"
-        checkForHiddenUnivLevels allUserLevelNames preDefs
-        addPreDefinitions preDefs
-        processDeriving headers
+  go :=
+    withAlwaysResolvedPromises views.size fun bodyPromises =>
+    withAlwaysResolvedPromises views.size fun tacPromises => do
+      let scopeLevelNames ← getLevelNames
+      let headers ← elabHeaders views bodyPromises tacPromises
+      let headers ← levelMVarToParamHeaders views headers
+      let allUserLevelNames := getAllUserLevelNames headers
+      withFunLocalDecls headers fun funFVars => do
+        for view in views, funFVar in funFVars do
+          addLocalVarInfo view.declId funFVar
+        let values ←
+          try
+            let values ← elabFunValues headers
+            Term.synthesizeSyntheticMVarsNoPostponing
+            values.mapM (instantiateMVars ·)
+          catch ex =>
+            logException ex
+            headers.mapM fun header => mkSorry header.type (synthetic := true)
+        let headers ← headers.mapM instantiateMVarsAtHeader
+        let letRecsToLift ← getLetRecsToLift
+        let letRecsToLift ← letRecsToLift.mapM instantiateMVarsAtLetRecToLift
+        checkLetRecsToLiftTypes funFVars letRecsToLift
+        withUsed vars headers values letRecsToLift fun vars => do
+          let preDefs ← MutualClosure.main vars headers funFVars values letRecsToLift
+          for preDef in preDefs do
+            trace[Elab.definition] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
+          let preDefs ← withLevelNames allUserLevelNames <| levelMVarToParamPreDecls preDefs
+          let preDefs ← instantiateMVarsAtPreDecls preDefs
+          let preDefs ← fixLevelParams preDefs scopeLevelNames allUserLevelNames
+          for preDef in preDefs do
+            trace[Elab.definition] "after eraseAuxDiscr, {preDef.declName} : {preDef.type} :=\n{preDef.value}"
+          checkForHiddenUnivLevels allUserLevelNames preDefs
+          addPreDefinitions preDefs
+          processDeriving headers
 
   processDeriving (headers : Array DefViewElabHeader) := do
     for header in headers, view in views do
@@ -842,12 +965,46 @@ end Term
 namespace Command
 
 def elabMutualDef (ds : Array Syntax) : CommandElabM Unit := do
-  let views ← ds.mapM fun d => do
-    let modifiers ← elabModifiers d[0]
-    if ds.size > 1 && modifiers.isNonrec then
-      throwErrorAt d "invalid use of 'nonrec' modifier in 'mutual' block"
-    mkDefView modifiers d[1]
-  runTermElabM fun vars => Term.elabMutualDef vars views
+  let opts ← getOptions
+  withAlwaysResolvedPromises ds.size fun headerPromises => do
+    let snap? := (← read).snap?
+    let mut views := #[]
+    let mut defs := #[]
+    let mut reusedAllHeaders := true
+    for h : i in [0:ds.size], headerPromise in headerPromises do
+      let d := ds[i]
+      let modifiers ← elabModifiers d[0]
+      if ds.size > 1 && modifiers.isNonrec then
+        throwErrorAt d "invalid use of 'nonrec' modifier in 'mutual' block"
+      let mut view ← mkDefView modifiers d[1]
+      let fullHeaderRef := mkNullNode #[d[0], view.headerRef]
+      if let some snap := snap? then
+        view := { view with headerSnap? := some {
+          old? := do
+            -- transitioning from `Context.snap?` to `DefView.headerSnap?` invariant: if the
+            -- elaboration context and state are unchanged, and the syntax of this as well as all
+            -- previous headers is unchanged, then the elaboration result for this header (which
+            -- includes state from elaboration of previous headers!) should be unchanged.
+            guard reusedAllHeaders
+            let old ← snap.old?
+            -- blocking wait, `HeadersParsedSnapshot` (and hopefully others) should be quick
+            let old ← old.val.get.toTyped? DefsParsedSnapshot
+            let oldParsed ← old.defs[i]?
+            guard <| fullHeaderRef.structRangeEqWithTraceReuse opts oldParsed.fullHeaderRef
+            -- no syntax guard to store, we already did the necessary checks
+            return ⟨.missing, oldParsed.headerProcessedSnap⟩
+          new := headerPromise
+        } }
+        defs := defs.push {
+          fullHeaderRef
+          headerProcessedSnap := { range? := d.getRange?, task := headerPromise.result }
+        }
+        reusedAllHeaders := reusedAllHeaders && view.headerSnap?.any (·.old?.isSome)
+      views := views.push view
+    if let some snap := snap? then
+      -- no non-fatal diagnostics at this point
+      snap.new.resolve <| .ofTyped { defs, diagnostics := .empty : DefsParsedSnapshot }
+    runTermElabM fun vars => Term.elabMutualDef vars views
 
 end Command
 end Lean.Elab

src/Lean/Elab/PreDefinition/Main.lean

@@ -90,6 +90,11 @@ private def addAsAxioms (preDefs : Array PreDefinition) : TermElabM Unit := do
     applyAttributesOf #[preDef] AttributeApplicationTime.afterTypeChecking
     applyAttributesOf #[preDef] AttributeApplicationTime.afterCompilation
 
+def ensureFunIndReservedNamesAvailable (preDefs : Array PreDefinition) : MetaM Unit := do
+  preDefs.forM fun preDef =>
+    withRef preDef.ref <| ensureReservedNameAvailable preDef.declName "induct"
+  withRef preDefs[0]!.ref <| ensureReservedNameAvailable preDefs[0]!.declName "mutual_induct"
+
 def addPreDefinitions (preDefs : Array PreDefinition) : TermElabM Unit := withLCtx {} {} do
   for preDef in preDefs do
     trace[Elab.definition.body] "{preDef.declName} : {preDef.type} :=\n{preDef.value}"
@@ -121,6 +126,7 @@ def addPreDefinitions (preDefs : Array PreDefinition) : TermElabM Unit := withLC
       addAndCompilePartial preDefs
       preDefs.forM (·.termination.ensureNone "partial")
     else
+      ensureFunIndReservedNamesAvailable preDefs
       try
         let hasHints := preDefs.any fun preDef => preDef.termination.isNotNone
         if hasHints then