fix: improve split discriminant generalization strategy

This commit also
- improves `split` error messages.
- adds `trace.split.failure` option.
- uses new convention for trace messages.

closes #4390

.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)
-            // disabled for now as this mostly just speeds up the test suite which is not a bottleneck
-            // let large = ${{ github.event_name != 'pull_request' && github.repository == 'leanprover/lean4' }} ? "-large" : "";
-            let matrix = [
-              {
-                // portable release build: use channel with older glibc (2.27)
-                "name": "Linux LLVM",
-                "os": "ubuntu-latest",
-                "release": false,
-                "quick": false,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                // reverse-ffi needs to be updated to link to LLVM libraries
-                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
-                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${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",
-                "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 +90,171 @@ 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",
+                "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
+                "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 +333,9 @@ 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)" >> $GITHUB_ENV
       - name: Build
         run: |
           mkdir build
@@ -352,8 +366,8 @@ jobs:
             OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ 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 +396,29 @@ 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$NPROC stage3
         if: matrix.test-speedcenter
       - name: Test Speedcenter Benchmarks
         run: |
@@ -418,11 +429,10 @@ jobs:
         if: matrix.test-speedcenter
       - name: Check rebootstrap
         run: |
-          cd build
           ulimit -c unlimited # coredumps
           # clean rebuild in case of Makefile changes
-          make update-stage0 && rm -rf ./stage* && make -j4
-        if: matrix.name == 'Linux' && needs.configure.outputs.quick == 'false'
+          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$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

@@ -298,6 +298,13 @@ jobs:
           ref: nightly-testing
           fetch-depth: 0 # This ensures we check out all tags and branches.
 
+      - name: install elan
+        run: |
+          set -o pipefail
+          curl -sSfL https://github.com/leanprover/elan/releases/download/v3.0.0/elan-x86_64-unknown-linux-gnu.tar.gz | tar xz
+          ./elan-init -y --default-toolchain none
+          echo "$HOME/.elan/bin" >> "${GITHUB_PATH}"
+
       - name: Check if tag exists
         if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
         id: check_mathlib_tag
@@ -322,7 +329,8 @@ jobs:
             echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
             git add lean-toolchain
             sed -i "s/require batteries from git \"https:\/\/github.com\/leanprover-community\/batteries\" @ \".\+\"/require batteries from git \"https:\/\/github.com\/leanprover-community\/batteries\" @ \"nightly-testing-${MOST_RECENT_NIGHTLY}\"/" lakefile.lean
-            git add lakefile.lean
+            lake update batteries
+            git add lakefile.lean lake-manifest.json
             git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           else
             echo "Branch already exists, pushing an empty commit."

.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

@@ -1,159 +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.
-
-v4.9.0 (development in progress)
+v4.9.0
 ---------
 
-* 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.
+Development in progress.
 
 v4.8.0
 ---------
 
-* **Executables configured with `supportInterpreter := true` on Windows should now be run via `lake exe` to function properly.**
-
-  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`.
-
-  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/dev/release_checklist.md

@@ -46,7 +46,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
   - We do this for the repositories:
     - [lean4checker](https://github.com/leanprover/lean4checker)
       - No dependencies
-      - Note: `lean4checker` uses a different version tagging scheme: use `toolchain/v4.6.0` rather than `v4.6.0`.
       - Toolchain bump PR
       - Create and push the tag
       - Merge the tag into `stable`
@@ -82,10 +81,8 @@ We'll use `v4.6.0` as the intended release version as a running example.
       - 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
-          `git checkout toolchain/v4.6.0` to the appropriate tag,
-          and then run `.github/workflows/mk_build_yml.sh`. Coordinate with
-          a Mathlib maintainer to get this merged.
+          in `.github/workflows/lean4checker.yml` update the line
+          `git checkout v4.6.0` to the appropriate tag. 
         - Push the PR branch to the main Mathlib repository rather than a fork, or CI may not work reliably
         - Create and push the tag
         - Create a new branch from the tag, push it, and open a pull request against `stable`.

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/make/osx-10.9.md

@@ -1,4 +1,4 @@
-# Install Packages on OS X 10.9
+# Install Packages on OS X 14.5
 
 We assume that you are using [homebrew][homebrew] as a package manager.
 
@@ -22,7 +22,7 @@ brew install gcc
 ```
 To install clang++-3.5 via homebrew, please execute:
 ```bash
-brew install llvm --with-clang --with-asan
+brew install llvm
 ```
 To use compilers other than the default one (Apple's clang++), you
 need to use `-DCMAKE_CXX_COMPILER` option to specify the compiler

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

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

src/Init.lean

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

src/Init/Core.lean

@@ -468,11 +468,11 @@ class Singleton (α : outParam <| Type u) (β : Type v) where
 export Singleton (singleton)
 
 /-- `insert x ∅ = {x}` -/
-class IsLawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
+class LawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
     Prop where
   /-- `insert x ∅ = {x}` -/
   insert_emptyc_eq (x : α) : (insert x ∅ : β) = singleton x
-export IsLawfulSingleton (insert_emptyc_eq)
+export LawfulSingleton (insert_emptyc_eq)
 
 /-- Type class used to implement the notation `{ a ∈ c | p a }` -/
 class Sep (α : outParam <| Type u) (γ : Type v) where

src/Init/Data/AC.lean

@@ -146,8 +146,8 @@ theorem Context.evalList_mergeIdem (ctx : Context α) (h : ContextInformation.is
     | nil =>
       simp [mergeIdem, mergeIdem.loop]
       split
-      case inl h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
-      rfl
+      next h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
+      next => rfl
     | cons z zs =>
       by_cases h₂ : x = y
       case pos =>
@@ -191,11 +191,11 @@ theorem Context.evalList_insert
     . simp [evalList, h.1, EvalInformation.evalOp]
   | step y z zs ih =>
     simp [insert] at *; split
-    case inl => rfl
-    case inr =>
+    next => rfl
+    next =>
       split
-      case inl => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
-      case inr => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
+      next => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
+      next => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
 
 theorem Context.evalList_sort_congr
   (ctx : Context α)

src/Init/Data/Array/DecidableEq.lean

@@ -27,17 +27,17 @@ decreasing_by decreasing_trivial_pre_omega
 theorem eq_of_isEqv [DecidableEq α] (a b : Array α) : Array.isEqv a b (fun x y => x = y) → a = b := by
   simp [Array.isEqv]
   split
-  case inr => intro; contradiction
-  case inl hsz =>
+  next hsz =>
    intro h
    have aux := eq_of_isEqvAux a b hsz 0 (Nat.zero_le ..) h
    exact ext a b hsz fun i h _ => aux i (Nat.zero_le ..) _
+  next => intro; contradiction
 
 theorem isEqvAux_self [DecidableEq α] (a : Array α) (i : Nat) : Array.isEqvAux a a rfl (fun x y => x = y) i = true := by
   unfold Array.isEqvAux
   split
-  case inl h => simp [h, isEqvAux_self a (i+1)]
-  case inr h => simp [h]
+  next h => simp [h, isEqvAux_self a (i+1)]
+  next h => simp [h]
 termination_by a.size - i
 decreasing_by decreasing_trivial_pre_omega
 

src/Init/Data/Array/Subarray.lean

@@ -15,13 +15,13 @@ 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]
+@[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. -/
@@ -150,12 +151,12 @@ end Int
 section Syntax
 
 /-- Notation for bit vector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
-scoped syntax:max term:max noWs "#" noWs term:max : term
-macro_rules | `($i#$n) => `(BitVec.ofNat $n $i)
+syntax:max num noWs "#" noWs term:max : term
+macro_rules | `($i:num#$n) => `(BitVec.ofNat $n $i)
 
 /-- Unexpander for bit vector literals. -/
 @[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
-  | `($(_) $n $i) => `($i#$n)
+  | `($(_) $n $i:num) => `($i:num#$n)
   | _ => throw ()
 
 /-- Notation for bit vector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLt i lt`. -/
@@ -503,7 +504,7 @@ equivalent to `a * 2^s`, modulo `2^n`.
 
 SMT-Lib name: `bvshl` except this operator uses a `Nat` shift value.
 -/
-protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := (a.toNat <<< s)#n
+protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (a.toNat <<< s)
 instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩
 
 /--
@@ -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

@@ -184,4 +184,55 @@ theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c
     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/Lemmas.lean

@@ -9,6 +9,8 @@ import Init.Data.Bool
 import Init.Data.BitVec.Basic
 import Init.Data.Fin.Lemmas
 import Init.Data.Nat.Lemmas
+import Init.Data.Nat.Mod
+import Init.Data.Int.Bitwise.Lemmas
 
 namespace BitVec
 
@@ -137,16 +139,19 @@ theorem ofBool_eq_iff_eq : ∀(b b' : Bool), BitVec.ofBool b = BitVec.ofBool b'
   getLsb (x#'lt) i = x.testBit i := by
   simp [getLsb, BitVec.ofNatLt]
 
-@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (x#w).toNat = x % 2^w := by
+@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
   simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
 
+@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' x (Nat.two_pow_pos w) := rfl
+
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
 theorem getLsb_ofNat (n : Nat) (x : Nat) (i : Nat) :
-  getLsb (x#n) i = (i < n && x.testBit i) := by
+  getLsb (BitVec.ofNat n x) 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]
 
@@ -173,8 +178,7 @@ 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]
@@ -221,17 +225,29 @@ 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]
   split
-  case inl g =>
+  next g =>
     rw [Int.bmod_pos] <;> simp only [←Int.ofNat_emod, toNat_mod_cancel]
     omega
-  case inr g =>
+  next g =>
     rw [Int.bmod_neg] <;> simp only [←Int.ofNat_emod, toNat_mod_cancel]
     omega
 
@@ -266,6 +282,9 @@ theorem toInt_ofNat {n : Nat} (x : Nat) :
   have p : 0 ≤ i % (2^n : Nat) := by omega
   simp [toInt_eq_toNat_bmod, Int.toNat_of_nonneg p]
 
+@[simp] theorem ofInt_natCast (w n : Nat) :
+  BitVec.ofInt w (n : Int) = BitVec.ofNat w n := rfl
+
 /-! ### zeroExtend and truncate -/
 
 @[simp, bv_toNat] theorem toNat_zeroExtend' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
@@ -297,19 +316,19 @@ theorem zeroExtend'_eq {x : BitVec w} (h : w ≤ v) : x.zeroExtend' h = x.zeroEx
   let ⟨x, lt_n⟩ := x
   simp [truncate, zeroExtend]
 
-@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m (0#n) = 0#m := by
+@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m 0#n = 0#m := by
   apply eq_of_toNat_eq
   simp [toNat_zeroExtend]
 
 @[simp] theorem truncate_eq (x : BitVec n) : truncate n x = x := zeroExtend_eq x
 
-@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : x.toNat#m = truncate m x := by
+@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = truncate m x := by
   apply eq_of_toNat_eq
   simp
 
 /-- Moves one-sided left toNat equality to BitVec equality. -/
 theorem toNat_eq_nat (x : BitVec w) (y : Nat)
-  : (x.toNat = y) ↔ (y < 2^w ∧ (x = y#w)) := by
+  : (x.toNat = y) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
   apply Iff.intro
   · intro eq
     simp at eq
@@ -321,7 +340,7 @@ theorem toNat_eq_nat (x : BitVec w) (y : Nat)
 
 /-- Moves one-sided right toNat equality to BitVec equality. -/
 theorem nat_eq_toNat (x : BitVec w) (y : Nat)
-  : (y = x.toNat) ↔ (y < 2^w ∧ (x = y#w)) := by
+  : (y = x.toNat) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
   rw [@eq_comm _ _ x.toNat]
   apply toNat_eq_nat
 
@@ -397,7 +416,7 @@ protected theorem extractLsb_ofFin {n} (x : Fin (2^n)) (hi lo : Nat) :
 
 @[simp]
 protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
-  extractLsb hi lo x#n = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
+  extractLsb hi lo (BitVec.ofNat n x) = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
   apply eq_of_getLsb_eq
   intro ⟨i, _lt⟩
   simp [BitVec.ofNat]
@@ -448,6 +467,11 @@ protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
   ext
   simp
 
+theorem or_assoc (x y z : BitVec w) :
+    x ||| y ||| z = x ||| (y ||| z) := by
+  ext i
+  simp [Bool.or_assoc]
+
 /-! ### and -/
 
 @[simp] theorem toNat_and (x y : BitVec v) :
@@ -474,6 +498,11 @@ protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
   ext
   simp
 
+theorem and_assoc (x y z : BitVec w) :
+    x &&& y &&& z = x &&& (y &&& z) := by
+  ext i
+  simp [Bool.and_assoc]
+
 /-! ### xor -/
 
 @[simp] theorem toNat_xor (x y : BitVec v) :
@@ -494,6 +523,11 @@ protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
   ext
   simp
 
+theorem xor_assoc (x y z : BitVec w) :
+    x ^^^ y ^^^ z = x ^^^ (y ^^^ z) := by
+  ext i
+  simp [Bool.xor_assoc]
+
 /-! ### not -/
 
 theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
@@ -608,6 +642,22 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
     (shiftLeftZeroExtend x i).msb = x.msb := by
   simp [shiftLeftZeroExtend_eq, BitVec.msb]
 
+theorem shiftLeft_add {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
+
+@[deprecated shiftLeft_add (since := "2024-06-02")]
+theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x <<< n) <<< m = x <<< (n + m) := by
+  rw [shiftLeft_add]
+
 /-! ### ushiftRight -/
 
 @[simp, bv_toNat] theorem toNat_ushiftRight (x : BitVec n) (i : Nat) :
@@ -617,6 +667,123 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
     getLsb (x >>> i) j = getLsb x (i+j) := by
   unfold getLsb ; simp
 
+/-! ### sshiftRight -/
+
+theorem sshiftRight_eq {x : BitVec n} {i : Nat} :
+    x.sshiftRight i = BitVec.ofInt n (x.toInt >>> i) := by
+  apply BitVec.eq_of_toInt_eq
+  simp [BitVec.sshiftRight]
+
+/-- if the msb is false, the arithmetic shift right equals logical shift right -/
+theorem sshiftRight_eq_of_msb_false {x : BitVec w} {s : Nat} (h : x.msb = false) :
+    (x.sshiftRight s) = x >>> s := by
+  apply BitVec.eq_of_toNat_eq
+  rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
+  have hxbound : 2 * x.toNat < 2 ^ w := (BitVec.msb_eq_false_iff_two_mul_lt x).mp h
+  simp only [hxbound, ↓reduceIte, Int.natCast_shiftRight, Int.ofNat_eq_coe, ofInt_natCast,
+    toNat_ofNat, toNat_ushiftRight]
+  replace hxbound : x.toNat >>> s < 2 ^ w := by
+    rw [Nat.shiftRight_eq_div_pow]
+    exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) x.isLt
+  apply Nat.mod_eq_of_lt hxbound
+
+/--
+If the msb is `true`, the arithmetic shift right equals negating,
+then logical shifting right, then negating again.
+The double negation preserves the lower bits that have been shifted,
+and the outer negation ensures that the high bits are '1'. -/
+theorem sshiftRight_eq_of_msb_true {x : BitVec w} {s : Nat} (h : x.msb = true) :
+    (x.sshiftRight s) = ~~~((~~~x) >>> s) := by
+  apply BitVec.eq_of_toNat_eq
+  rcases w with rfl | w
+  · simp
+  · rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
+    have hxbound : (2 * x.toNat ≥ 2 ^ (w + 1)) := (BitVec.msb_eq_true_iff_two_mul_ge x).mp h
+    replace hxbound : ¬ (2 * x.toNat < 2 ^ (w + 1)) := by omega
+    simp only [hxbound, ↓reduceIte, toNat_ofInt, toNat_not, toNat_ushiftRight]
+    rw [← Int.subNatNat_eq_coe, Int.subNatNat_of_lt (by omega),
+        Nat.pred_eq_sub_one, Int.negSucc_shiftRight,
+        Int.emod_negSucc, Int.natAbs_ofNat, Nat.succ_eq_add_one,
+        Int.subNatNat_of_le (by omega), Int.toNat_ofNat, Nat.mod_eq_of_lt,
+        Nat.sub_right_comm]
+    omega
+    · rw [Nat.shiftRight_eq_div_pow]
+      apply Nat.lt_of_le_of_lt (Nat.div_le_self _ _) (by omega)
+
+theorem getLsb_sshiftRight (x : BitVec w) (s i : Nat) :
+    getLsb (x.sshiftRight s) i =
+      (!decide (w ≤ i) && if s + i < w then x.getLsb (s + i) else x.msb) := by
+  rcases hmsb : x.msb with rfl | rfl
+  · simp only [sshiftRight_eq_of_msb_false hmsb, getLsb_ushiftRight, Bool.if_false_right]
+    by_cases hi : i ≥ w
+    · simp only [hi, decide_True, Bool.not_true, Bool.false_and]
+      apply getLsb_ge
+      omega
+    · simp only [hi, decide_False, Bool.not_false, Bool.true_and, Bool.iff_and_self,
+        decide_eq_true_eq]
+      intros hlsb
+      apply BitVec.lt_of_getLsb _ _ hlsb
+  · by_cases hi : i ≥ w
+    · simp [hi]
+    · simp only [sshiftRight_eq_of_msb_true hmsb, getLsb_not, getLsb_ushiftRight, Bool.not_and,
+        Bool.not_not, hi, decide_False, Bool.not_false, Bool.if_true_right, Bool.true_and,
+        Bool.and_iff_right_iff_imp, Bool.or_eq_true, Bool.not_eq_true', decide_eq_false_iff_not,
+        Nat.not_lt, decide_eq_true_eq]
+      omega
+
+/-! ### signExtend -/
+
+/-- Equation theorem for `Int.sub` when both arguments are `Int.ofNat` -/
+private theorem Int.ofNat_sub_ofNat_of_lt {n m : Nat} (hlt : n < m) :
+    (n : Int) - (m : Int) = -(↑(m - 1 - n) + 1) := by
+  omega
+
+/-- Equation theorem for `Int.mod` -/
+private theorem Int.negSucc_emod (m : Nat) (n : Int) :
+    -(m + 1) % n = Int.subNatNat (Int.natAbs n) ((m % Int.natAbs n) + 1) := rfl
+
+/-- The sign extension is the same as zero extending when `msb = false`. -/
+theorem signExtend_eq_not_zeroExtend_not_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
+    x.signExtend v = x.zeroExtend v := by
+  ext i
+  by_cases hv : i < v
+  · simp only [signExtend, getLsb, getLsb_zeroExtend, hv, decide_True, Bool.true_and, toNat_ofInt,
+      BitVec.toInt_eq_msb_cond, hmsb, ↓reduceIte]
+    rw [Int.ofNat_mod_ofNat, Int.toNat_ofNat, Nat.testBit_mod_two_pow]
+    simp [BitVec.testBit_toNat]
+  · simp only [getLsb_zeroExtend, hv, decide_False, Bool.false_and]
+    apply getLsb_ge
+    omega
+
+/--
+The sign extension is a bitwise not, followed by a zero extend, followed by another bitwise not
+when `msb = true`. The double bitwise not ensures that the high bits are '1',
+and the lower bits are preserved. -/
+theorem signExtend_eq_not_zeroExtend_not_of_msb_true {x : BitVec w} {v : Nat} (hmsb : x.msb = true) :
+    x.signExtend v = ~~~((~~~x).zeroExtend v) := by
+  apply BitVec.eq_of_toNat_eq
+  simp only [signExtend, BitVec.toInt_eq_msb_cond, toNat_ofInt, toNat_not,
+    toNat_truncate, hmsb, ↓reduceIte]
+  norm_cast
+  rw [Int.ofNat_sub_ofNat_of_lt, Int.negSucc_emod]
+  simp only [Int.natAbs_ofNat, Nat.succ_eq_add_one]
+  rw [Int.subNatNat_of_le]
+  · rw [Int.toNat_ofNat, Nat.add_comm, Nat.sub_add_eq]
+  · apply Nat.le_trans
+    · apply Nat.succ_le_of_lt
+      apply Nat.mod_lt
+      apply Nat.two_pow_pos
+    · apply Nat.le_refl
+  · omega
+
+@[simp] theorem getLsb_signExtend (x  : BitVec w) {v i : Nat} :
+    (x.signExtend v).getLsb i = (decide (i < v) && if i < w then x.getLsb i else x.msb) := by
+  rcases hmsb : x.msb with rfl | rfl
+  · rw [signExtend_eq_not_zeroExtend_not_of_msb_false hmsb]
+    by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
+  · rw [signExtend_eq_not_zeroExtend_not_of_msb_true hmsb]
+    by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
+
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -693,6 +860,16 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
   simp only [getLsb_append, cond_eq_if]
   split <;> simp [*]
 
+theorem shiftRight_add {w : Nat} (x : BitVec w) (n m : Nat) :
+    x >>> (n + m) = (x >>> n) >>> m:= by
+  ext i
+  simp [Nat.add_assoc n m i]
+
+@[deprecated shiftRight_add (since := "2024-06-02")]
+theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x >>> n) >>> m = x >>> (n + m) := by
+  rw [shiftRight_add]
+
 /-! ### rev -/
 
 theorem getLsb_rev (x : BitVec w) (i : Fin w) :
@@ -831,10 +1008,10 @@ Definition of bitvector addition as a nat.
 @[simp] theorem add_ofFin (x : BitVec n) (y : Fin (2^n)) :
   x + .ofFin y = .ofFin (x.toFin + y) := rfl
 
-theorem ofNat_add {n} (x y : Nat) : (x + y)#n = x#n + y#n := by
+theorem ofNat_add {n} (x y : Nat) : BitVec.ofNat n (x + y) = BitVec.ofNat n x + BitVec.ofNat n y := by
   apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
-theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n :=
+theorem ofNat_add_ofNat {n} (x y : Nat) : BitVec.ofNat n x + BitVec.ofNat n y = BitVec.ofNat n (x + y) :=
   (ofNat_add x y).symm
 
 protected theorem add_assoc (x y z : BitVec n) : x + y + z = x + (y + z) := by
@@ -880,10 +1057,10 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n (x.toNat + (2^n - y.toNa
   rfl
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
-theorem ofNat_sub_ofNat {n} (x y : Nat) : x#n - y#n = .ofNat n (x + (2^n - y % 2^n)) := by
+theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y = .ofNat n (x + (2^n - y % 2^n)) := by
   apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
-@[simp] protected theorem sub_zero (x : BitVec n) : x - (0#n) = x := by apply eq_of_toNat_eq ; simp
+@[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp
 
 @[simp] protected theorem sub_self (x : BitVec n) : x - x = 0#n := by
   apply eq_of_toNat_eq
@@ -895,11 +1072,15 @@ theorem ofNat_sub_ofNat {n} (x y : Nat) : x#n - y#n = .ofNat n (x + (2^n - y % 2
 @[simp, bv_toNat] theorem toNat_neg (x : BitVec n) : (- x).toNat = (2^n - x.toNat) % 2^n := by
   simp [Neg.neg, BitVec.neg]
 
+@[simp] theorem toFin_neg (x : BitVec n) :
+    (-x).toFin = Fin.ofNat' (2^n - x.toNat) (Nat.two_pow_pos _) :=
+  rfl
+
 theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
   apply eq_of_toNat_eq
   simp
 
-@[simp] theorem neg_zero (n:Nat) : -0#n = 0#n := by apply eq_of_toNat_eq ; simp
+@[simp] theorem neg_zero (n:Nat) : -BitVec.ofNat n 0 = BitVec.ofNat n 0 := by apply eq_of_toNat_eq ; simp
 
 theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
   apply eq_of_toNat_eq
@@ -976,7 +1157,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
   x ≤ BitVec.ofFin y ↔ x.toFin ≤ y := Iff.rfl
 @[simp] theorem ofFin_le (x : Fin (2^n)) (y : BitVec n) :
   BitVec.ofFin x ≤ y ↔ x ≤ y.toFin := Iff.rfl
-@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (x#n) ≤ (y#n) ↔ x % 2^n ≤ y % 2^n := by
+@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (BitVec.ofNat n x) ≤ (BitVec.ofNat n y) ↔ x % 2^n ≤ y % 2^n := by
   simp [le_def]
 
 @[bv_toNat] theorem lt_def (x y : BitVec n) :
@@ -986,7 +1167,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
   x < BitVec.ofFin y ↔ x.toFin < y := Iff.rfl
 @[simp] theorem ofFin_lt (x : Fin (2^n)) (y : BitVec n) :
   BitVec.ofFin x < y ↔ x < y.toFin := Iff.rfl
-@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : (x#n) < (y#n) ↔ x % 2^n < y % 2^n := by
+@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : BitVec.ofNat n x < BitVec.ofNat n y ↔ x % 2^n < y % 2^n := by
   simp [lt_def]
 
 protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x < y := by
@@ -999,7 +1180,7 @@ protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x
 /-! ### intMax -/
 
 /-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
-def intMax (w : Nat) : BitVec w  := (2^w - 1)#w
+def intMax (w : Nat) : BitVec w := BitVec.ofNat w (2^w - 1)
 
 theorem getLsb_intMax_eq (w : Nat) : (intMax w).getLsb i = decide (i < w) := by
   simp [intMax, getLsb]
@@ -1026,4 +1207,171 @@ 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]
+
+
+/--
+Accessing bits in `x.rotateLeft r` the range `[0, r)` is equal to
+accessing bits `x` in the range `[w - r, w)`.
+
+Proof by example:
+Let x := <6 5 4 3 2 1 0> : BitVec 7.
+x.rotateLeft 2 = (<6 5 | 4 3 2 1 0>).rotateLeft 2 = <3 2 1 0 | 6 5>
+
+(x.rotateLeft 2).getLsb ⟨i, i < 2⟩
+= <3 2 1 0 | 6 5>.getLsb ⟨i, i < 2⟩
+= <6 5>[i]
+= <6 5 | 4 3 2 1 0>[i + len(<4 3 2 1 0>)]
+= <6 5 | 4 3 2 1 0>[i + 7 - 2]
+-/
+theorem getLsb_rotateLeftAux_of_le {x : BitVec w} {r : Nat} {i : Nat} (hi : i < r) :
+    (x.rotateLeftAux r).getLsb i = x.getLsb (w - r + i) := by
+  rw [rotateLeftAux, getLsb_or, getLsb_ushiftRight]
+  suffices (x <<< r).getLsb i = false by
+    simp; omega
+  simp only [getLsb_shiftLeft, Bool.and_eq_false_imp, Bool.and_eq_true, decide_eq_true_eq,
+    Bool.not_eq_true', decide_eq_false_iff_not, Nat.not_lt, and_imp]
+  omega
+
+/--
+Accessing bits in `x.rotateLeft r` the range `[r, w)` is equal to
+accessing bits `x` in the range `[0, w - r)`.
+
+Proof by example:
+Let x := <6 5 4 3 2 1 0> : BitVec 7.
+x.rotateLeft 2 = (<6 5 | 4 3 2 1 0>).rotateLeft 2 = <3 2 1 0 | 6 5>
+
+(x.rotateLeft 2).getLsb ⟨i, i ≥ 2⟩
+= <3 2 1 0 | 6 5>.getLsb ⟨i, i ≥ 2⟩
+= <3 2 1 0>[i - 2]
+= <6 5 | 3 2 1 0>[i - 2]
+
+Intuitively, grab the full width (7), then move the marker `|` by `r` to the right `(-2)`
+Then, access the bit at `i` from the right `(+i)`.
+ -/
+theorem getLsb_rotateLeftAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ r) :
+    (x.rotateLeftAux r).getLsb i = (decide (i < w) && x.getLsb (i - r)) := by
+  rw [rotateLeftAux, getLsb_or]
+  suffices (x >>> (w - r)).getLsb i = false by
+    have hiltr : decide (i < r) = false := by
+      simp [hi]
+    simp [getLsb_shiftLeft, Bool.or_false, hi, hiltr, this]
+  simp only [getLsb_ushiftRight]
+  apply getLsb_ge
+  omega
+
+/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
+theorem getLsb_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
+    (x.rotateLeft r).getLsb i =
+      cond (i < r)
+      (x.getLsb (w - r + i))
+      (decide (i < w) && x.getLsb (i - r)) := by
+  · rw [rotateLeft_eq_rotateLeftAux_of_lt hr]
+    by_cases h : i < r
+    · simp [h, getLsb_rotateLeftAux_of_le h]
+    · simp [h, getLsb_rotateLeftAux_of_geq <| Nat.ge_of_not_lt h]
+
+@[simp]
+theorem getLsb_rotateLeft {x : BitVec w} {r i : Nat}  :
+    (x.rotateLeft r).getLsb i =
+      cond (i < r % w)
+      (x.getLsb (w - (r % w) + i))
+      (decide (i < w) && x.getLsb (i - (r % w))) := by
+  rcases w with ⟨rfl, w⟩
+  · simp
+  · rw [← rotateLeft_mod_eq_rotateLeft, getLsb_rotateLeft_of_le (Nat.mod_lt _ (by omega))]
+
+/-! ## Rotate Right -/
+
+/--
+Accessing bits in `x.rotateRight r` the range `[0, w-r)` is equal to
+accessing bits `x` in the range `[r, w)`.
+
+Proof by example:
+Let x := <6 5 4 3 2 1 0> : BitVec 7.
+x.rotateRight 2 = (<6 5 4 3 2 | 1 0>).rotateRight 2 = <1 0 | 6 5 4 3 2>
+
+(x.rotateLeft 2).getLsb ⟨i, i ≤ 7 - 2⟩
+= <1 0 | 6 5 4 3 2>.getLsb ⟨i, i ≤ 7 - 2⟩
+= <6 5 4 3 2>.getLsb i
+= <6 5 4 3 2 | 1 0>[i + 2]
+-/
+theorem getLsb_rotateRightAux_of_le {x : BitVec w} {r : Nat} {i : Nat} (hi : i < w - r) :
+    (x.rotateRightAux r).getLsb i = x.getLsb (r + i) := by
+  rw [rotateRightAux, getLsb_or, getLsb_ushiftRight]
+  suffices (x <<< (w - r)).getLsb i = false by
+    simp only [this, Bool.or_false]
+  simp only [getLsb_shiftLeft, Bool.and_eq_false_imp, Bool.and_eq_true, decide_eq_true_eq,
+    Bool.not_eq_true', decide_eq_false_iff_not, Nat.not_lt, and_imp]
+  omega
+
+/--
+Accessing bits in `x.rotateRight r` the range `[w-r, w)` is equal to
+accessing bits `x` in the range `[0, r)`.
+
+Proof by example:
+Let x := <6 5 4 3 2 1 0> : BitVec 7.
+x.rotateRight 2 = (<6 5 4 3 2 | 1 0>).rotateRight 2 = <1 0 | 6 5 4 3 2>
+
+(x.rotateLeft 2).getLsb ⟨i, i ≥ 7 - 2⟩
+= <1 0 | 6 5 4 3 2>.getLsb ⟨i, i ≤ 7 - 2⟩
+= <1 0>.getLsb (i - len(<6 5 4 3 2>)
+= <6 5 4 3 2 | 1 0> (i - len<6 4 4 3 2>)
+ -/
+theorem getLsb_rotateRightAux_of_geq {x : BitVec w} {r : Nat} {i : Nat} (hi : i ≥ w - r) :
+    (x.rotateRightAux r).getLsb i = (decide (i < w) && x.getLsb (i - (w - r))) := by
+  rw [rotateRightAux, getLsb_or]
+  suffices (x >>> r).getLsb i = false by
+    simp only [this, getLsb_shiftLeft, Bool.false_or]
+    by_cases hiw : i < w
+    <;> simp [hiw, hi]
+  simp only [getLsb_ushiftRight]
+  apply getLsb_ge
+  omega
+
+/-- `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]
+
+/-- When `r < w`, we give a formula for `(x.rotateRight r).getLsb i`. -/
+theorem getLsb_rotateRight_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
+    (x.rotateRight r).getLsb i =
+      cond (i < w - r)
+      (x.getLsb (r + i))
+      (decide (i < w) && x.getLsb (i - (w - r))) := by
+  · rw [rotateRight_eq_rotateRightAux_of_lt hr]
+    by_cases h : i < w - r
+    · simp [h, getLsb_rotateRightAux_of_le h]
+    · simp [h, getLsb_rotateRightAux_of_geq <| Nat.le_of_not_lt h]
+
+@[simp]
+theorem getLsb_rotateRight {x : BitVec w} {r i : Nat} :
+    (x.rotateRight r).getLsb i =
+      cond (i < w - (r % w))
+      (x.getLsb ((r % w) + i))
+      (decide (i < w) && x.getLsb (i - (w - (r % w)))) := by
+  rcases w with ⟨rfl, w⟩
+  · simp
+  · rw [← rotateRight_mod_eq_rotateRight, getLsb_rotateRight_of_le (Nat.mod_lt _ (by omega))]
+
 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/Basic.lean

@@ -40,7 +40,7 @@ theorem isValidUInt32 (n : Nat) (h : isValidCharNat n) : n < UInt32.size := by
     apply Nat.lt_trans h₂
     decide
 
-theorem isValidChar_of_isValidChar_Nat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
+theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
   match h with
   | Or.inl h        => Or.inl h
   | Or.inr ⟨h₁, h₂⟩ => Or.inr ⟨h₁, h₂⟩
@@ -52,6 +52,13 @@ theorem isValidChar_zero : isValidChar 0 :=
 @[inline] def toNat (c : Char) : Nat :=
   c.val.toNat
 
+/-- Convert a character into a `UInt8`, by truncating (reducing modulo 256) if necessary. -/
+@[inline] def toUInt8 (c : Char) : UInt8 :=
+  c.val.toUInt8
+
+/-- The numbers from 0 to 256 are all valid UTF-8 characters, so we can embed one in the other. -/
+def ofUInt8 (n : UInt8) : Char := ⟨n.toUInt32, .inl (Nat.lt_trans n.1.2 (by decide))⟩
+
 instance : Inhabited Char where
   default := 'A'
 

src/Init/Data/Char/Lemmas.lean

@@ -0,0 +1,34 @@
+/-
+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)
+
+theorem utf8Size_pos (c : Char) : 0 < c.utf8Size := by
+  simp only [utf8Size]
+  repeat (split; decide)
+  decide
+
+@[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by
+  rw [Char.ofNat, dif_pos]
+  rfl
+
+end Char

src/Init/Data/Fin/Fold.lean

@@ -6,6 +6,8 @@ Authors: François G. Dorais
 prelude
 import Init.Data.Nat.Linear
 
+namespace Fin
+
 /-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
 @[inline] def foldl (n) (f : α → Fin n → α) (init : α) : α := loop init 0 where
   /-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)`  -/
@@ -20,3 +22,5 @@ import Init.Data.Nat.Linear
   loop : {i // i ≤ n} → α → α
   | ⟨0, _⟩, x => x
   | ⟨i+1, h⟩, x => loop ⟨i, Nat.le_of_lt h⟩ (f ⟨i, h⟩ x)
+
+end Fin

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
@@ -62,7 +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
@@ -93,6 +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)
@@ -208,7 +221,6 @@ theorem val_add_one {n : Nat} (i : Fin (n + 1)) :
   | .inl h => cases Fin.eq_of_val_eq h; simp
   | .inr h => simpa [Fin.ne_of_lt h] using val_add_one_of_lt h
 
-unseal Nat.modCore in
 @[simp] theorem val_two {n : Nat} : (2 : Fin (n + 3)).val = 2 := rfl
 
 theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) < i + 1 := by
@@ -243,7 +255,6 @@ theorem succ_ne_zero {n} : ∀ k : Fin n, Fin.succ k ≠ 0
 
 @[simp] theorem succ_zero_eq_one : Fin.succ (0 : Fin (n + 1)) = 1 := rfl
 
-unseal Nat.modCore in
 /-- Version of `succ_one_eq_two` to be used by `dsimp` -/
 @[simp] theorem succ_one_eq_two : Fin.succ (1 : Fin (n + 2)) = 2 := rfl
 
@@ -395,7 +406,6 @@ theorem castSucc_lt_last (a : Fin n) : castSucc a < last n := a.is_lt
 
 @[simp] theorem castSucc_zero : castSucc (0 : Fin (n + 1)) = 0 := rfl
 
-unseal Nat.modCore in
 @[simp] theorem castSucc_one {n : Nat} : castSucc (1 : Fin (n + 2)) = 1 := rfl
 
 /-- `castSucc i` is positive when `i` is positive -/
@@ -825,27 +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/Format/Syntax.lean

@@ -20,24 +20,27 @@ private def formatInfo (showInfo : Bool) (info : SourceInfo) (f : Format) : Form
   | true, SourceInfo.synthetic pos endPos false     => f!"{pos}:{f}:{endPos}"
   | _,    _                                         => f
 
-partial def formatStxAux (maxDepth : Option Nat) (showInfo : Bool) : Nat → Syntax → Format
-  | _,     atom info val     => formatInfo showInfo info $ format (repr val)
-  | _,     ident info _ val _   => formatInfo showInfo info $ format "`" ++ format val
-  | _,     missing           => "<missing>"
-  | depth, node _ kind args  =>
+partial def formatStxAux (maxDepth : Option Nat) (showInfo : Bool) (depth : Nat) : Syntax → Format
+  | atom info val        => formatInfo showInfo info <| format (repr val)
+  | ident info _ val _   => formatInfo showInfo info <| format "`" ++ format val
+  | missing              => "<missing>"
+  | node info kind args  =>
     let depth := depth + 1;
     if kind == nullKind then
-      sbracket $
+      sbracket <|
         if args.size > 0 && depth > maxDepth.getD depth then
           ".."
         else
           joinSep (args.toList.map (formatStxAux maxDepth showInfo depth)) line
     else
-      let shorterName := kind.replacePrefix `Lean.Parser Name.anonymous;
-      let header      := format shorterName;
+      let shorterName := kind.replacePrefix `Lean.Parser Name.anonymous
+      let header      := formatInfo showInfo info <| format shorterName
       let body : List Format :=
-        if args.size > 0 && depth > maxDepth.getD depth then [".."] else args.toList.map (formatStxAux maxDepth showInfo depth);
-      paren $ joinSep (header :: body) line
+        if args.size > 0 && depth > maxDepth.getD depth then
+          [".."]
+        else
+          args.toList.map (formatStxAux maxDepth showInfo depth)
+      paren <| joinSep (header :: body) line
 
 /-- Pretty print the given syntax `stx` as a `Format`.
 Nodes deeper than `maxDepth` are omitted.

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

@@ -0,0 +1,37 @@
+/-
+Copyright (c) 2023 Siddharth Bhat. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Siddharth Bhat, Jeremy Avigad
+-/
+prelude
+import Init.Data.Nat.Bitwise.Lemmas
+import Init.Data.Int.Bitwise
+
+namespace Int
+
+theorem shiftRight_eq (n : Int) (s : Nat) : n >>> s = Int.shiftRight n s := rfl
+@[simp]
+theorem natCast_shiftRight (n s : Nat) : (n : Int) >>> s = n >>> s := rfl
+
+@[simp]
+theorem negSucc_shiftRight (m n : Nat) :
+    -[m+1] >>> n = -[m >>>n +1] := rfl
+
+theorem shiftRight_add (i : Int) (m n : Nat) :
+    i >>> (m + n) = i >>> m >>> n := by
+  simp only [shiftRight_eq, Int.shiftRight]
+  cases i <;> simp [Nat.shiftRight_add]
+
+theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
+    m >>> n = m / ((2 ^ n) : Nat) := by
+  simp only [shiftRight_eq, Int.shiftRight, Nat.shiftRight_eq_div_pow]
+  split
+  · simp
+  · rw [negSucc_ediv _ (by norm_cast; exact Nat.pow_pos (Nat.zero_lt_two))]
+    rfl
+
+@[simp]
+theorem zero_shiftRight (n : Nat) : (0 : Int) >>> n = 0 := by
+  simp [Int.shiftRight_eq_div_pow]
+
+end Int

src/Init/Data/Int/DivModLemmas.lean

@@ -420,6 +420,9 @@ theorem negSucc_emod (m : Nat) {b : Int} (bpos : 0 < b) : -[m+1] % b = b - 1 - m
   match b, eq_succ_of_zero_lt bpos with
   | _, ⟨n, rfl⟩ => rfl
 
+theorem emod_negSucc (m : Nat) (n : Int) :
+  (Int.negSucc m) % n = Int.subNatNat (Int.natAbs n) (Nat.succ (m % Int.natAbs n)) := rfl
+
 theorem ofNat_mod_ofNat (m n : Nat) : (m % n : Int) = ↑(m % n) := rfl
 
 theorem emod_nonneg : ∀ (a : Int) {b : Int}, b ≠ 0 → 0 ≤ a % b
@@ -1072,9 +1075,9 @@ theorem emod_mul_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n * y) n = Int.bmo
 theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n := by
   rw [bmod_def x n]
   split
-  case inl p =>
+  next p =>
     simp only [emod_add_bmod_congr]
-  case inr p =>
+  next p =>
     rw [Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg]
     simp
 
@@ -1085,9 +1088,9 @@ theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n
 theorem bmod_mul_bmod : Int.bmod (Int.bmod x n * y) n = Int.bmod (x * y) n := by
   rw [bmod_def x n]
   split
-  case inl p =>
+  next p =>
     simp
-  case inr p =>
+  next p =>
     rw [Int.sub_mul, Int.sub_eq_add_neg, ← Int.mul_neg]
     simp
 

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/Basic.lean

@@ -69,6 +69,8 @@ theorem length_add_eq_lengthTRAux (as : List α) (n : Nat) : as.length + n = as.
 @[simp] theorem length_nil : length ([] : List α) = 0 :=
   rfl
 
+@[simp 1100] theorem length_singleton (a : α) : length [a] = 1 := rfl
+
 /-- Auxiliary for `List.reverse`. `List.reverseAux l r = l.reverse ++ r`, but it is defined directly. -/
 def reverseAux : List α → List α → List α
   | [],   r => r

src/Init/Data/List/Lemmas.lean

@@ -755,8 +755,6 @@ theorem exists_cons_of_ne_nil : ∀ {l : List α}, l ≠ [] → ∃ b L, l = b :
 
 /-! ### length -/
 
-@[simp 1100] theorem length_singleton (a : α) : length [a] = 1 := rfl
-
 theorem length_pos_of_mem {a : α} : ∀ {l : List α}, a ∈ l → 0 < length l
   | _::_, _ => Nat.zero_lt_succ _
 
@@ -777,7 +775,6 @@ theorem exists_cons_of_length_succ :
     ∀ {l : List α}, l.length = n + 1 → ∃ h t, l = h :: t
   | _::_, _ => ⟨_, _, rfl⟩
 
-@[simp]
 theorem length_pos {l : List α} : 0 < length l ↔ l ≠ [] :=
   Nat.pos_iff_ne_zero.trans (not_congr length_eq_zero)
 

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

@@ -60,6 +60,13 @@ noncomputable def div2Induction {motive : Nat → Sort u}
   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]
@@ -74,7 +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]
@@ -191,8 +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 =>
@@ -236,7 +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
@@ -260,7 +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]
 

src/Init/Data/Nat/Div.lean

@@ -82,28 +82,34 @@ decreasing_by apply div_rec_lemma; assumption
 
 @[extern "lean_nat_mod"]
 protected def mod : @& Nat → @& Nat → Nat
-  /- These four cases are not needed mathematically, they are just special cases of the
-  general case. However, it makes `0 % n = 0` etc. true definitionally rather than just
-  propositionally.
+  /-
+  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. This was true in lean3 and it simplified things for mathlib if it remains true. -/
+  definition.
+   -/
   | 0, _ => 0
-  | 1, 0 => 0
-  | 1, 1 => 0
-  | 1, (_+2) => 1
-  | x@(_ + 2), 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
-  match x, y with
-  | 0, y =>
+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)
-  | 1, 0 => rw [Nat.modCore]; rfl
-  | 1, 1 => rw [Nat.modCore, Nat.modCore]; rfl
-  | 1, (_+2) => rw [Nat.modCore]; rfl
-  | (_ + 2), _ => 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/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 =>
@@ -789,10 +790,18 @@ theorem shiftRight_succ_inside : ∀m n, m >>> (n+1) = (m/2) >>> n
   | 0 => by simp [shiftRight]
   | n + 1 => by simp [shiftRight, zero_shiftRight n, shiftRight_succ]
 
+theorem shiftLeft_add (m n : Nat) : ∀ k, m <<< (n + k) = (m <<< n) <<< k
+  | 0 => rfl
+  | k + 1 => by simp [← Nat.add_assoc, shiftLeft_add _ _ k, shiftLeft_succ]
+
+@[deprecated shiftLeft_add (since := "2024-06-02")]
 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/Option/Lemmas.lean

@@ -101,7 +101,7 @@ theorem ball_ne_none {p : Option α → Prop} : (∀ x (_ : x ≠ none), p x)
 @[simp] theorem bind_none (x : Option α) : x.bind (fun _ => none (α := β)) = none := by
   cases x <;> rfl
 
-@[simp] theorem bind_eq_some : x.bind f = some b ↔ ∃ a, x = some a ∧ f a = some b := by
+theorem bind_eq_some : x.bind f = some b ↔ ∃ a, x = some a ∧ f a = some b := by
   cases x <;> simp
 
 @[simp] theorem bind_eq_none {o : Option α} {f : α → Option β} :
@@ -119,7 +119,7 @@ theorem bind_assoc (x : Option α) (f : α → Option β) (g : β → Option γ)
     (x.bind f).bind g = x.bind fun y => (f y).bind g := by cases x <;> rfl
 
 theorem join_eq_some : x.join = some a ↔ x = some (some a) := by
-  simp
+  simp [bind_eq_some]
 
 theorem join_ne_none : x.join ≠ none ↔ ∃ z, x = some (some z) := by
   simp only [ne_none_iff_exists', join_eq_some, iff_self]

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

@@ -1,12 +1,13 @@
 /-
 Copyright (c) 2016 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Author: Leonardo de Moura
+Author: Leonardo de Moura, Mario Carneiro
 -/
 prelude
 import Init.Data.List.Basic
 import Init.Data.Char.Basic
 import Init.Data.Option.Basic
+
 universe u
 
 def List.asString (s : List Char) : String :=
@@ -24,6 +25,14 @@ 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.
 
@@ -178,8 +187,9 @@ Returns the next position in a string after position `p`. If `p` is not a valid
 the result is unspecified.
 
 Examples:
-* `"abc".next ⟨1⟩ = String.Pos.mk 2`
-* `"L∃∀N".next ⟨1⟩ = String.Pos.mk 4`, since `'∃'` is a multi-byte UTF-8 character
+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`
@@ -196,22 +206,77 @@ 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
 
 /--
-Similar to `get` but runtime does not perform bounds check.
+Returns the character at position `p` of a string.
+If `p` is not a valid position, returns `(default : Char)`.
+
+Requires evidence, `h`, that `p` is within bounds
+instead of performing a runtime bounds check as in `get`.
+
+Examples:
+* `"abc".get' 0 (by decide) = 'a'`
+* `let lean := "L∃∀N"; lean.get' (0 |> lean.next |> lean.next) (by decide) = '∀'`
+
+A typical pattern combines `get'` with a dependent if-else expression
+to avoid the overhead of an additional bounds check. For example:
+```
+def getInBounds? (s : String) (p : String.Pos) : Option Char :=
+  if h : s.atEnd p then none else some (s.get' p h)
+```
+
+Even with evidence of `¬ s.atEnd p`,
+`p` may be invalid if a byte index points into the middle of a multi-byte UTF-8 character.
+For example, `"L∃∀N".get' ⟨2⟩ (by decide) = (default : Char)`.
 -/
 @[extern "lean_string_utf8_get_fast"]
 def get' (s : @& String) (p : @& Pos) (h : ¬ s.atEnd p) : Char :=
@@ -219,7 +284,21 @@ def get' (s : @& String) (p : @& Pos) (h : ¬ s.atEnd p) : Char :=
   | ⟨s⟩ => utf8GetAux s 0 p
 
 /--
-Similar to `next` but runtime does not perform bounds check.
+Returns the next position in a string after position `p`.
+If `p` is not a valid position, the result is unspecified.
+
+Requires evidence, `h`, that `p` is within bounds
+instead of performing a runtime bounds check as in `next`.
+
+Examples:
+* `let abc := "abc"; abc.get (abc.next' 0 (by decide)) = 'b'`
+
+A typical pattern combines `next'` with a dependent if-else expression
+to avoid the overhead of an additional bounds check. For example:
+```
+def next? (s: String) (p : String.Pos) : Option Char :=
+  if h : s.atEnd p then none else s.get (s.next' p h)
+```
 -/
 @[extern "lean_string_utf8_next_fast"]
 def next' (s : @& String) (p : @& Pos) (h : ¬ s.atEnd p) : Pos :=
@@ -260,6 +339,15 @@ def posOfAux (s : String) (c : Char) (stopPos : Pos) (pos : Pos) : Pos :=
   else pos
 termination_by stopPos.1 - pos.1
 
+/--
+Returns the position of the first occurrence of a character, `c`, in `s`.
+If `s` does not contain `c`, returns `s.endPos`.
+
+Examples:
+* `"abba".posOf 'a' = ⟨0⟩`
+* `"abba".posOf 'z' = ⟨4⟩`
+* `"L∃∀N".posOf '∀' = ⟨4⟩`
+-/
 @[inline] def posOf (s : String) (c : Char) : Pos :=
   posOfAux s c s.endPos 0
 
@@ -272,6 +360,15 @@ def revPosOfAux (s : String) (c : Char) (pos : Pos) : Option Pos :=
     else revPosOfAux s c pos
 termination_by pos.1
 
+/--
+Returns the position of the last occurrence of a character, `c`, in `s`.
+If `s` does not contain `c`, returns `none`.
+
+Examples:
+* `"abba".posOf 'a' = some ⟨3⟩`
+* `"abba".posOf 'z' = none`
+* `"L∃∀N".posOf '∀' = some ⟨4⟩`
+-/
 def revPosOf (s : String) (c : Char) : Option Pos :=
   revPosOfAux s c s.endPos
 
@@ -410,6 +507,7 @@ instance : Inhabited String := ⟨""⟩
 
 instance : Append String := ⟨String.append⟩
 
+@[deprecated push (since := "2024-04-06")]
 def str : String → Char → String := push
 
 def pushn (s : String) (c : Char) (n : Nat) : String :=
@@ -683,13 +781,15 @@ 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 :=
@@ -904,6 +1004,10 @@ 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
@@ -967,5 +1071,145 @@ def decapitalize (s : String) :=
 
 end String
 
-protected def Char.toString (c : Char) : String :=
+namespace Char
+
+protected def toString (c : Char) : String :=
   String.singleton c
+
+@[simp] theorem length_toString (c : Char) : c.toString.length = 1 := rfl
+
+end Char
+
+namespace String
+
+theorem ext {s₁ s₂ : String} (h : s₁.data = s₂.data) : s₁ = s₂ :=
+  show ⟨s₁.data⟩ = (⟨s₂.data⟩ : String) from h ▸ rfl
+
+theorem ext_iff {s₁ s₂ : String} : s₁ = s₂ ↔ s₁.data = s₂.data := ⟨fun h => h ▸ rfl, ext⟩
+
+@[simp] theorem default_eq : default = "" := rfl
+
+@[simp] theorem length_mk (s : List Char) : (String.mk s).length = s.length := rfl
+
+@[simp] theorem length_empty : "".length = 0 := rfl
+
+@[simp] theorem length_singleton (c : Char) : (String.singleton c).length = 1 := rfl
+
+@[simp] theorem length_push (c : Char) : (String.push s c).length = s.length + 1 := by
+  rw [push, length_mk, List.length_append, List.length_singleton, Nat.succ.injEq]
+  rfl
+
+@[simp] theorem length_pushn (c : Char) (n : Nat) : (pushn s c n).length = s.length + n := by
+  unfold pushn; induction n <;> simp [Nat.repeat, Nat.add_assoc, *]
+
+@[simp] theorem length_append (s t : String) : (s ++ t).length = s.length + t.length := by
+  simp only [length, append, List.length_append]
+
+@[simp] theorem data_push (s : String) (c : Char) : (s.push c).data = s.data ++ [c] := rfl
+
+@[simp] theorem data_append (s t : String) : (s ++ t).data = s.data ++ t.data := rfl
+
+attribute [simp] toList -- prefer `String.data` over `String.toList` in lemmas
+
+theorem lt_iff (s t : String) : s < t ↔ s.data < t.data := .rfl
+
+namespace Pos
+
+@[simp] theorem byteIdx_zero : (0 : Pos).byteIdx = 0 := rfl
+
+theorem byteIdx_mk (n : Nat) : byteIdx ⟨n⟩ = n := rfl
+
+@[simp] theorem mk_zero : ⟨0⟩ = (0 : Pos) := rfl
+
+@[simp] theorem mk_byteIdx (p : Pos) : ⟨p.byteIdx⟩ = p := rfl
+
+theorem ext {i₁ i₂ : Pos} (h : i₁.byteIdx = i₂.byteIdx) : i₁ = i₂ :=
+  show ⟨i₁.byteIdx⟩ = (⟨i₂.byteIdx⟩ : Pos) from h ▸ rfl
+
+theorem ext_iff {i₁ i₂ : Pos} : i₁ = i₂ ↔ i₁.byteIdx = i₂.byteIdx := ⟨fun h => h ▸ rfl, ext⟩
+
+@[simp] theorem add_byteIdx (p₁ p₂ : Pos) : (p₁ + p₂).byteIdx = p₁.byteIdx + p₂.byteIdx := rfl
+
+theorem add_eq (p₁ p₂ : Pos) : p₁ + p₂ = ⟨p₁.byteIdx + p₂.byteIdx⟩ := rfl
+
+@[simp] theorem sub_byteIdx (p₁ p₂ : Pos) : (p₁ - p₂).byteIdx = p₁.byteIdx - p₂.byteIdx := rfl
+
+theorem sub_eq (p₁ p₂ : Pos) : p₁ - p₂ = ⟨p₁.byteIdx - p₂.byteIdx⟩ := rfl
+
+@[simp] theorem addChar_byteIdx (p : Pos) (c : Char) : (p + c).byteIdx = p.byteIdx + csize c := rfl
+
+theorem addChar_eq (p : Pos) (c : Char) : p + c = ⟨p.byteIdx + csize c⟩ := rfl
+
+theorem zero_addChar_byteIdx (c : Char) : ((0 : Pos) + c).byteIdx = csize c := by
+  simp only [addChar_byteIdx, byteIdx_zero, Nat.zero_add]
+
+theorem zero_addChar_eq (c : Char) : (0 : Pos) + c = ⟨csize c⟩ := by rw [← zero_addChar_byteIdx]
+
+theorem addChar_right_comm (p : Pos) (c₁ c₂ : Char) : p + c₁ + c₂ = p + c₂ + c₁ := by
+  apply ext
+  repeat rw [pos_add_char]
+  apply Nat.add_right_comm
+
+theorem ne_of_lt {i₁ i₂ : Pos} (h : i₁ < i₂) : i₁ ≠ i₂ := mt ext_iff.1 (Nat.ne_of_lt h)
+
+theorem ne_of_gt {i₁ i₂ : Pos} (h : i₁ < i₂) : i₂ ≠ i₁ := (ne_of_lt h).symm
+
+@[simp] theorem addString_byteIdx (p : Pos) (s : String) :
+    (p + s).byteIdx = p.byteIdx + s.utf8ByteSize := rfl
+
+theorem addString_eq (p : Pos) (s : String) : p + s = ⟨p.byteIdx + s.utf8ByteSize⟩ := rfl
+
+theorem zero_addString_byteIdx (s : String) : ((0 : Pos) + s).byteIdx = s.utf8ByteSize := by
+  simp only [addString_byteIdx, byteIdx_zero, Nat.zero_add]
+
+theorem zero_addString_eq (s : String) : (0 : Pos) + s = ⟨s.utf8ByteSize⟩ := by
+  rw [← zero_addString_byteIdx]
+
+theorem le_iff {i₁ i₂ : Pos} : i₁ ≤ i₂ ↔ i₁.byteIdx ≤ i₂.byteIdx := .rfl
+
+@[simp] theorem mk_le_mk {i₁ i₂ : Nat} : Pos.mk i₁ ≤ Pos.mk i₂ ↔ i₁ ≤ i₂ := .rfl
+
+theorem lt_iff {i₁ i₂ : Pos} : i₁ < i₂ ↔ i₁.byteIdx < i₂.byteIdx := .rfl
+
+@[simp] theorem mk_lt_mk {i₁ i₂ : Nat} : Pos.mk i₁ < Pos.mk i₂ ↔ i₁ < i₂ := .rfl
+
+end Pos
+
+@[simp] theorem get!_eq_get (s : String) (p : Pos) : get! s p = get s p := rfl
+
+theorem lt_next' (s : String) (p : Pos) : p < next s p := lt_next ..
+
+@[simp] theorem prev_zero (s : String) : prev s 0 = 0 := rfl
+
+@[simp] theorem get'_eq (s : String) (p : Pos) (h) : get' s p h = get s p := rfl
+
+@[simp] theorem next'_eq (s : String) (p : Pos) (h) : next' s p h = next s p := rfl
+
+-- `toSubstring'` is just a synonym for `toSubstring` without the `@[inline]` attribute
+-- so for proving can be unfolded.
+attribute [simp] toSubstring'
+
+theorem singleton_eq (c : Char) : singleton c = ⟨[c]⟩ := rfl
+
+@[simp] theorem data_singleton (c : Char) : (singleton c).data = [c] := rfl
+
+@[simp] theorem append_empty (s : String) : s ++ "" = s := ext (List.append_nil _)
+
+@[simp] theorem empty_append (s : String) : "" ++ s = s := rfl
+
+theorem append_assoc (s₁ s₂ s₃ : String) : (s₁ ++ s₂) ++ s₃ = s₁ ++ (s₂ ++ s₃) :=
+  ext (List.append_assoc ..)
+
+end String
+
+open String
+
+namespace Substring
+
+@[simp] theorem prev_zero (s : Substring) : s.prev 0 = 0 := by simp [prev, Pos.add_eq, Pos.byteIdx_zero]
+
+@[simp] theorem prevn_zero (s : Substring) : ∀ n, s.prevn n 0 = 0
+  | 0 => rfl
+  | n+1 => by simp [prevn, prevn_zero s n]
+
+end Substring

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/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/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

@@ -253,17 +253,21 @@ instance : ToString TaskState := ⟨TaskState.toString⟩
 @[extern "lean_io_wait"] opaque wait (t : Task α) : BaseIO α :=
   return t.get
 
-local macro "nonempty_list" : tactic =>
-  `(tactic| exact Nat.zero_lt_succ _)
-
 /-- Wait until any of the tasks in the given list has finished, then return its result. -/
 @[extern "lean_io_wait_any"] opaque waitAny (tasks : @& List (Task α))
-    (h : tasks.length > 0 := by nonempty_list) : BaseIO α :=
+    (h : tasks.length > 0 := by exact Nat.zero_lt_succ _) : BaseIO α :=
   return tasks[0].get
 
 /-- 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).
 
@@ -786,6 +790,32 @@ 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

@@ -699,7 +699,37 @@ The `have` tactic is for adding hypotheses to the local context of the main goal
   For example, given `h : p ∧ q ∧ r`, `have ⟨h₁, h₂, h₃⟩ := h` produces the
   hypotheses `h₁ : p`, `h₂ : q`, and `h₃ : r`.
 -/
-macro "have " d:haveDecl : tactic => `(tactic| refine_lift have $d:haveDecl; ?_)
+syntax "have " haveDecl : tactic
+macro_rules
+  -- special case: when given a nested `by` block, move it outside of the `refine` to enable
+  -- incrementality
+  | `(tactic| have%$haveTk $id:haveId $bs* : $type := by%$byTk $tacs*) => do
+    /-
+    We want to create the syntax
+    ```
+    focus
+      refine no_implicit_lambda% (have $id:haveId $bs* : $type := ?body; ?_)
+      case body => $tacs*
+    ```
+    However, we need to be very careful with the syntax infos involved:
+    * We want most infos up to `tacs` to be independent of changes inside it so that incrementality
+      is not prematurely disabled; we use the `have` and then the `by` token as the reference for
+      this. Note that if we did nothing, the reference would be the entire `have` input and so any
+      change to `tacs` would change every token synthesized below.
+    * For the single node of the `case` body, we *should not* change the ref as this makes sure the
+      entire tactic block is included in any "unsaved goals" message (which is emitted after
+      execution of all nested tactics so it is indeed safe for `evalCase` to ignore it for
+      incrementality).
+    * Even after setting the ref, we still need a `with_annotate_state` to show the correct tactic
+      state on `by` as the synthetic info derived from the ref is ignored for this purpose.
+    -/
+    let tac ← Lean.withRef byTk `(tactic| with_annotate_state $byTk ($tacs*))
+    let tac ← `(tacticSeq| $tac:tactic)
+    let tac ← Lean.withRef byTk `(tactic| case body => $(.mk tac):tacticSeq)
+    Lean.withRef haveTk `(tactic| focus
+      refine no_implicit_lambda% (have $id:haveId $bs* : $type := ?body; ?_)
+      $tac)
+  | `(tactic| have $d:haveDecl) => `(tactic| refine_lift have $d:haveDecl; ?_)
 
 /--
 Given a main goal `ctx ⊢ t`, `suffices h : t' from e` replaces the main goal with `ctx ⊢ t'`,
@@ -833,14 +863,41 @@ syntax (name := cases) "cases " casesTarget,+ (" using " term)? (inductionAlts)?
 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 `Batteries` library provides `repeat'` which repeats separately in each subgoal.
+`repeat tac` repeatedly applies `tac` so long as it succeeds.
+The tactic `tac` may be a tactic sequence, and if `tac` fails at any point in its execution,
+`repeat` will revert any partial changes that `tac` made to the tactic state.
+
+The tactic `tac` should eventually fail, otherwise `repeat tac` will run indefinitely.
+
+See also:
+* `try tac` is like `repeat tac` but will apply `tac` at most once.
+* `repeat' tac` recursively applies `tac` to each goal.
+* `first | tac1 | tac2` implements the backtracking used by `repeat`
 -/
 syntax "repeat " tacticSeq : tactic
 macro_rules
   | `(tactic| repeat $seq) => `(tactic| first | ($seq); repeat $seq | skip)
 
+/--
+`repeat' tac` recursively applies `tac` on all of the goals so long as it succeeds.
+That is to say, if `tac` produces multiple subgoals, then `repeat' tac` is applied to each of them.
+
+See also:
+* `repeat tac` simply repeatedly applies `tac`.
+* `repeat1' tac` is `repeat' tac` but requires that `tac` succeed for some goal at least once.
+-/
+syntax (name := repeat') "repeat' " tacticSeq : tactic
+
+/--
+`repeat1' tac` recursively applies to `tac` on all of the goals so long as it succeeds,
+but `repeat1' tac` fails if `tac` succeeds on none of the initial goals.
+
+See also:
+* `repeat tac` simply applies `tac` repeatedly.
+* `repeat' tac` is like `repeat1' tac` but it does not require that `tac` succeed at least once.
+-/
+syntax (name := repeat1') "repeat1' " tacticSeq : tactic
+
 /--
 `trivial` tries different simple tactics (e.g., `rfl`, `contradiction`, ...)
 to close the current goal.
@@ -1041,18 +1098,6 @@ This can be used to simulate the `specialize` and `apply at` tactics of Coq.
 -/
 syntax (name := replace) "replace" haveDecl : tactic
 
-/--
-`repeat' tac` runs `tac` on all of the goals to produce a new list of goals,
-then runs `tac` again on all of those goals, and repeats until `tac` fails on all remaining goals.
--/
-syntax (name := repeat') "repeat' " tacticSeq : tactic
-
-/--
-`repeat1' tac` applies `tac` to main goal at least once. If the application succeeds,
-the tactic is applied recursively to the generated subgoals until it eventually fails.
--/
-syntax (name := repeat1') "repeat1' " tacticSeq : tactic
-
 /-- `and_intros` applies `And.intro` until it does not make progress. -/
 syntax "and_intros" : tactic
 macro_rules | `(tactic| and_intros) => `(tactic| repeat' refine And.intro ?_ ?_)
@@ -1425,6 +1470,16 @@ 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/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/ConstFolding.lean

@@ -193,12 +193,13 @@ def foldCharOfNat (beforeErasure : Bool) (a : Expr) : Option Expr := do
   else
     return mkUInt32Lit 0
 
-def foldToNat (_ : Bool) (a : Expr) : Option Expr := do
+def foldToNat (size : Nat) (_ : Bool) (a : Expr) : Option Expr := do
   let n ← getNumLit a
-  return mkRawNatLit n
+  return mkRawNatLit (n % size)
+
 
 def uintFoldToNatFns : List (Name × UnFoldFn) :=
-  numScalarTypes.foldl (fun r info => (info.toNatFn, foldToNat) :: r) []
+  numScalarTypes.foldl (fun r info => (info.toNatFn, foldToNat info.size) :: r) []
 
 def unFoldFns : List (Name × UnFoldFn) :=
   [(``Nat.succ, foldNatSucc),

src/Lean/Compiler/InitAttr.lean

@@ -5,6 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Lean.AddDecl
+import Lean.MonadEnv
 import Lean.Elab.InfoTree.Main
 
 namespace Lean
@@ -139,7 +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/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
@@ -83,6 +86,13 @@ structure Context where
   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.
@@ -199,16 +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 `act` and returns its result
+together with the saved monadic state after `act` including the heartbeats used by it. If
+`reusableResult?` on the other hand is `some (a, state)`, restores full `state` including heartbeats
+used and returns `(a, state)`.
+
+The intention is for steps that support incremental reuse to initially pass `none` as
+`reusableResult?` and store the result and state in a snapshot. In a further run, if reuse is
+possible, `reusableResult?` should be set to the previous result and state, 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`
+itself after calling `act` 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))
+    (act : CoreM α) : CoreM (α × SavedState) := do
+  if let some (val, state) := reusableResult? then
+    set state.toState
+    IO.addHeartbeats state.passedHearbeats.toUInt64
+    return (val, state)
+
+  let startHeartbeats ← IO.getNumHeartbeats
+  let a ← act
+  let s ← get
+  let stopHeartbeats ← IO.getNumHeartbeats
+  return (a, { 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 })
@@ -239,10 +278,18 @@ instance [MetaEval α] : MetaEval (CoreM α) where
 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
@@ -253,7 +300,7 @@ register_builtin_option debug.moduleNameAtTimeout : Bool := {
 def throwMaxHeartbeat (moduleName : Name) (optionName : Name) (max : Nat) : CoreM Unit := do
   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\nuse `set_option {diagnostics.name} true` to get diagnostic information"
+  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
@@ -287,11 +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
@@ -299,6 +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 }
@@ -330,7 +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` -/
@@ -405,19 +461,26 @@ 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 then
+    if ex.isInterrupt || ex.isRuntime then
+
       throw ex -- We should use `tryCatchRuntimeEx` for catching runtime exceptions
     else
       h ex

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/Elab/App.lean

@@ -59,7 +59,7 @@ private def mkProjAndCheck (structName : Name) (idx : Nat) (e : Expr) : MetaM Ex
 def synthesizeAppInstMVars (instMVars : Array MVarId) (app : Expr) : TermElabM Unit :=
   for mvarId in instMVars do
     unless (← synthesizeInstMVarCore mvarId) do
-      registerSyntheticMVarWithCurrRef mvarId SyntheticMVarKind.typeClass
+      registerSyntheticMVarWithCurrRef mvarId (.typeClass none)
       registerMVarErrorImplicitArgInfo mvarId (← getRef) app
 
 /-- Return `some namedArg` if `namedArgs` contains an entry for `binderName`. -/

src/Lean/Elab/Binders.lean

@@ -782,6 +782,9 @@ def elabLetDeclCore (stx : Syntax) (expectedType? : Option Expr) (useLetExpr : B
 @[builtin_term_elab «let_tmp»] def elabLetTmpDecl : TermElab :=
   fun stx expectedType? => elabLetDeclCore stx expectedType? (useLetExpr := true) (elabBodyFirst := false) (usedLetOnly := true)
 
-builtin_initialize registerTraceClass `Elab.let
+builtin_initialize
+  registerTraceClass `Elab.let
+  registerTraceClass `Elab.let.decl
+  registerTraceClass `Elab.autoParam
 
 end Lean.Elab.Term

src/Lean/Elab/BuiltinCommand.lean

@@ -461,7 +461,9 @@ def elabRunMeta : CommandElab := fun stx =>
   modifyScope fun scope => { scope with opts := options }
 
 @[builtin_macro Lean.Parser.Command.«in»] def expandInCmd : Macro
-  | `($cmd₁ in $cmd₂) => `(section $cmd₁:command $cmd₂ end)
+  | `($cmd₁ in%$tk $cmd₂) =>
+    -- Limit ref variability for incrementality; see Note [Incremental Macros]
+    withRef tk `(section $cmd₁:command $cmd₂ end)
   | _                 => Macro.throwUnsupported
 
 @[builtin_command_elab Parser.Command.addDocString] def elabAddDeclDoc : CommandElab := fun stx => do

src/Lean/Elab/BuiltinTerm.lean

@@ -190,8 +190,18 @@ private def mkFreshTypeMVarFor (expectedType? : Option Expr) : TermElabM Expr :=
     | some val => pure val
     | none     => throwIllFormedSyntax
   let typeMVar ← mkFreshTypeMVarFor expectedType?
-  let u ← getDecLevel typeMVar
-  let mvar ← mkInstMVar (mkApp2 (Lean.mkConst ``OfNat [u]) typeMVar (mkRawNatLit val))
+  let u ← try
+    getDecLevel typeMVar
+  catch ex =>
+    match expectedType? with
+    | some expectedType =>
+      if (← isProp expectedType) then
+        throwError m!"numerals are data in Lean, but the expected type is a proposition{indentExpr expectedType} : Prop"
+      else
+        throwError m!"numerals are data in Lean, but the expected type is universe polymorphic and may be a proposition{indentExpr expectedType} : {← inferType expectedType}"
+    | none => throw ex
+  let extraMsg := m!"numerals are polymorphic in Lean, but the numeral `{val}` cannot be used in a context where the expected type is{indentExpr typeMVar}\ndue to the absence of the instance above"
+  let mvar ← mkInstMVar (mkApp2 (Lean.mkConst ``OfNat [u]) typeMVar (mkRawNatLit val)) extraMsg
   let r := mkApp3 (Lean.mkConst ``OfNat.ofNat [u]) typeMVar (mkRawNatLit val) mvar
   registerMVarErrorImplicitArgInfo mvar.mvarId! stx r
   return r

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
@@ -160,17 +183,18 @@ private def runCore (x : CoreM α) : CommandElabM α := do
   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
-  }
+    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
@@ -215,6 +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 }
@@ -267,11 +296,29 @@ 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 -/
@@ -291,6 +338,26 @@ instance : MonadRecDepth CommandElabM where
 
 builtin_initialize registerTraceClass `Elab.command
 
+open Language in
+/-- Snapshot after macro expansion of a command. -/
+structure MacroExpandedSnapshot extends Snapshot where
+  /-- The declaration name of the macro. -/
+  macroDecl : Name
+  /-- The expanded syntax tree. -/
+  newStx    : Syntax
+  /-- `State.nextMacroScope` after expansion. -/
+  newNextMacroScope : Nat
+  /-- Whether any traces were present after expansion. -/
+  hasTraces : Bool
+  /--
+  Follow-up elaboration snapshots, one per command if `newStx` is a sequence of commands.
+  -/
+  next : Array (SnapshotTask DynamicSnapshot)
+deriving TypeName
+open Language in
+instance : ToSnapshotTree MacroExpandedSnapshot where
+  toSnapshotTree s := ⟨s.toSnapshot, s.next.map (·.map (sync := true) toSnapshotTree)⟩
+
 partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
   withLogging <| withRef stx <| withIncRecDepth <| withFreshMacroScope do
     match stx with
@@ -298,7 +365,10 @@ 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
+        -- Incrementality is currently limited to the common case where the sequence is the direct
+        -- output of a macro, see below.
+        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
@@ -308,7 +378,51 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
           withInfoTreeContext (mkInfoTree := mkInfoTree decl stx) do
             let stxNew ← liftMacroM <| liftExcept stxNew?
             withMacroExpansion stx stxNew do
-              elabCommand stxNew
+              -- Support incrementality; see also Note [Incremental Macros]
+              if let some snap := (←read).snap? then
+                -- Unpack nested commands; see `MacroExpandedSnapshot.next`
+                let cmds := if stxNew.isOfKind nullKind then stxNew.getArgs else #[stxNew]
+                let nextMacroScope := (← get).nextMacroScope
+                let hasTraces := (← getTraceState).traces.size > 0
+                let oldSnap? := do
+                  let oldSnap ← snap.old?
+                  let oldSnap ← oldSnap.val.get.toTyped? MacroExpandedSnapshot
+                  guard <| oldSnap.macroDecl == decl && oldSnap.newNextMacroScope == nextMacroScope
+                  -- check absence of traces; see Note [Incremental Macros]
+                  guard <| !oldSnap.hasTraces && !hasTraces
+                  return oldSnap
+                let oldCmds? := oldSnap?.map fun old =>
+                  if old.newStx.isOfKind nullKind then old.newStx.getArgs else #[old.newStx]
+                Language.withAlwaysResolvedPromises cmds.size fun promises => do
+                  snap.new.resolve <| .ofTyped {
+                    diagnostics := .empty
+                    macroDecl := decl
+                    newStx := stxNew
+                    newNextMacroScope := nextMacroScope
+                    hasTraces
+                    next := promises.zipWith cmds fun promise arg =>
+                      { range? := arg.getRange?, task := promise.result }
+                    : MacroExpandedSnapshot
+                  }
+                  -- After the first command whose syntax tree changed, we must disable
+                  -- incremental reuse
+                  let mut reusedCmds := true
+                  let opts ← getOptions
+                  -- For each command, associate it with new promise and old snapshot, if any, and
+                  -- elaborate recursively
+                  for cmd in cmds, promise in promises, i in [0:cmds.size] do
+                    let oldCmd? := oldCmds?.bind (·[i]?)
+                    withReader ({ · with snap? := some {
+                      new := promise
+                      old? := do
+                        guard reusedCmds
+                        let old ← oldSnap?
+                        return { stx := (← oldCmd?), val := (← old.next[i]?) }
+                    } }) do
+                      elabCommand cmd
+                    reusedCmds := reusedCmds && oldCmd?.any (·.structRangeEqWithTraceReuse opts cmd)
+              else
+                elabCommand stxNew
         | _ =>
           match commandElabAttribute.getEntries s.env k with
           | []      =>
@@ -321,11 +435,19 @@ 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
@@ -462,7 +584,12 @@ 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
@@ -528,6 +655,7 @@ def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
       ref := ← getRef
       tacticCache? := none
       snap? := none
+      cancelTk? := (← read).cancelTk?
     } |>.run {
       env := ← getEnv
       maxRecDepth := ← getMaxRecDepth
@@ -537,7 +665,7 @@ 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/DeclUtil.lean

@@ -9,19 +9,25 @@ import Lean.Meta.Check
 
 namespace Lean.Meta
 
-def forallTelescopeCompatibleAux {α} (k : Array Expr → Expr → Expr → MetaM α) : Nat → Expr → Expr → Array Expr → MetaM α
+def forallTelescopeCompatibleAux (k : Array Expr → Expr → Expr → MetaM α) : Nat → Expr → Expr → Array Expr → MetaM α
   | 0, type₁, type₂, xs   => k xs type₁ type₂
   | i+1, type₁, type₂, xs => do
     let type₁ ← whnf type₁
     let type₂ ← whnf type₂
     match type₁, type₂ with
-    | Expr.forallE n₁ d₁ b₁ c₁, Expr.forallE n₂ d₂ b₂ c₂ =>
-      unless n₁ == n₂ do
-        throwError "parameter name mismatch '{n₁}', expected '{n₂}'"
-      unless (← isDefEq d₁ d₂) do
-        throwError "parameter '{n₁}' {← mkHasTypeButIsExpectedMsg d₁ d₂}"
+    | .forallE n₁ d₁ b₁ c₁, .forallE n₂ d₂ b₂ c₂ =>
+      -- Remark: we use `mkIdent` to ensure macroscopes do not leak into error messages
       unless c₁ == c₂ do
-        throwError "binder annotation mismatch at parameter '{n₁}'"
+        throwError "binder annotation mismatch at parameter '{mkIdent n₁}'"
+      /-
+      Remark: recall that users may suppress parameter names for instance implicit arguments.
+      A fresh name (with macro scopes) is generated in this case. Thus, we allow the names
+      to be different in this case. See issue #4310.
+      -/
+      unless n₁ == n₂ || (c₁.isInstImplicit && n₁.hasMacroScopes && n₂.hasMacroScopes) do
+        throwError "parameter name mismatch '{mkIdent n₁}', expected '{mkIdent n₂}'"
+      unless (← isDefEq d₁ d₂) do
+        throwError "parameter '{mkIdent n₁}' {← mkHasTypeButIsExpectedMsg d₁ d₂}"
       withLocalDecl n₁ c₁ d₁ fun x =>
         let type₁ := b₁.instantiate1 x
         let type₂ := b₂.instantiate1 x
@@ -30,7 +36,7 @@ def forallTelescopeCompatibleAux {α} (k : Array Expr → Expr → Expr → Meta
 
 /-- Given two forall-expressions `type₁` and `type₂`, ensure the first `numParams` parameters are compatible, and
     then execute `k` with the parameters and remaining types. -/
-def forallTelescopeCompatible {α m} [Monad m] [MonadControlT MetaM m] (type₁ type₂ : Expr) (numParams : Nat) (k : Array Expr → Expr → Expr → m α) : m α :=
+def forallTelescopeCompatible [Monad m] [MonadControlT MetaM m] (type₁ type₂ : Expr) (numParams : Nat) (k : Array Expr → Expr → Expr → m α) : m α :=
   controlAt MetaM fun runInBase =>
     forallTelescopeCompatibleAux (fun xs type₁ type₂ => runInBase $ k xs type₁ type₂) numParams type₁ type₂ #[]
 

src/Lean/Elab/Declaration.lean

@@ -188,16 +188,28 @@ def elabClassInductive (modifiers : Modifiers) (stx : Syntax) : CommandElabM Uni
   let v ← classInductiveSyntaxToView modifiers stx
   elabInductiveViews #[v]
 
-@[builtin_command_elab declaration]
-def elabDeclaration : CommandElab := fun stx => do
-  match (← liftMacroM <| expandDeclNamespace? stx) with
+/--
+Macro that expands a declaration with a complex name into an explicit `namespace` block.
+Implementing this step as a macro means that reuse checking is handled by `elabCommand`.
+ -/
+@[builtin_macro Lean.Parser.Command.declaration]
+def expandNamespacedDeclaration : Macro := fun stx => do
+  match (← expandDeclNamespace? stx) with
   | some (ns, newStx) => do
-    let ns := mkIdentFrom stx ns
-    let newStx ← `(namespace $ns $(⟨newStx⟩) end $ns)
-    withMacroExpansion stx newStx <| elabCommand newStx
-  | none => do
-    let decl     := stx[1]
-    let declKind := decl.getKind
+    -- Limit ref variability for incrementality; see Note [Incremental Macros]
+    let declTk := stx[1][0]
+    let ns := mkIdentFrom declTk ns
+    withRef declTk `(namespace $ns $(⟨newStx⟩) end $ns)
+  | none => Macro.throwUnsupported
+
+@[builtin_command_elab declaration, builtin_incremental]
+def elabDeclaration : CommandElab := fun stx => do
+  let decl     := stx[1]
+  let declKind := decl.getKind
+  if isDefLike decl then
+    -- only case implementing incrementality currently
+    elabMutualDef #[stx]
+  else withoutCommandIncrementality true do
     if declKind == ``Lean.Parser.Command.«axiom» then
       let modifiers ← elabModifiers stx[0]
       elabAxiom modifiers decl
@@ -210,8 +222,6 @@ def elabDeclaration : CommandElab := fun stx => do
     else if declKind == ``Lean.Parser.Command.«structure» then
       let modifiers ← elabModifiers stx[0]
       elabStructure modifiers decl
-    else if isDefLike decl then
-      elabMutualDef #[stx]
     else
       throwError "unexpected declaration"
 
@@ -304,6 +314,10 @@ def expandMutualElement : Macro := fun stx => do
   let mut elemsNew := #[]
   let mut modified := false
   for elem in stx[1].getArgs do
+    -- Don't trigger the `expandNamespacedDecl` macro, the namespace is handled by the mutual def
+    -- elaborator directly instead
+    if elem.isOfKind ``Parser.Command.declaration then
+      continue
     match (← expandMacro? elem) with
     | some elemNew => elemsNew := elemsNew.push elemNew; modified := true
     | none         => elemsNew := elemsNew.push elem
@@ -322,14 +336,16 @@ 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/Do.lean

@@ -688,27 +688,15 @@ def getDoLetVars (doLet : Syntax) : TermElabM (Array Var) :=
   -- leading_parser "let " >> optional "mut " >> letDecl
   getLetDeclVars doLet[2]
 
-def getHaveIdLhsVar (optIdent : Syntax) : Var :=
-  if optIdent.getKind == hygieneInfoKind then
-    HygieneInfo.mkIdent optIdent[0] `this
-  else
-    optIdent
-
-def getDoHaveVars (doHave : Syntax) : TermElabM (Array Var) := do
-  -- doHave := leading_parser "have " >> Term.haveDecl
-  -- haveDecl := leading_parser haveIdDecl <|> letPatDecl <|> haveEqnsDecl
-  let arg := doHave[1][0]
-  if arg.getKind == ``Parser.Term.haveIdDecl then
-    -- haveIdDecl := leading_parser atomic (haveIdLhs >> " := ") >> termParser
-    -- haveIdLhs := (binderIdent <|> hygieneInfo) >> many letIdBinder >> optType
-    return #[getHaveIdLhsVar arg[0]]
-  else if arg.getKind == ``Parser.Term.letPatDecl then
-    getLetPatDeclVars arg
-  else if arg.getKind == ``Parser.Term.haveEqnsDecl then
-    -- haveEqnsDecl := leading_parser haveIdLhs >> matchAlts
-    return #[getHaveIdLhsVar arg[0]]
-  else
-    throwError "unexpected kind of have declaration"
+def getDoHaveVars : Syntax → TermElabM (Array Var)
+  -- NOTE: `hygieneInfo` case should come first as `id` will match anything else
+  | `(doElem| have $info:hygieneInfo $_params* $[$_:typeSpec]? := $_val)
+  | `(doElem| have $info:hygieneInfo $_params* $[$_:typeSpec]? $_eqns:matchAlts) =>
+    return #[HygieneInfo.mkIdent info `this]
+  | `(doElem| have $id $_params* $[$_:typeSpec]? := $_val)
+  | `(doElem| have $id $_params* $[$_:typeSpec]? $_eqns:matchAlts) => return #[id]
+  | `(doElem| have $pat:letPatDecl) => getLetPatDeclVars pat
+  | _ => throwError "unexpected kind of have declaration"
 
 def getDoLetRecVars (doLetRec : Syntax) : TermElabM (Array Var) := do
   -- letRecDecls is an array of `(group (optional attributes >> letDecl))`

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

@@ -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
@@ -268,8 +271,10 @@ 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 =>
@@ -430,7 +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
@@ -448,12 +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
 
@@ -519,7 +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

src/Lean/Elab/Level.lean

@@ -78,7 +78,7 @@ partial def elabLevel (stx : Syntax) : LevelElabM Level := withRef stx do
       if (← read).autoBoundImplicit && isValidAutoBoundLevelName paramName (relaxedAutoImplicit.get (← read).options) then
         modify fun s => { s with levelNames := paramName :: s.levelNames }
       else
-        throwError "unknown universe level '{paramName}'"
+        throwError "unknown universe level '{mkIdent paramName}'"
     return mkLevelParam paramName
   else if kind == `Lean.Parser.Level.addLit then
     let lvl ← elabLevel (stx.getArg 0)

src/Lean/Elab/MacroArgUtil.lean

@@ -56,13 +56,11 @@ where
           return ⟨Syntax.mkAntiquotNode kind term⟩
         | some (.category cat) =>
           return ⟨Syntax.mkAntiquotNode cat term (isPseudoKind := true)⟩
-        | none =>
+        | some (.alias _) =>
           let id := id.getId.eraseMacroScopes
-          if (← Parser.isParserAlias id) then
-            let kind := (← Parser.getSyntaxKindOfParserAlias? id).getD Name.anonymous
-            return ⟨Syntax.mkAntiquotNode kind term⟩
-          else
-            throwError "unknown parser declaration/category/alias '{id}'"
+          let kind := (← Parser.getSyntaxKindOfParserAlias? id).getD Name.anonymous
+          return ⟨Syntax.mkAntiquotNode kind term⟩
+        | _ => throwError "unknown parser declaration/category/alias '{id}'"
     | stx, term => do
       -- can't match against `` `(stx| ($stxs*)) `` as `*` is interpreted as the `stx` operator
       if stx.raw.isOfKind ``Parser.Syntax.paren then

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 +123,58 @@ 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
+      let mut oldBodySnap? := none
+      let mut oldTacSnap? := 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
+          -- 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
+          -- no syntax guard to store, we already did the necessary checks
+          oldBodySnap? := guard reuseBody *> pure ⟨.missing, old.bodySnap⟩
+          oldTacSnap? := do
+              guard reuseTac
+              some ⟨(← old.tacStx?), (← old.tacSnap?)⟩
+          let newHeader : DefViewElabHeader := { view, old.view with
+            bodySnap? := none, tacSnap? := none }  -- filled below
+          reusableResult? := some (newHeader, old.state)
+        else
+          reuseBody := false
+
+      let mut (newHeader, newState) ← withRestoreOrSaveFull reusableResult? 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 +202,62 @@ 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 newHeader : DefViewElabHeader := { view, newHeader with
+              bodySnap? := none, tacSnap? := none }
             check headers newHeader
             return newHeader
+      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 := newState
+          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? := oldTacSnap?, new := tacPromise }
+          bodySnap? := some { old? := oldBodySnap?, new := bodyPromise }
+        }
       headers := headers.push newHeader
     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 +329,44 @@ 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)
+
+    let (val, state) ← withRestoreOrSaveFull reusableResult? 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
+        mkLambdaFVars xs val
+    if let some snap := header.bodySnap? then
+      snap.new.resolve <| some {
+        diagnostics :=
+          (← Language.Snapshot.Diagnostics.ofMessageLog (← Core.getAndEmptyMessageLog))
+        state
+        value := val
+      }
+    return val
 
 private def collectUsed (headers : Array DefViewElabHeader) (values : Array Expr) (toLift : List LetRecToLift)
     : StateRefT CollectFVars.State MetaM Unit := do
@@ -640,7 +748,7 @@ 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 +904,40 @@ 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 +952,49 @@ 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
+
+builtin_initialize
+  registerTraceClass `Elab.definition.mkClosure
 
 end Command
 end Lean.Elab

src/Lean/Elab/PreDefinition/WF/Eqns.lean

@@ -9,6 +9,7 @@ import Lean.Meta.Tactic.Split
 import Lean.Elab.PreDefinition.Basic
 import Lean.Elab.PreDefinition.Eqns
 import Lean.Meta.ArgsPacker.Basic
+import Init.Data.Array.Basic
 
 namespace Lean.Elab.WF
 open Meta
@@ -39,41 +40,6 @@ private def rwFixEq (mvarId : MVarId) : MetaM MVarId := mvarId.withContext do
   mvarId.assign (← mkEqTrans h mvarNew)
   return mvarNew.mvarId!
 
-/--
-  Simplify `match`-expressions when trying to prove equation theorems for a recursive declaration defined using well-founded recursion.
-  It is similar to `simpMatch?`, but is also tries to fold `WellFounded.fix` applications occurring in discriminants.
-  See comment at `tryToFoldWellFoundedFix`.
--/
-def simpMatchWF? (mvarId : MVarId) : MetaM (Option MVarId) :=
-  mvarId.withContext do
-    let target ← instantiateMVars (← mvarId.getType)
-    let discharge? ← mvarId.withContext do SplitIf.mkDischarge?
-    let (targetNew, _) ← Simp.main target (← Split.getSimpMatchContext) (methods := { pre, discharge? })
-    let mvarIdNew ← applySimpResultToTarget mvarId target targetNew
-    if mvarId != mvarIdNew then return some mvarIdNew else return none
-where
-  pre (e : Expr) : SimpM Simp.Step := do
-    let some app ← matchMatcherApp? e
-      | return Simp.Step.continue
-    -- First try to reduce matcher
-    match (← reduceRecMatcher? e) with
-    | some e' => return Simp.Step.done { expr := e' }
-    | none    => Simp.simpMatchCore app.matcherName e
-
-/--
-  Given a goal of the form `|- f.{us} a_1 ... a_n b_1 ... b_m = ...`, return `(us, #[a_1, ..., a_n])`
-  where `f` is a constant named `declName`, and `n = info.fixedPrefixSize`.
--/
-private def getFixedPrefix (declName : Name) (info : EqnInfo) (mvarId : MVarId) : MetaM (List Level × Array Expr) := mvarId.withContext do
-  let target ← mvarId.getType'
-  let some (_, lhs, _) := target.eq? | unreachable!
-  let lhsArgs := lhs.getAppArgs
-  if lhsArgs.size < info.fixedPrefixSize || !lhs.getAppFn matches .const .. then
-    throwError "failed to generate equational theorem for '{declName}', unexpected number of arguments in the equation left-hand-side\n{mvarId}"
-  let result := lhsArgs[:info.fixedPrefixSize]
-  trace[Elab.definition.wf.eqns] "fixedPrefix: {result}"
-  return (lhs.getAppFn.constLevels!, result)
-
 private partial def mkProof (declName : Name) (type : Expr) : MetaM Expr := do
   trace[Elab.definition.wf.eqns] "proving: {type}"
   withNewMCtxDepth do
@@ -85,7 +51,7 @@ private partial def mkProof (declName : Name) (type : Expr) : MetaM Expr := do
         return ()
       else if (← tryContradiction mvarId) then
         return ()
-      else if let some mvarId ← simpMatchWF? mvarId then
+      else if let some mvarId ← simpMatch? mvarId then
         go mvarId
       else if let some mvarId ← simpIf? mvarId then
         go mvarId

src/Lean/Elab/PreDefinition/WF/TerminationArgument.lean

@@ -86,21 +86,23 @@ def TerminationArgument.delab (termArg : TerminationArgument) : MetaM (TSyntax `
     let e ← mkLambdaFVars ys[termArg.arity - termArg.extraParams:] e -- undo overshooting by lambdaTelescope
     pure (← delabCore e (delab := go termArg.extraParams #[])).1
   where
-    go : Nat → TSyntaxArray [`ident, `Lean.Parser.Term.hole] → DelabM (TSyntax ``terminationBy)
+    go : Nat → TSyntaxArray `ident → DelabM (TSyntax ``terminationBy)
     | 0, vars => do
+      let stxBody ← Delaborator.delab
+      let hole : TSyntax `Lean.Parser.Term.hole ← `(hole|_)
+
+      -- any variable not mentioned syntatically (it may appear in the `Expr`, so do not just use
+      -- `e.bindingBody!.hasLooseBVar`) should be delaborated as a hole.
+      let vars  : TSyntaxArray [`ident, `Lean.Parser.Term.hole] :=
+        Array.map (fun (i : Ident) => if hasIdent i.getId stxBody then i else hole) vars
       -- drop trailing underscores
       let mut vars := vars
       while ! vars.isEmpty && vars.back.raw.isOfKind ``hole do vars := vars.pop
       if vars.isEmpty then
-        `(terminationBy|termination_by $(← Delaborator.delab))
+        `(terminationBy|termination_by $stxBody)
       else
-        `(terminationBy|termination_by $vars* => $(← Delaborator.delab))
+        `(terminationBy|termination_by $vars* => $stxBody)
     | i+1, vars => do
       let e ← getExpr
       unless e.isLambda do return ← go 0 vars -- should not happen
-
-      -- Delaborate unused parameters with `_`
-      if e.bindingBody!.hasLooseBVar 0 then
-        withBindingBodyUnusedName fun n => go i (vars.push ⟨n⟩)
-      else
-        descend e.bindingBody! 1 (go i (vars.push (← `(hole|_))))
+      withBindingBodyUnusedName fun n => go i (vars.push ⟨n⟩)

src/Lean/Elab/Quotation.lean

@@ -223,9 +223,12 @@ def getQuotKind (stx : Syntax) : TermElabM SyntaxNodeKind := do
   | ``Parser.Tactic.quot => addNamedQuotInfo stx `tactic
   | ``Parser.Tactic.quotSeq => addNamedQuotInfo stx `tactic.seq
   | .str kind "quot" => addNamedQuotInfo stx kind
-  | ``dynamicQuot => match ← elabParserName stx[1] with
+  | ``dynamicQuot =>
+    let id := stx[1]
+    match (← elabParserName id) with
     | .parser n _ => return n
     | .category c => return c
+    | .alias _    => return (← Parser.getSyntaxKindOfParserAlias? id.getId.eraseMacroScopes).get!
   | k => throwError "unexpected quotation kind {k}"
 
 def mkSyntaxQuotation (stx : Syntax) (kind : Name) : TermElabM Syntax := do
@@ -687,5 +690,6 @@ builtin_initialize
   registerTraceClass `Elab.match_syntax
   registerTraceClass `Elab.match_syntax.alt (inherited := true)
   registerTraceClass `Elab.match_syntax.result (inherited := true)
+  registerTraceClass `Elab.match_syntax.onMatch
 
 end Lean.Elab.Term.Quotation

src/Lean/Elab/StructInst.lean

@@ -957,6 +957,8 @@ private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (sour
     else
       elabStructInstAux stx expectedType? sourceView
 
-builtin_initialize registerTraceClass `Elab.struct
+builtin_initialize
+  registerTraceClass `Elab.struct
+  registerTraceClass `Elab.struct.modifyOp
 
 end Lean.Elab.Term.StructInst

src/Lean/Elab/Syntax.lean

@@ -80,7 +80,7 @@ def checkLeftRec (stx : Syntax) : ToParserDescrM Bool := do
   markAsTrailingParser (prec?.getD 0)
   return true
 
-def elabParserName? (stx : Syntax.Ident) : TermElabM (Option Parser.ParserName) := do
+def elabParserName? (stx : Syntax.Ident) : TermElabM (Option Parser.ParserResolution) := do
   match ← Parser.resolveParserName stx with
   | [n@(.category cat)] =>
     addCategoryInfo stx cat
@@ -88,10 +88,12 @@ def elabParserName? (stx : Syntax.Ident) : TermElabM (Option Parser.ParserName)
   | [n@(.parser parser _)] =>
     addTermInfo' stx (Lean.mkConst parser)
     return n
+  | [n@(.alias _)] =>
+    return n
   | _::_::_ => throwErrorAt stx "ambiguous parser {stx}"
   | [] => return none
 
-def elabParserName (stx : Syntax.Ident) : TermElabM Parser.ParserName := do
+def elabParserName (stx : Syntax.Ident) : TermElabM Parser.ParserResolution := do
   match ← elabParserName? stx with
   | some n => return n
   | none => throwErrorAt stx "unknown parser {stx}"
@@ -194,12 +196,6 @@ where
   processNullaryOrCat (stx : Syntax) := do
     let ident := stx[0]
     let id := ident.getId.eraseMacroScopes
-    -- run when parser is neither a decl nor a cat
-    let default := do
-      if (← Parser.isParserAlias id) then
-        ensureNoPrec stx
-        return (← processAlias ident #[])
-      throwError "unknown parser declaration/category/alias '{id}'"
     match (← elabParserName? ident) with
     | some (.parser c (isDescr := true)) =>
       ensureNoPrec stx
@@ -209,14 +205,18 @@ where
     | some (.parser c (isDescr := false)) =>
       if (← Parser.getParserAliasInfo id).declName == c then
         -- prefer parser alias over base declaration because it has more metadata, #2249
-        return (← default)
+        ensureNoPrec stx
+        return (← processAlias ident #[])
       ensureNoPrec stx
       -- as usual, we assume that people using `Parser` know what they are doing
       let stackSz := 1
       return (← `(ParserDescr.parser $(quote c)), stackSz)
     | some (.category _) =>
       processParserCategory stx
-    | none => default
+    | some (.alias _) =>
+      ensureNoPrec stx
+      processAlias ident #[]
+    | none => throwError "unknown parser declaration/category/alias '{id}'"
 
   processSepBy (stx : Syntax) := do
     let p ← ensureUnaryOutput <$> withNestedParser do process stx[1]
@@ -442,4 +442,7 @@ def strLitToPattern (stx: Syntax) : MacroM Syntax :=
   | some str => return mkAtomFrom stx str
   | none     => Macro.throwUnsupported
 
+builtin_initialize
+  registerTraceClass `Elab.defaultInstance
+
 end Lean.Elab.Command

src/Lean/Elab/SyntheticMVars.lean

@@ -59,10 +59,10 @@ private def resumePostponed (savedContext : SavedContext) (stx : Syntax) (mvarId
 /--
   Similar to `synthesizeInstMVarCore`, but makes sure that `instMVar` local context and instances
   are used. It also logs any error message produced. -/
-private def synthesizePendingInstMVar (instMVar : MVarId) : TermElabM Bool :=
+private def synthesizePendingInstMVar (instMVar : MVarId) (extraErrorMsg? : Option MessageData := none): TermElabM Bool :=
   instMVar.withContext do
     try
-      synthesizeInstMVarCore instMVar
+      synthesizeInstMVarCore instMVar (extraErrorMsg? := extraErrorMsg?)
     catch
       | ex@(.error ..) => logException ex; return true
       | _              => unreachable!
@@ -180,7 +180,7 @@ private def synthesizeSomeUsingDefaultPrio (prio : Nat) : TermElabM Bool := do
     | mvarId :: pendingMVars =>
       let some mvarDecl ← getSyntheticMVarDecl? mvarId | visit pendingMVars (mvarId :: pendingMVarsNew)
       match mvarDecl.kind with
-      | .typeClass =>
+      | .typeClass .. => -- TODO: use `errorMsg?` in `typeClass`.
         if (← withRef mvarDecl.stx <| synthesizeUsingDefaultPrio mvarId prio) then
           modify fun s => { s with pendingMVars := pendingMVars.reverse ++ pendingMVarsNew }
           return true
@@ -211,12 +211,13 @@ def reportStuckSyntheticMVar (mvarId : MVarId) (ignoreStuckTC := false) : TermEl
   let some mvarSyntheticDecl ← getSyntheticMVarDecl? mvarId | return ()
   withRef mvarSyntheticDecl.stx do
     match mvarSyntheticDecl.kind with
-    | .typeClass =>
+    | .typeClass extraErrorMsg? =>
+      let extraErrorMsg := extraMsgToMsg extraErrorMsg?
       unless ignoreStuckTC do
          mvarId.withContext do
           let mvarDecl ← getMVarDecl mvarId
           unless (← MonadLog.hasErrors) do
-            throwError "typeclass instance problem is stuck, it is often due to metavariables{indentExpr mvarDecl.type}"
+            throwError "typeclass instance problem is stuck, it is often due to metavariables{indentExpr mvarDecl.type}{extraErrorMsg}"
     | .coe header expectedType e f? =>
       mvarId.withContext do
         throwTypeMismatchError header expectedType (← inferType e) e f?
@@ -324,7 +325,6 @@ mutual
   If `report := false`, then `runTactic` will not capture exceptions nor will report unsolved goals. Unsolved goals become exceptions.
   -/
   partial def runTactic (mvarId : MVarId) (tacticCode : Syntax) (report := true) : TermElabM Unit := withoutAutoBoundImplicit do
-    let code := tacticCode[1]
     instantiateMVarDeclMVars mvarId
     /-
     TODO: consider using `runPendingTacticsAt` at `mvarId` local context and target type.
@@ -346,7 +346,7 @@ mutual
               -- also put an info node on the `by` keyword specifically -- the token may be `canonical` and thus shown in the info
               -- view even though it is synthetic while a node like `tacticCode` never is (#1990)
               withTacticInfoContext tacticCode[0] do
-                evalTactic code
+                withNarrowedArgTacticReuse (argIdx := 1) (evalTactic ·) tacticCode
             synthesizeSyntheticMVars (postpone := .no)
           unless remainingGoals.isEmpty do
             if report then
@@ -366,7 +366,7 @@ mutual
     let some mvarSyntheticDecl ← getSyntheticMVarDecl? mvarId | return true -- The metavariable has already been synthesized
     withRef mvarSyntheticDecl.stx do
     match mvarSyntheticDecl.kind with
-    | .typeClass => synthesizePendingInstMVar mvarId
+    | .typeClass extraErrorMsg? => synthesizePendingInstMVar mvarId extraErrorMsg?
     | .coe _header? expectedType e _f? => mvarId.withContext do
       if (← withDefault do isDefEq (← inferType e) expectedType) then
         -- Types may be defeq now due to mvar assignments, type class

src/Lean/Elab/Tactic/Basic.lean

@@ -34,10 +34,6 @@ structure Context where
   -/
   recover    : Bool := true
 
-structure SavedState where
-  term   : Term.SavedState
-  tactic : State
-
 abbrev TacticM := ReaderT Context $ StateRefT State TermElabM
 abbrev Tactic  := Syntax → TacticM Unit
 
@@ -100,6 +96,16 @@ def SavedState.restore (b : SavedState) (restoreInfo := false) : TacticM Unit :=
   b.term.restore restoreInfo
   set b.tactic
 
+@[specialize, inherit_doc Core.withRestoreOrSaveFull]
+def withRestoreOrSaveFull (reusableResult? : Option (α × SavedState)) (act : TacticM α) :
+    TacticM (α × SavedState) := do
+  if let some (_, state) := reusableResult? then
+    set state.tactic
+  let reusableResult? := reusableResult?.map (fun (val, state) => (val, state.term))
+  let (a, term) ← controlAt TermElabM fun runInBase => do
+    Term.withRestoreOrSaveFull reusableResult? <| runInBase act
+  return (a, { term, tactic := (← get) })
+
 protected def getCurrMacroScope : TacticM MacroScope := do pure (← readThe Core.Context).currMacroScope
 protected def getMainModule     : TacticM Name       := do pure (← getEnv).mainModule
 
@@ -146,7 +152,10 @@ partial def evalTactic (stx : Syntax) : TacticM Unit := do
     | .node _ k _    =>
       if k == nullKind then
         -- Macro writers create a sequence of tactics `t₁ ... tₙ` using `mkNullNode #[t₁, ..., tₙ]`
-        stx.getArgs.forM evalTactic
+        -- We could support incrementality here by allocating `n` new snapshot bundles but the
+        -- practical value is not clear
+        Term.withoutTacticIncrementality true do
+          stx.getArgs.forM evalTactic
       else withTraceNode `Elab.step (fun _ => return stx) (tag := stx.getKind.toString) do
         let evalFns := tacticElabAttribute.getEntries (← getEnv) stx.getKind
         let macros  := macroAttribute.getEntries (← getEnv) stx.getKind
@@ -192,6 +201,37 @@ where
           withReader ({ · with elaborator := m.declName }) do
             withTacticInfoContext stx do
               let stx' ← adaptMacro m.value stx
+              -- Support incrementality; see also Note [Incremental Macros]
+              if evalFns.isEmpty && ms.isEmpty then  -- Only try incrementality in one branch
+                if let some snap := (← readThe Term.Context).tacSnap? then
+                  let nextMacroScope := (← getThe Core.State).nextMacroScope
+                  let traceState ← getTraceState
+                  let old? := do
+                    let old ← snap.old?
+                    -- If the kind is equal, we can assume the old version was a macro as well
+                    guard <| old.stx.isOfKind stx.getKind
+                    let state ← old.val.get.data.finished.get.state?
+                    guard <| state.term.meta.core.nextMacroScope == nextMacroScope
+                    -- check absence of traces; see Note [Incremental Macros]
+                    guard <| state.term.meta.core.traceState.traces.size == 0
+                    guard <| traceState.traces.size == 0
+                    return old.val.get
+                  Language.withAlwaysResolvedPromise fun promise => do
+                    -- Store new unfolding in the snapshot tree
+                    snap.new.resolve <| .mk {
+                      stx := stx'
+                      diagnostics := .empty
+                      finished := .pure { state? := (← Tactic.saveState) }
+                    } #[{ range? := stx'.getRange?, task := promise.result }]
+                    -- Update `tacSnap?` to old unfolding
+                    withTheReader Term.Context ({ · with tacSnap? := some {
+                      new := promise
+                      old? := do
+                        let old ← old?
+                        return ⟨old.data.stx, (← old.next.get? 0)⟩
+                    } }) do
+                      evalTactic stx'
+                  return
               evalTactic stx'
         catch ex => handleEx s failures ex (expandEval s ms evalFns)
 
@@ -200,7 +240,11 @@ where
       | []              => throwExs failures
       | evalFn::evalFns => do
         try
-          withReader ({ · with elaborator := evalFn.declName }) <| withTacticInfoContext stx <| evalFn.value stx
+          -- prevent unsupported tactics from accidentally accessing `Term.Context.tacSnap?`
+          Term.withoutTacticIncrementality (!(← isIncrementalElab evalFn.declName)) do
+          withReader ({ · with elaborator := evalFn.declName }) do
+          withTacticInfoContext stx do
+            evalFn.value stx
         catch ex => handleEx s failures ex (eval s evalFns)
 
 def throwNoGoalsToBeSolved : TacticM α :=

src/Lean/Elab/Tactic/BuiltinTactic.lean

@@ -21,24 +21,100 @@ namespace Lean.Elab.Tactic
 open Meta
 open Parser.Tactic
 
-@[builtin_tactic withAnnotateState] def evalWithAnnotateState : Tactic
-  | `(tactic| with_annotate_state $stx $t) =>
-    withTacticInfoContext stx (evalTactic t)
-  | _ => throwUnsupportedSyntax
+@[builtin_tactic withAnnotateState, builtin_incremental] def evalWithAnnotateState : Tactic :=
+  fun stx =>
+    withTacticInfoContext stx[1] do
+    Term.withNarrowedArgTacticReuse (argIdx := 2) evalTactic stx
 
 @[builtin_tactic Lean.Parser.Tactic.«done»] def evalDone : Tactic := fun _ =>
   done
 
-@[builtin_tactic seq1] def evalSeq1 : Tactic := fun stx => do
-  let args := stx[0].getArgs
-  for i in [:args.size] do
-    if i % 2 == 0 then
-      evalTactic args[i]!
-    else
-      saveTacticInfoForToken args[i]! -- add `TacticInfo` node for `;`
+open Language in
+/--
+Evaluates a tactic script in form of a syntax node with alternating tactics and separators as
+children.
+ -/
+partial def evalSepTactics : Tactic := goEven
+where
+  -- `stx[0]` is the next tactic step, if any
+  goEven stx := do
+    if stx.getNumArgs == 0 then
+      return
+    let tac := stx[0]
+    /-
+    Each `goEven` step creates three promises under incrementality and reuses their older versions
+    where possible:
+    * `finished` is resolved when `tac` finishes execution; if `tac` is wholly unchanged from the
+      previous version, its state is reused and `tac` execution is skipped. Note that this promise
+      is never turned into a `SnapshotTask` and added to the snapshot tree as incremental reporting
+      is already covered by the next two promises.
+    * `inner` is passed to `tac` if it is marked as supporting incrementality and can be used for
+      reporting and partial reuse inside of it; if the tactic is unsupported or `finished` is wholly
+      reused, it is ignored.
+    * `next` is used as the context when invoking `goOdd` and thus eventually used for the next
+      `goEven` step. Thus, the incremental state of a tactic script is ultimately represented as a
+      chain of `next` snapshots. Its reuse is disabled if `tac` or its following separator are
+      changed in any way.
+    -/
+    let mut oldInner? := none
+    if let some snap := (← readThe Term.Context).tacSnap? then
+      if let some old := snap.old? then
+        let oldParsed := old.val.get
+        oldInner? := oldParsed.next.get? 0 |>.map (⟨oldParsed.data.stx, ·⟩)
+    -- compare `stx[0]` for `finished`/`next` reuse, focus on remainder of script
+    Term.withNarrowedTacticReuse (stx := stx) (fun stx => (stx[0], mkNullNode stx.getArgs[1:])) fun stxs => do
+      let some snap := (← readThe Term.Context).tacSnap?
+        | do evalTactic tac; goOdd stxs
+      let mut reusableResult? := none
+      let mut oldNext? := none
+      if let some old := snap.old? then
+        -- `tac` must be unchanged given the narrow above; let's reuse `finished`'s state!
+        let oldParsed := old.val.get
+        if let some state := oldParsed.data.finished.get.state? then
+          reusableResult? := some ((), state)
+          -- only allow `next` reuse in this case
+          oldNext? := oldParsed.next.get? 1 |>.map (⟨old.stx, ·⟩)
 
-@[builtin_tactic paren] def evalParen : Tactic := fun stx =>
-  evalTactic stx[1]
+      withAlwaysResolvedPromise fun next => do
+        withAlwaysResolvedPromise fun finished => do
+          withAlwaysResolvedPromise fun inner => do
+            snap.new.resolve <| .mk {
+              stx := tac
+              diagnostics := (← Language.Snapshot.Diagnostics.ofMessageLog
+                (← Core.getAndEmptyMessageLog))
+              finished := finished.result
+            } #[
+              {
+                range? := tac.getRange?
+                task := inner.result },
+              {
+                range? := stxs |>.getRange?
+                task := next.result }]
+            let (_, state) ← withRestoreOrSaveFull reusableResult? do
+              -- set up nested reuse; `evalTactic` will check for `isIncrementalElab`
+              withTheReader Term.Context ({ · with
+                  tacSnap? := some { old? := oldInner?, new := inner } }) do
+                evalTactic tac
+            finished.resolve { state? := state }
+
+        withTheReader Term.Context ({ · with tacSnap? := some {
+          new := next
+          old? := oldNext?
+        } }) do
+          goOdd stxs
+  -- `stx[0]` is the next separator, if any
+  goOdd stx := do
+    if stx.getNumArgs == 0 then
+      return
+    saveTacticInfoForToken stx[0] -- add `TacticInfo` node for `;`
+    -- disable further reuse on separator change as to not reuse wrong `TacticInfo`
+    Term.withNarrowedTacticReuse (fun stx => (stx[0], mkNullNode stx.getArgs[1:])) goEven stx
+
+@[builtin_tactic seq1] def evalSeq1 : Tactic := fun stx =>
+  evalSepTactics stx[0]
+
+@[builtin_tactic paren, builtin_incremental] def evalParen : Tactic :=
+  Term.withNarrowedArgTacticReuse 1 evalTactic
 
 def isCheckpointableTactic (arg : Syntax) : TacticM Bool := do
   -- TODO: make it parametric
@@ -104,26 +180,20 @@ def addCheckpoints (stx : Syntax) : TacticM Syntax := do
   output := output ++ currentCheckpointBlock
   return stx.setArgs output
 
-/-- Evaluate `sepByIndent tactic "; " -/
-def evalSepByIndentTactic (stx : Syntax) : TacticM Unit := do
-  let stx ← addCheckpoints stx
-  for arg in stx.getArgs, i in [:stx.getArgs.size] do
-    if i % 2 == 0 then
-      evalTactic arg
-    else
-      saveTacticInfoForToken arg
+@[builtin_tactic tacticSeq1Indented, builtin_incremental]
+def evalTacticSeq1Indented : Tactic :=
+  Term.withNarrowedArgTacticReuse (argIdx := 0) evalSepTactics
 
-@[builtin_tactic tacticSeq1Indented] def evalTacticSeq1Indented : Tactic := fun stx =>
-  evalSepByIndentTactic stx[0]
-
-@[builtin_tactic tacticSeqBracketed] def evalTacticSeqBracketed : Tactic := fun stx => do
+@[builtin_tactic tacticSeqBracketed, builtin_incremental]
+def evalTacticSeqBracketed : Tactic := fun stx => do
   let initInfo ← mkInitialTacticInfo stx[0]
   withRef stx[2] <| closeUsingOrAdmit do
     -- save state before/after entering focus on `{`
     withInfoContext (pure ()) initInfo
-    evalSepByIndentTactic stx[1]
+    Term.withNarrowedArgTacticReuse (argIdx := 1) evalSepTactics stx
 
-@[builtin_tactic cdot] def evalTacticCDot : Tactic := fun stx => do
+@[builtin_tactic Lean.cdot, builtin_incremental]
+def evalTacticCDot : Tactic := fun stx => do
   -- adjusted copy of `evalTacticSeqBracketed`; we used to use the macro
   -- ``| `(tactic| $cdot:cdotTk $tacs) => `(tactic| {%$cdot ($tacs) }%$cdot)``
   -- but the token antiquotation does not copy trailing whitespace, leading to
@@ -132,14 +202,14 @@ def evalSepByIndentTactic (stx : Syntax) : TacticM Unit := do
   withRef stx[0] <| closeUsingOrAdmit do
     -- save state before/after entering focus on `·`
     withInfoContext (pure ()) initInfo
-    evalSepByIndentTactic stx[1]
+    Term.withNarrowedArgTacticReuse (argIdx := 1) evalTactic stx
 
-@[builtin_tactic Parser.Tactic.focus] def evalFocus : Tactic := fun stx => do
+@[builtin_tactic Parser.Tactic.focus, builtin_incremental] def evalFocus : Tactic := fun stx => do
   let mkInfo ← mkInitialTacticInfo stx[0]
   focus do
     -- show focused state on `focus`
     withInfoContext (pure ()) mkInfo
-    evalTactic stx[1]
+    Term.withNarrowedArgTacticReuse (argIdx := 1) evalTactic stx
 
 private def getOptRotation (stx : Syntax) : Nat :=
   if stx.isNone then 1 else stx[0].toNat
@@ -205,8 +275,9 @@ private def getOptRotation (stx : Syntax) : Nat :=
     throwError "failed on all goals"
   setGoals mvarIdsNew.toList
 
-@[builtin_tactic tacticSeq] def evalTacticSeq : Tactic := fun stx =>
-  evalTactic stx[0]
+@[builtin_tactic tacticSeq, builtin_incremental]
+def evalTacticSeq : Tactic :=
+  Term.withNarrowedArgTacticReuse (argIdx := 0) evalTactic
 
 partial def evalChoiceAux (tactics : Array Syntax) (i : Nat) : TacticM Unit :=
   if h : i < tactics.size then
@@ -392,7 +463,7 @@ def renameInaccessibles (mvarId : MVarId) (hs : TSyntaxArray ``binderIdent) : Ta
 private def getCaseGoals (tag : TSyntax ``binderIdent) : TacticM (MVarId × List MVarId) := do
   let gs ← getUnsolvedGoals
   let g ← if let `(binderIdent| $tag:ident) := tag then
-    let tag := tag.getId
+    let tag := tag.getId.eraseMacroScopes
     let some g ← findTag? gs tag | notFound gs tag
     pure g
   else
@@ -426,16 +497,16 @@ where
     .group <| .nest 2 <|
     .ofFormat .line ++ .joinSep items sep
 
-
-@[builtin_tactic «case»] def evalCase : Tactic
-  | stx@`(tactic| case $[$tag $hs*]|* =>%$arr $tac:tacticSeq) =>
+@[builtin_tactic «case», builtin_incremental]
+def evalCase : Tactic
+  | stx@`(tactic| case $[$tag $hs*]|* =>%$arr $tac:tacticSeq1Indented) =>
     for tag in tag, hs in hs do
       let (g, gs) ← getCaseGoals tag
       let g ← renameInaccessibles g hs
       setGoals [g]
       g.setTag Name.anonymous
-      withCaseRef arr tac do
-        closeUsingOrAdmit (withTacticInfoContext stx (evalTactic tac))
+      withCaseRef arr tac <| closeUsingOrAdmit <| withTacticInfoContext stx <|
+        Term.withNarrowedArgTacticReuse (argIdx := 3) (evalTactic ·) stx
       setGoals gs
   | _ => throwUnsupportedSyntax
 
@@ -499,7 +570,7 @@ where
   match stx with
   | `(tactic| replace $decl:haveDecl) =>
     withMainContext do
-      let vars ← Elab.Term.Do.getDoHaveVars <| mkNullNode #[.missing, decl]
+      let vars ← Elab.Term.Do.getDoHaveVars (← `(doElem| have $decl:haveDecl))
       let origLCtx ← getLCtx
       evalTactic $ ← `(tactic| have $decl:haveDecl)
       let mut toClear := #[]

src/Lean/Elab/Tactic/Calc.lean

@@ -11,15 +11,15 @@ namespace Lean.Elab.Tactic
 open Meta
 
 /-- Elaborator for the `calc` tactic mode variant. -/
-@[builtin_tactic calcTactic]
+@[builtin_tactic Lean.calcTactic]
 def evalCalc : Tactic := fun stx => withMainContext do
   let steps : TSyntax ``calcSteps := ⟨stx[1]⟩
   let (val, mvarIds) ← withCollectingNewGoalsFrom (tagSuffix := `calc) do
-    let target ← getMainTarget
+    let target := (← getMainTarget).consumeMData
     let tag ← getMainTag
     runTermElab do
     let mut val ← Term.elabCalcSteps steps
-    let mut valType ← inferType val
+    let mut valType ← instantiateMVars (← inferType val)
     unless (← isDefEq valType target) do
       let rec throwFailed :=
         throwError "'calc' tactic failed, has type{indentExpr valType}\nbut it is expected to have type{indentExpr target}"
@@ -32,3 +32,5 @@ def evalCalc : Tactic := fun stx => withMainContext do
     return val
   (← getMainGoal).assign val
   replaceMainGoal mvarIds
+
+end Lean.Elab.Tactic

src/Lean/Elab/Tactic/Induction.lean

@@ -54,23 +54,25 @@ private def getAltDArrow (alt : Syntax) : Syntax :=
 def isHoleRHS (rhs : Syntax) : Bool :=
   rhs.isOfKind ``Parser.Term.syntheticHole || rhs.isOfKind ``Parser.Term.hole
 
-def evalAlt (mvarId : MVarId) (alt : Syntax) (addInfo : TermElabM Unit) (remainingGoals : Array MVarId) : TacticM (Array MVarId) :=
+def evalAlt (mvarId : MVarId) (alt : Syntax) (addInfo : TermElabM Unit) : TacticM Unit :=
   let rhs := getAltRHS alt
   withCaseRef (getAltDArrow alt) rhs do
     if isHoleRHS rhs then
       addInfo
-      let gs' ← mvarId.withContext <| withTacticInfoContext rhs do
+      mvarId.withContext <| withTacticInfoContext rhs do
         let mvarDecl ← mvarId.getDecl
         let val ← elabTermEnsuringType rhs mvarDecl.type
         mvarId.assign val
         let gs' ← getMVarsNoDelayed val
         tagUntaggedGoals mvarDecl.userName `induction gs'.toList
-        pure gs'
-      return remainingGoals ++ gs'
+        setGoals <| (← getGoals) ++ gs'.toList
     else
-      setGoals [mvarId]
-      closeUsingOrAdmit (withTacticInfoContext alt (addInfo *> evalTactic rhs))
-      return remainingGoals
+      let goals ← getGoals
+      try
+        setGoals [mvarId]
+        closeUsingOrAdmit (withTacticInfoContext alt (addInfo *> evalTactic rhs))
+      finally
+        setGoals goals
 
 /-!
   Helper method for creating an user-defined eliminator/recursor application.
@@ -199,6 +201,9 @@ private def getAltNumFields (elimInfo : ElimInfo) (altName : Name) : TermElabM N
       return altInfo.numFields
   throwError "unknown alternative name '{altName}'"
 
+private def isWildcard (altStx : Syntax) : Bool :=
+  getAltName altStx == `_
+
 private def checkAltNames (alts : Array Alt) (altsSyntax : Array Syntax) : TacticM Unit :=
   for i in [:altsSyntax.size] do
     let altStx := altsSyntax[i]!
@@ -229,151 +234,184 @@ private def saveAltVarsInfo (altMVarId : MVarId) (altStx : Syntax) (fvarIds : Ar
           Term.addLocalVarInfo altVars[i]! (mkFVar fvarId)
           i := i + 1
 
-/--
-  If `altsSyntax` is not empty we reorder `alts` using the order the alternatives have been provided
-  in `altsSyntax`. Motivations:
-
-  1- It improves the effectiveness of the `checkpoint` and `save` tactics. Consider the following example:
-  ```lean
-  example (h₁ : p ∨ q) (h₂ : p → x = 0) (h₃ : q → y = 0) : x * y = 0 := by
-    cases h₁ with
-    | inr h =>
-      sleep 5000 -- sleeps for 5 seconds
-      save
-      have : y = 0 := h₃ h
-      -- We can confortably work here
-    | inl h => stop ...
-  ```
-  If we do reorder, the `inl` alternative will be executed first. Moreover, as we type in the `inr` alternative,
-  type errors will "swallow" the `inl` alternative and affect the tactic state at `save` making it ineffective.
-
-  2- The errors are produced in the same order the appear in the code above. This is not super important when using IDEs.
--/
-def reorderAlts (alts : Array Alt) (altsSyntax : Array Syntax) : Array Alt := Id.run do
-  if altsSyntax.isEmpty then
-    return alts
-  else
-    let mut alts := alts
-    let mut result := #[]
-    for altStx in altsSyntax do
-      let altName := getAltName altStx
-      let some i := alts.findIdx? (·.1 == altName) | return result ++ alts
-      result := result.push alts[i]!
-      alts := alts.eraseIdx i
-    return result ++ alts
-
-def evalAlts (elimInfo : ElimInfo) (alts : Array Alt) (optPreTac : Syntax) (altsSyntax : Array Syntax)
+open Language in
+def evalAlts (elimInfo : ElimInfo) (alts : Array Alt) (optPreTac : Syntax) (altStxs : Array Syntax)
     (initialInfo : Info)
     (numEqs : Nat := 0) (numGeneralized : Nat := 0) (toClear : Array FVarId := #[])
     (toTag : Array (Ident × FVarId) := #[]) : TacticM Unit := do
-  let hasAlts := altsSyntax.size > 0
+  let hasAlts := altStxs.size > 0
   if hasAlts then
     -- default to initial state outside of alts
     -- HACK: because this node has the same span as the original tactic,
     -- we need to take all the info trees we have produced so far and re-nest them
     -- inside this node as well
     let treesSaved ← getResetInfoTrees
-    withInfoContext ((modifyInfoState fun s => { s with trees := treesSaved }) *> go) (pure initialInfo)
-  else go
+    withInfoContext ((modifyInfoState fun s => { s with trees := treesSaved }) *> goWithInfo) (pure initialInfo)
+  else goWithInfo
 where
-  go := do
-    checkAltNames alts altsSyntax
-    let alts := reorderAlts alts altsSyntax
-    let hasAlts := altsSyntax.size > 0
-    let mut usedWildcard := false
-    let mut subgoals := #[] -- when alternatives are not provided, we accumulate subgoals here
-    let mut altsSyntax := altsSyntax
+  -- continuation in the correct info context
+  goWithInfo := do
+    let hasAlts := altStxs.size > 0
+
+    if hasAlts then
+      if let some tacSnap := (← readThe Term.Context).tacSnap? then
+        -- incrementality: create a new promise for each alternative, resolve current snapshot to
+        -- them, eventually put each of them back in `Context.tacSnap?` in `applyAltStx`
+        withAlwaysResolvedPromise fun finished => do
+          withAlwaysResolvedPromises altStxs.size fun altPromises => do
+            tacSnap.new.resolve <| .mk {
+              -- save all relevant syntax here for comparison with next document version
+              stx := mkNullNode altStxs
+              diagnostics := .empty
+              finished := finished.result
+            } (altStxs.zipWith altPromises fun stx prom =>
+                { range? := stx.getRange?, task := prom.result })
+            goWithIncremental <| altPromises.mapIdx fun i prom => {
+              old? := do
+                let old ← tacSnap.old?
+                -- waiting is fine here: this is the old version of the snapshot resolved above
+                -- immediately at the beginning of the tactic
+                let old := old.val.get
+                -- use old version of `mkNullNode altsSyntax` as guard, will be compared with new
+                -- version and picked apart in `applyAltStx`
+                return ⟨old.data.stx, (← old.next[i]?)⟩
+              new := prom
+            }
+            finished.resolve { state? := (← saveState) }
+        return
+
+    goWithIncremental #[]
+
+  -- continuation in the correct incrementality context
+  goWithIncremental (tacSnaps : Array (SnapshotBundle TacticParsedSnapshot)) := do
+    let hasAlts := altStxs.size > 0
+    let mut alts := alts
+
+    -- initial sanity checks: named cases should be known, wildcards should be last
+    checkAltNames alts altStxs
+
+    /-
+    First process `altsSyntax` in order, removing covered alternatives from `alts`. Previously we
+    did one loop through `alts`, looking up suitable alternatives from `altsSyntax`.
+    Motivations for the change:
+
+    1- It improves the effectiveness of incremental reuse. Consider the following example:
+    ```lean
+    example (h₁ : p ∨ q) (h₂ : p → x = 0) (h₃ : q → y = 0) : x * y = 0 := by
+      cases h₁ with
+      | inr h =>
+        sleep 5000 -- sleeps for 5 seconds
+        save
+        have : y = 0 := h₃ h
+        -- We can comfortably work here
+      | inl h => stop ...
+    ```
+    If we iterated through `alts` instead of `altsSyntax`, the `inl` alternative would be executed
+    first, making partial reuse in `inr` impossible (without support for reuse with position
+    adjustments).
+
+    2- The errors are produced in the same order the appear in the code above. This is not super
+    important when using IDEs.
+    -/
+    for altStxIdx in [0:altStxs.size] do
+      let altStx := altStxs[altStxIdx]!
+      let altName := getAltName altStx
+      if let some i := alts.findIdx? (·.1 == altName) then
+        -- cover named alternative
+        applyAltStx tacSnaps altStxIdx altStx alts[i]!
+        alts := alts.eraseIdx i
+      else if !alts.isEmpty && isWildcard altStx then
+        -- cover all alternatives
+        for alt in alts do
+          applyAltStx tacSnaps altStxIdx altStx alt
+        alts := #[]
+      else
+        throwErrorAt altStx "unused alternative '{altName}'"
+
+    -- now process remaining alternatives; these might either be unreachable or we're in `induction`
+    -- without `with`. In all other cases, remaining alternatives are flagged as errors.
     for { name := altName, info, mvarId := altMVarId } in alts do
       let numFields ← getAltNumFields elimInfo altName
-      let mut isWildcard := false
-      let altStx? ←
-        match altsSyntax.findIdx? (fun alt => getAltName alt == altName) with
-        | some idx =>
-          let altStx := altsSyntax[idx]!
-          altsSyntax := altsSyntax.eraseIdx idx
-          pure (some altStx)
-        | none => match altsSyntax.findIdx? (fun alt => getAltName alt == `_) with
-          | some idx =>
-            isWildcard := true
-            pure (some altsSyntax[idx]!)
-          | none =>
-            pure none
-      match altStx? with
-      | none =>
-        let mut (_, altMVarId) ← altMVarId.introN numFields
-        match (← Cases.unifyEqs? numEqs altMVarId {}) with
-        | none   => pure () -- alternative is not reachable
-        | some (altMVarId', subst) =>
-          altMVarId ← if info.provesMotive then
-            (_, altMVarId) ← altMVarId'.introNP numGeneralized
-            pure altMVarId
-          else
-            pure altMVarId'
-          for fvarId in toClear do
-            altMVarId ← altMVarId.tryClear fvarId
-          altMVarId.withContext do
-            for (stx, fvar) in toTag do
-              Term.addLocalVarInfo stx (subst.get fvar)
-          let altMVarIds ← applyPreTac altMVarId
-          if !hasAlts then
-            -- User did not provide alternatives using `|`
-            subgoals := subgoals ++ altMVarIds.toArray
-          else if altMVarIds.isEmpty then
-            pure ()
-          else
-            logError m!"alternative '{altName}' has not been provided"
-            altMVarIds.forM fun mvarId => admitGoal mvarId
-      | some altStx =>
-        (subgoals, usedWildcard) ← withRef altStx do
-          let altVars := getAltVars altStx
-          let numFieldsToName ← if altHasExplicitModifier altStx then pure numFields else getNumExplicitFields altMVarId numFields
-          if altVars.size > numFieldsToName then
-            logError m!"too many variable names provided at alternative '{altName}', #{altVars.size} provided, but #{numFieldsToName} expected"
-          let mut (fvarIds, altMVarId) ← altMVarId.introN numFields (altVars.toList.map getNameOfIdent') (useNamesForExplicitOnly := !altHasExplicitModifier altStx)
-          -- Delay adding the infos for the pattern LHS because we want them to nest
-          -- inside tacticInfo for the current alternative (in `evalAlt`)
-          let addInfo : TermElabM Unit := do
-            if (← getInfoState).enabled then
-              if let some declName := info.declName? then
-                addConstInfo (getAltNameStx altStx) declName
-              saveAltVarsInfo altMVarId altStx fvarIds
-          let unusedAlt := do
-            addInfo
-            if isWildcard then
-              pure (#[], usedWildcard)
-            else
-              throwError "alternative '{altName}' is not needed"
-          match (← Cases.unifyEqs? numEqs altMVarId {}) with
-          | none => unusedAlt
-          | some (altMVarId', subst) =>
-            altMVarId ← if info.provesMotive then
-              (_, altMVarId) ← altMVarId'.introNP numGeneralized
-              pure altMVarId
-            else
-              pure altMVarId'
-            for fvarId in toClear do
-              altMVarId ← altMVarId.tryClear fvarId
-            altMVarId.withContext do
-              for (stx, fvar) in toTag do
-                Term.addLocalVarInfo stx (subst.get fvar)
-            let altMVarIds ← applyPreTac altMVarId
-            if altMVarIds.isEmpty then
-              unusedAlt
-            else
-              let mut subgoals := subgoals
-              for altMVarId' in altMVarIds do
-                subgoals ← evalAlt altMVarId' altStx addInfo subgoals
-              pure (subgoals, usedWildcard || isWildcard)
-    if usedWildcard then
-      altsSyntax := altsSyntax.filter fun alt => getAltName alt != `_
-    unless altsSyntax.isEmpty do
-      logErrorAt altsSyntax[0]! "unused alternative"
-    setGoals subgoals.toList
+      let mut (_, altMVarId) ← altMVarId.introN numFields
+      let some (altMVarId', subst) ← Cases.unifyEqs? numEqs altMVarId {}
+        | continue  -- alternative is not reachable
+      altMVarId ← if info.provesMotive then
+        (_, altMVarId) ← altMVarId'.introNP numGeneralized
+        pure altMVarId
+      else
+        pure altMVarId'
+      for fvarId in toClear do
+        altMVarId ← altMVarId.tryClear fvarId
+      altMVarId.withContext do
+        for (stx, fvar) in toTag do
+          Term.addLocalVarInfo stx (subst.get fvar)
+      let altMVarIds ← applyPreTac altMVarId
+      if !hasAlts then
+        -- User did not provide alternatives using `|`
+        setGoals <| (← getGoals) ++ altMVarIds
+      else if !altMVarIds.isEmpty then
+        logError m!"alternative '{altName}' has not been provided"
+        altMVarIds.forM fun mvarId => admitGoal mvarId
+
+  /-- Applies syntactic alternative to alternative goal. -/
+  applyAltStx tacSnaps altStxIdx altStx alt := withRef altStx do
+    let { name := altName, info, mvarId := altMVarId } := alt
+    -- also checks for unknown alternatives
+    let numFields ← getAltNumFields elimInfo altName
+    let altVars := getAltVars altStx
+    let numFieldsToName ← if altHasExplicitModifier altStx then pure numFields else getNumExplicitFields altMVarId numFields
+    if altVars.size > numFieldsToName then
+      logError m!"too many variable names provided at alternative '{altName}', #{altVars.size} provided, but #{numFieldsToName} expected"
+    let mut (fvarIds, altMVarId) ← altMVarId.introN numFields (altVars.toList.map getNameOfIdent') (useNamesForExplicitOnly := !altHasExplicitModifier altStx)
+    -- Delay adding the infos for the pattern LHS because we want them to nest
+    -- inside tacticInfo for the current alternative (in `evalAlt`)
+    let addInfo : TermElabM Unit := do
+      if (← getInfoState).enabled then
+        if let some declName := info.declName? then
+          addConstInfo (getAltNameStx altStx) declName
+        saveAltVarsInfo altMVarId altStx fvarIds
+    let unusedAlt := do
+      addInfo
+      if !isWildcard altStx then
+        throwError "alternative '{altName}' is not needed"
+    let some (altMVarId', subst) ← Cases.unifyEqs? numEqs altMVarId {}
+      | unusedAlt
+    altMVarId ← if info.provesMotive then
+      (_, altMVarId) ← altMVarId'.introNP numGeneralized
+      pure altMVarId
+    else
+      pure altMVarId'
+    for fvarId in toClear do
+      altMVarId ← altMVarId.tryClear fvarId
+    altMVarId.withContext do
+      for (stx, fvar) in toTag do
+        Term.addLocalVarInfo stx (subst.get fvar)
+    let altMVarIds ← applyPreTac altMVarId
+    if altMVarIds.isEmpty then
+      return (← unusedAlt)
+
+    -- select corresponding snapshot bundle for incrementality of this alternative
+    -- note that `tacSnaps[altStxIdx]?` is `none` if `tacSnap?` was `none` to begin with
+    withTheReader Term.Context ({ · with tacSnap? := tacSnaps[altStxIdx]? }) do
+    -- all previous alternatives have to be unchanged for reuse
+    Term.withNarrowedArgTacticReuse (stx := mkNullNode altStxs) (argIdx := altStxIdx) fun altStx => do
+    -- everything up to rhs has to be unchanged for reuse
+    Term.withNarrowedArgTacticReuse (stx := altStx) (argIdx := 2) fun _rhs => do
+    -- disable reuse if rhs is run multiple times
+    Term.withoutTacticIncrementality (altMVarIds.length != 1 || isWildcard altStx) do
+      for altMVarId' in altMVarIds do
+        evalAlt altMVarId' altStx addInfo
+
+  /-- Applies `induction .. with $preTac | ..`, if any, to an alternative goal. -/
   applyPreTac (mvarId : MVarId) : TacticM (List MVarId) :=
     if optPreTac.isNone then
       return [mvarId]
     else
-      evalTacticAt optPreTac[0] mvarId
+      -- disable incrementality for the pre-tactic to avoid non-monotonic progress reporting; it
+      -- would be possible to include a custom task around the pre-tac with an appropriate range in
+      -- the snapshot such that it is cached as well if it turns out that this is valuable
+      Term.withoutTacticIncrementality true do
+        evalTacticAt optPreTac[0] mvarId
 
 end ElimApp
 
@@ -420,8 +458,24 @@ Return an array containing its alternatives.
 private def getAltsOfInductionAlts (inductionAlts : Syntax) : Array Syntax :=
   inductionAlts[2].getArgs
 
-private def getAltsOfOptInductionAlts (optInductionAlts : Syntax) : Array Syntax :=
-  if optInductionAlts.isNone then #[] else getAltsOfInductionAlts optInductionAlts[0]
+/--
+Given `inductionAlts` of the form
+```
+syntax inductionAlts := "with " (tactic)? withPosition( (colGe inductionAlt)+)
+```
+runs `cont alts` where `alts` is an array containing all `inductionAlt`s while disabling incremental
+reuse if any other syntax changed.
+-/
+private def withAltsOfOptInductionAlts (optInductionAlts : Syntax)
+    (cont : Array Syntax → TacticM α) : TacticM α :=
+  Term.withNarrowedTacticReuse (stx := optInductionAlts) (fun optInductionAlts =>
+    if optInductionAlts.isNone then
+      -- if there are no alternatives, what to compare is irrelevant as there will be no reuse
+      (mkNullNode #[], mkNullNode #[])
+    else
+      -- `with` and tactic applied to all branches must be unchanged for reuse
+      (mkNullNode optInductionAlts[0].getArgs[:2], optInductionAlts[0].getArg 2))
+    (fun alts => cont alts.getArgs)
 
 private def getOptPreTacOfOptInductionAlts (optInductionAlts : Syntax) : Syntax :=
   if optInductionAlts.isNone then mkNullNode else optInductionAlts[0][1]
@@ -582,12 +636,11 @@ private def generalizeTargets (exprs : Array Expr) : TacticM (Array Expr) := do
   else
     return exprs
 
-@[builtin_tactic Lean.Parser.Tactic.induction] def evalInduction : Tactic := fun stx =>
+@[builtin_tactic Lean.Parser.Tactic.induction, builtin_incremental]
+def evalInduction : Tactic := fun stx =>
   match expandInduction? stx with
   | some stxNew => withMacroExpansion stx stxNew <| evalTactic stxNew
   | _ => focus do
-    let optInductionAlts := stx[4]
-    let alts := getAltsOfOptInductionAlts optInductionAlts
     let targets ← withMainContext <| stx[1].getSepArgs.mapM (elabTerm · none)
     let targets ← generalizeTargets targets
     let elimInfo ← withMainContext <| getElimNameInfo stx[2] targets (induction := true)
@@ -605,10 +658,15 @@ private def generalizeTargets (exprs : Array Expr) : TacticM (Array Expr) := do
           ElimApp.mkElimApp elimInfo targets tag
         trace[Elab.induction] "elimApp: {result.elimApp}"
         ElimApp.setMotiveArg mvarId result.motive targetFVarIds
-        let optPreTac := getOptPreTacOfOptInductionAlts optInductionAlts
-        mvarId.assign result.elimApp
-        ElimApp.evalAlts elimInfo result.alts optPreTac alts initInfo (numGeneralized := n) (toClear := targetFVarIds)
-        appendGoals result.others.toList
+        -- drill down into old and new syntax: allow reuse of an rhs only if everything before it is
+        -- unchanged
+        -- everything up to the alternatives must be unchanged for reuse
+        Term.withNarrowedArgTacticReuse (stx := stx) (argIdx := 4) fun optInductionAlts => do
+        withAltsOfOptInductionAlts optInductionAlts fun alts => do
+          let optPreTac := getOptPreTacOfOptInductionAlts optInductionAlts
+          mvarId.assign result.elimApp
+          ElimApp.evalAlts elimInfo result.alts optPreTac alts initInfo (numGeneralized := n) (toClear := targetFVarIds)
+          appendGoals result.others.toList
 where
   checkTargets (targets : Array Expr) : MetaM Unit := do
     let mut foundFVars : FVarIdSet := {}
@@ -650,15 +708,13 @@ def elabCasesTargets (targets : Array Syntax) : TacticM (Array Expr × Array (Id
     else
       return (args.map (·.expr), #[])
 
-@[builtin_tactic Lean.Parser.Tactic.cases] def evalCases : Tactic := fun stx =>
+@[builtin_tactic Lean.Parser.Tactic.cases, builtin_incremental]
+def evalCases : Tactic := fun stx =>
   match expandCases? stx with
   | some stxNew => withMacroExpansion stx stxNew <| evalTactic stxNew
   | _ => focus do
     -- leading_parser nonReservedSymbol "cases " >> sepBy1 (group majorPremise) ", " >> usingRec >> optInductionAlts
     let (targets, toTag) ← elabCasesTargets stx[1].getSepArgs
-    let optInductionAlts := stx[3]
-    let optPreTac := getOptPreTacOfOptInductionAlts optInductionAlts
-    let alts :=  getAltsOfOptInductionAlts optInductionAlts
     let targetRef := stx[1]
     let elimInfo ← withMainContext <| getElimNameInfo stx[2] targets (induction := false)
     let mvarId ← getMainGoal
@@ -676,8 +732,14 @@ def elabCasesTargets (targets : Array Syntax) : TacticM (Array Expr × Array (Id
       mvarId.withContext do
         ElimApp.setMotiveArg mvarId elimArgs[elimInfo.motivePos]!.mvarId! targetsNew
         mvarId.assign result.elimApp
-        ElimApp.evalAlts elimInfo result.alts optPreTac alts initInfo
-          (numEqs := targets.size) (toClear := targetsNew) (toTag := toTag)
+        -- drill down into old and new syntax: allow reuse of an rhs only if everything before it is
+        -- unchanged
+        -- everything up to the alternatives must be unchanged for reuse
+        Term.withNarrowedArgTacticReuse (stx := stx) (argIdx := 3) fun optInductionAlts => do
+        withAltsOfOptInductionAlts optInductionAlts fun alts => do
+          let optPreTac := getOptPreTacOfOptInductionAlts optInductionAlts
+          ElimApp.evalAlts elimInfo result.alts optPreTac alts initInfo
+            (numEqs := targets.size) (toClear := targetsNew) (toTag := toTag)
 
 builtin_initialize
   registerTraceClass `Elab.cases

src/Lean/Elab/Tactic/Omega/Frontend.lean

@@ -217,8 +217,10 @@ partial def asLinearComboImpl (e : Expr) : OmegaM (LinearCombo × OmegaM Expr ×
         match groundInt? b with
         | some _ => rewrite e (mkApp2 (.const ``Int.pow_succ []) b k')
         | none => mkAtomLinearCombo e
-  | (``Nat.cast, #[.const ``Int [], i, n]) =>
-      handleNatCast e i n
+  | (``Nat.cast, #[α, i, n]) =>
+      match_expr α with
+      | Int => handleNatCast e i n
+      | _ => mkAtomLinearCombo e
   | (``Prod.fst, #[α, β, p]) => match p with
     | .app (.app (.app (.app (.const ``Prod.mk [u, v]) _) _) x) y =>
       rewrite e (mkApp4 (.const ``Prod.fst_mk [u, v]) α x β y)
@@ -423,65 +425,69 @@ partial def addFact (p : MetaProblem) (h : Expr) : OmegaM (MetaProblem × Nat) :
       else
         return (p, 0)
     | .app _ _ =>
-      match t.getAppFnArgs with
-      | (``Eq, #[.const ``Int [], x, y]) =>
-        match y.int? with
-        | some 0 => pure (← p.addIntEquality h x, 1)
-        | _ => p.addFact (mkApp3 (.const ``Int.sub_eq_zero_of_eq []) x y h)
-      | (``LE.le, #[.const ``Int [], _, x, y]) =>
-        match x.int? with
-        | some 0 => pure (← p.addIntInequality h y, 1)
-        | _ => p.addFact (mkApp3 (.const ``Int.sub_nonneg_of_le []) y x h)
-      | (``LT.lt, #[.const ``Int [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.add_one_le_of_lt []) x y h)
-      | (``GT.gt, #[.const ``Int [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.lt_of_gt []) x y h)
-      | (``GE.ge, #[.const ``Int [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.le_of_ge []) x y h)
-      | (``GT.gt, #[.const ``Nat [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Nat.lt_of_gt []) x y h)
-      | (``GE.ge, #[.const ``Nat [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Nat.le_of_ge []) x y h)
-      | (``Ne, #[.const ``Nat [], x, y]) =>
-        p.addFact (mkApp3 (.const ``Nat.lt_or_gt_of_ne []) x y h)
-      | (``Not, #[P]) => match ← pushNot h P with
+      match_expr t with
+      | Eq α x y =>
+        match_expr α with
+        | Int =>
+          match y.int? with
+          | some 0 => pure (← p.addIntEquality h x, 1)
+          | _ => p.addFact (mkApp3 (.const ``Int.sub_eq_zero_of_eq []) x y h)
+        | Nat => p.addFact (mkApp3 (.const ``Int.ofNat_congr []) x y h)
+        | Fin n => p.addFact (mkApp4 (.const ``Fin.val_congr []) n x y h)
+        | _ => pure (p, 0)
+      | LE.le α _ x y =>
+        match_expr α with
+        | Int =>
+          match x.int? with
+          | some 0 => pure (← p.addIntInequality h y, 1)
+          | _ => p.addFact (mkApp3 (.const ``Int.sub_nonneg_of_le []) y x h)
+        | Nat => p.addFact (mkApp3 (.const ``Int.ofNat_le_of_le []) x y h)
+        | Fin n => p.addFact (mkApp4 (.const ``Fin.val_le_of_le []) n x y h)
+        | _ => pure (p, 0)
+      | LT.lt α _ x y =>
+        match_expr α with
+        | Int => p.addFact (mkApp3 (.const ``Int.add_one_le_of_lt []) x y h)
+        | Nat => p.addFact (mkApp3 (.const ``Int.ofNat_lt_of_lt []) x y h)
+        | Fin n => p.addFact (mkApp4 (.const ``Fin.val_add_one_le_of_lt []) n x y h)
+        | _ => pure (p, 0)
+      | GT.gt α _ x y =>
+        match_expr α with
+        | Int => p.addFact (mkApp3 (.const ``Int.lt_of_gt []) x y h)
+        | Nat => p.addFact (mkApp3 (.const ``Nat.lt_of_gt []) x y h)
+        | Fin n => p.addFact (mkApp4 (.const ``Fin.val_add_one_le_of_gt []) n x y h)
+        | _ => pure (p, 0)
+      | GE.ge α _ x y =>
+        match_expr α with
+        | Int => p.addFact (mkApp3 (.const ``Int.le_of_ge []) x y h)
+        | Nat => p.addFact (mkApp3 (.const ``Nat.le_of_ge []) x y h)
+        | Fin n => p.addFact (mkApp4 (.const ``Fin.val_le_of_ge []) n x y h)
+        | _ => pure (p, 0)
+      | Ne α x y =>
+        match_expr α with
+        | Int => p.addFact (mkApp3 (.const ``Int.lt_or_gt_of_ne []) x y h)
+        | Nat => p.addFact (mkApp3 (.const ``Nat.lt_or_gt_of_ne []) x y h)
+        | _ => pure (p, 0)
+      | Dvd.dvd α _ k x =>
+        match_expr α with
+        | Int => p.addFact (mkApp3 (.const ``Int.emod_eq_zero_of_dvd []) k x h)
+        | Nat => p.addFact (mkApp3 (.const ``Nat.mod_eq_zero_of_dvd []) k x h)
+        | _ => pure (p, 0)
+      | Not P => match ← pushNot h P with
         | none => return (p, 0)
         | some h' => p.addFact h'
-      | (``Eq, #[.const ``Nat [], x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.ofNat_congr []) x y h)
-      | (``LT.lt, #[.const ``Nat [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.ofNat_lt_of_lt []) x y h)
-      | (``LE.le, #[.const ``Nat [], _, x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.ofNat_le_of_le []) x y h)
-      | (``Ne, #[.const ``Int [], x, y]) =>
-        p.addFact (mkApp3 (.const ``Int.lt_or_gt_of_ne []) x y h)
-      | (``Prod.Lex, _) => p.addFact (← mkAppM ``Prod.of_lex #[h])
-      | (``Dvd.dvd, #[.const ``Nat [], _, k, x]) =>
-        p.addFact (mkApp3 (.const ``Nat.mod_eq_zero_of_dvd []) k x h)
-      | (``Dvd.dvd, #[.const ``Int [], _, k, x]) =>
-        p.addFact (mkApp3 (.const ``Int.emod_eq_zero_of_dvd []) k x h)
-      | (``Eq, #[.app (.const ``Fin []) n, x, y]) =>
-        p.addFact (mkApp4 (.const ``Fin.val_congr []) n x y h)
-      | (``LE.le, #[.app (.const ``Fin []) n, _, x, y]) =>
-        p.addFact (mkApp4 (.const ``Fin.val_le_of_le []) n x y h)
-      | (``LT.lt, #[.app (.const ``Fin []) n, _, x, y]) =>
-        p.addFact (mkApp4 (.const ``Fin.val_add_one_le_of_lt []) n x y h)
-      | (``GE.ge, #[.app (.const ``Fin []) n, _, x, y]) =>
-        p.addFact (mkApp4 (.const ``Fin.val_le_of_ge []) n x y h)
-      | (``GT.gt, #[.app (.const ``Fin []) n, _, x, y]) =>
-        p.addFact (mkApp4 (.const ``Fin.val_add_one_le_of_gt []) n x y h)
-      | (``And, #[t₁, t₂]) => do
+      | Prod.Lex _ _ _ _ _ _ => p.addFact (← mkAppM ``Prod.of_lex #[h])
+      | And t₁ t₂ => do
           let (p₁, n₁) ← p.addFact (mkApp3 (.const ``And.left []) t₁ t₂ h)
           let (p₂, n₂) ← p₁.addFact (mkApp3 (.const ``And.right []) t₁ t₂ h)
           return (p₂, n₁ + n₂)
-      | (``Exists, #[α, P]) =>
+      | Exists α P =>
         p.addFact (mkApp3 (.const ``Exists.choose_spec [← getLevel α]) α P h)
-      | (``Subtype, #[α, P]) =>
+      | Subtype α P =>
         p.addFact (mkApp3 (.const ``Subtype.property [← getLevel α]) α P h)
-      | (``Iff, #[P₁, P₂]) =>
+      | Iff P₁ P₂ =>
         p.addFact (mkApp4 (.const ``Decidable.and_or_not_and_not_of_iff [])
           P₁ P₂ (.app (.const ``Classical.propDecidable []) P₂) h)
-      | (``Or, #[_, _]) =>
+      | Or _ _ =>
         if (← cfg).splitDisjunctions then
           return ({ p with disjunctions := p.disjunctions.insert h }, 1)
         else
@@ -532,7 +538,9 @@ Helpful error message when omega cannot find a solution
 def formatErrorMessage (p : Problem) : OmegaM MessageData := do
   if p.possible then
     if p.isEmpty then
-      return m!"it is false"
+      return m!"No usable constraints found. You may need to unfold definitions so `omega` can see \
+      linear arithmetic facts about `Nat` and `Int`, which may also involve multiplication, \
+      division, and modular remainder by constants."
     else
       let as ← atoms
       let mask ← mentioned p.constraints

src/Lean/Elab/Tactic/Omega/OmegaM.lean

@@ -71,7 +71,7 @@ abbrev OmegaM := StateRefT Cache OmegaM'
 
 /-- Run a computation in the `OmegaM` monad, starting with no recorded atoms. -/
 def OmegaM.run (m : OmegaM α) (cfg : OmegaConfig) : MetaM α :=
-  m.run' HashMap.empty |>.run' {} { cfg } |>.run
+  m.run' HashMap.empty |>.run' {} { cfg } |>.run'
 
 /-- Retrieve the user-specified configuration options. -/
 def cfg : OmegaM OmegaConfig := do pure (← read).cfg
@@ -150,7 +150,7 @@ partial def groundInt? (e : Expr) : Option Int :=
     | _, _ => none
   | _ => e.int?
 where op (f : Int → Int → Int) (x y : Expr) : Option Int :=
-  match groundNat? x, groundNat? y with
+  match groundInt? x, groundInt? y with
     | some x', some y' => some (f x' y')
     | _, _ => none
 
@@ -199,7 +199,7 @@ def analyzeAtom (e : Expr) : OmegaM (HashSet Expr) := do
       | some _ =>
         let b_pos := mkApp4 (.const ``LT.lt [0]) (.const ``Int []) (.const ``Int.instLTInt [])
           (toExpr (0 : Int)) b
-        let pow_pos := mkApp3 (.const ``Int.pos_pow_of_pos []) b exp (← mkDecideProof b_pos)
+        let pow_pos := mkApp3 (.const ``Lean.Omega.Int.pos_pow_of_pos []) b exp (← mkDecideProof b_pos)
         pure <| HashSet.empty.insert
           (mkApp3 (.const ``Int.emod_nonneg []) x k
               (mkApp3 (.const ``Int.ne_of_gt []) k (toExpr (0 : Int)) pow_pos)) |>.insert

src/Lean/Elab/Tactic/Simp.lean

@@ -153,6 +153,8 @@ inductive ResolveSimpIdResult where
   Elaborate extra simp theorems provided to `simp`. `stx` is of the form `"[" simpTheorem,* "]"`
   If `eraseLocal == true`, then we consider local declarations when resolving names for erased theorems (`- id`),
   this option only makes sense for `simp_all` or `*` is used.
+  When `recover := true`, try to recover from errors as much as possible so that users keep seeing
+  the current goal.
 -/
 def elabSimpArgs (stx : Syntax) (ctx : Simp.Context) (simprocs : Simp.SimprocsArray) (eraseLocal : Bool) (kind : SimpKind) : TacticM ElabSimpArgsResult := do
   if stx.isNone then
@@ -171,58 +173,62 @@ def elabSimpArgs (stx : Syntax) (ctx : Simp.Context) (simprocs : Simp.SimprocsAr
       let mut simprocs  := simprocs
       let mut starArg   := false
       for arg in stx[1].getSepArgs do
-        if arg.getKind == ``Lean.Parser.Tactic.simpErase then
-          let fvar ← if eraseLocal || starArg then Term.isLocalIdent? arg[1] else pure none
-          if let some fvar := fvar then
-            -- We use `eraseCore` because the simp theorem for the hypothesis was not added yet
-            thms := thms.eraseCore (.fvar fvar.fvarId!)
+        try -- like withLogging, but compatible with do-notation
+          if arg.getKind == ``Lean.Parser.Tactic.simpErase then
+            let fvar? ← if eraseLocal || starArg then Term.isLocalIdent? arg[1] else pure none
+            if let some fvar := fvar? then
+              -- We use `eraseCore` because the simp theorem for the hypothesis was not added yet
+              thms := thms.eraseCore (.fvar fvar.fvarId!)
+            else
+              let id := arg[1]
+              if let .ok declName ← observing (realizeGlobalConstNoOverloadWithInfo id) then
+                if (← Simp.isSimproc declName) then
+                  simprocs := simprocs.erase declName
+                else if ctx.config.autoUnfold then
+                  thms := thms.eraseCore (.decl declName)
+                else
+                  thms ← withRef id <| thms.erase (.decl declName)
+              else
+                -- If `id` could not be resolved, we should check whether it is a builtin simproc.
+                -- before returning error.
+                let name := id.getId.eraseMacroScopes
+                if (← Simp.isBuiltinSimproc name) then
+                  simprocs := simprocs.erase name
+                else
+                  withRef id <| throwUnknownConstant name
+          else if arg.getKind == ``Lean.Parser.Tactic.simpLemma then
+            let post :=
+              if arg[0].isNone then
+                true
+              else
+                arg[0][0].getKind == ``Parser.Tactic.simpPost
+            let inv  := !arg[1].isNone
+            let term := arg[2]
+            match (← resolveSimpIdTheorem? term) with
+            | .expr e  =>
+              let name ← mkFreshId
+              thms ← addDeclToUnfoldOrTheorem thms (.stx name arg) e post inv kind
+            | .simproc declName =>
+              simprocs ← simprocs.add declName post
+            | .ext (some ext₁) (some ext₂) _ =>
+              thmsArray := thmsArray.push (← ext₁.getTheorems)
+              simprocs  := simprocs.push (← ext₂.getSimprocs)
+            | .ext (some ext₁) none _ =>
+              thmsArray := thmsArray.push (← ext₁.getTheorems)
+            | .ext none (some ext₂) _ =>
+              simprocs  := simprocs.push (← ext₂.getSimprocs)
+            | .none    =>
+              let name ← mkFreshId
+              thms ← addSimpTheorem thms (.stx name arg) term post inv
+          else if arg.getKind == ``Lean.Parser.Tactic.simpStar then
+            starArg := true
           else
-            let id := arg[1]
-            let declNames? ← try pure (some (← realizeGlobalConst id)) catch _ => pure none
-            if let some declNames := declNames? then
-              let declName ← ensureNonAmbiguous id declNames
-              if (← Simp.isSimproc declName) then
-                simprocs := simprocs.erase declName
-              else if ctx.config.autoUnfold then
-                thms := thms.eraseCore (.decl declName)
-              else
-                thms ← thms.erase (.decl declName)
-            else
-              -- If `id` could not be resolved, we should check whether it is a builtin simproc.
-              -- before returning error.
-              let name := id.getId.eraseMacroScopes
-              if (← Simp.isBuiltinSimproc name) then
-                simprocs := simprocs.erase name
-              else
-                throwUnknownConstant name
-        else if arg.getKind == ``Lean.Parser.Tactic.simpLemma then
-          let post :=
-            if arg[0].isNone then
-              true
-            else
-              arg[0][0].getKind == ``Parser.Tactic.simpPost
-          let inv  := !arg[1].isNone
-          let term := arg[2]
-          match (← resolveSimpIdTheorem? term) with
-          | .expr e  =>
-            let name ← mkFreshId
-            thms ← addDeclToUnfoldOrTheorem thms (.stx name arg) e post inv kind
-          | .simproc declName =>
-            simprocs ← simprocs.add declName post
-          | .ext (some ext₁) (some ext₂) _ =>
-            thmsArray := thmsArray.push (← ext₁.getTheorems)
-            simprocs  := simprocs.push (← ext₂.getSimprocs)
-          | .ext (some ext₁) none _ =>
-            thmsArray := thmsArray.push (← ext₁.getTheorems)
-          | .ext none (some ext₂) _ =>
-            simprocs  := simprocs.push (← ext₂.getSimprocs)
-          | .none    =>
-            let name ← mkFreshId
-            thms ← addSimpTheorem thms (.stx name arg) term post inv
-        else if arg.getKind == ``Lean.Parser.Tactic.simpStar then
-          starArg := true
-        else
-          throwUnsupportedSyntax
+            throwUnsupportedSyntax
+        catch ex =>
+          if (← read).recover then
+            logException ex
+          else
+            throw ex
       return { ctx := { ctx with simpTheorems := thmsArray.set! 0 thms }, simprocs, starArg }
 where
   isSimproc? (e : Expr) : MetaM (Option Name) := do
@@ -338,7 +344,9 @@ def mkSimpOnly (stx : Syntax) (usedSimps : Simp.UsedSimps) : MetaM Syntax := do
   for (thm, _) in usedSimps.toArray.qsort (·.2 < ·.2) do
     match thm with
     | .decl declName post inv => -- global definitions in the environment
-      if env.contains declName && (inv || !simpOnlyBuiltins.contains declName) then
+      if env.contains declName
+         && (inv || !simpOnlyBuiltins.contains declName)
+         && !Match.isMatchEqnTheorem env declName then
         let decl : Term ← `($(mkIdent (← unresolveNameGlobal declName)):ident)
         let arg ← match post, inv with
           | true,  true  => `(Parser.Tactic.simpLemma| ← $decl:term)

src/Lean/Elab/Tactic/Split.lean

@@ -21,12 +21,12 @@ open Meta
       throwErrorAt stx[2] "'split' tactic failed, select a single target to split"
     if simplifyTarget then
       liftMetaTactic fun mvarId => do
-       let some mvarIds ← splitTarget? mvarId | Meta.throwTacticEx `split mvarId
+       let some mvarIds ← splitTarget? mvarId | Meta.throwTacticEx `split mvarId "consider using `set_option trace.split.failures true`"
         return mvarIds
     else
       let fvarId ← getFVarId hyps[0]!
       liftMetaTactic fun mvarId => do
-        let some mvarIds ← splitLocalDecl? mvarId fvarId | Meta.throwTacticEx `split mvarId
+        let some mvarIds ← splitLocalDecl? mvarId fvarId | Meta.throwTacticEx `split mvarId "consider using `set_option trace.split.failures true`"
         return mvarIds
   | Location.wildcard =>
     liftMetaTactic fun mvarId => do
@@ -34,7 +34,7 @@ open Meta
       for fvarId in fvarIds do
         if let some mvarIds ← splitLocalDecl? mvarId fvarId then
           return mvarIds
-      let some mvarIds ← splitTarget? mvarId | Meta.throwTacticEx `split mvarId
+      let some mvarIds ← splitTarget? mvarId | Meta.throwTacticEx `split mvarId "consider using `set_option trace.split.failures true`"
       return mvarIds
 
 end Lean.Elab.Tactic

src/Lean/Elab/Term.lean

@@ -13,6 +13,7 @@ import Lean.Elab.Config
 import Lean.Elab.Level
 import Lean.Elab.DeclModifiers
 import Lean.Elab.PreDefinition.WF.TerminationHint
+import Lean.Language.Basic
 
 namespace Lean.Elab
 
@@ -29,8 +30,12 @@ structure SavedContext where
 
 /-- We use synthetic metavariables as placeholders for pending elaboration steps. -/
 inductive SyntheticMVarKind where
-  /-- Use typeclass resolution to synthesize value for metavariable. -/
-  | typeClass
+  /--
+  Use typeclass resolution to synthesize value for metavariable.
+  If `extraErrorMsg?` is `some msg`, `msg` contains additional information to include in error messages
+  regarding type class synthesis failure.
+  -/
+  | typeClass (extraErrorMsg? : Option MessageData)
   /-- Use coercion to synthesize value for the metavariable.
   if `f?` is `some f`, we produce an application type mismatch error message.
   Otherwise, if `header?` is `some header`, we generate the error `(header ++ "has type" ++ eType ++ "but it is expected to have type" ++ expectedType)`
@@ -42,9 +47,15 @@ inductive SyntheticMVarKind where
   | postponed (ctx : SavedContext)
   deriving Inhabited
 
+/--
+Convert an "extra" optional error message into a message `"\n{msg}"` (if `some msg`) and `MessageData.nil` (if `none`)
+-/
+def extraMsgToMsg (extraErrorMsg? : Option MessageData) : MessageData :=
+  if let some msg := extraErrorMsg? then m!"\n{msg}" else .nil
+
 instance : ToString SyntheticMVarKind where
   toString
-    | .typeClass    => "typeclass"
+    | .typeClass .. => "typeclass"
     | .coe ..       => "coe"
     | .tactic ..    => "tactic"
     | .postponed .. => "postponed"
@@ -112,6 +123,14 @@ structure State where
   letRecsToLift     : List LetRecToLift := []
   deriving Inhabited
 
+/--
+  Backtrackable state for the `TermElabM` monad.
+-/
+structure SavedState where
+  meta   : Meta.SavedState
+  «elab» : State
+  deriving Nonempty
+
 end Term
 
 namespace Tactic
@@ -152,6 +171,42 @@ structure Cache where
    post : PHashMap CacheKey Snapshot := {}
    deriving Inhabited
 
+section Snapshot
+open Language
+
+structure SavedState where
+  term   : Term.SavedState
+  tactic : State
+
+/-- State after finishing execution of a tactic. -/
+structure TacticFinished where
+  /-- Reusable state, if no fatal exception occurred. -/
+  state? : Option SavedState
+deriving Inhabited
+
+/-- Snapshot just before execution of a tactic. -/
+structure TacticParsedSnapshotData extends Language.Snapshot where
+  /-- Syntax tree of the tactic, stored and compared for incremental reuse. -/
+  stx      : Syntax
+  /-- Task for state after tactic execution. -/
+  finished : Task TacticFinished
+deriving Inhabited
+
+/-- State after execution of a single synchronous tactic step. -/
+inductive TacticParsedSnapshot where
+  | mk (data : TacticParsedSnapshotData) (next : Array (SnapshotTask TacticParsedSnapshot))
+deriving Inhabited
+abbrev TacticParsedSnapshot.data : TacticParsedSnapshot → TacticParsedSnapshotData
+  | .mk data _ => data
+/-- Potential, potentially parallel, follow-up tactic executions. -/
+-- In the first, non-parallel version, each task will depend on its predecessor
+abbrev TacticParsedSnapshot.next : TacticParsedSnapshot → Array (SnapshotTask TacticParsedSnapshot)
+  | .mk _ next => next
+partial instance : ToSnapshotTree TacticParsedSnapshot where
+  toSnapshotTree := go where
+    go := fun ⟨s, next⟩ => ⟨s.toSnapshot, next.map (·.map (sync := true) go)⟩
+
+end Snapshot
 end Tactic
 
 namespace Term
@@ -211,6 +266,13 @@ structure Context where
   /-- Cache for the `save` tactic. It is only `some` in the LSP server. -/
   tacticCache?     : Option (IO.Ref Tactic.Cache) := none
   /--
+  Snapshot for incremental processing of current tactic, if any.
+
+  Invariant: if the bundle's `old?` is set, then the state *up to the start* of the tactic is
+  unchanged, i.e. reuse is possible.
+  -/
+  tacSnap?         : Option (Language.SnapshotBundle Tactic.TacticParsedSnapshot) := none
+  /--
   If `true`, we store in the `Expr` the `Syntax` for recursive applications (i.e., applications
   of free variables tagged with `isAuxDecl`). We store the `Syntax` using `mkRecAppWithSyntax`.
   We use the `Syntax` object to produce better error messages at `Structural.lean` and `WF.lean`. -/
@@ -241,14 +303,6 @@ open Meta
 instance : Inhabited (TermElabM α) where
   default := throw default
 
-/--
-  Backtrackable state for the `TermElabM` monad.
--/
-structure SavedState where
-  meta   : Meta.SavedState
-  «elab» : State
-  deriving Nonempty
-
 protected def saveState : TermElabM SavedState :=
   return { meta := (← Meta.saveState), «elab» := (← get) }
 
@@ -261,18 +315,87 @@ def SavedState.restore (s : SavedState) (restoreInfo : Bool := false) : TermElab
   unless restoreInfo do
     setInfoState infoState
 
-/--
-Restores full state including sources for unique identifiers. Only intended for incremental reuse
-between elaboration runs, not for backtracking within a single run.
--/
-def SavedState.restoreFull (s : SavedState) : TermElabM Unit := do
-  s.meta.restoreFull
-  set s.elab
+@[specialize, inherit_doc Core.withRestoreOrSaveFull]
+def withRestoreOrSaveFull (reusableResult? : Option (α × SavedState)) (act : TermElabM α) :
+    TermElabM (α × SavedState) := do
+  if let some (_, state) := reusableResult? then
+    set state.elab
+  let reusableResult? := reusableResult?.map (fun (val, state) => (val, state.meta))
+  let (a, meta) ← controlAt MetaM fun runInBase => do
+    Meta.withRestoreOrSaveFull reusableResult? <| runInBase act
+  return (a, { meta, «elab» := (← get) })
 
 instance : MonadBacktrack SavedState TermElabM where
   saveState      := Term.saveState
   restoreState b := b.restore
 
+/--
+Manages reuse information for nested tactics by `split`ting given syntax into an outer and inner
+part. `act` is then run on the inner part but with reuse information adjusted as following:
+* If the old (from `tacSnap?`'s `SyntaxGuarded.stx`) and new (from `stx`) outer syntax are not
+  identical according to `Syntax.structRangeEq`, reuse is disabled.
+* Otherwise, the old syntax as stored in `tacSnap?` is updated to the old *inner* syntax.
+* In any case, we also use `withRef` on the inner syntax to avoid leakage of the outer syntax into
+  `act` via this route.
+
+For any tactic that participates in reuse, `withNarrowedTacticReuse` should be applied to the
+tactic's syntax and `act` should be used to do recursive tactic evaluation of nested parts.
+-/
+def withNarrowedTacticReuse [Monad m] [MonadExceptOf Exception m] [MonadWithReaderOf Context m]
+    [MonadOptions m] [MonadRef m] (split : Syntax → Syntax × Syntax) (act : Syntax → m α)
+    (stx : Syntax) : m α := do
+  let (outer, inner) := split stx
+  let opts ← getOptions
+  withTheReader Term.Context (fun ctx => { ctx with tacSnap? := ctx.tacSnap?.map fun tacSnap =>
+    { tacSnap with old? := tacSnap.old?.bind fun old => do
+      let (oldOuter, oldInner) := split old.stx
+      guard <| outer.structRangeEqWithTraceReuse opts oldOuter
+      return { old with stx := oldInner }
+    }
+  }) do
+    withRef inner do
+      act inner
+
+/--
+A variant of `withNarrowedTacticReuse` that uses `stx[argIdx]` as the inner syntax and all `stx`
+child nodes before that as the outer syntax, i.e. reuse is disabled if there was any change before
+`argIdx`.
+
+NOTE: child nodes after `argIdx` are not tested (which would almost always disable reuse as they are
+necessarily shifted by changes at `argIdx`) so it must be ensured that the result of `arg` does not
+depend on them (i.e. they should not be inspected beforehand).
+-/
+def withNarrowedArgTacticReuse [Monad m] [MonadExceptOf Exception m] [MonadWithReaderOf Context m]
+    [MonadOptions m] [MonadRef m] (argIdx : Nat) (act : Syntax → m α) (stx : Syntax) : m α :=
+  withNarrowedTacticReuse (fun stx => (mkNullNode stx.getArgs[:argIdx], stx[argIdx])) act stx
+
+/--
+Disables incremental tactic reuse *and* reporting for `act` if `cond` is true by setting `tacSnap?`
+to `none`. This should be done for tactic blocks that are run multiple times as otherwise the
+reported progress will jump back and forth (and partial reuse for these kinds of tact blocks is
+similarly questionable).
+-/
+def withoutTacticIncrementality [Monad m] [MonadWithReaderOf Context m] [MonadOptions m] [MonadRef m]
+    (cond : Bool) (act : m α) : m α := do
+  let opts ← getOptions
+  withTheReader Term.Context (fun ctx => { ctx with tacSnap? := ctx.tacSnap?.filter fun tacSnap => Id.run do
+    if let some old := tacSnap.old? then
+      if cond && opts.getBool `trace.Elab.reuse then
+        dbg_trace "reuse stopped: guard failed at {old.stx}"
+    return !cond
+  }) act
+
+/-- Disables incremental tactic reuse for `act` if `cond` is true. -/
+def withoutTacticReuse [Monad m] [MonadWithReaderOf Context m] [MonadOptions m] [MonadRef m]
+    (cond : Bool) (act : m α) : m α := do
+  let opts ← getOptions
+  withTheReader Term.Context (fun ctx => { ctx with tacSnap? := ctx.tacSnap?.map fun tacSnap =>
+    { tacSnap with old? := tacSnap.old?.filter fun old => Id.run do
+      if cond && opts.getBool `trace.Elab.reuse then
+        dbg_trace "reuse stopped: guard failed at {old.stx}"
+      return !cond }
+  }) act
+
 abbrev TermElabResult (α : Type) := EStateM.Result Exception SavedState α
 
 /--
@@ -634,30 +757,35 @@ def mkFreshIdent [Monad m] [MonadQuotation m] (ref : Syntax) (canonical := false
 private def applyAttributesCore
     (declName : Name) (attrs : Array Attribute)
     (applicationTime? : Option AttributeApplicationTime) : TermElabM Unit := do profileitM Exception "attribute application" (← getOptions) do
-  for attr in attrs do
-    withRef attr.stx do withLogging do
-    let env ← getEnv
-    match getAttributeImpl env attr.name with
-    | Except.error errMsg => throwError errMsg
-    | Except.ok attrImpl  =>
-      let runAttr := attrImpl.add declName attr.stx attr.kind
-      let runAttr := do
-        -- not truly an elaborator, but a sensible target for go-to-definition
-        let elaborator := attrImpl.ref
-        if (← getInfoState).enabled && (← getEnv).contains elaborator then
-          withInfoContext (mkInfo := return .ofCommandInfo { elaborator, stx := attr.stx }) do
-            try runAttr
-            finally if attr.stx[0].isIdent || attr.stx[0].isAtom then
-              -- Add an additional node over the leading identifier if there is one to make it look more function-like.
-              -- Do this last because we want user-created infos to take precedence
-              pushInfoLeaf <| .ofCommandInfo { elaborator, stx := attr.stx[0] }
-        else
-          runAttr
-      match applicationTime? with
-      | none => runAttr
-      | some applicationTime =>
-        if applicationTime == attrImpl.applicationTime then
-          runAttr
+  /-
+  Remark: if the declaration has syntax errors, `declName` may be `.anonymous` see issue #4309
+  In this case, we skip attribute application.
+  -/
+  unless declName == .anonymous do
+    for attr in attrs do
+      withRef attr.stx do withLogging do
+      let env ← getEnv
+      match getAttributeImpl env attr.name with
+      | Except.error errMsg => throwError errMsg
+      | Except.ok attrImpl  =>
+        let runAttr := attrImpl.add declName attr.stx attr.kind
+        let runAttr := do
+          -- not truly an elaborator, but a sensible target for go-to-definition
+          let elaborator := attrImpl.ref
+          if (← getInfoState).enabled && (← getEnv).contains elaborator then
+            withInfoContext (mkInfo := return .ofCommandInfo { elaborator, stx := attr.stx }) do
+              try runAttr
+              finally if attr.stx[0].isIdent || attr.stx[0].isAtom then
+                -- Add an additional node over the leading identifier if there is one to make it look more function-like.
+                -- Do this last because we want user-created infos to take precedence
+                pushInfoLeaf <| .ofCommandInfo { elaborator, stx := attr.stx[0] }
+          else
+            runAttr
+        match applicationTime? with
+        | none => runAttr
+        | some applicationTime =>
+          if applicationTime == attrImpl.applicationTime then
+            runAttr
 
 /-- Apply given attributes **at** a given application time -/
 def applyAttributesAt (declName : Name) (attrs : Array Attribute) (applicationTime : AttributeApplicationTime) : TermElabM Unit :=
@@ -739,8 +867,12 @@ def containsPendingMVar (e : Expr) : MetaM Bool := do
   Return `true` if the instance was synthesized successfully, and `false` if
   the instance contains unassigned metavariables that are blocking the type class
   resolution procedure. Throw an exception if resolution or assignment irrevocably fails.
+
+  If `extraErrorMsg?` is not none, it contains additional information that should be attached
+  to type class synthesis failures.
 -/
-def synthesizeInstMVarCore (instMVar : MVarId) (maxResultSize? : Option Nat := none) : TermElabM Bool := do
+def synthesizeInstMVarCore (instMVar : MVarId) (maxResultSize? : Option Nat := none) (extraErrorMsg? : Option MessageData := none): TermElabM Bool := do
+  let extraErrorMsg := extraMsgToMsg extraErrorMsg?
   let instMVarDecl ← getMVarDecl instMVar
   let type := instMVarDecl.type
   let type ← instantiateMVars type
@@ -773,18 +905,18 @@ def synthesizeInstMVarCore (instMVar : MVarId) (maxResultSize? : Option Nat := n
         let oldValType ← inferType oldVal
         let valType ← inferType val
         unless (← isDefEq oldValType valType) do
-          throwError "synthesized type class instance type is not definitionally equal to expected type, synthesized{indentExpr val}\nhas type{indentExpr valType}\nexpected{indentExpr oldValType}"
-        throwError "synthesized type class instance is not definitionally equal to expression inferred by typing rules, synthesized{indentExpr val}\ninferred{indentExpr oldVal}"
+          throwError "synthesized type class instance type is not definitionally equal to expected type, synthesized{indentExpr val}\nhas type{indentExpr valType}\nexpected{indentExpr oldValType}{extraErrorMsg}"
+        throwError "synthesized type class instance is not definitionally equal to expression inferred by typing rules, synthesized{indentExpr val}\ninferred{indentExpr oldVal}{extraErrorMsg}"
     else
       unless (← isDefEq (mkMVar instMVar) val) do
-        throwError "failed to assign synthesized type class instance{indentExpr val}"
+        throwError "failed to assign synthesized type class instance{indentExpr val}{extraErrorMsg}"
     return true
   | .undef => return false -- we will try later
   | .none  =>
     if (← read).ignoreTCFailures then
       return false
     else
-      throwError "failed to synthesize instance{indentExpr type}"
+      throwError "failed to synthesize{indentExpr type}{extraErrorMsg}\n{useDiagnosticMsg}"
 
 def mkCoe (expectedType : Expr) (e : Expr) (f? : Option Expr := none) (errorMsgHeader? : Option String := none) : TermElabM Expr := do
   withTraceNode `Elab.coe (fun _ => return m!"adding coercion for {e} : {← inferType e} =?= {expectedType}") do
@@ -1485,11 +1617,11 @@ def adaptExpander (exp : Syntax → TermElabM Syntax) : TermElab := fun stx expe
   If type class resolution cannot be executed (e.g., it is stuck because of metavariables in `type`),
   register metavariable as a pending one.
 -/
-def mkInstMVar (type : Expr) : TermElabM Expr := do
+def mkInstMVar (type : Expr) (extraErrorMsg? : Option MessageData := none) : TermElabM Expr := do
   let mvar ← mkFreshExprMVar type MetavarKind.synthetic
   let mvarId := mvar.mvarId!
-  unless (← synthesizeInstMVarCore mvarId) do
-    registerSyntheticMVarWithCurrRef mvarId SyntheticMVarKind.typeClass
+  unless (← synthesizeInstMVarCore mvarId (extraErrorMsg? := extraErrorMsg?)) do
+    registerSyntheticMVarWithCurrRef mvarId (.typeClass extraErrorMsg?)
   return mvar
 
 /--
@@ -1531,7 +1663,7 @@ partial def withAutoBoundImplicit (k : TermElabM α) : TermElabM α := do
           | ex => match isAutoBoundImplicitLocalException? ex with
             | some n =>
               -- Restore state, declare `n`, and try again
-              s.restore
+              s.restore (restoreInfo := true)
               withLocalDecl n .implicit (← mkFreshTypeMVar) fun x =>
                 withReader (fun ctx => { ctx with autoBoundImplicits := ctx.autoBoundImplicits.push x } ) do
                   loop (← saveState)
@@ -1769,6 +1901,36 @@ builtin_initialize
   registerTraceClass `Elab.debug
   registerTraceClass `Elab.reuse
 
+builtin_initialize incrementalAttr : TagAttribute ←
+  registerTagAttribute `incremental "Marks an elaborator (tactic or command, currently) as \
+supporting incremental elaboration. For unmarked elaborators, the corresponding snapshot bundle \
+field in the elaboration context is unset so as to prevent accidental, incorrect reuse."
+
+builtin_initialize builtinIncrementalElabs : IO.Ref NameSet ← IO.mkRef {}
+
+def addBuiltinIncrementalElab (decl : Name) : IO Unit := do
+  builtinIncrementalElabs.modify fun s => s.insert decl
+
+builtin_initialize
+  registerBuiltinAttribute {
+    name            := `builtin_incremental
+    descr           := s!"(builtin) {incrementalAttr.attr.descr}"
+    applicationTime := .afterCompilation
+    add             := fun decl stx kind => do
+      Attribute.Builtin.ensureNoArgs stx
+      unless kind == AttributeKind.global do
+        throwError "invalid attribute 'builtin_incremental', must be global"
+      declareBuiltin decl <| mkApp (mkConst ``addBuiltinIncrementalElab) (toExpr decl)
+  }
+
+/-- Checks whether a declaration is annotated with `[builtin_incremental]` or `[incremental]`. -/
+def isIncrementalElab [Monad m] [MonadEnv m] [MonadLiftT IO m] (decl : Name) : m Bool :=
+  (return (← builtinIncrementalElabs.get (m := IO)).contains decl) <||>
+  (return incrementalAttr.hasTag (← getEnv) decl)
+
 export Term (TermElabM)
 
+builtin_initialize
+  registerTraceClass `Elab.implicitForall
+
 end Lean.Elab