chore: remove unneeded Batteries reference in repeat doc-string

this fixes a usability paper cut that just annoyed me. When editing a
larger simp proof, I usually want to see the goal state after the simp,
and this is what I see while the `simp` command is complete. But then,
when I start typing, and necessarily type incomplete lemma names, that
error makes `simp` do nothing again and I see the original goal state.
In fact, if a prefix of the simp theorem name I am typing is a valid
identifier, it jumps even more around.

With this PR, using `logException`, I still get the red squiggly lines
for the unknown identifer, but `simp` just ignores that argument and
still shows me the final goal. Much nicer.

I also demoted the message for `[-foo]` when `foo` isn’t `simp` to a
warning and gave it the correct `ref`.

See it in action here: (in the middle, when you suddenly see the
terminal,
I am switching lean versions.)


https://github.com/leanprover/lean4/assets/148037/8cb3c563-1354-4c2d-bcee-26dfa1005ae0

.github/workflows/ci.yml

@@ -20,8 +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
@@ -38,167 +40,6 @@ jobs:
       RELEASE_TAG: ${{ steps.set-release.outputs.RELEASE_TAG }}
 
     steps:
-      - name: Run quick CI?
-        id: set-quick
-        # 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 settings the `full-ci` label.
-        run: |
-          if [ "${{ github.event_name }}" == 'pull_request' ]
-          then
-            echo "quick=$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }} --jq '.labels | any(.name == "full-ci") | not')" >> "$GITHUB_OUTPUT"
-          else
-            echo "quick=false" >> "$GITHUB_OUTPUT"
-          fi
-        env:
-          GH_TOKEN: ${{ github.token }}
-
-      - 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
@@ -249,6 +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'
@@ -327,6 +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)" >> $GITHUB_ENV
       - name: Build
         run: |
           mkdir build
@@ -357,8 +366,8 @@ jobs:
             OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ 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
@@ -387,32 +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$NPROC stage3
         if: matrix.test-speedcenter
       - name: Test Speedcenter Benchmarks
         run: |
@@ -423,11 +429,10 @@ jobs:
         if: matrix.test-speedcenter
       - name: Check rebootstrap
         run: |
-          cd build
           ulimit -c unlimited # coredumps
           # clean rebuild in case of Makefile changes
-          make update-stage0 && rm -rf ./stage* && make -j4
-        if: matrix.name == 'Linux' && needs.configure.outputs.quick == 'false'
+          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
+        if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
       - name: CCache stats
         run: ccache -s
       - name: Show stacktrace for coredumps

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

@@ -7,7 +7,7 @@ on:
 jobs:
   restart-on-label:
     runs-on: ubuntu-latest
-    if: contains(github.event.label.name, 'full-ci')
+    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

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

@@ -1,171 +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.
-
-* 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`.
+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/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/Data/BitVec/Basic.lean

@@ -534,6 +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.
@@ -543,7 +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
@@ -554,7 +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

@@ -198,4 +198,41 @@ theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
 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
 
@@ -140,6 +142,8 @@ theorem ofBool_eq_iff_eq : ∀(b b' : Bool), BitVec.ofBool b = BitVec.ofBool b'
 @[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (x#w).toNat = x % 2^w := by
   simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
 
+@[simp] theorem toFin_ofNat (x : Nat) : toFin x#w = 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) :
@@ -174,8 +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]
@@ -222,9 +225,21 @@ theorem toInt_eq_toNat_cond (i : BitVec n) :
       if 2*i.toNat < 2^n then
         (i.toNat : Int)
       else
-        (i.toNat : Int) - (2^n : Nat) := by
-  unfold BitVec.toInt
-  split <;> omega
+        (i.toNat : Int) - (2^n : Nat) :=
+  rfl
+
+theorem msb_eq_false_iff_two_mul_lt (x : BitVec w) : x.msb = false ↔ 2 * x.toNat < 2^w := by
+  cases w <;> simp [Nat.pow_succ, Nat.mul_comm _ 2, msb_eq_decide]
+
+theorem msb_eq_true_iff_two_mul_ge (x : BitVec w) : x.msb = true ↔ 2 * x.toNat ≥ 2^w := by
+  simp [← Bool.ne_false_iff, msb_eq_false_iff_two_mul_lt]
+
+/-- Characterize `x.toInt` in terms of `x.msb`. -/
+theorem toInt_eq_msb_cond (x : BitVec w) :
+    x.toInt = if x.msb then (x.toNat : Int) - (2^w : Nat) else (x.toNat : Int) := by
+  simp only [BitVec.toInt, ← msb_eq_false_iff_two_mul_lt]
+  cases x.msb <;> rfl
+
 
 theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) := by
   simp only [toInt_eq_toNat_cond]
@@ -267,6 +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) :
@@ -449,6 +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) :
@@ -475,6 +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) :
@@ -495,6 +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
@@ -629,6 +662,70 @@ theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
     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
+
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -912,6 +1009,10 @@ 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
@@ -1043,4 +1144,171 @@ 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) :

src/Init/Data/Char.lean

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

src/Init/Data/Char/Lemmas.lean

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

src/Init/Data/Fin/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
@@ -94,6 +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)
@@ -823,27 +835,3 @@ protected theorem zero_mul (k : Fin (n + 1)) : (0 : Fin (n + 1)) * k = 0 := by
   simp [ext_iff, mul_def]
 
 end Fin
-
-namespace USize
-
-@[simp] theorem lt_def {a b : USize} : a < b ↔ a.toNat < b.toNat := .rfl
-
-@[simp] theorem le_def {a b : USize} : a ≤ b ↔ a.toNat ≤ b.toNat := .rfl
-
-@[simp] theorem zero_toNat : (0 : USize).toNat = 0 := Nat.zero_mod _
-
-@[simp] theorem mod_toNat (a b : USize) : (a % b).toNat = a.toNat % b.toNat :=
-  Fin.mod_val ..
-
-@[simp] theorem div_toNat (a b : USize) : (a / b).toNat = a.toNat / b.toNat :=
-  Fin.div_val ..
-
-@[simp] theorem modn_toNat (a : USize) (b : Nat) : (a.modn b).toNat = a.toNat % b :=
-  Fin.modn_val ..
-
-theorem mod_lt (a b : USize) (h : 0 < b) : a % b < b := USize.modn_lt _ (by simp at h; exact h)
-
-theorem toNat.inj : ∀ {a b : USize}, a.toNat = b.toNat → a = b
-  | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
-
-end USize

src/Init/Data/Int/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

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/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]

src/Init/Data/Nat/Lemmas.lean

@@ -794,6 +794,9 @@ theorem shiftLeft_shiftLeft (m n : Nat) : ∀ k, (m <<< n) <<< k = m <<< (n + k)
   | 0 => rfl
   | k + 1 => by simp [← Nat.add_assoc, shiftLeft_shiftLeft _ _ k, shiftLeft_succ]
 
+@[simp] theorem shiftLeft_shiftRight (x n : Nat) : x <<< n >>> n = x := by
+  rw [Nat.shiftLeft_eq, Nat.shiftRight_eq_div_pow, Nat.mul_div_cancel _ (Nat.two_pow_pos _)]
+
 theorem mul_add_div {m : Nat} (m_pos : m > 0) (x y : Nat) : (m * x + y) / m = x + y / m := by
   match x with
   | 0 => simp

src/Init/Data/Nat/Linear.lean

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

src/Init/Data/Option/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

@@ -186,8 +186,9 @@ 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`
@@ -204,16 +205,52 @@ def utf8PrevAux : List Char → Pos → Pos → Pos
     let i' := i + c
     if i' = p then i else utf8PrevAux cs i' p
 
+/--
+Returns the position in a string before a specified position, `p`. If `p = ⟨0⟩`, returns `0`.
+If `p` is not a valid position, the result is unspecified.
+
+Examples:
+Given `def abc := "abc"` and `def lean := "L∃∀N"`,
+* `abc.get (abc.endPos |> abc.prev) = 'c'`
+* `lean.get (lean.endPos |> lean.prev |> lean.prev |> lean.prev) = '∃'`
+* `"L∃∀N".prev ⟨3⟩` is unspecified, since byte 3 occurs in the middle of the multi-byte character `'∃'`.
+-/
 @[extern "lean_string_utf8_prev"]
 def prev : (@& String) → (@& Pos) → Pos
   | ⟨s⟩, p => if p = 0 then 0 else utf8PrevAux s 0 p
 
+/--
+Returns the first character in `s`. If `s = ""`, returns `(default : Char)`.
+
+Examples:
+* `"abc".front = 'a'`
+* `"".front = (default : Char)`
+-/
 def front (s : String) : Char :=
   get s 0
 
+/--
+Returns the last character in `s`. If `s = ""`, returns `(default : Char)`.
+
+Examples:
+* `"abc".back = 'c'`
+* `"".back = (default : Char)`
+-/
 def back (s : String) : Char :=
   get s (prev s s.endPos)
 
+/--
+Returns `true` if a specified position is greater than or equal to the position which
+points to the end of a string. Otherwise, returns `false`.
+
+Examples:
+Given `def abc := "abc"` and `def lean := "L∃∀N"`,
+* `(0 |> abc.next |> abc.next |> abc.atEnd) = false`
+* `(0 |> abc.next |> abc.next |> abc.next |> abc.next |> abc.atEnd) = true`
+* `(0 |> lean.next |> lean.next |> lean.next |> lean.next |> lean.atEnd) = true`
+
+Because `"L∃∀N"` contains multi-byte characters, `lean.next (lean.next 0)` is not equal to `abc.next (abc.next 0)`.
+-/
 @[extern "lean_string_utf8_at_end"]
 def atEnd : (@& String) → (@& Pos) → Bool
   | s, p => p.byteIdx ≥ utf8ByteSize s
@@ -914,6 +951,10 @@ def beq (ss1 ss2 : Substring) : Bool :=
 
 instance hasBeq : BEq Substring := ⟨beq⟩
 
+/-- Checks whether two substrings have the same position and content. -/
+def sameAs (ss1 ss2 : Substring) : Bool :=
+  ss1.startPos == ss2.startPos && ss1 == ss2
+
 end Substring
 
 namespace String

src/Init/Data/String/Extra.lean

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

src/Init/Data/String/Lemmas.lean

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

src/Init/Data/UInt.lean

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

src/Init/Data/UInt/Basic.lean

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

src/Init/Data/UInt/Lemmas.lean

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

src/Init/Grind.lean

@@ -7,3 +7,4 @@ 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/Tactics.lean

@@ -7,8 +7,19 @@ 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/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

@@ -264,6 +264,13 @@ local macro "nonempty_list" : tactic =>
 /-- Helper method for implementing "deterministic" timeouts. It is the number of "small" memory allocations performed by the current execution thread. -/
 @[extern "lean_io_get_num_heartbeats"] opaque getNumHeartbeats : BaseIO Nat
 
+/--
+Adjusts the heartbeat counter of the current thread by the given amount. This can be useful to give
+allocation-avoiding code additional "weight" and is also used to adjust the counter after resuming
+from a snapshot.
+-/
+@[extern "lean_io_add_heartbeats"] opaque addHeartbeats (count : UInt64) : BaseIO Unit
+
 /--
 The mode of a file handle (i.e., a set of `open` flags and an `fdopen` mode).
 
@@ -786,6 +793,32 @@ instance : MonadLift (ST IO.RealWorld) BaseIO := ⟨id⟩
 def mkRef (a : α) : BaseIO (IO.Ref α) :=
   ST.mkRef a
 
+/--
+Mutable cell that can be passed around for purposes of cooperative task cancellation: request
+cancellation with `CancelToken.set` and check for it with `CancelToken.isSet`.
+
+This is a more flexible alternative to `Task.cancel` as the token can be shared between multiple
+tasks.
+-/
+structure CancelToken where
+  private ref : IO.Ref Bool
+
+namespace CancelToken
+
+/-- Creates a new cancellation token. -/
+def new : BaseIO CancelToken :=
+  CancelToken.mk <$> IO.mkRef false
+
+/-- Activates a cancellation token. Idempotent. -/
+def set (tk : CancelToken) : BaseIO Unit :=
+  tk.ref.set true
+
+/-- Checks whether the cancellation token has been activated. -/
+def isSet (tk : CancelToken) : BaseIO Bool :=
+  tk.ref.get
+
+end CancelToken
+
 namespace FS
 namespace Stream
 

src/Init/Tactics.lean

@@ -835,7 +835,8 @@ 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.
+
+See also the tactic `repeat'` which repeats separately in each subgoal.
 -/
 syntax "repeat " tacticSeq : tactic
 macro_rules

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 := {
@@ -85,6 +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.
@@ -201,16 +209,45 @@ instance : MonadTrace CoreM where
   getTraceState := return (← get).traceState
   modifyTraceState f := modify fun s => { s with traceState := f s.traceState }
 
-/-- Restore backtrackable parts of the state. -/
-def restore (b : State) : CoreM Unit :=
-  modify fun s => { s with env := b.env, messages := b.messages, infoState := b.infoState }
+structure SavedState extends State where
+  /-- Number of heartbeats passed inside `withRestoreOrSaveFull`, not used otherwise. -/
+  passedHearbeats : Nat
+deriving Nonempty
+
+def saveState : CoreM SavedState := do
+  let s ← get
+  return { toState := s, passedHearbeats := 0 }
 
 /--
-Restores full state including sources for unique identifiers. Only intended for incremental reuse
-between elaboration runs, not for backtracking within a single run.
+Incremental reuse primitive: if `reusableResult?` is `none`, runs `cont` with an action `save` that
+on execution returns the saved monadic state at this point including the heartbeats used by `cont`
+so far. If `reusableResult?` on the other hand is `some (a, state)`, restores full `state` including
+heartbeats used and returns `a`.
+
+The intention is for steps that support incremental reuse to initially pass `none` as
+`reusableResult?` and call `save` as late as possible in `cont`. In a further run, if reuse is
+possible, `reusableResult?` should be set to the previous state and result, ensuring that the state
+after running `withRestoreOrSaveFull` is identical in both runs. Note however that necessarily this
+is only an approximation in the case of heartbeats as heartbeats used by `withRestoreOrSaveFull`, by
+the remainder of `cont` after calling `save`, as well as by reuse-handling code such as the one
+supplying `reusableResult?` are not accounted for.
 -/
-def restoreFull (b : State) : CoreM Unit :=
-  set b
+@[specialize] def withRestoreOrSaveFull (reusableResult? : Option (α × SavedState))
+    (cont : (save : CoreM SavedState) → CoreM α) : CoreM α := do
+  if let some (val, state) := reusableResult? then
+    set state.toState
+    IO.addHeartbeats state.passedHearbeats.toUInt64
+    return val
+
+  let startHeartbeats ← IO.getNumHeartbeats
+  cont (do
+    let s ← get
+    let stopHeartbeats ← IO.getNumHeartbeats
+    return { toState := s, passedHearbeats := stopHeartbeats - startHeartbeats })
+
+/-- Restore backtrackable parts of the state. -/
+def SavedState.restore (b : SavedState) : CoreM Unit :=
+  modify fun s => { s with env := b.env, messages := b.messages, infoState := b.infoState }
 
 private def mkFreshNameImp (n : Name) : CoreM Name := do
   let fresh ← modifyGet fun s => (s.nextMacroScope, { s with nextMacroScope := s.nextMacroScope + 1 })
@@ -241,10 +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
@@ -289,11 +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
@@ -301,6 +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 }
@@ -408,19 +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/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 -/
@@ -298,7 +345,10 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
       if k == nullKind then
         -- list of commands => elaborate in order
         -- The parser will only ever return a single command at a time, but syntax quotations can return multiple ones
-        args.forM elabCommand
+        -- TODO: support incrementality at least for some cases such as expansions of
+        -- `set_option in` or `def a.b`
+        withoutCommandIncrementality true do
+          args.forM elabCommand
       else withTraceNode `Elab.command (fun _ => return stx) (tag :=
         -- special case: show actual declaration kind for `declaration` commands
         (if stx.isOfKind ``Parser.Command.declaration then stx[1] else stx).getKind.toString) do
@@ -321,11 +371,19 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
 
 builtin_initialize registerTraceClass `Elab.input
 
+/-- Option for showing elaboration errors from partial syntax errors. -/
+register_builtin_option showPartialSyntaxErrors : Bool := {
+  defValue := false
+  descr    := "show elaboration errors from partial syntax trees (i.e. after parser recovery)"
+}
+
 /--
 `elabCommand` wrapper that should be used for the initial invocation, not for recursive calls after
 macro expansion etc.
 -/
 def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do profileitM Exception "elaboration" (← getOptions) do
+  withReader ({ · with suppressElabErrors :=
+    stx.hasMissing && !showPartialSyntaxErrors.get (← getOptions) }) do
   let initMsgs ← modifyGet fun st => (st.messages, { st with messages := {} })
   let initInfoTrees ← getResetInfoTrees
   try
@@ -462,7 +520,12 @@ def runTermElabM (elabFn : Array Expr → TermElabM α) : CommandElabM α := do
           Term.addAutoBoundImplicits' xs someType fun xs _ =>
             Term.withoutAutoBoundImplicit <| elabFn xs
 
-@[inline] def catchExceptions (x : CommandElabM Unit) : CommandElabCoreM Empty Unit := fun ctx ref =>
+/--
+Catches and logs exceptions occurring in `x`. Unlike `try catch` in `CommandElabM`, this function
+catches interrupt exceptions as well and thus is intended for use at the top level of elaboration.
+Interrupt and abort exceptions are caught but not logged.
+-/
+@[inline] def withLoggingExceptions (x : CommandElabM Unit) : CommandElabCoreM Empty Unit := fun ctx ref =>
   EIO.catchExceptions (withLogging x ctx ref) (fun _ => pure ())
 
 private def liftAttrM {α} (x : AttrM α) : CommandElabM α := do
@@ -528,6 +591,7 @@ def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
       ref := ← getRef
       tacticCache? := none
       snap? := none
+      cancelTk? := (← read).cancelTk?
     } |>.run {
       env := ← getEnv
       maxRecDepth := ← getMaxRecDepth
@@ -537,7 +601,7 @@ def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
     traceState.traces := coreState.traceState.traces ++ commandState.traceState.traces
     env := commandState.env
   }
-  if let some err := commandState.messages.msgs.toArray.find? (·.severity matches .error) then
+  if let some err := commandState.messages.toArray.find? (·.severity matches .error) then
     throwError err.data
   pure a
 

src/Lean/Elab/Declaration.lean

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

src/Lean/Elab/DefView.lean

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

src/Lean/Elab/Deriving/DecEq.lean

@@ -182,7 +182,8 @@ def mkDecEqEnum (declName : Name) : CommandElabM Unit := do
       fun x y =>
         if h : x.toCtorIdx = y.toCtorIdx then
           -- We use `rfl` in the following proof because the first script fails for unit-like datatypes due to etaStruct.
-          isTrue (by first | have aux := congrArg $ofNatIdent h; rw [$auxThmIdent:ident, $auxThmIdent:ident] at aux; assumption | rfl)
+          -- Temporarily avoiding tactic `have` for bootstrapping
+          isTrue (by first | refine_lift have aux := congrArg $ofNatIdent h; ?_; rw [$auxThmIdent:ident, $auxThmIdent:ident] at aux; assumption | rfl)
         else
           isFalse fun h => by subst h; contradiction
   )

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

src/Lean/Elab/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

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]

src/Lean/Elab/SyntheticMVars.lean

@@ -324,7 +324,6 @@ 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 +345,7 @@ 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

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))
+    (cont : TacticM SavedState → TacticM α) : TacticM α := do
+  if let some (_, state) := reusableResult? then
+    set state.tactic
+  let reusableResult? := reusableResult?.map (fun (val, state) => (val, state.term))
+  controlAt TermElabM fun runInBase =>
+    Term.withRestoreOrSaveFull reusableResult? fun restore =>
+      runInBase <| cont (return { term := (← restore), 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
@@ -200,7 +209,11 @@ 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

@@ -29,13 +29,90 @@ open Parser.Tactic
 @[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, state)
+          -- only allow `next` reuse in this case
+          oldNext? := oldParsed.next.get? 1 |>.map (⟨old.stx, ·⟩)
+
+      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? fun save => do
+              -- set up nested reuse; `evalTactic` will check for `isIncrementalElab`
+              withTheReader Term.Context ({ · with
+                  tacSnap? := some { old? := oldInner?, new := inner } }) do
+                evalTactic tac
+              save
+            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] def evalParen : Tactic := fun stx =>
   evalTactic stx[1]
@@ -104,26 +181,20 @@ 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 Lean.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
@@ -132,7 +203,7 @@ 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
   let mkInfo ← mkInitialTacticInfo stx[0]
@@ -205,8 +276,9 @@ 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 +464,7 @@ 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 +498,16 @@ 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 +571,7 @@ 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/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

@@ -532,7 +532,9 @@ 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/Simp.lean

@@ -153,6 +153,7 @@ 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.
+  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
@@ -171,56 +172,58 @@ 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]
-            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 ← 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 => logException ex
       return { ctx := { ctx with simpTheorems := thmsArray.set! 0 thms }, simprocs, starArg }
 where
   isSimproc? (e : Expr) : MetaM (Option Name) := do
@@ -336,7 +339,9 @@ 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/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
 
@@ -112,6 +113,14 @@ 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 +161,42 @@ 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 +256,13 @@ 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 +293,6 @@ 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 +305,87 @@ 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))
+    (cont : TermElabM SavedState → TermElabM α) : TermElabM α := do
+  if let some (_, state) := reusableResult? then
+    set state.elab
+  let reusableResult? := reusableResult?.map (fun (val, state) => (val, state.meta))
+  controlAt MetaM fun runInBase =>
+    Meta.withRestoreOrSaveFull reusableResult? fun restore =>
+      runInBase <| cont (return { meta := (← restore), «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
 
 /--
@@ -1531,7 +1644,7 @@ 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 +1882,33 @@ 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)
 
 end Lean.Elab

src/Lean/Elab/Util.lean

@@ -205,10 +205,13 @@ def logException [Monad m] [MonadLog m] [AddMessageContext m] [MonadOptions m] [
   match ex with
   | Exception.error ref msg => logErrorAt ref msg
   | Exception.internal id _ =>
-    unless isAbortExceptionId id do
+    unless isAbortExceptionId id || id == Core.interruptExceptionId do
       let name ← id.getName
       logError m!"internal exception: {name}"
 
+/--
+If `x` throws an exception, catch it and turn it into a log message (using `logException`).
+-/
 def withLogging [Monad m] [MonadLog m] [MonadExcept Exception m] [AddMessageContext m] [MonadOptions m] [MonadLiftT IO m]
     (x : m Unit) : m Unit := do
   try x catch ex => logException ex

src/Lean/Language/Basic.lean

@@ -17,8 +17,13 @@ set_option linter.missingDocs true
 
 namespace Lean.Language
 
-/-- `MessageLog` with interactive diagnostics. -/
+/--
+`MessageLog` with interactive diagnostics.
+
+Can be created using `Diagnostics.empty` or `Diagnostics.ofMessageLog`.
+-/
 structure Snapshot.Diagnostics where
+  private mk ::
   /-- Non-interactive message log. -/
   msgLog : MessageLog
   /--
@@ -133,8 +138,7 @@ checking if we can reuse `old?` if set or else redoing the corresponding elabora
 case, we derive new bundles for nested snapshots, if any, and finally `resolve` `new` to the result.
 
 Note that failing to `resolve` a created promise will block the language server indefinitely!
-Corresponding `IO.Promise.new` calls should come with a "definitely resolved in ..." comment
-explaining how this is avoided in each case.
+We use `withAlwaysResolvedPromise`/`withAlwaysResolvedPromises` to ensure this doesn't happen.
 
 In the future, the 1-element history `old?` may be replaced with a global cache indexed by strong
 hashes but the promise will still need to be passed through the elaborator.
@@ -151,6 +155,36 @@ structure SnapshotBundle (α : Type) where
   -/
   new  : IO.Promise α
 
+/--
+Runs `act` with a newly created promise and finally resolves it to `default` if not done by `act`.
+
+Always resolving promises involved in the snapshot tree is important to avoid deadlocking the
+language server.
+-/
+def withAlwaysResolvedPromise [Monad m] [MonadLiftT BaseIO m] [MonadFinally m] [Inhabited α]
+    (act : IO.Promise α → m Unit) : m Unit := do
+  let p ← IO.Promise.new
+  try
+    act p
+  finally
+    p.resolve default
+
+/--
+Runs `act` with `count` newly created promises and finally resolves them to `default` if not done by
+`act`.
+
+Always resolving promises involved in the snapshot tree is important to avoid deadlocking the
+language server.
+-/
+def withAlwaysResolvedPromises [Monad m] [MonadLiftT BaseIO m] [MonadFinally m] [Inhabited α]
+    (count : Nat) (act : Array (IO.Promise α) → m Unit) : m Unit := do
+  let ps ← List.iota count |>.toArray.mapM fun _ => IO.Promise.new
+  try
+    act ps
+  finally
+    for p in ps do
+      p.resolve default
+
 /--
   Tree of snapshots where each snapshot comes with an array of asynchronous further subtrees. Used
   for asynchronously collecting information about the entirety of snapshots in the language server.

src/Lean/Language/Lean.lean

@@ -63,36 +63,61 @@ we remain at "go two commands up" at this point.
 
 Because of Lean's use of persistent data structures, incremental reuse of fully elaborated commands
 is easy because we can simply snapshot the entire state after each command and then restart
-elaboration using the stored state at the point of change. However, incrementality within
-elaboration of a single command such as between tactic steps is much harder because we cannot simply
-return from those points to the language processor in a way that we can later resume from there.
-Instead, we exchange the need for continuations with some limited mutability: by allocating an
-`IO.Promise` "cell" in the language processor, we can both pass it to the elaborator to eventually
-fill it using `Promise.resolve` as well as convert it to a `Task` that will wait on that resolution
-using `Promise.result` and return it as part of the command snapshot created by the language
-processor. The elaborator can then create new promises itself and store their `result` when
-resolving an outer promise to create an arbitrary tree of promise-backed snapshot tasks. Thus, we
-can enable incremental reporting and reuse inside the elaborator using the same snapshot tree data
-structures as outside without having to change the elaborator's control flow.
+elaboration using the stored state at the next command above the point of change. However,
+incrementality *within* elaboration of a single command such as between tactic steps is much harder
+because the existing control flow does not allow us to simply return from those points to the
+language processor in a way that we can later resume from there. Instead, we exchange the need for
+continuations with some limited mutability: by allocating an `IO.Promise` "cell" in the language
+processor, we can both pass it to the elaborator to eventually fill it using `Promise.resolve` as
+well as convert it to a `Task` that will wait on that resolution using `Promise.result` and return
+it as part of the command snapshot created by the language processor. The elaborator can then in
+turn create new promises itself and store their `result` when resolving an outer promise to create
+an arbitrary tree of promise-backed snapshot tasks. Thus, we can enable incremental reporting and
+reuse inside the elaborator using the same snapshot tree data structures as outside without having
+to change the elaborator's control flow.
 
 While ideally we would decide what can be reused during command elaboration using strong hashes over
-the state and inputs, currently we rely on simpler syntactic checks: if all the syntax inspected up
-to a certain point is unchanged, we can assume that the old state can be reused.  The central
-`SnapshotBundle` type passed inwards through the elaborator for this purpose combines the following
-data:
+the full state and inputs, currently we rely on simpler syntactic checks: if all the syntax
+inspected up to a certain point is unchanged, we can assume that the old state can be reused. The
+central `SnapshotBundle` type passed inwards through the elaborator for this purpose combines the
+following data:
 * the `IO.Promise` to be resolved to an elaborator snapshot (whose type depends on the specific
-  elaborator part we're in, e.g. `)
+  elaborator part we're in, e.g. `TacticParsedSnapshot`, `BodyProcessedSnapshot`)
 * if there was a previous run:
   * a `SnapshotTask` holding the corresponding snapshot of the run
   * the relevant `Syntax` of the previous run to be compared before any reuse
 
 Note that as we do not wait for the previous run to finish before starting to elaborate the next
-one, the `SnapshotTask` task may not be finished yet. Indeed, if we do find that we can reuse the
-contained state, we will want to explicitly wait for it instead of redoing the work. On the other
-hand, the `Syntax` is not surrounded by a task so that we can immediately access it for comparisons,
-even if the snapshot task may, eventually, give access to the same syntax tree.
+one, the old `SnapshotTask` task may not be finished yet. Indeed, if we do find that we can reuse
+the contained state because of a successful syntax comparison, we always want to explicitly wait for
+the task instead of redoing the work. On the other hand, the `Syntax` is not surrounded by a task so
+that we can immediately access it for comparisons, even if the snapshot task may, eventually, give
+access to the same syntax tree.
 
-TODO: tactic examples
+For the most part, inside an elaborator participating in incrementality, we just have to ensure that
+we stop forwarding the old run's data as soon as we notice a relevant difference between old and new
+syntax tree. For example, allowing incrementality inside the cdot tactic combinator is as simple as
+```
+builtin_initialize registerBuiltinIncrementalTactic ``cdot
+@[builtin_tactic cdot] def evalTacticCDot : Tactic := fun stx => do
+  ...
+  closeUsingOrAdmit do
+    -- save state before/after entering focus on `·`
+    ...
+    Term.withNarrowedArgTacticReuse (argIdx := 1) evalTactic stx
+```
+The `Term.withNarrowedArgTacticReuse` combinator will focus on the given argument of `stx`, which in
+this case is the nested tactic sequence, and run `evalTactic` on it. But crucially, it will first
+compare all preceding arguments, in this case the cdot token itself, with the old syntax in the
+current snapshot bundle, which in the case of tactics is stored in `Term.Context.tacSnap?`. Indeed
+it is important here to check if the cdot token is identical because its position has been saved in
+the info tree, so it would be bad if we later restored some old state that uses a different position
+for it even if everything else is unchanged.  If there is any mismatch, the bundle's old value is
+set to `none` in order to prevent reuse from this point on. Note that in any case we still want to
+forward the "new" promise in order to provide incremental reporting as well as to construct a
+snapshot tree for reuse in future document versions! Note also that we explicitly opted into
+incrementality using `registerBuiltinIncrementalTactic` as any tactic combinator not written with
+these concerns in mind would likely misbehave under incremental reuse.
 
 While it is generally true that we can provide incremental reporting even without reuse, we
 generally want to avoid that when it would be confusing/annoying, e.g. when a tactic block is run
@@ -101,12 +126,24 @@ purpose, we can disable both incremental modes using `Term.withoutTacticIncremen
 opted into incrementality because of other parts of the combinator. `induction` is an example of
 this because there are some induction alternatives that are run multiple times, so we disable all of
 incrementality for them.
+
+Using `induction` as a more complex example than `cdot` as it calls into `evalTactic` multiple
+times, here is a summary of what it has to do to implement incrementality:
+* `Narrow` down to the syntax of alternatives, disabling reuse if anything before them changed
+* allocate one new promise for each given alternative, immediately resolve passed promise to a new
+  snapshot tree node holding them so that the language server can wait on them
+* when executing an alternative,
+  * we put the corresponding promise into the context
+  * we disable reuse if anything in front of the contained tactic block has changed, including
+    previous alternatives
+  * we disable reuse *and reporting* if the tactic block is run multiple times, e.g. in the case of
+    a wildcard pattern
 -/
 
 set_option linter.missingDocs true
 
 namespace Lean.Language.Lean
-open Lean.Elab
+open Lean.Elab Command
 open Lean.Parser
 
 private def pushOpt (a? : Option α) (as : Array α) : Array α :=
@@ -121,12 +158,6 @@ register_builtin_option stderrAsMessages : Bool := {
   descr    := "(server) capture output to the Lean stderr channel (such as from `dbg_trace`) during elaboration of a command as a diagnostic message"
 }
 
-/-- 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)"
-}
-
 /-! The hierarchy of Lean snapshot types -/
 
 /-- Snapshot after elaboration of the entire command. -/
@@ -165,7 +196,7 @@ deriving Nonempty
 abbrev CommandParsedSnapshot.data : CommandParsedSnapshot → CommandParsedSnapshotData
   | mk data _ => data
 /-- Next command, unless this is a terminal command. -/
-abbrev CommandParsedSnapshot.next? : CommandParsedSnapshot →
+abbrev CommandParsedSnapshot.nextCmdSnap? : CommandParsedSnapshot →
     Option (SnapshotTask CommandParsedSnapshot)
   | mk _ next? => next?
 partial instance : ToSnapshotTree CommandParsedSnapshot where
@@ -173,18 +204,7 @@ partial instance : ToSnapshotTree CommandParsedSnapshot where
     go s := ⟨s.data.toSnapshot,
       #[s.data.elabSnap.map (sync := true) toSnapshotTree,
         s.data.finishedSnap.map (sync := true) toSnapshotTree] |>
-        pushOpt (s.next?.map (·.map (sync := true) go))⟩
-
-
-/-- Cancels all significant computations from this snapshot onwards. -/
-partial def CommandParsedSnapshot.cancel (snap : CommandParsedSnapshot) : BaseIO Unit := do
-  -- This is the only relevant computation right now, everything else is promises
-  -- TODO: cancel additional elaboration tasks (which will be tricky with `DynamicSnapshot`) if we
-  -- add them without switching to implicit cancellation
-  snap.data.finishedSnap.cancel
-  if let some next := snap.next? then
-    -- recurse on next command (which may have been spawned just before we cancelled above)
-    let _ ← IO.mapTask (sync := true) (·.cancel) next.task
+        pushOpt (s.nextCmdSnap?.map (·.map (sync := true) go))⟩
 
 /-- State after successful importing. -/
 structure HeaderProcessedState where
@@ -218,6 +238,8 @@ structure HeaderParsedSnapshot extends Snapshot where
   /-- State after successful parsing. -/
   result? : Option HeaderParsedState
   isFatal := result?.isNone
+  /-- Cancellation token for interrupting processing of this run. -/
+  cancelTk? : Option IO.CancelToken
 
 instance : ToSnapshotTree HeaderParsedSnapshot where
   toSnapshotTree s := ⟨s.toSnapshot,
@@ -235,6 +257,10 @@ abbrev InitialSnapshot := HeaderParsedSnapshot
 structure LeanProcessingContext extends ProcessingContext where
   /-- Position of the first file difference if there was a previous invocation. -/
   firstDiffPos? : Option String.Pos
+  /-- Cancellation token of the previous invocation, if any. -/
+  oldCancelTk? : Option IO.CancelToken
+  /-- Cancellation token of the current run. -/
+  newCancelTk : IO.CancelToken
 
 /-- Monad transformer holding all relevant data for Lean processing. -/
 abbrev LeanProcessingT m := ReaderT LeanProcessingContext m
@@ -247,6 +273,18 @@ instance : MonadLift LeanProcessingM (LeanProcessingT IO) where
 instance : MonadLift (ProcessingT m) (LeanProcessingT m) where
   monadLift := fun act ctx => act ctx.toProcessingContext
 
+/--
+Embeds a `LeanProcessingM` action into `ProcessingM`, optionally using the old input string to speed
+up reuse analysis and supplying a cancellation token that should be triggered as soon as reuse is
+ruled out.
+-/
+def LeanProcessingM.run (act : LeanProcessingM α) (oldInputCtx? : Option InputContext)
+    (oldCancelTk? : Option IO.CancelToken := none) : ProcessingM α := do
+  -- compute position of syntactic change once
+  let firstDiffPos? := oldInputCtx?.map (·.input.firstDiffPos (← read).input)
+  let newCancelTk ← IO.CancelToken.new
+  ReaderT.adapt ({ · with firstDiffPos?, oldCancelTk?, newCancelTk }) act
+
 /--
 Returns true if there was a previous run and the given position is before any textual change
 compared to it.
@@ -291,8 +329,7 @@ General notes:
   state. As there is no cheap way to check whether the `Environment` is unchanged, i.e. *semantic*
   change detection is currently not possible, we must make sure to pass `none` as all follow-up
   "previous states" from the first *syntactic* change onwards.
-* We must make sure to use `CommandParsedSnapshot.cancel` on such tasks when discarding them, i.e.
-  when not passing them along in `old?`.
+* We must make sure to trigger `oldCancelTk?` as soon as discarding `old?`.
 * Control flow up to finding the last still-valid snapshot (which should be quick) is synchronous so
   as not to report this "fast forwarding" to the user as well as to make sure the next run sees all
   fast-forwarded snapshots without having to wait on tasks.
@@ -300,40 +337,47 @@ General notes:
 partial def process
     (setupImports : Syntax → ProcessingT IO (Except HeaderProcessedSnapshot SetupImportsResult))
     (old? : Option InitialSnapshot) : ProcessingM InitialSnapshot := do
-  -- compute position of syntactic change once
-  let firstDiffPos? := old?.map (·.ictx.input.firstDiffPos (← read).input)
-  ReaderT.adapt ({ · with firstDiffPos? }) do
-    parseHeader old?
+  parseHeader old? |>.run (old?.map (·.ictx)) (old?.bind (·.cancelTk?))
 where
   parseHeader (old? : Option HeaderParsedSnapshot) : LeanProcessingM HeaderParsedSnapshot := do
     let ctx ← read
     let ictx := ctx.toInputContext
-    let unchanged old :=
+    let unchanged old newParserState :=
       -- when header syntax is unchanged, reuse import processing task as is and continue with
       -- parsing the first command, synchronously if possible
+      -- NOTE: even if the syntax tree is functionally unchanged, the new parser state may still
+      -- have changed because of trailing whitespace and comments etc., so it is passed separately
+      -- from `old`
       if let some oldSuccess := old.result? then
-        return { old with ictx, result? := some { oldSuccess with
-          processedSnap := (← oldSuccess.processedSnap.bindIO (sync := true) fun oldProcessed => do
-            if let some oldProcSuccess := oldProcessed.result? then
-              -- also wait on old command parse snapshot as parsing is cheap and may allow for
-              -- elaboration reuse
-              oldProcSuccess.firstCmdSnap.bindIO (sync := true) fun oldCmd =>
-                return .pure { oldProcessed with result? := some { oldProcSuccess with
-                  firstCmdSnap := (← parseCmd oldCmd oldSuccess.parserState oldProcSuccess.cmdState ctx) } }
-            else
-              return .pure oldProcessed) } }
+        return {
+          ictx
+          stx := old.stx
+          diagnostics := old.diagnostics
+          cancelTk? := ctx.newCancelTk
+          result? := some { oldSuccess with
+            processedSnap := (← oldSuccess.processedSnap.bindIO (sync := true) fun oldProcessed => do
+              if let some oldProcSuccess := oldProcessed.result? then
+                -- also wait on old command parse snapshot as parsing is cheap and may allow for
+                -- elaboration reuse
+                oldProcSuccess.firstCmdSnap.bindIO (sync := true) fun oldCmd =>
+                  return .pure { oldProcessed with result? := some { oldProcSuccess with
+                    firstCmdSnap := (← parseCmd oldCmd newParserState oldProcSuccess.cmdState ctx) } }
+              else
+                return .pure oldProcessed) } }
       else return old
 
     -- fast path: if we have parsed the header successfully...
     if let some old := old? then
-      if let some (some processed) ← old.processedResult.get? then
-        -- ...and the edit location is after the next command (see note [Incremental Parsing])...
-        if let some nextCom ← processed.firstCmdSnap.get? then
-          if (← isBeforeEditPos nextCom.data.parserState.pos) then
-            -- ...go immediately to next snapshot
-            return (← unchanged old)
+      if let some oldSuccess := old.result? then
+        if let some (some processed) ← old.processedResult.get? then
+          -- ...and the edit location is after the next command (see note [Incremental Parsing])...
+          if let some nextCom ← processed.firstCmdSnap.get? then
+            if (← isBeforeEditPos nextCom.data.parserState.pos) then
+              -- ...go immediately to next snapshot
+              return (← unchanged old oldSuccess.parserState)
 
-    withHeaderExceptions ({ · with ictx, stx := .missing, result? := none }) do
+    withHeaderExceptions ({ · with
+        ictx, stx := .missing, result? := none, cancelTk? := none }) do
       -- parsing the header should be cheap enough to do synchronously
       let (stx, parserState, msgLog) ← Parser.parseHeader ictx
       if msgLog.hasErrors then
@@ -341,6 +385,7 @@ where
           ictx, stx
           diagnostics := (← Snapshot.Diagnostics.ofMessageLog msgLog)
           result? := none
+          cancelTk? := none
         }
 
       -- semi-fast path: go to next snapshot if syntax tree is unchanged AND we're still in front
@@ -351,14 +396,11 @@ where
       -- influence the range of error messages such as from a trailing `exact`
       if let some old := old? then
         if (← isBeforeEditPos parserState.pos) && old.stx == stx then
-          return (← unchanged old)
-        -- on first change, make sure to cancel all further old tasks
-        if let some oldSuccess := old.result? then
-          oldSuccess.processedSnap.cancel
-          let _ ← BaseIO.mapTask (t := oldSuccess.processedSnap.task) fun processed => do
-            if let some oldProcSuccess := processed.result? then
-              let _ ← BaseIO.mapTask (·.cancel) oldProcSuccess.firstCmdSnap.task
-
+          -- Here we must make sure to pass the *new* parser state; see NOTE in `unchanged`
+          return (← unchanged old parserState)
+        -- on first change, make sure to cancel old invocation
+        if let some tk := ctx.oldCancelTk? then
+          tk.set
       return {
         ictx, stx
         diagnostics := (← Snapshot.Diagnostics.ofMessageLog msgLog)
@@ -366,6 +408,7 @@ where
           parserState
           processedSnap := (← processHeader stx parserState)
         }
+        cancelTk? := ctx.newCancelTk
       }
 
   processHeader (stx : Syntax) (parserState : Parser.ModuleParserState) :
@@ -417,7 +460,7 @@ where
 
     -- check for cancellation, most likely during elaboration of previous command, before starting
     -- processing of next command
-    if (← IO.checkCanceled) then
+    if (← ctx.newCancelTk.isSet) then
       -- this is a bit ugly as we don't want to adjust our API with `Option`s just for cancellation
       -- (as no-one should look at this result in that case) but anything containing `Environment`
       -- is not `Inhabited`
@@ -428,22 +471,25 @@ where
         tacticCache := (← IO.mkRef {})
       }
 
-    let unchanged old : BaseIO CommandParsedSnapshot :=
+    let unchanged old newParserState : BaseIO CommandParsedSnapshot :=
       -- when syntax is unchanged, reuse command processing task as is
-      if let some oldNext := old.next? then
+      -- NOTE: even if the syntax tree is functionally unchanged, the new parser state may still
+      -- have changed because of trailing whitespace and comments etc., so it is passed separately
+      -- from `old`
+      if let some oldNext := old.nextCmdSnap? then
         return .mk (data := old.data)
           (nextCmdSnap? := (← old.data.finishedSnap.bindIO (sync := true) fun oldFinished =>
-              -- also wait on old command parse snapshot as parsing is cheap and may allow for
-              -- elaboration reuse
-              oldNext.bindIO (sync := true) fun oldNext => do
-                parseCmd oldNext old.data.parserState oldFinished.cmdState ctx))
+            -- also wait on old command parse snapshot as parsing is cheap and may allow for
+            -- elaboration reuse
+            oldNext.bindIO (sync := true) fun oldNext => do
+              parseCmd oldNext newParserState oldFinished.cmdState ctx))
       else return old  -- terminal command, we're done!
 
     -- fast path, do not even start new task for this snapshot
     if let some old := old? then
-      if let some nextCom ← old.next?.bindM (·.get?) then
+      if let some nextCom ← old.nextCmdSnap?.bindM (·.get?) then
         if (← isBeforeEditPos nextCom.data.parserState.pos) then
-          return .pure (← unchanged old)
+          return .pure (← unchanged old old.data.parserState)
 
     SnapshotTask.ofIO (some ⟨parserState.pos, ctx.input.endPos⟩) do
       let beginPos := parserState.pos
@@ -458,15 +504,19 @@ where
       -- semi-fast path
       if let some old := old? then
         if (← isBeforeEditPos parserState.pos ctx) && old.data.stx == stx then
-          return (← unchanged old)
-        -- on first change, make sure to cancel all further old tasks
-        old.cancel
+          -- Here we must make sure to pass the *new* parser state; see NOTE in `unchanged`
+          return (← unchanged old parserState)
+        -- on first change, make sure to cancel old invocation
+        -- TODO: pass token into incrementality-aware elaborators to improve reuse of still-valid,
+        -- still-running elaboration steps?
+        if let some tk := ctx.oldCancelTk? then
+          tk.set
 
       -- definitely resolved in `doElab` task
       let elabPromise ← IO.Promise.new
       let tacticCache ← old?.map (·.data.tacticCache) |>.getDM (IO.mkRef {})
       let finishedSnap ←
-        doElab stx cmdState msgLog.hasErrors beginPos
+        doElab stx cmdState beginPos
           { old? := old?.map fun old => ⟨old.data.stx, old.data.elabSnap⟩, new := elabPromise }
           tacticCache
           ctx
@@ -479,19 +529,24 @@ where
         diagnostics := (← Snapshot.Diagnostics.ofMessageLog msgLog)
         stx
         parserState
-        elabSnap := { range? := finishedSnap.range?, task := elabPromise.result }
+        elabSnap := { range? := stx.getRange?, task := elabPromise.result }
         finishedSnap
         tacticCache
       }
 
-  doElab (stx : Syntax) (cmdState : Command.State) (hasParseError : Bool) (beginPos : String.Pos)
+  doElab (stx : Syntax) (cmdState : Command.State) (beginPos : String.Pos)
       (snap : SnapshotBundle DynamicSnapshot) (tacticCache : IO.Ref Tactic.Cache) :
       LeanProcessingM (SnapshotTask CommandFinishedSnapshot) := do
     let ctx ← read
-
-    -- signature elaboration task; for now, does full elaboration
-    -- TODO: do tactic snapshots, reuse old state for them
-    SnapshotTask.ofIO (stx.getRange?.getD ⟨beginPos, beginPos⟩) do
+    -- (Try to) use last line of command as range for final snapshot task. This ensures we do not
+    -- retract the progress bar to a previous position in case the command support incremental
+    -- reporting but has significant work after resolving its last incremental promise, such as
+    -- final type checking; if it does not support incrementality, `elabSnap` constructed in
+    -- `parseCmd` and containing the entire range of the command will determine the reported
+    -- progress and be resolved effectively at the same time as this snapshot task, so `tailPos` is
+    -- irrelevant in this case.
+    let tailPos := stx.getTailPos? |>.getD beginPos
+    SnapshotTask.ofIO (some ⟨tailPos, tailPos⟩) do
       let scope := cmdState.scopes.head!
       let cmdStateRef ← IO.mkRef { cmdState with messages := .empty }
       /-
@@ -505,26 +560,18 @@ where
         cmdPos       := beginPos
         tacticCache? := some tacticCacheNew
         snap?        := some snap
+        cancelTk?    := some ctx.newCancelTk
       }
       let (output, _) ←
         IO.FS.withIsolatedStreams (isolateStderr := stderrAsMessages.get scope.opts) do
           liftM (m := BaseIO) do
-            Elab.Command.catchExceptions
+            withLoggingExceptions
               (getResetInfoTrees *> Elab.Command.elabCommandTopLevel stx)
               cmdCtx cmdStateRef
       let postNew := (← tacticCacheNew.get).post
       tacticCache.modify fun _ => { pre := postNew, post := {} }
       let cmdState ← cmdStateRef.get
       let mut messages := cmdState.messages
-      -- `stx.hasMissing` should imply `hasParseError`, but the latter should be cheaper to check in
-      -- general
-      if !showPartialSyntaxErrors.get cmdState.scopes[0]!.opts && hasParseError &&
-          stx.hasMissing then
-        -- discard elaboration errors, except for a few important and unlikely misleading ones, on
-        -- parse error
-        messages := ⟨messages.msgs.filter fun msg =>
-          msg.data.hasTag (fun tag => tag == `Elab.synthPlaceholder ||
-            tag == `Tactic.unsolvedGoals || (`_traceMsg).isSuffixOf tag)⟩
       if !output.isEmpty then
         messages := messages.add {
           fileName := ctx.fileName
@@ -541,13 +588,25 @@ where
         cmdState
       }
 
+/--
+Convenience function for tool uses of the language processor that skips header handling.
+-/
+def processCommands (inputCtx : Parser.InputContext) (parserState : Parser.ModuleParserState)
+    (commandState : Command.State)
+    (old? : Option (Parser.InputContext × CommandParsedSnapshot) := none) :
+    BaseIO (SnapshotTask CommandParsedSnapshot) := do
+  process.parseCmd (old?.map (·.2)) parserState commandState
+    |>.run (old?.map (·.1))
+    |>.run { inputCtx with }
+
+
 /-- Waits for and returns final environment, if importing was successful. -/
 partial def waitForFinalEnv? (snap : InitialSnapshot) : Option Environment := do
   let snap ← snap.result?
   let snap ← snap.processedSnap.get.result?
   goCmd snap.firstCmdSnap.get
 where goCmd snap :=
-  if let some next := snap.next? then
+  if let some next := snap.nextCmdSnap? then
     goCmd next.get
   else
     snap.data.finishedSnap.get.cmdState.env

src/Lean/Message.lean

@@ -57,27 +57,37 @@ inductive MessageData where
   This constructor is inspected in various hacks. -/
   | ofFormatWithInfos : FormatWithInfos → MessageData
   | ofGoal            : MVarId → MessageData
+  /-- A widget instance.
+
+  In `ofWidget wi alt`,
+  the nested message `alt` should approximate the contents of the widget
+  without itself using `ofWidget wi _`.
+  This is used as fallback in environments that cannot display user widgets.
+  `alt` may nest any structured message,
+  for example `ofGoal` to approximate a tactic state widget,
+  and, if necessary, even other widget instances
+  (for which approximations are computed recursively). -/
+  | ofWidget          : Widget.WidgetInstance → MessageData → MessageData
   /-- `withContext ctx d` specifies the pretty printing context `(env, mctx, lctx, opts)` for the nested expressions in `d`. -/
   | withContext       : MessageDataContext → MessageData → MessageData
   | withNamingContext : NamingContext → MessageData → MessageData
   /-- Lifted `Format.nest` -/
-  |  nest              : Nat → MessageData → MessageData
+  | nest              : Nat → MessageData → MessageData
   /-- Lifted `Format.group` -/
-  |  group             : MessageData → MessageData
+  | group             : MessageData → MessageData
   /-- Lifted `Format.compose` -/
-  |  compose           : MessageData → MessageData → MessageData
+  | compose           : MessageData → MessageData → MessageData
   /-- Tagged sections. `Name` should be viewed as a "kind", and is used by `MessageData` inspector functions.
     Example: an inspector that tries to find "definitional equality failures" may look for the tag "DefEqFailure". -/
   | tagged            : Name → MessageData → MessageData
   | trace (data : TraceData) (msg : MessageData) (children : Array MessageData)
   /-- A lazy message.
   The provided thunk will not be run until it is about to be displayed.
-  This can save computation in cases where the message may never be seen,
-  e.g. when nested inside a collapsed trace.
+  This can save computation in cases where the message may never be seen.
 
   The `Dynamic` value is expected to be a `MessageData`,
   which is a workaround for the positivity restriction.
-     
+
   If the thunked message is produced for a term that contains a synthetic sorry,
   `hasSyntheticSorry` should return `true`.
   This is used to filter out certain messages. -/
@@ -160,6 +170,7 @@ partial def formatAux : NamingContext → Option MessageDataContext → MessageD
   | _, _,            ofFormatWithInfos fmt    => return fmt.1
   | _,    none,      ofGoal mvarId            => return "goal " ++ format (mkMVar mvarId)
   | nCtx, some ctx,  ofGoal mvarId            => ppGoal (mkPPContext nCtx ctx) mvarId
+  | nCtx, ctx,       ofWidget _ d             => formatAux nCtx ctx d
   | nCtx, _,         withContext ctx d        => formatAux nCtx ctx d
   | _,    ctx,       withNamingContext nCtx d => formatAux nCtx ctx d
   | nCtx, ctx,       tagged _ d               => formatAux nCtx ctx d
@@ -298,47 +309,69 @@ protected def toJson (msg : Message) : IO Json := do
 
 end Message
 
-/-- A persistent array of messages. -/
+/--
+A persistent array of messages.
+
+In the Lean elaborator, we use a fresh message log per command but may also report diagnostics at
+various points inside a command, which will empty `unreported` and updated `hadErrors` accordingly
+(see `CoreM.getAndEmptyMessageLog`).
+-/
 structure MessageLog where
-  msgs : PersistentArray Message := {}
+  /--
+  If true, there was an error in the log previously that has already been reported to the user and
+  removed from the log. Thus we say that in the current context (usually the current command), we
+  "have errors" if either this flag is set or there is an error in `msgs`; see
+  `MessageLog.hasErrors`. If we have errors, we suppress some error messages that are often the
+  result of a previous error.
+  -/
+  /-
+  Design note: We considered introducing a `hasErrors` field instead that already includes the
+  presence of errors in `msgs` but this would not be compatible with e.g.
+  `MessageLog.errorsToWarnings`.
+  -/
+  hadErrors : Bool := false
+  /-- The list of messages not already reported, in insertion order. -/
+  unreported : PersistentArray Message := {}
   deriving Inhabited
 
 namespace MessageLog
-def empty : MessageLog := ⟨{}⟩
+def empty : MessageLog := {}
 
-def isEmpty (log : MessageLog) : Bool :=
-  log.msgs.isEmpty
+@[deprecated "renamed to `unreported`; direct access should in general be avoided in favor of \
+using `MessageLog.toList/toArray`"]
+def msgs : MessageLog → PersistentArray Message := unreported
+
+def hasUnreported (log : MessageLog) : Bool :=
+  !log.unreported.isEmpty
 
 def add (msg : Message) (log : MessageLog) : MessageLog :=
-  ⟨log.msgs.push msg⟩
+  { log with unreported := log.unreported.push msg }
 
 protected def append (l₁ l₂ : MessageLog) : MessageLog :=
-  ⟨l₁.msgs ++ l₂.msgs⟩
+  { hadErrors := l₁.hadErrors || l₂.hadErrors, unreported := l₁.unreported ++ l₂.unreported }
 
 instance : Append MessageLog :=
   ⟨MessageLog.append⟩
 
 def hasErrors (log : MessageLog) : Bool :=
-  log.msgs.any fun m => match m.severity with
-    | MessageSeverity.error => true
-    | _                     => false
+  log.hadErrors || log.unreported.any (·.severity matches .error)
 
 def errorsToWarnings (log : MessageLog) : MessageLog :=
-  { msgs := log.msgs.map (fun m => match m.severity with | MessageSeverity.error => { m with severity := MessageSeverity.warning } | _ => m) }
+  { unreported := log.unreported.map (fun m => match m.severity with | MessageSeverity.error => { m with severity := MessageSeverity.warning } | _ => m) }
 
 def getInfoMessages (log : MessageLog) : MessageLog :=
-  { msgs := log.msgs.filter fun m => match m.severity with | MessageSeverity.information => true | _ => false }
+  { unreported := log.unreported.filter fun m => match m.severity with | MessageSeverity.information => true | _ => false }
 
 def forM {m : Type → Type} [Monad m] (log : MessageLog) (f : Message → m Unit) : m Unit :=
-  log.msgs.forM f
+  log.unreported.forM f
 
-/-- Converts the log to a list, oldest message first. -/
+/-- Converts the unreported messages to a list, oldest message first. -/
 def toList (log : MessageLog) : List Message :=
-  log.msgs.toList
+  log.unreported.toList
 
-/-- Converts the log to an array, oldest message first. -/
+/-- Converts the unreported messages to an array, oldest message first. -/
 def toArray (log : MessageLog) : Array Message :=
-  log.msgs.toArray
+  log.unreported.toArray
 
 end MessageLog
 

src/Lean/Meta/Basic.lean

@@ -304,7 +304,7 @@ structure State where
   Backtrackable state for the `MetaM` monad.
 -/
 structure SavedState where
-  core        : Core.State
+  core        : Core.SavedState
   meta        : State
   deriving Nonempty
 
@@ -410,20 +410,22 @@ instance : AddMessageContext MetaM where
   addMessageContext := addMessageContextFull
 
 protected def saveState : MetaM SavedState :=
-  return { core := (← getThe Core.State), meta := (← get) }
+  return { core := (← Core.saveState), meta := (← get) }
 
 /-- Restore backtrackable parts of the state. -/
 def SavedState.restore (b : SavedState) : MetaM Unit := do
-  Core.restore b.core
+  b.core.restore
   modify fun s => { s with mctx := b.meta.mctx, zetaDeltaFVarIds := b.meta.zetaDeltaFVarIds, postponed := b.meta.postponed }
 
-/--
-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 (b : SavedState) : MetaM Unit := do
-  Core.restoreFull b.core
-  set b.meta
+@[specialize, inherit_doc Core.withRestoreOrSaveFull]
+def withRestoreOrSaveFull (reusableResult? : Option (α × SavedState))
+    (cont : MetaM SavedState → MetaM α) : MetaM α := do
+  if let some (_, state) := reusableResult? then
+    set state.meta
+  let reusableResult? := reusableResult?.map (fun (val, state) => (val, state.core))
+  controlAt CoreM fun runInCoreM =>
+    Core.withRestoreOrSaveFull reusableResult? fun restore =>
+      runInCoreM <| cont (return { core := (← restore), meta := (← get) })
 
 instance : MonadBacktrack SavedState MetaM where
   saveState      := Meta.saveState

src/Lean/Meta/CtorRecognizer.lean

@@ -14,13 +14,11 @@ private def getConstructorVal? (env : Environment) (ctorName : Name) : Option Co
   | some (.ctorInfo v) => v
   | _                  => none
 
-
 /--
-If `e` is a constructor application or a builtin literal defeq to a constructor application,
+If `e` is a constructor application,
 then return the corresponding `ConstructorVal`.
 -/
-def isConstructorApp? (e : Expr) : MetaM (Option ConstructorVal) := do
-  let e ← litToCtor e
+def isConstructorAppCore? (e : Expr) : MetaM (Option ConstructorVal) := do
   let .const n _ := e.getAppFn | return none
   let some v := getConstructorVal? (← getEnv) n | return none
   if v.numParams + v.numFields == e.getAppNumArgs then
@@ -28,6 +26,13 @@ def isConstructorApp? (e : Expr) : MetaM (Option ConstructorVal) := do
   else
     return none
 
+/--
+If `e` is a constructor application or a builtin literal defeq to a constructor application,
+then return the corresponding `ConstructorVal`.
+-/
+def isConstructorApp? (e : Expr) : MetaM (Option ConstructorVal) := do
+  isConstructorAppCore? (← litToCtor e)
+
 /--
 Similar to `isConstructorApp?`, but uses `whnf`.
 -/

src/Lean/Meta/LitValues.lean

@@ -99,6 +99,8 @@ def getUInt64Value? (e : Expr) : MetaM (Option UInt64) := OptionT.run do
   let (n, _) ← getOfNatValue? e ``UInt64
   return UInt64.ofNat n
 
+-- TODO: extensibility
+
 /--
 If `e` is a literal value, ensure it is encoded using the standard representation.
 Otherwise, just return `e`.
@@ -117,6 +119,23 @@ def normLitValue (e : Expr) : MetaM Expr := do
   if let some n ← getUInt64Value? e then return toExpr n
   return e
 
+/--
+Returns `true` if `e` is a literal value.
+-/
+def isLitValue (e : Expr) : MetaM Bool := do
+  let e ← instantiateMVars e
+  if (← getNatValue? e).isSome then return true
+  if (← getIntValue? e).isSome then return true
+  if (← getFinValue? e).isSome then return true
+  if (← getBitVecValue? e).isSome then return true
+  if (getStringValue? e).isSome then return true
+  if (← getCharValue? e).isSome then return true
+  if (← getUInt8Value? e).isSome then return true
+  if (← getUInt16Value? e).isSome then return true
+  if (← getUInt32Value? e).isSome then return true
+  if (← getUInt64Value? e).isSome then return true
+  return false
+
 /--
 If `e` is a `Nat`, `Int`, or `Fin` literal value, converts it into a constructor application.
 Otherwise, just return `e`.

src/Lean/Meta/Match/MatchEqsExt.lean

@@ -19,14 +19,18 @@ def MatchEqns.size (e : MatchEqns) : Nat :=
 
 structure MatchEqnsExtState where
   map : PHashMap Name MatchEqns := {}
+  eqns : PHashSet Name := {}
   deriving Inhabited
 
 /- We generate the equations and splitter on demand, and do not save them on .olean files. -/
 builtin_initialize matchEqnsExt : EnvExtension MatchEqnsExtState ←
   registerEnvExtension (pure {})
 
-def registerMatchEqns (matchDeclName : Name) (matchEqns : MatchEqns) : CoreM Unit :=
-  modifyEnv fun env => matchEqnsExt.modifyState env fun s => { s with map := s.map.insert matchDeclName matchEqns }
+def registerMatchEqns (matchDeclName : Name) (matchEqns : MatchEqns) : CoreM Unit := do
+  modifyEnv fun env => matchEqnsExt.modifyState env fun { map, eqns } => {
+    eqns := matchEqns.eqnNames.foldl (init := eqns) fun eqns eqn => eqns.insert eqn
+    map := map.insert matchDeclName matchEqns
+  }
 
 /-
   Forward definition. We want to use `getEquationsFor` in the simplifier,
@@ -34,4 +38,10 @@ def registerMatchEqns (matchDeclName : Name) (matchEqns : MatchEqns) : CoreM Uni
 @[extern "lean_get_match_equations_for"]
 opaque getEquationsFor (matchDeclName : Name) : MetaM MatchEqns
 
+/--
+Returns `true` if `declName` is the name of a `match` equational theorem.
+-/
+def isMatchEqnTheorem (env : Environment) (declName : Name) : Bool :=
+  matchEqnsExt.getState env |>.eqns.contains declName
+
 end Lean.Meta.Match

src/Lean/Meta/Tactic/Cases.lean

@@ -200,7 +200,7 @@ private def toCasesSubgoals (s : Array InductionSubgoal) (ctorNames : Array Name
     { ctorName           := ctorName,
       toInductionSubgoal := s }
 
-partial def unifyEqs? (numEqs : Nat) (mvarId : MVarId) (subst : FVarSubst) (caseName? : Option Name := none): MetaM (Option (MVarId × FVarSubst)) := do
+partial def unifyEqs? (numEqs : Nat) (mvarId : MVarId) (subst : FVarSubst) (caseName? : Option Name := none): MetaM (Option (MVarId × FVarSubst)) := withIncRecDepth do
   if numEqs == 0 then
     return some (mvarId, subst)
   else

src/Lean/Meta/Tactic/Grind.lean

@@ -9,3 +9,6 @@ import Lean.Meta.Tactic.Grind.RevertAll
 import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.Preprocessor
 import Lean.Meta.Tactic.Grind.Util
+import Lean.Meta.Tactic.Grind.Cases
+import Lean.Meta.Tactic.Grind.Injection
+import Lean.Meta.Tactic.Grind.Core

src/Lean/Meta/Tactic/Grind/Attr.lean

@@ -16,4 +16,54 @@ builtin_initialize grindNormExt : SimpExtension ←
 builtin_initialize grindNormSimprocExt : SimprocExtension ←
   registerSimprocAttr `grind_norm_proc "simplification/normalization procedured for `grind`" none
 
+builtin_initialize grindCasesExt : SimpleScopedEnvExtension Name NameSet ←
+  registerSimpleScopedEnvExtension {
+    initial        := {}
+    addEntry       := fun s declName => s.insert declName
+  }
+
+/--
+Returns `true` if `declName` has been tagged with attribute `[grind_cases]`.
+-/
+def isGrindCasesTarget (declName : Name) : CoreM Bool :=
+  return grindCasesExt.getState (← getEnv) |>.contains declName
+
+private def getAlias? (value : Expr) : MetaM (Option Name) :=
+  lambdaTelescope value fun _ body => do
+    if let .const declName _ := body.getAppFn' then
+      return some declName
+    else
+      return none
+
+/--
+Throws an error if `declName` cannot be annotated with attribute `[grind_cases]`.
+We support the following cases:
+- `declName` is a non-recursive datatype.
+- `declName` is an abbreviation for a non-recursive datatype.
+-/
+private partial def validateGrindCasesAttr (declName : Name) : CoreM Unit := do
+  match (← getConstInfo declName) with
+  | .inductInfo info =>
+    if info.isRec then
+      throwError "`{declName}` is a recursive datatype"
+  | .defnInfo info =>
+    let failed := throwError "`{declName}` is a definition, but it is not an alias/abbreviation for an inductive datatype"
+    let some declName ← getAlias? info.value |>.run' {} {}
+      | failed
+    try
+      validateGrindCasesAttr declName
+    catch _ =>
+      failed
+  | _ =>
+    throwError "`{declName}` is not an inductive datatype or an alias for one"
+
+builtin_initialize
+  registerBuiltinAttribute {
+    name  := `grind_cases
+    descr := "`grind` tactic applies `cases` to (non-recursive) inductives during pre-processing step"
+    add   := fun declName _ attrKind => do
+      validateGrindCasesAttr declName
+      grindCasesExt.add declName attrKind
+  }
+
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Cases.lean

@@ -0,0 +1,62 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Cases
+
+namespace Lean.Meta.Grind
+/--
+The `grind` tactic includes an auxiliary `cases` tactic that is not intended for direct use by users.
+This method implements it.
+This tactic is automatically applied when introducing local declarations with a type tagged with `[grind_cases]`.
+It differs from the user-facing Lean `cases` tactic in the following ways:
+
+- It avoids unnecessary `revert` and `intro` operations.
+
+- It does not introduce new local declarations for each minor premise. Instead, the `grind` tactic preprocessor is responsible for introducing them.
+
+- It assumes that the major premise (i.e., the parameter `fvarId`) is the latest local declaration in the current goal.
+
+- If the major premise type is an indexed family, auxiliary declarations and (heterogeneous) equalities are introduced.
+  However, these equalities are not resolved using `unifyEqs`. Instead, the `grind` tactic employs union-find and
+  congruence closure to process these auxiliary equalities. This approach avoids applying substitution to propositions
+  that have already been internalized by `grind`.
+-/
+def cases (mvarId : MVarId) (fvarId : FVarId) : MetaM (List MVarId) := mvarId.withContext do
+  let tag ← mvarId.getTag
+  let type ← whnf (← fvarId.getType)
+  let .const declName _ := type.getAppFn | throwInductiveExpected type
+  let .inductInfo _ ← getConstInfo declName | throwInductiveExpected type
+  let recursorInfo ← mkRecursorInfo (mkCasesOnName declName)
+  let k (mvarId : MVarId) (fvarId : FVarId) (indices : Array Expr) (clearMajor : Bool) : MetaM (List MVarId) := do
+    let recursor ← mkRecursorAppPrefix mvarId `grind.cases fvarId recursorInfo indices
+    let mut recursor := mkApp (mkAppN recursor indices) (mkFVar fvarId)
+    let mut recursorType ← inferType recursor
+    let mut mvarIdsNew := #[]
+    for _ in [:recursorInfo.numMinors] do
+      let .forallE _ targetNew recursorTypeNew _ ← whnf recursorType
+        | throwTacticEx `grind.cases mvarId "unexpected recursor type"
+      recursorType := recursorTypeNew
+      let mvar ← mkFreshExprSyntheticOpaqueMVar targetNew tag
+      recursor := mkApp recursor mvar
+      let mvarIdNew ← if clearMajor then
+        mvar.mvarId!.clear fvarId
+      else
+        pure mvar.mvarId!
+      mvarIdsNew := mvarIdsNew.push mvarIdNew
+    mvarId.assign recursor
+    return mvarIdsNew.toList
+  if recursorInfo.numIndices > 0 then
+    let s ← generalizeIndices mvarId fvarId
+    s.mvarId.withContext do
+      k s.mvarId s.fvarId (s.indicesFVarIds.map mkFVar) (clearMajor := false)
+  else
+    let indices ← getMajorTypeIndices mvarId `grind.cases recursorInfo type
+    k mvarId fvarId indices (clearMajor := true)
+where
+  throwInductiveExpected {α} (type : Expr) : MetaM α := do
+    throwTacticEx `grind.cases mvarId m!"(non-recursive) inductive type expected at {mkFVar fvarId}{indentExpr type}"
+
+end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Core.lean

@@ -0,0 +1,157 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Grind.Types
+import Lean.Meta.LitValues
+
+namespace Lean.Meta.Grind
+/--
+Returns `true` if `e` is `True`, `False`, or a literal value.
+See `LitValues` for supported literals.
+-/
+def isInterpreted (e : Expr) : MetaM Bool := do
+  if e.isTrue || e.isFalse then return true
+  isLitValue e
+
+/--
+Creates an `ENode` for `e` if one does not already exist.
+This method assumes `e` has been hashconsed.
+-/
+def mkENode (e : Expr) (generation : Nat := 0) : GoalM Unit := do
+  if (← getENode? e).isSome then return ()
+  let ctor := (← isConstructorAppCore? e).isSome
+  let interpreted ← isInterpreted e
+  mkENodeCore e interpreted ctor generation
+
+/--
+Returns the root element in the equivalence class of `e`.
+-/
+def getRoot (e : Expr) : GoalM Expr := do
+  let some n ← getENode? e | return e
+  return n.root
+
+/--
+Returns the next element in the equivalence class of `e`.
+-/
+def getNext (e : Expr) : GoalM Expr := do
+  let some n ← getENode? e | return e
+  return n.next
+
+@[inline] def isSameExpr (a b : Expr) : Bool :=
+  -- It is safe to use pointer equality because we hashcons all expressions
+  -- inserted into the E-graph
+  unsafe ptrEq a b
+
+private def pushNewEqCore (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit :=
+  modify fun s => { s with newEqs := s.newEqs.push { lhs, rhs, proof, isHEq } }
+
+@[inline] private def pushNewEq (lhs rhs proof : Expr) : GoalM Unit :=
+  pushNewEqCore lhs rhs proof (isHEq := false)
+
+@[inline] private def pushNewHEq (lhs rhs proof : Expr) : GoalM Unit :=
+  pushNewEqCore lhs rhs proof (isHEq := true)
+
+/--
+The fields `target?` and `proof?` in `e`'s `ENode` are encoding a transitivity proof
+from `e` to the root of the equivalence class
+This method "inverts" the proof, and makes it to go from the root of the equivalence class to `e`.
+
+We use this method when merging two equivalence classes.
+-/
+private partial def invertTrans (e : Expr) : GoalM Unit := do
+  go e false none none
+where
+  go (e : Expr) (flippedNew : Bool) (targetNew? : Option Expr) (proofNew? : Option Expr) : GoalM Unit := do
+    let some node ← getENode? e | unreachable!
+    if let some target := node.target? then
+      go target (!node.flipped) (some e) node.proof?
+    setENode e { node with
+      target? := targetNew?
+      flipped := flippedNew
+      proof?  := proofNew?
+    }
+
+private def markAsInconsistent : GoalM Unit :=
+  modify fun s => { s with inconsistent := true }
+
+private partial def addEqStep (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit := do
+  let some lhsNode ← getENode? lhs | return () -- `lhs` has not been internalized yet
+  let some rhsNode ← getENode? rhs | return () -- `rhs` has not been internalized yet
+  if isSameExpr lhsNode.root rhsNode.root then return () -- `lhs` and `rhs` are already in the same equivalence class.
+  let some lhsRoot ← getENode? lhsNode.root | unreachable!
+  let some rhsRoot ← getENode? rhsNode.root | unreachable!
+  if    (lhsRoot.interpreted && !rhsRoot.interpreted)
+     || (lhsRoot.ctor && !rhsRoot.ctor)
+     || (lhsRoot.size > rhsRoot.size && !rhsRoot.interpreted && !rhsRoot.ctor) then
+    go rhs lhs rhsNode lhsNode rhsRoot lhsRoot true
+  else
+    go lhs rhs lhsNode rhsNode lhsRoot rhsRoot false
+where
+  go (lhs rhs : Expr) (lhsNode rhsNode lhsRoot rhsRoot : ENode) (flipped : Bool) : GoalM Unit := do
+    let mut valueInconsistency := false
+    if lhsRoot.interpreted && rhsRoot.interpreted then
+      if lhsNode.root.isTrue || rhsNode.root.isTrue then
+        markAsInconsistent
+      else
+        valueInconsistency := true
+    -- TODO: process valueInconsistency := true
+    /-
+    We have the following `target?/proof?`
+    `lhs -> ... -> lhsNode.root`
+    `rhs -> ... -> rhsNode.root`
+    We want to convert it to
+    `lhsNode.root -> ... -> lhs -*-> rhs -> ... -> rhsNode.root`
+    where step `-*->` is justified by `proof` (or `proof.symm` if `flipped := true`)
+    -/
+    invertTrans lhs
+    setENode lhs { lhsNode with
+      target? := rhs
+      proof?  := proof
+      flipped
+    }
+    -- TODO: Remove parents from congruence table
+    -- TODO: set propagateBool
+    updateRoots lhs rhsNode.root true -- TODO
+    -- TODO: Reinsert parents into congruence table
+    setENode lhsNode.root { lhsRoot with
+      next := rhsRoot.next
+    }
+    setENode rhsNode.root { rhsRoot with
+      next := lhsRoot.next
+      size := rhsRoot.size + lhsRoot.size
+      hasLambdas := rhsRoot.hasLambdas || lhsRoot.hasLambdas
+      heqProofs  := isHEq || rhsRoot.heqProofs || lhsRoot.heqProofs
+    }
+    -- TODO: copy parentst from lhsRoot parents to rhsRoot parents
+
+  updateRoots (lhs : Expr) (rootNew : Expr) (_propagateBool : Bool) : GoalM Unit := do
+    let rec loop (e : Expr) : GoalM Unit := do
+      -- TODO: propagateBool
+      let some n ← getENode? e | unreachable!
+      setENode e { n with root := rootNew }
+      if isSameExpr lhs n.next then return ()
+      loop n.next
+    loop lhs
+
+partial def addEqCore (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit := do
+  addEqStep lhs rhs proof isHEq
+  processTodo
+where
+  processTodo : GoalM Unit := do
+    if (← get).inconsistent then
+      modify fun s => { s with newEqs := #[] }
+      return ()
+    let some { lhs, rhs, proof, isHEq } := (← get).newEqs.back? | return ()
+    addEqStep lhs rhs proof isHEq
+    processTodo
+
+def addEq (lhs rhs proof : Expr) : GoalM Unit := do
+  addEqCore lhs rhs proof false
+
+def addHEq (lhs rhs proof : Expr) : GoalM Unit := do
+  addEqCore lhs rhs proof true
+
+end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Injection.lean

@@ -0,0 +1,39 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.CtorRecognizer
+import Lean.Meta.Tactic.Util
+import Lean.Meta.Tactic.Clear
+
+namespace Lean.Meta.Grind
+/--
+The `grind` tactic includes an auxiliary `injection?` tactic that is not intended for direct use by users.
+This tactic is automatically applied when introducing non-dependent propositions.
+It differs from the user-facing Lean `injection` tactic in the following ways:
+
+- It does not introduce new propositions. Instead, the `grind` tactic preprocessor is responsible for introducing them.
+- It assumes that `fvarId` is the latest local declaration in the current goal.
+- It does not handle cases where the constructors are different because the simplifier already reduces such equalities to `False`.
+- It does not have support for heterogeneous equality. Recall that the simplifier already reduces them to `Eq` if
+  the types are definitionally equal.
+-/
+def injection? (mvarId : MVarId) (fvarId : FVarId) : MetaM (Option MVarId) := mvarId.withContext do
+  let decl ← fvarId.getDecl
+  let_expr Eq _ a b := decl.type | return none
+  match (← isConstructorAppCore? a), (← isConstructorAppCore? b) with
+  | some aCtor, some bCtor =>
+    if aCtor.name != bCtor.name then return none -- Simplifier handles this case
+    let target ← mvarId.getType
+    let val ← mkNoConfusion target (mkFVar fvarId)
+    let .forallE _ targetNew _ _ ← whnfD (← inferType val) | return none
+    let targetNew := targetNew.headBeta
+    let tag ← mvarId.getTag
+    let mvarNew ← mkFreshExprSyntheticOpaqueMVar targetNew tag
+    mvarId.assign (mkApp val mvarNew)
+    return some (← mvarNew.mvarId!.clear fvarId)
+  | _, _ => return none
+
+end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Preprocessor.lean

@@ -13,6 +13,9 @@ import Lean.Meta.Tactic.Grind.Attr
 import Lean.Meta.Tactic.Grind.RevertAll
 import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.Util
+import Lean.Meta.Tactic.Grind.Cases
+import Lean.Meta.Tactic.Grind.Injection
+import Lean.Meta.Tactic.Grind.Core
 
 namespace Lean.Meta.Grind
 namespace Preprocessor
@@ -27,6 +30,7 @@ structure Context where
 
 structure State where
   simpStats : Simp.Stats := {}
+  goals     : PArray Goal := {}
   deriving Inhabited
 
 abbrev PreM := ReaderT Context $ StateRefT State GrindM
@@ -41,21 +45,17 @@ def PreM.run (x : PreM α) : GrindM α := do
   }
   x { simp, simprocs } |>.run' {}
 
-def simp (e : Expr) : PreM Simp.Result := do
+def simp (_goal : Goal) (e : Expr) : PreM Simp.Result := do
+  -- TODO: use `goal` state in the simplifier
   let simpStats := (← get).simpStats
   let (r, simpStats) ← Meta.simp e (← read).simp (← read).simprocs (stats := simpStats)
   modify fun s => { s with simpStats }
   return r
 
-def simpHyp? (mvarId : MVarId) (fvarId : FVarId) : PreM (Option (FVarId × MVarId)) := do
-  let simpStats := (← get).simpStats
-  let (result, simpStats) ← simpLocalDecl mvarId fvarId (← read).simp (← read).simprocs (stats := simpStats)
-  modify fun s => { s with simpStats }
-  return result
-
 inductive IntroResult where
   | done
   | newHyp (fvarId : FVarId) (goal : Goal)
+  | newDepHyp (goal : Goal)
   | newLocal (fvarId : FVarId) (goal : Goal)
 
 def introNext (goal : Goal) : PreM IntroResult := do
@@ -69,7 +69,7 @@ def introNext (goal : Goal) : PreM IntroResult := do
       else
         let tag ← goal.mvarId.getTag
         let q := target.bindingBody!
-        let r ← simp p
+        let r ← simp goal p
         let p' := r.expr
         let p' ← canon p'
         let p' ← shareCommon p'
@@ -95,44 +95,73 @@ def introNext (goal : Goal) : PreM IntroResult := do
       if (← isProp localDecl.type) then
         -- Add a non-dependent copy
         let mvarId ← mvarId.assert localDecl.userName localDecl.type (mkFVar fvarId)
-        return .newLocal fvarId { goal with mvarId }
+        return .newDepHyp { goal with mvarId }
       else
         return .newLocal fvarId { goal with mvarId }
   else
     return .done
 
 def pushResult (goal : Goal) : PreM Unit :=
-  modifyThe Grind.State fun s => { s with goals := s.goals.push goal }
+  modify fun s => { s with goals := s.goals.push goal }
 
-partial def preprocess (goal : Goal) : PreM Unit := do
-  trace[Meta.debug] "{goal.mvarId}"
+def isCasesCandidate (fvarId : FVarId) : MetaM Bool := do
+  let .const declName _ := (← fvarId.getType).getAppFn | return false
+  isGrindCasesTarget declName
+
+def applyCases? (goal : Goal) (fvarId : FVarId) : MetaM (Option (List Goal)) := goal.mvarId.withContext do
+  if (← isCasesCandidate fvarId) then
+    let mvarIds ← cases goal.mvarId fvarId
+    return mvarIds.map fun mvarId => { goal with mvarId }
+  else
+    return none
+
+def applyInjection? (goal : Goal) (fvarId : FVarId) : MetaM (Option Goal) := do
+  if let some mvarId ← injection? goal.mvarId fvarId then
+    return some { goal with mvarId }
+  else
+    return none
+
+partial def loop (goal : Goal) : PreM Unit := do
   match (← introNext goal) with
   | .done =>
     if let some mvarId ← goal.mvarId.byContra? then
-      preprocess { goal with mvarId }
+      loop { goal with mvarId }
     else
       pushResult goal
   | .newHyp fvarId goal =>
-    -- TODO: apply eliminators
-    let clause ← goal.mvarId.withContext do mkInputClause fvarId
-    preprocess { goal with clauses := goal.clauses.push clause }
-  | .newLocal _ goal =>
-    -- TODO: apply eliminators
-    preprocess goal
+    if let some goals ← applyCases? goal fvarId then
+      goals.forM loop
+    else if let some goal ← applyInjection? goal fvarId then
+      loop goal
+    else
+      let clause ← goal.mvarId.withContext do mkInputClause fvarId
+      loop { goal with clauses := goal.clauses.push clause }
+  | .newDepHyp goal =>
+    loop goal
+  | .newLocal fvarId goal =>
+    if let some goals ← applyCases? goal fvarId then
+      goals.forM loop
+    else
+      loop goal
+
+def preprocess (mvarId : MVarId) : PreM State := do
+  loop (← mkGoal mvarId)
+  get
 
 end Preprocessor
 
 open Preprocessor
 
-partial def main (mvarId : MVarId) (mainDeclName : Name) : MetaM Grind.State := do
+partial def main (mvarId : MVarId) (mainDeclName : Name) : MetaM (List MVarId) := do
   mvarId.ensureProp
   mvarId.ensureNoMVar
+  let mvarId ← mvarId.clearAuxDecls
   let mvarId ← mvarId.revertAll
   mvarId.ensureNoMVar
   let mvarId ← mvarId.abstractNestedProofs mainDeclName
   let mvarId ← mvarId.unfoldReducible
   let mvarId ← mvarId.betaReduce
-  let s ← (preprocess { mvarId } *> getThe Grind.State) |>.run |>.run mainDeclName
-  return s
+  let s ← preprocess mvarId |>.run |>.run mainDeclName
+  return s.goals.toList.map (·.mvarId)
 
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Types.lean

@@ -11,6 +11,47 @@ import Lean.Meta.Canonicalizer
 import Lean.Meta.Tactic.Util
 
 namespace Lean.Meta.Grind
+
+structure Context where
+  mainDeclName : Name
+
+structure State where
+  canon      : Canonicalizer.State := {}
+  /-- `ShareCommon` (aka `Hashconsing`) state. -/
+  scState    : ShareCommon.State.{0} ShareCommon.objectFactory := ShareCommon.State.mk _
+  /-- Next index for creating auxiliary theorems. -/
+  nextThmIdx : Nat := 1
+
+abbrev GrindM := ReaderT Context $ StateRefT State MetaM
+
+@[inline] def GrindM.run (x : GrindM α) (mainDeclName : Name) : MetaM α :=
+  x { mainDeclName } |>.run' {}
+
+def abstractNestedProofs (e : Expr) : GrindM Expr := do
+  let nextIdx := (← get).nextThmIdx
+  let (e, s') ← AbstractNestedProofs.visit e |>.run { baseName := (← read).mainDeclName } |>.run |>.run { nextIdx }
+  modify fun s => { s with nextThmIdx := s'.nextIdx }
+  return e
+
+def shareCommon (e : Expr) : GrindM Expr := do
+  modifyGet fun { canon, scState, nextThmIdx } =>
+    let (e, scState) := ShareCommon.State.shareCommon scState e
+    (e, { canon, scState, nextThmIdx })
+
+def canon (e : Expr) : GrindM Expr := do
+  let canonS ← modifyGet fun s => (s.canon, { s with canon := {} })
+  let (e, canonS) ← Canonicalizer.CanonM.run (canonRec e) (s := canonS)
+  modify fun s => { s with canon := canonS }
+  return e
+where
+  canonRec (e : Expr) : CanonM Expr := do
+    let post (e : Expr) : CanonM TransformStep := do
+      if e.isApp then
+        return .done (← Meta.canon e)
+      else
+        return .done e
+    transform e post
+
 /--
 Stores information for a node in the egraph.
 Each internalized expression `e` has an `ENode` associated with it.
@@ -43,6 +84,9 @@ structure ENode where
   on heterogeneous equality.
   -/
   heqProofs : Bool := false
+  generation : Nat := 0
+  /-- Modification time -/
+  mt : Nat := 0
   -- TODO: see Lean 3 implementation
 
 structure Clause where
@@ -53,58 +97,57 @@ structure Clause where
 def mkInputClause (fvarId : FVarId) : MetaM Clause :=
   return { expr := (← fvarId.getType), proof := mkFVar fvarId }
 
-structure Goal where
-  mvarId  : MVarId
-  clauses : PArray Clause := {}
-  enodes  : PHashMap UInt64 ENode := {}
-  -- TODO: occurrences for propagation, etc
-  deriving Inhabited
+structure NewEq where
+  lhs   : Expr
+  rhs   : Expr
+  proof : Expr
+  isHEq : Bool
 
-def mkGoal (mvarId : MVarId) : Goal :=
-  { mvarId }
+structure Goal where
+  mvarId       : MVarId
+  clauses      : PArray Clause := {}
+  enodes       : PHashMap USize ENode := {}
+  newEqs       : Array NewEq := #[]
+  /-- `inconsistent := true` if `ENode`s for `True` and `False` are in the same equivalence class. -/
+  inconsistent : Bool := false
+  /-- Goal modification time. -/
+  gmt          : Nat := 0
+  deriving Inhabited
 
 def Goal.admit (goal : Goal) : MetaM Unit :=
   goal.mvarId.admit
 
-structure Context where
-  mainDeclName : Name
+abbrev GoalM := StateRefT Goal GrindM
 
-structure State where
-  canon      : Canonicalizer.State := {}
-  /-- `ShareCommon` (aka `Hashconsing`) state. -/
-  scState    : ShareCommon.State.{0} ShareCommon.objectFactory := ShareCommon.State.mk _
-  /-- Next index for creating auxiliary theorems. -/
-  nextThmIdx : Nat := 1
-  goals      : PArray Goal := {}
+@[inline] def GoalM.run (goal : Goal) (x : GoalM α) : GrindM (α × Goal) :=
+  StateRefT'.run x goal
 
-abbrev GrindM := ReaderT Context $ StateRefT State MetaM
+@[inline] def GoalM.run' (goal : Goal) (x : GoalM Unit) : GrindM Goal :=
+  StateRefT'.run' (x *> get) goal
 
-def GrindM.run (x : GrindM α) (mainDeclName : Name) : MetaM α :=
-  x { mainDeclName } |>.run' {}
+/--
+Returns `some n` if `e` has already been "internalized" into the
+Otherwise, returns `none`s.
+-/
+def getENode? (e : Expr) : GoalM (Option ENode) :=
+  return (← get).enodes.find? (unsafe ptrAddrUnsafe e)
 
-def abstractNestedProofs (e : Expr) : GrindM Expr := do
-  let nextIdx := (← get).nextThmIdx
-  let (e, s') ← AbstractNestedProofs.visit e |>.run { baseName := (← read).mainDeclName } |>.run |>.run { nextIdx }
-  modify fun s => { s with nextThmIdx := s'.nextIdx }
-  return e
+def setENode (e : Expr) (n : ENode) : GoalM Unit :=
+  modify fun s => { s with enodes := s.enodes.insert (unsafe ptrAddrUnsafe e) n }
 
-def shareCommon (e : Expr) : GrindM Expr := do
-  modifyGet fun { canon, scState, nextThmIdx, goals } =>
-    let (e, scState) := ShareCommon.State.shareCommon scState e
-    (e, { canon, scState, nextThmIdx, goals })
+def mkENodeCore (e : Expr) (interpreted ctor : Bool) (generation : Nat) : GoalM Unit := do
+  setENode e {
+    next := e, root := e, cgRoot := e, size := 1
+    flipped := false
+    heqProofs := false
+    hasLambdas := e.isLambda
+    mt := (← get).gmt
+    interpreted, ctor, generation
+  }
 
-def canon (e : Expr) : GrindM Expr := do
-  let canonS ← modifyGet fun s => (s.canon, { s with canon := {} })
-  let (e, canonS) ← Canonicalizer.CanonM.run (canonRec e) (s := canonS)
-  modify fun s => { s with canon := canonS }
-  return e
-where
-  canonRec (e : Expr) : CanonM Expr := do
-    let post (e : Expr) : CanonM TransformStep := do
-      if e.isApp then
-        return .done (← Meta.canon e)
-      else
-        return .done e
-    transform e post
+def mkGoal (mvarId : MVarId) : GrindM Goal := do
+  GoalM.run' { mvarId } do
+    mkENodeCore (← shareCommon (mkConst ``True)) (interpreted := true) (ctor := false) (generation := 0)
+    mkENodeCore (← shareCommon (mkConst ``False)) (interpreted := true) (ctor := false) (generation := 0)
 
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Grind/Util.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Lean.Meta.AbstractNestedProofs
 import Lean.Meta.Tactic.Util
+import Lean.Meta.Tactic.Clear
 
 namespace Lean.Meta.Grind
 /--
@@ -66,7 +67,7 @@ def _root_.Lean.MVarId.betaReduce (mvarId : MVarId) : MetaM MVarId :=
 If the target is not `False`, apply `byContradiction`.
 -/
 def _root_.Lean.MVarId.byContra? (mvarId : MVarId) : MetaM (Option MVarId) := mvarId.withContext do
-  mvarId.checkNotAssigned `grind
+  mvarId.checkNotAssigned `grind.by_contra
   let target ← mvarId.getType
   if target.isFalse then return none
   let targetNew ← mkArrow (mkNot target) (mkConst ``False)
@@ -75,4 +76,24 @@ def _root_.Lean.MVarId.byContra? (mvarId : MVarId) : MetaM (Option MVarId) := mv
   mvarId.assign <| mkApp2 (mkConst ``Classical.byContradiction) target mvarNew
   return mvarNew.mvarId!
 
+/--
+Clear auxiliary decls used to encode recursive declarations.
+`grind` eliminates them to ensure they are not accidentaly used by its proof automation.
+-/
+def _root_.Lean.MVarId.clearAuxDecls (mvarId : MVarId) : MetaM MVarId := mvarId.withContext do
+  mvarId.checkNotAssigned `grind.clear_aux_decls
+  let mut toClear := []
+  for localDecl in (← getLCtx) do
+    if localDecl.isAuxDecl then
+      toClear := localDecl.fvarId :: toClear
+  if toClear.isEmpty then
+    return mvarId
+  let mut mvarId := mvarId
+  for fvarId in toClear do
+    try
+      mvarId ← mvarId.clear fvarId
+    catch _ =>
+      throwTacticEx `grind.clear_aux_decls mvarId "failed to clear local auxiliary declaration"
+  return mvarId
+
 end Lean.Meta.Grind

src/Lean/Meta/Tactic/Induction.lean

@@ -120,8 +120,75 @@ private partial def finalize
       pure subgoals
   loop (recursorInfo.paramsPos.length + 1) 0 recursor recursorType false #[]
 
-private def throwUnexpectedMajorType {α} (mvarId : MVarId) (majorType : Expr) : MetaM α :=
-  throwTacticEx `induction mvarId m!"unexpected major premise type{indentExpr majorType}"
+private def throwUnexpectedMajorType (tacticName : Name) (mvarId : MVarId) (majorType : Expr) : MetaM α :=
+  throwTacticEx tacticName mvarId m!"unexpected major premise type{indentExpr majorType}"
+
+/--
+Auxiliary method for implementing `induction`-like tactics.
+It retrieves indices from `majorType` using `recursorInfo`.
+Remark: `mvarId` and `tacticName` are used to generate error messages.
+-/
+def getMajorTypeIndices (mvarId : MVarId) (tacticName : Name) (recursorInfo : RecursorInfo) (majorType : Expr) : MetaM (Array Expr) := do
+  let majorTypeArgs := majorType.getAppArgs
+  recursorInfo.indicesPos.toArray.mapM fun idxPos => do
+    if idxPos ≥ majorTypeArgs.size then throwTacticEx tacticName mvarId m!"major premise type is ill-formed{indentExpr majorType}"
+    let idx := majorTypeArgs.get! idxPos
+    unless idx.isFVar do throwTacticEx tacticName mvarId m!"major premise type index {idx} is not a variable{indentExpr majorType}"
+    majorTypeArgs.size.forM fun i => do
+      let arg := majorTypeArgs[i]!
+      if i != idxPos && arg == idx then
+        throwTacticEx tacticName mvarId m!"'{idx}' is an index in major premise, but it occurs more than once{indentExpr majorType}"
+      if i < idxPos then
+        if (← exprDependsOn arg idx.fvarId!) then
+          throwTacticEx tacticName mvarId m!"'{idx}' is an index in major premise, but it occurs in previous arguments{indentExpr majorType}"
+      -- If arg is also and index and a variable occurring after `idx`, we need to make sure it doesn't depend on `idx`.
+      -- Note that if `arg` is not a variable, we will fail anyway when we visit it.
+      if i > idxPos && recursorInfo.indicesPos.contains i && arg.isFVar then
+        let idxDecl ← idx.fvarId!.getDecl
+        if (← localDeclDependsOn idxDecl arg.fvarId!) then
+          throwTacticEx tacticName mvarId m!"'{idx}' is an index in major premise, but it depends on index occurring at position #{i+1}"
+    return idx
+
+/--
+Auxiliary method for implementing `induction`-like tactics.
+It creates the prefix of a recursor application up-to `motive`.
+The motive is computed by abstracting `major` and `indices` at `mvarId.getType`.
+It retrieves indices from `majorType` using `recursorInfo`.
+Remark: `mvarId` and `tacticName` are used to generate error messages.
+-/
+def mkRecursorAppPrefix (mvarId : MVarId) (tacticName : Name) (majorFVarId : FVarId) (recursorInfo : RecursorInfo) (indices : Array Expr) : MetaM Expr := do
+  let major := mkFVar majorFVarId
+  let target ← mvarId.getType
+  let targetLevel ← getLevel target
+  let targetLevel ← normalizeLevel targetLevel
+  let majorLocalDecl ← majorFVarId.getDecl
+  let some majorType ← whnfUntil majorLocalDecl.type recursorInfo.typeName
+    | throwUnexpectedMajorType tacticName mvarId majorLocalDecl.type
+  majorType.withApp fun majorTypeFn majorTypeArgs => do
+    match majorTypeFn with
+    | .const _ majorTypeFnLevels => do
+      let majorTypeFnLevels := majorTypeFnLevels.toArray
+      let (recursorLevels, foundTargetLevel) ← recursorInfo.univLevelPos.foldlM (init := (#[], false))
+          fun (recursorLevels, foundTargetLevel) (univPos : RecursorUnivLevelPos) => do
+            match univPos with
+            | RecursorUnivLevelPos.motive => pure (recursorLevels.push targetLevel, true)
+            | RecursorUnivLevelPos.majorType idx =>
+              if idx ≥ majorTypeFnLevels.size then throwTacticEx tacticName mvarId "ill-formed recursor"
+              pure (recursorLevels.push (majorTypeFnLevels.get! idx), foundTargetLevel)
+      if !foundTargetLevel && !targetLevel.isZero then
+        throwTacticEx tacticName mvarId m!"recursor '{recursorInfo.recursorName}' can only eliminate into Prop"
+      let recursor := mkConst recursorInfo.recursorName recursorLevels.toList
+      let recursor ← addRecParams mvarId majorTypeArgs recursorInfo.paramsPos recursor
+      -- Compute motive
+      let motive := target
+      let motive ← if recursorInfo.depElim then
+        pure <| mkLambda `x BinderInfo.default (← inferType major) (← motive.abstractM #[major])
+      else
+        pure motive
+      let motive ← mkLambdaFVars indices motive
+      return mkApp recursor motive
+    | _ =>
+      throwTacticEx tacticName mvarId "major premise is not of the form (C ...)"
 
 def _root_.Lean.MVarId.induction (mvarId : MVarId) (majorFVarId : FVarId) (recursorName : Name) (givenNames : Array AltVarNames := #[]) : MetaM (Array InductionSubgoal) :=
   mvarId.withContext do
@@ -129,30 +196,14 @@ def _root_.Lean.MVarId.induction (mvarId : MVarId) (majorFVarId : FVarId) (recur
     mvarId.checkNotAssigned `induction
     let majorLocalDecl ← majorFVarId.getDecl
     let recursorInfo ← mkRecursorInfo recursorName
-    let some majorType ← whnfUntil majorLocalDecl.type recursorInfo.typeName | throwUnexpectedMajorType mvarId majorLocalDecl.type
+    let some majorType ← whnfUntil majorLocalDecl.type recursorInfo.typeName
+      | throwUnexpectedMajorType `induction mvarId majorLocalDecl.type
     majorType.withApp fun _ majorTypeArgs => do
       recursorInfo.paramsPos.forM fun paramPos? => do
         match paramPos? with
         | none          => pure ()
         | some paramPos => if paramPos ≥ majorTypeArgs.size then throwTacticEx `induction mvarId m!"major premise type is ill-formed{indentExpr majorType}"
-      let indices ← recursorInfo.indicesPos.toArray.mapM fun idxPos => do
-        if idxPos ≥ majorTypeArgs.size then throwTacticEx `induction mvarId m!"major premise type is ill-formed{indentExpr majorType}"
-        let idx := majorTypeArgs.get! idxPos
-        unless idx.isFVar do throwTacticEx `induction mvarId m!"major premise type index {idx} is not a variable{indentExpr majorType}"
-        majorTypeArgs.size.forM fun i => do
-          let arg := majorTypeArgs[i]!
-          if i != idxPos && arg == idx then
-            throwTacticEx `induction mvarId m!"'{idx}' is an index in major premise, but it occurs more than once{indentExpr majorType}"
-          if i < idxPos then
-            if (← exprDependsOn arg idx.fvarId!) then
-              throwTacticEx `induction mvarId m!"'{idx}' is an index in major premise, but it occurs in previous arguments{indentExpr majorType}"
-          -- If arg is also and index and a variable occurring after `idx`, we need to make sure it doesn't depend on `idx`.
-          -- Note that if `arg` is not a variable, we will fail anyway when we visit it.
-          if i > idxPos && recursorInfo.indicesPos.contains i && arg.isFVar then
-            let idxDecl ← idx.fvarId!.getDecl
-            if (← localDeclDependsOn idxDecl arg.fvarId!) then
-              throwTacticEx `induction mvarId m!"'{idx}' is an index in major premise, but it depends on index occurring at position #{i+1}"
-        pure idx
+      let indices ← getMajorTypeIndices mvarId `induction recursorInfo majorType
       let target ← mvarId.getType
       if (← pure !recursorInfo.depElim <&&> exprDependsOn target majorFVarId) then
         throwTacticEx `induction mvarId m!"recursor '{recursorName}' does not support dependent elimination, but conclusion depends on major premise"
@@ -175,37 +226,8 @@ def _root_.Lean.MVarId.induction (mvarId : MVarId) (majorFVarId : FVarId) (recur
       let majorFVarId := majorFVarId'
       let major := mkFVar majorFVarId
       mvarId.withContext do
-        let target ← mvarId.getType
-        let targetLevel ← getLevel target
-        let targetLevel ← normalizeLevel targetLevel
-        let majorLocalDecl ← majorFVarId.getDecl
-        let some majorType ← whnfUntil majorLocalDecl.type recursorInfo.typeName | throwUnexpectedMajorType mvarId majorLocalDecl.type
-        majorType.withApp fun majorTypeFn majorTypeArgs => do
-          match majorTypeFn with
-          | Expr.const _ majorTypeFnLevels => do
-            let majorTypeFnLevels := majorTypeFnLevels.toArray
-            let (recursorLevels, foundTargetLevel) ← recursorInfo.univLevelPos.foldlM (init := (#[], false))
-                fun (recursorLevels, foundTargetLevel) (univPos : RecursorUnivLevelPos) => do
-                  match univPos with
-                  | RecursorUnivLevelPos.motive => pure (recursorLevels.push targetLevel, true)
-                  | RecursorUnivLevelPos.majorType idx =>
-                    if idx ≥ majorTypeFnLevels.size then throwTacticEx `induction mvarId "ill-formed recursor"
-                    pure (recursorLevels.push (majorTypeFnLevels.get! idx), foundTargetLevel)
-            if !foundTargetLevel && !targetLevel.isZero then
-              throwTacticEx `induction mvarId m!"recursor '{recursorName}' can only eliminate into Prop"
-            let recursor := mkConst recursorName recursorLevels.toList
-            let recursor ← addRecParams mvarId majorTypeArgs recursorInfo.paramsPos recursor
-            -- Compute motive
-            let motive := target
-            let motive ← if recursorInfo.depElim then
-              pure <| mkLambda `x BinderInfo.default (← inferType major) (← motive.abstractM #[major])
-            else
-              pure motive
-            let motive ← mkLambdaFVars indices motive
-            let recursor := mkApp recursor motive
-            finalize mvarId givenNames recursorInfo reverted major indices baseSubst recursor
-          | _ =>
-           throwTacticEx `induction mvarId "major premise is not of the form (C ...)"
+        let recursor ← mkRecursorAppPrefix mvarId `induction majorFVarId recursorInfo indices
+        finalize mvarId givenNames recursorInfo reverted major indices baseSubst recursor
 
 @[deprecated MVarId.induction (since := "2022-07-15")]
 def induction (mvarId : MVarId) (majorFVarId : FVarId) (recursorName : Name) (givenNames : Array AltVarNames := #[]) : MetaM (Array InductionSubgoal) :=

src/Lean/Meta/Tactic/Simp/SimpTheorems.lean

@@ -221,13 +221,14 @@ partial def SimpTheorems.eraseCore (d : SimpTheorems) (thmId : Origin) : SimpThe
   else
     d
 
-def SimpTheorems.erase [Monad m] [MonadError m] (d : SimpTheorems) (thmId : Origin) : m SimpTheorems := do
+def SimpTheorems.erase [Monad m] [MonadLog m] [AddMessageContext m] [MonadOptions m]
+    (d : SimpTheorems) (thmId : Origin) : m SimpTheorems := do
   unless d.isLemma thmId ||
     match thmId with
     | .decl declName .. => d.isDeclToUnfold declName || d.toUnfoldThms.contains declName
     | _ => false
   do
-    throwError "'{thmId.key}' does not have [simp] attribute"
+    logWarning m!"'{thmId.key}' does not have [simp] attribute"
   return d.eraseCore thmId
 
 private partial def isPerm : Expr → Expr → MetaM Bool

src/Lean/Meta/Tactic/UnifyEq.lean

@@ -21,6 +21,11 @@ structure UnifyEqResult where
   subst     : FVarSubst
   numNewEqs : Nat := 0
 
+private def toOffset? (e : Expr) : MetaM (Option (Expr × Nat)) := do
+  match (← evalNat e) with
+  | some k => return some (mkNatLit 0, k)
+  | none => isOffset? e
+
 /--
   Helper method for methods such as `Cases.unifyEqs?`.
   Given the given goal `mvarId` containing the local hypothesis `eqFVarId`, it performs the following operations:
@@ -69,7 +74,30 @@ def unifyEq? (mvarId : MVarId) (eqFVarId : FVarId) (subst : FVarSubst := {})
             return none -- this alternative has been solved
           else
             throwError "dependent elimination failed, failed to solve equation{indentExpr eqDecl.type}"
+        /- Special support for offset equalities -/
+        let injectionOffset? (a b : Expr) := do
+          unless (← getEnv).contains ``Nat.elimOffset do return none
+          let some (xa, ka) ← toOffset? a | return none
+          let some (xb, kb) ← toOffset? b | return none
+          if ka == 0 || kb == 0 then return none -- use default noConfusion
+          let (x, y, k) ← if ka < kb then
+            pure (xa, (← mkAdd xb (mkNatLit (kb - ka))), ka)
+          else if ka = kb then
+            pure (xa, xb, ka)
+          else
+            pure ((← mkAdd xa (mkNatLit (ka - kb))), xb, kb)
+          let target ← mvarId.getType
+          let u ← getLevel target
+          let newTarget ← mkArrow (← mkEq x y) target
+          let tag ← mvarId.getTag
+          let newMVar ← mkFreshExprSyntheticOpaqueMVar newTarget tag
+          let val := mkAppN (mkConst ``Nat.elimOffset [u]) #[target, x, y, mkNatLit k, eqDecl.toExpr, newMVar]
+          mvarId.assign val
+          let mvarId ← newMVar.mvarId!.tryClear eqDecl.fvarId
+          return some mvarId
         let rec injection (a b : Expr) := do
+          if let some mvarId ← injectionOffset? a b then
+            return some { mvarId, numNewEqs := 1, subst }
           if (← isConstructorApp a <&&> isConstructorApp b) then
             /- ctor_i ... = ctor_j ... -/
             match (← injectionCore mvarId eqFVarId) with

src/Lean/Parser/Basic.lean

@@ -558,6 +558,8 @@ partial def whitespace : ParserFn := fun c s =>
     let curr := input.get' i h
     if curr == '\t' then
       s.mkUnexpectedError (pushMissing := false) "tabs are not allowed; please configure your editor to expand them"
+    else if curr == '\r' then
+      s.mkUnexpectedError (pushMissing := false) "isolated carriage returns are not allowed"
     else if curr.isWhitespace then whitespace c (s.next' input i h)
     else if curr == '-' then
       let i    := input.next' i h
@@ -621,9 +623,8 @@ def hexDigitFn : ParserFn := fun c s =>
 /--
 Parses the whitespace after the `\` when there is a string gap.
 Raises an error if the whitespace does not contain exactly one newline character.
-Processes `\r\n` as a newline.
 -/
-partial def stringGapFn (seenNewline afterCR : Bool) : ParserFn := fun c s =>
+partial def stringGapFn (seenNewline : Bool) : ParserFn := fun c s =>
   let i := s.pos
   if h : c.input.atEnd i then s -- let strLitFnAux handle the EOI error if !seenNewline
   else
@@ -633,13 +634,9 @@ partial def stringGapFn (seenNewline afterCR : Bool) : ParserFn := fun c s =>
         -- Having more than one newline in a string gap is visually confusing
         s.mkUnexpectedError "unexpected additional newline in string gap"
       else
-        stringGapFn true false c (s.next' c.input i h)
-    else if curr == '\r' then
-      stringGapFn seenNewline true c (s.next' c.input i h)
-    else if afterCR then
-      s.mkUnexpectedError "expecting newline after carriage return"
+        stringGapFn true c (s.next' c.input i h)
     else if curr.isWhitespace then
-      stringGapFn seenNewline false c (s.next' c.input i h)
+      stringGapFn seenNewline c (s.next' c.input i h)
     else if seenNewline then
       s
     else
@@ -663,8 +660,8 @@ def quotedCharCoreFn (isQuotable : Char → Bool) (inString : Bool) : ParserFn :
       andthenFn hexDigitFn hexDigitFn c (s.next' input i h)
     else if curr == 'u' then
       andthenFn hexDigitFn (andthenFn hexDigitFn (andthenFn hexDigitFn hexDigitFn)) c (s.next' input i h)
-    else if inString && (curr == '\n' || curr == '\r') then
-      stringGapFn false false c s
+    else if inString && curr == '\n' then
+      stringGapFn false c s
     else
       s.mkUnexpectedError "invalid escape sequence"
 

src/Lean/Parser/Command.lean

@@ -94,8 +94,41 @@ def declSig          := leading_parser
 /-- `optDeclSig` matches the signature of a declaration with optional type: a list of binders and then possibly `: type` -/
 def optDeclSig       := leading_parser
   many (ppSpace >> (Term.binderIdent <|> Term.bracketedBinder)) >> Term.optType
+/-- Right-hand side of a `:=` in a declaration, a term. -/
+def declBody : Parser :=
+  /-
+  We want to make sure that bodies starting with `by` in fact create a single `by` node instead of
+  accidentally parsing some remnants after it as well. This can especially happen when starting to
+  type comments inside tactic blocks where
+  ```
+  by
+    sleep 2000
+    unfold f
+    -starting comment here
+  ```
+  is parsed as
+  ```
+  (by
+    sleep 2000
+    unfold f
+    ) - (starting comment here)
+  ```
+  where the new nesting will discard incrementality data. By using `byTactic`'s precedence, the
+  stray `-` will be flagged as an unexpected token and will not disturb the syntax tree up to it. We
+  do not call `byTactic` directly to avoid differences in pretty printing or behavior or error
+  reporting between the two branches.
+  -/
+  lookahead (setExpected [] "by") >> termParser leadPrec <|>
+  termParser
+
+-- As the pretty printer ignores `lookahead`, we need a custom parenthesizer to choose the correct
+-- precedence
+open PrettyPrinter in
+@[combinator_parenthesizer declBody] def declBody.parenthesizer : Parenthesizer :=
+  Parenthesizer.categoryParser.parenthesizer `term 0
+
 def declValSimple    := leading_parser
-  " :=" >> ppHardLineUnlessUngrouped >> termParser >> Termination.suffix >> optional Term.whereDecls
+  " :=" >> ppHardLineUnlessUngrouped >> declBody >> Termination.suffix >> optional Term.whereDecls
 def declValEqns      := leading_parser
   Term.matchAltsWhereDecls
 def whereStructField := leading_parser

src/Lean/Parser/Extension.lean

@@ -437,11 +437,12 @@ def getSyntaxNodeKinds (env : Environment) : List SyntaxNodeKind :=
 def getTokenTable (env : Environment) : TokenTable :=
   (parserExtension.getState env).tokens
 
-def mkInputContext (input : String) (fileName : String) : InputContext := {
-  input    := input,
-  fileName := fileName,
-  fileMap  := input.toFileMap
-}
+-- Note: `crlfToLf` preserves logical line and column numbers for each character.
+def mkInputContext (input : String) (fileName : String) (normalizeLineEndings := true) : InputContext :=
+  let input' := if normalizeLineEndings then input.crlfToLf else input
+  { input    := input',
+    fileName := fileName,
+    fileMap  := input'.toFileMap }
 
 def mkParserState (input : String) : ParserState :=
   { cache := initCacheForInput input }
@@ -453,7 +454,7 @@ def runParserCategory (env : Environment) (catName : Name) (input : String) (fil
   let s := p.run ictx { env, options := {} } (getTokenTable env) (mkParserState input)
   if !s.allErrors.isEmpty  then
     Except.error (s.toErrorMsg ictx)
-  else if input.atEnd s.pos then
+  else if ictx.input.atEnd s.pos then
     Except.ok s.stxStack.back
   else
     Except.error ((s.mkError "end of input").toErrorMsg ictx)
@@ -614,15 +615,30 @@ def withOpenDeclFn (p : ParserFn) : ParserFn := fun c s =>
 
 @[inline] def withOpenDecl : Parser → Parser := withFn withOpenDeclFn
 
-inductive ParserName
+/--
+Helper environment extension that gives us access to built-in aliases in pure parser functions.
+-/
+builtin_initialize aliasExtension : EnvExtension (NameMap ParserAliasValue) ←
+  registerEnvExtension parserAliasesRef.get
+
+/-- Result of resolving a parser name. -/
+inductive ParserResolution where
+  /-- Reference to a category. -/
   | category (cat : Name)
+  /--
+  Reference to a parser declaration in the environment.  A `(Trailing)ParserDescr` if `isDescr` is
+  true.
+  -/
   | parser (decl : Name) (isDescr : Bool)
-  -- TODO(gabriel): add parser aliases (this is blocked on doing IO in parsers)
-  deriving Repr
+  /--
+  Reference to a parser alias. Note that as aliases are built-in, a corresponding declaration may
+  not be in the environment (yet).
+  -/
+  | alias (p : ParserAliasValue)
 
 /-- Resolve the given parser name and return a list of candidates. -/
 def resolveParserNameCore (env : Environment) (currNamespace : Name)
-    (openDecls : List OpenDecl) (ident : Ident) : List ParserName := Id.run do
+    (openDecls : List OpenDecl) (ident : Ident) : List ParserResolution := Id.run do
   let ⟨.ident (val := val) (preresolved := pre) ..⟩ := ident | return []
 
   let rec isParser (name : Name) : Option Bool :=
@@ -642,16 +658,24 @@ def resolveParserNameCore (env : Environment) (currNamespace : Name)
   if isParserCategory env erased then
     return [.category erased]
 
-  ResolveName.resolveGlobalName env currNamespace openDecls val |>.filterMap fun
-      | (name, []) => (isParser name).map fun isDescr => .parser name isDescr
-      | _ => none
+  let resolved ← ResolveName.resolveGlobalName env currNamespace openDecls val |>.filterMap fun
+    | (name, []) => (isParser name).map fun isDescr => .parser name isDescr
+    | _ => none
+  unless resolved.isEmpty do
+    return resolved
+
+  -- Aliases are considered global declarations and so should be tried after scope-aware resolution
+  if let some alias := aliasExtension.getState env |>.find? erased then
+    return [.alias alias]
+
+  return []
 
 /-- Resolve the given parser name and return a list of candidates. -/
-def ParserContext.resolveParserName (ctx : ParserContext) (id : Ident) : List ParserName :=
+def ParserContext.resolveParserName (ctx : ParserContext) (id : Ident) : List ParserResolution :=
   Parser.resolveParserNameCore ctx.env ctx.currNamespace ctx.openDecls id
 
 /-- Resolve the given parser name and return a list of candidates. -/
-def resolveParserName (id : Ident) : CoreM (List ParserName) :=
+def resolveParserName (id : Ident) : CoreM (List ParserResolution) :=
   return resolveParserNameCore (← getEnv) (← getCurrNamespace) (← getOpenDecls) id
 
 def parserOfStackFn (offset : Nat) : ParserFn := fun ctx s => Id.run do
@@ -660,23 +684,27 @@ def parserOfStackFn (offset : Nat) : ParserFn := fun ctx s => Id.run do
     return s.mkUnexpectedError ("failed to determine parser using syntax stack, stack is too small")
   let parserName@(.ident ..) := stack.get! (stack.size - offset - 1)
     | s.mkUnexpectedError ("failed to determine parser using syntax stack, the specified element on the stack is not an identifier")
-  match ctx.resolveParserName ⟨parserName⟩ with
-  | [.category cat] =>
-    categoryParserFn cat ctx s
-  | [.parser parserName _] =>
-    let iniSz := s.stackSize
-    let s := adaptUncacheableContextFn (fun ctx =>
-      if !internal.parseQuotWithCurrentStage.get ctx.options then
-        -- static quotations such as `(e) do not use the interpreter unless the above option is set,
-        -- so for consistency neither should dynamic quotations using this function
-        { ctx with options := ctx.options.setBool `interpreter.prefer_native true }
-      else ctx) (evalParserConst parserName) ctx s
-    if !s.hasError && s.stackSize != iniSz + 1 then
-      s.mkUnexpectedError "expected parser to return exactly one syntax object"
-    else
-      s
-  | _::_::_ => s.mkUnexpectedError s!"ambiguous parser name {parserName}"
-  | [] => s.mkUnexpectedError s!"unknown parser {parserName}"
+  let iniSz := s.stackSize
+  let s ← match ctx.resolveParserName ⟨parserName⟩ with
+    | [.category cat] =>
+      categoryParserFn cat ctx s
+    | [.parser parserName _] =>
+      adaptUncacheableContextFn (fun ctx =>
+        if !internal.parseQuotWithCurrentStage.get ctx.options then
+          -- static quotations such as `(e) do not use the interpreter unless the above option is set,
+          -- so for consistency neither should dynamic quotations using this function
+          { ctx with options := ctx.options.setBool `interpreter.prefer_native true }
+        else ctx) (evalParserConst parserName) ctx s
+    | [.alias alias] =>
+      match alias with
+      | .const p => p.fn ctx s
+      | _ =>
+        return s.mkUnexpectedError s!"parser alias {parserName}, must not take parameters"
+    | _::_::_ => return s.mkUnexpectedError s!"ambiguous parser name {parserName}"
+    | [] => return s.mkUnexpectedError s!"unknown parser {parserName}"
+  if !s.hasError && s.stackSize != iniSz + 1 then
+    return s.mkUnexpectedError "expected parser to return exactly one syntax object"
+  s
 
 def parserOfStack (offset : Nat) (prec : Nat := 0) : Parser where
   fn := adaptCacheableContextFn ({ · with prec }) (parserOfStackFn offset)

src/Lean/Parser/Module.lean

@@ -141,7 +141,7 @@ partial def testParseModuleAux (env : Environment) (inputCtx : InputContext) (s
     match parseCommand inputCtx { env := env, options := {} } state msgs with
     | (stx, state, msgs) =>
       if isTerminalCommand stx then
-        if msgs.isEmpty then
+        if !msgs.hasUnreported then
           pure stxs
         else do
           msgs.forM fun msg => msg.toString >>= IO.println

src/Lean/Parser/Term.lean

@@ -542,8 +542,11 @@ It is often used when building macros.
 @[builtin_term_parser] def «let_tmp» := leading_parser:leadPrec
   withPosition ("let_tmp " >> letDecl) >> optSemicolon termParser
 
+def haveId := leading_parser (withAnonymousAntiquot := false)
+  (ppSpace >> binderIdent) <|> hygieneInfo
 /- like `let_fun` but with optional name -/
-def haveIdLhs    := ((ppSpace >> binderIdent) <|> hygieneInfo) >> many (ppSpace >> letIdBinder) >> optType
+def haveIdLhs    :=
+  haveId >> many (ppSpace >> letIdBinder) >> optType
 def haveIdDecl   := leading_parser (withAnonymousAntiquot := false)
   atomic (haveIdLhs >> " := ") >> termParser
 def haveEqnsDecl := leading_parser (withAnonymousAntiquot := false)
@@ -786,7 +789,7 @@ def isIdent (stx : Syntax) : Bool :=
   checkStackTop isIdent "expected preceding identifier" >>
   checkNoWsBefore "no space before '.{'" >> ".{" >>
   sepBy1 levelParser ", " >> "}"
-/-- `x@e` or `x:h@e` matches the pattern `e` and binds its value to the identifier `x`.
+/-- `x@e` or `x@h:e` matches the pattern `e` and binds its value to the identifier `x`.
 If present, the identifier `h` is bound to a proof of `x = e`. -/
 @[builtin_term_parser] def namedPattern : TrailingParser := trailing_parser
   checkStackTop isIdent "expected preceding identifier" >>

src/Lean/Server/FileWorker.lean

@@ -196,7 +196,7 @@ This option can only be set on the command line, not in the lakefile or via `set
         return .pure ()
   where
     go (node : SnapshotTree) (st : ReportSnapshotsState) : BaseIO (Task ReportSnapshotsState) := do
-      if !node.element.diagnostics.msgLog.isEmpty then
+      if node.element.diagnostics.msgLog.hasUnreported then
         let diags ←
           if let some memorized ← node.element.diagnostics.interactiveDiagsRef?.bindM fun ref => do
               return (← ref.get).bind (·.get? MemorizedInteractiveDiagnostics) then
@@ -705,12 +705,9 @@ def initAndRunWorker (i o e : FS.Stream) (opts : Options) : IO UInt32 := do
   let initParams ← i.readLspRequestAs "initialize" InitializeParams
   let ⟨_, param⟩ ← i.readLspNotificationAs "textDocument/didOpen" LeanDidOpenTextDocumentParams
   let doc := param.textDocument
-  /- NOTE(WN): `toFileMap` marks line beginnings as immediately following
-    "\n", which should be enough to handle both LF and CRLF correctly.
-    This is because LSP always refers to characters by (line, column),
-    so if we get the line number correct it shouldn't matter that there
-    is a CR there. -/
-  let meta : DocumentMeta := ⟨doc.uri, doc.version, doc.text.toFileMap, param.dependencyBuildMode?.getD .always⟩
+  /- Note (kmill): LSP always refers to characters by (line, column),
+     so converting CRLF to LF preserves line and column numbers. -/
+  let meta : DocumentMeta := ⟨doc.uri, doc.version, doc.text.crlfToLf.toFileMap, param.dependencyBuildMode?.getD .always⟩
   let e := e.withPrefix s!"[{param.textDocument.uri}] "
   let _ ← IO.setStderr e
   let (ctx, st) ← try

src/Lean/Server/FileWorker/Utils.lean

@@ -15,22 +15,6 @@ namespace Lean.Server.FileWorker
 open Snapshots
 open IO
 
-structure CancelToken where
-  ref : IO.Ref Bool
-
-namespace CancelToken
-
-def new : IO CancelToken :=
-  CancelToken.mk <$> IO.mkRef false
-
-def set (tk : CancelToken) : BaseIO Unit :=
-  tk.ref.set true
-
-def isSet (tk : CancelToken) : BaseIO Bool :=
-  tk.ref.get
-
-end CancelToken
-
 -- TEMP: translate from new heterogeneous snapshot tree to old homogeneous async list
 private partial def mkCmdSnaps (initSnap : Language.Lean.InitialSnapshot) :
     AsyncList IO.Error Snapshot := Id.run do
@@ -49,7 +33,7 @@ where
         stx := cmdParsed.data.stx
         mpState := cmdParsed.data.parserState
         cmdState := finished.cmdState
-      } (match cmdParsed.next? with
+      } (match cmdParsed.nextCmdSnap? with
         | some next => .delayed <| next.task.bind go
         | none => .nil)
 

src/Lean/Server/Snapshots.lean

@@ -59,6 +59,7 @@ def runCommandElabM (snap : Snapshot) (meta : DocumentMeta) (c : CommandElabM α
     fileMap := meta.text,
     tacticCache? := none
     snap? := none
+    cancelTk? := none
   }
   c.run ctx |>.run' snap.cmdState
 

src/Lean/Server/Utils.lean

@@ -75,7 +75,10 @@ structure DocumentMeta where
   uri                 : Lsp.DocumentUri
   /-- Version number of the document. Incremented whenever the document is edited. -/
   version             : Nat
-  /-- Current text of the document. -/
+  /--
+  Current text of the document.
+  It is maintained such that it is normalized using `String.crlfToLf`, which preserves logical line/column numbers.
+  (Note: we assume that edit operations never split or merge `\r\n` line endings.) -/
   text                : FileMap
   /--
   Controls when dependencies of the document are built on `textDocument/didOpen` notifications.
@@ -98,7 +101,11 @@ def replaceLspRange (text : FileMap) (r : Lsp.Range) (newText : String) : FileMa
   let «end» := text.lspPosToUtf8Pos r.«end»
   let pre := text.source.extract 0 start
   let post := text.source.extract «end» text.source.endPos
-  (pre ++ newText ++ post).toFileMap
+  -- `pre` and `post` already have normalized line endings, so only `newText` needs its endings normalized.
+  -- Note: this assumes that editing never separates a `\r\n`.
+  -- If `pre` ends with `\r` and `newText` begins with `\n`, the result is potentially inaccurate.
+  -- If this is ever a problem, we could store a second unnormalized FileMap, edit it, and normalize it here.
+  (pre ++ newText.crlfToLf ++ post).toFileMap
 
 open IO
 
@@ -125,7 +132,7 @@ def applyDocumentChange (oldText : FileMap) : (change : Lsp.TextDocumentContentC
   | TextDocumentContentChangeEvent.rangeChange (range : Range) (newText : String) =>
     replaceLspRange oldText range newText
   | TextDocumentContentChangeEvent.fullChange (newText : String) =>
-    newText.toFileMap
+    newText.crlfToLf.toFileMap
 
 /-- Returns the document contents with all changes applied. -/
 def foldDocumentChanges (changes : Array Lsp.TextDocumentContentChangeEvent) (oldText : FileMap) : FileMap :=

src/Lean/Server/Watchdog.lean

@@ -728,12 +728,9 @@ end RequestHandling
 section NotificationHandling
   def handleDidOpen (p : LeanDidOpenTextDocumentParams) : ServerM Unit :=
     let doc := p.textDocument
-    /- NOTE(WN): `toFileMap` marks line beginnings as immediately following
-       "\n", which should be enough to handle both LF and CRLF correctly.
-       This is because LSP always refers to characters by (line, column),
-       so if we get the line number correct it shouldn't matter that there
-       is a CR there. -/
-    startFileWorker ⟨doc.uri, doc.version, doc.text.toFileMap, p.dependencyBuildMode?.getD .always⟩
+    /- Note (kmill): LSP always refers to characters by (line, column),
+      so converting CRLF to LF preserves line and column numbers. -/
+    startFileWorker ⟨doc.uri, doc.version, doc.text.crlfToLf.toFileMap, p.dependencyBuildMode?.getD .always⟩
 
   def handleDidChange (p : DidChangeTextDocumentParams) : ServerM Unit := do
     let doc := p.textDocument

src/Lean/Syntax.lean

@@ -30,6 +30,9 @@ def SourceInfo.updateTrailing (trailing : Substring) : SourceInfo → SourceInfo
   | SourceInfo.original leading pos _ endPos => SourceInfo.original leading pos trailing endPos
   | info                                     => info
 
+def SourceInfo.getRange? (canonicalOnly := false) (info : SourceInfo) : Option String.Range :=
+  return ⟨(← info.getPos? canonicalOnly), (← info.getTailPos? canonicalOnly)⟩
+
 /-! # Syntax AST -/
 
 inductive IsNode : Syntax → Prop where
@@ -80,6 +83,34 @@ end SyntaxNode
 
 namespace Syntax
 
+/--
+Compare syntax structures and position ranges, but not whitespace.
+We generally assume that if syntax trees equal in this way generate the same elaboration output,
+including positions contained in e.g. diagnostics and the info tree.
+-/
+partial def structRangeEq : Syntax → Syntax → Bool
+  | .missing, .missing => true
+  | .node info k args, .node info' k' args' =>
+    info.getRange? == info'.getRange? && k == k' && args.isEqv args' structRangeEq
+  | .atom info val, .atom info' val' => info.getRange? == info'.getRange? && val == val'
+  | .ident info rawVal val preresolved, .ident info' rawVal' val' preresolved' =>
+    info.getRange? == info'.getRange? && rawVal == rawVal' && val == val' &&
+    preresolved == preresolved'
+  | _, _ => false
+
+/-- Like `structRangeEq` but prints trace on failure if `trace.Elab.reuse` is activated. -/
+def structRangeEqWithTraceReuse (opts : Options) (stx1 stx2 : Syntax) : Bool :=
+  if stx1.structRangeEq stx2 then
+    true
+  else
+    if opts.getBool `trace.Elab.reuse then
+      dbg_trace "reuse stopped:
+{stx1.formatStx (showInfo := true)} !=
+{stx2.formatStx (showInfo := true)}"
+      false
+    else
+      false
+
 def getAtomVal : Syntax → String
   | atom _ val => val
   | _          => ""
@@ -187,13 +218,6 @@ partial def updateTrailing (trailing : Substring) : Syntax → Syntax
      Syntax.node info k args
   | s => s
 
-partial def getTailWithPos : Syntax → Option Syntax
-  | stx@(atom info _)   => info.getPos?.map fun _ => stx
-  | stx@(ident info ..) => info.getPos?.map fun _ => stx
-  | node SourceInfo.none _ args => args.findSomeRev? getTailWithPos
-  | stx@(node ..) => stx
-  | _ => none
-
 open SourceInfo in
 /-- Split an `ident` into its dot-separated components while preserving source info.
 Macro scopes are first erased.  For example, `` `foo.bla.boo._@._hyg.4 `` ↦ `` [`foo, `bla, `boo] ``.