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/ISSUE_TEMPLATE/bug_report.md

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

.github/workflows/ci.yml

@@ -6,7 +6,6 @@ on:
     tags:
       - '*'
   pull_request:
-    types: [opened, synchronize, reopened, labeled]
   merge_group:
   schedule:
     - cron: '0 7 * * *'  # 8AM CET/11PM PT
@@ -21,8 +20,10 @@ jobs:
   configure:
     runs-on: ubuntu-latest
     outputs:
-      # Should we run only a quick CI? Yes on a pull request without the full-ci label
-      quick: ${{ steps.set-quick.outputs.quick }}
+      # 0: PRs without special label
+      # 1: PRs with `merge-ci` label, merge queue checks, master commits
+      # 2: PRs with `release-ci` label, releases (incl. nightlies)
+      check-level: ${{ steps.set-level.outputs.check-level }}
       # The build matrix, dynamically generated here
       matrix: ${{ steps.set-matrix.outputs.result }}
       # Should we make a nightly release? If so, this output contains the lean version string, else it is empty
@@ -39,161 +40,6 @@ jobs:
       RELEASE_TAG: ${{ steps.set-release.outputs.RELEASE_TAG }}
 
     steps:
-      - name: Run quick CI?
-        id: set-quick
-        env:
-          quick: ${{
-            github.event_name == 'pull_request' && !contains( github.event.pull_request.labels.*.name, 'full-ci')
-           }}
-        run: |
-          echo "quick=${{env.quick}}" >> "$GITHUB_OUTPUT"
-
-      - name: Configure build matrix
-        id: set-matrix
-        uses: actions/github-script@v7
-        with:
-          script: |
-            const quick = ${{ steps.set-quick.outputs.quick }};
-            console.log(`quick: ${quick}`);
-            // use large runners outside PRs where available (original repo)
-            // disabled for now as this mostly just speeds up the test suite which is not a bottleneck
-            // let large = ${{ github.event_name != 'pull_request' && github.repository == 'leanprover/lean4' }} ? "-large" : "";
-            let matrix = [
-              {
-                // portable release build: use channel with older glibc (2.27)
-                "name": "Linux LLVM",
-                "os": "ubuntu-latest",
-                "release": false,
-                "quick": false,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                // reverse-ffi needs to be updated to link to LLVM libraries
-                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
-                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
-              },
-              {
-                "name": "Linux release",
-                "os": "ubuntu-latest",
-                "release": true,
-                "quick": true,
-                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
-                "binary-check": "ldd -v",
-                // foreign code may be linked against more recent glibc
-                "CTEST_OPTIONS": "-E 'foreign'"
-              },
-              {
-                "name": "Linux",
-                "os": "ubuntu-latest",
-                "check-stage3": true,
-                "test-speedcenter": true,
-                "quick": false,
-              },
-              {
-                "name": "Linux Debug",
-                "os": "ubuntu-latest",
-                "quick": false,
-                "CMAKE_OPTIONS": "-DCMAKE_BUILD_TYPE=Debug",
-                // exclude seriously slow tests
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
-              },
-              // TODO: suddenly started failing in CI
-              /*{
-                "name": "Linux fsanitize",
-                "os": "ubuntu-latest",
-                "quick": false,
-                // turn off custom allocator & symbolic functions to make LSAN do its magic
-                "CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-fsanitize=address,undefined -DLEANC_EXTRA_FLAGS='-fsanitize=address,undefined -fsanitize-link-c++-runtime' -DSMALL_ALLOCATOR=OFF -DBSYMBOLIC=OFF",
-                // exclude seriously slow/problematic tests (laketests crash)
-                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
-              },*/
-              {
-                "name": "macOS",
-                "os": "macos-13",
-                "release": true,
-                "quick": false,
-                "shell": "bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
-                "binary-check": "otool -L",
-                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
-              },
-              {
-                "name": "macOS aarch64",
-                "os": "macos-13",
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "cross_target": "aarch64-apple-darwin",
-                "shell": "bash -euxo pipefail {0}",
-                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm-aarch64-* lean-llvm-x86_64-*",
-                "binary-check": "otool -L",
-                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
-              },
-              {
-                "name": "Windows",
-                "os": "windows-2022",
-                "release": true,
-                "quick": false,
-                "shell": "msys2 {0}",
-                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
-                // for reasons unknown, interactivetests are flaky on Windows
-                "CTEST_OPTIONS": "--repeat until-pass:2",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
-                "binary-check": "ldd"
-              },
-              {
-                "name": "Linux aarch64",
-                "os": "ubuntu-latest",
-                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "cross_target": "aarch64-unknown-linux-gnu",
-                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
-                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
-                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
-              },
-              {
-                "name": "Linux 32bit",
-                "os": "ubuntu-latest",
-                // Use 32bit on stage0 and stage1 to keep oleans compatible
-                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86",
-                "cmultilib": true,
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "shell": "bash -euxo pipefail {0}"
-              },
-              {
-                "name": "Web Assembly",
-                "os": "ubuntu-latest",
-                // Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
-                "CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
-                "wasm": true,
-                "cmultilib": true,
-                "release": true,
-                "quick": false,
-                "cross": true,
-                "shell": "bash -euxo pipefail {0}",
-                // Just a few selected tests because wasm is slow
-                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean\""
-              }
-            ];
-            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
-            if (quick) {
-              return matrix.filter((job) => job.quick)
-            } else {
-              return matrix
-            }
-
       - name: Checkout
         uses: actions/checkout@v3
         # don't schedule nightlies on forks
@@ -244,6 +90,171 @@ jobs:
             echo "Tag ${TAG_NAME} did not match SemVer regex."
           fi
 
+      - name: Set check level
+        id: set-level
+        # We do not use github.event.pull_request.labels.*.name here because
+        # re-running a run does not update that list, and we do want to be able to
+        # rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
+        run: |
+          check_level=0
+
+          if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" ]]; then
+            check_level=2
+          elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
+            check_level=1
+          else
+            labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }}) --jq '.labels'"
+            if echo "$labels" | grep -q "release-ci"; then
+              check_level=2
+            elif echo "$labels" | grep -q "merge-ci"; then
+              check_level=1
+            fi
+          fi
+
+          echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
+        env:
+          GH_TOKEN: ${{ github.token }}
+
+      - name: Configure build matrix
+        id: set-matrix
+        uses: actions/github-script@v7
+        with:
+          script: |
+            const level = ${{ steps.set-level.outputs.check-level }};
+            console.log(`level: ${level}`);
+            // use large runners outside PRs where available (original repo)
+            // disabled for now as this mostly just speeds up the test suite which is not a bottleneck
+            // let large = ${{ github.event_name != 'pull_request' && github.repository == 'leanprover/lean4' }} ? "-large" : "";
+            let matrix = [
+              {
+                // portable release build: use channel with older glibc (2.27)
+                "name": "Linux LLVM",
+                "os": "ubuntu-latest",
+                "release": false,
+                "check-level": 2,
+                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "binary-check": "ldd -v",
+                // foreign code may be linked against more recent glibc
+                // reverse-ffi needs to be updated to link to LLVM libraries
+                "CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
+                "CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
+              },
+              {
+                "name": "Linux release",
+                "os": "ubuntu-latest",
+                "release": true,
+                "check-level": 0,
+                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
+                "binary-check": "ldd -v",
+                // foreign code may be linked against more recent glibc
+                "CTEST_OPTIONS": "-E 'foreign'"
+              },
+              {
+                "name": "Linux",
+                "os": "ubuntu-latest",
+                "check-stage3": level >= 2,
+                "test-speedcenter": level >= 2,
+                "check-level": 1,
+              },
+              {
+                "name": "Linux Debug",
+                "os": "ubuntu-latest",
+                "check-level": 2,
+                "CMAKE_PRESET": "debug",
+                // exclude seriously slow tests
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
+              },
+              // TODO: suddenly started failing in CI
+              /*{
+                "name": "Linux fsanitize",
+                "os": "ubuntu-latest",
+                "check-level": 2,
+                // turn off custom allocator & symbolic functions to make LSAN do its magic
+                "CMAKE_PRESET": "sanitize",
+                // exclude seriously slow/problematic tests (laketests crash)
+                "CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
+              },*/
+              {
+                "name": "macOS",
+                "os": "macos-13",
+                "release": true,
+                "check-level": 2,
+                "shell": "bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
+                "binary-check": "otool -L",
+                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
+              },
+              {
+                "name": "macOS aarch64",
+                "os": "macos-14",
+                "CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
+                "release": true,
+                "check-level": 1,
+                "shell": "bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
+                "binary-check": "otool -L",
+                "tar": "gtar" // https://github.com/actions/runner-images/issues/2619
+              },
+              {
+                "name": "Windows",
+                "os": "windows-2022",
+                "release": true,
+                "check-level": 2,
+                "shell": "msys2 {0}",
+                "CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
+                // for reasons unknown, interactivetests are flaky on Windows
+                "CTEST_OPTIONS": "--repeat until-pass:2",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
+                "binary-check": "ldd"
+              },
+              {
+                "name": "Linux aarch64",
+                "os": "ubuntu-latest",
+                "CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
+                "release": true,
+                "check-level": 2,
+                "cross": true,
+                "cross_target": "aarch64-unknown-linux-gnu",
+                "shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
+                "llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
+                "prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
+              },
+              {
+                "name": "Linux 32bit",
+                "os": "ubuntu-latest",
+                // Use 32bit on stage0 and stage1 to keep oleans compatible
+                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86",
+                "cmultilib": true,
+                "release": true,
+                "check-level": 2,
+                "cross": true,
+                "shell": "bash -euxo pipefail {0}"
+              },
+              {
+                "name": "Web Assembly",
+                "os": "ubuntu-latest",
+                // Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
+                "CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
+                "wasm": true,
+                "cmultilib": true,
+                "release": true,
+                "check-level": 2,
+                "cross": true,
+                "shell": "bash -euxo pipefail {0}",
+                // Just a few selected tests because wasm is slow
+                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean\""
+              }
+            ];
+            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
+            return matrix.filter((job) => level >= job["check-level"])
+
   build:
     needs: [configure]
     if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
@@ -322,6 +333,9 @@ jobs:
           # store in current directory, for easy uploading together with binary
           echo $PWD/coredumps/%e.%p.%t | sudo tee /proc/sys/kernel/core_pattern
         if: runner.os == 'Linux'
+      - name: Set up NPROC
+        run: |
+          echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
       - name: Build
         run: |
           mkdir build
@@ -352,8 +366,8 @@ jobs:
             OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }})
           fi
           # contortion to support empty OPTIONS with old macOS bash
-          cmake .. ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
-          make -j4
+          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
+          make -j$NPROC
           make install
       - name: Check Binaries
         run: ${{ matrix.binary-check }} lean-*/bin/* || true
@@ -382,32 +396,29 @@ jobs:
           build/stage1/bin/lean --stats src/Lean.lean
         if: ${{ !matrix.cross }}
       - name: Test
+        id: test
         run: |
-          cd build/stage1
           ulimit -c unlimited # coredumps
-          # exclude nonreproducible test
-          ctest -j4 --progress --output-junit test-results.xml --output-on-failure ${{ matrix.CTEST_OPTIONS }} < /dev/null
-        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
+          ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
+        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.check-level >= 1
       - name: Test Summary
         uses: test-summary/action@v2
         with:
           paths: build/stage1/test-results.xml
         # prefix `if` above with `always` so it's run even if tests failed
-        if: always() && (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
+        if: always() && steps.test.conclusion != 'skipped'
       - name: Check Test Binary
         run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
-        if: ${{ !matrix.cross && needs.configure.outputs.quick == 'false' }}
+        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
       - name: Build Stage 2
         run: |
-          cd build
           ulimit -c unlimited # coredumps
-          make -j4 stage2
+          make -C build -j$NPROC stage2
         if: matrix.test-speedcenter
       - name: Check Stage 3
         run: |
-          cd build
           ulimit -c unlimited # coredumps
-          make -j4 check-stage3
+          make -C build -j$NPROC stage3
         if: matrix.test-speedcenter
       - name: Test Speedcenter Benchmarks
         run: |
@@ -418,11 +429,10 @@ jobs:
         if: matrix.test-speedcenter
       - name: Check rebootstrap
         run: |
-          cd build
           ulimit -c unlimited # coredumps
           # clean rebuild in case of Makefile changes
-          make update-stage0 && rm -rf ./stage* && make -j4
-        if: matrix.name == 'Linux' && needs.configure.outputs.quick == 'false'
+          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
+        if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
       - name: CCache stats
         run: ccache -s
       - name: Show stacktrace for coredumps

.github/workflows/nix-ci.yml

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

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

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

CMakePresets.json

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

RELEASES.md

@@ -1,148 +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
 ---------
 
-v4.8.0 
+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.lean

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

src/Init/Data/Array/Subarray.lean

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

src/Init/Data/BitVec/Basic.lean

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

src/Init/Data/BitVec/Bitblast.lean

@@ -184,4 +184,55 @@ theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c
     simp [← sub_toAdd, BitVec.sub_add_cancel]
   · simp [bit_not_testBit x _]
 
+/-! ### Inequalities (le / lt) -/
+
+theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true := by
+  simp only [BitVec.ult, carry, toNat_mod_cancel, toNat_not, toNat_true, ge_iff_le, ← decide_not,
+    Nat.not_le, decide_eq_decide]
+  rw [Nat.mod_eq_of_lt (by omega)]
+  omega
+
+theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
+  simp [BitVec.ule, BitVec.ult, ← decide_not]
+
+theorem ule_eq_carry (x y : BitVec w) : x.ule y = carry w y (~~~x) true := by
+  simp [ule_eq_not_ult, ult_eq_not_carry]
+
+/-- If two bitvectors have the same `msb`, then signed and unsigned comparisons coincide -/
+theorem slt_eq_ult_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) :
+    x.slt y = x.ult y := by
+  simp only [BitVec.slt, toInt_eq_msb_cond, BitVec.ult, decide_eq_decide, h]
+  cases y.msb <;> simp
+
+/-- If two bitvectors have different `msb`s, then unsigned comparison is determined by this bit -/
+theorem ult_eq_msb_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
+    x.ult y = y.msb := by
+  simp only [BitVec.ult, msb_eq_decide, ne_eq, decide_eq_decide] at *
+  omega
+
+/-- If two bitvectors have different `msb`s, then signed and unsigned comparisons are opposites -/
+theorem slt_eq_not_ult_of_msb_neq {x y : BitVec w} (h : x.msb ≠ y.msb) :
+    x.slt y = !x.ult y := by
+  simp only [BitVec.slt, toInt_eq_msb_cond, Bool.eq_not_of_ne h, ult_eq_msb_of_msb_neq h]
+  cases y.msb <;> (simp; omega)
+
+theorem slt_eq_ult (x y : BitVec w) :
+    x.slt y = (x.msb != y.msb).xor (x.ult y) := by
+  by_cases h : x.msb = y.msb
+  · simp [h, slt_eq_ult_of_msb_eq]
+  · have h' : x.msb != y.msb := by simp_all
+    simp [slt_eq_not_ult_of_msb_neq h, h']
+
+theorem slt_eq_not_carry (x y : BitVec w) :
+    x.slt y = (x.msb == y.msb).xor (carry w x (~~~y) true) := by
+  simp only [slt_eq_ult, bne, ult_eq_not_carry]
+  cases x.msb == y.msb <;> simp
+
+theorem sle_eq_not_slt (x y : BitVec w) : x.sle y = !y.slt x := by
+  simp only [BitVec.sle, BitVec.slt, ← decide_not, decide_eq_decide]; omega
+
+theorem sle_eq_carry (x y : BitVec w) :
+    x.sle y = !((x.msb == y.msb).xor (carry w y (~~~x) true)) := by
+  rw [sle_eq_not_slt, slt_eq_not_carry, beq_comm]
+
 end BitVec

src/Init/Data/BitVec/Lemmas.lean

@@ -9,6 +9,8 @@ import Init.Data.Bool
 import Init.Data.BitVec.Basic
 import Init.Data.Fin.Lemmas
 import Init.Data.Nat.Lemmas
+import Init.Data.Nat.Mod
+import Init.Data.Int.Bitwise.Lemmas
 
 namespace BitVec
 
@@ -140,13 +142,16 @@ 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) :
   getLsb (x#n) i = (i < n && x.testBit i) := by
   simp [getLsb, BitVec.ofNat, Fin.val_ofNat']
 
-@[simp, deprecated toNat_ofNat] theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
+@[simp, deprecated toNat_ofNat (since := "2024-02-22")]
+theorem toNat_zero (n : Nat) : (0#n).toNat = 0 := by trivial
 
 @[simp] theorem getLsb_zero : (0#w).getLsb i = false := by simp [getLsb]
 
@@ -173,8 +178,7 @@ theorem msb_eq_getLsb_last (x : BitVec w) :
     x.getLsb (w-1) = decide (2 ^ (w-1) ≤ x.toNat) := by
   rcases w with rfl | w
   · simp
-  · simp only [Nat.zero_lt_succ, decide_True, getLsb, Nat.testBit, Nat.succ_sub_succ_eq_sub,
-    Nat.sub_zero, Nat.and_one_is_mod, Bool.true_and, Nat.shiftRight_eq_div_pow]
+  · simp only [getLsb, Nat.testBit_to_div_mod, Nat.succ_sub_succ_eq_sub, Nat.sub_zero]
     rcases (Nat.lt_or_ge (BitVec.toNat x) (2 ^ w)) with h | h
     · simp [Nat.div_eq_of_lt h, h]
     · simp only [h]
@@ -221,9 +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]
@@ -245,6 +261,12 @@ theorem eq_of_toInt_eq {i j : BitVec n} : i.toInt = j.toInt → i = j := by
   have _jlt := j.isLt
   split <;> split <;> omega
 
+theorem toInt_inj (x y : BitVec n) : x.toInt = y.toInt ↔ x = y :=
+  Iff.intro eq_of_toInt_eq (congrArg BitVec.toInt)
+
+theorem toInt_ne (x y : BitVec n) : x.toInt ≠ y.toInt ↔ x ≠ y  := by
+  rw [Ne, toInt_inj]
+
 @[simp] theorem toNat_ofInt {n : Nat} (i : Int) :
   (BitVec.ofInt n i).toNat = (i % (2^n : Nat)).toNat := by
   unfold BitVec.ofInt
@@ -260,6 +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) :
@@ -442,6 +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) :
@@ -468,6 +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) :
@@ -488,6 +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
@@ -602,6 +642,17 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
     (shiftLeftZeroExtend x i).msb = x.msb := by
   simp [shiftLeftZeroExtend_eq, BitVec.msb]
 
+theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x <<< n) <<< m = x <<< (n + m) := by
+  ext i
+  simp only [getLsb_shiftLeft, Fin.is_lt, decide_True, Bool.true_and]
+  rw [show i - (n + m) = (i - m - n) by omega]
+  cases h₂ : decide (i < m) <;>
+  cases h₃ : decide (i - m < w) <;>
+  cases h₄ : decide (i - m < n) <;>
+  cases h₅ : decide (i < n + m) <;>
+    simp at * <;> omega
+
 /-! ### ushiftRight -/
 
 @[simp, bv_toNat] theorem toNat_ushiftRight (x : BitVec n) (i : Nat) :
@@ -611,6 +662,70 @@ theorem shiftLeftZeroExtend_eq {x : BitVec w} :
     getLsb (x >>> i) j = getLsb x (i+j) := by
   unfold getLsb ; simp
 
+/-! ### sshiftRight -/
+
+theorem sshiftRight_eq {x : BitVec n} {i : Nat} :
+    x.sshiftRight i = BitVec.ofInt n (x.toInt >>> i) := by
+  apply BitVec.eq_of_toInt_eq
+  simp [BitVec.sshiftRight]
+
+/-- if the msb is false, the arithmetic shift right equals logical shift right -/
+theorem sshiftRight_eq_of_msb_false {x : BitVec w} {s : Nat} (h : x.msb = false) :
+    (x.sshiftRight s) = x >>> s := by
+  apply BitVec.eq_of_toNat_eq
+  rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
+  have hxbound : 2 * x.toNat < 2 ^ w := (BitVec.msb_eq_false_iff_two_mul_lt x).mp h
+  simp only [hxbound, ↓reduceIte, Int.natCast_shiftRight, Int.ofNat_eq_coe, ofInt_natCast,
+    toNat_ofNat, toNat_ushiftRight]
+  replace hxbound : x.toNat >>> s < 2 ^ w := by
+    rw [Nat.shiftRight_eq_div_pow]
+    exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) x.isLt
+  apply Nat.mod_eq_of_lt hxbound
+
+/--
+If the msb is `true`, the arithmetic shift right equals negating,
+then logical shifting right, then negating again.
+The double negation preserves the lower bits that have been shifted,
+and the outer negation ensures that the high bits are '1'. -/
+theorem sshiftRight_eq_of_msb_true {x : BitVec w} {s : Nat} (h : x.msb = true) :
+    (x.sshiftRight s) = ~~~((~~~x) >>> s) := by
+  apply BitVec.eq_of_toNat_eq
+  rcases w with rfl | w
+  · simp
+  · rw [BitVec.sshiftRight_eq, BitVec.toInt_eq_toNat_cond]
+    have hxbound : (2 * x.toNat ≥ 2 ^ (w + 1)) := (BitVec.msb_eq_true_iff_two_mul_ge x).mp h
+    replace hxbound : ¬ (2 * x.toNat < 2 ^ (w + 1)) := by omega
+    simp only [hxbound, ↓reduceIte, toNat_ofInt, toNat_not, toNat_ushiftRight]
+    rw [← Int.subNatNat_eq_coe, Int.subNatNat_of_lt (by omega),
+        Nat.pred_eq_sub_one, Int.negSucc_shiftRight,
+        Int.emod_negSucc, Int.natAbs_ofNat, Nat.succ_eq_add_one,
+        Int.subNatNat_of_le (by omega), Int.toNat_ofNat, Nat.mod_eq_of_lt,
+        Nat.sub_right_comm]
+    omega
+    · rw [Nat.shiftRight_eq_div_pow]
+      apply Nat.lt_of_le_of_lt (Nat.div_le_self _ _) (by omega)
+
+theorem getLsb_sshiftRight (x : BitVec w) (s i : Nat) :
+    getLsb (x.sshiftRight s) i =
+      (!decide (w ≤ i) && if s + i < w then x.getLsb (s + i) else x.msb) := by
+  rcases hmsb : x.msb with rfl | rfl
+  · simp only [sshiftRight_eq_of_msb_false hmsb, getLsb_ushiftRight, Bool.if_false_right]
+    by_cases hi : i ≥ w
+    · simp only [hi, decide_True, Bool.not_true, Bool.false_and]
+      apply getLsb_ge
+      omega
+    · simp only [hi, decide_False, Bool.not_false, Bool.true_and, Bool.iff_and_self,
+        decide_eq_true_eq]
+      intros hlsb
+      apply BitVec.lt_of_getLsb _ _ hlsb
+  · by_cases hi : i ≥ w
+    · simp [hi]
+    · simp only [sshiftRight_eq_of_msb_true hmsb, getLsb_not, getLsb_ushiftRight, Bool.not_and,
+        Bool.not_not, hi, decide_False, Bool.not_false, Bool.if_true_right, Bool.true_and,
+        Bool.and_iff_right_iff_imp, Bool.or_eq_true, Bool.not_eq_true', decide_eq_false_iff_not,
+        Nat.not_lt, decide_eq_true_eq]
+      omega
+
 /-! ### append -/
 
 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -687,6 +802,11 @@ theorem msb_append {x : BitVec w} {y : BitVec v} :
   simp only [getLsb_append, cond_eq_if]
   split <;> simp [*]
 
+theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x >>> n) >>> m = x >>> (n + m) := by
+  ext i
+  simp [Nat.add_assoc n m i]
+
 /-! ### rev -/
 
 theorem getLsb_rev (x : BitVec w) (i : Fin w) :
@@ -889,6 +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
@@ -897,7 +1021,7 @@ theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
 
 theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
   apply eq_of_toNat_eq
-  have y_toNat_le := Nat.le_of_lt y.toNat_lt
+  have y_toNat_le := Nat.le_of_lt y.isLt
   rw [toNat_sub, toNat_add, Nat.mod_add_mod, Nat.add_assoc, ← Nat.add_sub_assoc y_toNat_le,
     Nat.add_sub_cancel_left, Nat.add_mod_right, toNat_mod_cancel]
 
@@ -1020,4 +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) :
@@ -360,7 +362,8 @@ def toNat (b:Bool) : Nat := cond b 1 0
 theorem toNat_le (c : Bool) : c.toNat ≤ 1 := by
   cases c <;> trivial
 
-@[deprecated toNat_le] abbrev toNat_le_one := toNat_le
+@[deprecated toNat_le (since := "2024-02-23")]
+abbrev toNat_le_one := toNat_le
 
 theorem toNat_lt (b : Bool) : b.toNat < 2 :=
   Nat.lt_succ_of_le (toNat_le _)

src/Init/Data/Char.lean

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

src/Init/Data/Char/Lemmas.lean

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

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

src/Init/Data/Int/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

@@ -14,6 +14,8 @@ import Init.RCases
 # Lemmas about integer division needed to bootstrap `omega`.
 -/
 
+-- Remove after the next stage0 update
+set_option allowUnsafeReducibility true
 
 open Nat (succ)
 
@@ -142,12 +144,14 @@ theorem eq_one_of_mul_eq_one_left {a b : Int} (H : 0 ≤ b) (H' : a * b = 1) : b
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => show -ofNat _ = _ by simp
 
+unseal Nat.div in
 @[simp] protected theorem div_zero : ∀ a : Int, div a 0 = 0
   | ofNat _ => show ofNat _ = _ by simp
   | -[_+1] => rfl
 
 @[simp] theorem zero_fdiv (b : Int) : fdiv 0 b = 0 := by cases b <;> rfl
 
+unseal Nat.div in
 @[simp] protected theorem fdiv_zero : ∀ a : Int, fdiv a 0 = 0
   | 0      => rfl
   | succ _ => rfl
@@ -178,7 +182,7 @@ theorem fdiv_eq_div {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : fdiv a b = div a
 
 @[simp] theorem mod_zero : ∀ a : Int, mod a 0 = a
   | ofNat _ => congrArg ofNat <| Nat.mod_zero _
-  | -[_+1] => rfl
+  | -[_+1] => congrArg (fun n => -ofNat n) <| Nat.mod_zero _
 
 @[simp] theorem zero_fmod (b : Int) : fmod 0 b = 0 := by cases b <;> rfl
 
@@ -225,7 +229,9 @@ theorem mod_add_div : ∀ a b : Int, mod a b + b * (a.div b) = a
   | ofNat m, -[n+1] => by
     show (m % succ n + -↑(succ n) * -↑(m / succ n) : Int) = m
     rw [Int.neg_mul_neg]; exact congrArg ofNat (Nat.mod_add_div ..)
-  | -[_+1], 0 => rfl
+  | -[m+1], 0 => by
+    show -(↑((succ m) % 0) : Int) + 0 * -↑(succ m / 0) = -↑(succ m)
+    rw [Nat.mod_zero, Int.zero_mul, Int.add_zero]
   | -[m+1], ofNat n => by
     show -(↑((succ m) % n) : Int) + ↑n * -↑(succ m / n) = -↑(succ m)
     rw [Int.mul_neg, ← Int.neg_add]
@@ -414,6 +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
@@ -763,11 +772,13 @@ theorem ediv_eq_ediv_of_mul_eq_mul {a b c d : Int}
   | (n:Nat) => congrArg ofNat (Nat.div_one _)
   | -[n+1] => by simp [Int.div, neg_ofNat_succ]; rfl
 
+unseal Nat.div in
 @[simp] protected theorem div_neg : ∀ a b : Int, a.div (-b) = -(a.div b)
   | ofNat m, 0 => show ofNat (m / 0) = -↑(m / 0) by rw [Nat.div_zero]; rfl
   | ofNat m, -[n+1] | -[m+1], succ n => (Int.neg_neg _).symm
   | ofNat m, succ n | -[m+1], 0 | -[m+1], -[n+1] => rfl
 
+unseal Nat.div in
 @[simp] protected theorem neg_div : ∀ a b : Int, (-a).div b = -(a.div b)
   | 0, n => by simp [Int.neg_zero]
   | succ m, (n:Nat) | -[m+1], 0 | -[m+1], -[n+1] => rfl
@@ -936,6 +947,7 @@ theorem fdiv_nonneg {a b : Int} (Ha : 0 ≤ a) (Hb : 0 ≤ b) : 0 ≤ a.fdiv b :
   match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
   | _, _, ⟨_, rfl⟩, ⟨_, rfl⟩ => ofNat_fdiv .. ▸ ofNat_zero_le _
 
+unseal Nat.div in
 theorem fdiv_nonpos : ∀ {a b : Int}, 0 ≤ a → b ≤ 0 → a.fdiv b ≤ 0
   | 0, 0, _, _ | 0, -[_+1], _, _ | succ _, 0, _, _ | succ _, -[_+1], _, _ => ⟨_⟩
 

src/Init/Data/Int/Order.lean

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

src/Init/Data/List/Lemmas.lean

@@ -777,7 +777,6 @@ theorem exists_cons_of_length_succ :
     ∀ {l : List α}, l.length = n + 1 → ∃ h t, l = h :: t
   | _::_, _ => ⟨_, _, rfl⟩
 
-@[simp]
 theorem length_pos {l : List α} : 0 < length l ↔ l ≠ [] :=
   Nat.pos_iff_ne_zero.trans (not_congr length_eq_zero)
 

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

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

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

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

src/Init/Data/Nat/Div.lean

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

src/Init/Data/Nat/Gcd.lean

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

src/Init/Data/Nat/Lemmas.lean

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

src/Init/Data/Nat/Linear.lean

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

src/Init/Data/Option/Basic.lean

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

src/Init/Data/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/Stream.lean

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

src/Init/Data/String.lean

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

src/Init/Data/String/Basic.lean

@@ -24,6 +24,14 @@ instance : LT String :=
 instance decLt (s₁ s₂ : @& String) : Decidable (s₁ < s₂) :=
   List.hasDecidableLt s₁.data s₂.data
 
+@[reducible] protected def le (a b : String) : Prop := ¬ b < a
+
+instance : LE String :=
+  ⟨String.le⟩
+
+instance decLE (s₁ s₂ : String) : Decidable (s₁ ≤ s₂) :=
+  inferInstanceAs (Decidable (Not _))
+
 /--
 Returns the length of a string in Unicode code points.
 
@@ -178,8 +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`
@@ -196,16 +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
@@ -683,13 +728,15 @@ def substrEq (s1 : String) (off1 : String.Pos) (s2 : String) (off2 : String.Pos)
   off1.byteIdx + sz ≤ s1.endPos.byteIdx && off2.byteIdx + sz ≤ s2.endPos.byteIdx && loop off1 off2 { byteIdx := off1.byteIdx + sz }
 where
   loop (off1 off2 stop1 : Pos) :=
-    if h : off1.byteIdx < stop1.byteIdx then
+    if _h : off1.byteIdx < stop1.byteIdx then
       let c₁ := s1.get off1
       let c₂ := s2.get off2
-      have := Nat.sub_lt_sub_left h (Nat.add_lt_add_left (one_le_csize c₁) off1.1)
       c₁ == c₂ && loop (off1 + c₁) (off2 + c₂) stop1
     else true
   termination_by stop1.1 - off1.1
+  decreasing_by
+    have := Nat.sub_lt_sub_left _h (Nat.add_lt_add_left (one_le_csize c₁) off1.1)
+    decreasing_tactic
 
 /-- Return true iff `p` is a prefix of `s` -/
 def isPrefixOf (p : String) (s : String) : Bool :=
@@ -904,6 +951,10 @@ def beq (ss1 ss2 : Substring) : Bool :=
 
 instance hasBeq : BEq Substring := ⟨beq⟩
 
+/-- Checks whether two substrings have the same position and content. -/
+def sameAs (ss1 ss2 : Substring) : Bool :=
+  ss1.startPos == ss2.startPos && ss1 == ss2
+
 end Substring
 
 namespace String

src/Init/Data/String/Extra.lean

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

src/Init/Data/String/Lemmas.lean

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

src/Init/Data/UInt.lean

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

src/Init/Data/UInt/Basic.lean

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

src/Init/Data/UInt/Lemmas.lean

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

src/Init/Grind.lean

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

src/Init/Grind/Cases.lean

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

src/Init/Grind/Lemmas.lean

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

src/Init/Grind/Norm.lean

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

src/Init/Grind/Tactics.lean

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

src/Init/MetaTypes.lean

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

src/Init/NotationExtra.lean

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

src/Init/Prelude.lean

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

src/Init/System/IO.lean

@@ -210,8 +210,44 @@ def sleep (ms : UInt32) : BaseIO Unit :=
 /-- Request cooperative cancellation of the task. The task must explicitly call `IO.checkCanceled` to react to the cancellation. -/
 @[extern "lean_io_cancel"] opaque cancel : @& Task α → BaseIO Unit
 
+/-- The current state of a `Task` in the Lean runtime's task manager. -/
+inductive TaskState
+  /--
+  The `Task` is waiting to be run.
+  It can be waiting for dependencies to complete or
+  sitting in the task manager queue waiting for a thread to run on.
+  -/
+  | waiting
+  /--
+  The `Task` is actively running on a thread or,
+  in the case of a `Promise`, waiting for a call to `IO.Promise.resolve`.
+  -/
+  | running
+  /--
+  The `Task` has finished running and its result is available.
+  Calling `Task.get` or `IO.wait` on the task will not block.
+  -/
+  | finished
+  deriving Inhabited, Repr, DecidableEq, Ord
+
+instance : LT TaskState := ltOfOrd
+instance : LE TaskState := leOfOrd
+instance : Min TaskState := minOfLe
+instance : Max TaskState := maxOfLe
+
+protected def TaskState.toString : TaskState → String
+  | .waiting => "waiting"
+  | .running => "running"
+  | .finished => "finished"
+
+instance : ToString TaskState := ⟨TaskState.toString⟩
+
+/-- Returns current state of the `Task` in the Lean runtime's task manager. -/
+@[extern "lean_io_get_task_state"] opaque getTaskState : @& Task α → BaseIO TaskState
+
 /-- Check if the task has finished execution, at which point calling `Task.get` will return immediately. -/
-@[extern "lean_io_has_finished"] opaque hasFinished : @& Task α → BaseIO Bool
+@[inline] def hasFinished (task : Task α) : BaseIO Bool := do
+  return (← getTaskState task) matches .finished
 
 /-- Wait for the task to finish, then return its result. -/
 @[extern "lean_io_wait"] opaque wait (t : Task α) : BaseIO α :=
@@ -228,6 +264,13 @@ local macro "nonempty_list" : tactic =>
 /-- Helper method for implementing "deterministic" timeouts. It is the number of "small" memory allocations performed by the current execution thread. -/
 @[extern "lean_io_get_num_heartbeats"] opaque getNumHeartbeats : BaseIO Nat
 
+/--
+Adjusts the heartbeat counter of the current thread by the given amount. This can be useful to give
+allocation-avoiding code additional "weight" and is also used to adjust the counter after resuming
+from a snapshot.
+-/
+@[extern "lean_io_add_heartbeats"] opaque addHeartbeats (count : UInt64) : BaseIO Unit
+
 /--
 The mode of a file handle (i.e., a set of `open` flags and an `fdopen` mode).
 
@@ -750,6 +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
@@ -1425,6 +1426,16 @@ If there are several with the same priority, it is uses the "most recent one". E
 -/
 syntax (name := simp) "simp" (Tactic.simpPre <|> Tactic.simpPost)? (ppSpace prio)? : attr
 
+/--
+Theorems tagged with the `grind_norm` attribute are used by the `grind` tactic normalizer/pre-processor.
+-/
+syntax (name := grind_norm) "grind_norm" (Tactic.simpPre <|> Tactic.simpPost)? (ppSpace prio)? : attr
+
+/--
+Simplification procedures tagged with the `grind_norm_proc` attribute are used by the `grind` tactic normalizer/pre-processor.
+-/
+syntax (name := grind_norm_proc) "grind_norm_proc" (Tactic.simpPre <|> Tactic.simpPost)? : attr
+
 
 /-- The possible `norm_cast` kinds: `elim`, `move`, or `squash`. -/
 syntax normCastLabel := &"elim" <|> &"move" <|> &"squash"

src/Lean.lean

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

src/Lean/AddDecl.lean

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

src/Lean/Attributes.lean

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

src/Lean/Compiler/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

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

src/Lean/Compiler/Old.lean

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

src/Lean/CoreM.lean

@@ -11,6 +11,7 @@ import Lean.Eval
 import Lean.ResolveName
 import Lean.Elab.InfoTree.Types
 import Lean.MonadEnv
+import Lean.Elab.Exception
 
 namespace Lean
 register_builtin_option diagnostics : Bool := {
@@ -30,6 +31,8 @@ register_builtin_option maxHeartbeats : Nat := {
   descr := "maximum amount of heartbeats per command. A heartbeat is number of (small) memory allocations (in thousands), 0 means no limit"
 }
 
+def useDiagnosticMsg := s!"use `set_option {diagnostics.name} true` to get diagnostic information"
+
 namespace Core
 
 builtin_initialize registerTraceClass `Kernel
@@ -79,16 +82,17 @@ structure Context where
   maxHeartbeats  : Nat := getMaxHeartbeats options
   currMacroScope : MacroScope := firstFrontendMacroScope
   /--
-  If `catchRuntimeEx = false`, then given `try x catch ex => h ex`,
-  an runtime exception occurring in `x` is not handled by `h`.
-  Recall that runtime exceptions are `maxRecDepth` or `maxHeartbeats`.
-  -/
-  catchRuntimeEx : Bool := false
-  /--
   If `diag := true`, different parts of the system collect diagnostics.
   Use the `set_option diag true` to set it to true.
   -/
   diag           : Bool := false
+  /-- If set, used to cancel elaboration from outside when results are not needed anymore. -/
+  cancelTk?      : Option IO.CancelToken := none
+  /--
+  If set (when `showPartialSyntaxErrors` is not set and parsing failed), suppresses most elaboration
+  errors; see also `logMessage` below.
+  -/
+  suppressElabErrors : Bool := false
   deriving Nonempty
 
 /-- CoreM is a monad for manipulating the Lean environment.
@@ -205,16 +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 })
@@ -245,13 +278,29 @@ 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
+  group    := "debug"
+  descr    := "include module name in deterministic timeout error messages.\nRemark: we set this option to false to increase the stability of our test suite"
+}
 
 def throwMaxHeartbeat (moduleName : Name) (optionName : Name) (max : Nat) : CoreM Unit := do
-  let msg := s!"(deterministic) timeout at `{moduleName}`, maximum number of heartbeats ({max/1000}) has been reached\nuse `set_option {optionName} <num>` to set the limit\nuse `set_option {diagnostics.name} true` to get diagnostic information"
+  let includeModuleName := debug.moduleNameAtTimeout.get (← getOptions)
+  let atModuleName := if includeModuleName then s!" at `{moduleName}`" else ""
+  let msg := s!"(deterministic) timeout{atModuleName}, maximum number of heartbeats ({max/1000}) has been reached\nuse `set_option {optionName} <num>` to set the limit\n{useDiagnosticMsg}"
   throw <| Exception.error (← getRef) (MessageData.ofFormat (Std.Format.text msg))
 
 def checkMaxHeartbeatsCore (moduleName : String) (optionName : Name) (max : Nat) : CoreM Unit := do
@@ -285,11 +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
@@ -297,6 +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 }
@@ -328,7 +385,8 @@ export Core (CoreM mkFreshUserName checkSystem withCurrHeartbeats)
   We used a similar hack at `Exception.isMaxRecDepth` -/
 def Exception.isMaxHeartbeat (ex : Exception) : Bool :=
   match ex with
-  | Exception.error _ (MessageData.ofFormat (Std.Format.text msg)) => "(deterministic) timeout".isPrefixOf msg
+  | Exception.error _ (MessageData.ofFormatWithInfos ⟨Std.Format.text msg, _⟩) =>
+    "(deterministic) timeout".isPrefixOf msg
   | _ => false
 
 /-- Creates the expression `d → b` -/
@@ -338,15 +396,6 @@ def mkArrow (d b : Expr) : CoreM Expr :=
 /-- Iterated `mkArrow`, creates the expression `a₁ → a₂ → … → aₙ → b`. Also see `arrowDomainsN`. -/
 def mkArrowN (ds : Array Expr) (e : Expr) : CoreM Expr := ds.foldrM mkArrow e
 
-def addDecl (decl : Declaration) : CoreM Unit := do
-  profileitM Exception "type checking" (← getOptions) do
-    withTraceNode `Kernel (fun _ => return m!"typechecking declaration") do
-      if !(← MonadLog.hasErrors) && decl.hasSorry then
-        logWarning "declaration uses 'sorry'"
-      match (← getEnv).addDecl decl with
-      | Except.ok    env => setEnv env
-      | Except.error ex  => throwKernelException ex
-
 private def supportedRecursors :=
   #[``Empty.rec, ``False.rec, ``Eq.ndrec, ``Eq.rec, ``Eq.recOn, ``Eq.casesOn, ``False.casesOn, ``Empty.casesOn, ``And.rec, ``And.casesOn]
 
@@ -400,10 +449,6 @@ def compileDecls (decls : List Name) : CoreM Unit := do
   | Except.error ex =>
     throwKernelException ex
 
-def addAndCompile (decl : Declaration) : CoreM Unit := do
-  addDecl decl;
-  compileDecl decl
-
 def getDiag (opts : Options) : Bool :=
   diagnostics.get opts
 
@@ -416,42 +461,55 @@ def ImportM.runCoreM (x : CoreM α) : ImportM α := do
   let (a, _) ← (withOptions (fun _ => ctx.opts) x).toIO { fileName := "<ImportM>", fileMap := default } { env := ctx.env }
   return a
 
-/-- Return `true` if the exception was generated by one our resource limits. -/
+/-- Return `true` if the exception was generated by one of our resource limits. -/
 def Exception.isRuntime (ex : Exception) : Bool :=
   ex.isMaxHeartbeat || ex.isMaxRecDepth
 
+/-- Returns `true` if the exception is an interrupt generated by `checkInterrupted`. -/
+def Exception.isInterrupt : Exception → Bool
+  | Exception.internal id _ => id == Core.interruptExceptionId
+  | _ => false
+
 /--
-Custom `try-catch` for all monads based on `CoreM`. We don't want to catch "runtime exceptions"
-in these monads, but on `CommandElabM`. See issues #2775 and #2744 as well as `MonadAlwayExcept`.
+Custom `try-catch` for all monads based on `CoreM`. We usually don't want to catch "runtime
+exceptions" these monads, but on `CommandElabM`. See issues #2775 and #2744 as well as
+`MonadAlwaysExcept`. Also, we never want to catch interrupt exceptions inside the elaborator.
 -/
 @[inline] protected def Core.tryCatch (x : CoreM α) (h : Exception → CoreM α) : CoreM α := do
   try
     x
   catch ex =>
-    if ex.isRuntime && !(← read).catchRuntimeEx then
-      throw ex
+    if ex.isInterrupt || ex.isRuntime then
+
+      throw ex -- We should use `tryCatchRuntimeEx` for catching runtime exceptions
     else
       h ex
 
+@[inline] protected def Core.tryCatchRuntimeEx (x : CoreM α) (h : Exception → CoreM α) : CoreM α := do
+  try
+    x
+  catch ex =>
+    h ex
+
 instance : MonadExceptOf Exception CoreM where
   throw    := throw
   tryCatch := Core.tryCatch
 
-@[inline] def Core.withCatchingRuntimeEx (flag : Bool) (x : CoreM α) : CoreM α :=
-  withReader (fun ctx => { ctx with catchRuntimeEx := flag }) x
+class MonadRuntimeException (m : Type → Type) where
+  tryCatchRuntimeEx (body : m α) (handler : Exception → m α) : m α
+
+export MonadRuntimeException (tryCatchRuntimeEx)
+
+instance : MonadRuntimeException CoreM where
+  tryCatchRuntimeEx := Core.tryCatchRuntimeEx
+
+@[inline] instance [MonadRuntimeException m] : MonadRuntimeException (ReaderT ρ m) where
+  tryCatchRuntimeEx := fun x c r => tryCatchRuntimeEx (x r) (fun e => (c e) r)
+
+@[inline] instance [MonadRuntimeException m] : MonadRuntimeException (StateRefT' ω σ m) where
+  tryCatchRuntimeEx := fun x c s => tryCatchRuntimeEx (x s) (fun e => c e s)
 
 @[inline] def mapCoreM [MonadControlT CoreM m] [Monad m] (f : forall {α}, CoreM α → CoreM α) {α} (x : m α) : m α :=
   controlAt CoreM fun runInBase => f <| runInBase x
 
-/--
-Execute `x` with `catchRuntimeEx = flag`. That is, given `try x catch ex => h ex`,
-if `x` throws a runtime exception, the handler `h` will be invoked if `flag = true`
-Recall that
--/
-@[inline] def withCatchingRuntimeEx [MonadControlT CoreM m] [Monad m] (x : m α) : m α :=
-  mapCoreM (Core.withCatchingRuntimeEx true) x
-
-@[inline] def withoutCatchingRuntimeEx [MonadControlT CoreM m] [Monad m] (x : m α) : m α :=
-  mapCoreM (Core.withCatchingRuntimeEx false) x
-
 end Lean

src/Lean/Data/HashMap.lean

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

src/Lean/Data/Position.lean

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

src/Lean/Data/RBTree.lean

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

src/Lean/Elab/Binders.lean

@@ -7,6 +7,7 @@ prelude
 import Lean.Elab.Quotation.Precheck
 import Lean.Elab.Term
 import Lean.Elab.BindersUtil
+import Lean.Elab.SyntheticMVars
 import Lean.Elab.PreDefinition.WF.TerminationHint
 
 namespace Lean.Elab.Term
@@ -646,7 +647,29 @@ def elabLetDeclAux (id : Syntax) (binders : Array Syntax) (typeStx : Syntax) (va
     (expectedType? : Option Expr) (useLetExpr : Bool) (elabBodyFirst : Bool) (usedLetOnly : Bool) : TermElabM Expr := do
   let (type, val, binders) ← elabBindersEx binders fun xs => do
     let (binders, fvars) := xs.unzip
-    let type ← elabType typeStx
+    /-
+    We use `withSynthesize` to ensure that any postponed elaboration problem
+    and nested tactics in `type` are resolved before elaborating `val`.
+    Resolved: we want to avoid synthethic opaque metavariables in `type`.
+    Recall that this kind of metavariable is non-assignable, and `isDefEq`
+    may waste a lot of time unfolding declarations before failing.
+    See issue #4051 for an example.
+
+    Here is the analysis for issue #4051.
+    - Given `have x : type := value; body`, we were previously elaborating `value` even
+      if `type` contained postponed elaboration problems.
+    - Moreover, the metavariables in `type` corresponding to postponed elaboration
+      problems cannot be assigned by `isDefEq` since the elaborator is supposed to assign them.
+    - Then, when checking whether type of `value` is definitionally equal to `type`,
+      a very long-time was spent unfolding a bunch of declarations before it failed.
+      In #4051, it was unfolding `Array.swaps` which is defined by well-founded recursion.
+      After the failure, the elaborator inserted a postponed coercion
+      that would be resolved later as soon as the types don't have unassigned metavariables.
+
+    We use `postpone := .partial` to allow type class (TC) resolution problems to be postponed
+    Recall that TC resolution does **not** produce synthetic opaque metavariables.
+    -/
+    let type ← withSynthesize (postpone := .partial) <| elabType typeStx
     registerCustomErrorIfMVar type typeStx "failed to infer 'let' declaration type"
     if elabBodyFirst then
       let type ← mkForallFVars fvars type

src/Lean/Elab/BuiltinCommand.lean

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

src/Lean/Elab/BuiltinNotation.lean

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

src/Lean/Elab/Calc.lean

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

src/Lean/Elab/Command.lean

@@ -47,8 +47,9 @@ structure Context where
   ref            : Syntax := Syntax.missing
   tacticCache?   : Option (IO.Ref Tactic.Cache)
   /--
-  Snapshot for incremental reuse and reporting of command elaboration. Currently unused in Lean
-  itself.
+  Snapshot for incremental reuse and reporting of command elaboration. Currently only used for
+  (mutual) defs and contained tactics, in which case the `DynamicSnapshot` is a
+  `HeadersParsedSnapshot`.
 
   Definitely resolved in `Language.Lean.process.doElab`.
 
@@ -56,6 +57,13 @@ structure Context where
   old elaboration are identical.
   -/
   snap?          : Option (Language.SnapshotBundle Language.DynamicSnapshot)
+  /-- Cancellation token forwarded to `Core.cancelTk?`. -/
+  cancelTk?      : Option IO.CancelToken
+  /--
+  If set (when `showPartialSyntaxErrors` is not set and parsing failed), suppresses most elaboration
+  errors; see also `logMessage` below.
+  -/
+  suppressElabErrors : Bool := false
 
 abbrev CommandElabCoreM (ε) := ReaderT Context $ StateRefT State $ EIO ε
 abbrev CommandElabM := CommandElabCoreM Exception
@@ -73,6 +81,21 @@ Remark: see comment at TermElabM
 @[always_inline]
 instance : Monad CommandElabM := let i := inferInstanceAs (Monad CommandElabM); { pure := i.pure, bind := i.bind }
 
+/-- Like `Core.tryCatch` but do catch runtime exceptions. -/
+@[inline] protected def tryCatch (x : CommandElabM α) (h : Exception → CommandElabM α) :
+    CommandElabM α := do
+  try
+    x
+  catch ex =>
+    if ex.isInterrupt then
+      throw ex
+    else
+      h ex
+
+instance : MonadExceptOf Exception CommandElabM where
+  throw    := throw
+  tryCatch := Command.tryCatch
+
 def mkState (env : Environment) (messages : MessageLog := {}) (opts : Options := {}) : State := {
   env         := env
   messages    := messages
@@ -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/Extra.lean

@@ -188,7 +188,7 @@ private partial def toTree (s : Syntax) : TermElabM Tree := do
   the macro declaration names in the `op` nodes.
   -/
   let result ← go s
-  synthesizeSyntheticMVars (mayPostpone := true)
+  synthesizeSyntheticMVars (postpone := .yes)
   return result
 where
   go (s : Syntax) := do
@@ -241,7 +241,10 @@ private def hasCoe (fromType toType : Expr) : TermElabM Bool := do
 
 private structure AnalyzeResult where
   max?            : Option Expr := none
-  hasUncomparable : Bool := false -- `true` if there are two types `α` and `β` where we don't have coercions in any direction.
+  /-- `true` if there are two types `α` and `β` where we don't have coercions in any direction. -/
+  hasUncomparable : Bool := false
+  /-- `true` if there are any leaf terms with an unknown type (according to `isUnknown`). -/
+  hasUnknown      : Bool := false
 
 private def isUnknown : Expr → Bool
   | .mvar ..        => true
@@ -255,7 +258,7 @@ private def analyze (t : Tree) (expectedType? : Option Expr) : TermElabM Analyze
     match expectedType? with
     | none => pure none
     | some expectedType =>
-      let expectedType ← instantiateMVars expectedType
+      let expectedType := (← instantiateMVars expectedType).cleanupAnnotations
       if isUnknown expectedType then pure none else pure (some expectedType)
   (go t *> get).run' { max? }
 where
@@ -268,8 +271,10 @@ where
        | .binop _ _ _ lhs rhs => go lhs; go rhs
        | .unop _ _ arg => go arg
        | .term _ _ val =>
-         let type ← instantiateMVars (← inferType val)
-         unless isUnknown type do
+         let type := (← instantiateMVars (← inferType val)).cleanupAnnotations
+         if isUnknown type then
+           modify fun s => { s with hasUnknown := true }
+         else
            match (← get).max? with
            | none     => modify fun s => { s with max? := type }
            | some max =>
@@ -430,7 +435,7 @@ mutual
       | .unop ref f arg =>
         return .unop ref f (← go arg none false false)
       | .term ref trees e =>
-        let type ← instantiateMVars (← inferType e)
+        let type := (← instantiateMVars (← inferType e)).cleanupAnnotations
         trace[Elab.binop] "visiting {e} : {type} =?= {maxType}"
         if isUnknown type then
           if let some f := f? then
@@ -448,12 +453,17 @@ mutual
 
   private partial def toExpr (tree : Tree) (expectedType? : Option Expr) : TermElabM Expr := do
     let r ← analyze tree expectedType?
-    trace[Elab.binop] "hasUncomparable: {r.hasUncomparable}, maxType: {r.max?}"
+    trace[Elab.binop] "hasUncomparable: {r.hasUncomparable}, hasUnknown: {r.hasUnknown}, maxType: {r.max?}"
     if r.hasUncomparable || r.max?.isNone then
       let result ← toExprCore tree
       ensureHasType expectedType? result
     else
       let result ← toExprCore (← applyCoe tree r.max?.get! (isPred := false))
+      unless r.hasUnknown do
+        -- Record the resulting maxType calculation.
+        -- We can do this when all the types are known, since in this case `hasUncomparable` is valid.
+        -- If they're not known, recording maxType like this can lead to heterogeneous operations failing to elaborate.
+        discard <| isDefEqGuarded (← inferType result) r.max?.get!
       trace[Elab.binop] "result: {result}"
       ensureHasType expectedType? result
 
@@ -486,7 +496,6 @@ def elabBinRelCore (noProp : Bool) (stx : Syntax) (expectedType? : Option Expr)
   | some f => withSynthesizeLight do
     /-
     We used to use `withSynthesize (mayPostpone := true)` here instead of `withSynthesizeLight` here.
-    Recall that `withSynthesizeLight` is equivalent to `withSynthesize (mayPostpone := true) (synthesizeDefault := false)`.
     It seems too much to apply default instances at binary relations. For example, we cannot elaborate
     ```
     def as : List Int := [-1, 2, 0, -3, 4]
@@ -520,7 +529,7 @@ def elabBinRelCore (noProp : Bool) (stx : Syntax) (expectedType? : Option Expr)
     let rhs ← withRef rhsStx <| toTree rhsStx
     let tree := .binop stx .regular f lhs rhs
     let r ← analyze tree none
-    trace[Elab.binrel] "hasUncomparable: {r.hasUncomparable}, maxType: {r.max?}"
+    trace[Elab.binrel] "hasUncomparable: {r.hasUncomparable}, hasUnknown: {r.hasUnknown}, maxType: {r.max?}"
     if r.hasUncomparable || r.max?.isNone then
       -- Use default elaboration strategy + `toBoolIfNecessary`
       let lhs ← toExprCore lhs

src/Lean/Elab/Frontend.lean

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

src/Lean/Elab/Inductive.lean

@@ -324,7 +324,7 @@ private def elabCtors (indFVars : Array Expr) (indFVar : Expr) (params : Array E
           | some ctorType =>
             let type ← Term.elabType ctorType
             trace[Elab.inductive] "elabType {ctorView.declName} : {type} "
-            Term.synthesizeSyntheticMVars (mayPostpone := true)
+            Term.synthesizeSyntheticMVars (postpone := .yes)
             let type ← instantiateMVars type
             let type ← checkParamOccs type
             forallTelescopeReducing type fun _ resultingType => do

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/PreDefinition/Main.lean

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

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

@@ -9,6 +9,7 @@ import Lean.Meta.Tactic.Split
 import Lean.Elab.PreDefinition.Basic
 import Lean.Elab.PreDefinition.Eqns
 import Lean.Meta.ArgsPacker.Basic
+import Init.Data.Array.Basic
 
 namespace Lean.Elab.WF
 open Meta
@@ -39,41 +40,6 @@ private def rwFixEq (mvarId : MVarId) : MetaM MVarId := mvarId.withContext do
   mvarId.assign (← mkEqTrans h mvarNew)
   return mvarNew.mvarId!
 
-/--
-  Simplify `match`-expressions when trying to prove equation theorems for a recursive declaration defined using well-founded recursion.
-  It is similar to `simpMatch?`, but is also tries to fold `WellFounded.fix` applications occurring in discriminants.
-  See comment at `tryToFoldWellFoundedFix`.
--/
-def simpMatchWF? (mvarId : MVarId) : MetaM (Option MVarId) :=
-  mvarId.withContext do
-    let target ← instantiateMVars (← mvarId.getType)
-    let discharge? ← mvarId.withContext do SplitIf.mkDischarge?
-    let (targetNew, _) ← Simp.main target (← Split.getSimpMatchContext) (methods := { pre, discharge? })
-    let mvarIdNew ← applySimpResultToTarget mvarId target targetNew
-    if mvarId != mvarIdNew then return some mvarIdNew else return none
-where
-  pre (e : Expr) : SimpM Simp.Step := do
-    let some app ← matchMatcherApp? e
-      | return Simp.Step.continue
-    -- First try to reduce matcher
-    match (← reduceRecMatcher? e) with
-    | some e' => return Simp.Step.done { expr := e' }
-    | none    => Simp.simpMatchCore app.matcherName e
-
-/--
-  Given a goal of the form `|- f.{us} a_1 ... a_n b_1 ... b_m = ...`, return `(us, #[a_1, ..., a_n])`
-  where `f` is a constant named `declName`, and `n = info.fixedPrefixSize`.
--/
-private def getFixedPrefix (declName : Name) (info : EqnInfo) (mvarId : MVarId) : MetaM (List Level × Array Expr) := mvarId.withContext do
-  let target ← mvarId.getType'
-  let some (_, lhs, _) := target.eq? | unreachable!
-  let lhsArgs := lhs.getAppArgs
-  if lhsArgs.size < info.fixedPrefixSize || !lhs.getAppFn matches .const .. then
-    throwError "failed to generate equational theorem for '{declName}', unexpected number of arguments in the equation left-hand-side\n{mvarId}"
-  let result := lhsArgs[:info.fixedPrefixSize]
-  trace[Elab.definition.wf.eqns] "fixedPrefix: {result}"
-  return (lhs.getAppFn.constLevels!, result)
-
 private partial def mkProof (declName : Name) (type : Expr) : MetaM Expr := do
   trace[Elab.definition.wf.eqns] "proving: {type}"
   withNewMCtxDepth do
@@ -81,11 +47,11 @@ private partial def mkProof (declName : Name) (type : Expr) : MetaM Expr := do
     let (_, mvarId) ← main.mvarId!.intros
     let rec go (mvarId : MVarId) : MetaM Unit := do
       trace[Elab.definition.wf.eqns] "step\n{MessageData.ofGoal mvarId}"
-      if (← tryURefl mvarId) then
+      if ← withAtLeastTransparency .all (tryURefl mvarId) then
         return ()
       else if (← tryContradiction mvarId) then
         return ()
-      else if let some mvarId ← simpMatchWF? mvarId then
+      else if let some mvarId ← simpMatch? mvarId then
         go mvarId
       else if let some mvarId ← simpIf? mvarId then
         go mvarId

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

@@ -132,12 +132,15 @@ def wfRecursion (preDefs : Array PreDefinition) : TermElabM Unit := do
       return { unaryPreDef with value }
   trace[Elab.definition.wf] ">> {preDefNonRec.declName} :=\n{preDefNonRec.value}"
   let preDefs ← preDefs.mapM fun d => eraseRecAppSyntax d
-  if (← isOnlyOneUnaryDef preDefs fixedPrefixSize) then
-    addNonRec preDefNonRec (applyAttrAfterCompilation := false)
-  else
-    withEnableInfoTree false do
+  -- Do not complain if the user sets @[semireducible], which usually is a noop,
+  -- we recognize that below and then do not set @[irreducible]
+  withOptions (allowUnsafeReducibility.set · true) do
+    if (← isOnlyOneUnaryDef preDefs fixedPrefixSize) then
       addNonRec preDefNonRec (applyAttrAfterCompilation := false)
-    addNonRecPreDefs fixedPrefixSize argsPacker preDefs preDefNonRec
+    else
+      withEnableInfoTree false do
+        addNonRec preDefNonRec (applyAttrAfterCompilation := false)
+      addNonRecPreDefs fixedPrefixSize argsPacker preDefs preDefNonRec
   -- We create the `_unsafe_rec` before we abstract nested proofs.
   -- Reason: the nested proofs may be referring to the _unsafe_rec.
   addAndCompilePartialRec preDefs
@@ -146,6 +149,10 @@ def wfRecursion (preDefs : Array PreDefinition) : TermElabM Unit := do
   for preDef in preDefs do
     markAsRecursive preDef.declName
     applyAttributesOf #[preDef] AttributeApplicationTime.afterCompilation
+    -- Unless the user asks for something else, mark the definition as irreducible
+    unless preDef.modifiers.attrs.any fun a =>
+      a.name = `reducible || a.name = `semireducible do
+      setIrreducibleAttribute preDef.declName
 
 builtin_initialize registerTraceClass `Elab.definition.wf
 

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/StructInst.lean

@@ -939,7 +939,7 @@ private def elabStructInstAux (stx : Syntax) (expectedType? : Option Expr) (sour
 
      TODO: investigate whether this design decision may have unintended side effects or produce confusing behavior.
   -/
-  let { val := r, struct, instMVars } ← withSynthesize (mayPostpone := true) <| elabStruct struct expectedType?
+  let { val := r, struct, instMVars } ← withSynthesize (postpone := .yes) <| elabStruct struct expectedType?
   trace[Elab.struct] "before propagate {r}"
   DefaultFields.propagate struct
   synthesizeAppInstMVars instMVars r

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

@@ -288,6 +288,32 @@ private def processPostponedUniverseContraints : TermElabM Unit := do
 private def markAsResolved (mvarId : MVarId) : TermElabM Unit :=
   modify fun s => { s with syntheticMVars := s.syntheticMVars.erase mvarId }
 
+/--
+Auxiliary type for `synthesizeSyntheticMVars`. It specifies
+whether pending synthetic metavariables can be postponed or not.
+-/
+inductive PostponeBehavior where
+  /--
+  Any kind of pending synthetic metavariable can be postponed.
+  Universe constrains may also be postponed.
+  -/
+  | yes
+  /--
+  Pending synthetic metavariables cannot be postponed.
+  -/
+  | no
+  /--
+  Synthectic metavariables associated with type class resolution can be postponed.
+  Motivation: this kind of metavariable are not synthethic opaque, and can be assigned by `isDefEq`.
+  Unviverse constraints can also be postponed.
+  -/
+  | «partial»
+  deriving Inhabited, Repr, BEq
+
+def PostponeBehavior.ofBool : Bool → PostponeBehavior
+  | true  => .yes
+  | false => .no
+
 mutual
 
   /--
@@ -298,7 +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.
@@ -314,26 +339,26 @@ mutual
     Regarding issue #1380, we addressed the issue by avoiding the elaboration postponement step. However, the same issue can happen
     in more complicated scenarios.
     -/
-    try
-      let remainingGoals ← withInfoHole mvarId <| Tactic.run mvarId do
-        withTacticInfoContext tacticCode do
-          -- 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
-        synthesizeSyntheticMVars (mayPostpone := false)
-      unless remainingGoals.isEmpty do
-        if report then
-          reportUnsolvedGoals remainingGoals
+    tryCatchRuntimeEx
+      (do let remainingGoals ← withInfoHole mvarId <| Tactic.run mvarId do
+            withTacticInfoContext tacticCode do
+              -- 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
+                withNarrowedArgTacticReuse (argIdx := 1) (evalTactic ·) tacticCode
+            synthesizeSyntheticMVars (postpone := .no)
+          unless remainingGoals.isEmpty do
+            if report then
+              reportUnsolvedGoals remainingGoals
+            else
+              throwError "unsolved goals\n{goalsToMessageData remainingGoals}")
+      fun ex => do
+        if report && (← read).errToSorry then
+          for mvarId in (← getMVars (mkMVar mvarId)) do
+            mvarId.admit
+          logException ex
         else
-          throwError "unsolved goals\n{goalsToMessageData remainingGoals}"
-    catch ex =>
-      if report && (← read).errToSorry then
-        for mvarId in (← getMVars (mkMVar mvarId)) do
-          mvarId.admit
-        logException ex
-      else
-        throw ex
+          throw ex
 
   /-- Try to synthesize the given pending synthetic metavariable. -/
   private partial def synthesizeSyntheticMVar (mvarId : MVarId) (postponeOnError : Bool) (runTactics : Bool) : TermElabM Bool := do
@@ -388,25 +413,27 @@ mutual
     return numSyntheticMVars != remainingPendingMVars.length
 
   /--
-    Try to process pending synthetic metavariables. If `mayPostpone == false`,
-    then `pendingMVars` is `[]` after executing this method.
+    Try to process pending synthetic metavariables.
+
+    If `postpone == .no`,then `pendingMVars` is `[]` after executing this method.
+    If `postpone == .partial`, then `pendingMVars` contains only `.tc` and `.coe` kinds.
 
     It keeps executing `synthesizeSyntheticMVarsStep` while progress is being made.
-    If `mayPostpone == false`, then it applies default instances to `SyntheticMVarKind.typeClass` (if available)
+    If `postpone != .yes`, then it applies default instances to `SyntheticMVarKind.typeClass` (if available)
     metavariables that are still unresolved, and then tries to resolve metavariables
-    with `mayPostpone == false`. That is, we force them to produce error messages and/or commit to
-    a "best option". If, after that, we still haven't made progress, we report "stuck" errors.
+    with `postponeOnError == false`. That is, we force them to produce error messages and/or commit to
+    a "best option". If, after that, we still haven't made progress, we report "stuck" errors If `postpone == .no`.
 
     Remark: we set `ignoreStuckTC := true` when elaborating `simp` arguments. Then,
     pending TC problems become implicit parameters for the simp theorem.
   -/
-  partial def synthesizeSyntheticMVars (mayPostpone := true) (ignoreStuckTC := false) : TermElabM Unit := do
+  partial def synthesizeSyntheticMVars (postpone := PostponeBehavior.yes) (ignoreStuckTC := false) : TermElabM Unit := do
     let rec loop (_ : Unit) : TermElabM Unit := do
       withRef (← getSomeSyntheticMVarsRef) <| withIncRecDepth do
         unless (← get).pendingMVars.isEmpty do
           if ← synthesizeSyntheticMVarsStep (postponeOnError := false) (runTactics := false) then
             loop ()
-          else if !mayPostpone then
+          else if postpone != .yes then
             /- Resume pending metavariables with "elaboration postponement" disabled.
                We postpone elaboration errors in this step by setting `postponeOnError := true`.
                Example:
@@ -431,48 +458,58 @@ mutual
               loop ()
             else if ← synthesizeSyntheticMVarsStep (postponeOnError := false) (runTactics := true) then
               loop ()
-            else
+            else if postpone == .no then
               reportStuckSyntheticMVars ignoreStuckTC
     loop ()
-    unless mayPostpone do
+    if postpone == .no then
      processPostponedUniverseContraints
 end
 
 def synthesizeSyntheticMVarsNoPostponing (ignoreStuckTC := false) : TermElabM Unit :=
-  synthesizeSyntheticMVars (mayPostpone := false) (ignoreStuckTC := ignoreStuckTC)
+  synthesizeSyntheticMVars (postpone := .no) (ignoreStuckTC := ignoreStuckTC)
 
 /-- Keep invoking `synthesizeUsingDefault` until it returns false. -/
 private partial def synthesizeUsingDefaultLoop : TermElabM Unit := do
   if (← synthesizeUsingDefault) then
-    synthesizeSyntheticMVars (mayPostpone := true)
+    synthesizeSyntheticMVars (postpone := .yes)
     synthesizeUsingDefaultLoop
 
 def synthesizeSyntheticMVarsUsingDefault : TermElabM Unit := do
-  synthesizeSyntheticMVars (mayPostpone := true)
+  synthesizeSyntheticMVars (postpone := .yes)
   synthesizeUsingDefaultLoop
 
-private partial def withSynthesizeImp {α} (k : TermElabM α) (mayPostpone : Bool) (synthesizeDefault : Bool) : TermElabM α := do
-  let pendingMVarsSaved := (← get).pendingMVars
-  modify fun s => { s with pendingMVars := [] }
-  try
-    let a ← k
-    synthesizeSyntheticMVars mayPostpone
-    if mayPostpone && synthesizeDefault then
-      synthesizeUsingDefaultLoop
-    return a
-  finally
-    modify fun s => { s with pendingMVars := s.pendingMVars ++ pendingMVarsSaved }
+private partial def withSynthesizeImp (k : TermElabM α) (postpone : PostponeBehavior) : TermElabM α := do
+   let pendingMVarsSaved := (← get).pendingMVars
+   modify fun s => { s with pendingMVars := [] }
+   try
+     let a ← k
+     synthesizeSyntheticMVars (postpone := postpone)
+     if postpone == .yes then
+       synthesizeUsingDefaultLoop
+     return a
+   finally
+     modify fun s => { s with pendingMVars := s.pendingMVars ++ pendingMVarsSaved }
 
 /--
   Execute `k`, and synthesize pending synthetic metavariables created while executing `k` are solved.
   If `mayPostpone == false`, then all of them must be synthesized.
   Remark: even if `mayPostpone == true`, the method still uses `synthesizeUsingDefault` -/
-@[inline] def withSynthesize [MonadFunctorT TermElabM m] [Monad m] (k : m α) (mayPostpone := false) : m α :=
-  monadMap (m := TermElabM) (withSynthesizeImp · mayPostpone (synthesizeDefault := true)) k
+@[inline] def withSynthesize [MonadFunctorT TermElabM m] [Monad m] (k : m α) (postpone := PostponeBehavior.no) : m α :=
+  monadMap (m := TermElabM) (withSynthesizeImp · postpone) k
 
-/-- Similar to `withSynthesize`, but sets `mayPostpone` to `true`, and do not use `synthesizeUsingDefault` -/
+private partial def withSynthesizeLightImp (k : TermElabM α) : TermElabM α := do
+  let pendingMVarsSaved := (← get).pendingMVars
+  modify fun s => { s with pendingMVars := [] }
+  try
+    let a ← k
+    synthesizeSyntheticMVars (postpone := .yes)
+    return a
+  finally
+    modify fun s => { s with pendingMVars := s.pendingMVars ++ pendingMVarsSaved }
+
+/-- Similar to `withSynthesize`, but uses `postpone := .true`, does not use use `synthesizeUsingDefault` -/
 @[inline] def withSynthesizeLight [MonadFunctorT TermElabM m] [Monad m] (k : m α) : m α :=
-  monadMap (m := TermElabM) (withSynthesizeImp · (mayPostpone := true) (synthesizeDefault := false)) k
+  monadMap (m := TermElabM) (withSynthesizeLightImp ·) k
 
 /-- Elaborate `stx`, and make sure all pending synthetic metavariables created while elaborating `stx` are solved. -/
 def elabTermAndSynthesize (stx : Syntax) (expectedType? : Option Expr) : TermElabM Expr :=

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 :=
@@ -231,15 +244,15 @@ def closeUsingOrAdmit (tac : TacticM Unit) : TacticM Unit := do
   /- Important: we must define `closeUsingOrAdmit` before we define
      the instance `MonadExcept` for `TacticM` since it backtracks the state including error messages. -/
   let mvarId :: mvarIds ← getUnsolvedGoals | throwNoGoalsToBeSolved
-  try
-    focusAndDone tac
-  catch ex =>
-    if (← read).recover then
-      logException ex
-      admitGoal mvarId
-      setGoals mvarIds
-    else
-      throw ex
+  tryCatchRuntimeEx
+    (focusAndDone tac)
+    fun ex => do
+      if (← read).recover then
+        logException ex
+        admitGoal mvarId
+        setGoals mvarIds
+      else
+        throw ex
 
 instance : MonadBacktrack SavedState TacticM where
   saveState := Tactic.saveState

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 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
@@ -270,7 +342,7 @@ where
       pure (fvarId, [mvarId])
     if let some typeStx := typeStx? then
       withMainContext do
-        let type ← Term.withSynthesize (mayPostpone := true) <| Term.elabType typeStx
+        let type ← Term.withSynthesize (postpone := .yes) <| Term.elabType typeStx
         let fvar := mkFVar fvarId
         let fvarType ← inferType fvar
         unless (← isDefEqGuarded type fvarType) do
@@ -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/Calc.lean

@@ -11,7 +11,7 @@ namespace Lean.Elab.Tactic
 open Meta
 
 /-- Elaborator for the `calc` tactic mode variant. -/
-@[builtin_tactic calcTactic]
+@[builtin_tactic Lean.calcTactic]
 def evalCalc : Tactic := fun stx => withMainContext do
   let steps : TSyntax ``calcSteps := ⟨stx[1]⟩
   let (val, mvarIds) ← withCollectingNewGoalsFrom (tagSuffix := `calc) do
@@ -32,3 +32,5 @@ def evalCalc : Tactic := fun stx => withMainContext do
     return val
   (← getMainGoal).assign val
   replaceMainGoal mvarIds
+
+end Lean.Elab.Tactic

src/Lean/Elab/Tactic/ElabTerm.lean

@@ -29,7 +29,7 @@ def runTermElab (k : TermElabM α) (mayPostpone := false) : TacticM α := do
   else
     Term.withoutErrToSorry go
 where
-  go := k <* Term.synthesizeSyntheticMVars (mayPostpone := mayPostpone)
+  go := k <* Term.synthesizeSyntheticMVars (postpone := .ofBool mayPostpone)
 
 /-- Elaborate `stx` in the current `MVarContext`. If given, the `expectedType` will be used to help
 elaboration but not enforced (use `elabTermEnsuringType` to enforce an expected type). -/

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]
@@ -524,7 +578,7 @@ private def elabTermForElim (stx : Syntax) : TermElabM Expr := do
       return e
   Term.withoutErrToSorry <| Term.withoutHeedElabAsElim do
     let e ← Term.elabTerm stx none (implicitLambda := false)
-    Term.synthesizeSyntheticMVars (mayPostpone := false) (ignoreStuckTC := true)
+    Term.synthesizeSyntheticMVars (postpone := .no) (ignoreStuckTC := true)
     let e ← instantiateMVars e
     let e := e.eta
     if e.hasMVar then
@@ -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/Meta.lean

@@ -14,7 +14,7 @@ open Term
 def runTactic (mvarId : MVarId) (tacticCode : Syntax) (ctx : Context := {}) (s : State := {}) : MetaM (List MVarId × State) := do
   instantiateMVarDeclMVars mvarId
   let go : TermElabM (List MVarId) :=
-    withSynthesize (mayPostpone := false) do Tactic.run mvarId (Tactic.evalTactic tacticCode *> Tactic.pruneSolvedGoals)
+    withSynthesize do Tactic.run mvarId (Tactic.evalTactic tacticCode *> Tactic.pruneSolvedGoals)
   go.run ctx s
 
 end Lean.Elab

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/Omega/OmegaM.lean

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

src/Lean/Elab/Tactic/Simp.lean

@@ -46,7 +46,7 @@ def tacticToDischarge (tacticCode : Syntax) : TacticM (IO.Ref Term.State × Simp
            So, we must not save references to them at `Term.State`.
         -/
         withoutModifyingStateWithInfoAndMessages do
-          Term.withSynthesize (mayPostpone := false) do
+          Term.withSynthesize (postpone := .no) do
             Term.runTactic (report := false) mvar.mvarId! tacticCode
           let result ← instantiateMVars mvar
           if result.hasExprMVar then
@@ -121,7 +121,7 @@ private def addDeclToUnfoldOrTheorem (thms : SimpTheorems) (id : Origin) (e : Ex
 private def addSimpTheorem (thms : SimpTheorems) (id : Origin) (stx : Syntax) (post : Bool) (inv : Bool) : TermElabM SimpTheorems := do
   let (levelParams, proof) ← Term.withoutModifyingElabMetaStateWithInfo <| withRef stx <| Term.withoutErrToSorry do
     let e ← Term.elabTerm stx none
-    Term.synthesizeSyntheticMVars (mayPostpone := false) (ignoreStuckTC := true)
+    Term.synthesizeSyntheticMVars (postpone := .no) (ignoreStuckTC := true)
     let e ← instantiateMVars e
     let e := e.eta
     if e.hasMVar then
@@ -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
@@ -171,58 +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]
-            let declNames? ← try pure (some (← realizeGlobalConst id)) catch _ => pure none
-            if let some declNames := declNames? then
-              let declName ← ensureNonAmbiguous id declNames
-              if (← Simp.isSimproc declName) then
-                simprocs := simprocs.erase declName
-              else if ctx.config.autoUnfold then
-                thms := thms.eraseCore (.decl declName)
-              else
-                thms ← thms.erase (.decl declName)
-            else
-              -- If `id` could not be resolved, we should check whether it is a builtin simproc.
-              -- before returning error.
-              let name := id.getId.eraseMacroScopes
-              if (← Simp.isBuiltinSimproc name) then
-                simprocs := simprocs.erase name
-              else
-                throwUnknownConstant name
-        else if arg.getKind == ``Lean.Parser.Tactic.simpLemma then
-          let post :=
-            if arg[0].isNone then
-              true
-            else
-              arg[0][0].getKind == ``Parser.Tactic.simpPost
-          let inv  := !arg[1].isNone
-          let term := arg[2]
-          match (← resolveSimpIdTheorem? term) with
-          | .expr e  =>
-            let name ← mkFreshId
-            thms ← addDeclToUnfoldOrTheorem thms (.stx name arg) e post inv kind
-          | .simproc declName =>
-            simprocs ← simprocs.add declName post
-          | .ext (some ext₁) (some ext₂) _ =>
-            thmsArray := thmsArray.push (← ext₁.getTheorems)
-            simprocs  := simprocs.push (← ext₂.getSimprocs)
-          | .ext (some ext₁) none _ =>
-            thmsArray := thmsArray.push (← ext₁.getTheorems)
-          | .ext none (some ext₂) _ =>
-            simprocs  := simprocs.push (← ext₂.getSimprocs)
-          | .none    =>
-            let name ← mkFreshId
-            thms ← addSimpTheorem thms (.stx name arg) term post inv
-        else if arg.getKind == ``Lean.Parser.Tactic.simpStar then
-          starArg := true
-        else
-          throwUnsupportedSyntax
+            throwUnsupportedSyntax
+        catch ex => logException ex
       return { ctx := { ctx with simpTheorems := thmsArray.set! 0 thms }, simprocs, starArg }
 where
   isSimproc? (e : Expr) : MetaM (Option Name) := do
@@ -338,7 +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
 
 /--
@@ -784,7 +897,7 @@ def synthesizeInstMVarCore (instMVar : MVarId) (maxResultSize? : Option Nat := n
     if (← read).ignoreTCFailures then
       return false
     else
-      throwError "failed to synthesize instance{indentExpr type}"
+      throwError "failed to synthesize{indentExpr type}\n{useDiagnosticMsg}"
 
 def mkCoe (expectedType : Expr) (e : Expr) (f? : Option Expr := none) (errorMsgHeader? : Option String := none) : TermElabM Expr := do
   withTraceNode `Elab.coe (fun _ => return m!"adding coercion for {e} : {← inferType e} =?= {expectedType}") do
@@ -1523,14 +1636,15 @@ partial def withAutoBoundImplicit (k : TermElabM α) : TermElabM α := do
   let flag := autoImplicit.get (← getOptions)
   if flag then
     withReader (fun ctx => { ctx with autoBoundImplicit := flag, autoBoundImplicits := {} }) do
-      let rec loop (s : SavedState) : TermElabM α := do
+      let rec loop (s : SavedState) : TermElabM α := withIncRecDepth do
+        checkSystem "auto-implicit"
         try
           k
         catch
           | 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)
@@ -1634,6 +1748,7 @@ def isLetRecAuxMVar (mvarId : MVarId) : TermElabM Bool := do
   Remark: fresh universe metavariables are created if the constant has more universe
   parameters than `explicitLevels`. -/
 def mkConst (constName : Name) (explicitLevels : List Level := []) : TermElabM Expr := do
+  Linter.checkDeprecated constName -- TODO: check is occurring too early if there are multiple alternatives. Fix if it is not ok in practice
   let cinfo ← getConstInfo constName
   if explicitLevels.length > cinfo.levelParams.length then
     throwError "too many explicit universe levels for '{constName}'"
@@ -1645,7 +1760,6 @@ def mkConst (constName : Name) (explicitLevels : List Level := []) : TermElabM E
 private def mkConsts (candidates : List (Name × List String)) (explicitLevels : List Level) : TermElabM (List (Expr × List String)) := do
   candidates.foldlM (init := []) fun result (declName, projs) => do
     -- TODO: better support for `mkConst` failure. We may want to cache the failures, and report them if all candidates fail.
-    Linter.checkDeprecated declName -- TODO: check is occurring too early if there are multiple alternatives. Fix if it is not ok in practice
     let const ← mkConst declName explicitLevels
     return (const, projs) :: result
 
@@ -1768,6 +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