feat: maximum?_eq_some_iff'

fix: discrepancy theorem vs example (#4493 )
When the type of an `example` is a proposition, we should elaborate on them as we elaborate on theorems. This is particularly important for examples that are often used in educational material. Recall that when elaborating theorem headers, we convert unassigned universe metavariables into universe parameters. The motivation is that the proof of a theorem should not influence its statement. However, before this commit, this was not the case for examples when their type was a proposition. This discrepancy often confused users. Additionally, we considered extending the above behavior to definitions when 1- When their type is a proposition. However, it still caused disruption in Mathlib. 2- When their type is provided. That is, we would keep the current behavior only if `: <type>` was omitted. This would make the elaborator for `def` much closer to the one for `theorem`, but it proved to be too restrictive. For example, the following instance in `Core.lean` would fail: ``` instance {α : Sort u} [Setoid α] : HasEquiv α := ⟨Setoid.r⟩ ``` and we would have to write instead: ``` instance {α : Sort u} [Setoid α] : HasEquiv.{u, 0} α := ⟨Setoid.r⟩ ``` There are other failures like this in the core, and we assume many more in Mathlib. closes #4398 closes #4482 Remark: PR #4482 implements option 1 above. We may consider it again in the future.
2026-03-18 10:54:09 +00:00 · 2024-06-24 21:44:42 +10:00 · 2024-06-24 01:18:41 +00:00 · 2024-06-24 01:04:04 +00:00 · 2024-06-24 00:38:22 +00:00 · 2024-06-23 22:37:02 +00:00
1220 changed files with 12615 additions and 5619 deletions
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -122,9 +122,8 @@ jobs:
          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" : "";
+            // use large runners where available (original repo)
+            let large = ${{ github.repository == 'leanprover/lean4' }};
            let matrix = [
              {
                // portable release build: use channel with older glibc (2.27)
@@ -143,7 +142,7 @@ jobs:
              },
              {
                "name": "Linux release",
-                "os": "ubuntu-latest",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
                "release": true,
                "check-level": 0,
                "shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
@@ -155,7 +154,7 @@ jobs:
              },
              {
                "name": "Linux",
-                "os": "ubuntu-latest",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
                "check-stage3": level >= 2,
                "test-speedcenter": level >= 2,
                "check-level": 1,
@@ -281,16 +280,8 @@ jobs:
      CXX: c++
      MACOSX_DEPLOYMENT_TARGET: 10.15
    steps:
-      - name: Checkout
-        uses: actions/checkout@v3
-        with:
-          submodules: true
-          # the default is to use a virtual merge commit between the PR and master: just use the PR
-          ref: ${{ github.event.pull_request.head.sha }}
      - name: Install Nix
-        uses: cachix/install-nix-action@v18
-        with:
-          install_url: https://releases.nixos.org/nix/nix-2.12.0/install
+        uses: DeterminateSystems/nix-installer-action@main
        if: runner.os == 'Linux' && !matrix.cmultilib
      - name: Install MSYS2
        uses: msys2/setup-msys2@v2
@@ -303,6 +294,20 @@ jobs:
        run: |
          brew install ccache tree zstd coreutils gmp
        if: runner.os == 'macOS'
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          # the default is to use a virtual merge commit between the PR and master: just use the PR
+          ref: ${{ github.event.pull_request.head.sha }}
+      # Do check out some CI-relevant files from virtual merge commit to accommodate CI changes on
+      # master (as the workflow files themselves are always taken from the merge)
+      # (needs to be after "Install *" to use the right shell)
+      - name: CI Merge Checkout
+        run: |
+          git fetch --depth=1 origin ${{ github.sha }}
+          git checkout FETCH_HEAD flake.nix flake.lock
+        if: github.event_name == 'pull_request'
+      # (needs to be after "Checkout" so files don't get overriden)
      - name: Setup emsdk
        uses: mymindstorm/setup-emsdk@v12
        with:
@@ -318,20 +323,14 @@ jobs:
        uses: actions/cache@v3
        with:
          path: .ccache
-          key: ${{ matrix.name }}-build-v3-${{ github.sha }}
+          key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
          # fall back to (latest) previous cache
          restore-keys: |
            ${{ matrix.name }}-build-v3
+      # open nix-shell once for initial setup
      - name: Setup
        run: |
-          # open nix-shell once for initial setup
-          true
-        if: runner.os == 'Linux'
-      - name: Set up core dumps
-        run: |
-          mkdir -p $PWD/coredumps
-          # store in current directory, for easy uploading together with binary
-          echo $PWD/coredumps/%e.%p.%t | sudo tee /proc/sys/kernel/core_pattern
+          ccache --zero-stats
        if: runner.os == 'Linux'
      - name: Set up NPROC
        run: |
@@ -340,7 +339,6 @@ jobs:
        run: |
          mkdir build
          cd build
-          ulimit -c unlimited # coredumps
          # arguments passed to `cmake`
          # this also enables githash embedding into stage 1 library
          OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
@@ -367,8 +365,10 @@ jobs:
          fi
          # contortion to support empty OPTIONS with old macOS bash
          cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
-          make -j$NPROC
-          make install
+          time make -j$NPROC
+      - name: Install
+        run: |
+          make -C build install
      - name: Check Binaries
        run: ${{ matrix.binary-check }} lean-*/bin/* || true
      - name: List Install Tree
@@ -398,8 +398,7 @@ jobs:
      - name: Test
        id: test
        run: |
-          ulimit -c unlimited # coredumps
-          ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
+          time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
        if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.check-level >= 1
      - name: Test Summary
        uses: test-summary/action@v2
@@ -412,51 +411,28 @@ jobs:
        if: (!matrix.cross) && steps.test.conclusion != 'skipped'
      - name: Build Stage 2
        run: |
-          ulimit -c unlimited # coredumps
          make -C build -j$NPROC stage2
        if: matrix.test-speedcenter
      - name: Check Stage 3
        run: |
-          ulimit -c unlimited # coredumps
          make -C build -j$NPROC stage3
        if: matrix.test-speedcenter
      - name: Test Speedcenter Benchmarks
        run: |
-          echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
+          # Necessary for some timing metrics but does not work on Namespace runners
+          # and we just want to test that the benchmarks run at all here
+          #echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
          export BUILD=$PWD/build PATH=$PWD/build/stage1/bin:$PATH
          cd tests/bench
          nix shell .#temci -c temci exec --config speedcenter.yaml --included_blocks fast --runs 1
        if: matrix.test-speedcenter
      - name: Check rebootstrap
        run: |
-          ulimit -c unlimited # coredumps
          # clean rebuild in case of Makefile changes
          make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
        if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
      - name: CCache stats
        run: ccache -s
-      - name: Show stacktrace for coredumps
-        if: ${{ failure() && runner.os == 'Linux' }}
-        run: |
-          for c in coredumps/*; do
-            progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
-            echo bt | $GDB/bin/gdb -q $progbin $c || true
-          done
-      # has not been used in a long while, would need to be adapted to new
-      # shared libs
-      #- name: Upload coredumps
-      #  uses: actions/upload-artifact@v3
-      #  if: ${{ failure() && runner.os == 'Linux' }}
-      #  with:
-      #    name: coredumps-${{ matrix.name }}
-      #    path: |
-      #      ./coredumps
-      #      ./build/stage0/bin/lean
-      #      ./build/stage0/lib/lean/libleanshared.so
-      #      ./build/stage1/bin/lean
-      #      ./build/stage1/lib/lean/libleanshared.so
-      #      ./build/stage2/bin/lean
-      #      ./build/stage2/lib/lean/libleanshared.so

  # This job collects results from all the matrix jobs
  # This can be made the “required” job, instead of listing each
@@ -491,6 +467,7 @@ jobs:
        with:
          files: artifacts/*/*
          fail_on_unmatched_files: true
+          prerelease: ${{ !startsWith(github.ref, 'refs/tags/v') || contains(github.ref, '-rc') }}
        env:
          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}

--- a/.github/workflows/nix-ci.yml
+++ b/.github/workflows/nix-ci.yml
@@ -13,18 +13,36 @@ concurrency:
  cancel-in-progress: true

 jobs:
+  # see ci.yml
+  configure:
+    runs-on: ubuntu-latest
+    outputs:
+      matrix: ${{ steps.set-matrix.outputs.result }}
+    steps:
+      - name: Configure build matrix
+        id: set-matrix
+        uses: actions/github-script@v7
+        with:
+          script: |
+            let large = ${{ github.repository == 'leanprover/lean4' }};
+            let matrix = [
+              {
+                "name": "Nix Linux",
+                "os": large ? "nscloud-ubuntu-22.04-amd64-8x8" : "ubuntu-latest",
+              }
+            ];
+            console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
+            return matrix;
+
  Build:
+    needs: [configure]
    runs-on: ${{ matrix.os }}
    defaults:
      run:
        shell: nix run .#ciShell -- bash -euxo pipefail {0}
    strategy:
      matrix:
-        include:
-          - name: Nix Linux
-            os: ubuntu-latest
-          #- name: Nix macOS
-          #  os: macos-latest
+        include: ${{fromJson(needs.configure.outputs.matrix)}}
      # complete all jobs
      fail-fast: false
    name: ${{ matrix.name }}
--- a/.github/workflows/pr-release.yml
+++ b/.github/workflows/pr-release.yml
@@ -298,6 +298,13 @@ jobs:
          ref: nightly-testing
          fetch-depth: 0 # This ensures we check out all tags and branches.

+      - name: install elan
+        run: |
+          set -o pipefail
+          curl -sSfL https://github.com/leanprover/elan/releases/download/v3.0.0/elan-x86_64-unknown-linux-gnu.tar.gz | tar xz
+          ./elan-init -y --default-toolchain none
+          echo "$HOME/.elan/bin" >> "${GITHUB_PATH}"
+
      - name: Check if tag exists
        if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
        id: check_mathlib_tag
@@ -322,7 +329,8 @@ jobs:
            echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
            git add lean-toolchain
            sed -i "s/require batteries from git \"https:\/\/github.com\/leanprover-community\/batteries\" @ \".\+\"/require batteries from git \"https:\/\/github.com\/leanprover-community\/batteries\" @ \"nightly-testing-${MOST_RECENT_NIGHTLY}\"/" lakefile.lean
-            git add lakefile.lean
+            lake update batteries
+            git add lakefile.lean lake-manifest.json
            git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
          else
            echo "Branch already exists, pushing an empty commit."
--- a/.gitignore
+++ b/.gitignore
@@ -4,8 +4,10 @@
 *.lock
 .lake
 lake-manifest.json
-build
-!/src/lake/Lake/Build
+/build
+/src/lakefile.toml
+/tests/lakefile.toml
+/lakefile.toml
 GPATH
 GRTAGS
 GSYMS
--- a/RELEASES.md
+++ b/RELEASES.md
@@ -1,23 +1,515 @@
 # 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.

-v4.9.0
---------
+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.

+v4.10.0
+----------
 Development in progress.

+v4.9.0
+---------- 
+Release candidate, release notes will be copied from branch `releases/v4.9.0` once completed.
+
 v4.8.0
 ---------

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

 v4.7.0
 ---------
--- a/doc/char.md
+++ b/doc/char.md
@@ -1 +1,11 @@
 # Characters
+
+A value of type `Char`, also known as a character, is a [Unicode scalar value](https://www.unicode.org/glossary/#unicode_scalar_value). It is represented using an unsigned 32-bit integer and is statically guaranteed to be a valid Unicode scalar value.
+
+Syntactically, character literals are enclosed in single quotes.
+```lean
+#eval 'a' -- 'a'
+#eval '∀' -- '∀'
+```
+
+Characters are ordered and can be decidably compared using the relational operators `=`, `<`, `≤`, `>`, `≥`.
--- a/doc/dev/release_checklist.md
+++ b/doc/dev/release_checklist.md
@@ -46,7 +46,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
  - We do this for the repositories:
    - [lean4checker](https://github.com/leanprover/lean4checker)
      - No dependencies
-      - Note: `lean4checker` uses a different version tagging scheme: use `toolchain/v4.6.0` rather than `v4.6.0`.
      - Toolchain bump PR
      - Create and push the tag
      - Merge the tag into `stable`
@@ -82,10 +81,8 @@ We'll use `v4.6.0` as the intended release version as a running example.
      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Batteries`, `doc-gen4`, `import-graph`
      - Toolchain bump PR notes:
        - In addition to updating the `lean-toolchain` and `lakefile.lean`,
-          in `.github/workflows/build.yml.in` in the `lean4checker` section update the line
-          `git checkout toolchain/v4.6.0` to the appropriate tag,
-          and then run `.github/workflows/mk_build_yml.sh`. Coordinate with
-          a Mathlib maintainer to get this merged.
+          in `.github/workflows/lean4checker.yml` update the line
+          `git checkout v4.6.0` to the appropriate tag. 
        - Push the PR branch to the main Mathlib repository rather than a fork, or CI may not work reliably
        - Create and push the tag
        - Create a new branch from the tag, push it, and open a pull request against `stable`.
--- a/doc/examples/compiler/.gitignore
+++ b/doc/examples/compiler/.gitignore
@@ -0,0 +1 @@
+build
--- a/flake.nix
+++ b/flake.nix
@@ -35,26 +35,28 @@
      lean-packages = pkgs.callPackage (./nix/packages.nix) { src = ./.; inherit nix lean4-mode; };

      devShellWithDist = pkgsDist: pkgs.mkShell.override {
-	  stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
-	} ({
-	  buildInputs = with pkgs; [
-	    cmake gmp ccache
-	    lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
-	    # TODO: only add when proven to not affect the flakification
-	    #pkgs.python3
-	  ];
-	  # https://github.com/NixOS/nixpkgs/issues/60919
-	  hardeningDisable = [ "all" ];
-	  # more convenient `ctest` output
-	  CTEST_OUTPUT_ON_FAILURE = 1;
-	} // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
-	  GMP = pkgsDist.gmp.override { withStatic = true; };
-	  GLIBC = pkgsDist.glibc;
-	  GLIBC_DEV = pkgsDist.glibc.dev;
-	  GCC_LIB = pkgsDist.gcc.cc.lib;
-	  ZLIB = pkgsDist.zlib;
-	  GDB = pkgsDist.gdb;
-	});
+          stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
+        } ({
+          buildInputs = with pkgs; [
+            cmake gmp ccache
+            lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
+            gdb
+            # TODO: only add when proven to not affect the flakification
+            #pkgs.python3
+            tree  # for CI
+          ];
+          # https://github.com/NixOS/nixpkgs/issues/60919
+          hardeningDisable = [ "all" ];
+          # more convenient `ctest` output
+          CTEST_OUTPUT_ON_FAILURE = 1;
+        } // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
+          GMP = pkgsDist.gmp.override { withStatic = true; };
+          GLIBC = pkgsDist.glibc;
+          GLIBC_DEV = pkgsDist.glibc.dev;
+          GCC_LIB = pkgsDist.gcc.cc.lib;
+          ZLIB = pkgsDist.zlib;
+          GDB = pkgsDist.gdb;
+        });
    in {
      packages = lean-packages // rec {
        debug = lean-packages.override { debug = true; };
--- a/nix/bootstrap.nix
+++ b/nix/bootstrap.nix
@@ -87,7 +87,8 @@ rec {
        leanFlags = [ "-DwarningAsError=true" ];
      } // args);
      Init' = build { name = "Init"; deps = []; };
-      Lean' = build { name = "Lean"; deps = [ Init' ]; };
+      Std' = build { name = "Std"; deps = [ Init' ]; };
+      Lean' = build { name = "Lean"; deps = [ Std' ]; };
      attachSharedLib = sharedLib: pkg: pkg // {
        inherit sharedLib;
        mods = mapAttrs (_: m: m // { inherit sharedLib; propagatedLoadDynlibs = []; }) pkg.mods;
@@ -95,7 +96,8 @@ rec {
    in (all: all // all.lean) rec {
      inherit (Lean) emacs-dev emacs-package vscode-dev vscode-package;
      Init = attachSharedLib leanshared Init';
-      Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Init ]; };
+      Std = attachSharedLib leanshared Std' // { allExternalDeps = [ Init ]; };
+      Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Std ]; };
      Lake = build {
        name = "Lake";
        src = src + "/src/lake";
@@ -109,23 +111,22 @@ rec {
        linkFlags = lib.optional stdenv.isLinux "-rdynamic";
        src = src + "/src/lake";
      };
-      stdlib = [ Init Lean Lake ];
+      stdlib = [ Init Std Lean Lake ];
      modDepsFiles = symlinkJoin { name = "modDepsFiles"; paths = map (l: l.modDepsFile) (stdlib ++ [ Leanc ]); };
      depRoots = symlinkJoin { name = "depRoots"; paths = map (l: l.depRoots) stdlib; };
      iTree = symlinkJoin { name = "ileans"; paths = map (l: l.iTree) stdlib; };
      Leanc = build { name = "Leanc"; src = lean-bin-tools-unwrapped.leanc_src; deps = stdlib; roots = [ "Leanc" ]; };
-      stdlibLinkFlags = "-L${Init.staticLib} -L${Lean.staticLib} -L${Lake.staticLib} -L${leancpp}/lib/lean";
+      stdlibLinkFlags = "${lib.concatMapStringsSep " " (l: "-L${l.staticLib}") stdlib} -L${leancpp}/lib/lean";
      libInit_shared = runCommand "libInit_shared" { buildInputs = [ stdenv.cc ]; libName = "libInit_shared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
        mkdir $out
-        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared -Wl,-Bsymbolic \
-          -Wl,--whole-archive -lInit ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++ -lm ${stdlibLinkFlags} \
-          $(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
-          -o $out/$libName
+        touch empty.c
+        ${stdenv.cc}/bin/cc -shared -o $out/$libName empty.c
      '';
      leanshared = runCommand "leanshared" { buildInputs = [ stdenv.cc ]; libName = "libleanshared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
        mkdir $out
-        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared -Wl,-Bsymbolic \
-          ${libInit_shared}/* -Wl,--whole-archive -lLean -lleancpp -Wl,--no-whole-archive -lstdc++ -lm ${stdlibLinkFlags} \
+        LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared ${lib.optionalString stdenv.isLinux "-Wl,-Bsymbolic"} \
+          ${if stdenv.isDarwin then "-Wl,-force_load,${Init.staticLib}/libInit.a -Wl,-force_load,${Lean.staticLib}/libStd.a -Wl,-force_load,${Lean.staticLib}/libLean.a -Wl,-force_load,${leancpp}/lib/lean/libleancpp.a ${leancpp}/lib/libleanrt_initial-exec.a -lc++"
+            else "-Wl,--whole-archive -lInit -lStd -lLean -lleancpp ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++"} -lm ${stdlibLinkFlags} \
          $(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
          -o $out/$libName
      '';
@@ -151,11 +152,9 @@ rec {
        '';
        meta.mainProgram = "lean";
      };
-      cacheRoots = linkFarmFromDrvs "cacheRoots" [
+      cacheRoots = linkFarmFromDrvs "cacheRoots" ([
        stage0 lean leanc lean-all iTree modDepsFiles depRoots Leanc.src
-        # .o files are not a runtime dependency on macOS because of lack of thin archives
-        Lean.oTree Lake.oTree
-      ];
+      ] ++ map (lib: lib.oTree) stdlib);
      test = buildCMake {
        name = "lean-test-${desc}";
        realSrc = lib.sourceByRegex src [ "src.*" "tests.*" ];
@@ -170,7 +169,7 @@ rec {
          ln -sf ${lean-all}/* .
        '';
        buildPhase = ''
-          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)|leanlaketest_init' -j$NIX_BUILD_CORES
+          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)' -j$NIX_BUILD_CORES
        '';
        installPhase = ''
          mkdir $out
@@ -178,7 +177,7 @@ rec {
        '';
      };
      update-stage0 =
-        let cTree = symlinkJoin { name = "cs"; paths = [ Init.cTree Lean.cTree ]; }; in
+        let cTree = symlinkJoin { name = "cs"; paths = map (lib: lib.cTree) stdlib; }; in
        writeShellScriptBin "update-stage0" ''
          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
        '';
--- a/nix/buildLeanPackage.nix
+++ b/nix/buildLeanPackage.nix
@@ -5,7 +5,7 @@ let lean-final' = lean-final; in
 lib.makeOverridable (
 { name, src, fullSrc ? src, srcPrefix ? "", srcPath ? "$PWD/${srcPrefix}",
  # Lean dependencies. Each entry should be an output of buildLeanPackage.
-  deps ? [ lean.Lean ],
+  deps ? [ lean.Init lean.Std lean.Lean ],
  # Static library dependencies. Each derivation `static` should contain a static library in the directory `${static}`.
  staticLibDeps ? [],
  # Whether to wrap static library inputs in a -Wl,--start-group [...] -Wl,--end-group to ensure dependencies are resolved.
@@ -249,7 +249,7 @@ in rec {
    ${if stdenv.isDarwin then "-Wl,-force_load,${staticLib}/lib${libName}.a" else "-Wl,--whole-archive ${staticLib}/lib${libName}.a -Wl,--no-whole-archive"} \
    ${lib.concatStringsSep " " (map (d: "${d.sharedLib}/*") deps)}'';
  executable = lib.makeOverridable ({ withSharedStdlib ? true }: let
-      objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.libInit_shared}/* ${lean-final.leanshared}/*";
+      objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.leanshared}/*";
    in runCommand executableName { buildInputs = [ stdenv.cc leanc ]; } ''
      mkdir -p $out/bin
      leanc ${staticLibLinkWrapper (lib.concatStringsSep " " (objPaths ++ map (d: "${d}/*.a") allStaticLibDeps))} \
--- a/releases_drafts/messagedata.md
+++ b/releases_drafts/messagedata.md
@@ -1,13 +0,0 @@
-* 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
--- a/releases_drafts/varCtorNameLint.md
+++ b/releases_drafts/varCtorNameLint.md
@@ -0,0 +1,45 @@
+A new linter flags situations where a local variable's name is one of
+the argumentless constructors of its type. This can arise when a user either
+doesn't open a namespace or doesn't add a dot or leading qualifier, as
+in the following:
+
+````
+inductive Tree (α : Type) where
+  | leaf
+  | branch (left : Tree α) (val : α) (right : Tree α)
+
+def depth : Tree α → Nat
+  | leaf => 0
+````
+
+With this linter, the `leaf` pattern is highlighted as a local
+variable whose name overlaps with the constructor `Tree.leaf`.
+
+The linter can be disabled with `set_option linter.constructorNameAsVariable false`.
+
+Additionally, the error message that occurs when a name in a pattern that takes arguments isn't valid now suggests similar names that would be valid. This means that the following definition:
+
+```
+def length (list : List α) : Nat :=
+  match list with
+  | nil => 0
+  | cons x xs => length xs + 1
+```
+
+now results in the following warning:
+
+```
+warning: Local variable 'nil' resembles constructor 'List.nil' - write '.nil' (with a dot) or 'List.nil' to use the constructor.
+note: this linter can be disabled with `set_option linter.constructorNameAsVariable false`
+```
+
+and error:
+
+```
+invalid pattern, constructor or constant marked with '[match_pattern]' expected
+
+Suggestion: 'List.cons' is similar
+```
+
+
+#4301
--- a/releases_drafts/wf.md
+++ b/releases_drafts/wf.md
@@ -1,12 +0,0 @@
-Functions defined by well-founded recursion are now marked as
-`@[irreducible]`, which should prevent expensive and often unfruitful
-unfolding of such definitions.
-
-Existing proofs that hold by definitional equality (e.g. `rfl`) can be
-rewritten to explictly unfold the function definition (using `simp`,
-`unfold`, `rw`), or the recursive function can be temporariliy made
-semireducible (using `unseal f in` before the command) or the function
-definition itself can be marked as `@[semireducible]` to get the previous
-behavor.
-
-#4061
--- a/script/lib/update-stage0
+++ b/script/lib/update-stage0
@@ -15,4 +15,19 @@ for f in $(git ls-files src ':!:src/lake/*' ':!:src/Leanc.lean'); do
        cp $f stage0/$f
    fi
 done
+
+# special handling for Lake files due to its nested directory
+# copy the README to ensure the `stage0/src/lake` directory is comitted
+for f in $(git ls-files 'src/lake/Lake/*' src/lake/Lake.lean src/lake/README.md ':!:src/lakefile.toml'); do
+    if [[ $f == *.lean ]]; then
+        f=${f#src/lake}
+        f=${f%.lean}.c
+        mkdir -p $(dirname stage0/stdlib/$f)
+        cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
+    else
+        mkdir -p $(dirname stage0/$f)
+        cp $f stage0/$f
+    fi
+done
+
 git add stage0
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -9,7 +9,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 9)
+set(LEAN_VERSION_MINOR 10)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -73,6 +73,7 @@ option(USE_GMP "USE_GMP" ON)

 # development-specific options
 option(CHECK_OLEAN_VERSION "Only load .olean files compiled with the current version of Lean" OFF)
+option(USE_LAKE "Use Lake instead of lean.mk for building core libs from language server" OFF)

 set(LEAN_EXTRA_MAKE_OPTS  ""                           CACHE STRING "extra options to lean --make")
 set(LEANC_CC              ${CMAKE_C_COMPILER}          CACHE STRING "C compiler to use in `leanc`")
@@ -312,7 +313,7 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
  set(LEAN_CXX_STDLIB "-lc++")
 endif()

-string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
+string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " ${LEAN_CXX_STDLIB} -lStd")
 string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")

 # in local builds, link executables and not just dynlibs against C++ stdlib as well,
@@ -513,11 +514,11 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
 endif()

 if(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
-  set(LEANSHARED_LINKER_FLAGS "-Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libInit.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLean.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libleancpp.a ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
+  set(LEANSHARED_LINKER_FLAGS "-Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libInit.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libStd.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLean.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libleancpp.a ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
 elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
-  set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLean.a.export -lleancpp -Wl,--no-whole-archive -lInit_shared -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libleanshared.dll.a")
+  set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libStd.a.export ${CMAKE_BINARY_DIR}/lib/temp/libLean.a.export -lleancpp -Wl,--no-whole-archive -lInit_shared -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libleanshared.dll.a")
 else()
-  set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit -lLean -lleancpp -Wl,--no-whole-archive ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
+  set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit -lStd -lLean -lleancpp -Wl,--no-whole-archive ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
 endif()

 if (${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
@@ -539,7 +540,7 @@ add_custom_target(make_stdlib ALL
  # The actual rule is in a separate makefile because we want to prefix it with '+' to use the Make job server
  # for a parallelized nested build, but CMake doesn't let us do that.
  # We use `lean` from the previous stage, but `leanc`, headers, etc. from the current stage
-  COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Lean
+  COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Std Lean
  VERBATIM)

 # if we have LLVM enabled, then build `lean.h.bc` which has the LLVM bitcode
@@ -577,11 +578,7 @@ else()
  string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared")
 endif()

-if(${STAGE} GREATER 0 AND NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  if(NOT EXISTS ${LEAN_SOURCE_DIR}/lake/Lake.lean)
-    message(FATAL_ERROR "src/lake does not exist. Please check out the Lake submodule using `git submodule update --init src/lake`.")
-  endif()
-
+if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
  add_custom_target(lake ALL
    WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
    DEPENDS leanshared
@@ -658,3 +655,9 @@ endif()
 string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE "${CMAKE_EXE_LINKER_FLAGS}")
 string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE_MAKE "${CMAKE_EXE_LINKER_FLAGS_MAKE}")
 configure_file(${LEAN_SOURCE_DIR}/stdlib.make.in ${CMAKE_BINARY_DIR}/stdlib.make)
+
+if(USE_LAKE AND STAGE EQUAL 1)
+  configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/lakefile.toml)
+  configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../tests/lakefile.toml)
+  configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../lakefile.toml)
+endif()
--- a/src/Init/Control/Except.lean
+++ b/src/Init/Control/Except.lean
@@ -131,7 +131,7 @@ protected def adapt {ε' α : Type u} (f : ε → ε') : ExceptT ε m α → Exc
 end ExceptT

@[always_inline]
-instance (m : Type u → Type v) (ε₁ : Type u) (ε₂ : Type u) [Monad m] [MonadExceptOf ε₁ m] : MonadExceptOf ε₁ (ExceptT ε₂ m) where
+instance (m : Type u → Type v) (ε₁ : Type u) (ε₂ : Type u) [MonadExceptOf ε₁ m] : MonadExceptOf ε₁ (ExceptT ε₂ m) where
  throw e := ExceptT.mk <| throwThe ε₁ e
  tryCatch x handle := ExceptT.mk <| tryCatchThe ε₁ x handle

--- a/src/Init/Control/Lawful/Basic.lean
+++ b/src/Init/Control/Lawful/Basic.lean
@@ -9,7 +9,7 @@ import Init.Meta

 open Function

-@[simp] theorem monadLift_self [Monad m] (x : m α) : monadLift x = x :=
+@[simp] theorem monadLift_self {m : Type u → Type v} (x : m α) : monadLift x = x :=
  rfl

 /--
--- a/src/Init/Control/Lawful/Instances.lean
+++ b/src/Init/Control/Lawful/Instances.lean
@@ -14,7 +14,7 @@ open Function

 namespace ExceptT

-theorem ext [Monad m] {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
+theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
  simp [run] at h
  assumption

@@ -50,7 +50,7 @@ theorem run_bind [Monad m] (x : ExceptT ε m α)
 protected theorem seq_eq {α β ε : Type u} [Monad m] (mf : ExceptT ε m (α → β)) (x : ExceptT ε m α) : mf <*> x = mf >>= fun f => f <$> x :=
  rfl

-protected theorem bind_pure_comp [Monad m] [LawfulMonad m] (f : α → β) (x : ExceptT ε m α) : x >>= pure ∘ f = f <$> x := by
+protected theorem bind_pure_comp [Monad m] (f : α → β) (x : ExceptT ε m α) : x >>= pure ∘ f = f <$> x := by
  intros; rfl

 protected theorem seqLeft_eq {α β ε : Type u} {m : Type u → Type v} [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x <* y = const β <$> x <*> y := by
@@ -200,11 +200,11 @@ theorem ext {x y : StateT σ m α} (h : ∀ s, x.run s = y.run s) : x = y :=
  show (f >>= fun g => g <$> x).run s = _
  simp

-@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x *> y).run s = (x.run s >>= fun p => y.run p.2) := by
+@[simp] theorem run_seqRight [Monad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x *> y).run s = (x.run s >>= fun p => y.run p.2) := by
  show (x >>= fun _ => y).run s = _
  simp

-@[simp] theorem run_seqLeft {α β σ : Type u} [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x <* y).run s = (x.run s >>= fun p => y.run p.2 >>= fun p' => pure (p.1, p'.2)) := by
+@[simp] theorem run_seqLeft {α β σ : Type u} [Monad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x <* y).run s = (x.run s >>= fun p => y.run p.2 >>= fun p' => pure (p.1, p'.2)) := by
  show (x >>= fun a => y >>= fun _ => pure a).run s = _
  simp

--- a/src/Init/Control/Option.lean
+++ b/src/Init/Control/Option.lean
@@ -67,7 +67,7 @@ instance : MonadExceptOf Unit (OptionT m) where
  throw    := fun _ => OptionT.fail
  tryCatch := OptionT.tryCatch

-instance (ε : Type u) [Monad m] [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
+instance (ε : Type u) [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
  throw e           := OptionT.mk <| throwThe ε e
  tryCatch x handle := OptionT.mk <| tryCatchThe ε x handle

--- a/src/Init/Control/Reader.lean
+++ b/src/Init/Control/Reader.lean
@@ -32,7 +32,7 @@ instance : MonadControl m (ReaderT ρ m) where
  restoreM x _ := x

@[always_inline]
-instance ReaderT.tryFinally [MonadFinally m] [Monad m] : MonadFinally (ReaderT ρ m) where
+instance ReaderT.tryFinally [MonadFinally m] : MonadFinally (ReaderT ρ m) where
  tryFinally' x h ctx := tryFinally' (x ctx) (fun a? => h a? ctx)

@[reducible] def ReaderM (ρ : Type u) := ReaderT ρ Id
--- a/src/Init/Control/State.lean
+++ b/src/Init/Control/State.lean
@@ -87,7 +87,7 @@ protected def lift {α : Type u} (t : m α) : StateT σ m α :=
 instance : MonadLift m (StateT σ m) := ⟨StateT.lift⟩

@[always_inline]
-instance (σ m) [Monad m] : MonadFunctor m (StateT σ m) := ⟨fun f x s => f (x s)⟩
+instance (σ m) : MonadFunctor m (StateT σ m) := ⟨fun f x s => f (x s)⟩

@[always_inline]
 instance (ε) [MonadExceptOf ε m] : MonadExceptOf ε (StateT σ m) := {
--- a/src/Init/Control/StateCps.lean
+++ b/src/Init/Control/StateCps.lean
@@ -14,16 +14,18 @@ def StateCpsT (σ : Type u) (m : Type u → Type v) (α : Type u) := (δ : Type

 namespace StateCpsT

+variable {α σ : Type u} {m : Type u → Type v}
+
@[always_inline, inline]
-def runK {α σ : Type u} {m : Type u → Type v}  (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
+def runK (x : StateCpsT σ m α) (s : σ) (k : α → σ → m β) : m β :=
  x _ s k

@[always_inline, inline]
-def run {α σ : Type u} {m : Type u → Type v} [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
+def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
  runK x s (fun a s => pure (a, s))

@[always_inline, inline]
-def run' {α σ : Type u} {m : Type u → Type v}  [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
+def run' [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
  runK x s (fun a _ => pure a)

@[always_inline]
@@ -48,29 +50,29 @@ protected def lift [Monad m] (x : m α) : StateCpsT σ m α :=
 instance [Monad m] : MonadLift m (StateCpsT σ m) where
  monadLift := StateCpsT.lift

-@[simp] theorem runK_pure {m : Type u → Type v} (a : α) (s : σ) (k : α → σ → m β) : (pure a : StateCpsT σ m α).runK s k = k a s := rfl
+@[simp] theorem runK_pure (a : α) (s : σ) (k : α → σ → m β) : (pure a : StateCpsT σ m α).runK s k = k a s := rfl

-@[simp] theorem runK_get {m : Type u → Type v} (s : σ) (k : σ → σ → m β) : (get : StateCpsT σ m σ).runK s k = k s s := rfl
+@[simp] theorem runK_get (s : σ) (k : σ → σ → m β) : (get : StateCpsT σ m σ).runK s k = k s s := rfl

-@[simp] theorem runK_set {m : Type u → Type v} (s s' : σ) (k : PUnit → σ → m β) : (set s' : StateCpsT σ m PUnit).runK s k = k ⟨⟩ s' := rfl
+@[simp] theorem runK_set (s s' : σ) (k : PUnit → σ → m β) : (set s' : StateCpsT σ m PUnit).runK s k = k ⟨⟩ s' := rfl

-@[simp] theorem runK_modify {m : Type u → Type v} (f : σ → σ) (s : σ) (k : PUnit → σ → m β) : (modify f : StateCpsT σ m PUnit).runK s k = k ⟨⟩ (f s) := rfl
+@[simp] theorem runK_modify (f : σ → σ) (s : σ) (k : PUnit → σ → m β) : (modify f : StateCpsT σ m PUnit).runK s k = k ⟨⟩ (f s) := rfl

-@[simp] theorem runK_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) (k : α → σ → m β) : (StateCpsT.lift x : StateCpsT σ m α).runK s k = x >>= (k . s) := rfl
+@[simp] theorem runK_lift [Monad m] (x : m α) (s : σ) (k : α → σ → m β) : (StateCpsT.lift x : StateCpsT σ m α).runK s k = x >>= (k . s) := rfl

-@[simp] theorem runK_monadLift {σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) (k : α → σ → m β)
+@[simp] theorem runK_monadLift [Monad m] [MonadLiftT n m] (x : n α) (s : σ) (k : α → σ → m β)
    : (monadLift x : StateCpsT σ m α).runK s k = (monadLift x : m α) >>= (k . s) := rfl

-@[simp] theorem runK_bind_pure {α σ : Type u} [Monad m] (a : α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (pure a >>= f).runK s k = (f a).runK s k := rfl
+@[simp] theorem runK_bind_pure (a : α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (pure a >>= f).runK s k = (f a).runK s k := rfl

-@[simp] theorem runK_bind_lift {α σ : Type u} [Monad m] (x : m α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ)
+@[simp] theorem runK_bind_lift [Monad m] (x : m α) (f : α → StateCpsT σ m β) (s : σ) (k : β → σ → m γ)
    : (StateCpsT.lift x >>= f).runK s k = x >>= fun a => (f a).runK s k := rfl

-@[simp] theorem runK_bind_get {σ : Type u} [Monad m] (f : σ → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (get >>= f).runK s k = (f s).runK s k := rfl
+@[simp] theorem runK_bind_get (f : σ → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (get >>= f).runK s k = (f s).runK s k := rfl

-@[simp] theorem runK_bind_set {σ : Type u} [Monad m] (f : PUnit → StateCpsT σ m β) (s s' : σ) (k : β → σ → m γ) : (set s' >>= f).runK s k = (f ⟨⟩).runK s' k := rfl
+@[simp] theorem runK_bind_set (f : PUnit → StateCpsT σ m β) (s s' : σ) (k : β → σ → m γ) : (set s' >>= f).runK s k = (f ⟨⟩).runK s' k := rfl

-@[simp] theorem runK_bind_modify {σ : Type u} [Monad m] (f : σ → σ) (g : PUnit → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (modify f >>= g).runK s k = (g ⟨⟩).runK (f s) k := rfl
+@[simp] theorem runK_bind_modify (f : σ → σ) (g : PUnit → StateCpsT σ m β) (s : σ) (k : β → σ → m γ) : (modify f >>= g).runK s k = (g ⟨⟩).runK (f s) k := rfl

@[simp] theorem run_eq [Monad m] (x : StateCpsT σ m α) (s : σ) : x.run s = x.runK s (fun a s => pure (a, s)) := rfl

--- a/src/Init/Control/StateRef.lean
+++ b/src/Init/Control/StateRef.lean
@@ -34,22 +34,22 @@ protected def lift (x : m α) : StateRefT' ω σ m α :=

 instance [Monad m] : Monad (StateRefT' ω σ m) := inferInstanceAs (Monad (ReaderT _ _))
 instance : MonadLift m (StateRefT' ω σ m) := ⟨StateRefT'.lift⟩
-instance (σ m) [Monad m] : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
+instance (σ m) : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
 instance [Alternative m] [Monad m] : Alternative (StateRefT' ω σ m) := inferInstanceAs (Alternative (ReaderT _ _))

@[inline]
-protected def get [Monad m] [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
+protected def get [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
  fun ref => ref.get

@[inline]
-protected def set [Monad m] [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
+protected def set [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
  fun ref => ref.set s

@[inline]
-protected def modifyGet [Monad m] [MonadLiftT (ST ω) m] (f : σ → α × σ) : StateRefT' ω σ m α :=
+protected def modifyGet [MonadLiftT (ST ω) m] (f : σ → α × σ) : StateRefT' ω σ m α :=
  fun ref => ref.modifyGet f

-instance [MonadLiftT (ST ω) m] [Monad m] : MonadStateOf σ (StateRefT' ω σ m) where
+instance [MonadLiftT (ST ω) m] : MonadStateOf σ (StateRefT' ω σ m) where
  get       := StateRefT'.get
  set       := StateRefT'.set
  modifyGet := StateRefT'.modifyGet
--- a/src/Init/Core.lean
+++ b/src/Init/Core.lean
@@ -468,11 +468,11 @@ class Singleton (α : outParam <| Type u) (β : Type v) where
 export Singleton (singleton)

 /-- `insert x ∅ = {x}` -/
-class IsLawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
+class LawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
    Prop where
  /-- `insert x ∅ = {x}` -/
  insert_emptyc_eq (x : α) : (insert x ∅ : β) = singleton x
-export IsLawfulSingleton (insert_emptyc_eq)
+export LawfulSingleton (insert_emptyc_eq)

 /-- Type class used to implement the notation `{ a ∈ c | p a }` -/
 class Sep (α : outParam <| Type u) (γ : Type v) where
@@ -642,7 +642,7 @@ instance : LawfulBEq String := inferInstance

 /-! # Logical connectives and equality -/

-@[inherit_doc True.intro] def trivial : True := ⟨⟩
+@[inherit_doc True.intro] theorem trivial : True := ⟨⟩

 theorem mt {a b : Prop} (h₁ : a → b) (h₂ : ¬b) : ¬a :=
  fun ha => h₂ (h₁ ha)
@@ -1173,7 +1173,7 @@ def Prod.lexLt [LT α] [LT β] (s : α × β) (t : α × β) : Prop :=
  s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)

 instance Prod.lexLtDec
-    [LT α] [LT β] [DecidableEq α] [DecidableEq β]
+    [LT α] [LT β] [DecidableEq α]
    [(a b : α) → Decidable (a < b)] [(a b : β) → Decidable (a < b)]
    : (s t : α × β) → Decidable (Prod.lexLt s t) :=
  fun _ _ => inferInstanceAs (Decidable (_ ∨ _))
@@ -1191,6 +1191,11 @@ def Prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂
    (f : α₁ → α₂) (g : β₁ → β₂) : α₁ × β₁ → α₂ × β₂
  | (a, b) => (f a, g b)

+@[simp] theorem Prod.map_apply (f : α → β) (g : γ → δ) (x) (y) :
+    Prod.map f g (x, y) = (f x, g y) := rfl
+@[simp] theorem Prod.map_fst (f : α → β) (g : γ → δ) (x) : (Prod.map f g x).1 = f x.1 := rfl
+@[simp] theorem Prod.map_snd (f : α → β) (g : γ → δ) (x) : (Prod.map f g x).2 = g x.2 := rfl
+
 /-! # Dependent products -/

 theorem ex_of_PSigma {α : Type u} {p : α → Prop} : (PSigma (fun x => p x)) → Exists (fun x => p x)
--- a/src/Init/Data/AC.lean
+++ b/src/Init/Data/AC.lean
@@ -146,8 +146,8 @@ theorem Context.evalList_mergeIdem (ctx : Context α) (h : ContextInformation.is
    | nil =>
      simp [mergeIdem, mergeIdem.loop]
      split
-      case inl h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
-      rfl
+      next h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
+      next => rfl
    | cons z zs =>
      by_cases h₂ : x = y
      case pos =>
@@ -191,11 +191,11 @@ theorem Context.evalList_insert
    . simp [evalList, h.1, EvalInformation.evalOp]
  | step y z zs ih =>
    simp [insert] at *; split
-    case inl => rfl
-    case inr =>
+    next => rfl
+    next =>
      split
-      case inl => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
-      case inr => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
+      next => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
+      next => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]

 theorem Context.evalList_sort_congr
  (ctx : Context α)
--- a/src/Init/Data/Array/Basic.lean
+++ b/src/Init/Data/Array/Basic.lean
@@ -481,7 +481,7 @@ def all (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool
  Id.run <| as.allM p start stop

 def contains [BEq α] (as : Array α) (a : α) : Bool :=
-  as.any fun b => a == b
+  as.any (· == a)

 def elem [BEq α] (a : α) (as : Array α) : Bool :=
  as.contains a
@@ -791,11 +791,11 @@ def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
 theorem ext' {as bs : Array α} (h : as.data = bs.data) : as = bs := by
  cases as; cases bs; simp at h; rw [h]

-theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
+@[simp] theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
  induction as generalizing acc <;> simp [*, List.toArrayAux, Array.push, List.append_assoc, List.concat_eq_append]

 theorem data_toArray (as : List α) : as.toArray.data = as := by
-  simp [List.toArray, toArrayAux_eq, Array.mkEmpty]
+  simp [List.toArray, Array.mkEmpty]

 theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
  apply ext'
--- a/src/Init/Data/Array/BasicAux.lean
+++ b/src/Init/Data/Array/BasicAux.lean
@@ -9,7 +9,7 @@ import Init.Data.Nat.Linear
 import Init.NotationExtra

 theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : as = bs ∧ a = b := by
-  simp [push] at h
+  simp only [push, mk.injEq] at h
  have ⟨h₁, h₂⟩ := List.of_concat_eq_concat h
  cases as; cases bs
  simp_all
--- a/src/Init/Data/Array/DecidableEq.lean
+++ b/src/Init/Data/Array/DecidableEq.lean
@@ -27,17 +27,17 @@ decreasing_by decreasing_trivial_pre_omega
 theorem eq_of_isEqv [DecidableEq α] (a b : Array α) : Array.isEqv a b (fun x y => x = y) → a = b := by
  simp [Array.isEqv]
  split
-  case inr => intro; contradiction
-  case inl hsz =>
+  next hsz =>
   intro h
   have aux := eq_of_isEqvAux a b hsz 0 (Nat.zero_le ..) h
   exact ext a b hsz fun i h _ => aux i (Nat.zero_le ..) _
+  next => intro; contradiction

 theorem isEqvAux_self [DecidableEq α] (a : Array α) (i : Nat) : Array.isEqvAux a a rfl (fun x y => x = y) i = true := by
  unfold Array.isEqvAux
  split
-  case inl h => simp [h, isEqvAux_self a (i+1)]
-  case inr h => simp [h]
+  next h => simp [h, isEqvAux_self a (i+1)]
+  next h => simp [h]
 termination_by a.size - i
 decreasing_by decreasing_trivial_pre_omega

--- a/src/Init/Data/Array/Lemmas.lean
+++ b/src/Init/Data/Array/Lemmas.lean
@@ -14,7 +14,7 @@ import Init.TacticsExtra
 /-!
 ## Bootstrapping theorems about arrays

-This file contains some theorems about `Array` and `List` needed for `Std.List.Basic`.
+This file contains some theorems about `Array` and `List` needed for `Init.Data.List.Impl`.
 -/

 namespace Array
@@ -34,9 +34,13 @@ attribute [simp] data_toArray uset

@[simp] theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp [size]

-theorem getElem_eq_data_get (a : Array α) (h : i < a.size) : a[i] = a.data.get ⟨i, h⟩ := by
+theorem getElem_eq_data_getElem (a : Array α) (h : i < a.size) : a[i] = a.data[i] := by
  by_cases i < a.size <;> (try simp [*]) <;> rfl

+@[deprecated getElem_eq_data_getElem (since := "2024-06-12")]
+theorem getElem_eq_data_get (a : Array α) (h : i < a.size) : a[i] = a.data.get ⟨i, h⟩ := by
+  simp [getElem_eq_data_getElem]
+
 theorem foldlM_eq_foldlM_data.aux [Monad m]
    (f : β → α → m β) (arr : Array α) (i j) (H : arr.size ≤ i + j) (b) :
    foldlM.loop f arr arr.size (Nat.le_refl _) i j b = (arr.data.drop j).foldlM f b := by
@@ -114,11 +118,11 @@ theorem foldr_push (f : α → β → β) (init : β) (arr : Array α) (a : α)
 theorem get_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
    have : i < (a.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
    (a.push x)[i] = a[i] := by
-  simp only [push, getElem_eq_data_get, List.concat_eq_append, List.get_append_left, h]
+  simp only [push, getElem_eq_data_getElem, List.concat_eq_append, List.getElem_append_left, h]

@[simp] theorem get_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
-  simp only [push, getElem_eq_data_get, List.concat_eq_append]
-  rw [List.get_append_right] <;> simp [getElem_eq_data_get, Nat.zero_lt_one]
+  simp only [push, getElem_eq_data_getElem, List.concat_eq_append]
+  rw [List.getElem_append_right] <;> simp [getElem_eq_data_getElem, Nat.zero_lt_one]

 theorem get_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size) :
    (a.push x)[i] = if h : i < a.size then a[i] else x := by
@@ -135,7 +139,8 @@ where
      mapM.map f arr i r = (arr.data.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
    unfold mapM.map; split
    · rw [← List.get_drop_eq_drop _ i ‹_›]
-      simp [aux (i+1), map_eq_pure_bind]; rfl
+      simp only [aux (i + 1), map_eq_pure_bind, data_length, List.foldlM_cons, bind_assoc, pure_bind]
+      rfl
    · rw [List.drop_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
  termination_by arr.size - i
  decreasing_by decreasing_trivial_pre_omega
@@ -233,11 +238,11 @@ theorem get!_eq_getD [Inhabited α] (a : Array α) : a.get! n = a.getD n default
@[simp] theorem getElem_set_eq (a : Array α) (i : Fin a.size) (v : α) {j : Nat}
      (eq : i.val = j) (p : j < (a.set i v).size) :
    (a.set i v)[j]'p = v := by
-  simp [set, getElem_eq_data_get, ←eq]
+  simp [set, getElem_eq_data_getElem, ←eq]

@[simp] theorem getElem_set_ne (a : Array α) (i : Fin a.size) (v : α) {j : Nat} (pj : j < (a.set i v).size)
    (h : i.val ≠ j) : (a.set i v)[j]'pj = a[j]'(size_set a i v ▸ pj) := by
-  simp only [set, getElem_eq_data_get, List.get_set_ne _ h]
+  simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]

 theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
    (h : j < (a.set i v).size) :
@@ -321,7 +326,7 @@ termination_by n - i
@[simp] theorem mkArray_data (n : Nat) (v : α) : (mkArray n v).data = List.replicate n v := rfl

@[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
-    (mkArray n v)[i] = v := by simp [Array.getElem_eq_data_get]
+    (mkArray n v)[i] = v := by simp [Array.getElem_eq_data_getElem]

 /-- # mem -/

@@ -332,7 +337,7 @@ theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
 /-- # get lemmas -/

 theorem getElem?_mem {l : Array α} {i : Fin l.size} : l[i] ∈ l := by
-  erw [Array.mem_def, getElem_eq_data_get]
+  erw [Array.mem_def, getElem_eq_data_getElem]
  apply List.get_mem

 theorem getElem_fin_eq_data_get (a : Array α) (i : Fin _) : a[i] = a.data.get i := rfl
@@ -347,7 +352,7 @@ theorem get?_len_le (a : Array α) (i : Nat) (h : a.size ≤ i) : a[i]? = none :
  simp [getElem?_neg, h]

 theorem getElem_mem_data (a : Array α) (h : i < a.size) : a[i] ∈ a.data := by
-  simp only [getElem_eq_data_get, List.get_mem]
+  simp only [getElem_eq_data_getElem, List.getElem_mem]

 theorem getElem?_eq_data_get? (a : Array α) (i : Nat) : a[i]? = a.data.get? i := by
  by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]; rfl
@@ -395,7 +400,7 @@ theorem get?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x el

 theorem get_set_eq (a : Array α) (i : Fin a.size) (v : α) :
    (a.set i v)[i.1] = v := by
-  simp only [set, getElem_eq_data_get, List.get_set_eq]
+  simp only [set, getElem_eq_data_getElem, List.getElem_set_eq]

 theorem get?_set_eq (a : Array α) (i : Fin a.size) (v : α) :
    (a.set i v)[i.1]? = v := by simp [getElem?_pos, i.2]
@@ -414,7 +419,7 @@ theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v :

@[simp] theorem get_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α) (hj : j < a.size)
    (h : i.1 ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
-  simp only [set, getElem_eq_data_get, List.get_set_ne _ h]
+  simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]

 theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
  (setD a i v)[i] = v := by
@@ -452,7 +457,7 @@ theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :

@[simp] theorem getElem_pop (a : Array α) (i : Nat) (hi : i < a.pop.size) :
    a.pop[i] = a[i]'(Nat.lt_of_lt_of_le (a.size_pop ▸ hi) (Nat.sub_le _ _)) :=
-  List.get_dropLast ..
+  List.getElem_dropLast ..

 theorem eq_empty_of_size_eq_zero {as : Array α} (h : as.size = 0) : as = #[] := by
  apply ext
@@ -500,27 +505,28 @@ theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
    simp only [mkEmpty_eq, size_push] at *
    omega

+set_option linter.deprecated false in
@[simp] theorem reverse_data (a : Array α) : a.reverse.data = a.data.reverse := by
  let rec go (as : Array α) (i j hj)
      (h : i + j + 1 = a.size) (h₂ : as.size = a.size)
      (H : ∀ k, as.data.get? k = if i ≤ k ∧ k ≤ j then a.data.get? k else a.data.reverse.get? k)
      (k) : (reverse.loop as i ⟨j, hj⟩).data.get? k = a.data.reverse.get? k := by
    rw [reverse.loop]; dsimp; split <;> rename_i h₁
-    · have := reverse.termination h₁
+    · have p := reverse.termination h₁
      match j with | j+1 => ?_
-      simp at *
+      simp only [Nat.add_sub_cancel] at p ⊢
      rw [(go · (i+1) j)]
      · rwa [Nat.add_right_comm i]
      · simp [size_swap, h₂]
      · intro k
        rw [← getElem?_eq_data_get?, get?_swap]
-        simp [getElem?_eq_data_get?, getElem_eq_data_get, ← List.get?_eq_get, H, Nat.le_of_lt h₁]
+        simp only [H, getElem_eq_data_get, ← List.get?_eq_get, Nat.le_of_lt h₁, getElem?_eq_data_get?]
        split <;> rename_i h₂
-        · simp [← h₂, Nat.not_le.2 (Nat.lt_succ_self _)]
-          exact (List.get?_reverse' _ _ (Eq.trans (by simp_arith) h)).symm
+        · simp only [← h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
+          exact (List.get?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
        split <;> rename_i h₃
-        · simp [← h₃, Nat.not_le.2 (Nat.lt_succ_self _)]
-          exact (List.get?_reverse' _ _ (Eq.trans (by simp_arith) h)).symm
+        · simp only [← h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
+          exact (List.get?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
        simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
          Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
    · rw [H]; split <;> rename_i h₂
@@ -529,13 +535,17 @@ theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
        exact (List.get?_reverse' _ _ h).symm
      · rfl
    termination_by j - i
-  simp only [reverse]; split
+  simp only [reverse]
+  split
  · match a with | ⟨[]⟩ | ⟨[_]⟩ => rfl
  · have := Nat.sub_add_cancel (Nat.le_of_not_le ‹_›)
-    refine List.ext <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
-    split; {rfl}; rename_i h
-    simp [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this] at h
-    rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.data.length_reverse ▸ ‹_›)]
+    refine List.ext_get? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
+    split
+    · rfl
+    · rename_i h
+      simp only [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this, Nat.zero_le,
+        true_and, Nat.not_lt] at h
+      rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.data.length_reverse ▸ ‹_›)]

 /-! ### foldl / foldr -/

@@ -740,7 +750,7 @@ theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
  exact this #[]
  induction l
  · simp_all [Id.run]
-  · simp_all [Id.run]
+  · simp_all [Id.run, List.filterMap_cons]
    split <;> simp_all

@[simp] theorem mem_filterMap (f : α → Option β) (l : Array α) {b : β} :
@@ -765,17 +775,17 @@ theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size :=

 theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
    (as ++ bs)[i] = as[i] := by
-  simp only [getElem_eq_data_get]
+  simp only [getElem_eq_data_getElem]
  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
-  conv => rhs; rw [← List.get_append_left (bs:=bs.data) (h':=h')]
+  conv => rhs; rw [← List.getElem_append_left (bs := bs.data) (h' := h')]
  apply List.get_of_eq; rw [append_data]

 theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
    (hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
    (as ++ bs)[i] = bs[i - as.size] := by
-  simp only [getElem_eq_data_get]
+  simp only [getElem_eq_data_getElem]
  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
-  conv => rhs; rw [← List.get_append_right (h':=h') (h:=Nat.not_lt_of_ge hle)]
+  conv => rhs; rw [← List.getElem_append_right (h' := h') (h := Nat.not_lt_of_ge hle)]
  apply List.get_of_eq; rw [append_data]

@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
@@ -983,13 +993,13 @@ theorem all_eq_true (p : α → Bool) (as : Array α) : all as p ↔ ∀ i : Fin
  simp [all_iff_forall, Fin.isLt]

 theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.data.all p := by
-  rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_get]
+  rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_getElem]
  constructor
-  · rintro w x ⟨r, rfl⟩
-    rw [← getElem_eq_data_get]
-    apply w
+  · rintro w x ⟨r, h, rfl⟩
+    rw [← getElem_eq_data_getElem]
+    exact w ⟨r, h⟩
  · intro w i
-    exact w as[i] ⟨i, (getElem_eq_data_get as i.2).symm⟩
+    exact w as[i] ⟨i, i.2, (getElem_eq_data_getElem as i.2).symm⟩

 theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
  simp only [all_def, List.all_eq_true, mem_def]
--- a/src/Init/Data/BitVec/Basic.lean
+++ b/src/Init/Data/BitVec/Basic.lean
@@ -151,12 +151,12 @@ end Int
 section Syntax

 /-- Notation for bit vector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
-scoped syntax:max term:max noWs "#" noWs term:max : term
-macro_rules | `($i#$n) => `(BitVec.ofNat $n $i)
+syntax:max num noWs "#" noWs term:max : term
+macro_rules | `($i:num#$n) => `(BitVec.ofNat $n $i)

 /-- Unexpander for bit vector literals. -/
@[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
-  | `($(_) $n $i) => `($i#$n)
+  | `($(_) $n $i:num) => `($i:num#$n)
  | _ => throw ()

 /-- Notation for bit vector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLt i lt`. -/
@@ -198,7 +198,7 @@ instance : Add (BitVec n) := ⟨BitVec.add⟩
 Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
 modulo `2^n`.
 -/
-protected def sub (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + (2^n - y.toNat))
+protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
 instance : Sub (BitVec n) := ⟨BitVec.sub⟩

 /--
@@ -504,7 +504,7 @@ equivalent to `a * 2^s`, modulo `2^n`.

 SMT-Lib name: `bvshl` except this operator uses a `Nat` shift value.
 -/
-protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := (a.toNat <<< s)#n
+protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (a.toNat <<< s)
 instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩

 /--
@@ -614,6 +614,13 @@ theorem ofBool_append (msb : Bool) (lsbs : BitVec w) :
    ofBool msb ++ lsbs = (cons msb lsbs).cast (Nat.add_comm ..) :=
  rfl

+/--
+`twoPow w i` is the bitvector `2^i` if `i < w`, and `0` otherwise.
+That is, 2 to the power `i`.
+For the bitwise point of view, it has the `i`th bit as `1` and all other bits as `0`.
+-/
+def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i
+
 end bitwise

 section normalization_eqs
--- a/src/Init/Data/BitVec/Lemmas.lean
+++ b/src/Init/Data/BitVec/Lemmas.lean
@@ -139,15 +139,15 @@ theorem ofBool_eq_iff_eq : ∀(b b' : Bool), BitVec.ofBool b = BitVec.ofBool b'
  getLsb (x#'lt) i = x.testBit i := by
  simp [getLsb, BitVec.ofNatLt]

-@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (x#w).toNat = x % 2^w := by
+@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
  simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']

-@[simp] theorem toFin_ofNat (x : Nat) : toFin x#w = Fin.ofNat' x (Nat.two_pow_pos w) := rfl
+@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' x (Nat.two_pow_pos w) := rfl

 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
 theorem getLsb_ofNat (n : Nat) (x : Nat) (i : Nat) :
-  getLsb (x#n) i = (i < n && x.testBit i) := by
+  getLsb (BitVec.ofNat n x) i = (i < n && x.testBit i) := by
  simp [getLsb, BitVec.ofNat, Fin.val_ofNat']

@[simp, deprecated toNat_ofNat (since := "2024-02-22")]
@@ -184,8 +184,7 @@ theorem msb_eq_getLsb_last (x : BitVec w) :
    · simp only [h]
      rw [Nat.div_eq_sub_div (Nat.two_pow_pos w) h, Nat.div_eq_of_lt]
      · decide
-      · have : BitVec.toNat x < 2^w + 2^w := by simpa [Nat.pow_succ, Nat.mul_two] using x.isLt
-        omega
+      · omega

@[bv_toNat] theorem getLsb_succ_last (x : BitVec (w + 1)) :
    x.getLsb w = decide (2 ^ w ≤ x.toNat) := getLsb_last x
@@ -244,10 +243,10 @@ theorem toInt_eq_msb_cond (x : BitVec w) :
 theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) := by
  simp only [toInt_eq_toNat_cond]
  split
-  case inl g =>
+  next g =>
    rw [Int.bmod_pos] <;> simp only [←Int.ofNat_emod, toNat_mod_cancel]
    omega
-  case inr g =>
+  next g =>
    rw [Int.bmod_neg] <;> simp only [←Int.ofNat_emod, toNat_mod_cancel]
    omega

@@ -316,31 +315,28 @@ theorem zeroExtend'_eq {x : BitVec w} (h : w ≤ v) : x.zeroExtend' h = x.zeroEx
  let ⟨x, lt_n⟩ := x
  simp [truncate, zeroExtend]

-@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m (0#n) = 0#m := by
+@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m 0#n = 0#m := by
  apply eq_of_toNat_eq
  simp [toNat_zeroExtend]

@[simp] theorem truncate_eq (x : BitVec n) : truncate n x = x := zeroExtend_eq x

-@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : x.toNat#m = truncate m x := by
+@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = truncate m x := by
  apply eq_of_toNat_eq
  simp

 /-- Moves one-sided left toNat equality to BitVec equality. -/
 theorem toNat_eq_nat (x : BitVec w) (y : Nat)
-  : (x.toNat = y) ↔ (y < 2^w ∧ (x = y#w)) := by
+  : (x.toNat = y) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
  apply Iff.intro
  · intro eq
-    simp at eq
-    have lt := x.isLt
-    simp [eq] at lt
-    simp [←eq, lt, x.isLt]
+    simp [←eq, x.isLt]
  · intro eq
    simp [Nat.mod_eq_of_lt, eq]

 /-- Moves one-sided right toNat equality to BitVec equality. -/
 theorem nat_eq_toNat (x : BitVec w) (y : Nat)
-  : (y = x.toNat) ↔ (y < 2^w ∧ (x = y#w)) := by
+  : (y = x.toNat) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
  rw [@eq_comm _ _ x.toNat]
  apply toNat_eq_nat

@@ -416,7 +412,7 @@ protected theorem extractLsb_ofFin {n} (x : Fin (2^n)) (hi lo : Nat) :

@[simp]
 protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
-  extractLsb hi lo x#n = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
+  extractLsb hi lo (BitVec.ofNat n x) = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
  apply eq_of_getLsb_eq
  intro ⟨i, _lt⟩
  simp [BitVec.ofNat]
@@ -642,8 +638,8 @@ 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
+theorem shiftLeft_add {w : Nat} (x : BitVec w) (n m : Nat) :
+    x <<< (n + m) = (x <<< n) <<< m := by
  ext i
  simp only [getLsb_shiftLeft, Fin.is_lt, decide_True, Bool.true_and]
  rw [show i - (n + m) = (i - m - n) by omega]
@@ -653,6 +649,11 @@ theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
  cases h₅ : decide (i < n + m) <;>
    simp at * <;> omega

+@[deprecated shiftLeft_add (since := "2024-06-02")]
+theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x <<< n) <<< m = x <<< (n + m) := by
+  rw [shiftLeft_add]
+
 /-! ### ushiftRight -/

@[simp, bv_toNat] theorem toNat_ushiftRight (x : BitVec n) (i : Nat) :
@@ -726,6 +727,59 @@ theorem getLsb_sshiftRight (x : BitVec w) (s i : Nat) :
        Nat.not_lt, decide_eq_true_eq]
      omega

+/-! ### signExtend -/
+
+/-- Equation theorem for `Int.sub` when both arguments are `Int.ofNat` -/
+private theorem Int.ofNat_sub_ofNat_of_lt {n m : Nat} (hlt : n < m) :
+    (n : Int) - (m : Int) = -(↑(m - 1 - n) + 1) := by
+  omega
+
+/-- Equation theorem for `Int.mod` -/
+private theorem Int.negSucc_emod (m : Nat) (n : Int) :
+    -(m + 1) % n = Int.subNatNat (Int.natAbs n) ((m % Int.natAbs n) + 1) := rfl
+
+/-- The sign extension is the same as zero extending when `msb = false`. -/
+theorem signExtend_eq_not_zeroExtend_not_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
+    x.signExtend v = x.zeroExtend v := by
+  ext i
+  by_cases hv : i < v
+  · simp only [signExtend, getLsb, getLsb_zeroExtend, hv, decide_True, Bool.true_and, toNat_ofInt,
+      BitVec.toInt_eq_msb_cond, hmsb, ↓reduceIte]
+    rw [Int.ofNat_mod_ofNat, Int.toNat_ofNat, Nat.testBit_mod_two_pow]
+    simp [BitVec.testBit_toNat]
+  · simp only [getLsb_zeroExtend, hv, decide_False, Bool.false_and]
+    apply getLsb_ge
+    omega
+
+/--
+The sign extension is a bitwise not, followed by a zero extend, followed by another bitwise not
+when `msb = true`. The double bitwise not ensures that the high bits are '1',
+and the lower bits are preserved. -/
+theorem signExtend_eq_not_zeroExtend_not_of_msb_true {x : BitVec w} {v : Nat} (hmsb : x.msb = true) :
+    x.signExtend v = ~~~((~~~x).zeroExtend v) := by
+  apply BitVec.eq_of_toNat_eq
+  simp only [signExtend, BitVec.toInt_eq_msb_cond, toNat_ofInt, toNat_not,
+    toNat_truncate, hmsb, ↓reduceIte]
+  norm_cast
+  rw [Int.ofNat_sub_ofNat_of_lt, Int.negSucc_emod]
+  simp only [Int.natAbs_ofNat, Nat.succ_eq_add_one]
+  rw [Int.subNatNat_of_le]
+  · rw [Int.toNat_ofNat, Nat.add_comm, Nat.sub_add_eq]
+  · apply Nat.le_trans
+    · apply Nat.succ_le_of_lt
+      apply Nat.mod_lt
+      apply Nat.two_pow_pos
+    · apply Nat.le_refl
+  · omega
+
+@[simp] theorem getLsb_signExtend (x  : BitVec w) {v i : Nat} :
+    (x.signExtend v).getLsb i = (decide (i < v) && if i < w then x.getLsb i else x.msb) := by
+  rcases hmsb : x.msb with rfl | rfl
+  · rw [signExtend_eq_not_zeroExtend_not_of_msb_false hmsb]
+    by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
+  · rw [signExtend_eq_not_zeroExtend_not_of_msb_true hmsb]
+    by_cases (i < v) <;> by_cases (i < w) <;> simp_all <;> omega
+
 /-! ### append -/

 theorem append_def (x : BitVec v) (y : BitVec w) :
@@ -802,11 +856,16 @@ 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
+theorem shiftRight_add {w : Nat} (x : BitVec w) (n m : Nat) :
+    x >>> (n + m) = (x >>> n) >>> m:= by
  ext i
  simp [Nat.add_assoc n m i]

+@[deprecated shiftRight_add (since := "2024-06-02")]
+theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
+    (x >>> n) >>> m = x >>> (n + m) := by
+  rw [shiftRight_add]
+
 /-! ### rev -/

 theorem getLsb_rev (x : BitVec w) (i : Fin w) :
@@ -945,10 +1004,10 @@ Definition of bitvector addition as a nat.
@[simp] theorem add_ofFin (x : BitVec n) (y : Fin (2^n)) :
  x + .ofFin y = .ofFin (x.toFin + y) := rfl

-theorem ofNat_add {n} (x y : Nat) : (x + y)#n = x#n + y#n := by
+theorem ofNat_add {n} (x y : Nat) : BitVec.ofNat n (x + y) = BitVec.ofNat n x + BitVec.ofNat n y := by
  apply eq_of_toNat_eq ; simp [BitVec.ofNat]

-theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n :=
+theorem ofNat_add_ofNat {n} (x y : Nat) : BitVec.ofNat n x + BitVec.ofNat n y = BitVec.ofNat n (x + y) :=
  (ofNat_add x y).symm

 protected theorem add_assoc (x y z : BitVec n) : x + y + z = x + (y + z) := by
@@ -982,10 +1041,10 @@ theorem ofInt_add {n} (x y : Int) : BitVec.ofInt n (x + y) =

 /-! ### sub/neg -/

-theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n (x.toNat + (2^n - y.toNat)) := by rfl
+theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toNat) := by rfl

@[simp, bv_toNat] theorem toNat_sub {n} (x y : BitVec n) :
-  (x - y).toNat = ((x.toNat + (2^n - y.toNat)) % 2^n) := rfl
+  (x - y).toNat = (((2^n - y.toNat) + x.toNat) % 2^n) := rfl
@[simp] theorem toFin_sub (x y : BitVec n) : (x - y).toFin = toFin x - toFin y := rfl

@[simp] theorem ofFin_sub (x : Fin (2^n)) (y : BitVec n) : .ofFin x - y = .ofFin (x - y.toFin) :=
@@ -994,15 +1053,15 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n (x.toNat + (2^n - y.toNa
  rfl
 -- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
 -- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
-theorem ofNat_sub_ofNat {n} (x y : Nat) : x#n - y#n = .ofNat n (x + (2^n - y % 2^n)) := by
+theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y = .ofNat n ((2^n - y % 2^n) + x) := by
  apply eq_of_toNat_eq ; simp [BitVec.ofNat]

-@[simp] protected theorem sub_zero (x : BitVec n) : x - (0#n) = x := by apply eq_of_toNat_eq ; simp
+@[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp

@[simp] protected theorem sub_self (x : BitVec n) : x - x = 0#n := by
  apply eq_of_toNat_eq
  simp only [toNat_sub]
-  rw [Nat.add_sub_of_le]
+  rw [Nat.add_comm, Nat.add_sub_of_le]
  · simp
  · exact Nat.le_of_lt x.isLt

@@ -1016,14 +1075,15 @@ theorem ofNat_sub_ofNat {n} (x y : Nat) : x#n - y#n = .ofNat n (x + (2^n - y % 2
 theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
  apply eq_of_toNat_eq
  simp
+  rw [Nat.add_comm]

-@[simp] theorem neg_zero (n:Nat) : -0#n = 0#n := by apply eq_of_toNat_eq ; simp
+@[simp] theorem neg_zero (n:Nat) : -BitVec.ofNat n 0 = BitVec.ofNat n 0 := by apply eq_of_toNat_eq ; simp

 theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
  apply eq_of_toNat_eq
  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]
+  rw [toNat_sub, toNat_add, Nat.add_comm, Nat.mod_add_mod, Nat.add_assoc, ← Nat.add_sub_assoc y_toNat_le,
+      Nat.add_sub_cancel_left, Nat.add_mod_right, toNat_mod_cancel]

 theorem sub_add_cancel (x y : BitVec w) : x - y + y = x := by
  rw [sub_toAdd, BitVec.add_assoc, BitVec.add_comm _ y,
@@ -1094,7 +1154,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
  x ≤ BitVec.ofFin y ↔ x.toFin ≤ y := Iff.rfl
@[simp] theorem ofFin_le (x : Fin (2^n)) (y : BitVec n) :
  BitVec.ofFin x ≤ y ↔ x ≤ y.toFin := Iff.rfl
-@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (x#n) ≤ (y#n) ↔ x % 2^n ≤ y % 2^n := by
+@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (BitVec.ofNat n x) ≤ (BitVec.ofNat n y) ↔ x % 2^n ≤ y % 2^n := by
  simp [le_def]

@[bv_toNat] theorem lt_def (x y : BitVec n) :
@@ -1104,7 +1164,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
  x < BitVec.ofFin y ↔ x.toFin < y := Iff.rfl
@[simp] theorem ofFin_lt (x : Fin (2^n)) (y : BitVec n) :
  BitVec.ofFin x < y ↔ x < y.toFin := Iff.rfl
-@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : (x#n) < (y#n) ↔ x % 2^n < y % 2^n := by
+@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : BitVec.ofNat n x < BitVec.ofNat n y ↔ x % 2^n < y % 2^n := by
  simp [lt_def]

 protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x < y := by
@@ -1117,7 +1177,7 @@ protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x
 /-! ### intMax -/

 /-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
-def intMax (w : Nat) : BitVec w  := (2^w - 1)#w
+def intMax (w : Nat) : BitVec w := BitVec.ofNat w (2^w - 1)

 theorem getLsb_intMax_eq (w : Nat) : (intMax w).getLsb i = decide (i < w) := by
  simp [intMax, getLsb]
@@ -1176,11 +1236,7 @@ x.rotateLeft 2 = (<6 5 | 4 3 2 1 0>).rotateLeft 2 = <3 2 1 0 | 6 5>
 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
+  simp; omega

 /--
 Accessing bits in `x.rotateLeft r` the range `[r, w)` is equal to
@@ -1311,4 +1367,51 @@ theorem getLsb_rotateRight {x : BitVec w} {r i : Nat} :
  · simp
  · rw [← rotateRight_mod_eq_rotateRight, getLsb_rotateRight_of_le (Nat.mod_lt _ (by omega))]

+/- ## twoPow -/
+
+@[simp, bv_toNat]
+theorem toNat_twoPow (w : Nat) (i : Nat) : (twoPow w i).toNat = 2^i % 2^w := by
+  rcases w with rfl | w
+  · simp [Nat.mod_one]
+  · simp only [twoPow, toNat_shiftLeft, toNat_ofNat]
+    have h1 : 1 < 2 ^ (w + 1) := Nat.one_lt_two_pow (by omega)
+    rw [Nat.mod_eq_of_lt h1, Nat.shiftLeft_eq, Nat.one_mul]
+
+@[simp]
+theorem getLsb_twoPow (i j : Nat) : (twoPow w i).getLsb j = ((i < w) && (i = j)) := by
+  rcases w with rfl | w
+  · simp; omega
+  · simp only [twoPow, getLsb_shiftLeft, getLsb_ofNat]
+    by_cases hj : j < i
+    · simp only [hj, decide_True, Bool.not_true, Bool.and_false, Bool.false_and, Bool.false_eq,
+      Bool.and_eq_false_imp, decide_eq_true_eq, decide_eq_false_iff_not]
+      omega
+    · by_cases hi : Nat.testBit 1 (j - i)
+      · obtain hi' := Nat.testBit_one_eq_true_iff_self_eq_zero.mp hi
+        have hij : j = i := by omega
+        simp_all
+      · have hij : i ≠ j := by
+          intro h; subst h
+          simp at hi
+        simp_all
+
+theorem and_twoPow_eq (x : BitVec w) (i : Nat) :
+    x &&& (twoPow w i) = if x.getLsb i then twoPow w i else 0#w := by
+  ext j
+  simp only [getLsb_and, getLsb_twoPow]
+  by_cases hj : i = j <;> by_cases hx : x.getLsb i <;> simp_all
+
+@[simp]
+theorem mul_twoPow_eq_shiftLeft (x : BitVec w) (i : Nat) :
+    x * (twoPow w i) = x <<< i := by
+  apply eq_of_toNat_eq
+  simp only [toNat_mul, toNat_twoPow, toNat_shiftLeft, Nat.shiftLeft_eq]
+  by_cases hi : i < w
+  · have hpow : 2^i < 2^w := Nat.pow_lt_pow_of_lt (by omega) (by omega)
+    rw [Nat.mod_eq_of_lt hpow]
+  · have hpow : 2 ^ i % 2 ^ w = 0 := by
+      rw [Nat.mod_eq_zero_of_dvd]
+      apply Nat.pow_dvd_pow 2 (by omega)
+    simp [Nat.mul_mod, hpow]
+
 end BitVec
--- a/src/Init/Data/Char/Basic.lean
+++ b/src/Init/Data/Char/Basic.lean
@@ -40,7 +40,7 @@ theorem isValidUInt32 (n : Nat) (h : isValidCharNat n) : n < UInt32.size := by
    apply Nat.lt_trans h₂
    decide

-theorem isValidChar_of_isValidChar_Nat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
+theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
  match h with
  | Or.inl h        => Or.inl h
  | Or.inr ⟨h₁, h₂⟩ => Or.inr ⟨h₁, h₂⟩
@@ -52,6 +52,13 @@ theorem isValidChar_zero : isValidChar 0 :=
@[inline] def toNat (c : Char) : Nat :=
  c.val.toNat

+/-- Convert a character into a `UInt8`, by truncating (reducing modulo 256) if necessary. -/
+@[inline] def toUInt8 (c : Char) : UInt8 :=
+  c.val.toUInt8
+
+/-- The numbers from 0 to 256 are all valid UTF-8 characters, so we can embed one in the other. -/
+def ofUInt8 (n : UInt8) : Char := ⟨n.toUInt32, .inl (Nat.lt_trans n.1.2 (by decide))⟩
+
 instance : Inhabited Char where
  default := 'A'

--- a/src/Init/Data/Char/Lemmas.lean
+++ b/src/Init/Data/Char/Lemmas.lean
@@ -22,4 +22,20 @@ protected theorem le_total (a b : Char) : a ≤ b ∨ b ≤ a := UInt32.le_total
 protected theorem lt_asymm {a b : Char} (h : a < b) : ¬ b < a := UInt32.lt_asymm h
 protected theorem ne_of_lt {a b : Char} (h : a < b) : a ≠ b := Char.ne_of_val_ne (UInt32.ne_of_lt h)

+theorem utf8Size_eq (c : Char) : c.utf8Size = 1 ∨ c.utf8Size = 2 ∨ c.utf8Size = 3 ∨ c.utf8Size = 4 := by
+  have := c.utf8Size_pos
+  have := c.utf8Size_le_four
+  omega
+
+@[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by
+  rw [Char.ofNat, dif_pos]
+  rfl
+
+@[ext] theorem Char.ext : {a b : Char} → a.val = b.val → a = b
+  | ⟨_,_⟩, ⟨_,_⟩, rfl => rfl
+
+theorem Char.ext_iff {x y : Char} : x = y ↔ x.val = y.val := ⟨congrArg _, Char.ext⟩
+
 end Char
+
+@[deprecated Char.utf8Size (since := "2024-06-04")] abbrev String.csize := Char.utf8Size
--- a/src/Init/Data/Fin/Basic.lean
+++ b/src/Init/Data/Fin/Basic.lean
@@ -66,7 +66,24 @@ protected def mul : Fin n → Fin n → Fin n

 /-- Subtraction modulo `n` -/
 protected def sub : Fin n → Fin n → Fin n
-  | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + (n - b)) % n, mlt h⟩
+  /-
+  The definition of `Fin.sub` has been updated to improve performance.
+  The right-hand-side of the following `match` was originally
+  ```
+  ⟨(a + (n - b)) % n, mlt h⟩
+  ```
+  This caused significant performance issues when testing definitional equality,
+  such as `x =?= x - 1` where `x : Fin n` and `n` is a big number,
+  as Lean spent a long time reducing
+  ```
+  ((n - 1) + x.val) % n
+  ```
+  For example, this was an issue for `Fin 2^64` (i.e., `UInt64`).
+  This change improves performance by leveraging the fact that `Nat.add` is defined
+  using recursion on the second argument.
+  See issue #4413.
+  -/
+  | ⟨a, h⟩, ⟨b, _⟩ => ⟨((n - b) + a) % n, mlt h⟩

 /-!
 Remark: land/lor can be defined without using (% n), but
@@ -193,4 +210,7 @@ theorem val_add_one_le_of_lt {n : Nat} {a b : Fin n} (h : a < b) : (a : Nat) + 1

 theorem val_add_one_le_of_gt {n : Nat} {a b : Fin n} (h : a > b) : (b : Nat) + 1 ≤ (a : Nat) := h

+theorem exists_iff {p : Fin n → Prop} : (Exists fun i => p i) ↔ Exists fun i => Exists fun h => p ⟨i, h⟩ :=
+  ⟨fun ⟨⟨i, hi⟩, hpi⟩ => ⟨i, hi, hpi⟩, fun ⟨i, hi, hpi⟩ => ⟨⟨i, hi⟩, hpi⟩⟩
+
 end Fin
--- a/src/Init/Data/Fin/Lemmas.lean
+++ b/src/Init/Data/Fin/Lemmas.lean
@@ -24,7 +24,7 @@ theorem mod_def (a m : Fin n) : a % m = Fin.mk (a % m) (Nat.lt_of_le_of_lt (Nat.

 theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.size_pos) := rfl

-theorem sub_def (a b : Fin n) : a - b = Fin.mk ((a + (n - b)) % n) (Nat.mod_lt _ a.size_pos) := rfl
+theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.size_pos) := rfl

 theorem size_pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.size_pos

@@ -43,9 +43,6 @@ theorem ext_iff {a b : Fin n} : a = b ↔ a.1 = b.1 := val_inj.symm

 theorem val_ne_iff {a b : Fin n} : a.1 ≠ b.1 ↔ a ≠ b := not_congr val_inj

-theorem exists_iff {p : Fin n → Prop} : (∃ i, p i) ↔ ∃ i h, p ⟨i, h⟩ :=
-  ⟨fun ⟨⟨i, hi⟩, hpi⟩ => ⟨i, hi, hpi⟩, fun ⟨i, hi, hpi⟩ => ⟨⟨i, hi⟩, hpi⟩⟩
-
 theorem forall_iff {p : Fin n → Prop} : (∀ i, p i) ↔ ∀ i h, p ⟨i, h⟩ :=
  ⟨fun h i hi => h ⟨i, hi⟩, fun h ⟨i, hi⟩ => h i hi⟩

@@ -381,7 +378,7 @@ theorem castSucc_lt_succ (i : Fin n) : Fin.castSucc i < i.succ :=
  lt_def.2 <| by simp only [coe_castSucc, val_succ, Nat.lt_succ_self]

 theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ Fin.castSucc j ↔ i < j.succ := by
-  simpa [lt_def, le_def] using Nat.succ_le_succ_iff.symm
+  simpa only [lt_def, le_def] using Nat.add_one_le_add_one_iff.symm

 theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
    Fin.castSucc i < j ↔ i.succ ≤ j := .rfl
@@ -762,16 +759,16 @@ theorem addCases_right {m n : Nat} {motive : Fin (m + n) → Sort _} {left right

 /-! ### sub -/

-protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = (a + (n - b)) % n := by
+protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
  cases a; cases b; rfl

@[simp] theorem ofNat'_sub (x : Nat) (lt : 0 < n) (y : Fin n) :
-    Fin.ofNat' x lt - y = Fin.ofNat' (x + (n - y.val)) lt := by
+    Fin.ofNat' x lt - y = Fin.ofNat' ((n - y.val) + x) lt := by
  apply Fin.eq_of_val_eq
  simp [Fin.ofNat', Fin.sub_def]

@[simp] theorem sub_ofNat' (x : Fin n) (y : Nat) (lt : 0 < n) :
-    x - Fin.ofNat' y lt = Fin.ofNat' (x.val + (n - y % n)) lt := by
+    x - Fin.ofNat' y lt = Fin.ofNat' ((n - y % n) + x.val) lt := by
  apply Fin.eq_of_val_eq
  simp [Fin.ofNat', Fin.sub_def]

@@ -782,7 +779,7 @@ private theorem _root_.Nat.mod_eq_sub_of_lt_two_mul {x n} (h₁ : n ≤ x) (h₂
 theorem coe_sub_iff_le {a b : Fin n} : (↑(a - b) : Nat) = a - b ↔ b ≤ a := by
  rw [sub_def, le_def]
  dsimp only
-  if h : n ≤ a + (n - b) then
+  if h : n ≤ (n - b) + a then
    rw [Nat.mod_eq_sub_of_lt_two_mul h]
    all_goals omega
  else
@@ -792,7 +789,7 @@ theorem coe_sub_iff_le {a b : Fin n} : (↑(a - b) : Nat) = a - b ↔ b ≤ a :=
 theorem coe_sub_iff_lt {a b : Fin n} : (↑(a - b) : Nat) = n + a - b ↔ a < b := by
  rw [sub_def, lt_def]
  dsimp only
-  if h : n ≤ a + (n - b) then
+  if h : n ≤ (n - b) + a then
    rw [Nat.mod_eq_sub_of_lt_two_mul h]
    all_goals omega
  else
--- a/src/Init/Data/Format/Syntax.lean
+++ b/src/Init/Data/Format/Syntax.lean
@@ -20,24 +20,27 @@ private def formatInfo (showInfo : Bool) (info : SourceInfo) (f : Format) : Form
  | true, SourceInfo.synthetic pos endPos false     => f!"{pos}:{f}:{endPos}"
  | _,    _                                         => f

-partial def formatStxAux (maxDepth : Option Nat) (showInfo : Bool) : Nat → Syntax → Format
-  | _,     atom info val     => formatInfo showInfo info $ format (repr val)
-  | _,     ident info _ val _   => formatInfo showInfo info $ format "`" ++ format val
-  | _,     missing           => "<missing>"
-  | depth, node _ kind args  =>
+partial def formatStxAux (maxDepth : Option Nat) (showInfo : Bool) (depth : Nat) : Syntax → Format
+  | atom info val        => formatInfo showInfo info <| format (repr val)
+  | ident info _ val _   => formatInfo showInfo info <| format "`" ++ format val
+  | missing              => "<missing>"
+  | node info kind args  =>
    let depth := depth + 1;
    if kind == nullKind then
-      sbracket $
+      sbracket <|
        if args.size > 0 && depth > maxDepth.getD depth then
          ".."
        else
          joinSep (args.toList.map (formatStxAux maxDepth showInfo depth)) line
    else
-      let shorterName := kind.replacePrefix `Lean.Parser Name.anonymous;
-      let header      := format shorterName;
+      let shorterName := kind.replacePrefix `Lean.Parser Name.anonymous
+      let header      := formatInfo showInfo info <| format shorterName
      let body : List Format :=
-        if args.size > 0 && depth > maxDepth.getD depth then [".."] else args.toList.map (formatStxAux maxDepth showInfo depth);
-      paren $ joinSep (header :: body) line
+        if args.size > 0 && depth > maxDepth.getD depth then
+          [".."]
+        else
+          args.toList.map (formatStxAux maxDepth showInfo depth)
+      paren <| joinSep (header :: body) line

 /-- Pretty print the given syntax `stx` as a `Format`.
 Nodes deeper than `maxDepth` are omitted.
--- a/src/Init/Data/Int/DivModLemmas.lean
+++ b/src/Init/Data/Int/DivModLemmas.lean
@@ -636,7 +636,7 @@ theorem sub_ediv_of_dvd (a : Int) {b c : Int}
  have := Int.mul_ediv_cancel 1 H; rwa [Int.one_mul] at this

@[simp]
-theorem Int.emod_sub_cancel (x y : Int): (x - y)%y = x%y := by
+theorem emod_sub_cancel (x y : Int): (x - y)%y = x%y := by
  by_cases h : y = 0
  · simp [h]
  · simp only [Int.emod_def, Int.sub_ediv_of_dvd, Int.dvd_refl, Int.ediv_self h, Int.mul_sub]
@@ -1075,9 +1075,9 @@ theorem emod_mul_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n * y) n = Int.bmo
 theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n := by
  rw [bmod_def x n]
  split
-  case inl p =>
+  next p =>
    simp only [emod_add_bmod_congr]
-  case inr p =>
+  next p =>
    rw [Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg]
    simp

@@ -1088,9 +1088,9 @@ theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n
 theorem bmod_mul_bmod : Int.bmod (Int.bmod x n * y) n = Int.bmod (x * y) n := by
  rw [bmod_def x n]
  split
-  case inl p =>
+  next p =>
    simp
-  case inr p =>
+  next p =>
    rw [Int.sub_mul, Int.sub_eq_add_neg, ← Int.mul_neg]
    simp

--- a/src/Init/Data/Int/Order.lean
+++ b/src/Init/Data/Int/Order.lean
@@ -127,9 +127,14 @@ protected theorem lt_iff_le_not_le {a b : Int} : a < b ↔ a ≤ b ∧ ¬b ≤ a
  · exact Int.le_antisymm h h'
  · subst h'; apply Int.le_refl

+protected theorem lt_of_not_ge {a b : Int} (h : ¬a ≤ b) : b < a :=
+  Int.lt_iff_le_not_le.mpr ⟨(Int.le_total ..).resolve_right h, h⟩
+
+protected theorem not_le_of_gt {a b : Int} (h : b < a) : ¬a ≤ b :=
+  (Int.lt_iff_le_not_le.mp h).right
+
 protected theorem not_le {a b : Int} : ¬a ≤ b ↔ b < a :=
-  ⟨fun h => Int.lt_iff_le_not_le.2 ⟨(Int.le_total ..).resolve_right h, h⟩,
-   fun h => (Int.lt_iff_le_not_le.1 h).2⟩
+  Iff.intro Int.lt_of_not_ge Int.not_le_of_gt

 protected theorem not_lt {a b : Int} : ¬a < b ↔ b ≤ a :=
  by rw [← Int.not_le, Decidable.not_not]
@@ -509,9 +514,6 @@ theorem mem_toNat' : ∀ (a : Int) (n : Nat), toNat' a = some n ↔ a = n

 /-! ## Order properties of the integers -/

-protected theorem lt_of_not_ge {a b : Int} : ¬a ≤ b → b < a := Int.not_le.mp
-protected theorem not_le_of_gt {a b : Int} : b < a → ¬a ≤ b := Int.not_le.mpr
-
 protected theorem le_of_not_le {a b : Int} : ¬ a ≤ b → b ≤ a := (Int.le_total a b).resolve_left

@[simp] theorem negSucc_not_pos (n : Nat) : 0 < -[n+1] ↔ False := by
@@ -586,7 +588,10 @@ theorem add_one_le_iff {a b : Int} : a + 1 ≤ b ↔ a < b := .rfl
 theorem lt_add_one_iff {a b : Int} : a < b + 1 ↔ a ≤ b := Int.add_le_add_iff_right _

@[simp] theorem succ_ofNat_pos (n : Nat) : 0 < (n : Int) + 1 :=
-  lt_add_one_iff.2 (ofNat_zero_le _)
+  lt_add_one_iff.mpr (ofNat_zero_le _)
+
+theorem not_ofNat_neg (n : Nat) : ¬((n : Int) < 0) :=
+  Int.not_lt.mpr (ofNat_zero_le ..)

 theorem le_add_one {a b : Int} (h : a ≤ b) : a ≤ b + 1 :=
  Int.le_of_lt (Int.lt_add_one_iff.2 h)
@@ -801,6 +806,12 @@ protected theorem lt_add_of_neg_lt_sub_right {a b c : Int} (h : -b < a - c) : c
 protected theorem neg_lt_sub_right_of_lt_add {a b c : Int} (h : c < a + b) : -b < a - c :=
  Int.lt_sub_left_of_add_lt (Int.sub_right_lt_of_lt_add h)

+protected theorem add_lt_iff (a b c : Int) : a + b < c ↔ a < -b + c := by
+  rw [← Int.add_lt_add_iff_left (-b), Int.add_comm (-b), Int.add_neg_cancel_right]
+
+protected theorem sub_lt_iff (a b c : Int) : a - b < c ↔ a < c + b :=
+  Iff.intro Int.lt_add_of_sub_right_lt Int.sub_right_lt_of_lt_add
+
 protected theorem sub_lt_of_sub_lt {a b c : Int} (h : a - b < c) : a - c < b :=
  Int.sub_left_lt_of_lt_add (Int.lt_add_of_sub_right_lt h)

--- a/src/Init/Data/List.lean
+++ b/src/Init/Data/List.lean
@@ -10,3 +10,4 @@ import Init.Data.List.Control
 import Init.Data.List.Lemmas
 import Init.Data.List.Impl
 import Init.Data.List.TakeDrop
+import Init.Data.List.Notation
--- a/src/Init/Data/List/Basic.lean
+++ b/src/Init/Data/List/Basic.lean
--- a/src/Init/Data/List/BasicAux.lean
+++ b/src/Init/Data/List/BasicAux.lean
@@ -5,7 +5,6 @@ Author: Leonardo de Moura
 -/
 prelude
 import Init.Data.Nat.Linear
-import Init.Ext

 universe u

@@ -13,6 +12,10 @@ namespace List
 /-! The following functions can't be defined at `Init.Data.List.Basic`, because they depend on `Init.Util`,
   and `Init.Util` depends on `Init.Data.List.Basic`. -/

+/-! ## Alternative getters -/
+
+/-! ### get! -/
+
 /--
 Returns the `i`-th element in the list (zero-based).

@@ -24,108 +27,12 @@ def get! [Inhabited α] : (as : List α) → (i : Nat) → α
  | _::as, n+1 => get! as n
  | _,     _   => panic! "invalid index"

-/--
-Returns the `i`-th element in the list (zero-based).
+theorem get!_nil [Inhabited α] (n : Nat) : [].get! n = (default : α) := rfl
+theorem get!_cons_succ [Inhabited α] (l : List α) (a : α) (n : Nat) :
+    (a::l).get! (n+1) = get! l n := rfl
+theorem get!_cons_zero [Inhabited α] (l : List α) (a : α) : (a::l).get! 0 = a := rfl

-If the index is out of bounds (`i ≥ as.length`), this function returns `none`.
-Also see `get`, `getD` and `get!`.
-/
-def get? : (as : List α) → (i : Nat) → Option α
-  | a::_,  0   => some a
-  | _::as, n+1 => get? as n
-  | _,     _   => none
-
-/--
-Returns the `i`-th element in the list (zero-based).
-
-If the index is out of bounds (`i ≥ as.length`), this function returns `fallback`.
-See also `get?` and `get!`.
-/
-def getD (as : List α) (i : Nat) (fallback : α) : α :=
-  (as.get? i).getD fallback
-
-@[ext] theorem ext : ∀ {l₁ l₂ : List α}, (∀ n, l₁.get? n = l₂.get? n) → l₁ = l₂
-  | [], [], _ => rfl
-  | a :: l₁, [], h => nomatch h 0
-  | [], a' :: l₂, h => nomatch h 0
-  | a :: l₁, a' :: l₂, h => by
-    have h0 : some a = some a' := h 0
-    injection h0 with aa; simp only [aa, ext fun n => h (n+1)]
-
-/--
-Returns the first element in the list.
-
-If the list is empty, this function panics when executed, and returns `default`.
-See `head` and `headD` for safer alternatives.
-/
-def head! [Inhabited α] : List α → α
-  | []   => panic! "empty list"
-  | a::_ => a
-
-/--
-Returns the first element in the list.
-
-If the list is empty, this function returns `none`.
-Also see `headD` and `head!`.
-/
-def head? : List α → Option α
-  | []   => none
-  | a::_ => some a
-
-/--
-Returns the first element in the list.
-
-If the list is empty, this function returns `fallback`.
-Also see `head?` and `head!`.
-/
-def headD : (as : List α) → (fallback : α) → α
-  | [],   fallback => fallback
-  | a::_, _  => a
-
-/--
-Returns the first element of a non-empty list.
-/
-def head : (as : List α) → as ≠ [] → α
-  | a::_, _ => a
-
-/--
-Drops the first element of the list.
-
-If the list is empty, this function panics when executed, and returns the empty list.
-See `tail` and `tailD` for safer alternatives.
-/
-def tail! : List α → List α
-  | []    => panic! "empty list"
-  | _::as => as
-
-/--
-Drops the first element of the list.
-
-If the list is empty, this function returns `none`.
-Also see `tailD` and `tail!`.
-/
-def tail? : List α → Option (List α)
-  | []    => none
-  | _::as => some as
-
-/--
-Drops the first element of the list.
-
-If the list is empty, this function returns `fallback`.
-Also see `head?` and `head!`.
-/
-def tailD (list fallback : List α) : List α :=
-  match list with
-  | [] => fallback
-  | _ :: tl => tl
-
-/--
-Returns the last element of a non-empty list.
-/
-def getLast : ∀ (as : List α), as ≠ [] → α
-  | [],       h => absurd rfl h
-  | [a],      _ => a
-  | _::b::as, _ => getLast (b::as) (fun h => List.noConfusion h)
+/-! ### getLast! -/

 /--
 Returns the last element in the list.
@@ -137,61 +44,118 @@ def getLast! [Inhabited α] : List α → α
  | []    => panic! "empty list"
  | a::as => getLast (a::as) (fun h => List.noConfusion h)

-/--
-Returns the last element in the list.
+/-! ## Head and tail -/

-If the list is empty, this function returns `none`.
-Also see `getLastD` and `getLast!`.
-/
-def getLast? : List α → Option α
-  | []    => none
-  | a::as => some (getLast (a::as) (fun h => List.noConfusion h))
+/-! ### head! -/

 /--
-Returns the last element in the list.
+Returns the first element in the list.

-If the list is empty, this function returns `fallback`.
-Also see `getLast?` and `getLast!`.
+If the list is empty, this function panics when executed, and returns `default`.
+See `head` and `headD` for safer alternatives.
 -/
-def getLastD : (as : List α) → (fallback : α) → α
-  | [],   a₀ => a₀
-  | a::as, _ => getLast (a::as) (fun h => List.noConfusion h)
+def head! [Inhabited α] : List α → α
+  | []   => panic! "empty list"
+  | a::_ => a
+
+/-! ### tail! -/

 /--
-`O(n)`. Rotates the elements of `xs` to the left such that the element at
-`xs[i]` rotates to `xs[(i - n) % l.length]`.
-* `rotateLeft [1, 2, 3, 4, 5] 3 = [4, 5, 1, 2, 3]`
-* `rotateLeft [1, 2, 3, 4, 5] 5 = [1, 2, 3, 4, 5]`
-* `rotateLeft [1, 2, 3, 4, 5] = [2, 3, 4, 5, 1]`
+Drops the first element of the list.
+
+If the list is empty, this function panics when executed, and returns the empty list.
+See `tail` and `tailD` for safer alternatives.
 -/
-def rotateLeft (xs : List α) (n : Nat := 1) : List α :=
-  let len := xs.length
-  if len ≤ 1 then
-    xs
-  else
-    let n := n % len
-    let b := xs.take n
-    let e := xs.drop n
-    e ++ b
+def tail! : List α → List α
+  | []    => panic! "empty list"
+  | _::as => as
+
+@[simp] theorem tail!_cons : @tail! α (a::l) = l := rfl
+
+/-! ### partitionM -/

 /--
-`O(n)`. Rotates the elements of `xs` to the right such that the element at
-`xs[i]` rotates to `xs[(i + n) % l.length]`.
-* `rotateRight [1, 2, 3, 4, 5] 3 = [3, 4, 5, 1, 2]`
-* `rotateRight [1, 2, 3, 4, 5] 5 = [1, 2, 3, 4, 5]`
-* `rotateRight [1, 2, 3, 4, 5] = [5, 1, 2, 3, 4]`
-/
-def rotateRight (xs : List α) (n : Nat := 1) : List α :=
-  let len := xs.length
-  if len ≤ 1 then
-    xs
-  else
-    let n := len - n % len
-    let b := xs.take n
-    let e := xs.drop n
-    e ++ b
+Monadic generalization of `List.partition`.

-theorem get_append_left (as bs : List α) (h : i < as.length) {h'} : (as ++ bs).get ⟨i, h'⟩ = as.get ⟨i, h⟩ := by
+This uses `Array.toList` and which isn't imported by `Init.Data.List.Basic` or `Init.Data.List.Control`.
+```
+def posOrNeg (x : Int) : Except String Bool :=
+  if x > 0 then pure true
+  else if x < 0 then pure false
+  else throw "Zero is not positive or negative"
+
+partitionM posOrNeg [-1, 2, 3] = Except.ok ([2, 3], [-1])
+partitionM posOrNeg [0, 2, 3] = Except.error "Zero is not positive or negative"
+```
+-/
+@[inline] def partitionM [Monad m] (p : α → m Bool) (l : List α) : m (List α × List α) :=
+  go l #[] #[]
+where
+  /-- Auxiliary for `partitionM`:
+  `partitionM.go p l acc₁ acc₂` returns `(acc₁.toList ++ left, acc₂.toList ++ right)`
+  if `partitionM p l` returns `(left, right)`. -/
+  @[specialize] go : List α → Array α → Array α → m (List α × List α)
+  | [], acc₁, acc₂ => pure (acc₁.toList, acc₂.toList)
+  | x :: xs, acc₁, acc₂ => do
+    if ← p x then
+      go xs (acc₁.push x) acc₂
+    else
+      go xs acc₁ (acc₂.push x)
+
+/-! ### partitionMap -/
+
+/--
+Given a function `f : α → β ⊕ γ`, `partitionMap f l` maps the list by `f`
+whilst partitioning the result into a pair of lists, `List β × List γ`,
+partitioning the `.inl _` into the left list, and the `.inr _` into the right List.
+```
+partitionMap (id : Nat ⊕ Nat → Nat ⊕ Nat) [inl 0, inr 1, inl 2] = ([0, 2], [1])
+```
+-/
+@[inline] def partitionMap (f : α → β ⊕ γ) (l : List α) : List β × List γ := go l #[] #[] where
+  /-- Auxiliary for `partitionMap`:
+  `partitionMap.go f l acc₁ acc₂ = (acc₁.toList ++ left, acc₂.toList ++ right)`
+  if `partitionMap f l = (left, right)`. -/
+  @[specialize] go : List α → Array β → Array γ → List β × List γ
+  | [], acc₁, acc₂ => (acc₁.toList, acc₂.toList)
+  | x :: xs, acc₁, acc₂ =>
+    match f x with
+    | .inl a => go xs (acc₁.push a) acc₂
+    | .inr b => go xs acc₁ (acc₂.push b)
+
+/-! ### mapMono
+
+This is a performance optimization for `List.mapM` that avoids allocating a new list when the result of each `f a` is a pointer equal value `a`.
+
+For verification purposes, `List.mapMono = List.map`.
+-/
+
+@[specialize] private unsafe def mapMonoMImp [Monad m] (as : List α) (f : α → m α) : m (List α) := do
+  match as with
+  | [] => return as
+  | b :: bs =>
+    let b'  ← f b
+    let bs' ← mapMonoMImp bs f
+    if ptrEq b' b && ptrEq bs' bs then
+      return as
+    else
+      return b' :: bs'
+
+/--
+Monomorphic `List.mapM`. The internal implementation uses pointer equality, and does not allocate a new list
+if the result of each `f a` is a pointer equal value `a`.
+-/
+@[implemented_by mapMonoMImp] def mapMonoM [Monad m] (as : List α) (f : α → m α) : m (List α) :=
+  match as with
+  | [] => return []
+  | a :: as => return (← f a) :: (← mapMonoM as f)
+
+def mapMono (as : List α) (f : α → α) : List α :=
+  Id.run <| as.mapMonoM f
+
+/-! ## Additional lemmas required for bootstrapping `Array`. -/
+
+theorem getElem_append_left (as bs : List α) (h : i < as.length) {h'} : (as ++ bs)[i] = as[i] := by
  induction as generalizing i with
  | nil => trivial
  | cons a as ih =>
@@ -199,7 +163,7 @@ theorem get_append_left (as bs : List α) (h : i < as.length) {h'} : (as ++ bs).
    | zero => rfl
    | succ i => apply ih

-theorem get_append_right (as bs : List α) (h : ¬ i < as.length) {h' h''} : (as ++ bs).get ⟨i, h'⟩ = bs.get ⟨i - as.length, h''⟩ := by
+theorem getElem_append_right (as bs : List α) (h : ¬ i < as.length) {h' h''} : (as ++ bs)[i]'h' = bs[i - as.length]'h'' := by
  induction as generalizing i with
  | nil => trivial
  | cons a as ih =>
@@ -285,74 +249,4 @@ theorem le_antisymm [LT α] [s : Antisymm (¬ · < · : α → α → Prop)] {as
 instance [LT α] [Antisymm (¬ · < · : α → α → Prop)] : Antisymm (· ≤ · : List α → List α → Prop) where
  antisymm h₁ h₂ := le_antisymm h₁ h₂

-@[specialize] private unsafe def mapMonoMImp [Monad m] (as : List α) (f : α → m α) : m (List α) := do
-  match as with
-  | [] => return as
-  | b :: bs =>
-    let b'  ← f b
-    let bs' ← mapMonoMImp bs f
-    if ptrEq b' b && ptrEq bs' bs then
-      return as
-    else
-      return b' :: bs'
-
-/--
-Monomorphic `List.mapM`. The internal implementation uses pointer equality, and does not allocate a new list
-if the result of each `f a` is a pointer equal value `a`.
-/
-@[implemented_by mapMonoMImp] def mapMonoM [Monad m] (as : List α) (f : α → m α) : m (List α) :=
-  match as with
-  | [] => return []
-  | a :: as => return (← f a) :: (← mapMonoM as f)
-
-def mapMono (as : List α) (f : α → α) : List α :=
-  Id.run <| as.mapMonoM f
-
-/--
-Monadic generalization of `List.partition`.
-
-This uses `Array.toList` and which isn't imported by `Init.Data.List.Basic`.
-```
-def posOrNeg (x : Int) : Except String Bool :=
-  if x > 0 then pure true
-  else if x < 0 then pure false
-  else throw "Zero is not positive or negative"
-
-partitionM posOrNeg [-1, 2, 3] = Except.ok ([2, 3], [-1])
-partitionM posOrNeg [0, 2, 3] = Except.error "Zero is not positive or negative"
-```
-/
-@[inline] def partitionM [Monad m] (p : α → m Bool) (l : List α) : m (List α × List α) :=
-  go l #[] #[]
-where
-  /-- Auxiliary for `partitionM`:
-  `partitionM.go p l acc₁ acc₂` returns `(acc₁.toList ++ left, acc₂.toList ++ right)`
-  if `partitionM p l` returns `(left, right)`. -/
-  @[specialize] go : List α → Array α → Array α → m (List α × List α)
-  | [], acc₁, acc₂ => pure (acc₁.toList, acc₂.toList)
-  | x :: xs, acc₁, acc₂ => do
-    if ← p x then
-      go xs (acc₁.push x) acc₂
-    else
-      go xs acc₁ (acc₂.push x)
-
-/--
-Given a function `f : α → β ⊕ γ`, `partitionMap f l` maps the list by `f`
-whilst partitioning the result it into a pair of lists, `List β × List γ`,
-partitioning the `.inl _` into the left list, and the `.inr _` into the right List.
-```
-partitionMap (id : Nat ⊕ Nat → Nat ⊕ Nat) [inl 0, inr 1, inl 2] = ([0, 2], [1])
-```
-/
-@[inline] def partitionMap (f : α → β ⊕ γ) (l : List α) : List β × List γ := go l #[] #[] where
-  /-- Auxiliary for `partitionMap`:
-  `partitionMap.go f l acc₁ acc₂ = (acc₁.toList ++ left, acc₂.toList ++ right)`
-  if `partitionMap f l = (left, right)`. -/
-  @[specialize] go : List α → Array β → Array γ → List β × List γ
-  | [], acc₁, acc₂ => (acc₁.toList, acc₂.toList)
-  | x :: xs, acc₁, acc₂ =>
-    match f x with
-    | .inl a => go xs (acc₁.push a) acc₂
-    | .inr b => go xs acc₁ (acc₂.push b)
-
 end List
--- a/src/Init/Data/List/Control.lean
+++ b/src/Init/Data/List/Control.lean
@@ -151,6 +151,11 @@ protected def foldlM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w
    let s' ← f s a
    List.foldlM f s' as

+@[simp] theorem foldlM_nil [Monad m] (f : β → α → m β) (b) : [].foldlM f b = pure b := rfl
+@[simp] theorem foldlM_cons [Monad m] (f : β → α → m β) (b) (a) (l : List α) :
+    (a :: l).foldlM f b = f b a >>= l.foldlM f := by
+  simp [List.foldlM]
+
 /--
 Folds a monadic function over a list from right to left:
 ```
@@ -165,6 +170,8 @@ foldrM f x₀ [a, b, c] = do
 def foldrM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} (f : α → s → m s) (init : s) (l : List α) : m s :=
  l.reverse.foldlM (fun s a => f a s) init

+@[simp] theorem foldrM_nil [Monad m] (f : α → β → m β) (b) : [].foldrM f b = pure b := rfl
+
 /--
 Maps `f` over the list and collects the results with `<|>`.
 ```
--- a/src/Init/Data/List/Impl.lean
+++ b/src/Init/Data/List/Impl.lean
@@ -16,7 +16,44 @@ so these are in a separate file to minimize imports.

 namespace List

-/-- Tail recursive version of `erase`. -/
+/-! ## Basic `List` operations.
+
+The following operations are already tail-recursive, and do not need `@[csimp]` replacements:
+`get`, `foldl`, `beq`, `isEqv`, `reverse`, `elem` (and hence `contains`), `drop`, `dropWhile`,
+`partition`, `isPrefixOf`, `isPrefixOf?`, `find?`, `findSome?`, `lookup`, `any` (and hence `or`),
+`all` (and hence `and`) , `range`, `eraseDups`, `eraseReps`, `span`, `groupBy`.
+
+The following operations are still missing `@[csimp]` replacements:
+`concat`, `zipWithAll`.
+
+The following operations are not recursive to begin with
+(or are defined in terms of recursive primitives):
+`isEmpty`, `isSuffixOf`, `isSuffixOf?`, `rotateLeft`, `rotateRight`, `insert`, `zip`, `enum`,
+`minimum?`, `maximum?`, and `removeAll`.
+
+The following operations are given `@[csimp]` replacements below:
+`length`, `set`, `map`, `filter`, `filterMap`, `foldr`, `append`, `bind`, `join`, `replicate`,
+`take`, `takeWhile`, `dropLast`, `replace`, `erase`, `eraseIdx`, `zipWith`, `unzip`, `iota`,
+`enumFrom`, `intersperse`, and `intercalate`.
+
+-/
+
+/-! ### length -/
+
+theorem length_add_eq_lengthTRAux (as : List α) (n : Nat) : as.length + n = as.lengthTRAux n := by
+  induction as generalizing n with
+  | nil  => simp [length, lengthTRAux]
+  | cons a as ih =>
+    simp [length, lengthTRAux, ← ih, Nat.succ_add]
+    rfl
+
+@[csimp] theorem length_eq_lengthTR : @List.length = @List.lengthTR := by
+  apply funext; intro α; apply funext; intro as
+  simp [lengthTR, ← length_add_eq_lengthTRAux]
+
+/-! ### set -/
+
+/-- Tail recursive version of `List.set`. -/
@[inline] def setTR (l : List α) (n : Nat) (a : α) : List α := go l n #[] where
  /-- Auxiliary for `setTR`: `setTR.go l a xs n acc = acc.toList ++ set xs a`,
  unless `n ≥ l.length` in which case it returns `l` -/
@@ -31,10 +68,214 @@ namespace List
    setTR.go l a xs n acc = acc.data ++ xs.set n a
  | [], _ => fun h => by simp [setTR.go, set, h]
  | x::xs, 0 => by simp [setTR.go, set]
-  | x::xs, n+1 => fun h => by simp [setTR.go, set]; rw [go _ xs]; {simp}; simp [h]
+  | x::xs, n+1 => fun h => by simp only [setTR.go, set]; rw [go _ xs] <;> simp [h]
  exact (go #[] _ _ rfl).symm

-/-- Tail recursive version of `erase`. -/
+/-! ### map -/
+
+/-- Tail-recursive version of `List.map`. -/
+@[inline] def mapTR (f : α → β) (as : List α) : List β :=
+  loop as []
+where
+  @[specialize] loop : List α → List β → List β
+  | [],    bs => bs.reverse
+  | a::as, bs => loop as (f a :: bs)
+
+theorem mapTR_loop_eq (f : α → β) (as : List α) (bs : List β) :
+    mapTR.loop f as bs = bs.reverse ++ map f as := by
+  induction as generalizing bs with
+  | nil => simp [mapTR.loop, map]
+  | cons a as ih =>
+    simp only [mapTR.loop, map]
+    rw [ih (f a :: bs), reverse_cons, append_assoc]
+    rfl
+
+@[csimp] theorem map_eq_mapTR : @map = @mapTR :=
+  funext fun α => funext fun β => funext fun f => funext fun as => by
+    simp [mapTR, mapTR_loop_eq]
+
+/-! ### filter -/
+
+/-- Tail-recursive version of `List.filter`. -/
+@[inline] def filterTR (p : α → Bool) (as : List α) : List α :=
+  loop as []
+where
+  @[specialize] loop : List α → List α → List α
+  | [],    rs => rs.reverse
+  | a::as, rs => match p a with
+     | true  => loop as (a::rs)
+     | false => loop as rs
+
+theorem filterTR_loop_eq (p : α → Bool) (as bs : List α) :
+    filterTR.loop p as bs = bs.reverse ++ filter p as := by
+  induction as generalizing bs with
+  | nil => simp [filterTR.loop, filter]
+  | cons a as ih =>
+    simp only [filterTR.loop, filter]
+    split <;> simp_all
+
+@[csimp] theorem filter_eq_filterTR : @filter = @filterTR := by
+  apply funext; intro α; apply funext; intro p; apply funext; intro as
+  simp [filterTR, filterTR_loop_eq]
+
+/-! ### filterMap -/
+
+/-- Tail recursive version of `filterMap`. -/
+@[inline] def filterMapTR (f : α → Option β) (l : List α) : List β := go l #[] where
+  /-- Auxiliary for `filterMap`: `filterMap.go f l = acc.toList ++ filterMap f l` -/
+  @[specialize] go : List α → Array β → List β
+  | [], acc => acc.toList
+  | a::as, acc => match f a with
+    | none => go as acc
+    | some b => go as (acc.push b)
+
+@[csimp] theorem filterMap_eq_filterMapTR : @List.filterMap = @filterMapTR := by
+  funext α β f l
+  let rec go : ∀ as acc, filterMapTR.go f as acc = acc.data ++ as.filterMap f
+    | [], acc => by simp [filterMapTR.go, filterMap]
+    | a::as, acc => by
+      simp only [filterMapTR.go, go as, Array.push_data, append_assoc, singleton_append, filterMap]
+      split <;> simp [*]
+  exact (go l #[]).symm
+
+/-! ### foldr -/
+
+/-- Tail recursive version of `List.foldr`. -/
+@[specialize] def foldrTR (f : α → β → β) (init : β) (l : List α) : β := l.toArray.foldr f init
+
+@[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
+  funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_data, -Array.size_toArray]
+
+/-! ### bind  -/
+
+/-- Tail recursive version of `List.bind`. -/
+@[inline] def bindTR (as : List α) (f : α → List β) : List β := go as #[] where
+  /-- Auxiliary for `bind`: `bind.go f as = acc.toList ++ bind f as` -/
+  @[specialize] go : List α → Array β → List β
+  | [], acc => acc.toList
+  | x::xs, acc => go xs (acc ++ f x)
+
+@[csimp] theorem bind_eq_bindTR : @List.bind = @bindTR := by
+  funext α β as f
+  let rec go : ∀ as acc, bindTR.go f as acc = acc.data ++ as.bind f
+    | [], acc => by simp [bindTR.go, bind]
+    | x::xs, acc => by simp [bindTR.go, bind, go xs]
+  exact (go as #[]).symm
+
+/-! ### join -/
+
+/-- Tail recursive version of `List.join`. -/
+@[inline] def joinTR (l : List (List α)) : List α := bindTR l id
+
+@[csimp] theorem join_eq_joinTR : @join = @joinTR := by
+  funext α l; rw [← List.bind_id, List.bind_eq_bindTR]; rfl
+
+/-! ### replicate -/
+
+/-- Tail-recursive version of `List.replicate`. -/
+def replicateTR {α : Type u} (n : Nat) (a : α) : List α :=
+  let rec loop : Nat → List α → List α
+    | 0, as => as
+    | n+1, as => loop n (a::as)
+  loop n []
+
+theorem replicateTR_loop_replicate_eq (a : α) (m n : Nat) :
+  replicateTR.loop a n (replicate m a) = replicate (n + m) a := by
+  induction n generalizing m with simp [replicateTR.loop]
+  | succ n ih => simp [Nat.succ_add]; exact ih (m+1)
+
+theorem replicateTR_loop_eq : ∀ n, replicateTR.loop a n acc = replicate n a ++ acc
+  | 0 => rfl
+  | n+1 => by rw [← replicateTR_loop_replicate_eq _ 1 n, replicate, replicate,
+    replicateTR.loop, replicateTR_loop_eq n, replicateTR_loop_eq n, append_assoc]; rfl
+
+@[csimp] theorem replicate_eq_replicateTR : @List.replicate = @List.replicateTR := by
+  apply funext; intro α; apply funext; intro n; apply funext; intro a
+  exact (replicateTR_loop_replicate_eq _ 0 n).symm
+
+/-! ## Sublists -/
+
+/-! ### take -/
+
+/-- Tail recursive version of `List.take`. -/
+@[inline] def takeTR (n : Nat) (l : List α) : List α := go l n #[] where
+  /-- Auxiliary for `take`: `take.go l xs n acc = acc.toList ++ take n xs`,
+  unless `n ≥ xs.length` in which case it returns `l`. -/
+  @[specialize] go : List α → Nat → Array α → List α
+  | [], _, _ => l
+  | _::_, 0, acc => acc.toList
+  | a::as, n+1, acc => go as n (acc.push a)
+
+@[csimp] theorem take_eq_takeTR : @take = @takeTR := by
+  funext α n l; simp [takeTR]
+  suffices ∀ xs acc, l = acc.data ++ xs → takeTR.go l xs n acc = acc.data ++ xs.take n from
+    (this l #[] (by simp)).symm
+  intro xs; induction xs generalizing n with intro acc
+  | nil => cases n <;> simp [take, takeTR.go]
+  | cons x xs IH =>
+    cases n with simp only [take, takeTR.go]
+    | zero => simp
+    | succ n => intro h; rw [IH] <;> simp_all
+
+/-! ### takeWhile -/
+
+/-- Tail recursive version of `List.takeWhile`. -/
+@[inline] def takeWhileTR (p : α → Bool) (l : List α) : List α := go l #[] where
+  /-- Auxiliary for `takeWhile`: `takeWhile.go p l xs acc = acc.toList ++ takeWhile p xs`,
+  unless no element satisfying `p` is found in `xs` in which case it returns `l`. -/
+  @[specialize] go : List α → Array α → List α
+  | [], _ => l
+  | a::as, acc => bif p a then go as (acc.push a) else acc.toList
+
+@[csimp] theorem takeWhile_eq_takeWhileTR : @takeWhile = @takeWhileTR := by
+  funext α p l; simp [takeWhileTR]
+  suffices ∀ xs acc, l = acc.data ++ xs →
+      takeWhileTR.go p l xs acc = acc.data ++ xs.takeWhile p from
+    (this l #[] (by simp)).symm
+  intro xs; induction xs with intro acc
+  | nil => simp [takeWhile, takeWhileTR.go]
+  | cons x xs IH =>
+    simp only [takeWhileTR.go, Array.toList_eq, takeWhile]
+    split
+    · intro h; rw [IH] <;> simp_all
+    · simp [*]
+
+/-! ### dropLast -/
+
+/-- Tail recursive version of `dropLast`. -/
+@[inline] def dropLastTR (l : List α) : List α := l.toArray.pop.toList
+
+@[csimp] theorem dropLast_eq_dropLastTR : @dropLast = @dropLastTR := by
+  funext α l; simp [dropLastTR]
+
+/-! ## Manipulating elements -/
+
+/-! ### replace -/
+
+/-- Tail recursive version of `List.replace`. -/
+@[inline] def replaceTR [BEq α] (l : List α) (b c : α) : List α := go l #[] where
+  /-- Auxiliary for `replace`: `replace.go l b c xs acc = acc.toList ++ replace xs b c`,
+  unless `b` is not found in `xs` in which case it returns `l`. -/
+  @[specialize] go : List α → Array α → List α
+  | [], _ => l
+  | a::as, acc => bif b == a then acc.toListAppend (c::as) else go as (acc.push a)
+
+@[csimp] theorem replace_eq_replaceTR : @List.replace = @replaceTR := by
+  funext α _ l b c; simp [replaceTR]
+  suffices ∀ xs acc, l = acc.data ++ xs →
+      replaceTR.go l b c xs acc = acc.data ++ xs.replace b c from
+    (this l #[] (by simp)).symm
+  intro xs; induction xs with intro acc
+  | nil => simp [replace, replaceTR.go]
+  | cons x xs IH =>
+    simp only [replaceTR.go, Array.toListAppend_eq, replace]
+    split
+    · simp [*]
+    · intro h; rw [IH] <;> simp_all
+
+/-! ### erase -/
+
+/-- Tail recursive version of `List.erase`. -/
@[inline] def eraseTR [BEq α] (l : List α) (a : α) : List α := go l #[] where
  /-- Auxiliary for `eraseTR`: `eraseTR.go l a xs acc = acc.toList ++ erase xs a`,
  unless `a` is not present in which case it returns `l` -/
@@ -49,11 +290,14 @@ namespace List
  intro xs; induction xs with intro acc h
  | nil => simp [List.erase, eraseTR.go, h]
  | cons x xs IH =>
-    simp [List.erase, eraseTR.go]
-    cases x == a <;> simp
-    · rw [IH]; simp; simp; exact h
+    simp only [eraseTR.go, Array.toListAppend_eq, List.erase]
+    cases x == a
+    · rw [IH] <;> simp_all
+    · simp

-/-- Tail recursive version of `eraseIdx`. -/
+/-! ### eraseIdx -/
+
+/-- Tail recursive version of `List.eraseIdx`. -/
@[inline] def eraseIdxTR (l : List α) (n : Nat) : List α := go l n #[] where
  /-- Auxiliary for `eraseIdxTR`: `eraseIdxTR.go l n xs acc = acc.toList ++ eraseIdx xs a`,
  unless `a` is not present in which case it returns `l` -/
@@ -72,109 +316,14 @@ namespace List
    match n with
    | 0 => simp [eraseIdx, eraseIdxTR.go]
    | n+1 =>
-      simp [eraseIdx, eraseIdxTR.go]
+      simp only [eraseIdxTR.go, eraseIdx]
      rw [IH]; simp; simp; exact h

-/-- Tail recursive version of `bind`. -/
-@[inline] def bindTR (as : List α) (f : α → List β) : List β := go as #[] where
-  /-- Auxiliary for `bind`: `bind.go f as = acc.toList ++ bind f as` -/
-  @[specialize] go : List α → Array β → List β
-  | [], acc => acc.toList
-  | x::xs, acc => go xs (acc ++ f x)
+/-! ## Zippers -/

-@[csimp] theorem bind_eq_bindTR : @List.bind = @bindTR := by
-  funext α β as f
-  let rec go : ∀ as acc, bindTR.go f as acc = acc.data ++ as.bind f
-    | [], acc => by simp [bindTR.go, bind]
-    | x::xs, acc => by simp [bindTR.go, bind, go xs]
-  exact (go as #[]).symm
+/-! ### zipWith -/

-/-- Tail recursive version of `join`. -/
-@[inline] def joinTR (l : List (List α)) : List α := bindTR l id
-
-@[csimp] theorem join_eq_joinTR : @join = @joinTR := by
-  funext α l; rw [← List.bind_id, List.bind_eq_bindTR]; rfl
-
-/-- Tail recursive version of `filterMap`. -/
-@[inline] def filterMapTR (f : α → Option β) (l : List α) : List β := go l #[] where
-  /-- Auxiliary for `filterMap`: `filterMap.go f l = acc.toList ++ filterMap f l` -/
-  @[specialize] go : List α → Array β → List β
-  | [], acc => acc.toList
-  | a::as, acc => match f a with
-    | none => go as acc
-    | some b => go as (acc.push b)
-
-@[csimp] theorem filterMap_eq_filterMapTR : @List.filterMap = @filterMapTR := by
-  funext α β f l
-  let rec go : ∀ as acc, filterMapTR.go f as acc = acc.data ++ as.filterMap f
-    | [], acc => by simp [filterMapTR.go, filterMap]
-    | a::as, acc => by simp [filterMapTR.go, filterMap, go as]; split <;> simp [*]
-  exact (go l #[]).symm
-
-/-- Tail recursive version of `replace`. -/
-@[inline] def replaceTR [BEq α] (l : List α) (b c : α) : List α := go l #[] where
-  /-- Auxiliary for `replace`: `replace.go l b c xs acc = acc.toList ++ replace xs b c`,
-  unless `b` is not found in `xs` in which case it returns `l`. -/
-  @[specialize] go : List α → Array α → List α
-  | [], _ => l
-  | a::as, acc => bif a == b then acc.toListAppend (c::as) else go as (acc.push a)
-
-@[csimp] theorem replace_eq_replaceTR : @List.replace = @replaceTR := by
-  funext α _ l b c; simp [replaceTR]
-  suffices ∀ xs acc, l = acc.data ++ xs →
-      replaceTR.go l b c xs acc = acc.data ++ xs.replace b c from
-    (this l #[] (by simp)).symm
-  intro xs; induction xs with intro acc
-  | nil => simp [replace, replaceTR.go]
-  | cons x xs IH =>
-    simp [replace, replaceTR.go]; split <;> simp [*]
-    · intro h; rw [IH]; simp; simp; exact h
-
-/-- Tail recursive version of `take`. -/
-@[inline] def takeTR (n : Nat) (l : List α) : List α := go l n #[] where
-  /-- Auxiliary for `take`: `take.go l xs n acc = acc.toList ++ take n xs`,
-  unless `n ≥ xs.length` in which case it returns `l`. -/
-  @[specialize] go : List α → Nat → Array α → List α
-  | [], _, _ => l
-  | _::_, 0, acc => acc.toList
-  | a::as, n+1, acc => go as n (acc.push a)
-
-@[csimp] theorem take_eq_takeTR : @take = @takeTR := by
-  funext α n l; simp [takeTR]
-  suffices ∀ xs acc, l = acc.data ++ xs → takeTR.go l xs n acc = acc.data ++ xs.take n from
-    (this l #[] (by simp)).symm
-  intro xs; induction xs generalizing n with intro acc
-  | nil => cases n <;> simp [take, takeTR.go]
-  | cons x xs IH =>
-    cases n with simp [take, takeTR.go]
-    | succ n => intro h; rw [IH]; simp; simp; exact h
-
-/-- Tail recursive version of `takeWhile`. -/
-@[inline] def takeWhileTR (p : α → Bool) (l : List α) : List α := go l #[] where
-  /-- Auxiliary for `takeWhile`: `takeWhile.go p l xs acc = acc.toList ++ takeWhile p xs`,
-  unless no element satisfying `p` is found in `xs` in which case it returns `l`. -/
-  @[specialize] go : List α → Array α → List α
-  | [], _ => l
-  | a::as, acc => bif p a then go as (acc.push a) else acc.toList
-
-@[csimp] theorem takeWhile_eq_takeWhileTR : @takeWhile = @takeWhileTR := by
-  funext α p l; simp [takeWhileTR]
-  suffices ∀ xs acc, l = acc.data ++ xs →
-      takeWhileTR.go p l xs acc = acc.data ++ xs.takeWhile p from
-    (this l #[] (by simp)).symm
-  intro xs; induction xs with intro acc
-  | nil => simp [takeWhile, takeWhileTR.go]
-  | cons x xs IH =>
-    simp [takeWhile, takeWhileTR.go]; split <;> simp [*]
-    · intro h; rw [IH]; simp; simp; exact h
-
-/-- Tail recursive version of `foldr`. -/
-@[specialize] def foldrTR (f : α → β → β) (init : β) (l : List α) : β := l.toArray.foldr f init
-
-@[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
-  funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_data, -Array.size_toArray]
-
-/-- Tail recursive version of `zipWith`. -/
+/-- Tail recursive version of `List.zipWith`. -/
@[inline] def zipWithTR (f : α → β → γ) (as : List α) (bs : List β) : List γ := go as bs #[] where
  /-- Auxiliary for `zipWith`: `zipWith.go f as bs acc = acc.toList ++ zipWith f as bs` -/
  go : List α → List β → Array γ → List γ
@@ -188,14 +337,37 @@ namespace List
    | a::as, b::bs, acc => by simp [zipWithTR.go, zipWith, go as bs]
  exact (go as bs #[]).symm

-/-- Tail recursive version of `unzip`. -/
+/-! ### unzip -/
+
+/-- Tail recursive version of `List.unzip`. -/
 def unzipTR (l : List (α × β)) : List α × List β :=
  l.foldr (fun (a, b) (al, bl) => (a::al, b::bl)) ([], [])

@[csimp] theorem unzip_eq_unzipTR : @unzip = @unzipTR := by
  funext α β l; simp [unzipTR]; induction l <;> simp [*]

-/-- Tail recursive version of `enumFrom`. -/
+/-! ## Ranges and enumeration -/
+
+/-! ### iota -/
+
+/-- Tail-recursive version of `List.iota`. -/
+def iotaTR (n : Nat) : List Nat :=
+  let rec go : Nat → List Nat → List Nat
+    | 0, r => r.reverse
+    | m@(n+1), r => go n (m::r)
+  go n []
+
+@[csimp]
+theorem iota_eq_iotaTR : @iota = @iotaTR :=
+  have aux (n : Nat) (r : List Nat) : iotaTR.go n r = r.reverse ++ iota n := by
+    induction n generalizing r with
+    | zero => simp [iota, iotaTR.go]
+    | succ n ih => simp [iota, iotaTR.go, ih, append_assoc]
+  funext fun n => by simp [iotaTR, aux]
+
+/-! ### enumFrom -/
+
+/-- Tail recursive version of `List.enumFrom`. -/
 def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
  let arr := l.toArray
  (arr.foldr (fun a (n, acc) => (n-1, (n-1, a) :: acc)) (n + arr.size, [])).2
@@ -211,18 +383,11 @@ def enumFromTR (n : Nat) (l : List α) : List (Nat × α) :=
  rw [Array.foldr_eq_foldr_data]
  simp [go]

-theorem replicateTR_loop_eq : ∀ n, replicateTR.loop a n acc = replicate n a ++ acc
-  | 0 => rfl
-  | n+1 => by rw [← replicateTR_loop_replicate_eq _ 1 n, replicate, replicate,
-    replicateTR.loop, replicateTR_loop_eq n, replicateTR_loop_eq n, append_assoc]; rfl
+/-! ## Other list operations -/

-/-- Tail recursive version of `dropLast`. -/
-@[inline] def dropLastTR (l : List α) : List α := l.toArray.pop.toList
+/-! ### intersperse -/

-@[csimp] theorem dropLast_eq_dropLastTR : @dropLast = @dropLastTR := by
-  funext α l; simp [dropLastTR]
-
-/-- Tail recursive version of `intersperse`. -/
+/-- Tail recursive version of `List.intersperse`. -/
 def intersperseTR (sep : α) : List α → List α
  | [] => []
  | [x] => [x]
@@ -234,7 +399,9 @@ def intersperseTR (sep : α) : List α → List α
  | [] | [_] => rfl
  | x::y::xs => simp [intersperse]; induction xs generalizing y <;> simp [*]

-/-- Tail recursive version of `intercalate`. -/
+/-! ### intercalate -/
+
+/-- Tail recursive version of `List.intercalate`. -/
 def intercalateTR (sep : List α) : List (List α) → List α
  | [] => []
  | [x] => x
--- a/src/Init/Data/List/Lemmas.lean
+++ b/src/Init/Data/List/Lemmas.lean
--- a/src/Init/Data/List/Notation.lean
+++ b/src/Init/Data/List/Notation.lean
@@ -0,0 +1,53 @@
+/-
+Copyright (c) 2016 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Author: Leonardo de Moura
+-/
+prelude
+import Init.Data.Nat.Div
+
+/-!
+# Notation for `List` literals.
+-/
+
+set_option linter.missingDocs true -- keep it documented
+open Decidable List
+
+/--
+The syntax `[a, b, c]` is shorthand for `a :: b :: c :: []`, or
+`List.cons a (List.cons b (List.cons c List.nil))`. It allows conveniently constructing
+list literals.
+
+For lists of length at least 64, an alternative desugaring strategy is used
+which uses let bindings as intermediates as in
+`let left := [d, e, f]; a :: b :: c :: left` to avoid creating very deep expressions.
+Note that this changes the order of evaluation, although it should not be observable
+unless you use side effecting operations like `dbg_trace`.
+-/
+syntax "[" withoutPosition(term,*,?) "]"  : term
+
+/--
+Auxiliary syntax for implementing `[$elem,*]` list literal syntax.
+The syntax `%[a,b,c|tail]` constructs a value equivalent to `a::b::c::tail`.
+It uses binary partitioning to construct a tree of intermediate let bindings as in
+`let left := [d, e, f]; a :: b :: c :: left` to avoid creating very deep expressions.
+-/
+syntax "%[" withoutPosition(term,*,? " | " term) "]" : term
+
+namespace Lean
+
+macro_rules
+  | `([ $elems,* ]) => do
+    -- NOTE: we do not have `TSepArray.getElems` yet at this point
+    let rec expandListLit (i : Nat) (skip : Bool) (result : TSyntax `term) : MacroM Syntax := do
+      match i, skip with
+      | 0,   _     => pure result
+      | i+1, true  => expandListLit i false result
+      | i+1, false => expandListLit i true  (← ``(List.cons $(⟨elems.elemsAndSeps.get! i⟩) $result))
+    let size := elems.elemsAndSeps.size
+    if size < 64 then
+      expandListLit size (size % 2 == 0) (← ``(List.nil))
+    else
+      `(%[ $elems,* | List.nil ])
+
+end Lean
--- a/src/Init/Data/List/TakeDrop.lean
+++ b/src/Init/Data/List/TakeDrop.lean
@@ -8,10 +8,10 @@ import Init.Data.List.Lemmas
 import Init.Data.Nat.Lemmas

 /-!
-# Lemmas about `List.take`, `List.drop`, `List.zip` and `List.zipWith`.
+# Further lemmas about `List.take`, `List.drop`, `List.zip` and `List.zipWith`.

 These are in a separate file from most of the list lemmas
-as they required importing more lemmas about natural numbers.
+as they required importing more lemmas about natural numbers, and use `omega`.
 -/

 namespace List
@@ -20,8 +20,6 @@ open Nat

 /-! ### take -/

-abbrev take_succ_cons := @take_cons_succ
-
@[simp] theorem length_take : ∀ (i : Nat) (l : List α), length (take i l) = min i (length l)
  | 0, l => by simp [Nat.zero_min]
  | succ n, [] => by simp [Nat.min_zero]
@@ -34,17 +32,6 @@ theorem length_take_le' (n) (l : List α) : length (take n l) ≤ l.length :=

 theorem length_take_of_le (h : n ≤ length l) : length (take n l) = n := by simp [Nat.min_eq_left h]

-theorem take_all_of_le {n} {l : List α} (h : length l ≤ n) : take n l = l :=
-  take_length_le h
-
-@[simp]
-theorem take_left : ∀ l₁ l₂ : List α, take (length l₁) (l₁ ++ l₂) = l₁
-  | [], _ => rfl
-  | a :: l₁, l₂ => congrArg (cons a) (take_left l₁ l₂)
-
-theorem take_left' {l₁ l₂ : List α} {n} (h : length l₁ = n) : take n (l₁ ++ l₂) = l₁ := by
-  rw [← h]; apply take_left
-
 theorem take_take : ∀ (n m) (l : List α), take n (take m l) = take (min n m) l
  | n, 0, l => by rw [Nat.min_zero, take_zero, take_nil]
  | 0, m, l => by rw [Nat.zero_min, take_zero, take_zero]
@@ -52,16 +39,15 @@ theorem take_take : ∀ (n m) (l : List α), take n (take m l) = take (min n m)
  | succ n, succ m, a :: l => by
    simp only [take, succ_min_succ, take_take n m l]

-theorem take_replicate (a : α) : ∀ n m : Nat, take n (replicate m a) = replicate (min n m) a
+@[simp] theorem take_replicate (a : α) : ∀ n m : Nat, take n (replicate m a) = replicate (min n m) a
  | n, 0 => by simp [Nat.min_zero]
  | 0, m => by simp [Nat.zero_min]
-  | succ n, succ m => by simp [succ_min_succ, take_replicate]
+  | succ n, succ m => by simp [replicate_succ, succ_min_succ, take_replicate]

-theorem map_take (f : α → β) :
-    ∀ (L : List α) (i : Nat), (L.take i).map f = (L.map f).take i
-  | [], i => by simp
-  | _, 0 => by simp
-  | h :: t, n + 1 => by dsimp; rw [map_take f t n]
+@[simp] theorem drop_replicate (a : α) : ∀ n m : Nat, drop n (replicate m a) = replicate (m - n) a
+  | n, 0 => by simp
+  | 0, m => by simp
+  | succ n, succ m => by simp [replicate_succ, succ_sub_succ, drop_replicate]

 /-- Taking the first `n` elements in `l₁ ++ l₂` is the same as appending the first `n` elements
 of `l₁` to the first `n - l₁.length` elements of `l₂`. -/
@@ -88,55 +74,51 @@ theorem take_append {l₁ l₂ : List α} (i : Nat) :

 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the big list to the small list. -/
-theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
-    get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ :=
-  get_of_eq (take_append_drop j L).symm _ ▸ get_append ..
+theorem getElem_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
+    L[i] = (L.take j)[i]'(length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩) :=
+  getElem_of_eq (take_append_drop j L).symm _ ▸ getElem_append ..

 /-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
 length `> i`. Version designed to rewrite from the small list to the big list. -/
+theorem getElem_take' (L : List α) {j i : Nat} {h : i < (L.take j).length} :
+    (L.take j)[i] =
+    L[i]'(Nat.lt_of_lt_of_le h (length_take_le' _ _)) := by
+  rw [length_take, Nat.lt_min] at h; rw [getElem_take L _ h.1]
+
+/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
+length `> i`. Version designed to rewrite from the big list to the small list. -/
+@[deprecated getElem_take (since := "2024-06-12")]
+theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
+    get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ := by
+  simp [getElem_take _ hi hj]
+
+/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
+length `> i`. Version designed to rewrite from the small list to the big list. -/
+@[deprecated getElem_take (since := "2024-06-12")]
 theorem get_take' (L : List α) {j i} :
    get (L.take j) i =
    get L ⟨i.1, Nat.lt_of_lt_of_le i.2 (length_take_le' _ _)⟩ := by
-  let ⟨i, hi⟩ := i; rw [length_take, Nat.lt_min] at hi; rw [get_take L _ hi.1]
+  simp [getElem_take']

-theorem get?_take {l : List α} {n m : Nat} (h : m < n) : (l.take n).get? m = l.get? m := by
-  induction n generalizing l m with
-  | zero =>
-    exact absurd h (Nat.not_lt_of_le m.zero_le)
-  | succ _ hn =>
-    cases l with
-    | nil => simp only [take_nil]
-    | cons hd tl =>
-      cases m
-      · simp only [get?, take]
-      · simpa only using hn (Nat.lt_of_succ_lt_succ h)
+theorem getElem?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
+    (l.take n)[m]? = none :=
+  getElem?_eq_none <| Nat.le_trans (length_take_le _ _) h

+@[deprecated getElem?_take_eq_none (since := "2024-06-12")]
 theorem get?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
-    (l.take n).get? m = none :=
-  get?_eq_none.mpr <| Nat.le_trans (length_take_le _ _) h
+    (l.take n).get? m = none := by
+  simp [getElem?_take_eq_none h]

+theorem getElem?_take_eq_if {l : List α} {n m : Nat} :
+    (l.take n)[m]? = if m < n then l[m]? else none := by
+  split
+  · next h => exact getElem?_take h
+  · next h => exact getElem?_take_eq_none (Nat.le_of_not_lt h)
+
+@[deprecated getElem?_take_eq_if (since := "2024-06-12")]
 theorem get?_take_eq_if {l : List α} {n m : Nat} :
    (l.take n).get? m = if m < n then l.get? m else none := by
-  split
-  · next h => exact get?_take h
-  · next h => exact get?_take_eq_none (Nat.le_of_not_lt h)
-
-@[simp]
-theorem nth_take_of_succ {l : List α} {n : Nat} : (l.take (n + 1)).get? n = l.get? n :=
-  get?_take (Nat.lt_succ_self n)
-
-theorem take_succ {l : List α} {n : Nat} : l.take (n + 1) = l.take n ++ (l.get? n).toList := by
-  induction l generalizing n with
-  | nil =>
-    simp only [Option.toList, get?, take_nil, append_nil]
-  | cons hd tl hl =>
-    cases n
-    · simp only [Option.toList, get?, eq_self_iff_true, take, nil_append]
-    · simp only [hl, cons_append, get?, eq_self_iff_true, take]
-
-@[simp]
-theorem take_eq_nil_iff {l : List α} {k : Nat} : l.take k = [] ↔ l = [] ∨ k = 0 := by
-  cases l <;> cases k <;> simp [Nat.succ_ne_zero]
+  simp [getElem?_take_eq_if]

@[simp]
 theorem take_eq_take :
@@ -158,20 +140,6 @@ theorem take_add (l : List α) (m n : Nat) : l.take (m + n) = l.take m ++ (l.dro
  · apply length_take_le
  · apply Nat.le_add_right

-theorem take_eq_nil_of_eq_nil : ∀ {as : List α} {i}, as = [] → as.take i = []
-  | _, _, rfl => take_nil
-
-theorem ne_nil_of_take_ne_nil {as : List α} {i : Nat} (h: as.take i ≠ []) : as ≠ [] :=
-  mt take_eq_nil_of_eq_nil h
-
-theorem dropLast_eq_take (l : List α) : l.dropLast = l.take l.length.pred := by
-  cases l with
-  | nil => simp [dropLast]
-  | cons x l =>
-    induction l generalizing x with
-    | nil => simp [dropLast]
-    | cons hd tl hl => simp [dropLast, hl]
-
 theorem dropLast_take {n : Nat} {l : List α} (h : n < l.length) :
    (l.take n).dropLast = l.take n.pred := by
  simp only [dropLast_eq_take, length_take, Nat.le_of_lt h, take_take, pred_le, Nat.min_eq_left]
@@ -188,19 +156,6 @@ theorem map_eq_append_split {f : α → β} {l : List α} {s₁ s₂ : List β}

 /-! ### drop -/

-@[simp]
-theorem drop_eq_nil_iff_le {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by
-  refine' ⟨fun h => _, drop_eq_nil_of_le⟩
-  induction k generalizing l with
-  | zero =>
-    simp only [drop] at h
-    simp [h]
-  | succ k hk =>
-    cases l
-    · simp
-    · simp only [drop] at h
-      simpa [Nat.succ_le_succ_iff] using hk h
-
 theorem drop_length_cons {l : List α} (h : l ≠ []) (a : α) :
    (a :: l).drop l.length = [l.getLast h] := by
  induction l generalizing a with
@@ -237,15 +192,6 @@ theorem drop_append {l₁ l₂ : List α} (i : Nat) : drop (l₁.length + i) (l
  rw [drop_append_eq_append_drop, drop_eq_nil_of_le] <;>
    simp [Nat.add_sub_cancel_left, Nat.le_add_right]

-theorem drop_sizeOf_le [SizeOf α] (l : List α) (n : Nat) : sizeOf (l.drop n) ≤ sizeOf l := by
-  induction l generalizing n with
-  | nil => rw [drop_nil]; apply Nat.le_refl
-  | cons _ _ lih =>
-    induction n with
-    | zero => apply Nat.le_refl
-    | succ n =>
-      exact Trans.trans (lih _) (Nat.le_add_left _ _)
-
 theorem lt_length_drop (L : List α) {i j : Nat} (h : i + j < L.length) : j < (L.drop i).length := by
  have A : i < L.length := Nat.lt_of_le_of_lt (Nat.le.intro rfl) h
  rw [(take_append_drop i L).symm] at h
@@ -254,24 +200,40 @@ theorem lt_length_drop (L : List α) {i j : Nat} (h : i + j < L.length) : j < (L

 /-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
 dropping the first `i` elements. Version designed to rewrite from the big list to the small list. -/
-theorem get_drop (L : List α) {i j : Nat} (h : i + j < L.length) :
-    get L ⟨i + j, h⟩ = get (L.drop i) ⟨j, lt_length_drop L h⟩ := by
+theorem getElem_drop (L : List α) {i j : Nat} (h : i + j < L.length) :
+    L[i + j] = (L.drop i)[j]'(lt_length_drop L h) := by
  have : i ≤ L.length := Nat.le_trans (Nat.le_add_right _ _) (Nat.le_of_lt h)
-  rw [get_of_eq (take_append_drop i L).symm ⟨i + j, h⟩, get_append_right'] <;>
+  rw [getElem_of_eq (take_append_drop i L).symm h, getElem_append_right'] <;>
    simp [Nat.min_eq_left this, Nat.add_sub_cancel_left, Nat.le_add_right]

+/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
+dropping the first `i` elements. Version designed to rewrite from the big list to the small list. -/
+@[deprecated getElem_drop (since := "2024-06-12")]
+theorem get_drop (L : List α) {i j : Nat} (h : i + j < L.length) :
+    get L ⟨i + j, h⟩ = get (L.drop i) ⟨j, lt_length_drop L h⟩ := by
+  simp [getElem_drop]
+
 /-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
 dropping the first `i` elements. Version designed to rewrite from the small list to the big list. -/
+theorem getElem_drop' (L : List α) {i : Nat} {j : Nat} {h : j < (L.drop i).length} :
+    (L.drop i)[j] = L[i + j]'(by
+      rw [Nat.add_comm]
+      exact Nat.add_lt_of_lt_sub (length_drop i L ▸ h)) := by
+  rw [getElem_drop]
+
+/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
+dropping the first `i` elements. Version designed to rewrite from the small list to the big list. -/
+@[deprecated getElem_drop' (since := "2024-06-12")]
 theorem get_drop' (L : List α) {i j} :
    get (L.drop i) j = get L ⟨i + j, by
      rw [Nat.add_comm]
      exact Nat.add_lt_of_lt_sub (length_drop i L ▸ j.2)⟩ := by
-  rw [get_drop]
+  simp [getElem_drop']

@[simp]
-theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j) := by
+theorem getElem?_drop (L : List α) (i j : Nat) : (L.drop i)[j]? = L[i + j]? := by
  ext
-  simp only [get?_eq_some, get_drop', Option.mem_def]
+  simp only [getElem?_eq_some, getElem_drop', Option.mem_def]
  constructor <;> intro ⟨h, ha⟩
  · exact ⟨_, ha⟩
  · refine ⟨?_, ha⟩
@@ -279,19 +241,36 @@ theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j)
    rw [Nat.add_comm] at h
    apply Nat.lt_sub_of_add_lt h

-@[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (n + m) l
-  | m, [] => by simp
-  | 0, l => by simp
-  | m + 1, a :: l =>
-    calc
-      drop n (drop (m + 1) (a :: l)) = drop n (drop m l) := rfl
-      _ = drop (n + m) l := drop_drop n m l
-      _ = drop (n + (m + 1)) (a :: l) := rfl
+@[deprecated getElem?_drop (since := "2024-06-12")]
+theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j) := by
+  simp

-theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (take (m + n) l)
-  | 0, _, _ => by simp
-  | _, _, [] => by simp
-  | _+1, _, _ :: _ => by simpa [Nat.succ_add, take_succ_cons, drop_succ_cons] using take_drop ..
+theorem set_eq_take_append_cons_drop {l : List α} {n : Nat} {a : α} :
+    l.set n a = if n < l.length then l.take n ++ a :: l.drop (n + 1) else l := by
+  split <;> rename_i h
+  · ext1 m
+    by_cases h' : m < n
+    · rw [getElem?_append (by simp [length_take]; omega), getElem?_set_ne (by omega),
+        getElem?_take h']
+    · by_cases h'' : m = n
+      · subst h''
+        rw [getElem?_set_eq (by simp; omega), getElem?_append_right, length_take,
+          Nat.min_eq_left (by omega), Nat.sub_self, getElem?_cons_zero]
+        rw [length_take]
+        exact Nat.min_le_left m l.length
+      · have h''' : n < m := by omega
+        rw [getElem?_set_ne (by omega), getElem?_append_right, length_take,
+          Nat.min_eq_left (by omega)]
+        · obtain ⟨k, rfl⟩ := Nat.exists_eq_add_of_lt h'''
+          have p : n + k + 1 - n = k + 1 := by omega
+          rw [p]
+          rw [getElem?_cons_succ, getElem?_drop]
+          congr 1
+          omega
+        · rw [length_take]
+          exact Nat.le_trans (Nat.min_le_left _ _) (by omega)
+  · rw [set_eq_of_length_le]
+    omega

 theorem drop_take : ∀ (m n : Nat) (l : List α), drop n (take m l) = take (m - n) (drop n l)
  | 0, _, _ => by simp
@@ -302,15 +281,7 @@ theorem drop_take : ∀ (m n : Nat) (l : List α), drop n (take m l) = take (m -
    congr 1
    omega

-theorem map_drop (f : α → β) :
-    ∀ (L : List α) (i : Nat), (L.drop i).map f = (L.map f).drop i
-  | [], i => by simp
-  | L, 0 => by simp
-  | h :: t, n + 1 => by
-    dsimp
-    rw [map_drop f t]
-
-theorem reverse_take {α} {xs : List α} (n : Nat) (h : n ≤ xs.length) :
+theorem take_reverse {α} {xs : List α} (n : Nat) (h : n ≤ xs.length) :
    xs.reverse.take n = (xs.drop (xs.length - n)).reverse := by
  induction xs generalizing n <;>
    simp only [reverse_cons, drop, reverse_nil, Nat.zero_sub, length, take_nil]
@@ -330,19 +301,33 @@ theorem reverse_take {α} {xs : List α} (n : Nat) (h : n ≤ xs.length) :
    rw [length_append, length_reverse]
    rfl

-@[simp]
-theorem get_cons_drop : ∀ (l : List α) i, get l i :: drop (i + 1) l = drop i l
-  | _::_, ⟨0, _⟩ => rfl
-  | _::_, ⟨i+1, _⟩ => get_cons_drop _ ⟨i, _⟩
+@[deprecated (since := "2024-06-15")] abbrev reverse_take := @take_reverse

-theorem drop_eq_get_cons {n} {l : List α} (h) : drop n l = get l ⟨n, h⟩ :: drop (n + 1) l :=
-  (get_cons_drop _ ⟨n, h⟩).symm
+/-! ### rotateLeft -/

-theorem drop_eq_nil_of_eq_nil : ∀ {as : List α} {i}, as = [] → as.drop i = []
-  | _, _, rfl => drop_nil
+@[simp] theorem rotateLeft_replicate (n) (a : α) : rotateLeft (replicate m a) n = replicate m a := by
+  cases n with
+  | zero => simp
+  | succ n =>
+    suffices 1 < m → m - (n + 1) % m + min ((n + 1) % m) m = m by
+      simpa [rotateLeft]
+    intro h
+    rw [Nat.min_eq_left (Nat.le_of_lt (Nat.mod_lt _ (by omega)))]
+    have : (n + 1) % m < m := Nat.mod_lt _ (by omega)
+    omega

-theorem ne_nil_of_drop_ne_nil {as : List α} {i : Nat} (h: as.drop i ≠ []) : as ≠ [] :=
-  mt drop_eq_nil_of_eq_nil h
+/-! ### rotateRight -/
+
+@[simp] theorem rotateRight_replicate (n) (a : α) : rotateRight (replicate m a) n = replicate m a := by
+  cases n with
+  | zero => simp
+  | succ n =>
+    suffices 1 < m → m - (m - (n + 1) % m) + min (m - (n + 1) % m) m = m by
+      simpa [rotateRight]
+    intro h
+    have : (n + 1) % m < m := Nat.mod_lt _ (by omega)
+    rw [Nat.min_eq_left (by omega)]
+    omega

 /-! ### zipWith -/

@@ -351,10 +336,52 @@ theorem ne_nil_of_drop_ne_nil {as : List α} {i : Nat} (h: as.drop i ≠ []) : a
  induction l₁ generalizing l₂ <;> cases l₂ <;>
    simp_all [succ_min_succ, Nat.zero_min, Nat.min_zero]

+theorem zipWith_eq_zipWith_take_min : ∀ (l₁ : List α) (l₂ : List β),
+    zipWith f l₁ l₂ = zipWith f (l₁.take (min l₁.length l₂.length)) (l₂.take (min l₁.length l₂.length))
+  | [], _ => by simp
+  | _, [] => by simp
+  | a :: l₁, b :: l₂ => by simp [succ_min_succ, zipWith_eq_zipWith_take_min l₁ l₂]
+
+@[simp] theorem zipWith_replicate {a : α} {b : β} {m n : Nat} :
+    zipWith f (replicate m a) (replicate n b) = replicate (min m n) (f a b) := by
+  rw [zipWith_eq_zipWith_take_min]
+  simp
+
 /-! ### zip -/

@[simp] theorem length_zip (l₁ : List α) (l₂ : List β) :
    length (zip l₁ l₂) = min (length l₁) (length l₂) := by
  simp [zip]

+theorem zip_eq_zip_take_min : ∀ (l₁ : List α) (l₂ : List β),
+    zip l₁ l₂ = zip (l₁.take (min l₁.length l₂.length)) (l₂.take (min l₁.length l₂.length))
+  | [], _ => by simp
+  | _, [] => by simp
+  | a :: l₁, b :: l₂ => by simp [succ_min_succ, zip_eq_zip_take_min l₁ l₂]
+
+@[simp] theorem zip_replicate {a : α} {b : β} {m n : Nat} :
+    zip (replicate m a) (replicate n b) = replicate (min m n) (a, b) := by
+  rw [zip_eq_zip_take_min]
+  simp
+
+/-! ### minimum? -/
+
+-- A specialization of `minimum?_eq_some_iff` to Nat.
+theorem minimum?_eq_some_iff' {xs : List Nat} :
+    xs.minimum? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, a ≤ b) :=
+  minimum?_eq_some_iff
+    (le_refl := Nat.le_refl)
+    (min_eq_or := fun _ _ => by omega)
+    (le_min_iff := fun _ _ _ => by omega)
+
+/-! ### maximum? -/
+
+-- A specialization of `maximum?_eq_some_iff` to Nat.
+theorem maximum?_eq_some_iff' {xs : List Nat} :
+    xs.maximum? = some a ↔ (a ∈ xs ∧ ∀ b ∈ xs, b ≤ a) :=
+  maximum?_eq_some_iff
+    (le_refl := Nat.le_refl)
+    (max_eq_or := fun _ _ => by omega)
+    (max_le_iff := fun _ _ _ => by omega)
+
 end List
--- a/src/Init/Data/Nat/Basic.lean
+++ b/src/Init/Data/Nat/Basic.lean
@@ -200,6 +200,9 @@ protected theorem eq_zero_of_add_eq_zero_left (h : n + m = 0) : m = 0 :=
 theorem mul_succ (n m : Nat) : n * succ m = n * m + n :=
  rfl

+theorem mul_add_one (n m : Nat) : n * (m + 1) = n * m + n :=
+  rfl
+
@[simp] protected theorem zero_mul : ∀ (n : Nat), 0 * n = 0
  | 0      => rfl
  | succ n => mul_succ 0 n ▸ (Nat.zero_mul n).symm ▸ rfl
@@ -209,6 +212,8 @@ theorem succ_mul (n m : Nat) : (succ n) * m = (n * m) + m := by
  | zero => rfl
  | succ m ih => rw [mul_succ, add_succ, ih, mul_succ, add_succ, Nat.add_right_comm]

+theorem add_one_mul (n m : Nat) : (n + 1) * m = (n * m) + m := succ_mul n m
+
 protected theorem mul_comm : ∀ (n m : Nat), n * m = m * n
  | n, 0      => (Nat.zero_mul n).symm ▸ (Nat.mul_zero n).symm ▸ rfl
  | n, succ m => (mul_succ n m).symm ▸ (succ_mul m n).symm ▸ (Nat.mul_comm n m).symm ▸ rfl
@@ -256,14 +261,24 @@ theorem succ_lt_succ {n m : Nat} : n < m → succ n < succ m := succ_le_succ

 theorem lt_succ_of_le {n m : Nat} : n ≤ m → n < succ m := succ_le_succ

+theorem le_of_lt_add_one {n m : Nat} : n < m + 1 → n ≤ m := le_of_succ_le_succ
+
+theorem lt_add_one_of_le {n m : Nat} : n ≤ m → n < m + 1 := succ_le_succ
+
@[simp] protected theorem sub_zero (n : Nat) : n - 0 = n := rfl

+theorem not_add_one_le_zero (n : Nat) : ¬ n + 1 ≤ 0 := nofun
+
+theorem not_add_one_le_self : (n : Nat) → ¬ n + 1 ≤ n := Nat.not_succ_le_self
+
+theorem add_one_pos (n : Nat) : 0 < n + 1 := Nat.zero_lt_succ n
+
 theorem succ_sub_succ_eq_sub (n m : Nat) : succ n - succ m = n - m := by
  induction m with
  | zero      => exact rfl
  | succ m ih => apply congrArg pred ih

-@[simp] theorem pred_le : ∀ (n : Nat), pred n ≤ n
+theorem pred_le : ∀ (n : Nat), pred n ≤ n
  | zero   => Nat.le.refl
  | succ _ => le_succ _

@@ -271,7 +286,9 @@ theorem pred_lt : ∀ {n : Nat}, n ≠ 0 → pred n < n
  | zero,   h => absurd rfl h
  | succ _, _ => lt_succ_of_le (Nat.le_refl _)

-theorem sub_le (n m : Nat) : n - m ≤ n := by
+theorem sub_one_lt : ∀ {n : Nat}, n ≠ 0 → n - 1 < n := pred_lt
+
+@[simp] theorem sub_le (n m : Nat) : n - m ≤ n := by
  induction m with
  | zero      => exact Nat.le_refl (n - 0)
  | succ m ih => apply Nat.le_trans (pred_le (n - m)) ih
@@ -340,6 +357,8 @@ theorem lt.base (n : Nat) : n < succ n := Nat.le_refl (succ n)

@[simp] theorem lt_succ_self (n : Nat) : n < succ n := lt.base n

+@[simp] protected theorem lt_add_one (n : Nat) : n < n + 1 := lt.base n
+
 protected theorem le_total (m n : Nat) : m ≤ n ∨ n ≤ m :=
  match Nat.lt_or_ge m n with
  | Or.inl h => Or.inl (Nat.le_of_lt h)
@@ -370,6 +389,9 @@ theorem le_or_eq_of_le_succ {m n : Nat} (h : m ≤ succ n) : m ≤ n ∨ m = suc
       have : succ m ≤ succ n := succ_le_of_lt this
       Or.inl (le_of_succ_le_succ this))

+theorem le_or_eq_of_le_add_one {m n : Nat} (h : m ≤ n + 1) : m ≤ n ∨ m = n + 1 :=
+  le_or_eq_of_le_succ h
+
 theorem le_add_right : ∀ (n k : Nat), n ≤ n + k
  | n, 0   => Nat.le_refl n
  | n, k+1 => le_succ_of_le (le_add_right n k)
@@ -377,12 +399,25 @@ theorem le_add_right : ∀ (n k : Nat), n ≤ n + k
 theorem le_add_left (n m : Nat): n ≤ m + n :=
  Nat.add_comm n m ▸ le_add_right n m

+theorem le_of_add_right_le {n m k : Nat} (h : n + k ≤ m) : n ≤ m :=
+  Nat.le_trans (le_add_right n k) h
+
+theorem le_add_right_of_le {n m k : Nat} (h : n ≤ m) : n ≤ m + k :=
+  Nat.le_trans h (le_add_right m k)
+
+theorem lt_of_add_one_le {n m : Nat} (h : n + 1 ≤ m) : n < m := h
+
+theorem add_one_le_of_lt {n m : Nat} (h : n < m) : n + 1 ≤ m := h
+
 protected theorem lt_add_left (c : Nat) (h : a < b) : a < c + b :=
  Nat.lt_of_lt_of_le h (Nat.le_add_left ..)

 protected theorem lt_add_right (c : Nat) (h : a < b) : a < b + c :=
  Nat.lt_of_lt_of_le h (Nat.le_add_right ..)

+theorem lt_of_add_right_lt {n m k : Nat} (h : n + k < m) : n < m :=
+  Nat.lt_of_le_of_lt (Nat.le_add_right ..) h
+
 theorem le.dest : ∀ {n m : Nat}, n ≤ m → Exists (fun k => n + k = m)
  | zero,   zero,   _ => ⟨0, rfl⟩
  | zero,   succ n, _ => ⟨succ n, Nat.add_comm 0 (succ n) ▸ rfl⟩
@@ -537,9 +572,14 @@ protected theorem le_iff_lt_or_eq {n m : Nat} : n ≤ m ↔ n < m ∨ n = m :=

 protected theorem lt_succ_iff : m < succ n ↔ m ≤ n := ⟨le_of_lt_succ, lt_succ_of_le⟩

+protected theorem lt_add_one_iff : m < n + 1 ↔ m ≤ n := ⟨le_of_lt_succ, lt_succ_of_le⟩
+
 protected theorem lt_succ_iff_lt_or_eq : m < succ n ↔ m < n ∨ m = n :=
  Nat.lt_succ_iff.trans Nat.le_iff_lt_or_eq

+protected theorem lt_add_one_iff_lt_or_eq : m < n + 1 ↔ m < n ∨ m = n :=
+  Nat.lt_add_one_iff.trans Nat.le_iff_lt_or_eq
+
 protected theorem eq_of_lt_succ_of_not_lt (hmn : m < n + 1) (h : ¬ m < n) : m = n :=
  (Nat.lt_succ_iff_lt_or_eq.1 hmn).resolve_left h

@@ -571,12 +611,18 @@ attribute [simp] zero_lt_succ

 theorem succ_ne_self (n) : succ n ≠ n := Nat.ne_of_gt (lt_succ_self n)

+theorem add_one_ne_self (n) : n + 1 ≠ n := Nat.ne_of_gt (lt_succ_self n)
+
 theorem succ_le : succ n ≤ m ↔ n < m := .rfl

+theorem add_one_le_iff : n + 1 ≤ m ↔ n < m := .rfl
+
 theorem lt_succ : m < succ n ↔ m ≤ n := ⟨le_of_lt_succ, lt_succ_of_le⟩

 theorem lt_succ_of_lt (h : a < b) : a < succ b := le_succ_of_le h

+theorem lt_add_one_of_lt (h : a < b) : a < b + 1 := le_succ_of_le h
+
 theorem succ_pred_eq_of_ne_zero : ∀ {n}, n ≠ 0 → succ (pred n) = n
  | _+1, _ => rfl

@@ -590,12 +636,21 @@ theorem succ_le_succ_iff : succ a ≤ succ b ↔ a ≤ b := ⟨le_of_succ_le_suc

 theorem succ_lt_succ_iff : succ a < succ b ↔ a < b := ⟨lt_of_succ_lt_succ, succ_lt_succ⟩

+theorem add_one_inj : a + 1 = b + 1 ↔ a = b := succ_inj'
+
+theorem add_one_le_add_one_iff : a + 1 ≤ b + 1 ↔ a ≤ b := succ_le_succ_iff
+
+theorem add_one_lt_add_one_iff : a + 1 < b + 1 ↔ a < b := succ_lt_succ_iff
+
 theorem pred_inj : ∀ {a b}, 0 < a → 0 < b → pred a = pred b → a = b
  | _+1, _+1, _, _ => congrArg _

 theorem pred_ne_self : ∀ {a}, a ≠ 0 → pred a ≠ a
  | _+1, _ => (succ_ne_self _).symm

+theorem sub_one_ne_self : ∀ {a}, a ≠ 0 → a - 1 ≠ a
+  | _+1, _ => (succ_ne_self _).symm
+
 theorem pred_lt_self : ∀ {a}, 0 < a → pred a < a
  | _+1, _ => lt_succ_self _

@@ -628,9 +683,17 @@ theorem le_sub_one_of_lt : a < b → a ≤ b - 1 := Nat.le_pred_of_lt

 theorem lt_of_le_pred (h : 0 < m) : n ≤ pred m → n < m := (le_pred_iff_lt h).1

+theorem lt_of_le_sub_one (h : 0 < m) : n ≤ m - 1 → n < m := (le_pred_iff_lt h).1
+
+protected theorem le_sub_one_iff_lt (h : 0 < m) : n ≤ m - 1 ↔ n < m :=
+  ⟨Nat.lt_of_le_sub_one h, Nat.le_sub_one_of_lt⟩
+
 theorem exists_eq_succ_of_ne_zero : ∀ {n}, n ≠ 0 → Exists fun k => n = succ k
  | _+1, _ => ⟨_, rfl⟩

+theorem exists_eq_add_one_of_ne_zero : ∀ {n}, n ≠ 0 → Exists fun k => n = k + 1
+  | _+1, _ => ⟨_, rfl⟩
+
 /-! # Basic theorems for comparing numerals -/

 theorem ctor_eq_zero : Nat.zero = 0 :=
@@ -686,6 +749,9 @@ theorem eq_of_mul_eq_mul_right {n m k : Nat} (hm : 0 < m) (h : n * m = k * m) :
 protected theorem pow_succ (n m : Nat) : n^(succ m) = n^m * n :=
  rfl

+protected theorem pow_add_one (n m : Nat) : n^(m + 1) = n^m * n :=
+  rfl
+
 protected theorem pow_zero (n : Nat) : n^0 = 1 := rfl

 theorem pow_le_pow_of_le_left {n m : Nat} (h : n ≤ m) : ∀ (i : Nat), n^i ≤ m^i
@@ -737,9 +803,15 @@ theorem not_eq_zero_of_lt (h : b < a) : a ≠ 0 := by
  exact absurd h (Nat.not_lt_zero _)
  apply Nat.noConfusion

-theorem pred_lt' {n m : Nat} (h : m < n) : pred n < n :=
+theorem pred_lt_of_lt {n m : Nat} (h : m < n) : pred n < n :=
  pred_lt (not_eq_zero_of_lt h)

+set_option linter.missingDocs false in
+@[deprecated (since := "2024-06-01")] abbrev pred_lt' := @pred_lt_of_lt
+
+theorem sub_one_lt_of_lt {n m : Nat} (h : m < n) : n - 1 < n :=
+  sub_one_lt (not_eq_zero_of_lt h)
+
 /-! # pred theorems -/

@[simp] protected theorem pred_zero : pred 0 = 0 := rfl
@@ -750,12 +822,21 @@ theorem succ_pred {a : Nat} (h : a ≠ 0) : a.pred.succ = a := by
  | zero => contradiction
  | succ => rfl

+theorem sub_one_add_one {a : Nat} (h : a ≠ 0) : a - 1 + 1 = a := by
+  induction a with
+  | zero => contradiction
+  | succ => rfl
+
 theorem succ_pred_eq_of_pos : ∀ {n}, 0 < n → succ (pred n) = n
  | _+1, _ => rfl

 theorem sub_one_add_one_eq_of_pos : ∀ {n}, 0 < n → (n - 1) + 1 = n
  | _+1, _ => rfl

+theorem eq_zero_or_eq_sub_one_add_one : ∀ {n}, n = 0 ∨ n = n - 1 + 1
+  | 0 => Or.inl rfl
+  | _+1 => Or.inr rfl
+
@[simp] theorem pred_eq_sub_one : pred n = n - 1 := rfl

 /-! # sub theorems -/
@@ -806,6 +887,9 @@ theorem add_sub_of_le {a b : Nat} (h : a ≤ b) : a + (b - a) = b := by
    have : a ≤ b := Nat.le_of_succ_le h
    rw [sub_succ, Nat.succ_add, ← Nat.add_succ, Nat.succ_pred hne, ih this]

+theorem sub_one_cancel : ∀ {a b : Nat}, 0 < a → 0 < b → a - 1 = b - 1 → a = b
+  | _+1, _+1, _, _ => congrArg _
+
@[simp] protected theorem sub_add_cancel {n m : Nat} (h : m ≤ n) : n - m + m = n := by
  rw [Nat.add_comm, Nat.add_sub_of_le h]

@@ -857,6 +941,17 @@ protected theorem sub_lt_sub_left : ∀ {k m n : Nat}, k < m → k < n → m - n
  | zero => rfl
  | succ n ih => simp only [ih, Nat.sub_succ]; decide

+protected theorem sub_lt_sub_right : ∀ {a b c : Nat}, c ≤ a → a < b → a - c < b - c
+  | 0, _, _, hle, h => by
+    rw [Nat.eq_zero_of_le_zero hle, Nat.sub_zero, Nat.sub_zero]
+    exact h
+  | _, _, 0, _, h => by
+    rw [Nat.sub_zero, Nat.sub_zero]
+    exact h
+  | _+1, _+1, _+1, hle, h => by
+    rw [Nat.add_sub_add_right, Nat.add_sub_add_right]
+    exact Nat.sub_lt_sub_right (le_of_succ_le_succ hle) (lt_of_succ_lt_succ h)
+
 protected theorem sub_self_add (n m : Nat) : n - (n + m) = 0 := by
  show (n + 0) - (n + m) = 0
  rw [Nat.add_sub_add_left, Nat.zero_sub]
@@ -935,6 +1030,9 @@ protected theorem sub_le_sub_right {n m : Nat} (h : n ≤ m) : ∀ k, n - k ≤
  | 0   => h
  | z+1 => pred_le_pred (Nat.sub_le_sub_right h z)

+protected theorem sub_le_add_right_sub (a i j : Nat) : a - i ≤ a + j - i :=
+  Nat.sub_le_sub_right (Nat.le_add_right ..) ..
+
 protected theorem lt_of_sub_ne_zero (h : n - m ≠ 0) : m < n :=
  Nat.not_le.1 (mt Nat.sub_eq_zero_of_le h)

@@ -947,6 +1045,9 @@ protected theorem lt_of_sub_pos (h : 0 < n - m) : m < n :=
 protected theorem lt_of_sub_eq_succ (h : m - n = succ l) : n < m :=
  Nat.lt_of_sub_pos (h ▸ Nat.zero_lt_succ _)

+protected theorem lt_of_sub_eq_sub_one (h : m - n = l + 1) : n < m :=
+  Nat.lt_of_sub_pos (h ▸ Nat.zero_lt_succ _)
+
 protected theorem sub_lt_left_of_lt_add {n k m : Nat} (H : n ≤ k) (h : k < n + m) : k - n < m := by
  have := Nat.sub_le_sub_right (succ_le_of_lt h) n
  rwa [Nat.add_sub_cancel_left, Nat.succ_sub H] at this
@@ -974,21 +1075,35 @@ protected theorem sub_eq_iff_eq_add {c : Nat} (h : b ≤ a) : a - b = c ↔ a =
 protected theorem sub_eq_iff_eq_add' {c : Nat} (h : b ≤ a) : a - b = c ↔ a = b + c := by
  rw [Nat.add_comm, Nat.sub_eq_iff_eq_add h]

-theorem mul_pred_left (n m : Nat) : pred n * m = n * m - m := by
+/-! ## Mul sub distrib -/
+
+theorem pred_mul (n m : Nat) : pred n * m = n * m - m := by
  cases n with
  | zero   => simp
  | succ n => rw [Nat.pred_succ, succ_mul, Nat.add_sub_cancel]

-/-! ## Mul sub distrib -/
+set_option linter.missingDocs false in
+@[deprecated (since := "2024-06-01")] abbrev mul_pred_left := @pred_mul

-theorem mul_pred_right (n m : Nat) : n * pred m = n * m - n := by
-  rw [Nat.mul_comm, mul_pred_left, Nat.mul_comm]
+protected theorem sub_one_mul  (n m : Nat) : (n - 1) * m = n * m - m := by
+  cases n with
+  | zero   => simp
+  | succ n =>
+    rw [Nat.add_sub_cancel, add_one_mul, Nat.add_sub_cancel]

+theorem mul_pred (n m : Nat) : n * pred m = n * m - n := by
+  rw [Nat.mul_comm, pred_mul, Nat.mul_comm]
+
+set_option linter.missingDocs false in
+@[deprecated (since := "2024-06-01")] abbrev mul_pred_right := @mul_pred
+
+theorem mul_sub_one (n m : Nat) : n * (m - 1) = n * m - n := by
+  rw [Nat.mul_comm, Nat.sub_one_mul , Nat.mul_comm]

 protected theorem mul_sub_right_distrib (n m k : Nat) : (n - m) * k = n * k - m * k := by
  induction m with
  | zero => simp
-  | succ m ih => rw [Nat.sub_succ, Nat.mul_pred_left, ih, succ_mul, Nat.sub_sub]; done
+  | succ m ih => rw [Nat.sub_succ, Nat.pred_mul, ih, succ_mul, Nat.sub_sub]; done

 protected theorem mul_sub_left_distrib (n m k : Nat) : n * (m - k) = n * m - n * k := by
  rw [Nat.mul_comm, Nat.mul_sub_right_distrib, Nat.mul_comm m n, Nat.mul_comm n k]
--- a/src/Init/Data/Nat/Bitwise/Lemmas.lean
+++ b/src/Init/Data/Nat/Bitwise/Lemmas.lean
@@ -90,6 +90,10 @@ noncomputable def div2Induction {motive : Nat → Sort u}
  unfold testBit
  simp [shiftRight_succ_inside]

+@[simp] theorem testBit_add_one (x i : Nat) : testBit x (i + 1) = testBit (x/2) i := by
+  unfold testBit
+  simp [shiftRight_succ_inside]
+
 theorem testBit_to_div_mod {x : Nat} : testBit x i = decide (x / 2^i % 2 = 1) := by
  induction i generalizing x with
  | zero =>
@@ -306,6 +310,11 @@ theorem testBit_bool_to_nat (b : Bool) (i : Nat) :
        ←Nat.div_div_eq_div_mul _ 2, one_div_two,
        Nat.mod_eq_of_lt]

+/-- `testBit 1 i` is true iff the index `i` equals 0. -/
+theorem testBit_one_eq_true_iff_self_eq_zero {i : Nat} :
+    Nat.testBit 1 i = true ↔ i = 0 := by
+  cases i <;> simp
+
 /-! ### bitwise -/

 theorem testBit_bitwise
--- a/src/Init/Data/Nat/Div.lean
+++ b/src/Init/Data/Nat/Div.lean
@@ -251,10 +251,10 @@ theorem div_mul_le_self : ∀ (m n : Nat), m / n * n ≤ m
 theorem div_lt_iff_lt_mul (Hk : 0 < k) : x / k < y ↔ x < y * k := by
  rw [← Nat.not_le, ← Nat.not_le]; exact not_congr (le_div_iff_mul_le Hk)

-@[simp] theorem add_div_right (x : Nat) {z : Nat} (H : 0 < z) : (x + z) / z = succ (x / z) := by
+@[simp] theorem add_div_right (x : Nat) {z : Nat} (H : 0 < z) : (x + z) / z = (x / z) + 1 := by
  rw [div_eq_sub_div H (Nat.le_add_left _ _), Nat.add_sub_cancel]

-@[simp] theorem add_div_left (x : Nat) {z : Nat} (H : 0 < z) : (z + x) / z = succ (x / z) := by
+@[simp] theorem add_div_left (x : Nat) {z : Nat} (H : 0 < z) : (z + x) / z = (x / z) + 1 := by
  rw [Nat.add_comm, add_div_right x H]

 theorem add_mul_div_left (x z : Nat) {y : Nat} (H : 0 < y) : (x + y * z) / y = x / y + z := by
@@ -285,7 +285,7 @@ theorem add_mul_div_right (x y : Nat) {z : Nat} (H : 0 < z) : (x + y * z) / z =
@[simp] theorem mul_mod_left (m n : Nat) : (m * n) % n = 0 := by
  rw [Nat.mul_comm, mul_mod_right]

-protected theorem div_eq_of_lt_le (lo : k * n ≤ m) (hi : m < succ k * n) : m / n = k :=
+protected theorem div_eq_of_lt_le (lo : k * n ≤ m) (hi : m < (k + 1) * n) : m / n = k :=
 have npos : 0 < n := (eq_zero_or_pos _).resolve_left fun hn => by
  rw [hn, Nat.mul_zero] at hi lo; exact absurd lo (Nat.not_le_of_gt hi)
 Nat.le_antisymm
@@ -307,7 +307,7 @@ theorem sub_mul_div (x n p : Nat) (h₁ : n*p ≤ x) : (x - n*p) / n = x / n - p
      rw [sub_succ, ← IH h₂, div_eq_sub_div h₀ h₃]
      simp [Nat.pred_succ, mul_succ, Nat.sub_sub]

-theorem mul_sub_div (x n p : Nat) (h₁ : x < n*p) : (n * p - succ x) / n = p - succ (x / n) := by
+theorem mul_sub_div (x n p : Nat) (h₁ : x < n*p) : (n * p - (x + 1)) / n = p - ((x / n) + 1) := by
  have npos : 0 < n := (eq_zero_or_pos _).resolve_left fun n0 => by
    rw [n0, Nat.zero_mul] at h₁; exact not_lt_zero _ h₁
  apply Nat.div_eq_of_lt_le
--- a/src/Init/Data/Nat/Gcd.lean
+++ b/src/Init/Data/Nat/Gcd.lean
@@ -43,6 +43,9 @@ def gcd (m n : @& Nat) : Nat :=
 theorem gcd_succ (x y : Nat) : gcd (succ x) y = gcd (y % succ x) (succ x) := by
  rw [gcd]; rfl

+theorem gcd_add_one (x y : Nat) : gcd (x + 1) y = gcd (y % (x + 1)) (x + 1) := by
+  rw [gcd]; rfl
+
@[simp] theorem gcd_one_left (n : Nat) : gcd 1 n = 1 := by
  rw [gcd_succ, mod_one]
  rfl
--- a/src/Init/Data/Nat/Lemmas.lean
+++ b/src/Init/Data/Nat/Lemmas.lean
@@ -101,6 +101,10 @@ protected theorem one_sub : ∀ n, 1 - n = if n = 0 then 1 else 0
 theorem succ_sub_sub_succ (n m k) : succ n - m - succ k = n - m - k := by
  rw [Nat.sub_sub, Nat.sub_sub, add_succ, succ_sub_succ]

+theorem add_sub_sub_add_right (n m k l : Nat) :
+    (n + l) - m - (k + l) = n - m - k := by
+  rw [Nat.sub_sub, Nat.sub_sub, ←Nat.add_assoc, Nat.add_sub_add_right]
+
 protected theorem sub_right_comm (m n k : Nat) : m - n - k = m - k - n := by
  rw [Nat.sub_sub, Nat.sub_sub, Nat.add_comm]

@@ -176,10 +180,12 @@ protected theorem sub_add_lt_sub (h₁ : m + k ≤ n) (h₂ : 0 < k) : n - (m +
  rw [← Nat.sub_sub]; exact Nat.sub_lt_of_pos_le h₂ (Nat.le_sub_of_add_le' h₁)

 theorem sub_one_lt_of_le (h₀ : 0 < a) (h₁ : a ≤ b) : a - 1 < b :=
-  Nat.lt_of_lt_of_le (Nat.pred_lt' h₀) h₁
+  Nat.lt_of_lt_of_le (Nat.pred_lt_of_lt h₀) h₁

 theorem sub_lt_succ (a b) : a - b < succ a := lt_succ_of_le (sub_le a b)

+theorem sub_lt_add_one (a b) : a - b < a + 1 := lt_add_one_of_le (sub_le a b)
+
 theorem sub_one_sub_lt (h : i < n) : n - 1 - i < n := by
  rw [Nat.sub_right_comm]; exact Nat.sub_one_lt_of_le (Nat.sub_pos_of_lt h) (Nat.sub_le ..)

@@ -206,13 +212,19 @@ instance : Std.IdempotentOp (α := Nat) min := ⟨Nat.min_self⟩

@[simp] protected theorem min_zero (a) : min a 0 = 0 := Nat.min_eq_right (Nat.zero_le _)

-protected theorem min_assoc : ∀ (a b c : Nat), min (min a b) c = min a (min b c)
+@[simp] protected theorem min_assoc : ∀ (a b c : Nat), min (min a b) c = min a (min b c)
  | 0, _, _ => by rw [Nat.zero_min, Nat.zero_min, Nat.zero_min]
  | _, 0, _ => by rw [Nat.zero_min, Nat.min_zero, Nat.zero_min]
  | _, _, 0 => by rw [Nat.min_zero, Nat.min_zero, Nat.min_zero]
  | _+1, _+1, _+1 => by simp only [Nat.succ_min_succ]; exact congrArg succ <| Nat.min_assoc ..
 instance : Std.Associative (α := Nat) min := ⟨Nat.min_assoc⟩

+@[simp] protected theorem min_self_assoc {m n : Nat} : min m (min m n) = min m n := by
+  rw [← Nat.min_assoc, Nat.min_self]
+
+@[simp] protected theorem min_self_assoc' {m n : Nat} : min n (min m n) = min n m := by
+  rw [Nat.min_comm m n, ← Nat.min_assoc, Nat.min_self]
+
 protected theorem sub_sub_eq_min : ∀ (a b : Nat), a - (a - b) = min a b
  | 0, _ => by rw [Nat.zero_sub, Nat.zero_min]
  | _, 0 => by rw [Nat.sub_zero, Nat.sub_self, Nat.min_zero]
@@ -479,6 +491,9 @@ 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 add_one_mul_add_one (a b : Nat) : (a + 1) * (b + 1) = a * b + a + b + 1 := by
+  rw [add_one_mul, mul_add_one]; rfl
+
 theorem mul_le_add_right (m k n : Nat) : k * m ≤ m + n ↔ (k-1) * m ≤ n := by
  match k with
  | 0 =>
@@ -562,6 +577,9 @@ theorem add_mod (a b n : Nat) : (a + b) % n = ((a % n) + (b % n)) % n := by
 theorem pow_succ' {m n : Nat} : m ^ n.succ = m * m ^ n := by
  rw [Nat.pow_succ, Nat.mul_comm]

+theorem pow_add_one' {m n : Nat} : m ^ (n + 1) = m * m ^ n := by
+  rw [Nat.pow_add_one, Nat.mul_comm]
+
@[simp] theorem pow_eq {m n : Nat} : m.pow n = m ^ n := rfl

 theorem one_shiftLeft (n : Nat) : 1 <<< n = 2 ^ n := by rw [shiftLeft_eq, Nat.one_mul]
@@ -790,6 +808,11 @@ theorem shiftRight_succ_inside : ∀m n, m >>> (n+1) = (m/2) >>> n
  | 0 => by simp [shiftRight]
  | n + 1 => by simp [shiftRight, zero_shiftRight n, shiftRight_succ]

+theorem shiftLeft_add (m n : Nat) : ∀ k, m <<< (n + k) = (m <<< n) <<< k
+  | 0 => rfl
+  | k + 1 => by simp [← Nat.add_assoc, shiftLeft_add _ _ k, shiftLeft_succ]
+
+@[deprecated shiftLeft_add (since := "2024-06-02")]
 theorem shiftLeft_shiftLeft (m n : Nat) : ∀ k, (m <<< n) <<< k = m <<< (n + k)
  | 0 => rfl
  | k + 1 => by simp [← Nat.add_assoc, shiftLeft_shiftLeft _ _ k, shiftLeft_succ]
--- a/src/Init/Data/Nat/Linear.lean
+++ b/src/Init/Data/Nat/Linear.lean
@@ -583,8 +583,6 @@ theorem PolyCnstr.denote_mul (ctx : Context) (k : Nat) (c : PolyCnstr) : (c.mul
  have : k ≠ 0 → k + 1 ≠ 1 := by intro h; match k with | 0 => contradiction | k+1 => simp [Nat.succ.injEq]
  have : ¬ (k == 0) → (k + 1 == 1) = false := fun h => beq_false_of_ne (this (ne_of_beq_false (Bool.of_not_eq_true h)))
  have : ¬ ((k + 1 == 0) = true)  := fun h => absurd (eq_of_beq h) (Nat.succ_ne_zero k)
-  have : (1 == (0 : Nat)) = false := rfl
-  have : (1 == (1 : Nat)) = true  := rfl
  by_cases he : eq = true <;> simp [he, PolyCnstr.mul, PolyCnstr.denote, Poly.denote_le, Poly.denote_eq]
     <;> by_cases hk : k == 0 <;> (try simp [eq_of_beq hk]) <;> simp [*] <;> apply Iff.intro <;> intro h
  · exact Nat.eq_of_mul_eq_mul_left (Nat.zero_lt_succ _) h
--- a/src/Init/Data/Option/Basic.lean
+++ b/src/Init/Data/Option/Basic.lean
@@ -119,7 +119,7 @@ def merge (fn : α → α → α) : Option α → Option α → Option α


 /-- An elimination principle for `Option`. It is a nondependent version of `Option.recOn`. -/
-@[simp, inline] protected def elim : Option α → β → (α → β) → β
+@[inline] protected def elim : Option α → β → (α → β) → β
  | some x, _, f => f x
  | none, y, _ => y

--- a/src/Init/Data/Option/Instances.lean
+++ b/src/Init/Data/Option/Instances.lean
@@ -26,7 +26,7 @@ instance : Membership α (Option α) := ⟨fun a b => b = some a⟩
 instance [DecidableEq α] (j : α) (o : Option α) : Decidable (j ∈ o) :=
  inferInstanceAs <| Decidable (o = some j)

-theorem isNone_iff_eq_none {o : Option α} : o.isNone ↔ o = none :=
+@[simp] theorem isNone_iff_eq_none {o : Option α} : o.isNone ↔ o = none :=
  ⟨Option.eq_none_of_isNone, fun e => e.symm ▸ rfl⟩

 theorem some_inj {a b : α} : some a = some b ↔ a = b := by simp; rfl
@@ -72,7 +72,7 @@ satisfy `p`, using the proof to apply `f`.

 /-- Map a monadic function which returns `Unit` over an `Option`. -/
@[inline] protected def forM [Pure m] : Option α → (α → m PUnit) → m PUnit
-  | none  , _ => pure ()
+  | none  , _ => pure ⟨⟩
  | some a, f => f a

 instance : ForM m (Option α) α :=
--- a/src/Init/Data/Option/Lemmas.lean
+++ b/src/Init/Data/Option/Lemmas.lean
@@ -208,9 +208,9 @@ theorem liftOrGet_eq_or_eq {f : α → α → α} (h : ∀ a b, f a b = a ∨ f
@[simp] theorem liftOrGet_some_some {f} {a b : α} :
  liftOrGet f (some a) (some b) = f a b := rfl

-theorem elim_none (x : β) (f : α → β) : none.elim x f = x := rfl
+@[simp] theorem elim_none (x : β) (f : α → β) : none.elim x f = x := rfl

-theorem elim_some (x : β) (f : α → β) (a : α) : (some a).elim x f = f a := rfl
+@[simp] theorem elim_some (x : β) (f : α → β) (a : α) : (some a).elim x f = f a := rfl

@[simp] theorem getD_map (f : α → β) (x : α) (o : Option α) :
  (o.map f).getD (f x) = f (getD o x) := by cases o <;> rfl
--- a/src/Init/Data/String/Basic.lean
+++ b/src/Init/Data/String/Basic.lean
@@ -1,12 +1,13 @@
 /-
 Copyright (c) 2016 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Author: Leonardo de Moura
+Author: Leonardo de Moura, Mario Carneiro
 -/
 prelude
 import Init.Data.List.Basic
 import Init.Data.Char.Basic
 import Init.Data.Option.Basic
+
 universe u

 def List.asString (s : List Char) : String :=
@@ -256,7 +257,26 @@ def atEnd : (@& String) → (@& Pos) → Bool
  | s, p => p.byteIdx ≥ utf8ByteSize s

 /--
-Similar to `get` but runtime does not perform bounds check.
+Returns the character at position `p` of a string.
+If `p` is not a valid position, returns `(default : Char)`.
+
+Requires evidence, `h`, that `p` is within bounds
+instead of performing a runtime bounds check as in `get`.
+
+Examples:
+* `"abc".get' 0 (by decide) = 'a'`
+* `let lean := "L∃∀N"; lean.get' (0 |> lean.next |> lean.next) (by decide) = '∀'`
+
+A typical pattern combines `get'` with a dependent if-else expression
+to avoid the overhead of an additional bounds check. For example:
+```
+def getInBounds? (s : String) (p : String.Pos) : Option Char :=
+  if h : s.atEnd p then none else some (s.get' p h)
+```
+
+Even with evidence of `¬ s.atEnd p`,
+`p` may be invalid if a byte index points into the middle of a multi-byte UTF-8 character.
+For example, `"L∃∀N".get' ⟨2⟩ (by decide) = (default : Char)`.
 -/
@[extern "lean_string_utf8_get_fast"]
 def get' (s : @& String) (p : @& Pos) (h : ¬ s.atEnd p) : Char :=
@@ -264,22 +284,41 @@ def get' (s : @& String) (p : @& Pos) (h : ¬ s.atEnd p) : Char :=
  | ⟨s⟩ => utf8GetAux s 0 p

 /--
-Similar to `next` but runtime does not perform bounds check.
+Returns the next position in a string after position `p`.
+If `p` is not a valid position, the result is unspecified.
+
+Requires evidence, `h`, that `p` is within bounds
+instead of performing a runtime bounds check as in `next`.
+
+Examples:
+* `let abc := "abc"; abc.get (abc.next' 0 (by decide)) = 'b'`
+
+A typical pattern combines `next'` with a dependent if-else expression
+to avoid the overhead of an additional bounds check. For example:
+```
+def next? (s: String) (p : String.Pos) : Option Char :=
+  if h : s.atEnd p then none else s.get (s.next' p h)
+```
 -/
@[extern "lean_string_utf8_next_fast"]
 def next' (s : @& String) (p : @& Pos) (h : ¬ s.atEnd p) : Pos :=
  let c := get s p
  p + c

-theorem one_le_csize (c : Char) : 1 ≤ csize c := by
-  repeat first | apply iteInduction (motive := (1 ≤ UInt32.toNat ·)) <;> intros | decide
+theorem _root_.Char.utf8Size_pos (c : Char) : 0 < c.utf8Size := by
+  repeat first | apply iteInduction (motive := (0 < ·)) <;> intros | decide
+
+theorem _root_.Char.utf8Size_le_four (c : Char) : c.utf8Size ≤ 4 := by
+  repeat first | apply iteInduction (motive := (· ≤ 4)) <;> intros | decide
+
+@[deprecated Char.utf8Size_pos (since := "2026-06-04")] abbrev one_le_csize := Char.utf8Size_pos

@[simp] theorem pos_lt_eq (p₁ p₂ : Pos) : (p₁ < p₂) = (p₁.1 < p₂.1) := rfl

-@[simp] theorem pos_add_char (p : Pos) (c : Char) : (p + c).byteIdx = p.byteIdx + csize c := rfl
+@[simp] theorem pos_add_char (p : Pos) (c : Char) : (p + c).byteIdx = p.byteIdx + c.utf8Size := rfl

 theorem lt_next (s : String) (i : Pos) : i.1 < (s.next i).1 :=
-  Nat.add_lt_add_left (one_le_csize _) _
+  Nat.add_lt_add_left (Char.utf8Size_pos _) _

 theorem utf8PrevAux_lt_of_pos : ∀ (cs : List Char) (i p : Pos), p ≠ 0 →
    (utf8PrevAux cs i p).1 < p.1
@@ -289,7 +328,7 @@ theorem utf8PrevAux_lt_of_pos : ∀ (cs : List Char) (i p : Pos), p ≠ 0 →
  | c::cs, i, p, h => by
    simp [utf8PrevAux]
    apply iteInduction (motive := (Pos.byteIdx · < _)) <;> intro h'
-    next => exact h' ▸ Nat.add_lt_add_left (one_le_csize _) _
+    next => exact h' ▸ Nat.add_lt_add_left (Char.utf8Size_pos _) _
    next => exact utf8PrevAux_lt_of_pos _ _ _ h

 theorem prev_lt_of_pos (s : String) (i : Pos) (h : i ≠ 0) : (s.prev i).1 < i.1 := by
@@ -305,6 +344,15 @@ def posOfAux (s : String) (c : Char) (stopPos : Pos) (pos : Pos) : Pos :=
  else pos
 termination_by stopPos.1 - pos.1

+/--
+Returns the position of the first occurrence of a character, `c`, in `s`.
+If `s` does not contain `c`, returns `s.endPos`.
+
+Examples:
+* `"abba".posOf 'a' = ⟨0⟩`
+* `"abba".posOf 'z' = ⟨4⟩`
+* `"L∃∀N".posOf '∀' = ⟨4⟩`
+-/
@[inline] def posOf (s : String) (c : Char) : Pos :=
  posOfAux s c s.endPos 0

@@ -317,6 +365,15 @@ def revPosOfAux (s : String) (c : Char) (pos : Pos) : Option Pos :=
    else revPosOfAux s c pos
 termination_by pos.1

+/--
+Returns the position of the last occurrence of a character, `c`, in `s`.
+If `s` does not contain `c`, returns `none`.
+
+Examples:
+* `"abba".posOf 'a' = some ⟨3⟩`
+* `"abba".posOf 'z' = none`
+* `"L∃∀N".posOf '∀' = some ⟨4⟩`
+-/
 def revPosOf (s : String) (c : Char) : Option Pos :=
  revPosOfAux s c s.endPos

@@ -424,7 +481,7 @@ decreasing_by
  focus
    rename_i i₀ j₀ _ eq h'
    rw [show (s.next i₀ - sep.next j₀).1 = (i₀ - j₀).1 by
-      show (_ + csize _) - (_ + csize _) = _
+      show (_ + Char.utf8Size _) - (_ + Char.utf8Size _) = _
      rw [(beq_iff_eq ..).1 eq, Nat.add_sub_add_right]; rfl]
    right; exact Nat.sub_lt_sub_left
      (Nat.lt_of_le_of_lt (Nat.le_add_right ..) (Nat.gt_of_not_le (mt decide_eq_true h')))
@@ -455,6 +512,7 @@ instance : Inhabited String := ⟨""⟩

 instance : Append String := ⟨String.append⟩

+@[deprecated push (since := "2024-04-06")]
 def str : String → Char → String := push

 def pushn (s : String) (c : Char) (n : Nat) : String :=
@@ -671,18 +729,18 @@ theorem set_next_add (s : String) (i : Pos) (c : Char) (b₁ b₂)
  simp [next, get, set, endPos, utf8ByteSize] at h ⊢
  rw [Nat.add_comm i.1, Nat.add_assoc] at h ⊢
  let rec foo : ∀ cs a b₁ b₂,
-    csize (utf8GetAux cs a i) + b₁ = utf8ByteSize.go cs + b₂ →
-    csize (utf8GetAux (utf8SetAux c cs a i) a i) + b₁ = utf8ByteSize.go (utf8SetAux c cs a i) + b₂
+    (utf8GetAux cs a i).utf8Size + b₁ = utf8ByteSize.go cs + b₂ →
+    (utf8GetAux (utf8SetAux c cs a i) a i).utf8Size + b₁ = utf8ByteSize.go (utf8SetAux c cs a i) + b₂
  | [], _, _, _, h => h
  | c'::cs, a, b₁, b₂, h => by
    unfold utf8SetAux
-    apply iteInduction (motive := fun p => csize (utf8GetAux p a i) + b₁ = utf8ByteSize.go p + b₂) <;>
+    apply iteInduction (motive := fun p => (utf8GetAux p a i).utf8Size + b₁ = utf8ByteSize.go p + b₂) <;>
      intro h' <;> simp [utf8GetAux, h', utf8ByteSize.go] at h ⊢
    next =>
      rw [Nat.add_assoc, Nat.add_left_comm] at h ⊢; rw [Nat.add_left_cancel h]
    next =>
      rw [Nat.add_assoc] at h ⊢
-      refine foo cs (a + c') b₁ (csize c' + b₂) h
+      refine foo cs (a + c') b₁ (c'.utf8Size + b₂) h
  exact foo s.1 0 _ _ h

 theorem mapAux_lemma (s : String) (i : Pos) (c : Char) (h : ¬s.atEnd i) :
@@ -735,7 +793,7 @@ where
    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)
+    have := Nat.sub_lt_sub_left _h (Nat.add_lt_add_left c₁.utf8Size_pos off1.1)
    decreasing_tactic

 /-- Return true iff `p` is a prefix of `s` -/
@@ -1018,5 +1076,145 @@ def decapitalize (s : String) :=

 end String

-protected def Char.toString (c : Char) : String :=
+namespace Char
+
+protected def toString (c : Char) : String :=
  String.singleton c
+
+@[simp] theorem length_toString (c : Char) : c.toString.length = 1 := rfl
+
+end Char
+
+namespace String
+
+theorem ext {s₁ s₂ : String} (h : s₁.data = s₂.data) : s₁ = s₂ :=
+  show ⟨s₁.data⟩ = (⟨s₂.data⟩ : String) from h ▸ rfl
+
+theorem ext_iff {s₁ s₂ : String} : s₁ = s₂ ↔ s₁.data = s₂.data := ⟨fun h => h ▸ rfl, ext⟩
+
+@[simp] theorem default_eq : default = "" := rfl
+
+@[simp] theorem length_mk (s : List Char) : (String.mk s).length = s.length := rfl
+
+@[simp] theorem length_empty : "".length = 0 := rfl
+
+@[simp] theorem length_singleton (c : Char) : (String.singleton c).length = 1 := rfl
+
+@[simp] theorem length_push (c : Char) : (String.push s c).length = s.length + 1 := by
+  rw [push, length_mk, List.length_append, List.length_singleton, Nat.succ.injEq]
+  rfl
+
+@[simp] theorem length_pushn (c : Char) (n : Nat) : (pushn s c n).length = s.length + n := by
+  unfold pushn; induction n <;> simp [Nat.repeat, Nat.add_assoc, *]
+
+@[simp] theorem length_append (s t : String) : (s ++ t).length = s.length + t.length := by
+  simp only [length, append, List.length_append]
+
+@[simp] theorem data_push (s : String) (c : Char) : (s.push c).data = s.data ++ [c] := rfl
+
+@[simp] theorem data_append (s t : String) : (s ++ t).data = s.data ++ t.data := rfl
+
+attribute [simp] toList -- prefer `String.data` over `String.toList` in lemmas
+
+theorem lt_iff (s t : String) : s < t ↔ s.data < t.data := .rfl
+
+namespace Pos
+
+@[simp] theorem byteIdx_zero : (0 : Pos).byteIdx = 0 := rfl
+
+theorem byteIdx_mk (n : Nat) : byteIdx ⟨n⟩ = n := rfl
+
+@[simp] theorem mk_zero : ⟨0⟩ = (0 : Pos) := rfl
+
+@[simp] theorem mk_byteIdx (p : Pos) : ⟨p.byteIdx⟩ = p := rfl
+
+theorem ext {i₁ i₂ : Pos} (h : i₁.byteIdx = i₂.byteIdx) : i₁ = i₂ :=
+  show ⟨i₁.byteIdx⟩ = (⟨i₂.byteIdx⟩ : Pos) from h ▸ rfl
+
+theorem ext_iff {i₁ i₂ : Pos} : i₁ = i₂ ↔ i₁.byteIdx = i₂.byteIdx := ⟨fun h => h ▸ rfl, ext⟩
+
+@[simp] theorem add_byteIdx (p₁ p₂ : Pos) : (p₁ + p₂).byteIdx = p₁.byteIdx + p₂.byteIdx := rfl
+
+theorem add_eq (p₁ p₂ : Pos) : p₁ + p₂ = ⟨p₁.byteIdx + p₂.byteIdx⟩ := rfl
+
+@[simp] theorem sub_byteIdx (p₁ p₂ : Pos) : (p₁ - p₂).byteIdx = p₁.byteIdx - p₂.byteIdx := rfl
+
+theorem sub_eq (p₁ p₂ : Pos) : p₁ - p₂ = ⟨p₁.byteIdx - p₂.byteIdx⟩ := rfl
+
+@[simp] theorem addChar_byteIdx (p : Pos) (c : Char) : (p + c).byteIdx = p.byteIdx + c.utf8Size := rfl
+
+theorem addChar_eq (p : Pos) (c : Char) : p + c = ⟨p.byteIdx + c.utf8Size⟩ := rfl
+
+theorem zero_addChar_byteIdx (c : Char) : ((0 : Pos) + c).byteIdx = c.utf8Size := by
+  simp only [addChar_byteIdx, byteIdx_zero, Nat.zero_add]
+
+theorem zero_addChar_eq (c : Char) : (0 : Pos) + c = ⟨c.utf8Size⟩ := by rw [← zero_addChar_byteIdx]
+
+theorem addChar_right_comm (p : Pos) (c₁ c₂ : Char) : p + c₁ + c₂ = p + c₂ + c₁ := by
+  apply ext
+  repeat rw [pos_add_char]
+  apply Nat.add_right_comm
+
+theorem ne_of_lt {i₁ i₂ : Pos} (h : i₁ < i₂) : i₁ ≠ i₂ := mt ext_iff.1 (Nat.ne_of_lt h)
+
+theorem ne_of_gt {i₁ i₂ : Pos} (h : i₁ < i₂) : i₂ ≠ i₁ := (ne_of_lt h).symm
+
+@[simp] theorem addString_byteIdx (p : Pos) (s : String) :
+    (p + s).byteIdx = p.byteIdx + s.utf8ByteSize := rfl
+
+theorem addString_eq (p : Pos) (s : String) : p + s = ⟨p.byteIdx + s.utf8ByteSize⟩ := rfl
+
+theorem zero_addString_byteIdx (s : String) : ((0 : Pos) + s).byteIdx = s.utf8ByteSize := by
+  simp only [addString_byteIdx, byteIdx_zero, Nat.zero_add]
+
+theorem zero_addString_eq (s : String) : (0 : Pos) + s = ⟨s.utf8ByteSize⟩ := by
+  rw [← zero_addString_byteIdx]
+
+theorem le_iff {i₁ i₂ : Pos} : i₁ ≤ i₂ ↔ i₁.byteIdx ≤ i₂.byteIdx := .rfl
+
+@[simp] theorem mk_le_mk {i₁ i₂ : Nat} : Pos.mk i₁ ≤ Pos.mk i₂ ↔ i₁ ≤ i₂ := .rfl
+
+theorem lt_iff {i₁ i₂ : Pos} : i₁ < i₂ ↔ i₁.byteIdx < i₂.byteIdx := .rfl
+
+@[simp] theorem mk_lt_mk {i₁ i₂ : Nat} : Pos.mk i₁ < Pos.mk i₂ ↔ i₁ < i₂ := .rfl
+
+end Pos
+
+@[simp] theorem get!_eq_get (s : String) (p : Pos) : get! s p = get s p := rfl
+
+theorem lt_next' (s : String) (p : Pos) : p < next s p := lt_next ..
+
+@[simp] theorem prev_zero (s : String) : prev s 0 = 0 := rfl
+
+@[simp] theorem get'_eq (s : String) (p : Pos) (h) : get' s p h = get s p := rfl
+
+@[simp] theorem next'_eq (s : String) (p : Pos) (h) : next' s p h = next s p := rfl
+
+-- `toSubstring'` is just a synonym for `toSubstring` without the `@[inline]` attribute
+-- so for proving can be unfolded.
+attribute [simp] toSubstring'
+
+theorem singleton_eq (c : Char) : singleton c = ⟨[c]⟩ := rfl
+
+@[simp] theorem data_singleton (c : Char) : (singleton c).data = [c] := rfl
+
+@[simp] theorem append_empty (s : String) : s ++ "" = s := ext (List.append_nil _)
+
+@[simp] theorem empty_append (s : String) : "" ++ s = s := rfl
+
+theorem append_assoc (s₁ s₂ s₃ : String) : (s₁ ++ s₂) ++ s₃ = s₁ ++ (s₂ ++ s₃) :=
+  ext (List.append_assoc ..)
+
+end String
+
+open String
+
+namespace Substring
+
+@[simp] theorem prev_zero (s : Substring) : s.prev 0 = 0 := by simp [prev, Pos.add_eq, Pos.byteIdx_zero]
+
+@[simp] theorem prevn_zero (s : Substring) : ∀ n, s.prevn n 0 = 0
+  | 0 => rfl
+  | n+1 => by simp [prevn, prevn_zero s n]
+
+end Substring
--- a/src/Init/Data/String/Extra.lean
+++ b/src/Init/Data/String/Extra.lean
@@ -63,23 +63,23 @@ where
  loop (i : Nat) : Option Unit := do
    if i < a.size then
      let c ← utf8DecodeChar? a i
-      loop (i + csize c)
+      loop (i + c.utf8Size)
    else pure ()
  termination_by a.size - i
-  decreasing_by exact Nat.sub_lt_sub_left ‹_› (Nat.lt_add_of_pos_right (one_le_csize c))
+  decreasing_by exact Nat.sub_lt_sub_left ‹_› (Nat.lt_add_of_pos_right c.utf8Size_pos)

 /-- Converts a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded `ByteArray` string to `String`. -/
-@[extern "lean_string_from_utf8"]
+@[extern "lean_string_from_utf8_unchecked"]
 def fromUTF8 (a : @& ByteArray) (h : validateUTF8 a) : String :=
  loop 0 ""
 where
  loop (i : Nat) (acc : String) : String :=
    if i < a.size then
      let c := (utf8DecodeChar? a i).getD default
-      loop (i + csize c) (acc.push c)
+      loop (i + c.utf8Size) (acc.push c)
    else acc
  termination_by a.size - i
-  decreasing_by exact Nat.sub_lt_sub_left ‹_› (Nat.lt_add_of_pos_right (one_le_csize c))
+  decreasing_by exact Nat.sub_lt_sub_left ‹_› (Nat.lt_add_of_pos_right c.utf8Size_pos)

 /-- Converts a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded `ByteArray` string to `String`,
 or returns `none` if `a` is not properly UTF-8 encoded. -/
@@ -108,8 +108,8 @@ def utf8EncodeChar (c : Char) : List UInt8 :=
     (v >>>  6).toUInt8 &&& 0x3f ||| 0x80,
              v.toUInt8 &&& 0x3f ||| 0x80]

-@[simp] theorem length_utf8EncodeChar (c : Char) : (utf8EncodeChar c).length = csize c := by
-  simp [csize, utf8EncodeChar, Char.utf8Size]
+@[simp] theorem length_utf8EncodeChar (c : Char) : (utf8EncodeChar c).length = c.utf8Size := by
+  simp [Char.utf8Size, utf8EncodeChar]
  cases Decidable.em (c.val ≤ 0x7f) <;> simp [*]
  cases Decidable.em (c.val ≤ 0x7ff) <;> simp [*]
  cases Decidable.em (c.val ≤ 0xffff) <;> simp [*]
@@ -221,11 +221,11 @@ where
  termination_by text.utf8ByteSize - pos.byteIdx
  decreasing_by
    decreasing_with
-      show text.utf8ByteSize - (text.next' (text.next' pos _) _).byteIdx < text.utf8ByteSize - pos.byteIdx
+      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
+      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 _ _)

--- a/src/Init/GetElem.lean
+++ b/src/Init/GetElem.lean
@@ -141,12 +141,16 @@ instance : GetElem (List α) Nat α fun as i => i < as.length where

 instance : LawfulGetElem (List α) Nat α fun as i => i < as.length where

-@[simp] theorem cons_getElem_zero (a : α) (as : List α) (h : 0 < (a :: as).length) : getElem (a :: as) 0 h = a := by
+@[simp] theorem getElem_cons_zero (a : α) (as : List α) (h : 0 < (a :: as).length) : getElem (a :: as) 0 h = a := by
  rfl

-@[simp] theorem cons_getElem_succ (a : α) (as : List α) (i : Nat) (h : i + 1 < (a :: as).length) : getElem (a :: as) (i+1) h = getElem as i (Nat.lt_of_succ_lt_succ h) := by
+@[deprecated (since := "2024-6-12")] abbrev cons_getElem_zero := @getElem_cons_zero
+
+@[simp] theorem getElem_cons_succ (a : α) (as : List α) (i : Nat) (h : i + 1 < (a :: as).length) : getElem (a :: as) (i+1) h = getElem as i (Nat.lt_of_succ_lt_succ h) := by
  rfl

+@[deprecated (since := "2024-6-12")] abbrev cons_getElem_succ := @getElem_cons_succ
+
 theorem get_drop_eq_drop (as : List α) (i : Nat) (h : i < as.length) : as[i] :: as.drop (i+1) = as.drop i :=
  match as, i with
  | _::_, 0   => rfl
--- a/src/Init/Meta.lean
+++ b/src/Init/Meta.lean
@@ -1278,12 +1278,46 @@ def Occurrences.isAll : Occurrences → Bool
  | all => true
  | _   => false

+/--
+Controls which new mvars are turned in to goals by the `apply` tactic.
+- `nonDependentFirst`  mvars that don't depend on other goals appear first in the goal list.
+- `nonDependentOnly` only mvars that don't depend on other goals are added to goal list.
+- `all` all unassigned mvars are added to the goal list.
+-/
+-- TODO: Consider renaming to `Apply.NewGoals`
+inductive ApplyNewGoals where
+  | nonDependentFirst | nonDependentOnly | all
+
+/-- Configures the behaviour of the `apply` tactic. -/
+-- TODO: Consider renaming to `Apply.Config`
+structure ApplyConfig where
+  newGoals := ApplyNewGoals.nonDependentFirst
+  /--
+  If `synthAssignedInstances` is `true`, then `apply` will synthesize instance implicit arguments
+  even if they have assigned by `isDefEq`, and then check whether the synthesized value matches the
+  one inferred. The `congr` tactic sets this flag to false.
+  -/
+  synthAssignedInstances := true
+  /--
+  If `allowSynthFailures` is `true`, then `apply` will return instance implicit arguments
+  for which typeclass search failed as new goals.
+  -/
+  allowSynthFailures := false
+  /--
+  If `approx := true`, then we turn on `isDefEq` approximations. That is, we use
+  the `approxDefEq` combinator.
+  -/
+  approx : Bool := true
+
 namespace Rewrite

+abbrev NewGoals := ApplyNewGoals
+
 structure Config where
-  transparency : TransparencyMode := TransparencyMode.reducible
+  transparency : TransparencyMode := .reducible
  offsetCnstrs : Bool := true
-  occs : Occurrences := Occurrences.all
+  occs : Occurrences := .all
+  newGoals : NewGoals := .nonDependentFirst

 end Rewrite

--- a/src/Init/MetaTypes.lean
+++ b/src/Init/MetaTypes.lean
@@ -42,23 +42,67 @@ inductive EtaStructMode where

 namespace DSimp

+/--
+The configuration for `dsimp`.
+Passed to `dsimp` using, for example, the `dsimp (config := {zeta := false})` syntax.
+
+Implementation note: this structure is only used for processing the `(config := ...)` syntax, and it is not used internally.
+It is immediately converted to `Lean.Meta.Simp.Config` by `Lean.Elab.Tactic.elabSimpConfig`.
+-/
 structure Config where
-  /-- `let x := v; e[x]` reduces to `e[v]`. -/
+  /--
+  When `true` (default: `true`), performs zeta reduction of let expressions.
+  That is, `let x := v; e[x]` reduces to `e[v]`.
+  See also `zetaDelta`.
+  -/
  zeta              : Bool := true
+  /--
+  When `true` (default: `true`), performs beta reduction of applications of `fun` expressions.
+  That is, `(fun x => e[x]) v` reduces to `e[v]`.
+  -/
  beta              : Bool := true
+  /--
+  TODO (currently unimplemented). When `true` (default: `true`), performs eta reduction for `fun` expressions.
+  That is, `(fun x => f x)` reduces to `f`.
+  -/
  eta               : Bool := true
+  /--
+  Configures how to determine definitional equality between two structure instances.
+  See documentation for `Lean.Meta.EtaStructMode`.
+  -/
  etaStruct         : EtaStructMode := .all
+  /--
+  When `true` (default: `true`), reduces `match` expressions applied to constructors.
+  -/
  iota              : Bool := true
+  /--
+  When `true` (default: `true`), reduces projections of structure constructors.
+  -/
  proj              : Bool := true
+  /--
+  When `true` (default: `false`), rewrites a proposition `p` to `True` or `False` by inferring
+  a `Decidable p` instance and reducing it.
+  -/
  decide            : Bool := false
+  /--
+  When `true` (default: `false`), unfolds definitions.
+  This can be enabled using the `simp!` syntax.
+  -/
  autoUnfold        : Bool := false
-  /-- If `failIfUnchanged := true`, then calls to `simp`, `dsimp`, or `simp_all`
-  will fail if they do not make progress. -/
+  /--
+  If `failIfUnchanged` is `true` (default: `true`), then calls to `simp`, `dsimp`, or `simp_all`
+  will fail if they do not make progress.
+  -/
  failIfUnchanged   : Bool := true
-  /-- If `unfoldPartialApp := true`, then calls to `simp`, `dsimp`, or `simp_all`
-  will unfold even partial applications of `f` when we request `f` to be unfolded. -/
+  /--
+  If `unfoldPartialApp` is `true` (default: `false`), then calls to `simp`, `dsimp`, or `simp_all`
+  will unfold even partial applications of `f` when we request `f` to be unfolded.
+  -/
  unfoldPartialApp  : Bool := false
-  /-- Given a local context containing entry `x : t := e`, free variable `x` reduces to `e`. -/
+  /--
+  When `true` (default: `false`), local definitions are unfolded.
+  That is, given a local context containing entry `x : t := e`, the free variable `x` reduces to `e`.
+  -/
  zetaDelta         : Bool := false
  deriving Inhabited, BEq

@@ -72,7 +116,7 @@ def defaultMaxSteps := 100000
 The configuration for `simp`.
 Passed to `simp` using, for example, the `simp (config := {contextual := true})` syntax.

-See also `Lean.Meta.Simp.neutralConfig`.
+See also `Lean.Meta.Simp.neutralConfig` and `Lean.Meta.DSimp.Config`.
 -/
 structure Config where
  /--
--- a/src/Init/Notation.lean
+++ b/src/Init/Notation.lean
@@ -558,6 +558,22 @@ syntax (name := runMeta) "run_meta " doSeq : command
 set_option linter.missingDocs false in
 syntax guardMsgsFilterSeverity := &"info" <|> &"warning" <|> &"error" <|> &"all"

+/--
+`#reduce <expression>` reduces the expression `<expression>` to its normal form. This
+involves applying reduction rules until no further reduction is possible.
+
+By default, proofs and types within the expression are not reduced. Use modifiers
+`(proofs := true)`  and `(types := true)` to reduce them.
+Recall that propositions are types in Lean.
+
+**Warning:** This can be a computationally expensive operation,
+especially for complex expressions.
+
+Consider using `#eval <expression>` for simple evaluation/execution
+of expressions.
+-/
+syntax (name := reduceCmd) "#reduce " (atomic("(" &"proofs" " := " &"true" ")"))? (atomic("(" &"types" " := " &"true" ")"))? term : command
+
 /--
 A message filter specification for `#guard_msgs`.
 - `info`, `warning`, `error`: capture messages with the given severity level.
--- a/src/Init/Omega/Int.lean
+++ b/src/Init/Omega/Int.lean
@@ -187,7 +187,7 @@ theorem ofNat_val_add {x y : Fin n} :
    (((x + y : Fin n)) : Int) = ((x : Int) + (y : Int)) % n := rfl

 theorem ofNat_val_sub {x y : Fin n} :
-    (((x - y : Fin n)) : Int) = ((x : Int) + ((n - y : Nat) : Int)) % n := rfl
+    (((x - y : Fin n)) : Int) = (((n - y : Nat) + (x : Int) : Int)) % n := rfl

 theorem ofNat_val_mul {x y : Fin n} :
    (((x * y : Fin n)) : Int) = ((x : Int) * (y : Int)) % n := rfl
--- a/src/Init/Omega/IntList.lean
+++ b/src/Init/Omega/IntList.lean
@@ -28,8 +28,8 @@ def get (xs : IntList) (i : Nat) : Int := (xs.get? i).getD 0
@[simp] theorem get_cons_succ : get (x :: xs) (i+1) = get xs i := rfl

 theorem get_map {xs : IntList} (h : f 0 = 0) : get (xs.map f) i = f (xs.get i) := by
-  simp only [get, List.get?_map]
-  cases xs.get? i <;> simp_all
+  simp only [get, List.get?_eq_getElem?, List.getElem?_map]
+  cases xs[i]? <;> simp_all

 theorem get_of_length_le {xs : IntList} (h : xs.length ≤ i) : xs.get i = 0 := by
  rw [get, List.get?_eq_none.mpr h]
@@ -66,8 +66,8 @@ theorem add_def (xs ys : IntList) :
  rfl

@[simp] theorem add_get (xs ys : IntList) (i : Nat) : (xs + ys).get i = xs.get i + ys.get i := by
-  simp only [add_def, get, List.zipWithAll_get?, List.get?_eq_none]
-  cases xs.get? i <;> cases ys.get? i <;> simp
+  simp only [get, add_def, List.get?_eq_getElem?, List.getElem?_zipWithAll]
+  cases xs[i]? <;> cases ys[i]? <;> simp

@[simp] theorem add_nil (xs : IntList) : xs + [] = xs := by simp [add_def]
@[simp] theorem nil_add (xs : IntList) : [] + xs = xs := by simp [add_def]
@@ -83,8 +83,8 @@ theorem mul_def (xs ys : IntList) : xs * ys = List.zipWith (· * ·) xs ys :=
  rfl

@[simp] theorem mul_get (xs ys : IntList) (i : Nat) : (xs * ys).get i = xs.get i * ys.get i := by
-  simp only [mul_def, get, List.zipWith_get?]
-  cases xs.get? i <;> cases ys.get? i <;> simp
+  simp only [get, mul_def, List.get?_eq_getElem?, List.getElem?_zipWith]
+  cases xs[i]? <;> cases ys[i]? <;> simp

@[simp] theorem mul_nil_left : ([] : IntList) * ys = [] := rfl
@[simp] theorem mul_nil_right : xs * ([] : IntList) = [] := List.zipWith_nil_right
@@ -98,8 +98,8 @@ instance : Neg IntList := ⟨neg⟩
 theorem neg_def (xs : IntList) : - xs = xs.map fun x => -x := rfl

@[simp] theorem neg_get (xs : IntList) (i : Nat) : (- xs).get i = - xs.get i := by
-  simp only [neg_def, get, List.get?_map]
-  cases xs.get? i <;> simp
+  simp only [get, neg_def, List.get?_eq_getElem?, List.getElem?_map]
+  cases xs[i]? <;> simp

@[simp] theorem neg_nil : (- ([] : IntList)) = [] := rfl
@[simp] theorem neg_cons : (- (x::xs : IntList)) = -x :: -xs := rfl
@@ -124,8 +124,8 @@ instance : HMul Int IntList IntList where
 theorem smul_def (xs : IntList) (i : Int) : i * xs = xs.map fun x => i * x := rfl

@[simp] theorem smul_get (xs : IntList) (a : Int) (i : Nat) : (a * xs).get i = a * xs.get i := by
-  simp only [smul_def, get, List.get?_map]
-  cases xs.get? i <;> simp
+  simp only [get, smul_def, List.get?_eq_getElem?, List.getElem?_map]
+  cases xs[i]? <;> simp

@[simp] theorem smul_nil {i : Int} : i * ([] : IntList) = [] := rfl
@[simp] theorem smul_cons {i : Int} : i * (x::xs : IntList) = i * x :: i * xs := rfl
@@ -173,7 +173,7 @@ theorem mul_neg_left (xs ys : IntList) : (-xs) * ys = -(xs * ys) := by
 attribute [local simp] add_def neg_def sub_def in
 theorem sub_eq_add_neg (xs ys : IntList) : xs - ys = xs + (-ys) := by
  induction xs generalizing ys with
-  | nil => simp; rfl
+  | nil => simp
  | cons x xs ih =>
    cases ys with
    | nil => simp
--- a/src/Init/Prelude.lean
+++ b/src/Init/Prelude.lean
@@ -740,7 +740,7 @@ prove `p` given any element `x : α`, then `p` holds. Note that it is essential
 that `p` is a `Prop` here; the version with `p` being a `Sort u` is equivalent
 to `Classical.choice`.
 -/
-protected def Nonempty.elim {α : Sort u} {p : Prop} (h₁ : Nonempty α) (h₂ : α → p) : p :=
+protected theorem Nonempty.elim {α : Sort u} {p : Prop} (h₁ : Nonempty α) (h₂ : α → p) : p :=
  match h₁ with
  | intro a => h₂ a

@@ -914,6 +914,9 @@ is `Bool` valued instead of `Prop` valued, and it also does not have any
 axioms like being reflexive or agreeing with `=`. It is mainly intended for
 programming applications. See `LawfulBEq` for a version that requires that
 `==` and `=` coincide.
+
+Typically we prefer to put the "more variable" term on the left,
+and the "more constant" term on the right.
 -/
 class BEq (α : Type u) where
  /-- Boolean equality, notated as `a == b`. -/
@@ -1068,11 +1071,15 @@ This type is special-cased by both the kernel and the compiler:
  library (usually [GMP](https://gmplib.org/)).
 -/
 inductive Nat where
-  /-- `Nat.zero`, normally written `0 : Nat`, is the smallest natural number.
-  This is one of the two constructors of `Nat`. -/
+  /-- `Nat.zero`, is the smallest natural number. This is one of the two
+  constructors of `Nat`. Using `Nat.zero` should usually be avoided in favor of
+  `0 : Nat` or simply `0`, in order to remain compatible with the simp normal
+  form defined by `Nat.zero_eq`. -/
  | zero : Nat
  /-- The successor function on natural numbers, `succ n = n + 1`.
-  This is one of the two constructors of `Nat`. -/
+  This is one of the two constructors of `Nat`. Using `succ n` should usually
+  be avoided in favor of `n + 1`, in order to remain compatible with the simp
+  normal form defined by `Nat.succ_eq_add_one`. -/
  | succ (n : Nat) : Nat

 instance : Inhabited Nat where
@@ -2196,15 +2203,11 @@ instance : DecidableEq Char :=
    | isFalse h => isFalse (Char.ne_of_val_ne h)

 /-- Returns the number of bytes required to encode this `Char` in UTF-8. -/
-def Char.utf8Size (c : Char) : UInt32 :=
+def Char.utf8Size (c : Char) : Nat :=
  let v := c.val
-  ite (LE.le v (UInt32.ofNatCore 0x7F (by decide)))
-    (UInt32.ofNatCore 1 (by decide))
-    (ite (LE.le v (UInt32.ofNatCore 0x7FF (by decide)))
-      (UInt32.ofNatCore 2 (by decide))
-      (ite (LE.le v (UInt32.ofNatCore 0xFFFF (by decide)))
-        (UInt32.ofNatCore 3 (by decide))
-        (UInt32.ofNatCore 4 (by decide))))
+  ite (LE.le v (UInt32.ofNatCore 0x7F (by decide))) 1
+    (ite (LE.le v (UInt32.ofNatCore 0x7FF (by decide))) 2
+      (ite (LE.le v (UInt32.ofNatCore 0xFFFF (by decide))) 3 4))

 /--
 `Option α` is the type of values which are either `some a` for some `a : α`,
@@ -2303,24 +2306,6 @@ protected def List.hasDecEq {α : Type u} [DecidableEq α] : (a b : List α) →

 instance {α : Type u} [DecidableEq α] : DecidableEq (List α) := List.hasDecEq

-/--
-Folds a function over a list from the left:
-`foldl f z [a, b, c] = f (f (f z a) b) c`
-/
-@[specialize]
-def List.foldl {α : Type u} {β : Type v} (f : α → β → α) : (init : α) → List β → α
-  | a, nil      => a
-  | a, cons b l => foldl f (f a b) l
-
-/--
-`l.set n a` sets the value of list `l` at (zero-based) index `n` to `a`:
-`[a, b, c, d].set 1 b' = [a, b', c, d]`
-/
-def List.set : List α → Nat → α → List α
-  | cons _ as, 0,          b => cons b as
-  | cons a as, Nat.succ n, b => cons a (set as n b)
-  | nil,       _,          _ => nil
-
 /--
 The length of a list: `[].length = 0` and `(a :: l).length = l.length + 1`.

@@ -2344,14 +2329,6 @@ without running out of stack space.
 def List.lengthTR (as : List α) : Nat :=
  lengthTRAux as 0

-@[simp] theorem List.length_cons {α} (a : α) (as : List α) : Eq (cons a as).length as.length.succ :=
-  rfl
-
-/-- `l.concat a` appends `a` at the *end* of `l`, that is, `l ++ [a]`. -/
-def List.concat {α : Type u} : List α → α → List α
-  | nil,       b => cons b nil
-  | cons a as, b => cons a (concat as b)
-
 /--
 `as.get i` returns the `i`'th element of the list `as`.
 This version of the function uses `i : Fin as.length` to ensure that it will
@@ -2361,6 +2338,29 @@ def List.get {α : Type u} : (as : List α) → Fin as.length → α
  | cons a _,  ⟨0, _⟩ => a
  | cons _ as, ⟨Nat.succ i, h⟩ => get as ⟨i, Nat.le_of_succ_le_succ h⟩

+/--
+`l.set n a` sets the value of list `l` at (zero-based) index `n` to `a`:
+`[a, b, c, d].set 1 b' = [a, b', c, d]`
+-/
+def List.set : List α → Nat → α → List α
+  | cons _ as, 0,          b => cons b as
+  | cons a as, Nat.succ n, b => cons a (set as n b)
+  | nil,       _,          _ => nil
+
+/--
+Folds a function over a list from the left:
+`foldl f z [a, b, c] = f (f (f z a) b) c`
+-/
+@[specialize]
+def List.foldl {α : Type u} {β : Type v} (f : α → β → α) : (init : α) → List β → α
+  | a, nil      => a
+  | a, cons b l => foldl f (f a b) l
+
+/-- `l.concat a` appends `a` at the *end* of `l`, that is, `l ++ [a]`. -/
+def List.concat {α : Type u} : List α → α → List α
+  | nil,       b => cons b nil
+  | cons a as, b => cons a (concat as b)
+
 /--
 `String` is the type of (UTF-8 encoded) strings.

@@ -2433,10 +2433,6 @@ instance : Inhabited Substring where
@[inline] def Substring.bsize : Substring → Nat
  | ⟨_, b, e⟩ => e.byteIdx.sub b.byteIdx

-/-- Returns the number of bytes required to encode this `Char` in UTF-8. -/
-def String.csize (c : Char) : Nat :=
-  c.utf8Size.toNat
-
 /--
 The UTF-8 byte length of this string.
 This is overridden by the compiler to be cached and O(1).
@@ -2447,7 +2443,7 @@ def String.utf8ByteSize : (@& String) → Nat
 where
  go : List Char → Nat
   | .nil       => 0
-   | .cons c cs => hAdd (go cs) (csize c)
+   | .cons c cs => hAdd (go cs) c.utf8Size

 instance : HAdd String.Pos String.Pos String.Pos where
  hAdd p₁ p₂ := { byteIdx := hAdd p₁.byteIdx p₂.byteIdx }
@@ -2456,7 +2452,7 @@ instance : HSub String.Pos String.Pos String.Pos where
  hSub p₁ p₂ := { byteIdx := HSub.hSub p₁.byteIdx p₂.byteIdx }

 instance : HAdd String.Pos Char String.Pos where
-  hAdd p c := { byteIdx := hAdd p.byteIdx (String.csize c) }
+  hAdd p c := { byteIdx := hAdd p.byteIdx c.utf8Size }

 instance : HAdd String.Pos String String.Pos where
  hAdd p s := { byteIdx := hAdd p.byteIdx s.utf8ByteSize }
@@ -2977,7 +2973,7 @@ def MonadExcept.ofExcept [Monad m] [MonadExcept ε m] : Except ε α → m α

 export MonadExcept (throw tryCatch ofExcept)

-instance (ε : outParam (Type u)) (m : Type v → Type w) [MonadExceptOf ε m] : MonadExcept ε m where
+instance (ε : Type u) (m : Type v → Type w) [MonadExceptOf ε m] : MonadExcept ε m where
  throw    := throwThe ε
  tryCatch := tryCatchThe ε

@@ -3151,7 +3147,7 @@ instance (ρ : Type u) (m : Type u → Type v) [MonadWithReaderOf ρ m] : MonadW
 instance {ρ : Type u} {m : Type u → Type v} {n : Type u → Type v} [MonadFunctor m n] [MonadWithReaderOf ρ m] : MonadWithReaderOf ρ n where
  withReader f := monadMap (m := m) (withTheReader ρ f)

-instance {ρ : Type u} {m : Type u → Type v} [Monad m] : MonadWithReaderOf ρ (ReaderT ρ m) where
+instance {ρ : Type u} {m : Type u → Type v} : MonadWithReaderOf ρ (ReaderT ρ m) where
  withReader f x := fun ctx => x (f ctx)

 /--
@@ -3234,7 +3230,7 @@ def modify {σ : Type u} {m : Type u → Type v} [MonadState σ m] (f : σ →
 of the state. It is equivalent to `get <* modify f` but may be more efficient.
 -/
@[always_inline, inline]
-def getModify {σ : Type u} {m : Type u → Type v} [MonadState σ m] [Monad m] (f : σ → σ) : m σ :=
+def getModify {σ : Type u} {m : Type u → Type v} [MonadState σ m] (f : σ → σ) : m σ :=
  modifyGet fun s => (s, f s)

 -- NOTE: The Ordering of the following two instances determines that the top-most `StateT` Monad layer
--- a/src/Init/System/IO.lean
+++ b/src/Init/System/IO.lean
@@ -253,12 +253,9 @@ instance : ToString TaskState := ⟨TaskState.toString⟩
@[extern "lean_io_wait"] opaque wait (t : Task α) : BaseIO α :=
  return t.get

-local macro "nonempty_list" : tactic =>
-  `(tactic| exact Nat.zero_lt_succ _)
-
 /-- Wait until any of the tasks in the given list has finished, then return its result. -/
@[extern "lean_io_wait_any"] opaque waitAny (tasks : @& List (Task α))
-    (h : tasks.length > 0 := by nonempty_list) : BaseIO α :=
+    (h : tasks.length > 0 := by exact Nat.zero_lt_succ _) : BaseIO α :=
  return tasks[0].get

 /-- Helper method for implementing "deterministic" timeouts. It is the number of "small" memory allocations performed by the current execution thread. -/
--- a/src/Init/Tactics.lean
+++ b/src/Init/Tactics.lean
@@ -267,7 +267,9 @@ syntax (name := case') "case' " sepBy1(caseArg, " | ") " => " tacticSeq : tactic
 `next x₁ ... xₙ => tac` additionally renames the `n` most recent hypotheses with
 inaccessible names to the given names.
 -/
-macro "next " args:binderIdent* " => " tac:tacticSeq : tactic => `(tactic| case _ $args* => $tac)
+macro "next " args:binderIdent* arrowTk:" => " tac:tacticSeq : tactic =>
+  -- Limit ref variability for incrementality; see Note [Incremental Macros]
+  withRef arrowTk `(tactic| case _ $args* =>%$arrowTk $tac)

 /-- `all_goals tac` runs `tac` on each goal, concatenating the resulting goals, if any. -/
 syntax (name := allGoals) "all_goals " tacticSeq : tactic
@@ -371,7 +373,8 @@ reflexivity theorems (e.g., `Iff.rfl`).
 macro "rfl" : tactic => `(tactic| case' _ => fail "The rfl tactic failed. Possible reasons:
 - The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma).
 - The arguments of the relation are not equal.
-Try using the reflexivitiy lemma for your relation explicitly, e.g. `exact Eq.rfl`.")
+Try using the reflexivity lemma for your relation explicitly, e.g. `exact Eq.refl _` or
+`exact HEq.rfl` etc.")

 macro_rules | `(tactic| rfl) => `(tactic| eq_refl)
 macro_rules | `(tactic| rfl) => `(tactic| exact HEq.rfl)
@@ -699,7 +702,37 @@ The `have` tactic is for adding hypotheses to the local context of the main goal
  For example, given `h : p ∧ q ∧ r`, `have ⟨h₁, h₂, h₃⟩ := h` produces the
  hypotheses `h₁ : p`, `h₂ : q`, and `h₃ : r`.
 -/
-macro "have " d:haveDecl : tactic => `(tactic| refine_lift have $d:haveDecl; ?_)
+syntax "have " haveDecl : tactic
+macro_rules
+  -- special case: when given a nested `by` block, move it outside of the `refine` to enable
+  -- incrementality
+  | `(tactic| have%$haveTk $id:haveId $bs* : $type := by%$byTk $tacs*) => do
+    /-
+    We want to create the syntax
+    ```
+    focus
+      refine no_implicit_lambda% (have $id:haveId $bs* : $type := ?body; ?_)
+      case body => $tacs*
+    ```
+    However, we need to be very careful with the syntax infos involved:
+    * We want most infos up to `tacs` to be independent of changes inside it so that incrementality
+      is not prematurely disabled; we use the `have` and then the `by` token as the reference for
+      this. Note that if we did nothing, the reference would be the entire `have` input and so any
+      change to `tacs` would change every token synthesized below.
+    * For the single node of the `case` body, we *should not* change the ref as this makes sure the
+      entire tactic block is included in any "unsaved goals" message (which is emitted after
+      execution of all nested tactics so it is indeed safe for `evalCase` to ignore it for
+      incrementality).
+    * Even after setting the ref, we still need a `with_annotate_state` to show the correct tactic
+      state on `by` as the synthetic info derived from the ref is ignored for this purpose.
+    -/
+    let tac ← Lean.withRef byTk `(tactic| with_annotate_state $byTk ($tacs*))
+    let tac ← `(tacticSeq| $tac:tactic)
+    let tac ← Lean.withRef byTk `(tactic| case body => $(.mk tac):tacticSeq)
+    Lean.withRef haveTk `(tactic| focus
+      refine no_implicit_lambda% (have $id:haveId $bs* : $type := ?body; ?_)
+      $tac)
+  | `(tactic| have $d:haveDecl) => `(tactic| refine_lift have $d:haveDecl; ?_)

 /--
 Given a main goal `ctx ⊢ t`, `suffices h : t' from e` replaces the main goal with `ctx ⊢ t'`,
@@ -833,14 +866,41 @@ syntax (name := cases) "cases " casesTarget,+ (" using " term)? (inductionAlts)?
 syntax (name := renameI) "rename_i" (ppSpace colGt binderIdent)+ : tactic

 /--
-`repeat tac` repeatedly applies `tac` to the main goal until it fails.
-That is, if `tac` produces multiple subgoals, only subgoals up to the first failure will be visited.
-The `Batteries` library provides `repeat'` which repeats separately in each subgoal.
+`repeat tac` repeatedly applies `tac` so long as it succeeds.
+The tactic `tac` may be a tactic sequence, and if `tac` fails at any point in its execution,
+`repeat` will revert any partial changes that `tac` made to the tactic state.
+
+The tactic `tac` should eventually fail, otherwise `repeat tac` will run indefinitely.
+
+See also:
+* `try tac` is like `repeat tac` but will apply `tac` at most once.
+* `repeat' tac` recursively applies `tac` to each goal.
+* `first | tac1 | tac2` implements the backtracking used by `repeat`
 -/
 syntax "repeat " tacticSeq : tactic
 macro_rules
  | `(tactic| repeat $seq) => `(tactic| first | ($seq); repeat $seq | skip)

+/--
+`repeat' tac` recursively applies `tac` on all of the goals so long as it succeeds.
+That is to say, if `tac` produces multiple subgoals, then `repeat' tac` is applied to each of them.
+
+See also:
+* `repeat tac` simply repeatedly applies `tac`.
+* `repeat1' tac` is `repeat' tac` but requires that `tac` succeed for some goal at least once.
+-/
+syntax (name := repeat') "repeat' " tacticSeq : tactic
+
+/--
+`repeat1' tac` recursively applies to `tac` on all of the goals so long as it succeeds,
+but `repeat1' tac` fails if `tac` succeeds on none of the initial goals.
+
+See also:
+* `repeat tac` simply applies `tac` repeatedly.
+* `repeat' tac` is like `repeat1' tac` but it does not require that `tac` succeed at least once.
+-/
+syntax (name := repeat1') "repeat1' " tacticSeq : tactic
+
 /--
 `trivial` tries different simple tactics (e.g., `rfl`, `contradiction`, ...)
 to close the current goal.
@@ -1041,18 +1101,6 @@ This can be used to simulate the `specialize` and `apply at` tactics of Coq.
 -/
 syntax (name := replace) "replace" haveDecl : tactic

-/--
-`repeat' tac` runs `tac` on all of the goals to produce a new list of goals,
-then runs `tac` again on all of those goals, and repeats until `tac` fails on all remaining goals.
-/
-syntax (name := repeat') "repeat' " tacticSeq : tactic
-
-/--
-`repeat1' tac` applies `tac` to main goal at least once. If the application succeeds,
-the tactic is applied recursively to the generated subgoals until it eventually fails.
-/
-syntax (name := repeat1') "repeat1' " tacticSeq : tactic
-
 /-- `and_intros` applies `And.intro` until it does not make progress. -/
 syntax "and_intros" : tactic
 macro_rules | `(tactic| and_intros) => `(tactic| repeat' refine And.intro ?_ ?_)
@@ -1414,6 +1462,7 @@ have been simplified by using the modifier `↓`. Here is an example
 ```

 When multiple simp theorems are applicable, the simplifier uses the one with highest priority.
+The equational theorems of function are applied at very low priority (100 and below).
 If there are several with the same priority, it is uses the "most recent one". Example:
 ```lean
@[simp high] theorem cond_true (a b : α) : cond true a b = a := rfl
--- a/src/Init/TacticsExtra.lean
+++ b/src/Init/TacticsExtra.lean
@@ -31,15 +31,19 @@ private def expandIfThenElse
      pure (hole, #[case])
  let (posHole, posCase) ← mkCase thenTk pos `(?pos)
  let (negHole, negCase) ← mkCase elseTk neg `(?neg)
-  `(tactic| (open Classical in refine%$ifTk $(← mkIf posHole negHole); $[$(posCase ++ negCase)]*))
+  `(tactic| ((open Classical in refine%$ifTk $(← mkIf posHole negHole)); $[$(posCase ++ negCase)]*))

 macro_rules
  | `(tactic| if%$tk $h : $c then%$ttk $pos else%$etk $neg) =>
-    expandIfThenElse tk ttk etk pos neg fun pos neg => `(if $h : $c then $pos else $neg)
+    -- Limit ref variability for incrementality; see Note [Incremental Macros]
+    withRef tk do
+      expandIfThenElse tk ttk etk pos neg fun pos neg => `(if $h : $c then $pos else $neg)

 macro_rules
  | `(tactic| if%$tk $c then%$ttk $pos else%$etk $neg) =>
-    expandIfThenElse tk ttk etk pos neg fun pos neg => `(if h : $c then $pos else $neg)
+    -- Limit ref variability for incrementality; see Note [Incremental Macros]
+    withRef tk do
+      expandIfThenElse tk ttk etk pos neg fun pos neg => `(if h : $c then $pos else $neg)

 /--
 `iterate n tac` runs `tac` exactly `n` times.
--- a/src/Init/WF.lean
+++ b/src/Init/WF.lean
@@ -37,7 +37,7 @@ noncomputable abbrev Acc.ndrecOn.{u1, u2} {α : Sort u2} {r : α → α → Prop
 namespace Acc
 variable {α : Sort u} {r : α → α → Prop}

-def inv {x y : α} (h₁ : Acc r x) (h₂ : r y x) : Acc r y :=
+theorem inv {x y : α} (h₁ : Acc r x) (h₂ : r y x) : Acc r y :=
  h₁.recOn (fun _ ac₁ _ h₂ => ac₁ y h₂) h₂

 end Acc
@@ -58,7 +58,7 @@ class WellFoundedRelation (α : Sort u) where
  wf  : WellFounded rel

 namespace WellFounded
-def apply {α : Sort u} {r : α → α → Prop} (wf : WellFounded r) (a : α) : Acc r a :=
+theorem apply {α : Sort u} {r : α → α → Prop} (wf : WellFounded r) (a : α) : Acc r a :=
  wf.rec (fun p => p) a

 section
@@ -78,7 +78,7 @@ noncomputable def fixF (x : α) (a : Acc r x) : C x := by
  induction a with
  | intro x₁ _ ih => exact F x₁ ih

-def fixFEq (x : α) (acx : Acc r x) : fixF F x acx = F x (fun (y : α) (p : r y x) => fixF F y (Acc.inv acx p)) := by
+theorem fixFEq (x : α) (acx : Acc r x) : fixF F x acx = F x (fun (y : α) (p : r y x) => fixF F y (Acc.inv acx p)) := by
  induction acx with
  | intro x r _ => exact rfl

@@ -112,14 +112,14 @@ def emptyWf {α : Sort u} : WellFoundedRelation α where
 namespace Subrelation
 variable {α : Sort u} {r q : α → α → Prop}

-def accessible {a : α} (h₁ : Subrelation q r) (ac : Acc r a) : Acc q a := by
+theorem accessible {a : α} (h₁ : Subrelation q r) (ac : Acc r a) : Acc q a := by
  induction ac with
  | intro x _ ih =>
    apply Acc.intro
    intro y h
    exact ih y (h₁ h)

-def wf (h₁ : Subrelation q r) (h₂ : WellFounded r) : WellFounded q :=
+theorem wf (h₁ : Subrelation q r) (h₂ : WellFounded r) : WellFounded q :=
  ⟨fun a => accessible @h₁ (apply h₂ a)⟩
 end Subrelation

@@ -136,10 +136,10 @@ private def accAux (f : α → β) {b : β} (ac : Acc r b) : (x : α) → f x =
    subst x
    apply ih (f y) lt y rfl

-def accessible {a : α} (f : α → β) (ac : Acc r (f a)) : Acc (InvImage r f) a :=
+theorem accessible {a : α} (f : α → β) (ac : Acc r (f a)) : Acc (InvImage r f) a :=
  accAux f ac a rfl

-def wf (f : α → β) (h : WellFounded r) : WellFounded (InvImage r f) :=
+theorem wf (f : α → β) (h : WellFounded r) : WellFounded (InvImage r f) :=
  ⟨fun a => accessible f (apply h (f a))⟩
 end InvImage

@@ -151,7 +151,7 @@ end InvImage
 namespace TC
 variable {α : Sort u} {r : α → α → Prop}

-def accessible {z : α} (ac : Acc r z) : Acc (TC r) z := by
+theorem accessible {z : α} (ac : Acc r z) : Acc (TC r) z := by
  induction ac with
  | intro x acx ih =>
    apply Acc.intro x
@@ -160,7 +160,7 @@ def accessible {z : α} (ac : Acc r z) : Acc (TC r) z := by
    | base a b rab => exact ih a rab
    | trans a b c rab _ _ ih₂ => apply Acc.inv (ih₂ acx ih) rab

-def wf (h : WellFounded r) : WellFounded (TC r) :=
+theorem wf (h : WellFounded r) : WellFounded (TC r) :=
  ⟨fun a => accessible (apply h a)⟩
 end TC

@@ -251,7 +251,7 @@ instance [αeqDec : DecidableEq α] {r : α → α → Prop} [rDec : DecidableRe
        apply isFalse; intro contra; cases contra <;> contradiction

 -- TODO: generalize
-def right' {a₁ : Nat} {b₁ : β} (h₁ : a₁ ≤ a₂) (h₂ : rb b₁ b₂) : Prod.Lex Nat.lt rb (a₁, b₁) (a₂, b₂) :=
+theorem right' {a₁ : Nat} {b₁ : β} (h₁ : a₁ ≤ a₂) (h₂ : rb b₁ b₂) : Prod.Lex Nat.lt rb (a₁, b₁) (a₂, b₂) :=
  match Nat.eq_or_lt_of_le h₁ with
  | Or.inl h => h ▸ Prod.Lex.right a₁ h₂
  | Or.inr h => Prod.Lex.left b₁ _ h
@@ -268,7 +268,7 @@ section
 variable {α : Type u} {β : Type v}
 variable {ra  : α → α → Prop} {rb  : β → β → Prop}

-def lexAccessible {a : α} (aca : Acc ra a) (acb : (b : β) → Acc rb b) (b : β) : Acc (Prod.Lex ra rb) (a, b) := by
+theorem lexAccessible {a : α} (aca : Acc ra a) (acb : (b : β) → Acc rb b) (b : β) : Acc (Prod.Lex ra rb) (a, b) := by
  induction aca generalizing b with
  | intro xa _ iha =>
    induction (acb b) with
@@ -347,7 +347,7 @@ variable {α : Sort u} {β : Sort v}
 def lexNdep (r : α → α → Prop) (s : β → β → Prop) :=
  Lex r (fun _ => s)

-def lexNdepWf {r  : α → α → Prop} {s : β → β → Prop} (ha : WellFounded r) (hb : WellFounded s) : WellFounded (lexNdep r s) :=
+theorem lexNdepWf {r  : α → α → Prop} {s : β → β → Prop} (ha : WellFounded r) (hb : WellFounded s) : WellFounded (lexNdep r s) :=
  WellFounded.intro fun ⟨a, b⟩ => lexAccessible (WellFounded.apply ha a) (fun _ => hb) b
 end

@@ -365,7 +365,7 @@ open WellFounded
 variable {α : Sort u} {β : Sort v}
 variable {r  : α → α → Prop} {s : β → β → Prop}

-def revLexAccessible {b} (acb : Acc s b) (aca : (a : α) → Acc r a): (a : α) → Acc (RevLex r s) ⟨a, b⟩ := by
+theorem revLexAccessible {b} (acb : Acc s b) (aca : (a : α) → Acc r a): (a : α) → Acc (RevLex r s) ⟨a, b⟩ := by
  induction acb with
  | intro xb _ ihb =>
    intro a
@@ -377,7 +377,7 @@ def revLexAccessible {b} (acb : Acc s b) (aca : (a : α) → Acc r a): (a : α)
      | left  => apply iha; assumption
      | right => apply ihb; assumption

-def revLex (ha : WellFounded r) (hb : WellFounded s) : WellFounded (RevLex r s) :=
+theorem revLex (ha : WellFounded r) (hb : WellFounded s) : WellFounded (RevLex r s) :=
  WellFounded.intro fun ⟨a, b⟩ => revLexAccessible (apply hb b) (WellFounded.apply ha) a
 end

@@ -389,7 +389,7 @@ def skipLeft (α : Type u) {β : Type v} (hb : WellFoundedRelation β) : WellFou
  rel := SkipLeft α hb.rel
  wf  := revLex emptyWf.wf hb.wf

-def mkSkipLeft {α : Type u} {β : Type v} {b₁ b₂ : β} {s : β → β → Prop} (a₁ a₂ : α) (h : s b₁ b₂) : SkipLeft α s ⟨a₁, b₁⟩ ⟨a₂, b₂⟩ :=
+theorem mkSkipLeft {α : Type u} {β : Type v} {b₁ b₂ : β} {s : β → β → Prop} (a₁ a₂ : α) (h : s b₁ b₂) : SkipLeft α s ⟨a₁, b₁⟩ ⟨a₂, b₂⟩ :=
  RevLex.right _ _ h
 end

--- a/src/Init/WFTactics.lean
+++ b/src/Init/WFTactics.lean
@@ -32,7 +32,7 @@ before `omega` is available.
 -/
 syntax "decreasing_trivial_pre_omega" : tactic
 macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.sub_succ_lt_self; assumption) -- a - (i+1) < a - i if i < a
-macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt'; assumption) -- i-1 < i if j < i
+macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt_of_lt; assumption) -- i-1 < i if j < i
 macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt; assumption)  -- i-1 < i if i ≠ 0


--- a/src/Lean/Attributes.lean
+++ b/src/Lean/Attributes.lean
@@ -53,7 +53,7 @@ structure AttributeImpl extends AttributeImplCore where
  erase (decl : Name) : AttrM Unit := throwError "attribute cannot be erased"
  deriving Inhabited

-builtin_initialize attributeMapRef : IO.Ref (PersistentHashMap Name AttributeImpl) ← IO.mkRef {}
+builtin_initialize attributeMapRef : IO.Ref (HashMap Name AttributeImpl) ← IO.mkRef {}

 /-- Low level attribute registration function. -/
 def registerBuiltinAttribute (attr : AttributeImpl) : IO Unit := do
@@ -185,7 +185,7 @@ structure ParametricAttributeImpl (α : Type) extends AttributeImplCore where
  afterSet : Name → α → AttrM Unit := fun _ _ _ => pure ()
  afterImport : Array (Array (Name × α)) → ImportM Unit := fun _ => pure ()

-def registerParametricAttribute [Inhabited α] (impl : ParametricAttributeImpl α) : IO (ParametricAttribute α) := do
+def registerParametricAttribute (impl : ParametricAttributeImpl α) : IO (ParametricAttribute α) := do
  let ext : PersistentEnvExtension (Name × α) (Name × α) (NameMap α) ← registerPersistentEnvExtension {
    name            := impl.ref
    mkInitial       := pure {}
@@ -239,7 +239,7 @@ structure EnumAttributes (α : Type) where
  ext   : PersistentEnvExtension (Name × α) (Name × α) (NameMap α)
  deriving Inhabited

-def registerEnumAttributes [Inhabited α] (attrDescrs : List (Name × String × α))
+def registerEnumAttributes (attrDescrs : List (Name × String × α))
    (validate : Name → α → AttrM Unit := fun _ _ => pure ())
    (applicationTime := AttributeApplicationTime.afterTypeChecking)
    (ref : Name := by exact decl_name%) : IO (EnumAttributes α) := do
@@ -317,7 +317,7 @@ inductive AttributeExtensionOLeanEntry where

 structure AttributeExtensionState where
  newEntries : List AttributeExtensionOLeanEntry := []
-  map        : PersistentHashMap Name AttributeImpl
+  map        : HashMap Name AttributeImpl
  deriving Inhabited

 abbrev AttributeExtension := PersistentEnvExtension AttributeExtensionOLeanEntry (AttributeExtensionOLeanEntry × AttributeImpl) AttributeExtensionState
@@ -348,7 +348,7 @@ private def AttributeExtension.addImported (es : Array (Array AttributeExtension
  let map ← es.foldlM
    (fun map entries =>
      entries.foldlM
-        (fun (map : PersistentHashMap Name AttributeImpl) entry => do
+        (fun (map : HashMap Name AttributeImpl) entry => do
          let attrImpl ← mkAttributeImplOfEntry ctx.env ctx.opts entry
          return map.insert attrImpl.name attrImpl)
        map)
@@ -374,7 +374,7 @@ def isBuiltinAttribute (n : Name) : IO Bool := do

 /-- Return the name of all registered attributes. -/
 def getBuiltinAttributeNames : IO (List Name) :=
-  return (← attributeMapRef.get).foldl (init := []) fun r n _ => n::r
+  return (← attributeMapRef.get).fold (init := []) fun r n _ => n::r

 def getBuiltinAttributeImpl (attrName : Name) : IO AttributeImpl := do
  let m ← attributeMapRef.get
@@ -392,7 +392,7 @@ def isAttribute (env : Environment) (attrName : Name) : Bool :=

 def getAttributeNames (env : Environment) : List Name :=
  let m := (attributeExtension.getState env).map
-  m.foldl (fun r n _ => n::r) []
+  m.fold (fun r n _ => n::r) []

 def getAttributeImpl (env : Environment) (attrName : Name) : Except String AttributeImpl :=
  let m := (attributeExtension.getState env).map
@@ -427,7 +427,7 @@ def Attribute.erase (declName : Name) (attrName : Name) : AttrM Unit := do
 def updateEnvAttributesImpl (env : Environment) : IO Environment := do
  let map ← attributeMapRef.get
  let s := attributeExtension.getState env
-  let s := map.foldl (init := s) fun s attrName attrImpl =>
+  let s := map.fold (init := s) fun s attrName attrImpl =>
    if s.map.contains attrName then
      s
    else
--- a/src/Lean/AuxRecursor.lean
+++ b/src/Lean/AuxRecursor.lean
@@ -13,16 +13,17 @@ def recOnSuffix         := "recOn"
 def brecOnSuffix        := "brecOn"
 def binductionOnSuffix  := "binductionOn"
 def belowSuffix         := "below"
+def ibelowSuffix        := "ibelow"

 def mkCasesOnName (indDeclName : Name) : Name := Name.mkStr indDeclName casesOnSuffix
 def mkRecOnName (indDeclName : Name) : Name   := Name.mkStr indDeclName recOnSuffix
 def mkBRecOnName (indDeclName : Name) : Name  := Name.mkStr indDeclName brecOnSuffix
 def mkBInductionOnName (indDeclName : Name) : Name  := Name.mkStr indDeclName binductionOnSuffix
 def mkBelowName (indDeclName : Name) : Name := Name.mkStr indDeclName belowSuffix
+def mkIBelowName (indDeclName : Name) : Name := Name.mkStr indDeclName ibelowSuffix

 builtin_initialize auxRecExt : TagDeclarationExtension ← mkTagDeclarationExtension

-@[export lean_mark_aux_recursor]
 def markAuxRecursor (env : Environment) (declName : Name) : Environment :=
  auxRecExt.tag env declName

@@ -50,7 +51,6 @@ def isBRecOnRecursor (env : Environment) (declName : Name) : Bool :=

 builtin_initialize noConfusionExt : TagDeclarationExtension ← mkTagDeclarationExtension

-@[export lean_mark_no_confusion]
 def markNoConfusion (env : Environment) (n : Name) : Environment :=
  noConfusionExt.tag env n

--- a/src/Lean/BuiltinDocAttr.lean
+++ b/src/Lean/BuiltinDocAttr.lean
@@ -5,12 +5,12 @@ Authors: Mario Carneiro
 -/
 prelude
 import Lean.Compiler.InitAttr
-import Lean.DocString
+import Lean.DocString.Extension

 namespace Lean

 def declareBuiltinDocStringAndRanges (declName : Name) : AttrM Unit := do
-  if let some doc ← findDocString? (← getEnv) declName (includeBuiltin := false) then
+  if let some doc ← findSimpleDocString? (← getEnv) declName (includeBuiltin := false) then
    declareBuiltin (declName ++ `docString) (mkAppN (mkConst ``addBuiltinDocString) #[toExpr declName, toExpr doc])
  if let some declRanges ← findDeclarationRanges? declName then
    declareBuiltin (declName ++ `declRange) (mkAppN (mkConst ``addBuiltinDeclarationRanges) #[toExpr declName, toExpr declRanges])
--- a/src/Lean/Compiler/FFI.lean
+++ b/src/Lean/Compiler/FFI.lean
@@ -18,6 +18,13 @@ private opaque getLeancExtraFlags : Unit → String
 def getCFlags (leanSysroot : FilePath) : Array String :=
  #["-I", (leanSysroot / "include").toString] ++ (getLeancExtraFlags ()).trim.splitOn

+@[extern "lean_get_leanc_internal_flags"]
+private opaque getLeancInternalFlags : Unit → String
+
+/-- Return C compiler flags needed to use the C compiler bundled with the Lean toolchain. -/
+def getInternalCFlags (leanSysroot : FilePath) : Array String :=
+  (getLeancInternalFlags ()).trim.splitOn.toArray.map (·.replace "ROOT" leanSysroot.toString)
+
@[extern "lean_get_linker_flags"]
 private opaque getBuiltinLinkerFlags (linkStatic : Bool) : String

@@ -25,4 +32,11 @@ private opaque getBuiltinLinkerFlags (linkStatic : Bool) : String
 def getLinkerFlags (leanSysroot : FilePath) (linkStatic := true) : Array String :=
  #["-L", (leanSysroot / "lib" / "lean").toString] ++ (getBuiltinLinkerFlags linkStatic).trim.splitOn

+@[extern "lean_get_internal_linker_flags"]
+private opaque getBuiltinInternalLinkerFlags : Unit → String
+
+/-- Return linker flags needed to use the linker bundled with the Lean toolchain. -/
+def getInternalLinkerFlags (leanSysroot : FilePath) : Array String :=
+  (getBuiltinInternalLinkerFlags ()).trim.splitOn.toArray.map (·.replace "ROOT" leanSysroot.toString)
+
 end Lean.Compiler.FFI
--- a/src/Lean/Compiler/IR/Basic.lean
+++ b/src/Lean/Compiler/IR/Basic.lean
@@ -24,12 +24,12 @@ abbrev Index := Nat
 /-- Variable identifier -/
 structure VarId where
  idx : Index
-  deriving Inhabited
+  deriving Inhabited, Repr

 /-- Join point identifier -/
 structure JoinPointId where
  idx : Index
-  deriving Inhabited
+  deriving Inhabited, Repr

 abbrev Index.lt (a b : Index) : Bool := a < b

@@ -83,7 +83,7 @@ inductive IRType where
  | irrelevant | object | tobject
  | struct (leanTypeName : Option Name) (types : Array IRType) : IRType
  | union (leanTypeName : Name) (types : Array IRType) : IRType
-  deriving Inhabited
+  deriving Inhabited, Repr

 namespace IRType

@@ -236,7 +236,7 @@ structure Param where
  x : VarId
  borrow : Bool
  ty : IRType
-  deriving Inhabited
+  deriving Inhabited, Repr

@[export lean_ir_mk_param]
 def mkParam (x : VarId) (borrow : Bool) (ty : IRType) : Param := ⟨x, borrow, ty⟩
--- a/src/Lean/Compiler/IR/Borrow.lean
+++ b/src/Lean/Compiler/IR/Borrow.lean
@@ -258,7 +258,8 @@ def preserveTailCall (x : VarId) (v : Expr) (b : FnBody) : M Unit := do
  let ctx ← read
  match v, b with
  | (Expr.fap g ys), (FnBody.ret (Arg.var z)) =>
-    if ctx.decls.any (·.name == g) && x == z then
+    -- NOTE: we currently support TCO for self-calls only
+    if ctx.currFn == g && x == z then
      let ps ← getParamInfo (ParamMap.Key.decl g)
      ownParamsUsingArgs ys ps
  | _, _ => pure ()
--- a/src/Lean/Compiler/IR/EmitC.lean
+++ b/src/Lean/Compiler/IR/EmitC.lean
@@ -499,7 +499,11 @@ def emitLit (z : VarId) (t : IRType) (v : LitVal) : M Unit := do
  emitLhs z;
  match v with
  | LitVal.num v => emitNumLit t v; emitLn ";"
-  | LitVal.str v => emit "lean_mk_string_from_bytes("; emit (quoteString v); emit ", "; emit v.utf8ByteSize; emitLn ");"
+  | LitVal.str v =>
+    emit "lean_mk_string_unchecked(";
+    emit (quoteString v); emit ", ";
+    emit v.utf8ByteSize; emit ", ";
+    emit v.length; emitLn ");"

 def emitVDecl (z : VarId) (t : IRType) (v : Expr) : M Unit :=
  match v with
--- a/src/Lean/Compiler/IR/EmitLLVM.lean
+++ b/src/Lean/Compiler/IR/EmitLLVM.lean
@@ -178,14 +178,14 @@ def callLeanUnsignedToNatFn (builder : LLVM.Builder llvmctx)
  let nv ← constIntUnsigned n
  LLVM.buildCall2 builder fnty f #[nv] name

-def callLeanMkStringFromBytesFn (builder : LLVM.Builder llvmctx)
-    (strPtr nBytes : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do
-  let fnName :=  "lean_mk_string_from_bytes"
+def callLeanMkStringUncheckedFn (builder : LLVM.Builder llvmctx)
+    (strPtr nBytes nChars : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do
+  let fnName :=  "lean_mk_string_unchecked"
  let retty ← LLVM.voidPtrType llvmctx
-  let argtys :=  #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx]
+  let argtys :=  #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx, ← LLVM.size_tType llvmctx]
  let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys
  let fnty ← LLVM.functionType retty argtys
-  LLVM.buildCall2 builder fnty fn #[strPtr, nBytes] name
+  LLVM.buildCall2 builder fnty fn #[strPtr, nBytes, nChars] name

 def callLeanMkString (builder : LLVM.Builder llvmctx)
    (strPtr : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do
@@ -772,7 +772,8 @@ def emitLit (builder : LLVM.Builder llvmctx)
                                (← LLVM.opaquePointerTypeInContext llvmctx)
                                str_global #[zero] ""
                 let nbytes ← constIntSizeT v.utf8ByteSize
-                 callLeanMkStringFromBytesFn builder strPtr nbytes ""
+                 let nchars ← constIntSizeT v.length
+                 callLeanMkStringUncheckedFn builder strPtr nbytes nchars ""
  LLVM.buildStore builder zv zslot
  return zslot

--- a/src/Lean/CoreM.lean
+++ b/src/Lean/CoreM.lean
@@ -219,31 +219,31 @@ def saveState : CoreM SavedState := do
  return { toState := s, passedHearbeats := 0 }

 /--
-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`.
+Incremental reuse primitive: if `reusableResult?` is `none`, runs `act` and returns its result
+together with the saved monadic state after `act` including the heartbeats used by it. If
+`reusableResult?` on the other hand is `some (a, state)`, restores full `state` including heartbeats
+used and returns `(a, state)`.

 The intention is for steps that support incremental reuse to initially pass `none` as
-`reusableResult?` and 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
+`reusableResult?` and store the result and state in a snapshot. In a further run, if reuse is
+possible, `reusableResult?` should be set to the previous result and state, ensuring that the state
 after running `withRestoreOrSaveFull` is identical in both runs. Note however that necessarily this
-is only an approximation in the case of heartbeats as heartbeats used by `withRestoreOrSaveFull`, 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.
+is only an approximation in the case of heartbeats as heartbeats used by `withRestoreOrSaveFull`
+itself after calling `act` as well as by reuse-handling code such as the one supplying
+`reusableResult?` are not accounted for.
 -/
@[specialize] def withRestoreOrSaveFull (reusableResult? : Option (α × SavedState))
-    (cont : (save : CoreM SavedState) → CoreM α) : CoreM α := do
+    (act : CoreM α) : CoreM (α × SavedState) := do
  if let some (val, state) := reusableResult? then
    set state.toState
    IO.addHeartbeats state.passedHearbeats.toUInt64
-    return val
+    return (val, state)

  let startHeartbeats ← IO.getNumHeartbeats
-  cont (do
-    let s ← get
-    let stopHeartbeats ← IO.getNumHeartbeats
-    return { toState := s, passedHearbeats := stopHeartbeats - startHeartbeats })
+  let a ← act
+  let s ← get
+  let stopHeartbeats ← IO.getNumHeartbeats
+  return (a, { toState := s, passedHearbeats := stopHeartbeats - startHeartbeats })

 /-- Restore backtrackable parts of the state. -/
 def SavedState.restore (b : SavedState) : CoreM Unit :=
--- a/src/Lean/Data/HashMap.lean
+++ b/src/Lean/Data/HashMap.lean
@@ -15,6 +15,10 @@ def HashMapBucket.update {α : Type u} {β : Type v} (data : HashMapBucket α β
  ⟨ data.val.uset i d h,
    by erw [Array.size_set]; apply data.property ⟩

+@[simp] theorem HashMapBucket.size_update {α : Type u} {β : Type v} (data : HashMapBucket α β) (i : USize) (d : AssocList α β)
+    (h : i.toNat < data.val.size) : (data.update i d h).val.size = data.val.size := by
+  simp [update, Array.uset]
+
 structure HashMapImp (α : Type u) (β : Type v) where
  size       : Nat
  buckets    : HashMapBucket α β
@@ -108,7 +112,9 @@ def expand [Hashable α] (size : Nat) (buckets : HashMapBucket α β) : HashMapI
    let ⟨i, h⟩ := mkIdx (hash a) buckets.property
    let bkt    := buckets.val[i]
    if bkt.contains a then
-      (⟨size, buckets.update i (bkt.replace a b) h⟩, true)
+      -- make sure `bkt` is used linearly in the following call to `replace`
+      let buckets' := buckets.update i .nil h
+      (⟨size, buckets'.update i (bkt.replace a b) (by simpa [buckets'])⟩, true)
    else
      let size'    := size + 1
      let buckets' := buckets.update i (AssocList.cons a b bkt) h
@@ -139,7 +145,9 @@ def erase [BEq α] [Hashable α] (m : HashMapImp α β) (a : α) : HashMapImp α
    let ⟨i, h⟩ := mkIdx (hash a) buckets.property
    let bkt    := buckets.val[i]
    if bkt.contains a then
-      ⟨size - 1, buckets.update i (bkt.erase a) h⟩
+      -- make sure `bkt` is used linearly in the following call to `erase`
+      let buckets' := buckets.update i .nil h
+      ⟨size - 1, buckets'.update i (bkt.erase a) (by simpa [buckets'])⟩
    else
      ⟨size, buckets⟩

--- a/src/Lean/Data/HashSet.lean
+++ b/src/Lean/Data/HashSet.lean
@@ -16,6 +16,10 @@ def HashSetBucket.update {α : Type u} (data : HashSetBucket α) (i : USize) (d
  ⟨ data.val.uset i d h,
    by erw [Array.size_set]; apply data.property ⟩

+@[simp] theorem HashSetBucket.size_update {α : Type u} (data : HashSetBucket α) (i : USize) (d : List α) (h : i.toNat < data.val.size) :
+    (data.update i d h).val.size = data.val.size := by
+  simp [update, Array.uset]
+
 structure HashSetImp (α : Type u) where
  size       : Nat
  buckets    : HashSetBucket α
@@ -100,7 +104,10 @@ def insert [BEq α] [Hashable α] (m : HashSetImp α) (a : α) : HashSetImp α :
    let ⟨i, h⟩ := mkIdx (hash a) buckets.property
    let bkt    := buckets.val[i]
    if bkt.contains a
-    then ⟨size, buckets.update i (bkt.replace a a) h⟩
+    then
+      -- make sure `bkt` is used linearly in the following call to `replace`
+      let buckets' := buckets.update i .nil h
+      ⟨size, buckets'.update i (bkt.replace a a) (by simpa [buckets'])⟩
    else
      let size'    := size + 1
      let buckets' := buckets.update i (a :: bkt) h
@@ -114,7 +121,9 @@ def erase [BEq α] [Hashable α] (m : HashSetImp α) (a : α) : HashSetImp α :=
    let ⟨i, h⟩ := mkIdx (hash a) buckets.property
    let bkt    := buckets.val[i]
    if bkt.contains a then
-      ⟨size - 1, buckets.update i (bkt.erase a) h⟩
+      -- make sure `bkt` is used linearly in the following call to `erase`
+      let buckets' := buckets.update i .nil h
+      ⟨size - 1, buckets'.update i (bkt.erase a) (by simpa [buckets'])⟩
    else
      ⟨size, buckets⟩

--- a/src/Lean/Data/Lsp/LanguageFeatures.lean
+++ b/src/Lean/Data/Lsp/LanguageFeatures.lean
@@ -333,8 +333,8 @@ def SemanticTokenType.names : Array String :=
    "event", "method", "macro", "modifier", "comment", "string", "number",
    "regexp", "operator", "decorator", "leanSorryLike"]

-def SemanticTokenType.toNat (type : SemanticTokenType) : Nat :=
-  type.toCtorIdx
+def SemanticTokenType.toNat (tokenType : SemanticTokenType) : Nat :=
+  tokenType.toCtorIdx

 -- sanity check
 -- TODO: restore after update-stage0
--- a/src/Lean/Data/Name.lean
+++ b/src/Lean/Data/Name.lean
@@ -120,6 +120,26 @@ def isInternalOrNum : Name → Bool
  | .num _ _ => true
  | _       => false

+/--
+Returns true if this a part of name that is internal or dynamically
+generated so that it may easily be changed.
+
+Generally, user code should not explicitly use internal names.
+-/
+def isInternalDetail : Name → Bool
+  | .str p s     =>
+    s.startsWith "_"
+      || matchPrefix s "eq_"
+      || matchPrefix s "match_"
+      || matchPrefix s "proof_"
+      || p.isInternalOrNum
+  | .num _ _     => true
+  | p            => p.isInternalOrNum
+where
+  /-- Check that a string begins with the given prefix, and then is only digit characters. -/
+  matchPrefix (s : String) (pre : String) :=
+    s.startsWith pre && (s |>.drop pre.length |>.all Char.isDigit)
+
 /--
 Checks whether the name is an implementation-detail hypothesis name.

--- a/src/Lean/Data/NameMap.lean
+++ b/src/Lean/Data/NameMap.lean
@@ -27,7 +27,7 @@ def insert (m : NameMap α) (n : Name) (a : α) := RBMap.insert m n a

 def contains (m : NameMap α) (n : Name) : Bool := RBMap.contains m n

-@[inline] def find? (m : NameMap α) (n : Name) : Option α := RBMap.find? m n
+def find? (m : NameMap α) (n : Name) : Option α := RBMap.find? m n

 instance : ForIn m (NameMap α) (Name × α) :=
  inferInstanceAs (ForIn _ (RBMap ..) ..)
--- a/src/Lean/Data/PersistentHashMap.lean
+++ b/src/Lean/Data/PersistentHashMap.lean
@@ -23,6 +23,13 @@ inductive Node (α : Type u) (β : Type v) : Type (max u v) where
  | entries   (es : Array (Entry α β (Node α β))) : Node α β
  | collision (ks : Array α) (vs : Array β) (h : ks.size = vs.size) : Node α β

+partial def Node.isEmpty : Node α β → Bool
+  | .collision .. => false
+  | .entries es => es.all fun
+    | .entry .. => false
+    | .ref n    => n.isEmpty
+    | .null     => true
+
 instance {α β} : Inhabited (Node α β) := ⟨Node.entries #[]⟩

 abbrev shift         : USize  := 5
@@ -36,8 +43,7 @@ def mkEmptyEntriesArray {α β} : Array (Entry α β (Node α β)) :=
 end PersistentHashMap

 structure PersistentHashMap (α : Type u) (β : Type v) [BEq α] [Hashable α] where
-  root    : PersistentHashMap.Node α β := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray
-  size    : Nat                        := 0
+  root : PersistentHashMap.Node α β := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray

 abbrev PHashMap (α : Type u) (β : Type v) [BEq α] [Hashable α] := PersistentHashMap α β

@@ -45,8 +51,8 @@ namespace PersistentHashMap

 def empty [BEq α] [Hashable α] : PersistentHashMap α β := {}

-def isEmpty [BEq α] [Hashable α] (m : PersistentHashMap α β) : Bool :=
-  m.size == 0
+def isEmpty {_ : BEq α} {_ : Hashable α} : PersistentHashMap α β → Bool
+  | { root } => root.isEmpty

 instance [BEq α] [Hashable α] : Inhabited (PersistentHashMap α β) := ⟨{}⟩

@@ -130,7 +136,7 @@ partial def insertAux [BEq α] [Hashable α] : Node α β → USize → USize
        else Entry.ref $ mkCollisionNode k' v' k v

 def insert {_ : BEq α} {_ : Hashable α} : PersistentHashMap α β → α → β → PersistentHashMap α β
-  | { root := n, size := sz }, k, v => { root := insertAux n (hash k |>.toUSize) 1 k v, size := sz + 1 }
+  | { root }, k, v => { root := insertAux root (hash k |>.toUSize) 1 k v }

 partial def findAtAux [BEq α] (keys : Array α) (vals : Array β) (heq : keys.size = vals.size) (i : Nat) (k : α) : Option β :=
  if h : i < keys.size then
@@ -150,7 +156,7 @@ partial def findAux [BEq α] : Node α β → USize → α → Option β
  | Node.collision keys vals heq, _, k => findAtAux keys vals heq 0 k

 def find? {_ : BEq α} {_ : Hashable α} : PersistentHashMap α β → α → Option β
-  | { root := n, .. }, k => findAux n (hash k |>.toUSize) k
+  | { root }, k => findAux root (hash k |>.toUSize) k

 instance {_ : BEq α} {_ : Hashable α} : GetElem (PersistentHashMap α β) α (Option β) fun _ _ => True where
  getElem m i _ := m.find? i
@@ -183,7 +189,7 @@ partial def findEntryAux [BEq α] : Node α β → USize → α → Option (α
  | Node.collision keys vals heq, _, k => findEntryAtAux keys vals heq 0 k

 def findEntry? {_ : BEq α} {_ : Hashable α} : PersistentHashMap α β → α → Option (α × β)
-  | { root := n, .. }, k => findEntryAux n (hash k |>.toUSize) k
+  | { root }, k => findEntryAux root (hash k |>.toUSize) k

 partial def containsAtAux [BEq α] (keys : Array α) (vals : Array β) (heq : keys.size = vals.size) (i : Nat) (k : α) : Bool :=
  if h : i < keys.size then
@@ -202,7 +208,7 @@ partial def containsAux [BEq α] : Node α β → USize → α → Bool
  | Node.collision keys vals heq, _, k => containsAtAux keys vals heq 0 k

 def contains [BEq α] [Hashable α] : PersistentHashMap α β → α → Bool
-  | { root := n, .. }, k => containsAux n (hash k |>.toUSize) k
+  | { root }, k => containsAux root (hash k |>.toUSize) k

 partial def isUnaryEntries (a : Array (Entry α β (Node α β))) (i : Nat) (acc : Option (α × β)) : Option (α × β) :=
  if h : i < a.size then
@@ -225,7 +231,7 @@ def isUnaryNode : Node α β → Option (α × β)
    else
      none

-partial def eraseAux [BEq α] : Node α β → USize → α → Node α β × Bool
+partial def eraseAux [BEq α] : Node α β → USize → α → Node α β
  | n@(Node.collision keys vals heq), _, k =>
    match keys.indexOf? k with
    | some idx =>
@@ -234,28 +240,26 @@ partial def eraseAux [BEq α] : Node α β → USize → α → Node α β × Bo
      let vals' := vals.feraseIdx (Eq.ndrec idx heq)
      have veq := vals.size_feraseIdx (Eq.ndrec idx heq)
      have : keys.size - 1 = vals.size - 1 := by rw [heq]
-      (Node.collision keys' vals' (keq.trans (this.trans veq.symm)), true)
-    | none     => (n, false)
+      Node.collision keys' vals' (keq.trans (this.trans veq.symm))
+    | none     => n
  | n@(Node.entries entries), h, k =>
    let j       := (mod2Shift h shift).toNat
    let entry   := entries.get! j
    match entry with
-    | Entry.null       => (n, false)
+    | Entry.null       => n
    | Entry.entry k' _ =>
-      if k == k' then (Node.entries (entries.set! j Entry.null), true) else (n, false)
+      if k == k' then Node.entries (entries.set! j Entry.null) else n
    | Entry.ref node   =>
      let entries := entries.set! j Entry.null
-      let (newNode, deleted) := eraseAux node (div2Shift h shift) k
-      if !deleted then (n, false)
-      else match isUnaryNode newNode with
-        | none        => (Node.entries (entries.set! j (Entry.ref newNode)), true)
-        | some (k, v) => (Node.entries (entries.set! j (Entry.entry k v)), true)
+      let newNode := eraseAux node (div2Shift h shift) k
+      match isUnaryNode newNode with
+      | none        => Node.entries (entries.set! j (Entry.ref newNode))
+      | some (k, v) => Node.entries (entries.set! j (Entry.entry k v))

 def erase {_ : BEq α} {_ : Hashable α} : PersistentHashMap α β → α → PersistentHashMap α β
-  | { root := n, size := sz }, k =>
+  | { root }, k =>
    let h := hash k |>.toUSize
-    let (n, del) := eraseAux n h k
-    { root := n, size := if del then sz - 1 else sz }
+    { root := eraseAux root h k }

 section
 variable {m : Type w → Type w'} [Monad m]
@@ -317,7 +321,7 @@ partial def mapMAux {α : Type u} {β : Type v} {σ : Type u} {m : Type u → Ty

 def mapM {α : Type u} {β : Type v} {σ : Type u} {m : Type u → Type w} [Monad m] {_ : BEq α} {_ : Hashable α} (pm : PersistentHashMap α β) (f : β → m σ) : m (PersistentHashMap α σ) := do
  let root ← mapMAux f pm.root
-  return { pm with root }
+  return { root }

 def map {α : Type u} {β : Type v} {σ : Type u} {_ : BEq α} {_ : Hashable α} (pm : PersistentHashMap α β) (f : β → σ) : PersistentHashMap α σ :=
  Id.run <| pm.mapM f
--- a/src/Lean/Data/PersistentHashSet.lean
+++ b/src/Lean/Data/PersistentHashSet.lean
@@ -44,9 +44,6 @@ variable {_ : BEq α} {_ : Hashable α}
@[inline] def contains (s : PersistentHashSet α) (a : α) : Bool :=
  s.set.contains a

-@[inline] def size (s : PersistentHashSet α) : Nat :=
-  s.set.size
-
@[inline] def foldM {β : Type v} {m : Type v → Type v} [Monad m] (f : β → α → m β) (init : β) (s : PersistentHashSet α) : m β :=
  s.set.foldlM (init := init) fun d a _ => f d a

--- a/src/Lean/Data/SMap.lean
+++ b/src/Lean/Data/SMap.lean
@@ -74,6 +74,12 @@ def forM [Monad m] (s : SMap α β) (f : α → β → m PUnit) : m PUnit := do
  s.map₁.forM f
  s.map₂.forM f

+instance : ForM m (SMap α β) (α × β) where
+  forM s f := forM s fun x y => f (x, y)
+
+instance : ForIn m (SMap α β) (α × β) where
+  forIn := ForM.forIn
+
 /-- Move from stage 1 into stage 2. -/
 def switch (m : SMap α β) : SMap α β :=
  if m.stage₁ then { m with stage₁ := false } else m
@@ -84,12 +90,6 @@ def switch (m : SMap α β) : SMap α β :=
 def fold {σ : Type w} (f : σ → α → β → σ) (init : σ) (m : SMap α β) : σ :=
  m.map₂.foldl f $ m.map₁.fold f init

-def size (m : SMap α β) : Nat :=
-  m.map₁.size + m.map₂.size
-
-def stageSizes (m : SMap α β) : Nat × Nat :=
-  (m.map₁.size, m.map₂.size)
-
 def numBuckets (m : SMap α β) : Nat :=
  m.map₁.numBuckets

--- a/src/Lean/Data/SSet.lean
+++ b/src/Lean/Data/SSet.lean
@@ -34,9 +34,6 @@ abbrev switch (s : SSet α) : SSet α :=
 abbrev fold (f : σ → α → σ) (init : σ) (s : SSet α) : σ :=
  SMap.fold (fun d a _ => f d a) init s

-abbrev size (s : SSet α) : Nat :=
-  SMap.size s
-
 def toList (m : SSet α) : List α :=
  m.fold (init := []) fun es a => a::es

--- a/src/Lean/Declaration.lean
+++ b/src/Lean/Declaration.lean
@@ -35,7 +35,7 @@ inductive ReducibilityHints where
  | opaque  : ReducibilityHints
  | abbrev  : ReducibilityHints
  | regular : UInt32 → ReducibilityHints
-  deriving Inhabited
+  deriving Inhabited, BEq

@[export lean_mk_reducibility_hints_regular]
 def mkReducibilityHintsRegularEx (h : UInt32) : ReducibilityHints :=
@@ -117,7 +117,7 @@ structure DefinitionVal extends ConstantVal where
    are compiled using recursors and `WellFounded.fix`.
  -/
  all : List Name := [name]
-  deriving Inhabited
+  deriving Inhabited, BEq

@[export lean_mk_definition_val]
 def mkDefinitionValEx (name : Name) (levelParams : List Name) (type : Expr) (value : Expr) (hints : ReducibilityHints) (safety : DefinitionSafety) (all : List Name) : DefinitionVal := {
@@ -161,13 +161,13 @@ def mkOpaqueValEx (name : Name) (levelParams : List Name) (type : Expr) (value :
 structure Constructor where
  name : Name
  type : Expr
-  deriving Inhabited
+  deriving Inhabited, BEq

 structure InductiveType where
  name : Name
  type : Expr
  ctors : List Constructor
-  deriving Inhabited
+  deriving Inhabited, BEq

 /-- Declaration object that can be sent to the kernel. -/
 inductive Declaration where
@@ -178,7 +178,7 @@ inductive Declaration where
  | quotDecl
  | mutualDefnDecl  (defns : List DefinitionVal) -- All definitions must be marked as `unsafe` or `partial`
  | inductDecl      (lparams : List Name) (nparams : Nat) (types : List InductiveType) (isUnsafe : Bool)
-  deriving Inhabited
+  deriving Inhabited, BEq

@[export lean_mk_inductive_decl]
 def mkInductiveDeclEs (lparams : List Name) (nparams : Nat) (types : List InductiveType) (isUnsafe : Bool) : Declaration :=
@@ -189,6 +189,10 @@ def Declaration.isUnsafeInductiveDeclEx : Declaration → Bool
  | Declaration.inductDecl _ _ _ isUnsafe => isUnsafe
  | _ => false

+def Declaration.definitionVal! : Declaration → DefinitionVal
+  | .defnDecl val => val
+  | _ => panic! "Expected a `Declaration.defnDecl`."
+
@[specialize] def Declaration.foldExprM {α} {m : Type → Type} [Monad m] (d : Declaration) (f : α → Expr → m α) (a : α) : m α :=
  match d with
  | Declaration.quotDecl                                        => pure a
--- a/src/Lean/DocString.lean
+++ b/src/Lean/DocString.lean
@@ -4,58 +4,26 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
-import Lean.DeclarationRange
-import Lean.MonadEnv
-import Init.Data.String.Extra
+import Lean.DocString.Extension
+import Lean.Parser.Tactic.Doc
+
+set_option linter.missingDocs true
+
+-- This module contains the main query interface for docstrings, which assembles user-visible
+-- docstrings.
+-- The module `Lean.DocString.Extension` contains the underlying data.

 namespace Lean
+open Lean.Parser.Tactic.Doc

-private builtin_initialize builtinDocStrings : IO.Ref (NameMap String) ← IO.mkRef {}
-private builtin_initialize docStringExt : MapDeclarationExtension String ← mkMapDeclarationExtension
+/--
+Finds the docstring for a name, taking tactic alternate forms and documentation extensions into
+account.

-def addBuiltinDocString (declName : Name) (docString : String) : IO Unit :=
-  builtinDocStrings.modify (·.insert declName docString.removeLeadingSpaces)
-
-def addDocString [Monad m] [MonadError m] [MonadEnv m] (declName : Name) (docString : String) : m Unit := do
-  unless (← getEnv).getModuleIdxFor? declName |>.isNone do
-    throwError s!"invalid doc string, declaration '{declName}' is in an imported module"
-  modifyEnv fun env => docStringExt.insert env declName docString.removeLeadingSpaces
-
-def addDocString' [Monad m] [MonadError m] [MonadEnv m] (declName : Name) (docString? : Option String) : m Unit :=
-  match docString? with
-  | some docString => addDocString declName docString
-  | none => return ()
-
-def findDocString? (env : Environment) (declName : Name) (includeBuiltin := true) : IO (Option String) :=
-  if let some docStr := docStringExt.find? env declName then
-    return some docStr
-  else if includeBuiltin then
-    return (← builtinDocStrings.get).find? declName
-  else
-    return none
-
-structure ModuleDoc where
-  doc : String
-  declarationRange : DeclarationRange
-
-private builtin_initialize moduleDocExt : SimplePersistentEnvExtension ModuleDoc (PersistentArray ModuleDoc) ← registerSimplePersistentEnvExtension {
-  addImportedFn := fun _ => {}
-  addEntryFn    := fun s e => s.push e
-  toArrayFn     := fun es => es.toArray
-}
-
-def addMainModuleDoc (env : Environment) (doc : ModuleDoc) : Environment :=
-  moduleDocExt.addEntry env doc
-
-def getMainModuleDoc (env : Environment) : PersistentArray ModuleDoc :=
-  moduleDocExt.getState env
-
-def getModuleDoc? (env : Environment) (moduleName : Name) : Option (Array ModuleDoc) :=
-  env.getModuleIdx? moduleName |>.map fun modIdx => moduleDocExt.getModuleEntries env modIdx
-
-def getDocStringText [Monad m] [MonadError m] [MonadRef m] (stx : TSyntax `Lean.Parser.Command.docComment) : m String :=
-  match stx.raw[1] with
-  | Syntax.atom _ val => return val.extract 0 (val.endPos - ⟨2⟩)
-  | _                 => throwErrorAt stx "unexpected doc string{indentD stx.raw[1]}"
-
-end Lean
+Use `Lean.findSimpleDocString?` to look up the raw docstring without resolving alternate forms or
+including extensions.
+-/
+def findDocString? (env : Environment) (declName : Name) (includeBuiltin := true) : IO (Option String) := do
+  let declName := alternativeOfTactic env declName |>.getD declName
+  let exts := getTacticExtensionString env declName
+  return (← findSimpleDocString? env declName (includeBuiltin := includeBuiltin)).map (· ++ exts)
--- a/src/Lean/DocString/Extension.lean
+++ b/src/Lean/DocString/Extension.lean
@@ -0,0 +1,69 @@
+/-
+Copyright (c) 2021 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.DeclarationRange
+import Lean.MonadEnv
+import Init.Data.String.Extra
+
+-- This module contains the underlying data for docstrings, with as few imports as possible, so that
+-- docstrings can be saved in as much of the compiler as possible.
+-- The module `Lean.DocString` contains the query interface, which needs to look at additional data
+-- to construct user-visible docstrings.
+
+namespace Lean
+
+private builtin_initialize builtinDocStrings : IO.Ref (NameMap String) ← IO.mkRef {}
+private builtin_initialize docStringExt : MapDeclarationExtension String ← mkMapDeclarationExtension
+
+def addBuiltinDocString (declName : Name) (docString : String) : IO Unit :=
+  builtinDocStrings.modify (·.insert declName docString.removeLeadingSpaces)
+
+def addDocString [Monad m] [MonadError m] [MonadEnv m] (declName : Name) (docString : String) : m Unit := do
+  unless (← getEnv).getModuleIdxFor? declName |>.isNone do
+    throwError s!"invalid doc string, declaration '{declName}' is in an imported module"
+  modifyEnv fun env => docStringExt.insert env declName docString.removeLeadingSpaces
+
+def addDocString' [Monad m] [MonadError m] [MonadEnv m] (declName : Name) (docString? : Option String) : m Unit :=
+  match docString? with
+  | some docString => addDocString declName docString
+  | none => return ()
+
+/--
+Finds a docstring without performing any alias resolution or enrichment with extra metadata.
+
+Docstrings to be shown to a user should be looked up with `Lean.findDocString?` instead.
+-/
+def findSimpleDocString? (env : Environment) (declName : Name) (includeBuiltin := true) : IO (Option String) :=
+  if let some docStr := docStringExt.find? env declName then
+    return some docStr
+  else if includeBuiltin then
+    return (← builtinDocStrings.get).find? declName
+  else
+    return none
+
+structure ModuleDoc where
+  doc : String
+  declarationRange : DeclarationRange
+
+private builtin_initialize moduleDocExt : SimplePersistentEnvExtension ModuleDoc (PersistentArray ModuleDoc) ← registerSimplePersistentEnvExtension {
+  addImportedFn := fun _ => {}
+  addEntryFn    := fun s e => s.push e
+  toArrayFn     := fun es => es.toArray
+}
+
+def addMainModuleDoc (env : Environment) (doc : ModuleDoc) : Environment :=
+  moduleDocExt.addEntry env doc
+
+def getMainModuleDoc (env : Environment) : PersistentArray ModuleDoc :=
+  moduleDocExt.getState env
+
+def getModuleDoc? (env : Environment) (moduleName : Name) : Option (Array ModuleDoc) :=
+  env.getModuleIdx? moduleName |>.map fun modIdx => moduleDocExt.getModuleEntries env modIdx
+
+def getDocStringText [Monad m] [MonadError m] (stx : TSyntax `Lean.Parser.Command.docComment) : m String :=
+  match stx.raw[1] with
+  | Syntax.atom _ val => return val.extract 0 (val.endPos - ⟨2⟩)
+  | _                 => throwErrorAt stx "unexpected doc string{indentD stx.raw[1]}"
--- a/src/Lean/Elab.lean
+++ b/src/Lean/Elab.lean
@@ -50,3 +50,4 @@ import Lean.Elab.ParseImportsFast
 import Lean.Elab.GuardMsgs
 import Lean.Elab.CheckTactic
 import Lean.Elab.MatchExpr
+import Lean.Elab.Tactic.Doc
--- a/src/Lean/Elab/App.lean
+++ b/src/Lean/Elab/App.lean
@@ -59,7 +59,7 @@ private def mkProjAndCheck (structName : Name) (idx : Nat) (e : Expr) : MetaM Ex
 def synthesizeAppInstMVars (instMVars : Array MVarId) (app : Expr) : TermElabM Unit :=
  for mvarId in instMVars do
    unless (← synthesizeInstMVarCore mvarId) do
-      registerSyntheticMVarWithCurrRef mvarId SyntheticMVarKind.typeClass
+      registerSyntheticMVarWithCurrRef mvarId (.typeClass none)
      registerMVarErrorImplicitArgInfo mvarId (← getRef) app

 /-- Return `some namedArg` if `namedArgs` contains an entry for `binderName`. -/
@@ -233,9 +233,7 @@ def eraseNamedArg (binderName : Name) : M Unit :=
 private def addNewArg (argName : Name) (arg : Expr) : M Unit := do
  modify fun s => { s with f := mkApp s.f arg, fType := s.fType.bindingBody!.instantiate1 arg }
  if arg.isMVar then
-    let mvarId := arg.mvarId!
-    if let some mvarErrorInfo ← getMVarErrorInfo? mvarId then
-      registerMVarErrorInfo { mvarErrorInfo with argName? := argName }
+    registerMVarArgName arg.mvarId! argName

 /--
  Elaborate the given `Arg` and add it to the result. See `addNewArg`.
@@ -833,9 +831,7 @@ private def elabArg (arg : Arg) (argExpectedType : Expr) : M Expr := do
 /-- Save information for producing error messages. -/
 def saveArgInfo (arg : Expr) (binderName : Name) : M Unit := do
  if arg.isMVar then
-    let mvarId := arg.mvarId!
-    if let some mvarErrorInfo ← getMVarErrorInfo? mvarId then
-      registerMVarErrorInfo { mvarErrorInfo with argName? := binderName }
+    registerMVarArgName arg.mvarId! binderName

 /-- Create an implicit argument using the given `BinderInfo`. -/
 def mkImplicitArg (argExpectedType : Expr) (bi : BinderInfo) : M Expr := do
--- a/src/Lean/Elab/Attributes.lean
+++ b/src/Lean/Elab/Attributes.lean
@@ -39,7 +39,7 @@ def toAttributeKind (attrKindStx : Syntax) : MacroM AttributeKind := do
 def mkAttrKindGlobal : Syntax :=
  mkNode ``Lean.Parser.Term.attrKind #[mkNullNode]

-def elabAttr [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMacroAdapter m] [MonadRecDepth m] [MonadTrace m] [MonadOptions m] [AddMessageContext m] [MonadInfoTree m] [MonadLiftT IO m] (attrInstance : Syntax) : m Attribute := do
+def elabAttr [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMacroAdapter m] [MonadRecDepth m] [MonadTrace m] [MonadOptions m] [AddMessageContext m] [MonadLiftT IO m] (attrInstance : Syntax) : m Attribute := do
  /- attrInstance     := ppGroup $ leading_parser attrKind >> attrParser -/
  let attrKind ← liftMacroM <| toAttributeKind attrInstance[0]
  let attr := attrInstance[1]
@@ -55,7 +55,7 @@ def elabAttr [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMa
     So, we expand them before here before we invoke the attributer handlers implemented using `AttrM`. -/
  return { kind := attrKind, name := attrName, stx := attr }

-def elabAttrs [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMacroAdapter m] [MonadRecDepth m] [MonadTrace m] [MonadOptions m] [AddMessageContext m] [MonadLog m] [MonadInfoTree m] [MonadLiftT IO m] (attrInstances : Array Syntax) : m (Array Attribute) := do
+def elabAttrs [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMacroAdapter m] [MonadRecDepth m] [MonadTrace m] [MonadOptions m] [AddMessageContext m] [MonadLog m] [MonadLiftT IO m] (attrInstances : Array Syntax) : m (Array Attribute) := do
  let mut attrs := #[]
  for attr in attrInstances do
    try
@@ -65,7 +65,7 @@ def elabAttrs [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadM
  return attrs

 -- leading_parser "@[" >> sepBy1 attrInstance ", " >> "]"
-def elabDeclAttrs [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMacroAdapter m] [MonadRecDepth m] [MonadTrace m] [MonadOptions m] [AddMessageContext m] [MonadLog m] [MonadInfoTree m] [MonadLiftT IO m] (stx : Syntax) : m (Array Attribute) :=
+def elabDeclAttrs [Monad m] [MonadEnv m] [MonadResolveName m] [MonadError m] [MonadMacroAdapter m] [MonadRecDepth m] [MonadTrace m] [MonadOptions m] [AddMessageContext m] [MonadLog m] [MonadLiftT IO m] (stx : Syntax) : m (Array Attribute) :=
  elabAttrs stx[1].getSepArgs

 end Lean.Elab
--- a/src/Lean/Elab/Binders.lean
+++ b/src/Lean/Elab/Binders.lean
@@ -782,6 +782,9 @@ def elabLetDeclCore (stx : Syntax) (expectedType? : Option Expr) (useLetExpr : B
@[builtin_term_elab «let_tmp»] def elabLetTmpDecl : TermElab :=
  fun stx expectedType? => elabLetDeclCore stx expectedType? (useLetExpr := true) (elabBodyFirst := false) (usedLetOnly := true)

-builtin_initialize registerTraceClass `Elab.let
+builtin_initialize
+  registerTraceClass `Elab.let
+  registerTraceClass `Elab.let.decl
+  registerTraceClass `Elab.autoParam

 end Lean.Elab.Term
--- a/src/Lean/Elab/BuiltinCommand.lean
+++ b/src/Lean/Elab/BuiltinCommand.lean
@@ -229,7 +229,7 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
@[builtin_command_elab «variable»] def elabVariable : CommandElab
  | `(variable $binders*) => do
    -- Try to elaborate `binders` for sanity checking
-    runTermElabM fun _ => Term.withAutoBoundImplicit <|
+    runTermElabM fun _ => Term.withSynthesize <| Term.withAutoBoundImplicit <|
      Term.elabBinders binders fun _ => pure ()
    for binder in binders do
      let binders ← replaceBinderAnnotation binder
@@ -262,16 +262,22 @@ def elabCheckCore (ignoreStuckTC : Bool) : CommandElab

@[builtin_command_elab Lean.Parser.Command.check] def elabCheck : CommandElab := elabCheckCore (ignoreStuckTC := true)

-@[builtin_command_elab Lean.Parser.Command.reduce] def elabReduce : CommandElab
-  | `(#reduce%$tk $term) => withoutModifyingEnv <| runTermElabM fun _ => Term.withDeclName `_reduce do
-    let e ← Term.elabTerm term none
-    Term.synthesizeSyntheticMVarsNoPostponing
-    let e ← Term.levelMVarToParam (← instantiateMVars e)
-    -- TODO: add options or notation for setting the following parameters
-    withTheReader Core.Context (fun ctx => { ctx with options := ctx.options.setBool `smartUnfolding false }) do
-      let e ← withTransparency (mode := TransparencyMode.all) <| reduce e (skipProofs := false) (skipTypes := false)
-      logInfoAt tk e
+@[builtin_command_elab Lean.reduceCmd] def elabReduce : CommandElab
+  | `(#reduce%$tk $term) => go tk term
+  | `(#reduce%$tk (proofs := true) $term) => go tk term (skipProofs := false)
+  | `(#reduce%$tk (types := true) $term) => go tk term (skipTypes := false)
+  | `(#reduce%$tk (proofs := true) (types := true) $term) => go tk term (skipProofs := false) (skipTypes := false)
  | _ => throwUnsupportedSyntax
+where
+  go (tk : Syntax) (term : Syntax) (skipProofs := true) (skipTypes := true) : CommandElabM Unit :=
+    withoutModifyingEnv <| runTermElabM fun _ => Term.withDeclName `_reduce do
+      let e ← Term.elabTerm term none
+      Term.synthesizeSyntheticMVarsNoPostponing
+      let e ← Term.levelMVarToParam (← instantiateMVars e)
+      -- TODO: add options or notation for setting the following parameters
+      withTheReader Core.Context (fun ctx => { ctx with options := ctx.options.setBool `smartUnfolding false }) do
+        let e ← withTransparency (mode := TransparencyMode.all) <| reduce e (skipProofs := skipProofs) (skipTypes := skipTypes)
+        logInfoAt tk e

 def hasNoErrorMessages : CommandElabM Bool := do
  return !(← get).messages.hasErrors
@@ -461,7 +467,9 @@ def elabRunMeta : CommandElab := fun stx =>
  modifyScope fun scope => { scope with opts := options }

@[builtin_macro Lean.Parser.Command.«in»] def expandInCmd : Macro
-  | `($cmd₁ in $cmd₂) => `(section $cmd₁:command $cmd₂ end)
+  | `($cmd₁ in%$tk $cmd₂) =>
+    -- Limit ref variability for incrementality; see Note [Incremental Macros]
+    withRef tk `(section $cmd₁:command $cmd₂ end)
  | _                 => Macro.throwUnsupported

@[builtin_command_elab Parser.Command.addDocString] def elabAddDeclDoc : CommandElab := fun stx => do
--- a/src/Lean/Elab/BuiltinTerm.lean
+++ b/src/Lean/Elab/BuiltinTerm.lean
@@ -190,8 +190,18 @@ private def mkFreshTypeMVarFor (expectedType? : Option Expr) : TermElabM Expr :=
    | some val => pure val
    | none     => throwIllFormedSyntax
  let typeMVar ← mkFreshTypeMVarFor expectedType?
-  let u ← getDecLevel typeMVar
-  let mvar ← mkInstMVar (mkApp2 (Lean.mkConst ``OfNat [u]) typeMVar (mkRawNatLit val))
+  let u ← try
+    getDecLevel typeMVar
+  catch ex =>
+    match expectedType? with
+    | some expectedType =>
+      if (← isProp expectedType) then
+        throwError m!"numerals are data in Lean, but the expected type is a proposition{indentExpr expectedType} : Prop"
+      else
+        throwError m!"numerals are data in Lean, but the expected type is universe polymorphic and may be a proposition{indentExpr expectedType} : {← inferType expectedType}"
+    | none => throw ex
+  let extraMsg := m!"numerals are polymorphic in Lean, but the numeral `{val}` cannot be used in a context where the expected type is{indentExpr typeMVar}\ndue to the absence of the instance above"
+  let mvar ← mkInstMVar (mkApp2 (Lean.mkConst ``OfNat [u]) typeMVar (mkRawNatLit val)) extraMsg
  let r := mkApp3 (Lean.mkConst ``OfNat.ofNat [u]) typeMVar (mkRawNatLit val) mvar
  registerMVarErrorImplicitArgInfo mvar.mvarId! stx r
  return r
--- a/src/Lean/Elab/CheckTactic.lean
+++ b/src/Lean/Elab/CheckTactic.lean
@@ -17,6 +17,7 @@ namespace Lean.Elab.CheckTactic

 open Lean.Meta CheckTactic
 open Lean.Elab.Tactic
+open Lean.Elab.Term
 open Lean.Elab.Command

@[builtin_command_elab Lean.Parser.checkTactic]
@@ -24,7 +25,7 @@ def elabCheckTactic : CommandElab := fun stx => do
  let `(#check_tactic $t ~> $result by $tac) := stx | throwUnsupportedSyntax
  withoutModifyingEnv $ do
    runTermElabM $ fun _vars => do
-      let u ← Lean.Elab.Term.elabTerm t none
+      let u ← withSynthesize (postpone := .no) <| Lean.Elab.Term.elabTerm t none
      let type ← inferType u
      let checkGoalType ← mkCheckGoalType u type
      let mvar ← mkFreshExprMVar (.some checkGoalType)
--- a/src/Lean/Elab/Command.lean
+++ b/src/Lean/Elab/Command.lean
@@ -338,6 +338,26 @@ instance : MonadRecDepth CommandElabM where

 builtin_initialize registerTraceClass `Elab.command

+open Language in
+/-- Snapshot after macro expansion of a command. -/
+structure MacroExpandedSnapshot extends Snapshot where
+  /-- The declaration name of the macro. -/
+  macroDecl : Name
+  /-- The expanded syntax tree. -/
+  newStx    : Syntax
+  /-- `State.nextMacroScope` after expansion. -/
+  newNextMacroScope : Nat
+  /-- Whether any traces were present after expansion. -/
+  hasTraces : Bool
+  /--
+  Follow-up elaboration snapshots, one per command if `newStx` is a sequence of commands.
+  -/
+  next : Array (SnapshotTask DynamicSnapshot)
+deriving TypeName
+open Language in
+instance : ToSnapshotTree MacroExpandedSnapshot where
+  toSnapshotTree s := ⟨s.toSnapshot, s.next.map (·.map (sync := true) toSnapshotTree)⟩
+
 partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
  withLogging <| withRef stx <| withIncRecDepth <| withFreshMacroScope do
    match stx with
@@ -345,8 +365,8 @@ 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
-        -- TODO: support incrementality at least for some cases such as expansions of
-        -- `set_option in` or `def a.b`
+        -- Incrementality is currently limited to the common case where the sequence is the direct
+        -- output of a macro, see below.
        withoutCommandIncrementality true do
          args.forM elabCommand
      else withTraceNode `Elab.command (fun _ => return stx) (tag :=
@@ -358,7 +378,55 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
          withInfoTreeContext (mkInfoTree := mkInfoTree decl stx) do
            let stxNew ← liftMacroM <| liftExcept stxNew?
            withMacroExpansion stx stxNew do
-              elabCommand stxNew
+              -- Support incrementality; see also Note [Incremental Macros]
+              if let some snap := (←read).snap? then
+                -- Unpack nested commands; see `MacroExpandedSnapshot.next`
+                let cmds := if stxNew.isOfKind nullKind then stxNew.getArgs else #[stxNew]
+                let nextMacroScope := (← get).nextMacroScope
+                let hasTraces := (← getTraceState).traces.size > 0
+                let oldSnap? := do
+                  let oldSnap ← snap.old?
+                  let oldSnap ← oldSnap.val.get.toTyped? MacroExpandedSnapshot
+                  guard <| oldSnap.macroDecl == decl && oldSnap.newNextMacroScope == nextMacroScope
+                  -- check absence of traces; see Note [Incremental Macros]
+                  guard <| !oldSnap.hasTraces && !hasTraces
+                  return oldSnap
+                let oldCmds? := oldSnap?.map fun old =>
+                  if old.newStx.isOfKind nullKind then old.newStx.getArgs else #[old.newStx]
+                Language.withAlwaysResolvedPromises cmds.size fun cmdPromises => do
+                  snap.new.resolve <| .ofTyped {
+                    diagnostics := .empty
+                    macroDecl := decl
+                    newStx := stxNew
+                    newNextMacroScope := nextMacroScope
+                    hasTraces
+                    next := cmdPromises.zipWith cmds fun cmdPromise cmd =>
+                      { range? := cmd.getRange?, task := cmdPromise.result }
+                    : MacroExpandedSnapshot
+                  }
+                  -- After the first command whose syntax tree changed, we must disable
+                  -- incremental reuse
+                  let mut reusedCmds := true
+                  let opts ← getOptions
+                  -- For each command, associate it with new promise and old snapshot, if any, and
+                  -- elaborate recursively
+                  for cmd in cmds, cmdPromise in cmdPromises, i in [0:cmds.size] do
+                    let oldCmd? := oldCmds?.bind (·[i]?)
+                    withReader ({ · with snap? := some {
+                      new := cmdPromise
+                      old? := do
+                        guard reusedCmds
+                        let old ← oldSnap?
+                        return { stx := (← oldCmd?), val := (← old.next[i]?) }
+                    } }) do
+                      elabCommand cmd
+                      -- Resolve promise for commands not supporting incrementality; waiting for
+                      -- `withAlwaysResolvedPromises` to do this could block reporting by later
+                      -- commands
+                      cmdPromise.resolve default
+                    reusedCmds := reusedCmds && oldCmd?.any (·.eqWithInfoAndTraceReuse opts cmd)
+              else
+                elabCommand stxNew
        | _ =>
          match commandElabAttribute.getEntries s.env k with
          | []      =>
@@ -377,6 +445,10 @@ register_builtin_option showPartialSyntaxErrors : Bool := {
  descr    := "show elaboration errors from partial syntax trees (i.e. after parser recovery)"
 }

+builtin_initialize
+  registerTraceClass `Elab.info
+  registerTraceClass `Elab.snapshotTree
+
 /--
 `elabCommand` wrapper that should be used for the initial invocation, not for recursive calls after
 macro expansion etc.
@@ -399,6 +471,12 @@ def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do pro
    let mut msgs := (← get).messages
    for tree in (← getInfoTrees) do
      trace[Elab.info] (← tree.format)
+    if let some snap := (← read).snap? then
+      -- We can assume that the root command snapshot is not involved in parallelism yet, so this
+      -- should be true iff the command supports incrementality
+      if (← IO.hasFinished snap.new.result) then
+        trace[Elab.snapshotTree]
+          Language.ToSnapshotTree.toSnapshotTree snap.new.result.get |>.format
    modify fun st => { st with
      messages := initMsgs ++ msgs
      infoState := { st.infoState with trees := initInfoTrees ++ st.infoState.trees }
--- a/src/Lean/Elab/DeclModifiers.lean
+++ b/src/Lean/Elab/DeclModifiers.lean
@@ -81,10 +81,14 @@ def Modifiers.isNonrec : Modifiers → Bool
  | { recKind := .nonrec, .. } => true
  | _                          => false

-/-- Store `attr` in `modifiers` -/
-def Modifiers.addAttribute (modifiers : Modifiers) (attr : Attribute) : Modifiers :=
+/-- Adds attribute `attr` in `modifiers` -/
+def Modifiers.addAttr (modifiers : Modifiers) (attr : Attribute) : Modifiers :=
  { modifiers with attrs := modifiers.attrs.push attr }

+/-- Filters attributes using `p` -/
+def Modifiers.filterAttrs (modifiers : Modifiers) (p : Attribute → Bool) : Modifiers :=
+  { modifiers with attrs := modifiers.attrs.filter p }
+
 instance : ToFormat Modifiers := ⟨fun m =>
  let components : List Format :=
    (match m.docString? with
--- a/Show More
+++ b/Show More