chore: remove dead code

This is intended to fail at present: it just adds a test case containing
a minimization of a Mathlib slowdown from #3807.

Prior to #3807, the declaration `exists_algHom_adjoin_of_splits'''` at
the end of the file would take around 16,000 heartbeats. Now it takes
around 210,000 heartbeats.

---------

Co-authored-by: Leonardo de Moura <leomoura@amazon.com>

.github/workflows/ci.yml

@@ -383,8 +383,14 @@ jobs:
           cd build/stage1
           ulimit -c unlimited # coredumps
           # exclude nonreproducible test
-          ctest -j4 --output-on-failure ${{ matrix.CTEST_OPTIONS }} < /dev/null
+          ctest -j4 --progress --output-junit test-results.xml --output-on-failure ${{ matrix.CTEST_OPTIONS }} < /dev/null
         if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
+      - name: Test Summary
+        uses: test-summary/action@v2
+        with:
+          paths: build/stage1/test-results.xml
+        # prefix `if` above with `always` so it's run even if tests failed
+        if: always() && (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
       - name: Check Test Binary
         run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
         if: ${{ !matrix.cross && needs.configure.outputs.quick == 'false' }}

.github/workflows/copyright-header.yml

@@ -10,7 +10,7 @@ jobs:
 
     - name: Verify .lean files start with a copyright header.
       run: |
-        FILES=$(find . -type d \( -path "./tests" -o -path "./doc" -o -path "./src/lake/examples" -o -path "./src/lake/tests" -o -path "./build" -o -path "./nix" \) -prune -o -type f -name "*.lean" -exec perl -ne 'BEGIN { $/ = undef; } print "$ARGV\n" if !m{\A/-\nCopyright}; exit;' {} \;)
+        FILES=$(find ./src -type d \( -path "./src/lake/examples" -o -path "./src/lake/tests" \) -prune -o -type f -name "*.lean" -exec perl -ne 'BEGIN { $/ = undef; } print "$ARGV\n" if !m{\A/-\nCopyright}; exit;' {} \;)
         if [ -n "$FILES" ]; then
           echo "Found .lean files which do not have a copyright header:"
           echo "$FILES"

.github/workflows/nix-ci.yml

@@ -77,7 +77,13 @@ jobs:
           nix build $NIX_BUILD_ARGS .#cacheRoots -o push-build
       - name: Test
         run: |
-          nix build $NIX_BUILD_ARGS .#test -o push-test
+          nix build --keep-failed $NIX_BUILD_ARGS .#test -o push-test || (ln -s /tmp/nix-build-*/source/src/build/ ./push-test; false)
+      - name: Test Summary
+        uses: test-summary/action@v2
+        with:
+          paths: push-test/test-results.xml
+        if: always()
+        continue-on-error: true
       - name: Build manual
         run: |
           nix build $NIX_BUILD_ARGS --update-input lean --no-write-lock-file ./doc#{lean-mdbook,leanInk,alectryon,test,inked} -o push-doc

.github/workflows/pr-release.yml

@@ -149,7 +149,9 @@ jobs:
             echo "but 'git merge-base origin/master HEAD' reported: $MERGE_BASE_SHA"
             git -C lean4.git log -10 origin/master
 
-            MESSAGE="- ❗ Std/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_SHA\`."
+            git -C lean4.git fetch origin nightly-with-mathlib 
+            NIGHTLY_WITH_MATHLIB_SHA="$(git -C lean4.git rev-parse "origin/nightly-with-mathlib")"
+            MESSAGE="- ❗ Std/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MATHLIB_SHA\`."
           fi
 
           if [[ -n "$MESSAGE" ]]; then

CMakeLists.txt

@@ -78,6 +78,10 @@ add_custom_target(update-stage0
   COMMAND $(MAKE) -C stage1 update-stage0
   DEPENDS stage1)
 
+add_custom_target(update-stage0-commit
+  COMMAND $(MAKE) -C stage1 update-stage0-commit
+  DEPENDS stage1)
+
 add_custom_target(test
   COMMAND $(MAKE) -C stage1 test
   DEPENDS stage1)

CODEOWNERS

@@ -21,3 +21,23 @@
 /src/Lean/Server/ @mhuisi
 /src/Lean/Widget/ @Vtec234
 /src/runtime/io.cpp @joehendrix
+/src/Lean/Elab/Tactic/RCases.lean @digama0
+/src/Init/RCases.lean @digama0
+/src/Lean/Elab/Tactic/Ext.lean @digama0
+/src/Init/Ext.lean @digama0
+/src/Lean/Elab/Tactic/Simpa.lean @digama0
+/src/Lean/Elab/Tactic/NormCast.lean @digama0
+/src/Lean/Meta/Tactic/NormCast.lean @digama0
+/src/Lean/Meta/Tactic/TryThis.lean @digama0
+/src/Lean/Elab/Tactic/SimpTrace.lean @digama0
+/src/Lean/Elab/Tactic/NoMatch.lean @digama0
+/src/Lean/Elab/Tactic/ShowTerm.lean @digama0
+/src/Lean/Elab/Tactic/Repeat.lean @digama0
+/src/Lean/Meta/Tactic/Repeat.lean @digama0
+/src/Lean/Meta/CoeAttr.lean @digama0
+/src/Lean/Elab/GuardMsgs.lean @digama0
+/src/Lean/Elab/Tactic/Guard.lean @digama0
+/src/Init/Guard.lean @digama0
+/src/Lean/Server/CodeActions/ @digama0
+/src/Init/Data/Array/Subarray.lean @david-christiansen
+

RELEASES.md

@@ -21,17 +21,16 @@ v4.8.0 (development in progress)
 
 * 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).
 
-* New command `derive_functional_induction`:
+* Functional induction principles.
 
-  Derived from the definition of a (possibly mutually) recursive function
-  defined by well-founded recursion, a **functional induction principle** is
-  tailored to proofs about that function. For example from:
+  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)
-  derive_functional_induction ackermann
   ```
   we get
   ```
@@ -41,6 +40,11 @@ v4.8.0 (development in progress)
     (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
@@ -53,6 +57,15 @@ v4.8.0 (development in progress)
   ```
   is recognized without having to say `termination_by arr.size - i`.
 
+* Shorter instances names. There is a new algorithm for generating names for anonymous instances.
+  Across Std and Mathlib, the median ratio between lengths of new names and of old names is about 72%.
+  With the old algorithm, the longest name was 1660 characters, and now the longest name is 202 characters.
+  The new algorithm's 95th percentile name length is 67 characters, versus 278 for the old algorithm.
+  While the new algorithm produces names that are 1.2% less unique,
+  it avoids cross-project collisions by adding a module-based suffix
+  when it does not refer to declarations from the same "project" (modules that share the same root).
+  PR [#3089](https://github.com/leanprover/lean4/pull/3089).
+
 * Attribute `@[pp_using_anonymous_constructor]` to make structures pretty print like `⟨x, y, z⟩`
   rather than `{a := x, b := y, c := z}`.
   This attribute is applied to `Sigma`, `PSigma`, `PProd`, `Subtype`, `And`, and `Fin`.
@@ -65,6 +78,31 @@ v4.8.0 (development in progress)
   to enable pretty printing function applications using generalized field notation (defaults to true).
   Field notation can be disabled on a function-by-function basis using the `@[pp_nodot]` attribute.
 
+* Added options `pp.mvars` (default: true) and `pp.mvars.withType` (default: false).
+  When `pp.mvars` is false, metavariables pretty print as `?_`,
+  and when `pp.mvars.withType` is true, metavariables pretty print with a type ascription.
+  These can be set when using `#guard_msgs` to make tests not rely on the unique ids assigned to anonymous metavariables.
+  [#3798](https://github.com/leanprover/lean4/pull/3798).
+
+* Added `@[induction_eliminator]` and `@[cases_eliminator]` attributes to be able to define custom eliminators
+  for the `induction` and `cases` tactics, replacing the `@[eliminator]` attribute.
+  Gives custom eliminators for `Nat` so that `induction` and `cases` put goal states into terms of `0` and `n + 1`
+  rather than `Nat.zero` and `Nat.succ n`.
+  Added option `tactic.customEliminators` to control whether to use custom eliminators.
+  Added a hack for `rcases`/`rintro`/`obtain` to use the custom eliminator for `Nat`.
+  [#3629](https://github.com/leanprover/lean4/pull/3629),
+  [#3655](https://github.com/leanprover/lean4/pull/3655), and
+  [#3747](https://github.com/leanprover/lean4/pull/3747).
+
+* The `#guard_msgs` command now has options to change whitespace normalization and sensitivity to message ordering.
+  For example, `#guard_msgs (whitespace := lax) in cmd` collapses whitespace before checking messages,
+  and `#guard_msgs (ordering := sorted) in cmd` sorts the messages in lexicographic order before checking.
+  PR [#3883](https://github.com/leanprover/lean4/pull/3883).
+
+* The `#guard_msgs` command now supports showing a diff between the expected and actual outputs. This feature is currently
+  disabled by default, but can be enabled with `set_option guard_msgs.diff true`. Depending on user feedback, this option
+  may default to `true` in a future version of Lean.
+
 Breaking changes:
 
 * Automatically generated equational theorems are now named using suffix `.eq_<idx>` instead of `._eq_<idx>`, and `.def` instead of `._unfold`. Example:
@@ -94,6 +132,12 @@ fact.def :
 
 * 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
 ---------
 

doc/dev/bootstrap.md

@@ -81,20 +81,8 @@ or using Github CLI with
 gh workflow run update-stage0.yml
 ```
 
-Leaving stage0 updates to the CI automation is preferrable, but should you need
-to do it locally, you can use `make update-stage0` in `build/release`, to
-update `stage0` from `stage1`, `make -C stageN update-stage0` to update from
-another stage, or `nix run .#update-stage0-commit` to update using nix.
-
-Updates to `stage0` should be their own commits in the Git history. So should
-you have to include the stage0 update in your PR (rather than using above
-automation after merging changes), commit your work before running `make
-update-stage0`, commit the updated `stage0` compiler code with the commit
-message:
-```
-chore: update stage0
-```
-and coordinate with the admins to not squash your PR.
+Leaving stage0 updates to the CI automation is preferable, but should you need to do it locally, you can use `make update-stage0-commit` in `build/release` to update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to update from another stage.
+This command will automatically stage the updated files and introduce a commit, so make sure to commit your work before that. Then coordinate with the admins to not squash your PR so that stage 0 updates are preserved as separate commits.
 
 ## Further Bootstrapping Complications
 

doc/dev/release_checklist.md

@@ -21,7 +21,7 @@ We'll use `v4.6.0` as the intended release version as a running example.
   - Reconcile discrepancies in the `v4.6.0` section,
     usually via copy and paste and a commit to `releases/v4.6.0`.
 - `git tag v4.6.0`
-- `git push origin v4.6.0`
+- `git push $REMOTE v4.6.0`, where `$REMOTE` is the upstream Lean repository (e.g., `origin`, `upstream`)
 - Now wait, while CI runs.
   - You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`,
     looking for the `v4.6.0` tag.
@@ -34,48 +34,76 @@ We'll use `v4.6.0` as the intended release version as a running example.
     (e.g. `v4.6.0-rc1`), and quickly sanity check.
 - Next, we will move a curated list of downstream repos to the latest stable release.
   - For each of the repositories listed below:
-    - Make a PR to `master`/`main` changing the toolchain to `v4.6.0`.
-      The PR title should be "chore: bump toolchain to v4.6.0".
-      Since the `v4.6.0` release should be functionally identical to the last release candidate,
-      which the repository should already be on, this PR is a no-op besides changing the toolchain.
-    - Once this is merged, create the tag `v4.6.0` from `master`/`main` and push it.
-    - Merge the tag `v4.6.0` into the stable branch.
+    - Make a PR to `master`/`main` changing the toolchain to `v4.6.0`
+      - Update the toolchain file
+      - In the Lakefile, if there are dependencies on specific version tags of dependencies that you've already pushed as part of this process, update them to the new tag.
+        If they depend on `main` or `master`, don't change this; you've just updated the dependency, so it will work and be saved in the manifest
+      - Run `lake update`
+      - The PR title should be "chore: bump toolchain to v4.6.0".
+    - Merge the PR once CI completes.
+    - Create the tag `v4.6.0` from `master`/`main` and push it.
+    - Merge the tag `v4.6.0` into the `stable` branch and push it.
   - We do this for the repositories:
     - [lean4checker](https://github.com/leanprover/lean4checker)
-      - `lean4checker` uses a different version tagging scheme: use `toolchain/v4.6.0` rather than `v4.6.0`.
-    - [Std](https://github.com/leanprover-community/repl)
+      - 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`
+    - [Std](https://github.com/leanprover-community/std4)
+      - No dependencies
+      - Toolchain bump PR
+      - Create and push the tag
+      - Merge the tag into `stable`
     - [ProofWidgets4](https://github.com/leanprover-community/ProofWidgets4)
-      - `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
-        which does not refer to the toolchain being used.
-      - Make a new release in this sequence after merging the toolchain bump PR.
-      - `ProofWidgets` does not maintain a `stable` branch.
+      - Dependencies: `Std`
+      - Note on versions and branches:
+        - `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
+          which does not refer to the toolchain being used.
+        - Make a new release in this sequence after merging the toolchain bump PR.
+        - `ProofWidgets` does not maintain a `stable` branch.
+      - Toolchain bump PR
+      - Create and push the tag, following the version convention of the repository
     - [Aesop](https://github.com/leanprover-community/aesop)
+      - Dependencies: `Std`
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - Merge the tag into `stable`
+    - [doc-gen4](https://github.com/leanprover/doc-gen4)
+      - Dependencies: exist, but they're not part of the release workflow
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
+    - [import-graph](https://github.com/leanprover-community/import-graph)
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - There is no `stable` branch; skip this step
     - [Mathlib](https://github.com/leanprover-community/mathlib4)
-      - 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`.
+      - Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Std`, `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.
+        - 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`.
+          Coordinate with a Mathlib maintainer to get this merged.
     - [REPL](https://github.com/leanprover-community/repl)
+      - Dependencies: `Mathlib` (for test code)
       - Note that there are two copies of `lean-toolchain`/`lakefile.lean`:
-        in the root, and in `test/Mathlib/`.
-  - Note that there are dependencies between these packages:
-    you should update the lakefile so that you are using the `v4.6.0` tag of upstream repositories
-    (or the sequential tag for `ProofWidgets4`), and run `lake update` before committing.
-  - This means that this process is sequential; each repository must have its bump PR merged,
-    and the new tag pushed, before you can make the PR for the downstream repositories.
-    - `lean4checker` has no dependencies
-    - `Std` has no dependencies
-    - `Aesop` depends on `Std`
-    - `ProofWidgets4` depends on `Std`
-    - `Mathlib` depends on `Aesop`, `ProofWidgets4`, and `lean4checker` (and transitively on `Std`)
-    - `REPL` depends on `Mathlib` (this dependency is only for testing).
+        in the root, and in `test/Mathlib/`. Edit both, and run `lake update` in both directories.
+      - Toolchain bump PR including updated Lake manifest
+      - Create and push the tag
+      - Merge the tag into `stable`
 - Merge the release announcement PR for the Lean website - it will be deployed automatically
 - Finally, make an announcement!
   This should go in https://leanprover.zulipchat.com/#narrow/stream/113486-announce, with topic `v4.6.0`.
   Please see previous announcements for suggested language.
   You will want a few bullet points for main topics from the release notes.
   Link to the blog post from the Zulip announcement.
-  Please also make sure that whoever is handling social media knows the release is out.
+- Make sure that whoever is handling social media knows the release is out.
 
 ## Optimistic(?) time estimates:
 - Initial checks and push the tag: 30 minutes.

doc/flake.nix

@@ -27,7 +27,7 @@
         src = inputs.mdBook;
         cargoDeps = drv.cargoDeps.overrideAttrs (_: {
           inherit src;
-          outputHash = "sha256-1YlPS6cqgxE4fjy9G8pWrpP27YrrbCDnfeyIsX81ZNw=";
+          outputHash = "sha256-CO3A9Kpp4sIvkT9X3p+GTidazk7Fn4jf0AP2PINN44A=";
         });
         doCheck = false;
       });

flake.lock

@@ -1,12 +1,31 @@
 {
   "nodes": {
-    "flake-utils": {
+    "flake-compat": {
+      "flake": false,
       "locked": {
-        "lastModified": 1656928814,
-        "narHash": "sha256-RIFfgBuKz6Hp89yRr7+NR5tzIAbn52h8vT6vXkYjZoM=",
+        "lastModified": 1673956053,
+        "narHash": "sha256-4gtG9iQuiKITOjNQQeQIpoIB6b16fm+504Ch3sNKLd8=",
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "rev": "35bb57c0c8d8b62bbfd284272c928ceb64ddbde9",
+        "type": "github"
+      },
+      "original": {
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "type": "github"
+      }
+    },
+    "flake-utils": {
+      "inputs": {
+        "systems": "systems"
+      },
+      "locked": {
+        "lastModified": 1710146030,
+        "narHash": "sha256-SZ5L6eA7HJ/nmkzGG7/ISclqe6oZdOZTNoesiInkXPQ=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "7e2a3b3dfd9af950a856d66b0a7d01e3c18aa249",
+        "rev": "b1d9ab70662946ef0850d488da1c9019f3a9752a",
         "type": "github"
       },
       "original": {
@@ -18,11 +37,11 @@
     "lean4-mode": {
       "flake": false,
       "locked": {
-        "lastModified": 1676498134,
-        "narHash": "sha256-u3WvyKxOViZG53hkb8wd2/Og6muTecbh+NdflIgVeyk=",
+        "lastModified": 1709737301,
+        "narHash": "sha256-uT9JN2kLNKJK9c/S/WxLjiHmwijq49EgLb+gJUSDpz0=",
         "owner": "leanprover",
         "repo": "lean4-mode",
-        "rev": "2c6ef33f476fdf5eb5e4fa4fa023ba8b11372440",
+        "rev": "f1f24c15134dee3754b82c9d9924866fe6bc6b9f",
         "type": "github"
       },
       "original": {
@@ -31,34 +50,35 @@
         "type": "github"
       }
     },
-    "lowdown-src": {
+    "libgit2": {
       "flake": false,
       "locked": {
-        "lastModified": 1633514407,
-        "narHash": "sha256-Dw32tiMjdK9t3ETl5fzGrutQTzh2rufgZV4A/BbxuD4=",
-        "owner": "kristapsdz",
-        "repo": "lowdown",
-        "rev": "d2c2b44ff6c27b936ec27358a2653caaef8f73b8",
+        "lastModified": 1697646580,
+        "narHash": "sha256-oX4Z3S9WtJlwvj0uH9HlYcWv+x1hqp8mhXl7HsLu2f0=",
+        "owner": "libgit2",
+        "repo": "libgit2",
+        "rev": "45fd9ed7ae1a9b74b957ef4f337bc3c8b3df01b5",
         "type": "github"
       },
       "original": {
-        "owner": "kristapsdz",
-        "repo": "lowdown",
+        "owner": "libgit2",
+        "repo": "libgit2",
         "type": "github"
       }
     },
     "nix": {
       "inputs": {
-        "lowdown-src": "lowdown-src",
+        "flake-compat": "flake-compat",
+        "libgit2": "libgit2",
         "nixpkgs": "nixpkgs",
         "nixpkgs-regression": "nixpkgs-regression"
       },
       "locked": {
-        "lastModified": 1657097207,
-        "narHash": "sha256-SmeGmjWM3fEed3kQjqIAO8VpGmkC2sL1aPE7kKpK650=",
+        "lastModified": 1711102798,
+        "narHash": "sha256-CXOIJr8byjolqG7eqCLa+Wfi7rah62VmLoqSXENaZnw=",
         "owner": "NixOS",
         "repo": "nix",
-        "rev": "f6316b49a0c37172bca87ede6ea8144d7d89832f",
+        "rev": "a22328066416650471c3545b0b138669ea212ab4",
         "type": "github"
       },
       "original": {
@@ -69,16 +89,16 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1653988320,
-        "narHash": "sha256-ZaqFFsSDipZ6KVqriwM34T739+KLYJvNmCWzErjAg7c=",
+        "lastModified": 1709083642,
+        "narHash": "sha256-7kkJQd4rZ+vFrzWu8sTRtta5D1kBG0LSRYAfhtmMlSo=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "2fa57ed190fd6c7c746319444f34b5917666e5c1",
+        "rev": "b550fe4b4776908ac2a861124307045f8e717c8e",
         "type": "github"
       },
       "original": {
         "owner": "NixOS",
-        "ref": "nixos-22.05-small",
+        "ref": "release-23.11",
         "repo": "nixpkgs",
         "type": "github"
       }
@@ -118,11 +138,11 @@
     },
     "nixpkgs_2": {
       "locked": {
-        "lastModified": 1686089707,
-        "narHash": "sha256-LTNlJcru2qJ0XhlhG9Acp5KyjB774Pza3tRH0pKIb3o=",
+        "lastModified": 1710889954,
+        "narHash": "sha256-Pr6F5Pmd7JnNEMHHmspZ0qVqIBVxyZ13ik1pJtm2QXk=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "af21c31b2a1ec5d361ed8050edd0303c31306397",
+        "rev": "7872526e9c5332274ea5932a0c3270d6e4724f3b",
         "type": "github"
       },
       "original": {
@@ -140,6 +160,21 @@
         "nixpkgs": "nixpkgs_2",
         "nixpkgs-old": "nixpkgs-old"
       }
+    },
+    "systems": {
+      "locked": {
+        "lastModified": 1681028828,
+        "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
+        "owner": "nix-systems",
+        "repo": "default",
+        "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nix-systems",
+        "repo": "default",
+        "type": "github"
+      }
     }
   },
   "root": "root",

nix/bootstrap.nix

@@ -170,10 +170,11 @@ rec {
           ln -sf ${lean-all}/* .
         '';
         buildPhase = ''
-          ctest --output-on-failure -E 'leancomptest_(doc_example|foreign)' -j$NIX_BUILD_CORES
+          ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)' -j$NIX_BUILD_CORES
         '';
         installPhase = ''
-          touch $out
+          mkdir $out
+          mv test-results.xml $out
         '';
       };
       update-stage0 =

script/collideProfiles.lean

@@ -0,0 +1,28 @@
+import Lean.Util.Profiler
+
+/-!
+
+Usage:
+```sh
+lean --run ./script/collideProfiles.lean **/*.lean.json ... > merged.json
+```
+
+Merges multiple `trace.profiler.output` profiles into a single one while deduplicating samples with
+the same stack. This is useful for building cumulative profiles of medium-to-large projects because
+Firefox Profiler cannot handle hundreds of tracks and the deduplication will also ensure that the
+profile is small enough for uploading.
+
+As ordering of samples is not meaningful after this transformation, only "Call Tree" and "Flame
+Graph" are useful for such profiles.
+-/
+
+open Lean
+
+def main (args : List String) : IO Unit := do
+  let profiles ← args.toArray.mapM fun path => do
+    let json ← IO.FS.readFile ⟨path⟩
+    let profile ← IO.ofExcept $ Json.parse json
+    IO.ofExcept <| fromJson? profile
+  -- NOTE: `collide` should not be interpreted
+  let profile := Firefox.Profile.collide profiles
+  IO.println <| Json.compress <| toJson profile

src/CMakeLists.txt

@@ -588,6 +588,10 @@ if(PREV_STAGE)
     COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/update-stage0'
     DEPENDS make_stdlib
     WORKING_DIRECTORY "${LEAN_SOURCE_DIR}/..")
+
+  add_custom_target(update-stage0-commit
+    COMMAND git commit -m "chore: update stage0"
+    DEPENDS update-stage0)
 endif()
 
 # use Bash version for building, use Lean version in bin/ for tests & distribution

src/Init.lean

@@ -33,3 +33,4 @@ import Init.SizeOfLemmas
 import Init.BinderPredicates
 import Init.Ext
 import Init.Omega
+import Init.MacroTrace

src/Init/Control/Basic.lean

@@ -20,8 +20,29 @@ def Functor.discard {f : Type u → Type v} {α : Type u} [Functor f] (x : f α)
 
 export Functor (discard)
 
+/--
+An `Alternative` functor is an `Applicative` functor that can "fail" or be "empty"
+and a binary operation `<|>` that “collects values” or finds the “left-most success”.
+
+Important instances include
+* `Option`, where `failure := none` and `<|>` returns the left-most `some`.
+* Parser combinators typically provide an `Applicative` instance for error-handling and
+  backtracking.
+  
+Error recovery and state can interact subtly. For example, the implementation of `Alternative` for `OptionT (StateT σ Id)` keeps modifications made to the state while recovering from failure, while `StateT σ (OptionT Id)` discards them.
+-/
+-- NB: List instance is in mathlib. Once upstreamed, add
+-- * `List`, where `failure` is the empty list and `<|>` concatenates.
 class Alternative (f : Type u → Type v) extends Applicative f : Type (max (u+1) v) where
+  /--
+  Produces an empty collection or recoverable failure.  The `<|>` operator collects values or recovers
+  from failures. See `Alternative` for more details.
+  -/
   failure : {α : Type u} → f α
+  /--
+  Depending on the `Alternative` instance, collects values or recovers from `failure`s by
+  returning the leftmost success. Can be written using the `<|>` operator syntax.
+  -/
   orElse  : {α : Type u} → f α → (Unit → f α) → f α
 
 instance (f : Type u → Type v) (α : Type u) [Alternative f] : OrElse (f α) := ⟨Alternative.orElse⟩
@@ -30,9 +51,15 @@ variable {f : Type u → Type v} [Alternative f] {α : Type u}
 
 export Alternative (failure)
 
+/--
+If the proposition `p` is true, does nothing, else fails (using `failure`).
+-/
 @[always_inline, inline] def guard {f : Type → Type v} [Alternative f] (p : Prop) [Decidable p] : f Unit :=
   if p then pure () else failure
 
+/--
+Returns `some x` if `f` succeeds with value `x`, else returns `none`.
+-/
 @[always_inline, inline] def optional (x : f α) : f (Option α) :=
   some <$> x <|> pure none
 

src/Init/Control/Lawful/Basic.lean

@@ -12,6 +12,15 @@ open Function
 @[simp] theorem monadLift_self [Monad m] (x : m α) : monadLift x = x :=
   rfl
 
+/--
+The `Functor` typeclass only contains the operations of a functor.
+`LawfulFunctor` further asserts that these operations satisfy the laws of a functor,
+including the preservation of the identity and composition laws:
+```
+id <$> x = x
+(h ∘ g) <$> x = h <$> g <$> x
+```
+-/
 class LawfulFunctor (f : Type u → Type v) [Functor f] : Prop where
   map_const          : (Functor.mapConst : α → f β → f α) = Functor.map ∘ const β
   id_map   (x : f α) : id <$> x = x
@@ -24,6 +33,16 @@ attribute [simp] id_map
 @[simp] theorem id_map' [Functor m] [LawfulFunctor m] (x : m α) : (fun a => a) <$> x = x :=
   id_map x
 
+/--
+The `Applicative` typeclass only contains the operations of an applicative functor.
+`LawfulApplicative` further asserts that these operations satisfy the laws of an applicative functor:
+```
+pure id <*> v = v
+pure (·∘·) <*> u <*> v <*> w = u <*> (v <*> w)
+pure f <*> pure x = pure (f x)
+u <*> pure y = pure (· y) <*> u
+```
+-/
 class LawfulApplicative (f : Type u → Type v) [Applicative f] extends LawfulFunctor f : Prop where
   seqLeft_eq  (x : f α) (y : f β)     : x <* y = const β <$> x <*> y
   seqRight_eq (x : f α) (y : f β)     : x *> y = const α id <$> x <*> y
@@ -42,6 +61,18 @@ attribute [simp] map_pure seq_pure
 @[simp] theorem pure_id_seq [Applicative f] [LawfulApplicative f] (x : f α) : pure id <*> x = x := by
   simp [pure_seq]
 
+/--
+The `Monad` typeclass only contains the operations of a monad.
+`LawfulMonad` further asserts that these operations satisfy the laws of a monad,
+including associativity and identity laws for `bind`:
+```
+pure x >>= f = f x
+x >>= pure = x
+x >>= f >>= g = x >>= (fun x => f x >>= g)
+```
+
+`LawfulMonad.mk'` is an alternative constructor containing useful defaults for many fields.
+-/
 class LawfulMonad (m : Type u → Type v) [Monad m] extends LawfulApplicative m : Prop where
   bind_pure_comp (f : α → β) (x : m α) : x >>= (fun a => pure (f a)) = f <$> x
   bind_map       {α β : Type u} (f : m (α → β)) (x : m α) : f >>= (. <$> x) = f <*> x

src/Init/Control/Lawful/Instances.lean

@@ -235,13 +235,13 @@ end StateT
 
 instance : LawfulMonad (EStateM ε σ) := .mk'
   (id_map := fun x => funext <| fun s => by
-    dsimp only [EStateM.instMonadEStateM, EStateM.map]
+    dsimp only [EStateM.instMonad, EStateM.map]
     match x s with
     | .ok _ _ => rfl
     | .error _ _ => rfl)
   (pure_bind := fun _ _ => rfl)
   (bind_assoc := fun x _ _ => funext <| fun s => by
-    dsimp only [EStateM.instMonadEStateM, EStateM.bind]
+    dsimp only [EStateM.instMonad, EStateM.bind]
     match x s with
     | .ok _ _ => rfl
     | .error _ _ => rfl)

src/Init/Conv.lean

@@ -6,7 +6,7 @@ Authors: Leonardo de Moura
 Notation for operators defined at Prelude.lean
 -/
 prelude
-import Init.Meta
+import Init.Tactics
 
 namespace Lean.Parser.Tactic.Conv
 
@@ -201,7 +201,7 @@ macro (name := anyGoals) tk:"any_goals " s:convSeq : conv =>
   with inaccessible names to the given names.
 * `case tag₁ | tag₂ => tac` is equivalent to `(case tag₁ => tac); (case tag₂ => tac)`.
 -/
-macro (name := case) tk:"case " args:sepBy1(caseArg, " | ") arr:" => " s:convSeq : conv =>
+macro (name := case) tk:"case " args:sepBy1(caseArg, "|") arr:" => " s:convSeq : conv =>
   `(conv| tactic' => case%$tk $args|* =>%$arr conv' => ($s); all_goals rfl)
 
 /--
@@ -210,7 +210,7 @@ has been solved after applying `tac`, nor admits the goal if `tac` failed.
 Recall that `case` closes the goal using `sorry` when `tac` fails, and
 the tactic execution is not interrupted.
 -/
-macro (name := case') tk:"case' " args:sepBy1(caseArg, " | ") arr:" => " s:convSeq : conv =>
+macro (name := case') tk:"case' " args:sepBy1(caseArg, "|") arr:" => " s:convSeq : conv =>
   `(conv| tactic' => case'%$tk $args|* =>%$arr conv' => $s)
 
 /--

src/Init/Core.lean

@@ -1308,7 +1308,6 @@ gen_injective_theorems% Fin
 gen_injective_theorems% Array
 gen_injective_theorems% Sum
 gen_injective_theorems% PSum
-gen_injective_theorems% Nat
 gen_injective_theorems% Option
 gen_injective_theorems% List
 gen_injective_theorems% Except
@@ -1316,6 +1315,12 @@ gen_injective_theorems% EStateM.Result
 gen_injective_theorems% Lean.Name
 gen_injective_theorems% Lean.Syntax
 
+theorem Nat.succ.inj {m n : Nat} : m.succ = n.succ → m = n :=
+  fun x => Nat.noConfusion x id
+
+theorem Nat.succ.injEq (u v : Nat) : (u.succ = v.succ) = (u = v) :=
+  Eq.propIntro Nat.succ.inj (congrArg Nat.succ)
+
 @[simp] theorem beq_iff_eq [BEq α] [LawfulBEq α] (a b : α) : a == b ↔ a = b :=
   ⟨eq_of_beq, by intro h; subst h; exact LawfulBEq.rfl⟩
 

src/Init/Data.lean

@@ -14,6 +14,7 @@ import Init.Data.String
 import Init.Data.List
 import Init.Data.Int
 import Init.Data.Array
+import Init.Data.Array.Subarray.Split
 import Init.Data.ByteArray
 import Init.Data.FloatArray
 import Init.Data.Fin

src/Init/Data/Array/Basic.lean

@@ -10,7 +10,7 @@ import Init.Data.Fin.Basic
 import Init.Data.UInt.Basic
 import Init.Data.Repr
 import Init.Data.ToString.Basic
-import Init.Util
+import Init.GetElem
 universe u v w
 
 namespace Array
@@ -59,6 +59,8 @@ def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
 instance : GetElem (Array α) USize α fun xs i => i.toNat < xs.size where
   getElem xs i h := xs.uget i h
 
+instance : LawfulGetElem (Array α) USize α fun xs i => i.toNat < xs.size where
+
 def back [Inhabited α] (a : Array α) : α :=
   a.get! (a.size - 1)
 
@@ -730,10 +732,8 @@ def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
     a.pop
 termination_by a.size - i.val
 
-derive_functional_induction feraseIdx
-
 theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
-  induction a, i using feraseIdx.induct with
+  induction a, i using Array.feraseIdx.induct with
   | @case1 a i h a' _ _ ih =>
     unfold feraseIdx
     simp [h, a', ih]

src/Init/Data/Array/Subarray.lean

@@ -9,29 +9,46 @@ import Init.Data.Array.Basic
 universe u v w
 
 structure Subarray (α : Type u)  where
-  as : Array α
+  array : Array α
   start : Nat
   stop : Nat
-  h₁ : start ≤ stop
-  h₂ : stop ≤ as.size
+  start_le_stop : start ≤ stop
+  stop_le_array_size : stop ≤ array.size
+
+@[deprecated Subarray.array]
+abbrev Subarray.as (s : Subarray α) : Array α := s.array
+
+@[deprecated Subarray.start_le_stop]
+theorem Subarray.h₁ (s : Subarray α) : s.start ≤ s.stop := s.start_le_stop
+
+@[deprecated Subarray.stop_le_array_size]
+theorem Subarray.h₂ (s : Subarray α) : s.stop ≤ s.as.size := s.stop_le_array_size
 
 namespace Subarray
 
 def size (s : Subarray α) : Nat :=
   s.stop - s.start
 
+theorem size_le_array_size {s : Subarray α} : s.size ≤ s.array.size := by
+  let {array, start, stop, start_le_stop, stop_le_array_size} := s
+  simp [size]
+  apply Nat.le_trans (Nat.sub_le stop start)
+  assumption
+
 def get (s : Subarray α) (i : Fin s.size) : α :=
-  have : s.start + i.val < s.as.size := by
-   apply Nat.lt_of_lt_of_le _ s.h₂
+  have : s.start + i.val < s.array.size := by
+   apply Nat.lt_of_lt_of_le _ s.stop_le_array_size
    have := i.isLt
    simp [size] at this
    rw [Nat.add_comm]
    exact Nat.add_lt_of_lt_sub this
-  s.as[s.start + i.val]
+  s.array[s.start + i.val]
 
 instance : GetElem (Subarray α) Nat α fun xs i => i < xs.size where
   getElem xs i h := xs.get ⟨i, h⟩
 
+instance : LawfulGetElem (Subarray α) Nat α fun xs i => i < xs.size where
+
 @[inline] def getD (s : Subarray α) (i : Nat) (v₀ : α) : α :=
   if h : i < s.size then s.get ⟨i, h⟩ else v₀
 
@@ -40,7 +57,7 @@ abbrev get! [Inhabited α] (s : Subarray α) (i : Nat) : α :=
 
 def popFront (s : Subarray α) : Subarray α :=
   if h : s.start < s.stop then
-    { s with start := s.start + 1, h₁ := Nat.le_of_lt_succ (Nat.add_lt_add_right h 1) }
+    { s with start := s.start + 1, start_le_stop := Nat.le_of_lt_succ (Nat.add_lt_add_right h 1) }
   else
     s
 
@@ -48,7 +65,7 @@ def popFront (s : Subarray α) : Subarray α :=
   let sz := USize.ofNat s.stop
   let rec @[specialize] loop (i : USize) (b : β) : m β := do
     if i < sz then
-      let a := s.as.uget i lcProof
+      let a := s.array.uget i lcProof
       match (← f a b) with
       | ForInStep.done  b => pure b
       | ForInStep.yield b => loop (i+1) b
@@ -66,27 +83,27 @@ instance : ForIn m (Subarray α) α where
 
 @[inline]
 def foldlM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : β → α → m β) (init : β) (as : Subarray α) : m β :=
-  as.as.foldlM f (init := init) (start := as.start) (stop := as.stop)
+  as.array.foldlM f (init := init) (start := as.start) (stop := as.stop)
 
 @[inline]
 def foldrM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → β → m β) (init : β) (as : Subarray α) : m β :=
-  as.as.foldrM f (init := init) (start := as.stop) (stop := as.start)
+  as.array.foldrM f (init := init) (start := as.stop) (stop := as.start)
 
 @[inline]
 def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Subarray α) : m Bool :=
-  as.as.anyM p (start := as.start) (stop := as.stop)
+  as.array.anyM p (start := as.start) (stop := as.stop)
 
 @[inline]
 def allM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as : Subarray α) : m Bool :=
-  as.as.allM p (start := as.start) (stop := as.stop)
+  as.array.allM p (start := as.start) (stop := as.stop)
 
 @[inline]
 def forM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Subarray α) : m PUnit :=
-  as.as.forM f (start := as.start) (stop := as.stop)
+  as.array.forM f (start := as.start) (stop := as.stop)
 
 @[inline]
 def forRevM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Subarray α) : m PUnit :=
-  as.as.forRevM f (start := as.stop) (stop := as.start)
+  as.array.forRevM f (start := as.stop) (stop := as.start)
 
 @[inline]
 def foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : Subarray α) : β :=
@@ -133,15 +150,25 @@ variable {α : Type u}
 
 def toSubarray (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : Subarray α :=
   if h₂ : stop ≤ as.size then
-     if h₁ : start ≤ stop then
-       { as := as, start := start, stop := stop, h₁ := h₁, h₂ := h₂ }
-     else
-       { as := as, start := stop, stop := stop, h₁ := Nat.le_refl _, h₂ := h₂ }
+    if h₁ : start ≤ stop then
+      { array := as, start := start, stop := stop,
+        start_le_stop := h₁, stop_le_array_size := h₂ }
+    else
+      { array := as, start := stop, stop := stop,
+        start_le_stop := Nat.le_refl _, stop_le_array_size := h₂ }
   else
-     if h₁ : start ≤ as.size then
-       { as := as, start := start, stop := as.size, h₁ := h₁, h₂ := Nat.le_refl _ }
-     else
-       { as := as, start := as.size, stop := as.size, h₁ := Nat.le_refl _, h₂ := Nat.le_refl _ }
+    if h₁ : start ≤ as.size then
+      { array := as,
+        start := start,
+        stop := as.size,
+        start_le_stop := h₁,
+        stop_le_array_size := Nat.le_refl _ }
+    else
+      { array := as,
+        start := as.size,
+        stop := as.size,
+        start_le_stop := Nat.le_refl _,
+        stop_le_array_size := Nat.le_refl _ }
 
 @[coe]
 def ofSubarray (s : Subarray α) : Array α := Id.run do

src/Init/Data/Array/Subarray/Split.lean

@@ -0,0 +1,71 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: David Thrane Christiansen
+-/
+
+prelude
+import Init.Data.Array.Basic
+import Init.Data.Array.Subarray
+import Init.Omega
+
+/-
+This module contains splitting operations on subarrays that crucially rely on `omega` for proof
+automation. Placing them in another module breaks an import cycle, because `omega` itself uses the
+array library.
+-/
+
+namespace Subarray
+/--
+Splits a subarray into two parts.
+-/
+def split (s : Subarray α) (i : Fin s.size.succ) : (Subarray α × Subarray α) :=
+  let ⟨i', isLt⟩ := i
+  have := s.start_le_stop
+  have := s.stop_le_array_size
+  have : i' ≤ s.stop - s.start := Nat.lt_succ.mp isLt
+  have : s.start + i' ≤ s.stop := by omega
+  have : s.start + i' ≤ s.array.size := by omega
+  have : s.start + i' ≤ s.stop := by
+    simp only [size] at isLt
+    omega
+  let pre := {s with
+    stop := s.start + i',
+    start_le_stop := by omega,
+    stop_le_array_size := by assumption
+  }
+  let post := {s with
+    start := s.start + i'
+    start_le_stop := by assumption
+  }
+  (pre, post)
+
+/--
+Removes the first `i` elements of the subarray. If there are `i` or fewer elements, the resulting
+subarray is empty.
+-/
+def drop (arr : Subarray α) (i : Nat) : Subarray α where
+  array := arr.array
+  start := min (arr.start + i) arr.stop
+  stop := arr.stop
+  start_le_stop := by
+    rw [Nat.min_def]
+    split <;> simp only [Nat.le_refl, *]
+  stop_le_array_size := arr.stop_le_array_size
+
+/--
+Keeps only the first `i` elements of the subarray. If there are `i` or fewer elements, the resulting
+subarray is empty.
+-/
+def take (arr : Subarray α) (i : Nat) : Subarray α where
+  array := arr.array
+  start := arr.start
+  stop := min (arr.start + i) arr.stop
+  start_le_stop := by
+    have := arr.start_le_stop
+    rw [Nat.min_def]
+    split <;> omega
+  stop_le_array_size := by
+    have := arr.stop_le_array_size
+    rw [Nat.min_def]
+    split <;> omega

src/Init/Data/BitVec/Basic.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer
+Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed
 -/
 prelude
 import Init.Data.Fin.Basic
@@ -34,7 +34,7 @@ structure BitVec (w : Nat) where
   O(1), because we use `Fin` as the internal representation of a bitvector. -/
   toFin : Fin (2^w)
 
-@[deprecated] abbrev Std.BitVec := _root_.BitVec
+@[deprecated] protected abbrev Std.BitVec := _root_.BitVec
 
 -- We manually derive the `DecidableEq` instances for `BitVec` because
 -- we want to have builtin support for bit-vector literals, and we

src/Init/Data/BitVec/Lemmas.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix
+Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed,
 -/
 prelude
 import Init.Data.Bool
@@ -728,8 +728,7 @@ theorem toNat_cons' {x : BitVec w} :
   rw [← BitVec.msb, msb_cons]
 
 @[simp] theorem getMsb_cons_succ : (cons a x).getMsb (i + 1) = x.getMsb i := by
-  simp [cons, cond_eq_if]
-  omega
+  simp [cons, Nat.le_add_left 1 i]
 
 theorem truncate_succ (x : BitVec w) :
     truncate (i+1) x = cons (getLsb x i) (truncate i x) := by
@@ -818,9 +817,13 @@ Definition of bitvector addition as a nat.
   .ofFin x + y = .ofFin (x + y.toFin) := rfl
 @[simp] theorem add_ofFin (x : BitVec n) (y : Fin (2^n)) :
   x + .ofFin y = .ofFin (x.toFin + y) := rfl
-@[simp] theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n := by
+
+theorem ofNat_add {n} (x y : Nat) : (x + y)#n = x#n + y#n := by
   apply eq_of_toNat_eq ; simp [BitVec.ofNat]
 
+theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n :=
+  (ofNat_add x y).symm
+
 protected theorem add_assoc (x y z : BitVec n) : x + y + z = x + (y + z) := by
   apply eq_of_toNat_eq ; simp [Nat.add_assoc]
 
@@ -836,6 +839,15 @@ theorem truncate_add (x y : BitVec w) (h : i ≤ w) :
   have dvd : 2^i ∣ 2^w := Nat.pow_dvd_pow _ h
   simp [bv_toNat, h, Nat.mod_mod_of_dvd _ dvd]
 
+@[simp, bv_toNat] theorem toInt_add (x y : BitVec w) :
+  (x + y).toInt = (x.toInt + y.toInt).bmod (2^w) := by
+  simp [toInt_eq_toNat_bmod]
+
+theorem ofInt_add {n} (x y : Int) : BitVec.ofInt n (x + y) =
+    BitVec.ofInt n x + BitVec.ofInt n y := by
+  apply eq_of_toInt_eq
+  simp
+
 /-! ### sub/neg -/
 
 theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n (x.toNat + (2^n - y.toNat)) := by rfl
@@ -912,6 +924,15 @@ instance : Std.Associative (fun (x y : BitVec w) => x * y) := ⟨BitVec.mul_asso
 instance : Std.LawfulCommIdentity (fun (x y : BitVec w) => x * y) (1#w) where
   right_id := BitVec.mul_one
 
+@[simp, bv_toNat] theorem toInt_mul (x y : BitVec w) :
+  (x * y).toInt = (x.toInt * y.toInt).bmod (2^w) := by
+  simp [toInt_eq_toNat_bmod]
+
+theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
+    BitVec.ofInt n x * BitVec.ofInt n y := by
+  apply eq_of_toInt_eq
+  simp
+
 /-! ### le and lt -/
 
 @[bv_toNat] theorem le_def (x y : BitVec n) :

src/Init/Data/Bool.lean

@@ -220,6 +220,12 @@ due to `beq_iff_eq`.
 
 /-! ### coercision related normal forms -/
 
+theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
+    (a == b) = decide (a = b) := by
+  cases h : a == b
+  · simp [ne_of_beq_false h]
+  · simp [eq_of_beq h]
+
 @[simp] theorem not_eq_not : ∀ {a b : Bool}, ¬a = !b ↔ a = b := by decide
 
 @[simp] theorem not_not_eq : ∀ {a b : Bool}, ¬(!a) = b ↔ a = b := by decide
@@ -230,6 +236,11 @@ due to `beq_iff_eq`.
 @[simp] theorem coe_false_iff_true  : ∀(a b : Bool), (a = false ↔ b) ↔ (!a) = b := by decide
 @[simp] theorem coe_false_iff_false : ∀(a b : Bool), (a = false ↔ b = false) ↔ (!a) = (!b) := by decide
 
+/-! ### beq properties -/
+
+theorem beq_comm {α} [BEq α] [LawfulBEq α] {a b : α} : (a == b) = (b == a) :=
+  (Bool.coe_iff_coe (a == b) (b == a)).mp (by simp [@eq_comm α])
+
 /-! ### xor -/
 
 theorem false_xor : ∀ (x : Bool), xor false x = x := false_bne

src/Init/Data/ByteArray/Basic.lean

@@ -52,9 +52,13 @@ def get : (a : @& ByteArray) → (@& Fin a.size) → UInt8
 instance : GetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
   getElem xs i h := xs.get ⟨i, h⟩
 
+instance : LawfulGetElem ByteArray Nat UInt8 fun xs i => i < xs.size where
+
 instance : GetElem ByteArray USize UInt8 fun xs i => i.val < xs.size where
   getElem xs i h := xs.uget i h
 
+instance : LawfulGetElem ByteArray USize UInt8 fun xs i => i.val < xs.size where
+
 @[extern "lean_byte_array_set"]
 def set! : ByteArray → (@& Nat) → UInt8 → ByteArray
   | ⟨bs⟩, i, b => ⟨bs.set! i b⟩
@@ -195,18 +199,6 @@ instance : ToString ByteArray := ⟨fun bs => bs.toList.toString⟩
 
 /-- Interpret a `ByteArray` of size 8 as a little-endian `UInt64`. -/
 def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
-  assert! bs.size == 8
-  (bs.get! 0).toUInt64 <<< 0x38 |||
-  (bs.get! 1).toUInt64 <<< 0x30 |||
-  (bs.get! 2).toUInt64 <<< 0x28 |||
-  (bs.get! 3).toUInt64 <<< 0x20 |||
-  (bs.get! 4).toUInt64 <<< 0x18 |||
-  (bs.get! 5).toUInt64 <<< 0x10 |||
-  (bs.get! 6).toUInt64 <<< 0x8  |||
-  (bs.get! 7).toUInt64
-
-/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
-def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
   assert! bs.size == 8
   (bs.get! 7).toUInt64 <<< 0x38 |||
   (bs.get! 6).toUInt64 <<< 0x30 |||
@@ -216,3 +208,15 @@ def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
   (bs.get! 2).toUInt64 <<< 0x10 |||
   (bs.get! 1).toUInt64 <<< 0x8  |||
   (bs.get! 0).toUInt64
+
+/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
+def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
+  assert! bs.size == 8
+  (bs.get! 0).toUInt64 <<< 0x38 |||
+  (bs.get! 1).toUInt64 <<< 0x30 |||
+  (bs.get! 2).toUInt64 <<< 0x28 |||
+  (bs.get! 3).toUInt64 <<< 0x20 |||
+  (bs.get! 4).toUInt64 <<< 0x18 |||
+  (bs.get! 5).toUInt64 <<< 0x10 |||
+  (bs.get! 6).toUInt64 <<< 0x8  |||
+  (bs.get! 7).toUInt64

src/Init/Data/Fin/Basic.lean

@@ -4,9 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura, Robert Y. Lewis, Keeley Hoek, Mario Carneiro
 -/
 prelude
-import Init.Data.Nat.Div
 import Init.Data.Nat.Bitwise.Basic
-import Init.Coe
 
 open Nat
 
@@ -15,17 +13,40 @@ namespace Fin
 instance coeToNat : CoeOut (Fin n) Nat :=
   ⟨fun v => v.val⟩
 
+/--
+From the empty type `Fin 0`, any desired result `α` can be derived. This is simlar to `Empty.elim`.
+-/
 def elim0.{u} {α : Sort u} : Fin 0 → α
   | ⟨_, h⟩ => absurd h (not_lt_zero _)
 
+/--
+Returns the successor of the argument.
+
+The bound in the result type is increased:
+```
+(2 : Fin 3).succ = (3 : Fin 4)
+```
+This differs from addition, which wraps around:
+```
+(2 : Fin 3) + 1 = (0 : Fin 3)
+```
+-/
 def succ : Fin n → Fin n.succ
   | ⟨i, h⟩ => ⟨i+1, Nat.succ_lt_succ h⟩
 
 variable {n : Nat}
 
+/--
+Returns `a` modulo `n + 1` as a `Fin n.succ`.
+-/
 protected def ofNat {n : Nat} (a : Nat) : Fin n.succ :=
   ⟨a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)⟩
 
+/--
+Returns `a` modulo `n` as a `Fin n`.
+
+The assumption `n > 0` ensures that `Fin n` is nonempty.
+-/
 protected def ofNat' {n : Nat} (a : Nat) (h : n > 0) : Fin n :=
   ⟨a % n, Nat.mod_lt _ h⟩
 
@@ -35,12 +56,15 @@ private theorem mlt {b : Nat} : {a : Nat} → a < n → b % n < n
     have : n > 0 := Nat.lt_trans (Nat.zero_lt_succ _) h;
     Nat.mod_lt _ this
 
+/-- Addition modulo `n` -/
 protected def add : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + b) % n, mlt h⟩
 
+/-- Multiplication modulo `n` -/
 protected def mul : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a * b) % n, mlt h⟩
 
+/-- Subtraction modulo `n` -/
 protected def sub : Fin n → Fin n → Fin n
   | ⟨a, h⟩, ⟨b, _⟩ => ⟨(a + (n - b)) % n, mlt h⟩
 
@@ -170,9 +194,3 @@ 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
 
 end Fin
-
-instance [GetElem cont Nat elem dom] : GetElem cont (Fin n) elem fun xs i => dom xs i where
-  getElem xs i h := getElem xs i.1 h
-
-macro_rules
-  | `(tactic| get_elem_tactic_trivial) => `(tactic| apply Fin.val_lt_of_le; get_elem_tactic_trivial; done)

src/Init/Data/Fin/Lemmas.lean

@@ -541,7 +541,7 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
     ∀ {a b : Fin (n + 1)} {ha : a ≠ 0} {hb : b ≠ 0}, a.pred ha = b.pred hb ↔ a = b
   | ⟨0, _⟩, _, ha, _ => by simp only [mk_zero, ne_eq, not_true] at ha
   | ⟨i + 1, _⟩, ⟨0, _⟩, _, hb => by simp only [mk_zero, ne_eq, not_true] at hb
-  | ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [ext_iff]
+  | ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [ext_iff, Nat.succ.injEq]
 
 @[simp] theorem pred_one {n : Nat} :
     Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
@@ -683,6 +683,7 @@ and `cast` defines the inductive step using `motive i.succ`, inducting downwards
 termination_by n + 1 - i
 decreasing_by decreasing_with
   -- FIXME: we put the proof down here to avoid getting a dummy `have` in the definition
+  try simp only [Nat.succ_sub_succ_eq_sub]
   exact Nat.add_sub_add_right .. ▸ Nat.sub_lt_sub_left i.2 (Nat.lt_succ_self i)
 
 @[simp] theorem reverseInduction_last {n : Nat} {motive : Fin (n + 1) → Sort _} {zero succ} :

src/Init/Data/FloatArray/Basic.lean

@@ -58,9 +58,13 @@ def get? (ds : FloatArray) (i : Nat) : Option Float :=
 instance : GetElem FloatArray Nat Float fun xs i => i < xs.size where
   getElem xs i h := xs.get ⟨i, h⟩
 
+instance : LawfulGetElem FloatArray Nat Float fun xs i => i < xs.size where
+
 instance : GetElem FloatArray USize Float fun xs i => i.val < xs.size where
   getElem xs i h := xs.uget i h
 
+instance : LawfulGetElem FloatArray USize Float fun xs i => i.val < xs.size where
+
 @[extern "lean_float_array_uset"]
 def uset : (a : FloatArray) → (i : USize) → Float → i.toNat < a.size → FloatArray
   | ⟨ds⟩, i, v, h => ⟨ds.uset i v h⟩

src/Init/Data/Int/Basic.lean

@@ -100,7 +100,7 @@ protected def neg (n : @& Int) : Int :=
   ```
 -/
 @[default_instance mid]
-instance : Neg Int where
+instance instNegInt : Neg Int where
   neg := Int.neg
 
 /-- Subtraction of two natural numbers. -/
@@ -173,13 +173,13 @@ inductive NonNeg : Int → Prop where
 /-- Definition of `a ≤ b`, encoded as `b - a ≥ 0`. -/
 protected def le (a b : Int) : Prop := NonNeg (b - a)
 
-instance : LE Int where
+instance instLEInt : LE Int where
   le := Int.le
 
 /-- Definition of `a < b`, encoded as `a + 1 ≤ b`. -/
 protected def lt (a b : Int) : Prop := (a + 1) ≤ b
 
-instance : LT Int where
+instance instLTInt : LT Int where
   lt := Int.lt
 
 set_option bootstrap.genMatcherCode false in

src/Init/Data/Int/DivModLemmas.lean

@@ -8,6 +8,7 @@ prelude
 import Init.Data.Int.DivMod
 import Init.Data.Int.Order
 import Init.Data.Nat.Dvd
+import Init.RCases
 
 /-!
 # Lemmas about integer division needed to bootstrap `omega`.
@@ -1053,19 +1054,39 @@ theorem emod_add_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n + y) n = Int.bmo
   simp [Int.emod_def, Int.sub_eq_add_neg]
   rw [←Int.mul_neg, Int.add_right_comm,  Int.bmod_add_mul_cancel]
 
+@[simp]
+theorem emod_mul_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n * y) n = Int.bmod (x * y) n := by
+  simp [Int.emod_def, Int.sub_eq_add_neg]
+  rw [←Int.mul_neg, Int.add_mul, Int.mul_assoc, Int.bmod_add_mul_cancel]
+
 @[simp]
 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 =>
+    simp only [emod_add_bmod_congr]
+  case inr p =>
+    rw [Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg]
+    simp
+
+@[simp] theorem add_bmod_bmod : Int.bmod (x + Int.bmod y n) n = Int.bmod (x + y) n := by
+  rw [Int.add_comm x, Int.bmod_add_bmod_congr, Int.add_comm y]
+
+@[simp]
+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 =>
     simp
   case inr p =>
-    rw [Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg]
+    rw [Int.sub_mul, Int.sub_eq_add_neg, ← Int.mul_neg]
     simp
 
-@[simp]
-theorem add_bmod_bmod : Int.bmod (x + Int.bmod y n) n = Int.bmod (x + y) n := by
-  rw [Int.add_comm x, Int.bmod_add_bmod_congr, Int.add_comm y]
+@[simp] theorem mul_bmod_bmod : Int.bmod (x * Int.bmod y n) n = Int.bmod (x * y) n := by
+  rw [Int.mul_comm x, bmod_mul_bmod, Int.mul_comm x]
+
+theorem add_bmod (a b : Int) (n : Nat) : (a + b).bmod n = (a.bmod n + b.bmod n).bmod n := by
+  simp
 
 theorem emod_bmod {x : Int} {m : Nat} : bmod (x % m) m = bmod x m := by
   simp [bmod]

src/Init/Data/Int/Lemmas.lean

@@ -6,7 +6,7 @@ Authors: Jeremy Avigad, Deniz Aydin, Floris van Doorn, Mario Carneiro
 prelude
 import Init.Data.Int.Basic
 import Init.Conv
-import Init.PropLemmas
+import Init.NotationExtra
 
 namespace Int
 

src/Init/Data/Int/Order.lean

@@ -6,7 +6,6 @@ Authors: Jeremy Avigad, Deniz Aydin, Floris van Doorn, Mario Carneiro
 prelude
 import Init.Data.Int.Lemmas
 import Init.ByCases
-import Init.RCases
 
 /-!
 # Results about the order properties of the integers, and the integers as an ordered ring.
@@ -999,7 +998,8 @@ theorem natAbs_add_le (a b : Int) : natAbs (a + b) ≤ natAbs a + natAbs b := by
   refine fun a b => subNatNat_elim a b.succ
     (fun m n i => n = b.succ → natAbs i ≤ (m + b).succ) ?_
     (fun i n (e : (n + i).succ = _) => ?_) rfl
-  · rintro i n rfl
+  · intro i n h
+    subst h
     rw [Nat.add_comm _ i, Nat.add_assoc]
     exact Nat.le_add_right i (b.succ + b).succ
   · apply succ_le_succ

src/Init/Data/List.lean

@@ -8,3 +8,4 @@ import Init.Data.List.Basic
 import Init.Data.List.BasicAux
 import Init.Data.List.Control
 import Init.Data.List.Lemmas
+import Init.Data.List.Impl

src/Init/Data/List/Basic.lean

@@ -7,6 +7,7 @@ prelude
 import Init.SimpLemmas
 import Init.Data.Nat.Basic
 import Init.Data.Nat.Div
+
 set_option linter.missingDocs true -- keep it documented
 open Decidable List
 
@@ -54,15 +55,6 @@ variable {α : Type u} {β : Type v} {γ : Type w}
 
 namespace List
 
-instance : GetElem (List α) Nat α fun as i => i < as.length where
-  getElem as i h := as.get ⟨i, h⟩
-
-@[simp] theorem cons_getElem_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
-  rfl
-
 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]
@@ -520,11 +512,6 @@ def drop : Nat → List α → List α
 @[simp] theorem drop_nil : ([] : List α).drop i = [] := by
   cases i <;> rfl
 
-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
-  | _::_, i+1 => get_drop_eq_drop _ i _
-
 /--
 `O(min n |xs|)`. Returns the first `n` elements of `xs`, or the whole list if `n` is too large.
 * `take 0 [a, b, c, d, e] = []`

src/Init/Data/List/BasicAux.lean

@@ -12,60 +12,139 @@ 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`. -/
 
-def get! [Inhabited α] : List α → Nat → α
+/--
+Returns the `i`-th element in the list (zero-based).
+
+If the index is out of bounds (`i ≥ as.length`), this function panics when executed, and returns
+`default`. See `get?` and `getD` for safer alternatives.
+-/
+def get! [Inhabited α] : (as : List α) → (i : Nat) → α
   | a::_,  0   => a
   | _::as, n+1 => get! as n
   | _,     _   => panic! "invalid index"
 
-def get? : List α → Nat → Option α
+/--
+Returns the `i`-th element in the list (zero-based).
+
+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
 
-def getD (as : List α) (idx : Nat) (a₀ : α) : α :=
-  (as.get? idx).getD a₀
+/--
+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
+
+/--
+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
 
-def headD : List α → α → α
-  | [],   a₀ => a₀
+/--
+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
 
-def tailD : List α → List α → List α
-  | [],   as₀ => as₀
-  | _::as, _  => 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)
 
+/--
+Returns the last element in the list.
+
+If the list is empty, this function panics when executed, and returns `default`.
+See `getLast` and `getLastD` for safer alternatives.
+-/
 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.
+
+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))
 
-def getLastD : List α → α → α
+/--
+Returns the last element in the list.
+
+If the list is empty, this function returns `fallback`.
+Also see `getLast?` and `getLast!`.
+-/
+def getLastD : (as : List α) → (fallback : α) → α
   | [],   a₀ => a₀
   | a::as, _ => getLast (a::as) (fun h => List.noConfusion h)
 

src/Init/Data/List/Control.lean

@@ -40,6 +40,13 @@ Finally, we rarely use `mapM` with something that is not a `Monad`.
 Users that want to use `mapM` with `Applicative` should use `mapA` instead.
 -/
 
+/--
+Applies the monadic action `f` on every element in the list, left-to-right, and returns the list of
+results.
+
+See `List.forM` for the variant that discards the results.
+See `List.mapA` for the variant that works with `Applicative`.
+-/
 @[inline]
 def mapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m β) (as : List α) : m (List β) :=
   let rec @[specialize] loop
@@ -47,17 +54,42 @@ def mapM {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α
     | a :: as, bs => do loop as ((← f a)::bs)
   loop as []
 
+/--
+Applies the applicative action `f` on every element in the list, left-to-right, and returns the list of
+results.
+
+NB: If `m` is also a `Monad`, then using `mapM` can be more efficient.
+
+See `List.forA` for the variant that discards the results.
+See `List.mapM` for the variant that works with `Monad`.
+
+**Warning**: this function is not tail-recursive, meaning that it may fail with a stack overflow on long lists.
+-/
 @[specialize]
 def mapA {m : Type u → Type v} [Applicative m] {α : Type w} {β : Type u} (f : α → m β) : List α → m (List β)
   | []    => pure []
   | a::as => List.cons <$> f a <*> mapA f as
 
+/--
+Applies the monadic action `f` on every element in the list, left-to-right.
+
+See `List.mapM` for the variant that collects results.
+See `List.forA` for the variant that works with `Applicative`.
+-/
 @[specialize]
 protected def forM {m : Type u → Type v} [Monad m] {α : Type w} (as : List α) (f : α → m PUnit) : m PUnit :=
   match as with
   | []      => pure ⟨⟩
   | a :: as => do f a; List.forM as f
 
+/--
+Applies the applicative action `f` on every element in the list, left-to-right.
+
+NB: If `m` is also a `Monad`, then using `forM` can be more efficient.
+
+See `List.mapA` for the variant that collects results.
+See `List.forM` for the variant that works with `Monad`.
+-/
 @[specialize]
 def forA {m : Type u → Type v} [Applicative m] {α : Type w} (as : List α) (f : α → m PUnit) : m PUnit :=
   match as with
@@ -71,15 +103,27 @@ def filterAuxM {m : Type → Type v} [Monad m] {α : Type} (f : α → m Bool) :
     let b ← f h
     filterAuxM f t (cond b (h :: acc) acc)
 
+/--
+Applies the monadic predicate `p` on every element in the list, left-to-right, and returns those
+elements `x` for which `p x` returns `true`.
+-/
 @[inline]
-def filterM {m : Type → Type v} [Monad m] {α : Type} (f : α → m Bool) (as : List α) : m (List α) := do
-  let as ← filterAuxM f as []
+def filterM {m : Type → Type v} [Monad m] {α : Type} (p : α → m Bool) (as : List α) : m (List α) := do
+  let as ← filterAuxM p as []
   pure as.reverse
 
+/--
+Applies the monadic predicate `p` on every element in the list, right-to-left, and returns those
+elements `x` for which `p x` returns `true`.
+-/
 @[inline]
-def filterRevM {m : Type → Type v} [Monad m] {α : Type} (f : α → m Bool) (as : List α) : m (List α) :=
-  filterAuxM f as.reverse []
+def filterRevM {m : Type → Type v} [Monad m] {α : Type} (p : α → m Bool) (as : List α) : m (List α) :=
+  filterAuxM p as.reverse []
 
+/--
+Applies the monadic function `f` on every element `x` in the list, left-to-right, and returns those
+results `y` for which `f x` returns `some y`.
+-/
 @[inline]
 def filterMapM {m : Type u → Type v} [Monad m] {α β : Type u} (f : α → m (Option β)) (as : List α) : m (List β) :=
   let rec @[specialize] loop
@@ -90,6 +134,16 @@ def filterMapM {m : Type u → Type v} [Monad m] {α β : Type u} (f : α → m
       | some b => loop as (b::bs)
   loop as.reverse []
 
+/--
+Folds a monadic function over a list from left to right:
+```
+foldlM f x₀ [a, b, c] = do
+  let x₁ ← f x₀ a
+  let x₂ ← f x₁ b
+  let x₃ ← f x₂ c
+  pure x₃
+```
+-/
 @[specialize]
 protected def foldlM {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} : (f : s → α → m s) → (init : s) → List α → m s
   | _, s, []      => pure s
@@ -97,10 +151,26 @@ 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
 
+/--
+Folds a monadic function over a list from right to left:
+```
+foldrM f x₀ [a, b, c] = do
+  let x₁ ← f c x₀
+  let x₂ ← f b x₁
+  let x₃ ← f a x₂
+  pure x₃
+```
+-/
 @[inline]
 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
 
+/--
+Maps `f` over the list and collects the results with `<|>`.
+```
+firstM f [a, b, c] = f a <|> f b <|> f c <|> failure
+```
+-/
 @[specialize]
 def firstM {m : Type u → Type v} [Alternative m] {α : Type w} {β : Type u} (f : α → m β) : List α → m β
   | []    => failure

src/Init/Data/List/Impl.lean

@@ -0,0 +1,261 @@
+/-
+Copyright (c) 2016 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+
+prelude
+import Init.Data.Array.Lemmas
+
+/-!
+## Tail recursive implementations for `List` definitions.
+
+Many of the proofs require theorems about `Array`,
+so these are in a separate file to minimize imports.
+-/
+
+namespace List
+
+/-- Tail recursive version of `erase`. -/
+@[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` -/
+  go : List α → Nat → Array α → List α
+  | [], _, _ => l
+  | _::xs, 0, acc => acc.toListAppend (a::xs)
+  | x::xs, n+1, acc => go xs n (acc.push x)
+
+@[csimp] theorem set_eq_setTR : @set = @setTR := by
+  funext α l n a; simp [setTR]
+  let rec go (acc) : ∀ xs n, l = acc.data ++ xs →
+    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]
+  exact (go #[] _ _ rfl).symm
+
+/-- Tail recursive version of `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` -/
+  go : List α → Array α → List α
+  | [], _ => l
+  | x::xs, acc => bif x == a then acc.toListAppend xs else go xs (acc.push x)
+
+@[csimp] theorem erase_eq_eraseTR : @List.erase = @eraseTR := by
+  funext α _ l a; simp [eraseTR]
+  suffices ∀ xs acc, l = acc.data ++ xs → eraseTR.go l a xs acc = acc.data ++ xs.erase a from
+    (this l #[] (by simp)).symm
+  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
+
+/-- Tail recursive version of `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` -/
+  go : List α → Nat → Array α → List α
+  | [], _, _ => l
+  | _::as, 0, acc => acc.toListAppend as
+  | a::as, n+1, acc => go as n (acc.push a)
+
+@[csimp] theorem eraseIdx_eq_eraseIdxTR : @eraseIdx = @eraseIdxTR := by
+  funext α l n; simp [eraseIdxTR]
+  suffices ∀ xs acc, l = acc.data ++ xs → eraseIdxTR.go l xs n acc = acc.data ++ xs.eraseIdx n from
+    (this l #[] (by simp)).symm
+  intro xs; induction xs generalizing n with intro acc h
+  | nil => simp [eraseIdx, eraseIdxTR.go, h]
+  | cons x xs IH =>
+    match n with
+    | 0 => simp [eraseIdx, eraseIdxTR.go]
+    | n+1 =>
+      simp [eraseIdx, eraseIdxTR.go]
+      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)
+
+@[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
+
+/-- 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`. -/
+@[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
+  | a::as, b::bs, acc => go as bs (acc.push (f a b))
+  | _, _, acc => acc.toList
+
+@[csimp] theorem zipWith_eq_zipWithTR : @zipWith = @zipWithTR := by
+  funext α β γ f as bs
+  let rec go : ∀ as bs acc, zipWithTR.go f as bs acc = acc.data ++ as.zipWith f bs
+    | [], _, acc | _::_, [], acc => by simp [zipWithTR.go, zipWith]
+    | a::as, b::bs, acc => by simp [zipWithTR.go, zipWith, go as bs]
+  exact (go as bs #[]).symm
+
+/-- Tail recursive version of `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`. -/
+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
+
+@[csimp] theorem enumFrom_eq_enumFromTR : @enumFrom = @enumFromTR := by
+  funext α n l; simp [enumFromTR, -Array.size_toArray]
+  let f := fun (a : α) (n, acc) => (n-1, (n-1, a) :: acc)
+  let rec go : ∀ l n, l.foldr f (n + l.length, []) = (n, enumFrom n l)
+    | [], n => rfl
+    | a::as, n => by
+      rw [← show _ + as.length = n + (a::as).length from Nat.succ_add .., foldr, go as]
+      simp [enumFrom, f]
+  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
+
+/-- 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]
+
+/-- Tail recursive version of `intersperse`. -/
+def intersperseTR (sep : α) : List α → List α
+  | [] => []
+  | [x] => [x]
+  | x::y::xs => x :: sep :: y :: xs.foldr (fun a r => sep :: a :: r) []
+
+@[csimp] theorem intersperse_eq_intersperseTR : @intersperse = @intersperseTR := by
+  funext α sep l; simp [intersperseTR]
+  match l with
+  | [] | [_] => rfl
+  | x::y::xs => simp [intersperse]; induction xs generalizing y <;> simp [*]
+
+/-- Tail recursive version of `intercalate`. -/
+def intercalateTR (sep : List α) : List (List α) → List α
+  | [] => []
+  | [x] => x
+  | x::xs => go sep.toArray x xs #[]
+where
+  /-- Auxiliary for `intercalateTR`:
+  `intercalateTR.go sep x xs acc = acc.toList ++ intercalate sep.toList (x::xs)` -/
+  go (sep : Array α) : List α → List (List α) → Array α → List α
+  | x, [], acc => acc.toListAppend x
+  | x, y::xs, acc => go sep y xs (acc ++ x ++ sep)
+
+@[csimp] theorem intercalate_eq_intercalateTR : @intercalate = @intercalateTR := by
+  funext α sep l; simp [intercalate, intercalateTR]
+  match l with
+  | [] => rfl
+  | [_] => simp
+  | x::y::xs =>
+    let rec go {acc x} : ∀ xs,
+      intercalateTR.go sep.toArray x xs acc = acc.data ++ join (intersperse sep (x::xs))
+    | [] => by simp [intercalateTR.go]
+    | _::_ => by simp [intercalateTR.go, go]
+    simp [intersperse, go]
+
+end List

src/Init/Data/List/Lemmas.lean

@@ -249,12 +249,14 @@ theorem getD_eq_get? : ∀ l n (a : α), getD l n a = (get? l n).getD a
 theorem get?_append_right : ∀ {l₁ l₂ : List α} {n : Nat}, l₁.length ≤ n →
   (l₁ ++ l₂).get? n = l₂.get? (n - l₁.length)
 | [], _, n, _ => rfl
-| a :: l, _, n+1, h₁ => by rw [cons_append]; simp [get?_append_right (Nat.lt_succ.1 h₁)]
+| a :: l, _, n+1, h₁ => by
+  rw [cons_append]
+  simp [Nat.succ_sub_succ_eq_sub, get?_append_right (Nat.lt_succ.1 h₁)]
 
 theorem get?_reverse' : ∀ {l : List α} (i j), i + j + 1 = length l →
     get? l.reverse i = get? l j
   | [], _, _, _ => rfl
-  | a::l, i, 0, h => by simp at h; simp [h, get?_append_right]
+  | a::l, i, 0, h => by simp [Nat.succ.injEq] at h; simp [h, get?_append_right, Nat.succ.injEq]
   | a::l, i, j+1, h => by
     have := Nat.succ.inj h; simp at this ⊢
     rw [get?_append, get?_reverse' _ j this]
@@ -711,3 +713,5 @@ theorem minimum?_eq_some_iff [Min α] [LE α] [anti : Antisymm ((· : α) ≤ ·
   | _ :: l, i + 1, j + 1 => by
     have g : i ≠ j := h ∘ congrArg (· + 1)
     simp [get_set_ne l g]
+
+end List

src/Init/Data/Nat.lean

@@ -19,3 +19,4 @@ import Init.Data.Nat.Lemmas
 import Init.Data.Nat.Mod
 import Init.Data.Nat.Lcm
 import Init.Data.Nat.Compare
+import Init.Data.Nat.Simproc

src/Init/Data/Nat/Basic.lean

@@ -174,7 +174,7 @@ protected theorem add_right_comm (n m k : Nat) : (n + m) + k = (n + k) + m := by
 protected theorem add_left_cancel {n m k : Nat} : n + m = n + k → m = k := by
   induction n with
   | zero => simp
-  | succ n ih => simp [succ_add]; intro h; apply ih h
+  | succ n ih => simp [succ_add, succ.injEq]; intro h; apply ih h
 
 protected theorem add_right_cancel {n m k : Nat} (h : n + m = k + m) : n = k := by
   rw [Nat.add_comm n m, Nat.add_comm k m] at h
@@ -248,7 +248,7 @@ theorem lt_succ_of_le {n m : Nat} : n ≤ m → n < succ m := succ_le_succ
 
 @[simp] protected theorem sub_zero (n : Nat) : n - 0 = n := rfl
 
-@[simp] theorem succ_sub_succ_eq_sub (n m : Nat) : succ n - succ m = n - m := by
+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
@@ -574,7 +574,7 @@ theorem eq_zero_or_eq_succ_pred : ∀ n, n = 0 ∨ n = succ (pred n)
   | 0 => .inl rfl
   | _+1 => .inr rfl
 
-theorem succ_inj' : succ a = succ b ↔ a = b := ⟨succ.inj, congrArg _⟩
+theorem succ_inj' : succ a = succ b ↔ a = b := (Nat.succ.injEq a b).to_iff
 
 theorem succ_le_succ_iff : succ a ≤ succ b ↔ a ≤ b := ⟨le_of_succ_le_succ, succ_le_succ⟩
 
@@ -802,7 +802,7 @@ theorem add_sub_of_le {a b : Nat} (h : a ≤ b) : a + (b - a) = b := by
 protected theorem add_sub_add_right (n k m : Nat) : (n + k) - (m + k) = n - m := by
   induction k with
   | zero => simp
-  | succ k ih => simp [← Nat.add_assoc, ih]
+  | succ k ih => simp [← Nat.add_assoc, succ_sub_succ_eq_sub, ih]
 
 protected theorem add_sub_add_left (k n m : Nat) : (k + n) - (k + m) = n - m := by
   rw [Nat.add_comm k n, Nat.add_comm k m, Nat.add_sub_add_right]

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

@@ -9,6 +9,7 @@ import Init.Data.Bool
 import Init.Data.Int.Pow
 import Init.Data.Nat.Bitwise.Basic
 import Init.Data.Nat.Lemmas
+import Init.Data.Nat.Simproc
 import Init.TacticsExtra
 import Init.Omega
 
@@ -271,7 +272,7 @@ theorem testBit_two_pow_sub_succ (h₂ : x < 2 ^ n) (i : Nat) :
   induction i generalizing n x with
   | zero =>
     match n with
-    | 0 => simp
+    | 0 => simp [succ_sub_succ_eq_sub]
     | n+1 =>
       simp [not_decide_mod_two_eq_one]
       omega
@@ -279,7 +280,7 @@ theorem testBit_two_pow_sub_succ (h₂ : x < 2 ^ n) (i : Nat) :
     simp only [testBit_succ]
     match n with
     | 0 =>
-      simp [decide_eq_false]
+      simp [decide_eq_false, succ_sub_succ_eq_sub]
     | n+1 =>
       rw [Nat.two_pow_succ_sub_succ_div_two, ih]
       · simp [Nat.succ_lt_succ_iff]

src/Init/Data/Nat/Div.lean

@@ -28,7 +28,7 @@ protected def div (x y : @& Nat) : Nat :=
     0
 decreasing_by apply div_rec_lemma; assumption
 
-instance : Div Nat := ⟨Nat.div⟩
+instance instDiv : Div Nat := ⟨Nat.div⟩
 
 theorem div_eq (x y : Nat) : x / y = if 0 < y ∧ y ≤ x then (x - y) / y + 1 else 0 := by
   show Nat.div x y = _
@@ -90,7 +90,7 @@ protected def mod : @& Nat → @& Nat → Nat
   | 0, _ => 0
   | x@(_ + 1), y => Nat.modCore x y
 
-instance : Mod Nat := ⟨Nat.mod⟩
+instance instMod : Mod Nat := ⟨Nat.mod⟩
 
 protected theorem modCore_eq_mod (x y : Nat) : Nat.modCore x y = x % y := by
   cases x with

src/Init/Data/Nat/Gcd.lean

@@ -10,6 +10,24 @@ import Init.RCases
 
 namespace Nat
 
+/--
+Computes the greatest common divisor of two natural numbers.
+
+This reference implementation via the Euclidean algorithm
+is overridden in both the kernel and the compiler to efficiently
+evaluate using the "bignum" representation (see `Nat`).
+The definition provided here is the logical model
+(and it is soundness-critical that they coincide).
+
+The GCD of two natural numbers is the largest natural number
+that divides both arguments.
+In particular, the GCD of a number and `0` is the number itself:
+```
+example : Nat.gcd 10 15 = 5 := rfl
+example : Nat.gcd 0 5 = 5 := rfl
+example : Nat.gcd 7 0 = 7 := rfl
+```
+-/
 @[extern "lean_nat_gcd"]
 def gcd (m n : @& Nat) : Nat :=
   if m = 0 then

src/Init/Data/Nat/Lemmas.lean

@@ -88,7 +88,7 @@ protected theorem add_pos_right (m) (h : 0 < n) : 0 < m + n :=
   Nat.lt_of_lt_of_le h (Nat.le_add_left ..)
 
 protected theorem add_self_ne_one : ∀ n, n + n ≠ 1
-  | n+1, h => by rw [Nat.succ_add, Nat.succ_inj'] at h; contradiction
+  | n+1, h => by rw [Nat.succ_add, Nat.succ.injEq] at h; contradiction
 
 /-! ## sub -/
 

src/Init/Data/Nat/Linear.lean

@@ -580,7 +580,7 @@ attribute [-simp] Nat.right_distrib Nat.left_distrib
 
 theorem PolyCnstr.denote_mul (ctx : Context) (k : Nat) (c : PolyCnstr) : (c.mul (k+1)).denote ctx = c.denote ctx := by
   cases c; rename_i eq lhs rhs
-  have : k ≠ 0 → k + 1 ≠ 1 := by intro h; match k with | 0 => contradiction | k+1 => simp
+  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

src/Init/Data/Nat/Simproc.lean

@@ -0,0 +1,108 @@
+/-
+Copyright (c) 2023 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joe Hendrix
+-/
+prelude
+import Init.Data.Bool
+import Init.Data.Nat.Basic
+import Init.Data.Nat.Lemmas
+
+/-!
+This contains lemmas used by the Nat simprocs for simplifying arithmetic
+addition offsets.
+-/
+namespace Nat.Simproc
+
+/- Sub proofs -/
+
+theorem sub_add_eq_comm (a b c : Nat) : a - (b + c) = a - c - b := by
+  rw [Nat.add_comm b c]
+  exact Nat.sub_add_eq a c b
+
+theorem add_sub_add_le (a c : Nat) {b d : Nat} (h : b ≤ d) : a + b - (c + d) = a - (c + (d-b)) := by
+  induction b generalizing a c d with
+  | zero =>
+    simp
+  | succ b ind =>
+    match d with
+    | 0 =>
+      contradiction
+    | d + 1 =>
+      have g := Nat.le_of_succ_le_succ h
+      rw [Nat.add_succ a, Nat.add_succ c, Nat.succ_sub_succ, Nat.succ_sub_succ,
+          ind _ _ g]
+
+theorem add_sub_add_ge (a c : Nat) {b d : Nat} (h : b ≥ d) : a + b - (c + d) = a + (b - d) - c := by
+  rw [Nat.add_comm c d, Nat.sub_add_eq, Nat.add_sub_assoc h a]
+
+theorem add_sub_le (a : Nat) {b c : Nat} (h : b ≤ c) : a + b - c = a - (c - b) := by
+  have p := add_sub_add_le a 0 h
+  simp only [Nat.zero_add] at p
+  exact p
+
+/- Eq proofs -/
+
+theorem add_eq_gt (a : Nat) {b c : Nat} (h : b > c) : (a + b = c) = False :=
+  eq_false (Nat.ne_of_gt (Nat.lt_of_lt_of_le h (le_add_left b a)))
+
+theorem eq_add_gt (a : Nat) {b c : Nat} (h : c > a) : (a = b + c) = False := by
+  rw [@Eq.comm Nat a (b + c)]
+  exact add_eq_gt b h
+
+theorem add_eq_add_le (a c : Nat) {b d : Nat} (h : b ≤ d) : (a + b = c + d) = (a = c + (d - b)) := by
+  have g : b ≤ c + d := Nat.le_trans h (le_add_left d c)
+  rw [← Nat.add_sub_assoc h, @Eq.comm _ a, Nat.sub_eq_iff_eq_add g, @Eq.comm _ (a + b)]
+
+theorem add_eq_add_ge (a c : Nat) {b d : Nat} (h : b ≥ d) : (a + b = c + d) = (a + (b - d) = c) := by
+  rw [@Eq.comm _ (a + b) _, add_eq_add_le c a h, @Eq.comm _ _ c]
+
+theorem add_eq_le (a : Nat) {b c : Nat} (h : b ≤ c) : (a + b = c) = (a = c - b) := by
+  have r := add_eq_add_le a 0 h
+  simp only [Nat.zero_add] at r
+  exact r
+
+theorem eq_add_le {a : Nat} (b : Nat) {c : Nat} (h : c ≤ a) : (a = b + c) = (b = a - c) := by
+  rw [@Eq.comm Nat a (b + c)]
+  exact add_eq_le b h
+
+/- Lemmas for lifting Eq proofs to beq -/
+
+theorem beqEqOfEqEq {a b c d : Nat} (p : (a = b) = (c = d)) : (a == b) = (c == d) := by
+  simp only [Bool.beq_eq_decide_eq, p]
+
+theorem beqFalseOfEqFalse {a b : Nat} (p : (a = b) = False) : (a == b) = false := by
+  simp [Bool.beq_eq_decide_eq, p]
+
+theorem bneEqOfEqEq {a b c d : Nat} (p : (a = b) = (c = d)) : (a != b) = (c != d) := by
+  simp only [bne, beqEqOfEqEq p]
+
+theorem bneTrueOfEqFalse {a b : Nat} (p : (a = b) = False) : (a != b) = true := by
+  simp [bne, beqFalseOfEqFalse p]
+
+/- le proofs -/
+
+theorem add_le_add_le (a c : Nat) {b d : Nat} (h : b ≤ d) : (a + b ≤ c + d) = (a ≤ c + (d - b)) := by
+  rw [← Nat.add_sub_assoc h, Nat.le_sub_iff_add_le]
+  exact Nat.le_trans h (le_add_left d c)
+
+theorem add_le_add_ge (a c : Nat) {b d : Nat} (h : b ≥ d) : (a + b ≤ c + d) = (a + (b - d) ≤ c) := by
+  rw [← Nat.add_sub_assoc h, Nat.sub_le_iff_le_add]
+
+theorem add_le_le (a : Nat) {b c : Nat} (h : b ≤ c) : (a + b ≤ c) = (a ≤ c - b) := by
+  have r := add_le_add_le a 0 h
+  simp only [Nat.zero_add] at r
+  exact r
+
+theorem add_le_gt (a : Nat) {b c : Nat} (h : b > c) : (a + b ≤ c) = False :=
+  eq_false (Nat.not_le_of_gt (Nat.lt_of_lt_of_le h (le_add_left b a)))
+
+theorem le_add_le (a : Nat) {b c : Nat} (h : a ≤ c) : (a ≤ b + c) = True :=
+  eq_true (Nat.le_trans h (le_add_left c b))
+
+theorem le_add_ge (a : Nat) {b c : Nat} (h : a ≥ c) : (a ≤ b + c) = (a - c ≤ b) := by
+  have r := add_le_add_ge 0 b h
+  simp only [Nat.zero_add] at r
+  exact r
+
+end Nat.Simproc

src/Init/Data/Option/Basic.lean

@@ -13,29 +13,38 @@ namespace Option
 deriving instance DecidableEq for Option
 deriving instance BEq for Option
 
-def toMonad [Monad m] [Alternative m] : Option α → m α
+/-- Lifts an optional value to any `Alternative`, sending `none` to `failure`. -/
+def getM [Alternative m] : Option α → m α
   | none     => failure
   | some a   => pure a
 
+@[deprecated getM] def toMonad [Monad m] [Alternative m] : Option α → m α :=
+  getM
+
 @[inline] def toBool : Option α → Bool
   | some _ => true
   | none   => false
 
+/-- Returns `true` on `some x` and `false` on `none`. -/
 @[inline] def isSome : Option α → Bool
   | some _ => true
   | none   => false
 
+/-- Returns `true` on `none` and `false` on `some x`. -/
 @[inline] def isNone : Option α → Bool
   | some _ => false
   | none   => true
 
+/--
+`x?.isEqSome y` is equivalent to `x? == some y`, but avoids an allocation.
+-/
 @[inline] def isEqSome [BEq α] : Option α → α → Bool
   | some a, b => a == b
   | none,   _ => false
 
 @[inline] protected def bind : Option α → (α → Option β) → Option β
   | none,   _ => none
-  | some a, b => b a
+  | some a, f => f a
 
 /-- Runs `f` on `o`'s value, if any, and returns its result, or else returns `none`.  -/
 @[inline] protected def bindM [Monad m] (f : α → m (Option β)) (o : Option α) : m (Option β) := do
@@ -44,6 +53,10 @@ def toMonad [Monad m] [Alternative m] : Option α → m α
   else
     return none
 
+/--
+Runs a monadic function `f` on an optional value.
+If the optional value is `none` the function is not called.
+-/
 @[inline] protected def mapM [Monad m] (f : α → m β) (o : Option α) : m (Option β) := do
   if let some a := o then
     return some (← f a)
@@ -53,18 +66,24 @@ def toMonad [Monad m] [Alternative m] : Option α → m α
 theorem map_id : (Option.map id : Option α → Option α) = id :=
   funext (fun o => match o with | none => rfl | some _ => rfl)
 
+/-- Keeps an optional value only if it satisfies the predicate `p`. -/
 @[always_inline, inline] protected def filter (p : α → Bool) : Option α → Option α
   | some a => if p a then some a else none
   | none   => none
 
+/-- Checks that an optional value satisfies a predicate `p` or is `none`. -/
 @[always_inline, inline] protected def all (p : α → Bool) : Option α → Bool
   | some a => p a
   | none   => true
 
+/-- Checks that an optional value is not `none` and the value satisfies a predicate `p`. -/
 @[always_inline, inline] protected def any (p : α → Bool) : Option α → Bool
   | some a => p a
   | none   => false
 
+/--
+Implementation of `OrElse`'s `<|>` syntax for `Option`.
+-/
 @[always_inline, macro_inline] protected def orElse : Option α → (Unit → Option α) → Option α
   | some a, _ => some a
   | none,   b => b ()

src/Init/Data/Ord.lean

@@ -114,7 +114,18 @@ by `cmp₂` to break the tie.
 @[inline] def compareLex (cmp₁ cmp₂ : α → β → Ordering) (a : α) (b : β) : Ordering :=
   (cmp₁ a b).then (cmp₂ a b)
 
+/--
+`Ord α` provides a computable total order on `α`, in terms of the
+`compare : α → α → Ordering` function.
+
+Typically instances will be transitive, reflexive, and antisymmetric,
+but this is not enforced by the typeclass.
+
+There is a derive handler, so appending `deriving Ord` to an inductive type or structure
+will attempt to create an `Ord` instance.
+-/
 class Ord (α : Type u) where
+  /-- Compare two elements in `α` using the comparator contained in an `[Ord α]` instance. -/
   compare : α → α → Ordering
 
 export Ord (compare)

src/Init/Data/Repr.lean

@@ -13,11 +13,24 @@ open Sum Subtype Nat
 
 open Std
 
+/--
+A typeclass that specifies the standard way of turning values of some type into `Format`.
+
+When rendered this `Format` should be as close as possible to something that can be parsed as the
+input value.
+-/
 class Repr (α : Type u) where
+  /--
+  Turn a value of type `α` into `Format` at a given precedence. The precedence value can be used
+  to avoid parentheses if they are not necessary.
+  -/
   reprPrec : α → Nat → Format
 
 export Repr (reprPrec)
 
+/--
+Turn `a` into `Format` using its `Repr` instance. The precedence level is initially set to 0.
+-/
 abbrev repr [Repr α] (a : α) : Format :=
   reprPrec a 0
 
@@ -103,6 +116,11 @@ instance {p : α → Prop} [Repr α] : Repr (Subtype p) where
 
 namespace Nat
 
+/-
+We have pure functions for calculating the decimal representation of a `Nat` (`toDigits`), but also
+a fast variant that handles small numbers (`USize`) via C code (`lean_string_of_usize`).
+-/
+
 def digitChar (n : Nat) : Char :=
   if n = 0 then '0' else
   if n = 1 then '1' else
@@ -133,6 +151,20 @@ def toDigitsCore (base : Nat) : Nat → Nat → List Char → List Char
 def toDigits (base : Nat) (n : Nat) : List Char :=
   toDigitsCore base (n+1) n []
 
+@[extern "lean_string_of_usize"]
+protected def _root_.USize.repr (n : @& USize) : String :=
+  (toDigits 10 n.toNat).asString
+
+/-- We statically allocate and memoize reprs for small natural numbers. -/
+private def reprArray : Array String := Id.run do
+  List.range 128 |>.map (·.toUSize.repr) |> Array.mk
+
+private def reprFast (n : Nat) : String :=
+  if h : n < 128 then Nat.reprArray.get ⟨n, h⟩ else
+  if h : n < USize.size then (USize.ofNatCore n h).repr
+  else (toDigits 10 n).asString
+
+@[implemented_by reprFast]
 protected def repr (n : Nat) : String :=
   (toDigits 10 n).asString
 
@@ -162,6 +194,32 @@ def toSuperDigits (n : Nat) : List Char :=
 def toSuperscriptString (n : Nat) : String :=
   (toSuperDigits n).asString
 
+def subDigitChar (n : Nat) : Char :=
+  if n = 0 then '₀' else
+  if n = 1 then '₁' else
+  if n = 2 then '₂' else
+  if n = 3 then '₃' else
+  if n = 4 then '₄' else
+  if n = 5 then '₅' else
+  if n = 6 then '₆' else
+  if n = 7 then '₇' else
+  if n = 8 then '₈' else
+  if n = 9 then '₉' else
+  '*'
+
+partial def toSubDigitsAux : Nat → List Char → List Char
+  | n, ds =>
+    let d  := subDigitChar <| n % 10;
+    let n' := n / 10;
+    if n' = 0 then d::ds
+    else toSubDigitsAux n' (d::ds)
+
+def toSubDigits (n : Nat) : List Char :=
+  toSubDigitsAux n []
+
+def toSubscriptString (n : Nat) : String :=
+  (toSubDigits n).asString
+
 end Nat
 
 instance : Repr Nat where

src/Init/Data/Stream.lean

@@ -94,7 +94,8 @@ instance : Stream (Subarray α) α where
   next? s :=
     if h : s.start < s.stop then
       have : s.start + 1 ≤ s.stop := Nat.succ_le_of_lt h
-      some (s.as.get ⟨s.start, Nat.lt_of_lt_of_le h s.h₂⟩, { s with start := s.start + 1, h₁ := this })
+      some (s.as.get ⟨s.start, Nat.lt_of_lt_of_le h s.stop_le_array_size⟩,
+        { s with start := s.start + 1, start_le_stop := this })
     else
       none
 

src/Init/Data/String/Basic.lean

@@ -44,6 +44,16 @@ def append : String → (@& String) → String
 def toList (s : String) : List Char :=
   s.data
 
+/-- Returns true if `p` is a valid UTF-8 position in the string `s`, meaning that `p ≤ s.endPos`
+and `p` lies on a UTF-8 character boundary. This has an O(1) implementation in the runtime. -/
+@[extern "lean_string_is_valid_pos"]
+def Pos.isValid (s : @&String) (p : @& Pos) : Bool :=
+  go s.data 0
+where
+  go : List Char → Pos → Bool
+  | [],    i => i = p
+  | c::cs, i => if i = p then true else go cs (i + c)
+
 def utf8GetAux : List Char → Pos → Pos → Char
   | [],    _, _ => default
   | c::cs, i, p => if i = p then c else utf8GetAux cs (i + c) p
@@ -245,12 +255,21 @@ termination_by s.endPos.1 - i.1
 @[specialize] def split (s : String) (p : Char → Bool) : List String :=
   splitAux s p 0 0 []
 
+/--
+Auxiliary for `splitOn`. Preconditions:
+* `sep` is not empty
+* `b <= i` are indexes into `s`
+* `j` is an index into `sep`, and not at the end
+
+It represents the state where we have currently parsed some split parts into `r` (in reverse order),
+`b` is the beginning of the string / the end of the previous match of `sep`, and the first `j` bytes
+of `sep` match the bytes `i-j .. i` of `s`.
+-/
 def splitOnAux (s sep : String) (b : Pos) (i : Pos) (j : Pos) (r : List String) : List String :=
-  if h : s.atEnd i then
+  if s.atEnd i then
     let r := (s.extract b i)::r
     r.reverse
   else
-    have := Nat.sub_lt_sub_left (Nat.gt_of_not_le (mt decide_eq_true h)) (lt_next s _)
     if s.get i == sep.get j then
       let i := s.next i
       let j := sep.next j
@@ -259,9 +278,42 @@ def splitOnAux (s sep : String) (b : Pos) (i : Pos) (j : Pos) (r : List String)
       else
         splitOnAux s sep b i j r
     else
-      splitOnAux s sep b (s.next i) 0 r
-termination_by s.endPos.1 - i.1
+      splitOnAux s sep b (s.next (i - j)) 0 r
+termination_by (s.endPos.1 - (i - j).1, sep.endPos.1 - j.1)
+decreasing_by
+  all_goals simp_wf
+  focus
+    rename_i h _ _
+    left; exact Nat.sub_lt_sub_left
+      (Nat.lt_of_le_of_lt (Nat.sub_le ..) (Nat.gt_of_not_le (mt decide_eq_true h)))
+      (Nat.lt_of_le_of_lt (Nat.sub_le ..) (lt_next s _))
+  focus
+    rename_i i₀ j₀ _ eq h'
+    rw [show (s.next i₀ - sep.next j₀).1 = (i₀ - j₀).1 by
+      show (_ + csize _) - (_ + csize _) = _
+      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')))
+      (lt_next sep _)
+  focus
+    rename_i h _
+    left; exact Nat.sub_lt_sub_left
+      (Nat.lt_of_le_of_lt (Nat.sub_le ..) (Nat.gt_of_not_le (mt decide_eq_true h)))
+      (lt_next s _)
 
+/--
+Splits a string `s` on occurrences of the separator `sep`. When `sep` is empty, it returns `[s]`;
+when `sep` occurs in overlapping patterns, the first match is taken. There will always be exactly
+`n+1` elements in the returned list if there were `n` nonoverlapping matches of `sep` in the string.
+The default separator is `" "`. The separators are not included in the returned substrings.
+
+```
+"here is some text ".splitOn = ["here", "is", "some", "text", ""]
+"here is some text ".splitOn "some" = ["here is ", " text "]
+"here is some text ".splitOn "" = ["here is some text "]
+"ababacabac".splitOn "aba" = ["", "bac", "c"]
+```
+-/
 def splitOn (s : String) (sep : String := " ") : List String :=
   if sep == "" then [s] else splitOnAux s sep 0 0 0 []
 

src/Init/Data/String/Extra.lean

@@ -17,14 +17,25 @@ def toNat! (s : String) : Nat :=
   else
     panic! "Nat expected"
 
-/--
-  Convert a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded `ByteArray` string to `String`.
-  The result is unspecified if `a` is not properly UTF-8 encoded.
--/
-@[extern "lean_string_from_utf8_unchecked"]
-opaque fromUTF8Unchecked (a : @& ByteArray) : String
+/-- Returns true if the given byte array consists of valid UTF-8. -/
+@[extern "lean_string_validate_utf8"]
+opaque validateUTF8 (a : @& ByteArray) : Bool
 
-/-- Convert the given `String` to a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded byte array. -/
+/-- Converts a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded `ByteArray` string to `String`. -/
+@[extern "lean_string_from_utf8"]
+opaque fromUTF8 (a : @& ByteArray) (h : validateUTF8 a) : String
+
+/-- 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. -/
+@[inline] def fromUTF8? (a : ByteArray) : Option String :=
+  if h : validateUTF8 a then fromUTF8 a h else none
+
+/-- Converts a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded `ByteArray` string to `String`,
+or panics if `a` is not properly UTF-8 encoded. -/
+@[inline] def fromUTF8! (a : ByteArray) : String :=
+  if h : validateUTF8 a then fromUTF8 a h else panic! "invalid UTF-8 string"
+
+/-- Converts the given `String` to a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded byte array. -/
 @[extern "lean_string_to_utf8"]
 opaque toUTF8 (a : @& String) : ByteArray
 
@@ -62,4 +73,40 @@ namespace Iterator
 
 end Iterator
 
+private def findLeadingSpacesSize (s : String) : Nat :=
+  let it := s.iter
+  let it := it.find (· == '\n') |>.next
+  consumeSpaces it 0 s.length
+where
+  consumeSpaces (it : String.Iterator) (curr min : Nat) : Nat :=
+    if it.atEnd then min
+    else if it.curr == ' ' || it.curr == '\t' then consumeSpaces it.next (curr + 1) min
+    else if it.curr == '\n' then findNextLine it.next min
+    else findNextLine it.next (Nat.min curr min)
+  findNextLine (it : String.Iterator) (min : Nat) : Nat :=
+    if it.atEnd then min
+    else if it.curr == '\n' then consumeSpaces it.next 0 min
+    else findNextLine it.next min
+
+private def removeNumLeadingSpaces (n : Nat) (s : String) : String :=
+  consumeSpaces n s.iter ""
+where
+  consumeSpaces (n : Nat) (it : String.Iterator) (r : String) : String :=
+     match n with
+     | 0 => saveLine it r
+     | n+1 =>
+       if it.atEnd then r
+       else if it.curr == ' ' || it.curr == '\t' then consumeSpaces n it.next r
+       else saveLine it r
+  termination_by (it, 1)
+  saveLine (it : String.Iterator) (r : String) : String :=
+    if it.atEnd then r
+    else if it.curr == '\n' then consumeSpaces n it.next (r.push '\n')
+    else saveLine it.next (r.push it.curr)
+  termination_by (it, 0)
+
+def removeLeadingSpaces (s : String) : String :=
+  let n := findLeadingSpacesSize s
+  if n == 0 then s else removeNumLeadingSpaces n s
+
 end String

src/Init/Data/UInt/Basic.lean

@@ -103,7 +103,7 @@ def UInt16.shiftLeft (a b : UInt16) : UInt16 := ⟨a.val <<< (modn b 16).val⟩
 @[extern "lean_uint16_to_uint8"]
 def UInt16.toUInt8 (a : UInt16) : UInt8 := a.toNat.toUInt8
 @[extern "lean_uint8_to_uint16"]
-def UInt8.toUInt16 (a : UInt8) : UInt16 := a.toNat.toUInt16
+def UInt8.toUInt16 (a : UInt8) : UInt16 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
 @[extern "lean_uint16_shift_right"]
 def UInt16.shiftRight (a b : UInt16) : UInt16 := ⟨a.val >>> (modn b 16).val⟩
 def UInt16.lt (a b : UInt16) : Prop := a.val < b.val
@@ -186,9 +186,9 @@ def UInt32.toUInt8 (a : UInt32) : UInt8 := a.toNat.toUInt8
 @[extern "lean_uint32_to_uint16"]
 def UInt32.toUInt16 (a : UInt32) : UInt16 := a.toNat.toUInt16
 @[extern "lean_uint8_to_uint32"]
-def UInt8.toUInt32 (a : UInt8) : UInt32 := a.toNat.toUInt32
+def UInt8.toUInt32 (a : UInt8) : UInt32 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
 @[extern "lean_uint16_to_uint32"]
-def UInt16.toUInt32 (a : UInt16) : UInt32 := a.toNat.toUInt32
+def UInt16.toUInt32 (a : UInt16) : UInt32 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
 
 instance UInt32.instOfNat : OfNat UInt32 n := ⟨UInt32.ofNat n⟩
 instance : Add UInt32       := ⟨UInt32.add⟩
@@ -244,11 +244,11 @@ def UInt64.toUInt16 (a : UInt64) : UInt16 := a.toNat.toUInt16
 @[extern "lean_uint64_to_uint32"]
 def UInt64.toUInt32 (a : UInt64) : UInt32 := a.toNat.toUInt32
 @[extern "lean_uint8_to_uint64"]
-def UInt8.toUInt64 (a : UInt8) : UInt64 := a.toNat.toUInt64
+def UInt8.toUInt64 (a : UInt8) : UInt64 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
 @[extern "lean_uint16_to_uint64"]
-def UInt16.toUInt64 (a : UInt16) : UInt64 := a.toNat.toUInt64
+def UInt16.toUInt64 (a : UInt16) : UInt64 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
 @[extern "lean_uint32_to_uint64"]
-def UInt32.toUInt64 (a : UInt32) : UInt64 := a.toNat.toUInt64
+def UInt32.toUInt64 (a : UInt32) : UInt64 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
 
 instance UInt64.instOfNat : OfNat UInt64 n := ⟨UInt64.ofNat n⟩
 instance : Add UInt64       := ⟨UInt64.add⟩
@@ -321,7 +321,7 @@ def USize.shiftLeft (a b : USize) : USize := ⟨a.val <<< (modn b System.Platfor
 @[extern "lean_usize_shift_right"]
 def USize.shiftRight (a b : USize) : USize := ⟨a.val >>> (modn b System.Platform.numBits).val⟩
 @[extern "lean_uint32_to_usize"]
-def UInt32.toUSize (a : UInt32) : USize := a.toNat.toUSize
+def UInt32.toUSize (a : UInt32) : USize := USize.ofNat32 a.val a.1.2
 @[extern "lean_usize_to_uint32"]
 def USize.toUInt32 (a : USize) : UInt32 := a.toNat.toUInt32
 

src/Init/Ext.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Gabriel Ebner, Mario Carneiro
 -/
 prelude
+import Init.Data.ToString.Macro
 import Init.TacticsExtra
 import Init.RCases
 

src/Init/GetElem.lean

@@ -0,0 +1,173 @@
+/-
+Copyright (c) 2020 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura, Mario Carneiro
+-/
+prelude
+import Init.Util
+
+@[never_extract]
+private def outOfBounds [Inhabited α] : α :=
+  panic! "index out of bounds"
+
+/--
+The class `GetElem coll idx elem valid` implements the `xs[i]` notation.
+Given `xs[i]` with `xs : coll` and `i : idx`, Lean looks for an instance of
+`GetElem coll idx elem valid` and uses this to infer the type of return
+value `elem` and side conditions `valid` required to ensure `xs[i]` yields
+a valid value of type `elem`.
+
+For example, the instance for arrays looks like
+`GetElem (Array α) Nat α (fun xs i => i < xs.size)`.
+
+The proof side-condition `valid xs i` is automatically dispatched by the
+`get_elem_tactic` tactic, which can be extended by adding more clauses to
+`get_elem_tactic_trivial`.
+-/
+class GetElem (coll : Type u) (idx : Type v) (elem : outParam (Type w))
+              (valid : outParam (coll → idx → Prop)) where
+  /--
+  The syntax `arr[i]` gets the `i`'th element of the collection `arr`. If there
+  are proof side conditions to the application, they will be automatically
+  inferred by the `get_elem_tactic` tactic.
+
+  The actual behavior of this class is type-dependent, but here are some
+  important implementations:
+  * `arr[i] : α` where `arr : Array α` and `i : Nat` or `i : USize`: does array
+    indexing with no bounds check and a proof side goal `i < arr.size`.
+  * `l[i] : α` where `l : List α` and `i : Nat`: index into a list, with proof
+    side goal `i < l.length`.
+  * `stx[i] : Syntax` where `stx : Syntax` and `i : Nat`: get a syntax argument,
+    no side goal (returns `.missing` out of range)
+
+  There are other variations on this syntax:
+  * `arr[i]!` is syntax for `getElem! arr i` which should panic and return
+    `default : α` if the index is not valid.
+  * `arr[i]?` is syntax for `getElem?` which should return `none` if the index
+    is not valid.
+  * `arr[i]'h` is syntax for `getElem arr i h` with `h` an explicit proof the
+    index is valid.
+  -/
+  getElem (xs : coll) (i : idx) (h : valid xs i) : elem
+
+  getElem? (xs : coll) (i : idx) [Decidable (valid xs i)] : Option elem :=
+    if h : _ then some (getElem xs i h) else none
+
+  getElem! [Inhabited elem] (xs : coll) (i : idx) [Decidable (valid xs i)] : elem :=
+    match getElem? xs i with | some e => e | none => outOfBounds
+
+export GetElem (getElem getElem! getElem?)
+
+@[inherit_doc getElem]
+syntax:max term noWs "[" withoutPosition(term) "]" : term
+macro_rules | `($x[$i]) => `(getElem $x $i (by get_elem_tactic))
+
+@[inherit_doc getElem]
+syntax term noWs "[" withoutPosition(term) "]'" term:max : term
+macro_rules | `($x[$i]'$h) => `(getElem $x $i $h)
+
+/--
+The syntax `arr[i]?` gets the `i`'th element of the collection `arr` or
+returns `none` if `i` is out of bounds.
+-/
+macro:max x:term noWs "[" i:term "]" noWs "?" : term => `(getElem? $x $i)
+
+/--
+The syntax `arr[i]!` gets the `i`'th element of the collection `arr` and
+panics `i` is out of bounds.
+-/
+macro:max x:term noWs "[" i:term "]" noWs "!" : term => `(getElem! $x $i)
+
+class LawfulGetElem (cont : Type u) (idx : Type v) (elem : outParam (Type w))
+   (dom : outParam (cont → idx → Prop)) [ge : GetElem cont idx elem dom] : Prop where
+
+  getElem?_def (c : cont) (i : idx) [Decidable (dom c i)] :
+    c[i]? = if h : dom c i then some (c[i]'h) else none := by intros; eq_refl
+  getElem!_def [Inhabited elem] (c : cont) (i : idx) [Decidable (dom c i)] :
+    c[i]! = match c[i]? with | some e => e | none => default := by intros; eq_refl
+
+export LawfulGetElem (getElem?_def getElem!_def)
+
+theorem getElem?_pos [GetElem cont idx elem dom] [LawfulGetElem cont idx elem dom]
+    (c : cont) (i : idx) (h : dom c i) [Decidable (dom c i)] : c[i]? = some (c[i]'h) := by
+  rw [getElem?_def]
+  exact dif_pos h
+
+theorem getElem?_neg [GetElem cont idx elem dom] [LawfulGetElem cont idx elem dom]
+    (c : cont) (i : idx) (h : ¬dom c i) [Decidable (dom c i)] : c[i]? = none := by
+  rw [getElem?_def]
+  exact dif_neg h
+
+theorem getElem!_pos [GetElem cont idx elem dom] [LawfulGetElem cont idx elem dom]
+    [Inhabited elem] (c : cont) (i : idx) (h : dom c i) [Decidable (dom c i)] :
+    c[i]! = c[i]'h := by
+  simp only [getElem!_def, getElem?_def, h]
+
+theorem getElem!_neg [GetElem cont idx elem dom] [LawfulGetElem cont idx elem dom]
+    [Inhabited elem] (c : cont) (i : idx) (h : ¬dom c i) [Decidable (dom c i)] : c[i]! = default := by
+  simp only [getElem!_def, getElem?_def, h]
+
+namespace Fin
+
+instance instGetElemFinVal [GetElem cont Nat elem dom] : GetElem cont (Fin n) elem fun xs i => dom xs i where
+  getElem xs i h := getElem xs i.1 h
+  getElem? xs i := getElem? xs i.val
+  getElem! xs i := getElem! xs i.val
+
+instance [GetElem cont Nat elem dom] [h : LawfulGetElem cont Nat elem dom] :
+      LawfulGetElem cont (Fin n) elem fun xs i => dom xs i where
+
+  getElem?_def _c _i _d := h.getElem?_def ..
+  getElem!_def _c _i _d := h.getElem!_def ..
+
+@[simp] theorem getElem_fin [GetElem Cont Nat Elem Dom] (a : Cont) (i : Fin n) (h : Dom a i) :
+    a[i] = a[i.1] := rfl
+
+@[simp] theorem getElem?_fin [h : GetElem Cont Nat Elem Dom] (a : Cont) (i : Fin n)
+    [Decidable (Dom a i)] : a[i]? = a[i.1]? := by rfl
+
+@[simp] theorem getElem!_fin [GetElem Cont Nat Elem Dom] (a : Cont) (i : Fin n)
+    [Decidable (Dom a i)] [Inhabited Elem] : a[i]! = a[i.1]! := rfl
+
+macro_rules
+  | `(tactic| get_elem_tactic_trivial) => `(tactic| apply Fin.val_lt_of_le; get_elem_tactic_trivial; done)
+
+end Fin
+
+namespace List
+
+instance : GetElem (List α) Nat α fun as i => i < as.length where
+  getElem as i h := as.get ⟨i, h⟩
+
+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
+  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
+  rfl
+
+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
+  | _::_, i+1 => get_drop_eq_drop _ i _
+
+end List
+
+namespace Array
+
+instance : GetElem (Array α) Nat α fun xs i => i < xs.size where
+  getElem xs i h := xs.get ⟨i, h⟩
+
+instance : LawfulGetElem (Array α) Nat α fun xs i => i < xs.size where
+
+end Array
+
+namespace Lean.Syntax
+
+instance : GetElem Syntax Nat Syntax fun _ _ => True where
+  getElem stx i _ := stx.getArg i
+
+instance : LawfulGetElem Syntax Nat Syntax fun _ _ => True where
+
+end Lean.Syntax

src/Init/MacroTrace.lean

@@ -0,0 +1,18 @@
+/-
+Copyright (c) 2020 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+
+Extra notation that depends on Init/Meta
+-/
+
+prelude
+import Init.Data.ToString.Macro
+import Init.Meta
+
+namespace Lean
+
+macro "Macro.trace[" id:ident "]" s:interpolatedStr(term) : term =>
+  `(Macro.trace $(quote id.getId.eraseMacroScopes) (s! $s))
+
+end Lean

src/Init/Meta.lean

@@ -9,7 +9,6 @@ prelude
 import Init.MetaTypes
 import Init.Data.Array.Basic
 import Init.Data.Option.BasicAux
-import Init.Data.String.Extra
 
 namespace Lean
 
@@ -105,43 +104,6 @@ def idBeginEscape := '«'
 def idEndEscape   := '»'
 def isIdBeginEscape (c : Char) : Bool := c = idBeginEscape
 def isIdEndEscape (c : Char) : Bool := c = idEndEscape
-
-private def findLeadingSpacesSize (s : String) : Nat :=
-  let it := s.iter
-  let it := it.find (· == '\n') |>.next
-  consumeSpaces it 0 s.length
-where
-  consumeSpaces (it : String.Iterator) (curr min : Nat) : Nat :=
-    if it.atEnd then min
-    else if it.curr == ' ' || it.curr == '\t' then consumeSpaces it.next (curr + 1) min
-    else if it.curr == '\n' then findNextLine it.next min
-    else findNextLine it.next (Nat.min curr min)
-  findNextLine (it : String.Iterator) (min : Nat) : Nat :=
-    if it.atEnd then min
-    else if it.curr == '\n' then consumeSpaces it.next 0 min
-    else findNextLine it.next min
-
-private def removeNumLeadingSpaces (n : Nat) (s : String) : String :=
-  consumeSpaces n s.iter ""
-where
-  consumeSpaces (n : Nat) (it : String.Iterator) (r : String) : String :=
-     match n with
-     | 0 => saveLine it r
-     | n+1 =>
-       if it.atEnd then r
-       else if it.curr == ' ' || it.curr == '\t' then consumeSpaces n it.next r
-       else saveLine it r
-  termination_by (it, 1)
-  saveLine (it : String.Iterator) (r : String) : String :=
-    if it.atEnd then r
-    else if it.curr == '\n' then consumeSpaces n it.next (r.push '\n')
-    else saveLine it.next (r.push it.curr)
-  termination_by (it, 0)
-
-def removeLeadingSpaces (s : String) : String :=
-  let n := findLeadingSpacesSize s
-  if n == 0 then s else removeNumLeadingSpaces n s
-
 namespace Name
 
 def getRoot : Name → Name
@@ -1232,14 +1194,6 @@ instance : Coe (Lean.Term) (Lean.TSyntax `Lean.Parser.Term.funBinder) where
 
 end Lean.Syntax
 
-set_option linter.unusedVariables.funArgs false in
-/--
-  Gadget for automatic parameter support. This is similar to the `optParam` gadget, but it uses
-  the given tactic.
-  Like `optParam`, this gadget only affects elaboration.
-  For example, the tactic will *not* be invoked during type class resolution. -/
-abbrev autoParam.{u} (α : Sort u) (tactic : Lean.Syntax) : Sort u := α
-
 /-! # Helper functions for manipulating interpolated strings -/
 
 namespace Lean.Syntax

src/Init/MetaTypes.lean

@@ -68,38 +68,106 @@ namespace Simp
 
 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`.
+-/
 structure Config where
+  /--
+  The maximum number of subexpressions to visit when performing simplification.
+  The default is 100000.
+  -/
   maxSteps          : Nat  := defaultMaxSteps
+  /--
+  When simp discharges side conditions for conditional lemmas, it can recursively apply simplification.
+  The `maxDischargeDepth` (default: 2) is the maximum recursion depth when recursively applying simplification to side conditions.
+  -/
   maxDischargeDepth : Nat  := 2
+  /--
+  When `contextual` is true (default: `false`) and simplification encounters an implication `p → q`
+  it includes `p` as an additional simp lemma when simplifying `q`.
+  -/
   contextual        : Bool := false
+  /--
+  When true (default: `true`) then the simplifier caches the result of simplifying each subexpression, if possible.
+  -/
   memoize           : Bool := true
+  /--
+  When `singlePass` is `true` (default: `false`), the simplifier runs through a single round of simplification,
+  which consists of running pre-methods, recursing using congruence lemmas, and then running post-methods.
+  Otherwise, when it is `false`, it iteratively applies this simplification procedure.
+  -/
   singlePass        : Bool := false
-  /-- `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`), simplifies simple arithmetic expressions. -/
   arith             : Bool := false
+  /--
+  When `true` (default: `false`), unfolds definitions.
+  This can be enabled using the `simp!` syntax.
+  -/
   autoUnfold        : Bool := false
   /--
-    If `dsimp := true`, then switches to `dsimp` on dependent arguments where there is no congruence theorem that allows
-    `simp` to visit them. If `dsimp := false`, then argument is not visited.
+  When `true` (default: `true`) then switches to `dsimp` on dependent arguments
+  if there is no congruence theorem that would allow `simp` to visit them.
+  When `dsimp` is `false`, then the argument is not visited.
   -/
   dsimp             : Bool := true
-  /-- 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 `ground := true`, then ground terms are reduced. A term is ground when
-  it does not contain free or meta variables. Reduction is interrupted at a function application `f ...`
-  if `f` is marked to not be unfolded. -/
+  /--
+  If `ground` is `true` (default: `false`), then ground terms are reduced.
+  A term is ground when it does not contain free or meta variables.
+  Reduction is interrupted at a function application `f ...` if `f` is marked to not be unfolded.
+  Ground term reduction applies `@[seval]` lemmas.
+  -/
   ground            : Bool := false
-  /-- 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
 
@@ -107,6 +175,9 @@ structure Config where
 structure ConfigCtx extends Config where
   contextual := true
 
+/--
+A neutral configuration for `simp`, turning off all reductions and other built-in simplifications.
+-/
 def neutralConfig : Simp.Config := {
   zeta              := false
   beta              := false

src/Init/Notation.lean

@@ -552,15 +552,52 @@ except that it doesn't print an empty diagnostic.
 -/
 syntax (name := runMeta) "run_meta " doSeq : command
 
-/-- Element that can be part of a `#guard_msgs` specification. -/
-syntax guardMsgsSpecElt := &"drop"? (&"info" <|> &"warning" <|> &"error" <|> &"all")
+set_option linter.missingDocs false in
+syntax guardMsgsFilterSeverity := &"info" <|> &"warning" <|> &"error" <|> &"all"
 
-/-- Specification for `#guard_msgs` command. -/
+/--
+A message filter specification for `#guard_msgs`.
+- `info`, `warning`, `error`: capture messages with the given severity level.
+- `all`: capture all messages (the default).
+- `drop info`, `drop warning`, `drop error`: drop messages with the given severity level.
+- `drop all`: drop every message.
+These filters are processed in left-to-right order.
+-/
+syntax guardMsgsFilter := &"drop"? guardMsgsFilterSeverity
+
+set_option linter.missingDocs false in
+syntax guardMsgsWhitespaceArg := &"exact" <|> &"normalized" <|> &"lax"
+
+/--
+Whitespace handling for `#guard_msgs`:
+- `whitespace := exact` requires an exact whitespace match.
+- `whitespace := normalized` converts all newline characters to a space before matching
+  (the default). This allows breaking long lines.
+- `whitespace := lax` collapses whitespace to a single space before matching.
+In all cases, leading and trailing whitespace is trimmed before matching.
+-/
+syntax guardMsgsWhitespace := &"whitespace" " := " guardMsgsWhitespaceArg
+
+set_option linter.missingDocs false in
+syntax guardMsgsOrderingArg := &"exact" <|> &"sorted"
+
+/--
+Message ordering for `#guard_msgs`:
+- `ordering := exact` uses the exact ordering of the messages (the default).
+- `ordering := sorted` sorts the messages in lexicographic order.
+  This helps with testing commands that are non-deterministic in their ordering.
+-/
+syntax guardMsgsOrdering := &"ordering" " := " guardMsgsOrderingArg
+
+set_option linter.missingDocs false in
+syntax guardMsgsSpecElt := guardMsgsFilter <|> guardMsgsWhitespace <|> guardMsgsOrdering
+
+set_option linter.missingDocs false in
 syntax guardMsgsSpec := "(" guardMsgsSpecElt,* ")"
 
 /--
-`#guard_msgs` captures the messages generated by another command and checks that they
-match the contents of the docstring attached to the `#guard_msgs` command.
+`/-- ... -/ #guard_msgs in cmd` captures the messages generated by the command `cmd`
+and checks that they match the contents of the docstring.
 
 Basic example:
 ```lean
@@ -570,10 +607,10 @@ error: unknown identifier 'x'
 #guard_msgs in
 example : α := x
 ```
-This checks that there is such an error and then consumes the message entirely.
+This checks that there is such an error and then consumes the message.
 
-By default, the command intercepts all messages, but there is a way to specify which types
-of messages to consider. For example, we can select only warnings:
+By default, the command captures all messages, but the filter condition can be adjusted.
+For example, we can select only warnings:
 ```lean
 /--
 warning: declaration uses 'sorry'
@@ -586,29 +623,37 @@ or only errors
 #guard_msgs(error) in
 example : α := sorry
 ```
-In this last example, since the message is not intercepted there is a warning on `sorry`.
+In the previous example, since warnings are not captured there is a warning on `sorry`.
 We can drop the warning completely with
 ```lean
 #guard_msgs(error, drop warning) in
 example : α := sorry
 ```
 
-Syntax description:
+In general, `#guard_msgs` accepts a comma-separated list of configuration clauses in parentheses:
 ```
-#guard_msgs (drop? info|warning|error|all,*)? in cmd
+#guard_msgs (configElt,*) in cmd
 ```
+By default, the configuration list is `(all, whitespace := normalized, ordering := exact)`.
 
-If there is no specification, `#guard_msgs` intercepts all messages.
-Otherwise, if there is one, the specification is considered in left-to-right order, and the first
-that applies chooses the outcome of the message:
-- `info`, `warning`, `error`: intercept a message with the given severity level.
-- `all`: intercept any message (so `#guard_msgs in cmd` and `#guard_msgs (all) in cmd`
-  are equivalent).
-- `drop info`, `drop warning`, `drop error`: intercept a message with the given severity
-  level and then drop it. These messages are not checked.
-- `drop all`: intercept a message and drop it.
+Message filters (processed in left-to-right order):
+- `info`, `warning`, `error`: capture messages with the given severity level.
+- `all`: capture all messages (the default).
+- `drop info`, `drop warning`, `drop error`: drop messages with the given severity level.
+- `drop all`: drop every message.
 
-For example, `#guard_msgs (error, drop all) in cmd` means to check warnings and then drop
+Whitespace handling (after trimming leading and trailing whitespace):
+- `whitespace := exact` requires an exact whitespace match.
+- `whitespace := normalized` converts all newline characters to a space before matching
+  (the default). This allows breaking long lines.
+- `whitespace := lax` collapses whitespace to a single space before matching.
+
+Message ordering:
+- `ordering := exact` uses the exact ordering of the messages (the default).
+- `ordering := sorted` sorts the messages in lexicographic order.
+  This helps with testing commands that are non-deterministic in their ordering.
+
+For example, `#guard_msgs (error, drop all) in cmd` means to check warnings and drop
 everything else.
 -/
 syntax (name := guardMsgsCmd)

src/Init/NotationExtra.lean

@@ -6,14 +6,12 @@ Authors: Leonardo de Moura
 Extra notation that depends on Init/Meta
 -/
 prelude
-import Init.Meta
+import Init.Data.ToString.Basic
 import Init.Data.Array.Subarray
-import Init.Data.ToString
 import Init.Conv
-namespace Lean
+import Init.Meta
 
-macro "Macro.trace[" id:ident "]" s:interpolatedStr(term) : term =>
-  `(Macro.trace $(quote id.getId.eraseMacroScopes) (s! $s))
+namespace Lean
 
 -- Auxiliary parsers and functions for declaring notation with binders
 
@@ -224,35 +222,35 @@ macro tk:"calc" steps:calcSteps : conv =>
   | _ => throw ()
 
 @[app_unexpander Name.mkStr1] def unexpandMkStr1 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a.getString}"]
+  | `($(_) $a:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++  a.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr2] def unexpandMkStr2 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}"]
+  | `($(_) $a1:str $a2:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr3] def unexpandMkStr3 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}.{a3.getString}"]
+  | `($(_) $a1:str $a2:str $a3:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr4] def unexpandMkStr4 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}.{a3.getString}.{a4.getString}"]
+  | `($(_) $a1:str $a2:str $a3:str $a4:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr5] def unexpandMkStr5 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}.{a3.getString}.{a4.getString}.{a5.getString}"]
+  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr6] def unexpandMkStr6 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}.{a3.getString}.{a4.getString}.{a5.getString}.{a6.getString}"]
+  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString ++ "." ++ a6.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr7] def unexpandMkStr7 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str $a7:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}.{a3.getString}.{a4.getString}.{a5.getString}.{a6.getString}.{a7.getString}"]
+  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str $a7:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString ++ "." ++ a6.getString ++ "." ++ a7.getString)]
   | _  => throw ()
 
 @[app_unexpander Name.mkStr8] def unexpandMkStr8 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str $a7:str $a8:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit s!"`{a1.getString}.{a2.getString}.{a3.getString}.{a4.getString}.{a5.getString}.{a6.getString}.{a7.getString}.{a8.getString}"]
+  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str $a7:str $a8:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString ++ "." ++ a6.getString ++ "." ++ a7.getString ++ "." ++ a8.getString)]
   | _  => throw ()
 
 @[app_unexpander Array.empty] def unexpandArrayEmpty : Lean.PrettyPrinter.Unexpander

src/Init/Omega/Int.lean

@@ -137,11 +137,13 @@ theorem add_le_iff_le_sub (a b c : Int) : a + b ≤ c ↔ a ≤ c - b := by
     lhs
     rw [← Int.add_zero c, ← Int.sub_self (-b), Int.sub_eq_add_neg, ← Int.add_assoc, Int.neg_neg,
       Int.add_le_add_iff_right]
+  try rfl -- stage0 update TODO: Change this to rfl or remove
 
 theorem le_add_iff_sub_le (a b c : Int) : a ≤ b + c ↔ a - c ≤ b := by
   conv =>
     lhs
     rw [← Int.neg_neg c, ← Int.sub_eq_add_neg, ← add_le_iff_le_sub]
+  try rfl -- stage0 update TODO: Change this to rfl or remove
 
 theorem add_le_zero_iff_le_neg (a b : Int) : a + b ≤ 0 ↔ a ≤ - b := by
   rw [add_le_iff_le_sub, Int.zero_sub]

src/Init/Omega/LinearCombo.lean

@@ -5,6 +5,7 @@ Authors: Scott Morrison
 -/
 prelude
 import Init.Omega.Coeffs
+import Init.Data.ToString.Macro
 
 /-!
 # Linear combinations

src/Init/Prelude.lean

@@ -477,6 +477,8 @@ and `Prod.snd p` respectively. You can also write `p.fst` and `p.snd`.
 For more information: [Constructors with Arguments](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html?highlight=Prod#constructors-with-arguments)
 -/
 structure Prod (α : Type u) (β : Type v) where
+  /-- Constructs a pair from two terms. -/
+  mk ::
   /-- The first projection out of a pair. if `p : α × β` then `p.1 : α`. -/
   fst : α
   /-- The second projection out of a pair. if `p : α × β` then `p.2 : β`. -/
@@ -1096,7 +1098,7 @@ class OfNat (α : Type u) (_ : Nat) where
   ofNat : α
 
 @[default_instance 100] /- low prio -/
-instance (n : Nat) : OfNat Nat n where
+instance instOfNatNat (n : Nat) : OfNat Nat n where
   ofNat := n
 
 /-- `LE α` is the typeclass which supports the notation `x ≤ y` where `x y : α`.-/
@@ -1430,31 +1432,31 @@ class ShiftRight (α : Type u) where
   shiftRight : α → α → α
 
 @[default_instance]
-instance [Add α] : HAdd α α α where
+instance instHAdd [Add α] : HAdd α α α where
   hAdd a b := Add.add a b
 
 @[default_instance]
-instance [Sub α] : HSub α α α where
+instance instHSub [Sub α] : HSub α α α where
   hSub a b := Sub.sub a b
 
 @[default_instance]
-instance [Mul α] : HMul α α α where
+instance instHMul [Mul α] : HMul α α α where
   hMul a b := Mul.mul a b
 
 @[default_instance]
-instance [Div α] : HDiv α α α where
+instance instHDiv [Div α] : HDiv α α α where
   hDiv a b := Div.div a b
 
 @[default_instance]
-instance [Mod α] : HMod α α α where
+instance instHMod [Mod α] : HMod α α α where
   hMod a b := Mod.mod a b
 
 @[default_instance]
-instance [Pow α β] : HPow α β α where
+instance instHPow [Pow α β] : HPow α β α where
   hPow a b := Pow.pow a b
 
 @[default_instance]
-instance [NatPow α] : Pow α Nat where
+instance instPowNat [NatPow α] : Pow α Nat where
   pow a n := NatPow.pow a n
 
 @[default_instance]
@@ -1521,7 +1523,7 @@ protected def Nat.add : (@& Nat) → (@& Nat) → Nat
   | a, Nat.zero   => a
   | a, Nat.succ b => Nat.succ (Nat.add a b)
 
-instance : Add Nat where
+instance instAddNat : Add Nat where
   add := Nat.add
 
 /- We mark the following definitions as pattern to make sure they can be used in recursive equations,
@@ -1541,7 +1543,7 @@ protected def Nat.mul : (@& Nat) → (@& Nat) → Nat
   | _, 0          => 0
   | a, Nat.succ b => Nat.add (Nat.mul a b) a
 
-instance : Mul Nat where
+instance instMulNat : Mul Nat where
   mul := Nat.mul
 
 set_option bootstrap.genMatcherCode false in
@@ -1557,7 +1559,7 @@ protected def Nat.pow (m : @& Nat) : (@& Nat) → Nat
   | 0      => 1
   | succ n => Nat.mul (Nat.pow m n) m
 
-instance : NatPow Nat := ⟨Nat.pow⟩
+instance instNatPowNat : NatPow Nat := ⟨Nat.pow⟩
 
 set_option bootstrap.genMatcherCode false in
 /--
@@ -1634,14 +1636,14 @@ protected inductive Nat.le (n : Nat) : Nat → Prop
   /-- If `n ≤ m`, then `n ≤ m + 1`. -/
   | step {m} : Nat.le n m → Nat.le n (succ m)
 
-instance : LE Nat where
+instance instLENat : LE Nat where
   le := Nat.le
 
 /-- The strict less than relation on natural numbers is defined as `n < m := n + 1 ≤ m`. -/
 protected def Nat.lt (n m : Nat) : Prop :=
   Nat.le (succ n) m
 
-instance : LT Nat where
+instance instLTNat : LT Nat where
   lt := Nat.lt
 
 theorem Nat.not_succ_le_zero : ∀ (n : Nat), LE.le (succ n) 0 → False
@@ -1793,7 +1795,7 @@ protected def Nat.sub : (@& Nat) → (@& Nat) → Nat
   | a, 0      => a
   | a, succ b => pred (Nat.sub a b)
 
-instance : Sub Nat where
+instance instSubNat : Sub Nat where
   sub := Nat.sub
 
 /--
@@ -1820,6 +1822,8 @@ It is the "canonical type with `n` elements".
 -/
 @[pp_using_anonymous_constructor]
 structure Fin (n : Nat) where
+  /-- Creates a `Fin n` from `i : Nat` and a proof that `i < n`. -/
+  mk ::
   /-- If `i : Fin n`, then `i.val : ℕ` is the described number. It can also be
   written as `i.1` or just `i` when the target type is known. -/
   val  : Nat
@@ -2543,43 +2547,6 @@ def panic {α : Type u} [Inhabited α] (msg : String) : α :=
 -- TODO: this be applied directly to `Inhabited`'s definition when we remove the above workaround
 attribute [nospecialize] Inhabited
 
-/--
-The class `GetElem cont idx elem dom` implements the `xs[i]` notation.
-When you write this, given `xs : cont` and `i : idx`, Lean looks for an instance
-of `GetElem cont idx elem dom`. Here `elem` is the type of `xs[i]`, while
-`dom` is whatever proof side conditions are required to make this applicable.
-For example, the instance for arrays looks like
-`GetElem (Array α) Nat α (fun xs i => i < xs.size)`.
-
-The proof side-condition `dom xs i` is automatically dispatched by the
-`get_elem_tactic` tactic, which can be extended by adding more clauses to
-`get_elem_tactic_trivial`.
--/
-class GetElem (cont : Type u) (idx : Type v) (elem : outParam (Type w)) (dom : outParam (cont → idx → Prop)) where
-  /--
-  The syntax `arr[i]` gets the `i`'th element of the collection `arr`.
-  If there are proof side conditions to the application, they will be automatically
-  inferred by the `get_elem_tactic` tactic.
-
-  The actual behavior of this class is type-dependent,
-  but here are some important implementations:
-  * `arr[i] : α` where `arr : Array α` and `i : Nat` or `i : USize`:
-    does array indexing with no bounds check and a proof side goal `i < arr.size`.
-  * `l[i] : α` where `l : List α` and `i : Nat`: index into a list,
-    with proof side goal `i < l.length`.
-  * `stx[i] : Syntax` where `stx : Syntax` and `i : Nat`: get a syntax argument,
-    no side goal (returns `.missing` out of range)
-
-  There are other variations on this syntax:
-  * `arr[i]`: proves the proof side goal by `get_elem_tactic`
-  * `arr[i]!`: panics if the side goal is false
-  * `arr[i]?`: returns `none` if the side goal is false
-  * `arr[i]'h`: uses `h` to prove the side goal
-  -/
-  getElem (xs : cont) (i : idx) (h : dom xs i) : elem
-
-export GetElem (getElem)
-
 /--
 `Array α` is the type of [dynamic arrays](https://en.wikipedia.org/wiki/Dynamic_array)
 with elements from `α`. This type has special support in the runtime.
@@ -2637,9 +2604,6 @@ def Array.get {α : Type u} (a : @& Array α) (i : @& Fin a.size) : α :=
 def Array.get! {α : Type u} [Inhabited α] (a : @& Array α) (i : @& Nat) : α :=
   Array.getD a i default
 
-instance : GetElem (Array α) Nat α fun xs i => LT.lt i xs.size where
-  getElem xs i h := xs.get ⟨i, h⟩
-
 /--
 Push an element onto the end of an array. This is amortized O(1) because
 `Array α` is internally a dynamic array.
@@ -3397,7 +3361,7 @@ protected def seqRight (x : EStateM ε σ α) (y : Unit → EStateM ε σ β) :
   | Result.error e s => Result.error e s
 
 @[always_inline]
-instance : Monad (EStateM ε σ) where
+instance instMonad : Monad (EStateM ε σ) where
   bind     := EStateM.bind
   pure     := EStateM.pure
   map      := EStateM.map
@@ -3907,9 +3871,6 @@ def getArg (stx : Syntax) (i : Nat) : Syntax :=
   | Syntax.node _ _ args => args.getD i Syntax.missing
   | _                    => Syntax.missing
 
-instance : GetElem Syntax Nat Syntax fun _ _ => True where
-  getElem stx i _ := stx.getArg i
-
 /-- Gets the list of arguments of the syntax node, or `#[]` if it's not a `node`. -/
 def getArgs (stx : Syntax) : Array Syntax :=
   match stx with

src/Init/RCases.lean

@@ -5,7 +5,8 @@ Authors: Mario Carneiro, Jacob von Raumer
 -/
 prelude
 import Init.Tactics
-import Init.NotationExtra
+import Init.Meta
+
 
 /-!
 # Recursive cases (`rcases`) tactic and related tactics
@@ -127,7 +128,7 @@ the input expression). An `rcases` pattern has the following grammar:
   and so on.
 * A `@` before a tuple pattern as in `@⟨p1, p2, p3⟩` will bind all arguments in the constructor,
   while leaving the `@` off will only use the patterns on the explicit arguments.
-* An alteration pattern `p1 | p2 | p3`, which matches an inductive type with multiple constructors,
+* An alternation pattern `p1 | p2 | p3`, which matches an inductive type with multiple constructors,
   or a nested disjunction like `a ∨ b ∨ c`.
 
 A pattern like `⟨a, b, c⟩ | ⟨d, e⟩` will do a split over the inductive datatype,

src/Init/System/IO.lean

@@ -311,6 +311,8 @@ Note that EOF does not actually close a stream, so further reads may block and r
   -/
   getLine : IO String
   putStr  : String → IO Unit
+  /-- Returns true if a stream refers to a Windows console or Unix terminal. -/
+  isTty   : BaseIO Bool
   deriving Inhabited
 
 open FS
@@ -360,6 +362,9 @@ Will succeed even if no lock has been acquired.
 -/
 @[extern "lean_io_prim_handle_unlock"] opaque unlock (h : @& Handle) : IO Unit
 
+/-- Returns true if a handle refers to a Windows console or Unix terminal. -/
+@[extern "lean_io_prim_handle_is_tty"] opaque isTty (h : @& Handle) : BaseIO Bool
+
 @[extern "lean_io_prim_handle_flush"] opaque flush (h : @& Handle) : IO Unit
 /-- Rewinds the read/write cursor to the beginning of the handle. -/
 @[extern "lean_io_prim_handle_rewind"] opaque rewind (h : @& Handle) : IO Unit
@@ -743,36 +748,41 @@ namespace FS
 namespace Stream
 
 @[export lean_stream_of_handle]
-def ofHandle (h : Handle) : Stream := {
-  flush   := Handle.flush h,
-  read    := Handle.read h,
-  write   := Handle.write h,
-  getLine := Handle.getLine h,
-  putStr  := Handle.putStr h,
-}
+def ofHandle (h : Handle) : Stream where
+  flush   := Handle.flush h
+  read    := Handle.read h
+  write   := Handle.write h
+  getLine := Handle.getLine h
+  putStr  := Handle.putStr h
+  isTty   := Handle.isTty h
 
 structure Buffer where
   data : ByteArray := ByteArray.empty
   pos  : Nat := 0
 
-def ofBuffer (r : Ref Buffer) : Stream := {
-  flush   := pure (),
+def ofBuffer (r : Ref Buffer) : Stream where
+  flush   := pure ()
   read    := fun n => r.modifyGet fun b =>
     let data := b.data.extract b.pos (b.pos + n.toNat)
-    (data, { b with pos := b.pos + data.size }),
+    (data, { b with pos := b.pos + data.size })
   write   := fun data => r.modify fun b =>
     -- set `exact` to `false` so that repeatedly writing to the stream does not impose quadratic run time
-    { b with data := data.copySlice 0 b.data b.pos data.size false, pos := b.pos + data.size },
-  getLine := r.modifyGet fun b =>
-    let pos := match b.data.findIdx? (start := b.pos) fun u => u == 0 || u = '\n'.toNat.toUInt8 with
-      -- include '\n', but not '\0'
-      | some pos => if b.data.get! pos == 0 then pos else pos + 1
-      | none     => b.data.size
-    (String.fromUTF8Unchecked <| b.data.extract b.pos pos, { b with pos := pos }),
+    { b with data := data.copySlice 0 b.data b.pos data.size false, pos := b.pos + data.size }
+  getLine := do
+    let buf ← r.modifyGet fun b =>
+      let pos := match b.data.findIdx? (start := b.pos) fun u => u == 0 || u = '\n'.toNat.toUInt8 with
+        -- include '\n', but not '\0'
+        | some pos => if b.data.get! pos == 0 then pos else pos + 1
+        | none     => b.data.size
+      (b.data.extract b.pos pos, { b with pos := pos })
+    match String.fromUTF8? buf with
+    | some str => pure str
+    | none => throw (.userError "invalid UTF-8")
   putStr  := fun s => r.modify fun b =>
     let data := s.toUTF8
-    { b with data := data.copySlice 0 b.data b.pos data.size false, pos := b.pos + data.size },
-}
+    { b with data := data.copySlice 0 b.data b.pos data.size false, pos := b.pos + data.size }
+  isTty   := pure false
+
 end Stream
 
 /-- Run action with `stdin` emptied and `stdout+stderr` captured into a `String`. -/
@@ -785,7 +795,7 @@ def withIsolatedStreams [Monad m] [MonadFinally m] [MonadLiftT BaseIO m] (x : m
       (if isolateStderr then withStderr (Stream.ofBuffer bOut) else id) <|
         x
   let bOut ← liftM (m := BaseIO) bOut.get
-  let out := String.fromUTF8Unchecked bOut.data
+  let out := String.fromUTF8! bOut.data
   pure (out, r)
 
 end FS
@@ -802,7 +812,7 @@ class Eval (α : Type u) where
   -- We take `Unit → α` instead of `α` because ‵α` may contain effectful debugging primitives (e.g., `dbg_trace`)
   eval : (Unit → α) → (hideUnit : Bool := true) → IO Unit
 
-instance [ToString α] : Eval α where
+instance instEval [ToString α] : Eval α where
   eval a _ := IO.println (toString (a ()))
 
 instance [Repr α] : Eval α where

src/Init/System/Uri.lean

@@ -50,7 +50,7 @@ def decodeUri (uri : String) : String := Id.run do
         ((decoded.push c).push h1, i + 2)
     else
       (decoded.push c, i + 1)
-  return String.fromUTF8Unchecked decoded
+  return String.fromUTF8! decoded
 where hexDigitToUInt8? (c : UInt8) : Option UInt8 :=
   if zero ≤ c ∧ c ≤ nine then some (c - zero)
   else if lettera ≤ c ∧ c ≤ letterf then some (c - lettera + 10)

src/Init/Tactics.lean

@@ -354,6 +354,9 @@ macro:1 x:tactic tk:" <;> " y:tactic:2 : tactic => `(tactic|
     with_annotate_state $tk skip
     all_goals $y:tactic)
 
+/-- `fail msg` is a tactic that always fails, and produces an error using the given message. -/
+syntax (name := fail) "fail" (ppSpace str)? : tactic
+
 /-- `eq_refl` is equivalent to `exact rfl`, but has a few optimizations. -/
 syntax (name := eqRefl) "eq_refl" : tactic
 
@@ -365,13 +368,18 @@ for new reflexive relations.
 Remark: `rfl` is an extensible tactic. We later add `macro_rules` to try different
 reflexivity theorems (e.g., `Iff.rfl`).
 -/
-macro "rfl" : tactic => `(tactic| eq_refl)
+macro "rfl" : tactic => `(tactic| 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`.")
 
+macro_rules | `(tactic| rfl) => `(tactic| eq_refl)
 macro_rules | `(tactic| rfl) => `(tactic| exact HEq.rfl)
 
 /--
-This tactic applies to a goal whose target has the form `x ~ x`, where `~` is a reflexive
-relation, that is, a relation which has a reflexive lemma tagged with the attribute [refl].
+This tactic applies to a goal whose target has the form `x ~ x`,
+where `~` is a reflexive relation other than `=`,
+that is, a relation which has a reflexive lemma tagged with the attribute @[refl].
 -/
 syntax (name := applyRfl) "apply_rfl" : tactic
 
@@ -907,9 +915,6 @@ example : ∀ x : Nat, x = x := by unhygienic
 -/
 macro "unhygienic " t:tacticSeq : tactic => `(tactic| set_option tactic.hygienic false in $t)
 
-/-- `fail msg` is a tactic that always fails, and produces an error using the given message. -/
-syntax (name := fail) "fail" (ppSpace str)? : tactic
-
 /--
 `checkpoint tac` acts the same as `tac`, but it caches the input and output of `tac`,
 and if the file is re-elaborated and the input matches, the tactic is not re-run and
@@ -1517,16 +1522,16 @@ macro "get_elem_tactic" : tactic =>
   - Use `a[i]'h` notation instead, where `h` is a proof that index is valid"
    )
 
-@[inherit_doc getElem]
-syntax:max term noWs "[" withoutPosition(term) "]" : term
-macro_rules | `($x[$i]) => `(getElem $x $i (by get_elem_tactic))
-
-@[inherit_doc getElem]
-syntax term noWs "[" withoutPosition(term) "]'" term:max : term
-macro_rules | `($x[$i]'$h) => `(getElem $x $i $h)
-
 /--
 Searches environment for definitions or theorems that can be substituted in
 for `exact?% to solve the goal.
  -/
 syntax (name := Lean.Parser.Syntax.exact?) "exact?%" : term
+
+set_option linter.unusedVariables.funArgs false in
+/--
+  Gadget for automatic parameter support. This is similar to the `optParam` gadget, but it uses
+  the given tactic.
+  Like `optParam`, this gadget only affects elaboration.
+  For example, the tactic will *not* be invoked during type class resolution. -/
+abbrev autoParam.{u} (α : Sort u) (tactic : Lean.Syntax) : Sort u := α

src/Init/Util.lean

@@ -73,19 +73,6 @@ def withPtrEq {α : Type u} (a b : α) (k : Unit → Bool) (h : a = b → k () =
 @[implemented_by withPtrAddrUnsafe]
 def withPtrAddr {α : Type u} {β : Type v} (a : α) (k : USize → β) (h : ∀ u₁ u₂, k u₁ = k u₂) : β := k 0
 
-@[never_extract]
-private def outOfBounds [Inhabited α] : α :=
-  panic! "index out of bounds"
-
-@[inline] def getElem! [GetElem cont idx elem dom] [Inhabited elem] (xs : cont) (i : idx) [Decidable (dom xs i)] : elem :=
-  if h : _ then getElem xs i h else outOfBounds
-
-@[inline] def getElem? [GetElem cont idx elem dom] (xs : cont) (i : idx) [Decidable (dom xs i)] : Option elem :=
-  if h : _ then some (getElem xs i h) else none
-
-macro:max x:term noWs "[" i:term "]" noWs "?" : term => `(getElem? $x $i)
-macro:max x:term noWs "[" i:term "]" noWs "!" : term => `(getElem! $x $i)
-
 /--
   Marks given value and its object graph closure as multi-threaded if currently
   marked single-threaded. This will make reference counter updates atomic and

src/Init/WF.lean

@@ -9,7 +9,18 @@ import Init.Data.Nat.Basic
 
 universe u v
 
+/--
+`Acc` is the accessibility predicate. Given some relation `r` (e.g. `<`) and a value `x`,
+`Acc r x` means that `x` is accessible through `r`:
+
+`x` is accessible if there exists no infinite sequence `... < y₂ < y₁ < y₀ < x`.
+-/
 inductive Acc {α : Sort u} (r : α → α → Prop) : α → Prop where
+  /--
+  A value is accessible if for all `y` such that `r y x`, `y` is also accessible.
+  Note that if there exists no `y` such that `r y x`, then `x` is accessible. Such an `x` is called a
+  _base case_.
+  -/
   | intro (x : α) (h : (y : α) → r y x → Acc r y) : Acc r x
 
 noncomputable abbrev Acc.ndrec.{u1, u2} {α : Sort u2} {r : α → α → Prop} {C : α → Sort u1}
@@ -31,6 +42,14 @@ def inv {x y : α} (h₁ : Acc r x) (h₂ : r y x) : Acc r y :=
 
 end Acc
 
+/--
+A relation `r` is `WellFounded` if all elements of `α` are accessible within `r`.
+If a relation is `WellFounded`, it does not allow for an infinite descent along the relation.
+
+If the arguments of the recursive calls in a function definition decrease according to
+a well founded relation, then the function terminates.
+Well-founded relations are sometimes called _Artinian_ or said to satisfy the “descending chain condition”.
+-/
 inductive WellFounded {α : Sort u} (r : α → α → Prop) : Prop where
   | intro (h : ∀ a, Acc r a) : WellFounded r
 

src/Lean/BuiltinDocAttr.lean

@@ -0,0 +1,27 @@
+/-
+Copyright (c) 2024 Mario Carneiro. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Mario Carneiro
+-/
+prelude
+import Lean.Compiler.InitAttr
+import Lean.DocString
+
+namespace Lean
+
+def declareBuiltinDocStringAndRanges (declName : Name) : AttrM Unit := do
+  if let some doc ← findDocString? (← 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])
+
+builtin_initialize
+  registerBuiltinAttribute {
+    name  := `builtin_doc
+    descr := "make the docs and location of this declaration available as a builtin"
+    add   := fun decl stx _ => do
+      Attribute.Builtin.ensureNoArgs stx
+      declareBuiltinDocStringAndRanges decl
+  }
+
+end Lean

src/Lean/Compiler/IR/EmitLLVM.lean

@@ -147,7 +147,7 @@ def callLeanRefcountFn (builder : LLVM.Builder llvmctx)
     (delta : Option (LLVM.Value llvmctx) := Option.none) : M llvmctx Unit := do
   let fnName :=  s!"lean_{kind}{if checkRef? then "" else "_ref"}{if delta.isNone then "" else "_n"}"
   let retty ← LLVM.voidType llvmctx
-  let argtys := if delta.isNone then #[← LLVM.voidPtrType llvmctx] else #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx]
+  let argtys ← if delta.isNone then pure #[← LLVM.voidPtrType llvmctx] else pure #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx]
   let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys
   let fnty ← LLVM.functionType retty argtys
   match delta with

src/Lean/Compiler/LCNF/LambdaLifting.lean

@@ -88,7 +88,7 @@ occurring in `decl`.
 -/
 def mkAuxDecl (closure : Array Param) (decl : FunDecl) : LiftM LetDecl := do
   let nameNew ← mkAuxDeclName
-  let inlineAttr? := if (← read).inheritInlineAttrs then (← read).mainDecl.inlineAttr? else none
+  let inlineAttr? ← if (← read).inheritInlineAttrs then pure (← read).mainDecl.inlineAttr? else pure none
   let auxDecl ← go nameNew (← read).mainDecl.safe inlineAttr? |>.run' {}
   let us := auxDecl.levelParams.map mkLevelParam
   let auxDeclName ← match (← cacheAuxDecl auxDecl) with

src/Lean/Compiler/Main.lean

@@ -12,7 +12,8 @@ Run the code generation pipeline for all declarations in `declNames`
 that fulfill the requirements of `shouldGenerateCode`.
 -/
 def compile (declNames : Array Name) : CoreM Unit := do profileitM Exception "compiler new" (← getOptions) do
-  discard <| LCNF.compile declNames
+  withTraceNode `Compiler (fun _ => return m!"compiling: {declNames}") do
+    discard <| LCNF.compile declNames
 
 builtin_initialize
   registerTraceClass `Compiler

src/Lean/CoreM.lean

@@ -177,6 +177,13 @@ instance : MonadTrace CoreM where
 def restore (b : State) : CoreM Unit :=
   modify fun s => { s with env := b.env, messages := b.messages, infoState := b.infoState }
 
+/--
+Restores full state including sources for unique identifiers. Only intended for incremental reuse
+between elaboration runs, not for backtracking within a single run.
+-/
+def restoreFull (b : State) : CoreM Unit :=
+  set b
+
 private def mkFreshNameImp (n : Name) : CoreM Name := do
   let fresh ← modifyGet fun s => (s.nextMacroScope, { s with nextMacroScope := s.nextMacroScope + 1 })
   return addMacroScope (← getEnv).mainModule n fresh
@@ -245,6 +252,13 @@ def resetMessageLog : CoreM Unit :=
 def getMessageLog : CoreM MessageLog :=
   return (← get).messages
 
+/--
+Returns the current log and then resets its messages but does NOT reset `MessageLog.hadErrors`. Used
+for incremental reporting during elaboration of a single command.
+-/
+def getAndEmptyMessageLog : CoreM MessageLog :=
+  modifyGet fun log => ({ log with msgs := {} }, log)
+
 instance : MonadLog CoreM where
   getRef      := getRef
   getFileMap  := return (← read).fileMap
@@ -330,10 +344,13 @@ opaque compileDeclsNew (declNames : List Name) : CoreM Unit
 
 def compileDecl (decl : Declaration) : CoreM Unit := do
   let opts ← getOptions
+  let decls := Compiler.getDeclNamesForCodeGen decl
   if compiler.enableNew.get opts then
-    compileDeclsNew (Compiler.getDeclNamesForCodeGen decl)
-  match (← getEnv).compileDecl opts decl with
-  | Except.ok env   => setEnv env
+    compileDeclsNew decls
+  let res ← withTraceNode `compiler (fun _ => return m!"compiling old: {decls}") do
+    return (← getEnv).compileDecl opts decl
+  match res with
+  | Except.ok env => setEnv env
   | Except.error (KernelException.other msg) =>
     checkUnsupported decl -- Generate nicer error message for unsupported recursors and axioms
     throwError msg

src/Lean/Data/HashMap.lean

@@ -122,7 +122,7 @@ 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 let some b := bkt.find? a then
-      (m, some b)
+      (⟨size, buckets⟩, some b)
     else
       let size'    := size + 1
       let buckets' := buckets.update i (AssocList.cons a b bkt) h
@@ -137,8 +137,10 @@ def erase [BEq α] [Hashable α] (m : HashMapImp α β) (a : α) : HashMapImp α
   | ⟨ size, buckets ⟩ =>
     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⟩
-    else m
+    if bkt.contains a then
+      ⟨size - 1, buckets.update i (bkt.erase a) h⟩
+    else
+      ⟨size, buckets⟩
 
 inductive WellFormed [BEq α] [Hashable α] : HashMapImp α β → Prop where
   | mkWff          : ∀ n,                    WellFormed (mkHashMapImp n)
@@ -212,6 +214,8 @@ def insertIfNew (m : HashMap α β) (a : α) (b : β) : HashMap α β × Option
 instance : GetElem (HashMap α β) α (Option β) fun _ _ => True where
   getElem m k _ := m.find? k
 
+instance : LawfulGetElem (HashMap α β) α (Option β) fun _ _ => True where
+
 @[inline] def contains (m : HashMap α β) (a : α) : Bool :=
   match m with
   | ⟨ m, _ ⟩ => m.contains a

src/Lean/Data/HashSet.lean

@@ -112,8 +112,10 @@ def erase [BEq α] [Hashable α] (m : HashSetImp α) (a : α) : HashSetImp α :=
   | ⟨ size, buckets ⟩ =>
     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⟩
-    else m
+    if bkt.contains a then
+      ⟨size - 1, buckets.update i (bkt.erase a) h⟩
+    else
+      ⟨size, buckets⟩
 
 inductive WellFormed [BEq α] [Hashable α] : HashSetImp α → Prop where
   | mkWff     : ∀ n,                  WellFormed (mkHashSetImp n)

src/Lean/Data/Json/Basic.lean

@@ -10,6 +10,8 @@ import Init.Data.Range
 import Init.Data.OfScientific
 import Init.Data.Hashable
 import Lean.Data.RBMap
+import Init.Data.ToString.Macro
+
 namespace Lean
 
 -- mantissa * 10^-exponent

src/Lean/Data/Json/Stream.lean

@@ -18,7 +18,7 @@ open IO
 /-- Consumes `nBytes` bytes from the stream, interprets the bytes as a utf-8 string and the string as a valid JSON object. -/
 def readJson (h : FS.Stream) (nBytes : Nat) : IO Json := do
   let bytes ← h.read (USize.ofNat nBytes)
-  let s := String.fromUTF8Unchecked bytes
+  let some s := String.fromUTF8? bytes | throw (IO.userError "invalid UTF-8")
   ofExcept (Json.parse s)
 
 def writeJson (h : FS.Stream) (j : Json) : IO Unit := do

src/Lean/Data/Lsp/LanguageFeatures.lean

@@ -324,7 +324,7 @@ inductive SemanticTokenType where
   | decorator
   -- Extensions
   | leanSorryLike
-  deriving ToJson, FromJson
+  deriving ToJson, FromJson, BEq, Hashable
 
 -- must be in the same order as the constructors
 def SemanticTokenType.names : Array String :=

src/Lean/Data/Parsec.lean

@@ -5,7 +5,7 @@ Author: Dany Fabian
 -/
 prelude
 import Init.NotationExtra
-import Init.Data.ToString.Basic
+import Init.Data.ToString.Macro
 
 namespace Lean
 

src/Lean/Data/PersistentArray.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 import Init.NotationExtra
+import Init.Data.ToString.Macro
 
 universe u v w
 
@@ -71,6 +72,8 @@ def get! [Inhabited α] (t : PersistentArray α) (i : Nat) : α :=
 instance [Inhabited α] : GetElem (PersistentArray α) Nat α fun as i => i < as.size where
   getElem xs i _ := xs.get! i
 
+instance [Inhabited α] : LawfulGetElem (PersistentArray α) Nat α fun as i => i < as.size where
+
 partial def setAux : PersistentArrayNode α → USize → USize → α → PersistentArrayNode α
   | node cs, i, shift, a =>
     let j     := div2Shift i shift

src/Lean/Data/PersistentHashMap.lean

@@ -5,6 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.Data.Array.BasicAux
+import Init.Data.ToString.Macro
 
 namespace Lean
 universe u v w w'
@@ -154,6 +155,8 @@ def find? {_ : BEq α} {_ : Hashable α} : PersistentHashMap α β → α → Op
 instance {_ : BEq α} {_ : Hashable α} : GetElem (PersistentHashMap α β) α (Option β) fun _ _ => True where
   getElem m i _ := m.find? i
 
+instance {_ : BEq α} {_ : Hashable α} : LawfulGetElem (PersistentHashMap α β) α (Option β) fun _ _ => True where
+
 @[inline] def findD {_ : BEq α} {_ : Hashable α} (m : PersistentHashMap α β) (a : α) (b₀ : β) : β :=
   (m.find? a).getD b₀
 
@@ -322,6 +325,9 @@ def map {α : Type u} {β : Type v} {σ : Type u} {_ : BEq α} {_ : Hashable α}
 def toList {_ : BEq α} {_ : Hashable α} (m : PersistentHashMap α β) : List (α × β) :=
   m.foldl (init := []) fun ps k v => (k, v) :: ps
 
+def toArray {_ : BEq α} {_ : Hashable α} (m : PersistentHashMap α β) : Array (α × β) :=
+  m.foldl (init := #[]) fun ps k v => ps.push (k, v)
+
 structure Stats where
   numNodes      : Nat := 0
   numNull       : Nat := 0

src/Lean/Data/Rat.lean

@@ -5,7 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import Init.NotationExtra
-import Init.Data.ToString.Basic
+import Init.Data.ToString.Macro
 import Init.Data.Int.DivMod
 import Init.Data.Nat.Gcd
 namespace Lean

src/Lean/Data/Xml/Basic.lean

@@ -5,6 +5,8 @@ Author: Dany Fabian
 -/
 prelude
 import Lean.Data.RBMap
+import Init.Data.ToString.Macro
+
 namespace Lean
 namespace Xml
 

src/Lean/Declaration.lean

@@ -49,13 +49,26 @@ def ReducibilityHints.getHeightEx (h : ReducibilityHints) : UInt32 :=
 
 namespace ReducibilityHints
 
+-- Recall that if `lt h₁ h₂`, we want to reduce declaration associated with `h₁`.
 def lt : ReducibilityHints → ReducibilityHints → Bool
   | .abbrev,     .abbrev     => false
   | .abbrev,     _           => true
-  | .regular d₁, .regular d₂ => d₁ < d₂
+  | .regular d₁, .regular d₂ => d₁ > d₂
   | .regular _,  .opaque     => true
   | _,           _           => false
 
+protected def compare : ReducibilityHints → ReducibilityHints → Ordering
+  | .abbrev,     .abbrev     => .eq
+  | .abbrev,     _           => .lt
+  | .regular _,  .abbrev     => .gt
+  | .regular d₁, .regular d₂ => Ord.compare d₂ d₁
+  | .regular _,  .opaque     => .lt
+  | .opaque,     .opaque     => .eq
+  | .opaque,     _           => .gt
+
+instance : Ord ReducibilityHints where
+  compare := ReducibilityHints.compare
+
 def isAbbrev : ReducibilityHints → Bool
   | .abbrev => true
   | _       => false

src/Lean/DocString.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Lean.DeclarationRange
 import Lean.MonadEnv
+import Init.Data.String.Extra
 
 namespace Lean
 
@@ -13,12 +14,14 @@ private builtin_initialize builtinDocStrings : IO.Ref (NameMap String) ← IO.mk
 private builtin_initialize docStringExt : MapDeclarationExtension String ← mkMapDeclarationExtension
 
 def addBuiltinDocString (declName : Name) (docString : String) : IO Unit :=
-  builtinDocStrings.modify (·.insert declName (removeLeadingSpaces docString))
+  builtinDocStrings.modify (·.insert declName docString.removeLeadingSpaces)
 
-def addDocString [MonadEnv m] (declName : Name) (docString : String) : m Unit :=
-  modifyEnv fun env => docStringExt.insert env declName (removeLeadingSpaces docString)
+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] [MonadEnv m] (declName : Name) (docString? : Option String) : m Unit :=
+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 ()

src/Lean/Elab/App.lean

@@ -1149,7 +1149,7 @@ private partial def mkBaseProjections (baseStructName : Name) (structName : Name
 private def typeMatchesBaseName (type : Expr) (baseName : Name) : MetaM Bool := do
   if baseName == `Function then
     return (← whnfR type).isForall
-  else if type.consumeMData.isAppOf baseName then
+  else if type.cleanupAnnotations.isAppOf baseName then
     return true
   else
     return (← whnfR type).isAppOf baseName
@@ -1194,13 +1194,24 @@ private def addLValArg (baseName : Name) (fullName : Name) (e : Expr) (args : Ar
           argIdx := argIdx + 1
     throwError "invalid field notation, function '{fullName}' does not have argument with type ({baseName} ...) that can be used, it must be explicit or implicit with a unique name"
 
+/-- Adds the `TermInfo` for the field of a projection. See `Lean.Parser.Term.identProjKind`. -/
+private def addProjTermInfo
+    (stx            : Syntax)
+    (e              : Expr)
+    (expectedType?  : Option Expr := none)
+    (lctx?          : Option LocalContext := none)
+    (elaborator     : Name := Name.anonymous)
+    (isBinder force : Bool := false)
+    : TermElabM Expr :=
+  addTermInfo (Syntax.node .none Parser.Term.identProjKind #[stx]) e expectedType? lctx? elaborator isBinder force
+
 private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (expectedType? : Option Expr) (explicit ellipsis : Bool)
     (f : Expr) (lvals : List LVal) : TermElabM Expr :=
   let rec loop : Expr → List LVal → TermElabM Expr
   | f, []          => elabAppArgs f namedArgs args expectedType? explicit ellipsis
   | f, lval::lvals => do
-    if let LVal.fieldName (ref := fieldStx) (targetStx := targetStx) .. := lval then
-      addDotCompletionInfo targetStx f expectedType? fieldStx
+    if let LVal.fieldName (fullRef := fullRef) .. := lval then
+      addDotCompletionInfo fullRef f expectedType?
     let hasArgs := !namedArgs.isEmpty || !args.isEmpty
     let (f, lvalRes) ← resolveLVal f lval hasArgs
     match lvalRes with
@@ -1214,7 +1225,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
         if isPrivateNameFromImportedModule (← getEnv) info.projFn then
           throwError "field '{fieldName}' from structure '{structName}' is private"
         let projFn ← mkConst info.projFn
-        let projFn ← addTermInfo lval.getRef projFn
+        let projFn ← addProjTermInfo lval.getRef projFn
         if lvals.isEmpty then
           let namedArgs ← addNamedArg namedArgs { name := `self, val := Arg.expr f }
           elabAppArgs projFn namedArgs args expectedType? explicit ellipsis
@@ -1226,7 +1237,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
     | LValResolution.const baseStructName structName constName =>
       let f ← if baseStructName != structName then mkBaseProjections baseStructName structName f else pure f
       let projFn ← mkConst constName
-      let projFn ← addTermInfo lval.getRef projFn
+      let projFn ← addProjTermInfo lval.getRef projFn
       if lvals.isEmpty then
         let projFnType ← inferType projFn
         let (args, namedArgs) ← addLValArg baseStructName constName f args namedArgs projFnType
@@ -1235,7 +1246,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
         let f ← elabAppArgs projFn #[] #[Arg.expr f] (expectedType? := none) (explicit := false) (ellipsis := false)
         loop f lvals
     | LValResolution.localRec baseName fullName fvar =>
-      let fvar ← addTermInfo lval.getRef fvar
+      let fvar ← addProjTermInfo lval.getRef fvar
       if lvals.isEmpty then
         let fvarType ← inferType fvar
         let (args, namedArgs) ← addLValArg baseName fullName f args namedArgs fvarType
@@ -1340,7 +1351,7 @@ private partial def elabAppFn (f : Syntax) (lvals : List LVal) (namedArgs : Arra
     let elabFieldName (e field : Syntax) := do
       let newLVals := field.identComponents.map fun comp =>
         -- We use `none` in `suffix?` since `field` can't be part of a composite name
-        LVal.fieldName comp comp.getId.getString! none e
+        LVal.fieldName comp comp.getId.getString! none f
       elabAppFn e (newLVals ++ lvals) namedArgs args expectedType? explicit ellipsis overloaded acc
     let elabFieldIdx (e idxStx : Syntax) := do
       let some idx := idxStx.isFieldIdx? | throwError "invalid field index"

src/Lean/Elab/BuiltinCommand.lean

@@ -119,64 +119,6 @@ private partial def elabChoiceAux (cmds : Array Syntax) (i : Nat) : CommandElabM
 @[builtin_command_elab choice] def elabChoice : CommandElab := fun stx =>
   elabChoiceAux stx.getArgs 0
 
-/-- Declares one or more universe variables.
-
-`universe u v`
-
-`Prop`, `Type`, `Type u` and `Sort u` are types that classify other types, also known as
-*universes*. In `Type u` and `Sort u`, the variable `u` stands for the universe's *level*, and a
-universe at level `u` can only classify universes that are at levels lower than `u`. For more
-details on type universes, please refer to [the relevant chapter of Theorem Proving in Lean][tpil
-universes].
-
-Just as type arguments allow polymorphic definitions to be used at many different types, universe
-parameters, represented by universe variables, allow a definition to be used at any required level.
-While Lean mostly handles universe levels automatically, declaring them explicitly can provide more
-control when writing signatures. The `universe` keyword allows the declared universe variables to be
-used in a collection of definitions, and Lean will ensure that these definitions use them
-consistently.
-
-[tpil universes]: https://lean-lang.org/theorem_proving_in_lean4/dependent_type_theory.html#types-as-objects
-(Type universes on Theorem Proving in Lean)
-
-```lean
-/- Explicit type-universe parameter. -/
-def id₁.{u} (α : Type u) (a : α) := a
-
-/- Implicit type-universe parameter, equivalent to `id₁`.
-  Requires option `autoImplicit true`, which is the default. -/
-def id₂ (α : Type u) (a : α) := a
-
-/- Explicit standalone universe variable declaration, equivalent to `id₁` and `id₂`. -/
-universe u
-def id₃ (α : Type u) (a : α) := a
-```
-
-On a more technical note, using a universe variable only in the right-hand side of a definition
-causes an error if the universe has not been declared previously.
-
-```lean
-def L₁.{u} := List (Type u)
-
--- def L₂ := List (Type u) -- error: `unknown universe level 'u'`
-
-universe u
-def L₃ := List (Type u)
-```
-
-## Examples
-
-```lean
-universe u v w
-
-structure Pair (α : Type u) (β : Type v) : Type (max u v) where
-  a : α
-  b : β
-
-#check Pair.{v, w}
--- Pair : Type v → Type w → Type (max v w)
-```
--/
 @[builtin_command_elab «universe»] def elabUniverse : CommandElab := fun n => do
   n[1].forArgsM addUnivLevel
 
@@ -185,30 +127,6 @@ structure Pair (α : Type u) (β : Type v) : Type (max u v) where
   | Except.ok env   => setEnv env
   | Except.error ex => throwError (ex.toMessageData (← getOptions))
 
-/-- Adds names from other namespaces to the current namespace.
-
-The command `export Some.Namespace (name₁ name₂)` makes `name₁` and `name₂`:
-
-- visible in the current namespace without prefix `Some.Namespace`, like `open`, and
-- visible from outside the current namespace `N` as `N.name₁` and `N.name₂`.
-
-## Examples
-
-```lean
-namespace Morning.Sky
-  def star := "venus"
-end Morning.Sky
-
-namespace Evening.Sky
-  export Morning.Sky (star)
-  -- `star` is now in scope
-  #check star
-end Evening.Sky
-
--- `star` is visible in `Evening.Sky`
-#check Evening.Sky.star
-```
--/
 @[builtin_command_elab «export»] def elabExport : CommandElab := fun stx => do
   let `(export $ns ($ids*)) := stx | throwUnsupportedSyntax
   let nss ← resolveNamespace ns
@@ -223,118 +141,6 @@ end Evening.Sky
     aliases := aliases.push (currNamespace ++ id, declName)
   modify fun s => { s with env := aliases.foldl (init := s.env) fun env p => addAlias env p.1 p.2 }
 
-/-- Makes names from other namespaces visible without writing the namespace prefix.
-
-Names that are made available with `open` are visible within the current `section` or `namespace`
-block. This makes referring to (type) definitions and theorems easier, but note that it can also
-make [scoped instances], notations, and attributes from a different namespace available.
-
-The `open` command can be used in a few different ways:
-
-* `open Some.Namespace.Path1 Some.Namespace.Path2` makes all non-protected names in
-  `Some.Namespace.Path1` and `Some.Namespace.Path2` available without the prefix, so that
-  `Some.Namespace.Path1.x` and `Some.Namespace.Path2.y` can be referred to by writing only `x` and
-  `y`.
-
-* `open Some.Namespace.Path hiding def1 def2` opens all non-protected names in `Some.Namespace.Path`
-  except `def1` and `def2`.
-
-* `open Some.Namespace.Path (def1 def2)` only makes `Some.Namespace.Path.def1` and
-  `Some.Namespace.Path.def2` available without the full prefix, so `Some.Namespace.Path.def3` would
-  be unaffected.
-
-  This works even if `def1` and `def2` are `protected`.
-
-* `open Some.Namespace.Path renaming def1 → def1', def2 → def2'` same as `open Some.Namespace.Path
-  (def1 def2)` but `def1`/`def2`'s names are changed to `def1'`/`def2'`.
-
-  This works even if `def1` and `def2` are `protected`.
-
-* `open scoped Some.Namespace.Path1 Some.Namespace.Path2` **only** opens [scoped instances],
-  notations, and attributes from `Namespace1` and `Namespace2`; it does **not** make any other name
-  available.
-
-* `open <any of the open shapes above> in` makes the names `open`-ed visible only in the next
-  command or expression.
-
-[scoped instance]: https://lean-lang.org/theorem_proving_in_lean4/type_classes.html#scoped-instances
-(Scoped instances in Theorem Proving in Lean)
-
-
-## Examples
-
-```lean
-/-- SKI combinators https://en.wikipedia.org/wiki/SKI_combinator_calculus -/
-namespace Combinator.Calculus
-  def I (a : α) : α := a
-  def K (a : α) : β → α := fun _ => a
-  def S (x : α → β → γ) (y : α → β) (z : α) : γ := x z (y z)
-end Combinator.Calculus
-
-section
-  -- open everything under `Combinator.Calculus`, *i.e.* `I`, `K` and `S`,
-  -- until the section ends
-  open Combinator.Calculus
-
-  theorem SKx_eq_K : S K x = I := rfl
-end
-
--- open everything under `Combinator.Calculus` only for the next command (the next `theorem`, here)
-open Combinator.Calculus in
-theorem SKx_eq_K' : S K x = I := rfl
-
-section
-  -- open only `S` and `K` under `Combinator.Calculus`
-  open Combinator.Calculus (S K)
-
-  theorem SKxy_eq_y : S K x y = y := rfl
-
-  -- `I` is not in scope, we have to use its full path
-  theorem SKxy_eq_Iy : S K x y = Combinator.Calculus.I y := rfl
-end
-
-section
-  open Combinator.Calculus
-    renaming
-      I → identity,
-      K → konstant
-
-  #check identity
-  #check konstant
-end
-
-section
-  open Combinator.Calculus
-    hiding S
-
-  #check I
-  #check K
-end
-
-section
-  namespace Demo
-    inductive MyType
-    | val
-
-    namespace N1
-      scoped infix:68 " ≋ " => BEq.beq
-
-      scoped instance : BEq MyType where
-        beq _ _ := true
-
-      def Alias := MyType
-    end N1
-  end Demo
-
-  -- bring `≋` and the instance in scope, but not `Alias`
-  open scoped Demo.N1
-
-  #check Demo.MyType.val == Demo.MyType.val
-  #check Demo.MyType.val ≋ Demo.MyType.val
-  -- #check Alias -- unknown identifier 'Alias'
-end
-```
--/
 @[builtin_command_elab «open»] def elabOpen : CommandElab
   | `(open $decl:openDecl) => do
     let openDecls ← elabOpenDecl decl
@@ -420,102 +226,6 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
   else
     return #[binder]
 
-/-- Declares one or more typed variables, or modifies whether already-declared variables are
-implicit.
-
-Introduces variables that can be used in definitions within the same `namespace` or `section` block.
-When a definition mentions a variable, Lean will add it as an argument of the definition. The
-`variable` command is also able to add typeclass parameters. This is useful in particular when
-writing many definitions that have parameters in common (see below for an example).
-
-Variable declarations have the same flexibility as regular function paramaters. In particular they
-can be [explicit, implicit][binder docs], or [instance implicit][tpil classes] (in which case they
-can be anonymous). This can be changed, for instance one can turn explicit variable `x` into an
-implicit one with `variable {x}`. Note that currently, you should avoid changing how variables are
-bound and declare new variables at the same time; see [issue 2789] for more on this topic.
-
-See [*Variables and Sections* from Theorem Proving in Lean][tpil vars] for a more detailed
-discussion.
-
-[tpil vars]: https://lean-lang.org/theorem_proving_in_lean4/dependent_type_theory.html#variables-and-sections
-(Variables and Sections on Theorem Proving in Lean)
-[tpil classes]: https://lean-lang.org/theorem_proving_in_lean4/type_classes.html
-(Type classes on Theorem Proving in Lean)
-[binder docs]: https://leanprover-community.github.io/mathlib4_docs/Lean/Expr.html#Lean.BinderInfo
-(Documentation for the BinderInfo type)
-[issue 2789]: https://github.com/leanprover/lean4/issues/2789
-(Issue 2789 on github)
-
-## Examples
-
-```lean
-section
-  variable
-    {α : Type u}      -- implicit
-    (a : α)           -- explicit
-    [instBEq : BEq α] -- instance implicit, named
-    [Hashable α]      -- instance implicit, anonymous
-
-  def isEqual (b : α) : Bool :=
-    a == b
-
-  #check isEqual
-  -- isEqual.{u} {α : Type u} (a : α) [instBEq : BEq α] (b : α) : Bool
-
-  variable
-    {a} -- `a` is implicit now
-
-  def eqComm {b : α} := a == b ↔ b == a
-
-  #check eqComm
-  -- eqComm.{u} {α : Type u} {a : α} [instBEq : BEq α] {b : α} : Prop
-end
-```
-
-The following shows a typical use of `variable` to factor out definition arguments:
-
-```lean
-variable (Src : Type)
-
-structure Logger where
-  trace : List (Src × String)
-#check Logger
--- Logger (Src : Type) : Type
-
-namespace Logger
-  -- switch `Src : Type` to be implicit until the `end Logger`
-  variable {Src}
-
-  def empty : Logger Src where
-    trace := []
-  #check empty
-  -- Logger.empty {Src : Type} : Logger Src
-
-  variable (log : Logger Src)
-
-  def len :=
-    log.trace.length
-  #check len
-  -- Logger.len {Src : Type} (log : Logger Src) : Nat
-
-  variable (src : Src) [BEq Src]
-
-  -- at this point all of `log`, `src`, `Src` and the `BEq` instance can all become arguments
-
-  def filterSrc :=
-    log.trace.filterMap
-      fun (src', str') => if src' == src then some str' else none
-  #check filterSrc
-  -- Logger.filterSrc {Src : Type} (log : Logger Src) (src : Src) [inst✝ : BEq Src] : List String
-
-  def lenSrc :=
-    log.filterSrc src |>.length
-  #check lenSrc
-  -- Logger.lenSrc {Src : Type} (log : Logger Src) (src : Src) [inst✝ : BEq Src] : Nat
-end Logger
-```
-
--/
 @[builtin_command_elab «variable»] def elabVariable : CommandElab
   | `(variable $binders*) => do
     -- Try to elaborate `binders` for sanity checking
@@ -538,10 +248,7 @@ def elabCheckCore (ignoreStuckTC : Bool) : CommandElab
       try
         for c in (← realizeGlobalConstWithInfos term) do
           addCompletionInfo <| .id term id.getId (danglingDot := false) {} none
-          logInfoAt tk <| .ofPPFormat { pp := fun
-            | some ctx => ctx.runMetaM <| PrettyPrinter.ppSignature c
-            | none     => return f!"{c}"  -- should never happen
-          }
+          logInfoAt tk <| .signature c
           return
       catch _ => pure ()  -- identifier might not be a constant but constant + projection
     let e ← Term.elabTerm term none
@@ -749,7 +456,7 @@ def elabRunMeta : CommandElab := fun stx =>
     pure ()
 
 @[builtin_command_elab «set_option»] def elabSetOption : CommandElab := fun stx => do
-  let options ← Elab.elabSetOption stx[1] stx[2]
+  let options ← Elab.elabSetOption stx[1] stx[3]
   modify fun s => { s with maxRecDepth := maxRecDepth.get options }
   modifyScope fun scope => { scope with opts := options }
 

src/Lean/Elab/BuiltinTerm.lean

@@ -232,7 +232,7 @@ def elabScientificLit : TermElab := fun stx expectedType? => do
 
 @[builtin_term_elab Parser.Term.withDeclName] def elabWithDeclName : TermElab := fun stx expectedType? => do
   let id := stx[2].getId
-  let id := if stx[1].isNone then id else (← getCurrNamespace) ++ id
+  let id ← if stx[1].isNone then pure id else pure <| (← getCurrNamespace) ++ id
   let e := stx[3]
   withMacroExpansion stx e <| withDeclName id <| elabTerm e expectedType?
 
@@ -312,9 +312,9 @@ private def mkSilentAnnotationIfHole (e : Expr) : TermElabM Expr := do
     popScope
 
 @[builtin_term_elab «set_option»] def elabSetOption : TermElab := fun stx expectedType? => do
-  let options ← Elab.elabSetOption stx[1] stx[2]
+  let options ← Elab.elabSetOption stx[1] stx[3]
   withTheReader Core.Context (fun ctx => { ctx with maxRecDepth := maxRecDepth.get options, options := options }) do
-    elabTerm stx[4] expectedType?
+    elabTerm stx[5] expectedType?
 
 @[builtin_term_elab withAnnotateTerm] def elabWithAnnotateTerm : TermElab := fun stx expectedType? => do
   match stx with

src/Lean/Elab/Command.lean

@@ -7,6 +7,7 @@ prelude
 import Lean.Elab.Binders
 import Lean.Elab.SyntheticMVars
 import Lean.Elab.SetOption
+import Lean.Language.Basic
 
 namespace Lean.Elab.Command
 
@@ -30,7 +31,6 @@ structure State where
   scopes         : List Scope := [{ header := "" }]
   nextMacroScope : Nat := firstFrontendMacroScope + 1
   maxRecDepth    : Nat
-  nextInstIdx    : Nat := 1 -- for generating anonymous instance names
   ngen           : NameGenerator := {}
   infoState      : InfoState := {}
   traceState     : TraceState := {}
@@ -45,6 +45,16 @@ structure Context where
   currMacroScope : MacroScope := firstFrontendMacroScope
   ref            : Syntax := Syntax.missing
   tacticCache?   : Option (IO.Ref Tactic.Cache)
+  /--
+  Snapshot for incremental reuse and reporting of command elaboration. Currently unused in Lean
+  itself.
+
+  Definitely resolved in `Language.Lean.process.doElab`.
+
+  Invariant: if the bundle's `old?` is set, the context and state at the beginning of current and
+  old elaboration are identical.
+  -/
+  snap?          : Option (Language.SnapshotBundle Language.DynamicSnapshot)
 
 abbrev CommandElabCoreM (ε) := ReaderT Context $ StateRefT State $ EIO ε
 abbrev CommandElabM := CommandElabCoreM Exception
@@ -147,10 +157,13 @@ private def addTraceAsMessagesCore (ctx : Context) (log : MessageLog) (traceStat
 
 private def addTraceAsMessages : CommandElabM Unit := do
   let ctx ← read
-  modify fun s => { s with
-    messages          := addTraceAsMessagesCore ctx s.messages s.traceState
-    traceState.traces := {}
-  }
+  -- do not add trace messages if `trace.profiler.output` is set as it would be redundant and
+  -- pretty printing the trace messages is expensive
+  if trace.profiler.output.get? (← getOptions) |>.isNone then
+    modify fun s => { s with
+      messages          := addTraceAsMessagesCore ctx s.messages s.traceState
+      traceState.traces := {}
+    }
 
 def liftCoreM (x : CoreM α) : CommandElabM α := do
   let s ← get
@@ -207,7 +220,8 @@ def runLinters (stx : Syntax) : CommandElabM Unit := do
       let linters ← lintersRef.get
       unless linters.isEmpty do
         for linter in linters do
-          withTraceNode `Elab.lint (fun _ => return m!"running linter: {linter.name}") do
+          withTraceNode `Elab.lint (fun _ => return m!"running linter: {linter.name}")
+              (tag := linter.name.toString) do
             let savedState ← get
             try
               linter.run stx
@@ -279,7 +293,9 @@ partial def elabCommand (stx : Syntax) : CommandElabM Unit := do
         -- list of commands => elaborate in order
         -- The parser will only ever return a single command at a time, but syntax quotations can return multiple ones
         args.forM elabCommand
-      else withTraceNode `Elab.command (fun _ => return stx) do
+      else withTraceNode `Elab.command (fun _ => return stx) (tag :=
+        -- special case: show actual declaration kind for `declaration` commands
+        (if stx.isOfKind ``Parser.Command.declaration then stx[1] else stx).getKind.toString) do
         let s ← get
         match (← liftMacroM <| expandMacroImpl? s.env stx) with
         | some (decl, stxNew?) =>
@@ -515,6 +531,7 @@ def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
       fileMap := ← getFileMap
       ref := ← getRef
       tacticCache? := none
+      snap? := none
     } |>.run {
       env := ← getEnv
       maxRecDepth := ← getMaxRecDepth
@@ -535,9 +552,9 @@ first evaluates any local `set_option ... in ...` clauses and then invokes `cmd`
 partial def withSetOptionIn (cmd : CommandElab) : CommandElab := fun stx => do
   if stx.getKind == ``Lean.Parser.Command.in &&
      stx[0].getKind == ``Lean.Parser.Command.set_option then
-      let opts ← Elab.elabSetOption stx[0][1] stx[0][2]
+      let opts ← Elab.elabSetOption stx[0][1] stx[0][3]
       Command.withScope (fun scope => { scope with opts }) do
-        withSetOptionIn cmd stx[1]
+        withSetOptionIn cmd stx[2]
   else
     cmd stx
 

src/Lean/Elab/DeclNameGen.lean

@@ -0,0 +1,256 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kyle Miller
+-/
+prelude
+import Lean.Elab.Command
+
+/-!
+# Name generator for declarations
+
+This module provides functionality to generate a name for a declaration using its binders and its type.
+This is used to generate names for anonymous instances.
+
+It uses heuristics to generate an informative but terse name given its namespace, supplied binders, and type.
+It tries to make these relatively unique,
+and it uses suffixes derived from the module to ensure cross-project uniqueness
+when the instance doesn't refer to anything defined in the current project.
+
+The name generator can be thought of as a kind of pretty printer, rendering an expression in textual form.
+The general structure of this generator is
+1. `Lean.Elab.Command.NameGen.winnowExpr` takes an expression and re-uses `Expr` as a data structure
+   to record the "Syntax"-like structure.
+2. `Lean.Elab.Command.NameGen.mkBaseNameCore` formats the result of that as a string.
+   It actually does a bit more computation than that, since it further removes duplicate expressions,
+   reporting only the first occurrence of each subexpression.
+-/
+
+namespace Lean.Elab.Command
+
+open Meta
+
+namespace NameGen
+
+/--
+If `e` is an application of a projection to a parent structure, returns the term being projected.
+-/
+private def getParentProjArg (e : Expr) : MetaM (Option Expr) := do
+  let .const c@(.str _ field) _ := e.getAppFn | return none
+  let env ← getEnv
+  let some info := env.getProjectionFnInfo? c | return none
+  unless e.getAppNumArgs == info.numParams + 1 do return none
+  let some (.ctorInfo cVal) := env.find? info.ctorName | return none
+  if isSubobjectField? env cVal.induct (Name.mkSimple field) |>.isNone then return none
+  return e.appArg!
+
+/--
+Strips out universes and arguments we decide are unnecessary for naming.
+The resulting expression can have loose fvars and be mangled in other ways.
+Expressions can also be replaced by `.bvar 0` if they shouldn't be mentioned.
+-/
+private partial def winnowExpr (e : Expr) : MetaM Expr := do
+  let rec visit (e : Expr) : MonadCacheT Expr Expr MetaM Expr := checkCache e fun _ => do
+    if ← isProof e then
+      return .bvar 0
+    match e with
+    | .app .. =>
+      if let some e' ← getParentProjArg e then
+        return (← visit e')
+      e.withApp fun f args => do
+        -- Visit only the explicit arguments to `f` and also its type (and type family) arguments.
+        -- The reason we visit type arguments is so that, for example, `Decidable (_ < _)` has
+        -- a chance to insert type information. Type families are for reporting things such as type constructors and monads.
+        let mut fty ← inferType f
+        let mut j := 0
+        let mut e' ← visit f
+        for i in [0:args.size] do
+          unless fty.isForall do
+            fty ← withTransparency .all <| whnf <| fty.instantiateRevRange j i args
+            j := i
+          let .forallE _ _ fty' bi := fty | failure
+          fty := fty'
+          let arg := args[i]!
+          if ← pure bi.isExplicit <||> (pure !arg.isSort <&&> isTypeFormer arg) then
+            unless (← isProof arg) do
+              e' := .app e' (← visit arg)
+        return e'
+    | .forallE n ty body bi =>
+      withLocalDecl n bi ty fun arg => do
+        -- In a dependent forall the body implies `ty`, so we won't mention it.
+        let ty' ← if body.hasLooseBVars then pure (.bvar 0) else visit ty
+        return .forallE n ty' (← visit (body.instantiate1 arg)) bi
+    | .lam n ty body bi =>
+      if let some e := Expr.etaExpandedStrict? e then
+        visit e
+      else
+        withLocalDecl n bi ty fun arg => do
+          -- Don't record the `.lam` since `ty` should be recorded elsewhere in the expression.
+          visit (body.instantiate1 arg)
+    | .letE _n _t v b _ => visit (b.instantiate1 v)
+    | .sort .. =>
+      if e.isProp then return .sort levelZero
+      else if e.isType then return .sort levelOne
+      else return .sort (.param `u)
+    | .const name .. => return .const name []
+    | .mdata _ e' => visit e'
+    | _ => return .bvar 0
+  visit e |>.run
+
+/--
+State for name generation.
+-/
+private structure MkNameState where
+  /-- Keeps track of expressions already visited so that we do not include them again. -/
+  seen : ExprSet := {}
+  /-- Keeps track of constants that appear in the generated name. -/
+  consts : NameSet := {}
+
+/--
+Monad for name generation.
+-/
+private abbrev MkNameM := StateRefT MkNameState MetaM
+
+/--
+Core algorithm for generating a name. The provided expression should be a winnowed expression.
+
+- `omitTopForall` if true causes "Forall" to not be included if the binding type results in an empty string.
+-/
+private def mkBaseNameCore (e : Expr) (omitTopForall : Bool := false) : MkNameM String :=
+  visit e omitTopForall
+where
+  visit (e : Expr) (omitTopForall : Bool := false) : MkNameM String := do
+    if (← get).seen.contains e then
+      return ""
+    else
+      let s ← visit' e omitTopForall
+      modify fun st => {st with seen := st.seen.insert e}
+      return s
+  visit' (e : Expr) (omitTopForall : Bool) : MkNameM String := do
+    match e with
+    | .const name .. =>
+      modify (fun st => {st with consts := st.consts.insert name})
+      return match name.eraseMacroScopes with
+              | .str _ str => str.capitalize
+              | _ => ""
+    | .app f x => (· ++ ·) <$> visit f <*> visit x
+    | .forallE _ ty body _ =>
+      let sty ← visit ty
+      if omitTopForall && sty == "" then
+        visit body true
+      else
+        ("Forall" ++ sty ++ ·) <$> visit body
+    | .sort .zero => return "Prop"
+    | .sort (.succ _) => return "Type"
+    | .sort _ => return "Sort"
+    | _ => return ""
+
+/--
+Generate a name, while naming the top-level foralls using "Of".
+The provided expression should be a winnowed expression.
+-/
+private partial def mkBaseNameAux (e : Expr) : MkNameM String := do
+  let (foralls, sb) ← visit e
+  return sb ++ String.join foralls
+where
+  visit (e : Expr) : MkNameM (List String × String) := do
+    match e with
+    | .forallE _ ty body _ =>
+      let (foralls, sb) ← visit body
+      let st ← mkBaseNameCore ty (omitTopForall := true)
+      if st == "" then
+        return (foralls, sb)
+      else
+        return (("Of" ++ st) :: foralls, sb)
+    | _ => return ([], ← mkBaseNameCore e)
+
+/--
+Adds all prefixes of `ns` as seen constants.
+-/
+private def visitNamespace (ns : Name) : MkNameM Unit := do
+  match ns with
+  | .anonymous => pure ()
+  | .num ns' _ => visitNamespace ns'
+  | .str ns' _ =>
+    let env ← getEnv
+    if env.contains ns then
+      modify fun st => {st with seen := st.seen.insert (.const ns []), consts := st.consts.insert ns}
+    visitNamespace ns'
+
+/--
+Given an expression, generates a "base name" for a declaration.
+The top-level foralls in `e` are treated as being binders, so use the `...Of...` naming convention.
+The current namespace is used to seed the seen expressions with each prefix of the namespace that's a global constant.
+
+Collects all constants that contribute to the name in the `MkInstM` state.
+This can be used to decide whether to further transform the generated name;
+in particular, this enables checking whether the generated name mentions declarations
+from the current module or project.
+-/
+def mkBaseName (e : Expr) : MkNameM String := do
+  let e ← instantiateMVars e
+  visitNamespace (← getCurrNamespace)
+  mkBaseNameAux (← winnowExpr e)
+
+/--
+Converts a module name into a suffix. Includes a leading `_`,
+so for example `Lean.Elab.DefView` becomes `_lean_elab_defView`.
+-/
+private def moduleToSuffix : Name → String
+  | .anonymous => ""
+  | .num n _ => moduleToSuffix n
+  | .str n s => moduleToSuffix n ++ "_" ++ s.decapitalize
+
+/--
+Uses heuristics to generate an informative but terse base name for a term of the given type, using `mkBaseName`.
+Makes use of the current namespace.
+It tries to make these names relatively unique ecosystem-wide,
+and it adds suffixes using the current module if the resulting name doesn't refer to anything defined in this module.
+-/
+def mkBaseNameWithSuffix (pre : String) (type : Expr) : MetaM String := do
+  let (name, st) ← mkBaseName type |>.run {}
+  let name := pre ++ name
+  let project := (← getMainModule).getRoot
+  -- Collect the modules for each constant that appeared.
+  let modules ← st.consts.foldM (init := Array.mkEmpty st.consts.size) fun mods name => return mods.push (← findModuleOf? name)
+  -- We can avoid adding the suffix if the instance refers to module-local names.
+  let isModuleLocal := modules.any Option.isNone
+  -- We can also avoid adding the full module suffix if the instance refers to "project"-local names.
+  let isProjectLocal := isModuleLocal || modules.any fun mod? => mod?.map (·.getRoot) == project
+  if !isProjectLocal then
+    return s!"{name}{moduleToSuffix project}"
+  else
+    return name
+
+/--
+Elaborates the binders and type and then uses `mkBaseNameWithSuffix` to generate a name.
+Furthermore, uses `mkUnusedBaseName` on the result.
+-/
+def mkBaseNameWithSuffix' (pre : String) (binders : Array Syntax) (type : Syntax) : TermElabM Name := do
+  let name ←
+    try
+      Term.withAutoBoundImplicit <| Term.elabBinders binders fun binds => Term.withoutErrToSorry do
+        let ty ← mkForallFVars binds (← Term.elabType type)
+        mkBaseNameWithSuffix pre ty
+    catch _ =>
+      pure pre
+  liftMacroM <| mkUnusedBaseName <| Name.mkSimple name
+
+end NameGen
+
+/--
+Generates an instance name for a declaration that has the given binders and type.
+It tries to make these names relatively unique ecosystem-wide.
+
+Note that this elaborates the binders and the type.
+This means that when elaborating an instance declaration, we elaborate these twice.
+-/
+def mkInstanceName (binders : Array Syntax) (type : Syntax) : CommandElabM Name := do
+  let savedState ← get
+  try
+    -- Unfortunately we can't include any of the binders from `runTermElabM` since, without
+    -- elaborating the body of the instance, we have no idea which of these binders are
+    -- actually used.
+    runTermElabM fun _ => NameGen.mkBaseNameWithSuffix' "inst" binders type
+  finally
+    set savedState

src/Lean/Elab/DeclUtil.lean

@@ -54,14 +54,6 @@ def expandDeclSig (stx : Syntax) : Syntax × Syntax :=
   let typeSpec := stx[1]
   (binders, typeSpec[1])
 
-def mkFreshInstanceName (env : Environment) (nextIdx : Nat) : Name :=
-  (env.mainModule ++ `_instance).appendIndexAfter nextIdx
-
-def isFreshInstanceName (name : Name) : Bool :=
-  match name with
-  | .str _ s => "_instance".isPrefixOf s
-  | _        => false
-
 /--
   Sort the given list of `usedParams` using the following order:
   - If it is an explicit level `allUserParams`, then use user given order.

src/Lean/Elab/Declaration.lean

@@ -353,14 +353,14 @@ def elabMutual : CommandElab := fun stx => do
     for builtin simprocs.
     -/
     let declNames ←
-       try
-         realizeGlobalConst ident
-       catch _ =>
-         let name := ident.getId.eraseMacroScopes
-         if (← Simp.isBuiltinSimproc name) then
-           pure [name]
-         else
-           throwUnknownConstant name
+      try
+        realizeGlobalConstWithInfos ident
+      catch _ =>
+        let name := ident.getId.eraseMacroScopes
+        if (← Simp.isBuiltinSimproc name) then
+          pure [name]
+        else
+          throwUnknownConstant name
     let declName ← ensureNonAmbiguous ident declNames
     Term.applyAttributes declName attrs
     for attrName in toErase do

src/Lean/Elab/DefView.lean

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Sebastian Ullrich
 -/
 prelude
-import Lean.Meta.ForEachExpr
 import Lean.Elab.Command
+import Lean.Elab.DeclNameGen
 import Lean.Elab.DeclUtil
 
 namespace Lean.Elab
@@ -66,41 +66,6 @@ def mkDefViewOfTheorem (modifiers : Modifiers) (stx : Syntax) : DefView :=
   { ref := stx, kind := DefKind.theorem, modifiers,
     declId := stx[1], binders, type? := some type, value := stx[3] }
 
-def mkFreshInstanceName : CommandElabM Name := do
-  let s ← get
-  let idx := s.nextInstIdx
-  modify fun s => { s with nextInstIdx := s.nextInstIdx + 1 }
-  return Lean.Elab.mkFreshInstanceName s.env idx
-
-/--
-  Generate a name for an instance with the given type.
-  Note that we elaborate the type twice. Once for producing the name, and another when elaborating the declaration. -/
-def mkInstanceName (binders : Array Syntax) (type : Syntax) : CommandElabM Name := do
-  let savedState ← get
-  try
-    let result ← runTermElabM fun _ => Term.withAutoBoundImplicit <| Term.elabBinders binders fun _ => Term.withoutErrToSorry do
-      let type ← instantiateMVars (← Term.elabType type)
-      let ref ← IO.mkRef ""
-      Meta.forEachExpr type fun e => do
-        if e.isForall then ref.modify (· ++ "ForAll")
-        else if e.isProp then ref.modify (· ++ "Prop")
-        else if e.isType then ref.modify (· ++ "Type")
-        else if e.isSort then ref.modify (· ++ "Sort")
-        else if e.isConst then
-          match e.constName!.eraseMacroScopes with
-          | .str _ str =>
-              if str.front.isLower then
-                ref.modify (· ++ str.capitalize)
-              else
-                ref.modify (· ++ str)
-          | _ => pure ()
-      ref.get
-    set savedState
-    liftMacroM <| mkUnusedBaseName <| Name.mkSimple ("inst" ++ result)
-  catch _ =>
-    set savedState
-    mkFreshInstanceName
-
 def mkDefViewOfInstance (modifiers : Modifiers) (stx : Syntax) : CommandElabM DefView := do
   -- leading_parser Term.attrKind >> "instance " >> optNamedPrio >> optional declId >> declSig >> declVal
   let attrKind        ← liftMacroM <| toAttributeKind stx[0]
@@ -109,9 +74,14 @@ def mkDefViewOfInstance (modifiers : Modifiers) (stx : Syntax) : CommandElabM De
   let (binders, type) := expandDeclSig stx[4]
   let modifiers       := modifiers.addAttribute { kind := attrKind, name := `instance, stx := attrStx }
   let declId ← match stx[3].getOptional? with
-    | some declId => pure declId
+    | some declId =>
+      if ← isTracingEnabledFor `Elab.instance.mkInstanceName then
+        let id ← mkInstanceName binders.getArgs type
+        trace[Elab.instance.mkInstanceName] "generated {(← getCurrNamespace) ++ id} for {declId}"
+      pure declId
     | none        =>
       let id ← mkInstanceName binders.getArgs type
+      trace[Elab.instance.mkInstanceName] "generated {(← getCurrNamespace) ++ id}"
       pure <| mkNode ``Parser.Command.declId #[mkIdentFrom stx id, mkNullNode]
   return {
     ref := stx, kind := DefKind.def, modifiers := modifiers,
@@ -166,6 +136,7 @@ def mkDefView (modifiers : Modifiers) (stx : Syntax) : CommandElabM DefView :=
     throwError "unexpected kind of definition"
 
 builtin_initialize registerTraceClass `Elab.definition
+builtin_initialize registerTraceClass `Elab.instance.mkInstanceName
 
 end Command
 end Lean.Elab

src/Lean/Elab/Deriving/DecEq.lean

@@ -27,8 +27,9 @@ where
       let rhs ← if isProof then
         `(have h : @$a = @$b := rfl; by subst h; exact $(← mkSameCtorRhs todo):term)
       else
+        let sameCtor ← mkSameCtorRhs todo
         `(if h : @$a = @$b then
-           by subst h; exact $(← mkSameCtorRhs todo):term
+           by subst h; exact $sameCtor:term
           else
            isFalse (by intro n; injection n; apply h _; assumption))
       if let some auxFunName := recField then

src/Lean/Elab/Deriving/Ord.lean

@@ -49,10 +49,7 @@ where
             let b := mkIdent (← mkFreshUserName `b)
             ctorArgs1 := ctorArgs1.push a
             ctorArgs2 := ctorArgs2.push b
-            rhsCont := fun rhs => `(match compare $a $b with
-              | Ordering.lt => Ordering.lt
-              | Ordering.gt => Ordering.gt
-              | Ordering.eq => $rhs) >>= rhsCont
+            rhsCont := fun rhs => `(Ordering.then (compare $a $b) $rhs) >>= rhsCont
         let lPat ← `(@$(mkIdent ctorName):ident $ctorArgs1:term*)
         let rPat ← `(@$(mkIdent ctorName):ident $ctorArgs2:term*)
         let patterns := indPatterns ++ #[lPat, rPat]

src/Lean/Elab/Do.lean

@@ -63,8 +63,9 @@ private def letDeclHasBinders (letDecl : Syntax) : Bool :=
 /-- Return true if we should generate an error message when lifting a method over this kind of syntax. -/
 private def liftMethodForbiddenBinder (stx : Syntax) : Bool :=
   let k := stx.getKind
+  -- TODO: make this extensible in the future.
   if k == ``Parser.Term.fun || k == ``Parser.Term.matchAlts ||
-     k == ``Parser.Term.doLetRec || k == ``Parser.Term.letrec  then
+     k == ``Parser.Term.doLetRec || k == ``Parser.Term.letrec then
      -- It is never ok to lift over this kind of binder
     true
   -- The following kinds of `let`-expressions require extra checks to decide whether they contain binders or not
@@ -77,12 +78,15 @@ private def liftMethodForbiddenBinder (stx : Syntax) : Bool :=
   else
     false
 
+-- TODO: we must track whether we are inside a quotation or not.
 private partial def hasLiftMethod : Syntax → Bool
   | Syntax.node _ k args =>
     if liftMethodDelimiter k then false
     -- NOTE: We don't check for lifts in quotations here, which doesn't break anything but merely makes this rare case a
     -- bit slower
     else if k == ``Parser.Term.liftMethod then true
+    -- For `pure` if-then-else, we only lift `(<- ...)` occurring in the condition.
+    else if k == ``termDepIfThenElse || k == ``termIfThenElse then args.size >= 2 && hasLiftMethod args[1]!
     else args.any hasLiftMethod
   | _ => false
 
@@ -1321,6 +1325,12 @@ private partial def expandLiftMethodAux (inQuot : Bool) (inBinder : Bool) : Synt
       return .node i k (alts.map (·.1))
     else if liftMethodDelimiter k then
       return stx
+    -- For `pure` if-then-else, we only lift `(<- ...)` occurring in the condition.
+    else if args.size >= 2 && (k == ``termDepIfThenElse || k == ``termIfThenElse) then do
+      let inAntiquot := stx.isAntiquot && !stx.isEscapedAntiquot
+      let arg1 ← expandLiftMethodAux (inQuot && !inAntiquot || stx.isQuot) inBinder args[1]!
+      let args := args.set! 1 arg1
+      return Syntax.node i k args
     else if k == ``Parser.Term.liftMethod && !inQuot then withFreshMacroScope do
       if inBinder then
         throwErrorAt stx "cannot lift `(<- ...)` over a binder, this error usually happens when you are trying to lift a method nested in a `fun`, `let`, or `match`-alternative, and it can often be fixed by adding a missing `do`"