chore: test for issue #4064

closes #4064

.github/workflows/check-stage0.yml

@@ -0,0 +1,57 @@
+name: Check for stage0 changes
+
+on:
+  merge_group:
+  pull_request:
+
+jobs:
+  check-stage0-on-queue:
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v4
+      with:
+        ref: ${{ github.event.pull_request.head.sha }}
+        filter: blob:none
+        fetch-depth: 0
+
+    - name: Find base commit
+      if: github.event_name == 'pull_request'
+      run: echo "BASE=$(git merge-base origin/${{ github.base_ref }} HEAD)" >> "$GITHUB_ENV"
+
+    - name: Identify stage0 changes
+      run: |
+        git diff "${BASE:-HEAD^}..HEAD" --name-only -- stage0 |
+          grep -v -x -F $'stage0/src/stdlib_flags.h\nstage0/src/lean.mk.in' \
+          > "$RUNNER_TEMP/stage0" || true
+        if test -s "$RUNNER_TEMP/stage0"
+        then
+          echo "CHANGES=yes" >> "$GITHUB_ENV"
+        else
+          echo "CHANGES=no" >> "$GITHUB_ENV"
+        fi
+      shell: bash
+
+    - if: github.event_name == 'pull_request'
+      name: Set label
+      uses: actions/github-script@v7
+      with:
+        script: |
+          const { owner, repo, number: issue_number  } = context.issue;
+          if (process.env.CHANGES == 'yes') {
+            await github.rest.issues.addLabels({ owner, repo, issue_number, labels: ['changes-stage0'] }).catch(() => {});
+          } else {
+            await github.rest.issues.removeLabel({ owner, repo, issue_number, name: 'changes-stage0' }).catch(() => {});
+          }
+
+    - if: env.CHANGES == 'yes'
+      name: Report changes
+      run: |
+        echo "Found changes to stage0/, please do not merge using the merge queue." | tee "$GITHUB_STEP_SUMMARY"
+        # shellcheck disable=SC2129
+        echo '```'                  >> "$GITHUB_STEP_SUMMARY"
+        cat  "$RUNNER_TEMP/stage0"  >> "$GITHUB_STEP_SUMMARY"
+        echo '```'                  >> "$GITHUB_STEP_SUMMARY"
+
+    - if: github.event_name == 'merge_group' && env.CHANGES == 'yes'
+      name: Fail when on the merge queue
+      run: exit 1

.github/workflows/ci.yml

@@ -54,7 +54,10 @@ jobs:
         with:
           script: |
             const quick = ${{ steps.set-quick.outputs.quick }};
-            console.log(`quick: ${quick}`)
+            console.log(`quick: ${quick}`);
+            // use large runners outside PRs where available (original repo)
+            // disabled for now as this mostly just speeds up the test suite which is not a bottleneck
+            // let large = ${{ github.event_name != 'pull_request' && github.repository == 'leanprover/lean4' }} ? "-large" : "";
             let matrix = [
               {
                 // portable release build: use channel with older glibc (2.27)
@@ -110,7 +113,7 @@ jobs:
               },*/
               {
                 "name": "macOS",
-                "os": "macos-latest",
+                "os": "macos-13",
                 "release": true,
                 "quick": false,
                 "shell": "bash -euxo pipefail {0}",
@@ -121,7 +124,7 @@ jobs:
               },
               {
                 "name": "macOS aarch64",
-                "os": "macos-latest",
+                "os": "macos-13",
                 "release": true,
                 "quick": false,
                 "cross": true,
@@ -277,18 +280,18 @@ jobs:
         uses: cachix/install-nix-action@v18
         with:
           install_url: https://releases.nixos.org/nix/nix-2.12.0/install
-        if: matrix.os == 'ubuntu-latest' && !matrix.cmultilib
+        if: runner.os == 'Linux' && !matrix.cmultilib
       - name: Install MSYS2
         uses: msys2/setup-msys2@v2
         with:
           msystem: clang64
           # `:p` means prefix with appropriate msystem prefix
           pacboy: "make python cmake:p clang:p ccache:p gmp:p git zip unzip diffutils binutils tree zstd:p tar"
-        if: matrix.os == 'windows-2022'
+        if: runner.os == 'Windows'
       - name: Install Brew Packages
         run: |
           brew install ccache tree zstd coreutils gmp
-        if: matrix.os == 'macos-latest'
+        if: runner.os == 'macOS'
       - name: Setup emsdk
         uses: mymindstorm/setup-emsdk@v12
         with:
@@ -312,13 +315,13 @@ jobs:
         run: |
           # open nix-shell once for initial setup
           true
-        if: matrix.os == 'ubuntu-latest'
+        if: runner.os == 'Linux'
       - name: Set up core dumps
         run: |
           mkdir -p $PWD/coredumps
           # store in current directory, for easy uploading together with binary
           echo $PWD/coredumps/%e.%p.%t | sudo tee /proc/sys/kernel/core_pattern
-        if: matrix.os == 'ubuntu-latest'
+        if: runner.os == 'Linux'
       - name: Build
         run: |
           mkdir build
@@ -423,7 +426,7 @@ jobs:
       - name: CCache stats
         run: ccache -s
       - name: Show stacktrace for coredumps
-        if: ${{ failure() && matrix.os == 'ubuntu-latest' }}
+        if: ${{ failure() && runner.os == 'Linux' }}
         run: |
           for c in coredumps/*; do
             progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
@@ -433,7 +436,7 @@ jobs:
       # shared libs
       #- name: Upload coredumps
       #  uses: actions/upload-artifact@v3
-      #  if: ${{ failure() && matrix.os == 'ubuntu-latest' }}
+      #  if: ${{ failure() && runner.os == 'Linux' }}
       #  with:
       #    name: coredumps-${{ matrix.name }}
       #    path: |

CODEOWNERS

@@ -6,7 +6,6 @@
 
 /.github/ @Kha @semorrison
 /RELEASES.md @semorrison
-/src/Init/IO.lean @joehendrix
 /src/kernel/ @leodemoura
 /src/lake/ @tydeu
 /src/Lean/Compiler/ @leodemoura
@@ -20,7 +19,11 @@
 /src/Lean/PrettyPrinter/Delaborator/ @kmill
 /src/Lean/Server/ @mhuisi
 /src/Lean/Widget/ @Vtec234
-/src/runtime/io.cpp @joehendrix
+/src/Init/Data/ @semorrison
+/src/Init/Data/Array/Lemmas.lean @digama0
+/src/Init/Data/List/Lemmas.lean @digama0
+/src/Init/Data/List/BasicAux.lean @digama0
+/src/Init/Data/Array/Subarray.lean @david-christiansen
 /src/Lean/Elab/Tactic/RCases.lean @digama0
 /src/Init/RCases.lean @digama0
 /src/Lean/Elab/Tactic/Ext.lean @digama0
@@ -39,5 +42,4 @@
 /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
 

README.md

@@ -22,4 +22,4 @@ Please read our [Contribution Guidelines](CONTRIBUTING.md) first.
 
 # Building from Source
 
-See [Building Lean](https://lean-lang.org/lean4/doc/make/index.html).
+See [Building Lean](https://lean-lang.org/lean4/doc/make/index.html) (documentation source: [doc/make/index.md](doc/make/index.md)).

RELEASES.md

@@ -8,7 +8,10 @@ This file contains work-in-progress notes for the upcoming release, as well as p
 Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
 of each version.
 
-v4.8.0 (development in progress)
+v4.9.0 (development in progress)
+---------
+
+v4.8.0 
 ---------
 
 * **Executables configured with `supportInterpreter := true` on Windows should now be run via `lake exe` to function properly.**
@@ -79,10 +82,13 @@ v4.8.0 (development in progress)
   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).
+  When `pp.mvars` is false, expression metavariables pretty print as `?_` and universe metavariables pretty print as `_`.
+  When `pp.mvars.withType` is true, expression metavariables pretty print with a type ascription.
+  These can be set when using `#guard_msgs` to make tests not depend on the particular names of metavariables.
+  [#3798](https://github.com/leanprover/lean4/pull/3798) and
+  [#3978](https://github.com/leanprover/lean4/pull/3978).
+
+* Hovers for terms in `match` expressions in the Infoview now reliably show the correct term.
 
 * Added `@[induction_eliminator]` and `@[cases_eliminator]` attributes to be able to define custom eliminators
   for the `induction` and `cases` tactics, replacing the `@[eliminator]` attribute.

doc/dev/bootstrap.md

@@ -75,14 +75,28 @@ The github repository will automatically update stage0 on `master` once
 
 If you have write access to the lean4 repository, you can also also manually
 trigger that process, for example to be able to use new features in the compiler itself.
-You can do that on <https://github.com/nomeata/lean4/actions/workflows/update-stage0.yml>
+You can do that on <https://github.com/leanprover/lean4/actions/workflows/update-stage0.yml>
 or using Github CLI with
 ```
 gh workflow run update-stage0.yml
 ```
 
-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.
+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.
+
+If you rebased the branch (either onto a newer version of `master`, or fixing
+up some commits prior to the stage0 update, recreate the stage0 update commits.
+The script `script/rebase-stage0.sh` can be used for that.
+
+The CI should prevent PRs with changes to stage0 (besides `stdlib_flags.h`)
+from entering `master` through the (squashing!) merge queue, and label such PRs
+with the `changes-stage0` label. Such PRs should have a cleaned up history,
+with separate stage0 update commits; then coordinate with the admins to merge
+your PR using rebase merge, bypassing the merge queue.
+
 
 ## Further Bootstrapping Complications
 

doc/dev/ffi.md

@@ -53,10 +53,59 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
   Its runtime value is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number (`lean_box`/`lean_unbox`).
 * A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
 * Any other type is represented by `lean_object *`.
-  Its runtime value is a pointer to an object of a subtype of `lean_object` (see respective declarations in `lean.h`) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
+  Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
 
   Example: the runtime value of `u : Unit` is always `lean_box(0)`.
 
+#### Inductive types
+
+For inductive types which are in the fallback `lean_object *` case above and not trivial constructors, the type is stored as a `lean_ctor_object`, and `lean_is_ctor` will return true. A `lean_ctor_object` stores the constructor index in the header, and the fields are stored in the `m_objs` portion of the object.
+
+The memory order of the fields is derived from the types and order of the fields in the declaration. They are ordered as follows:
+
+* Non-scalar fields stored as `lean_object *`
+* Fields of type `USize`
+* Other scalar fields, in decreasing order by size
+
+Within each group the fields are ordered in declaration order. **Warning**: Trivial wrapper types still count toward a field being treated as non-scalar for this purpose.
+
+* To access fields of the first kind, use `lean_ctor_get(val, i)` to get the `i`th non-scalar field.
+* To access `USize` fields, use `lean_ctor_get_usize(val, n+i)` to get the `i`th usize field and `n` is the total number of fields of the first kind.
+* To access other scalar fields, use `lean_ctor_get_uintN(val, off)` or `lean_ctor_get_usize(val, off)` as appropriate. Here `off` is the byte offset of the field in the structure, starting at `n*sizeof(void*)` where `n` is the number of fields of the first two kinds.
+
+For example, a structure such as
+```lean
+structure S where
+  ptr_1 : Array Nat
+  usize_1 : USize
+  sc64_1 : UInt64
+  ptr_2 : { x : UInt64 // x > 0 } -- wrappers don't count as scalars
+  sc64_2 : Float -- `Float` is 64 bit
+  sc8_1 : Bool
+  sc16_1 : UInt16
+  sc8_2 : UInt8
+  sc64_3 : UInt64
+  usize_2 : USize
+  ptr_3 : Char -- trivial wrapper around `UInt32`
+  sc32_1 : UInt32
+  sc16_2 : UInt16
+```
+would get re-sorted into the following memory order:
+
+* `S.ptr_1` - `lean_ctor_get(val, 0)`
+* `S.ptr_2` - `lean_ctor_get(val, 1)`
+* `S.ptr_3` - `lean_ctor_get(val, 2)`
+* `S.usize_1` - `lean_ctor_get_usize(val, 3)`
+* `S.usize_2` - `lean_ctor_get_usize(val, 4)`
+* `S.sc64_1` - `lean_ctor_get_uint64(val, sizeof(void*)*5)`
+* `S.sc64_2` - `lean_ctor_get_float(val, sizeof(void*)*5 + 8)`
+* `S.sc64_3` - `lean_ctor_get_uint64(val, sizeof(void*)*5 + 16)`
+* `S.sc32_1` - `lean_ctor_get_uint32(val, sizeof(void*)*5 + 24)`
+* `S.sc16_1` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 28)`
+* `S.sc16_2` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 30)`
+* `S.sc8_1` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 32)`
+* `S.sc8_2` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 33)`
+
 ### Borrowing
 
 By default, all `lean_object *` parameters of an `@[extern]` function are considered *owned*, i.e. the external code is passed a "virtual RC token" and is responsible for passing this token along to another consuming function (exactly once) or freeing it via `lean_dec`.

doc/examples/Certora2022/ex8.lean

@@ -4,16 +4,16 @@ def ack : Nat → Nat → Nat
   | 0,   y   => y+1
   | x+1, 0   => ack x 1
   | x+1, y+1 => ack x (ack (x+1) y)
-termination_by ack x y => (x, y)
+termination_by x y => (x, y)
 
 def sum (a : Array Int) : Int :=
   let rec go (i : Nat) :=
-     if i < a.size then
+     if _ : i < a.size then
         a[i] + go (i+1)
      else
         0
+  termination_by a.size - i
   go 0
-termination_by go i => a.size - i
 
 set_option pp.proofs true
 #print sum.go

doc/examples/ICERM2022/ctor.lean

@@ -4,43 +4,42 @@ open Lean Meta
 
 def ctor (mvarId : MVarId) (idx : Nat) : MetaM (List MVarId) := do
   /- Set `MetaM` context using `mvarId` -/
-  withMVarContext mvarId do 
+  mvarId.withContext do
     /- Fail if the metavariable is already assigned. -/
-    checkNotAssigned mvarId `ctor
+    mvarId.checkNotAssigned `ctor
     /- Retrieve the target type, instantiateMVars, and use `whnf`. -/
-    let target ← getMVarType' mvarId
+    let target ← mvarId.getType'
     let .const declName us := target.getAppFn
       | throwTacticEx `ctor mvarId "target is not an inductive datatype"
     let .inductInfo { ctors, .. } ← getConstInfo declName
       | throwTacticEx `ctor mvarId "target is not an inductive datatype"
     if idx = 0 then
-      throwTacticEx `ctor mvarId "invalid index, it must be > 0"  
+      throwTacticEx `ctor mvarId "invalid index, it must be > 0"
     else if h : idx - 1 < ctors.length then
-      apply mvarId (.const ctors[idx - 1] us)
+      mvarId.apply (.const ctors[idx - 1] us)
     else
-      throwTacticEx `ctor mvarId "invalid index, inductive datatype has only {ctors.length} contructors"  
+      throwTacticEx `ctor mvarId "invalid index, inductive datatype has only {ctors.length} contructors"
 
 open Elab Tactic
 
-elab "ctor" idx:num : tactic => 
+elab "ctor" idx:num : tactic =>
   liftMetaTactic (ctor · idx.getNat)
 
-example (p : Prop) : p := by 
+example (p : Prop) : p := by
   ctor 1 -- Error
 
-example (h : q) : p ∨ q := by 
+example (h : q) : p ∨ q := by
   ctor 0 -- Error
   exact h
 
-example (h : q) : p ∨ q := by 
+example (h : q) : p ∨ q := by
   ctor 3 -- Error
   exact h
 
-example (h : q) : p ∨ q := by 
+example (h : q) : p ∨ q := by
   ctor 2
   exact h
 
-example (h : q) : p ∨ q := by 
+example (h : q) : p ∨ q := by
   ctor 1
-  exact h -- Error 
-
+  exact h -- Error

doc/examples/ICERM2022/meta.lean

@@ -5,15 +5,15 @@ open Lean Meta
 def ex1 (declName : Name) : MetaM Unit := do
   let info ← getConstInfo declName
   IO.println s!"{declName} : {← ppExpr info.type}"
-  if let some val := info.value? then 
+  if let some val := info.value? then
     IO.println s!"{declName} : {← ppExpr val}"
-    
+
 #eval ex1 ``Nat
 
 def ex2 (declName : Name) : MetaM Unit := do
   let info ← getConstInfo declName
   trace[Meta.debug] "{declName} : {info.type}"
-  if let some val := info.value? then 
+  if let some val := info.value? then
     trace[Meta.debug] "{declName} : {val}"
 
 #eval ex2 ``Add.add
@@ -30,9 +30,9 @@ def ex3 (declName : Name) : MetaM Unit := do
       trace[Meta.debug] "{x} : {← inferType x}"
 
 def myMin [LT α] [DecidableRel (α := α) (·<·)] (a b : α) : α :=
-  if a < b then 
+  if a < b then
     a
-  else 
+  else
     b
 
 set_option trace.Meta.debug true in
@@ -40,7 +40,7 @@ set_option trace.Meta.debug true in
 
 def ex4 : MetaM Unit := do
   let nat := mkConst ``Nat
-  withLocalDeclD `a nat fun a => 
+  withLocalDeclD `a nat fun a =>
   withLocalDeclD `b nat fun b => do
     let e ← mkAppM ``HAdd.hAdd #[a, b]
     trace[Meta.debug] "{e} : {← inferType e}"
@@ -66,15 +66,17 @@ open Elab Term
 
 def ex5 : TermElabM Unit := do
   let nat := Lean.mkConst ``Nat
-  withLocalDeclD `a nat fun a => do 
+  withLocalDeclD `a nat fun a => do
   withLocalDeclD `b nat fun b => do
     let ab ← mkAppM ``HAdd.hAdd #[a, b]
-    let stx ← `(fun x => if x < 10 then $(← exprToSyntax ab) + x else x + $(← exprToSyntax a))
+    let abStx ← exprToSyntax ab
+    let aStx ← exprToSyntax a
+    let stx ← `(fun x => if x < 10 then $abStx + x else x + $aStx)
     let e ← elabTerm stx none
     trace[Meta.debug] "{e} : {← inferType e}"
     let e := mkApp e (mkNatLit 5)
     let e ← whnf e
     trace[Meta.debug] "{e}"
-       
+
 set_option trace.Meta.debug true in
 #eval ex5

doc/examples/NFM2022/nfm8.lean

@@ -4,16 +4,16 @@ def ack : Nat → Nat → Nat
   | 0,   y   => y+1
   | x+1, 0   => ack x 1
   | x+1, y+1 => ack x (ack (x+1) y)
-termination_by ack x y => (x, y)
+termination_by x y => (x, y)
 
 def sum (a : Array Int) : Int :=
   let rec go (i : Nat) :=
-     if i < a.size then
+     if _ : i < a.size then
         a[i] + go (i+1)
      else
         0
+  termination_by a.size - i
   go 0
-termination_by go i => a.size - i
 
 set_option pp.proofs true
 #print sum.go

nix/bootstrap.nix

@@ -180,7 +180,7 @@ rec {
       update-stage0 =
         let cTree = symlinkJoin { name = "cs"; paths = [ Init.cTree Lean.cTree ]; }; in
         writeShellScriptBin "update-stage0" ''
-          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/update-stage0"}
+          CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
         '';
       update-stage0-commit = writeShellScriptBin "update-stage0-commit" ''
         set -euo pipefail

script/issues_summary.sh

@@ -0,0 +1,39 @@
+#!/bin/bash
+
+# https://chat.openai.com/share/7469c7c3-aceb-4d80-aee5-62982e1f1538
+
+# Output CSV Header
+echo '"Issue URL","Title","Days Since Creation","Days Since Last Update","Total Reactions","Assignee","Labels"'
+
+# Get the current date in YYYY-MM-DD format
+today=$(date +%Y-%m-%d)
+
+# Fetch only open issues (excluding PRs and closed issues) from the repository 'leanprover/lean4'
+issues=$(gh api repos/leanprover/lean4/issues --paginate --jq '.[] | select(.pull_request == null and .state == "open") | {url: .html_url, title: .title, created_at: (.created_at | split("T")[0]), updated_at: (.updated_at | split("T")[0]), number: .number, assignee: (.assignee.login // ""), labels: [.labels[].name] | join(",")}')
+
+# Process each JSON object
+echo "$issues" | while IFS= read -r issue; do
+    # Extract fields from JSON
+    url=$(echo "$issue" | jq -r '.url')
+    title=$(echo "$issue" | jq -r '.title')
+    created_at=$(echo "$issue" | jq -r '.created_at')
+    updated_at=$(echo "$issue" | jq -r '.updated_at')
+    issue_number=$(echo "$issue" | jq -r '.number')
+    assignee=$(echo "$issue" | jq -r '.assignee')
+    labels=$(echo "$issue" | jq -r '.labels')
+
+    # Calculate days since creation and update using macOS compatible date calculation
+    days_since_created=$(( ($(date -jf "%Y-%m-%d" "$today" +%s) - $(date -jf "%Y-%m-%d" "$created_at" +%s)) / 86400 ))
+    days_since_updated=$(( ($(date -jf "%Y-%m-%d" "$today" +%s) - $(date -jf "%Y-%m-%d" "$updated_at" +%s)) / 86400 ))
+
+    # Fetch the total number of reactions for each issue
+    reaction_data=$(gh api repos/leanprover/lean4/issues/$issue_number/reactions --paginate --jq 'length' 2>&1)
+    if [[ $reaction_data == *"Not Found"* ]]; then
+        total_reactions="Error fetching reactions"
+    else
+        total_reactions=$reaction_data
+    fi
+
+    # Format output as CSV by escaping quotes and delimiting with commas
+    echo "\"$url\",\"${title//\"/\"\"}\",\"$days_since_created\",\"$days_since_updated\",\"$total_reactions\",\"$assignee\",\"$labels\""
+done

script/lib/README.md

@@ -0,0 +1,2 @@
+This directory contains various scripts that are *not* meant to be called
+directly, but through other scripts or makefiles.

script/lib/rebase-editor.sh

@@ -0,0 +1,19 @@
+#!/usr/bin/env bash
+
+
+# Script internal to `./script/rebase-stage0.sh`
+
+# Determine OS type for sed in-place editing
+SED_CMD=("sed" "-i")
+if [[ "$OSTYPE" == "darwin"* ]]
+then
+    # macOS requires an empty string argument with -i for in-place editing
+    SED_CMD=("sed" "-i" "")
+fi
+
+if [ "$STAGE0_WITH_NIX" = true ]
+then
+  "${SED_CMD[@]}" '/chore: update stage0/ s,.*,x nix run .#update-stage0-commit,' "$1"
+else
+  "${SED_CMD[@]}" '/chore: update stage0/ s,.*,x make -j32 -C build/release update-stage0 \&\& git commit -m "chore: update stage0",' "$1"
+fi

script/rebase-stage0.sh

@@ -0,0 +1,24 @@
+#!/usr/bin/env bash
+
+# This script rebases onto the given branch/commit, and updates
+# all `chore: update stage0` commits along the way.
+
+# Whether to use nix or make to update stage0
+if [ "$1" = "-nix" ]
+then
+   export STAGE0_WITH_NIX=true
+   shift
+fi
+
+# Check if an argument is provided
+if [ "$#" -eq 0 ]; then
+    echo "Usage: $0 [-nix] <options to git rebase -i>"
+    exit 1
+fi
+
+REPO_ROOT=$(git rev-parse --show-toplevel)
+
+# Run git rebase in interactive mode, but automatically edit the todo list
+# using the defined GIT_SEQUENCE_EDITOR command
+GIT_SEQUENCE_EDITOR="$REPO_ROOT/script/lib/rebase-editor.sh" git rebase -i "$@"
+

src/CMakeLists.txt

@@ -9,7 +9,7 @@ endif()
 include(ExternalProject)
 project(LEAN CXX C)
 set(LEAN_VERSION_MAJOR 4)
-set(LEAN_VERSION_MINOR 8)
+set(LEAN_VERSION_MINOR 9)
 set(LEAN_VERSION_PATCH 0)
 set(LEAN_VERSION_IS_RELEASE 0)  # This number is 1 in the release revision, and 0 otherwise.
 set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -315,6 +315,12 @@ endif()
 string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
 string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
 
+# in local builds, link executables and not just dynlibs against C++ stdlib as well,
+# which is required for e.g. asan
+if(NOT LEAN_STANDALONE)
+  string(APPEND CMAKE_EXE_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
+endif()
+
 # flags for user binaries = flags for toolchain binaries + Lake
 string(APPEND LEANC_STATIC_LINKER_FLAGS " ${TOOLCHAIN_STATIC_LINKER_FLAGS} -lLake")
 
@@ -585,7 +591,7 @@ endif()
 
 if(PREV_STAGE)
   add_custom_target(update-stage0
-    COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/update-stage0'
+    COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/lib/update-stage0'
     DEPENDS make_stdlib
     WORKING_DIRECTORY "${LEAN_SOURCE_DIR}/..")
 

src/Init/ByCases.lean

@@ -63,3 +63,16 @@ theorem ite_some_none_eq_none [Decidable P] :
 @[simp] theorem ite_some_none_eq_some [Decidable P] :
     (if P then some x else none) = some y ↔ P ∧ x = y := by
   split <;> simp_all
+
+-- This is not marked as `simp` as it is already handled by `dite_eq_right_iff`.
+theorem dite_some_none_eq_none [Decidable P] {x : P → α} :
+    (if h : P then some (x h) else none) = none ↔ ¬P := by
+  simp only [dite_eq_right_iff]
+  rfl
+
+@[simp] theorem dite_some_none_eq_some [Decidable P] {x : P → α} {y : α} :
+    (if h : P then some (x h) else none) = some y ↔ ∃ h : P, x h = y := by
+  by_cases h : P <;> simp only [h, dite_cond_eq_true, dite_cond_eq_false, Option.some.injEq,
+    false_iff, not_exists]
+  case pos => exact ⟨fun h_eq ↦ Exists.intro h h_eq, fun h_exists => h_exists.2⟩
+  case neg => exact fun h_false _ ↦ h_false

src/Init/Core.lean

@@ -1114,9 +1114,6 @@ theorem eta (a : {x // p x}) (h : p (val a)) : mk (val a) h = a := by
   cases a
   exact rfl
 
-instance {α : Type u} {p : α → Prop} {a : α} (h : p a) : Inhabited {x // p x} where
-  default := ⟨a, h⟩
-
 instance {α : Type u} {p : α → Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
   fun ⟨a, h₁⟩ ⟨b, h₂⟩ =>
     if h : a = b then isTrue (by subst h; exact rfl)
@@ -2040,4 +2037,8 @@ class LawfulCommIdentity (op : α → α → α) (o : outParam α) [hc : Commuta
   left_id a := Eq.trans (hc.comm o a) (right_id a)
   right_id a := Eq.trans (hc.comm a o) (left_id a)
 
+instance : Commutative Or := ⟨fun _ _ => propext or_comm⟩
+instance : Commutative And := ⟨fun _ _ => propext and_comm⟩
+instance : Commutative Iff := ⟨fun _ _ => propext iff_comm⟩
+
 end Std

src/Init/Data/Array/Basic.lean

@@ -31,6 +31,7 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
   go (i : Nat) (acc : Array α) : Array α :=
     if h : i < n then go (i+1) (acc.push (f ⟨i, h⟩)) else acc
 termination_by n - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 /-- The array `#[0, 1, ..., n - 1]`. -/
 def range (n : Nat) : Array Nat :=
@@ -43,7 +44,7 @@ instance : EmptyCollection (Array α) := ⟨Array.empty⟩
 instance : Inhabited (Array α) where
   default := Array.empty
 
-def isEmpty (a : Array α) : Bool :=
+@[simp] def isEmpty (a : Array α) : Bool :=
   a.size = 0
 
 def singleton (v : α) : Array α :=
@@ -52,7 +53,7 @@ def singleton (v : α) : Array α :=
 /-- Low-level version of `fget` which is as fast as a C array read.
    `Fin` values are represented as tag pointers in the Lean runtime. Thus,
    `fget` may be slightly slower than `uget`. -/
-@[extern "lean_array_uget"]
+@[extern "lean_array_uget", simp]
 def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
   a[i.toNat]
 
@@ -306,6 +307,7 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
     else
       pure r
   termination_by as.size - i
+  decreasing_by simp_wf; decreasing_trivial_pre_omega
   map 0 (mkEmpty as.size)
 
 @[inline]
@@ -378,6 +380,7 @@ def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as :
       else
         pure false
       termination_by stop - j
+      decreasing_by simp_wf; decreasing_trivial_pre_omega
     loop start
   if h : stop ≤ as.size then
     any stop h
@@ -463,6 +466,7 @@ def findIdx? {α : Type u} (as : Array α) (p : α → Bool) : Option Nat :=
       if p as[j] then some j else loop (j + 1)
     else none
     termination_by as.size - j
+    decreasing_by simp_wf; decreasing_trivial_pre_omega
   loop 0
 
 def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
@@ -557,6 +561,7 @@ def isEqvAux (a b : Array α) (hsz : a.size = b.size) (p : α → α → Bool) (
   else
     true
 termination_by a.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def isEqv (a b : Array α) (p : α → α → Bool) : Bool :=
   if h : a.size = b.size then
@@ -661,6 +666,7 @@ def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size)
     else indexOfAux a v (i+1)
   else none
 termination_by a.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
   indexOfAux a v 0
@@ -703,6 +709,7 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
   else
     as
 termination_by as.size
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def takeWhile (p : α → Bool) (as : Array α) : Array α :=
   let rec go (i : Nat) (r : Array α) : Array α :=
@@ -715,6 +722,7 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
     else
       r
     termination_by as.size - i
+    decreasing_by simp_wf; decreasing_trivial_pre_omega
   go 0 #[]
 
 /-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.
@@ -725,16 +733,15 @@ def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
   if h : i.val + 1 < a.size then
     let a' := a.swap ⟨i.val + 1, h⟩ i
     let i' : Fin a'.size := ⟨i.val + 1, by simp [a', h]⟩
-    have : a'.size - i' < a.size - i := by
-      simp [a', Nat.sub_succ_lt_self _ _ i.isLt]
     a'.feraseIdx i'
   else
     a.pop
 termination_by a.size - i.val
+decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
 
 theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
   induction a, i using Array.feraseIdx.induct with
-  | @case1 a i h a' _ _ ih =>
+  | @case1 a i h a' _ ih =>
     unfold feraseIdx
     simp [h, a', ih]
   | case2 a i h =>
@@ -763,6 +770,7 @@ def erase [BEq α] (as : Array α) (a : α) : Array α :=
     else
       as
     termination_by j.1
+    decreasing_by simp_wf; decreasing_trivial_pre_omega
   let j := as.size
   let as := as.push a
   loop as ⟨j, size_push .. ▸ j.lt_succ_self⟩
@@ -816,6 +824,7 @@ def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : N
   else
     true
 termination_by as.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 /-- Return true iff `as` is a prefix of `bs`.
 That is, `bs = as ++ t` for some `t : List α`.-/
@@ -837,6 +846,7 @@ private def allDiffAux [BEq α] (as : Array α) (i : Nat) : Bool :=
   else
     true
 termination_by as.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def allDiff [BEq α] (as : Array α) : Bool :=
   allDiffAux as 0
@@ -852,6 +862,7 @@ def allDiff [BEq α] (as : Array α) : Bool :=
   else
     cs
 termination_by as.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 @[inline] def zipWith (as : Array α) (bs : Array β) (f : α → β → γ) : Array γ :=
   zipWithAux f as bs 0 #[]

src/Init/Data/Array/BasicAux.lean

@@ -48,6 +48,7 @@ where
       let b ← f as[i]
       go (i+1) ⟨acc.val.push b, by simp [acc.property]⟩ hlt
   termination_by as.size - i
+  decreasing_by decreasing_trivial_pre_omega
 
 @[inline] private unsafe def mapMonoMImp [Monad m] (as : Array α) (f : α → m α) : m (Array α) :=
   go 0 as

src/Init/Data/Array/DecidableEq.lean

@@ -21,6 +21,8 @@ theorem eq_of_isEqvAux [DecidableEq α] (a b : Array α) (hsz : a.size = b.size)
     subst heq
     exact absurd (Nat.lt_of_lt_of_le high low) (Nat.lt_irrefl j)
 termination_by a.size - i
+decreasing_by decreasing_trivial_pre_omega
+
 
 theorem eq_of_isEqv [DecidableEq α] (a b : Array α) : Array.isEqv a b (fun x y => x = y) → a = b := by
   simp [Array.isEqv]
@@ -37,6 +39,7 @@ theorem isEqvAux_self [DecidableEq α] (a : Array α) (i : Nat) : Array.isEqvAux
   case inl h => simp [h, isEqvAux_self a (i+1)]
   case inr h => simp [h]
 termination_by a.size - i
+decreasing_by decreasing_trivial_pre_omega
 
 theorem isEqv_self [DecidableEq α] (a : Array α) : Array.isEqv a a (fun x y => x = y) = true := by
   simp [isEqv, isEqvAux_self]

src/Init/Data/Array/Lemmas.lean

@@ -5,6 +5,7 @@ Authors: Mario Carneiro
 -/
 prelude
 import Init.Data.Nat.MinMax
+import Init.Data.Nat.Lemmas
 import Init.Data.List.Lemmas
 import Init.Data.Fin.Basic
 import Init.Data.Array.Mem
@@ -20,6 +21,13 @@ namespace Array
 
 attribute [simp] data_toArray uset
 
+@[simp] theorem singleton_def (v : α) : singleton v = #[v] := rfl
+
+@[simp] theorem toArray_data : (a : Array α) → a.data.toArray = a
+  | ⟨l⟩ => ext' (data_toArray l)
+
+@[simp] theorem data_length {l : Array α} : l.data.length = l.size := rfl
+
 @[simp] theorem mkEmpty_eq (α n) : @mkEmpty α n = #[] := rfl
 
 @[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
@@ -130,6 +138,7 @@ where
       simp [aux (i+1), map_eq_pure_bind]; rfl
     · rw [List.drop_length_le (Nat.ge_of_not_lt ‹_›)]; rfl
   termination_by arr.size - i
+  decreasing_by decreasing_trivial_pre_omega
 
 @[simp] theorem map_data (f : α → β) (arr : Array α) : (arr.map f).data = arr.data.map f := by
   rw [map, mapM_eq_foldlM]
@@ -139,7 +148,8 @@ where
   simp [H]
 
 @[simp] theorem size_map (f : α → β) (arr : Array α) : (arr.map f).size = arr.size := by
-  simp [size]
+  simp only [← data_length]
+  simp
 
 @[simp] theorem pop_data (arr : Array α) : arr.pop.data = arr.data.dropLast := rfl
 
@@ -187,7 +197,8 @@ theorem anyM_stop_le_start [Monad m] (p : α → m Bool) (as : Array α) (start
 theorem mem_def (a : α) (as : Array α) : a ∈ as ↔ a ∈ as.data :=
   ⟨fun | .mk h => h, Array.Mem.mk⟩
 
-/-- # get -/
+/-! # get -/
+
 @[simp] theorem get_eq_getElem (a : Array α) (i : Fin _) : a.get i = a[i.1] := rfl
 
 theorem getElem?_lt
@@ -217,7 +228,7 @@ theorem get!_eq_getD [Inhabited α] (a : Array α) : a.get! n = a.getD n default
 @[simp] theorem get!_eq_getElem? [Inhabited α] (a : Array α) (i : Nat) : a.get! i = (a.get? i).getD default := by
   by_cases p : i < a.size <;> simp [getD_get?, get!_eq_getD, p]
 
-/-- # set -/
+/-! # set -/
 
 @[simp] theorem getElem_set_eq (a : Array α) (i : Fin a.size) (v : α) {j : Nat}
       (eq : i.val = j) (p : j < (a.set i v).size) :
@@ -240,7 +251,7 @@ theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
     (ne : i.val ≠ j) : (a.set i v)[j]? = a[j]? := by
   by_cases h : j < a.size <;> simp [getElem?_lt, getElem?_ge, Nat.ge_of_not_lt, ne, h]
 
-/- # setD -/
+/-! # setD -/
 
 @[simp] theorem set!_is_setD : @set! = @setD := rfl
 
@@ -266,4 +277,788 @@ theorem getElem?_setD_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) : (a
   by_cases h : i < a.size <;>
     simp [setD, Nat.not_lt_of_le, h,  getD_get?]
 
+/-! # ofFn -/
+
+@[simp] theorem size_ofFn_go {n} (f : Fin n → α) (i acc) :
+    (ofFn.go f i acc).size = acc.size + (n - i) := by
+  if hin : i < n then
+    unfold ofFn.go
+    have : 1 + (n - (i + 1)) = n - i :=
+      Nat.sub_sub .. ▸ Nat.add_sub_cancel' (Nat.le_sub_of_add_le (Nat.add_comm .. ▸ hin))
+    rw [dif_pos hin, size_ofFn_go f (i+1), size_push, Nat.add_assoc, this]
+  else
+    have : n - i = 0 := Nat.sub_eq_zero_of_le (Nat.le_of_not_lt hin)
+    unfold ofFn.go
+    simp [hin, this]
+termination_by n - i
+
+@[simp] theorem size_ofFn (f : Fin n → α) : (ofFn f).size = n := by simp [ofFn]
+
+theorem getElem_ofFn_go (f : Fin n → α) (i) {acc k}
+    (hki : k < n) (hin : i ≤ n) (hi : i = acc.size)
+    (hacc : ∀ j, ∀ hj : j < acc.size, acc[j] = f ⟨j, Nat.lt_of_lt_of_le hj (hi ▸ hin)⟩) :
+    haveI : acc.size + (n - acc.size) = n := Nat.add_sub_cancel' (hi ▸ hin)
+    (ofFn.go f i acc)[k]'(by simp [*]) = f ⟨k, hki⟩ := by
+  unfold ofFn.go
+  if hin : i < n then
+    have : 1 + (n - (i + 1)) = n - i :=
+      Nat.sub_sub .. ▸ Nat.add_sub_cancel' (Nat.le_sub_of_add_le (Nat.add_comm .. ▸ hin))
+    simp only [dif_pos hin]
+    rw [getElem_ofFn_go f (i+1) _ hin (by simp [*]) (fun j hj => ?hacc)]
+    cases (Nat.lt_or_eq_of_le <| Nat.le_of_lt_succ (by simpa using hj)) with
+    | inl hj => simp [get_push, hj, hacc j hj]
+    | inr hj => simp [get_push, *]
+  else
+    simp [hin, hacc k (Nat.lt_of_lt_of_le hki (Nat.le_of_not_lt (hi ▸ hin)))]
+termination_by n - i
+
+@[simp] theorem getElem_ofFn (f : Fin n → α) (i : Nat) (h) :
+    (ofFn f)[i] = f ⟨i, size_ofFn f ▸ h⟩ :=
+  getElem_ofFn_go _ _ _ (by simp) (by simp) nofun
+
+/-- # mkArray -/
+
+@[simp] theorem mkArray_data (n : Nat) (v : α) : (mkArray n v).data = List.replicate n v := rfl
+
+@[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
+    (mkArray n v)[i] = v := by simp [Array.getElem_eq_data_get]
+
+/-- # mem -/
+
+theorem mem_data {a : α} {l : Array α} : a ∈ l.data ↔ a ∈ l := (mem_def _ _).symm
+
+theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
+
+/-- # get lemmas -/
+
+theorem getElem?_mem {l : Array α} {i : Fin l.size} : l[i] ∈ l := by
+  erw [Array.mem_def, getElem_eq_data_get]
+  apply List.get_mem
+
+theorem getElem_fin_eq_data_get (a : Array α) (i : Fin _) : a[i] = a.data.get i := rfl
+
+@[simp] theorem ugetElem_eq_getElem (a : Array α) {i : USize} (h : i.toNat < a.size) :
+  a[i] = a[i.toNat] := rfl
+
+theorem getElem?_eq_getElem (a : Array α) (i : Nat) (h : i < a.size) : a[i]? = a[i] :=
+  getElem?_pos ..
+
+theorem get?_len_le (a : Array α) (i : Nat) (h : a.size ≤ i) : a[i]? = none := by
+  simp [getElem?_neg, h]
+
+theorem getElem_mem_data (a : Array α) (h : i < a.size) : a[i] ∈ a.data := by
+  simp only [getElem_eq_data_get, List.get_mem]
+
+theorem getElem?_eq_data_get? (a : Array α) (i : Nat) : a[i]? = a.data.get? i := by
+  by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]; rfl
+
+theorem get?_eq_data_get? (a : Array α) (i : Nat) : a.get? i = a.data.get? i :=
+  getElem?_eq_data_get? ..
+
+theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
+  simp [get!_eq_getD]
+
+@[simp] theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
+  simp [back, back?]
+
+@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
+  simp [back?, getElem?_eq_data_get?]
+
+theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
+
+theorem get?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
+    (a.push x)[i]? = some a[i] := by
+  rw [getElem?_pos, get_push_lt]
+
+theorem get?_push_eq (a : Array α) (x : α) : (a.push x)[a.size]? = some x := by
+  rw [getElem?_pos, get_push_eq]
+
+theorem get?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x else a[i]? := by
+  match Nat.lt_trichotomy i a.size with
+  | Or.inl g =>
+    have h1 : i < a.size + 1 := by omega
+    have h2 : i ≠ a.size := by omega
+    simp [getElem?, size_push, g, h1, h2, get_push_lt]
+  | Or.inr (Or.inl heq) =>
+    simp [heq, getElem?_pos, get_push_eq]
+  | Or.inr (Or.inr g) =>
+    simp only [getElem?, size_push]
+    have h1 : ¬ (i < a.size) := by omega
+    have h2 : ¬ (i < a.size + 1) := by omega
+    have h3 : i ≠ a.size := by omega
+    simp [h1, h2, h3]
+
+@[simp] theorem get?_size {a : Array α} : a[a.size]? = none := by
+  simp only [getElem?, Nat.lt_irrefl, dite_false]
+
+@[simp] theorem data_set (a : Array α) (i v) : (a.set i v).data = a.data.set i.1 v := rfl
+
+theorem get_set_eq (a : Array α) (i : Fin a.size) (v : α) :
+    (a.set i v)[i.1] = v := by
+  simp only [set, getElem_eq_data_get, List.get_set_eq]
+
+theorem get?_set_eq (a : Array α) (i : Fin a.size) (v : α) :
+    (a.set i v)[i.1]? = v := by simp [getElem?_pos, i.2]
+
+@[simp] theorem get?_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α)
+    (h : i.1 ≠ j) : (a.set i v)[j]? = a[j]? := by
+  by_cases j < a.size <;> simp [getElem?_pos, getElem?_neg, *]
+
+theorem get?_set (a : Array α) (i : Fin a.size) (j : Nat) (v : α) :
+    (a.set i v)[j]? = if i.1 = j then some v else a[j]? := by
+  if h : i.1 = j then subst j; simp [*] else simp [*]
+
+theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v : α) :
+    (a.set i v)[j]'(by simp [*]) = if i = j then v else a[j] := by
+  if h : i.1 = j then subst j; simp [*] else simp [*]
+
+@[simp] theorem get_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α) (hj : j < a.size)
+    (h : i.1 ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
+  simp only [set, getElem_eq_data_get, List.get_set_ne _ h]
+
+theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
+  (setD a i v)[i] = v := by
+  simp at h
+  simp only [setD, h, dite_true, get_set, ite_true]
+
+theorem set_set (a : Array α) (i : Fin a.size) (v v' : α) :
+    (a.set i v).set ⟨i, by simp [i.2]⟩ v' = a.set i v' := by simp [set, List.set_set]
+
+private theorem fin_cast_val (e : n = n') (i : Fin n) : e ▸ i = ⟨i.1, e ▸ i.2⟩ := by cases e; rfl
+
+theorem swap_def (a : Array α) (i j : Fin a.size) :
+    a.swap i j = (a.set i (a.get j)).set ⟨j.1, by simp [j.2]⟩ (a.get i) := by
+  simp [swap, fin_cast_val]
+
+theorem data_swap (a : Array α) (i j : Fin a.size) :
+    (a.swap i j).data = (a.data.set i (a.get j)).set j (a.get i) := by simp [swap_def]
+
+theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
+    if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
+  simp [swap_def, get?_set, ← getElem_fin_eq_data_get]
+
+@[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
+    a.swapAt i v = (a[i.1], a.set i v) := rfl
+
+-- @[simp] -- FIXME: gives a weird linter error
+theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
+    a.swapAt! i v = (a[i], a.set ⟨i, h⟩ v) := by simp [swapAt!, h]
+
+@[simp] theorem data_pop (a : Array α) : a.pop.data = a.data.dropLast := by simp [pop]
+
+@[simp] theorem pop_empty : (#[] : Array α).pop = #[] := rfl
+
+@[simp] theorem pop_push (a : Array α) : (a.push x).pop = a := by simp [pop]
+
+@[simp] theorem getElem_pop (a : Array α) (i : Nat) (hi : i < a.pop.size) :
+    a.pop[i] = a[i]'(Nat.lt_of_lt_of_le (a.size_pop ▸ hi) (Nat.sub_le _ _)) :=
+  List.get_dropLast ..
+
+theorem eq_empty_of_size_eq_zero {as : Array α} (h : as.size = 0) : as = #[] := by
+  apply ext
+  · simp [h]
+  · intros; contradiction
+
+theorem eq_push_pop_back_of_size_ne_zero [Inhabited α] {as : Array α} (h : as.size ≠ 0) :
+    as = as.pop.push as.back := by
+  apply ext
+  · simp [Nat.sub_add_cancel (Nat.zero_lt_of_ne_zero h)]
+  · intros i h h'
+    if hlt : i < as.pop.size then
+      rw [get_push_lt (h:=hlt), getElem_pop]
+    else
+      have heq : i = as.pop.size :=
+        Nat.le_antisymm (size_pop .. ▸ Nat.le_pred_of_lt h) (Nat.le_of_not_gt hlt)
+      cases heq; rw [get_push_eq, back, ←size_pop, get!_eq_getD, getD, dif_pos h]; rfl
+
+theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size ≠ 0) :
+    ∃ (bs : Array α) (c : α), as = bs.push c :=
+  let _ : Inhabited α := ⟨as[0]⟩
+  ⟨as.pop, as.back, eq_push_pop_back_of_size_ne_zero h⟩
+
+theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
+
+@[simp] theorem size_swap! (a : Array α) (i j) :
+    (a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
+
+@[simp] theorem size_reverse (a : Array α) : a.reverse.size = a.size := by
+  let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
+    rw [reverse.loop]
+    if h : i < j then
+      have := reverse.termination h
+      simp [(go · (i+1) ⟨j-1, ·⟩), h]
+    else simp [h]
+    termination_by j - i
+  simp only [reverse]; split <;> simp [go]
+
+@[simp] theorem size_range {n : Nat} : (range n).size = n := by
+  unfold range
+  induction n with
+  | zero      => simp [Nat.fold]
+  | succ k ih =>
+    rw [Nat.fold, flip]
+    simp only [mkEmpty_eq, size_push] at *
+    omega
+
+@[simp] theorem reverse_data (a : Array α) : a.reverse.data = a.data.reverse := by
+  let rec go (as : Array α) (i j hj)
+      (h : i + j + 1 = a.size) (h₂ : as.size = a.size)
+      (H : ∀ k, as.data.get? k = if i ≤ k ∧ k ≤ j then a.data.get? k else a.data.reverse.get? k)
+      (k) : (reverse.loop as i ⟨j, hj⟩).data.get? k = a.data.reverse.get? k := by
+    rw [reverse.loop]; dsimp; split <;> rename_i h₁
+    · have := reverse.termination h₁
+      match j with | j+1 => ?_
+      simp at *
+      rw [(go · (i+1) j)]
+      · rwa [Nat.add_right_comm i]
+      · simp [size_swap, h₂]
+      · intro k
+        rw [← getElem?_eq_data_get?, get?_swap]
+        simp [getElem?_eq_data_get?, getElem_eq_data_get, ← List.get?_eq_get, H, Nat.le_of_lt h₁]
+        split <;> rename_i h₂
+        · simp [← h₂, Nat.not_le.2 (Nat.lt_succ_self _)]
+          exact (List.get?_reverse' _ _ (Eq.trans (by simp_arith) h)).symm
+        split <;> rename_i h₃
+        · simp [← h₃, Nat.not_le.2 (Nat.lt_succ_self _)]
+          exact (List.get?_reverse' _ _ (Eq.trans (by simp_arith) h)).symm
+        simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
+          Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
+    · rw [H]; split <;> rename_i h₂
+      · cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
+        cases Nat.le_antisymm h₂.1 h₂.2
+        exact (List.get?_reverse' _ _ h).symm
+      · rfl
+    termination_by j - i
+  simp only [reverse]; split
+  · match a with | ⟨[]⟩ | ⟨[_]⟩ => rfl
+  · have := Nat.sub_add_cancel (Nat.le_of_not_le ‹_›)
+    refine List.ext <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
+    split; {rfl}; rename_i h
+    simp [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := a.size - 1), this] at h
+    rw [List.get?_eq_none.2 ‹_›, List.get?_eq_none.2 (a.data.length_reverse ▸ ‹_›)]
+
+/-! ### foldl / foldr -/
+
+-- This proof is the pure version of `Array.SatisfiesM_foldlM`,
+-- reproduced to avoid a dependency on `SatisfiesM`.
+theorem foldl_induction
+    {as : Array α} (motive : Nat → β → Prop) {init : β} (h0 : motive 0 init) {f : β → α → β}
+    (hf : ∀ i : Fin as.size, ∀ b, motive i.1 b → motive (i.1 + 1) (f b as[i])) :
+    motive as.size (as.foldl f init) := by
+  let rec go {i j b} (h₁ : j ≤ as.size) (h₂ : as.size ≤ i + j) (H : motive j b) :
+    (motive as.size) (foldlM.loop (m := Id) f as as.size (Nat.le_refl _) i j b) := by
+    unfold foldlM.loop; split
+    · next hj =>
+      split
+      · cases Nat.not_le_of_gt (by simp [hj]) h₂
+      · exact go hj (by rwa [Nat.succ_add] at h₂) (hf ⟨j, hj⟩ b H)
+    · next hj => exact Nat.le_antisymm h₁ (Nat.ge_of_not_lt hj) ▸ H
+  simpa [foldl, foldlM] using go (Nat.zero_le _) (Nat.le_refl _) h0
+
+-- This proof is the pure version of `Array.SatisfiesM_foldrM`,
+-- reproduced to avoid a dependency on `SatisfiesM`.
+theorem foldr_induction
+    {as : Array α} (motive : Nat → β → Prop) {init : β} (h0 : motive as.size init) {f : α → β → β}
+    (hf : ∀ i : Fin as.size, ∀ b, motive (i.1 + 1) b → motive i.1 (f as[i] b)) :
+    motive 0 (as.foldr f init) := by
+  let rec go {i b} (hi : i ≤ as.size) (H : motive i b) :
+    (motive 0) (foldrM.fold (m := Id) f as 0 i hi b) := by
+    unfold foldrM.fold; simp; split
+    · next hi => exact (hi ▸ H)
+    · next hi =>
+      split; {simp at hi}
+      · next i hi' =>
+        exact go _ (hf ⟨i, hi'⟩ b H)
+  simp [foldr, foldrM]; split; {exact go _ h0}
+  · next h => exact (Nat.eq_zero_of_not_pos h ▸ h0)
+
+/-! ### map -/
+
+@[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
+  simp only [mem_def, map_data, List.mem_map]
+
+theorem mapM_eq_mapM_data [Monad m] [LawfulMonad m] (f : α → m β) (arr : Array α) :
+    arr.mapM f = return mk (← arr.data.mapM f) := by
+  rw [mapM_eq_foldlM, foldlM_eq_foldlM_data, ← List.foldrM_reverse]
+  conv => rhs; rw [← List.reverse_reverse arr.data]
+  induction arr.data.reverse with
+  | nil => simp; rfl
+  | cons a l ih => simp [ih]; simp [map_eq_pure_bind, push]
+
+theorem mapM_map_eq_foldl (as : Array α) (f : α → β) (i) :
+    mapM.map (m := Id) f as i b = as.foldl (start := i) (fun r a => r.push (f a)) b := by
+  unfold mapM.map
+  split <;> rename_i h
+  · simp only [Id.bind_eq]
+    dsimp [foldl, Id.run, foldlM]
+    rw [mapM_map_eq_foldl, dif_pos (by omega), foldlM.loop, dif_pos h]
+    -- Calling `split` here gives a bad goal.
+    have : size as - i = Nat.succ (size as - i - 1) := by omega
+    rw [this]
+    simp [foldl, foldlM, Id.run, Nat.sub_add_eq]
+  · dsimp [foldl, Id.run, foldlM]
+    rw [dif_pos (by omega), foldlM.loop, dif_neg h]
+    rfl
+termination_by as.size - i
+
+theorem map_eq_foldl (as : Array α) (f : α → β) :
+    as.map f = as.foldl (fun r a => r.push (f a)) #[] :=
+  mapM_map_eq_foldl _ _ _
+
+theorem map_induction (as : Array α) (f : α → β) (motive : Nat → Prop) (h0 : motive 0)
+    (p : Fin as.size → β → Prop) (hs : ∀ i, motive i.1 → p i (f as[i]) ∧ motive (i+1)) :
+    motive as.size ∧
+      ∃ eq : (as.map f).size = as.size, ∀ i h, p ⟨i, h⟩ ((as.map f)[i]) := by
+  have t := foldl_induction (as := as) (β := Array β)
+    (motive := fun i arr => motive i ∧ arr.size = i ∧ ∀ i h2, p i arr[i.1])
+    (init := #[]) (f := fun r a => r.push (f a)) ?_ ?_
+  obtain ⟨m, eq, w⟩ := t
+  · refine ⟨m, by simpa [map_eq_foldl] using eq, ?_⟩
+    intro i h
+    simp [eq] at w
+    specialize w ⟨i, h⟩ h
+    simpa [map_eq_foldl] using w
+  · exact ⟨h0, rfl, nofun⟩
+  · intro i b ⟨m, ⟨eq, w⟩⟩
+    refine ⟨?_, ?_, ?_⟩
+    · exact (hs _ m).2
+    · simp_all
+    · intro j h
+      simp at h ⊢
+      by_cases h' : j < size b
+      · rw [get_push]
+        simp_all
+      · rw [get_push, dif_neg h']
+        simp only [show j = i by omega]
+        exact (hs _ m).1
+
+theorem map_spec (as : Array α) (f : α → β) (p : Fin as.size → β → Prop)
+    (hs : ∀ i, p i (f as[i])) :
+    ∃ eq : (as.map f).size = as.size, ∀ i h, p ⟨i, h⟩ ((as.map f)[i]) := by
+  simpa using map_induction as f (fun _ => True) trivial p (by simp_all)
+
+@[simp] theorem getElem_map (f : α → β) (as : Array α) (i : Nat) (h) :
+    ((as.map f)[i]) = f (as[i]'(size_map .. ▸ h)) := by
+  have := map_spec as f (fun i b => b = f (as[i]))
+  simp only [implies_true, true_implies] at this
+  obtain ⟨eq, w⟩ := this
+  apply w
+  simp_all
+
+/-! ### mapIdx -/
+
+-- This could also be prove from `SatisfiesM_mapIdxM`.
+theorem mapIdx_induction (as : Array α) (f : Fin as.size → α → β)
+    (motive : Nat → Prop) (h0 : motive 0)
+    (p : Fin as.size → β → Prop)
+    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
+    motive as.size ∧ ∃ eq : (Array.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) := by
+  let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : ∀ i h h', p ⟨i, h⟩ bs[i]) (hm : motive j) :
+    let arr : Array β := Array.mapIdxM.map (m := Id) as f i j h bs
+    motive as.size ∧ ∃ eq : arr.size = as.size, ∀ i h, p ⟨i, h⟩ arr[i] := by
+    induction i generalizing j bs with simp [mapIdxM.map]
+    | zero =>
+      have := (Nat.zero_add _).symm.trans h
+      exact ⟨this ▸ hm, h₁ ▸ this, fun _ _ => h₂ ..⟩
+    | succ i ih =>
+      apply @ih (bs.push (f ⟨j, by omega⟩ as[j])) (j + 1) (by omega) (by simp; omega)
+      · intro i i_lt h'
+        rw [get_push]
+        split
+        · apply h₂
+        · simp only [size_push] at h'
+          obtain rfl : i = j := by omega
+          apply (hs ⟨i, by omega⟩ hm).1
+      · exact (hs ⟨j, by omega⟩ hm).2
+  simp [mapIdx, mapIdxM]; exact go rfl nofun h0
+
+theorem mapIdx_spec (as : Array α) (f : Fin as.size → α → β)
+    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
+    ∃ eq : (Array.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
+  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+
+@[simp] theorem size_mapIdx (a : Array α) (f : Fin a.size → α → β) : (a.mapIdx f).size = a.size :=
+  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+
+@[simp] theorem size_zipWithIndex (as : Array α) : as.zipWithIndex.size = as.size :=
+  Array.size_mapIdx _ _
+
+@[simp] theorem getElem_mapIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat)
+    (h : i < (mapIdx a f).size) :
+    haveI : i < a.size := by simp_all
+    (a.mapIdx f)[i] = f ⟨i, this⟩ a[i] :=
+  (mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
+
+/-! ### modify -/
+
+@[simp] theorem size_modify (a : Array α) (i : Nat) (f : α → α) : (a.modify i f).size = a.size := by
+  unfold modify modifyM Id.run
+  split <;> simp
+
+theorem get_modify {arr : Array α} {x i} (h : i < arr.size) :
+    (arr.modify x f).get ⟨i, by simp [h]⟩ =
+    if x = i then f (arr.get ⟨i, h⟩) else arr.get ⟨i, h⟩ := by
+  simp [modify, modifyM, Id.run]; split
+  · simp [get_set _ _ _ h]; split <;> simp [*]
+  · rw [if_neg (mt (by rintro rfl; exact h) ‹_›)]
+
+/-! ### filter -/
+
+@[simp] theorem filter_data (p : α → Bool) (l : Array α) :
+    (l.filter p).data = l.data.filter p := by
+  dsimp only [filter]
+  rw [foldl_eq_foldl_data]
+  generalize l.data = l
+  suffices ∀ a, (List.foldl (fun r a => if p a = true then push r a else r) a l).data =
+      a.data ++ List.filter p l by
+    simpa using this #[]
+  induction l with simp
+  | cons => split <;> simp [*]
+
+@[simp] theorem filter_filter (q) (l : Array α) :
+    filter p (filter q l) = filter (fun a => p a ∧ q a) l := by
+  apply ext'
+  simp only [filter_data, List.filter_filter]
+
+@[simp] theorem mem_filter : x ∈ filter p as ↔ x ∈ as ∧ p x := by
+  simp only [mem_def, filter_data, List.mem_filter]
+
+theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
+  (mem_filter.mp h).1
+
+/-! ### filterMap -/
+
+@[simp] theorem filterMap_data (f : α → Option β) (l : Array α) :
+    (l.filterMap f).data = l.data.filterMap f := by
+  dsimp only [filterMap, filterMapM]
+  rw [foldlM_eq_foldlM_data]
+  generalize l.data = l
+  have this : ∀ a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).data =
+    a.data ++ List.filterMap f l := ?_
+  exact this #[]
+  induction l
+  · simp_all [Id.run]
+  · simp_all [Id.run]
+    split <;> simp_all
+
+@[simp] theorem mem_filterMap (f : α → Option β) (l : Array α) {b : β} :
+    b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
+  simp only [mem_def, filterMap_data, List.mem_filterMap]
+
+/-! ### empty -/
+
+theorem size_empty : (#[] : Array α).size = 0 := rfl
+
+theorem empty_data : (#[] : Array α).data = [] := rfl
+
+/-! ### append -/
+
+theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] := rfl
+
+@[simp] theorem mem_append {a : α} {s t : Array α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
+  simp only [mem_def, append_data, List.mem_append]
+
+theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
+  simp only [size, append_data, List.length_append]
+
+theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
+    (as ++ bs)[i] = as[i] := by
+  simp only [getElem_eq_data_get]
+  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
+  conv => rhs; rw [← List.get_append_left (bs:=bs.data) (h':=h')]
+  apply List.get_of_eq; rw [append_data]
+
+theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
+    (hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
+    (as ++ bs)[i] = bs[i - as.size] := by
+  simp only [getElem_eq_data_get]
+  have h' : i < (as.data ++ bs.data).length := by rwa [← data_length, append_data] at h
+  conv => rhs; rw [← List.get_append_right (h':=h') (h:=Nat.not_lt_of_ge hle)]
+  apply List.get_of_eq; rw [append_data]
+
+@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
+  apply ext'; simp only [append_data, empty_data, List.append_nil]
+
+@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
+  apply ext'; simp only [append_data, empty_data, List.nil_append]
+
+theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
+  apply ext'; simp only [append_data, List.append_assoc]
+
+/-! ### extract -/
+
+theorem extract_loop_zero (as bs : Array α) (start : Nat) : extract.loop as 0 start bs = bs := by
+  rw [extract.loop]; split <;> rfl
+
+theorem extract_loop_succ (as bs : Array α) (size start : Nat) (h : start < as.size) :
+    extract.loop as (size+1) start bs = extract.loop as size (start+1) (bs.push as[start]) := by
+  rw [extract.loop, dif_pos h]; rfl
+
+theorem extract_loop_of_ge (as bs : Array α) (size start : Nat) (h : start ≥ as.size) :
+    extract.loop as size start bs = bs := by
+  rw [extract.loop, dif_neg (Nat.not_lt_of_ge h)]
+
+theorem extract_loop_eq_aux (as bs : Array α) (size start : Nat) :
+    extract.loop as size start bs = bs ++ extract.loop as size start #[] := by
+  induction size using Nat.recAux generalizing start bs with
+  | zero => rw [extract_loop_zero, extract_loop_zero, append_nil]
+  | succ size ih =>
+    if h : start < as.size then
+      rw [extract_loop_succ (h:=h), ih (bs.push _), push_eq_append_singleton]
+      rw [extract_loop_succ (h:=h), ih (#[].push _), push_eq_append_singleton, nil_append]
+      rw [append_assoc]
+    else
+      rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
+      rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
+      rw [append_nil]
+
+theorem extract_loop_eq (as bs : Array α) (size start : Nat) (h : start + size ≤ as.size) :
+  extract.loop as size start bs = bs ++ as.extract start (start + size) := by
+  simp [extract]; rw [extract_loop_eq_aux, Nat.min_eq_left h, Nat.add_sub_cancel_left]
+
+theorem size_extract_loop (as bs : Array α) (size start : Nat) :
+    (extract.loop as size start bs).size = bs.size + min size (as.size - start) := by
+  induction size using Nat.recAux generalizing start bs with
+  | zero => rw [extract_loop_zero, Nat.zero_min, Nat.add_zero]
+  | succ size ih =>
+    if h : start < as.size then
+      rw [extract_loop_succ (h:=h), ih, size_push, Nat.add_assoc, ←Nat.add_min_add_left,
+        Nat.sub_succ, Nat.one_add, Nat.one_add, Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt h)]
+    else
+      have h := Nat.le_of_not_gt h
+      rw [extract_loop_of_ge (h:=h), Nat.sub_eq_zero_of_le h, Nat.min_zero, Nat.add_zero]
+
+@[simp] theorem size_extract (as : Array α) (start stop : Nat) :
+    (as.extract start stop).size = min stop as.size - start := by
+  simp [extract]; rw [size_extract_loop, size_empty, Nat.zero_add, Nat.sub_min_sub_right,
+    Nat.min_assoc, Nat.min_self]
+
+theorem get_extract_loop_lt_aux (as bs : Array α) (size start : Nat) (hlt : i < bs.size) :
+    i < (extract.loop as size start bs).size := by
+  rw [size_extract_loop]
+  apply Nat.lt_of_lt_of_le hlt
+  exact Nat.le_add_right ..
+
+theorem get_extract_loop_lt (as bs : Array α) (size start : Nat) (hlt : i < bs.size)
+    (h := get_extract_loop_lt_aux as bs size start hlt) :
+    (extract.loop as size start bs)[i] = bs[i] := by
+  apply Eq.trans _ (get_append_left (bs:=extract.loop as size start #[]) hlt)
+  · rw [size_append]; exact Nat.lt_of_lt_of_le hlt (Nat.le_add_right ..)
+  · congr; rw [extract_loop_eq_aux]
+
+theorem get_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
+    (h : i < (extract.loop as size start bs).size) : start + i - bs.size < as.size := by
+  have h : i < bs.size + (as.size - start) := by
+      apply Nat.lt_of_lt_of_le h
+      rw [size_extract_loop]
+      apply Nat.add_le_add_left
+      exact Nat.min_le_right ..
+  rw [Nat.add_sub_assoc hge]
+  apply Nat.add_lt_of_lt_sub'
+  exact Nat.sub_lt_left_of_lt_add hge h
+
+theorem get_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i ≥ bs.size)
+    (h : i < (extract.loop as size start bs).size)
+    (h' := get_extract_loop_ge_aux as bs size start hge h) :
+    (extract.loop as size start bs)[i] = as[start + i - bs.size] := by
+  induction size using Nat.recAux generalizing start bs with
+  | zero =>
+    rw [size_extract_loop, Nat.zero_min, Nat.add_zero] at h
+    omega
+  | succ size ih =>
+    have : start < as.size := by
+      apply Nat.lt_of_le_of_lt (Nat.le_add_right start (i - bs.size))
+      rwa [← Nat.add_sub_assoc hge]
+    have : i < (extract.loop as size (start+1) (bs.push as[start])).size := by
+      rwa [← extract_loop_succ]
+    have heq : (extract.loop as (size+1) start bs)[i] =
+        (extract.loop as size (start+1) (bs.push as[start]))[i] := by
+      congr 1; rw [extract_loop_succ]
+    rw [heq]
+    if hi : bs.size = i then
+      cases hi
+      have h₁ : bs.size < (bs.push as[start]).size := by rw [size_push]; exact Nat.lt_succ_self ..
+      have h₂ : bs.size < (extract.loop as size (start+1) (bs.push as[start])).size := by
+        rw [size_extract_loop]; apply Nat.lt_of_lt_of_le h₁; exact Nat.le_add_right ..
+      have h : (extract.loop as size (start + 1) (push bs as[start]))[bs.size] = as[start] := by
+        rw [get_extract_loop_lt as (bs.push as[start]) size (start+1) h₁ h₂, get_push_eq]
+      rw [h]; congr; rw [Nat.add_sub_cancel]
+    else
+      have hge : bs.size + 1 ≤ i := Nat.lt_of_le_of_ne hge hi
+      rw [ih (bs.push as[start]) (start+1) ((size_push ..).symm ▸ hge)]
+      congr 1; rw [size_push, Nat.add_right_comm, Nat.add_sub_add_right]
+
+theorem get_extract_aux {as : Array α} {start stop : Nat} (h : i < (as.extract start stop).size) :
+    start + i < as.size := by
+  rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
+  apply Nat.sub_le_sub_right; apply Nat.min_le_right
+
+@[simp] theorem get_extract {as : Array α} {start stop : Nat}
+    (h : i < (as.extract start stop).size) :
+    (as.extract start stop)[i] = as[start + i]'(get_extract_aux h) :=
+  show (extract.loop as (min stop as.size - start) start #[])[i]
+    = as[start + i]'(get_extract_aux h) by rw [get_extract_loop_ge]; rfl; exact Nat.zero_le _
+
+@[simp] theorem extract_all (as : Array α) : as.extract 0 as.size = as := by
+  apply ext
+  · rw [size_extract, Nat.min_self, Nat.sub_zero]
+  · intros; rw [get_extract]; congr; rw [Nat.zero_add]
+
+theorem extract_empty_of_stop_le_start (as : Array α) {start stop : Nat} (h : stop ≤ start) :
+    as.extract start stop = #[] := by
+  simp [extract]; rw [←Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.zero_min,
+    extract_loop_zero]
+
+theorem extract_empty_of_size_le_start (as : Array α) {start stop : Nat} (h : as.size ≤ start) :
+    as.extract start stop = #[] := by
+  simp [extract]; rw [←Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.min_zero,
+    extract_loop_zero]
+
+@[simp] theorem extract_empty (start stop : Nat) : (#[] : Array α).extract start stop = #[] :=
+  extract_empty_of_size_le_start _ (Nat.zero_le _)
+
+/-! ### any -/
+
+-- Auxiliary for `any_iff_exists`.
+theorem anyM_loop_iff_exists (p : α → Bool) (as : Array α) (start stop) (h : stop ≤ as.size) :
+    anyM.loop (m := Id) p as stop h start = true ↔
+      ∃ i : Fin as.size, start ≤ ↑i ∧ ↑i < stop ∧ p as[i] = true := by
+  unfold anyM.loop
+  split <;> rename_i h₁
+  · dsimp
+    split <;> rename_i h₂
+    · simp only [true_iff]
+      refine ⟨⟨start, by omega⟩, by dsimp; omega, by dsimp; omega, h₂⟩
+    · rw [anyM_loop_iff_exists]
+      constructor
+      · rintro ⟨i, ge, lt, h⟩
+        have : start ≠ i := by rintro rfl; omega
+        exact ⟨i, by omega, lt, h⟩
+      · rintro ⟨i, ge, lt, h⟩
+        have : start ≠ i := by rintro rfl; erw [h] at h₂; simp_all
+        exact ⟨i, by omega, lt, h⟩
+  · simp
+    omega
+termination_by stop - start
+
+-- This could also be proved from `SatisfiesM_anyM_iff_exists` in `Std.Data.Array.Init.Monadic`
+theorem any_iff_exists (p : α → Bool) (as : Array α) (start stop) :
+    any as p start stop ↔ ∃ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop ∧ p as[i] := by
+  dsimp [any, anyM, Id.run]
+  split
+  · rw [anyM_loop_iff_exists]; rfl
+  · rw [anyM_loop_iff_exists]
+    constructor
+    · rintro ⟨i, ge, _, h⟩
+      exact ⟨i, by omega, by omega, h⟩
+    · rintro ⟨i, ge, _, h⟩
+      exact ⟨i, by omega, by omega, h⟩
+
+theorem any_eq_true (p : α → Bool) (as : Array α) :
+    any as p ↔ ∃ i : Fin as.size, p as[i] := by simp [any_iff_exists, Fin.isLt]
+
+theorem any_def {p : α → Bool} (as : Array α) : as.any p = as.data.any p := by
+  rw [Bool.eq_iff_iff, any_eq_true, List.any_eq_true]; simp only [List.mem_iff_get]
+  exact ⟨fun ⟨i, h⟩ => ⟨_, ⟨i, rfl⟩, h⟩, fun ⟨_, ⟨i, rfl⟩, h⟩ => ⟨i, h⟩⟩
+
+/-! ### all -/
+
+theorem all_eq_not_any_not (p : α → Bool) (as : Array α) (start stop) :
+    all as p start stop = !(any as (!p ·) start stop) := by
+  dsimp [all, allM]
+  rfl
+
+theorem all_iff_forall (p : α → Bool) (as : Array α) (start stop) :
+    all as p start stop ↔ ∀ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop → p as[i] := by
+  rw [all_eq_not_any_not]
+  suffices ¬(any as (!p ·) start stop = true) ↔
+      ∀ i : Fin as.size, start ≤ i.1 ∧ i.1 < stop → p as[i] by
+    simp_all
+  rw [any_iff_exists]
+  simp
+
+theorem all_eq_true (p : α → Bool) (as : Array α) : all as p ↔ ∀ i : Fin as.size, p as[i] := by
+  simp [all_iff_forall, Fin.isLt]
+
+theorem all_def {p : α → Bool} (as : Array α) : as.all p = as.data.all p := by
+  rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_get]
+  constructor
+  · rintro w x ⟨r, rfl⟩
+    rw [← getElem_eq_data_get]
+    apply w
+  · intro w i
+    exact w as[i] ⟨i, (getElem_eq_data_get as i.2).symm⟩
+
+theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
+  simp only [all_def, List.all_eq_true, mem_def]
+
+/-! ### contains -/
+
+theorem contains_def [DecidableEq α] {a : α} {as : Array α} : as.contains a ↔ a ∈ as := by
+  rw [mem_def, contains, any_def, List.any_eq_true]; simp [and_comm]
+
+instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a ∈ as) :=
+  decidable_of_iff _ contains_def
+
+/-! ### swap -/
+
+open Fin
+
+@[simp] theorem get_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.val] = a[i] :=
+  by simp only [swap, fin_cast_val, get_eq_getElem, getElem_set_eq, getElem_fin]
+
+@[simp] theorem get_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.val] = a[j] :=
+  if he : ((Array.size_set _ _ _).symm ▸ j).val = i.val then by
+    simp only [←he, fin_cast_val, get_swap_right, getElem_fin]
+  else by
+    apply Eq.trans
+    · apply Array.get_set_ne
+      · simp only [size_set, Fin.isLt]
+      · assumption
+    · simp [get_set_ne]
+
+@[simp] theorem get_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
+    (hi : p ≠ i) (hj : p ≠ j) : (a.swap i j)[p]'(a.size_swap .. |>.symm ▸ hp) = a[p] := by
+  apply Eq.trans
+  · have : ((a.size_set i (a.get j)).symm ▸ j).val = j.val := by simp only [fin_cast_val]
+    apply Array.get_set_ne
+    · simp only [this]
+      apply Ne.symm
+      · assumption
+  · apply Array.get_set_ne
+    · apply Ne.symm
+      · assumption
+
+theorem get_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk: k < a.size) :
+    (a.swap i j)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i]  else a[k] := by
+  split
+  · simp_all only [get_swap_left]
+  · split <;> simp_all
+
+theorem get_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk' : k < (a.swap i j).size) :
+    (a.swap i j)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
+  apply get_swap
+
+@[simp] theorem swap_swap (a : Array α) {i j : Fin a.size} :
+    (a.swap i j).swap ⟨i.1, (a.size_swap ..).symm ▸i.2⟩ ⟨j.1, (a.size_swap ..).symm ▸j.2⟩ = a := by
+  apply ext
+  · simp only [size_swap]
+  · intros
+    simp only [get_swap']
+    split
+    · simp_all
+    · split <;> simp_all
+
+theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i := by
+  apply ext
+  · simp only [size_swap]
+  · intros
+    simp only [get_swap']
+    split
+    · split <;> simp_all
+    · split <;> simp_all
+
+
 end Array

src/Init/Data/Array/Mem.lean

@@ -27,13 +27,20 @@ theorem sizeOf_lt_of_mem [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a <
   cases as with | _ as =>
   exact Nat.lt_trans (List.sizeOf_get ..) (by simp_arith)
 
+@[simp] theorem sizeOf_getElem [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) :
+  sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _
+
 /-- This tactic, added to the `decreasing_trivial` toolbox, proves that
 `sizeOf arr[i] < sizeOf arr`, which is useful for well founded recursions
 over a nested inductive like `inductive T | mk : Array T → T`. -/
 macro "array_get_dec" : tactic =>
   `(tactic| first
-    | apply sizeOf_get
-    | apply Nat.lt_trans (sizeOf_get ..); simp_arith)
+    -- subsumed by simp
+    -- | with_reducible apply sizeOf_get
+    -- | with_reducible apply sizeOf_getElem
+    | (with_reducible apply Nat.lt_trans (sizeOf_get ..)); simp_arith
+    | (with_reducible apply Nat.lt_trans (sizeOf_getElem ..)); simp_arith
+    )
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_get_dec)
 
@@ -43,9 +50,10 @@ provided that `a ∈ arr` which is useful for well founded recursions over a nes
 -- NB: This is analogue to tactic `sizeOf_list_dec`
 macro "array_mem_dec" : tactic =>
   `(tactic| first
-    | apply Array.sizeOf_lt_of_mem; assumption; done
-    | apply Nat.lt_trans (Array.sizeOf_lt_of_mem ?h)
-      case' h => assumption
+    | with_reducible apply Array.sizeOf_lt_of_mem; assumption; done
+    | with_reducible
+        apply Nat.lt_trans (Array.sizeOf_lt_of_mem ?h)
+        case' h => assumption
       simp_arith)
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_mem_dec)

src/Init/Data/Array/QSort.lean

@@ -27,6 +27,7 @@ def qpartition (as : Array α) (lt : α → α → Bool) (lo hi : Nat) : Nat ×
       let as := as.swap! i hi
       (i, as)
     termination_by hi - j
+    decreasing_by all_goals simp_wf; decreasing_trivial_pre_omega
   loop as lo lo
 
 @[inline] partial def qsort (as : Array α) (lt : α → α → Bool) (low := 0) (high := as.size - 1) : Array α :=

src/Init/Data/BitVec/Bitblast.lean

@@ -159,4 +159,29 @@ theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := b
 theorem allOnes_sub_eq_not (x : BitVec w) : allOnes w - x = ~~~x := by
   rw [← add_not_self x, BitVec.add_comm, add_sub_cancel]
 
+/-! ### Negation -/
+
+theorem bit_not_testBit (x : BitVec w) (i : Fin w) :
+  getLsb (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) i.val = !(getLsb x i.val) := by
+  apply iunfoldr_getLsb (fun _ => ()) i (by simp)
+
+theorem bit_not_add_self (x : BitVec w) :
+  ((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd + x  = -1 := by
+  simp only [add_eq_adc]
+  apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
+  intro i; simp only [ BitVec.not, adcb, testBit_toNat]
+  rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd)]
+  <;> simp [bit_not_testBit, negOne_eq_allOnes, getLsb_allOnes]
+
+theorem bit_not_eq_not (x : BitVec w) :
+  ((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd = ~~~ x := by
+  simp [←allOnes_sub_eq_not, BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), ←negOne_eq_allOnes]
+
+theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) (BitVec.ofNat w 1) false).snd:= by
+  simp only [← add_eq_adc]
+  rw [iunfoldr_replace_snd ((fun _ => ())) (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) _ rfl]
+  · rw [BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), sub_toAdd, BitVec.add_comm _ (-x)]
+    simp [← sub_toAdd, BitVec.sub_add_cancel]
+  · simp [bit_not_testBit x _]
+
 end BitVec

src/Init/Data/BitVec/Folds.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
 -/
 prelude
 import Init.Data.BitVec.Lemmas
@@ -48,6 +48,51 @@ private theorem iunfoldr.eq_test
     intro i
     simp_all [truncate_succ]
 
+theorem iunfoldr_getLsb' {f : Fin w → α → α × Bool} (state : Nat → α)
+    (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :
+  (∀ i : Fin w, getLsb (iunfoldr f (state 0)).snd i.val = (f i (state i.val)).snd)
+  ∧ (iunfoldr f (state 0)).fst = state w := by
+  unfold iunfoldr
+  simp
+  apply Fin.hIterate_elim
+        (fun j (p : α × BitVec j) => (hj : j ≤ w) →
+         (∀ i : Fin j,  getLsb p.snd i.val = (f ⟨i.val, Nat.lt_of_lt_of_le i.isLt hj⟩ (state i.val)).snd)
+          ∧ p.fst = state j)
+  case hj => simp
+  case init =>
+    intro
+    apply And.intro
+    · intro i
+      have := Fin.size_pos i
+      contradiction
+    · rfl
+  case step =>
+    intro j ⟨s, v⟩ ih hj
+    apply And.intro
+    case left =>
+      intro i
+      simp only [getLsb_cons]
+      have hj2 : j.val ≤ w := by simp
+      cases (Nat.lt_or_eq_of_le (Nat.lt_succ.mp i.isLt)) with
+      | inl h3 => simp [if_neg, (Nat.ne_of_lt h3)]
+                  exact (ih hj2).1 ⟨i.val, h3⟩
+      | inr h3 => simp [h3, if_pos]
+                  cases (Nat.eq_zero_or_pos j.val) with
+                  | inl hj3 => congr
+                               rw [← (ih hj2).2]
+                  | inr hj3 => congr
+                               exact (ih hj2).2
+    case right =>
+      simp
+      have hj2 : j.val ≤ w := by simp
+      rw [← ind j, ← (ih hj2).2]
+
+
+theorem iunfoldr_getLsb {f : Fin w → α → α × Bool} (state : Nat → α) (i : Fin w)
+    (ind : ∀(i : Fin w), (f i (state i.val)).fst = state (i.val+1)) :
+  getLsb (iunfoldr f (state 0)).snd i.val = (f i (state i.val)).snd := by
+  exact (iunfoldr_getLsb' state ind).1 i
+
 /--
 Correctness theorem for `iunfoldr`.
 -/
@@ -58,4 +103,11 @@ theorem iunfoldr_replace
     iunfoldr f a = (state w, value) := by
   simp [iunfoldr.eq_test state value a init step]
 
+theorem iunfoldr_replace_snd
+  {f : Fin w → α → α × Bool} (state : Nat → α) (value : BitVec w) (a : α)
+    (init : state 0 = a)
+    (step : ∀(i : Fin w), f i (state i.val) = (state (i.val+1), value.getLsb i.val)) :
+    (iunfoldr f a).snd = value := by
+  simp [iunfoldr.eq_test state value a init step]
+
 end BitVec

src/Init/Data/BitVec/Lemmas.lean

@@ -2,6 +2,7 @@
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed,
+
 -/
 prelude
 import Init.Data.Bool
@@ -103,7 +104,13 @@ theorem eq_of_getMsb_eq {x y : BitVec w}
     have q := pred ⟨w - 1 - i, q_lt⟩
     simpa [q_lt, Nat.sub_sub_self, r] using q
 
-@[simp] theorem of_length_zero {x : BitVec 0} : x = 0#0 := by ext; simp
+-- This cannot be a `@[simp]` lemma, as it would be tried at every term.
+theorem of_length_zero {x : BitVec 0} : x = 0#0 := by ext; simp
+
+@[simp] theorem toNat_zero_length (x : BitVec 0) : x.toNat = 0 := by simp [of_length_zero]
+@[simp] theorem getLsb_zero_length (x : BitVec 0) : x.getLsb i = false := by simp [of_length_zero]
+@[simp] theorem getMsb_zero_length (x : BitVec 0) : x.getMsb i = false := by simp [of_length_zero]
+@[simp] theorem msb_zero_length (x : BitVec 0) : x.msb = false := by simp [BitVec.msb, of_length_zero]
 
 theorem eq_of_toFin_eq : ∀ {x y : BitVec w}, x.toFin = y.toFin → x = y
   | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
@@ -336,7 +343,7 @@ theorem nat_eq_toNat (x : BitVec w) (y : Nat)
 @[simp] theorem getMsb_zeroExtend_add {x : BitVec w} (h : k ≤ i) :
     (x.zeroExtend (w + k)).getMsb i = x.getMsb (i - k) := by
   by_cases h : w = 0
-  · subst h; simp
+  · subst h; simp [of_length_zero]
   simp only [getMsb, getLsb_zeroExtend]
   by_cases h₁ : i < w + k <;> by_cases h₂ : i - k < w <;> by_cases h₃ : w + k - 1 - i < w + k
     <;> simp [h₁, h₂, h₃]
@@ -826,13 +833,18 @@ theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n :=
 
 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]
+instance : Std.Associative (α := BitVec n) (· + ·) := ⟨BitVec.add_assoc⟩
 
 protected theorem add_comm (x y : BitVec n) : x + y = y + x := by
   simp [add_def, Nat.add_comm]
+instance : Std.Commutative (α := BitVec n) (· + ·) := ⟨BitVec.add_comm⟩
 
 @[simp] protected theorem add_zero (x : BitVec n) : x + 0#n = x := by simp [add_def]
 
 @[simp] protected theorem zero_add (x : BitVec n) : 0#n + x = x := by simp [add_def]
+instance : Std.LawfulIdentity (α := BitVec n) (· + ·) 0#n where
+  left_id := BitVec.zero_add
+  right_id := BitVec.add_zero
 
 theorem truncate_add (x y : BitVec w) (h : i ≤ w) :
     (x + y).truncate i = x.truncate i + y.truncate i := by
@@ -889,6 +901,15 @@ theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
   rw [toNat_sub, toNat_add, Nat.mod_add_mod, Nat.add_assoc, ← Nat.add_sub_assoc y_toNat_le,
     Nat.add_sub_cancel_left, Nat.add_mod_right, toNat_mod_cancel]
 
+theorem sub_add_cancel (x y : BitVec w) : x - y + y = x := by
+  rw [sub_toAdd, BitVec.add_assoc, BitVec.add_comm _ y,
+      ← BitVec.add_assoc, ← sub_toAdd, add_sub_cancel]
+
+theorem eq_sub_iff_add_eq {x y z : BitVec w} : x = z - y ↔ x + y = z := by
+  apply Iff.intro <;> intro h
+  · simp [h, sub_add_cancel]
+  · simp [←h, add_sub_cancel]
+
 theorem negOne_eq_allOnes : -1#w = allOnes w := by
   apply eq_of_toNat_eq
   if g : w = 0 then

src/Init/Data/Bool.lean

@@ -74,6 +74,7 @@ Added for confluence with `not_and_self` `and_not_self` on term
 @[simp] theorem eq_false_and_eq_true_self : ∀(b : Bool), (b = false ∧ b = true) ↔ False := by decide
 
 theorem and_comm : ∀ (x y : Bool), (x && y) = (y && x) := by decide
+instance : Std.Commutative (· && ·) := ⟨and_comm⟩
 
 theorem and_left_comm : ∀ (x y z : Bool), (x && (y && z)) = (y && (x && z)) := by decide
 theorem and_right_comm : ∀ (x y z : Bool), ((x && y) && z) = ((x && z) && y) := by decide
@@ -120,6 +121,7 @@ Needed for confluence of term `(a || b) ↔ a` which reduces to `(a || b) = a` v
 @[simp] theorem iff_or_self : ∀(a b : Bool), (b = (a || b)) ↔ (a → b) := by decide
 
 theorem or_comm : ∀ (x y : Bool), (x || y) = (y || x) := by decide
+instance : Std.Commutative (· || ·) := ⟨or_comm⟩
 
 theorem or_left_comm : ∀ (x y z : Bool), (x || (y || z)) = (y || (x || z)) := by decide
 theorem or_right_comm : ∀ (x y z : Bool), ((x || y) || z) = ((x || z) || y) := by decide
@@ -186,12 +188,18 @@ in false_eq and true_eq.
 @[simp] theorem true_beq  : ∀b, (true  == b) =  b := by decide
 @[simp] theorem false_beq : ∀b, (false == b) = !b := by decide
 @[simp] theorem beq_true  : ∀b, (b == true)  =  b := by decide
+instance : Std.LawfulIdentity (· == ·) true where
+  left_id := true_beq
+  right_id := beq_true
 @[simp] theorem beq_false : ∀b, (b == false) = !b := by decide
 
 @[simp] theorem true_bne  : ∀(b : Bool), (true  != b) = !b := by decide
 @[simp] theorem false_bne : ∀(b : Bool), (false != b) =  b := by decide
 @[simp] theorem bne_true  : ∀(b : Bool), (b != true)  = !b := by decide
 @[simp] theorem bne_false : ∀(b : Bool), (b != false) =  b := by decide
+instance : Std.LawfulIdentity (· != ·) false where
+  left_id := false_bne
+  right_id := bne_false
 
 @[simp] theorem not_beq_self : ∀ (x : Bool), ((!x) == x) = false := by decide
 @[simp] theorem beq_not_self : ∀ (x : Bool), (x   == !x) = false := by decide
@@ -214,6 +222,7 @@ due to `beq_iff_eq`.
 @[simp] theorem not_bne_not : ∀ (x y : Bool), ((!x) != (!y)) = (x != y) := by decide
 
 @[simp] theorem bne_assoc : ∀ (x y z : Bool), ((x != y) != z) = (x != (y != z)) := by decide
+instance : Std.Associative (· != ·) := ⟨bne_assoc⟩
 
 @[simp] theorem bne_left_inj  : ∀ (x y z : Bool), (x != y) = (x != z) ↔ y = z := by decide
 @[simp] theorem bne_right_inj : ∀ (x y z : Bool), (x != z) = (y != z) ↔ x = y := by decide

src/Init/Data/Fin/Fold.lean

@@ -12,6 +12,7 @@ import Init.Data.Nat.Linear
   loop (x : α) (i : Nat) : α :=
     if h : i < n then loop (f x ⟨i, h⟩) (i+1) else x
   termination_by n - i
+  decreasing_by decreasing_trivial_pre_omega
 
 /-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
 @[inline] def foldr (n) (f : Fin n → α → α) (init : α) : α := loop ⟨n, Nat.le_refl n⟩ init where

src/Init/Data/Fin/Iterate.lean

@@ -23,6 +23,7 @@ def hIterateFrom (P : Nat → Sort _) {n} (f : ∀(i : Fin n), P i.val → P (i.
     have p : i = n := (or_iff_left g).mp (Nat.eq_or_lt_of_le ubnd)
     _root_.cast (congrArg P p) a
   termination_by n - i
+  decreasing_by decreasing_trivial_pre_omega
 
 /--
 `hIterate` is a heterogenous iterative operation that applies a

src/Init/Data/Fin/Lemmas.lean

@@ -602,6 +602,7 @@ A version of `Fin.succRec` taking `i : Fin n` as the first argument. -/
     @Fin.succRecOn (n + 1) i.succ motive zero succ = succ n i (Fin.succRecOn i zero succ) := by
   cases i; rfl
 
+
 /-- Define `motive i` by induction on `i : Fin (n + 1)` via induction on the underlying `Nat` value.
 This function has two arguments: `zero` handles the base case on `motive 0`,
 and `succ` defines the inductive step using `motive i.castSucc`.
@@ -610,8 +611,12 @@ and `succ` defines the inductive step using `motive i.castSucc`.
 @[elab_as_elim] def induction {motive : Fin (n + 1) → Sort _} (zero : motive 0)
     (succ : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
     ∀ i : Fin (n + 1), motive i
-  | ⟨0, hi⟩ => by rwa [Fin.mk_zero]
-  | ⟨i+1, hi⟩ => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (induction zero succ ⟨i, Nat.lt_of_succ_lt hi⟩)
+  | ⟨i, hi⟩ => go i hi
+where
+  -- Use a curried function so that this is structurally recursive
+  go : ∀ (i : Nat) (hi : i < n + 1), motive ⟨i, hi⟩
+  | 0, hi => by rwa [Fin.mk_zero]
+  | i+1, hi => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (go i (Nat.lt_of_succ_lt hi))
 
 @[simp] theorem induction_zero {motive : Fin (n + 1) → Sort _} (zero : motive 0)
     (hs : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
@@ -793,15 +798,20 @@ protected theorem mul_one (k : Fin (n + 1)) : k * 1 = k := by
 
 protected theorem mul_comm (a b : Fin n) : a * b = b * a :=
   ext <| by rw [mul_def, mul_def, Nat.mul_comm]
+instance : Std.Commutative (α := Fin n) (· * ·) := ⟨Fin.mul_comm⟩
 
 protected theorem mul_assoc (a b c : Fin n) : a * b * c = a * (b * c) := by
   apply eq_of_val_eq
   simp only [val_mul]
   rw [← Nat.mod_eq_of_lt a.isLt, ← Nat.mod_eq_of_lt b.isLt, ← Nat.mod_eq_of_lt c.isLt]
   simp only [← Nat.mul_mod, Nat.mul_assoc]
+instance : Std.Associative (α := Fin n) (· * ·) := ⟨Fin.mul_assoc⟩
 
 protected theorem one_mul (k : Fin (n + 1)) : (1 : Fin (n + 1)) * k = k := by
   rw [Fin.mul_comm, Fin.mul_one]
+instance : Std.LawfulIdentity (α := Fin (n + 1)) (· * ·) 1 where
+  left_id := Fin.one_mul
+  right_id := Fin.mul_one
 
 protected theorem mul_zero (k : Fin (n + 1)) : k * 0 = 0 := by simp [ext_iff, mul_def]
 

src/Init/Data/Int/Lemmas.lean

@@ -137,12 +137,16 @@ protected theorem add_comm : ∀ a b : Int, a + b = b + a
   | ofNat _, -[_+1]  => rfl
   | -[_+1],  ofNat _ => rfl
   | -[_+1],  -[_+1]  => by simp [Nat.add_comm]
+instance : Std.Commutative (α := Int) (· + ·) := ⟨Int.add_comm⟩
 
 @[simp] protected theorem add_zero : ∀ a : Int, a + 0 = a
   | ofNat _ => rfl
   | -[_+1]  => rfl
 
 @[simp] protected theorem zero_add (a : Int) : 0 + a = a := Int.add_comm .. ▸ a.add_zero
+instance : Std.LawfulIdentity (α := Int) (· + ·) 0 where
+  left_id := Int.zero_add
+  right_id := Int.add_zero
 
 theorem ofNat_add_negSucc_of_lt (h : m < n.succ) : ofNat m + -[n+1] = -[n - m+1] :=
   show subNatNat .. = _ by simp [succ_sub (le_of_lt_succ h), subNatNat]
@@ -196,6 +200,7 @@ where
     simp
     rw [Int.add_comm, subNatNat_add_negSucc]
     simp [Nat.add_comm, Nat.add_left_comm, Nat.add_assoc]
+instance : Std.Associative (α := Int) (· + ·) := ⟨Int.add_assoc⟩
 
 protected theorem add_left_comm (a b c : Int) : a + (b + c) = b + (a + c) := by
   rw [← Int.add_assoc, Int.add_comm a, Int.add_assoc]
@@ -351,6 +356,7 @@ protected theorem sub_right_inj (i j k : Int) : (i - k = j - k) ↔ i = j := by
 
 protected theorem mul_comm (a b : Int) : a * b = b * a := by
   cases a <;> cases b <;> simp [Nat.mul_comm]
+instance : Std.Commutative (α := Int) (· * ·) := ⟨Int.mul_comm⟩
 
 theorem ofNat_mul_negOfNat (m n : Nat) : (m : Nat) * negOfNat n = negOfNat (m * n) := by
   cases n <;> rfl
@@ -369,6 +375,7 @@ attribute [local simp] ofNat_mul_negOfNat negOfNat_mul_ofNat
 
 protected theorem mul_assoc (a b c : Int) : a * b * c = a * (b * c) := by
   cases a <;> cases b <;> cases c <;> simp [Nat.mul_assoc]
+instance : Std.Associative (α := Int) (· * ·) := ⟨Int.mul_assoc⟩
 
 protected theorem mul_left_comm (a b c : Int) : a * (b * c) = b * (a * c) := by
   rw [← Int.mul_assoc, ← Int.mul_assoc, Int.mul_comm a]
@@ -458,6 +465,9 @@ protected theorem sub_mul (a b c : Int) : (a - b) * c = a * c - b * c := by
   | -[n+1]  => show -[1 * n +1] = -[n+1] by rw [Nat.one_mul]
 
 @[simp] protected theorem mul_one (a : Int) : a * 1 = a := by rw [Int.mul_comm, Int.one_mul]
+instance : Std.LawfulIdentity (α := Int) (· * ·) 1 where
+  left_id := Int.one_mul
+  right_id := Int.mul_one
 
 protected theorem mul_neg_one (a : Int) : a * -1 = -a := by rw [Int.mul_neg, Int.mul_one]
 

src/Init/Data/Int/Order.lean

@@ -187,6 +187,7 @@ protected theorem min_comm (a b : Int) : min a b = min b a := by
   by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
   · exact Int.le_antisymm h₁ h₂
   · cases not_or_intro h₁ h₂ <| Int.le_total ..
+instance : Std.Commutative (α := Int) min := ⟨Int.min_comm⟩
 
 protected theorem min_le_right (a b : Int) : min a b ≤ b := by rw [Int.min_def]; split <;> simp [*]
 
@@ -206,6 +207,7 @@ protected theorem max_comm (a b : Int) : max a b = max b a := by
   by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
   · exact Int.le_antisymm h₂ h₁
   · cases not_or_intro h₁ h₂ <| Int.le_total ..
+instance : Std.Commutative (α := Int) max := ⟨Int.max_comm⟩
 
 protected theorem le_max_left (a b : Int) : a ≤ max a b := by rw [Int.max_def]; split <;> simp [*]
 

src/Init/Data/List.lean

@@ -9,3 +9,4 @@ import Init.Data.List.BasicAux
 import Init.Data.List.Control
 import Init.Data.List.Lemmas
 import Init.Data.List.Impl
+import Init.Data.List.TakeDrop

src/Init/Data/List/Basic.lean

@@ -127,6 +127,9 @@ instance : Append (List α) := ⟨List.append⟩
   | nil => rfl
   | cons a as ih =>
     simp_all [HAppend.hAppend, Append.append, List.append]
+instance : Std.LawfulIdentity (α := List α) (· ++ ·) [] where
+  left_id := nil_append
+  right_id := append_nil
 
 @[simp] theorem cons_append (a : α) (as bs : List α) : (a::as) ++ bs = a::(as ++ bs) := rfl
 
@@ -136,6 +139,7 @@ theorem append_assoc (as bs cs : List α) : (as ++ bs) ++ cs = as ++ (bs ++ cs)
   induction as with
   | nil => rfl
   | cons a as ih => simp [ih]
+instance : Std.Associative (α := List α) (· ++ ·) := ⟨append_assoc⟩
 
 theorem append_cons (as : List α) (b : α) (bs : List α) : as ++ b :: bs = as ++ [b] ++ bs := by
   induction as with

src/Init/Data/List/BasicAux.lean

@@ -5,6 +5,7 @@ Author: Leonardo de Moura
 -/
 prelude
 import Init.Data.Nat.Linear
+import Init.Ext
 
 universe u
 
@@ -43,6 +44,14 @@ See also `get?` and `get!`.
 def getD (as : List α) (i : Nat) (fallback : α) : α :=
   (as.get? i).getD fallback
 
+@[ext] theorem ext : ∀ {l₁ l₂ : List α}, (∀ n, l₁.get? n = l₂.get? n) → l₁ = l₂
+  | [], [], _ => rfl
+  | a :: l₁, [], h => nomatch h 0
+  | [], a' :: l₂, h => nomatch h 0
+  | a :: l₁, a' :: l₂, h => by
+    have h0 : some a = some a' := h 0
+    injection h0 with aa; simp only [aa, ext fun n => h (n+1)]
+
 /--
 Returns the first element in the list.
 
@@ -148,6 +157,13 @@ def getLastD : (as : List α) → (fallback : α) → α
   | [],   a₀ => a₀
   | a::as, _ => getLast (a::as) (fun h => List.noConfusion h)
 
+/--
+`O(n)`. Rotates the elements of `xs` to the left such that the element at
+`xs[i]` rotates to `xs[(i - n) % l.length]`.
+* `rotateLeft [1, 2, 3, 4, 5] 3 = [4, 5, 1, 2, 3]`
+* `rotateLeft [1, 2, 3, 4, 5] 5 = [1, 2, 3, 4, 5]`
+* `rotateLeft [1, 2, 3, 4, 5] = [2, 3, 4, 5, 1]`
+-/
 def rotateLeft (xs : List α) (n : Nat := 1) : List α :=
   let len := xs.length
   if len ≤ 1 then
@@ -158,6 +174,13 @@ def rotateLeft (xs : List α) (n : Nat := 1) : List α :=
     let e := xs.drop n
     e ++ b
 
+/--
+`O(n)`. Rotates the elements of `xs` to the right such that the element at
+`xs[i]` rotates to `xs[(i + n) % l.length]`.
+* `rotateRight [1, 2, 3, 4, 5] 3 = [3, 4, 5, 1, 2]`
+* `rotateRight [1, 2, 3, 4, 5] 5 = [1, 2, 3, 4, 5]`
+* `rotateRight [1, 2, 3, 4, 5] = [5, 1, 2, 3, 4]`
+-/
 def rotateRight (xs : List α) (n : Nat := 1) : List α :=
   let len := xs.length
   if len ≤ 1 then
@@ -203,9 +226,10 @@ theorem sizeOf_lt_of_mem [SizeOf α] {as : List α} (h : a ∈ as) : sizeOf a <
 over a nested inductive like `inductive T | mk : List T → T`. -/
 macro "sizeOf_list_dec" : tactic =>
   `(tactic| first
-    | apply sizeOf_lt_of_mem; assumption; done
-    | apply Nat.lt_trans (sizeOf_lt_of_mem ?h)
-      case' h => assumption
+    | with_reducible apply sizeOf_lt_of_mem; assumption; done
+    | with_reducible
+        apply Nat.lt_trans (sizeOf_lt_of_mem ?h)
+        case' h => assumption
       simp_arith)
 
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| sizeOf_list_dec)
@@ -288,6 +312,15 @@ def mapMono (as : List α) (f : α → α) : List α :=
 Monadic generalization of `List.partition`.
 
 This uses `Array.toList` and which isn't imported by `Init.Data.List.Basic`.
+```
+def posOrNeg (x : Int) : Except String Bool :=
+  if x > 0 then pure true
+  else if x < 0 then pure false
+  else throw "Zero is not positive or negative"
+
+partitionM posOrNeg [-1, 2, 3] = Except.ok ([2, 3], [-1])
+partitionM posOrNeg [0, 2, 3] = Except.error "Zero is not positive or negative"
+```
 -/
 @[inline] def partitionM [Monad m] (p : α → m Bool) (l : List α) : m (List α × List α) :=
   go l #[] #[]

src/Init/Data/List/TakeDrop.lean

@@ -0,0 +1,360 @@
+/-
+Copyright (c) 2014 Parikshit Khanna. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
+-/
+prelude
+import Init.Data.List.Lemmas
+import Init.Data.Nat.Lemmas
+
+/-!
+# Lemmas about `List.take`, `List.drop`, `List.zip` and `List.zipWith`.
+
+These are in a separate file from most of the list lemmas
+as they required importing more lemmas about natural numbers.
+-/
+
+namespace List
+
+open Nat
+
+/-! ### take -/
+
+abbrev take_succ_cons := @take_cons_succ
+
+@[simp] theorem length_take : ∀ (i : Nat) (l : List α), length (take i l) = min i (length l)
+  | 0, l => by simp [Nat.zero_min]
+  | succ n, [] => by simp [Nat.min_zero]
+  | succ n, _ :: l => by simp [Nat.succ_min_succ, length_take]
+
+theorem length_take_le (n) (l : List α) : length (take n l) ≤ n := by simp [Nat.min_le_left]
+
+theorem length_take_le' (n) (l : List α) : length (take n l) ≤ l.length :=
+  by simp [Nat.min_le_right]
+
+theorem length_take_of_le (h : n ≤ length l) : length (take n l) = n := by simp [Nat.min_eq_left h]
+
+theorem take_all_of_le {n} {l : List α} (h : length l ≤ n) : take n l = l :=
+  take_length_le h
+
+@[simp]
+theorem take_left : ∀ l₁ l₂ : List α, take (length l₁) (l₁ ++ l₂) = l₁
+  | [], _ => rfl
+  | a :: l₁, l₂ => congrArg (cons a) (take_left l₁ l₂)
+
+theorem take_left' {l₁ l₂ : List α} {n} (h : length l₁ = n) : take n (l₁ ++ l₂) = l₁ := by
+  rw [← h]; apply take_left
+
+theorem take_take : ∀ (n m) (l : List α), take n (take m l) = take (min n m) l
+  | n, 0, l => by rw [Nat.min_zero, take_zero, take_nil]
+  | 0, m, l => by rw [Nat.zero_min, take_zero, take_zero]
+  | succ n, succ m, nil => by simp only [take_nil]
+  | succ n, succ m, a :: l => by
+    simp only [take, succ_min_succ, take_take n m l]
+
+theorem take_replicate (a : α) : ∀ n m : Nat, take n (replicate m a) = replicate (min n m) a
+  | n, 0 => by simp [Nat.min_zero]
+  | 0, m => by simp [Nat.zero_min]
+  | succ n, succ m => by simp [succ_min_succ, take_replicate]
+
+theorem map_take (f : α → β) :
+    ∀ (L : List α) (i : Nat), (L.take i).map f = (L.map f).take i
+  | [], i => by simp
+  | _, 0 => by simp
+  | h :: t, n + 1 => by dsimp; rw [map_take f t n]
+
+/-- Taking the first `n` elements in `l₁ ++ l₂` is the same as appending the first `n` elements
+of `l₁` to the first `n - l₁.length` elements of `l₂`. -/
+theorem take_append_eq_append_take {l₁ l₂ : List α} {n : Nat} :
+    take n (l₁ ++ l₂) = take n l₁ ++ take (n - l₁.length) l₂ := by
+  induction l₁ generalizing n
+  · simp
+  · cases n
+    · simp [*]
+    · simp only [cons_append, take_cons_succ, length_cons, succ_eq_add_one, cons.injEq,
+        append_cancel_left_eq, true_and, *]
+      congr 1
+      omega
+
+theorem take_append_of_le_length {l₁ l₂ : List α} {n : Nat} (h : n ≤ l₁.length) :
+    (l₁ ++ l₂).take n = l₁.take n := by
+  simp [take_append_eq_append_take, Nat.sub_eq_zero_of_le h]
+
+/-- Taking the first `l₁.length + i` elements in `l₁ ++ l₂` is the same as appending the first
+`i` elements of `l₂` to `l₁`. -/
+theorem take_append {l₁ l₂ : List α} (i : Nat) :
+    take (l₁.length + i) (l₁ ++ l₂) = l₁ ++ take i l₂ := by
+  rw [take_append_eq_append_take, take_all_of_le (Nat.le_add_right _ _), Nat.add_sub_cancel_left]
+
+/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
+length `> i`. Version designed to rewrite from the big list to the small list. -/
+theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
+    get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ :=
+  get_of_eq (take_append_drop j L).symm _ ▸ get_append ..
+
+/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
+length `> i`. Version designed to rewrite from the small list to the big list. -/
+theorem get_take' (L : List α) {j i} :
+    get (L.take j) i =
+    get L ⟨i.1, Nat.lt_of_lt_of_le i.2 (length_take_le' _ _)⟩ := by
+  let ⟨i, hi⟩ := i; rw [length_take, Nat.lt_min] at hi; rw [get_take L _ hi.1]
+
+theorem get?_take {l : List α} {n m : Nat} (h : m < n) : (l.take n).get? m = l.get? m := by
+  induction n generalizing l m with
+  | zero =>
+    exact absurd h (Nat.not_lt_of_le m.zero_le)
+  | succ _ hn =>
+    cases l with
+    | nil => simp only [take_nil]
+    | cons hd tl =>
+      cases m
+      · simp only [get?, take]
+      · simpa only using hn (Nat.lt_of_succ_lt_succ h)
+
+theorem get?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
+    (l.take n).get? m = none :=
+  get?_eq_none.mpr <| Nat.le_trans (length_take_le _ _) h
+
+theorem get?_take_eq_if {l : List α} {n m : Nat} :
+    (l.take n).get? m = if m < n then l.get? m else none := by
+  split
+  · next h => exact get?_take h
+  · next h => exact get?_take_eq_none (Nat.le_of_not_lt h)
+
+@[simp]
+theorem nth_take_of_succ {l : List α} {n : Nat} : (l.take (n + 1)).get? n = l.get? n :=
+  get?_take (Nat.lt_succ_self n)
+
+theorem take_succ {l : List α} {n : Nat} : l.take (n + 1) = l.take n ++ (l.get? n).toList := by
+  induction l generalizing n with
+  | nil =>
+    simp only [Option.toList, get?, take_nil, append_nil]
+  | cons hd tl hl =>
+    cases n
+    · simp only [Option.toList, get?, eq_self_iff_true, take, nil_append]
+    · simp only [hl, cons_append, get?, eq_self_iff_true, take]
+
+@[simp]
+theorem take_eq_nil_iff {l : List α} {k : Nat} : l.take k = [] ↔ l = [] ∨ k = 0 := by
+  cases l <;> cases k <;> simp [Nat.succ_ne_zero]
+
+@[simp]
+theorem take_eq_take :
+    ∀ {l : List α} {m n : Nat}, l.take m = l.take n ↔ min m l.length = min n l.length
+  | [], m, n => by simp [Nat.min_zero]
+  | _ :: xs, 0, 0 => by simp
+  | x :: xs, m + 1, 0 => by simp [Nat.zero_min, succ_min_succ]
+  | x :: xs, 0, n + 1 => by simp [Nat.zero_min, succ_min_succ]
+  | x :: xs, m + 1, n + 1 => by simp [succ_min_succ, take_eq_take]; omega
+
+theorem take_add (l : List α) (m n : Nat) : l.take (m + n) = l.take m ++ (l.drop m).take n := by
+  suffices take (m + n) (take m l ++ drop m l) = take m l ++ take n (drop m l) by
+    rw [take_append_drop] at this
+    assumption
+  rw [take_append_eq_append_take, take_all_of_le, append_right_inj]
+  · simp only [take_eq_take, length_take, length_drop]
+    omega
+  apply Nat.le_trans (m := m)
+  · apply length_take_le
+  · apply Nat.le_add_right
+
+theorem take_eq_nil_of_eq_nil : ∀ {as : List α} {i}, as = [] → as.take i = []
+  | _, _, rfl => take_nil
+
+theorem ne_nil_of_take_ne_nil {as : List α} {i : Nat} (h: as.take i ≠ []) : as ≠ [] :=
+  mt take_eq_nil_of_eq_nil h
+
+theorem dropLast_eq_take (l : List α) : l.dropLast = l.take l.length.pred := by
+  cases l with
+  | nil => simp [dropLast]
+  | cons x l =>
+    induction l generalizing x with
+    | nil => simp [dropLast]
+    | cons hd tl hl => simp [dropLast, hl]
+
+theorem dropLast_take {n : Nat} {l : List α} (h : n < l.length) :
+    (l.take n).dropLast = l.take n.pred := by
+  simp only [dropLast_eq_take, length_take, Nat.le_of_lt h, take_take, pred_le, Nat.min_eq_left]
+
+theorem map_eq_append_split {f : α → β} {l : List α} {s₁ s₂ : List β}
+    (h : map f l = s₁ ++ s₂) : ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = s₁ ∧ map f l₂ = s₂ := by
+  have := h
+  rw [← take_append_drop (length s₁) l] at this ⊢
+  rw [map_append] at this
+  refine ⟨_, _, rfl, append_inj this ?_⟩
+  rw [length_map, length_take, Nat.min_eq_left]
+  rw [← length_map l f, h, length_append]
+  apply Nat.le_add_right
+
+/-! ### drop -/
+
+@[simp]
+theorem drop_eq_nil_iff_le {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by
+  refine' ⟨fun h => _, drop_eq_nil_of_le⟩
+  induction k generalizing l with
+  | zero =>
+    simp only [drop] at h
+    simp [h]
+  | succ k hk =>
+    cases l
+    · simp
+    · simp only [drop] at h
+      simpa [Nat.succ_le_succ_iff] using hk h
+
+theorem drop_length_cons {l : List α} (h : l ≠ []) (a : α) :
+    (a :: l).drop l.length = [l.getLast h] := by
+  induction l generalizing a with
+  | nil =>
+    cases h rfl
+  | cons y l ih =>
+    simp only [drop, length]
+    by_cases h₁ : l = []
+    · simp [h₁]
+    rw [getLast_cons' _ h₁]
+    exact ih h₁ y
+
+/-- Dropping the elements up to `n` in `l₁ ++ l₂` is the same as dropping the elements up to `n`
+in `l₁`, dropping the elements up to `n - l₁.length` in `l₂`, and appending them. -/
+theorem drop_append_eq_append_drop {l₁ l₂ : List α} {n : Nat} :
+    drop n (l₁ ++ l₂) = drop n l₁ ++ drop (n - l₁.length) l₂ := by
+  induction l₁ generalizing n
+  · simp
+  · cases n
+    · simp [*]
+    · simp only [cons_append, drop_succ_cons, length_cons, succ_eq_add_one, append_cancel_left_eq, *]
+      congr 1
+      omega
+
+theorem drop_append_of_le_length {l₁ l₂ : List α} {n : Nat} (h : n ≤ l₁.length) :
+    (l₁ ++ l₂).drop n = l₁.drop n ++ l₂ := by
+  simp [drop_append_eq_append_drop, Nat.sub_eq_zero_of_le h]
+
+
+/-- Dropping the elements up to `l₁.length + i` in `l₁ + l₂` is the same as dropping the elements
+up to `i` in `l₂`. -/
+@[simp]
+theorem drop_append {l₁ l₂ : List α} (i : Nat) : drop (l₁.length + i) (l₁ ++ l₂) = drop i l₂ := by
+  rw [drop_append_eq_append_drop, drop_eq_nil_of_le] <;>
+    simp [Nat.add_sub_cancel_left, Nat.le_add_right]
+
+theorem drop_sizeOf_le [SizeOf α] (l : List α) (n : Nat) : sizeOf (l.drop n) ≤ sizeOf l := by
+  induction l generalizing n with
+  | nil => rw [drop_nil]; apply Nat.le_refl
+  | cons _ _ lih =>
+    induction n with
+    | zero => apply Nat.le_refl
+    | succ n =>
+      exact Trans.trans (lih _) (Nat.le_add_left _ _)
+
+theorem lt_length_drop (L : List α) {i j : Nat} (h : i + j < L.length) : j < (L.drop i).length := by
+  have A : i < L.length := Nat.lt_of_le_of_lt (Nat.le.intro rfl) h
+  rw [(take_append_drop i L).symm] at h
+  simpa only [Nat.le_of_lt A, Nat.min_eq_left, Nat.add_lt_add_iff_left, length_take,
+    length_append] using h
+
+/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
+dropping the first `i` elements. Version designed to rewrite from the big list to the small list. -/
+theorem get_drop (L : List α) {i j : Nat} (h : i + j < L.length) :
+    get L ⟨i + j, h⟩ = get (L.drop i) ⟨j, lt_length_drop L h⟩ := by
+  have : i ≤ L.length := Nat.le_trans (Nat.le_add_right _ _) (Nat.le_of_lt h)
+  rw [get_of_eq (take_append_drop i L).symm ⟨i + j, h⟩, get_append_right'] <;>
+    simp [Nat.min_eq_left this, Nat.add_sub_cancel_left, Nat.le_add_right]
+
+/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
+dropping the first `i` elements. Version designed to rewrite from the small list to the big list. -/
+theorem get_drop' (L : List α) {i j} :
+    get (L.drop i) j = get L ⟨i + j, by
+      rw [Nat.add_comm]
+      exact Nat.add_lt_of_lt_sub (length_drop i L ▸ j.2)⟩ := by
+  rw [get_drop]
+
+@[simp]
+theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j) := by
+  ext
+  simp only [get?_eq_some, get_drop', Option.mem_def]
+  constructor <;> intro ⟨h, ha⟩
+  · exact ⟨_, ha⟩
+  · refine ⟨?_, ha⟩
+    rw [length_drop]
+    rw [Nat.add_comm] at h
+    apply Nat.lt_sub_of_add_lt h
+
+@[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (n + m) l
+  | m, [] => by simp
+  | 0, l => by simp
+  | m + 1, a :: l =>
+    calc
+      drop n (drop (m + 1) (a :: l)) = drop n (drop m l) := rfl
+      _ = drop (n + m) l := drop_drop n m l
+      _ = drop (n + (m + 1)) (a :: l) := rfl
+
+theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (take (m + n) l)
+  | 0, _, _ => by simp
+  | _, _, [] => by simp
+  | _+1, _, _ :: _ => by simpa [Nat.succ_add, take_succ_cons, drop_succ_cons] using take_drop ..
+
+theorem drop_take : ∀ (m n : Nat) (l : List α), drop n (take m l) = take (m - n) (drop n l)
+  | 0, _, _ => by simp
+  | _, 0, _ => by simp
+  | _, _, [] => by simp
+  | m+1, n+1, h :: t => by
+    simp [take_succ_cons, drop_succ_cons, drop_take m n t]
+    congr 1
+    omega
+
+theorem map_drop (f : α → β) :
+    ∀ (L : List α) (i : Nat), (L.drop i).map f = (L.map f).drop i
+  | [], i => by simp
+  | L, 0 => by simp
+  | h :: t, n + 1 => by
+    dsimp
+    rw [map_drop f t]
+
+theorem reverse_take {α} {xs : List α} (n : Nat) (h : n ≤ xs.length) :
+    xs.reverse.take n = (xs.drop (xs.length - n)).reverse := by
+  induction xs generalizing n <;>
+    simp only [reverse_cons, drop, reverse_nil, Nat.zero_sub, length, take_nil]
+  next xs_hd xs_tl xs_ih =>
+  cases Nat.lt_or_eq_of_le h with
+  | inl h' =>
+    have h' := Nat.le_of_succ_le_succ h'
+    rw [take_append_of_le_length, xs_ih _ h']
+    rw [show xs_tl.length + 1 - n = succ (xs_tl.length - n) from _, drop]
+    · rwa [succ_eq_add_one, Nat.sub_add_comm]
+    · rwa [length_reverse]
+  | inr h' =>
+    subst h'
+    rw [length, Nat.sub_self, drop]
+    suffices xs_tl.length + 1 = (xs_tl.reverse ++ [xs_hd]).length by
+      rw [this, take_length, reverse_cons]
+    rw [length_append, length_reverse]
+    rfl
+
+@[simp]
+theorem get_cons_drop : ∀ (l : List α) i, get l i :: drop (i + 1) l = drop i l
+  | _::_, ⟨0, _⟩ => rfl
+  | _::_, ⟨i+1, _⟩ => get_cons_drop _ ⟨i, _⟩
+
+theorem drop_eq_get_cons {n} {l : List α} (h) : drop n l = get l ⟨n, h⟩ :: drop (n + 1) l :=
+  (get_cons_drop _ ⟨n, h⟩).symm
+
+theorem drop_eq_nil_of_eq_nil : ∀ {as : List α} {i}, as = [] → as.drop i = []
+  | _, _, rfl => drop_nil
+
+theorem ne_nil_of_drop_ne_nil {as : List α} {i : Nat} (h: as.drop i ≠ []) : as ≠ [] :=
+  mt drop_eq_nil_of_eq_nil h
+
+/-! ### zipWith -/
+
+@[simp] theorem length_zipWith (f : α → β → γ) (l₁ l₂) :
+    length (zipWith f l₁ l₂) = min (length l₁) (length l₂) := by
+  induction l₁ generalizing l₂ <;> cases l₂ <;>
+    simp_all [succ_min_succ, Nat.zero_min, Nat.min_zero]
+
+/-! ### zip -/
+
+@[simp] theorem length_zip (l₁ : List α) (l₂ : List β) :
+    length (zip l₁ l₂) = min (length l₁) (length l₂) := by
+  simp [zip]
+
+end List

src/Init/Data/Nat/Basic.lean

@@ -137,6 +137,9 @@ instance : LawfulBEq Nat where
 @[simp] protected theorem zero_add : ∀ (n : Nat), 0 + n = n
   | 0   => rfl
   | n+1 => congrArg succ (Nat.zero_add n)
+instance : Std.LawfulIdentity (α := Nat) (· + ·) 0 where
+  left_id := Nat.zero_add
+  right_id := Nat.add_zero
 
 theorem succ_add : ∀ (n m : Nat), (succ n) + m = succ (n + m)
   | _, 0   => rfl
@@ -160,10 +163,12 @@ protected theorem add_comm : ∀ (n m : Nat), n + m = m + n
     have : succ (n + m) = succ (m + n) := by apply congrArg; apply Nat.add_comm
     rw [succ_add m n]
     apply this
+instance : Std.Commutative (α := Nat) (· + ·) := ⟨Nat.add_comm⟩
 
 protected theorem add_assoc : ∀ (n m k : Nat), (n + m) + k = n + (m + k)
   | _, _, 0      => rfl
   | n, m, succ k => congrArg succ (Nat.add_assoc n m k)
+instance : Std.Associative (α := Nat) (· + ·) := ⟨Nat.add_assoc⟩
 
 protected theorem add_left_comm (n m k : Nat) : n + (m + k) = m + (n + k) := by
   rw [← Nat.add_assoc, Nat.add_comm n m, Nat.add_assoc]
@@ -207,12 +212,16 @@ theorem succ_mul (n m : Nat) : (succ n) * m = (n * m) + m := by
 protected theorem mul_comm : ∀ (n m : Nat), n * m = m * n
   | n, 0      => (Nat.zero_mul n).symm ▸ (Nat.mul_zero n).symm ▸ rfl
   | n, succ m => (mul_succ n m).symm ▸ (succ_mul m n).symm ▸ (Nat.mul_comm n m).symm ▸ rfl
+instance : Std.Commutative (α := Nat) (· * ·) := ⟨Nat.mul_comm⟩
 
 @[simp] protected theorem mul_one : ∀ (n : Nat), n * 1 = n :=
   Nat.zero_add
 
 @[simp] protected theorem one_mul (n : Nat) : 1 * n = n :=
   Nat.mul_comm n 1 ▸ Nat.mul_one n
+instance : Std.LawfulIdentity (α := Nat) (· * ·) 1 where
+  left_id := Nat.one_mul
+  right_id := Nat.mul_one
 
 protected theorem left_distrib (n m k : Nat) : n * (m + k) = n * m + n * k := by
   induction n with
@@ -231,6 +240,7 @@ protected theorem add_mul (n m k : Nat) : (n + m) * k = n * k + m * k :=
 protected theorem mul_assoc : ∀ (n m k : Nat), (n * m) * k = n * (m * k)
   | n, m, 0      => rfl
   | n, m, succ k => by simp [mul_succ, Nat.mul_assoc n m k, Nat.left_distrib]
+instance : Std.Associative (α := Nat) (· * ·) := ⟨Nat.mul_assoc⟩
 
 protected theorem mul_left_comm (n m k : Nat) : n * (m * k) = m * (n * k) := by
   rw [← Nat.mul_assoc, Nat.mul_comm n m, Nat.mul_assoc]

src/Init/Data/Nat/Gcd.lean

@@ -54,9 +54,13 @@ theorem gcd_succ (x y : Nat) : gcd (succ x) y = gcd (y % succ x) (succ x) :=
     -- `simp [gcd_succ]` produces an invalid term unless `gcd_succ` is proved with `id rfl` instead
     rw [gcd_succ]
     exact gcd_zero_left _
+instance : Std.LawfulIdentity gcd 0 where
+  left_id := gcd_zero_left
+  right_id := gcd_zero_right
 
 @[simp] theorem gcd_self (n : Nat) : gcd n n = n := by
   cases n <;> simp [gcd_succ]
+instance : Std.IdempotentOp gcd := ⟨gcd_self⟩
 
 theorem gcd_rec (m n : Nat) : gcd m n = gcd (n % m) m :=
   match m with
@@ -97,6 +101,7 @@ theorem gcd_comm (m n : Nat) : gcd m n = gcd n m :=
   Nat.dvd_antisymm
     (dvd_gcd (gcd_dvd_right m n) (gcd_dvd_left m n))
     (dvd_gcd (gcd_dvd_right n m) (gcd_dvd_left n m))
+instance : Std.Commutative gcd := ⟨gcd_comm⟩
 
 theorem gcd_eq_left_iff_dvd : m ∣ n ↔ gcd m n = m :=
   ⟨fun h => by rw [gcd_rec, mod_eq_zero_of_dvd h, gcd_zero_left],

src/Init/Data/Nat/Lcm.lean

@@ -14,6 +14,7 @@ def lcm (m n : Nat) : Nat := m * n / gcd m n
 
 theorem lcm_comm (m n : Nat) : lcm m n = lcm n m := by
   rw [lcm, lcm, Nat.mul_comm n m, gcd_comm n m]
+instance : Std.Commutative lcm := ⟨lcm_comm⟩
 
 @[simp] theorem lcm_zero_left (m : Nat) : lcm 0 m = 0 := by simp [lcm]
 
@@ -22,11 +23,15 @@ theorem lcm_comm (m n : Nat) : lcm m n = lcm n m := by
 @[simp] theorem lcm_one_left (m : Nat) : lcm 1 m = m := by simp [lcm]
 
 @[simp] theorem lcm_one_right (m : Nat) : lcm m 1 = m := by simp [lcm]
+instance : Std.LawfulIdentity lcm 1 where
+  left_id := lcm_one_left
+  right_id := lcm_one_right
 
 @[simp] theorem lcm_self (m : Nat) : lcm m m = m := by
   match eq_zero_or_pos m with
   | .inl h => rw [h, lcm_zero_left]
   | .inr h => simp [lcm, Nat.mul_div_cancel _ h]
+instance : Std.IdempotentOp lcm := ⟨lcm_self⟩
 
 theorem dvd_lcm_left (m n : Nat) : m ∣ lcm m n :=
   ⟨n / gcd m n, by rw [← Nat.mul_div_assoc m (Nat.gcd_dvd_right m n)]; rfl⟩
@@ -54,6 +59,7 @@ Nat.dvd_antisymm
     (Nat.dvd_trans (dvd_lcm_left m n) (dvd_lcm_left (lcm m n) k))
     (lcm_dvd (Nat.dvd_trans (dvd_lcm_right m n) (dvd_lcm_left (lcm m n) k))
       (dvd_lcm_right (lcm m n) k)))
+instance : Std.Associative lcm := ⟨lcm_assoc⟩
 
 theorem lcm_ne_zero (hm : m ≠ 0) (hn : n ≠ 0) : lcm m n ≠ 0 := by
   intro h

src/Init/Data/Nat/Lemmas.lean

@@ -200,6 +200,7 @@ theorem succ_min_succ (x y) : min (succ x) (succ y) = succ (min x y) := by
   | inr h => rw [Nat.min_eq_right h, Nat.min_eq_right (Nat.succ_le_succ h)]
 
 @[simp] protected theorem min_self (a : Nat) : min a a = a := Nat.min_eq_left (Nat.le_refl _)
+instance : Std.IdempotentOp (α := Nat) min := ⟨Nat.min_self⟩
 
 @[simp] protected theorem zero_min (a) : min 0 a = 0 := Nat.min_eq_left (Nat.zero_le _)
 
@@ -210,6 +211,7 @@ protected theorem min_assoc : ∀ (a b c : Nat), min (min a b) c = min a (min b
   | _, 0, _ => by rw [Nat.zero_min, Nat.min_zero, Nat.zero_min]
   | _, _, 0 => by rw [Nat.min_zero, Nat.min_zero, Nat.min_zero]
   | _+1, _+1, _+1 => by simp only [Nat.succ_min_succ]; exact congrArg succ <| Nat.min_assoc ..
+instance : Std.Associative (α := Nat) min := ⟨Nat.min_assoc⟩
 
 protected theorem sub_sub_eq_min : ∀ (a b : Nat), a - (a - b) = min a b
   | 0, _ => by rw [Nat.zero_sub, Nat.zero_min]
@@ -249,16 +251,21 @@ protected theorem max_lt {a b c : Nat} : max a b < c ↔ a < c ∧ b < c := by
   rw [← Nat.succ_le, ← Nat.succ_max_succ a b]; exact Nat.max_le
 
 @[simp] protected theorem max_self (a : Nat) : max a a = a := Nat.max_eq_right (Nat.le_refl _)
+instance : Std.IdempotentOp (α := Nat) max := ⟨Nat.max_self⟩
 
 @[simp] protected theorem zero_max (a) : max 0 a = a := Nat.max_eq_right (Nat.zero_le _)
 
 @[simp] protected theorem max_zero (a) : max a 0 = a := Nat.max_eq_left (Nat.zero_le _)
+instance : Std.LawfulIdentity (α := Nat) max 0 where
+  left_id := Nat.zero_max
+  right_id := Nat.max_zero
 
 protected theorem max_assoc : ∀ (a b c : Nat), max (max a b) c = max a (max b c)
   | 0, _, _ => by rw [Nat.zero_max, Nat.zero_max]
   | _, 0, _ => by rw [Nat.zero_max, Nat.max_zero]
   | _, _, 0 => by rw [Nat.max_zero, Nat.max_zero]
   | _+1, _+1, _+1 => by simp only [Nat.succ_max_succ]; exact congrArg succ <| Nat.max_assoc ..
+instance : Std.Associative (α := Nat) max := ⟨Nat.max_assoc⟩
 
 protected theorem sub_add_eq_max (a b : Nat) : a - b + b = max a b := by
   match Nat.le_total a b with

src/Init/Data/Nat/MinMax.lean

@@ -17,6 +17,7 @@ protected theorem min_comm (a b : Nat) : min a b = min b a := by
   | .inl h => simp [Nat.min_def, h, Nat.le_of_lt, Nat.not_le_of_lt]
   | .inr (.inl h) => simp [Nat.min_def, h]
   | .inr (.inr h) => simp [Nat.min_def, h, Nat.le_of_lt, Nat.not_le_of_lt]
+instance : Std.Commutative (α := Nat) min := ⟨Nat.min_comm⟩
 
 protected theorem min_le_right (a b : Nat) : min a b ≤ b := by
   by_cases (a <= b) <;> simp [Nat.min_def, *]
@@ -47,6 +48,7 @@ protected theorem max_comm (a b : Nat) : max a b = max b a := by
   by_cases h₁ : a ≤ b <;> by_cases h₂ : b ≤ a <;> simp [h₁, h₂]
   · exact Nat.le_antisymm h₂ h₁
   · cases not_or_intro h₁ h₂ <| Nat.le_total ..
+instance : Std.Commutative (α := Nat) max := ⟨Nat.max_comm⟩
 
 protected theorem le_max_left ( a b : Nat) : a ≤ max a b := by
   by_cases (a <= b) <;> simp [Nat.max_def, *]

src/Init/Data/String/Extra.lean

@@ -132,13 +132,17 @@ theorem Iterator.sizeOf_next_lt_of_hasNext (i : String.Iterator) (h : i.hasNext)
   cases i; rename_i s pos; simp [Iterator.next, Iterator.sizeOf_eq]; simp [Iterator.hasNext] at h
   exact Nat.sub_lt_sub_left h (String.lt_next s pos)
 
-macro_rules | `(tactic| decreasing_trivial) => `(tactic| apply String.Iterator.sizeOf_next_lt_of_hasNext; assumption)
+macro_rules
+| `(tactic| decreasing_trivial) =>
+  `(tactic| with_reducible apply String.Iterator.sizeOf_next_lt_of_hasNext; assumption)
 
 theorem Iterator.sizeOf_next_lt_of_atEnd (i : String.Iterator) (h : ¬ i.atEnd = true) : sizeOf i.next < sizeOf i :=
   have h : i.hasNext := decide_eq_true <| Nat.gt_of_not_le <| mt decide_eq_true h
   sizeOf_next_lt_of_hasNext i h
 
-macro_rules | `(tactic| decreasing_trivial) => `(tactic| apply String.Iterator.sizeOf_next_lt_of_atEnd; assumption)
+macro_rules
+| `(tactic| decreasing_trivial) =>
+  `(tactic| with_reducible apply String.Iterator.sizeOf_next_lt_of_atEnd; assumption)
 
 namespace Iterator
 

src/Init/Meta.lean

@@ -1057,6 +1057,7 @@ where
     else
       Syntax.mkCApp (Name.mkStr2 "Array" ("mkArray" ++ toString xs.size)) args
   termination_by xs.size - i
+  decreasing_by decreasing_trivial_pre_omega
 
 instance [Quote α `term] : Quote (Array α) `term where
   quote := quoteArray

src/Init/Notation.lean

@@ -296,7 +296,7 @@ macro_rules | `($x - $y)   => `(binop% HSub.hSub $x $y)
 macro_rules | `($x * $y)   => `(binop% HMul.hMul $x $y)
 macro_rules | `($x / $y)   => `(binop% HDiv.hDiv $x $y)
 macro_rules | `($x % $y)   => `(binop% HMod.hMod $x $y)
--- exponentiation should be considered a right action (#2220)
+-- exponentiation should be considered a right action (#2854)
 macro_rules | `($x ^ $y)   => `(rightact% HPow.hPow $x $y)
 macro_rules | `($x ++ $y)  => `(binop% HAppend.hAppend $x $y)
 macro_rules | `(- $x)      => `(unop% Neg.neg $x)
@@ -492,9 +492,12 @@ The attribute `@[deprecated]` on a declaration indicates that the declaration
 is discouraged for use in new code, and/or should be migrated away from in
 existing code. It may be removed in a future version of the library.
 
-`@[deprecated myBetterDef]` means that `myBetterDef` is the suggested replacement.
+* `@[deprecated myBetterDef]` means that `myBetterDef` is the suggested replacement.
+* `@[deprecated myBetterDef "use myBetterDef instead"]` allows customizing the deprecation message.
+* `@[deprecated (since := "2024-04-21")]` records when the deprecation was first applied.
 -/
-syntax (name := deprecated) "deprecated" (ppSpace ident)? : attr
+syntax (name := deprecated) "deprecated" (ppSpace ident)? (ppSpace str)?
+    (" (" &"since" " := " str ")")? : attr
 
 /--
 The `@[coe]` attribute on a function (which should also appear in a
@@ -684,4 +687,27 @@ syntax (name := checkSimp) "#check_simp " term "~>" term : command
 -/
 syntax (name := checkSimpFailure) "#check_simp " term "!~>" : command
 
+/--
+The `seal foo` command ensures that the definition of `foo` is sealed, meaning it is marked as `[irreducible]`.
+This command is particularly useful in contexts where you want to prevent the reduction of `foo` in proofs.
+
+In terms of functionality, `seal foo` is equivalent to `attribute [local irreducible] foo`.
+This attribute specifies that `foo` should be treated as irreducible only within the local scope,
+which helps in maintaining the desired abstraction level without affecting global settings.
+-/
+syntax "seal " (ppSpace ident)+ : command
+
+/--
+The `unseal foo` command ensures that the definition of `foo` is unsealed, meaning it is marked as `[semireducible]`, the
+default reducibility setting. This command is useful when you need to allow some level of reduction of `foo` in proofs.
+
+Functionally, `unseal foo` is equivalent to `attribute [local semireducible] foo`.
+Applying this attribute makes `foo` semireducible only within the local scope.
+-/
+syntax "unseal " (ppSpace ident)+ : command
+
+macro_rules
+  | `(seal $fs:ident*) => `(attribute [local irreducible] $fs:ident*)
+  | `(unseal $fs:ident*) => `(attribute [local semireducible] $fs:ident*)
+
 end Parser

src/Init/Prelude.lean

@@ -4335,8 +4335,13 @@ def addMacroScope (mainModule : Name) (n : Name) (scp : MacroScope) : Name :=
     Name.mkNum (Name.mkStr (Name.appendCore (Name.mkStr n "_@") mainModule) "_hyg") scp
 
 /--
-Append two names that may have macro scopes. The macro scopes in `b` are always erased.
-If `a` has macro scopes, then they are propagated to the result of `append a b`.
+Appends two names `a` and `b`, propagating macro scopes from `a` or `b`, if any, to the result.
+Panics if both `a` and `b` have macro scopes.
+
+This function is used for the `Append Name` instance.
+
+See also `Lean.Name.appendCore`, which appends names without any consideration for macro scopes.
+Also consider `Lean.Name.eraseMacroScopes` to erase macro scopes before appending, if appropriate.
 -/
 def Name.append (a b : Name) : Name :=
   match a.hasMacroScopes, b.hasMacroScopes with
@@ -4367,7 +4372,7 @@ def defaultMaxRecDepth := 512
 
 /-- The message to display on stack overflow. -/
 def maxRecDepthErrorMessage : String :=
-  "maximum recursion depth has been reached (use `set_option maxRecDepth <num>` to increase limit)"
+  "maximum recursion depth has been reached\nuse `set_option maxRecDepth <num>` to increase limit\nuse `set_option diagnostics true` to get diagnostic information"
 
 namespace Syntax
 

src/Init/SimpLemmas.lean

@@ -103,18 +103,26 @@ end SimprocHelperLemmas
 
 @[simp] theorem and_true (p : Prop) : (p ∧ True) = p := propext ⟨(·.1), (⟨·, trivial⟩)⟩
 @[simp] theorem true_and (p : Prop) : (True ∧ p) = p := propext ⟨(·.2), (⟨trivial, ·⟩)⟩
+instance : Std.LawfulIdentity And True where
+  left_id := true_and
+  right_id := and_true
 @[simp] theorem and_false (p : Prop) : (p ∧ False) = False := eq_false (·.2)
 @[simp] theorem false_and (p : Prop) : (False ∧ p) = False := eq_false (·.1)
 @[simp] theorem and_self (p : Prop) : (p ∧ p) = p := propext ⟨(·.left), fun h => ⟨h, h⟩⟩
+instance : Std.IdempotentOp And := ⟨and_self⟩
 @[simp] theorem and_not_self : ¬(a ∧ ¬a) | ⟨ha, hn⟩ => absurd ha hn
 @[simp] theorem not_and_self : ¬(¬a ∧ a) := and_not_self ∘ And.symm
 @[simp] theorem and_imp : (a ∧ b → c) ↔ (a → b → c) := ⟨fun h ha hb => h ⟨ha, hb⟩, fun h ⟨ha, hb⟩ => h ha hb⟩
 @[simp] theorem not_and : ¬(a ∧ b) ↔ (a → ¬b) := and_imp
 @[simp] theorem or_self (p : Prop) : (p ∨ p) = p := propext ⟨fun | .inl h | .inr h => h, .inl⟩
+instance : Std.IdempotentOp Or := ⟨or_self⟩
 @[simp] theorem or_true (p : Prop) : (p ∨ True) = True := eq_true (.inr trivial)
 @[simp] theorem true_or (p : Prop) : (True ∨ p) = True := eq_true (.inl trivial)
 @[simp] theorem or_false (p : Prop) : (p ∨ False) = p := propext ⟨fun (.inl h) => h, .inl⟩
 @[simp] theorem false_or (p : Prop) : (False ∨ p) = p := propext ⟨fun (.inr h) => h, .inr⟩
+instance : Std.LawfulIdentity Or False where
+  left_id := false_or
+  right_id := or_false
 @[simp] theorem iff_self (p : Prop) : (p ↔ p) = True := eq_true .rfl
 @[simp] theorem iff_true (p : Prop) : (p ↔ True) = p := propext ⟨(·.2 trivial), fun h => ⟨fun _ => trivial, fun _ => h⟩⟩
 @[simp] theorem true_iff (p : Prop) : (True ↔ p) = p := propext ⟨(·.1 trivial), fun h => ⟨fun _ => h, fun _ => trivial⟩⟩
@@ -140,6 +148,7 @@ theorem and_congr_left (h : c → (a ↔ b)) : a ∧ c ↔ b ∧ c :=
 theorem and_assoc : (a ∧ b) ∧ c ↔ a ∧ (b ∧ c) :=
   Iff.intro (fun ⟨⟨ha, hb⟩, hc⟩ => ⟨ha, hb, hc⟩)
             (fun ⟨ha, hb, hc⟩ => ⟨⟨ha, hb⟩, hc⟩)
+instance : Std.Associative And := ⟨fun _ _ _ => propext and_assoc⟩
 
 @[simp] theorem and_self_left  : a ∧ (a ∧ b) ↔ a ∧ b := by rw [←propext and_assoc, and_self]
 @[simp] theorem and_self_right : (a ∧ b) ∧ b ↔ a ∧ b := by rw [ propext and_assoc, and_self]
@@ -167,6 +176,7 @@ theorem Or.imp_right (f : b → c) : a ∨ b → a ∨ c := .imp id f
 theorem or_assoc : (a ∨ b) ∨ c ↔ a ∨ (b ∨ c) :=
   Iff.intro (.rec (.imp_right .inl) (.inr ∘ .inr))
             (.rec (.inl ∘ .inl) (.imp_left .inr))
+instance : Std.Associative Or := ⟨fun _ _ _ => propext or_assoc⟩
 
 @[simp] theorem or_self_left  : a ∨ (a ∨ b) ↔ a ∨ b := by rw [←propext or_assoc, or_self]
 @[simp] theorem or_self_right : (a ∨ b) ∨ b ↔ a ∨ b := by rw [ propext or_assoc, or_self]
@@ -187,8 +197,12 @@ theorem or_iff_left_of_imp  (hb : b → a) : (a ∨ b) ↔ a  := Iff.intro (Or.r
 @[simp] theorem Bool.or_false (b : Bool) : (b || false) = b  := by cases b <;> rfl
 @[simp] theorem Bool.or_true (b : Bool) : (b || true) = true := by cases b <;> rfl
 @[simp] theorem Bool.false_or (b : Bool) : (false || b) = b  := by cases b <;> rfl
+instance : Std.LawfulIdentity (· || ·) false where
+  left_id := Bool.false_or
+  right_id := Bool.or_false
 @[simp] theorem Bool.true_or (b : Bool) : (true || b) = true := by cases b <;> rfl
 @[simp] theorem Bool.or_self (b : Bool) : (b || b) = b       := by cases b <;> rfl
+instance : Std.IdempotentOp (· || ·) := ⟨Bool.or_self⟩
 @[simp] theorem Bool.or_eq_true (a b : Bool) : ((a || b) = true) = (a = true ∨ b = true) := by
   cases a <;> cases b <;> decide
 
@@ -196,14 +210,20 @@ theorem or_iff_left_of_imp  (hb : b → a) : (a ∨ b) ↔ a  := Iff.intro (Or.r
 @[simp] theorem Bool.and_true (b : Bool) : (b && true) = b       := by cases b <;> rfl
 @[simp] theorem Bool.false_and (b : Bool) : (false && b) = false := by cases b <;> rfl
 @[simp] theorem Bool.true_and (b : Bool) : (true && b) = b       := by cases b <;> rfl
+instance : Std.LawfulIdentity (· && ·) true where
+  left_id := Bool.true_and
+  right_id := Bool.and_true
 @[simp] theorem Bool.and_self (b : Bool) : (b && b) = b          := by cases b <;> rfl
+instance : Std.IdempotentOp (· && ·) := ⟨Bool.and_self⟩
 @[simp] theorem Bool.and_eq_true (a b : Bool) : ((a && b) = true) = (a = true ∧ b = true) := by
   cases a <;> cases b <;> decide
 
 theorem Bool.and_assoc (a b c : Bool) : (a && b && c) = (a && (b && c)) := by
   cases a <;> cases b <;> cases c <;> decide
+instance : Std.Associative (· && ·) := ⟨Bool.and_assoc⟩
 theorem Bool.or_assoc (a b c : Bool) : (a || b || c) = (a || (b || c)) := by
   cases a <;> cases b <;> cases c <;> decide
+instance : Std.Associative (· || ·) := ⟨Bool.or_assoc⟩
 
 @[simp] theorem Bool.not_not (b : Bool) : (!!b) = b := by cases b <;> rfl
 @[simp] theorem Bool.not_true  : (!true) = false := by decide

src/Init/System/IO.lean

@@ -625,7 +625,13 @@ partial def FS.removeDirAll (p : FilePath) : IO Unit := do
 
 namespace Process
 
-/-- Returns the process ID of the current process. -/
+/-- Returns the current working directory of the calling process. -/
+@[extern "lean_io_process_get_current_dir"] opaque getCurrentDir : IO FilePath
+
+/-- Sets the current working directory of the calling process. -/
+@[extern "lean_io_process_set_current_dir"] opaque setCurrentDir (path : @& FilePath) : IO Unit
+
+/-- Returns the process ID of the calling process. -/
 @[extern "lean_io_process_get_pid"] opaque getPID : BaseIO UInt32
 
 inductive Stdio where

src/Init/Tactics.lean

@@ -368,7 +368,7 @@ 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| fail "The rfl tactic failed. Possible reasons:
+macro "rfl" : tactic => `(tactic| case' _ => fail "The rfl tactic failed. Possible reasons:
 - The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma).
 - The arguments of the relation are not equal.
 Try using the reflexivitiy lemma for your relation explicitly, e.g. `exact Eq.rfl`.")
@@ -1542,7 +1542,7 @@ macro "get_elem_tactic" : tactic =>
 
 /--
 Searches environment for definitions or theorems that can be substituted in
-for `exact?% to solve the goal.
+for `exact?%` to solve the goal.
  -/
 syntax (name := Lean.Parser.Syntax.exact?) "exact?%" : term
 

src/Init/WFTactics.lean

@@ -25,9 +25,16 @@ syntax "decreasing_trivial" : tactic
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| (simp (config := { arith := true, failIfUnchanged := false })) <;> done)
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| omega)
 macro_rules | `(tactic| decreasing_trivial) => `(tactic| assumption)
-macro_rules | `(tactic| decreasing_trivial) => `(tactic| apply Nat.sub_succ_lt_self; assumption) -- a - (i+1) < a - i if i < a
-macro_rules | `(tactic| decreasing_trivial) => `(tactic| apply Nat.pred_lt'; assumption) -- i-1 < i if j < i
-macro_rules | `(tactic| decreasing_trivial) => `(tactic| apply Nat.pred_lt; assumption)  -- i-1 < i if i ≠ 0
+
+/--
+Variant of `decreasing_trivial` that does not use `omega`, intended to be used in core modules
+before `omega` is available.
+-/
+syntax "decreasing_trivial_pre_omega" : tactic
+macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.sub_succ_lt_self; assumption) -- a - (i+1) < a - i if i < a
+macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt'; assumption) -- i-1 < i if j < i
+macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt; assumption)  -- i-1 < i if i ≠ 0
+
 
 /-- Constructs a proof of decreasing along a well founded relation, by applying
 lexicographic order lemmas and using `ts` to solve the base case. If it fails,

src/Lean/Attributes.lean

@@ -183,7 +183,6 @@ structure ParametricAttribute (α : Type) where
   deriving Inhabited
 
 structure ParametricAttributeImpl (α : Type) extends AttributeImplCore where
-  /-- This is used as the target for go-to-definition queries for simple attributes -/
   getParam : Name → Syntax → AttrM α
   afterSet : Name → α → AttrM Unit := fun _ _ _ => pure ()
   afterImport : Array (Array (Name × α)) → ImportM Unit := fun _ => pure ()

src/Lean/Compiler/ExternAttr.lean

@@ -66,12 +66,13 @@ builtin_initialize externAttr : ParametricAttribute ExternAttrData ←
     descr := "builtin and foreign functions"
     getParam := fun _ stx => syntaxToExternAttrData stx
     afterSet := fun declName _ => do
-      let mut env ← getEnv
-      if env.isProjectionFn declName || env.isConstructor declName then do
-        env ← ofExcept <| addExtern env declName
+      let env ← getEnv
+      if env.isProjectionFn declName || env.isConstructor declName then
+        if let some (.thmInfo ..) := env.find? declName then
+          -- We should not mark theorems as extern
+          return ()
+        let env ← ofExcept <| addExtern env declName
         setEnv env
-      else
-        pure ()
   }
 
 @[export lean_get_extern_attr_data]

src/Lean/Compiler/IR/RC.lean

@@ -9,9 +9,10 @@ import Lean.Compiler.IR.CompilerM
 import Lean.Compiler.IR.LiveVars
 
 namespace Lean.IR.ExplicitRC
-/-! Insert explicit RC instructions. So, it assumes the input code does not contain `inc` nor `dec` instructions.
-   This transformation is applied before lower level optimizations
-   that introduce the instructions `release` and `set`
+/-!
+Insert explicit RC instructions. So, it assumes the input code does not contain `inc` nor `dec` instructions.
+This transformation is applied before lower level optimizations
+that introduce the instructions `release` and `set`
 -/
 
 structure VarInfo where

src/Lean/Compiler/IR/ResetReuse.lean

@@ -9,21 +9,24 @@ import Lean.Compiler.IR.LiveVars
 import Lean.Compiler.IR.Format
 
 namespace Lean.IR.ResetReuse
-/-! Remark: the insertResetReuse transformation is applied before we have
-   inserted `inc/dec` instructions, and performed lower level optimizations
-   that introduce the instructions `release` and `set`. -/
+/-!
+Remark: the insertResetReuse transformation is applied before we have
+inserted `inc/dec` instructions, and performed lower level optimizations
+that introduce the instructions `release` and `set`.
+-/
 
-/-! Remark: the functions `S`, `D` and `R` defined here implement the
-  corresponding functions in the paper "Counting Immutable Beans"
+/-!
+Remark: the functions `S`, `D` and `R` defined here implement the
+corresponding functions in the paper "Counting Immutable Beans"
 
-  Here are the main differences:
-  - We use the State monad to manage the generation of fresh variable names.
-  - Support for join points, and `uset` and `sset` instructions for unboxed data.
-  - `D` uses the auxiliary function `Dmain`.
-  - `Dmain` returns a pair `(b, found)` to avoid quadratic behavior when checking
-    the last occurrence of the variable `x`.
-  - Because we have join points in the actual implementation, a variable may be live even if it
-    does not occur in a function body. See example at `livevars.lean`.
+Here are the main differences:
+- We use the State monad to manage the generation of fresh variable names.
+- Support for join points, and `uset` and `sset` instructions for unboxed data.
+- `D` uses the auxiliary function `Dmain`.
+- `Dmain` returns a pair `(b, found)` to avoid quadratic behavior when checking
+  the last occurrence of the variable `x`.
+- Because we have join points in the actual implementation, a variable may be live even if it
+  does not occur in a function body. See example at `livevars.lean`.
 -/
 
 private def mayReuse (c₁ c₂ : CtorInfo) : Bool :=
@@ -33,39 +36,68 @@ private def mayReuse (c₁ c₂ : CtorInfo) : Bool :=
      because it produces counterintuitive behavior. -/
   c₁.name.getPrefix == c₂.name.getPrefix
 
+/--
+Replace `ctor` applications with `reuse` applications if compatible.
+`w` contains the "memory cell" being reused.
+-/
 private partial def S (w : VarId) (c : CtorInfo) : FnBody → FnBody
-  | FnBody.vdecl x t v@(Expr.ctor c' ys) b   =>
+  | .vdecl x t v@(.ctor c' ys) b   =>
     if mayReuse c c' then
       let updtCidx := c.cidx != c'.cidx
-      FnBody.vdecl x t (Expr.reuse w c' updtCidx ys) b
+      .vdecl x t (.reuse w c' updtCidx ys) b
     else
-      FnBody.vdecl x t v (S w c b)
-  | FnBody.jdecl j ys v b   =>
+      .vdecl x t v (S w c b)
+  | .jdecl j ys v b   =>
     let v' := S w c v
-    if v == v' then FnBody.jdecl j ys v (S w c b)
-    else FnBody.jdecl j ys v' b
-  | FnBody.case tid x xType alts    => FnBody.case tid x xType <| alts.map fun alt => alt.modifyBody (S w c)
+    if v == v' then
+      .jdecl j ys v (S w c b)
+    else
+      .jdecl j ys v' b
+  | .case tid x xType alts =>
+    .case tid x xType <| alts.map fun alt => alt.modifyBody (S w c)
   | b =>
-    if b.isTerminal then b
+    if b.isTerminal then
+      b
     else let
       (instr, b) := b.split
       instr.setBody (S w c b)
 
+structure Context where
+  lctx      : LocalContext := {}
+  /--
+  Contains all variables in `cases` statements in the current path.
+  We use this information to prevent double-reset in code such as
+  ```
+  case x_i : obj of
+  Prod.mk →
+    case x_i : obj of
+    Prod.mk →
+    ...
+  ```
+  -/
+  casesVars : PHashSet VarId := {}
+
 /-- We use `Context` to track join points in scope. -/
-abbrev M := ReaderT LocalContext (StateT Index Id)
+abbrev M := ReaderT Context (StateT Index Id)
 
 private def mkFresh : M VarId := do
-  let idx ← getModify (fun n => n + 1)
-  pure { idx := idx }
+  let idx ← getModify fun n => n + 1
+  return { idx := idx }
 
+/--
+Helper function for applying `S`. We only introduce a `reset` if we managed
+to replace a `ctor` withe `reuse` in `b`.
+-/
 private def tryS (x : VarId) (c : CtorInfo) (b : FnBody) : M FnBody := do
   let w ← mkFresh
   let b' := S w c b
-  if b == b' then pure b
-  else pure $ FnBody.vdecl w IRType.object (Expr.reset c.size x) b'
+  if b == b' then
+    return b
+  else
+    return .vdecl w IRType.object (.reset c.size x) b'
 
 private def Dfinalize (x : VarId) (c : CtorInfo) : FnBody × Bool → M FnBody
-  | (b, true)  => pure b
+  | (b, true)  => return b
   | (b, false) => tryS x c b
 
 private def argsContainsVar (ys : Array Arg) (x : VarId) : Bool :=
@@ -75,75 +107,85 @@ private def argsContainsVar (ys : Array Arg) (x : VarId) : Bool :=
 
 private def isCtorUsing (b : FnBody) (x : VarId) : Bool :=
   match b with
-  | (FnBody.vdecl _ _ (Expr.ctor _ ys) _) => argsContainsVar ys x
+  | .vdecl _ _ (.ctor _ ys) _ => argsContainsVar ys x
   | _ => false
 
-/-- Given `Dmain b`, the resulting pair `(new_b, flag)` contains the new body `new_b`,
-   and `flag == true` if `x` is live in `b`.
+/--
+Given `Dmain b`, the resulting pair `(new_b, flag)` contains the new body `new_b`,
+and `flag == true` if `x` is live in `b`.
 
-   Note that, in the function `D` defined in the paper, for each `let x := e; F`,
-   `D` checks whether `x` is live in `F` or not. This is great for clarity but it
-   is expensive: `O(n^2)` where `n` is the size of the function body. -/
-private partial def Dmain (x : VarId) (c : CtorInfo) : FnBody → M (FnBody × Bool)
-  | e@(FnBody.case tid y yType alts) => do
-    let ctx ← read
-    if e.hasLiveVar ctx x then do
+Note that, in the function `D` defined in the paper, for each `let x := e; F`,
+`D` checks whether `x` is live in `F` or not. This is great for clarity but it
+is expensive: `O(n^2)` where `n` is the size of the function body. -/
+private partial def Dmain (x : VarId) (c : CtorInfo) (e : FnBody) : M (FnBody × Bool) := do
+  match e with
+  | .case tid y yType alts =>
+    if e.hasLiveVar (← read).lctx x then
       /- If `x` is live in `e`, we recursively process each branch. -/
       let alts ← alts.mapM fun alt => alt.mmodifyBody fun b => Dmain x c b >>= Dfinalize x c
-      pure (FnBody.case tid y yType alts, true)
-    else pure (e, false)
-  | FnBody.jdecl j ys v b   => do
-    let (b, found) ← withReader (fun ctx => ctx.addJP j ys v) (Dmain x c b)
+      return (.case tid y yType alts, true)
+    else
+      return (e, false)
+  | .jdecl j ys v b =>
+    let (b, found) ← withReader (fun ctx => { ctx with lctx := ctx.lctx.addJP j ys v }) (Dmain x c b)
     let (v, _ /- found' -/) ← Dmain x c v
     /- If `found' == true`, then `Dmain b` must also have returned `(b, true)` since
        we assume the IR does not have dead join points. So, if `x` is live in `j` (i.e., `v`),
        then it must also live in `b` since `j` is reachable from `b` with a `jmp`.
        On the other hand, `x` may be live in `b` but dead in `j` (i.e., `v`). -/
-    pure (FnBody.jdecl j ys v b, found)
-  | e => do
-    let ctx ← read
+    return (.jdecl j ys v b, found)
+  | e =>
     if e.isTerminal then
-      pure (e, e.hasLiveVar ctx x)
+      return (e, e.hasLiveVar (← read).lctx x)
     else do
       let (instr, b) := e.split
       if isCtorUsing instr x then
         /- If the scrutinee `x` (the one that is providing memory) is being
            stored in a constructor, then reuse will probably not be able to reuse memory at runtime.
            It may work only if the new cell is consumed, but we ignore this case. -/
-        pure (e, true)
+        return (e, true)
       else
         let (b, found) ← Dmain x c b
         /- Remark: it is fine to use `hasFreeVar` instead of `hasLiveVar`
-           since `instr` is not a `FnBody.jmp` (it is not a terminal) nor it is a `FnBody.jdecl`. -/
+           since `instr` is not a `FnBody.jmp` (it is not a terminal) nor
+           it is a `FnBody.jdecl`. -/
         if found || !instr.hasFreeVar x then
-          pure (instr.setBody b, found)
+          return (instr.setBody b, found)
         else
           let b ← tryS x c b
-          pure (instr.setBody b, true)
+          return (instr.setBody b, true)
 
 private def D (x : VarId) (c : CtorInfo) (b : FnBody) : M FnBody :=
   Dmain x c b >>= Dfinalize x c
 
-partial def R : FnBody → M FnBody
-  | FnBody.case tid x xType alts   => do
+partial def R (e : FnBody) : M FnBody := do
+  match e with
+  | .case tid x xType alts =>
+    let alreadyFound := (← read).casesVars.contains x
+    withReader (fun ctx => { ctx with casesVars := ctx.casesVars.insert x }) do
       let alts ← alts.mapM fun alt => do
         let alt ← alt.mmodifyBody R
         match alt with
-        | Alt.ctor c b =>
-          if c.isScalar then pure alt
-          else Alt.ctor c <$> D x c b
-        | _            => pure alt
-      pure $ FnBody.case tid x xType alts
-  | FnBody.jdecl j ys v b   => do
+        | .ctor c b =>
+          if c.isScalar || alreadyFound then
+            -- If `alreadyFound`, then we don't try to reuse memory cell to avoid
+            -- double reset.
+            return alt
+          else
+            .ctor c <$> D x c b
+        | _ => return alt
+      return .case tid x xType alts
+  | .jdecl j ys v b =>
     let v ← R v
-    let b ← withReader (fun ctx => ctx.addJP j ys v) (R b)
-    pure $ FnBody.jdecl j ys v b
-  | e => do
-    if e.isTerminal then pure e
-    else do
+    let b ← withReader (fun ctx => { ctx with lctx := ctx.lctx.addJP j ys v }) (R b)
+    return .jdecl j ys v b
+  | e =>
+    if e.isTerminal then
+      return e
+    else
       let (instr, b) := e.split
       let b ← R b
-      pure (instr.setBody b)
+      return instr.setBody b
 
 end ResetReuse
 
@@ -151,7 +193,7 @@ open ResetReuse
 
 def Decl.insertResetReuse (d : Decl) : Decl :=
   match d with
-  | .fdecl (body := b) ..=>
+  | .fdecl (body := b) .. =>
     let nextIndex := d.maxIndex + 1
     let bNew      := (R b {}).run' nextIndex
     d.updateBody! bNew

src/Lean/CoreM.lean

@@ -13,13 +13,25 @@ import Lean.Elab.InfoTree.Types
 import Lean.MonadEnv
 
 namespace Lean
-namespace Core
+register_builtin_option diagnostics : Bool := {
+  defValue := false
+  group    := "diagnostics"
+  descr    := "collect diagnostic information"
+}
+
+register_builtin_option diagnostics.threshold : Nat := {
+  defValue := 20
+  group    := "diagnostics"
+  descr    := "only diagnostic counters above this threshold are reported by the definitional equality"
+}
 
 register_builtin_option maxHeartbeats : Nat := {
   defValue := 200000
   descr := "maximum amount of heartbeats per command. A heartbeat is number of (small) memory allocations (in thousands), 0 means no limit"
 }
 
+namespace Core
+
 builtin_initialize registerTraceClass `Kernel
 
 def getMaxHeartbeats (opts : Options) : Nat :=
@@ -72,6 +84,11 @@ structure Context where
   Recall that runtime exceptions are `maxRecDepth` or `maxHeartbeats`.
   -/
   catchRuntimeEx : Bool := false
+  /--
+  If `diag := true`, different parts of the system collect diagnostics.
+  Use the `set_option diag true` to set it to true.
+  -/
+  diag           : Bool := false
   deriving Nonempty
 
 /-- CoreM is a monad for manipulating the Lean environment.
@@ -104,7 +121,22 @@ instance : MonadOptions CoreM where
   getOptions := return (← read).options
 
 instance : MonadWithOptions CoreM where
-  withOptions f x := withReader (fun ctx => { ctx with options := f ctx.options }) x
+  withOptions f x := do
+    let options := f (← read).options
+    let diag := diagnostics.get options
+    if Kernel.isDiagnosticsEnabled (← getEnv) != diag then
+      modifyEnv fun env => Kernel.enableDiag env diag
+    withReader
+      (fun ctx =>
+        { ctx with
+          options
+          diag
+          maxRecDepth := maxRecDepth.get options })
+      x
+
+-- Helper function for ensuring fields that depend on `options` have the correct value.
+@[inline] private def withConsistentCtx (x : CoreM α) : CoreM α := do
+  withOptions id x
 
 instance : AddMessageContext CoreM where
   addMessageContext := addMessageContextPartial
@@ -192,7 +224,7 @@ def mkFreshUserName (n : Name) : CoreM Name :=
   mkFreshNameImp n
 
 @[inline] def CoreM.run (x : CoreM α) (ctx : Context) (s : State) : EIO Exception (α × State) :=
-  (x ctx).run s
+  ((withConsistentCtx x) ctx).run s
 
 @[inline] def CoreM.run' (x : CoreM α) (ctx : Context) (s : State) : EIO Exception α :=
   Prod.fst <$> x.run ctx s
@@ -206,7 +238,7 @@ def mkFreshUserName (n : Name) : CoreM Name :=
 instance [MetaEval α] : MetaEval (CoreM α) where
   eval env opts x _ := do
     let x : CoreM α := do try x finally printTraces
-    let (a, s) ← x.toIO { maxRecDepth := maxRecDepth.get opts, options := opts, fileName := "<CoreM>", fileMap := default } { env := env }
+    let (a, s) ← (withConsistentCtx x).toIO { fileName := "<CoreM>", fileMap := default, options := opts } { env := env }
     MetaEval.eval s.env opts a (hideUnit := true)
 
 -- withIncRecDepth for a monad `m` such that `[MonadControlT CoreM n]`
@@ -219,7 +251,7 @@ protected def withIncRecDepth [Monad m] [MonadControlT CoreM m] (x : m α) : m
     throw <| Exception.error .missing "elaboration interrupted"
 
 def throwMaxHeartbeat (moduleName : Name) (optionName : Name) (max : Nat) : CoreM Unit := do
-  let msg := s!"(deterministic) timeout at '{moduleName}', maximum number of heartbeats ({max/1000}) has been reached (use 'set_option {optionName} <num>' to set the limit)"
+  let msg := s!"(deterministic) timeout at `{moduleName}`, maximum number of heartbeats ({max/1000}) has been reached\nuse `set_option {optionName} <num>` to set the limit\nuse `set_option {diagnostics.name} true` to get diagnostic information"
   throw <| Exception.error (← getRef) (MessageData.ofFormat (Std.Format.text msg))
 
 def checkMaxHeartbeatsCore (moduleName : String) (optionName : Name) (max : Nat) : CoreM Unit := do
@@ -372,9 +404,16 @@ def addAndCompile (decl : Declaration) : CoreM Unit := do
   addDecl decl;
   compileDecl decl
 
+def getDiag (opts : Options) : Bool :=
+  diagnostics.get opts
+
+/-- Return `true` if diagnostic information collection is enabled. -/
+def isDiagnosticsEnabled : CoreM Bool :=
+  return (← read).diag
+
 def ImportM.runCoreM (x : CoreM α) : ImportM α := do
   let ctx ← read
-  let (a, _) ← x.toIO { options := ctx.opts, fileName := "<ImportM>", fileMap := default } { env := ctx.env }
+  let (a, _) ← (withOptions (fun _ => ctx.opts) x).toIO { fileName := "<ImportM>", fileMap := default } { env := ctx.env }
   return a
 
 /-- Return `true` if the exception was generated by one our resource limits. -/

src/Lean/Data/HashMap.lean

@@ -92,6 +92,7 @@ def moveEntries [Hashable α] (i : Nat) (source : Array (AssocList α β)) (targ
      moveEntries (i+1) source target
   else target
 termination_by source.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def expand [Hashable α] (size : Nat) (buckets : HashMapBucket α β) : HashMapImp α β :=
   let bucketsNew : HashMapBucket α β := ⟨

src/Lean/Data/HashSet.lean

@@ -84,6 +84,7 @@ def moveEntries [Hashable α] (i : Nat) (source : Array (List α)) (target : Has
   else
     target
 termination_by source.size - i
+decreasing_by simp_wf; decreasing_trivial_pre_omega
 
 def expand [Hashable α] (size : Nat) (buckets : HashSetBucket α) : HashSetImp α :=
   let bucketsNew : HashSetBucket α := ⟨

src/Lean/Declaration.lean

@@ -135,6 +135,11 @@ structure TheoremVal extends ConstantVal where
   all : List Name := [name]
   deriving Inhabited, BEq
 
+@[export lean_mk_theorem_val]
+def mkTheoremValEx (name : Name) (levelParams : List Name) (type : Expr) (value : Expr) (all : List Name) : TheoremVal := {
+  name, levelParams, type, value, all
+}
+
 /-- Value for an opaque constant declaration `opaque x : t := e` -/
 structure OpaqueVal extends ConstantVal where
   value : Expr

src/Lean/Elab/Binders.lean

@@ -70,30 +70,34 @@ def kindOfBinderName (binderName : Name) : LocalDeclKind :=
   else
     .default
 
-partial def quoteAutoTactic : Syntax → TermElabM Syntax
-  | stx@(.ident ..) => throwErrorAt stx "invalid auto tactic, identifier is not allowed"
+partial def quoteAutoTactic : Syntax → CoreM Expr
+  | .ident _ _ val preresolved =>
+    return mkApp4 (.const ``Syntax.ident [])
+      (.const ``SourceInfo.none [])
+      (.app (.const ``String.toSubstring []) (mkStrLit (toString val)))
+      (toExpr val)
+      (toExpr preresolved)
   | stx@(.node _ k args) => do
     if stx.isAntiquot then
       throwErrorAt stx "invalid auto tactic, antiquotation is not allowed"
     else
-      let mut quotedArgs ← `(Array.empty)
+      let ty := .const ``Syntax []
+      let mut quotedArgs := mkApp (.const ``Array.empty [.zero]) ty
       for arg in args do
         if k == nullKind && (arg.isAntiquotSuffixSplice || arg.isAntiquotSplice) then
           throwErrorAt arg "invalid auto tactic, antiquotation is not allowed"
         else
           let quotedArg ← quoteAutoTactic arg
-          quotedArgs ← `(Array.push $quotedArgs $quotedArg)
-      `(Syntax.node SourceInfo.none $(quote k) $quotedArgs)
-  | .atom _ val => `(mkAtom $(quote val))
+          quotedArgs := mkApp3 (.const ``Array.push [.zero]) ty quotedArgs quotedArg
+      return mkApp3 (.const ``Syntax.node []) (.const ``SourceInfo.none []) (toExpr k) quotedArgs
+  | .atom _ val => return .app (.const ``mkAtom []) (toExpr val)
   | .missing    => throwError "invalid auto tactic, tactic is missing"
 
 def declareTacticSyntax (tactic : Syntax) : TermElabM Name :=
   withFreshMacroScope do
     let name ← MonadQuotation.addMacroScope `_auto
     let type := Lean.mkConst `Lean.Syntax
-    let tactic ← quoteAutoTactic tactic
-    let value ← elabTerm tactic type
-    let value ← instantiateMVars value
+    let value ← quoteAutoTactic tactic
     trace[Elab.autoParam] value
     let decl := Declaration.defnDecl { name, levelParams := [], type, value, hints := .opaque,
                                        safety := DefinitionSafety.safe }

src/Lean/Elab/BuiltinNotation.lean

@@ -388,7 +388,7 @@ private def withLocalIdentFor (stx : Term) (e : Expr) (k : Term → TermElabM Ex
                return (← mkEqRec motive h (← mkEqSymm heq), none)
          let motive ← mkMotive lhs expectedAbst
          if badMotive?.isSome || !(← isTypeCorrect motive) then
-           -- Before failing try tos use `subst`
+           -- Before failing try to use `subst`
            if ← (isSubstCandidate lhs rhs <||> isSubstCandidate rhs lhs) then
              withLocalIdentFor heqStx heq fun heqStx => do
                let h ← instantiateMVars h
@@ -408,7 +408,13 @@ private def withLocalIdentFor (stx : Term) (e : Expr) (k : Term → TermElabM Ex
        | none =>
          let h ← elabTerm hStx none
          let hType ← inferType h
-         let hTypeAbst ← kabstract hType lhs
+         let mut hTypeAbst ← kabstract hType lhs
+         unless hTypeAbst.hasLooseBVars do
+           hTypeAbst ← kabstract hType rhs
+           unless hTypeAbst.hasLooseBVars do
+             throwError "invalid `▸` notation, the equality{indentExpr heq}\nhas type {indentExpr heqType}\nbut neither side of the equality is mentioned in the type{indentExpr hType}"
+           heq ← mkEqSymm heq
+           (lhs, rhs) := (rhs, lhs)
          let motive ← mkMotive lhs hTypeAbst
          unless (← isTypeCorrect motive) do
            throwError "invalid `▸` notation, failed to compute motive for the substitution"

src/Lean/Elab/BuiltinTerm.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
+import Lean.Meta.Diagnostics
 import Lean.Elab.Open
 import Lean.Elab.SetOption
 import Lean.Elab.Eval
@@ -313,8 +314,12 @@ private def mkSilentAnnotationIfHole (e : Expr) : TermElabM Expr := do
 
 @[builtin_term_elab «set_option»] def elabSetOption : TermElab := fun stx expectedType? => do
   let options ← Elab.elabSetOption stx[1] stx[3]
-  withTheReader Core.Context (fun ctx => { ctx with maxRecDepth := maxRecDepth.get options, options := options }) do
-    elabTerm stx[5] expectedType?
+  withOptions (fun _ => options) do
+    try
+      elabTerm stx[5] expectedType?
+    finally
+      if stx[1].getId == `diagnostics then
+        reportDiag
 
 @[builtin_term_elab withAnnotateTerm] def elabWithAnnotateTerm : TermElab := fun stx expectedType? => do
   match stx with

src/Lean/Elab/Command.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura, Gabriel Ebner
 -/
 prelude
+import Lean.Meta.Diagnostics
 import Lean.Elab.Binders
 import Lean.Elab.SyntheticMVars
 import Lean.Elab.SetOption
@@ -127,19 +128,6 @@ def mkMessageAux (ctx : Context) (ref : Syntax) (msgData : MessageData) (severit
   let endPos := ref.getTailPos?.getD pos
   mkMessageCore ctx.fileName ctx.fileMap msgData severity pos endPos
 
-private def mkCoreContext (ctx : Context) (s : State) (heartbeats : Nat) : Core.Context :=
-  let scope        := s.scopes.head!
-  { fileName       := ctx.fileName
-    fileMap        := ctx.fileMap
-    options        := scope.opts
-    currRecDepth   := ctx.currRecDepth
-    maxRecDepth    := s.maxRecDepth
-    ref            := ctx.ref
-    currNamespace  := scope.currNamespace
-    openDecls      := scope.openDecls
-    initHeartbeats := heartbeats
-    currMacroScope := ctx.currMacroScope }
-
 private def addTraceAsMessagesCore (ctx : Context) (log : MessageLog) (traceState : TraceState) : MessageLog := Id.run do
   if traceState.traces.isEmpty then return log
   let mut traces : HashMap (String.Pos × String.Pos) (Array MessageData) := ∅
@@ -165,31 +153,49 @@ private def addTraceAsMessages : CommandElabM Unit := do
       traceState.traces := {}
     }
 
-def liftCoreM (x : CoreM α) : CommandElabM α := do
+private def runCore (x : CoreM α) : CommandElabM α := do
   let s ← get
   let ctx ← read
   let heartbeats ← IO.getNumHeartbeats
-  let Eα := Except Exception α
-  let x : CoreM Eα := try let a ← x; pure <| Except.ok a catch ex => pure <| Except.error ex
-  let x : EIO Exception (Eα × Core.State) := (ReaderT.run x (mkCoreContext ctx s heartbeats)).run { env := s.env, ngen := s.ngen, traceState := s.traceState, messages := {}, infoState.enabled := s.infoState.enabled }
+  let env := Kernel.resetDiag s.env
+  let scope := s.scopes.head!
+  let coreCtx : Core.Context := {
+    fileName       := ctx.fileName
+    fileMap        := ctx.fileMap
+    currRecDepth   := ctx.currRecDepth
+    maxRecDepth    := s.maxRecDepth
+    ref            := ctx.ref
+    currNamespace  := scope.currNamespace
+    openDecls      := scope.openDecls
+    initHeartbeats := heartbeats
+    currMacroScope := ctx.currMacroScope
+    options        := scope.opts
+  }
+  let x : EIO _ _ := x.run coreCtx {
+    env
+    ngen := s.ngen
+    nextMacroScope := s.nextMacroScope
+    infoState.enabled := s.infoState.enabled
+    traceState := s.traceState
+  }
   let (ea, coreS) ← liftM x
   modify fun s => { s with
-    env := coreS.env
-    ngen := coreS.ngen
-    messages := s.messages ++ coreS.messages
+    env               := coreS.env
+    nextMacroScope    := coreS.nextMacroScope
+    ngen              := coreS.ngen
+    infoState.trees   := s.infoState.trees.append coreS.infoState.trees
     traceState.traces := coreS.traceState.traces.map fun t => { t with ref := replaceRef t.ref ctx.ref }
-    infoState.trees := s.infoState.trees.append coreS.infoState.trees
+    messages          := s.messages ++ coreS.messages
   }
-  match ea with
-  | Except.ok a    => pure a
-  | Except.error e => throw e
+  return ea
+
+def liftCoreM (x : CoreM α) : CommandElabM α := do
+  MonadExcept.ofExcept (← runCore (observing x))
 
 private def ioErrorToMessage (ctx : Context) (ref : Syntax) (err : IO.Error) : Message :=
   let ref := getBetterRef ref ctx.macroStack
   mkMessageAux ctx ref (toString err) MessageSeverity.error
 
-@[inline] def liftEIO {α} (x : EIO Exception α) : CommandElabM α := liftM x
-
 @[inline] def liftIO {α} (x : IO α) : CommandElabM α := do
   let ctx ← read
   IO.toEIO (fun (ex : IO.Error) => Exception.error ctx.ref ex.toString) x
@@ -269,7 +275,7 @@ private def elabCommandUsing (s : State) (stx : Syntax) : List (KeyedDeclsAttrib
       (fun _ => do set s; elabCommandUsing s stx elabFns)
 
 /-- Elaborate `x` with `stx` on the macro stack -/
-def withMacroExpansion {α} (beforeStx afterStx : Syntax) (x : CommandElabM α) : CommandElabM α :=
+def withMacroExpansion (beforeStx afterStx : Syntax) (x : CommandElabM α) : CommandElabM α :=
   withInfoContext (mkInfo := pure <| .ofMacroExpansionInfo { stx := beforeStx, output := afterStx, lctx := .empty }) do
     withReader (fun ctx => { ctx with macroStack := { before := beforeStx, after := afterStx } :: ctx.macroStack }) x
 
@@ -402,7 +408,6 @@ def printExpr (e : Expr) : MetaM Unit := do
 def liftTermElabM (x : TermElabM α) : CommandElabM α := do
   let ctx ← read
   let s   ← get
-  let heartbeats ← IO.getNumHeartbeats
   -- dbg_trace "heartbeats: {heartbeats}"
   let scope := s.scopes.head!
   -- We execute `x` with an empty message log. Thus, `x` cannot modify/view messages produced by previous commands.
@@ -411,18 +416,9 @@ def liftTermElabM (x : TermElabM α) : CommandElabM α := do
   -- make sure `observing` below also catches runtime exceptions (like we do by default in
   -- `CommandElabM`)
   let _ := MonadAlwaysExcept.except (m := TermElabM)
-  let x : MetaM _      := (observing x).run (mkTermContext ctx s) { levelNames := scope.levelNames }
-  let x : CoreM _      := x.run mkMetaContext {}
-  let x : EIO _ _      := x.run (mkCoreContext ctx s heartbeats) { env := s.env, ngen := s.ngen, nextMacroScope := s.nextMacroScope, infoState.enabled := s.infoState.enabled, traceState := s.traceState }
-  let (((ea, _), _), coreS) ← liftEIO x
-  modify fun s => { s with
-    env               := coreS.env
-    nextMacroScope    := coreS.nextMacroScope
-    ngen              := coreS.ngen
-    infoState.trees   := s.infoState.trees.append coreS.infoState.trees
-    traceState.traces := coreS.traceState.traces.map fun t => { t with ref := replaceRef t.ref ctx.ref }
-    messages          := s.messages ++ coreS.messages
-  }
+  let x : MetaM _ := (observing (try x finally Meta.reportDiag)).run (mkTermContext ctx s) { levelNames := scope.levelNames }
+  let x : CoreM _ := x.run mkMetaContext {}
+  let ((ea, _), _) ← runCore x
   MonadExcept.ofExcept ea
 
 /--

src/Lean/Elab/Extra.lean

@@ -96,7 +96,7 @@ Here are brief descriptions of each of the operator types:
 - `rightact% f a b` elaborates `f a b` as a right action (the `b` operand "acts upon" the `a` operand).
   Only `a` participates in the protocol since `b` can have an unrelated type.
   This is used by `HPow` since, for example, there are both `Real -> Nat -> Real` and `Real -> Real -> Real`
-  exponentiation functions, and we prefer the former in the case of `x ^ 2`, but `binop%` would choose the latter. (#2220)
+  exponentiation functions, and we prefer the former in the case of `x ^ 2`, but `binop%` would choose the latter. (#2854)
 - There are also `binrel%` and `binrel_no_prop%` (see the docstring for `elabBinRelCore`).
 
 The elaborator works as follows:
@@ -449,7 +449,7 @@ def elabOp : TermElab := fun stx expectedType? => do
 
   - `binrel% R x y` elaborates `R x y` using the `binop%/...` expression trees in both `x` and `y`.
     It is similar to how `binop% R x y` elaborates but with a significant difference:
-    it does not use the expected type when computing the types of the operads.
+    it does not use the expected type when computing the types of the operands.
   - `binrel_no_prop% R x y` elaborates `R x y` like `binrel% R x y`, but if the resulting type for `x` and `y`
     is `Prop` they are coerced to `Bool`.
     This is used for relations such as `==` which do not support `Prop`, but we still want

src/Lean/Elab/Inductive.lean

@@ -686,8 +686,8 @@ private def computeFixedIndexBitMask (numParams : Nat) (indType : InductiveType)
               maskRef.modify fun mask => mask.set! i false
           for x in xs[numParams:] do
             let xType ← inferType x
-            let cond (e : Expr) := indFVars.any (fun indFVar => e.getAppFn == indFVar) && e.getAppNumArgs > numParams
-            xType.forEachWhere cond fun e => do
+            let cond (e : Expr) := indFVars.any (fun indFVar => e.getAppFn == indFVar)
+            xType.forEachWhere (stopWhenVisited := true) cond fun e => do
               let eArgs := e.getAppArgs
               for i in [numParams:eArgs.size] do
                 if i >= typeArgs.size then
@@ -695,6 +695,19 @@ private def computeFixedIndexBitMask (numParams : Nat) (indType : InductiveType)
                 else
                   unless eArgs[i]! == typeArgs[i]! do
                     maskRef.modify (resetMaskAt · i)
+              /-If an index is missing in the arguments of the inductive type, then it must be non-fixed.
+                Consider the following example:
+                ```lean
+                inductive All {I : Type u} (P : I → Type v) : List I → Type (max u v) where
+                  | cons : P x → All P xs → All P (x :: xs)
+
+                inductive Iμ {I : Type u}  : I → Type (max u v) where
+                  | mk : (i : I)  → All Iμ [] → Iμ i
+                ```
+                because `i` doesn't appear in `All Iμ []`, the index shouldn't be fixed.
+              -/
+              for i in [eArgs.size:arity] do
+                maskRef.modify (resetMaskAt · i)
         go ctors
     go indType.ctors
 

src/Lean/Elab/InfoTree/Main.lean

@@ -102,8 +102,10 @@ def ContextInfo.runCoreM (info : ContextInfo) (x : CoreM α) : IO α := do
     have been used in `lctx` and `info.mctx`.
   -/
   (·.1) <$>
-    x.toIO { options := info.options, currNamespace := info.currNamespace, openDecls := info.openDecls, fileName := "<InfoTree>", fileMap := default }
-           { env := info.env, ngen := info.ngen }
+    (withOptions (fun _ => info.options) x).toIO
+      { currNamespace := info.currNamespace, openDecls := info.openDecls
+        fileName := "<InfoTree>", fileMap := default }
+      { env := info.env, ngen := info.ngen }
 
 def ContextInfo.runMetaM (info : ContextInfo) (lctx : LocalContext) (x : MetaM α) : IO α := do
   (·.1) <$> info.runCoreM (x.run { lctx := lctx } { mctx := info.mctx })

src/Lean/Elab/PreDefinition/Eqns.lean

@@ -228,20 +228,23 @@ private def shouldUseSimpMatch (e : Expr) : MetaM Bool := do
             throwThe Unit ()
   return (← (find e).run) matches .error _
 
-partial def mkEqnTypes (declNames : Array Name) (mvarId : MVarId) : MetaM (Array Expr) := do
+partial def mkEqnTypes (tryRefl : Bool) (declNames : Array Name) (mvarId : MVarId) : MetaM (Array Expr) := do
   let (_, eqnTypes) ← go mvarId |>.run { declNames } |>.run #[]
   return eqnTypes
 where
   go (mvarId : MVarId) : ReaderT Context (StateRefT (Array Expr) MetaM) Unit := do
     trace[Elab.definition.eqns] "mkEqnTypes step\n{MessageData.ofGoal mvarId}"
-    if (← tryURefl mvarId) then
-      saveEqn mvarId
-      return ()
+    if tryRefl then
+      if (← tryURefl mvarId) then
+        saveEqn mvarId
+        return ()
 
     if let some mvarId ← expandRHS? mvarId then
       return (← go mvarId)
---  The following `funext?` was producing an overapplied `lhs`. Possible refinement: only do it if we want to apply `splitMatch` on the body of the lambda
-/-    if let some mvarId ← funext? mvarId then
+
+    --  The following `funext?` was producing an overapplied `lhs`. Possible refinement: only do it
+    --  if we want to apply `splitMatch` on the body of the lambda
+    /- if let some mvarId ← funext? mvarId then
         return (← go mvarId) -/
 
     if (← shouldUseSimpMatch (← mvarId.getType')) then

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

@@ -62,7 +62,7 @@ def mkEqns (info : EqnInfo) : MetaM (Array Name) :=
     let us := info.levelParams.map mkLevelParam
     let target ← mkEq (mkAppN (Lean.mkConst info.declName us) xs) body
     let goal ← mkFreshExprSyntheticOpaqueMVar target
-    mkEqnTypes #[info.declName] goal.mvarId!
+    mkEqnTypes (tryRefl := true) #[info.declName] goal.mvarId!
   let baseName := info.declName
   let mut thmNames := #[]
   for i in [: eqnTypes.size] do

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

@@ -114,7 +114,8 @@ def mkEqns (declName : Name) (info : EqnInfo) : MetaM (Array Name) :=
     let us := info.levelParams.map mkLevelParam
     let target ← mkEq (mkAppN (Lean.mkConst declName us) xs) body
     let goal ← mkFreshExprSyntheticOpaqueMVar target
-    mkEqnTypes info.declNames goal.mvarId!
+    withReducible do
+      mkEqnTypes (tryRefl := false) info.declNames goal.mvarId!
   let mut thmNames := #[]
   for i in [: eqnTypes.size] do
     let type := eqnTypes[i]!

src/Lean/Elab/Print.lean

@@ -65,8 +65,36 @@ private def printInduct (id : Name) (levelParams : List Name) (numParams : Nat)
     m := m ++ Format.line ++ ctor ++ " : " ++ cinfo.type
   logInfo m
 
+open Meta in
+private def printStructure (id : Name) (levelParams : List Name) (numParams : Nat) (type : Expr)
+    (ctor : Name) (fields : Array Name) (isUnsafe : Bool) (isClass : Bool) : CommandElabM Unit := do
+  let kind := if isClass then "class" else "structure"
+  let mut m ← mkHeader' kind id levelParams type isUnsafe
+  m := m ++ Format.line ++ "number of parameters: " ++ toString numParams
+  m := m ++ Format.line ++ "constructor:"
+  let cinfo ← getConstInfo ctor
+  m := m ++ Format.line ++ ctor ++ " : " ++ cinfo.type
+  m := m ++ Format.line ++ "fields:" ++ (← doFields)
+  logInfo m
+where
+  doFields := liftTermElabM do
+    forallTelescope (← getConstInfo id).type fun params type =>
+      withLocalDeclD `self type fun self => do
+        let params := params.push self
+        let mut m : Format := ""
+        for field in fields do
+          match getProjFnForField? (← getEnv) id field with
+          | some proj =>
+            let field : Format := if isPrivateName proj then "private " ++ toString field else toString field
+            let cinfo ← getConstInfo proj
+            let ftype ← instantiateForall cinfo.type params
+            m := m ++ Format.line ++ field ++ " : " ++ (← ppExpr ftype) -- Why ppExpr here?
+          | none => panic! "missing structure field info"
+        return m
+
 private def printIdCore (id : Name) : CommandElabM Unit := do
-  match (← getEnv).find? id with
+  let env ← getEnv
+  match env.find? id with
   | ConstantInfo.axiomInfo { levelParams := us, type := t, isUnsafe := u, .. } => printAxiomLike "axiom" id us t u
   | ConstantInfo.defnInfo  { levelParams := us, type := t, value := v, safety := s, .. } => printDefLike "def" id us t v s
   | ConstantInfo.thmInfo  { levelParams := us, type := t, value := v, .. } => printDefLike "theorem" id us t v
@@ -75,7 +103,11 @@ private def printIdCore (id : Name) : CommandElabM Unit := do
   | ConstantInfo.ctorInfo { levelParams := us, type := t, isUnsafe := u, .. } => printAxiomLike "constructor" id us t u
   | ConstantInfo.recInfo { levelParams := us, type := t, isUnsafe := u, .. } => printAxiomLike "recursor" id us t u
   | ConstantInfo.inductInfo { levelParams := us, numParams, type := t, ctors, isUnsafe := u, .. } =>
-    printInduct id us numParams t ctors u
+    match getStructureInfo? env id with
+    | some { fieldNames, .. } =>
+      let [ctor] := ctors | panic! "structures have only one constructor"
+      printStructure id us numParams t ctor fieldNames u (isClass env id)
+    | none => printInduct id us numParams t ctors u
   | none => throwUnknownId id
 
 private def printId (id : Syntax) : CommandElabM Unit := do

src/Lean/Elab/StructInst.lean

@@ -821,7 +821,9 @@ partial def reduce (structNames : Array Name) (e : Expr) : MetaM Expr := do
     | some r => reduce structNames r
     | none   => return e.updateProj! (← reduce structNames b)
   | .app f .. =>
-    match (← reduceProjOf? e structNames.contains) with
+    -- Recall that proposition fields are theorems. Thus, we must set transparency to .all
+    -- to ensure they are unfolded here
+    match (← withTransparency .all <| reduceProjOf? e structNames.contains) with
     | some r => reduce structNames r
     | none   =>
       let f := f.getAppFn

src/Lean/Elab/Structure.lean

@@ -82,15 +82,6 @@ def StructFieldInfo.isSubobject (info : StructFieldInfo) : Bool :=
   | StructFieldKind.subobject => true
   | _                         => false
 
-structure ElabStructResult where
-  decl            : Declaration
-  projInfos       : List ProjectionInfo
-  projInstances   : List Name -- projections (to parent classes) that must be marked as instances.
-  mctx            : MetavarContext
-  lctx            : LocalContext
-  localInsts      : LocalInstances
-  defaultAuxDecls : Array (Name × Expr × Expr)
-
 private def defaultCtorName := `mk
 
 /-
@@ -713,8 +704,8 @@ private def registerStructure (structName : Name) (infos : Array StructFieldInfo
           subobject? :=
             if info.kind == StructFieldKind.subobject then
               match env.find? info.declName with
-              | some (ConstantInfo.defnInfo val) =>
-                match val.type.getForallBody.getAppFn with
+              | some info =>
+                match info.type.getForallBody.getAppFn with
                 | Expr.const parentName .. => some parentName
                 | _ => panic! "ill-formed structure"
               | _ => panic! "ill-formed environment"

src/Lean/Elab/Tactic/BuiltinTactic.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
+import Lean.Meta.Diagnostics
 import Lean.Meta.Tactic.Apply
 import Lean.Meta.Tactic.Assumption
 import Lean.Meta.Tactic.Contradiction
@@ -163,8 +164,12 @@ private def getOptRotation (stx : Syntax) : Nat :=
 
 @[builtin_tactic Parser.Tactic.set_option] def elabSetOption : Tactic := fun stx => do
   let options ← Elab.elabSetOption stx[1] stx[3]
-  withTheReader Core.Context (fun ctx => { ctx with maxRecDepth := maxRecDepth.get options, options := options }) do
-    evalTactic stx[5]
+  withOptions (fun _ => options) do
+    try
+      evalTactic stx[5]
+    finally
+      if stx[1].getId == `diagnostics then
+        reportDiag
 
 @[builtin_tactic Parser.Tactic.allGoals] def evalAllGoals : Tactic := fun stx => do
   let mvarIds ← getGoals

src/Lean/Elab/Tactic/LibrarySearch.lean

@@ -68,11 +68,8 @@ def elabExact?Term : TermElab := fun stx expectedType? => do
     let (_, introdGoal) ← goal.mvarId!.intros
     introdGoal.withContext do
       if let some suggestions ← librarySearch introdGoal then
-        reportOutOfHeartbeats `library_search stx
-        for suggestion in suggestions do
-          withMCtx suggestion.2 do
-            addTermSuggestion stx (← instantiateMVars goal).headBeta
-        if suggestions.isEmpty then logError "exact?# didn't find any relevant lemmas"
+        if suggestions.isEmpty then logError "`exact?%` didn't find any relevant lemmas"
+        else logError "`exact?%` could not close the goal. Try `by apply` to see partial suggestions."
         mkSorry expectedType (synthetic := true)
       else
         addTermSuggestion stx (← instantiateMVars goal).headBeta

src/Lean/Elab/Tactic/NormCast.lean

@@ -146,7 +146,9 @@ It tries to rewrite an expression using the elim and move lemmas.
 On failure, it calls the splitting procedure heuristic.
 -/
 partial def upwardAndElim (up : SimpTheorems) (e : Expr) : SimpM Simp.Step := do
-  let r ← withDischarger prove do
+  -- Remark: we set `wellBehavedDischarge := false` because `prove` may access arbitrary elements in the local context.
+  -- See comment at `Methods.wellBehavedDischarge`
+  let r ← withDischarger prove (wellBehavedDischarge := false) do
     Simp.rewrite? e up.post up.erased (tag := "squash") (rflOnly := false)
   let r := r.getD { expr := e }
   let r ← r.mkEqTrans (← splittingProcedure r.expr)

src/Lean/Elab/Tactic/Simp.lean

@@ -15,7 +15,6 @@ import Lean.Elab.Tactic.Config
 namespace Lean.Elab.Tactic
 open Meta
 open TSyntax.Compat
-open Simp (UsedSimps)
 
 declare_config_elab elabSimpConfigCore    Meta.Simp.Config
 declare_config_elab elabSimpConfigCtxCore Meta.Simp.ConfigCtx
@@ -327,7 +326,7 @@ If `stx` is the syntax of a `simp`, `simp_all` or `dsimp` tactic invocation, and
 creates the syntax of an equivalent `simp only`, `simp_all only` or `dsimp only`
 invocation.
 -/
-def mkSimpOnly (stx : Syntax) (usedSimps : UsedSimps) : MetaM Syntax := do
+def mkSimpOnly (stx : Syntax) (usedSimps : Simp.UsedSimps) : MetaM Syntax := do
   let isSimpAll := stx.isOfKind ``Parser.Tactic.simpAll
   let mut stx := stx
   if stx[3].isNone then
@@ -379,7 +378,7 @@ def mkSimpOnly (stx : Syntax) (usedSimps : UsedSimps) : MetaM Syntax := do
   let argsStx := if args.isEmpty then #[] else #[mkAtom "[", (mkAtom ",").mkSep args, mkAtom "]"]
   return stx.setArg 4 (mkNullNode argsStx)
 
-def traceSimpCall (stx : Syntax) (usedSimps : UsedSimps) : MetaM Unit := do
+def traceSimpCall (stx : Syntax) (usedSimps : Simp.UsedSimps) : MetaM Unit := do
   logInfoAt stx[0] m!"Try this: {← mkSimpOnly stx usedSimps}"
 
 /--
@@ -396,7 +395,7 @@ For many tactics other than the simplifier,
 one should use the `withLocation` tactic combinator
 when working with a `location`.
 -/
-def simpLocation (ctx : Simp.Context) (simprocs : Simp.SimprocsArray) (discharge? : Option Simp.Discharge := none) (loc : Location) : TacticM UsedSimps := do
+def simpLocation (ctx : Simp.Context) (simprocs : Simp.SimprocsArray) (discharge? : Option Simp.Discharge := none) (loc : Location) : TacticM Simp.Stats := do
   match loc with
   | Location.targets hyps simplifyTarget =>
     withMainContext do
@@ -406,33 +405,39 @@ def simpLocation (ctx : Simp.Context) (simprocs : Simp.SimprocsArray) (discharge
     withMainContext do
       go (← (← getMainGoal).getNondepPropHyps) (simplifyTarget := true)
 where
-  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM UsedSimps := do
+  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM Simp.Stats := do
     let mvarId ← getMainGoal
-    let (result?, usedSimps) ← simpGoal mvarId ctx (simprocs := simprocs) (simplifyTarget := simplifyTarget) (discharge? := discharge?) (fvarIdsToSimp := fvarIdsToSimp)
+    let (result?, stats) ← simpGoal mvarId ctx (simprocs := simprocs) (simplifyTarget := simplifyTarget) (discharge? := discharge?) (fvarIdsToSimp := fvarIdsToSimp)
     match result? with
     | none => replaceMainGoal []
     | some (_, mvarId) => replaceMainGoal [mvarId]
-    return usedSimps
+    return stats
+
+def withSimpDiagnostics (x : TacticM Simp.Diagnostics) : TacticM Unit := do
+  let stats ← x
+  Simp.reportDiag stats
 
 /-
   "simp" (config)? (discharger)? (" only")? (" [" ((simpStar <|> simpErase <|> simpLemma),*,?) "]")?
   (location)?
 -/
-@[builtin_tactic Lean.Parser.Tactic.simp] def evalSimp : Tactic := fun stx => withMainContext do
+@[builtin_tactic Lean.Parser.Tactic.simp] def evalSimp : Tactic := fun stx => withMainContext do withSimpDiagnostics do
   let { ctx, simprocs, dischargeWrapper } ← mkSimpContext stx (eraseLocal := false)
-  let usedSimps ← dischargeWrapper.with fun discharge? =>
+  let stats ← dischargeWrapper.with fun discharge? =>
     simpLocation ctx simprocs discharge? (expandOptLocation stx[5])
   if tactic.simp.trace.get (← getOptions) then
-    traceSimpCall stx usedSimps
+    traceSimpCall stx stats.usedTheorems
+  return stats.diag
 
-@[builtin_tactic Lean.Parser.Tactic.simpAll] def evalSimpAll : Tactic := fun stx => withMainContext do
+@[builtin_tactic Lean.Parser.Tactic.simpAll] def evalSimpAll : Tactic := fun stx => withMainContext do withSimpDiagnostics do
   let { ctx, simprocs, .. } ← mkSimpContext stx (eraseLocal := true) (kind := .simpAll) (ignoreStarArg := true)
-  let (result?, usedSimps) ← simpAll (← getMainGoal) ctx (simprocs := simprocs)
+  let (result?, stats) ← simpAll (← getMainGoal) ctx (simprocs := simprocs)
   match result? with
   | none => replaceMainGoal []
   | some mvarId => replaceMainGoal [mvarId]
   if tactic.simp.trace.get (← getOptions) then
-    traceSimpCall stx usedSimps
+    traceSimpCall stx stats.usedTheorems
+  return stats.diag
 
 def dsimpLocation (ctx : Simp.Context) (simprocs : Simp.SimprocsArray) (loc : Location) : TacticM Unit := do
   match loc with
@@ -444,14 +449,15 @@ def dsimpLocation (ctx : Simp.Context) (simprocs : Simp.SimprocsArray) (loc : Lo
     withMainContext do
       go (← (← getMainGoal).getNondepPropHyps) (simplifyTarget := true)
 where
-  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM Unit := do
+  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM Unit := withSimpDiagnostics do
     let mvarId ← getMainGoal
-    let (result?, usedSimps) ← dsimpGoal mvarId ctx simprocs (simplifyTarget := simplifyTarget) (fvarIdsToSimp := fvarIdsToSimp)
+    let (result?, stats) ← dsimpGoal mvarId ctx simprocs (simplifyTarget := simplifyTarget) (fvarIdsToSimp := fvarIdsToSimp)
     match result? with
     | none => replaceMainGoal []
     | some mvarId => replaceMainGoal [mvarId]
     if tactic.simp.trace.get (← getOptions) then
-      mvarId.withContext <| traceSimpCall (← getRef) usedSimps
+      mvarId.withContext <| traceSimpCall (← getRef) stats.usedTheorems
+    return stats.diag
 
 @[builtin_tactic Lean.Parser.Tactic.dsimp] def evalDSimp : Tactic := fun stx => do
   let { ctx, simprocs, .. } ← withMainContext <| mkSimpContext stx (eraseLocal := false) (kind := .dsimp)

src/Lean/Elab/Tactic/SimpTrace.lean

@@ -25,39 +25,41 @@ def mkSimpCallStx (stx : Syntax) (usedSimps : UsedSimps) : MetaM (TSyntax `tacti
 @[builtin_tactic simpTrace] def evalSimpTrace : Tactic := fun stx =>
   match stx with
   | `(tactic|
-      simp?%$tk $[!%$bang]? $(config)? $(discharger)? $[only%$o]? $[[$args,*]]? $(loc)?) => withMainContext do
+      simp?%$tk $[!%$bang]? $(config)? $(discharger)? $[only%$o]? $[[$args,*]]? $(loc)?) => withMainContext do withSimpDiagnostics do
     let stx ← if bang.isSome then
       `(tactic| simp!%$tk $(config)? $(discharger)? $[only%$o]? $[[$args,*]]? $(loc)?)
     else
       `(tactic| simp%$tk $(config)? $(discharger)? $[only%$o]? $[[$args,*]]? $(loc)?)
     let { ctx, simprocs, dischargeWrapper } ← mkSimpContext stx (eraseLocal := false)
-    let usedSimps ← dischargeWrapper.with fun discharge? =>
+    let stats ← dischargeWrapper.with fun discharge? =>
       simpLocation ctx (simprocs := simprocs) discharge? <|
         (loc.map expandLocation).getD (.targets #[] true)
-    let stx ← mkSimpCallStx stx usedSimps
+    let stx ← mkSimpCallStx stx stats.usedTheorems
     addSuggestion tk stx (origSpan? := ← getRef)
+    return stats.diag
   | _ => throwUnsupportedSyntax
 
 @[builtin_tactic simpAllTrace] def evalSimpAllTrace : Tactic := fun stx =>
   match stx with
-  | `(tactic| simp_all?%$tk $[!%$bang]? $(config)? $(discharger)? $[only%$o]? $[[$args,*]]?) => do
+  | `(tactic| simp_all?%$tk $[!%$bang]? $(config)? $(discharger)? $[only%$o]? $[[$args,*]]?) => withSimpDiagnostics do
     let stx ← if bang.isSome then
       `(tactic| simp_all!%$tk $(config)? $(discharger)? $[only%$o]? $[[$args,*]]?)
     else
       `(tactic| simp_all%$tk $(config)? $(discharger)? $[only%$o]? $[[$args,*]]?)
     let { ctx, .. } ← mkSimpContext stx (eraseLocal := true)
       (kind := .simpAll) (ignoreStarArg := true)
-    let (result?, usedSimps) ← simpAll (← getMainGoal) ctx
+    let (result?, stats) ← simpAll (← getMainGoal) ctx
     match result? with
     | none => replaceMainGoal []
     | some mvarId => replaceMainGoal [mvarId]
-    let stx ← mkSimpCallStx stx usedSimps
+    let stx ← mkSimpCallStx stx stats.usedTheorems
     addSuggestion tk stx (origSpan? := ← getRef)
+    return stats.diag
   | _ => throwUnsupportedSyntax
 
 /-- Implementation of `dsimp?`. -/
 def dsimpLocation' (ctx : Simp.Context) (simprocs : SimprocsArray) (loc : Location) :
-    TacticM Simp.UsedSimps := do
+    TacticM Simp.Stats := do
   match loc with
   | Location.targets hyps simplifyTarget =>
     withMainContext do
@@ -68,25 +70,26 @@ def dsimpLocation' (ctx : Simp.Context) (simprocs : SimprocsArray) (loc : Locati
       go (← (← getMainGoal).getNondepPropHyps) (simplifyTarget := true)
 where
   /-- Implementation of `dsimp?`. -/
-  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM Simp.UsedSimps := do
+  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM Simp.Stats := do
     let mvarId ← getMainGoal
-    let (result?, usedSimps) ← dsimpGoal mvarId ctx simprocs (simplifyTarget := simplifyTarget)
+    let (result?, stats) ← dsimpGoal mvarId ctx simprocs (simplifyTarget := simplifyTarget)
       (fvarIdsToSimp := fvarIdsToSimp)
     match result? with
     | none => replaceMainGoal []
     | some mvarId => replaceMainGoal [mvarId]
-    pure usedSimps
+    pure stats
 
 @[builtin_tactic dsimpTrace] def evalDSimpTrace : Tactic := fun stx =>
   match stx with
-  | `(tactic| dsimp?%$tk $[!%$bang]? $(config)? $[only%$o]? $[[$args,*]]? $(loc)?) => do
+  | `(tactic| dsimp?%$tk $[!%$bang]? $(config)? $[only%$o]? $[[$args,*]]? $(loc)?) => withSimpDiagnostics do
     let stx ← if bang.isSome then
       `(tactic| dsimp!%$tk $(config)? $[only%$o]? $[[$args,*]]? $(loc)?)
     else
       `(tactic| dsimp%$tk $(config)? $[only%$o]? $[[$args,*]]? $(loc)?)
     let { ctx, simprocs, .. } ←
       withMainContext <| mkSimpContext stx (eraseLocal := false) (kind := .dsimp)
-    let usedSimps ← dsimpLocation' ctx simprocs <| (loc.map expandLocation).getD (.targets #[] true)
-    let stx ← mkSimpCallStx stx usedSimps
+    let stats ← dsimpLocation' ctx simprocs <| (loc.map expandLocation).getD (.targets #[] true)
+    let stx ← mkSimpCallStx stx stats.usedTheorems
     addSuggestion tk stx (origSpan? := ← getRef)
+    return stats.diag
   | _ => throwUnsupportedSyntax

src/Lean/Elab/Tactic/Simpa.lean

@@ -31,7 +31,7 @@ deriving instance Repr for UseImplicitLambdaResult
 @[builtin_tactic Lean.Parser.Tactic.simpa] def evalSimpa : Tactic := fun stx => do
   match stx with
   | `(tactic| simpa%$tk $[?%$squeeze]? $[!%$unfold]? $(cfg)? $(disch)? $[only%$only]?
-        $[[$args,*]]? $[using $usingArg]?) => Elab.Tactic.focus do
+        $[[$args,*]]? $[using $usingArg]?) => Elab.Tactic.focus do withSimpDiagnostics do
     let stx ← `(tactic| simp $(cfg)? $(disch)? $[only%$only]? $[[$args,*]]?)
     let { ctx, simprocs, dischargeWrapper } ←
       withMainContext <| mkSimpContext stx (eraseLocal := false)
@@ -39,12 +39,13 @@ deriving instance Repr for UseImplicitLambdaResult
     -- TODO: have `simpa` fail if it doesn't use `simp`.
     let ctx := { ctx with config := { ctx.config with failIfUnchanged := false } }
     dischargeWrapper.with fun discharge? => do
-      let (some (_, g), usedSimps) ← simpGoal (← getMainGoal) ctx (simprocs := simprocs)
+      let (some (_, g), stats) ← simpGoal (← getMainGoal) ctx (simprocs := simprocs)
           (simplifyTarget := true) (discharge? := discharge?)
         | if getLinterUnnecessarySimpa (← getOptions) then
             logLint linter.unnecessarySimpa (← getRef) "try 'simp' instead of 'simpa'"
+          return {}
       g.withContext do
-      let usedSimps ← if let some stx := usingArg then
+      let stats ← if let some stx := usingArg then
         setGoals [g]
         g.withContext do
         let e ← Tactic.elabTerm stx none (mayPostpone := true)
@@ -52,8 +53,8 @@ deriving instance Repr for UseImplicitLambdaResult
           pure (h, g)
         else
           (← g.assert `h (← inferType e) e).intro1
-        let (result?, usedSimps) ← simpGoal g ctx (simprocs := simprocs) (fvarIdsToSimp := #[h])
-          (simplifyTarget := false) (usedSimps := usedSimps) (discharge? := discharge?)
+        let (result?, stats) ← simpGoal g ctx (simprocs := simprocs) (fvarIdsToSimp := #[h])
+          (simplifyTarget := false) (stats := stats) (discharge? := discharge?)
         match result? with
         | some (xs, g) =>
           let h := match xs with | #[h] | #[] => h | _ => unreachable!
@@ -66,18 +67,18 @@ deriving instance Repr for UseImplicitLambdaResult
             if (← getLCtx).getRoundtrippingUserName? h |>.isSome then
               logLint linter.unnecessarySimpa (← getRef)
                 m!"try 'simp at {Expr.fvar h}' instead of 'simpa using {Expr.fvar h}'"
-        pure usedSimps
+        pure stats
       else if let some ldecl := (← getLCtx).findFromUserName? `this then
-        if let (some (_, g), usedSimps) ← simpGoal g ctx (simprocs := simprocs)
-            (fvarIdsToSimp := #[ldecl.fvarId]) (simplifyTarget := false) (usedSimps := usedSimps)
+        if let (some (_, g), stats) ← simpGoal g ctx (simprocs := simprocs)
+            (fvarIdsToSimp := #[ldecl.fvarId]) (simplifyTarget := false) (stats := stats)
             (discharge? := discharge?) then
-          g.assumption; pure usedSimps
+          g.assumption; pure stats
         else
-          pure usedSimps
+          pure stats
       else
-        g.assumption; pure usedSimps
+        g.assumption; pure stats
       if tactic.simp.trace.get (← getOptions) || squeeze.isSome then
-        let stx ← match ← mkSimpOnly stx usedSimps with
+        let stx ← match ← mkSimpOnly stx stats.usedTheorems with
           | `(tactic| simp $(cfg)? $(disch)? $[only%$only]? $[[$args,*]]?) =>
             if unfold.isSome then
               `(tactic| simpa! $(cfg)? $(disch)? $[only%$only]? $[[$args,*]]? $[using $usingArg]?)
@@ -85,6 +86,7 @@ deriving instance Repr for UseImplicitLambdaResult
               `(tactic| simpa $(cfg)? $(disch)? $[only%$only]? $[[$args,*]]? $[using $usingArg]?)
           | _ => unreachable!
         TryThis.addSuggestion tk stx (origSpan? := ← getRef)
+      return stats.diag
     | _ => throwUnsupportedSyntax
 
 end Lean.Elab.Tactic.Simpa

src/Lean/Environment.lean

@@ -901,6 +901,55 @@ builtin_initialize namespacesExt : SimplePersistentEnvExtension Name NameSSet
     addEntryFn      := fun s n => s.insert n
   }
 
+structure Kernel.Diagnostics where
+  /-- Number of times each declaration has been unfolded by the kernel. -/
+  unfoldCounter : PHashMap Name Nat := {}
+  /-- If `enabled = true`, kernel records declarations that have been unfolded. -/
+  enabled : Bool := false
+  deriving Inhabited
+
+/--
+Extension for storting diagnostic information.
+
+Remark: We store kernel diagnostic information in an environment extension to simplify
+the interface with the kernel implemented in C/C++. Thus, we can only track
+declarations in methods, such as `addDecl`, which return a new environment.
+`Kernel.isDefEq` and `Kernel.whnf` do not update the statistics. We claim
+this is ok since these methods are mainly used for debugging.
+-/
+builtin_initialize diagExt : EnvExtension Kernel.Diagnostics ←
+  registerEnvExtension (pure {})
+
+@[export lean_kernel_diag_is_enabled]
+def Kernel.Diagnostics.isEnabled (d : Diagnostics) : Bool :=
+  d.enabled
+
+/-- Enables/disables kernel diagnostics. -/
+def Kernel.enableDiag (env : Environment) (flag : Bool) : Environment :=
+  diagExt.modifyState env fun s => { s with enabled := flag }
+
+def Kernel.isDiagnosticsEnabled (env : Environment) : Bool :=
+  diagExt.getState env |>.enabled
+
+def Kernel.resetDiag (env : Environment) : Environment :=
+  diagExt.modifyState env fun s => { s with unfoldCounter := {} }
+
+@[export lean_kernel_record_unfold]
+def Kernel.Diagnostics.recordUnfold (d : Diagnostics) (declName : Name) : Diagnostics :=
+  if d.enabled then
+    let cNew := if let some c := d.unfoldCounter.find? declName then c + 1 else 1
+    { d with unfoldCounter := d.unfoldCounter.insert declName cNew }
+  else
+    d
+
+@[export lean_kernel_get_diag]
+def Kernel.getDiagnostics (env : Environment) : Diagnostics :=
+  diagExt.getState env
+
+@[export lean_kernel_set_diag]
+def Kernel.setDiagnostics (env : Environment) (diag : Diagnostics) : Environment :=
+  diagExt.setState env diag
+
 namespace Environment
 
 /-- Register a new namespace in the environment. -/

src/Lean/Level.lean

@@ -428,15 +428,18 @@ def Result.imax : Result → Result → Result
   | f, Result.imaxNode Fs => Result.imaxNode (f::Fs)
   | f₁, f₂                => Result.imaxNode [f₁, f₂]
 
-def toResult : Level → Result
+def toResult (l : Level) (mvars : Bool) : Result :=
+  match l with
   | zero       => Result.num 0
-  | succ l     => Result.succ (toResult l)
-  | max l₁ l₂  => Result.max (toResult l₁) (toResult l₂)
-  | imax l₁ l₂ => Result.imax (toResult l₁) (toResult l₂)
+  | succ l     => Result.succ (toResult l mvars)
+  | max l₁ l₂  => Result.max (toResult l₁ mvars) (toResult l₂ mvars)
+  | imax l₁ l₂ => Result.imax (toResult l₁ mvars) (toResult l₂ mvars)
   | param n    => Result.leaf n
   | mvar n     =>
-    let n := n.name.replacePrefix `_uniq (Name.mkSimple "?u");
-    Result.leaf n
+    if mvars then
+      Result.leaf <| n.name.replacePrefix `_uniq (Name.mkSimple "?u")
+    else
+      Result.leaf `_
 
 private def parenIfFalse : Format → Bool → Format
   | f, true  => f
@@ -471,17 +474,17 @@ protected partial def Result.quote (r : Result) (prec : Nat) : Syntax.Level :=
 
 end PP
 
-protected def format (u : Level) : Format :=
-  (PP.toResult u).format true
+protected def format (u : Level) (mvars : Bool) : Format :=
+  (PP.toResult u mvars).format true
 
 instance : ToFormat Level where
-  format u := Level.format u
+  format u := Level.format u (mvars := true)
 
 instance : ToString Level where
-  toString u := Format.pretty (Level.format u)
+  toString u := Format.pretty (format u)
 
-protected def quote (u : Level) (prec : Nat := 0) : Syntax.Level :=
-  (PP.toResult u).quote prec
+protected def quote (u : Level) (prec : Nat := 0) (mvars : Bool := true) : Syntax.Level :=
+  (PP.toResult u (mvars := mvars)).quote prec
 
 instance : Quote Level `level where
   quote := Level.quote

src/Lean/Linter/Deprecated.lean

@@ -15,17 +15,23 @@ register_builtin_option linter.deprecated : Bool := {
   descr := "if true, generate deprecation warnings"
 }
 
-builtin_initialize deprecatedAttr : ParametricAttribute (Option Name) ←
+structure DeprecationEntry where
+  newName? : Option Name := none
+  text? : Option String := none
+  since? : Option String := none
+  deriving Inhabited
+
+builtin_initialize deprecatedAttr : ParametricAttribute DeprecationEntry ←
   registerParametricAttribute {
     name := `deprecated
     descr := "mark declaration as deprecated",
     getParam := fun _ stx => do
-     match stx with
-     | `(attr| deprecated $[$id?]?) =>
-       let some id := id? | return none
-       let declNameNew ← Elab.realizeGlobalConstNoOverloadWithInfo id
-       return some declNameNew
-     | _  => throwError "invalid `[deprecated]` attribute"
+      let `(attr| deprecated $[$id?]? $[$text?]? $[(since := $since?)]?) := stx
+        | throwError "invalid `[deprecated]` attribute"
+      let newName? ← id?.mapM Elab.realizeGlobalConstNoOverloadWithInfo
+      let text? := text?.map TSyntax.getString
+      let since? := since?.map TSyntax.getString
+      return { newName?, text?, since? }
   }
 
 def isDeprecated (env : Environment) (declName : Name) : Bool :=
@@ -34,12 +40,13 @@ def isDeprecated (env : Environment) (declName : Name) : Bool :=
 def _root_.Lean.MessageData.isDeprecationWarning (msg : MessageData) : Bool :=
   msg.hasTag (· == ``deprecatedAttr)
 
-def getDeprecatedNewName (env : Environment) (declName : Name) : Option Name :=
-  (deprecatedAttr.getParam? env declName).getD none
+def getDeprecatedNewName (env : Environment) (declName : Name) : Option Name := do
+  (← deprecatedAttr.getParam? env declName).newName?
 
 def checkDeprecated [Monad m] [MonadEnv m] [MonadLog m] [AddMessageContext m] [MonadOptions m] (declName : Name) : m Unit := do
   if getLinterValue linter.deprecated (← getOptions) then
-    match deprecatedAttr.getParam? (← getEnv) declName with
-    | none => pure ()
-    | some none => logWarning <| .tagged ``deprecatedAttr m!"`{declName}` has been deprecated"
-    | some (some newName) => logWarning <| .tagged ``deprecatedAttr m!"`{declName}` has been deprecated, use `{newName}` instead"
+    let some attr := deprecatedAttr.getParam? (← getEnv) declName | pure ()
+    logWarning <| .tagged ``deprecatedAttr <| attr.text?.getD <|
+      match attr.newName? with
+      | none => s!"`{declName}` has been deprecated"
+      | some newName => s!"`{declName}` has been deprecated, use `{newName}` instead"

src/Lean/Message.lean

@@ -120,7 +120,13 @@ def ofExpr (e : Expr) : MessageData :=
     hasSyntheticSorry := (instantiateMVarsCore · e |>.1.hasSyntheticSorry)
   }
 
-def ofLevel (l : Level) : MessageData := ofFormat (format l)
+def ofLevel (l : Level) : MessageData :=
+  .ofPPFormat {
+    pp := fun
+      | some ctx => ppLevel ctx l
+      | none => return format l
+  }
+
 def ofName (n : Name) : MessageData := ofFormat (format n)
 
 partial def hasSyntheticSorry (msg : MessageData) : Bool :=

src/Lean/Meta.lean

@@ -49,3 +49,4 @@ import Lean.Meta.LazyDiscrTree
 import Lean.Meta.LitValues
 import Lean.Meta.CheckTactic
 import Lean.Meta.Canonicalizer
+import Lean.Meta.Diagnostics

src/Lean/Meta/Basic.lean

@@ -110,6 +110,14 @@ structure Config where
   trackZetaDelta     : Bool := false
   /-- Eta for structures configuration mode. -/
   etaStruct          : EtaStructMode := .all
+  /--
+  When `univApprox` is set to true,
+  we use approximations when solving postponed universe constraints.
+  Examples:
+  - `max u ?v =?= u` is solved with `?v := u` and ignoring the solution `?v := 0`.
+  - `max u w =?= mav u ?v` is solved with `?v := w` ignoring the solution `?v := max u w`
+  -/
+  univApprox : Bool := true
 
 /--
   Function parameter information cache.
@@ -258,6 +266,15 @@ structure PostponedEntry where
   ctx? : Option DefEqContext
   deriving Inhabited
 
+structure Diagnostics where
+  /-- Number of times each declaration has been unfolded -/
+  unfoldCounter : PHashMap Name Nat := {}
+  /-- Number of times `f a =?= f b` heuristic has been used per function `f`. -/
+  heuristicCounter : PHashMap Name Nat := {}
+  /-- Number of times a TC instance is used. -/
+  instanceCounter : PHashMap Name Nat := {}
+  deriving Inhabited
+
 /--
   `MetaM` monad state.
 -/
@@ -268,6 +285,7 @@ structure State where
   zetaDeltaFVarIds : FVarIdSet := {}
   /-- Array of postponed universe level constraints -/
   postponed        : PersistentArray PostponedEntry := {}
+  diag             : Diagnostics := {}
   deriving Inhabited
 
 /--
@@ -300,6 +318,17 @@ structure Context where
     A predicate to control whether a constant can be unfolded or not at `whnf`.
     Note that we do not cache results at `whnf` when `canUnfold?` is not `none`. -/
   canUnfold?        : Option (Config → ConstantInfo → CoreM Bool) := none
+  /--
+  When `Config.univApprox := true`, this flag is set to `true` when there is no
+  progress processing universe constraints.
+  -/
+  univApprox        : Bool := false
+  /--
+  `inTypeClassResolution := true` when `isDefEq` is invoked at `tryResolve` in the type class
+   resolution module. We don't use `isDefEqProjDelta` when performing TC resolution due to performance issues.
+   This is not a great solution, but a proper solution would require a more sophisticased caching mechanism.
+  -/
+  inTypeClassResolution : Bool := false
 
 /--
 The `MetaM` monad is a core component of Lean's metaprogramming framework, facilitating the
@@ -421,7 +450,7 @@ section Methods
 variable [MonadControlT MetaM n] [Monad n]
 
 @[inline] def modifyCache (f : Cache → Cache) : MetaM Unit :=
-  modify fun { mctx, cache, zetaDeltaFVarIds, postponed } => { mctx, cache := f cache, zetaDeltaFVarIds, postponed }
+  modify fun { mctx, cache, zetaDeltaFVarIds, postponed, diag } => { mctx, cache := f cache, zetaDeltaFVarIds, postponed, diag }
 
 @[inline] def modifyInferTypeCache (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
   modifyCache fun ⟨ic, c1, c2, c3, c4, c5, c6⟩ => ⟨f ic, c1, c2, c3, c4, c5, c6⟩
@@ -435,6 +464,28 @@ variable [MonadControlT MetaM n] [Monad n]
 @[inline] def resetDefEqPermCaches : MetaM Unit :=
   modifyDefEqPermCache fun _ => {}
 
+@[inline] def modifyDiag (f : Diagnostics → Diagnostics) : MetaM Unit := do
+  if (← isDiagnosticsEnabled) then
+    modify fun { mctx, cache, zetaDeltaFVarIds, postponed, diag } => { mctx, cache, zetaDeltaFVarIds, postponed, diag := f diag }
+
+/-- If diagnostics are enabled, record that `declName` has been unfolded. -/
+def recordUnfold (declName : Name) : MetaM Unit := do
+  modifyDiag fun { unfoldCounter, heuristicCounter, instanceCounter } =>
+    let newC := if let some c := unfoldCounter.find? declName then c + 1 else 1
+    { unfoldCounter := unfoldCounter.insert declName newC, heuristicCounter, instanceCounter }
+
+/-- If diagnostics are enabled, record that heuristic for solving `f a =?= f b` has been used. -/
+def recordDefEqHeuristic (declName : Name) : MetaM Unit := do
+  modifyDiag fun { unfoldCounter, heuristicCounter, instanceCounter } =>
+    let newC := if let some c := heuristicCounter.find? declName then c + 1 else 1
+    { unfoldCounter, heuristicCounter := heuristicCounter.insert declName newC, instanceCounter }
+
+/-- If diagnostics are enabled, record that instance `declName` was used during TC resolution. -/
+def recordInstance (declName : Name) : MetaM Unit := do
+  modifyDiag fun { unfoldCounter, heuristicCounter, instanceCounter } =>
+    let newC := if let some c := instanceCounter.find? declName then c + 1 else 1
+    { unfoldCounter, heuristicCounter, instanceCounter := instanceCounter.insert declName newC }
+
 def getLocalInstances : MetaM LocalInstances :=
   return (← read).localInstances
 
@@ -1690,6 +1741,10 @@ partial def processPostponed (mayPostpone : Bool := true) (exceptionOnFailure :=
               return true
             else if numPostponed' < numPostponed then
               loop
+            -- If we cannot pospone anymore, `Config.univApprox := true`, but we haven't tried universe approximations yet,
+            -- then try approximations before failing.
+            else if !mayPostpone && (← getConfig).univApprox && !(← read).univApprox then
+              withReader (fun ctx => { ctx with univApprox := true }) loop
             else
               trace[Meta.isLevelDefEq.postponed] "no progress solving pending is-def-eq level constraints"
               return mayPostpone

src/Lean/Meta/Diagnostics.lean

@@ -0,0 +1,90 @@
+/-
+Copyright (c) 2023 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.PrettyPrinter
+import Lean.Meta.Basic
+import Lean.Meta.Instances
+
+namespace Lean.Meta
+
+def collectAboveThreshold [BEq α] [Hashable α] (counters : PHashMap α Nat) (threshold : Nat) (p : α → Bool) (lt : α → α → Bool) : Array (α × Nat) := Id.run do
+  let mut r := #[]
+  for (declName, counter) in counters do
+    if counter > threshold then
+    if p declName then
+      r := r.push (declName, counter)
+  return r.qsort fun (d₁, c₁) (d₂, c₂) => if c₁ == c₂ then lt d₁ d₂ else c₁ > c₂
+
+def subCounters [BEq α] [Hashable α] (newCounters oldCounters : PHashMap α Nat) : PHashMap α Nat := Id.run do
+  let mut result := {}
+  for (a, counterNew) in newCounters do
+    if let some counterOld := oldCounters.find? a then
+      result := result.insert a (counterNew - counterOld)
+    else
+      result := result.insert a counterNew
+  return result
+
+structure DiagSummary where
+  data  : Array MessageData := #[]
+  max   : Nat := 0
+  deriving Inhabited
+
+def DiagSummary.isEmpty (s : DiagSummary) : Bool :=
+  s.data.isEmpty
+
+def mkDiagSummary (counters : PHashMap Name Nat) (p : Name → Bool := fun _ => true) : MetaM DiagSummary := do
+  let threshold := diagnostics.threshold.get (← getOptions)
+  let entries := collectAboveThreshold counters threshold p Name.lt
+  if entries.isEmpty then
+    return {}
+  else
+    let mut data := #[]
+    for (declName, counter) in entries do
+      data := data.push m!"{if data.isEmpty then "  " else "\n"}{MessageData.ofConst (← mkConstWithLevelParams declName)} ↦ {counter}"
+    return { data, max := entries[0]!.2 }
+
+def mkDiagSummaryForUnfolded (counters : PHashMap Name Nat) (instances := false) : MetaM DiagSummary := do
+  let env ← getEnv
+  mkDiagSummary counters fun declName =>
+    getReducibilityStatusCore env declName matches .semireducible
+    && isInstanceCore env declName == instances
+
+def mkDiagSummaryForUnfoldedReducible (counters : PHashMap Name Nat) : MetaM DiagSummary := do
+  let env ← getEnv
+  mkDiagSummary counters fun declName =>
+    getReducibilityStatusCore env declName matches .reducible
+
+def mkDiagSummaryForUsedInstances : MetaM DiagSummary := do
+  mkDiagSummary (← get).diag.instanceCounter
+
+def appendSection (m : MessageData) (cls : Name) (header : String) (s : DiagSummary) : MessageData :=
+  if s.isEmpty then
+    m
+  else
+    let header := s!"{header} (max: {s.max}, num: {s.data.size}):"
+    m ++ .trace { cls } header s.data
+
+def reportDiag : MetaM Unit := do
+  if (← isDiagnosticsEnabled) then
+    let unfoldCounter := (← get).diag.unfoldCounter
+    let unfoldDefault ← mkDiagSummaryForUnfolded unfoldCounter
+    let unfoldInstance ← mkDiagSummaryForUnfolded unfoldCounter (instances := true)
+    let unfoldReducible ← mkDiagSummaryForUnfoldedReducible unfoldCounter
+    let heu ← mkDiagSummary (← get).diag.heuristicCounter
+    let inst ← mkDiagSummaryForUsedInstances
+    let unfoldKernel ← mkDiagSummary (Kernel.getDiagnostics (← getEnv)).unfoldCounter
+    unless unfoldDefault.isEmpty && unfoldInstance.isEmpty && unfoldReducible.isEmpty && heu.isEmpty && inst.isEmpty do
+      let m := MessageData.nil
+      let m := appendSection m `reduction "unfolded declarations" unfoldDefault
+      let m := appendSection m `reduction "unfolded instances" unfoldInstance
+      let m := appendSection m `reduction "unfolded reducible declarations" unfoldReducible
+      let m := appendSection m `type_class "used instances" inst
+      let m := appendSection m `def_eq "heuristic for solving `f a =?= f b`" heu
+      let m := appendSection m `kernel "unfolded declarations" unfoldKernel
+      let m := m ++ "use `set_option diagnostics.threshold <num>` to control threshold for reporting counters"
+      logInfo m
+
+end Lean.Meta

src/Lean/Meta/ExprDefEq.lean

@@ -10,6 +10,18 @@ import Lean.Util.OccursCheck
 
 namespace Lean.Meta
 
+register_builtin_option backward.isDefEq.lazyProjDelta : Bool := {
+  defValue := true
+  group    := "backward compatibility"
+  descr    := "use lazy delta reduction when solving unification constrains of the form `(f a).i =?= (g b).i`"
+}
+
+register_builtin_option backward.isDefEq.lazyWhnfCore : Bool := {
+  defValue := true
+  group    := "backward compatibility"
+  descr    := "specifies transparency mode when normalizing constraints of the form `(f a).i =?= s`, if `true` only reducible definitions and instances are unfolded when reducing `f a`. Otherwise, the default setting is used"
+}
+
 /--
   Return `true` if `e` is of the form `fun (x_1 ... x_n) => ?m y_1 ... y_k)`, and `?m` is unassigned.
   Remark: `n`, `k` may be 0.
@@ -108,9 +120,9 @@ private def isDefEqEta (a b : Expr) : MetaM LBool := do
     let bType ← inferType b
     let bType ← whnfD bType
     match bType with
-    | Expr.forallE n d _ c =>
+    | .forallE n d _ c =>
       let b' := mkLambda n c d (mkApp b (mkBVar 0))
-      toLBoolM <| checkpointDefEq <| Meta.isExprDefEqAux a b'
+      toLBoolM <| Meta.isExprDefEqAux a b'
     | _ => return .undef
   else
     return .undef
@@ -334,10 +346,12 @@ private partial def isDefEqArgs (f : Expr) (args₁ args₂ : Array Expr) : Meta
       k
   loop 0
 
-/-- Auxiliary function for `isDefEqBinding` for handling binders `forall/fun`.
-   It accumulates the new free variables in `fvars`, and declare them at `lctx`.
-   We use the domain types of `e₁` to create the new free variables.
-   We store the domain types of `e₂` at `ds₂`. -/
+/--
+Auxiliary function for `isDefEqBinding` for handling binders `forall/fun`.
+It accumulates the new free variables in `fvars`, and declare them at `lctx`.
+We use the domain types of `e₁` to create the new free variables.
+We store the domain types of `e₂` at `ds₂`.
+-/
 private partial def isDefEqBindingAux (lctx : LocalContext) (fvars : Array Expr) (e₁ e₂ : Expr) (ds₂ : Array Expr) : MetaM Bool :=
   let process (n : Name) (d₁ d₂ b₁ b₂ : Expr) : MetaM Bool := do
     let d₁     := d₁.instantiateRev fvars
@@ -374,34 +388,34 @@ private def checkTypesAndAssign (mvar : Expr) (v : Expr) : MetaM Bool :=
         pure false
 
 /--
-  Auxiliary method for solving constraints of the form `?m xs := v`.
-  It creates a lambda using `mkLambdaFVars ys v`, where `ys` is a superset of `xs`.
-  `ys` is often equal to `xs`. It is a bigger when there are let-declaration dependencies in `xs`.
-  For example, suppose we have `xs` of the form `#[a, c]` where
-  ```
-  a : Nat
-  b : Nat := f a
-  c : b = a
-  ```
-  In this scenario, the type of `?m` is `(x1 : Nat) -> (x2 : f x1 = x1) -> C[x1, x2]`,
-  and type of `v` is `C[a, c]`. Note that, `?m a c` is type correct since `f a = a` is definitionally equal
-  to the type of `c : b = a`, and the type of `?m a c` is equal to the type of `v`.
-  Note that `fun xs => v` is the term `fun (x1 : Nat) (x2 : b = x1) => v` which has type
-  `(x1 : Nat) -> (x2 : b = x1) -> C[x1, x2]` which is not definitionally equal to the type of `?m`,
-  and may not even be type correct.
-  The issue here is that we are not capturing the `let`-declarations.
+Auxiliary method for solving constraints of the form `?m xs := v`.
+It creates a lambda using `mkLambdaFVars ys v`, where `ys` is a superset of `xs`.
+`ys` is often equal to `xs`. It is a bigger when there are let-declaration dependencies in `xs`.
+For example, suppose we have `xs` of the form `#[a, c]` where
+```
+a : Nat
+b : Nat := f a
+c : b = a
+```
+In this scenario, the type of `?m` is `(x1 : Nat) -> (x2 : f x1 = x1) -> C[x1, x2]`,
+and type of `v` is `C[a, c]`. Note that, `?m a c` is type correct since `f a = a` is definitionally equal
+to the type of `c : b = a`, and the type of `?m a c` is equal to the type of `v`.
+Note that `fun xs => v` is the term `fun (x1 : Nat) (x2 : b = x1) => v` which has type
+`(x1 : Nat) -> (x2 : b = x1) -> C[x1, x2]` which is not definitionally equal to the type of `?m`,
+and may not even be type correct.
+The issue here is that we are not capturing the `let`-declarations.
 
-  This method collects let-declarations `y` occurring between `xs[0]` and `xs.back` s.t.
-  some `x` in `xs` depends on `y`.
-  `ys` is the `xs` with these extra let-declarations included.
+This method collects let-declarations `y` occurring between `xs[0]` and `xs.back` s.t.
+some `x` in `xs` depends on `y`.
+`ys` is the `xs` with these extra let-declarations included.
 
-  In the example above, `ys` is `#[a, b, c]`, and `mkLambdaFVars ys v` produces
-  `fun a => let b := f a; fun (c : b = a) => v` which has a type definitionally equal to the type of `?m`.
+In the example above, `ys` is `#[a, b, c]`, and `mkLambdaFVars ys v` produces
+`fun a => let b := f a; fun (c : b = a) => v` which has a type definitionally equal to the type of `?m`.
 
-  Recall that the method `checkAssignment` ensures `v` does not contain offending `let`-declarations.
+Recall that the method `checkAssignment` ensures `v` does not contain offending `let`-declarations.
 
-  This method assumes that for any `xs[i]` and `xs[j]` where `i < j`, we have that `index of xs[i]` < `index of xs[j]`.
-  where the index is the position in the local context.
+This method assumes that for any `xs[i]` and `xs[j]` where `i < j`, we have that `index of xs[i]` < `index of xs[j]`.
+where the index is the position in the local context.
 -/
 private partial def mkLambdaFVarsWithLetDeps (xs : Array Expr) (v : Expr) : MetaM (Option Expr) := do
   if not (← hasLetDeclsInBetween) then
@@ -435,13 +449,13 @@ where
     let rec visit (e : Expr) : MonadCacheT Expr Unit (ReaderT Nat (StateRefT FVarIdHashSet MetaM)) Unit :=
       checkCache e fun _ => do
         match e with
-        | Expr.forallE _ d b _   => visit d; visit b
-        | Expr.lam _ d b _       => visit d; visit b
-        | Expr.letE _ t v b _    => visit t; visit v; visit b
-        | Expr.app f a           => visit f; visit a
-        | Expr.mdata _ b         => visit b
-        | Expr.proj _ _ b        => visit b
-        | Expr.fvar fvarId       =>
+        | .forallE _ d b _   => visit d; visit b
+        | .lam _ d b _       => visit d; visit b
+        | .letE _ t v b _    => visit t; visit v; visit b
+        | .app f a           => visit f; visit a
+        | .mdata _ b         => visit b
+        | .proj _ _ b        => visit b
+        | .fvar fvarId       =>
           let localDecl ← fvarId.getDecl
           if localDecl.isLet && localDecl.index > (← read) then
             modify fun s => s.insert localDecl.fvarId
@@ -834,18 +848,18 @@ mutual
       return e
     else checkCache e fun _ =>
       match e with
-      | Expr.mdata _ b       => return e.updateMData! (← check b)
-      | Expr.proj _ _ s      => return e.updateProj! (← check s)
-      | Expr.lam _ d b _     => return e.updateLambdaE! (← check d) (← check b)
-      | Expr.forallE _ d b _ => return e.updateForallE! (← check d) (← check b)
-      | Expr.letE _ t v b _  => return e.updateLet! (← check t) (← check v) (← check b)
-      | Expr.bvar ..         => return e
-      | Expr.sort ..         => return e
-      | Expr.const ..        => return e
-      | Expr.lit ..          => return e
-      | Expr.fvar ..         => checkFVar e
-      | Expr.mvar ..         => checkMVar e
-      | Expr.app ..          =>
+      | .mdata _ b       => return e.updateMData! (← check b)
+      | .proj _ _ s      => return e.updateProj! (← check s)
+      | .lam _ d b _     => return e.updateLambdaE! (← check d) (← check b)
+      | .forallE _ d b _ => return e.updateForallE! (← check d) (← check b)
+      | .letE _ t v b _  => return e.updateLet! (← check t) (← check v) (← check b)
+      | .bvar ..         => return e
+      | .sort ..         => return e
+      | .const ..        => return e
+      | .lit ..          => return e
+      | .fvar ..         => checkFVar e
+      | .mvar ..         => checkMVar e
+      | .app ..          =>
         try
           checkApp e
         catch ex => match ex with
@@ -890,24 +904,24 @@ partial def check
     if !e.hasExprMVar && !e.hasFVar then
       true
     else match e with
-    | Expr.mdata _ b       => visit b
-    | Expr.proj _ _ s      => visit s
-    | Expr.app f a         => visit f && visit a
-    | Expr.lam _ d b _     => visit d && visit b
-    | Expr.forallE _ d b _ => visit d && visit b
-    | Expr.letE _ t v b _  => visit t && visit v && visit b
-    | Expr.bvar ..         => true
-    | Expr.sort ..         => true
-    | Expr.const ..        => true
-    | Expr.lit ..          => true
-    | Expr.fvar fvarId ..  =>
+    | .mdata _ b       => visit b
+    | .proj _ _ s      => visit s
+    | .app f a         => visit f && visit a
+    | .lam _ d b _     => visit d && visit b
+    | .forallE _ d b _ => visit d && visit b
+    | .letE _ t v b _  => visit t && visit v && visit b
+    | .bvar ..         => true
+    | .sort ..         => true
+    | .const ..        => true
+    | .lit ..          => true
+    | .fvar fvarId ..  =>
       if mvarDecl.lctx.contains fvarId then true
       else match lctx.find? fvarId with
         | some (LocalDecl.ldecl ..) => false -- need expensive CheckAssignment.check
         | _ =>
           if fvars.any fun x => x.fvarId! == fvarId then true
           else false -- We could throw an exception here, but we would have to use ExceptM. So, we let CheckAssignment.check do it
-    | Expr.mvar mvarId'    =>
+    | .mvar mvarId'    =>
       match mctx.getExprAssignmentCore? mvarId' with
       | some _ => false -- use CheckAssignment.check to instantiate
       | none   =>
@@ -1239,6 +1253,7 @@ private def tryHeuristic (t s : Expr) : MetaM Bool := do
     unless t.hasExprMVar || s.hasExprMVar do
       return false
   withTraceNodeBefore `Meta.isDefEq.delta (return m!"{t} =?= {s}") do
+    recordDefEqHeuristic tFn.constName!
     /-
       We process arguments before universe levels to reduce a source of brittleness in the TC procedure.
 
@@ -1462,8 +1477,8 @@ private def expandDelayedAssigned? (t : Expr) : MetaM (Option Expr) := do
   return some (mkAppRange (mkMVar mvarIdPending) fvars.size tArgs.size tArgs)
 
 private def isAssignable : Expr → MetaM Bool
-  | Expr.mvar mvarId => do let b ← mvarId.isReadOnlyOrSyntheticOpaque; pure (!b)
-  | _                => pure false
+  | .mvar mvarId => do let b ← mvarId.isReadOnlyOrSyntheticOpaque; pure (!b)
+  | _            => pure false
 
 private def etaEq (t s : Expr) : Bool :=
   match t.etaExpanded? with
@@ -1538,7 +1553,7 @@ private def isDefEqMVarSelf (mvar : Expr) (args₁ args₂ : Array Expr) : MetaM
 Removes unnecessary let-decls (both true `let`s and `let_fun`s).
 -/
 private partial def consumeLet : Expr → Expr
-  | e@(Expr.letE _ _ _ b _) => if b.hasLooseBVars then e else consumeLet b
+  | e@(.letE _ _ _ b _) => if b.hasLooseBVars then e else consumeLet b
   | e =>
     if let some (_, _, _, b) := e.letFun? then
       if b.hasLooseBVars then e else consumeLet b
@@ -1708,11 +1723,10 @@ private partial def isDefEqQuickMVarMVar (t s : Expr) : MetaM LBool := do
 end
 
 @[inline] def whenUndefDo (x : MetaM LBool) (k : MetaM Bool) : MetaM Bool := do
-  let status ← x
-  match status with
-  | LBool.true  => pure true
-  | LBool.false => pure false
-  | LBool.undef => k
+  match (← x) with
+  | .true  => return true
+  | .false => return false
+  | .undef => k
 
 @[specialize] private def unstuckMVar (e : Expr) (successK : Expr → MetaM Bool) (failK : MetaM Bool): MetaM Bool := do
   match (← getStuckMVar? e) with
@@ -1757,10 +1771,21 @@ private def isDefEqDeltaStep (t s : Expr) : MetaM DeltaStepResult := do
     | .lt => unfold t (return .unknown) (k · s)
     | .gt => unfold s (return .unknown) (k t ·)
     | .eq =>
-      unfold t
-        (unfold s (return .unknown) (k t ·))
-        (fun t => unfold s (k t s) (k t ·))
+      -- Remark: if `t` and `s` are both some `f`-application, we use `tryHeuristic`
+      -- if `f` is not a projection. The projection case generates a performance regression.
+      if tInfo.name == sInfo.name then
+        if t.isApp && s.isApp && (← tryHeuristic t s) then
+          return .eq
+        else
+          unfoldBoth t s
+      else
+        unfoldBoth t s
 where
+  unfoldBoth (t s : Expr) : MetaM DeltaStepResult := do
+    unfold t
+      (unfold s (return .unknown) (k t ·))
+      (fun t => unfold s (k t s) (k t ·))
+
   k (t s : Expr) : MetaM DeltaStepResult := do
     let t ← whnfCore t
     let s ← whnfCore s
@@ -1792,8 +1817,13 @@ where
     | _, _ => Meta.isExprDefEqAux t s
 
 private def isDefEqProj : Expr → Expr → MetaM Bool
-  | .proj m i t, .proj n j s =>
-    if i == j && m == n then
+  | .proj m i t, .proj n j s => do
+    if (← read).inTypeClassResolution then
+      -- See comment at `inTypeClassResolution`
+      pure (i == j && m == n) <&&> Meta.isExprDefEqAux t s
+    else if !backward.isDefEq.lazyProjDelta.get (← getOptions) then
+      pure (i == j && m == n) <&&> Meta.isExprDefEqAux t s
+    else if i == j && m == n then
       isDefEqProjDelta t s i
     else
       return false
@@ -1966,6 +1996,12 @@ private def cacheResult (keyInfo : DefEqCacheKeyInfo) (result : Bool) : MetaM Un
     let key := (← instantiateMVars key.1, ← instantiateMVars key.2)
     modifyDefEqTransientCache fun c => c.update mode key result
 
+private def whnfCoreAtDefEq (e : Expr) : MetaM Expr := do
+  if backward.isDefEq.lazyWhnfCore.get (← getOptions) then
+    whnfCore e (config := { proj := .yesWithDeltaI })
+  else
+    whnfCore e
+
 @[export lean_is_expr_def_eq]
 partial def isExprDefEqAuxImpl (t : Expr) (s : Expr) : MetaM Bool := withIncRecDepth do
   withTraceNodeBefore `Meta.isDefEq (return m!"{t} =?= {s}") do
@@ -1978,7 +2014,7 @@ partial def isExprDefEqAuxImpl (t : Expr) (s : Expr) : MetaM Bool := withIncRecD
     we only want to unify negation (and not all other field operations as well).
     Unifying the field instances slowed down unification: https://github.com/leanprover/lean4/issues/1986
 
-    Note that ew use `proj := .yesWithDeltaI` to ensure `whnfAtMostI` is used to reduce the projection structure.
+    Note that we use `proj := .yesWithDeltaI` to ensure `whnfAtMostI` is used to reduce the projection structure.
     We added this refinement to address a performance issue in code such as
     ```
     let val : Test := bar c1 key
@@ -2007,8 +2043,8 @@ partial def isExprDefEqAuxImpl (t : Expr) (s : Expr) : MetaM Bool := withIncRecD
     `whnfCore t (config := { proj := .yes })` which more conservative than `.yesWithDeltaI`,
     and it only created performance issues when handling TC unification problems.
   -/
-  let t' ← whnfCore t (config := { proj := .yesWithDeltaI })
-  let s' ← whnfCore s (config := { proj := .yesWithDeltaI })
+  let t' ← whnfCoreAtDefEq t
+  let s' ← whnfCoreAtDefEq s
   if t != t' || s != s' then
     isExprDefEqAuxImpl t' s'
   else

src/Lean/Meta/ExprLens.lean

@@ -21,27 +21,28 @@ section ExprLens
 
 open Lean.SubExpr
 
-variable {M} [Monad M] [MonadLiftT MetaM M] [MonadControlT MetaM M] [MonadError M]
+variable [Monad M] [MonadLiftT MetaM M] [MonadControlT MetaM M] [MonadError M]
 
 /-- Given a constructor index for Expr, runs `g` on the value of that subexpression and replaces it.
 If the subexpression is under a binder it will instantiate and abstract the binder body correctly.
 Mdata is ignored. An index of 3 is interpreted as the type of the expression. An index of 3 will throw since we can't replace types.
 
 See also `Lean.Meta.transform`, `Lean.Meta.traverseChildren`. -/
-private def lensCoord (g : Expr → M Expr) : Nat → Expr → M Expr
-  | 0, e@(Expr.app f a)         => return e.updateApp! (← g f) a
-  | 1, e@(Expr.app f a)         => return e.updateApp! f (← g a)
-  | 0, e@(Expr.lam _ y b _)     => return e.updateLambdaE! (← g y) b
-  | 1,   (Expr.lam n y b c)     => withLocalDecl n c y fun x => do mkLambdaFVars #[x] <|← g <| b.instantiateRev #[x]
-  | 0, e@(Expr.forallE _ y b _) => return e.updateForallE! (← g y) b
-  | 1,   (Expr.forallE n y b c) => withLocalDecl n c y fun x => do mkForallFVars #[x] <|← g <| b.instantiateRev #[x]
-  | 0, e@(Expr.letE _ y a b _)  => return e.updateLet! (← g y) a b
-  | 1, e@(Expr.letE _ y a b _)  => return e.updateLet! y (← g a) b
-  | 2,   (Expr.letE n y a b _)  => withLetDecl n y a fun x => do mkLetFVars #[x] <|← g <| b.instantiateRev #[x]
-  | 0, e@(Expr.proj _ _ b)      => e.updateProj! <$> g b
-  | n, e@(Expr.mdata _ a)       => e.updateMData! <$> lensCoord g n a
-  | 3, _                        => throwError "Lensing on types is not supported"
-  | c, e                        => throwError "Invalid coordinate {c} for {e}"
+private def lensCoord (g : Expr → M Expr) (n : Nat) (e : Expr) : M Expr := do
+  match n, e with
+  | 0, .app f a         => return e.updateApp! (← g f) a
+  | 1, .app f a         => return e.updateApp! f (← g a)
+  | 0, .lam _ y b _     => return e.updateLambdaE! (← g y) b
+  | 1, .lam n y b c     => withLocalDecl n c y fun x => do mkLambdaFVars #[x] <|← g <| b.instantiateRev #[x]
+  | 0, .forallE _ y b _ => return e.updateForallE! (← g y) b
+  | 1, .forallE n y b c => withLocalDecl n c y fun x => do mkForallFVars #[x] <|← g <| b.instantiateRev #[x]
+  | 0, .letE _ y a b _  => return e.updateLet! (← g y) a b
+  | 1, .letE _ y a b _  => return e.updateLet! y (← g a) b
+  | 2, .letE n y a b _  => withLetDecl n y a fun x => do mkLetFVars #[x] <|← g <| b.instantiateRev #[x]
+  | 0, .proj _ _ b      => e.updateProj! <$> g b
+  | n, .mdata _ a       => e.updateMData! <$> lensCoord g n a
+  | 3, _                => throwError "Lensing on types is not supported"
+  | c, e                => throwError "Invalid coordinate {c} for {e}"
 
 private def lensAux (g : Expr → M Expr) : List Nat → Expr → M Expr
   | [], e => g e
@@ -56,20 +57,21 @@ def replaceSubexpr (replace : (subexpr : Expr) → M Expr) (p : Pos) (root : Exp
 /-- Runs `k` on the given coordinate, including handling binders properly.
 The subexpression value passed to `k` is not instantiated with respect to the
 array of free variables. -/
-private def viewCoordAux (k : Array Expr → Expr → M α) (fvars: Array Expr) : Nat → Expr → M α
-  | 3, _                      => throwError "Internal: Types should be handled by viewAux"
-  | 0, (Expr.app f _)         => k fvars f
-  | 1, (Expr.app _ a)         => k fvars a
-  | 0, (Expr.lam _ y _ _)     => k fvars y
-  | 1, (Expr.lam n y b c)     => withLocalDecl n c (y.instantiateRev fvars) fun x => k (fvars.push x) b
-  | 0, (Expr.forallE _ y _ _) => k fvars y
-  | 1, (Expr.forallE n y b c) => withLocalDecl n c (y.instantiateRev fvars) fun x => k (fvars.push x) b
-  | 0, (Expr.letE _ y _ _ _)  => k fvars y
-  | 1, (Expr.letE _ _ a _ _)  => k fvars a
-  | 2, (Expr.letE n y a b _)  => withLetDecl n (y.instantiateRev fvars) (a.instantiateRev fvars) fun x => k (fvars.push x) b
-  | 0, (Expr.proj _ _ b)      => k fvars b
-  | n, (Expr.mdata _ a)       => viewCoordAux k fvars n a
-  | c, e                      => throwError "Invalid coordinate {c} for {e}"
+private def viewCoordAux (k : Array Expr → Expr → M α) (fvars: Array Expr) (n : Nat) (e : Expr) : M α := do
+  match n, e with
+  | 3, _                => throwError "Internal: Types should be handled by viewAux"
+  | 0, .app f _         => k fvars f
+  | 1, .app _ a         => k fvars a
+  | 0, .lam _ y _ _     => k fvars y
+  | 1, .lam n y b c     => withLocalDecl n c (y.instantiateRev fvars) fun x => k (fvars.push x) b
+  | 0, .forallE _ y _ _ => k fvars y
+  | 1, .forallE n y b c => withLocalDecl n c (y.instantiateRev fvars) fun x => k (fvars.push x) b
+  | 0, .letE _ y _ _ _  => k fvars y
+  | 1, .letE _ _ a _ _  => k fvars a
+  | 2, .letE n y a b _  => withLetDecl n (y.instantiateRev fvars) (a.instantiateRev fvars) fun x => k (fvars.push x) b
+  | 0, .proj _ _ b      => k fvars b
+  | n, .mdata _ a       => viewCoordAux k fvars n a
+  | c, e                => throwError "Invalid coordinate {c} for {e}"
 
 private def viewAux (k : Array Expr → Expr → M α) (fvars : Array Expr) : List Nat → Expr → M α
   | [],         e => k fvars <| e.instantiateRev fvars
@@ -119,24 +121,24 @@ open Lean.SubExpr
 
 section ViewRaw
 
-variable {M} [Monad M] [MonadError M]
+variable [Monad M] [MonadError M]
 
 /-- Get the raw subexpression without performing any instantiation. -/
-private def viewCoordRaw: Expr → Nat → M Expr
-  | e                     , 3 => throwError "Can't viewRaw the type of {e}"
-  | (Expr.app f _)        , 0 => pure f
-  | (Expr.app _ a)        , 1 => pure a
-  | (Expr.lam _ y _ _)    , 0 => pure y
-  | (Expr.lam _ _ b _)    , 1 => pure b
-  | (Expr.forallE _ y _ _), 0 => pure y
-  | (Expr.forallE _ _ b _), 1 => pure b
-  | (Expr.letE _ y _ _ _) , 0 => pure y
-  | (Expr.letE _ _ a _ _) , 1 => pure a
-  | (Expr.letE _ _ _ b _) , 2 => pure b
-  | (Expr.proj _ _ b)     , 0 => pure b
-  | (Expr.mdata _ a)      , n => viewCoordRaw a n
-  | e                     , c => throwError "Bad coordinate {c} for {e}"
-
+private def viewCoordRaw (e : Expr) (n : Nat) : M Expr := do
+  match e, n with
+  | e,                3 => throwError "Can't viewRaw the type of {e}"
+  | .app f _,         0 => pure f
+  | .app _ a,         1 => pure a
+  | .lam _ y _ _,     0 => pure y
+  | .lam _ _ b _,     1 => pure b
+  | .forallE _ y _ _, 0 => pure y
+  | .forallE _ _ b _, 1 => pure b
+  | .letE _ y _ _ _,  0 => pure y
+  | .letE _ _ a _ _,  1 => pure a
+  | .letE _ _ _ b _,  2 => pure b
+  | .proj _ _ b,      0 => pure b
+  | .mdata _ a,       n => viewCoordRaw a n
+  | e,                c => throwError "Bad coordinate {c} for {e}"
 
 /-- Given a valid `SubExpr`, return the raw current expression without performing any instantiation.
 If the given `SubExpr` has a type subexpression coordinate, then throw an error.
@@ -148,21 +150,20 @@ def viewSubexpr (p : Pos) (root : Expr) : M Expr :=
   p.foldlM viewCoordRaw root
 
 private def viewBindersCoord : Nat → Expr → Option (Name × Expr)
-  | 1, (Expr.lam n y _ _)     => some (n, y)
-  | 1, (Expr.forallE n y _ _) => some (n, y)
-  | 2, (Expr.letE n y _ _ _)  => some (n, y)
-  | _, _                      => none
+  | 1, .lam n y _ _     => some (n, y)
+  | 1, .forallE n y _ _ => some (n, y)
+  | 2, .letE n y _ _ _  => some (n, y)
+  | _, _                => none
 
 /-- `viewBinders p e` returns a list of all of the binders (name, type) above the given position `p` in the root expression `e` -/
 def viewBinders (p : Pos) (root : Expr) : M (Array (Name × Expr)) := do
-  let (acc, _) ← p.foldlM (fun (acc, e) c => do
+  let (acc, _) ← p.foldlM (init := (#[], root)) fun (acc, e) c => do
     let e₂ ← viewCoordRaw e c
     let acc :=
       match viewBindersCoord c e with
       | none => acc
       | some b => acc.push b
     return (acc, e₂)
-  ) (#[], root)
   return acc
 
 /-- Returns the number of binders above a given subexpr position. -/

src/Lean/Meta/Injective.lean

@@ -31,6 +31,35 @@ def elimOptParam (type : Expr) : CoreM Expr := do
     else
       return .continue
 
+
+/-- Returns true if `e` occurs either in `t`, or in the type of a sub-expression of `t`.
+  Consider the following example:
+  ```lean
+  inductive Tyₛ : Type (u+1)
+  | SPi : (T : Type u) -> (T -> Tyₛ) -> Tyₛ
+
+  inductive Tmₛ.{u} :  Tyₛ.{u} -> Type (u+1)
+  | app : Tmₛ (.SPi T A) -> (arg : T) -> Tmₛ (A arg)```
+  ```
+  When looking for fixed arguments in `Tmₛ.app`, if we only consider occurences in the term `Tmₛ (A arg)`,
+  `T` is considered non-fixed despite the fact that `A : T -> Tyₛ`.
+  This leads to an ill-typed injectivity theorem signature:
+  ```lean
+  theorem Tmₛ.app.inj {T : Type u} {A : T → Tyₛ} {a : Tmₛ (Tyₛ.SPi T A)} {arg : T} {T_1 : Type u} {a_1 : Tmₛ (Tyₛ.SPi T_1 A)} :
+  Tmₛ.app a arg = Tmₛ.app a_1 arg →
+    T = T_1 ∧ HEq a a_1 := fun x => Tmₛ.noConfusion x fun T_eq A_eq a_eq arg_eq => eq_of_heq a_eq
+  ```
+  Instead of checking the type of every subterm, we only need to check the type of free variables, since free variables introduced in
+  the constructor may only appear in the type of other free variables introduced after them.
+-/
+def occursOrInType (e : Expr) (t : Expr) : MetaM Bool := do
+  let_fun f (s : Expr) := do
+    if !s.isFVar then
+      return s == e
+    let ty ← inferType s
+    return s == e || e.occurs ty
+  return (← t.findM? f).isSome
+
 private partial def mkInjectiveTheoremTypeCore? (ctorVal : ConstructorVal) (useEq : Bool) : MetaM (Option Expr) := do
   let us := ctorVal.levelParams.map mkLevelParam
   let type ← elimOptParam ctorVal.type
@@ -58,7 +87,7 @@ private partial def mkInjectiveTheoremTypeCore? (ctorVal : ConstructorVal) (useE
         match (← whnf type) with
         | Expr.forallE n d b _ =>
           let arg1 := args1.get ⟨i, h⟩
-          if arg1.occurs resultType then
+          if ← occursOrInType arg1 resultType then
             mkArgs2 (i + 1) (b.instantiate1 arg1) (args2.push arg1) args2New
           else
             withLocalDecl n (if useEq then BinderInfo.default else BinderInfo.implicit) d fun arg2 =>

src/Lean/Meta/Instances.lean

@@ -114,7 +114,7 @@ For example:
 
 (The type of `inst` must not contain mvars.)
 -/
-partial def computeSynthOrder (inst : Expr) : MetaM (Array Nat) :=
+private partial def computeSynthOrder (inst : Expr) : MetaM (Array Nat) :=
   withReducible do
   let instTy ← inferType inst
 
@@ -217,8 +217,11 @@ def getGlobalInstancesIndex : CoreM (DiscrTree InstanceEntry) :=
 def getErasedInstances : CoreM (PHashSet Name) :=
   return Meta.instanceExtension.getState (← getEnv) |>.erased
 
+def isInstanceCore (env : Environment) (declName : Name) : Bool :=
+  Meta.instanceExtension.getState env |>.instanceNames.contains declName
+
 def isInstance (declName : Name) : CoreM Bool :=
-  return Meta.instanceExtension.getState (← getEnv) |>.instanceNames.contains declName
+  return isInstanceCore (← getEnv) declName
 
 def getInstancePriority? (declName : Name) : CoreM (Option Nat) := do
   let some entry := Meta.instanceExtension.getState (← getEnv) |>.instanceNames.find? declName | return none

src/Lean/Meta/LazyDiscrTree.lean

@@ -745,7 +745,6 @@ instance : Append (PreDiscrTree α) where
 end PreDiscrTree
 
 /-- Initial entry in lazy discrimination tree -/
-@[reducible]
 structure InitEntry (α : Type) where
   /-- Return root key for an entry. -/
   key : Key
@@ -978,12 +977,13 @@ def createImportedDiscrTree [Monad m] [MonadLog m] [AddMessageContext m] [MonadO
 
 /-- Creates the core context used for initializing a tree using the current context. -/
 private def createTreeCtx (ctx : Core.Context) : Core.Context := {
-    fileName := ctx.fileName,
-    fileMap := ctx.fileMap,
-    options := ctx.options,
-    maxRecDepth := ctx.maxRecDepth,
-    maxHeartbeats := 0,
-    ref := ctx.ref,
+    fileName := ctx.fileName
+    fileMap := ctx.fileMap
+    options := ctx.options
+    maxRecDepth := ctx.maxRecDepth
+    maxHeartbeats := 0
+    ref := ctx.ref
+    diag := getDiag ctx.options
   }
 
 def findImportMatches

src/Lean/Meta/LevelDefEq.lean

@@ -16,26 +16,62 @@ namespace Lean.Meta
   That is, `lvl` is a proper level subterm of some `u_i`. -/
 private def strictOccursMax (lvl : Level) : Level → Bool
   | Level.max u v => visit u || visit v
-  | _               => false
+  | _             => false
 where
   visit : Level → Bool
     | Level.max u v => visit u || visit v
-    | u               => u != lvl && lvl.occurs u
+    | u             => u != lvl && lvl.occurs u
 
 /-- `mkMaxArgsDiff mvarId (max u_1 ... (mvar mvarId) ... u_n) v` => `max v u_1 ... u_n` -/
 private def mkMaxArgsDiff (mvarId : LMVarId) : Level → Level → Level
   | Level.max u v,     acc => mkMaxArgsDiff mvarId v <| mkMaxArgsDiff mvarId u acc
   | l@(Level.mvar id), acc => if id != mvarId then mkLevelMax' acc l else acc
-  | l,                   acc => mkLevelMax' acc l
+  | l,                 acc => mkLevelMax' acc l
 
 /--
-  Solve `?m =?= max ?m v` by creating a fresh metavariable `?n`
-  and assigning `?m := max ?n v` -/
+Solves `?m =?= max ?m v` by creating a fresh metavariable `?n`
+and assigning `?m := max ?n v`
+-/
 private def solveSelfMax (mvarId : LMVarId) (v : Level) : MetaM Unit := do
   assert! v.isMax
   let n ← mkFreshLevelMVar
   assignLevelMVar mvarId <| mkMaxArgsDiff mvarId v n
 
+/--
+Returns true if `v` is `max u ?m` (or variant). That is, we solve `u =?= max u ?m` as `?m := u`.
+This is an approximation. For example, we ignore the solution `?m := 0`.
+-/
+-- TODO: investigate whether we need to improve this approximation.
+private def tryApproxSelfMax (u v : Level) : MetaM Bool := do
+  match v with
+  | .max v' (.mvar mvarId) => solve v' mvarId
+  | .max (.mvar mvarId) v' => solve v' mvarId
+  | _ => return false
+where
+  solve (v' : Level) (mvarId : LMVarId) : MetaM Bool := do
+    if u == v' then
+      assignLevelMVar mvarId u
+      return true
+    else
+      return false
+
+/--
+Returns true if `u` of the form `max u₁ u₂` and `v` of the form `max u₁ ?w` (or variant).
+That is, we solve `max u₁ u₂ =?= max u₁ ?v` as `?v := u₂`.
+This is an approximation. For example, we ignore the solution `?w := max u₁ u₂`.
+-/
+-- TODO: investigate whether we need to improve this approximation.
+private def tryApproxMaxMax (u v : Level) : MetaM Bool := do
+  match u, v with
+  | .max u₁ u₂, .max v' (.mvar mvarId) => solve u₁ u₂ v' mvarId
+  | .max u₁ u₂, .max (.mvar mvarId) v' => solve u₁ u₂ v' mvarId
+  | _, _ => return false
+where
+  solve (u₁ u₂ v' : Level) (mvarId : LMVarId) : MetaM Bool := do
+    if u₁ == v' then assignLevelMVar mvarId u₂; return true
+    else if u₂ == v' then assignLevelMVar mvarId u₁; return true
+    else return false
+
 private def postponeIsLevelDefEq (lhs : Level) (rhs : Level) : MetaM Unit := do
   let ref ← getRef
   let ctx ← read
@@ -82,7 +118,13 @@ mutual
         match (← Meta.decLevel? v) with
         | some v => Bool.toLBool <$> isLevelDefEqAux u v
         | none   => return LBool.undef
-    | _, _ => return LBool.undef
+    | _, _ =>
+      if (← read).univApprox then
+        if (← tryApproxSelfMax u v) then
+          return LBool.true
+        if (← tryApproxMaxMax u v) then
+          return LBool.true
+      return LBool.undef
 
   @[export lean_is_level_def_eq]
   partial def isLevelDefEqAuxImpl : Level → Level → MetaM Bool

src/Lean/Meta/SynthInstance.lean

@@ -25,6 +25,12 @@ register_builtin_option synthInstance.maxSize : Nat := {
   descr := "maximum number of instances used to construct a solution in the type class instance synthesis procedure"
 }
 
+register_builtin_option backward.synthInstance.canonInstances : Bool := {
+  defValue := true
+  group    := "backward compatibility"
+  descr := "use optimization that relies on 'morally canonical' instances during type class resolution"
+}
+
 namespace SynthInstance
 
 def getMaxHeartbeats (opts : Options) : Nat :=
@@ -41,6 +47,14 @@ structure GeneratorNode where
   mctx            : MetavarContext
   instances       : Array Instance
   currInstanceIdx : Nat
+  /--
+  `typeHasMVars := true` if type of `mvar` contains metavariables.
+  We store this information to implement an optimization that relies on the fact
+  that instances are "morally canonical."
+  That is, we need to find at most one answer for this generator node if the type
+  does not have metavariables.
+  -/
+  typeHasMVars    : Bool
   deriving Inhabited
 
 structure ConsumerNode where
@@ -56,8 +70,8 @@ inductive Waiter where
   | root         : Waiter
 
 def Waiter.isRoot : Waiter → Bool
-  | Waiter.consumerNode _ => false
-  | Waiter.root           => true
+  | .consumerNode _ => false
+  | .root           => true
 
 /-!
   In tabled resolution, we creating a mapping from goals (e.g., `Coe Nat ?x`) to
@@ -98,10 +112,10 @@ partial def normLevel (u : Level) : M Level := do
   if !u.hasMVar then
     return u
   else match u with
-    | Level.succ v      => return u.updateSucc! (← normLevel v)
-    | Level.max v w     => return u.updateMax! (← normLevel v) (← normLevel w)
-    | Level.imax v w    => return u.updateIMax! (← normLevel v) (← normLevel w)
-    | Level.mvar mvarId =>
+    | .succ v      => return u.updateSucc! (← normLevel v)
+    | .max v w     => return u.updateMax! (← normLevel v) (← normLevel w)
+    | .imax v w    => return u.updateIMax! (← normLevel v) (← normLevel w)
+    | .mvar mvarId =>
       if (← getMCtx).getLevelDepth mvarId != (← getMCtx).depth then
         return u
       else
@@ -118,15 +132,15 @@ partial def normExpr (e : Expr) : M Expr := do
   if !e.hasMVar then
     pure e
   else match e with
-    | Expr.const _ us      => return e.updateConst! (← us.mapM normLevel)
-    | Expr.sort u          => return e.updateSort! (← normLevel u)
-    | Expr.app f a         => return e.updateApp! (← normExpr f) (← normExpr a)
-    | Expr.letE _ t v b _  => return e.updateLet! (← normExpr t) (← normExpr v) (← normExpr b)
-    | Expr.forallE _ d b _ => return e.updateForallE! (← normExpr d) (← normExpr b)
-    | Expr.lam _ d b _     => return e.updateLambdaE! (← normExpr d) (← normExpr b)
-    | Expr.mdata _ b       => return e.updateMData! (← normExpr b)
-    | Expr.proj _ _ b      => return e.updateProj! (← normExpr b)
-    | Expr.mvar mvarId     =>
+    | .const _ us      => return e.updateConst! (← us.mapM normLevel)
+    | .sort u          => return e.updateSort! (← normLevel u)
+    | .app f a         => return e.updateApp! (← normExpr f) (← normExpr a)
+    | .letE _ t v b _  => return e.updateLet! (← normExpr t) (← normExpr v) (← normExpr b)
+    | .forallE _ d b _ => return e.updateForallE! (← normExpr d) (← normExpr b)
+    | .lam _ d b _     => return e.updateLambdaE! (← normExpr d) (← normExpr b)
+    | .mdata _ b       => return e.updateMData! (← normExpr b)
+    | .proj _ _ b      => return e.updateProj! (← normExpr b)
+    | .mvar mvarId     =>
       if !(← mvarId.isAssignable) then
         return e
       else
@@ -202,7 +216,7 @@ def getInstances (type : Expr) : MetaM (Array Instance) := do
       let result := result.insertionSort fun e₁ e₂ => e₁.priority < e₂.priority
       let erasedInstances ← getErasedInstances
       let mut result ← result.filterMapM fun e => match e.val with
-        | Expr.const constName us =>
+        | .const constName us =>
           if erasedInstances.contains constName then
             return none
           else
@@ -234,6 +248,7 @@ def mkGeneratorNode? (key mvar : Expr) : MetaM (Option GeneratorNode) := do
     let mctx ← getMCtx
     return some {
       mvar, key, mctx, instances
+      typeHasMVars := mvarType.hasMVar
       currInstanceIdx := instances.size
     }
 
@@ -347,11 +362,14 @@ private def mkLambdaFVars' (xs : Array Expr) (e : Expr) : MetaM Expr :=
   If it succeeds, the result is a new updated metavariable context and a new list of subgoals.
   A subgoal is created for each instance implicit parameter of `inst`. -/
 def tryResolve (mvar : Expr) (inst : Instance) : MetaM (Option (MetavarContext × List Expr)) := do
+  if (← isDiagnosticsEnabled) then
+    if let .const declName _ := inst.val.getAppFn then
+      recordInstance declName
   let mvarType   ← inferType mvar
   let lctx       ← getLCtx
   let localInsts ← getLocalInstances
   forallTelescopeReducing mvarType fun xs mvarTypeBody => do
-    let ⟨subgoals, instVal, instTypeBody⟩ ← getSubgoals lctx localInsts xs inst
+    let { subgoals, instVal, instTypeBody } ← getSubgoals lctx localInsts xs inst
     withTraceNode `Meta.synthInstance.tryResolve (withMCtx (← getMCtx) do
         return m!"{exceptOptionEmoji ·} {← instantiateMVars mvarTypeBody} ≟ {← instantiateMVars instTypeBody}") do
     if (← isDefEq mvarTypeBody instTypeBody) then
@@ -373,7 +391,7 @@ def tryAnswer (mctx : MetavarContext) (mvar : Expr) (answer : Answer) : SynthM (
 
 /-- Move waiters that are waiting for the given answer to the resume stack. -/
 def wakeUp (answer : Answer) : Waiter → SynthM Unit
-  | Waiter.root               => do
+  | .root               => do
     /- Recall that we now use `ignoreLevelMVarDepth := true`. Thus, we should allow solutions
        containing universe metavariables, and not check `answer.result.paramNames.isEmpty`.
        We use `openAbstractMVarsResult` to construct the universe metavariables
@@ -383,7 +401,7 @@ def wakeUp (answer : Answer) : Waiter → SynthM Unit
     else
       let (_, _, answerExpr) ← openAbstractMVarsResult answer.result
       trace[Meta.synthInstance] "skip answer containing metavariables {answerExpr}"
-  | Waiter.consumerNode cNode =>
+  | .consumerNode cNode =>
     modify fun s => { s with resumeStack := s.resumeStack.push (cNode, answer) }
 
 def isNewAnswer (oldAnswers : Array Answer) (answer : Answer) : Bool :=
@@ -407,18 +425,18 @@ private def mkAnswer (cNode : ConsumerNode) : MetaM Answer :=
 def addAnswer (cNode : ConsumerNode) : SynthM Unit := do
   withMCtx cNode.mctx do
   if cNode.size ≥ (← read).maxResultSize then
-      trace[Meta.synthInstance.answer] "{crossEmoji} {← instantiateMVars (← inferType cNode.mvar)}{Format.line}(size: {cNode.size} ≥ {(← read).maxResultSize})"
+    trace[Meta.synthInstance.answer] "{crossEmoji} {← instantiateMVars (← inferType cNode.mvar)}{Format.line}(size: {cNode.size} ≥ {(← read).maxResultSize})"
   else
     withTraceNode `Meta.synthInstance.answer
       (fun _ => return m!"{checkEmoji} {← instantiateMVars (← inferType cNode.mvar)}") do
     let answer ← mkAnswer cNode
     -- Remark: `answer` does not contain assignable or assigned metavariables.
     let key := cNode.key
-    let entry ← getEntry key
-    if isNewAnswer entry.answers answer then
-      let newEntry := { entry with answers := entry.answers.push answer }
+    let { waiters, answers } ← getEntry key
+    if isNewAnswer answers answer then
+      let newEntry := { waiters, answers := answers.push answer }
       modify fun s => { s with tableEntries := s.tableEntries.insert key newEntry }
-      entry.waiters.forM (wakeUp answer)
+      waiters.forM (wakeUp answer)
 
 /--
   Return `true` if a type of the form `(a_1 : A_1) → ... → (a_n : A_n) → B` has an unused argument `a_i`.
@@ -426,7 +444,7 @@ def addAnswer (cNode : ConsumerNode) : SynthM Unit := do
   Remark: This is syntactic check and no reduction is performed.
 -/
 private def hasUnusedArguments : Expr → Bool
-  | Expr.forallE _ _ b _ => !b.hasLooseBVar 0 || hasUnusedArguments b
+  | .forallE _ _ b _ => !b.hasLooseBVar 0 || hasUnusedArguments b
   | _ => false
 
 /--
@@ -539,6 +557,18 @@ def generate : SynthM Unit := do
     let inst := gNode.instances.get! idx
     let mctx := gNode.mctx
     let mvar := gNode.mvar
+    /- See comment at `typeHasMVars` -/
+    if backward.synthInstance.canonInstances.get (← getOptions) then
+      unless gNode.typeHasMVars do
+        if let some entry := (← get).tableEntries.find? key then
+          unless entry.answers.isEmpty do
+            /-
+            We already have an answer for this node, and since its type does not have metavariables,
+            we can skip other solutions because we assume instances are "morally canonical".
+            We have added this optimization to address issue #3996.
+            -/
+            modify fun s => { s with generatorStack := s.generatorStack.pop }
+            return
     discard do withMCtx mctx do
       withTraceNode `Meta.synthInstance
         (return m!"{exceptOptionEmoji ·} apply {inst.val} to {← instantiateMVars (← inferType mvar)}") do
@@ -667,7 +697,7 @@ private partial def preprocessArgs (type : Expr) (i : Nat) (args : Array Expr) (
 private def preprocessOutParam (type : Expr) : MetaM Expr :=
   forallTelescope type fun xs typeBody => do
     match typeBody.getAppFn with
-    | c@(Expr.const declName _) =>
+    | c@(.const declName _) =>
       let env ← getEnv
       if let some outParamsPos := getOutParamPositions? env declName then
         unless outParamsPos.isEmpty do
@@ -690,7 +720,8 @@ def synthInstance? (type : Expr) (maxResultSize? : Option Nat := none) : MetaM (
   withTraceNode `Meta.synthInstance
     (return m!"{exceptOptionEmoji ·} {← instantiateMVars type}") do
   withConfig (fun config => { config with isDefEqStuckEx := true, transparency := TransparencyMode.instances,
-                                          foApprox := true, ctxApprox := true, constApprox := false }) do
+                                          foApprox := true, ctxApprox := true, constApprox := false, univApprox := false }) do
+  withReader (fun ctx => { ctx with inTypeClassResolution := true }) do
     let localInsts ← getLocalInstances
     let type ← instantiateMVars type
     let type ← preprocess type
@@ -775,8 +806,7 @@ def synthInstance (type : Expr) (maxResultSize? : Option Nat := none) : MetaM Ex
 private def synthPendingImp (mvarId : MVarId) : MetaM Bool := withIncRecDepth <| mvarId.withContext do
   let mvarDecl ← mvarId.getDecl
   match mvarDecl.kind with
-  | MetavarKind.syntheticOpaque =>
-    return false
+  | .syntheticOpaque => return false
   | _ =>
     /- Check whether the type of the given metavariable is a class or not. If yes, then try to synthesize
        it using type class resolution. We only do it for `synthetic` and `natural` metavariables. -/

src/Lean/Meta/Tactic/LinearArith/Solver.lean

@@ -81,6 +81,7 @@ def Poly.add (e₁ e₂ : Poly) : Poly :=
       else
         { val := r }
     termination_by (e₁.size - i₁, e₂.size - i₂)
+    decreasing_by all_goals decreasing_with decreasing_trivial_pre_omega
   go 0 0 #[]
 
 def Poly.combine (d₁ : Int) (e₁ : Poly) (d₂ : Int) (e₂ : Poly) : Poly :=
@@ -108,6 +109,7 @@ def Poly.combine (d₁ : Int) (e₁ : Poly) (d₂ : Int) (e₂ : Poly) : Poly :=
       else
         { val := r }
     termination_by (e₁.size - i₁, e₂.size - i₂)
+    decreasing_by all_goals decreasing_with decreasing_trivial_pre_omega
   go 0 0 #[]
 
 def Poly.eval? (e : Poly) (a : Assignment) : Option Rat := Id.run do

src/Lean/Meta/Tactic/Simp.lean

@@ -14,6 +14,7 @@ import Lean.Meta.Tactic.Simp.Simproc
 import Lean.Meta.Tactic.Simp.BuiltinSimprocs
 import Lean.Meta.Tactic.Simp.RegisterCommand
 import Lean.Meta.Tactic.Simp.Attr
+import Lean.Meta.Tactic.Simp.Diagnostics
 
 namespace Lean
 

src/Lean/Meta/Tactic/Simp/BuiltinSimprocs/Nat.lean

@@ -275,7 +275,7 @@ def reduceLTLE (nm : Name) (arity : Nat) (isLT : Bool) (e : Expr) : SimpM Step :
       applySimprocConst (mkConst ``True) ``Nat.Simproc.le_add_le #[x, yb, yo, leProof]
     else
       let finExpr := mkLENat (toExpr (xn - yn)) yb
-      let geProof ← mkOfDecideEqTrue (mkGENat yo x)
+      let geProof ← mkOfDecideEqTrue (mkGENat x yo)
       applySimprocConst finExpr ``Nat.Simproc.le_add_ge #[x, yb, yo, geProof]
   | .offset xb xo xn, .offset yb yo yn => do
     if xn ≤ yn then

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

@@ -0,0 +1,48 @@
+/-
+Copyright (c) 2020 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Diagnostics
+import Lean.Meta.Tactic.Simp.Types
+
+namespace Lean.Meta.Simp
+
+def mkSimpDiagSummary (counters : PHashMap Origin Nat) (usedCounters? : Option (PHashMap Origin Nat) := none) : MetaM DiagSummary := do
+  let threshold := diagnostics.threshold.get (← getOptions)
+  let entries := collectAboveThreshold counters threshold (fun _ => true) (lt := (· < ·))
+  if entries.isEmpty then
+    return {}
+  else
+    let mut data := #[]
+    for (thmId, counter) in entries do
+      let key ← match thmId with
+        | .decl declName _ _ =>
+          if (← getEnv).contains declName then
+            pure m!"{MessageData.ofConst (← mkConstWithLevelParams declName)}"
+          else
+            pure m!"{declName} (builtin simproc)"
+        | .fvar fvarId => pure m!"{mkFVar fvarId}"
+        | _ => pure thmId.key
+      let usedMsg ← if let some usedCounters := usedCounters? then
+        if let some c := usedCounters.find? thmId then pure s!", succeeded: {c}" else pure s!" {crossEmoji}" -- not used
+      else
+        pure ""
+      data := data.push m!"{if data.isEmpty then "  " else "\n"}{key} ↦ {counter}{usedMsg}"
+    return { data, max := entries[0]!.2 }
+
+def reportDiag (diag : Simp.Diagnostics) : MetaM Unit := do
+  if (← isDiagnosticsEnabled) then
+    let used ← mkSimpDiagSummary diag.usedThmCounter
+    let tried ← mkSimpDiagSummary diag.triedThmCounter diag.usedThmCounter
+    let congr ← mkDiagSummary diag.congrThmCounter
+    unless used.isEmpty && tried.isEmpty && congr.isEmpty do
+      let m := MessageData.nil
+      let m := appendSection m `simp "used theorems" used
+      let m := appendSection m `simp "tried theorems" tried
+      let m := appendSection m `simp "tried congruence theorems" congr
+      let m := m ++ "use `set_option diagnostics.threshold <num>` to control threshold for reporting counters"
+      logInfo m
+
+end Lean.Meta.Simp

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

@@ -8,6 +8,7 @@ import Lean.Meta.Transform
 import Lean.Meta.Tactic.Replace
 import Lean.Meta.Tactic.UnifyEq
 import Lean.Meta.Tactic.Simp.Rewrite
+import Lean.Meta.Tactic.Simp.Diagnostics
 import Lean.Meta.Match.Value
 
 namespace Lean.Meta
@@ -243,28 +244,26 @@ def getSimpLetCase (n : Name) (t : Expr) (b : Expr) : MetaM SimpLetCase := do
 
 /--
 We use `withNewlemmas` whenever updating the local context.
-We use `withFreshCache` because the local context affects `simp` rewrites
-even when `contextual := false`.
-For example, the `discharger` may inspect the current local context. The default
-discharger does that when applying equational theorems, and the user may
-use `(discharger := assumption)` or `(discharger := omega)`.
-If the `wishFreshCache` introduces performance issues, we can design a better solution
-for the default discharger which is used most of the time.
 -/
-def withNewLemmas {α} (xs : Array Expr) (f : SimpM α) : SimpM α := withFreshCache do
+def withNewLemmas {α} (xs : Array Expr) (f : SimpM α) : SimpM α := do
   if (← getConfig).contextual then
-    let mut s ← getSimpTheorems
-    let mut updated := false
-    for x in xs do
-      if (← isProof x) then
-        s ← s.addTheorem (.fvar x.fvarId!) x
-        updated := true
-    if updated then
-      withTheReader Context (fun ctx => { ctx with simpTheorems := s }) f
-    else
-      f
-  else
+    withFreshCache do
+      let mut s ← getSimpTheorems
+      let mut updated := false
+      for x in xs do
+        if (← isProof x) then
+          s ← s.addTheorem (.fvar x.fvarId!) x
+          updated := true
+      if updated then
+        withTheReader Context (fun ctx => { ctx with simpTheorems := s }) f
+      else
+        f
+  else if (← getMethods).wellBehavedDischarge then
+    -- See comment at `Methods.wellBehavedDischarge` to understand why
+    -- we don't have to reset the cache
     f
+  else
+    withFreshCache do f
 
 def simpProj (e : Expr) : SimpM Result := do
   match (← reduceProj? e) with
@@ -519,6 +518,7 @@ def processCongrHypothesis (h : Expr) : SimpM Bool := do
 
 /-- Try to rewrite `e` children using the given congruence theorem -/
 def trySimpCongrTheorem? (c : SimpCongrTheorem) (e : Expr) : SimpM (Option Result) := withNewMCtxDepth do
+  recordCongrTheorem c.theoremName
   trace[Debug.Meta.Tactic.simp.congr] "{c.theoremName}, {e}"
   let thm ← mkConstWithFreshMVarLevels c.theoremName
   let (xs, bis, type) ← forallMetaTelescopeReducing (← inferType thm)
@@ -652,63 +652,75 @@ where
     trace[Meta.Tactic.simp.heads] "{repr e.toHeadIndex}"
     simpLoop e
 
-@[inline] def withSimpConfig (ctx : Context) (x : MetaM α) : MetaM α :=
+@[inline] def withSimpContext (ctx : Context) (x : MetaM α) : MetaM α :=
   withConfig (fun c => { c with etaStruct := ctx.config.etaStruct }) <| withReducible x
 
-def main (e : Expr) (ctx : Context) (usedSimps : UsedSimps := {}) (methods : Methods := {}) : MetaM (Result × UsedSimps) := do
-  let ctx := { ctx with config := (← ctx.config.updateArith) }
-  withSimpConfig ctx do withCatchingRuntimeEx do
+def main (e : Expr) (ctx : Context) (stats : Stats := {}) (methods : Methods := {}) : MetaM (Result × Stats) := do
+  let ctx := { ctx with config := (← ctx.config.updateArith), lctxInitIndices := (← getLCtx).numIndices }
+  withSimpContext ctx do
+    let (r, s) ← simpMain e methods.toMethodsRef ctx |>.run { stats with }
+    trace[Meta.Tactic.simp.numSteps] "{s.numSteps}"
+    return (r, { s with })
+where
+  simpMain (e : Expr) : SimpM Result := withCatchingRuntimeEx do
     try
-      withoutCatchingRuntimeEx do
-        let (r, s) ← simp e methods.toMethodsRef ctx |>.run { usedTheorems := usedSimps }
-        trace[Meta.Tactic.simp.numSteps] "{s.numSteps}"
-        return (r, s.usedTheorems)
+      withoutCatchingRuntimeEx <| simp e
     catch ex =>
-      if ex.isRuntime then throwNestedTacticEx `simp ex else throw ex
+      reportDiag (← get).diag
+      if ex.isRuntime then
+        throwNestedTacticEx `simp ex
+      else
+        throw ex
 
-def dsimpMain (e : Expr) (ctx : Context) (usedSimps : UsedSimps := {}) (methods : Methods := {}) : MetaM (Expr × UsedSimps) := do
-  withSimpConfig ctx do withCatchingRuntimeEx do
+def dsimpMain (e : Expr) (ctx : Context) (stats : Stats := {}) (methods : Methods := {}) : MetaM (Expr × Stats) := do
+  withSimpContext ctx do
+    let (r, s) ← dsimpMain e methods.toMethodsRef ctx |>.run { stats with }
+    pure (r, { s with })
+where
+  dsimpMain (e : Expr) : SimpM Expr := withCatchingRuntimeEx do
     try
-      withoutCatchingRuntimeEx do
-        let (r, s) ← dsimp e methods.toMethodsRef ctx |>.run { usedTheorems := usedSimps }
-        pure (r, s.usedTheorems)
+      withoutCatchingRuntimeEx <| dsimp e
     catch ex =>
-      if ex.isRuntime then throwNestedTacticEx `dsimp ex else throw ex
+      reportDiag (← get).diag
+      if ex.isRuntime then
+        throwNestedTacticEx `simp ex
+      else
+        throw ex
 
 end Simp
-open Simp (UsedSimps SimprocsArray)
+open Simp (SimprocsArray Stats)
 
 def simp (e : Expr) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
-    (usedSimps : UsedSimps := {}) : MetaM (Simp.Result × UsedSimps) := do profileitM Exception "simp" (← getOptions) do
+    (stats : Stats := {}) : MetaM (Simp.Result × Stats) := do profileitM Exception "simp" (← getOptions) do
   match discharge? with
-  | none   => Simp.main e ctx usedSimps (methods := Simp.mkDefaultMethodsCore simprocs)
-  | some d => Simp.main e ctx usedSimps (methods := Simp.mkMethods simprocs d)
+  | none   => Simp.main e ctx stats (methods := Simp.mkDefaultMethodsCore simprocs)
+  | some d => Simp.main e ctx stats (methods := Simp.mkMethods simprocs d (wellBehavedDischarge := false))
 
 def dsimp (e : Expr) (ctx : Simp.Context) (simprocs : SimprocsArray := #[])
-    (usedSimps : UsedSimps := {}) : MetaM (Expr × UsedSimps) := do profileitM Exception "dsimp" (← getOptions) do
-  Simp.dsimpMain e ctx usedSimps (methods := Simp.mkDefaultMethodsCore simprocs )
+    (stats : Stats := {}) : MetaM (Expr × Stats) := do profileitM Exception "dsimp" (← getOptions) do
+  Simp.dsimpMain e ctx stats (methods := Simp.mkDefaultMethodsCore simprocs )
 
 /-- See `simpTarget`. This method assumes `mvarId` is not assigned, and we are already using `mvarId`s local context. -/
 def simpTargetCore (mvarId : MVarId) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
-    (mayCloseGoal := true) (usedSimps : UsedSimps := {}) : MetaM (Option MVarId × UsedSimps) := do
+    (mayCloseGoal := true) (stats : Stats := {}) : MetaM (Option MVarId × Stats) := do
   let target ← instantiateMVars (← mvarId.getType)
-  let (r, usedSimps) ← simp target ctx simprocs discharge? usedSimps
+  let (r, stats) ← simp target ctx simprocs discharge? stats
   if mayCloseGoal && r.expr.isTrue then
     match r.proof? with
     | some proof => mvarId.assign (← mkOfEqTrue proof)
     | none => mvarId.assign (mkConst ``True.intro)
-    return (none, usedSimps)
+    return (none, stats)
   else
-    return (← applySimpResultToTarget mvarId target r, usedSimps)
+    return (← applySimpResultToTarget mvarId target r, stats)
 
 /--
   Simplify the given goal target (aka type). Return `none` if the goal was closed. Return `some mvarId'` otherwise,
   where `mvarId'` is the simplified new goal. -/
 def simpTarget (mvarId : MVarId) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
-    (mayCloseGoal := true) (usedSimps : UsedSimps := {}) : MetaM (Option MVarId × UsedSimps) :=
+    (mayCloseGoal := true) (stats : Stats := {}) : MetaM (Option MVarId × Stats) :=
   mvarId.withContext do
     mvarId.checkNotAssigned `simp
-    simpTargetCore mvarId ctx simprocs discharge? mayCloseGoal usedSimps
+    simpTargetCore mvarId ctx simprocs discharge? mayCloseGoal stats
 
 /--
   Apply the result `r` for `prop` (which is inhabited by `proof`). Return `none` if the goal was closed. Return `some (proof', prop')`
@@ -740,9 +752,9 @@ def applySimpResultToFVarId (mvarId : MVarId) (fvarId : FVarId) (r : Simp.Result
 
   This method assumes `mvarId` is not assigned, and we are already using `mvarId`s local context. -/
 def simpStep (mvarId : MVarId) (proof : Expr) (prop : Expr) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
-    (mayCloseGoal := true) (usedSimps : UsedSimps := {}) : MetaM (Option (Expr × Expr) × UsedSimps) := do
-  let (r, usedSimps) ← simp prop ctx simprocs discharge? usedSimps
-  return (← applySimpResultToProp mvarId proof prop r (mayCloseGoal := mayCloseGoal), usedSimps)
+    (mayCloseGoal := true) (stats : Stats := {}) : MetaM (Option (Expr × Expr) × Stats) := do
+  let (r, stats) ← simp prop ctx simprocs discharge? stats
+  return (← applySimpResultToProp mvarId proof prop r (mayCloseGoal := mayCloseGoal), stats)
 
 def applySimpResultToLocalDeclCore (mvarId : MVarId) (fvarId : FVarId) (r : Option (Expr × Expr)) : MetaM (Option (FVarId × MVarId)) := do
   match r with
@@ -773,99 +785,99 @@ def applySimpResultToLocalDecl (mvarId : MVarId) (fvarId : FVarId) (r : Simp.Res
     applySimpResultToLocalDeclCore mvarId fvarId (← applySimpResultToFVarId mvarId fvarId r mayCloseGoal)
 
 def simpLocalDecl (mvarId : MVarId) (fvarId : FVarId) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
-    (mayCloseGoal := true) (usedSimps : UsedSimps := {}) : MetaM (Option (FVarId × MVarId) × UsedSimps) := do
+    (mayCloseGoal := true) (stats : Stats := {}) : MetaM (Option (FVarId × MVarId) × Stats) := do
   mvarId.withContext do
     mvarId.checkNotAssigned `simp
     let type ← instantiateMVars (← fvarId.getType)
-    let (r, usedSimps) ← simpStep mvarId (mkFVar fvarId) type ctx simprocs discharge? mayCloseGoal usedSimps
-    return (← applySimpResultToLocalDeclCore mvarId fvarId r, usedSimps)
+    let (r, stats) ← simpStep mvarId (mkFVar fvarId) type ctx simprocs discharge? mayCloseGoal stats
+    return (← applySimpResultToLocalDeclCore mvarId fvarId r, stats)
 
 def simpGoal (mvarId : MVarId) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
     (simplifyTarget : Bool := true) (fvarIdsToSimp : Array FVarId := #[])
-    (usedSimps : UsedSimps := {}) : MetaM (Option (Array FVarId × MVarId) × UsedSimps) := do
+    (stats : Stats := {}) : MetaM (Option (Array FVarId × MVarId) × Stats) := do
   mvarId.withContext do
     mvarId.checkNotAssigned `simp
     let mut mvarIdNew := mvarId
     let mut toAssert := #[]
     let mut replaced := #[]
-    let mut usedSimps := usedSimps
+    let mut stats := stats
     for fvarId in fvarIdsToSimp do
       let localDecl ← fvarId.getDecl
       let type ← instantiateMVars localDecl.type
       let ctx := { ctx with simpTheorems := ctx.simpTheorems.eraseTheorem (.fvar localDecl.fvarId) }
-      let (r, usedSimps') ← simp type ctx simprocs discharge? usedSimps
-      usedSimps := usedSimps'
+      let (r, stats') ← simp type ctx simprocs discharge? stats
+      stats := stats'
       match r.proof? with
       | some _ => match (← applySimpResultToProp mvarIdNew (mkFVar fvarId) type r) with
-        | none => return (none, usedSimps)
+        | none => return (none, stats)
         | some (value, type) => toAssert := toAssert.push { userName := localDecl.userName, type := type, value := value }
       | none =>
         if r.expr.isFalse then
           mvarIdNew.assign (← mkFalseElim (← mvarIdNew.getType) (mkFVar fvarId))
-          return (none, usedSimps)
+          return (none, stats)
         -- TODO: if there are no forwards dependencies we may consider using the same approach we used when `r.proof?` is a `some ...`
         -- Reason: it introduces a `mkExpectedTypeHint`
         mvarIdNew ← mvarIdNew.replaceLocalDeclDefEq fvarId r.expr
         replaced := replaced.push fvarId
     if simplifyTarget then
-      match (← simpTarget mvarIdNew ctx simprocs discharge? (usedSimps := usedSimps)) with
-      | (none, usedSimps') => return (none, usedSimps')
-      | (some mvarIdNew', usedSimps') => mvarIdNew := mvarIdNew'; usedSimps := usedSimps'
+      match (← simpTarget mvarIdNew ctx simprocs discharge? (stats := stats)) with
+      | (none, stats') => return (none, stats')
+      | (some mvarIdNew', stats') => mvarIdNew := mvarIdNew'; stats := stats'
     let (fvarIdsNew, mvarIdNew') ← mvarIdNew.assertHypotheses toAssert
     mvarIdNew := mvarIdNew'
     let toClear := fvarIdsToSimp.filter fun fvarId => !replaced.contains fvarId
     mvarIdNew ← mvarIdNew.tryClearMany toClear
     if ctx.config.failIfUnchanged && mvarId == mvarIdNew then
       throwError "simp made no progress"
-    return (some (fvarIdsNew, mvarIdNew), usedSimps)
+    return (some (fvarIdsNew, mvarIdNew), stats)
 
 def simpTargetStar (mvarId : MVarId) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (discharge? : Option Simp.Discharge := none)
-    (usedSimps : UsedSimps := {}) : MetaM (TacticResultCNM × UsedSimps) := mvarId.withContext do
+    (stats : Stats := {}) : MetaM (TacticResultCNM × Stats) := mvarId.withContext do
   let mut ctx := ctx
   for h in (← getPropHyps) do
     let localDecl ← h.getDecl
     let proof  := localDecl.toExpr
     let simpTheorems ← ctx.simpTheorems.addTheorem (.fvar h) proof
     ctx := { ctx with simpTheorems }
-  match (← simpTarget mvarId ctx simprocs discharge? (usedSimps := usedSimps)) with
-  | (none, usedSimps) => return (TacticResultCNM.closed, usedSimps)
-  | (some mvarId', usedSimps') =>
+  match (← simpTarget mvarId ctx simprocs discharge? (stats := stats)) with
+  | (none, stats) => return (TacticResultCNM.closed, stats)
+  | (some mvarId', stats') =>
     if (← mvarId.getType) == (← mvarId'.getType) then
-      return (TacticResultCNM.noChange, usedSimps)
+      return (TacticResultCNM.noChange, stats)
     else
-      return (TacticResultCNM.modified mvarId', usedSimps')
+      return (TacticResultCNM.modified mvarId', stats')
 
 def dsimpGoal (mvarId : MVarId) (ctx : Simp.Context) (simprocs : SimprocsArray := #[]) (simplifyTarget : Bool := true) (fvarIdsToSimp : Array FVarId := #[])
-    (usedSimps : UsedSimps := {}) : MetaM (Option MVarId × UsedSimps) := do
+    (stats : Stats := {}) : MetaM (Option MVarId × Stats) := do
    mvarId.withContext do
     mvarId.checkNotAssigned `simp
     let mut mvarIdNew := mvarId
-    let mut usedSimps : UsedSimps := usedSimps
+    let mut stats : Stats := stats
     for fvarId in fvarIdsToSimp do
       let type ← instantiateMVars (← fvarId.getType)
-      let (typeNew, usedSimps') ← dsimp type ctx simprocs
-      usedSimps := usedSimps'
+      let (typeNew, stats') ← dsimp type ctx simprocs
+      stats := stats'
       if typeNew.isFalse then
         mvarIdNew.assign (← mkFalseElim (← mvarIdNew.getType) (mkFVar fvarId))
-        return (none, usedSimps)
+        return (none, stats)
       if typeNew != type then
         mvarIdNew ← mvarIdNew.replaceLocalDeclDefEq fvarId typeNew
     if simplifyTarget then
       let target ← mvarIdNew.getType
-      let (targetNew, usedSimps') ← dsimp target ctx simprocs usedSimps
-      usedSimps := usedSimps'
+      let (targetNew, stats') ← dsimp target ctx simprocs stats
+      stats := stats'
       if targetNew.isTrue then
         mvarIdNew.assign (mkConst ``True.intro)
-        return (none, usedSimps)
+        return (none, stats)
       if let some (_, lhs, rhs) := targetNew.consumeMData.eq? then
         if (← withReducible <| isDefEq lhs rhs) then
           mvarIdNew.assign (← mkEqRefl lhs)
-          return (none, usedSimps)
+          return (none, stats)
       if target != targetNew then
         mvarIdNew ← mvarIdNew.replaceTargetDefEq targetNew
       pure () -- FIXME: bug in do notation if this is removed?
     if ctx.config.failIfUnchanged && mvarId == mvarIdNew then
       throwError "dsimp made no progress"
-    return (some mvarIdNew, usedSimps)
+    return (some mvarIdNew, stats)
 
 end Lean.Meta

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

@@ -109,6 +109,7 @@ where
       return false
 
 private def tryTheoremCore (lhs : Expr) (xs : Array Expr) (bis : Array BinderInfo) (val : Expr) (type : Expr) (e : Expr) (thm : SimpTheorem) (numExtraArgs : Nat) : SimpM (Option Result) := do
+  recordTriedSimpTheorem thm.origin
   let rec go (e : Expr) : SimpM (Option Result) := do
     if (← isDefEq lhs e) then
       unless (← synthesizeArgs thm.origin bis xs) do
@@ -406,6 +407,7 @@ def mkSEvalMethods : CoreM Methods := do
     dpre       := dpreDefault #[s]
     dpost      := dpostDefault #[s]
     discharge? := dischargeGround
+    wellBehavedDischarge := true
   }
 
 def mkSEvalContext : CoreM Context := do
@@ -493,10 +495,16 @@ where
     | .forallE _ d b _ => (d.isEq || d.isHEq || b.hasLooseBVar 0) && go b
     | _ => e.isFalse
 
-def dischargeUsingAssumption? (e : Expr) : SimpM (Option Expr) := do
+private def dischargeUsingAssumption? (e : Expr) : SimpM (Option Expr) := do
+  let lctxInitIndices := (← readThe Simp.Context).lctxInitIndices
+  let contextual := (← getConfig).contextual
   (← getLCtx).findDeclRevM? fun localDecl => do
     if localDecl.isImplementationDetail then
       return none
+    -- The following test is needed to ensure `dischargeUsingAssumption?` is a
+    -- well-behaved discharger. See comment at `Methods.wellBehavedDischarge`
+    else if !contextual && localDecl.index >= lctxInitIndices then
+      return none
     else if (← isDefEq e localDecl.type) then
       return some localDecl.toExpr
     else
@@ -545,16 +553,17 @@ def dischargeDefault? (e : Expr) : SimpM (Option Expr) := do
 
 abbrev Discharge := Expr → SimpM (Option Expr)
 
-def mkMethods (s : SimprocsArray) (discharge? : Discharge) : Methods := {
+def mkMethods (s : SimprocsArray) (discharge? : Discharge) (wellBehavedDischarge : Bool) : Methods := {
   pre        := preDefault s
   post       := postDefault s
   dpre       := dpreDefault s
   dpost      := dpostDefault s
-  discharge? := discharge?
+  discharge?
+  wellBehavedDischarge
 }
 
 def mkDefaultMethodsCore (simprocs : SimprocsArray) : Methods :=
-  mkMethods simprocs dischargeDefault?
+  mkMethods simprocs dischargeDefault? (wellBehavedDischarge := true)
 
 def mkDefaultMethods : CoreM Methods := do
   if simprocs.get (← getOptions) then