test: beta reduction tests for grind

A small boost before #6691 made `modifyState` more complex, a larger
boost after.

.github/workflows/ci.yml

@@ -238,7 +238,7 @@ jobs:
                 "name": "Linux 32bit",
                 "os": "ubuntu-latest",
                 // Use 32bit on stage0 and stage1 to keep oleans compatible
-                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/",
+                "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DPKG_CONFIG_EXECUTABLE=/usr/bin/i386-linux-gnu-pkg-config",
                 "cmultilib": true,
                 "release": true,
                 "check-level": 2,
@@ -327,7 +327,7 @@ jobs:
         run: |
           sudo dpkg --add-architecture i386
           sudo apt-get update
-          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386
+          sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386 pkgconf:i386
         if: matrix.cmultilib
       - name: Cache
         uses: actions/cache@v4

CMakeLists.txt

@@ -18,6 +18,9 @@ foreach(var ${vars})
     if("${var}" MATCHES "LLVM*")
       list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
     endif()
+    if("${var}" MATCHES "PKG_CONFIG*")
+      list(APPEND STAGE0_ARGS "-D${var}=${${var}}")
+    endif()
   elseif(("${var}" MATCHES "CMAKE_.*") AND NOT ("${var}" MATCHES "CMAKE_BUILD_TYPE") AND NOT ("${var}" MATCHES "CMAKE_HOME_DIRECTORY"))
     list(APPEND PLATFORM_ARGS "-D${var}=${${var}}")
   endif()

doc/dev/commit_convention.md

@@ -33,6 +33,9 @@ Format of the commit message
  - chore (maintain, ex: travis-ci)
  - perf (performance improvement, optimization, ...)
 
+Every `feat` or `fix` commit must have a `changelog-*` label, and a commit message
+beginning with "This PR " that will be included in the changelog.
+
 ``<subject>`` has the following constraints:
 
  - use imperative, present tense: "change" not "changed" nor "changes"
@@ -44,6 +47,7 @@ Format of the commit message
  - just as in ``<subject>``, use imperative, present tense
  - includes motivation for the change and contrasts with previous
    behavior
+ - If a `changelog-*` label is present, the body must begin with "This PR ".
 
 ``<footer>`` is optional and may contain two items:
 
@@ -60,17 +64,21 @@ Examples
 
 fix: add declarations for operator<<(std::ostream&, expr const&) and operator<<(std::ostream&, context const&) in the kernel
 
+This PR adds declarations `operator<<` for raw printing.
 The actual implementation of these two operators is outside of the
-kernel. They are implemented in the file 'library/printer.cpp'. We
-declare them in the kernel to prevent the following problem. Suppose
-there is a file 'foo.cpp' that does not include 'library/printer.h',
-but contains
+kernel. They are implemented in the file 'library/printer.cpp'.
 
-    expr a;
-    ...
-    std::cout << a << "\n";
-    ...
+We declare them in the kernel to prevent the following problem.
+Suppose there is a file 'foo.cpp' that does not include 'library/printer.h',
+but contains
+```cpp
+expr a;
+...
+std::cout << a << "\n";
+...
+```
 
 The compiler does not generate an error message. It silently uses the
 operator bool() to coerce the expression into a Boolean. This produces
 counter-intuitive behavior, and may confuse developers.
+

doc/dev/index.md

@@ -80,3 +80,10 @@ Unlike most Lean projects, all submodules of the `Lean` module begin with the
 `prelude` keyword. This disables the automated import of `Init`, meaning that
 developers need to figure out their own subset of `Init` to import. This is done
 such that changing files in `Init` doesn't force a full rebuild of `Lean`.
+
+### Testing against Mathlib/Batteries
+You can test a Lean PR against Mathlib and Batteries by rebasing your PR
+on to `nightly-with-mathlib` branch. (It is fine to force push after rebasing.)
+CI will generate a branch of Mathlib and Batteries called `lean-pr-testing-NNNN`
+that uses the toolchain for your PR, and will report back to the Lean PR with results from Mathlib CI.
+See https://leanprover-community.github.io/contribute/tags_and_branches.html for more details.

doc/make/osx-10.9.md

@@ -32,12 +32,13 @@ following to use `g++`.
 cmake -DCMAKE_CXX_COMPILER=g++ ...
 ```
 
-## Required Packages: CMake, GMP, libuv
+## Required Packages: CMake, GMP, libuv, pkgconf
 
 ```bash
 brew install cmake
 brew install gmp
 brew install libuv
+brew install pkgconf
 ```
 
 ## Recommended Packages: CCache

doc/make/ubuntu.md

@@ -8,5 +8,5 @@ follow the [generic build instructions](index.md).
 ## Basic packages
 
 ```bash
-sudo apt-get install git libgmp-dev libuv1-dev cmake ccache clang
+sudo apt-get install git libgmp-dev libuv1-dev cmake ccache clang pkgconf
 ```

flake.nix

@@ -28,7 +28,7 @@
           stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
         } ({
           buildInputs = with pkgs; [
-            cmake gmp libuv ccache cadical
+            cmake gmp libuv ccache cadical pkg-config
             lean-packages.llvmPackages.llvm  # llvm-symbolizer for asan/lsan
             gdb
             tree  # for CI

nix/bootstrap.nix

@@ -1,12 +1,12 @@
 { src, debug ? false, stage0debug ? false, extraCMakeFlags ? [],
-  stdenv, lib, cmake, gmp, libuv, cadical, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
+  stdenv, lib, cmake, pkg-config, gmp, libuv, cadical, git, gnumake, bash, buildLeanPackage, writeShellScriptBin, runCommand, symlinkJoin, lndir, perl, gnused, darwin, llvmPackages, linkFarmFromDrvs,
   ... } @ args:
 with builtins;
 lib.warn "The Nix-based build is deprecated" rec {
   inherit stdenv;
   sourceByRegex = p: rs: lib.sourceByRegex p (map (r: "(/src/)?${r}") rs);
   buildCMake = args: stdenv.mkDerivation ({
-    nativeBuildInputs = [ cmake ];
+    nativeBuildInputs = [ cmake pkg-config ];
     buildInputs = [ gmp libuv llvmPackages.llvm ];
     # https://github.com/NixOS/nixpkgs/issues/60919
     hardeningDisable = [ "all" ];

script/push_repo_release_tag.py

@@ -0,0 +1,69 @@
+#!/usr/bin/env python3
+import sys
+import subprocess
+import requests
+
+def main():
+    if len(sys.argv) != 4:
+        print("Usage: ./push_repo_release_tag.py <repo> <branch> <version_tag>")
+        sys.exit(1)
+
+    repo, branch, version_tag = sys.argv[1], sys.argv[2], sys.argv[3]
+
+    if branch not in {"master", "main"}:
+        print(f"Error: Branch '{branch}' is not 'master' or 'main'.")
+        sys.exit(1)
+
+    # Get the `lean-toolchain` file content
+    lean_toolchain_url = f"https://raw.githubusercontent.com/{repo}/{branch}/lean-toolchain"
+    try:
+        response = requests.get(lean_toolchain_url)
+        response.raise_for_status()
+    except requests.exceptions.RequestException as e:
+        print(f"Error fetching 'lean-toolchain' file: {e}")
+        sys.exit(1)
+
+    lean_toolchain_content = response.text.strip()
+    expected_prefix = "leanprover/lean4:"
+    if not lean_toolchain_content.startswith(expected_prefix) or lean_toolchain_content != f"{expected_prefix}{version_tag}":
+        print(f"Error: 'lean-toolchain' content does not match '{expected_prefix}{version_tag}'.")
+        sys.exit(1)
+
+    # Create and push the tag using `gh`
+    try:
+        # Check if the tag already exists
+        list_tags_cmd = ["gh", "api", f"repos/{repo}/git/matching-refs/tags/v4", "--jq", ".[].ref"]
+        list_tags_output = subprocess.run(list_tags_cmd, capture_output=True, text=True)
+
+        if list_tags_output.returncode == 0:
+            existing_tags = list_tags_output.stdout.strip().splitlines()
+            if f"refs/tags/{version_tag}" in existing_tags:
+                print(f"Error: Tag '{version_tag}' already exists.")
+                print("Existing tags starting with 'v4':")
+                for tag in existing_tags:
+                    print(tag.replace("refs/tags/", ""))
+                sys.exit(1)
+
+        # Get the SHA of the branch
+        get_sha_cmd = [
+            "gh", "api", f"repos/{repo}/git/ref/heads/{branch}", "--jq", ".object.sha"
+        ]
+        sha_result = subprocess.run(get_sha_cmd, capture_output=True, text=True, check=True)
+        sha = sha_result.stdout.strip()
+
+        # Create the tag
+        create_tag_cmd = [
+            "gh", "api", f"repos/{repo}/git/refs",
+            "-X", "POST",
+            "-F", f"ref=refs/tags/{version_tag}",
+            "-F", f"sha={sha}"
+        ]
+        subprocess.run(create_tag_cmd, capture_output=True, text=True, check=True)
+
+        print(f"Successfully created and pushed tag '{version_tag}' to {repo}.")
+    except subprocess.CalledProcessError as e:
+        print(f"Error while creating/pushing tag: {e.stderr.strip() if e.stderr else e}")
+        sys.exit(1)
+
+if __name__ == "__main__":
+    main()

script/release_checklist.py

@@ -22,6 +22,36 @@ def get_github_token():
         print("Warning: 'gh' CLI not found. Some API calls may be rate-limited.")
     return None
 
+def strip_rc_suffix(toolchain):
+    """Remove -rcX suffix from the toolchain."""
+    return toolchain.split("-")[0]
+
+def branch_exists(repo_url, branch, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/branches/{branch}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    return response.status_code == 200
+
+def tag_exists(repo_url, tag_name, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/git/refs/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    return response.status_code == 200
+
+def release_page_exists(repo_url, tag_name, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    return response.status_code == 200
+
+def get_release_notes(repo_url, tag_name, github_token):
+    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/releases/tags/{tag_name}"
+    headers = {'Authorization': f'token {github_token}'} if github_token else {}
+    response = requests.get(api_url, headers=headers)
+    if response.status_code == 200:
+        return response.json().get("body", "").strip()
+    return None
+
 def get_branch_content(repo_url, branch, file_path, github_token):
     api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/contents/{file_path}?ref={branch}"
     headers = {'Authorization': f'token {github_token}'} if github_token else {}
@@ -35,11 +65,20 @@ def get_branch_content(repo_url, branch, file_path, github_token):
             return None
     return None
 
-def tag_exists(repo_url, tag_name, github_token):
-    api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + f"/git/refs/tags/{tag_name}"
-    headers = {'Authorization': f'token {github_token}'} if github_token else {}
-    response = requests.get(api_url, headers=headers)
-    return response.status_code == 200
+def parse_version(version_str):
+    # Remove 'v' prefix and extract version and release candidate suffix
+    if ':' in version_str:
+        version_str = version_str.split(':')[1]
+    version = version_str.lstrip('v')
+    parts = version.split('-')
+    base_version = tuple(map(int, parts[0].split('.')))
+    rc_part = parts[1] if len(parts) > 1 and parts[1].startswith('rc') else None
+    rc_number = int(rc_part[2:]) if rc_part else float('inf')  # Treat non-rc as higher than rc
+    return base_version + (rc_number,)
+
+def is_version_gte(version1, version2):
+    """Check if version1 >= version2, including proper handling of release candidates."""
+    return parse_version(version1) >= parse_version(version2)
 
 def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token):
     # First get the commit SHA for the tag
@@ -64,23 +103,38 @@ def is_merged_into_stable(repo_url, tag_name, stable_branch, github_token):
     stable_commits = [commit['sha'] for commit in commits_response.json()]
     return tag_sha in stable_commits
 
-def parse_version(version_str):
-    # Remove 'v' prefix and split into components
-    # Handle Lean toolchain format (leanprover/lean4:v4.x.y)
-    if ':' in version_str:
-        version_str = version_str.split(':')[1]
-    version = version_str.lstrip('v')
-    # Handle release candidates by removing -rc part for comparison
-    version = version.split('-')[0]
-    return tuple(map(int, version.split('.')))
-
-def is_version_gte(version1, version2):
-    """Check if version1 >= version2"""
-    return parse_version(version1) >= parse_version(version2)
-
 def is_release_candidate(version):
     return "-rc" in version
 
+def check_cmake_version(repo_url, branch, version_major, version_minor, github_token):
+    """Verify the CMake version settings in src/CMakeLists.txt."""
+    cmake_file_path = "src/CMakeLists.txt"
+    content = get_branch_content(repo_url, branch, cmake_file_path, github_token)
+    if content is None:
+        print(f"  ❌ Could not retrieve {cmake_file_path} from {branch}")
+        return False
+
+    expected_lines = [
+        f"set(LEAN_VERSION_MAJOR {version_major})",
+        f"set(LEAN_VERSION_MINOR {version_minor})",
+        f"set(LEAN_VERSION_PATCH 0)",
+        f"set(LEAN_VERSION_IS_RELEASE 1)"
+    ]
+
+    for line in expected_lines:
+        if not any(l.strip().startswith(line) for l in content.splitlines()):
+            print(f"  ❌ Missing or incorrect line in {cmake_file_path}: {line}")
+            return False
+
+    print(f"  ✅ CMake version settings are correct in {cmake_file_path}")
+    return True
+
+def extract_org_repo_from_url(repo_url):
+    """Extract the 'org/repo' part from a GitHub URL."""
+    if repo_url.startswith("https://github.com/"):
+        return repo_url.replace("https://github.com/", "").rstrip("/")
+    return repo_url
+
 def main():
     github_token = get_github_token()
 
@@ -89,6 +143,47 @@ def main():
         sys.exit(1)
 
     toolchain = sys.argv[1]
+    stripped_toolchain = strip_rc_suffix(toolchain)
+    lean_repo_url = "https://github.com/leanprover/lean4"
+
+    # Preliminary checks
+    print("\nPerforming preliminary checks...")
+
+    # Check for branch releases/v4.Y.0
+    version_major, version_minor, _ = map(int, stripped_toolchain.lstrip('v').split('.'))
+    branch_name = f"releases/v{version_major}.{version_minor}.0"
+    if branch_exists(lean_repo_url, branch_name, github_token):
+        print(f"  ✅ Branch {branch_name} exists")
+
+        # Check CMake version settings
+        check_cmake_version(lean_repo_url, branch_name, version_major, version_minor, github_token)
+    else:
+        print(f"  ❌ Branch {branch_name} does not exist")
+
+    # Check for tag v4.X.Y(-rcZ)
+    if tag_exists(lean_repo_url, toolchain, github_token):
+        print(f"  ✅ Tag {toolchain} exists")
+    else:
+        print(f"  ❌ Tag {toolchain} does not exist.")
+
+    # Check for release page
+    if release_page_exists(lean_repo_url, toolchain, github_token):
+        print(f"  ✅ Release page for {toolchain} exists")
+
+        # Check the first line of the release notes
+        release_notes = get_release_notes(lean_repo_url, toolchain, github_token)
+        if release_notes and release_notes.splitlines()[0].strip() == toolchain:
+            print(f"  ✅ Release notes look good.")
+        else:
+            previous_minor_version = version_minor - 1
+            previous_stable_branch = f"releases/v{version_major}.{previous_minor_version}.0"
+            previous_release = f"v{version_major}.{previous_minor_version}.0"
+            print(f"  ❌ Release notes not published. Please run `script/release_notes.py {previous_release}` on branch `{previous_stable_branch}`.")
+    else:
+        print(f"  ❌ Release page for {toolchain} does not exist")
+
+    # Load repositories and perform further checks
+    print("\nChecking repositories...")
 
     with open(os.path.join(os.path.dirname(__file__), "release_repos.yml")) as f:
         repos = yaml.safe_load(f)["repositories"]
@@ -117,7 +212,7 @@ def main():
         # Only check for tag if toolchain-tag is true
         if check_tag:
             if not tag_exists(url, toolchain, github_token):
-                print(f"  ❌ Tag {toolchain} does not exist")
+                print(f"  ❌ Tag {toolchain} does not exist. Run `script/push_repo_release_tag.py {extract_org_repo_from_url(url)} {branch} {toolchain}`.")
                 continue
             print(f"  ✅ Tag {toolchain} exists")
 

src/CMakeLists.txt

@@ -295,14 +295,15 @@ index 5e8e0166..f3b29134 100644
 	  PATCH_COMMAND git reset --hard HEAD && printf "${LIBUV_PATCH}" > patch.diff && git apply patch.diff
     BUILD_IN_SOURCE ON
     INSTALL_COMMAND "")
-  set(LIBUV_INCLUDE_DIR "${CMAKE_BINARY_DIR}/libuv/src/libuv/include")
-  set(LIBUV_LIBRARIES "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
+  set(LIBUV_INCLUDE_DIRS "${CMAKE_BINARY_DIR}/libuv/src/libuv/include")
+  set(LIBUV_LDFLAGS "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
 else()
   find_package(LibUV 1.0.0 REQUIRED)
 endif()
-include_directories(${LIBUV_INCLUDE_DIR})
+include_directories(${LIBUV_INCLUDE_DIRS})
 if(NOT LEAN_STANDALONE)
-  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LIBRARIES}")
+  string(JOIN " " LIBUV_LDFLAGS ${LIBUV_LDFLAGS})
+  string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LDFLAGS}")
 endif()
 
 # Windows SDK (for ICU)
@@ -698,12 +699,12 @@ else()
 endif()
 
 if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
-  add_custom_target(lake_lib ALL
+  add_custom_target(lake_lib
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS leanshared
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Lake
     VERBATIM)
-  add_custom_target(lake_shared ALL
+  add_custom_target(lake_shared
     WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
     DEPENDS lake_lib
     COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make libLake_shared

src/Init/Data/Array/Basic.lean

@@ -244,8 +244,7 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
 def range (n : Nat) : Array Nat :=
   ofFn fun (i : Fin n) => i
 
-def singleton (v : α) : Array α :=
-  mkArray 1 v
+@[inline] protected def singleton (v : α) : Array α := #[v]
 
 def back! [Inhabited α] (a : Array α) : α :=
   a[a.size - 1]!
@@ -456,7 +455,7 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
 /-- Variant of `mapIdxM` which receives the index as a `Fin as.size`. -/
 @[inline]
 def mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
-    (as : Array α) (f : Fin as.size → α → m β) : m (Array β) :=
+    (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → m β) : m (Array β) :=
   let rec @[specialize] map (i : Nat) (j : Nat) (inv : i + j = as.size) (bs : Array β) : m (Array β) := do
     match i, inv with
     | 0,    _  => pure bs
@@ -465,12 +464,12 @@ def mapFinIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m]
         rw [← inv, Nat.add_assoc, Nat.add_comm 1 j, Nat.add_comm]
         apply Nat.le_add_right
       have : i + (j + 1) = as.size := by rw [← inv, Nat.add_comm j 1, Nat.add_assoc]
-      map i (j+1) this (bs.push (← f ⟨j, j_lt⟩ (as.get j j_lt)))
+      map i (j+1) this (bs.push (← f j (as.get j j_lt) j_lt))
   map as.size 0 rfl (mkEmpty as.size)
 
 @[inline]
 def mapIdxM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : Nat → α → m β) (as : Array α) : m (Array β) :=
-  as.mapFinIdxM fun i a => f i a
+  as.mapFinIdxM fun i a _ => f i a
 
 @[inline]
 def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α → m (Option β)) (as : Array α) : m (Option β) := do
@@ -577,13 +576,19 @@ def foldl {α : Type u} {β : Type v} (f : β → α → β) (init : β) (as : A
 def foldr {α : Type u} {β : Type v} (f : α → β → β) (init : β) (as : Array α) (start := as.size) (stop := 0) : β :=
   Id.run <| as.foldrM f init start stop
 
+/-- Sum of an array.
+
+`Array.sum #[a, b, c] = a + (b + (c + 0))` -/
+def sum {α} [Add α] [Zero α] : Array α → α :=
+  foldr (· + ·) 0
+
 @[inline]
 def map {α : Type u} {β : Type v} (f : α → β) (as : Array α) : Array β :=
   Id.run <| as.mapM f
 
 /-- Variant of `mapIdx` which receives the index as a `Fin as.size`. -/
 @[inline]
-def mapFinIdx {α : Type u} {β : Type v} (as : Array α) (f : Fin as.size → α → β) : Array β :=
+def mapFinIdx {α : Type u} {β : Type v} (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → β) : Array β :=
   Id.run <| as.mapFinIdxM f
 
 @[inline]

src/Init/Data/Array/Bootstrap.lean

@@ -81,12 +81,18 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init
 
 @[simp] theorem toList_empty : (#[] : Array α).toList = [] := rfl
 
-@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
+@[simp] theorem append_empty (as : Array α) : as ++ #[] = as := by
   apply ext'; simp only [toList_append, toList_empty, List.append_nil]
 
-@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
+@[deprecated append_empty (since := "2025-01-13")]
+abbrev append_nil := @append_empty
+
+@[simp] theorem empty_append (as : Array α) : #[] ++ as = as := by
   apply ext'; simp only [toList_append, toList_empty, List.nil_append]
 
+@[deprecated empty_append (since := "2025-01-13")]
+abbrev nil_append := @empty_append
+
 @[simp] theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
   apply ext'; simp only [toList_append, List.append_assoc]
 

src/Init/Data/Array/Find.lean

@@ -74,12 +74,12 @@ theorem findSome?_append {l₁ l₂ : Array α} : (l₁ ++ l₂).findSome? f = (
 
 theorem getElem?_zero_flatten (L : Array (Array α)) :
     (flatten L)[0]? = L.findSome? fun l => l[0]? := by
-  cases L using array_array_induction
+  cases L using array₂_induction
   simp [← List.head?_eq_getElem?, List.head?_flatten, List.findSome?_map, Function.comp_def]
 
 theorem getElem_zero_flatten.proof {L : Array (Array α)} (h : 0 < L.flatten.size) :
     (L.findSome? fun l => l[0]?).isSome := by
-  cases L using array_array_induction
+  cases L using array₂_induction
   simp only [List.findSome?_toArray, List.findSome?_map, Function.comp_def, List.getElem?_toArray,
     List.findSome?_isSome_iff, isSome_getElem?]
   simp only [flatten_toArray_map_toArray, size_toArray, List.length_flatten,
@@ -95,7 +95,7 @@ theorem getElem_zero_flatten {L : Array (Array α)} (h) :
 
 theorem back?_flatten {L : Array (Array α)} :
     (flatten L).back? = (L.findSomeRev? fun l => l.back?) := by
-  cases L using array_array_induction
+  cases L using array₂_induction
   simp [List.getLast?_flatten, ← List.map_reverse, List.findSome?_map, Function.comp_def]
 
 theorem findSome?_mkArray : findSome? f (mkArray n a) = if n = 0 then none else f a := by
@@ -203,7 +203,7 @@ theorem get_find?_mem {xs : Array α} (h) : (xs.find? p).get h ∈ xs := by
 
 @[simp] theorem find?_flatten (xs : Array (Array α)) (p : α → Bool) :
     xs.flatten.find? p = xs.findSome? (·.find? p) := by
-  cases xs using array_array_induction
+  cases xs using array₂_induction
   simp [List.findSome?_map, Function.comp_def]
 
 theorem find?_flatten_eq_none {xs : Array (Array α)} {p : α → Bool} :
@@ -220,7 +220,7 @@ theorem find?_flatten_eq_some {xs : Array (Array α)} {p : α → Bool} {a : α}
       p a ∧ ∃ (as : Array (Array α)) (ys zs : Array α) (bs : Array (Array α)),
         xs = as.push (ys.push a ++ zs) ++ bs ∧
         (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
-  cases xs using array_array_induction
+  cases xs using array₂_induction
   simp only [flatten_toArray_map_toArray, List.find?_toArray, List.find?_flatten_eq_some]
   simp only [Bool.not_eq_eq_eq_not, Bool.not_true, exists_and_right, and_congr_right_iff]
   intro w

src/Init/Data/Array/MapIdx.lean

@@ -12,81 +12,82 @@ namespace Array
 /-! ### mapFinIdx -/
 
 -- This could also be proved from `SatisfiesM_mapIdxM` in Batteries.
-theorem mapFinIdx_induction (as : Array α) (f : Fin as.size → α → β)
+theorem mapFinIdx_induction (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → 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)) :
+    (p : (i : Nat) → β → (h : i < as.size) → Prop)
+    (hs : ∀ i h, motive i → p i (f i as[i] h) h ∧ motive (i + 1)) :
     motive as.size ∧ ∃ eq : (Array.mapFinIdx as f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((Array.mapFinIdx 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) :
+      ∀ i h, p i ((Array.mapFinIdx as f)[i]) h := by
+  let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : ∀ i h h', p i bs[i] h) (hm : motive j) :
     let arr : Array β := Array.mapFinIdxM.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
+    motive as.size ∧ ∃ eq : arr.size = as.size, ∀ i h, p i arr[i] h := by
     induction i generalizing j bs with simp [mapFinIdxM.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)
+      apply @ih (bs.push (f j as[j] (by omega))) (j + 1) (by omega) (by simp; omega)
       · intro i i_lt h'
         rw [getElem_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
+          apply (hs i (by omega) hm).1
+      · exact (hs j (by omega) hm).2
   simp [mapFinIdx, mapFinIdxM]; exact go rfl nofun h0
 
-theorem mapFinIdx_spec (as : Array α) (f : Fin as.size → α → β)
-    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
+theorem mapFinIdx_spec (as : Array α) (f : (i : Nat) → α → (h : i < as.size) → β)
+    (p : (i : Nat) → β → (h : i < as.size) → Prop) (hs : ∀ i h, p i (f i as[i] h) h) :
     ∃ eq : (Array.mapFinIdx as f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((Array.mapFinIdx as f)[i]) :=
-  (mapFinIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+      ∀ i h, p i ((Array.mapFinIdx as f)[i]) h :=
+  (mapFinIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
-@[simp] theorem size_mapFinIdx (a : Array α) (f : Fin a.size → α → β) : (a.mapFinIdx f).size = a.size :=
-  (mapFinIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+@[simp] theorem size_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) :
+    (a.mapFinIdx f).size = a.size :=
+  (mapFinIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
 @[simp] theorem size_zipWithIndex (as : Array α) : as.zipWithIndex.size = as.size :=
   Array.size_mapFinIdx _ _
 
-@[simp] theorem getElem_mapFinIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat)
+@[simp] theorem getElem_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) (i : Nat)
     (h : i < (mapFinIdx a f).size) :
-    (a.mapFinIdx f)[i] = f ⟨i, by simp_all⟩ (a[i]'(by simp_all)) :=
-  (mapFinIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
+    (a.mapFinIdx f)[i] = f i (a[i]'(by simp_all))  (by simp_all) :=
+  (mapFinIdx_spec _ _ (fun i b h => b = f i a[i] h) fun _ _ => rfl).2 i _
 
-@[simp] theorem getElem?_mapFinIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat) :
+@[simp] theorem getElem?_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) (i : Nat) :
     (a.mapFinIdx f)[i]? =
-      a[i]?.pbind fun b h => f ⟨i, (getElem?_eq_some_iff.1 h).1⟩ b := by
+      a[i]?.pbind fun b h => f i b (getElem?_eq_some_iff.1 h).1 := by
   simp only [getElem?_def, size_mapFinIdx, getElem_mapFinIdx]
   split <;> simp_all
 
-@[simp] theorem toList_mapFinIdx (a : Array α) (f : Fin a.size → α → β) :
-    (a.mapFinIdx f).toList = a.toList.mapFinIdx (fun i a => f ⟨i, by simp⟩ a) := by
+@[simp] theorem toList_mapFinIdx (a : Array α) (f : (i : Nat) → α → (h : i < a.size) → β) :
+    (a.mapFinIdx f).toList = a.toList.mapFinIdx (fun i a h => f i a (by simpa)) := by
   apply List.ext_getElem <;> simp
 
 /-! ### mapIdx -/
 
 theorem mapIdx_induction (f : Nat → α → β) (as : Array α)
     (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)) :
+    (p : (i : Nat) → β → (h : i < as.size) → Prop)
+    (hs : ∀ i h, motive i → p i (f i as[i]) h ∧ motive (i + 1)) :
     motive as.size ∧ ∃ eq : (as.mapIdx f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((as.mapIdx f)[i]) :=
-  mapFinIdx_induction as (fun i a => f i a) motive h0 p hs
+      ∀ i h, p i ((as.mapIdx f)[i]) h :=
+  mapFinIdx_induction as (fun i a _ => f i a) motive h0 p hs
 
 theorem mapIdx_spec (f : Nat → α → β) (as : Array α)
-    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
+    (p : (i : Nat) → β → (h : i < as.size) → Prop) (hs : ∀ i h, p i (f i as[i]) h) :
     ∃ eq : (as.mapIdx f).size = as.size,
-      ∀ i h, p ⟨i, h⟩ ((as.mapIdx f)[i]) :=
-  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+      ∀ i h, p i ((as.mapIdx f)[i]) h :=
+  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ _ => ⟨hs .., trivial⟩).2
 
 @[simp] theorem size_mapIdx (f : Nat → α → β) (as : Array α) : (as.mapIdx f).size = as.size :=
-  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+  (mapIdx_spec (p := fun _ _ _ => True) (hs := fun _ _ => trivial)).1
 
 @[simp] theorem getElem_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat)
     (h : i < (as.mapIdx f).size) :
     (as.mapIdx f)[i] = f i (as[i]'(by simp_all)) :=
-  (mapIdx_spec _ _ (fun i b => b = f i as[i]) fun _ => rfl).2 i (by simp_all)
+  (mapIdx_spec _ _ (fun i b h => b = f i as[i]) fun _ _ => rfl).2 i (by simp_all)
 
 @[simp] theorem getElem?_mapIdx (f : Nat → α → β) (as : Array α) (i : Nat) :
     (as.mapIdx f)[i]? =
@@ -101,7 +102,7 @@ end Array
 
 namespace List
 
-@[simp] theorem mapFinIdx_toArray (l : List α) (f : Fin l.length → α → β) :
+@[simp] theorem mapFinIdx_toArray (l : List α) (f : (i : Nat) → α → (h : i < l.length) → β) :
     l.toArray.mapFinIdx f = (l.mapFinIdx f).toArray := by
   ext <;> simp
 

src/Init/Data/BitVec/Lemmas.lean

@@ -1294,11 +1294,6 @@ theorem allOnes_shiftLeft_or_shiftLeft {x : BitVec w} {n : Nat} :
     BitVec.allOnes w <<< n ||| x <<< n = BitVec.allOnes w <<< n := by
   simp [← shiftLeft_or_distrib]
 
-@[deprecated shiftLeft_add (since := "2024-06-02")]
-theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
-    (x <<< n) <<< m = x <<< (n + m) := by
-  rw [shiftLeft_add]
-
 /-! ### shiftLeft reductions from BitVec to Nat -/
 
 @[simp]
@@ -1946,11 +1941,6 @@ theorem msb_shiftLeft {x : BitVec w} {n : Nat} :
     (x <<< n).msb = x.getMsbD n := by
   simp [BitVec.msb]
 
-@[deprecated shiftRight_add (since := "2024-06-02")]
-theorem shiftRight_shiftRight {w : Nat} (x : BitVec w) (n m : Nat) :
-    (x >>> n) >>> m = x >>> (n + m) := by
-  rw [shiftRight_add]
-
 /-! ### rev -/
 
 theorem getLsbD_rev (x : BitVec w) (i : Fin w) :
@@ -3539,7 +3529,7 @@ theorem getLsbD_intMax (w : Nat) : (intMax w).getLsbD i = decide (i + 1 < w) :=
 
 /-! ### Non-overflow theorems -/
 
-/-- If `x.toNat * y.toNat < 2^w`, then the multiplication `(x * y)` does not overflow. -/
+/-- If `x.toNat + y.toNat < 2^w`, then the addition `(x + y)` does not overflow. -/
 theorem toNat_add_of_lt {w} {x y : BitVec w} (h : x.toNat + y.toNat < 2^w) :
     (x + y).toNat = x.toNat + y.toNat := by
   rw [BitVec.toNat_add, Nat.mod_eq_of_lt h]

src/Init/Data/Char/Lemmas.lean

@@ -70,5 +70,3 @@ theorem utf8Size_eq (c : Char) : c.utf8Size = 1 ∨ c.utf8Size = 2 ∨ c.utf8Siz
   rfl
 
 end Char
-
-@[deprecated Char.utf8Size (since := "2024-06-04")] abbrev String.csize := Char.utf8Size

src/Init/Data/List/Basic.lean

@@ -258,9 +258,6 @@ theorem ext_get? : ∀ {l₁ l₂ : List α}, (∀ n, l₁.get? n = l₂.get? n)
     have h0 : some a = some a' := h 0
     injection h0 with aa; simp only [aa, ext_get? fun n => h (n+1)]
 
-/-- Deprecated alias for `ext_get?`. The preferred extensionality theorem is now `ext_getElem?`. -/
-@[deprecated ext_get? (since := "2024-06-07")] abbrev ext := @ext_get?
-
 /-! ### getD -/
 
 /--
@@ -606,11 +603,11 @@ set_option linter.missingDocs false in
 to get a list of lists, and then concatenates them all together.
 * `[2, 3, 2].bind range = [0, 1, 0, 1, 2, 0, 1]`
 -/
-@[inline] def flatMap {α : Type u} {β : Type v} (a : List α) (b : α → List β) : List β := flatten (map b a)
+@[inline] def flatMap {α : Type u} {β : Type v} (b : α → List β) (a : List α) : List β := flatten (map b a)
 
-@[simp] theorem flatMap_nil (f : α → List β) : List.flatMap [] f = [] := by simp [flatten, List.flatMap]
+@[simp] theorem flatMap_nil (f : α → List β) : List.flatMap f [] = [] := by simp [flatten, List.flatMap]
 @[simp] theorem flatMap_cons x xs (f : α → List β) :
-  List.flatMap (x :: xs) f = f x ++ List.flatMap xs f := by simp [flatten, List.flatMap]
+  List.flatMap f (x :: xs) = f x ++ List.flatMap f xs := by simp [flatten, List.flatMap]
 
 set_option linter.missingDocs false in
 @[deprecated flatMap (since := "2024-10-16")] abbrev bind := @flatMap
@@ -619,11 +616,6 @@ set_option linter.missingDocs false in
 set_option linter.missingDocs false in
 @[deprecated flatMap_cons (since := "2024-10-16")] abbrev cons_flatMap := @flatMap_cons
 
-set_option linter.missingDocs false in
-@[deprecated flatMap_nil (since := "2024-06-15")] abbrev nil_bind := @flatMap_nil
-set_option linter.missingDocs false in
-@[deprecated flatMap_cons (since := "2024-06-15")] abbrev cons_bind := @flatMap_cons
-
 /-! ### replicate -/
 
 /--
@@ -713,11 +705,6 @@ def elem [BEq α] (a : α) : List α → Bool
 theorem elem_cons [BEq α] {a : α} :
     (b::bs).elem a = match a == b with | true => true | false => bs.elem a := rfl
 
-/-- `notElem a l` is `!(elem a l)`. -/
-@[deprecated "Use `!(elem a l)` instead."(since := "2024-06-15")]
-def notElem [BEq α] (a : α) (as : List α) : Bool :=
-  !(as.elem a)
-
 /-! ### contains -/
 
 @[inherit_doc elem] abbrev contains [BEq α] (as : List α) (a : α) : Bool :=

src/Init/Data/List/Impl.lean

@@ -96,14 +96,14 @@ The following operations are given `@[csimp]` replacements below:
 /-! ### flatMap  -/
 
 /-- Tail recursive version of `List.flatMap`. -/
-@[inline] def flatMapTR (as : List α) (f : α → List β) : List β := go as #[] where
+@[inline] def flatMapTR (f : α → List β) (as : List α) : List β := go as #[] where
   /-- Auxiliary for `flatMap`: `flatMap.go f as = acc.toList ++ bind f as` -/
   @[specialize] go : List α → Array β → List β
   | [], acc => acc.toList
   | x::xs, acc => go xs (acc ++ f x)
 
 @[csimp] theorem flatMap_eq_flatMapTR : @List.flatMap = @flatMapTR := by
-  funext α β as f
+  funext α β f as
   let rec go : ∀ as acc, flatMapTR.go f as acc = acc.toList ++ as.flatMap f
     | [], acc => by simp [flatMapTR.go, flatMap]
     | x::xs, acc => by simp [flatMapTR.go, flatMap, go xs]
@@ -112,7 +112,7 @@ The following operations are given `@[csimp]` replacements below:
 /-! ### flatten -/
 
 /-- Tail recursive version of `List.flatten`. -/
-@[inline] def flattenTR (l : List (List α)) : List α := flatMapTR l id
+@[inline] def flattenTR (l : List (List α)) : List α := l.flatMapTR id
 
 @[csimp] theorem flatten_eq_flattenTR : @flatten = @flattenTR := by
   funext α l; rw [← List.flatMap_id, List.flatMap_eq_flatMapTR]; rfl

src/Init/Data/List/Lemmas.lean

@@ -813,11 +813,6 @@ theorem getElem_cons_length (x : α) (xs : List α) (i : Nat) (h : i = xs.length
     (x :: xs)[i]'(by simp [h]) = (x :: xs).getLast (cons_ne_nil x xs) := by
   rw [getLast_eq_getElem]; cases h; rfl
 
-@[deprecated getElem_cons_length (since := "2024-06-12")]
-theorem get_cons_length (x : α) (xs : List α) (n : Nat) (h : n = xs.length) :
-    (x :: xs).get ⟨n, by simp [h]⟩ = (x :: xs).getLast (cons_ne_nil x xs) := by
-  simp [getElem_cons_length, h]
-
 /-! ### getLast? -/
 
 @[simp] theorem getLast?_singleton (a : α) : getLast? [a] = a := rfl
@@ -1026,21 +1021,10 @@ theorem getLast?_tail (l : List α) : (tail l).getLast? = if l.length = 1 then n
   | _ :: _, 0 => by simp
   | _ :: l, i+1 => by simp [getElem?_map f l i]
 
-@[deprecated getElem?_map (since := "2024-06-12")]
-theorem get?_map (f : α → β) : ∀ l i, (map f l).get? i = (l.get? i).map f
-  | [], _ => rfl
-  | _ :: _, 0 => rfl
-  | _ :: l, i+1 => get?_map f l i
-
 @[simp] theorem getElem_map (f : α → β) {l} {i : Nat} {h : i < (map f l).length} :
     (map f l)[i] = f (l[i]'(length_map l f ▸ h)) :=
   Option.some.inj <| by rw [← getElem?_eq_getElem, getElem?_map, getElem?_eq_getElem]; rfl
 
-@[deprecated getElem_map (since := "2024-06-12")]
-theorem get_map (f : α → β) {l i} :
-    get (map f l) i = f (get l ⟨i, length_map l f ▸ i.2⟩) := by
-  simp
-
 @[simp] theorem map_id_fun : map (id : α → α) = id := by
   funext l
   induction l <;> simp_all
@@ -1076,9 +1060,31 @@ theorem forall_mem_map {f : α → β} {l : List α} {P : β → Prop} :
 
 @[deprecated forall_mem_map (since := "2024-07-25")] abbrev forall_mem_map_iff := @forall_mem_map
 
+@[simp] theorem map_eq_nil_iff {f : α → β} {l : List α} : map f l = [] ↔ l = [] := by
+  constructor <;> exact fun _ => match l with | [] => rfl
+
+@[deprecated map_eq_nil_iff (since := "2024-09-05")] abbrev map_eq_nil := @map_eq_nil_iff
+
+theorem eq_nil_of_map_eq_nil {f : α → β} {l : List α} (h : map f l = []) : l = [] :=
+  map_eq_nil_iff.mp h
+
 @[simp] theorem map_inj_left {f g : α → β} : map f l = map g l ↔ ∀ a ∈ l, f a = g a := by
   induction l <;> simp_all
 
+theorem map_inj_right {f : α → β} (w : ∀ x y, f x = f y → x = y) : map f l = map f l' ↔ l = l' := by
+  induction l generalizing l' with
+  | nil => simp
+  | cons a l ih =>
+    simp only [map_cons]
+    cases l' with
+    | nil => simp
+    | cons a' l' =>
+      simp only [map_cons, cons.injEq, ih, and_congr_left_iff]
+      intro h
+      constructor
+      · apply w
+      · simp +contextual
+
 theorem map_congr_left (h : ∀ a ∈ l, f a = g a) : map f l = map g l :=
   map_inj_left.2 h
 
@@ -1087,14 +1093,6 @@ theorem map_inj : map f = map g ↔ f = g := by
   · intro h; ext a; replace h := congrFun h [a]; simpa using h
   · intro h; subst h; rfl
 
-@[simp] theorem map_eq_nil_iff {f : α → β} {l : List α} : map f l = [] ↔ l = [] := by
-  constructor <;> exact fun _ => match l with | [] => rfl
-
-@[deprecated map_eq_nil_iff (since := "2024-09-05")] abbrev map_eq_nil := @map_eq_nil_iff
-
-theorem eq_nil_of_map_eq_nil {f : α → β} {l : List α} (h : map f l = []) : l = [] :=
-  map_eq_nil_iff.mp h
-
 theorem map_eq_cons_iff {f : α → β} {l : List α} :
     map f l = b :: l₂ ↔ ∃ a l₁, l = a :: l₁ ∧ f a = b ∧ map f l₁ = l₂ := by
   cases l
@@ -1272,8 +1270,6 @@ theorem filter_map (f : β → α) (l : List β) : filter p (map f l) = map f (f
   | nil => rfl
   | cons a l IH => by_cases h : p (f a) <;> simp [*]
 
-@[deprecated filter_map (since := "2024-06-15")] abbrev map_filter := @filter_map
-
 theorem map_filter_eq_foldr (f : α → β) (p : α → Bool) (as : List α) :
     map f (filter p as) = foldr (fun a bs => bif p a then f a :: bs else bs) [] as := by
   induction as with
@@ -1318,8 +1314,6 @@ theorem filter_congr {p q : α → Bool} :
     · simp [pa, h.1 ▸ pa, filter_congr h.2]
     · simp [pa, h.1 ▸ pa, filter_congr h.2]
 
-@[deprecated filter_congr (since := "2024-06-20")] abbrev filter_congr' := @filter_congr
-
 theorem head_filter_of_pos {p : α → Bool} {l : List α} (w : l ≠ []) (h : p (l.head w)) :
     (filter p l).head ((ne_nil_of_mem (mem_filter.2 ⟨head_mem w, h⟩))) = l.head w := by
   cases l with
@@ -1494,6 +1488,34 @@ theorem filterMap_eq_cons_iff {l} {b} {bs} :
 @[simp] theorem cons_append_fun (a : α) (as : List α) :
     (fun bs => ((a :: as) ++ bs)) = fun bs => a :: (as ++ bs) := rfl
 
+@[simp] theorem mem_append {a : α} {s t : List α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
+  induction s <;> simp_all [or_assoc]
+
+theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t) : a ∉ s ++ t :=
+  mt mem_append.1 $ not_or.mpr ⟨h₁, h₂⟩
+
+@[deprecated mem_append (since := "2025-01-13")]
+theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
+  propext mem_append
+
+@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
+@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
+
+/--
+See also `eq_append_cons_of_mem`, which proves a stronger version
+in which the initial list must not contain the element.
+-/
+theorem append_of_mem {a : α} {l : List α} : a ∈ l → ∃ s t : List α, l = s ++ a :: t
+  | .head l => ⟨[], l, rfl⟩
+  | .tail b h => let ⟨s, t, h'⟩ := append_of_mem h; ⟨b::s, t, by rw [h', cons_append]⟩
+
+theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
+  ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
+
+theorem forall_mem_append {p : α → Prop} {l₁ l₂ : List α} :
+    (∀ (x) (_ : x ∈ l₁ ++ l₂), p x) ↔ (∀ (x) (_ : x ∈ l₁), p x) ∧ (∀ (x) (_ : x ∈ l₂), p x) := by
+  simp only [mem_append, or_imp, forall_and]
+
 theorem getElem_append {l₁ l₂ : List α} (i : Nat) (h : i < (l₁ ++ l₂).length) :
     (l₁ ++ l₂)[i] = if h' : i < l₁.length then l₁[i] else l₂[i - l₁.length]'(by simp at h h'; exact Nat.sub_lt_left_of_lt_add h' h) := by
   split <;> rename_i h'
@@ -1519,11 +1541,6 @@ theorem getElem?_append {l₁ l₂ : List α} {i : Nat} :
   · exact getElem?_append_left h
   · exact getElem?_append_right (by simpa using h)
 
-@[deprecated getElem?_append_right (since := "2024-06-12")]
-theorem get?_append_right {l₁ l₂ : List α} {i : Nat} (h : l₁.length ≤ i) :
-    (l₁ ++ l₂).get? i = l₂.get? (i - l₁.length) := by
-  simp [getElem?_append_right, h]
-
 /-- Variant of `getElem_append_left` useful for rewriting from the small list to the big list. -/
 theorem getElem_append_left' (l₂ : List α) {l₁ : List α} {i : Nat} (hi : i < l₁.length) :
     l₁[i] = (l₁ ++ l₂)[i]'(by simpa using Nat.lt_add_right l₂.length hi) := by
@@ -1534,41 +1551,11 @@ theorem getElem_append_right' (l₁ : List α) {l₂ : List α} {i : Nat} (hi :
     l₂[i] = (l₁ ++ l₂)[i + l₁.length]'(by simpa [Nat.add_comm] using Nat.add_lt_add_left hi _) := by
   rw [getElem_append_right] <;> simp [*, le_add_left]
 
-@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
-theorem get_append_right_aux {l₁ l₂ : List α} {i : Nat}
-  (h₁ : l₁.length ≤ i) (h₂ : i < (l₁ ++ l₂).length) : i - l₁.length < l₂.length := by
-  rw [length_append] at h₂
-  exact Nat.sub_lt_left_of_lt_add h₁ h₂
-
-set_option linter.deprecated false in
-@[deprecated getElem_append_right (since := "2024-06-12")]
-theorem get_append_right' {l₁ l₂ : List α} {i : Nat} (h₁ : l₁.length ≤ i) (h₂) :
-    (l₁ ++ l₂).get ⟨i, h₂⟩ = l₂.get ⟨i - l₁.length, get_append_right_aux h₁ h₂⟩ :=
-  Option.some.inj <| by rw [← get?_eq_get, ← get?_eq_get, get?_append_right h₁]
-
 theorem getElem_of_append {l : List α} (eq : l = l₁ ++ a :: l₂) (h : l₁.length = i) :
     l[i]'(eq ▸ h ▸ by simp_arith) = a := Option.some.inj <| by
   rw [← getElem?_eq_getElem, eq, getElem?_append_right (h ▸ Nat.le_refl _), h]
   simp
 
-@[deprecated "Deprecated without replacement." (since := "2024-06-12")]
-theorem get_of_append_proof {l : List α}
-    (eq : l = l₁ ++ a :: l₂) (h : l₁.length = i) : i < length l := eq ▸ h ▸ by simp_arith
-
-set_option linter.deprecated false in
-@[deprecated getElem_of_append (since := "2024-06-12")]
-theorem get_of_append {l : List α} (eq : l = l₁ ++ a :: l₂) (h : l₁.length = i) :
-    l.get ⟨i, get_of_append_proof eq h⟩ = a := Option.some.inj <| by
-  rw [← get?_eq_get, eq, get?_append_right (h ▸ Nat.le_refl _), h, Nat.sub_self]; rfl
-
-/--
-See also `eq_append_cons_of_mem`, which proves a stronger version
-in which the initial list must not contain the element.
--/
-theorem append_of_mem {a : α} {l : List α} : a ∈ l → ∃ s t : List α, l = s ++ a :: t
-  | .head l => ⟨[], l, rfl⟩
-  | .tail b h => let ⟨s, t, h'⟩ := append_of_mem h; ⟨b::s, t, by rw [h', cons_append]⟩
-
 @[simp 1100] theorem singleton_append : [x] ++ l = x :: l := rfl
 
 theorem append_inj :
@@ -1585,8 +1572,8 @@ theorem append_inj_left (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length s₁ = le
 
 /-- Variant of `append_inj` instead requiring equality of the lengths of the second lists. -/
 theorem append_inj' (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length t₁ = length t₂) : s₁ = s₂ ∧ t₁ = t₂ :=
-  append_inj h <| @Nat.add_right_cancel _ (length t₁) _ <| by
-  let hap := congrArg length h; simp only [length_append, ← hl] at hap; exact hap
+  append_inj h <| @Nat.add_right_cancel _ t₁.length _ <| by
+    let hap := congrArg length h; simp only [length_append, ← hl] at hap; exact hap
 
 /-- Variant of `append_inj_right` instead requiring equality of the lengths of the second lists. -/
 theorem append_inj_right' (h : s₁ ++ t₁ = s₂ ++ t₂) (hl : length t₁ = length t₂) : t₁ = t₂ :=
@@ -1614,33 +1601,58 @@ theorem append_left_inj {s₁ s₂ : List α} (t) : s₁ ++ t = s₂ ++ t ↔ s
 @[simp] theorem self_eq_append_right {x y : List α} : x = x ++ y ↔ y = [] := by
   rw [eq_comm, append_right_eq_self]
 
-@[simp] theorem append_eq_nil : p ++ q = [] ↔ p = [] ∧ q = [] := by
-  cases p <;> simp
-
 theorem getLast_concat {a : α} : ∀ (l : List α), getLast (l ++ [a]) (by simp) = a
   | [] => rfl
   | a::t => by
     simp [getLast_cons _, getLast_concat t]
 
-@[deprecated getElem_append (since := "2024-06-12")]
-theorem get_append {l₁ l₂ : List α} (n : Nat) (h : n < l₁.length) :
-    (l₁ ++ l₂).get ⟨n, length_append .. ▸ Nat.lt_add_right _ h⟩ = l₁.get ⟨n, h⟩ := by
-  simp [getElem_append, h]
+@[simp] theorem append_eq_nil_iff : p ++ q = [] ↔ p = [] ∧ q = [] := by
+  cases p <;> simp
 
-@[deprecated getElem_append_left (since := "2024-06-12")]
-theorem get_append_left (as bs : List α) (h : i < as.length) {h'} :
-    (as ++ bs).get ⟨i, h'⟩ = as.get ⟨i, h⟩ := by
-  simp [getElem_append_left, h, h']
+@[deprecated append_eq_nil_iff (since := "2025-01-13")] abbrev append_eq_nil := @append_eq_nil_iff
 
-@[deprecated getElem_append_right (since := "2024-06-12")]
-theorem get_append_right (as bs : List α) (h : as.length ≤ i) {h' h''} :
-    (as ++ bs).get ⟨i, h'⟩ = bs.get ⟨i - as.length, h''⟩ := by
-  simp [getElem_append_right, h, h', h'']
+@[simp] theorem nil_eq_append_iff : [] = a ++ b ↔ a = [] ∧ b = [] := by
+  rw [eq_comm, append_eq_nil_iff]
 
-@[deprecated getElem?_append_left (since := "2024-06-12")]
-theorem get?_append {l₁ l₂ : List α} {n : Nat} (hn : n < l₁.length) :
-    (l₁ ++ l₂).get? n = l₁.get? n := by
-  simp [getElem?_append_left hn]
+@[deprecated nil_eq_append_iff (since := "2024-07-24")] abbrev nil_eq_append := @nil_eq_append_iff
+
+theorem append_ne_nil_of_left_ne_nil {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
+theorem append_ne_nil_of_right_ne_nil (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
+
+@[deprecated append_ne_nil_of_left_ne_nil (since := "2024-07-24")]
+theorem append_ne_nil_of_ne_nil_left {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
+@[deprecated append_ne_nil_of_right_ne_nil (since := "2024-07-24")]
+theorem append_ne_nil_of_ne_nil_right (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
+
+theorem append_eq_cons_iff :
+    a ++ b = x :: c ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
+  cases a with simp | cons a as => ?_
+  exact ⟨fun h => ⟨as, by simp [h]⟩, fun ⟨a', ⟨aeq, aseq⟩, h⟩ => ⟨aeq, by rw [aseq, h]⟩⟩
+
+@[deprecated append_eq_cons_iff (since := "2024-07-24")] abbrev append_eq_cons := @append_eq_cons_iff
+
+theorem cons_eq_append_iff :
+    x :: c = a ++ b ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
+  rw [eq_comm, append_eq_cons_iff]
+
+@[deprecated cons_eq_append_iff (since := "2024-07-24")] abbrev cons_eq_append := @cons_eq_append_iff
+
+theorem append_eq_singleton_iff :
+    a ++ b = [x] ↔ (a = [] ∧ b = [x]) ∨ (a = [x] ∧ b = []) := by
+  cases a <;> cases b <;> simp
+
+theorem singleton_eq_append_iff :
+    [x] = a ++ b ↔ (a = [] ∧ b = [x]) ∨ (a = [x] ∧ b = []) := by
+  cases a <;> cases b <;> simp [eq_comm]
+
+theorem append_eq_append_iff {a b c d : List α} :
+    a ++ b = c ++ d ↔ (∃ a', c = a ++ a' ∧ b = a' ++ d) ∨ ∃ c', a = c ++ c' ∧ d = c' ++ b := by
+  induction a generalizing c with
+  | nil => simp_all
+  | cons a as ih => cases c <;> simp [eq_comm, and_assoc, ih, and_or_left]
+
+@[deprecated append_inj (since := "2024-07-24")] abbrev append_inj_of_length_left := @append_inj
+@[deprecated append_inj' (since := "2024-07-24")] abbrev append_inj_of_length_right := @append_inj'
 
 @[simp] theorem head_append_of_ne_nil {l : List α} {w₁} (w₂) :
     head (l ++ l') w₁ = head l w₂ := by
@@ -1691,60 +1703,6 @@ theorem tail_append {l l' : List α} : (l ++ l').tail = if l.isEmpty then l'.tai
 
 @[deprecated tail_append_of_ne_nil (since := "2024-07-24")] abbrev tail_append_left := @tail_append_of_ne_nil
 
-theorem nil_eq_append_iff : [] = a ++ b ↔ a = [] ∧ b = [] := by
-  rw [eq_comm, append_eq_nil]
-
-@[deprecated nil_eq_append_iff (since := "2024-07-24")] abbrev nil_eq_append := @nil_eq_append_iff
-
-theorem append_ne_nil_of_left_ne_nil {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
-theorem append_ne_nil_of_right_ne_nil (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
-
-@[deprecated append_ne_nil_of_left_ne_nil (since := "2024-07-24")]
-theorem append_ne_nil_of_ne_nil_left {s : List α} (h : s ≠ []) (t : List α) : s ++ t ≠ [] := by simp_all
-@[deprecated append_ne_nil_of_right_ne_nil (since := "2024-07-24")]
-theorem append_ne_nil_of_ne_nil_right (s : List α) : t ≠ [] → s ++ t ≠ [] := by simp_all
-
-theorem append_eq_cons_iff :
-    a ++ b = x :: c ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
-  cases a with simp | cons a as => ?_
-  exact ⟨fun h => ⟨as, by simp [h]⟩, fun ⟨a', ⟨aeq, aseq⟩, h⟩ => ⟨aeq, by rw [aseq, h]⟩⟩
-
-@[deprecated append_eq_cons_iff (since := "2024-07-24")] abbrev append_eq_cons := @append_eq_cons_iff
-
-theorem cons_eq_append_iff :
-    x :: c = a ++ b ↔ (a = [] ∧ b = x :: c) ∨ (∃ a', a = x :: a' ∧ c = a' ++ b) := by
-  rw [eq_comm, append_eq_cons_iff]
-
-@[deprecated cons_eq_append_iff (since := "2024-07-24")] abbrev cons_eq_append := @cons_eq_append_iff
-
-theorem append_eq_append_iff {a b c d : List α} :
-    a ++ b = c ++ d ↔ (∃ a', c = a ++ a' ∧ b = a' ++ d) ∨ ∃ c', a = c ++ c' ∧ d = c' ++ b := by
-  induction a generalizing c with
-  | nil => simp_all
-  | cons a as ih => cases c <;> simp [eq_comm, and_assoc, ih, and_or_left]
-
-@[deprecated append_inj (since := "2024-07-24")] abbrev append_inj_of_length_left := @append_inj
-@[deprecated append_inj' (since := "2024-07-24")] abbrev append_inj_of_length_right := @append_inj'
-
-@[simp] theorem mem_append {a : α} {s t : List α} : a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
-  induction s <;> simp_all [or_assoc]
-
-theorem not_mem_append {a : α} {s t : List α} (h₁ : a ∉ s) (h₂ : a ∉ t) : a ∉ s ++ t :=
-  mt mem_append.1 $ not_or.mpr ⟨h₁, h₂⟩
-
-theorem mem_append_eq (a : α) (s t : List α) : (a ∈ s ++ t) = (a ∈ s ∨ a ∈ t) :=
-  propext mem_append
-
-@[deprecated mem_append_left (since := "2024-11-20")] abbrev mem_append_of_mem_left := @mem_append_left
-@[deprecated mem_append_right (since := "2024-11-20")] abbrev mem_append_of_mem_right := @mem_append_right
-
-theorem mem_iff_append {a : α} {l : List α} : a ∈ l ↔ ∃ s t : List α, l = s ++ a :: t :=
-  ⟨append_of_mem, fun ⟨s, t, e⟩ => e ▸ by simp⟩
-
-theorem forall_mem_append {p : α → Prop} {l₁ l₂ : List α} :
-    (∀ (x) (_ : x ∈ l₁ ++ l₂), p x) ↔ (∀ (x) (_ : x ∈ l₁), p x) ∧ (∀ (x) (_ : x ∈ l₂), p x) := by
-  simp only [mem_append, or_imp, forall_and]
-
 theorem set_append {s t : List α} :
     (s ++ t).set i x = if i < s.length then s.set i x ++ t else s ++ t.set (i - s.length) x := by
   induction s generalizing i with
@@ -1873,7 +1831,7 @@ theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ L b, l = concat L b
 
 /-! ### flatten -/
 
-@[simp] theorem length_flatten (L : List (List α)) : (flatten L).length = (L.map length).sum := by
+@[simp] theorem length_flatten (L : List (List α)) : L.flatten.length = (L.map length).sum := by
   induction L with
   | nil => rfl
   | cons =>
@@ -1888,6 +1846,9 @@ theorem flatten_singleton (l : List α) : [l].flatten = l := by simp
 @[simp] theorem flatten_eq_nil_iff {L : List (List α)} : L.flatten = [] ↔ ∀ l ∈ L, l = [] := by
   induction L <;> simp_all
 
+@[simp] theorem nil_eq_flatten_iff {L : List (List α)} : [] = L.flatten ↔ ∀ l ∈ L, l = [] := by
+  rw [eq_comm, flatten_eq_nil_iff]
+
 theorem flatten_ne_nil_iff {xs : List (List α)} : xs.flatten ≠ [] ↔ ∃ x, x ∈ xs ∧ x ≠ [] := by
   simp
 
@@ -1913,7 +1874,8 @@ theorem head?_flatten {L : List (List α)} : (flatten L).head? = L.findSome? fun
 -- `getLast?_flatten` is proved later, after the `reverse` section.
 -- `head_flatten` and `getLast_flatten` are proved in `Init.Data.List.Find`.
 
-@[simp] theorem map_flatten (f : α → β) (L : List (List α)) : map f (flatten L) = flatten (map (map f) L) := by
+@[simp] theorem map_flatten (f : α → β) (L : List (List α)) :
+    (flatten L).map f = (map (map f) L).flatten := by
   induction L <;> simp_all
 
 @[simp] theorem filterMap_flatten (f : α → Option β) (L : List (List α)) :
@@ -1966,6 +1928,26 @@ theorem flatten_eq_cons_iff {xs : List (List α)} {y : α} {ys : List α} :
   · rintro ⟨as, bs, cs, rfl, h₁, rfl⟩
     simp [flatten_eq_nil_iff.mpr h₁]
 
+theorem cons_eq_flatten_iff {xs : List (List α)} {y : α} {ys : List α} :
+    y :: ys = xs.flatten ↔
+      ∃ as bs cs, xs = as ++ (y :: bs) :: cs ∧ (∀ l, l ∈ as → l = []) ∧ ys = bs ++ cs.flatten := by
+  rw [eq_comm, flatten_eq_cons_iff]
+
+theorem flatten_eq_singleton_iff {xs : List (List α)} {y : α} :
+    xs.flatten = [y] ↔ ∃ as bs, xs = as ++ [y] :: bs ∧ (∀ l, l ∈ as → l = []) ∧ (∀ l, l ∈ bs → l = []) := by
+  rw [flatten_eq_cons_iff]
+  constructor
+  · rintro ⟨as, bs, cs, rfl, h₁, h₂⟩
+    simp at h₂
+    obtain ⟨rfl, h₂⟩ := h₂
+    exact ⟨as, cs, by simp, h₁, h₂⟩
+  · rintro ⟨as, bs, rfl, h₁, h₂⟩
+    exact ⟨as, [], bs, rfl, h₁, by simpa⟩
+
+theorem singleton_eq_flatten_iff {xs : List (List α)} {y : α} :
+    [y] = xs.flatten ↔ ∃ as bs, xs = as ++ [y] :: bs ∧ (∀ l, l ∈ as → l = []) ∧ (∀ l, l ∈ bs → l = []) := by
+  rw [eq_comm, flatten_eq_singleton_iff]
+
 theorem flatten_eq_append_iff {xs : List (List α)} {ys zs : List α} :
     xs.flatten = ys ++ zs ↔
       (∃ as bs, xs = as ++ bs ∧ ys = as.flatten ∧ zs = bs.flatten) ∨
@@ -1974,8 +1956,8 @@ theorem flatten_eq_append_iff {xs : List (List α)} {ys zs : List α} :
   constructor
   · induction xs generalizing ys with
     | nil =>
-      simp only [flatten_nil, nil_eq, append_eq_nil, and_false, cons_append, false_and, exists_const,
-        exists_false, or_false, and_imp, List.cons_ne_nil]
+      simp only [flatten_nil, nil_eq, append_eq_nil_iff, and_false, cons_append, false_and,
+        exists_const, exists_false, or_false, and_imp, List.cons_ne_nil]
       rintro rfl rfl
       exact ⟨[], [], by simp⟩
     | cons x xs ih =>
@@ -1994,6 +1976,13 @@ theorem flatten_eq_append_iff {xs : List (List α)} {ys zs : List α} :
     · simp
     · simp
 
+theorem append_eq_flatten_iff {xs : List (List α)} {ys zs : List α} :
+    ys ++ zs = xs.flatten ↔
+      (∃ as bs, xs = as ++ bs ∧ ys = as.flatten ∧ zs = bs.flatten) ∨
+        ∃ as bs c cs ds, xs = as ++ (bs ++ c :: cs) :: ds ∧ ys = as.flatten ++ bs ∧
+          zs = c :: cs ++ ds.flatten := by
+  rw [eq_comm, flatten_eq_append_iff]
+
 /-- Two lists of sublists are equal iff their flattens coincide, as well as the lengths of the
 sublists. -/
 theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
@@ -2014,12 +2003,14 @@ theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
 
 theorem flatMap_def (l : List α) (f : α → List β) : l.flatMap f = flatten (map f l) := by rfl
 
-@[simp] theorem flatMap_id (l : List (List α)) : List.flatMap l id = l.flatten := by simp [flatMap_def]
+@[simp] theorem flatMap_id (l : List (List α)) : l.flatMap id = l.flatten := by simp [flatMap_def]
+
+@[simp] theorem flatMap_id' (l : List (List α)) : l.flatMap (fun a => a) = l.flatten := by simp [flatMap_def]
 
 @[simp]
 theorem length_flatMap (l : List α) (f : α → List β) :
-    length (l.flatMap f) = sum (map (length ∘ f) l) := by
-  rw [List.flatMap, length_flatten, map_map]
+    length (l.flatMap f) = sum (map (fun a => (f a).length) l) := by
+  rw [List.flatMap, length_flatten, map_map, Function.comp_def]
 
 @[simp] theorem mem_flatMap {f : α → List β} {b} {l : List α} : b ∈ l.flatMap f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
   simp [flatMap_def, mem_flatten]
@@ -2032,7 +2023,7 @@ theorem mem_flatMap_of_mem {b : β} {l : List α} {f : α → List β} {a} (al :
     b ∈ l.flatMap f := mem_flatMap.2 ⟨a, al, h⟩
 
 @[simp]
-theorem flatMap_eq_nil_iff {l : List α} {f : α → List β} : List.flatMap l f = [] ↔ ∀ x ∈ l, f x = [] :=
+theorem flatMap_eq_nil_iff {l : List α} {f : α → List β} : l.flatMap f = [] ↔ ∀ x ∈ l, f x = [] :=
   flatten_eq_nil_iff.trans <| by
     simp only [mem_map, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
 
@@ -2141,10 +2132,6 @@ theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :
     (replicate n a)[m] = a :=
   eq_of_mem_replicate (getElem_mem _)
 
-@[deprecated getElem_replicate (since := "2024-06-12")]
-theorem get_replicate (a : α) {n : Nat} (m : Fin _) : (replicate n a).get m = a := by
-  simp
-
 theorem getElem?_replicate : (replicate n a)[m]? = if m < n then some a else none := by
   by_cases h : m < n
   · rw [getElem?_eq_getElem (by simpa), getElem_replicate, if_pos h]
@@ -2216,7 +2203,7 @@ theorem map_const' (l : List α) (b : β) : map (fun _ => b) l = replicate l.len
   · intro i h₁ h₂
     simp [getElem_set]
 
-@[simp] theorem append_replicate_replicate : replicate n a ++ replicate m a = replicate (n + m) a := by
+@[simp] theorem replicate_append_replicate : replicate n a ++ replicate m a = replicate (n + m) a := by
   rw [eq_replicate_iff]
   constructor
   · simp
@@ -2224,6 +2211,9 @@ theorem map_const' (l : List α) (b : β) : map (fun _ => b) l = replicate l.len
     simp only [mem_append, mem_replicate, ne_eq]
     rintro (⟨-, rfl⟩ | ⟨_, rfl⟩) <;> rfl
 
+@[deprecated replicate_append_replicate (since := "2025-01-16")]
+abbrev append_replicate_replicate := @replicate_append_replicate
+
 theorem append_eq_replicate_iff {l₁ l₂ : List α} {a : α} :
     l₁ ++ l₂ = replicate n a ↔
       l₁.length + l₂.length = n ∧ l₁ = replicate l₁.length a ∧ l₂ = replicate l₂.length a := by
@@ -2234,6 +2224,11 @@ theorem append_eq_replicate_iff {l₁ l₂ : List α} {a : α} :
 
 @[deprecated append_eq_replicate_iff (since := "2024-09-05")] abbrev append_eq_replicate := @append_eq_replicate_iff
 
+theorem replicate_eq_append_iff {l₁ l₂ : List α} {a : α} :
+    replicate n a = l₁ ++ l₂ ↔
+      l₁.length + l₂.length = n ∧ l₁ = replicate l₁.length a ∧ l₂ = replicate l₂.length a := by
+  rw [eq_comm, append_eq_replicate_iff]
+
 @[simp] theorem map_replicate : (replicate n a).map f = replicate n (f a) := by
   ext1 n
   simp only [getElem?_map, getElem?_replicate]
@@ -2285,7 +2280,7 @@ theorem filterMap_replicate_of_some {f : α → Option β} (h : f a = some b) :
   induction n with
   | zero => simp
   | succ n ih =>
-    simp only [replicate_succ, flatten_cons, ih, append_replicate_replicate, replicate_inj, or_true,
+    simp only [replicate_succ, flatten_cons, ih, replicate_append_replicate, replicate_inj, or_true,
       and_true, add_one_mul, Nat.add_comm]
 
 theorem flatMap_replicate {β} (f : α → List β) : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
@@ -2337,6 +2332,9 @@ theorem replicateRecOn {α : Type _} {p : List α → Prop} (m : List α)
     exact hi _ _ _ _ h hn (replicateRecOn (b :: l') h0 hr hi)
 termination_by m.length
 
+@[simp] theorem sum_replicate_nat (n : Nat) (a : Nat) : (replicate n a).sum = n * a := by
+  induction n <;> simp_all [replicate_succ, Nat.add_mul, Nat.add_comm]
+
 /-! ### reverse -/
 
 @[simp] theorem length_reverse (as : List α) : (as.reverse).length = as.length := by
@@ -2369,10 +2367,6 @@ theorem getElem?_reverse' : ∀ {l : List α} (i j), i + j + 1 = length l →
     rw [getElem?_append_left, getElem?_reverse' _ _ this]
     rw [length_reverse, ← this]; apply Nat.lt_add_of_pos_right (Nat.succ_pos _)
 
-@[deprecated getElem?_reverse' (since := "2024-06-12")]
-theorem get?_reverse' {l : List α} (i j) (h : i + j + 1 = length l) : get? l.reverse i = get? l j := by
-  simp [getElem?_reverse' _ _ h]
-
 @[simp]
 theorem getElem?_reverse {l : List α} {i} (h : i < length l) :
     l.reverse[i]? = l[l.length - 1 - i]? :=
@@ -2387,11 +2381,6 @@ theorem getElem_reverse {l : List α} {i} (h : i < l.reverse.length) :
   rw [← getElem?_eq_getElem, ← getElem?_eq_getElem]
   rw [getElem?_reverse (by simpa using h)]
 
-@[deprecated getElem?_reverse (since := "2024-06-12")]
-theorem get?_reverse {l : List α} {i} (h : i < length l) :
-    get? l.reverse i = get? l (l.length - 1 - i) := by
-  simp [getElem?_reverse h]
-
 theorem reverseAux_reverseAux_nil (as bs : List α) : reverseAux (reverseAux as bs) [] = reverseAux bs as := by
   induction as generalizing bs with
   | nil => rfl
@@ -2432,10 +2421,6 @@ theorem mem_of_mem_getLast? {l : List α} {a : α} (h : a ∈ getLast? l) : a
 @[simp] theorem map_reverse (f : α → β) (l : List α) : l.reverse.map f = (l.map f).reverse := by
   induction l <;> simp [*]
 
-@[deprecated map_reverse (since := "2024-06-20")]
-theorem reverse_map (f : α → β) (l : List α) : (l.map f).reverse = l.reverse.map f := by
-  simp
-
 @[simp] theorem filter_reverse (p : α → Bool) (l : List α) : (l.reverse.filter p) = (l.filter p).reverse := by
   induction l with
   | nil => simp
@@ -2899,11 +2884,6 @@ are often used for theorems about `Array.pop`.
   | _::_::_, 0, _ => rfl
   | _::_::_, i+1, h => getElem_dropLast _ i (Nat.add_one_lt_add_one_iff.mp h)
 
-@[deprecated getElem_dropLast (since := "2024-06-12")]
-theorem get_dropLast (xs : List α) (i : Fin xs.dropLast.length) :
-    xs.dropLast.get i = xs.get ⟨i, Nat.lt_of_lt_of_le i.isLt (length_dropLast .. ▸ Nat.pred_le _)⟩ := by
-  simp
-
 theorem getElem?_dropLast (xs : List α) (i : Nat) :
     xs.dropLast[i]? = if i < xs.length - 1 then xs[i]? else none := by
   split
@@ -3441,29 +3421,6 @@ theorem mem_iff_get? {a} {l : List α} : a ∈ l ↔ ∃ n, l.get? n = some a :=
 
 /-! ### Deprecations -/
 
-@[deprecated getD_eq_getElem?_getD (since := "2024-06-12")]
-theorem getD_eq_get? : ∀ l n (a : α), getD l n a = (get? l n).getD a := by simp
-@[deprecated getElem_singleton (since := "2024-06-12")]
-theorem get_singleton (a : α) (n : Fin 1) : get [a] n = a := by simp
-@[deprecated getElem?_concat_length (since := "2024-06-12")]
-theorem get?_concat_length (l : List α) (a : α) : (l ++ [a]).get? l.length = some a := by simp
-@[deprecated getElem_set_self (since := "2024-06-12")]
-theorem get_set_eq {l : List α} {i : Nat} {a : α} (h : i < (l.set i a).length) :
-    (l.set i a).get ⟨i, h⟩ = a := by
-  simp
-@[deprecated getElem_set_ne (since := "2024-06-12")]
-theorem get_set_ne {l : List α} {i j : Nat} (h : i ≠ j) {a : α}
-    (hj : j < (l.set i a).length) :
-    (l.set i a).get ⟨j, hj⟩ = l.get ⟨j, by simp at hj; exact hj⟩ := by
-  simp [h]
-@[deprecated getElem_set (since := "2024-06-12")]
-theorem get_set {l : List α} {m n} {a : α} (h) :
-    (set l m a).get ⟨n, h⟩ = if m = n then a else l.get ⟨n, length_set .. ▸ h⟩ := by
-  simp [getElem_set]
-@[deprecated cons_inj_right (since := "2024-06-15")] abbrev cons_inj := @cons_inj_right
-@[deprecated ne_nil_of_length_eq_add_one (since := "2024-06-16")]
-abbrev ne_nil_of_length_eq_succ := @ne_nil_of_length_eq_add_one
-
 @[deprecated "Deprecated without replacement." (since := "2024-07-09")]
 theorem get_cons_cons_one : (a₁ :: a₂ :: as).get (1 : Fin (as.length + 2)) = a₂ := rfl
 

src/Init/Data/List/MapIdx.lean

@@ -22,13 +22,13 @@ namespace List
 Given a list `as = [a₀, a₁, ...]` function `f : Fin as.length → α → β`, returns the list
 `[f 0 a₀, f 1 a₁, ...]`.
 -/
-@[inline] def mapFinIdx (as : List α) (f : Fin as.length → α → β) : List β := go as #[] (by simp) where
+@[inline] def mapFinIdx (as : List α) (f : (i : Nat) → α → (h : i < as.length) → β) : List β := go as #[] (by simp) where
   /-- Auxiliary for `mapFinIdx`:
   `mapFinIdx.go [a₀, a₁, ...] acc = acc.toList ++ [f 0 a₀, f 1 a₁, ...]` -/
   @[specialize] go : (bs : List α) → (acc : Array β) → bs.length + acc.size = as.length → List β
   | [], acc, h => acc.toList
   | a :: as, acc, h =>
-    go as (acc.push (f ⟨acc.size, by simp at h; omega⟩ a)) (by simp at h ⊢; omega)
+    go as (acc.push (f acc.size a (by simp at h; omega))) (by simp at h ⊢; omega)
 
 /--
 Given a function `f : Nat → α → β` and `as : List α`, `as = [a₀, a₁, ...]`, returns the list
@@ -44,7 +44,7 @@ Given a function `f : Nat → α → β` and `as : List α`, `as = [a₀, a₁,
 /-! ### mapFinIdx -/
 
 @[simp]
-theorem mapFinIdx_nil {f : Fin 0 → α → β} : mapFinIdx [] f = [] :=
+theorem mapFinIdx_nil {f : (i : Nat) → α → (h : i < 0) → β} : mapFinIdx [] f = [] :=
   rfl
 
 @[simp] theorem length_mapFinIdx_go :
@@ -53,13 +53,16 @@ theorem mapFinIdx_nil {f : Fin 0 → α → β} : mapFinIdx [] f = [] :=
   | nil => simpa using h
   | cons _ _ ih => simp [mapFinIdx.go, ih]
 
-@[simp] theorem length_mapFinIdx {as : List α} {f : Fin as.length → α → β} :
+@[simp] theorem length_mapFinIdx {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} :
     (as.mapFinIdx f).length = as.length := by
   simp [mapFinIdx, length_mapFinIdx_go]
 
-theorem getElem_mapFinIdx_go {as : List α} {f : Fin as.length → α → β} {i : Nat} {h} {w} :
+theorem getElem_mapFinIdx_go {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} {i : Nat} {h} {w} :
     (mapFinIdx.go as f bs acc h)[i] =
-      if w' : i < acc.size then acc[i] else f ⟨i, by simp at w; omega⟩ (bs[i - acc.size]'(by simp at w; omega)) := by
+      if w' : i < acc.size then
+        acc[i]
+      else
+        f i (bs[i - acc.size]'(by simp at w; omega)) (by simp at w; omega) := by
   induction bs generalizing acc with
   | nil =>
     simp only [length_mapFinIdx_go, length_nil, Nat.zero_add] at w h
@@ -78,29 +81,30 @@ theorem getElem_mapFinIdx_go {as : List α} {f : Fin as.length → α → β} {i
     · have h₃ : i - acc.size = (i - (acc.size + 1)) + 1 := by omega
       simp [h₃]
 
-@[simp] theorem getElem_mapFinIdx {as : List α} {f : Fin as.length → α → β} {i : Nat} {h} :
-    (as.mapFinIdx f)[i] = f ⟨i, by simp at h; omega⟩ (as[i]'(by simp at h; omega)) := by
+@[simp] theorem getElem_mapFinIdx {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} {i : Nat} {h} :
+    (as.mapFinIdx f)[i] = f i (as[i]'(by simp at h; omega)) (by simp at h; omega) := by
   simp [mapFinIdx, getElem_mapFinIdx_go]
 
-theorem mapFinIdx_eq_ofFn {as : List α} {f : Fin as.length → α → β} :
-    as.mapFinIdx f = List.ofFn fun i : Fin as.length => f i as[i] := by
+theorem mapFinIdx_eq_ofFn {as : List α} {f : (i : Nat) → α → (h : i < as.length) → β} :
+    as.mapFinIdx f = List.ofFn fun i : Fin as.length => f i as[i] i.2 := by
   apply ext_getElem <;> simp
 
-@[simp] theorem getElem?_mapFinIdx {l : List α} {f : Fin l.length → α → β} {i : Nat} :
-    (l.mapFinIdx f)[i]? = l[i]?.pbind fun x m => f ⟨i, by simp [getElem?_eq_some_iff] at m; exact m.1⟩ x := by
+@[simp] theorem getElem?_mapFinIdx {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} {i : Nat} :
+    (l.mapFinIdx f)[i]? = l[i]?.pbind fun x m => f i x (by simp [getElem?_eq_some_iff] at m; exact m.1) := by
   simp only [getElem?_def, length_mapFinIdx, getElem_mapFinIdx]
   split <;> simp
 
 @[simp]
-theorem mapFinIdx_cons {l : List α} {a : α} {f : Fin (l.length + 1) → α → β} :
-    mapFinIdx (a :: l) f = f 0 a :: mapFinIdx l (fun i => f i.succ) := by
+theorem mapFinIdx_cons {l : List α} {a : α} {f : (i : Nat) → α → (h : i < l.length + 1) → β} :
+    mapFinIdx (a :: l) f = f 0 a (by omega) :: mapFinIdx l (fun i a h => f (i + 1) a (by omega)) := by
   apply ext_getElem
   · simp
   · rintro (_|i) h₁ h₂ <;> simp
 
-theorem mapFinIdx_append {K L : List α} {f : Fin (K ++ L).length → α → β} :
+theorem mapFinIdx_append {K L : List α} {f : (i : Nat) → α → (h : i < (K ++ L).length) → β} :
     (K ++ L).mapFinIdx f =
-      K.mapFinIdx (fun i => f (i.castLE (by simp))) ++ L.mapFinIdx (fun i => f ((i.natAdd K.length).cast (by simp))) := by
+      K.mapFinIdx (fun i a h => f i a (by simp; omega)) ++
+        L.mapFinIdx (fun i a h => f (i + K.length) a (by simp; omega)) := by
   apply ext_getElem
   · simp
   · intro i h₁ h₂
@@ -108,60 +112,57 @@ theorem mapFinIdx_append {K L : List α} {f : Fin (K ++ L).length → α → β}
     simp only [getElem_mapFinIdx, length_mapFinIdx]
     split <;> rename_i h
     · rw [getElem_append_left]
-      congr
     · simp only [Nat.not_lt] at h
       rw [getElem_append_right h]
       congr
-      simp
       omega
 
-@[simp] theorem mapFinIdx_concat {l : List α} {e : α} {f : Fin (l ++ [e]).length → α → β}:
-    (l ++ [e]).mapFinIdx f = l.mapFinIdx (fun i => f (i.castLE (by simp))) ++ [f ⟨l.length, by simp⟩ e] := by
+@[simp] theorem mapFinIdx_concat {l : List α} {e : α} {f : (i : Nat) → α → (h : i < (l ++ [e]).length) → β}:
+    (l ++ [e]).mapFinIdx f = l.mapFinIdx (fun i a h => f i a (by simp; omega)) ++ [f l.length e (by simp)] := by
   simp [mapFinIdx_append]
-  congr
 
-theorem mapFinIdx_singleton {a : α} {f : Fin 1 → α → β} :
-    [a].mapFinIdx f = [f ⟨0, by simp⟩ a] := by
+theorem mapFinIdx_singleton {a : α} {f : (i : Nat) → α → (h : i < 1) → β} :
+    [a].mapFinIdx f = [f 0 a (by simp)] := by
   simp
 
-theorem mapFinIdx_eq_enum_map {l : List α} {f : Fin l.length → α → β} :
+theorem mapFinIdx_eq_enum_map {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
     l.mapFinIdx f = l.enum.attach.map
       fun ⟨⟨i, x⟩, m⟩ =>
-        f ⟨i, by rw [mk_mem_enum_iff_getElem?, getElem?_eq_some_iff] at m; exact m.1⟩ x := by
+        f i x (by rw [mk_mem_enum_iff_getElem?, getElem?_eq_some_iff] at m; exact m.1) := by
   apply ext_getElem <;> simp
 
 @[simp]
-theorem mapFinIdx_eq_nil_iff {l : List α} {f : Fin l.length → α → β} :
+theorem mapFinIdx_eq_nil_iff {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
     l.mapFinIdx f = [] ↔ l = [] := by
   rw [mapFinIdx_eq_enum_map, map_eq_nil_iff, attach_eq_nil_iff, enum_eq_nil_iff]
 
-theorem mapFinIdx_ne_nil_iff {l : List α} {f : Fin l.length → α → β} :
+theorem mapFinIdx_ne_nil_iff {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
     l.mapFinIdx f ≠ [] ↔ l ≠ [] := by
   simp
 
-theorem exists_of_mem_mapFinIdx {b : β} {l : List α} {f : Fin l.length → α → β}
-    (h : b ∈ l.mapFinIdx f) : ∃ (i : Fin l.length), f i l[i] = b := by
+theorem exists_of_mem_mapFinIdx {b : β} {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β}
+    (h : b ∈ l.mapFinIdx f) : ∃ (i : Nat) (h : i < l.length), f i l[i] h = b := by
   rw [mapFinIdx_eq_enum_map] at h
   replace h := exists_of_mem_map h
   simp only [mem_attach, true_and, Subtype.exists, Prod.exists, mk_mem_enum_iff_getElem?] at h
   obtain ⟨i, b, h, rfl⟩ := h
   rw [getElem?_eq_some_iff] at h
   obtain ⟨h', rfl⟩ := h
-  exact ⟨⟨i, h'⟩, rfl⟩
+  exact ⟨i, h', rfl⟩
 
-@[simp] theorem mem_mapFinIdx {b : β} {l : List α} {f : Fin l.length → α → β} :
-    b ∈ l.mapFinIdx f ↔ ∃ (i : Fin l.length), f i l[i] = b := by
+@[simp] theorem mem_mapFinIdx {b : β} {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
+    b ∈ l.mapFinIdx f ↔ ∃ (i : Nat) (h : i < l.length), f i l[i] h = b := by
   constructor
   · intro h
     exact exists_of_mem_mapFinIdx h
   · rintro ⟨i, h, rfl⟩
     rw [mem_iff_getElem]
-    exact ⟨i, by simp⟩
+    exact ⟨i, by simpa using h, by simp⟩
 
-theorem mapFinIdx_eq_cons_iff {l : List α} {b : β} {f : Fin l.length → α → β} :
+theorem mapFinIdx_eq_cons_iff {l : List α} {b : β} {f : (i : Nat) → α → (h : i < l.length) → β} :
     l.mapFinIdx f = b :: l₂ ↔
-      ∃ (a : α) (l₁ : List α) (h : l = a :: l₁),
-        f ⟨0, by simp [h]⟩ a = b ∧ l₁.mapFinIdx (fun i => f (i.succ.cast (by simp [h]))) = l₂ := by
+      ∃ (a : α) (l₁ : List α) (w : l = a :: l₁),
+        f 0 a (by simp [w]) = b ∧ l₁.mapFinIdx (fun i a h => f (i + 1) a (by simp [w]; omega)) = l₂ := by
   cases l with
   | nil => simp
   | cons x l' =>
@@ -169,39 +170,48 @@ theorem mapFinIdx_eq_cons_iff {l : List α} {b : β} {f : Fin l.length → α
       exists_and_left]
     constructor
     · rintro ⟨rfl, rfl⟩
-      refine ⟨x, rfl, l', by simp⟩
-    · rintro ⟨a, ⟨rfl, h⟩, ⟨_, ⟨rfl, rfl⟩, h⟩⟩
-      exact ⟨rfl, h⟩
+      refine ⟨x, l', ⟨rfl, rfl⟩, by simp⟩
+    · rintro ⟨a, l', ⟨rfl, rfl⟩, ⟨rfl, rfl⟩⟩
+      exact ⟨rfl, by simp⟩
 
-theorem mapFinIdx_eq_cons_iff' {l : List α} {b : β} {f : Fin l.length → α → β} :
+theorem mapFinIdx_eq_cons_iff' {l : List α} {b : β} {f : (i : Nat) → α → (h : i < l.length) → β} :
     l.mapFinIdx f = b :: l₂ ↔
-      l.head?.pbind (fun x m => (f ⟨0, by cases l <;> simp_all⟩ x)) = some b ∧
-        l.tail?.attach.map (fun ⟨t, m⟩ => t.mapFinIdx fun i => f (i.succ.cast (by cases l <;> simp_all))) = some l₂ := by
+      l.head?.pbind (fun x m => (f 0 x (by cases l <;> simp_all))) = some b ∧
+        l.tail?.attach.map (fun ⟨t, m⟩ => t.mapFinIdx fun i a h => f (i + 1) a (by cases l <;> simp_all)) = some l₂ := by
   cases l <;> simp
 
-theorem mapFinIdx_eq_iff {l : List α} {f : Fin l.length → α → β} :
-    l.mapFinIdx f = l' ↔ ∃ h : l'.length = l.length, ∀ (i : Nat) (h : i < l.length), l'[i] = f ⟨i, h⟩ l[i] := by
+theorem mapFinIdx_eq_iff {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} :
+    l.mapFinIdx f = l' ↔ ∃ h : l'.length = l.length, ∀ (i : Nat) (h : i < l.length), l'[i] = f i l[i] h := by
   constructor
   · rintro rfl
     simp
   · rintro ⟨h, w⟩
     apply ext_getElem <;> simp_all
 
-theorem mapFinIdx_eq_mapFinIdx_iff {l : List α} {f g : Fin l.length → α → β} :
-    l.mapFinIdx f = l.mapFinIdx g ↔ ∀ (i : Fin l.length), f i l[i] = g i l[i] := by
+theorem mapFinIdx_eq_mapFinIdx_iff {l : List α} {f g : (i : Nat) → α → (h : i < l.length) → β} :
+    l.mapFinIdx f = l.mapFinIdx g ↔ ∀ (i : Nat) (h : i < l.length), f i l[i] h = g i l[i] h := by
   rw [eq_comm, mapFinIdx_eq_iff]
   simp [Fin.forall_iff]
 
-@[simp] theorem mapFinIdx_mapFinIdx {l : List α} {f : Fin l.length → α → β} {g : Fin _ → β → γ} :
-    (l.mapFinIdx f).mapFinIdx g = l.mapFinIdx (fun i => g (i.cast (by simp)) ∘ f i) := by
+@[simp] theorem mapFinIdx_mapFinIdx {l : List α}
+    {f : (i : Nat) → α → (h : i < l.length) → β}
+    {g : (i : Nat) → β → (h : i < (l.mapFinIdx f).length) → γ} :
+    (l.mapFinIdx f).mapFinIdx g = l.mapFinIdx (fun i a h => g i (f i a h) (by simpa)) := by
   simp [mapFinIdx_eq_iff]
 
-theorem mapFinIdx_eq_replicate_iff {l : List α} {f : Fin l.length → α → β} {b : β} :
-    l.mapFinIdx f = replicate l.length b ↔ ∀ (i : Fin l.length), f i l[i] = b := by
-  simp [eq_replicate_iff, length_mapFinIdx, mem_mapFinIdx, forall_exists_index, true_and]
+theorem mapFinIdx_eq_replicate_iff {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} {b : β} :
+    l.mapFinIdx f = replicate l.length b ↔ ∀ (i : Nat) (h : i < l.length), f i l[i] h = b := by
+  rw [eq_replicate_iff, length_mapFinIdx]
+  simp only [mem_mapFinIdx, forall_exists_index, true_and]
+  constructor
+  · intro w i h
+    exact w (f i l[i] h) i h rfl
+  · rintro w b i h rfl
+    exact w i h
 
-@[simp] theorem mapFinIdx_reverse {l : List α} {f : Fin l.reverse.length → α → β} :
-    l.reverse.mapFinIdx f = (l.mapFinIdx (fun i => f ⟨l.length - 1 - i, by simp; omega⟩)).reverse := by
+@[simp] theorem mapFinIdx_reverse {l : List α} {f : (i : Nat) → α → (h : i < l.reverse.length) → β} :
+    l.reverse.mapFinIdx f =
+      (l.mapFinIdx (fun i a h => f (l.length - 1 - i) a (by simp; omega))).reverse := by
   simp [mapFinIdx_eq_iff]
   intro i h
   congr
@@ -262,13 +272,13 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {arr : Array β} {i : Nat},
   rw [← getElem?_eq_getElem, getElem?_mapIdx, getElem?_eq_getElem (by simpa using h)]
   simp
 
-@[simp] theorem mapFinIdx_eq_mapIdx {l : List α} {f : Fin l.length → α → β} {g : Nat → α → β}
-    (h : ∀ (i : Fin l.length), f i l[i] = g i l[i]) :
+@[simp] theorem mapFinIdx_eq_mapIdx {l : List α} {f : (i : Nat) → α → (h : i < l.length) → β} {g : Nat → α → β}
+    (h : ∀ (i : Nat) (h : i < l.length), f i l[i] h = g i l[i]) :
     l.mapFinIdx f = l.mapIdx g := by
   simp_all [mapFinIdx_eq_iff]
 
 theorem mapIdx_eq_mapFinIdx {l : List α} {f : Nat → α → β} :
-    l.mapIdx f = l.mapFinIdx (fun i => f i) := by
+    l.mapIdx f = l.mapFinIdx (fun i a _ => f i a) := by
   simp [mapFinIdx_eq_mapIdx]
 
 theorem mapIdx_eq_enum_map {l : List α} :

src/Init/Data/List/Nat/TakeDrop.lean

@@ -47,41 +47,16 @@ length `> i`. Version designed to rewrite from the small list to the big list. -
     L[i]'(Nat.lt_of_lt_of_le h (length_take_le' _ _)) := by
   rw [length_take, Nat.lt_min] at h; rw [getElem_take' L _ h.1]
 
-/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
-length `> i`. Version designed to rewrite from the big list to the small list. -/
-@[deprecated getElem_take' (since := "2024-06-12")]
-theorem get_take (L : List α) {i j : Nat} (hi : i < L.length) (hj : i < j) :
-    get L ⟨i, hi⟩ = get (L.take j) ⟨i, length_take .. ▸ Nat.lt_min.mpr ⟨hj, hi⟩⟩ := by
-  simp
-
-/-- The `i`-th element of a list coincides with the `i`-th element of any of its prefixes of
-length `> i`. Version designed to rewrite from the small list to the big list. -/
-@[deprecated getElem_take (since := "2024-06-12")]
-theorem get_take' (L : List α) {j i} :
-    get (L.take j) i =
-    get L ⟨i.1, Nat.lt_of_lt_of_le i.2 (length_take_le' _ _)⟩ := by
-  simp [getElem_take]
-
 theorem getElem?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
     (l.take n)[m]? = none :=
   getElem?_eq_none <| Nat.le_trans (length_take_le _ _) h
 
-@[deprecated getElem?_take_eq_none (since := "2024-06-12")]
-theorem get?_take_eq_none {l : List α} {n m : Nat} (h : n ≤ m) :
-    (l.take n).get? m = none := by
-  simp [getElem?_take_eq_none h]
-
 theorem getElem?_take {l : List α} {n m : Nat} :
     (l.take n)[m]? = if m < n then l[m]? else none := by
   split
   · next h => exact getElem?_take_of_lt h
   · next h => exact getElem?_take_eq_none (Nat.le_of_not_lt h)
 
-@[deprecated getElem?_take (since := "2024-06-12")]
-theorem get?_take_eq_if {l : List α} {n m : Nat} :
-    (l.take n).get? m = if m < n then l.get? m else none := by
-  simp [getElem?_take]
-
 theorem head?_take {l : List α} {n : Nat} :
     (l.take n).head? = if n = 0 then none else l.head? := by
   simp [head?_eq_getElem?, getElem?_take]
@@ -226,13 +201,6 @@ theorem getElem_drop' (L : List α) {i j : Nat} (h : i + j < L.length) :
   · simp [Nat.min_eq_left this, Nat.add_sub_cancel_left]
   · simp [Nat.min_eq_left this, Nat.le_add_right]
 
-/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
-dropping the first `i` elements. Version designed to rewrite from the big list to the small list. -/
-@[deprecated getElem_drop' (since := "2024-06-12")]
-theorem get_drop (L : List α) {i j : Nat} (h : i + j < L.length) :
-    get L ⟨i + j, h⟩ = get (L.drop i) ⟨j, lt_length_drop L h⟩ := by
-  simp [getElem_drop']
-
 /-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
 dropping the first `i` elements. Version designed to rewrite from the small list to the big list. -/
 @[simp] theorem getElem_drop (L : List α) {i : Nat} {j : Nat} {h : j < (L.drop i).length} :
@@ -241,15 +209,6 @@ dropping the first `i` elements. Version designed to rewrite from the small list
       exact Nat.add_lt_of_lt_sub (length_drop i L ▸ h)) := by
   rw [getElem_drop']
 
-/-- The `i + j`-th element of a list coincides with the `j`-th element of the list obtained by
-dropping the first `i` elements. Version designed to rewrite from the small list to the big list. -/
-@[deprecated getElem_drop' (since := "2024-06-12")]
-theorem get_drop' (L : List α) {i j} :
-    get (L.drop i) j = get L ⟨i + j, by
-      rw [Nat.add_comm]
-      exact Nat.add_lt_of_lt_sub (length_drop i L ▸ j.2)⟩ := by
-  simp
-
 @[simp]
 theorem getElem?_drop (L : List α) (i j : Nat) : (L.drop i)[j]? = L[i + j]? := by
   ext
@@ -261,10 +220,6 @@ theorem getElem?_drop (L : List α) (i j : Nat) : (L.drop i)[j]? = L[i + j]? :=
     rw [Nat.add_comm] at h
     apply Nat.lt_sub_of_add_lt h
 
-@[deprecated getElem?_drop (since := "2024-06-12")]
-theorem get?_drop (L : List α) (i j : Nat) : get? (L.drop i) j = get? L (i + j) := by
-  simp
-
 theorem mem_take_iff_getElem {l : List α} {a : α} :
     a ∈ l.take n ↔ ∃ (i : Nat) (hm : i < min n l.length), l[i] = a := by
   rw [mem_iff_getElem]

src/Init/Data/List/TakeDrop.lean

@@ -67,17 +67,9 @@ theorem getElem_cons_drop : ∀ (l : List α) (i : Nat) (h : i < l.length),
   | _::_, 0, _ => rfl
   | _::_, i+1, h => getElem_cons_drop _ i (Nat.add_one_lt_add_one_iff.mp h)
 
-@[deprecated getElem_cons_drop (since := "2024-06-12")]
-theorem get_cons_drop (l : List α) (i) : get l i :: drop (i + 1) l = drop i l := by
-  simp
-
 theorem drop_eq_getElem_cons {n} {l : List α} (h : n < l.length) : drop n l = l[n] :: drop (n + 1) l :=
   (getElem_cons_drop _ n h).symm
 
-@[deprecated drop_eq_getElem_cons (since := "2024-06-12")]
-theorem drop_eq_get_cons {n} {l : List α} (h) : drop n l = get l ⟨n, h⟩ :: drop (n + 1) l := by
-  simp [drop_eq_getElem_cons]
-
 @[simp]
 theorem getElem?_take_of_lt {l : List α} {n m : Nat} (h : m < n) : (l.take n)[m]? = l[m]? := by
   induction n generalizing l m with
@@ -91,10 +83,6 @@ theorem getElem?_take_of_lt {l : List α} {n m : Nat} (h : m < n) : (l.take n)[m
       · simp
       · simpa using hn (Nat.lt_of_succ_lt_succ h)
 
-@[deprecated getElem?_take_of_lt (since := "2024-06-12")]
-theorem get?_take {l : List α} {n m : Nat} (h : m < n) : (l.take n).get? m = l.get? m := by
-  simp [getElem?_take_of_lt, h]
-
 theorem getElem?_take_of_succ {l : List α} {n : Nat} : (l.take (n + 1))[n]? = l[n]? := by simp
 
 @[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (m + n) l
@@ -111,10 +99,6 @@ theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (t
   | _, _, [] => by simp
   | _+1, _, _ :: _ => by simpa [Nat.succ_add, take_succ_cons, drop_succ_cons] using take_drop ..
 
-@[deprecated drop_drop (since := "2024-06-15")]
-theorem drop_add (m n) (l : List α) : drop (m + n) l = drop n (drop m l) := by
-  simp [drop_drop]
-
 @[simp]
 theorem tail_drop (l : List α) (n : Nat) : (l.drop n).tail = l.drop (n + 1) := by
   induction l generalizing n with

src/Init/Data/List/ToArray.lean

@@ -46,7 +46,7 @@ theorem toArray_cons (a : α) (l : List α) : (a :: l).toArray = #[a] ++ l.toArr
 @[simp] theorem isEmpty_toArray (l : List α) : l.toArray.isEmpty = l.isEmpty := by
   cases l <;> simp [Array.isEmpty]
 
-@[simp] theorem toArray_singleton (a : α) : (List.singleton a).toArray = singleton a := rfl
+@[simp] theorem toArray_singleton (a : α) : (List.singleton a).toArray = Array.singleton a := rfl
 
 @[simp] theorem back!_toArray [Inhabited α] (l : List α) : l.toArray.back! = l.getLast! := by
   simp only [back!, size_toArray, Array.get!_eq_getElem!, getElem!_toArray, getLast!_eq_getElem!]
@@ -143,6 +143,9 @@ theorem forM_toArray [Monad m] (l : List α) (f : α → m PUnit) :
   subst h
   rw [foldl_toList]
 
+@[simp] theorem sum_toArray [Add α] [Zero α] (l : List α) : l.toArray.sum = l.sum := by
+  simp [Array.sum, List.sum]
+
 @[simp] theorem append_toArray (l₁ l₂ : List α) :
     l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
   apply ext'
@@ -394,4 +397,24 @@ theorem takeWhile_go_toArray (p : α → Bool) (l : List α) (i : Nat) :
 @[deprecated toArray_replicate (since := "2024-12-13")]
 abbrev _root_.Array.mkArray_eq_toArray_replicate := @toArray_replicate
 
+@[simp] theorem flatMap_empty {β} (f : α → Array β) : (#[] : Array α).flatMap f = #[] := rfl
+
+theorem flatMap_toArray_cons {β} (f : α → Array β) (a : α) (as : List α) :
+    (a :: as).toArray.flatMap f = f a ++ as.toArray.flatMap f := by
+  simp [Array.flatMap]
+  suffices ∀ cs, List.foldl (fun bs a => bs ++ f a) (f a ++ cs) as =
+      f a ++ List.foldl (fun bs a => bs ++ f a) cs as by
+    erw [empty_append] -- Why doesn't this work via `simp`?
+    simpa using this #[]
+  intro cs
+  induction as generalizing cs <;> simp_all
+
+@[simp] theorem flatMap_toArray {β} (f : α → Array β) (as : List α) :
+    as.toArray.flatMap f = (as.flatMap (fun a => (f a).toList)).toArray := by
+  induction as with
+  | nil => simp
+  | cons a as ih =>
+    apply ext'
+    simp [ih, flatMap_toArray_cons]
+
 end List

src/Init/Data/List/Zip.lean

@@ -76,15 +76,6 @@ theorem getElem?_zip_eq_some {l₁ : List α} {l₂ : List β} {z : α × β} {i
   · rintro ⟨h₀, h₁⟩
     exact ⟨_, _, h₀, h₁, rfl⟩
 
-@[deprecated getElem?_zipWith (since := "2024-06-12")]
-theorem get?_zipWith {f : α → β → γ} :
-    (List.zipWith f as bs).get? i = match as.get? i, bs.get? i with
-      | some a, some b => some (f a b) | _, _ => none := by
-  simp [getElem?_zipWith]
-
-set_option linter.deprecated false in
-@[deprecated getElem?_zipWith (since := "2024-06-07")] abbrev zipWith_get? := @get?_zipWith
-
 theorem head?_zipWith {f : α → β → γ} :
     (List.zipWith f as bs).head? = match as.head?, bs.head? with
       | some a, some b => some (f a b) | _, _ => none := by
@@ -203,11 +194,11 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {l₁ : List α} {l₂ : Li
     cases l₂ with
     | nil =>
       constructor
-      · simp only [zipWith_nil_right, nil_eq, append_eq_nil, exists_and_left, and_imp]
+      · simp only [zipWith_nil_right, nil_eq, append_eq_nil_iff, exists_and_left, and_imp]
         rintro rfl  rfl
         exact ⟨[], x₁ :: l₁, [], by simp⟩
       · rintro ⟨w, x, y, z, h₁, _, h₃, rfl, rfl⟩
-        simp only [nil_eq, append_eq_nil] at h₃
+        simp only [nil_eq, append_eq_nil_iff] at h₃
         obtain ⟨rfl, rfl⟩ := h₃
         simp
     | cons x₂ l₂ =>
@@ -369,15 +360,6 @@ theorem getElem?_zipWithAll {f : Option α → Option β → γ} {i : Nat} :
       cases i <;> simp_all
     | cons b bs => cases i <;> simp_all
 
-@[deprecated getElem?_zipWithAll (since := "2024-06-12")]
-theorem get?_zipWithAll {f : Option α → Option β → γ} :
-    (zipWithAll f as bs).get? i = match as.get? i, bs.get? i with
-      | none, none => .none | a?, b? => some (f a? b?) := by
-  simp [getElem?_zipWithAll]
-
-set_option linter.deprecated false in
-@[deprecated getElem?_zipWithAll (since := "2024-06-07")] abbrev zipWithAll_get? := @get?_zipWithAll
-
 theorem head?_zipWithAll {f : Option α → Option β → γ} :
     (zipWithAll f as bs).head? = match as.head?, bs.head? with
       | none, none => .none | a?, b? => some (f a? b?) := by

src/Init/Data/Nat/Basic.lean

@@ -788,9 +788,6 @@ theorem not_eq_zero_of_lt (h : b < a) : a ≠ 0 := by
 theorem pred_lt_of_lt {n m : Nat} (h : m < n) : pred n < n :=
   pred_lt (not_eq_zero_of_lt h)
 
-set_option linter.missingDocs false in
-@[deprecated pred_lt_of_lt (since := "2024-06-01")] abbrev pred_lt' := @pred_lt_of_lt
-
 theorem sub_one_lt_of_lt {n m : Nat} (h : m < n) : n - 1 < n :=
   sub_one_lt (not_eq_zero_of_lt h)
 
@@ -1074,9 +1071,6 @@ theorem pred_mul (n m : Nat) : pred n * m = n * m - m := by
   | zero   => simp
   | succ n => rw [Nat.pred_succ, succ_mul, Nat.add_sub_cancel]
 
-set_option linter.missingDocs false in
-@[deprecated pred_mul (since := "2024-06-01")] abbrev mul_pred_left := @pred_mul
-
 protected theorem sub_one_mul  (n m : Nat) : (n - 1) * m = n * m - m := by
   cases n with
   | zero   => simp
@@ -1086,9 +1080,6 @@ protected theorem sub_one_mul  (n m : Nat) : (n - 1) * m = n * m - m := by
 theorem mul_pred (n m : Nat) : n * pred m = n * m - n := by
   rw [Nat.mul_comm, pred_mul, Nat.mul_comm]
 
-set_option linter.missingDocs false in
-@[deprecated mul_pred (since := "2024-06-01")] abbrev mul_pred_right := @mul_pred
-
 theorem mul_sub_one (n m : Nat) : n * (m - 1) = n * m - n := by
   rw [Nat.mul_comm, Nat.sub_one_mul , Nat.mul_comm]
 

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

@@ -711,6 +711,32 @@ theorem mul_add_lt_is_or {b : Nat} (b_lt : b < 2^i) (a : Nat) : 2^i * a + b = 2^
   rw [mod_two_eq_one_iff_testBit_zero, testBit_shiftLeft]
   simp
 
+theorem testBit_mul_two_pow (x i n : Nat) :
+    (x * 2 ^ n).testBit i = (decide (n ≤ i) && x.testBit (i - n)) := by
+  rw [← testBit_shiftLeft, shiftLeft_eq]
+
+theorem bitwise_mul_two_pow (of_false_false : f false false = false := by rfl) :
+    (bitwise f x y) * 2 ^ n = bitwise f (x * 2 ^ n) (y * 2 ^ n) := by
+  apply Nat.eq_of_testBit_eq
+  simp only [testBit_mul_two_pow, testBit_bitwise of_false_false, Bool.if_false_right]
+  intro i
+  by_cases hn : n ≤ i
+  · simp [hn]
+  · simp [hn, of_false_false]
+
+theorem shiftLeft_bitwise_distrib {a b : Nat} (of_false_false : f false false = false := by rfl) :
+    (bitwise f a b) <<< i = bitwise f (a <<< i) (b <<< i) := by
+  simp [shiftLeft_eq, bitwise_mul_two_pow of_false_false]
+
+theorem shiftLeft_and_distrib {a b : Nat} : (a &&& b) <<< i = a <<< i &&& b <<< i :=
+  shiftLeft_bitwise_distrib
+
+theorem shiftLeft_or_distrib {a b : Nat} : (a ||| b) <<< i = a <<< i ||| b <<< i :=
+  shiftLeft_bitwise_distrib
+
+theorem shiftLeft_xor_distrib {a b : Nat} : (a ^^^ b) <<< i = a <<< i ^^^ b <<< i :=
+  shiftLeft_bitwise_distrib
+
 @[simp] theorem decide_shiftRight_mod_two_eq_one :
     decide (x >>> i % 2 = 1) = x.testBit i := by
   simp only [testBit, one_and_eq_mod_two, mod_two_bne_zero]

src/Init/Data/Nat/Lemmas.lean

@@ -622,6 +622,14 @@ protected theorem pos_of_mul_pos_right {a b : Nat} (h : 0 < a * b) : 0 < a := by
     0 < a * b ↔ 0 < a :=
   ⟨Nat.pos_of_mul_pos_right, fun w => Nat.mul_pos w h⟩
 
+protected theorem pos_of_lt_mul_left {a b c : Nat} (h : a < b * c) : 0 < c := by
+  replace h : 0 < b * c := by omega
+  exact Nat.pos_of_mul_pos_left h
+
+protected theorem pos_of_lt_mul_right {a b c : Nat} (h : a < b * c) : 0 < b := by
+  replace h : 0 < b * c := by omega
+  exact Nat.pos_of_mul_pos_right h
+
 /-! ### div/mod -/
 
 theorem mod_two_eq_zero_or_one (n : Nat) : n % 2 = 0 ∨ n % 2 = 1 :=
@@ -995,11 +1003,6 @@ theorem shiftLeft_add (m n : Nat) : ∀ k, m <<< (n + k) = (m <<< n) <<< k
   | 0 => rfl
   | k + 1 => by simp [← Nat.add_assoc, shiftLeft_add _ _ k, shiftLeft_succ]
 
-@[deprecated shiftLeft_add (since := "2024-06-02")]
-theorem shiftLeft_shiftLeft (m n : Nat) : ∀ k, (m <<< n) <<< k = m <<< (n + k)
-  | 0 => rfl
-  | k + 1 => by simp [← Nat.add_assoc, shiftLeft_shiftLeft _ _ k, shiftLeft_succ]
-
 @[simp] theorem shiftLeft_shiftRight (x n : Nat) : x <<< n >>> n = x := by
   rw [Nat.shiftLeft_eq, Nat.shiftRight_eq_div_pow, Nat.mul_div_cancel _ (Nat.two_pow_pos _)]
 

src/Init/Data/Option/Lemmas.lean

@@ -208,6 +208,15 @@ theorem comp_map (h : β → γ) (g : α → β) (x : Option α) : x.map (h ∘
 
 theorem mem_map_of_mem (g : α → β) (h : a ∈ x) : g a ∈ Option.map g x := h.symm ▸ map_some' ..
 
+theorem map_inj_right {f : α → β} {o o' : Option α} (w : ∀ x y, f x = f y → x = y) :
+    o.map f = o'.map f ↔ o = o' := by
+  cases o with
+  | none => cases o' <;> simp
+  | some a =>
+    cases o' with
+    | none => simp
+    | some a' => simpa using ⟨fun h => w _ _ h, fun h => congrArg f h⟩
+
 @[simp] theorem map_if {f : α → β} [Decidable c] :
      (if c then some a else none).map f = if c then some (f a) else none := by
   split <;> rfl
@@ -629,6 +638,15 @@ theorem pbind_eq_some_iff {o : Option α} {f : (a : α) → a ∈ o → Option
     · rintro ⟨h, rfl⟩
       rfl
 
+@[simp]
+theorem pmap_eq_map (p : α → Prop) (f : α → β) (o : Option α) (H) :
+    @pmap _ _ p (fun a _ => f a) o H = Option.map f o := by
+  cases o <;> simp
+
+theorem map_pmap {p : α → Prop} (g : β → γ) (f : ∀ a, p a → β) (o H) :
+    Option.map g (pmap f o H) = pmap (fun a h => g (f a h)) o H := by
+  cases o <;> simp
+
 /-! ### pelim -/
 
 @[simp] theorem pelim_none : pelim none b f = b := rfl

src/Init/Data/UInt/Bitwise.lean

@@ -13,11 +13,17 @@ macro "declare_bitwise_uint_theorems" typeName:ident bits:term:arg : command =>
 `(
 namespace $typeName
 
-@[simp] protected theorem toBitVec_and (a b : $typeName) : (a &&& b).toBitVec = a.toBitVec &&& b.toBitVec := rfl
-@[simp] protected theorem toBitVec_or (a b : $typeName) : (a ||| b).toBitVec = a.toBitVec ||| b.toBitVec := rfl
-@[simp] protected theorem toBitVec_xor (a b : $typeName) : (a ^^^ b).toBitVec = a.toBitVec ^^^ b.toBitVec := rfl
-@[simp] protected theorem toBitVec_shiftLeft (a b : $typeName) : (a <<< b).toBitVec = a.toBitVec <<< (b.toBitVec % $bits) := rfl
-@[simp] protected theorem toBitVec_shiftRight (a b : $typeName) : (a >>> b).toBitVec = a.toBitVec >>> (b.toBitVec % $bits) := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_add {a b : $typeName} : (a + b).toBitVec = a.toBitVec + b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_sub {a b : $typeName} : (a - b).toBitVec = a.toBitVec - b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_mul {a b : $typeName} : (a * b).toBitVec = a.toBitVec * b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_div {a b : $typeName} : (a / b).toBitVec = a.toBitVec / b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_mod {a b : $typeName} : (a % b).toBitVec = a.toBitVec % b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_not {a : $typeName} : (~~~a).toBitVec = ~~~a.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_and (a b : $typeName) : (a &&& b).toBitVec = a.toBitVec &&& b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_or (a b : $typeName) : (a ||| b).toBitVec = a.toBitVec ||| b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_xor (a b : $typeName) : (a ^^^ b).toBitVec = a.toBitVec ^^^ b.toBitVec := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_shiftLeft (a b : $typeName) : (a <<< b).toBitVec = a.toBitVec <<< (b.toBitVec % $bits) := rfl
+@[simp, int_toBitVec] protected theorem toBitVec_shiftRight (a b : $typeName) : (a >>> b).toBitVec = a.toBitVec >>> (b.toBitVec % $bits) := rfl
 
 @[simp] protected theorem toNat_and (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := by simp [toNat]
 @[simp] protected theorem toNat_or (a b : $typeName) : (a ||| b).toNat = a.toNat ||| b.toNat := by simp [toNat]
@@ -37,3 +43,31 @@ declare_bitwise_uint_theorems UInt16 16
 declare_bitwise_uint_theorems UInt32 32
 declare_bitwise_uint_theorems UInt64 64
 declare_bitwise_uint_theorems USize System.Platform.numBits
+
+@[simp, int_toBitVec]
+theorem Bool.toBitVec_toUInt8 {b : Bool} :
+    b.toUInt8.toBitVec = (BitVec.ofBool b).setWidth 8 := by
+  cases b <;> simp [toUInt8]
+
+@[simp, int_toBitVec]
+theorem Bool.toBitVec_toUInt16 {b : Bool} :
+    b.toUInt16.toBitVec = (BitVec.ofBool b).setWidth 16 := by
+  cases b <;> simp [toUInt16]
+
+@[simp, int_toBitVec]
+theorem Bool.toBitVec_toUInt32 {b : Bool} :
+    b.toUInt32.toBitVec = (BitVec.ofBool b).setWidth 32 := by
+  cases b <;> simp [toUInt32]
+
+@[simp, int_toBitVec]
+theorem Bool.toBitVec_toUInt64 {b : Bool} :
+    b.toUInt64.toBitVec = (BitVec.ofBool b).setWidth 64 := by
+  cases b <;> simp [toUInt64]
+
+@[simp, int_toBitVec]
+theorem Bool.toBitVec_toUSize {b : Bool} :
+    b.toUSize.toBitVec = (BitVec.ofBool b).setWidth System.Platform.numBits := by
+  cases b
+  · simp [toUSize]
+  · apply BitVec.eq_of_toNat_eq
+    simp [toUSize]

src/Init/Data/UInt/Lemmas.lean

@@ -41,9 +41,9 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   theorem toNat_ofNat_of_lt {n : Nat} (h : n < size) : (ofNat n).toNat = n := by
     rw [toNat, toBitVec_eq_of_lt h]
 
-  theorem le_def {a b : $typeName} : a ≤ b ↔ a.toBitVec ≤ b.toBitVec := .rfl
+  @[int_toBitVec] theorem le_def {a b : $typeName} : a ≤ b ↔ a.toBitVec ≤ b.toBitVec := .rfl
 
-  theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
+  @[int_toBitVec] theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
 
   theorem le_iff_toNat_le {a b : $typeName} : a ≤ b ↔ a.toNat ≤ b.toNat := .rfl
 
@@ -74,6 +74,11 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   protected theorem toBitVec_inj {a b : $typeName} : a.toBitVec = b.toBitVec ↔ a = b :=
     Iff.intro eq_of_toBitVec_eq toBitVec_eq_of_eq
 
+  open $typeName (eq_of_toBitVec_eq toBitVec_eq_of_eq) in
+  @[int_toBitVec]
+  protected theorem eq_iff_toBitVec_eq {a b : $typeName} : a = b ↔ a.toBitVec = b.toBitVec :=
+    Iff.intro toBitVec_eq_of_eq eq_of_toBitVec_eq
+
   open $typeName (eq_of_toBitVec_eq) in
   protected theorem eq_of_val_eq {a b : $typeName} (h : a.val = b.val) : a = b := by
     rcases a with ⟨⟨_⟩⟩; rcases b with ⟨⟨_⟩⟩; simp_all [val]
@@ -82,10 +87,19 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   protected theorem val_inj {a b : $typeName} : a.val = b.val ↔ a = b :=
     Iff.intro eq_of_val_eq (congrArg val)
 
+  open $typeName (eq_of_toBitVec_eq) in
+  protected theorem toBitVec_ne_of_ne {a b : $typeName} (h : a ≠ b) : a.toBitVec ≠ b.toBitVec :=
+    fun h' => h (eq_of_toBitVec_eq h')
+
   open $typeName (toBitVec_eq_of_eq) in
   protected theorem ne_of_toBitVec_ne {a b : $typeName} (h : a.toBitVec ≠ b.toBitVec) : a ≠ b :=
     fun h' => absurd (toBitVec_eq_of_eq h') h
 
+  open $typeName (ne_of_toBitVec_ne toBitVec_ne_of_ne) in
+  @[int_toBitVec]
+  protected theorem ne_iff_toBitVec_ne {a b : $typeName} : a ≠ b ↔ a.toBitVec ≠ b.toBitVec :=
+    Iff.intro toBitVec_ne_of_ne ne_of_toBitVec_ne
+
   open $typeName (ne_of_toBitVec_ne) in
   protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := by
     apply ne_of_toBitVec_ne
@@ -159,7 +173,7 @@ macro "declare_uint_theorems" typeName:ident bits:term:arg : command => do
   @[simp]
   theorem val_ofNat (n : Nat) : val (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
 
-  @[simp]
+  @[simp, int_toBitVec]
   theorem toBitVec_ofNat (n : Nat) : toBitVec (no_index (OfNat.ofNat n)) = BitVec.ofNat _ n := rfl
 
   @[simp]
@@ -220,23 +234,3 @@ theorem UInt32.toNat_le_of_le {n : UInt32} {m : Nat} (h : m < size) : n ≤ ofNa
 
 theorem UInt32.le_toNat_of_le {n : UInt32} {m : Nat} (h : m < size) : ofNat m ≤ n → m ≤ n.toNat := by
   simp [le_def, BitVec.le_def, UInt32.toNat, toBitVec_eq_of_lt h]
-
-@[deprecated UInt8.toNat_zero (since := "2024-06-23")] protected abbrev UInt8.zero_toNat := @UInt8.toNat_zero
-@[deprecated UInt8.toNat_div (since := "2024-06-23")] protected abbrev UInt8.div_toNat := @UInt8.toNat_div
-@[deprecated UInt8.toNat_mod (since := "2024-06-23")] protected abbrev UInt8.mod_toNat := @UInt8.toNat_mod
-
-@[deprecated UInt16.toNat_zero (since := "2024-06-23")] protected abbrev UInt16.zero_toNat := @UInt16.toNat_zero
-@[deprecated UInt16.toNat_div (since := "2024-06-23")] protected abbrev UInt16.div_toNat := @UInt16.toNat_div
-@[deprecated UInt16.toNat_mod (since := "2024-06-23")] protected abbrev UInt16.mod_toNat := @UInt16.toNat_mod
-
-@[deprecated UInt32.toNat_zero (since := "2024-06-23")] protected abbrev UInt32.zero_toNat := @UInt32.toNat_zero
-@[deprecated UInt32.toNat_div (since := "2024-06-23")] protected abbrev UInt32.div_toNat := @UInt32.toNat_div
-@[deprecated UInt32.toNat_mod (since := "2024-06-23")] protected abbrev UInt32.mod_toNat := @UInt32.toNat_mod
-
-@[deprecated UInt64.toNat_zero (since := "2024-06-23")] protected abbrev UInt64.zero_toNat := @UInt64.toNat_zero
-@[deprecated UInt64.toNat_div (since := "2024-06-23")] protected abbrev UInt64.div_toNat := @UInt64.toNat_div
-@[deprecated UInt64.toNat_mod (since := "2024-06-23")] protected abbrev UInt64.mod_toNat := @UInt64.toNat_mod
-
-@[deprecated USize.toNat_zero (since := "2024-06-23")] protected abbrev USize.zero_toNat := @USize.toNat_zero
-@[deprecated USize.toNat_div (since := "2024-06-23")] protected abbrev USize.div_toNat := @USize.toNat_div
-@[deprecated USize.toNat_mod (since := "2024-06-23")] protected abbrev USize.mod_toNat := @USize.toNat_mod

src/Init/Data/Vector/Basic.lean

@@ -170,6 +170,13 @@ result is empty. If `stop` is greater than the size of the vector, the size is u
 @[inline] def map (f : α → β) (v : Vector α n) : Vector β n :=
   ⟨v.toArray.map f, by simp⟩
 
+@[inline] def flatten (v : Vector (Vector α n) m) : Vector α (m * n) :=
+  ⟨(v.toArray.map Vector.toArray).flatten,
+    by rcases v; simp_all [Function.comp_def, Array.map_const']⟩
+
+@[inline] def flatMap (v : Vector α n) (f : α → Vector β m) : Vector β (n * m) :=
+  ⟨v.toArray.flatMap fun a => (f a).toArray, by simp [Array.map_const']⟩
+
 /-- Maps corresponding elements of two vectors of equal size using the function `f`. -/
 @[inline] def zipWith (a : Vector α n) (b : Vector β n) (f : α → β → φ) : Vector φ n :=
   ⟨Array.zipWith a.toArray b.toArray f, by simp⟩

src/Init/Data/Vector/Lemmas.lean

@@ -5,6 +5,7 @@ Authors: Shreyas Srinivas, Francois Dorais, Kim Morrison
 -/
 prelude
 import Init.Data.Vector.Basic
+import Init.Data.Array.Attach
 
 /-!
 ## Vectors
@@ -27,6 +28,9 @@ namespace Vector
 
 theorem toArray_mk (a : Array α) (h : a.size = n) : (Vector.mk a h).toArray = a := rfl
 
+@[simp] theorem mk_toArray (v : Vector α n) : mk v.toArray v.2 = v := by
+  rfl
+
 @[simp] theorem getElem_mk {data : Array α} {size : data.size = n} {i : Nat} (h : i < n) :
     (Vector.mk data size)[i] = data[i] := rfl
 
@@ -471,7 +475,7 @@ theorem singleton_inj : #v[a] = #v[b] ↔ a = b := by
 theorem mkVector_succ : mkVector (n + 1) a = (mkVector n a).push a := by
   simp [mkVector, Array.mkArray_succ]
 
-theorem mkVector_inj : mkVector n a = mkVector n b ↔ n = 0 ∨ a = b := by
+@[simp] theorem mkVector_inj : mkVector n a = mkVector n b ↔ n = 0 ∨ a = b := by
   simp [← toArray_inj, toArray_mkVector, Array.mkArray_inj]
 
 /-! ## L[i] and L[i]? -/
@@ -693,6 +697,24 @@ theorem forall_getElem {l : Vector α n} {p : α → Prop} :
   rcases l with ⟨l, rfl⟩
   simp [Array.forall_getElem]
 
+
+/-! ### cast -/
+
+@[simp] theorem getElem_cast (a : Vector α n) (h : n = m) (i : Nat) (hi : i < m) :
+    (a.cast h)[i] = a[i] := by
+  cases a
+  simp
+
+@[simp] theorem getElem?_cast {l : Vector α n} {m : Nat} {w : n = m} {i : Nat} :
+    (l.cast w)[i]? = l[i]? := by
+  rcases l with ⟨l, rfl⟩
+  simp
+
+@[simp] theorem mem_cast {a : α} {l : Vector α n} {m : Nat} {w : n = m} :
+    a ∈ l.cast w ↔ a ∈ l := by
+  rcases l with ⟨l, rfl⟩
+  simp
+
 /-! ### Decidability of bounded quantifiers -/
 
 instance {xs : Vector α n} {p : α → Prop} [DecidablePred p] :
@@ -1097,6 +1119,11 @@ theorem forall_mem_map {f : α → β} {l : Vector α n} {P : β → Prop} :
 @[simp] theorem map_inj_left {f g : α → β} : map f l = map g l ↔ ∀ a ∈ l, f a = g a := by
   cases l <;> simp_all
 
+theorem map_inj_right {f : α → β} (w : ∀ x y, f x = f y → x = y) : map f l = map f l' ↔ l = l' := by
+  cases l
+  cases l'
+  simp [Array.map_inj_right w]
+
 theorem map_congr_left (h : ∀ a ∈ l, f a = g a) : map f l = map g l :=
   map_inj_left.2 h
 
@@ -1167,6 +1194,644 @@ theorem map_eq_iff {f : α → β} {l : Vector α n} {l' : Vector β n} :
   cases as
   simp
 
+/--
+Use this as `induction ass using vector₂_induction` on a hypothesis of the form `ass : Vector (Vector α n) m`.
+The hypothesis `ass` will be replaced with a hypothesis `ass : Array (Array α)`
+along with additional hypotheses `h₁ : ass.size = m` and `h₂ : ∀ xs ∈ ass, xs.size = n`.
+Appearances of the original `ass` in the goal will be replaced with
+`Vector.mk (xss.attach.map (fun ⟨xs, m⟩ => Vector.mk xs ⋯)) ⋯`.
+-/
+-- We can't use `@[cases_eliminator]` here as
+-- `Lean.Meta.getCustomEliminator?` only looks at the top-level constant.
+theorem vector₂_induction (P : Vector (Vector α n) m → Prop)
+    (of : ∀ (xss : Array (Array α)) (h₁ : xss.size = m) (h₂ : ∀ xs ∈ xss, xs.size = n),
+      P (mk (xss.attach.map (fun ⟨xs, m⟩ => mk xs (h₂ xs m))) (by simpa using h₁)))
+    (ass : Vector (Vector α n) m) : P ass := by
+  specialize of (ass.map toArray).toArray (by simp) (by simp)
+  simpa [Array.map_attach, Array.pmap_map] using of
+
+/--
+Use this as `induction ass using vector₃_induction` on a hypothesis of the form `ass : Vector (Vector (Vector α n) m) k`.
+The hypothesis `ass` will be replaced with a hypothesis `ass : Array (Array (Array α))`
+along with additional hypotheses `h₁ : ass.size = k`, `h₂ : ∀ xs ∈ ass, xs.size = m`,
+and `h₃ : ∀ xs ∈ ass, ∀ x ∈ xs, x.size = n`.
+Appearances of the original `ass` in the goal will be replaced with
+`Vector.mk (xss.attach.map (fun ⟨xs, m⟩ => Vector.mk (xs.attach.map (fun ⟨x, m'⟩ => Vector.mk x ⋯)) ⋯)) ⋯`.
+-/
+theorem vector₃_induction (P : Vector (Vector (Vector α n) m) k → Prop)
+    (of : ∀ (xss : Array (Array (Array α))) (h₁ : xss.size = k) (h₂ : ∀ xs ∈ xss, xs.size = m)
+      (h₃ : ∀ xs ∈ xss, ∀ x ∈ xs, x.size = n),
+      P (mk (xss.attach.map (fun ⟨xs, m⟩ =>
+        mk (xs.attach.map (fun ⟨x, m'⟩ =>
+          mk x (h₃ xs m x m'))) (by simpa using h₂ xs m))) (by simpa using h₁)))
+    (ass : Vector (Vector (Vector α n) m) k) : P ass := by
+  specialize of (ass.map (fun as => (as.map toArray).toArray)).toArray (by simp) (by simp) (by simp)
+  simpa [Array.map_attach, Array.pmap_map] using of
+
+/-! ### singleton -/
+
+@[simp] theorem singleton_def (v : α) : Vector.singleton v = #v[v] := rfl
+
+/-! ### append -/
+
+@[simp] theorem append_push {as : Vector α n} {bs : Vector α m} {a : α} :
+    as ++ bs.push a = (as ++ bs).push a := by
+  cases as
+  cases bs
+  simp
+
+theorem singleton_eq_toVector_singleton (a : α) : #v[a] = #[a].toVector := rfl
+
+@[simp] theorem mem_append {a : α} {s : Vector α n} {t : Vector α m} :
+    a ∈ s ++ t ↔ a ∈ s ∨ a ∈ t := by
+  cases s
+  cases t
+  simp
+
+theorem mem_append_left {a : α} {s : Vector α n} {t : Vector α m} (h : a ∈ s) : a ∈ s ++ t :=
+  mem_append.2 (Or.inl h)
+
+theorem mem_append_right {a : α} {s : Vector α n} {t : Vector α m} (h : a ∈ t) : a ∈ s ++ t :=
+  mem_append.2 (Or.inr h)
+
+theorem not_mem_append {a : α} {s : Vector α n} {t : Vector α m} (h₁ : a ∉ s) (h₂ : a ∉ t) :
+    a ∉ s ++ t :=
+  mt mem_append.1 $ not_or.mpr ⟨h₁, h₂⟩
+
+/--
+See also `eq_push_append_of_mem`, which proves a stronger version
+in which the initial array must not contain the element.
+-/
+theorem append_of_mem {a : α} {l : Vector α n} (h : a ∈ l) :
+    ∃ (m k : Nat) (w : m + 1 + k = n) (s : Vector α m) (t : Vector α k),
+      l = (s.push a ++ t).cast w := by
+  rcases l with ⟨l, rfl⟩
+  obtain ⟨s, t, rfl⟩ := Array.append_of_mem (by simpa using h)
+  refine ⟨_, _, by simp, s.toVector, t.toVector, by simp_all⟩
+
+theorem mem_iff_append {a : α} {l : Vector α n} :
+    a ∈ l ↔ ∃ (m k : Nat) (w : m + 1 + k = n) (s : Vector α m) (t : Vector α k),
+      l = (s.push a ++ t).cast w :=
+  ⟨append_of_mem, by rintro ⟨m, k, rfl, s, t, rfl⟩; simp⟩
+
+theorem forall_mem_append {p : α → Prop} {l₁ : Vector α n} {l₂ : Vector α m} :
+    (∀ (x) (_ : x ∈ l₁ ++ l₂), p x) ↔ (∀ (x) (_ : x ∈ l₁), p x) ∧ (∀ (x) (_ : x ∈ l₂), p x) := by
+  simp only [mem_append, or_imp, forall_and]
+
+theorem empty_append (as : Vector α n) : (#v[] : Vector α 0) ++ as = as.cast (by omega) := by
+  rcases as with ⟨as, rfl⟩
+  simp
+
+theorem append_empty (as : Vector α n) : as ++ (#v[] : Vector α 0) = as := by
+  rw [← toArray_inj, toArray_append, Array.append_empty]
+
+theorem getElem_append (a : Vector α n) (b : Vector α m) (i : Nat) (hi : i < n + m) :
+    (a ++ b)[i] = if h : i < n then a[i] else b[i - n] := by
+  rcases a with ⟨a, rfl⟩
+  rcases b with ⟨b, rfl⟩
+  simp [Array.getElem_append, hi]
+
+theorem getElem_append_left {a : Vector α n} {b : Vector α m} {i : Nat} (hi : i < n) :
+    (a ++ b)[i] = a[i] := by simp [getElem_append, hi]
+
+theorem getElem_append_right {a : Vector α n} {b : Vector α m} {i : Nat} (h : i < n + m) (hi : n ≤ i) :
+    (a ++ b)[i] = b[i - n] := by
+  rw [getElem_append, dif_neg (by omega)]
+
+theorem getElem?_append_left {as : Vector α n} {bs : Vector α m} {i : Nat} (hn : i < n) :
+    (as ++ bs)[i]? = as[i]? := by
+  have hn' : i < n + m := by omega
+  simp_all [getElem?_eq_getElem, getElem_append]
+
+theorem getElem?_append_right {as : Vector α n} {bs : Vector α m} {i : Nat} (h : n ≤ i) :
+    (as ++ bs)[i]? = bs[i - n]? := by
+  rcases as with ⟨as, rfl⟩
+  rcases bs with ⟨bs, rfl⟩
+  simp [Array.getElem?_append_right, h]
+
+theorem getElem?_append {as : Vector α n} {bs : Vector α m} {i : Nat} :
+    (as ++ bs)[i]? = if i < n then as[i]? else bs[i - n]? := by
+  split <;> rename_i h
+  · exact getElem?_append_left h
+  · exact getElem?_append_right (by simpa using h)
+
+/-- Variant of `getElem_append_left` useful for rewriting from the small array to the big array. -/
+theorem getElem_append_left' (l₁ : Vector α m) {l₂ : Vector α n} {i : Nat} (hi : i < m) :
+    l₁[i] = (l₁ ++ l₂)[i] := by
+  rw [getElem_append_left] <;> simp
+
+/-- Variant of `getElem_append_right` useful for rewriting from the small array to the big array. -/
+theorem getElem_append_right' (l₁ : Vector α m) {l₂ : Vector α n} {i : Nat} (hi : i < n) :
+    l₂[i] = (l₁ ++ l₂)[i + m] := by
+  rw [getElem_append_right] <;> simp [*, Nat.le_add_left]
+
+theorem getElem_of_append {l : Vector α n} {l₁ : Vector α m} {l₂ : Vector α k}
+    (w : m + 1 + k = n) (eq : l = (l₁.push a ++ l₂).cast w) :
+    l[m] = a := Option.some.inj <| by
+  rw [← getElem?_eq_getElem, eq, getElem?_cast, getElem?_append_left (by simp)]
+  simp
+
+@[simp 1100] theorem append_singleton {a : α} {as : Vector α n} : as ++ #v[a] = as.push a := by
+  cases as
+  simp
+
+theorem append_inj {s₁ s₂ : Vector α n} {t₁ t₂ : Vector α m} (h : s₁ ++ t₁ = s₂ ++ t₂) :
+    s₁ = s₂ ∧ t₁ = t₂ := by
+  rcases s₁ with ⟨s₁, rfl⟩
+  rcases s₂ with ⟨s₂, hs⟩
+  rcases t₁ with ⟨t₁, rfl⟩
+  rcases t₂ with ⟨t₂, ht⟩
+  simpa using Array.append_inj (by simpa using h) (by omega)
+
+theorem append_inj_right {s₁ s₂ : Vector α n} {t₁ t₂ : Vector α m}
+    (h : s₁ ++ t₁ = s₂ ++ t₂) : t₁ = t₂ :=
+  (append_inj h).right
+
+theorem append_inj_left {s₁ s₂ : Vector α n} {t₁ t₂ : Vector α m}
+    (h : s₁ ++ t₁ = s₂ ++ t₂) : s₁ = s₂ :=
+  (append_inj h).left
+
+theorem append_right_inj {t₁ t₂ : Vector α m} (s : Vector α n) : s ++ t₁ = s ++ t₂ ↔ t₁ = t₂ :=
+  ⟨fun h => append_inj_right h, congrArg _⟩
+
+theorem append_left_inj {s₁ s₂ : Vector α n} (t : Vector α m) : s₁ ++ t = s₂ ++ t ↔ s₁ = s₂ :=
+  ⟨fun h => append_inj_left h, congrArg (· ++ _)⟩
+
+theorem append_eq_append_iff {a : Vector α n} {b : Vector α m} {c : Vector α k} {d : Vector α l}
+    (w : k + l = n + m) :
+    a ++ b = (c ++ d).cast w ↔
+      if h : n ≤ k then
+        ∃ a' : Vector α (k - n), c = (a ++ a').cast (by omega) ∧ b = (a' ++ d).cast (by omega)
+      else
+        ∃ c' : Vector α (n - k), a = (c ++ c').cast (by omega) ∧ d = (c' ++ b).cast (by omega) := by
+  rcases a with ⟨a, rfl⟩
+  rcases b with ⟨b, rfl⟩
+  rcases c with ⟨c, rfl⟩
+  rcases d with ⟨d, rfl⟩
+  simp only [mk_append_mk, Array.append_eq_append_iff, mk_eq, toArray_cast]
+  constructor
+  · rintro (⟨a', rfl, rfl⟩ | ⟨c', rfl, rfl⟩)
+    · rw [dif_pos (by simp)]
+      exact ⟨a'.toVector.cast (by simp; omega), by simp⟩
+    · split <;> rename_i h
+      · have hc : c'.size = 0 := by simp at h; omega
+        simp at hc
+        exact ⟨#v[].cast (by simp; omega), by simp_all⟩
+      · exact ⟨c'.toVector.cast (by simp; omega), by simp⟩
+  · split <;> rename_i h
+    · rintro ⟨a', hc, rfl⟩
+      left
+      refine ⟨a'.toArray, hc, rfl⟩
+    · rintro ⟨c', ha, rfl⟩
+      right
+      refine ⟨c'.toArray, ha, rfl⟩
+
+theorem set_append {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} (h : i < n + m) :
+    (s ++ t).set i x =
+      if h' : i < n then
+        s.set i x ++ t
+      else
+        s ++ t.set (i - n) x := by
+  rcases s with ⟨s, rfl⟩
+  rcases t with ⟨t, rfl⟩
+  simp only [mk_append_mk, set_mk, Array.set_append]
+  split <;> simp
+
+@[simp] theorem set_append_left {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} (h : i < n) :
+    (s ++ t).set i x = s.set i x ++ t := by
+  simp [set_append, h]
+
+@[simp] theorem set_append_right {s : Vector α n} {t : Vector α m} {i : Nat} {x : α}
+    (h' : i < n + m) (h : n ≤ i) :
+    (s ++ t).set i x = s ++ t.set (i - n) x := by
+  rw [set_append, dif_neg (by omega)]
+
+theorem setIfInBounds_append {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} :
+    (s ++ t).setIfInBounds i x =
+      if i < n then
+        s.setIfInBounds i x ++ t
+      else
+        s ++ t.setIfInBounds (i - n) x := by
+  rcases s with ⟨s, rfl⟩
+  rcases t with ⟨t, rfl⟩
+  simp only [mk_append_mk, setIfInBounds_mk, Array.setIfInBounds_append]
+  split <;> simp
+
+@[simp] theorem setIfInBounds_append_left {s : Vector α n} {t : Vector α m} {i : Nat} {x : α} (h : i < n) :
+    (s ++ t).setIfInBounds i x = s.setIfInBounds i x ++ t := by
+  simp [setIfInBounds_append, h]
+
+@[simp] theorem setIfInBounds_append_right {s : Vector α n} {t : Vector α m} {i : Nat} {x : α}
+    (h : n ≤ i) :
+    (s ++ t).setIfInBounds i x = s ++ t.setIfInBounds (i - n) x := by
+  rw [setIfInBounds_append, if_neg (by omega)]
+
+@[simp] theorem map_append (f : α → β) (l₁ : Vector α n) (l₂ : Vector α m) :
+    map f (l₁ ++ l₂) = map f l₁ ++ map f l₂ := by
+  rcases l₁ with ⟨l₁, rfl⟩
+  rcases l₂ with ⟨l₂, rfl⟩
+  simp
+
+theorem map_eq_append_iff {f : α → β} :
+    map f l = L₁ ++ L₂ ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = L₁ ∧ map f l₂ = L₂ := by
+  rcases l with ⟨l, h⟩
+  rcases L₁ with ⟨L₁, rfl⟩
+  rcases L₂ with ⟨L₂, rfl⟩
+  simp only [map_mk, mk_append_mk, eq_mk, Array.map_eq_append_iff, mk_eq, toArray_append,
+    toArray_map]
+  constructor
+  · rintro ⟨l₁, l₂, rfl, rfl, rfl⟩
+    exact ⟨l₁.toVector.cast (by simp), l₂.toVector.cast (by simp), by simp⟩
+  · rintro ⟨⟨l₁⟩, ⟨l₂⟩, rfl, h₁, h₂⟩
+    exact ⟨l₁, l₂, by simp_all⟩
+
+theorem append_eq_map_iff {f : α → β} :
+    L₁ ++ L₂ = map f l ↔ ∃ l₁ l₂, l = l₁ ++ l₂ ∧ map f l₁ = L₁ ∧ map f l₂ = L₂ := by
+  rw [eq_comm, map_eq_append_iff]
+
+/-! ### flatten -/
+
+@[simp] theorem flatten_mk (L : Array (Vector α n)) (h : L.size = m) :
+    (mk L h).flatten =
+      mk (L.map toArray).flatten (by simp [Function.comp_def, Array.map_const', h]) := by
+  simp [flatten]
+
+@[simp] theorem getElem_flatten (l : Vector (Vector β m) n) (i : Nat) (hi : i < n * m) :
+    l.flatten[i] =
+      haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
+      haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
+      l[i / m][i % m] := by
+  rcases l with ⟨⟨l⟩, rfl⟩
+  simp only [flatten_mk, List.map_toArray, getElem_mk, List.getElem_toArray, Array.flatten_toArray]
+  induction l generalizing i with
+  | nil => simp at hi
+  | cons a l ih =>
+    simp only [List.map_cons, List.map_map, List.flatten_cons]
+    by_cases h : i < m
+    · rw [List.getElem_append_left (by simpa)]
+      have h₁ : i / m = 0 := Nat.div_eq_of_lt h
+      have h₂ : i % m = i := Nat.mod_eq_of_lt h
+      simp [h₁, h₂]
+    · have h₁ : a.toList.length ≤ i := by simp; omega
+      rw [List.getElem_append_right h₁]
+      simp only [Array.length_toList, size_toArray]
+      specialize ih (i - m) (by simp_all [Nat.add_one_mul]; omega)
+      have h₂ : i / m = (i - m) / m + 1 := by
+        conv => lhs; rw [show i = i - m + m by omega]
+        rw [Nat.add_div_right]
+        exact Nat.pos_of_lt_mul_left hi
+      simp only [Array.length_toList, size_toArray] at h₁
+      have h₃ : (i - m) % m = i % m := (Nat.mod_eq_sub_mod h₁).symm
+      simp_all
+
+theorem getElem?_flatten (l : Vector (Vector β m) n) (i : Nat) :
+    l.flatten[i]? =
+      if hi : i < n * m then
+        haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
+        haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
+        some l[i / m][i % m]
+      else
+        none := by
+  simp [getElem?_def]
+
+@[simp] theorem flatten_singleton (l : Vector α n) : #v[l].flatten = l.cast (by simp) := by
+  simp [flatten]
+
+theorem mem_flatten {L : Vector (Vector α n) m} : a ∈ L.flatten ↔ ∃ l, l ∈ L ∧ a ∈ l := by
+  rcases L with ⟨L, rfl⟩
+  simp [Array.mem_flatten]
+  constructor
+  · rintro ⟨_, ⟨l, h₁, rfl⟩, h₂⟩
+    exact ⟨l, h₁, by simpa using h₂⟩
+  · rintro ⟨l, h₁, h₂⟩
+    exact ⟨l.toArray, ⟨l, h₁, rfl⟩, by simpa using h₂⟩
+
+theorem exists_of_mem_flatten : a ∈ flatten L → ∃ l, l ∈ L ∧ a ∈ l := mem_flatten.1
+
+theorem mem_flatten_of_mem (lL : l ∈ L) (al : a ∈ l) : a ∈ flatten L := mem_flatten.2 ⟨l, lL, al⟩
+
+theorem forall_mem_flatten {p : α → Prop} {L : Vector (Vector α n) m} :
+    (∀ (x) (_ : x ∈ flatten L), p x) ↔ ∀ (l) (_ : l ∈ L) (x) (_ : x ∈ l), p x := by
+  simp only [mem_flatten, forall_exists_index, and_imp]
+  constructor <;> (intros; solve_by_elim)
+
+@[simp] theorem map_flatten (f : α → β) (L : Vector (Vector α n) m) :
+    (flatten L).map f = (map (map f) L).flatten := by
+  induction L using vector₂_induction with
+  | of xss h₁ h₂ => simp
+
+@[simp] theorem flatten_append (L₁ : Vector (Vector α n) m₁) (L₂ : Vector (Vector α n) m₂) :
+    flatten (L₁ ++ L₂) = (flatten L₁ ++ flatten L₂).cast (by simp [Nat.add_mul]) := by
+  induction L₁ using vector₂_induction
+  induction L₂ using vector₂_induction
+  simp
+
+theorem flatten_push (L : Vector (Vector α n) m) (l : Vector α n) :
+    flatten (L.push l) = (flatten L ++ l).cast (by simp [Nat.add_mul]) := by
+  induction L using vector₂_induction
+  rcases l with ⟨l⟩
+  simp [Array.flatten_push]
+
+theorem flatten_flatten {L : Vector (Vector (Vector α n) m) k} :
+    flatten (flatten L) = (flatten (map flatten L)).cast (by simp [Nat.mul_assoc]) := by
+  induction L using vector₃_induction with
+  | of xss h₁ h₂ h₃ =>
+    -- simp [Array.flatten_flatten] -- FIXME: `simp` produces a bad proof here!
+    simp [Array.map_attach, Array.flatten_flatten, Array.map_pmap]
+
+/-- Two vectors of constant length vectors are equal iff their flattens coincide. -/
+theorem eq_iff_flatten_eq {L L' : Vector (Vector α n) m} :
+    L = L' ↔ L.flatten = L'.flatten := by
+  induction L using vector₂_induction with | of L h₁ h₂ =>
+  induction L' using vector₂_induction with | of L' h₁' h₂' =>
+  simp only [eq_mk, flatten_mk, Array.map_map, Function.comp_apply, Array.map_subtype,
+    Array.unattach_attach, Array.map_id_fun', id_eq]
+  constructor
+  · intro h
+    suffices L = L' by simp_all
+    apply Array.ext_getElem?
+    intro i
+    replace h := congrArg (fun x => x[i]?.map (fun x => x.toArray)) h
+    simpa [Option.map_pmap] using h
+  · intro h
+    have w : L.map Array.size = L'.map Array.size := by
+      ext i h h'
+      · simp_all
+      · simp only [Array.getElem_map]
+        rw [h₂ _ (by simp), h₂' _ (by simp)]
+    have := Array.eq_iff_flatten_eq.mpr ⟨h, w⟩
+    subst this
+    rfl
+
+
+/-! ### flatMap -/
+
+@[simp] theorem flatMap_mk (l : Array α) (h : l.size = m) (f : α → Vector β n) :
+    (mk l h).flatMap f =
+      mk (l.flatMap (fun a => (f a).toArray)) (by simp [Array.map_const', h]) := by
+  simp [flatMap]
+
+@[simp] theorem flatMap_toArray (l : Vector α n) (f : α → Vector β m) :
+    l.toArray.flatMap (fun a => (f a).toArray) = (l.flatMap f).toArray := by
+  rcases l with ⟨l, rfl⟩
+  simp
+
+theorem flatMap_def (l : Vector α n) (f : α → Vector β m) : l.flatMap f = flatten (map f l) := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.flatMap_def, Function.comp_def]
+
+@[simp] theorem getElem_flatMap (l : Vector α n) (f : α → Vector β m) (i : Nat) (hi : i < n * m) :
+    (l.flatMap f)[i] =
+      haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
+      haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
+      (f (l[i / m]))[i % m] := by
+  rw [flatMap_def, getElem_flatten, getElem_map]
+
+theorem getElem?_flatMap (l : Vector α n) (f : α → Vector β m) (i : Nat) :
+    (l.flatMap f)[i]? =
+      if hi : i < n * m then
+        haveI : i / m < n := by rwa [Nat.div_lt_iff_lt_mul (Nat.pos_of_lt_mul_left hi)]
+        haveI : i % m < m := Nat.mod_lt _ (Nat.pos_of_lt_mul_left hi)
+        some ((f (l[i / m]))[i % m])
+      else
+        none := by
+  simp [getElem?_def]
+
+@[simp] theorem flatMap_id (l : Vector (Vector α m) n) : l.flatMap id = l.flatten := by simp [flatMap_def]
+
+@[simp] theorem flatMap_id' (l : Vector (Vector α m) n) : l.flatMap (fun a => a) = l.flatten := by simp [flatMap_def]
+
+@[simp] theorem mem_flatMap {f : α → Vector β m} {b} {l : Vector α n} : b ∈ l.flatMap f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
+  simp [flatMap_def, mem_flatten]
+  exact ⟨fun ⟨_, ⟨a, h₁, rfl⟩, h₂⟩ => ⟨a, h₁, h₂⟩, fun ⟨a, h₁, h₂⟩ => ⟨_, ⟨a, h₁, rfl⟩, h₂⟩⟩
+
+theorem exists_of_mem_flatMap {b : β} {l : Vector α n} {f : α → Vector β m} :
+    b ∈ l.flatMap f → ∃ a, a ∈ l ∧ b ∈ f a := mem_flatMap.1
+
+theorem mem_flatMap_of_mem {b : β} {l : Vector α n} {f : α → Vector β m} {a} (al : a ∈ l) (h : b ∈ f a) :
+    b ∈ l.flatMap f := mem_flatMap.2 ⟨a, al, h⟩
+
+theorem forall_mem_flatMap {p : β → Prop} {l : Vector α n} {f : α → Vector β m} :
+    (∀ (x) (_ : x ∈ l.flatMap f), p x) ↔ ∀ (a) (_ : a ∈ l) (b) (_ : b ∈ f a), p b := by
+  simp only [mem_flatMap, forall_exists_index, and_imp]
+  constructor <;> (intros; solve_by_elim)
+
+theorem flatMap_singleton (f : α → Vector β m) (x : α) : #v[x].flatMap f = (f x).cast (by simp) := by
+  simp [flatMap_def]
+
+@[simp] theorem flatMap_singleton' (l : Vector α n) : (l.flatMap fun x => #v[x]) = l.cast (by simp) := by
+  rcases l with ⟨l, rfl⟩
+  simp
+
+@[simp] theorem flatMap_append (xs ys : Vector α n) (f : α → Vector β m) :
+    (xs ++ ys).flatMap f = (xs.flatMap f ++ ys.flatMap f).cast (by simp [Nat.add_mul]) := by
+  rcases xs with ⟨xs⟩
+  rcases ys with ⟨ys⟩
+  simp [flatMap_def, flatten_append]
+
+theorem flatMap_assoc {α β} (l : Vector α n) (f : α → Vector β m) (g : β → Vector γ k) :
+    (l.flatMap f).flatMap g = (l.flatMap fun x => (f x).flatMap g).cast (by simp [Nat.mul_assoc]) := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.flatMap_assoc]
+
+theorem map_flatMap (f : β → γ) (g : α → Vector β m) (l : Vector α n) :
+     (l.flatMap g).map f = l.flatMap fun a => (g a).map f := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.map_flatMap]
+
+theorem flatMap_map (f : α → β) (g : β → Vector γ k) (l : Vector α n) :
+     (map f l).flatMap g = l.flatMap (fun a => g (f a)) := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.flatMap_map]
+
+theorem map_eq_flatMap {α β} (f : α → β) (l : Vector α n) :
+    map f l = (l.flatMap fun x => #v[f x]).cast (by simp) := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.map_eq_flatMap]
+
+/-! ### mkVector -/
+
+@[simp] theorem mkVector_one : mkVector 1 a = #v[a] := rfl
+
+/-- Variant of `mkVector_succ` that prepends `a` at the beginning of the vector. -/
+theorem mkVector_succ' : mkVector (n + 1) a = (#v[a] ++ mkVector n a).cast (by omega) := by
+  rw [← toArray_inj]
+  simp [Array.mkArray_succ']
+
+@[simp] theorem mem_mkVector {a b : α} {n} : b ∈ mkVector n a ↔ n ≠ 0 ∧ b = a := by
+  unfold mkVector
+  simp
+
+theorem eq_of_mem_mkVector {a b : α} {n} (h : b ∈ mkVector n a) : b = a := (mem_mkVector.1 h).2
+
+theorem forall_mem_mkVector {p : α → Prop} {a : α} {n} :
+    (∀ b, b ∈ mkVector n a → p b) ↔ n = 0 ∨ p a := by
+  cases n <;> simp [mem_mkVector]
+
+@[simp] theorem getElem_mkVector (a : α) (n i : Nat) (h : i < n) : (mkVector n a)[i] = a := by
+  simp [mkVector]
+
+theorem getElem?_mkVector (a : α) (n i : Nat) : (mkVector n a)[i]? = if i < n then some a else none := by
+  simp [getElem?_def]
+
+@[simp] theorem getElem?_mkVector_of_lt {n : Nat} {m : Nat} (h : m < n) : (mkVector n a)[m]? = some a := by
+  simp [getElem?_mkVector, h]
+
+theorem eq_mkVector_of_mem {a : α} {l : Vector α n} (h : ∀ (b) (_ : b ∈ l), b = a) : l = mkVector n a := by
+  rw [← toArray_inj]
+  simpa using Array.eq_mkArray_of_mem (l := l.toArray) (by simpa using h)
+
+theorem eq_mkVector_iff {a : α} {n} {l : Vector α n} :
+    l = mkVector n a ↔ ∀ (b) (_ : b ∈ l), b = a := by
+  rw [← toArray_inj]
+  simpa using Array.eq_mkArray_iff (l := l.toArray) (n := n)
+
+theorem map_eq_mkVector_iff {l : Vector α n} {f : α → β} {b : β} :
+    l.map f = mkVector n b ↔ ∀ x ∈ l, f x = b := by
+  simp [eq_mkVector_iff]
+
+@[simp] theorem map_const (l : Vector α n) (b : β) : map (Function.const α b) l = mkVector n b :=
+  map_eq_mkVector_iff.mpr fun _ _ => rfl
+
+@[simp] theorem map_const_fun (x : β) : map (n := n) (Function.const α x) = fun _ => mkVector n x := by
+  funext l
+  simp
+
+/-- Variant of `map_const` using a lambda rather than `Function.const`. -/
+-- This can not be a `@[simp]` lemma because it would fire on every `List.map`.
+theorem map_const' (l : Vector α n) (b : β) : map (fun _ => b) l = mkVector n b :=
+  map_const l b
+
+@[simp] theorem set_mkVector_self : (mkVector n a).set i a h = mkVector n a := by
+  rw [← toArray_inj]
+  simp
+
+@[simp] theorem setIfInBounds_mkVector_self : (mkVector n a).setIfInBounds i a = mkVector n a := by
+  rw [← toArray_inj]
+  simp
+
+@[simp] theorem mkVector_append_mkVector : mkVector n a ++ mkVector m a = mkVector (n + m) a := by
+  rw [← toArray_inj]
+  simp
+
+theorem append_eq_mkVector_iff {l₁ : Vector α n} {l₂ : Vector α m} {a : α} :
+    l₁ ++ l₂ = mkVector (n + m) a ↔ l₁ = mkVector n a ∧ l₂ = mkVector m a := by
+  simp [← toArray_inj, Array.append_eq_mkArray_iff]
+
+theorem mkVector_eq_append_iff {l₁ : Vector α n} {l₂ : Vector α m} {a : α} :
+    mkVector (n + m) a = l₁ ++ l₂ ↔ l₁ = mkVector n a ∧ l₂ = mkVector m a := by
+  rw [eq_comm, append_eq_mkVector_iff]
+
+@[simp] theorem map_mkVector : (mkVector n a).map f = mkVector n (f a) := by
+  rw [← toArray_inj]
+  simp
+
+
+@[simp] theorem flatten_mkVector_empty : (mkVector n (#v[] : Vector α 0)).flatten = #v[] := by
+  rw [← toArray_inj]
+  simp
+
+@[simp] theorem flatten_mkVector_singleton : (mkVector n #v[a]).flatten = (mkVector n a).cast (by simp) := by
+  ext i h
+  simp [h]
+
+@[simp] theorem flatten_mkVector_mkVector : (mkVector n (mkVector m a)).flatten = mkVector (n * m) a := by
+  ext i h
+  simp [h]
+
+theorem flatMap_mkArray {β} (f : α → Vector β m) : (mkVector n a).flatMap f = (mkVector n (f a)).flatten := by
+  ext i h
+  simp [h]
+
+@[simp] theorem sum_mkArray_nat (n : Nat) (a : Nat) : (mkVector n a).sum = n * a := by
+  simp [toArray_mkVector]
+
+/-! ### reverse -/
+
+@[simp] theorem reverse_push (as : Vector α n) (a : α) :
+    (as.push a).reverse = (#v[a] ++ as.reverse).cast (by omega) := by
+  rcases as with ⟨as, rfl⟩
+  simp [Array.reverse_push]
+
+@[simp] theorem mem_reverse {x : α} {as : Vector α n} : x ∈ as.reverse ↔ x ∈ as := by
+  cases as
+  simp
+
+@[simp] theorem getElem_reverse (a : Vector α n) (i : Nat) (hi : i < n) :
+    (a.reverse)[i] = a[n - 1 - i] := by
+  rcases a with ⟨a, rfl⟩
+  simp
+
+/-- Variant of `getElem?_reverse` with a hypothesis giving the linear relation between the indices. -/
+theorem getElem?_reverse' {l : Vector α n} (i j) (h : i + j + 1 = n) : l.reverse[i]? = l[j]? := by
+  rcases l with ⟨l, rfl⟩
+  simpa using Array.getElem?_reverse' i j h
+
+@[simp]
+theorem getElem?_reverse {l : Vector α n} {i} (h : i < n) :
+    l.reverse[i]? = l[n - 1 - i]? := by
+  cases l
+  simp_all
+
+@[simp] theorem reverse_reverse (as : Vector α n) : as.reverse.reverse = as := by
+  rcases as with ⟨as, rfl⟩
+  simp [Array.reverse_reverse]
+
+theorem reverse_eq_iff {as bs : Vector α n} : as.reverse = bs ↔ as = bs.reverse := by
+  constructor <;> (rintro rfl; simp)
+
+@[simp] theorem reverse_inj {xs ys : Vector α n} : xs.reverse = ys.reverse ↔ xs = ys := by
+  simp [reverse_eq_iff]
+
+@[simp] theorem reverse_eq_push_iff {xs : Vector α (n + 1)} {ys : Vector α n} {a : α} :
+    xs.reverse = ys.push a ↔ xs = (#v[a] ++ ys.reverse).cast (by omega) := by
+  rcases xs with ⟨xs, h⟩
+  rcases ys with ⟨ys, rfl⟩
+  simp [Array.reverse_eq_push_iff]
+
+@[simp] theorem map_reverse (f : α → β) (l : Vector α n) : l.reverse.map f = (l.map f).reverse := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.map_reverse]
+
+@[simp] theorem reverse_append (as : Vector α n) (bs : Vector α m) :
+    (as ++ bs).reverse = (bs.reverse ++ as.reverse).cast (by omega) := by
+  rcases as with ⟨as, rfl⟩
+  rcases bs with ⟨bs, rfl⟩
+  simp [Array.reverse_append]
+
+@[simp] theorem reverse_eq_append_iff {xs : Vector α (n + m)} {ys : Vector α n} {zs : Vector α m} :
+    xs.reverse = ys ++ zs ↔ xs = (zs.reverse ++ ys.reverse).cast (by omega) := by
+  cases xs
+  cases ys
+  cases zs
+  simp
+
+/-- Reversing a flatten is the same as reversing the order of parts and reversing all parts. -/
+theorem reverse_flatten (L : Vector (Vector α m) n) :
+    L.flatten.reverse = (L.map reverse).reverse.flatten := by
+  cases L using vector₂_induction
+  simp [Array.reverse_flatten]
+
+/-- Flattening a reverse is the same as reversing all parts and reversing the flattened result. -/
+theorem flatten_reverse (L : Vector (Vector α m) n) :
+    L.reverse.flatten = (L.map reverse).flatten.reverse := by
+  cases L using vector₂_induction
+  simp [Array.flatten_reverse]
+
+theorem reverse_flatMap {β} (l : Vector α n) (f : α → Vector β m) :
+    (l.flatMap f).reverse = l.reverse.flatMap (reverse ∘ f) := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.reverse_flatMap, Function.comp_def]
+
+theorem flatMap_reverse {β} (l : Vector α n) (f : α → Vector β m) :
+    (l.reverse.flatMap f) = (l.flatMap (reverse ∘ f)).reverse := by
+  rcases l with ⟨l, rfl⟩
+  simp [Array.flatMap_reverse, Function.comp_def]
+
+@[simp] theorem reverse_mkVector (n) (a : α) : reverse (mkVector n a) = mkVector n a := by
+  rw [← toArray_inj]
+  simp
+
 /-! Content below this point has not yet been aligned with `List` and `Array`. -/
 
 @[simp] theorem getElem_ofFn {α n} (f : Fin n → α) (i : Nat) (h : i < n) :
@@ -1197,28 +1862,6 @@ defeq issues in the implicit size argument.
     subst h
     simp [pop, back, back!, ← Array.eq_push_pop_back!_of_size_ne_zero]
 
-/-! ### append -/
-
-theorem getElem_append (a : Vector α n) (b : Vector α m) (i : Nat) (hi : i < n + m) :
-    (a ++ b)[i] = if h : i < n then a[i] else b[i - n] := by
-  rcases a with ⟨a, rfl⟩
-  rcases b with ⟨b, rfl⟩
-  simp [Array.getElem_append, hi]
-
-theorem getElem_append_left {a : Vector α n} {b : Vector α m} {i : Nat} (hi : i < n) :
-    (a ++ b)[i] = a[i] := by simp [getElem_append, hi]
-
-theorem getElem_append_right {a : Vector α n} {b : Vector α m} {i : Nat} (h : i < n + m) (hi : n ≤ i) :
-    (a ++ b)[i] = b[i - n] := by
-  rw [getElem_append, dif_neg (by omega)]
-
-/-! ### cast -/
-
-@[simp] theorem getElem_cast (a : Vector α n) (h : n = m) (i : Nat) (hi : i < m) :
-    (a.cast h)[i] = a[i] := by
-  cases a
-  simp
-
 /-! ### extract -/
 
 @[simp] theorem getElem_extract (a : Vector α n) (start stop) (i : Nat) (hi : i < min stop n - start) :
@@ -1320,13 +1963,6 @@ theorem swap_comm (a : Vector α n) {i j : Nat} {hi hj} :
   cases a
   simp
 
-/-! ### reverse -/
-
-@[simp] theorem getElem_reverse (a : Vector α n) (i : Nat) (hi : i < n) :
-    (a.reverse)[i] = a[n - 1 - i] := by
-  rcases a with ⟨a, rfl⟩
-  simp
-
 /-! ### Decidable quantifiers. -/
 
 theorem forall_zero_iff {P : Vector α 0 → Prop} :

src/Init/Grind.lean

@@ -11,3 +11,4 @@ import Init.Grind.Cases
 import Init.Grind.Propagator
 import Init.Grind.Util
 import Init.Grind.Offset
+import Init.Grind.PP

src/Init/Grind/Lemmas.lean

@@ -12,6 +12,9 @@ import Init.Grind.Util
 
 namespace Lean.Grind
 
+theorem rfl_true : true = true :=
+  rfl
+
 theorem intro_with_eq (p p' q : Prop) (he : p = p') (h : p' → q) : p → q :=
   fun hp => h (he.mp hp)
 
@@ -66,6 +69,12 @@ theorem eq_eq_of_eq_true_right {a b : Prop} (h : b = True) : (a = b) = a := by s
 theorem eq_congr  {α : Sort u} {a₁ b₁ a₂ b₂ : α} (h₁ : a₁ = a₂) (h₂ : b₁ = b₂) : (a₁ = b₁) = (a₂ = b₂) := by simp [*]
 theorem eq_congr' {α : Sort u} {a₁ b₁ a₂ b₂ : α} (h₁ : a₁ = b₂) (h₂ : b₁ = a₂) : (a₁ = b₁) = (a₂ = b₂) := by rw [h₁, h₂, Eq.comm (a := a₂)]
 
+/- The following two helper theorems are used to case-split `a = b` representing `iff`. -/
+theorem of_eq_eq_true {a b : Prop} (h : (a = b) = True) : (¬a ∨ b) ∧ (¬b ∨ a) := by
+  by_cases a <;> by_cases b <;> simp_all
+theorem of_eq_eq_false {a b : Prop} (h : (a = b) = False) : (¬a ∨ ¬b) ∧ (b ∨ a) := by
+  by_cases a <;> by_cases b <;> simp_all
+
 /-! Forall -/
 
 theorem forall_propagator (p : Prop) (q : p → Prop) (q' : Prop) (h₁ : p = True) (h₂ : q (of_eq_true h₁) = q') : (∀ hp : p, q hp) = q' := by

src/Init/Grind/Norm.lean

@@ -12,110 +12,105 @@ import Init.ByCases
 namespace Lean.Grind
 /-!
 Normalization theorems for the `grind` tactic.
-
-We are also going to use simproc's in the future.
 -/
 
--- Not
-attribute [grind_norm] Classical.not_not
-
--- Ne
-attribute [grind_norm] ne_eq
-
--- Iff
-@[grind_norm] theorem iff_eq (p q : Prop) : (p ↔ q) = (p = q) := by
+theorem iff_eq (p q : Prop) : (p ↔ q) = (p = q) := by
   by_cases p <;> by_cases q <;> simp [*]
 
--- Eq
-attribute [grind_norm] eq_self heq_eq_eq
-
--- Prop equality
-@[grind_norm] theorem eq_true_eq (p : Prop) : (p = True) = p := by simp
-@[grind_norm] theorem eq_false_eq (p : Prop) : (p = False) = ¬p := by simp
-@[grind_norm] theorem not_eq_prop (p q : Prop) : (¬(p = q)) = (p = ¬q) := by
+theorem eq_true_eq (p : Prop) : (p = True) = p := by simp
+theorem eq_false_eq (p : Prop) : (p = False) = ¬p := by simp
+theorem not_eq_prop (p q : Prop) : (¬(p = q)) = (p = ¬q) := by
   by_cases p <;> by_cases q <;> simp [*]
 
--- True
-attribute [grind_norm] not_true
-
--- False
-attribute [grind_norm] not_false_eq_true
-
 -- Remark: we disabled the following normalization rule because we want this information when implementing splitting heuristics
 -- Implication as a clause
 theorem imp_eq (p q : Prop) : (p → q) = (¬ p ∨ q) := by
   by_cases p <;> by_cases q <;> simp [*]
 
--- And
-@[grind_norm↓] theorem not_and (p q : Prop) : (¬(p ∧ q)) = (¬p ∨ ¬q) := by
+theorem true_imp_eq (p : Prop) : (True → p) = p := by simp
+theorem false_imp_eq (p : Prop) : (False → p) = True := by simp
+theorem imp_true_eq (p : Prop) : (p → True) = True := by simp
+theorem imp_false_eq (p : Prop) : (p → False) = ¬p := by simp
+theorem imp_self_eq (p : Prop) : (p → p) = True := by simp
+
+theorem not_and (p q : Prop) : (¬(p ∧ q)) = (¬p ∨ ¬q) := by
   by_cases p <;> by_cases q <;> simp [*]
-attribute [grind_norm] and_true true_and and_false false_and and_assoc
 
--- Or
-attribute [grind_norm↓] not_or
-attribute [grind_norm] or_true true_or or_false false_or or_assoc
-
--- ite
-attribute [grind_norm] ite_true ite_false
-@[grind_norm↓] theorem not_ite {_ : Decidable p} (q r : Prop) : (¬ite p q r) = ite p (¬q) (¬r) := by
+theorem not_ite {_ : Decidable p} (q r : Prop) : (¬ite p q r) = ite p (¬q) (¬r) := by
   by_cases p <;> simp [*]
 
-@[grind_norm] theorem ite_true_false {_ : Decidable p} : (ite p True False) = p := by
+theorem ite_true_false {_ : Decidable p} : (ite p True False) = p := by
   by_cases p <;> simp
 
-@[grind_norm] theorem ite_false_true {_ : Decidable p} : (ite p False True) = ¬p := by
+theorem ite_false_true {_ : Decidable p} : (ite p False True) = ¬p := by
   by_cases p <;> simp
 
--- Forall
-@[grind_norm↓] theorem not_forall (p : α → Prop) : (¬∀ x, p x) = ∃ x, ¬p x := by simp
-attribute [grind_norm] forall_and
+theorem not_forall (p : α → Prop) : (¬∀ x, p x) = ∃ x, ¬p x := by simp
 
--- Exists
-@[grind_norm↓] theorem not_exists (p : α → Prop) : (¬∃ x, p x) = ∀ x, ¬p x := by simp
-attribute [grind_norm] exists_const exists_or exists_prop exists_and_left exists_and_right
+theorem not_exists (p : α → Prop) : (¬∃ x, p x) = ∀ x, ¬p x := by simp
 
--- Bool cond
-@[grind_norm] theorem cond_eq_ite (c : Bool) (a b : α) : cond c a b = ite c a b := by
+theorem cond_eq_ite (c : Bool) (a b : α) : cond c a b = ite c a b := by
   cases c <;> simp [*]
 
--- Bool or
-attribute [grind_norm]
-  Bool.or_false Bool.or_true Bool.false_or Bool.true_or Bool.or_eq_true Bool.or_assoc
-
--- Bool and
-attribute [grind_norm]
-  Bool.and_false Bool.and_true Bool.false_and Bool.true_and Bool.and_eq_true Bool.and_assoc
-
--- Bool not
-attribute [grind_norm]
-  Bool.not_not
-
--- beq
-attribute [grind_norm] beq_iff_eq
-
--- bne
-attribute [grind_norm] bne_iff_ne
-
--- Bool not eq true/false
-attribute [grind_norm] Bool.not_eq_true Bool.not_eq_false
-
--- decide
-attribute [grind_norm] decide_eq_true_eq decide_not not_decide_eq_true
-
--- Nat LE
-attribute [grind_norm] Nat.le_zero_eq
-
--- Nat/Int LT
-@[grind_norm] theorem Nat.lt_eq (a b : Nat) : (a < b) = (a + 1 ≤ b) := by
+theorem Nat.lt_eq (a b : Nat) : (a < b) = (a + 1 ≤ b) := by
   simp [Nat.lt, LT.lt]
 
-@[grind_norm] theorem Int.lt_eq (a b : Int) : (a < b) = (a + 1 ≤ b) := by
+theorem Int.lt_eq (a b : Int) : (a < b) = (a + 1 ≤ b) := by
   simp [Int.lt, LT.lt]
 
--- GT GE
-attribute [grind_norm] GT.gt GE.ge
+theorem ge_eq [LE α] (a b : α) : (a ≥ b) = (b ≤ a) := rfl
+theorem gt_eq [LT α] (a b : α) : (a > b) = (b < a) := rfl
 
--- Succ
-attribute [grind_norm] Nat.succ_eq_add_one
+init_grind_norm
+  /- Pre theorems -/
+  not_and not_or not_ite not_forall not_exists
+  |
+  /- Post theorems -/
+  Classical.not_not
+  ne_eq iff_eq eq_self heq_eq_eq
+  -- Prop equality
+  eq_true_eq eq_false_eq not_eq_prop
+  -- True
+  not_true
+  -- False
+  not_false_eq_true
+  -- Implication
+  true_imp_eq false_imp_eq imp_true_eq imp_false_eq imp_self_eq
+  -- And
+  and_true true_and and_false false_and and_assoc
+  -- Or
+  or_true true_or or_false false_or or_assoc
+  -- ite
+  ite_true ite_false ite_true_false ite_false_true
+  -- Forall
+  forall_and
+  -- Exists
+  exists_const exists_or exists_prop exists_and_left exists_and_right
+  -- Bool cond
+  cond_eq_ite
+  -- Bool or
+  Bool.or_false Bool.or_true Bool.false_or Bool.true_or Bool.or_eq_true Bool.or_assoc
+  -- Bool and
+  Bool.and_false Bool.and_true Bool.false_and Bool.true_and Bool.and_eq_true Bool.and_assoc
+  -- Bool not
+  Bool.not_not
+  -- beq
+  beq_iff_eq
+  -- bne
+  bne_iff_ne
+  -- Bool not eq true/false
+  Bool.not_eq_true Bool.not_eq_false
+  -- decide
+  decide_eq_true_eq decide_not not_decide_eq_true
+  -- Nat LE
+  Nat.le_zero_eq
+  -- Nat/Int LT
+  Nat.lt_eq
+  -- Nat.succ
+  Nat.succ_eq_add_one
+  -- Int
+  Int.lt_eq
+  -- GT GE
+  ge_eq gt_eq
 
 end Lean.Grind

src/Init/Grind/Offset.lean

@@ -7,159 +7,86 @@ prelude
 import Init.Core
 import Init.Omega
 
-namespace Lean.Grind.Offset
+namespace Lean.Grind
+abbrev isLt (x y : Nat) : Bool := x < y
+abbrev isLE (x y : Nat) : Bool := x ≤ y
 
-abbrev Var := Nat
-abbrev Context := Lean.RArray Nat
+/-! Theorems for transitivity. -/
+theorem Nat.le_ro (u w v k : Nat) : u ≤ w → w ≤ v + k → u ≤ v + k := by
+  omega
+theorem Nat.le_lo (u w v k : Nat) : u ≤ w → w + k ≤ v → u + k ≤ v := by
+  omega
+theorem Nat.lo_le (u w v k : Nat) : u + k ≤ w → w ≤ v → u + k ≤ v := by
+  omega
+theorem Nat.lo_lo (u w v k₁ k₂ : Nat) : u + k₁ ≤ w → w + k₂ ≤ v → u + (k₁ + k₂) ≤ v := by
+  omega
+theorem Nat.lo_ro_1 (u w v k₁ k₂ : Nat) : isLt k₂ k₁ = true → u + k₁ ≤ w → w ≤ v + k₂ → u + (k₁ - k₂) ≤ v := by
+  simp [isLt]; omega
+theorem Nat.lo_ro_2 (u w v k₁ k₂ : Nat) : u + k₁ ≤ w → w ≤ v + k₂ → u ≤ v + (k₂ - k₁) := by
+  omega
+theorem Nat.ro_le (u w v k : Nat) : u ≤ w + k → w ≤ v → u ≤ v + k := by
+  omega
+theorem Nat.ro_lo_1 (u w v k₁ k₂ : Nat) : u ≤ w + k₁ → w + k₂ ≤ v → u ≤ v + (k₁ - k₂) := by
+  omega
+theorem Nat.ro_lo_2 (u w v k₁ k₂ : Nat) : isLt k₁ k₂ = true → u ≤ w + k₁ → w + k₂ ≤ v → u + (k₂ - k₁) ≤ v := by
+  simp [isLt]; omega
+theorem Nat.ro_ro (u w v k₁ k₂ : Nat) : u ≤ w + k₁ → w ≤ v + k₂ → u ≤ v + (k₁ + k₂) := by
+  omega
 
-def fixedVar := 100000000 -- Any big number should work here
+/-! Theorems for negating constraints. -/
+theorem Nat.of_le_eq_false (u v : Nat) : ((u ≤ v) = False) → v + 1 ≤ u := by
+  simp; omega
+theorem Nat.of_lo_eq_false_1 (u v : Nat) : ((u + 1 ≤ v) = False) → v ≤ u := by
+  simp; omega
+theorem Nat.of_lo_eq_false (u v k : Nat) : ((u + k ≤ v) = False) → v ≤ u + (k-1) := by
+  simp; omega
+theorem Nat.of_ro_eq_false (u v k : Nat) : ((u ≤ v + k) = False) → v + (k+1) ≤ u := by
+  simp; omega
 
-def Var.denote (ctx : Context) (v : Var) : Nat :=
-  bif v == fixedVar then 1 else ctx.get v
+/-! Theorems for closing a goal. -/
+theorem Nat.unsat_le_lo (u v k : Nat) : isLt 0 k = true → u ≤ v → v + k ≤ u → False := by
+  simp [isLt]; omega
+theorem Nat.unsat_lo_lo (u v k₁ k₂ : Nat) : isLt 0 (k₁+k₂) = true → u + k₁ ≤ v → v + k₂ ≤ u → False := by
+  simp [isLt]; omega
+theorem Nat.unsat_lo_ro (u v k₁ k₂ : Nat) : isLt k₂ k₁ = true → u + k₁ ≤ v → v ≤ u + k₂ → False := by
+  simp [isLt]; omega
 
-structure Cnstr where
-  x : Var
-  y : Var
-  k : Nat  := 0
-  l : Bool := true
-  deriving Repr, DecidableEq, Inhabited
+/-! Theorems for propagating constraints to `True` -/
+theorem Nat.lo_eq_true_of_lo (u v k₁ k₂ : Nat) : isLE k₂ k₁ = true → u + k₁ ≤ v → (u + k₂ ≤ v) = True :=
+  by simp [isLt]; omega
+theorem Nat.le_eq_true_of_lo (u v k : Nat) : u + k ≤ v → (u ≤ v) = True :=
+  by simp; omega
+theorem Nat.le_eq_true_of_le (u v : Nat) : u ≤ v → (u ≤ v) = True :=
+  by simp
+theorem Nat.ro_eq_true_of_lo (u v k₁ k₂ : Nat) : u + k₁ ≤ v → (u ≤ v + k₂) = True :=
+  by simp; omega
+theorem Nat.ro_eq_true_of_le (u v k : Nat) : u ≤ v → (u ≤ v + k) = True :=
+  by simp; omega
+theorem Nat.ro_eq_true_of_ro (u v k₁ k₂ : Nat) : isLE k₁ k₂ = true → u ≤ v + k₁ → (u ≤ v + k₂) = True :=
+  by simp [isLE]; omega
 
-def Cnstr.denote (c : Cnstr) (ctx : Context) : Prop :=
-  if c.l then
-    c.x.denote ctx + c.k ≤ c.y.denote ctx
-  else
-    c.x.denote ctx ≤ c.y.denote ctx + c.k
+/-!
+Theorems for propagating constraints to `False`.
+They are variants of the theorems for closing a goal.
+-/
+theorem Nat.lo_eq_false_of_le (u v k : Nat) : isLt 0 k = true → u ≤ v → (v + k ≤ u) = False := by
+ simp [isLt]; omega
+theorem Nat.le_eq_false_of_lo (u v k : Nat) : isLt 0 k = true → u + k ≤ v → (v ≤ u) = False := by
+ simp [isLt]; omega
+theorem Nat.lo_eq_false_of_lo (u v k₁ k₂ : Nat) : isLt 0 (k₁+k₂) = true → u + k₁ ≤ v → (v + k₂ ≤ u) = False := by
+  simp [isLt]; omega
+theorem Nat.ro_eq_false_of_lo (u v k₁ k₂ : Nat) : isLt k₂ k₁ = true → u + k₁ ≤ v → (v ≤ u + k₂) = False := by
+  simp [isLt]; omega
+theorem Nat.lo_eq_false_of_ro (u v k₁ k₂ : Nat) : isLt k₁ k₂ = true → u ≤ v + k₁ → (v + k₂ ≤ u) = False := by
+  simp [isLt]; omega
 
-def trivialCnstr : Cnstr := { x := 0, y := 0, k := 0, l := true }
+/-!
+Helper theorems for equality propagation
+-/
 
-@[simp] theorem denote_trivial (ctx : Context) : trivialCnstr.denote ctx := by
-  simp [Cnstr.denote, trivialCnstr]
+theorem Nat.le_of_eq_1 (u v : Nat) : u = v → u ≤ v := by omega
+theorem Nat.le_of_eq_2 (u v : Nat) : u = v → v ≤ u := by omega
+theorem Nat.eq_of_le_of_le (u v : Nat) : u ≤ v → v ≤ u → u = v := by omega
+theorem Nat.le_offset (a k : Nat) : k ≤ a + k := by omega
 
-def Cnstr.trans (c₁ c₂ : Cnstr) : Cnstr :=
-  if c₁.y = c₂.x then
-    let { x, k := k₁, l := l₁, .. } := c₁
-    let { y, k := k₂, l := l₂, .. } := c₂
-    match l₁, l₂ with
-    | false, false =>
-      { x, y, k := k₁ + k₂, l := false }
-    | false, true =>
-      if k₁ < k₂ then
-        { x, y, k := k₂ - k₁, l := true }
-      else
-        { x, y, k := k₁ - k₂, l := false }
-    | true, false =>
-      if k₁ < k₂ then
-        { x, y, k := k₂ - k₁, l := false }
-      else
-        { x, y, k := k₁ - k₂, l := true }
-    | true, true =>
-      { x, y, k := k₁ + k₂, l := true }
-  else
-    trivialCnstr
-
-@[simp] theorem Cnstr.denote_trans_easy (ctx : Context) (c₁ c₂ : Cnstr) (h : c₁.y ≠ c₂.x) : (c₁.trans c₂).denote ctx := by
-  simp [*, Cnstr.trans]
-
-@[simp] theorem Cnstr.denote_trans (ctx : Context) (c₁ c₂ : Cnstr) : c₁.denote ctx → c₂.denote ctx → (c₁.trans c₂).denote ctx := by
-  by_cases c₁.y = c₂.x
-  case neg => simp [*]
-  simp [trans, *]
-  let { x, k := k₁, l := l₁, .. } := c₁
-  let { y, k := k₂, l := l₂, .. } := c₂
-  simp_all; split
-  · simp [denote]; omega
-  · split <;> simp [denote] <;> omega
-  · split <;> simp [denote] <;> omega
-  · simp [denote]; omega
-
-def Cnstr.isTrivial (c : Cnstr) : Bool := c.x == c.y && c.k == 0
-
-theorem Cnstr.of_isTrivial (ctx : Context) (c : Cnstr) : c.isTrivial = true → c.denote ctx := by
-  cases c; simp [isTrivial]; intros; simp [*, denote]
-
-def Cnstr.isFalse (c : Cnstr) : Bool := c.x == c.y && c.k != 0 && c.l == true
-
-theorem Cnstr.of_isFalse (ctx : Context) {c : Cnstr} : c.isFalse = true → ¬c.denote ctx := by
-  cases c; simp [isFalse]; intros; simp [*, denote]; omega
-
-def Cnstrs := List Cnstr
-
-def Cnstrs.denoteAnd' (ctx : Context) (c₁ : Cnstr) (c₂ : Cnstrs) : Prop :=
-  match c₂ with
-  | [] => c₁.denote ctx
-  | c::cs => c₁.denote ctx ∧ Cnstrs.denoteAnd' ctx c cs
-
-theorem Cnstrs.denote'_trans (ctx : Context) (c₁ c : Cnstr) (cs : Cnstrs) : c₁.denote ctx → denoteAnd' ctx c cs → denoteAnd' ctx (c₁.trans c) cs := by
-  induction cs
-  next => simp [denoteAnd', *]; apply Cnstr.denote_trans
-  next c cs ih => simp [denoteAnd']; intros; simp [*]
-
-def Cnstrs.trans' (c₁ : Cnstr) (c₂ : Cnstrs) : Cnstr :=
-  match c₂ with
-  | [] => c₁
-  | c::c₂ => trans' (c₁.trans c) c₂
-
-@[simp] theorem Cnstrs.denote'_trans' (ctx : Context) (c₁ : Cnstr) (c₂ : Cnstrs) : denoteAnd' ctx c₁ c₂ → (trans' c₁ c₂).denote ctx := by
-  induction c₂ generalizing c₁
-  next => intros; simp_all [trans', denoteAnd']
-  next c cs ih => simp [denoteAnd']; intros; simp [trans']; apply ih; apply denote'_trans <;> assumption
-
-def Cnstrs.denoteAnd (ctx : Context) (c : Cnstrs) : Prop :=
-  match c with
-  | [] => True
-  | c::cs => denoteAnd' ctx c cs
-
-def Cnstrs.trans (c : Cnstrs) : Cnstr :=
-  match c with
-  | []    => trivialCnstr
-  | c::cs => trans' c cs
-
-theorem Cnstrs.of_denoteAnd_trans {ctx : Context} {c : Cnstrs} : c.denoteAnd ctx → c.trans.denote ctx := by
-  cases c <;> simp [*, trans, denoteAnd] <;> intros <;> simp [*]
-
-def Cnstrs.isFalse (c : Cnstrs) : Bool :=
-  c.trans.isFalse
-
-theorem Cnstrs.unsat' (ctx : Context) (c : Cnstrs) : c.isFalse = true → ¬ c.denoteAnd ctx := by
-  simp [isFalse]; intro h₁ h₂
-  have := of_denoteAnd_trans h₂
-  have := Cnstr.of_isFalse ctx h₁
-  contradiction
-
-/-- `denote ctx [c_1, ..., c_n] C` is `c_1.denote ctx → ... → c_n.denote ctx → C` -/
-def Cnstrs.denote (ctx : Context) (cs : Cnstrs) (C : Prop) : Prop :=
-  match cs with
-  | [] => C
-  | c::cs => c.denote ctx → denote ctx cs C
-
-theorem Cnstrs.not_denoteAnd'_eq (ctx : Context) (c : Cnstr) (cs : Cnstrs) (C : Prop) : (denoteAnd' ctx c cs → C) = denote ctx (c::cs) C := by
-  simp [denote]
-  induction cs generalizing c
-  next => simp [denoteAnd', denote]
-  next c' cs ih =>
-    simp [denoteAnd', denote, *]
-
-theorem Cnstrs.not_denoteAnd_eq (ctx : Context) (cs : Cnstrs) (C : Prop) : (denoteAnd ctx cs → C) = denote ctx cs C := by
-  cases cs
-  next => simp [denoteAnd, denote]
-  next c cs => apply not_denoteAnd'_eq
-
-def Cnstr.isImpliedBy (cs : Cnstrs) (c : Cnstr) : Bool :=
-  cs.trans == c
-
-/-! Main theorems used by `grind`. -/
-
-/-- Auxiliary theorem used by `grind` to prove that a system of offset inequalities is unsatisfiable. -/
-theorem Cnstrs.unsat (ctx : Context) (cs : Cnstrs) : cs.isFalse = true → cs.denote ctx False := by
-  intro h
-  rw [← not_denoteAnd_eq]
-  apply unsat'
-  assumption
-
-/-- Auxiliary theorem used by `grind` to prove an implied offset inequality. -/
-theorem Cnstrs.imp (ctx : Context) (cs : Cnstrs) (c : Cnstr) (h : c.isImpliedBy cs = true)  : cs.denote ctx (c.denote ctx) := by
-  rw [← eq_of_beq h]
-  rw [← not_denoteAnd_eq]
-  apply of_denoteAnd_trans
-
-end Lean.Grind.Offset
+end Lean.Grind

src/Init/Grind/PP.lean

@@ -0,0 +1,30 @@
+/-
+Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.NotationExtra
+
+namespace Lean.Grind
+/-!
+This is a hackish module for hovering node information in the `grind` tactic state.
+-/
+
+inductive NodeDef where
+  | unit
+
+set_option linter.unusedVariables false in
+def node_def (_ : Nat) {α : Sort u} {a : α} : NodeDef := .unit
+
+@[app_unexpander node_def]
+def nodeDefUnexpander : PrettyPrinter.Unexpander := fun stx => do
+  match stx with
+  | `($_ $id:num) => return mkIdent <| Name.mkSimple $ "#" ++ toString id.getNat
+  | _ => throw ()
+
+@[app_unexpander NodeDef]
+def NodeDefUnexpander : PrettyPrinter.Unexpander := fun _ => do
+  return mkIdent <| Name.mkSimple "NodeDef"
+
+end Lean.Grind

src/Init/Grind/Tactics.lean

@@ -14,7 +14,9 @@ syntax grindEqRhs  := atomic("=" "_")
 syntax grindBwd    := "←"
 syntax grindFwd    := "→"
 
-syntax (name := grind) "grind" (grindEqBoth <|> grindEqRhs <|> grindEq <|> grindBwd <|> grindFwd)? : attr
+syntax grindThmMod := grindEqBoth <|> grindEqRhs <|> grindEq <|> grindBwd <|> grindFwd
+
+syntax (name := grind) "grind" (grindThmMod)? : attr
 
 end Lean.Parser.Attr
 
@@ -25,7 +27,7 @@ Passed to `grind` using, for example, the `grind (config := { matchEqs := true }
 -/
 structure Config where
   /-- Maximum number of case-splits in a proof search branch. It does not include splits performed during normalization. -/
-  splits : Nat := 5
+  splits : Nat := 8
   /-- Maximum number of E-matching (aka heuristic theorem instantiation) rounds before each case split. -/
   ematch : Nat := 5
   /--
@@ -45,6 +47,12 @@ structure Config where
   If `splitIndPred` is `true`, `grind` performs case-splitting on inductive predicates.
   Otherwise, it performs case-splitting only on types marked with `[grind_split]` attribute. -/
   splitIndPred : Bool := true
+  /-- By default, `grind` halts as soon as it encounters a sub-goal where no further progress can be made. -/
+  failures : Nat := 1
+  /-- Maximum number of heartbeats (in thousands) the canonicalizer can spend per definitional equality test. -/
+  canonHeartbeats : Nat := 1000
+  /-- If `ext` is `true`, `grind` uses extensionality theorems available in the environment. -/
+  ext : Bool := true
   deriving Inhabited, BEq
 
 end Lean.Grind
@@ -55,7 +63,13 @@ namespace Lean.Parser.Tactic
 `grind` tactic and related tactics.
 -/
 
--- TODO: parameters
-syntax (name := grind) "grind" optConfig ("on_failure " term)? : tactic
+syntax grindErase := "-" ident
+syntax grindLemma := (Attr.grindThmMod)? ident
+syntax grindParam := grindErase <|> grindLemma
+
+syntax (name := grind)
+  "grind" optConfig (&" only")?
+  (" [" withoutPosition(grindParam,*) "]")?
+  ("on_failure " term)? : tactic
 
 end Lean.Parser.Tactic

src/Init/Grind/Util.lean

@@ -9,7 +9,7 @@ import Init.Core
 namespace Lean.Grind
 
 /-- A helper gadget for annotating nested proofs in goals. -/
-def nestedProof (p : Prop) (h : p) : p := h
+def nestedProof (p : Prop) {h : p} : p := h
 
 /--
 Gadget for marking terms that should not be normalized by `grind`s simplifier.
@@ -28,7 +28,7 @@ When `EqMatch a b origin` is `True`, we mark `origin` as a resolved case-split.
 -/
 def EqMatch (a b : α) {_origin : α} : Prop := a = b
 
-theorem nestedProof_congr (p q : Prop) (h : p = q) (hp : p) (hq : q) : HEq (nestedProof p hp) (nestedProof q hq) := by
+theorem nestedProof_congr (p q : Prop) (h : p = q) (hp : p) (hq : q) : HEq (@nestedProof p hp) (@nestedProof q hq) := by
   subst h; apply HEq.refl
 
 end Lean.Grind

src/Init/Prelude.lean

@@ -150,6 +150,9 @@ It can also be written as `()`.
 /-- Marker for information that has been erased by the code generator. -/
 unsafe axiom lcErased : Type
 
+/-- Marker for type dependency that has been erased by the code generator. -/
+unsafe axiom lcAny : Type
+
 /--
 Auxiliary unsafe constant used by the Compiler when erasing proofs from code.
 

src/Init/Tactics.lean

@@ -1648,17 +1648,6 @@ If there are several with the same priority, it is uses the "most recent one". E
 -/
 syntax (name := simp) "simp" (Tactic.simpPre <|> Tactic.simpPost)? patternIgnore("← " <|> "<- ")? (ppSpace prio)? : attr
 
-/--
-Theorems tagged with the `grind_norm` attribute are used by the `grind` tactic normalizer/pre-processor.
--/
-syntax (name := grind_norm) "grind_norm" (Tactic.simpPre <|> Tactic.simpPost)? (ppSpace prio)? : attr
-
-/--
-Simplification procedures tagged with the `grind_norm_proc` attribute are used by the `grind` tactic normalizer/pre-processor.
--/
-syntax (name := grind_norm_proc) "grind_norm_proc" (Tactic.simpPre <|> Tactic.simpPost)? : attr
-
-
 /-- The possible `norm_cast` kinds: `elim`, `move`, or `squash`. -/
 syntax normCastLabel := &"elim" <|> &"move" <|> &"squash"
 

src/Lean/AddDecl.lean

@@ -14,26 +14,54 @@ register_builtin_option debug.skipKernelTC : Bool := {
   descr    := "skip kernel type checker. WARNING: setting this option to true may compromise soundness because your proofs will not be checked by the Lean kernel"
 }
 
-def Environment.addDecl (env : Environment) (opts : Options) (decl : Declaration)
-    (cancelTk? : Option IO.CancelToken := none) : Except KernelException Environment :=
+/-- Adds given declaration to the environment, respecting `debug.skipKernelTC`. -/
+def Kernel.Environment.addDecl (env : Environment) (opts : Options) (decl : Declaration)
+    (cancelTk? : Option IO.CancelToken := none) : Except Exception Environment :=
   if debug.skipKernelTC.get opts then
     addDeclWithoutChecking env decl
   else
     addDeclCore env (Core.getMaxHeartbeats opts).toUSize decl cancelTk?
 
-def Environment.addAndCompile (env : Environment) (opts : Options) (decl : Declaration)
-    (cancelTk? : Option IO.CancelToken := none) : Except KernelException Environment := do
-  let env ← addDecl env opts decl cancelTk?
-  compileDecl env opts decl
+private def Environment.addDeclAux (env : Environment) (opts : Options) (decl : Declaration)
+    (cancelTk? : Option IO.CancelToken := none) : Except Kernel.Exception Environment :=
+  env.addDeclCore (Core.getMaxHeartbeats opts).toUSize decl cancelTk? (!debug.skipKernelTC.get opts)
+
+@[deprecated "use `Lean.addDecl` instead to ensure new namespaces are registered" (since := "2024-12-03")]
+def Environment.addDecl (env : Environment) (opts : Options) (decl : Declaration)
+    (cancelTk? : Option IO.CancelToken := none) : Except Kernel.Exception Environment :=
+  Environment.addDeclAux env opts decl cancelTk?
+
+private def isNamespaceName : Name → Bool
+  | .str .anonymous _ => true
+  | .str p _          => isNamespaceName p
+  | _                 => false
+
+private def registerNamePrefixes (env : Environment) (name : Name) : Environment :=
+  match name with
+    | .str _ s =>
+      if s.get 0 == '_' then
+        -- Do not register namespaces that only contain internal declarations.
+        env
+      else
+        go env name
+    | _ => env
+where go env
+  | .str p _ => if isNamespaceName p then go (env.registerNamespace p) p else env
+  | _        => env
 
 def addDecl (decl : Declaration) : CoreM Unit := do
   profileitM Exception "type checking" (← getOptions) do
-    withTraceNode `Kernel (fun _ => return m!"typechecking declaration") do
+    let mut env ← withTraceNode `Kernel (fun _ => return m!"typechecking declaration") do
       if !(← MonadLog.hasErrors) && decl.hasSorry then
         logWarning "declaration uses 'sorry'"
-      match (← getEnv).addDecl (← getOptions) decl (← read).cancelTk? with
-      | .ok    env => setEnv env
-      | .error ex  => throwKernelException ex
+      (← getEnv).addDeclAux (← getOptions) decl (← read).cancelTk? |> ofExceptKernelException
+
+    -- register namespaces for newly added constants; this used to be done by the kernel itself
+    -- but that is incompatible with moving it to a separate task
+    env := decl.getNames.foldl registerNamePrefixes env
+    if let .inductDecl _ _ types _ := decl then
+      env := types.foldl (registerNamePrefixes · <| ·.name ++ `rec) env
+    setEnv env
 
 def addAndCompile (decl : Declaration) : CoreM Unit := do
   addDecl decl

src/Lean/Compiler/InitAttr.lean

@@ -144,11 +144,7 @@ def declareBuiltin (forDecl : Name) (value : Expr) : CoreM Unit := do
   let type := mkApp (mkConst `IO) (mkConst `Unit)
   let decl := Declaration.defnDecl { name, levelParams := [], type, value, hints := ReducibilityHints.opaque,
                                      safety := DefinitionSafety.safe }
-  match (← getEnv).addAndCompile {} decl with
-  -- TODO: pretty print error
-  | Except.error e => do
-    let msg ← (e.toMessageData {}).toString
-    throwError "failed to emit registration code for builtin '{forDecl}': {msg}"
-  | Except.ok env  => IO.ofExcept (setBuiltinInitAttr env name) >>= setEnv
+  addAndCompile decl
+  IO.ofExcept (setBuiltinInitAttr (← getEnv) name) >>= setEnv
 
 end Lean

src/Lean/Compiler/LCNF/MonoTypes.lean

@@ -74,8 +74,6 @@ partial def toMonoType (type : Expr) : CoreM Expr := do
   let type := type.headBeta
   if type.isErased then
     return erasedExpr
-  else if type.isErased then
-    return erasedExpr
   else if isTypeFormerType type then
     return erasedExpr
   else match type with

src/Lean/Compiler/LCNF/ToMono.lean

@@ -150,18 +150,7 @@ where
 
 def toMono : Pass where
   name     := `toMono
-  run      := fun decls => do
-    let decls ← decls.filterM fun decl => do
-      if hasLocalInst decl.type then
-        /-
-        Declaration is a "template" for the code specialization pass.
-        So, we should delete it before going to next phase.
-        -/
-        decl.erase
-        return false
-      else
-        return true
-    decls.mapM (·.toMono)
+  run      := (·.mapM (·.toMono))
   phase    := .base
   phaseOut := .mono
 

src/Lean/Compiler/Old.lean

@@ -53,18 +53,3 @@ def isUnsafeRecName? : Name → Option Name
   | _ => none
 
 end Compiler
-
-namespace Environment
-
-/--
-Compile the given block of mutual declarations.
-Assumes the declarations have already been added to the environment using `addDecl`.
--/
-@[extern "lean_compile_decls"]
-opaque compileDecls (env : Environment) (opt : @& Options) (decls : @& List Name) : Except KernelException Environment
-
-/-- Compile the given declaration, it assumes the declaration has already been added to the environment using `addDecl`. -/
-def compileDecl (env : Environment) (opt : @& Options) (decl : @& Declaration) : Except KernelException Environment :=
-  compileDecls env opt (Compiler.getDeclNamesForCodeGen decl)
-
-end Environment

src/Lean/CoreM.lean

@@ -514,16 +514,19 @@ register_builtin_option compiler.enableNew : Bool := {
 @[extern "lean_lcnf_compile_decls"]
 opaque compileDeclsNew (declNames : List Name) : CoreM Unit
 
+@[extern "lean_compile_decls"]
+opaque compileDeclsOld (env : Environment) (opt : @& Options) (decls : @& List Name) : Except Kernel.Exception Environment
+
 def compileDecl (decl : Declaration) : CoreM Unit := do
   let opts ← getOptions
   let decls := Compiler.getDeclNamesForCodeGen decl
   if compiler.enableNew.get opts then
     compileDeclsNew decls
   let res ← withTraceNode `compiler (fun _ => return m!"compiling old: {decls}") do
-    return (← getEnv).compileDecl opts decl
+    return compileDeclsOld (← getEnv) opts decls
   match res with
   | Except.ok env => setEnv env
-  | Except.error (KernelException.other msg) =>
+  | Except.error (.other msg) =>
     checkUnsupported decl -- Generate nicer error message for unsupported recursors and axioms
     throwError msg
   | Except.error ex =>
@@ -533,9 +536,9 @@ def compileDecls (decls : List Name) : CoreM Unit := do
   let opts ← getOptions
   if compiler.enableNew.get opts then
     compileDeclsNew decls
-  match (← getEnv).compileDecls opts decls with
+  match compileDeclsOld (← getEnv) opts decls with
   | Except.ok env   => setEnv env
-  | Except.error (KernelException.other msg) =>
+  | Except.error (.other msg) =>
     throwError msg
   | Except.error ex =>
     throwKernelException ex

src/Lean/Data/AssocList.lean

@@ -24,7 +24,7 @@ abbrev empty : AssocList α β :=
 
 instance : EmptyCollection (AssocList α β) := ⟨empty⟩
 
-abbrev insert (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
+abbrev insertNew (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
   m.cons k v
 
 def isEmpty : AssocList α β → Bool
@@ -77,6 +77,12 @@ def replace [BEq α] (a : α) (b : β) : AssocList α β → AssocList α β
     | true  => cons a b es
     | false => cons k v (replace a b es)
 
+def insert [BEq α] (m : AssocList α β) (k : α) (v : β) : AssocList α β :=
+  if m.contains k then
+    m.replace k v
+  else
+    m.insertNew k v
+
 def erase [BEq α] (a : α) : AssocList α β → AssocList α β
   | nil         => nil
   | cons k v es => match k == a with

src/Lean/Data/NameTrie.lean

@@ -54,6 +54,10 @@ instance : EmptyCollection (NameTrie β) where
 def NameTrie.find? (t : NameTrie β) (k : Name) : Option β :=
   PrefixTree.find? t (toKey k)
 
+@[inline, inherit_doc PrefixTree.findLongestPrefix?]
+def NameTrie.findLongestPrefix? (t : NameTrie β) (k : Name) : Option β :=
+  PrefixTree.findLongestPrefix? t (toKey k)
+
 @[inline]
 def NameTrie.foldMatchingM [Monad m] (t : NameTrie β) (k : Name) (init : σ) (f : β → σ → m σ) : m σ :=
   PrefixTree.foldMatchingM t (toKey k) init f

src/Lean/Data/PrefixTree.lean

@@ -48,6 +48,17 @@ partial def find? (t : PrefixTreeNode α β) (cmp : α → α → Ordering) (k :
       | some t => loop t ks
   loop t k
 
+/-- Returns the the value of the longest key in `t` that is a prefix of `k`, if any. -/
+@[specialize]
+partial def findLongestPrefix? (t : PrefixTreeNode α β) (cmp : α → α → Ordering) (k : List α) : Option β :=
+  let rec loop acc?
+    | PrefixTreeNode.Node val _, [] => val <|> acc?
+    | PrefixTreeNode.Node val m, k :: ks =>
+      match RBNode.find cmp m k with
+      | none   => val
+      | some t => loop (val <|> acc?) t ks
+  loop none t k
+
 @[specialize]
 partial def foldMatchingM [Monad m] (t : PrefixTreeNode α β) (cmp : α → α → Ordering) (k : List α) (init : σ) (f : β → σ → m σ) : m σ :=
   let rec fold : PrefixTreeNode α β → σ → m σ
@@ -92,6 +103,10 @@ def PrefixTree.insert (t : PrefixTree α β p) (k : List α) (v : β) : PrefixTr
 def PrefixTree.find? (t : PrefixTree α β p) (k : List α) : Option β :=
   t.val.find? p k
 
+@[inline, inherit_doc PrefixTreeNode.findLongestPrefix?]
+def PrefixTree.findLongestPrefix? (t : PrefixTree α β p) (k : List α) : Option β :=
+  t.val.findLongestPrefix? p k
+
 @[inline]
 def PrefixTree.foldMatchingM [Monad m] (t : PrefixTree α β p) (k : List α) (init : σ) (f : β → σ → m σ) : m σ :=
   t.val.foldMatchingM p k init f

src/Lean/Declaration.lean

@@ -193,6 +193,19 @@ def Declaration.definitionVal! : Declaration → DefinitionVal
   | .defnDecl val => val
   | _ => panic! "Expected a `Declaration.defnDecl`."
 
+/--
+Returns all top-level names to be defined by adding this declaration to the environment. This does
+not include auxiliary definitions such as projections.
+-/
+def Declaration.getNames : Declaration → List Name
+  | .axiomDecl val          => [val.name]
+  | .defnDecl val           => [val.name]
+  | .thmDecl val            => [val.name]
+  | .opaqueDecl val         => [val.name]
+  | .quotDecl               => [``Quot, ``Quot.mk, ``Quot.lift, ``Quot.ind]
+  | .mutualDefnDecl defns   => defns.map (·.name)
+  | .inductDecl _ _ types _ => types.map (·.name)
+
 @[specialize] def Declaration.foldExprM {α} {m : Type → Type} [Monad m] (d : Declaration) (f : α → Expr → m α) (a : α) : m α :=
   match d with
   | .quotDecl                                        => pure a
@@ -469,6 +482,10 @@ def isInductive : ConstantInfo → Bool
   | .inductInfo _ => true
   | _             => false
 
+def isDefinition : ConstantInfo → Bool
+  | .defnInfo _ => true
+  | _           => false
+
 def isTheorem : ConstantInfo → Bool
   | .thmInfo _ => true
   | _          => false

src/Lean/Elab/App.lean

@@ -1474,7 +1474,7 @@ where
     | field::fields, false => .fieldName field field.getId.getString! none fIdent :: toLVals fields false
 
 /-- Resolve `(.$id:ident)` using the expected type to infer namespace. -/
-private partial def resolveDotName (id : Syntax) (expectedType? : Option Expr) : TermElabM Name := do
+private partial def resolveDotName (id : Syntax) (expectedType? : Option Expr) : TermElabM Expr := do
   tryPostponeIfNoneOrMVar expectedType?
   let some expectedType := expectedType?
     | throwError "invalid dotted identifier notation, expected type must be known"
@@ -1489,7 +1489,7 @@ where
         withForallBody body k
       else
         k body
-  go (resultType : Expr) (expectedType : Expr) (previousExceptions : Array Exception) : TermElabM Name := do
+  go (resultType : Expr) (expectedType : Expr) (previousExceptions : Array Exception) : TermElabM Expr := do
     let resultType ← instantiateMVars resultType
     let resultTypeFn := resultType.cleanupAnnotations.getAppFn
     try
@@ -1497,9 +1497,12 @@ where
       let .const declName .. := resultTypeFn.cleanupAnnotations
         | throwError "invalid dotted identifier notation, expected type is not of the form (... → C ...) where C is a constant{indentExpr expectedType}"
       let idNew := declName ++ id.getId.eraseMacroScopes
-      unless (← getEnv).contains idNew do
+      if (← getEnv).contains idNew then
+        mkConst idNew
+      else if let some (fvar, []) ← resolveLocalName idNew then
+        return fvar
+      else
         throwError "invalid dotted identifier notation, unknown identifier `{idNew}` from expected type{indentExpr expectedType}"
-      return idNew
     catch
       | ex@(.error ..) =>
         match (← unfoldDefinition? resultType) with
@@ -1548,7 +1551,7 @@ private partial def elabAppFn (f : Syntax) (lvals : List LVal) (namedArgs : Arra
     | `(_)       => throwError "placeholders '_' cannot be used where a function is expected"
     | `(.$id:ident) =>
         addCompletionInfo <| CompletionInfo.dotId f id.getId (← getLCtx) expectedType?
-        let fConst ← mkConst (← resolveDotName id expectedType?)
+        let fConst ← resolveDotName id expectedType?
         let s ← observing do
           -- Use (force := true) because we want to record the result of .ident resolution even in patterns
           let fConst ← addTermInfo f fConst expectedType? (force := true)

src/Lean/Elab/BuiltinCommand.lean

@@ -124,9 +124,7 @@ private partial def elabChoiceAux (cmds : Array Syntax) (i : Nat) : CommandElabM
   n[1].forArgsM addUnivLevel
 
 @[builtin_command_elab «init_quot»] def elabInitQuot : CommandElab := fun _ => do
-  match (← getEnv).addDecl (← getOptions) Declaration.quotDecl with
-  | Except.ok env   => setEnv env
-  | Except.error ex => throwError (ex.toMessageData (← getOptions))
+  liftCoreM <| addDecl Declaration.quotDecl
 
 @[builtin_command_elab «export»] def elabExport : CommandElab := fun stx => do
   let `(export $ns ($ids*)) := stx | throwUnsupportedSyntax
@@ -294,7 +292,7 @@ def failIfSucceeds (x : CommandElabM Unit) : CommandElabM Unit := do
     modify fun s => { s with messages := {} };
     pure messages
   let restoreMessages (prevMessages : MessageLog) : CommandElabM Unit := do
-    modify fun s => { s with messages := prevMessages ++ s.messages.errorsToWarnings }
+    modify fun s => { s with messages := prevMessages ++ s.messages.errorsToInfos }
   let prevMessages ← resetMessages
   let succeeded ← try
     x

src/Lean/Elab/Import.lean

@@ -5,7 +5,7 @@ Authors: Leonardo de Moura, Sebastian Ullrich
 -/
 prelude
 import Lean.Parser.Module
-import Lean.Data.Json
+import Lean.Util.Paths
 
 namespace Lean.Elab
 
@@ -42,4 +42,12 @@ def printImports (input : String) (fileName : Option String) : IO Unit := do
     let fname ← findOLean dep.module
     IO.println fname
 
+@[export lean_print_import_srcs]
+def printImportSrcs (input : String) (fileName : Option String) : IO Unit := do
+  let sp ← initSrcSearchPath
+  let (deps, _, _) ← parseImports input fileName
+  for dep in deps do
+    let fname ← findLean sp dep.module
+    IO.println fname
+
 end Lean.Elab

src/Lean/Elab/Structure.lean

@@ -681,7 +681,7 @@ private partial def checkResultingUniversesForFields (fieldInfos : Array StructF
       throwErrorAt info.ref msg
 
 @[extern "lean_mk_projections"]
-private opaque mkProjections (env : Environment) (structName : Name) (projs : List Name) (isClass : Bool) : Except KernelException Environment
+private opaque mkProjections (env : Environment) (structName : Name) (projs : List Name) (isClass : Bool) : Except Kernel.Exception Environment
 
 private def addProjections (r : ElabHeaderResult) (fieldInfos : Array StructFieldInfo) : TermElabM Unit := do
   if r.type.isProp then

src/Lean/Elab/Tactic/BVDecide/Frontend/Attr.lean

@@ -38,6 +38,9 @@ declare_config_elab elabBVDecideConfig Lean.Elab.Tactic.BVDecide.Frontend.BVDeci
 builtin_initialize bvNormalizeExt : Meta.SimpExtension ←
   Meta.registerSimpAttr `bv_normalize "simp theorems used by bv_normalize"
 
+builtin_initialize intToBitVecExt : Meta.SimpExtension ←
+  Meta.registerSimpAttr `int_toBitVec "simp theorems used to convert UIntX/IntX statements into BitVec ones"
+
 /-- Builtin `bv_normalize` simprocs. -/
 builtin_initialize builtinBVNormalizeSimprocsRef : IO.Ref Meta.Simp.Simprocs ← IO.mkRef {}
 

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize.lean

@@ -4,342 +4,28 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Henrik Böving
 -/
 prelude
-import Lean.Meta.AppBuilder
-import Lean.Meta.Tactic.AC.Main
-import Lean.Elab.Tactic.Simp
 import Lean.Elab.Tactic.FalseOrByContra
-import Lean.Elab.Tactic.BVDecide.Frontend.Attr
-import Std.Tactic.BVDecide.Normalize
-import Std.Tactic.BVDecide.Syntax
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Rewrite
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlatten
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.EmbeddedConstraint
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC
 
 /-!
-This module contains the implementation of `bv_normalize` which is effectively a custom `bv_normalize`
-simp set that is called like this: `simp only [seval, bv_normalize]`. The rules in `bv_normalize`
-fulfill two goals:
-1. Turn all hypothesis involving `Bool` and `BitVec` into the form `x = true` where `x` only consists
-   of a operations on `Bool` and `BitVec`. In particular no `Prop` should be contained. This makes
-   the reflection procedure further down the pipeline much easier to implement.
-2. Apply simplification rules from the Bitwuzla SMT solver.
+This module contains the implementation of `bv_normalize`, the preprocessing tactic for `bv_decide`.
+It is in essence a (slightly reduced) version of the Bitwuzla preprocessor together with Lean
+specific details.
 -/
 
 namespace Lean.Elab.Tactic.BVDecide
 namespace Frontend.Normalize
 
 open Lean.Meta
-open Std.Tactic.BVDecide.Normalize
 
-builtin_simproc ↓ [bv_normalize] reduceCond (cond _ _ _) := fun e => do
-  let_expr f@cond α c tb eb := e | return .continue
-  let r ← Simp.simp c
-  if r.expr.cleanupAnnotations.isConstOf ``Bool.true then
-    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_pos f.constLevels!) α c tb eb) (← r.getProof)
-    return .visit { expr := tb, proof? := pr }
-  else if r.expr.cleanupAnnotations.isConstOf ``Bool.false then
-    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_neg f.constLevels!) α c tb eb) (← r.getProof)
-    return .visit { expr := eb, proof? := pr }
-  else
-    return .continue
-
-builtin_simproc [bv_normalize] eqToBEq (((_ : Bool) = (_ : Bool))) := fun e => do
-  let_expr Eq _ lhs rhs := e | return .continue
-  match_expr rhs with
-  | Bool.true => return .continue
-  | _ =>
-    let beqApp ← mkAppM ``BEq.beq #[lhs, rhs]
-    let new := mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) beqApp (mkConst ``Bool.true)
-    let proof := mkApp2 (mkConst ``Bool.eq_to_beq) lhs rhs
-    return .done { expr := new, proof? := some proof }
-
-builtin_simproc [bv_normalize] andOnes ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
-  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
-  let some ⟨w, rhsValue⟩ ← getBitVecValue? rhs | return .continue
-  if rhsValue == -1#w then
-    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.and_ones) (toExpr w) lhs
-    return .visit { expr := lhs, proof? := some proof }
-  else
-    return .continue
-
-builtin_simproc [bv_normalize] onesAnd ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
-  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
-  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
-  if lhsValue == -1#w then
-    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.ones_and) (toExpr w) rhs
-    return .visit { expr := rhs, proof? := some proof }
-  else
-    return .continue
-
-builtin_simproc [bv_normalize] maxUlt (BitVec.ult (_ : BitVec _) (_ : BitVec _)) := fun e => do
-  let_expr BitVec.ult _ lhs rhs := e | return .continue
-  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
-  if lhsValue == -1#w then
-    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.max_ult') (toExpr w) rhs
-    return .visit { expr := toExpr Bool.false, proof? := some proof }
-  else
-    return .continue
-
--- A specialised version of BitVec.neg_eq_not_add so it doesn't trigger on -constant
-builtin_simproc [bv_normalize] neg_eq_not_add (-(_ : BitVec _)) := fun e => do
-  let_expr Neg.neg typ _ val := e | return .continue
-  let_expr BitVec widthExpr := typ | return .continue
-  let some w ← getNatValue? widthExpr | return .continue
-  match ← getBitVecValue? val with
-  | some _ => return .continue
-  | none =>
-    let proof := mkApp2 (mkConst ``BitVec.neg_eq_not_add) (toExpr w) val
-    let expr ← mkAppM ``HAdd.hAdd #[← mkAppM ``Complement.complement #[val], (toExpr 1#w)]
-    return .visit { expr := expr, proof? := some proof }
-
-builtin_simproc [bv_normalize] bv_add_const ((_ : BitVec _) + ((_ : BitVec _) + (_ : BitVec _))) :=
-  fun e => do
-    let_expr HAdd.hAdd _ _ _ _ exp1 rhs := e | return .continue
-    let_expr HAdd.hAdd _ _ _ _ exp2 exp3 := rhs | return .continue
-    let some ⟨w, exp1Val⟩ ←  getBitVecValue? exp1 | return .continue
-    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
-    match ← getBitVecValue? exp2 with
-    | some ⟨w', exp2Val⟩ =>
-      if h : w = w' then
-        let newLhs := exp1Val + h ▸ exp2Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp3]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-    | none =>
-      let some ⟨w', exp3Val⟩ ← getBitVecValue? exp3 | return .continue
-      if h : w = w' then
-        let newLhs := exp1Val + h ▸ exp3Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-
-builtin_simproc [bv_normalize] bv_add_const' (((_ : BitVec _) + (_ : BitVec _)) + (_ : BitVec _)) :=
-  fun e => do
-    let_expr HAdd.hAdd _ _ _ _ lhs exp3 := e | return .continue
-    let_expr HAdd.hAdd _ _ _ _ exp1 exp2 := lhs | return .continue
-    let some ⟨w, exp3Val⟩ ←  getBitVecValue? exp3 | return .continue
-    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
-    match ← getBitVecValue? exp1 with
-    | some ⟨w', exp1Val⟩ =>
-      if h : w = w' then
-        let newLhs := exp3Val + h ▸ exp1Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left'
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-    | none =>
-      let some ⟨w', exp2Val⟩ ← getBitVecValue? exp2 | return .continue
-      if h : w = w' then
-        let newLhs := exp3Val + h ▸ exp2Val
-        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp1]
-        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right'
-        return .visit { expr := expr, proof? := some proof }
-      else
-        return .continue
-
-/-- Return a number `k` such that `2^k = n`. -/
-private def Nat.log2Exact (n : Nat) : Option Nat := do
-  guard <| n ≠ 0
-  let k := n.log2
-  guard <| Nat.pow 2 k == n
-  return k
-
--- Build an expression for `x ^ y`.
-def mkPow (x y : Expr) : MetaM Expr := mkAppM ``HPow.hPow #[x, y]
-
-builtin_simproc [bv_normalize] bv_udiv_of_two_pow (((_ : BitVec _) / (BitVec.ofNat _ _) : BitVec _)) := fun e => do
-  let_expr HDiv.hDiv _α _β _γ _self x y := e | return .continue
-  let some ⟨w, yVal⟩ ← getBitVecValue? y | return .continue
-  let n := yVal.toNat
-  -- BitVec.ofNat w n, where n =def= 2^k
-  let some k := Nat.log2Exact n | return .continue
-  -- check that k < w.
-  if k ≥ w then return .continue
-  let rhs ← mkAppM ``HShiftRight.hShiftRight #[x, mkNatLit k]
-  -- 2^k = n
-  let hk ← mkDecideProof (← mkEq (← mkPow (mkNatLit 2) (mkNatLit k)) (mkNatLit n))
-  -- k < w
-  let hlt ← mkDecideProof (← mkLt (mkNatLit k) (mkNatLit w))
-  let proof := mkAppN (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.udiv_ofNat_eq_of_lt)
-    #[mkNatLit w, x, mkNatLit n, mkNatLit k, hk, hlt]
-  return .done {
-      expr :=  rhs
-      proof? := some proof
-  }
-
-/--
-A pass in the normalization pipeline. Takes the current goal and produces a refined one or closes
-the goal fully, indicated by returning `none`.
--/
-structure Pass where
-  name : Name
-  run : MVarId → MetaM (Option MVarId)
-
-namespace Pass
-
-/--
-Repeatedly run a list of `Pass` until they either close the goal or an iteration doesn't change
-the goal anymore.
--/
-partial def fixpointPipeline (passes : List Pass) (goal : MVarId) : MetaM (Option MVarId) := do
-  let runPass (goal? : Option MVarId) (pass : Pass) : MetaM (Option MVarId) := do
-    let some goal := goal? | return none
-    withTraceNode `bv (fun _ => return s!"Running pass: {pass.name}") do
-      pass.run goal
-
-  let some newGoal := ← passes.foldlM (init := some goal) runPass | return none
-  if goal != newGoal then
-    trace[Meta.Tactic.bv] m!"Rerunning pipeline on:\n{newGoal}"
-    fixpointPipeline passes newGoal
-  else
-    trace[Meta.Tactic.bv] "Pipeline reached a fixpoint"
-    return newGoal
-
-/--
-Responsible for applying the Bitwuzla style rewrite rules.
--/
-def rewriteRulesPass (maxSteps : Nat) : Pass where
-  name := `rewriteRules
-  run goal := do
-    let bvThms ← bvNormalizeExt.getTheorems
-    let bvSimprocs ← bvNormalizeSimprocExt.getSimprocs
-    let sevalThms ← getSEvalTheorems
-    let sevalSimprocs ← Simp.getSEvalSimprocs
-
-    let simpCtx ← Simp.mkContext
-      (config := { failIfUnchanged := false, zetaDelta := true, maxSteps })
-      (simpTheorems := #[bvThms, sevalThms])
-      (congrTheorems := (← getSimpCongrTheorems))
-
-    let hyps ← goal.getNondepPropHyps
-    let ⟨result?, _⟩ ← simpGoal goal
-      (ctx := simpCtx)
-      (simprocs := #[bvSimprocs, sevalSimprocs])
-      (fvarIdsToSimp := hyps)
-    let some (_, newGoal) := result? | return none
-    return newGoal
-
-/--
-Flatten out ands. That is look for hypotheses of the form `h : (x && y) = true` and replace them
-with `h.left : x = true` and `h.right : y = true`. This can enable more fine grained substitutions
-in embedded constraint substitution.
--/
-partial def andFlatteningPass : Pass where
-  name := `andFlattening
-  run goal := do
-    goal.withContext do
-      let hyps ← goal.getNondepPropHyps
-      let mut newHyps := #[]
-      let mut oldHyps := #[]
-      for fvar in hyps do
-        let hyp : Hypothesis := {
-          userName := (← fvar.getDecl).userName
-          type := ← fvar.getType
-          value := mkFVar fvar
-        }
-        let sizeBefore := newHyps.size
-        newHyps ← splitAnds hyp newHyps
-        if newHyps.size > sizeBefore then
-          oldHyps := oldHyps.push fvar
-      if newHyps.size == 0 then
-        return goal
-      else
-        let (_, goal) ← goal.assertHypotheses newHyps
-        -- Given that we collected the hypotheses in the correct order above the invariant is given
-        let goal ← goal.tryClearMany oldHyps
-        return goal
-where
-  splitAnds (hyp : Hypothesis) (hyps : Array Hypothesis) (first : Bool := true) :
-      MetaM (Array Hypothesis) := do
-    match ← trySplit hyp with
-    | some (left, right) =>
-      let hyps ← splitAnds left hyps false
-      splitAnds right hyps false
-    | none =>
-      if first then
-        return hyps
-      else
-        return hyps.push hyp
-
-  trySplit (hyp : Hypothesis) : MetaM (Option (Hypothesis × Hypothesis)) := do
-    let typ := hyp.type
-    let_expr Eq α eqLhs eqRhs := typ | return none
-    let_expr Bool.and lhs rhs := eqLhs | return none
-    let_expr Bool.true := eqRhs | return none
-    let_expr Bool := α | return none
-    let mkEqTrue (lhs : Expr) : Expr :=
-      mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
-    let leftHyp : Hypothesis := {
-      userName := hyp.userName,
-      type := mkEqTrue lhs,
-      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hyp.value
-    }
-    let rightHyp : Hypothesis := {
-      userName := hyp.userName,
-      type := mkEqTrue rhs,
-      value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hyp.value
-    }
-    return some (leftHyp, rightHyp)
-
-/--
-Substitute embedded constraints. That is look for hypotheses of the form `h : x = true` and use
-them to substitute occurences of `x` within other hypotheses. Additionally this drops all
-redundant top level hypotheses.
--/
-def embeddedConstraintPass (maxSteps : Nat) : Pass where
-  name := `embeddedConstraintSubsitution
-  run goal := do
-    goal.withContext do
-      let hyps ← goal.getNondepPropHyps
-      let mut relevantHyps : SimpTheoremsArray := #[]
-      let mut seen : Std.HashSet Expr := {}
-      let mut duplicates : Array FVarId := #[]
-      for hyp in hyps do
-        let typ ← hyp.getType
-        let_expr Eq α lhs rhs := typ | continue
-        let_expr Bool.true := rhs | continue
-        let_expr Bool := α | continue
-        if seen.contains lhs then
-          -- collect and later remove duplicates on the fly
-          duplicates := duplicates.push hyp
-        else
-          seen := seen.insert lhs
-          let localDecl ← hyp.getDecl
-          let proof  := localDecl.toExpr
-          relevantHyps ← relevantHyps.addTheorem (.fvar hyp) proof
-
-      let goal ← goal.tryClearMany duplicates
-
-      let simpCtx ← Simp.mkContext
-        (config := { failIfUnchanged := false, maxSteps })
-        (simpTheorems := relevantHyps)
-        (congrTheorems := (← getSimpCongrTheorems))
-
-      let ⟨result?, _⟩ ← simpGoal goal (ctx := simpCtx) (fvarIdsToSimp := ← goal.getNondepPropHyps)
-      let some (_, newGoal) := result? | return none
-      return newGoal
-
-/--
-Normalize with respect to Associativity and Commutativity.
--/
-def acNormalizePass : Pass where
-  name := `ac_nf
-  run goal := do
-    let mut newGoal := goal
-    for hyp in (← goal.getNondepPropHyps) do
-      let result ← Lean.Meta.AC.acNfHypMeta newGoal hyp
-
-      if let .some nextGoal := result then
-        newGoal := nextGoal
-      else
-        return none
-
-    return newGoal
-
-def passPipeline (cfg : BVDecideConfig) : List Pass := Id.run do
-  let mut passPipeline := [rewriteRulesPass cfg.maxSteps]
+def passPipeline : PreProcessM (List Pass) := do
+  let mut passPipeline := [rewriteRulesPass]
+  let cfg ← PreProcessM.getConfig
 
   if cfg.acNf then
     passPipeline := passPipeline ++ [acNormalizePass]
@@ -348,18 +34,20 @@ def passPipeline (cfg : BVDecideConfig) : List Pass := Id.run do
     passPipeline := passPipeline ++ [andFlatteningPass]
 
   if cfg.embeddedConstraintSubst then
-    passPipeline := passPipeline ++ [embeddedConstraintPass cfg.maxSteps]
+    passPipeline := passPipeline ++ [embeddedConstraintPass]
 
   return passPipeline
 
-end Pass
-
 def bvNormalize (g : MVarId) (cfg : BVDecideConfig) : MetaM (Option MVarId) := do
-  withTraceNode `bv (fun _ => return "Normalizing goal") do
-    -- Contradiction proof
+  withTraceNode `bv (fun _ => return "Preprocessing goal") do
+    (go g).run cfg g
+where
+  go (g : MVarId) : PreProcessM (Option MVarId) := do
     let some g ← g.falseOrByContra | return none
+
     trace[Meta.Tactic.bv] m!"Running preprocessing pipeline on:\n{g}"
-    Pass.fixpointPipeline (Pass.passPipeline cfg) g
+    let pipeline ← passPipeline
+    Pass.fixpointPipeline pipeline g
 
 @[builtin_tactic Lean.Parser.Tactic.bvNormalize]
 def evalBVNormalize : Tactic := fun

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/AC.lean

@@ -0,0 +1,39 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
+import Lean.Meta.Tactic.AC.Main
+
+/-!
+This module contains the implementation of the associativity and commutativity normalisation pass
+in the fixpoint pipeline.
+-/
+
+namespace Lean.Elab.Tactic.BVDecide
+namespace Frontend.Normalize
+
+open Lean.Meta
+
+/--
+Normalize with respect to Associativity and Commutativity.
+-/
+def acNormalizePass : Pass where
+  name := `ac_nf
+  run' goal := do
+    let mut newGoal := goal
+    for hyp in (← goal.getNondepPropHyps) do
+      let result ← AC.acNfHypMeta newGoal hyp
+
+      if let .some nextGoal := result then
+        newGoal := nextGoal
+      else
+        return none
+
+    return newGoal
+
+
+end Frontend.Normalize
+end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/AndFlatten.lean

@@ -0,0 +1,99 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Std.Tactic.BVDecide.Normalize.Bool
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
+import Lean.Meta.Tactic.Assert
+
+/-!
+This module contains the implementation of the and flattening pass in the fixpoint pipeline, taking
+hypotheses of the form `h : x && y = true` and splitting them into `h1 : x = true` and
+`h2 : y = true` recursively.
+-/
+
+namespace Lean.Elab.Tactic.BVDecide
+namespace Frontend.Normalize
+
+open Lean.Meta
+
+structure AndFlattenState where
+  hypsToDelete : Array FVarId := #[]
+  hypsToAdd : Array Hypothesis := #[]
+  cache : Std.HashSet Expr := {}
+
+/--
+Flatten out ands. That is look for hypotheses of the form `h : (x && y) = true` and replace them
+with `h.left : x = true` and `h.right : y = true`. This can enable more fine grained substitutions
+in embedded constraint substitution.
+-/
+partial def andFlatteningPass : Pass where
+  name := `andFlattening
+  run' goal := do
+    let (_, { hypsToDelete, hypsToAdd, .. }) ← processGoal goal |>.run {}
+    if hypsToAdd.isEmpty then
+      return goal
+    else
+      let (_, goal) ← goal.assertHypotheses hypsToAdd
+      -- Given that we collected the hypotheses in the correct order above the invariant is given
+      let goal ← goal.tryClearMany hypsToDelete
+      return goal
+where
+  processGoal (goal : MVarId) : StateRefT AndFlattenState MetaM Unit := do
+    goal.withContext do
+      let hyps ← goal.getNondepPropHyps
+      hyps.forM processFVar
+
+  processFVar (fvar : FVarId) : StateRefT AndFlattenState MetaM Unit := do
+    let type ← fvar.getType
+    if (← get).cache.contains type then
+      modify (fun s => { s with hypsToDelete := s.hypsToDelete.push fvar })
+    else
+      let hyp := {
+        userName := (← fvar.getDecl).userName
+        type := type
+        value := mkFVar fvar
+      }
+      let some (lhs, rhs) ← trySplit hyp | return ()
+      modify (fun s => { s with hypsToDelete := s.hypsToDelete.push fvar })
+      splitAnds [lhs, rhs]
+
+  splitAnds (worklist : List Hypothesis) : StateRefT AndFlattenState MetaM Unit := do
+    match worklist with
+    | [] => return ()
+    | hyp :: worklist =>
+      match ← trySplit hyp with
+      | some (left, right) => splitAnds <| left :: right :: worklist
+      | none =>
+        modify (fun s => { s with hypsToAdd := s.hypsToAdd.push hyp })
+        splitAnds worklist
+
+  trySplit (hyp : Hypothesis) :
+      StateRefT AndFlattenState MetaM (Option (Hypothesis × Hypothesis)) := do
+    let typ := hyp.type
+    if (← get).cache.contains typ then
+      return none
+    else
+      modify (fun s => { s with cache := s.cache.insert typ })
+      let_expr Eq _ eqLhs eqRhs := typ | return none
+      let_expr Bool.and lhs rhs := eqLhs | return none
+      let_expr Bool.true := eqRhs | return none
+      let mkEqTrue (lhs : Expr) : Expr :=
+        mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) lhs (mkConst ``Bool.true)
+      let leftHyp : Hypothesis := {
+        userName := hyp.userName,
+        type := mkEqTrue lhs,
+        value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_left) lhs rhs hyp.value
+      }
+      let rightHyp : Hypothesis := {
+        userName := hyp.userName,
+        type := mkEqTrue rhs,
+        value := mkApp3 (mkConst ``Std.Tactic.BVDecide.Normalize.Bool.and_right) lhs rhs hyp.value
+      }
+      return some (leftHyp, rightHyp)
+
+
+end Frontend.Normalize
+end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/Basic.lean

@@ -0,0 +1,86 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Lean.Meta.Basic
+import Lean.Elab.Tactic.BVDecide.Frontend.Attr
+
+/-!
+This module contains the basic preprocessing pipeline framework for `bv_normalize`.
+-/
+
+namespace Lean.Elab.Tactic.BVDecide
+namespace Frontend.Normalize
+
+open Lean.Meta
+
+structure PreProcessState where
+  /--
+  Contains `FVarId` that we already know are in `bv_normalize` simp normal form and thus don't
+  need to be processed again when we visit the next time.
+  -/
+  rewriteCache : Std.HashSet FVarId := {}
+
+abbrev PreProcessM : Type → Type := ReaderT BVDecideConfig <| StateRefT PreProcessState MetaM
+
+namespace PreProcessM
+
+def getConfig : PreProcessM BVDecideConfig := read
+
+@[inline]
+def checkRewritten (fvar : FVarId) : PreProcessM Bool := do
+  let val := (← get).rewriteCache.contains fvar
+  trace[Meta.Tactic.bv] m!"{mkFVar fvar} was already rewritten? {val}"
+  return val
+
+@[inline]
+def rewriteFinished (fvar : FVarId) : PreProcessM Unit := do
+  trace[Meta.Tactic.bv] m!"Adding {mkFVar fvar} to the rewritten set"
+  modify (fun s => { s with rewriteCache := s.rewriteCache.insert fvar })
+
+def run (cfg : BVDecideConfig) (goal : MVarId) (x : PreProcessM α) : MetaM α := do
+  let hyps ← goal.getNondepPropHyps
+  ReaderT.run x cfg |>.run' { rewriteCache := Std.HashSet.empty hyps.size }
+
+end PreProcessM
+
+/--
+A pass in the normalization pipeline. Takes the current goal and produces a refined one or closes
+the goal fully, indicated by returning `none`.
+-/
+structure Pass where
+  name : Name
+  run' : MVarId → PreProcessM (Option MVarId)
+
+namespace Pass
+
+def run (pass : Pass) (goal : MVarId) : PreProcessM (Option MVarId) := do
+  withTraceNode `bv (fun _ => return m!"Running pass: {pass.name} on\n{goal}") do
+    pass.run' goal
+
+/--
+Repeatedly run a list of `Pass` until they either close the goal or an iteration doesn't change
+the goal anymore.
+-/
+partial def fixpointPipeline (passes : List Pass) (goal : MVarId) : PreProcessM (Option MVarId) := do
+  let mut newGoal := goal
+  for pass in passes do
+    if let some nextGoal ← pass.run newGoal then
+      newGoal := nextGoal
+    else
+      trace[Meta.Tactic.bv] "Fixpoint iteration solved the goal"
+      return none
+
+  if goal != newGoal then
+    trace[Meta.Tactic.bv] m!"Rerunning pipeline on:\n{newGoal}"
+    fixpointPipeline passes newGoal
+  else
+    trace[Meta.Tactic.bv] "Pipeline reached a fixpoint"
+    return newGoal
+
+end Pass
+
+end Frontend.Normalize
+end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/EmbeddedConstraint.lean

@@ -0,0 +1,62 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Std.Tactic.BVDecide.Normalize.Bool
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
+import Lean.Meta.Tactic.Simp
+
+/-!
+This module contains the implementation of the embedded constraint substitution pass in the fixpoint
+pipeline, substituting hypotheses of the form `h : x = true` in other hypotheses.
+-/
+
+namespace Lean.Elab.Tactic.BVDecide
+namespace Frontend.Normalize
+
+open Lean.Meta
+
+/--
+Substitute embedded constraints. That is look for hypotheses of the form `h : x = true` and use
+them to substitute occurences of `x` within other hypotheses. Additionally this drops all
+redundant top level hypotheses.
+-/
+def embeddedConstraintPass : Pass where
+  name := `embeddedConstraintSubsitution
+  run' goal := do
+    goal.withContext do
+      let hyps ← goal.getNondepPropHyps
+      let mut relevantHyps : SimpTheoremsArray := #[]
+      let mut seen : Std.HashSet Expr := {}
+      let mut duplicates : Array FVarId := #[]
+      for hyp in hyps do
+        let typ ← hyp.getType
+        let_expr Eq _ lhs rhs := typ | continue
+        let_expr Bool.true := rhs | continue
+        if seen.contains lhs then
+          duplicates := duplicates.push hyp
+        else
+          seen := seen.insert lhs
+          let localDecl ← hyp.getDecl
+          let proof := localDecl.toExpr
+          relevantHyps ← relevantHyps.addTheorem (.fvar hyp) proof
+
+      let goal ← goal.tryClearMany duplicates
+
+      if relevantHyps.isEmpty then
+        return goal
+
+      let cfg ← PreProcessM.getConfig
+      let simpCtx ← Simp.mkContext
+        (config := { failIfUnchanged := false, maxSteps := cfg.maxSteps })
+        (simpTheorems := relevantHyps)
+        (congrTheorems := (← getSimpCongrTheorems))
+      let ⟨result?, _⟩ ← simpGoal goal (ctx := simpCtx) (fvarIdsToSimp := ← goal.getNondepPropHyps)
+      let some (_, newGoal) := result? | return none
+      return newGoal
+
+
+end Frontend.Normalize
+end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/Rewrite.lean

@@ -0,0 +1,61 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Lean.Elab.Tactic.Simp
+import Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic
+import Lean.Elab.Tactic.BVDecide.Frontend.Attr
+
+/-!
+This module contains the implementation of the rewriting pass in the fixpoint pipeline, applying
+rules from the `bv_normalize` simp set.
+-/
+
+namespace Lean.Elab.Tactic.BVDecide
+namespace Frontend.Normalize
+
+open Lean.Meta
+
+/--
+Responsible for applying the Bitwuzla style rewrite rules.
+-/
+def rewriteRulesPass : Pass where
+  name := `rewriteRules
+  run' goal := do
+    let bvThms ← bvNormalizeExt.getTheorems
+    let bvSimprocs ← bvNormalizeSimprocExt.getSimprocs
+    let sevalThms ← getSEvalTheorems
+    let sevalSimprocs ← Simp.getSEvalSimprocs
+    let cfg ← PreProcessM.getConfig
+
+    let simpCtx ← Simp.mkContext
+      (config := { failIfUnchanged := false, zetaDelta := true, maxSteps := cfg.maxSteps })
+      (simpTheorems := #[bvThms, sevalThms])
+      (congrTheorems := (← getSimpCongrTheorems))
+
+    let hyps ← getHyps goal
+    if hyps.isEmpty then
+      return goal
+    else
+      let ⟨result?, _⟩ ← simpGoal goal
+        (ctx := simpCtx)
+        (simprocs := #[bvSimprocs, sevalSimprocs])
+        (fvarIdsToSimp := hyps)
+
+      let some (_, newGoal) := result? | return none
+      newGoal.withContext do
+        (← newGoal.getNondepPropHyps).forM PreProcessM.rewriteFinished
+      return newGoal
+where
+  getHyps (goal : MVarId) : PreProcessM (Array FVarId) := do
+    goal.withContext do
+      let mut hyps ← goal.getNondepPropHyps
+      let filter hyp := do
+        return !(← PreProcessM.checkRewritten hyp)
+      hyps.filterM filter
+
+
+end Frontend.Normalize
+end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/BVDecide/Frontend/Normalize/Simproc.lean

@@ -0,0 +1,164 @@
+/-
+Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Std.Tactic.BVDecide.Normalize
+import Std.Tactic.BVDecide.Syntax
+import Lean.Elab.Tactic.Simp
+import Lean.Elab.Tactic.BVDecide.Frontend.Attr
+
+/-!
+This module contains implementations of simprocs used in the `bv_normalize` simp set.
+-/
+
+namespace Lean.Elab.Tactic.BVDecide
+namespace Frontend.Normalize
+
+open Lean.Meta
+open Std.Tactic.BVDecide.Normalize
+
+builtin_simproc ↓ [bv_normalize] reduceCond (cond _ _ _) := fun e => do
+  let_expr f@cond α c tb eb := e | return .continue
+  let r ← Simp.simp c
+  if r.expr.cleanupAnnotations.isConstOf ``Bool.true then
+    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_pos f.constLevels!) α c tb eb) (← r.getProof)
+    return .visit { expr := tb, proof? := pr }
+  else if r.expr.cleanupAnnotations.isConstOf ``Bool.false then
+    let pr := mkApp (mkApp4 (mkConst ``Bool.cond_neg f.constLevels!) α c tb eb) (← r.getProof)
+    return .visit { expr := eb, proof? := pr }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] eqToBEq (((_ : Bool) = (_ : Bool))) := fun e => do
+  let_expr Eq _ lhs rhs := e | return .continue
+  match_expr rhs with
+  | Bool.true => return .continue
+  | _ =>
+    let beqApp ← mkAppM ``BEq.beq #[lhs, rhs]
+    let new := mkApp3 (mkConst ``Eq [1]) (mkConst ``Bool) beqApp (mkConst ``Bool.true)
+    let proof := mkApp2 (mkConst ``Bool.eq_to_beq) lhs rhs
+    return .done { expr := new, proof? := some proof }
+
+builtin_simproc [bv_normalize] andOnes ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
+  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
+  let some ⟨w, rhsValue⟩ ← getBitVecValue? rhs | return .continue
+  if rhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.and_ones) (toExpr w) lhs
+    return .visit { expr := lhs, proof? := some proof }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] onesAnd ((_ : BitVec _) &&& (_ : BitVec _)) := fun e => do
+  let_expr HAnd.hAnd _ _ _ _ lhs rhs := e | return .continue
+  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
+  if lhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.ones_and) (toExpr w) rhs
+    return .visit { expr := rhs, proof? := some proof }
+  else
+    return .continue
+
+builtin_simproc [bv_normalize] maxUlt (BitVec.ult (_ : BitVec _) (_ : BitVec _)) := fun e => do
+  let_expr BitVec.ult _ lhs rhs := e | return .continue
+  let some ⟨w, lhsValue⟩ ← getBitVecValue? lhs | return .continue
+  if lhsValue == -1#w then
+    let proof := mkApp2 (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.max_ult') (toExpr w) rhs
+    return .visit { expr := toExpr Bool.false, proof? := some proof }
+  else
+    return .continue
+
+-- A specialised version of BitVec.neg_eq_not_add so it doesn't trigger on -constant
+builtin_simproc [bv_normalize] neg_eq_not_add (-(_ : BitVec _)) := fun e => do
+  let_expr Neg.neg typ _ val := e | return .continue
+  let_expr BitVec widthExpr := typ | return .continue
+  let some w ← getNatValue? widthExpr | return .continue
+  match ← getBitVecValue? val with
+  | some _ => return .continue
+  | none =>
+    let proof := mkApp2 (mkConst ``BitVec.neg_eq_not_add) (toExpr w) val
+    let expr ← mkAppM ``HAdd.hAdd #[← mkAppM ``Complement.complement #[val], (toExpr 1#w)]
+    return .visit { expr := expr, proof? := some proof }
+
+builtin_simproc [bv_normalize] bv_add_const ((_ : BitVec _) + ((_ : BitVec _) + (_ : BitVec _))) :=
+  fun e => do
+    let_expr HAdd.hAdd _ _ _ _ exp1 rhs := e | return .continue
+    let_expr HAdd.hAdd _ _ _ _ exp2 exp3 := rhs | return .continue
+    let some ⟨w, exp1Val⟩ ←  getBitVecValue? exp1 | return .continue
+    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
+    match ← getBitVecValue? exp2 with
+    | some ⟨w', exp2Val⟩ =>
+      if h : w = w' then
+        let newLhs := exp1Val + h ▸ exp2Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp3]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+    | none =>
+      let some ⟨w', exp3Val⟩ ← getBitVecValue? exp3 | return .continue
+      if h : w = w' then
+        let newLhs := exp1Val + h ▸ exp3Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+
+builtin_simproc [bv_normalize] bv_add_const' (((_ : BitVec _) + (_ : BitVec _)) + (_ : BitVec _)) :=
+  fun e => do
+    let_expr HAdd.hAdd _ _ _ _ lhs exp3 := e | return .continue
+    let_expr HAdd.hAdd _ _ _ _ exp1 exp2 := lhs | return .continue
+    let some ⟨w, exp3Val⟩ ←  getBitVecValue? exp3 | return .continue
+    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
+    match ← getBitVecValue? exp1 with
+    | some ⟨w', exp1Val⟩ =>
+      if h : w = w' then
+        let newLhs := exp3Val + h ▸ exp1Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left'
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+    | none =>
+      let some ⟨w', exp2Val⟩ ← getBitVecValue? exp2 | return .continue
+      if h : w = w' then
+        let newLhs := exp3Val + h ▸ exp2Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp1]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right'
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+
+/-- Return a number `k` such that `2^k = n`. -/
+private def Nat.log2Exact (n : Nat) : Option Nat := do
+  guard <| n ≠ 0
+  let k := n.log2
+  guard <| Nat.pow 2 k == n
+  return k
+
+-- Build an expression for `x ^ y`.
+def mkPow (x y : Expr) : MetaM Expr := mkAppM ``HPow.hPow #[x, y]
+
+builtin_simproc [bv_normalize] bv_udiv_of_two_pow (((_ : BitVec _) / (BitVec.ofNat _ _) : BitVec _)) := fun e => do
+  let_expr HDiv.hDiv _α _β _γ _self x y := e | return .continue
+  let some ⟨w, yVal⟩ ← getBitVecValue? y | return .continue
+  let n := yVal.toNat
+  -- BitVec.ofNat w n, where n =def= 2^k
+  let some k := Nat.log2Exact n | return .continue
+  -- check that k < w.
+  if k ≥ w then return .continue
+  let rhs ← mkAppM ``HShiftRight.hShiftRight #[x, mkNatLit k]
+  -- 2^k = n
+  let hk ← mkDecideProof (← mkEq (← mkPow (mkNatLit 2) (mkNatLit k)) (mkNatLit n))
+  -- k < w
+  let hlt ← mkDecideProof (← mkLt (mkNatLit k) (mkNatLit w))
+  let proof := mkAppN (mkConst ``Std.Tactic.BVDecide.Normalize.BitVec.udiv_ofNat_eq_of_lt)
+    #[mkNatLit w, x, mkNatLit n, mkNatLit k, hk, hlt]
+  return .done {
+      expr :=  rhs
+      proof? := some proof
+  }
+
+end Frontend.Normalize
+end Lean.Elab.Tactic.BVDecide

src/Lean/Elab/Tactic/Ext.lean

@@ -5,6 +5,7 @@ Authors: Gabriel Ebner, Mario Carneiro
 -/
 prelude
 import Init.Ext
+import Lean.Meta.Tactic.Ext
 import Lean.Elab.DeclarationRange
 import Lean.Elab.Tactic.RCases
 import Lean.Elab.Tactic.Repeat
@@ -174,65 +175,8 @@ def realizeExtIffTheorem (extName : Name) : Elab.Command.CommandElabM Name := do
 ### Attribute
 -/
 
-/-- Information about an extensionality theorem, stored in the environment extension. -/
-structure ExtTheorem where
-  /-- Declaration name of the extensionality theorem. -/
-  declName : Name
-  /-- Priority of the extensionality theorem. -/
-  priority : Nat
-  /--
-  Key in the discrimination tree,
-  for the type in which the extensionality theorem holds.
-  -/
-  keys : Array DiscrTree.Key
-  deriving Inhabited, Repr, BEq, Hashable
-
-/-- The state of the `ext` extension environment -/
-structure ExtTheorems where
-  /-- The tree of `ext` extensions. -/
-  tree   : DiscrTree ExtTheorem := {}
-  /-- Erased `ext`s via `attribute [-ext]`. -/
-  erased  : PHashSet Name := {}
-  deriving Inhabited
-
-/-- The environment extension to track `@[ext]` theorems. -/
-builtin_initialize extExtension :
-    SimpleScopedEnvExtension ExtTheorem ExtTheorems ←
-  registerSimpleScopedEnvExtension {
-    addEntry := fun { tree, erased } thm =>
-      { tree := tree.insertCore thm.keys thm, erased := erased.erase thm.declName }
-    initial := {}
-  }
-
-/-- Gets the list of `@[ext]` theorems corresponding to the key `ty`,
-ordered from high priority to low. -/
-@[inline] def getExtTheorems (ty : Expr) : MetaM (Array ExtTheorem) := do
-  let extTheorems := extExtension.getState (← getEnv)
-  let arr ← extTheorems.tree.getMatch ty
-  let erasedArr := arr.filter fun thm => !extTheorems.erased.contains thm.declName
-  -- Using insertion sort because it is stable and the list of matches should be mostly sorted.
-  -- Most ext theorems have default priority.
-  return erasedArr.insertionSort (·.priority < ·.priority) |>.reverse
-
-/--
-Erases a name marked `ext` by adding it to the state's `erased` field and
-removing it from the state's list of `Entry`s.
-
-This is triggered by `attribute [-ext] name`.
--/
-def ExtTheorems.eraseCore (d : ExtTheorems) (declName : Name) : ExtTheorems :=
- { d with erased := d.erased.insert declName }
-
-/--
-Erases a name marked as a `ext` attribute.
-Check that it does in fact have the `ext` attribute by making sure it names a `ExtTheorem`
-found somewhere in the state's tree, and is not erased.
--/
-def ExtTheorems.erase [Monad m] [MonadError m] (d : ExtTheorems) (declName : Name) :
-    m ExtTheorems := do
-  unless d.tree.containsValueP (·.declName == declName) && !d.erased.contains declName do
-    throwError "'{declName}' does not have [ext] attribute"
-  return d.eraseCore declName
+abbrev extExtension := Meta.Ext.extExtension
+abbrev getExtTheorems := Meta.Ext.getExtTheorems
 
 builtin_initialize registerBuiltinAttribute {
   name := `ext

src/Lean/Elab/Tactic/Grind.lean

@@ -34,10 +34,69 @@ def elabGrindPattern : CommandElab := fun stx => do
         Grind.addEMatchTheorem declName xs.size patterns.toList
   | _ => throwUnsupportedSyntax
 
-def grind (mvarId : MVarId) (config : Grind.Config) (mainDeclName : Name) (fallback : Grind.Fallback) : MetaM Unit := do
-  let mvarIds ← Grind.main mvarId config mainDeclName fallback
-  unless mvarIds.isEmpty do
-    throwError "`grind` failed\n{goalsToMessageData mvarIds}"
+open Command Term in
+@[builtin_command_elab Lean.Parser.Command.initGrindNorm]
+def elabInitGrindNorm : CommandElab := fun stx =>
+  match stx with
+  | `(init_grind_norm $pre:ident* | $post*) =>
+    Command.liftTermElabM do
+      let pre ← pre.mapM fun id => realizeGlobalConstNoOverloadWithInfo id
+      let post ← post.mapM fun id => realizeGlobalConstNoOverloadWithInfo id
+      Grind.registerNormTheorems pre post
+  | _ => throwUnsupportedSyntax
+
+def elabGrindParams (params : Grind.Params) (ps :  TSyntaxArray ``Parser.Tactic.grindParam) : MetaM Grind.Params := do
+  let mut params := params
+  for p in ps do
+    match p with
+    | `(Parser.Tactic.grindParam| - $id:ident) =>
+      let declName ← realizeGlobalConstNoOverloadWithInfo id
+      if (← isInductivePredicate declName) then
+        throwErrorAt p "NIY"
+      else
+        params := { params with ematch := (← params.ematch.eraseDecl declName) }
+    | `(Parser.Tactic.grindParam| $[$mod?:grindThmMod]? $id:ident) =>
+      let declName ← realizeGlobalConstNoOverloadWithInfo id
+      let kind ← if let some mod := mod? then Grind.getTheoremKindCore mod else pure .default
+      if (← isInductivePredicate declName) then
+        throwErrorAt p "NIY"
+      else
+        let info ← getConstInfo declName
+        match info with
+        | .thmInfo _ =>
+          if kind == .eqBoth then
+            params := { params with extra := params.extra.push (← Grind.mkEMatchTheoremForDecl declName .eqLhs) }
+            params := { params with extra := params.extra.push (← Grind.mkEMatchTheoremForDecl declName .eqRhs) }
+          else
+            params := { params with extra := params.extra.push (← Grind.mkEMatchTheoremForDecl declName kind) }
+        | .defnInfo _ =>
+          if (← isReducible declName) then
+            throwErrorAt p "`{declName}` is a reducible definition, `grind` automatically unfolds them"
+          if kind != .eqLhs && kind != .default then
+            throwErrorAt p "invalid `grind` parameter, `{declName}` is a definition, the only acceptable (and redundant) modifier is '='"
+          let some thms ← Grind.mkEMatchEqTheoremsForDef? declName
+            | throwErrorAt p "failed to genereate equation theorems for `{declName}`"
+          params := { params with extra := params.extra ++ thms.toPArray' }
+        | _ =>
+          throwErrorAt p "invalid `grind` parameter, `{declName}` is not a theorem, definition, or inductive type"
+    | _ => throwError "unexpected `grind` parameter{indentD p}"
+  return params
+
+def mkGrindParams (config : Grind.Config) (only : Bool) (ps :  TSyntaxArray ``Parser.Tactic.grindParam) : MetaM Grind.Params := do
+  let params ← Grind.mkParams config
+  let ematch ← if only then pure {} else Grind.getEMatchTheorems
+  let params := { params with ematch }
+  elabGrindParams params ps
+
+def grind
+    (mvarId : MVarId) (config : Grind.Config)
+    (only : Bool)
+    (ps   :  TSyntaxArray ``Parser.Tactic.grindParam)
+    (mainDeclName : Name) (fallback : Grind.Fallback) : MetaM Unit := do
+  let params ← mkGrindParams config only ps
+  let goals ← Grind.main mvarId params mainDeclName fallback
+  unless goals.isEmpty do
+    throwError "`grind` failed\n{← Grind.goalsToMessageData goals config}"
 
 private def elabFallback (fallback? : Option Term) : TermElabM (Grind.GoalM Unit) := do
   let some fallback := fallback? | return (pure ())
@@ -56,14 +115,16 @@ private def elabFallback (fallback? : Option Term) : TermElabM (Grind.GoalM Unit
     pure auxDeclName
   unsafe evalConst (Grind.GoalM Unit) auxDeclName
 
-@[builtin_tactic Lean.Parser.Tactic.grind] def evalApplyRfl : Tactic := fun stx => do
+@[builtin_tactic Lean.Parser.Tactic.grind] def evalGrind : Tactic := fun stx => do
   match stx with
-  | `(tactic| grind $config:optConfig $[on_failure $fallback?]?) =>
+  | `(tactic| grind $config:optConfig $[only%$only]?  $[ [$params:grindParam,*] ]? $[on_failure $fallback?]?) =>
     let fallback ← elabFallback fallback?
+    let only := only.isSome
+    let params := if let some params := params then params.getElems else #[]
     logWarningAt stx "The `grind` tactic is experimental and still under development. Avoid using it in production projects"
     let declName := (← Term.getDeclName?).getD `_grind
     let config ← elabGrindConfig config
-    withMainContext do liftMetaFinishingTactic (grind · config declName fallback)
+    withMainContext do liftMetaFinishingTactic (grind · config only params declName fallback)
   | _ => throwUnsupportedSyntax
 
 end Lean.Elab.Tactic

src/Lean/Environment.lean

@@ -7,8 +7,10 @@ prelude
 import Init.Control.StateRef
 import Init.Data.Array.BinSearch
 import Init.Data.Stream
+import Init.System.Promise
 import Lean.ImportingFlag
 import Lean.Data.HashMap
+import Lean.Data.NameTrie
 import Lean.Data.SMap
 import Lean.Declaration
 import Lean.LocalContext
@@ -16,6 +18,50 @@ import Lean.Util.Path
 import Lean.Util.FindExpr
 import Lean.Util.Profile
 import Lean.Util.InstantiateLevelParams
+import Lean.PrivateName
+
+/-!
+# Note [Environment Branches]
+
+The kernel environment type `Lean.Kernel.Environment` enforces a linear order on the addition of
+declarations: `addDeclCore` takes an environment and returns a new one, assuming type checking
+succeeded. On the other hand, the metaprogramming-level `Lean.Environment` wrapper must allow for
+*branching* environment transformations so that multiple declarations can be elaborated
+concurrently while still being able to access information about preceding declarations that have
+also been branched out as soon as they are available.
+
+The basic function to introduce such branches is `addConstAsync`, which takes an environment and
+returns a structure containing two environments: one for the "main" branch that can be used in
+further branching and eventually contains all the declarations of the file and one for the "async"
+branch that can be used concurrently to the main branch to elaborate and add the declaration for
+which the branch was introduced. Branches are "joined" back together implicitly via the kernel
+environment, which as mentioned cannot be changed concurrently: when the main branch first tries to
+access it, evaluation is blocked until the kernel environment on the async branch is complete.
+Thus adding two declarations A and B concurrently can be visualized like this:
+```text
+o addConstAsync A
+|\
+| \
+|  \
+o addConstAsync B
+|\   \
+| \   o elaborate A
+|  \  |
+|   o elaborate B
+|   | |
+|   | o addDeclCore A
+|   |/
+|   o addDeclCore B
+|  /
+| /
+|/
+o .olean serialization calls Environment.toKernelEnv
+```
+While each edge represents a `Lean.Environment` that has its own view of the state of the module,
+the kernel environment really lives only in the right-most path, with all other paths merely holding
+an unfulfilled `Task` representing it and where forcing that task leads to the back-edges joining
+paths back together.
+-/
 
 namespace Lean
 /-- Opaque environment extension state. -/
@@ -88,11 +134,6 @@ structure EnvironmentHeader where
   -/
   trustLevel   : UInt32       := 0
   /--
-  `quotInit = true` if the command `init_quot` has already been executed for the environment, and
-  `Quot` declarations have been added to the environment.
-  -/
-  quotInit     : Bool         := false
-  /--
   Name of the module being compiled.
   -/
   mainModule   : Name         := default
@@ -106,6 +147,15 @@ structure EnvironmentHeader where
   moduleData   : Array ModuleData := #[]
   deriving Nonempty
 
+namespace Kernel
+
+structure 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
+
 /--
 An environment stores declarations provided by the user. The kernel
 currently supports different kinds of declarations such as definitions, theorems,
@@ -121,10 +171,33 @@ declared by users are stored in an environment extension. Users can declare new
 using meta-programming.
 -/
 structure Environment where
-  /-- The constructor of `Environment` is private to protect against modification
-  that bypasses the kernel. -/
+  /--
+  The constructor of `Environment` is private to protect against modification that bypasses the
+  kernel.
+  -/
   private mk ::
   /--
+  Mapping from constant name to `ConstantInfo`. It contains all constants (definitions, theorems,
+  axioms, etc) that have been already type checked by the kernel.
+  -/
+  constants   : ConstMap
+  /--
+  `quotInit = true` if the command `init_quot` has already been executed for the environment, and
+  `Quot` declarations have been added to the environment. When the flag is set, the type checker can
+  assume that the `Quot` declarations in the environment have indeed been added by the kernel and
+  not by the user.
+  -/
+  quotInit    : Bool := false
+  /--
+  Diagnostic information collected during kernel execution.
+
+  Remark: We store kernel diagnostic information in an environment field 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.
+  -/
+  diagnostics : Diagnostics := {}
+  /--
   Mapping from constant name to module (index) where constant has been declared.
   Recall that a Lean file has a header where previously compiled modules can be imported.
   Each imported module has a unique `ModuleIdx`.
@@ -134,96 +207,23 @@ structure Environment where
   the field `constants`. These auxiliary constants are invisible to the Lean kernel and elaborator.
   Only the code generator uses them.
   -/
-  const2ModIdx : Std.HashMap Name ModuleIdx
-  /--
-  Mapping from constant name to `ConstantInfo`. It contains all constants (definitions, theorems, axioms, etc)
-  that have been already type checked by the kernel.
-  -/
-  constants    : ConstMap
+  const2ModIdx            : Std.HashMap Name ModuleIdx
   /--
   Environment extensions. It also includes user-defined extensions.
   -/
-  extensions   : Array EnvExtensionState
+  private extensions      : Array EnvExtensionState
   /--
   Constant names to be saved in the field `extraConstNames` at `ModuleData`.
   It contains auxiliary declaration names created by the code generator which are not in `constants`.
   When importing modules, we want to insert them at `const2ModIdx`.
   -/
-  extraConstNames : NameSet
-  /-- The header contains additional information that is not updated often. -/
-  header       : EnvironmentHeader := {}
-  deriving Nonempty
+  private extraConstNames : NameSet
+  /-- The header contains additional information that is set at import time. -/
+  header                  : EnvironmentHeader := {}
+deriving Nonempty
 
-namespace Environment
-
-private def addAux (env : Environment) (cinfo : ConstantInfo) : Environment :=
-  { env with constants := env.constants.insert cinfo.name cinfo }
-
-/--
-Save an extra constant name that is used to populate `const2ModIdx` when we import
-.olean files. We use this feature to save in which module an auxiliary declaration
-created by the code generator has been created.
--/
-def addExtraName (env : Environment) (name : Name) : Environment :=
-  if env.constants.contains name then
-    env
-  else
-    { env with extraConstNames := env.extraConstNames.insert name }
-
-@[export lean_environment_find]
-def find? (env : Environment) (n : Name) : Option ConstantInfo :=
-  /- It is safe to use `find'` because we never overwrite imported declarations. -/
-  env.constants.find?' n
-
-def contains (env : Environment) (n : Name) : Bool :=
-  env.constants.contains n
-
-def imports (env : Environment) : Array Import :=
-  env.header.imports
-
-def allImportedModuleNames (env : Environment) : Array Name :=
-  env.header.moduleNames
-
-@[export lean_environment_set_main_module]
-def setMainModule (env : Environment) (m : Name) : Environment :=
-  { env with header := { env.header with mainModule := m } }
-
-@[export lean_environment_main_module]
-def mainModule (env : Environment) : Name :=
-  env.header.mainModule
-
-@[export lean_environment_mark_quot_init]
-private def markQuotInit (env : Environment) : Environment :=
-  { env with header := { env.header with quotInit := true } }
-
-@[export lean_environment_quot_init]
-private def isQuotInit (env : Environment) : Bool :=
-  env.header.quotInit
-
-@[export lean_environment_trust_level]
-private def getTrustLevel (env : Environment) : UInt32 :=
-  env.header.trustLevel
-
-def getModuleIdxFor? (env : Environment) (declName : Name) : Option ModuleIdx :=
-  env.const2ModIdx[declName]?
-
-def isConstructor (env : Environment) (declName : Name) : Bool :=
-  match env.find? declName with
-  | some (.ctorInfo _) => true
-  | _                  => false
-
-def isSafeDefinition (env : Environment) (declName : Name) : Bool :=
-  match env.find? declName with
-  | some (.defnInfo { safety := .safe, .. }) => true
-  | _ => false
-
-def getModuleIdx? (env : Environment) (moduleName : Name) : Option ModuleIdx :=
-  env.header.moduleNames.findIdx? (· == moduleName)
-
-end Environment
-
-/-- Exceptions that can be raised by the Kernel when type checking new declarations. -/
-inductive KernelException where
+/-- Exceptions that can be raised by the kernel when type checking new declarations. -/
+inductive Exception where
   | unknownConstant  (env : Environment) (name : Name)
   | alreadyDeclared  (env : Environment) (name : Name)
   | declTypeMismatch (env : Environment) (decl : Declaration) (givenType : Expr)
@@ -244,21 +244,500 @@ inductive KernelException where
 
 namespace Environment
 
-/--
-Type check given declaration and add it to the environment
--/
+@[export lean_environment_find]
+def find? (env : Environment) (n : Name) : Option ConstantInfo :=
+  /- It is safe to use `find'` because we never overwrite imported declarations. -/
+  env.constants.find?' n
+
+@[export lean_environment_mark_quot_init]
+private def markQuotInit (env : Environment) : Environment :=
+  { env with quotInit := true }
+
+@[export lean_environment_quot_init]
+private def isQuotInit (env : Environment) : Bool :=
+  env.quotInit
+
+/-- Type check given declaration and add it to the environment -/
 @[extern "lean_add_decl"]
 opaque addDeclCore (env : Environment) (maxHeartbeats : USize) (decl : @& Declaration)
-  (cancelTk? : @& Option IO.CancelToken) : Except KernelException Environment
+  (cancelTk? : @& Option IO.CancelToken) : Except Exception Environment
 
 /--
 Add declaration to kernel without type checking it.
+
 **WARNING** This function is meant for temporarily working around kernel performance issues.
 It compromises soundness because, for example, a buggy tactic may produce an invalid proof,
 and the kernel will not catch it if the new option is set to true.
 -/
 @[extern "lean_add_decl_without_checking"]
-opaque addDeclWithoutChecking (env : Environment) (decl : @& Declaration) : Except KernelException Environment
+opaque addDeclWithoutChecking (env : Environment) (decl : @& Declaration) : Except Exception Environment
+
+@[export lean_environment_add]
+private def add (env : Environment) (cinfo : ConstantInfo) : Environment :=
+  { env with constants := env.constants.insert cinfo.name cinfo }
+
+@[export lean_kernel_diag_is_enabled]
+def Diagnostics.isEnabled (d : Diagnostics) : Bool :=
+  d.enabled
+
+/-- Enables/disables kernel diagnostics. -/
+def enableDiag (env : Environment) (flag : Bool) : Environment :=
+  { env with diagnostics.enabled := flag }
+
+def isDiagnosticsEnabled (env : Environment) : Bool :=
+  env.diagnostics.enabled
+
+def resetDiag (env : Environment) : Environment :=
+  { env with diagnostics.unfoldCounter := {} }
+
+@[export lean_kernel_record_unfold]
+def 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 getDiagnostics (env : Environment) : Diagnostics :=
+  env.diagnostics
+
+@[export lean_kernel_set_diag]
+def setDiagnostics (env : Environment) (diag : Diagnostics) : Environment :=
+  { env with diagnostics := diag}
+
+end Kernel.Environment
+
+@[deprecated Kernel.Exception (since := "2024-12-12")]
+abbrev KernelException := Kernel.Exception
+
+inductive ConstantKind where
+  | defn | thm | «axiom» | «opaque» | quot | induct | ctor | recursor
+deriving Inhabited, BEq, Repr
+
+def ConstantKind.ofConstantInfo : ConstantInfo → ConstantKind
+  | .defnInfo   _ => .defn
+  | .thmInfo    _ => .thm
+  | .axiomInfo  _ => .axiom
+  | .opaqueInfo _ => .opaque
+  | .quotInfo   _ => .quot
+  | .inductInfo _ => .induct
+  | .ctorInfo   _ => .ctor
+  | .recInfo    _ => .recursor
+
+/-- `ConstantInfo` variant that allows for asynchronous filling of components via tasks. -/
+structure AsyncConstantInfo where
+  /-- The declaration name, known immediately. -/
+  name      : Name
+  /-- The kind of the constant, known immediately. -/
+  kind      : ConstantKind
+  /-- The "signature" including level params and type, potentially filled asynchronously. -/
+  sig       : Task ConstantVal
+  /-- The final, complete constant info, potentially filled asynchronously. -/
+  constInfo : Task ConstantInfo
+
+namespace AsyncConstantInfo
+
+def toConstantVal (c : AsyncConstantInfo) : ConstantVal :=
+  c.sig.get
+
+def toConstantInfo (c : AsyncConstantInfo) : ConstantInfo :=
+  c.constInfo.get
+
+def ofConstantInfo (c : ConstantInfo) : AsyncConstantInfo where
+  name := c.name
+  kind := .ofConstantInfo c
+  sig := .pure c.toConstantVal
+  constInfo := .pure c
+
+end AsyncConstantInfo
+
+/--
+Information about the current branch of the environment representing asynchronous elaboration.
+-/
+structure AsyncContext where
+  /--
+  Name of the declaration asynchronous elaboration was started for. All constants added to this
+  environment branch must have the name as a prefix, after erasing macro scopes and private name
+  prefixes.
+  -/
+  declPrefix : Name
+deriving Nonempty
+
+/--
+Checks whether a declaration named `n` may be added to the environment in the given context. See
+also `AsyncContext.declPrefix`.
+-/
+def AsyncContext.mayContain (ctx : AsyncContext) (n : Name) : Bool :=
+  ctx.declPrefix.isPrefixOf <| privateToUserName n.eraseMacroScopes
+
+/--
+Constant info and environment extension states eventually resulting from async elaboration.
+-/
+structure AsyncConst where
+  constInfo : AsyncConstantInfo
+  /--
+  Reported extension state eventually fulfilled by promise; may be missing for tasks (e.g. kernel
+  checking) that can eagerly guarantee they will not report any state.
+  -/
+  exts?     : Option (Task (Array EnvExtensionState))
+
+/-- Data structure holding a sequence of `AsyncConst`s optimized for efficient access. -/
+structure AsyncConsts where
+  toArray : Array AsyncConst := #[]
+  /-- Map from declaration name to const for fast direct access. -/
+  private map : NameMap AsyncConst := {}
+  /-- Trie of declaration names without private name prefixes for fast longest-prefix access. -/
+  private normalizedTrie : NameTrie AsyncConst := {}
+deriving Inhabited
+
+def AsyncConsts.add (aconsts : AsyncConsts) (aconst : AsyncConst) : AsyncConsts :=
+  { aconsts with
+    toArray := aconsts.toArray.push aconst
+    map := aconsts.map.insert aconst.constInfo.name aconst
+    normalizedTrie := aconsts.normalizedTrie.insert (privateToUserName aconst.constInfo.name) aconst
+  }
+
+def AsyncConsts.find? (aconsts : AsyncConsts) (declName : Name) : Option AsyncConst :=
+  aconsts.map.find? declName
+
+/-- Checks whether the name of any constant in the collection is a prefix of `declName`. -/
+def AsyncConsts.hasPrefix (aconsts : AsyncConsts) (declName : Name) : Bool :=
+  -- as macro scopes are a strict suffix,
+  aconsts.normalizedTrie.findLongestPrefix? (privateToUserName declName.eraseMacroScopes) |>.isSome
+
+/--
+Elaboration-specific extension of `Kernel.Environment` that adds tracking of asynchronously
+elaborated declarations.
+-/
+structure Environment where
+  /-
+  Like with `Kernel.Environment`, this constructor is private to protect consistency of the
+  environment, though there are no soundness concerns in this case given that it is used purely for
+  elaboration.
+  -/
+  private mk ::
+  /--
+  Kernel environment not containing any asynchronously elaborated declarations. Also stores
+  environment extension state for the current branch of the environment.
+
+  Ignoring extension state, this is guaranteed to be some prior version of `checked` that is eagerly
+  available. Thus we prefer taking information from it instead of `checked` whenever possible.
+  -/
+  checkedWithoutAsync : Kernel.Environment
+  /--
+  Kernel environment task that is fulfilled when all asynchronously elaborated declarations are
+  finished, containing the resulting environment. Also collects the environment extension state of
+  all environment branches that contributed contained declarations.
+  -/
+  checked             : Task Kernel.Environment := .pure checkedWithoutAsync
+  /--
+  Container of asynchronously elaborated declarations, i.e.
+  `checked = checkedWithoutAsync ⨃ asyncConsts`.
+  -/
+  private asyncConsts : AsyncConsts := {}
+  /-- Information about this asynchronous branch of the environment, if any. -/
+  private asyncCtx?   : Option AsyncContext := none
+deriving Nonempty
+
+namespace Environment
+
+@[export lean_elab_environment_of_kernel_env]
+def ofKernelEnv (env : Kernel.Environment) : Environment :=
+  { checkedWithoutAsync := env }
+
+@[export lean_elab_environment_to_kernel_env]
+def toKernelEnv (env : Environment) : Kernel.Environment :=
+  env.checked.get
+
+/-- Consistently updates synchronous and asynchronous parts of the environment without blocking. -/
+private def modifyCheckedAsync (env : Environment) (f : Kernel.Environment → Kernel.Environment) : Environment :=
+  { env with checked := env.checked.map (sync := true) f, checkedWithoutAsync := f env.checkedWithoutAsync }
+
+/-- Sets synchronous and asynchronous parts of the environment to the given kernel environment. -/
+private def setCheckedSync (env : Environment) (newChecked : Kernel.Environment) : Environment :=
+  { env with checked := .pure newChecked, checkedWithoutAsync := newChecked }
+
+@[extern "lean_elab_add_decl"]
+private opaque addDeclCheck (env : Environment) (maxHeartbeats : USize) (decl : @& Declaration)
+  (cancelTk? : @& Option IO.CancelToken) : Except Kernel.Exception Environment
+
+@[extern "lean_elab_add_decl_without_checking"]
+private opaque addDeclWithoutChecking (env : Environment) (decl : @& Declaration) :
+  Except Kernel.Exception Environment
+
+/--
+Adds given declaration to the environment, type checking it unless `doCheck` is false.
+
+This is a plumbing function for the implementation of `Lean.addDecl`, most users should use it
+instead.
+-/
+def addDeclCore (env : Environment) (maxHeartbeats : USize) (decl : @& Declaration)
+    (cancelTk? : @& Option IO.CancelToken) (doCheck := true) :
+    Except Kernel.Exception Environment := do
+  if let some ctx := env.asyncCtx? then
+    if let some n := decl.getNames.find? (!ctx.mayContain ·) then
+      throw <| .other s!"cannot add declaration {n} to environment as it is restricted to the \
+        prefix {ctx.declPrefix}"
+  if doCheck then
+    addDeclCheck env maxHeartbeats decl cancelTk?
+  else
+    addDeclWithoutChecking env decl
+
+@[inherit_doc Kernel.Environment.constants]
+def constants (env : Environment) : ConstMap :=
+  env.toKernelEnv.constants
+
+@[inherit_doc Kernel.Environment.const2ModIdx]
+def const2ModIdx (env : Environment) : Std.HashMap Name ModuleIdx :=
+  env.toKernelEnv.const2ModIdx
+
+-- only needed for the lakefile.lean cache
+@[export lake_environment_add]
+private def lakeAdd (env : Environment) (cinfo : ConstantInfo) : Environment :=
+  { env with checked := .pure <| env.checked.get.add cinfo }
+
+/--
+Save an extra constant name that is used to populate `const2ModIdx` when we import
+.olean files. We use this feature to save in which module an auxiliary declaration
+created by the code generator has been created.
+-/
+def addExtraName (env : Environment) (name : Name) : Environment :=
+  if env.constants.contains name then
+    env
+  else
+    env.modifyCheckedAsync fun env => { env with extraConstNames := env.extraConstNames.insert name }
+
+/-- Find base case: name did not match any asynchronous declaration. -/
+private def findNoAsync (env : Environment) (n : Name) : Option ConstantInfo := do
+  if env.asyncConsts.hasPrefix n then
+    -- Constant generated in a different environment branch: wait for final kernel environment. Rare
+    -- case when only proofs are elaborated asynchronously as they are rarely inspected. Could be
+    -- optimized in the future by having the elaboration thread publish an (incremental?) map of
+    -- generated declarations before kernel checking (which must wait on all previous threads).
+    env.checked.get.constants.find?' n
+  else
+    -- Not in the kernel environment nor in the name prefix of environment branch: undefined by
+    -- `addDeclCore` invariant.
+    none
+
+/--
+Looks up the given declaration name in the environment, avoiding forcing any in-progress elaboration
+tasks.
+-/
+def findAsync? (env : Environment) (n : Name) : Option AsyncConstantInfo := do
+  -- Check declarations already added to the kernel environment (e.g. because they were imported)
+  -- first as that should be the most common case. It is safe to use `find?'` because we never
+  -- overwrite imported declarations.
+  if let some c := env.checkedWithoutAsync.constants.find?' n then
+    some <| .ofConstantInfo c
+  else if let some asyncConst := env.asyncConsts.find? n then
+    -- Constant for which an asynchronous elaboration task was spawned
+    return asyncConst.constInfo
+  else env.findNoAsync n |>.map .ofConstantInfo
+
+/--
+Looks up the given declaration name in the environment, avoiding forcing any in-progress elaboration
+tasks for declaration bodies (which are not accessible from `ConstantVal`).
+-/
+def findConstVal? (env : Environment) (n : Name) : Option ConstantVal := do
+  if let some c := env.checkedWithoutAsync.constants.find?' n then
+    some c.toConstantVal
+  else if let some asyncConst := env.asyncConsts.find? n then
+    return asyncConst.constInfo.toConstantVal
+  else env.findNoAsync n |>.map (·.toConstantVal)
+
+/--
+Looks up the given declaration name in the environment, blocking on the corresponding elaboration
+task if not yet complete.
+-/
+def find? (env : Environment) (n : Name) : Option ConstantInfo :=
+  if let some c := env.checkedWithoutAsync.constants.find?' n then
+    some c
+  else if let some asyncConst := env.asyncConsts.find? n then
+    return asyncConst.constInfo.toConstantInfo
+  else
+    env.findNoAsync n
+
+/-- Returns debug output about the asynchronous state of the environment. -/
+def dbgFormatAsyncState (env : Environment) : BaseIO String :=
+  return s!"\
+    asyncCtx.declPrefix: {repr <| env.asyncCtx?.map (·.declPrefix)}\
+  \nasyncConsts: {repr <| env.asyncConsts.toArray.map (·.constInfo.name)}\
+  \ncheckedWithoutAsync.constants.map₂: {repr <|
+      env.checkedWithoutAsync.constants.map₂.toList.map (·.1)}"
+
+/-- Returns debug output about the synchronous state of the environment. -/
+def dbgFormatCheckedSyncState (env : Environment) : BaseIO String :=
+  return s!"checked.get.constants.map₂: {repr <| env.checked.get.constants.map₂.toList.map (·.1)}"
+
+/--
+Result of `Lean.Environment.addConstAsync` which is necessary to complete the asynchronous addition.
+-/
+structure AddConstAsyncResult where
+  /--
+  Resulting "main branch" environment which contains the declaration name as an asynchronous
+  constant. Accessing the constant or kernel environment will block until the corresponding
+  `AddConstAsyncResult.commit*` function has been called.
+  -/
+  mainEnv : Environment
+  /--
+  Resulting "async branch" environment which should be used to add the desired declaration in a new
+  task and then call `AddConstAsyncResult.commit*` to commit results back to the main environment.
+  One of `commitCheckEnv` or `commitFailure` must be called eventually to prevent deadlocks on main
+  branch accesses.
+  -/
+  asyncEnv : Environment
+  private constName : Name
+  private kind : ConstantKind
+  private sigPromise : IO.Promise ConstantVal
+  private infoPromise : IO.Promise ConstantInfo
+  private extensionsPromise : IO.Promise (Array EnvExtensionState)
+  private checkedEnvPromise : IO.Promise Kernel.Environment
+
+/--
+Starts the asynchronous addition of a constant to the environment. The environment is split into a
+"main" branch that holds a reference to the constant to be added but will block on access until the
+corresponding information has been added on the "async" environment branch and committed there; see
+the respective fields of `AddConstAsyncResult` as well as the [Environment Branches] note for more
+information.
+-/
+def addConstAsync (env : Environment) (constName : Name) (kind : ConstantKind) (reportExts := true) :
+    IO AddConstAsyncResult := do
+  let sigPromise ← IO.Promise.new
+  let infoPromise ← IO.Promise.new
+  let extensionsPromise ← IO.Promise.new
+  let checkedEnvPromise ← IO.Promise.new
+  let asyncConst := {
+    constInfo := {
+      name := constName
+      kind
+      sig := sigPromise.result
+      constInfo := infoPromise.result
+    }
+    exts? := guard reportExts *> some extensionsPromise.result
+  }
+  return {
+    constName, kind
+    mainEnv := { env with
+      asyncConsts := env.asyncConsts.add asyncConst
+      checked := checkedEnvPromise.result }
+    asyncEnv := { env with
+      asyncCtx? := some { declPrefix := privateToUserName constName.eraseMacroScopes }
+    }
+    sigPromise, infoPromise, extensionsPromise, checkedEnvPromise
+  }
+
+/--
+Commits the signature of the constant to the main environment branch. The declaration name must
+match the name originally given to `addConstAsync`. It is optional to call this function but can
+help in unblocking corresponding accesses to the constant on the main branch.
+-/
+def AddConstAsyncResult.commitSignature (res : AddConstAsyncResult) (sig : ConstantVal) :
+    IO Unit := do
+  if sig.name != res.constName then
+    throw <| .userError s!"AddConstAsyncResult.commitSignature: constant has name {sig.name} but expected {res.constName}"
+  res.sigPromise.resolve sig
+
+/--
+Commits the full constant info to the main environment branch. If `info?` is `none`, it is taken
+from the given environment. The declaration name and kind must match the original values given to
+`addConstAsync`. The signature must match the previous `commitSignature` call, if any.
+-/
+def AddConstAsyncResult.commitConst (res : AddConstAsyncResult) (env : Environment)
+    (info? : Option ConstantInfo := none) :
+    IO Unit := do
+  let info ← match info? <|> env.find? res.constName with
+    | some info => pure info
+    | none =>
+      throw <| .userError s!"AddConstAsyncResult.commitConst: constant {res.constName} not found in async context"
+  res.commitSignature info.toConstantVal
+  let kind' := .ofConstantInfo info
+  if res.kind != kind' then
+    throw <| .userError s!"AddConstAsyncResult.commitConst: constant has kind {repr kind'} but expected {repr res.kind}"
+  let sig := res.sigPromise.result.get
+  if sig.levelParams != info.levelParams then
+    throw <| .userError s!"AddConstAsyncResult.commitConst: constant has level params {info.levelParams} but expected {sig.levelParams}"
+  if sig.type != info.type then
+    throw <| .userError s!"AddConstAsyncResult.commitConst: constant has type {info.type} but expected {sig.type}"
+  res.infoPromise.resolve info
+  res.extensionsPromise.resolve env.checkedWithoutAsync.extensions
+
+/--
+Aborts async addition, filling in missing information with default values/sorries and leaving the
+kernel environment unchanged.
+-/
+def AddConstAsyncResult.commitFailure (res : AddConstAsyncResult) : BaseIO Unit := do
+  let val := if (← IO.hasFinished res.sigPromise.result) then
+    res.sigPromise.result.get
+  else {
+    name := res.constName
+    levelParams := []
+    type := mkApp2 (mkConst ``sorryAx [0]) (mkSort 0) (mkConst ``true)
+  }
+  res.sigPromise.resolve val
+  res.infoPromise.resolve <| match res.kind with
+    | .defn => .defnInfo { val with
+      value := mkApp2 (mkConst ``sorryAx [0]) val.type (mkConst ``true)
+      hints := .abbrev
+      safety := .safe
+    }
+    | .thm  => .thmInfo { val with
+      value := mkApp2 (mkConst ``sorryAx [0]) val.type (mkConst ``true)
+    }
+    | k => panic! s!"AddConstAsyncResult.commitFailure: unsupported constant kind {repr k}"
+  res.extensionsPromise.resolve #[]
+  let _ ← BaseIO.mapTask (t := res.asyncEnv.checked) (sync := true) res.checkedEnvPromise.resolve
+
+/--
+Assuming `Lean.addDecl` has been run for the constant to be added on the async environment branch,
+commits the full constant info from that call to the main environment, waits for the final kernel
+environment resulting from the `addDecl` call, and commits it to the main branch as well, unblocking
+kernel additions there. All `commitConst` preconditions apply.
+-/
+def AddConstAsyncResult.commitCheckEnv (res : AddConstAsyncResult) (env : Environment) :
+    IO Unit := do
+  let some _ := env.findAsync? res.constName
+    | throw <| .userError s!"AddConstAsyncResult.checkAndCommitEnv: constant {res.constName} not \
+      found in async context"
+  res.commitConst env
+  res.checkedEnvPromise.resolve env.checked.get
+
+def contains (env : Environment) (n : Name) : Bool :=
+  env.findAsync? n |>.isSome
+
+def header (env : Environment) : EnvironmentHeader :=
+  -- can be assumed to be in sync with `env.checked`; see `setMainModule`, the only modifier of the header
+  env.checkedWithoutAsync.header
+
+def imports (env : Environment) : Array Import :=
+  env.header.imports
+
+def allImportedModuleNames (env : Environment) : Array Name :=
+  env.header.moduleNames
+
+def setMainModule (env : Environment) (m : Name) : Environment :=
+  env.modifyCheckedAsync ({ · with header.mainModule := m })
+
+def mainModule (env : Environment) : Name :=
+  env.header.mainModule
+
+def getModuleIdxFor? (env : Environment) (declName : Name) : Option ModuleIdx :=
+  -- async constants are always from the current module
+  env.checkedWithoutAsync.const2ModIdx[declName]?
+
+def isConstructor (env : Environment) (declName : Name) : Bool :=
+  match env.find? declName with
+  | some (.ctorInfo _) => true
+  | _                  => false
+
+def isSafeDefinition (env : Environment) (declName : Name) : Bool :=
+  match env.find? declName with
+  | some (.defnInfo { safety := .safe, .. }) => true
+  | _ => false
+
+def getModuleIdx? (env : Environment) (moduleName : Name) : Option ModuleIdx :=
+  env.header.moduleNames.findIdx? (· == moduleName)
 
 end Environment
 
@@ -385,20 +864,22 @@ opaque EnvExtensionInterfaceImp : EnvExtensionInterface
 def EnvExtension (σ : Type) : Type := EnvExtensionInterfaceImp.ext σ
 
 private def ensureExtensionsArraySize (env : Environment) : IO Environment := do
-  let exts ← EnvExtensionInterfaceImp.ensureExtensionsSize env.extensions
-  return { env with extensions := exts }
+  let exts ← EnvExtensionInterfaceImp.ensureExtensionsSize env.checked.get.extensions
+  return env.modifyCheckedAsync ({ · with extensions := exts })
 
 namespace EnvExtension
 instance {σ} [s : Inhabited σ] : Inhabited (EnvExtension σ) := EnvExtensionInterfaceImp.inhabitedExt s
 
 def setState {σ : Type} (ext : EnvExtension σ) (env : Environment) (s : σ) : Environment :=
-  { env with extensions := EnvExtensionInterfaceImp.setState ext env.extensions s }
+  let checked := env.checked.get
+  env.setCheckedSync { checked with extensions := EnvExtensionInterfaceImp.setState ext checked.extensions s }
 
 def modifyState {σ : Type} (ext : EnvExtension σ) (env : Environment) (f : σ → σ) : Environment :=
-  { env with extensions := EnvExtensionInterfaceImp.modifyState ext env.extensions f }
+  let checked := env.checked.get
+  env.setCheckedSync { checked with extensions := EnvExtensionInterfaceImp.modifyState ext checked.extensions f }
 
 def getState {σ : Type} [Inhabited σ] (ext : EnvExtension σ) (env : Environment) : σ :=
-  EnvExtensionInterfaceImp.getState ext env.extensions
+  EnvExtensionInterfaceImp.getState ext env.checked.get.extensions
 
 end EnvExtension
 
@@ -418,11 +899,13 @@ def mkEmptyEnvironment (trustLevel : UInt32 := 0) : IO Environment := do
   if initializing then throw (IO.userError "environment objects cannot be created during initialization")
   let exts ← mkInitialExtensionStates
   pure {
-    const2ModIdx    := {}
-    constants       := {}
-    header          := { trustLevel := trustLevel }
-    extraConstNames := {}
-    extensions      := exts
+    checkedWithoutAsync := {
+      const2ModIdx    := {}
+      constants       := {}
+      header          := { trustLevel }
+      extraConstNames := {}
+      extensions      := exts
+    }
   }
 
 structure PersistentEnvExtensionState (α : Type) (σ : Type) where
@@ -706,11 +1189,12 @@ def mkModuleData (env : Environment) : IO ModuleData := do
   let entries := pExts.map fun pExt =>
     let state := pExt.getState env
     (pExt.name, pExt.exportEntriesFn state)
-  let constNames := env.constants.foldStage2 (fun names name _ => names.push name) #[]
-  let constants  := env.constants.foldStage2 (fun cs _ c => cs.push c) #[]
+  let kenv := env.toKernelEnv
+  let constNames := kenv.constants.foldStage2 (fun names name _ => names.push name) #[]
+  let constants  := kenv.constants.foldStage2 (fun cs _ c => cs.push c) #[]
   return {
     imports         := env.header.imports
-    extraConstNames := env.extraConstNames.toArray
+    extraConstNames := env.checked.get.extraConstNames.toArray
     constNames, constants, entries
   }
 
@@ -731,19 +1215,23 @@ def mkExtNameMap (startingAt : Nat) : IO (Std.HashMap Name Nat) := do
   return result
 
 private def setImportedEntries (env : Environment) (mods : Array ModuleData) (startingAt : Nat := 0) : IO Environment := do
-  let mut env := env
+  -- We work directly on the states array instead of `env` as `Environment.modifyState` introduces
+  -- significant overhead on such frequent calls
+  let mut states := env.checkedWithoutAsync.extensions
   let extDescrs ← persistentEnvExtensionsRef.get
   /- For extensions starting at `startingAt`, ensure their `importedEntries` array have size `mods.size`. -/
   for extDescr in extDescrs[startingAt:] do
-    env := extDescr.toEnvExtension.modifyState env fun s => { s with importedEntries := mkArray mods.size #[] }
+    states := EnvExtensionInterfaceImp.modifyState extDescr.toEnvExtension states fun s =>
+      { s with importedEntries := mkArray mods.size #[] }
   /- For each module `mod`, and `mod.entries`, if the extension name is one of the extensions after `startingAt`, set `entries` -/
   let extNameIdx ← mkExtNameMap startingAt
   for h : modIdx in [:mods.size] do
     let mod := mods[modIdx]
     for (extName, entries) in mod.entries do
       if let some entryIdx := extNameIdx[extName]? then
-        env := extDescrs[entryIdx]!.toEnvExtension.modifyState env fun s => { s with importedEntries := s.importedEntries.set! modIdx entries }
-  return env
+        states := EnvExtensionInterfaceImp.modifyState extDescrs[entryIdx]!.toEnvExtension states fun s =>
+          { s with importedEntries := s.importedEntries.set! modIdx entries }
+  return env.setCheckedSync { env.checkedWithoutAsync with extensions := states }
 
 /--
   "Forward declaration" needed for updating the attribute table with user-defined attributes.
@@ -873,17 +1361,17 @@ def finalizeImport (s : ImportState) (imports : Array Import) (opts : Options) (
   let constants : ConstMap := SMap.fromHashMap constantMap false
   let exts ← mkInitialExtensionStates
   let mut env : Environment := {
-    const2ModIdx    := const2ModIdx
-    constants       := constants
-    extraConstNames := {}
-    extensions      := exts
-    header          := {
-      quotInit     := !imports.isEmpty -- We assume `core.lean` initializes quotient module
-      trustLevel   := trustLevel
-      imports      := imports
-      regions      := s.regions
-      moduleNames  := s.moduleNames
-      moduleData   := s.moduleData
+    checkedWithoutAsync := {
+      const2ModIdx, constants
+      quotInit        := !imports.isEmpty -- We assume `core.lean` initializes quotient module
+      extraConstNames := {}
+      extensions      := exts
+      header     := {
+        trustLevel, imports
+        regions      := s.regions
+        moduleNames  := s.moduleNames
+        moduleData   := s.moduleData
+      }
     }
   }
   env ← setImportedEntries env s.moduleData
@@ -946,54 +1434,21 @@ 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
+@[inherit_doc Kernel.Environment.enableDiag]
+def Kernel.enableDiag (env : Lean.Environment) (flag : Bool) : Lean.Environment :=
+  env.modifyCheckedAsync (·.enableDiag flag)
 
-/--
-Extension for storting diagnostic information.
+def Kernel.isDiagnosticsEnabled (env : Lean.Environment) : Bool :=
+  env.checkedWithoutAsync.isDiagnosticsEnabled
 
-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 {})
+def Kernel.resetDiag (env : Lean.Environment) : Lean.Environment :=
+  env.modifyCheckedAsync (·.resetDiag)
 
-@[export lean_kernel_diag_is_enabled]
-def Kernel.Diagnostics.isEnabled (d : Diagnostics) : Bool :=
-  d.enabled
+def Kernel.getDiagnostics (env : Lean.Environment) : Diagnostics :=
+  env.checked.get.diagnostics
 
-/-- 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
+def Kernel.setDiagnostics (env : Lean.Environment) (diag : Diagnostics) : Lean.Environment :=
+  env.modifyCheckedAsync (·.setDiagnostics diag)
 
 namespace Environment
 
@@ -1009,27 +1464,9 @@ def isNamespace (env : Environment) (n : Name) : Bool :=
 def getNamespaceSet (env : Environment) : NameSSet :=
   namespacesExt.getState env
 
-private def isNamespaceName : Name → Bool
-  | .str .anonymous _ => true
-  | .str p _          => isNamespaceName p
-  | _                 => false
-
-private def registerNamePrefixes : Environment → Name → Environment
-  | env, .str p _ => if isNamespaceName p then registerNamePrefixes (registerNamespace env p) p else env
-  | env, _        => env
-
-@[export lean_environment_add]
-private def add (env : Environment) (cinfo : ConstantInfo) : Environment :=
-  let name := cinfo.name
-  let env := match name with
-    | .str _ s =>
-      if s.get 0 == '_' then
-        -- Do not register namespaces that only contain internal declarations.
-        env
-      else
-        registerNamePrefixes env name
-    | _ => env
-  env.addAux cinfo
+@[export lean_elab_environment_update_base_after_kernel_add]
+private def updateBaseAfterKernelAdd (env : Environment) (kernel : Kernel.Environment) : Environment :=
+  env.setCheckedSync kernel
 
 @[export lean_display_stats]
 def displayStats (env : Environment) : IO Unit := do
@@ -1039,7 +1476,7 @@ def displayStats (env : Environment) : IO Unit := do
   IO.println ("number of memory-mapped modules:       " ++ toString (env.header.regions.filter (·.isMemoryMapped) |>.size));
   IO.println ("number of buckets for imported consts: " ++ toString env.constants.numBuckets);
   IO.println ("trust level:                           " ++ toString env.header.trustLevel);
-  IO.println ("number of extensions:                  " ++ toString env.extensions.size);
+  IO.println ("number of extensions:                  " ++ toString env.checkedWithoutAsync.extensions.size);
   pExtDescrs.forM fun extDescr => do
     IO.println ("extension '" ++ toString extDescr.name ++ "'")
     let s := extDescr.toEnvExtension.getState env
@@ -1085,27 +1522,33 @@ namespace Kernel
 
 /--
   Kernel isDefEq predicate. We use it mainly for debugging purposes.
-  Recall that the Kernel type checker does not support metavariables.
+  Recall that the kernel type checker does not support metavariables.
   When implementing automation, consider using the `MetaM` methods. -/
+-- We use `Lean.Environment` for ease of use; as this is a debugging function, we forgo a
+-- `Kernel.Environment` base variant
 @[extern "lean_kernel_is_def_eq"]
-opaque isDefEq (env : Environment) (lctx : LocalContext) (a b : Expr) : Except KernelException Bool
+opaque isDefEq (env : Lean.Environment) (lctx : LocalContext) (a b : Expr) : Except Kernel.Exception Bool
 
-def isDefEqGuarded (env : Environment) (lctx : LocalContext) (a b : Expr) : Bool :=
+def isDefEqGuarded (env : Lean.Environment) (lctx : LocalContext) (a b : Expr) : Bool :=
   if let .ok result := isDefEq env lctx a b then result else false
 
 /--
   Kernel WHNF function. We use it mainly for debugging purposes.
-  Recall that the Kernel type checker does not support metavariables.
+  Recall that the kernel type checker does not support metavariables.
   When implementing automation, consider using the `MetaM` methods. -/
+-- We use `Lean.Environment` for ease of use; as this is a debugging function, we forgo a
+-- `Kernel.Environment` base variant
 @[extern "lean_kernel_whnf"]
-opaque whnf (env : Environment) (lctx : LocalContext) (a : Expr) : Except KernelException Expr
+opaque whnf (env : Lean.Environment) (lctx : LocalContext) (a : Expr) : Except Kernel.Exception Expr
 
 /--
   Kernel typecheck function. We use it mainly for debugging purposes.
   Recall that the Kernel type checker does not support metavariables.
   When implementing automation, consider using the `MetaM` methods. -/
+-- We use `Lean.Environment` for ease of use; as this is a debugging function, we forgo a
+-- `Kernel.Environment` base variant
 @[extern "lean_kernel_check"]
-opaque check (env : Environment) (lctx : LocalContext) (a : Expr) : Except KernelException Expr
+opaque check (env : Lean.Environment) (lctx : LocalContext) (a : Expr) : Except Kernel.Exception Expr
 
 end Kernel
 

src/Lean/Exception.lean

@@ -89,11 +89,11 @@ def ofExcept [Monad m] [MonadError m] [ToMessageData ε] (x : Except ε α) : m
 /--
 Throw an error exception for the given kernel exception.
 -/
-def throwKernelException [Monad m] [MonadError m] [MonadOptions m] (ex : KernelException) : m α := do
+def throwKernelException [Monad m] [MonadError m] [MonadOptions m] (ex : Kernel.Exception) : m α := do
   Lean.throwError <| ex.toMessageData (← getOptions)
 
 /-- Lift from `Except KernelException` to `m` when `m` can throw kernel exceptions. -/
-def ofExceptKernelException [Monad m] [MonadError m] [MonadOptions m] (x : Except KernelException α) : m α :=
+def ofExceptKernelException [Monad m] [MonadError m] [MonadOptions m] (x : Except Kernel.Exception α) : m α :=
   match x with
   | .ok a    => return a
   | .error e => throwKernelException e

src/Lean/Expr.lean

@@ -639,7 +639,7 @@ def mkFVar (fvarId : FVarId) : Expr :=
 /--
 `.mvar mvarId` is now the preferred form.
 This function is seldom used, metavariables are often created using functions such
-as `mkFresheExprMVar` at `MetaM`.
+as `mkFreshExprMVar` at `MetaM`.
 -/
 def mkMVar (mvarId : MVarId) : Expr :=
   .mvar mvarId

src/Lean/Message.lean

@@ -448,6 +448,9 @@ def markAllReported (log : MessageLog) : MessageLog :=
 def errorsToWarnings (log : MessageLog) : MessageLog :=
   { unreported := log.unreported.map (fun m => match m.severity with | MessageSeverity.error => { m with severity := MessageSeverity.warning } | _ => m) }
 
+def errorsToInfos (log : MessageLog) : MessageLog :=
+  { unreported := log.unreported.map (fun m => match m.severity with | MessageSeverity.error => { m with severity := MessageSeverity.information } | _ => m) }
+
 def getInfoMessages (log : MessageLog) : MessageLog :=
   { unreported := log.unreported.filter fun m => match m.severity with | MessageSeverity.information => true | _ => false }
 
@@ -537,12 +540,12 @@ macro_rules
 def toMessageList (msgs : Array MessageData) : MessageData :=
   indentD (MessageData.joinSep msgs.toList m!"\n\n")
 
-namespace KernelException
+namespace Kernel.Exception
 
 private def mkCtx (env : Environment) (lctx : LocalContext) (opts : Options) (msg : MessageData) : MessageData :=
-  MessageData.withContext { env := env, mctx := {}, lctx := lctx, opts := opts } msg
+  MessageData.withContext { env := .ofKernelEnv env, mctx := {}, lctx := lctx, opts := opts } msg
 
-def toMessageData (e : KernelException) (opts : Options) : MessageData :=
+def toMessageData (e : Kernel.Exception) (opts : Options) : MessageData :=
   match e with
   | unknownConstant env constName       => mkCtx env {} opts m!"(kernel) unknown constant '{constName}'"
   | alreadyDeclared env constName       => mkCtx env {} opts m!"(kernel) constant has already been declared '{.ofConstName constName true}'"
@@ -570,5 +573,5 @@ def toMessageData (e : KernelException) (opts : Options) : MessageData :=
   | deepRecursion                       => "(kernel) deep recursion detected"
   | interrupted                         => "(kernel) interrupted"
 
-end KernelException
+end Kernel.Exception
 end Lean

src/Lean/Meta/AppBuilder.lean

@@ -11,14 +11,14 @@ import Lean.Meta.DecLevel
 
 namespace Lean.Meta
 
-/-- Return `id e` -/
+/-- Returns `id e` -/
 def mkId (e : Expr) : MetaM Expr := do
   let type ← inferType e
   let u    ← getLevel type
   return mkApp2 (mkConst ``id [u]) type e
 
 /--
-  Given `e` s.t. `inferType e` is definitionally equal to `expectedType`, return
+  Given `e` s.t. `inferType e` is definitionally equal to `expectedType`, returns
   term `@id expectedType e`. -/
 def mkExpectedTypeHint (e : Expr) (expectedType : Expr) : MetaM Expr := do
   let u ← getLevel expectedType
@@ -38,13 +38,13 @@ def mkLetFun (x : Expr) (v : Expr) (e : Expr) : MetaM Expr := do
   let u2 ← getLevel ety
   return mkAppN (.const ``letFun [u1, u2]) #[α, β, v, f]
 
-/-- Return `a = b`. -/
+/-- Returns `a = b`. -/
 def mkEq (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getLevel aType
   return mkApp3 (mkConst ``Eq [u]) aType a b
 
-/-- Return `HEq a b`. -/
+/-- Returns `HEq a b`. -/
 def mkHEq (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let bType ← inferType b
@@ -52,7 +52,7 @@ def mkHEq (a b : Expr) : MetaM Expr := do
   return mkApp4 (mkConst ``HEq [u]) aType a bType b
 
 /--
-  If `a` and `b` have definitionally equal types, return `Eq a b`, otherwise return `HEq a b`.
+  If `a` and `b` have definitionally equal types, returns `Eq a b`, otherwise returns `HEq a b`.
 -/
 def mkEqHEq (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
@@ -63,25 +63,25 @@ def mkEqHEq (a b : Expr) : MetaM Expr := do
   else
     return mkApp4 (mkConst ``HEq [u]) aType a bType b
 
-/-- Return a proof of `a = a`. -/
+/-- Returns a proof of `a = a`. -/
 def mkEqRefl (a : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getLevel aType
   return mkApp2 (mkConst ``Eq.refl [u]) aType a
 
-/-- Return a proof of `HEq a a`. -/
+/-- Returns a proof of `HEq a a`. -/
 def mkHEqRefl (a : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getLevel aType
   return mkApp2 (mkConst ``HEq.refl [u]) aType a
 
-/-- Given `hp : P` and `nhp : Not P` returns an instance of type `e`. -/
+/-- Given `hp : P` and `nhp : Not P`, returns an instance of type `e`. -/
 def mkAbsurd (e : Expr) (hp hnp : Expr) : MetaM Expr := do
   let p ← inferType hp
   let u ← getLevel e
   return mkApp4 (mkConst ``absurd [u]) p e hp hnp
 
-/-- Given `h : False`, return an instance of type `e`. -/
+/-- Given `h : False`, returns an instance of type `e`. -/
 def mkFalseElim (e : Expr) (h : Expr) : MetaM Expr := do
   let u ← getLevel e
   return mkApp2 (mkConst ``False.elim [u]) e h
@@ -108,7 +108,7 @@ def mkEqSymm (h : Expr) : MetaM Expr := do
       return mkApp4 (mkConst ``Eq.symm [u]) α a b h
     | none => throwAppBuilderException ``Eq.symm ("equality proof expected" ++ hasTypeMsg h hType)
 
-/-- Given `h₁ : a = b` and `h₂ : b = c` returns a proof of `a = c`. -/
+/-- Given `h₁ : a = b` and `h₂ : b = c`, returns a proof of `a = c`. -/
 def mkEqTrans (h₁ h₂ : Expr) : MetaM Expr := do
   if h₁.isAppOf ``Eq.refl then
     return h₂
@@ -185,7 +185,7 @@ def mkHEqOfEq (h : Expr) : MetaM Expr := do
   return mkApp4 (mkConst ``heq_of_eq [u]) α a b h
 
 /--
-If `e` is `@Eq.refl α a`, return `a`.
+If `e` is `@Eq.refl α a`, returns `a`.
 -/
 def isRefl? (e : Expr) : Option Expr := do
   if e.isAppOfArity ``Eq.refl 2 then
@@ -194,7 +194,7 @@ def isRefl? (e : Expr) : Option Expr := do
     none
 
 /--
-If `e` is `@congrArg α β a b f h`, return `α`, `f` and `h`.
+If `e` is `@congrArg α β a b f h`, returns `α`, `f` and `h`.
 Also works if `e` can be turned into such an application (e.g. `congrFun`).
 -/
 def congrArg? (e : Expr) : MetaM (Option (Expr × Expr × Expr)) := do
@@ -336,13 +336,14 @@ private def withAppBuilderTrace [ToMessageData α] [ToMessageData β]
       throw ex
 
 /--
-  Return the application `constName xs`.
+  Returns the application `constName xs`.
   It tries to fill the implicit arguments before the last element in `xs`.
 
   Remark:
   ``mkAppM `arbitrary #[α]`` returns `@arbitrary.{u} α` without synthesizing
   the implicit argument occurring after `α`.
-  Given a `x : ([Decidable p] → Bool) × Nat`, ``mkAppM `Prod.fst #[x]`` returns `@Prod.fst ([Decidable p] → Bool) Nat x`.
+  Given a `x : ([Decidable p] → Bool) × Nat`, ``mkAppM `Prod.fst #[x]``,
+  returns `@Prod.fst ([Decidable p] → Bool) Nat x`.
 -/
 def mkAppM (constName : Name) (xs : Array Expr) : MetaM Expr := do
   withAppBuilderTrace constName xs do withNewMCtxDepth do
@@ -465,8 +466,9 @@ def mkPure (monad : Expr) (e : Expr) : MetaM Expr :=
   mkAppOptM ``Pure.pure #[monad, none, none, e]
 
 /--
-  `mkProjection s fieldName` returns an expression for accessing field `fieldName` of the structure `s`.
-  Remark: `fieldName` may be a subfield of `s`. -/
+`mkProjection s fieldName` returns an expression for accessing field `fieldName` of the structure `s`.
+Remark: `fieldName` may be a subfield of `s`.
+-/
 partial def mkProjection (s : Expr) (fieldName : Name) : MetaM Expr := do
   let type ← inferType s
   let type ← whnf type
@@ -520,11 +522,11 @@ def mkSome (type value : Expr) : MetaM Expr := do
   let u ← getDecLevel type
   return mkApp2 (mkConst ``Option.some [u]) type value
 
-/-- Return `Decidable.decide p` -/
+/-- Returns `Decidable.decide p` -/
 def mkDecide (p : Expr) : MetaM Expr :=
   mkAppOptM ``Decidable.decide #[p, none]
 
-/-- Return a proof for `p : Prop` using `decide p` -/
+/-- Returns a proof for `p : Prop` using `decide p` -/
 def mkDecideProof (p : Expr) : MetaM Expr := do
   let decP      ← mkDecide p
   let decEqTrue ← mkEq decP (mkConst ``Bool.true)
@@ -532,59 +534,75 @@ def mkDecideProof (p : Expr) : MetaM Expr := do
   let h         ← mkExpectedTypeHint h decEqTrue
   mkAppM ``of_decide_eq_true #[h]
 
-/-- Return `a < b` -/
+/-- Returns `a < b` -/
 def mkLt (a b : Expr) : MetaM Expr :=
   mkAppM ``LT.lt #[a, b]
 
-/-- Return `a <= b` -/
+/-- Returns `a <= b` -/
 def mkLe (a b : Expr) : MetaM Expr :=
   mkAppM ``LE.le #[a, b]
 
-/-- Return `Inhabited.default α` -/
+/-- Returns `Inhabited.default α` -/
 def mkDefault (α : Expr) : MetaM Expr :=
   mkAppOptM ``Inhabited.default #[α, none]
 
-/-- Return `@Classical.ofNonempty α _` -/
+/-- Returns `@Classical.ofNonempty α _` -/
 def mkOfNonempty (α : Expr) : MetaM Expr := do
   mkAppOptM ``Classical.ofNonempty #[α, none]
 
-/-- Return `funext h` -/
+/-- Returns `funext h` -/
 def mkFunExt (h : Expr) : MetaM Expr :=
   mkAppM ``funext #[h]
 
-/-- Return `propext h` -/
+/-- Returns `propext h` -/
 def mkPropExt (h : Expr) : MetaM Expr :=
   mkAppM ``propext #[h]
 
-/-- Return `let_congr h₁ h₂` -/
+/-- Returns `let_congr h₁ h₂` -/
 def mkLetCongr (h₁ h₂ : Expr) : MetaM Expr :=
   mkAppM ``let_congr #[h₁, h₂]
 
-/-- Return `let_val_congr b h` -/
+/-- Returns `let_val_congr b h` -/
 def mkLetValCongr (b h : Expr) : MetaM Expr :=
   mkAppM ``let_val_congr #[b, h]
 
-/-- Return `let_body_congr a h` -/
+/-- Returns `let_body_congr a h` -/
 def mkLetBodyCongr (a h : Expr) : MetaM Expr :=
   mkAppM ``let_body_congr #[a, h]
 
-/-- Return `of_eq_true h` -/
-def mkOfEqTrue (h : Expr) : MetaM Expr :=
-  mkAppM ``of_eq_true #[h]
+/-- Returns `@of_eq_true p h` -/
+def mkOfEqTrueCore (p : Expr) (h : Expr) : Expr :=
+  match_expr h with
+  | eq_true _ h => h
+  | _ => mkApp2 (mkConst ``of_eq_true) p h
 
-/-- Return `eq_true h` -/
-def mkEqTrue (h : Expr) : MetaM Expr :=
-  mkAppM ``eq_true #[h]
+/-- Returns `of_eq_true h` -/
+def mkOfEqTrue (h : Expr) : MetaM Expr := do
+  match_expr h with
+  | eq_true _ h => return h
+  | _ => mkAppM ``of_eq_true #[h]
+
+/-- Returns `eq_true h` -/
+def mkEqTrueCore (p : Expr) (h : Expr) : Expr :=
+  match_expr h with
+  | of_eq_true _ h => h
+  | _ => mkApp2 (mkConst ``eq_true) p h
+
+/-- Returns `eq_true h` -/
+def mkEqTrue (h : Expr) : MetaM Expr := do
+  match_expr h with
+  | of_eq_true _ h => return h
+  | _ => return mkApp2 (mkConst ``eq_true) (← inferType h) h
 
 /--
-  Return `eq_false h`
+  Returns `eq_false h`
   `h` must have type definitionally equal to `¬ p` in the current
   reducibility setting. -/
 def mkEqFalse (h : Expr) : MetaM Expr :=
   mkAppM ``eq_false #[h]
 
 /--
-  Return `eq_false' h`
+  Returns `eq_false' h`
   `h` must have type definitionally equal to `p → False` in the current
   reducibility setting. -/
 def mkEqFalse' (h : Expr) : MetaM Expr :=
@@ -602,7 +620,7 @@ def mkImpDepCongrCtx (h₁ h₂ : Expr) : MetaM Expr :=
 def mkForallCongr (h : Expr) : MetaM Expr :=
   mkAppM ``forall_congr #[h]
 
-/-- Return instance for `[Monad m]` if there is one -/
+/-- Returns instance for `[Monad m]` if there is one -/
 def isMonad? (m : Expr) : MetaM (Option Expr) :=
   try
     let monadType ← mkAppM `Monad #[m]
@@ -613,52 +631,52 @@ def isMonad? (m : Expr) : MetaM (Option Expr) :=
   catch _ =>
     pure none
 
-/-- Return `(n : type)`, a numeric literal of type `type`. The method fails if we don't have an instance `OfNat type n` -/
+/-- Returns `(n : type)`, a numeric literal of type `type`. The method fails if we don't have an instance `OfNat type n` -/
 def mkNumeral (type : Expr) (n : Nat) : MetaM Expr := do
   let u ← getDecLevel type
   let inst ← synthInstance (mkApp2 (mkConst ``OfNat [u]) type (mkRawNatLit n))
   return mkApp3 (mkConst ``OfNat.ofNat [u]) type (mkRawNatLit n) inst
 
 /--
-  Return `a op b`, where `op` has name `opName` and is implemented using the typeclass `className`.
-  This method assumes `a` and `b` have the same type, and typeclass `className` is heterogeneous.
-  Examples of supported classes: `HAdd`, `HSub`, `HMul`.
-  We use heterogeneous operators to ensure we have a uniform representation.
-  -/
+Returns `a op b`, where `op` has name `opName` and is implemented using the typeclass `className`.
+This method assumes `a` and `b` have the same type, and typeclass `className` is heterogeneous.
+Examples of supported classes: `HAdd`, `HSub`, `HMul`.
+We use heterogeneous operators to ensure we have a uniform representation.
+-/
 private def mkBinaryOp (className : Name) (opName : Name) (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getDecLevel aType
   let inst ← synthInstance (mkApp3 (mkConst className [u, u, u]) aType aType aType)
   return mkApp6 (mkConst opName [u, u, u]) aType aType aType inst a b
 
-/-- Return `a + b` using a heterogeneous `+`. This method assumes `a` and `b` have the same type. -/
+/-- Returns `a + b` using a heterogeneous `+`. This method assumes `a` and `b` have the same type. -/
 def mkAdd (a b : Expr) : MetaM Expr := mkBinaryOp ``HAdd ``HAdd.hAdd a b
 
-/-- Return `a - b` using a heterogeneous `-`. This method assumes `a` and `b` have the same type. -/
+/-- Returns `a - b` using a heterogeneous `-`. This method assumes `a` and `b` have the same type. -/
 def mkSub (a b : Expr) : MetaM Expr := mkBinaryOp ``HSub ``HSub.hSub a b
 
-/-- Return `a * b` using a heterogeneous `*`. This method assumes `a` and `b` have the same type. -/
+/-- Returns `a * b` using a heterogeneous `*`. This method assumes `a` and `b` have the same type. -/
 def mkMul (a b : Expr) : MetaM Expr := mkBinaryOp ``HMul ``HMul.hMul a b
 
 /--
-  Return `a r b`, where `r` has name `rName` and is implemented using the typeclass `className`.
-  This method assumes `a` and `b` have the same type.
-  Examples of supported classes: `LE` and `LT`.
-  We use heterogeneous operators to ensure we have a uniform representation.
-  -/
+Returns `a r b`, where `r` has name `rName` and is implemented using the typeclass `className`.
+This method assumes `a` and `b` have the same type.
+Examples of supported classes: `LE` and `LT`.
+We use heterogeneous operators to ensure we have a uniform representation.
+-/
 private def mkBinaryRel (className : Name) (rName : Name) (a b : Expr) : MetaM Expr := do
   let aType ← inferType a
   let u ← getDecLevel aType
   let inst ← synthInstance (mkApp (mkConst className [u]) aType)
   return mkApp4 (mkConst rName [u]) aType inst a b
 
-/-- Return `a ≤ b`. This method assumes `a` and `b` have the same type. -/
+/-- Returns `a ≤ b`. This method assumes `a` and `b` have the same type. -/
 def mkLE (a b : Expr) : MetaM Expr := mkBinaryRel ``LE ``LE.le a b
 
-/-- Return `a < b`. This method assumes `a` and `b` have the same type. -/
+/-- Returns `a < b`. This method assumes `a` and `b` have the same type. -/
 def mkLT (a b : Expr) : MetaM Expr := mkBinaryRel ``LT ``LT.lt a b
 
-/-- Given `h : a = b`, return a proof for `a ↔ b`. -/
+/-- Given `h : a = b`, returns a proof for `a ↔ b`. -/
 def mkIffOfEq (h : Expr) : MetaM Expr := do
   if h.isAppOfArity ``propext 3 then
     return h.appArg!

src/Lean/Meta/Basic.lean

@@ -1964,15 +1964,22 @@ def sortFVarIds (fvarIds : Array FVarId) : MetaM (Array FVarId) := do
 
 end Methods
 
+/--
+Return `some info` if `declName` is an inductive predicate where `info : InductiveVal`.
+That is, `inductive` type in `Prop`.
+-/
+def isInductivePredicate? (declName : Name) : MetaM (Option InductiveVal) := do
+  match (← getEnv).find? declName with
+  | some (.inductInfo info) =>
+    forallTelescopeReducing info.type fun _ type => do
+      match (← whnfD type) with
+      | .sort u .. => if u == levelZero then return some info else return none
+      | _ => return none
+  | _ => return none
+
 /-- Return `true` if `declName` is an inductive predicate. That is, `inductive` type in `Prop`. -/
 def isInductivePredicate (declName : Name) : MetaM Bool := do
-  match (← getEnv).find? declName with
-  | some (.inductInfo { type := type, ..}) =>
-    forallTelescopeReducing type fun _ type => do
-      match (← whnfD type) with
-      | .sort u .. => return u == levelZero
-      | _ => return false
-  | _ => return false
+  return (← isInductivePredicate? declName).isSome
 
 def isListLevelDefEqAux : List Level → List Level → MetaM Bool
   | [],    []    => return true

src/Lean/Meta/Constructions/CasesOn.lean

@@ -9,13 +9,13 @@ import Lean.Meta.Basic
 
 namespace Lean
 
-@[extern "lean_mk_cases_on"] opaque mkCasesOnImp (env : Environment) (declName : @& Name) : Except KernelException Declaration
+@[extern "lean_mk_cases_on"] opaque mkCasesOnImp (env : Kernel.Environment) (declName : @& Name) : Except Kernel.Exception Declaration
 
 open Meta
 
 def mkCasesOn (declName : Name) : MetaM Unit := do
   let name := mkCasesOnName declName
-  let decl ← ofExceptKernelException (mkCasesOnImp (← getEnv) declName)
+  let decl ← ofExceptKernelException (mkCasesOnImp (← getEnv).toKernelEnv declName)
   addDecl decl
   setReducibleAttribute name
   modifyEnv fun env => markAuxRecursor env name

src/Lean/Meta/Constructions/NoConfusion.lean

@@ -10,8 +10,8 @@ import Lean.Meta.CompletionName
 
 namespace Lean
 
-@[extern "lean_mk_no_confusion_type"] opaque mkNoConfusionTypeCoreImp (env : Environment) (declName : @& Name) : Except KernelException Declaration
-@[extern "lean_mk_no_confusion"] opaque mkNoConfusionCoreImp (env : Environment) (declName : @& Name) : Except KernelException Declaration
+@[extern "lean_mk_no_confusion_type"] opaque mkNoConfusionTypeCoreImp (env : Environment) (declName : @& Name) : Except Kernel.Exception Declaration
+@[extern "lean_mk_no_confusion"] opaque mkNoConfusionCoreImp (env : Environment) (declName : @& Name) : Except Kernel.Exception Declaration
 
 open Meta
 

src/Lean/Meta/Diagnostics.lean

@@ -72,12 +72,12 @@ def mkDiagSynthPendingFailure (failures : PHashMap Expr MessageData) : MetaM Dia
 /--
 We use below that this returns `m` unchanged if `s.isEmpty`
 -/
-def appendSection (m : MessageData) (cls : Name) (header : String) (s : DiagSummary) (resultSummary := true) : MessageData :=
+def appendSection (m : Array MessageData) (cls : Name) (header : String) (s : DiagSummary) (resultSummary := true) : Array MessageData :=
   if s.isEmpty then
     m
   else
     let header := if resultSummary then s!"{header} (max: {s.max}, num: {s.data.size}):" else header
-    m ++ .trace { cls } header s.data
+    m.push <| .trace { cls } header s.data
 
 def reportDiag : MetaM Unit := do
   if (← isDiagnosticsEnabled) then
@@ -89,7 +89,7 @@ def reportDiag : MetaM Unit := do
     let inst ← mkDiagSummaryForUsedInstances
     let synthPending ← mkDiagSynthPendingFailure (← get).diag.synthPendingFailures
     let unfoldKernel ← mkDiagSummary `kernel (Kernel.getDiagnostics (← getEnv)).unfoldCounter
-    let m := MessageData.nil
+    let m := #[]
     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
@@ -99,8 +99,8 @@ def reportDiag : MetaM Unit := do
               synthPending (resultSummary := false)
     let m := appendSection m `def_eq "heuristic for solving `f a =?= f b`" heu
     let m := appendSection m `kernel "unfolded declarations" unfoldKernel
-    unless m matches .nil do
-      let m := m ++ "use `set_option diagnostics.threshold <num>` to control threshold for reporting counters"
-      logInfo m
+    unless m.isEmpty do
+      let m := m.push "use `set_option diagnostics.threshold <num>` to control threshold for reporting counters"
+      logInfo <| .trace { cls := `diag, collapsed := false } "Diagnostics" m
 
 end Lean.Meta

src/Lean/Meta/ExprDefEq.lean

@@ -1233,10 +1233,7 @@ private def processAssignment' (mvarApp : Expr) (v : Expr) : MetaM Bool := do
 
 private def isDeltaCandidate? (t : Expr) : MetaM (Option ConstantInfo) := do
   match t.getAppFn with
-  | .const c _ =>
-    match (← getUnfoldableConst? c) with
-    | r@(some info) => if info.hasValue then return r else return none
-    | _             => return none
+  | .const c _ => getUnfoldableConst? c
   | _ => pure none
 
 /-- Auxiliary method for isDefEqDelta -/

src/Lean/Meta/GetUnfoldableConst.lean

@@ -30,7 +30,7 @@ def canUnfold (info : ConstantInfo) : MetaM Bool := do
 
 /--
 Look up a constant name, returning the `ConstantInfo`
-if it should be unfolded at the current reducibility settings,
+if it is a def/theorem that should be unfolded at the current reducibility settings,
 or `none` otherwise.
 
 This is part of the implementation of `whnf`.
@@ -40,7 +40,7 @@ def getUnfoldableConst? (constName : Name) : MetaM (Option ConstantInfo) := do
   match (← getEnv).find? constName with
   | some (info@(.thmInfo _))  => getTheoremInfo info
   | some (info@(.defnInfo _)) => if (← canUnfold info) then return info else return none
-  | some info                 => return some info
+  | some _                    => return none
   | none                      => throwUnknownConstant constName
 
 /--
@@ -50,7 +50,6 @@ def getUnfoldableConstNoEx? (constName : Name) : MetaM (Option ConstantInfo) :=
   match (← getEnv).find? constName with
   | some (info@(.thmInfo _))  => getTheoremInfo info
   | some (info@(.defnInfo _)) => if (← canUnfold info) then return info else return none
-  | some info                 => return some info
-  | none                      => return none
+  | _                         => return none
 
 end Meta

src/Lean/Meta/IndPredBelow.lean

@@ -296,7 +296,7 @@ where
     m.apply recursor
 
   applyCtors (ms : List MVarId) : MetaM $ List MVarId := do
-    let mss ← ms.toArray.mapIdxM fun _ m => do
+    let mss ← ms.toArray.mapM fun m => do
       let m ← introNPRec m
       (← m.getType).withApp fun below args =>
       m.withContext do

src/Lean/Meta/Tactic.lean

@@ -41,3 +41,4 @@ import Lean.Meta.Tactic.FunInd
 import Lean.Meta.Tactic.Rfl
 import Lean.Meta.Tactic.Rewrites
 import Lean.Meta.Tactic.Grind
+import Lean.Meta.Tactic.Ext

src/Lean/Meta/Tactic/Ext.lean

@@ -0,0 +1,76 @@
+/-
+Copyright (c) 2021 Gabriel Ebner. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Gabriel Ebner, Mario Carneiro
+-/
+prelude
+import Init.Data.Array.InsertionSort
+import Lean.Meta.DiscrTree
+
+namespace Lean.Meta.Ext
+
+/-!
+### Environment extension for `ext` theorems
+-/
+
+/-- Information about an extensionality theorem, stored in the environment extension. -/
+structure ExtTheorem where
+  /-- Declaration name of the extensionality theorem. -/
+  declName : Name
+  /-- Priority of the extensionality theorem. -/
+  priority : Nat
+  /--
+  Key in the discrimination tree,
+  for the type in which the extensionality theorem holds.
+  -/
+  keys : Array DiscrTree.Key
+  deriving Inhabited, Repr, BEq, Hashable
+
+/-- The state of the `ext` extension environment -/
+structure ExtTheorems where
+  /-- The tree of `ext` extensions. -/
+  tree   : DiscrTree ExtTheorem := {}
+  /-- Erased `ext`s via `attribute [-ext]`. -/
+  erased  : PHashSet Name := {}
+  deriving Inhabited
+
+/-- The environment extension to track `@[ext]` theorems. -/
+builtin_initialize extExtension :
+    SimpleScopedEnvExtension ExtTheorem ExtTheorems ←
+  registerSimpleScopedEnvExtension {
+    addEntry := fun { tree, erased } thm =>
+      { tree := tree.insertCore thm.keys thm, erased := erased.erase thm.declName }
+    initial := {}
+  }
+
+/-- Gets the list of `@[ext]` theorems corresponding to the key `ty`,
+ordered from high priority to low. -/
+@[inline] def getExtTheorems (ty : Expr) : MetaM (Array ExtTheorem) := do
+  let extTheorems := extExtension.getState (← getEnv)
+  let arr ← extTheorems.tree.getMatch ty
+  let erasedArr := arr.filter fun thm => !extTheorems.erased.contains thm.declName
+  -- Using insertion sort because it is stable and the list of matches should be mostly sorted.
+  -- Most ext theorems have default priority.
+  return erasedArr.insertionSort (·.priority < ·.priority) |>.reverse
+
+/--
+Erases a name marked `ext` by adding it to the state's `erased` field and
+removing it from the state's list of `Entry`s.
+
+This is triggered by `attribute [-ext] name`.
+-/
+def ExtTheorems.eraseCore (d : ExtTheorems) (declName : Name) : ExtTheorems :=
+ { d with erased := d.erased.insert declName }
+
+/--
+Erases a name marked as a `ext` attribute.
+Check that it does in fact have the `ext` attribute by making sure it names a `ExtTheorem`
+found somewhere in the state's tree, and is not erased.
+-/
+def ExtTheorems.erase [Monad m] [MonadError m] (d : ExtTheorems) (declName : Name) :
+    m ExtTheorems := do
+  unless d.tree.containsValueP (·.declName == declName) && !d.erased.contains declName do
+    throwError "'{declName}' does not have [ext] attribute"
+  return d.eraseCore declName
+
+end Lean.Meta.Ext

src/Lean/Meta/Tactic/FVarSubst.lean

@@ -35,7 +35,7 @@ def insert (s : FVarSubst) (fvarId : FVarId) (v : Expr) : FVarSubst :=
   if s.contains fvarId then s
   else
     let map := s.map.mapVal fun e => e.replaceFVarId fvarId v;
-    { map := map.insert fvarId v }
+    { map := map.insertNew fvarId v }
 
 def erase (s : FVarSubst) (fvarId : FVarId) : FVarSubst :=
   { map := s.map.erase fvarId }

src/Lean/Meta/Tactic/Grind.lean

@@ -24,6 +24,8 @@ import Lean.Meta.Tactic.Grind.EMatchTheorem
 import Lean.Meta.Tactic.Grind.EMatch
 import Lean.Meta.Tactic.Grind.Main
 import Lean.Meta.Tactic.Grind.CasesMatch
+import Lean.Meta.Tactic.Grind.Arith
+import Lean.Meta.Tactic.Grind.Ext
 
 namespace Lean
 
@@ -37,11 +39,21 @@ builtin_initialize registerTraceClass `grind.ematch.pattern
 builtin_initialize registerTraceClass `grind.ematch.pattern.search
 builtin_initialize registerTraceClass `grind.ematch.instance
 builtin_initialize registerTraceClass `grind.ematch.instance.assignment
+builtin_initialize registerTraceClass `grind.eqResolution
 builtin_initialize registerTraceClass `grind.issues
 builtin_initialize registerTraceClass `grind.simp
 builtin_initialize registerTraceClass `grind.split
 builtin_initialize registerTraceClass `grind.split.candidate
 builtin_initialize registerTraceClass `grind.split.resolved
+builtin_initialize registerTraceClass `grind.offset
+builtin_initialize registerTraceClass `grind.offset.dist
+builtin_initialize registerTraceClass `grind.offset.internalize
+builtin_initialize registerTraceClass `grind.offset.internalize.term (inherited := true)
+builtin_initialize registerTraceClass `grind.offset.propagate
+builtin_initialize registerTraceClass `grind.offset.eq
+builtin_initialize registerTraceClass `grind.offset.eq.to (inherited := true)
+builtin_initialize registerTraceClass `grind.offset.eq.from (inherited := true)
+builtin_initialize registerTraceClass `grind.beta
 
 /-! Trace options for `grind` developers -/
 builtin_initialize registerTraceClass `grind.debug
@@ -54,4 +66,9 @@ builtin_initialize registerTraceClass `grind.debug.final
 builtin_initialize registerTraceClass `grind.debug.forallPropagator
 builtin_initialize registerTraceClass `grind.debug.split
 builtin_initialize registerTraceClass `grind.debug.canon
+builtin_initialize registerTraceClass `grind.debug.offset
+builtin_initialize registerTraceClass `grind.debug.offset.proof
+builtin_initialize registerTraceClass `grind.debug.ematch.pattern
+builtin_initialize registerTraceClass `grind.debug.beta
+
 end Lean

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

@@ -0,0 +1,10 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Grind.Arith.Util
+import Lean.Meta.Tactic.Grind.Arith.Types
+import Lean.Meta.Tactic.Grind.Arith.Offset
+import Lean.Meta.Tactic.Grind.Arith.Main

src/Lean/Meta/Tactic/Grind/Arith/Internalize.lean

@@ -0,0 +1,14 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Grind.Arith.Offset
+
+namespace Lean.Meta.Grind.Arith
+
+def internalize (e : Expr) (parent? : Option Expr) : GoalM Unit := do
+  Offset.internalize e parent?
+
+end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Inv.lean

@@ -0,0 +1,14 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Grind.Arith.Offset
+
+namespace Lean.Meta.Grind.Arith
+
+def checkInvariants : GoalM Unit :=
+  Offset.checkInvariants
+
+end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Main.lean

@@ -0,0 +1,34 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Grind.PropagatorAttr
+import Lean.Meta.Tactic.Grind.Arith.Offset
+
+namespace Lean.Meta.Grind.Arith
+
+namespace Offset
+def isCnstr? (e : Expr) : GoalM (Option (Cnstr NodeId)) :=
+  return (← get).arith.offset.cnstrs.find? { expr := e }
+
+def assertTrue (c : Cnstr NodeId) (p : Expr) : GoalM Unit := do
+  addEdge c.u c.v c.k (← mkOfEqTrue p)
+
+def assertFalse (c : Cnstr NodeId) (p : Expr) : GoalM Unit := do
+  let p := mkOfNegEqFalse (← get').nodes c p
+  let c := c.neg
+  addEdge c.u c.v c.k p
+
+end Offset
+
+builtin_grind_propagator propagateLE ↓LE.le := fun e => do
+  if (← isEqTrue e) then
+    if let some c ← Offset.isCnstr? e then
+      Offset.assertTrue c (← mkEqTrueProof e)
+  if (← isEqFalse e) then
+    if let some c ← Offset.isCnstr? e then
+      Offset.assertFalse c (← mkEqFalseProof e)
+
+end Lean.Meta.Grind.Arith

src/Lean/Meta/Tactic/Grind/Arith/Model.lean

@@ -0,0 +1,46 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Basic
+import Lean.Meta.Tactic.Grind.Types
+import Lean.Meta.Tactic.Grind.Util
+
+namespace Lean.Meta.Grind.Arith.Offset
+/-- Construct a model that statisfies all offset constraints -/
+def mkModel (goal : Goal) : MetaM (Array (Expr × Nat)) := do
+  let s := goal.arith.offset
+  let nodes := s.nodes
+  let mut pre : Array (Option Int) := mkArray nodes.size none
+  for u in [:nodes.size] do
+    let val? := s.sources[u]!.foldl (init := @none Int) fun val? v k => Id.run do
+      let some va := pre[v]! | return val?
+      let val' := va - k
+      let some val := val? | return val'
+      if val' > val then return val' else val?
+    let val? := s.targets[u]!.foldl (init := val?) fun val? v k => Id.run do
+      let some va := pre[v]! | return val?
+      let val' := va + k
+      let some val := val? | return val'
+      if val' < val then return val' else val?
+    let val := val?.getD 0
+    pre := pre.set! u (some val)
+  let min := pre.foldl (init := 0) fun min val? => Id.run do
+    let some val := val? | return min
+    if val < min then val else min
+  let mut r := {}
+  for u in [:nodes.size] do
+    let some val := pre[u]! | unreachable!
+    let val := (val - min).toNat
+    let e := nodes[u]!
+    /-
+    We should not include the assignment for auxiliary offset terms since
+    they do not provide any additional information.
+    -/
+    if (isNatOffset? e).isNone && isNatNum? e != some 0 then
+      r := r.push (e, val)
+  return r
+
+end Lean.Meta.Grind.Arith.Offset

src/Lean/Meta/Tactic/Grind/Arith/Offset.lean

@@ -0,0 +1,335 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Grind.Offset
+import Lean.Meta.Tactic.Grind.Types
+import Lean.Meta.Tactic.Grind.Arith.ProofUtil
+
+namespace Lean.Meta.Grind.Arith.Offset
+/-!
+This module implements a decision procedure for offset constraints of the form:
+```
+x + k ≤ y
+x ≤ y + k
+```
+where `k` is a numeral.
+Each constraint is represented as an edge in a weighted graph.
+The constraint `x + k ≤ y` is represented as a negative edge.
+The shortest path between two nodes in the graph corresponds to an implied inequality.
+When adding a new edge, the state is considered unsatisfiable if the new edge creates a negative cycle.
+An incremental Floyd-Warshall algorithm is used to find the shortest paths between all nodes.
+This module can also handle offset equalities of the form `x + k = y` by representing them with two edges:
+```
+x + k ≤ y
+y ≤ x + k
+```
+The main advantage of this module over a full linear integer arithmetic procedure is
+its ability to efficiently detect all implied equalities and inequalities.
+-/
+
+def get' : GoalM State := do
+  return (← get).arith.offset
+
+@[inline] def modify' (f : State → State) : GoalM Unit := do
+  modify fun s => { s with arith.offset := f s.arith.offset }
+
+def mkNode (expr : Expr) : GoalM NodeId := do
+  if let some nodeId := (← get').nodeMap.find? { expr } then
+    return nodeId
+  let nodeId : NodeId := (← get').nodes.size
+  trace[grind.offset.internalize.term] "{expr} ↦ #{nodeId}"
+  modify' fun s => { s with
+    nodes   := s.nodes.push expr
+    nodeMap := s.nodeMap.insert { expr } nodeId
+    sources := s.sources.push {}
+    targets := s.targets.push {}
+    proofs  := s.proofs.push {}
+  }
+  markAsOffsetTerm expr
+  return nodeId
+
+private def getExpr (u : NodeId) : GoalM Expr := do
+  return (← get').nodes[u]!
+
+private def getDist? (u v : NodeId) : GoalM (Option Int) := do
+  return (← get').targets[u]!.find? v
+
+private def getProof? (u v : NodeId) : GoalM (Option ProofInfo) := do
+  return (← get').proofs[u]!.find? v
+
+private def getNodeId (e : Expr) : GoalM NodeId := do
+  let some nodeId := (← get').nodeMap.find? { expr := e }
+    | throwError "internal `grind` error, term has not been internalized by offset module{indentExpr e}"
+  return nodeId
+
+/--
+Returns a proof for `u + k ≤ v` (or `u ≤ v + k`) where `k` is the
+shortest path between `u` and `v`.
+-/
+private partial def mkProofForPath (u v : NodeId) : GoalM Expr := do
+  go (← getProof? u v).get!
+where
+  go (p : ProofInfo) : GoalM Expr := do
+    if u == p.w then
+      return p.proof
+    else
+      let p' := (← getProof? u p.w).get!
+      go (mkTrans (← get').nodes p' p v)
+
+/--
+Given a new edge edge `u --(kuv)--> v` justified by proof `huv` s.t.
+it creates a negative cycle with the existing path `v --{kvu}-->* u`, i.e., `kuv + kvu < 0`,
+this function closes the current goal by constructing a proof of `False`.
+-/
+private def setUnsat (u v : NodeId) (kuv : Int) (huv : Expr) (kvu : Int) : GoalM Unit := do
+  assert! kuv + kvu < 0
+  let hvu ← mkProofForPath v u
+  let u ← getExpr u
+  let v ← getExpr v
+  closeGoal (mkUnsatProof u v kuv huv kvu hvu)
+
+/-- Sets the new shortest distance `k` between nodes `u` and `v`. -/
+private def setDist (u v : NodeId) (k : Int) : GoalM Unit := do
+  trace[grind.offset.dist] "{({ u, v, k : Cnstr NodeId})}"
+  modify' fun s => { s with
+    targets := s.targets.modify u fun es => es.insert v k
+    sources := s.sources.modify v fun es => es.insert u k
+  }
+
+private def setProof (u v : NodeId) (p : ProofInfo) : GoalM Unit := do
+  modify' fun s => { s with
+    proofs := s.proofs.modify u fun es => es.insert v p
+  }
+
+@[inline]
+private def forEachSourceOf (u : NodeId) (f : NodeId → Int → GoalM Unit) : GoalM Unit := do
+  (← get').sources[u]!.forM f
+
+@[inline]
+private def forEachTargetOf (u : NodeId) (f : NodeId → Int → GoalM Unit) : GoalM Unit := do
+  (← get').targets[u]!.forM f
+
+/-- Returns `true` if `k` is smaller than the shortest distance between `u` and `v` -/
+private def isShorter (u v : NodeId) (k : Int) : GoalM Bool := do
+  if let some k' ← getDist? u v then
+    return k < k'
+  else
+    return true
+
+/--
+Tries to assign `e` to `True`, which is represented by constraint `c` (from `u` to `v`), using the
+path `u --(k)--> v`.
+-/
+private def propagateTrue (u v : NodeId) (k : Int) (c : Cnstr NodeId) (e : Expr) : GoalM Bool := do
+  if k ≤ c.k then
+    trace[grind.offset.propagate] "{{ u, v, k : Cnstr NodeId}} ==> {e} = True"
+    let kuv ← mkProofForPath u v
+    let u ← getExpr u
+    let v ← getExpr v
+    pushEqTrue e <| mkPropagateEqTrueProof u v k kuv c.k
+    return true
+  return false
+
+/--
+Tries to assign `e` to `False`, which is represented by constraint `c` (from `v` to `u`), using the
+path `u --(k)--> v`.
+-/
+private def propagateFalse (u v : NodeId) (k : Int) (c : Cnstr NodeId) (e : Expr) : GoalM Bool := do
+  if k + c.k < 0 then
+    trace[grind.offset.propagate] "{{ u, v, k : Cnstr NodeId}} ==> {e} = False"
+    let kuv ← mkProofForPath u v
+    let u ← getExpr u
+    let v ← getExpr v
+    pushEqFalse e <| mkPropagateEqFalseProof u v k kuv c.k
+  return false
+
+/--
+Auxiliary function for implementing `propagateAll`.
+Traverses the constraints `c` (representing an expression `e`) s.t.
+`c.u = u` and `c.v = v`, it removes `c` from the list of constraints
+associated with `(u, v)` IF
+- `e` is already assigned, or
+- `f c e` returns true
+-/
+@[inline]
+private def updateCnstrsOf (u v : NodeId) (f : Cnstr NodeId → Expr → GoalM Bool) : GoalM Unit := do
+  if let some cs := (← get').cnstrsOf.find? (u, v) then
+    let cs' ← cs.filterM fun (c, e) => do
+      if (← isEqTrue e <||> isEqFalse e) then
+        return false -- constraint was already assigned
+      else
+        return !(← f c e)
+    modify' fun s => { s with cnstrsOf := s.cnstrsOf.insert (u, v) cs' }
+
+/-- Equality propagation. -/
+private def propagateEq (u v : NodeId) (k : Int) : GoalM Unit := do
+  if k != 0 then return ()
+  let some k' ← getDist? v u | return ()
+  if k' != 0 then return ()
+  let ue ← getExpr u
+  let ve ← getExpr v
+  if (← isEqv ue ve) then return ()
+  let huv ← mkProofForPath u v
+  let hvu ← mkProofForPath v u
+  trace[grind.offset.eq.from] "{ue}, {ve}"
+  pushEq ue ve <| mkApp4 (mkConst ``Grind.Nat.eq_of_le_of_le) ue ve huv hvu
+
+/-- Performs constraint propagation. -/
+private def propagateAll (u v : NodeId) (k : Int) : GoalM Unit := do
+  updateCnstrsOf u v fun c e => return !(← propagateTrue u v k c e)
+  updateCnstrsOf v u fun c e => return !(← propagateFalse u v k c e)
+  propagateEq u v k
+
+/--
+If `isShorter u v k`, updates the shortest distance between `u` and `v`.
+`w` is the penultimate node in the path from `u` to `v`.
+-/
+private def updateIfShorter (u v : NodeId) (k : Int) (w : NodeId) : GoalM Unit := do
+  if (← isShorter u v k) then
+    setDist u v k
+    setProof u v (← getProof? w v).get!
+    propagateAll u v k
+
+/--
+Adds an edge `u --(k) --> v` justified by the proof term `p`, and then
+if no negative cycle was created, updates the shortest distance of affected
+node pairs.
+-/
+def addEdge (u : NodeId) (v : NodeId) (k : Int) (p : Expr) : GoalM Unit := do
+  if (← isInconsistent) then return ()
+  if let some k' ← getDist? v u then
+    if k'+k < 0 then
+      setUnsat u v k p k'
+      return ()
+  if (← isShorter u v k) then
+    setDist u v k
+    setProof u v { w := u, k, proof := p }
+    propagateAll u v k
+    update
+where
+  update : GoalM Unit := do
+    forEachTargetOf v fun j k₂ => do
+      /- Check whether new path: `u -(k)-> v -(k₂)-> j` is shorter -/
+      updateIfShorter u j (k+k₂) v
+    forEachSourceOf u fun i k₁ => do
+      /- Check whether new path: `i -(k₁)-> u -(k)-> v` is shorter -/
+      updateIfShorter i v (k₁+k) u
+      forEachTargetOf v fun j k₂ => do
+        /- Check whether new path: `i -(k₁)-> u -(k)-> v -(k₂) -> j` is shorter -/
+        updateIfShorter i j (k₁+k+k₂) v
+
+private def internalizeCnstr (e : Expr) (c : Cnstr Expr) : GoalM Unit := do
+  let u ← mkNode c.u
+  let v ← mkNode c.v
+  let c := { c with u, v }
+  if let some k ← getDist? u v then
+    if (← propagateTrue u v k c e) then
+      return ()
+  if let some k ← getDist? v u then
+    if (← propagateFalse v u k c e) then
+      return ()
+  trace[grind.offset.internalize] "{e} ↦ {c}"
+  modify' fun s => { s with
+    cnstrs   := s.cnstrs.insert { expr := e } c
+    cnstrsOf :=
+      let cs := if let some cs := s.cnstrsOf.find? (u, v) then (c, e) :: cs else [(c, e)]
+      s.cnstrsOf.insert (u, v) cs
+  }
+
+private def getZeroNode : GoalM NodeId := do
+  mkNode (← getNatZeroExpr)
+
+/-- Internalize `e` of the form `b + k` -/
+private def internalizeTerm (e : Expr) (b : Expr) (k : Nat) : GoalM Unit := do
+  -- `e` is of the form `b + k`
+  let u ← mkNode e
+  let v ← mkNode b
+  -- `u = v + k`. So, we add edges for `u ≤ v + k` and `v + k ≤ u`.
+  let h := mkApp (mkConst ``Nat.le_refl) e
+  addEdge u v k h
+  addEdge v u (-k) h
+  -- `0 + k ≤ u`
+  let z ← getZeroNode
+  addEdge z u (-k) <| mkApp2 (mkConst ``Grind.Nat.le_offset) b (toExpr k)
+
+/--
+Returns `true`, if `parent?` is relevant for internalization.
+For example, we do not want to internalize an offset term that
+is the child of an addition. This kind of term will be processed by the
+more general linear arithmetic module.
+-/
+private def isRelevantParent (parent? : Option Expr) : GoalM Bool := do
+  let some parent := parent? | return false
+  let z ← getNatZeroExpr
+  return !isNatAdd parent && (isNatOffsetCnstr? parent z).isNone
+
+private def isEqParent (parent? : Option Expr) : Bool := Id.run do
+  let some parent := parent? | return false
+  return parent.isEq
+
+def internalize (e : Expr) (parent? : Option Expr) : GoalM Unit := do
+  let z ← getNatZeroExpr
+  if let some c := isNatOffsetCnstr? e z then
+    internalizeCnstr e c
+  else if (← isRelevantParent parent?) then
+    if let some (b, k) := isNatOffset? e then
+      internalizeTerm e b k
+    else if let some k := isNatNum? e then
+      -- core module has support for detecting equality between literals
+      unless isEqParent parent? do
+        internalizeTerm e z k
+
+@[export lean_process_new_offset_eq]
+def processNewOffsetEqImpl (a b : Expr) : GoalM Unit := do
+  unless isSameExpr a b do
+    trace[grind.offset.eq.to] "{a}, {b}"
+    let u ← getNodeId a
+    let v ← getNodeId b
+    let h ← mkEqProof a b
+    addEdge u v 0 <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_1) a b h
+    addEdge v u 0 <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_2) a b h
+
+@[export lean_process_new_offset_eq_lit]
+def processNewOffsetEqLitImpl (a b : Expr) : GoalM Unit := do
+  unless isSameExpr a b do
+    trace[grind.offset.eq.to] "{a}, {b}"
+    let some k := isNatNum? b | unreachable!
+    let u ← getNodeId a
+    let z ← mkNode (← getNatZeroExpr)
+    let h ← mkEqProof a b
+    addEdge u z k <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_1) a b h
+    addEdge z u (-k) <| mkApp3 (mkConst ``Grind.Nat.le_of_eq_2) a b h
+
+def traceDists : GoalM Unit := do
+  let s ← get'
+  for u in [:s.targets.size], es in s.targets.toArray do
+    for (v, k) in es do
+      trace[grind.offset.dist] "#{u} -({k})-> #{v}"
+
+def Cnstr.toExpr (c : Cnstr NodeId) : GoalM Expr := do
+  let u := (← get').nodes[c.u]!
+  let v := (← get').nodes[c.v]!
+  if c.k == 0 then
+    return mkNatLE u v
+  else if c.k < 0 then
+    return mkNatLE (mkNatAdd u (Lean.toExpr ((-c.k).toNat))) v
+  else
+    return mkNatLE u (mkNatAdd v (Lean.toExpr c.k.toNat))
+
+def checkInvariants : GoalM Unit := do
+  let s ← get'
+  for u in [:s.targets.size], es in s.targets.toArray do
+    for (v, k) in es do
+      let c : Cnstr NodeId := { u, v, k }
+      trace[grind.debug.offset] "{c}"
+      let p ← mkProofForPath u v
+      trace[grind.debug.offset.proof] "{p} : {← inferType p}"
+      check p
+      unless (← withDefault <| isDefEq (← inferType p) (← Cnstr.toExpr c)) do
+        trace[grind.debug.offset.proof] "failed: {← inferType p} =?= {← Cnstr.toExpr c}"
+        unreachable!
+
+end Lean.Meta.Grind.Arith.Offset

src/Lean/Meta/Tactic/Grind/Arith/ProofUtil.lean

@@ -0,0 +1,168 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Grind.Offset
+import Init.Grind.Lemmas
+import Lean.Meta.Tactic.Grind.Types
+
+namespace Lean.Meta.Grind.Arith
+
+/-!
+Helper functions for constructing proof terms in the arithmetic procedures.
+-/
+
+namespace Offset
+
+/-- Returns a proof for `true = true` -/
+def rfl_true : Expr := mkConst ``Grind.rfl_true
+
+private def toExprN (n : Int) :=
+  assert! n >= 0
+  toExpr n.toNat
+
+open Lean.Grind in
+/--
+Assume `pi₁` is `{ w := u, k := k₁, proof := p₁ }` and `pi₂` is `{ w := w, k := k₂, proof := p₂ }`
+`p₁` is the proof for edge `u -(k₁) → w` and `p₂` the proof for edge `w -(k₂)-> v`.
+Then, this function returns a proof for edge `u -(k₁+k₂) -> v`.
+-/
+def mkTrans (nodes : PArray Expr) (pi₁ : ProofInfo) (pi₂ : ProofInfo) (v : NodeId) : ProofInfo :=
+  let { w := u, k := k₁, proof := p₁ } := pi₁
+  let { w, k := k₂, proof := p₂ } := pi₂
+  let u := nodes[u]!
+  let w := nodes[w]!
+  let v := nodes[v]!
+  let p := if k₁ == 0 then
+    if k₂ == 0 then
+      -- u ≤ w, w ≤ v
+      mkApp5 (mkConst ``Nat.le_trans) u w v p₁ p₂
+    else if k₂ > 0 then
+      -- u ≤ v, w ≤ v + k₂
+      mkApp6 (mkConst ``Nat.le_ro) u w v (toExprN k₂) p₁ p₂
+    else
+      let k₂ := - k₂
+      -- u ≤ w, w + k₂ ≤ v
+      mkApp6 (mkConst ``Nat.le_lo) u w v (toExprN k₂) p₁ p₂
+  else if k₁ < 0 then
+    let k₁ := -k₁
+    if k₂ == 0 then
+      mkApp6 (mkConst ``Nat.lo_le) u w v (toExprN k₁) p₁ p₂
+    else if k₂ < 0 then
+      let k₂ := -k₂
+      mkApp7 (mkConst ``Nat.lo_lo) u w v (toExprN k₁) (toExprN k₂) p₁ p₂
+    else
+      let ke₁ := toExprN k₁
+      let ke₂ := toExprN k₂
+      if k₁ > k₂ then
+        mkApp8 (mkConst ``Nat.lo_ro_1) u w v ke₁ ke₂ rfl_true p₁ p₂
+      else
+        mkApp7 (mkConst ``Nat.lo_ro_2) u w v ke₁ ke₂ p₁ p₂
+  else
+    let ke₁ := toExprN k₁
+    if k₂ == 0 then
+      mkApp6 (mkConst ``Nat.ro_le) u w v ke₁ p₁ p₂
+    else if k₂ < 0 then
+      let k₂  := -k₂
+      let ke₂ := toExprN k₂
+       if k₂ > k₁ then
+         mkApp8 (mkConst ``Nat.ro_lo_2) u w v ke₁ ke₂ rfl_true p₁ p₂
+       else
+         mkApp7 (mkConst ``Nat.ro_lo_1) u w v ke₁ ke₂ p₁ p₂
+    else
+      let ke₂ := toExprN k₂
+      mkApp7 (mkConst ``Nat.ro_ro) u w v ke₁ ke₂ p₁ p₂
+  { w := pi₁.w, k := k₁+k₂, proof := p }
+
+open Lean.Grind in
+def mkOfNegEqFalse (nodes : PArray Expr) (c : Cnstr NodeId) (h : Expr) : Expr :=
+  let u := nodes[c.u]!
+  let v := nodes[c.v]!
+  if c.k == 0 then
+    mkApp3 (mkConst ``Nat.of_le_eq_false) u v h
+  else if c.k == -1 then
+    mkApp3 (mkConst ``Nat.of_lo_eq_false_1) u v h
+  else if c.k < 0 then
+    mkApp4 (mkConst ``Nat.of_lo_eq_false) u v (toExprN (-c.k)) h
+  else
+    mkApp4 (mkConst ``Nat.of_ro_eq_false) u v (toExprN c.k) h
+
+/--
+Returns a proof of `False` using a negative cycle composed of
+- `u --(kuv)--> v` with proof `huv`
+- `v --(kvu)--> u` with proof `hvu`
+-/
+def mkUnsatProof (u v : Expr) (kuv : Int) (huv : Expr) (kvu : Int) (hvu : Expr) : Expr :=
+  if kuv == 0 then
+    assert! kvu < 0
+    mkApp6 (mkConst ``Grind.Nat.unsat_le_lo) u v (toExprN (-kvu)) rfl_true huv hvu
+  else if kvu == 0 then
+    mkApp6 (mkConst ``Grind.Nat.unsat_le_lo) v u (toExprN (-kuv)) rfl_true hvu huv
+  else if kuv < 0 then
+    if kvu > 0 then
+      mkApp7 (mkConst ``Grind.Nat.unsat_lo_ro) u v (toExprN (-kuv)) (toExprN kvu) rfl_true huv hvu
+    else
+      assert! kvu < 0
+      mkApp7 (mkConst ``Grind.Nat.unsat_lo_lo) u v (toExprN (-kuv)) (toExprN (-kvu)) rfl_true huv hvu
+  else
+    assert! kuv > 0 && kvu < 0
+    mkApp7 (mkConst ``Grind.Nat.unsat_lo_ro) v u (toExprN (-kvu)) (toExprN kuv) rfl_true hvu huv
+
+/--
+Given a path `u --(kuv)--> v` justified by proof `huv`,
+construct a proof of `e = True` where `e` is a term corresponding to the edgen `u --(k') --> v`
+s.t. `k ≤ k'`
+-/
+def mkPropagateEqTrueProof (u v : Expr) (k : Int) (huv : Expr) (k' : Int) : Expr :=
+  if k == 0 then
+    if k' == 0 then
+      mkApp3 (mkConst ``Grind.Nat.le_eq_true_of_le) u v huv
+    else
+      assert! k' > 0
+      mkApp4 (mkConst ``Grind.Nat.ro_eq_true_of_le) u v (toExprN k') huv
+  else if k < 0 then
+    let k := -k
+    if k' == 0 then
+      mkApp4 (mkConst ``Grind.Nat.le_eq_true_of_lo) u v (toExprN k) huv
+    else if k' < 0 then
+      let k' := -k'
+      mkApp6 (mkConst ``Grind.Nat.lo_eq_true_of_lo) u v (toExprN k) (toExprN k') rfl_true huv
+    else
+      assert! k' > 0
+      mkApp5 (mkConst ``Grind.Nat.ro_eq_true_of_lo) u v (toExprN k) (toExprN k') huv
+  else
+    assert! k > 0
+    assert! k' > 0
+    mkApp6 (mkConst ``Grind.Nat.ro_eq_true_of_ro) u v (toExprN k) (toExprN k') rfl_true huv
+
+/--
+Given a path `u --(kuv)--> v` justified by proof `huv`,
+construct a proof of `e = False` where `e` is a term corresponding to the edgen `v --(k') --> u`
+s.t. `k+k' < 0`
+-/
+def mkPropagateEqFalseProof (u v : Expr) (k : Int) (huv : Expr) (k' : Int) : Expr :=
+  if k == 0 then
+    assert! k' < 0
+    let k' := -k'
+    mkApp5 (mkConst ``Grind.Nat.lo_eq_false_of_le) u v (toExprN k') rfl_true huv
+  else if k < 0 then
+    let k := -k
+    if k' == 0 then
+      mkApp5 (mkConst ``Grind.Nat.le_eq_false_of_lo) u v (toExprN k) rfl_true huv
+    else if k' < 0 then
+      let k' := -k'
+      mkApp6 (mkConst ``Grind.Nat.lo_eq_false_of_lo) u v (toExprN k) (toExprN k') rfl_true huv
+    else
+      assert! k' > 0
+      mkApp6 (mkConst ``Grind.Nat.ro_eq_false_of_lo) u v (toExprN k) (toExprN k') rfl_true huv
+  else
+    assert! k > 0
+    assert! k' < 0
+    let k' := -k'
+    mkApp6 (mkConst ``Grind.Nat.lo_eq_false_of_ro) u v (toExprN k) (toExprN k') rfl_true huv
+
+end Offset
+
+end Lean.Meta.Grind.Arith

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

@@ -0,0 +1,66 @@
+/-
+Copyright (c) 2025 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.Data.PersistentArray
+import Lean.Meta.Tactic.Grind.ENodeKey
+import Lean.Meta.Tactic.Grind.Arith.Util
+
+namespace Lean.Meta.Grind.Arith
+
+namespace Offset
+
+abbrev NodeId := Nat
+
+instance : ToMessageData (Offset.Cnstr NodeId) where
+  toMessageData c := Offset.toMessageData (α := NodeId) (inst := { toMessageData n := m!"#{n}" }) c
+
+/-- Auxiliary structure used for proof extraction.  -/
+structure ProofInfo where
+  w     : NodeId
+  k     : Int
+  proof : Expr
+  deriving Inhabited
+
+/-- State of the constraint offset procedure. -/
+structure State where
+  /-- Mapping from `NodeId` to the `Expr` represented by the node. -/
+  nodes    : PArray Expr := {}
+  /-- Mapping from `Expr` to a node representing it. -/
+  nodeMap  : PHashMap ENodeKey NodeId := {}
+  /-- Mapping from `Expr` representing inequalites to constraints. -/
+  cnstrs   : PHashMap ENodeKey (Cnstr NodeId) := {}
+  /--
+  Mapping from pairs `(u, v)` to a list of offset constraints on `u` and `v`.
+  We use this mapping to implement exhaustive constraint propagation.
+  -/
+  cnstrsOf : PHashMap (NodeId × NodeId) (List (Cnstr NodeId × Expr)) := {}
+  /--
+  For each node with id `u`, `sources[u]` contains
+  pairs `(v, k)` s.t. there is a path from `v` to `u` with weight `k`.
+  -/
+  sources  : PArray (AssocList NodeId Int) := {}
+  /--
+  For each node with id `u`, `targets[u]` contains
+  pairs `(v, k)` s.t. there is a path from `u` to `v` with weight `k`.
+  -/
+  targets  : PArray (AssocList NodeId Int) := {}
+  /--
+  Proof reconstruction information. For each node with id `u`, `proofs[u]` contains
+  pairs `(v, { w, proof })` s.t. there is a path from `u` to `v`, and
+  `w` is the penultimate node in the path, and `proof` is the justification for
+  the last edge.
+  -/
+  proofs   : PArray (AssocList NodeId ProofInfo) := {}
+  deriving Inhabited
+
+end Offset
+
+/-- State for the arithmetic procedures. -/
+structure State where
+  offset : Offset.State := {}
+  deriving Inhabited
+
+end Lean.Meta.Grind.Arith

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

@@ -0,0 +1,102 @@
+/-
+Copyright (c) 2025 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.Expr
+import Lean.Message
+
+namespace Lean.Meta.Grind.Arith
+
+/-- Returns `true` if `e` is of the form `Nat` -/
+def isNatType (e : Expr) : Bool :=
+  e.isConstOf ``Nat
+
+/-- Returns `true` if `e` is of the form `@instHAdd Nat instAddNat` -/
+def isInstAddNat (e : Expr) : Bool :=
+  let_expr instHAdd a b := e | false
+  isNatType a && b.isConstOf ``instAddNat
+
+/-- Returns `true` if `e` is `instLENat` -/
+def isInstLENat (e : Expr) : Bool :=
+  e.isConstOf ``instLENat
+
+/--
+Returns `some (a, b)` if `e` is of the form
+```
+@HAdd.hAdd Nat Nat Nat (instHAdd Nat instAddNat) a b
+```
+-/
+def isNatAdd? (e : Expr) : Option (Expr × Expr) :=
+  let_expr HAdd.hAdd _ _ _ i a b := e | none
+  if isInstAddNat i then some (a, b) else none
+
+/--
+Returns `true` if `e` is of the form
+```
+@HAdd.hAdd Nat Nat Nat (instHAdd Nat instAddNat) _ _
+```
+-/
+def isNatAdd (e : Expr) : Bool :=
+  let_expr HAdd.hAdd _ _ _ i _ _ := e | false
+  isInstAddNat i
+
+/-- Returns `some k` if `e` `@OfNat.ofNat Nat _ (instOfNatNat k)` -/
+def isNatNum? (e : Expr) : Option Nat := Id.run do
+  let_expr OfNat.ofNat _ _ inst := e | none
+  let_expr instOfNatNat k := inst | none
+  let .lit (.natVal k) := k | none
+  some k
+
+/-- Returns `some (a, k)` if `e` is of the form `a + k`.  -/
+def isNatOffset? (e : Expr) : Option (Expr × Nat) := Id.run do
+  let some (a, b) := isNatAdd? e | none
+  let some k := isNatNum? b | none
+  some (a, k)
+
+/-- An offset constraint. -/
+structure Offset.Cnstr (α : Type) where
+  u  : α
+  v  : α
+  k  : Int := 0
+  deriving Inhabited
+
+def Offset.Cnstr.neg : Cnstr α → Cnstr α
+  | { u, v, k } => { u := v, v := u, k := -k - 1 }
+
+example (c : Offset.Cnstr α) : c.neg.neg = c := by
+  cases c; simp [Offset.Cnstr.neg]; omega
+
+def Offset.toMessageData [inst : ToMessageData α] (c : Offset.Cnstr α) : MessageData :=
+  match c.k with
+  | .ofNat 0   => m!"{c.u} ≤ {c.v}"
+  | .ofNat k   => m!"{c.u} ≤ {c.v} + {k}"
+  | .negSucc k => m!"{c.u} + {k + 1} ≤ {c.v}"
+
+instance : ToMessageData (Offset.Cnstr Expr) where
+  toMessageData c := Offset.toMessageData c
+
+/--
+Returns `some cnstr` if `e` is offset constraint.
+Remark: `z` is `0` numeral. It is an extra argument because we
+want to be able to provide the one that has already been internalized.
+-/
+def isNatOffsetCnstr? (e : Expr) (z : Expr) : Option (Offset.Cnstr Expr) :=
+  match_expr e with
+  | LE.le _ inst a b => if isInstLENat inst then go a b else none
+  | _ => none
+where
+  go (u v : Expr) :=
+    if let some (u, k) := isNatOffset? u then
+      some { u, k := - k, v }
+    else if let some (v, k) := isNatOffset? v then
+      some { u, v, k }
+    else if let some k := isNatNum? u then
+      some { u := z, v, k := - k }
+    else if let some k := isNatNum? v then
+      some { u, v := z, k }
+    else
+      some { u, v }
+
+end Lean.Meta.Grind.Arith

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

@@ -10,12 +10,6 @@ import Lean.Meta.Tactic.Simp.Simproc
 namespace Lean.Meta.Grind
 open Simp
 
-builtin_initialize grindNormExt : SimpExtension ←
-  registerSimpAttr `grind_norm "simplification/normalization theorems for `grind`"
-
-builtin_initialize grindNormSimprocExt : SimprocExtension ←
-  registerSimprocAttr `grind_norm_proc "simplification/normalization procedured for `grind`" none
-
 builtin_initialize grindCasesExt : SimpleScopedEnvExtension Name NameSet ←
   registerSimpleScopedEnvExtension {
     initial        := {}

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

@@ -0,0 +1,77 @@
+/-
+Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Lean.Meta.Tactic.Grind.Types
+
+namespace Lean.Meta.Grind
+
+/-- Returns all lambda expressions in the equivalence class with root `root`. -/
+def getEqcLambdas (root : ENode) : GoalM (Array Expr) := do
+  unless root.hasLambdas do return #[]
+  foldEqc root.self (init := #[]) fun n lams =>
+    if n.self.isLambda then return lams.push n.self else return lams
+
+/--
+Returns the root of the functions in the equivalence class containing `e`.
+That is, if `f a` is in `root`s equivalence class, results contains the root of `f`.
+-/
+def getFnRoots (e : Expr) : GoalM (Array Expr) := do
+  foldEqc e (init := #[]) fun n fns => do
+    let fn := n.self.getAppFn
+    let fnRoot := (← getRoot? fn).getD fn
+    if Option.isNone <| fns.find? (isSameExpr · fnRoot) then
+      return fns.push fnRoot
+    else
+      return fns
+
+/--
+For each `lam` in `lams` s.t. `lam` and `f` are in the same equivalence class,
+propagate `f args = lam args`.
+-/
+def propagateBetaEqs (lams : Array Expr) (f : Expr) (args : Array Expr) : GoalM Unit := do
+  if args.isEmpty then return ()
+  for lam in lams do
+    let rhs := lam.beta args
+    unless rhs.isLambda do
+      let mut gen := Nat.max (← getGeneration lam) (← getGeneration f)
+      let lhs := mkAppN f args
+      if (← hasSameType f lam) then
+        let mut h ← mkEqProof f lam
+        for arg in args do
+          gen := Nat.max gen (← getGeneration arg)
+          h ← mkCongrFun h arg
+        let eq ← mkEq lhs rhs
+        trace[grind.beta] "{eq}, using {lam}"
+        addNewFact h eq (gen+1)
+
+private def isPropagateBetaTarget (e : Expr) : GoalM Bool := do
+  let .app f _ := e | return false
+  go f
+where
+  go (f : Expr) : GoalM Bool := do
+    if let some root ← getRootENode? f then
+      return root.hasLambdas
+    let .app f _ := f | return false
+    go f
+
+/--
+Applies beta-reduction for lambdas in `f`s equivalence class.
+We use this function while internalizing new applications.
+-/
+def propagateBetaForNewApp (e : Expr) : GoalM Unit := do
+  unless (← isPropagateBetaTarget e) do return ()
+  let mut e := e
+  let mut args := #[]
+  repeat
+    unless args.isEmpty do
+      if let some root ← getRootENode? e then
+        if root.hasLambdas then
+          propagateBetaEqs (← getEqcLambdas root) e args.reverse
+    let .app f arg := e | return ()
+    e := f
+    args := args.push arg
+
+end Lean.Meta.Grind

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

@@ -10,6 +10,7 @@ import Lean.Meta.FunInfo
 import Lean.Util.FVarSubset
 import Lean.Util.PtrSet
 import Lean.Util.FVarSubset
+import Lean.Meta.Tactic.Grind.Types
 
 namespace Lean.Meta.Grind
 namespace Canon
@@ -40,42 +41,37 @@ additions will still use structurally different (and definitionally different) i
 Furthermore, `grind` will not be able to infer that  `HEq (a + a) (b + b)` even if we add the assumptions `n = m` and `HEq a b`.
 -/
 
-structure State where
-  argMap     : PHashMap (Expr × Nat) (List Expr) := {}
-  canon      : PHashMap Expr Expr := {}
-  proofCanon : PHashMap Expr Expr := {}
-  deriving Inhabited
+@[inline] private def get' : GoalM State :=
+  return (← get).canon
 
-inductive CanonElemKind where
-  | /--
-    Type class instances are canonicalized using `TransparencyMode.instances`.
-    -/
-    instance
-  | /--
-    Types and Type formers are canonicalized using `TransparencyMode.default`.
-    Remark: propositions are just visited. We do not invoke `canonElemCore` for them.
-    -/
-    type
-  | /--
-    Implicit arguments that are not types, type formers, or instances, are canonicalized
-    using `TransparencyMode.reducible`
-    -/
-    implicit
-  deriving BEq
+@[inline] private def modify' (f : State → State) : GoalM Unit :=
+  modify fun s => { s with canon := f s.canon }
 
-def CanonElemKind.explain : CanonElemKind → String
-  | .instance => "type class instances"
-  | .type => "types (or type formers)"
-  | .implicit => "implicit arguments (which are not type class instances or types)"
+/--
+Helper function for `canonElemCore`. It tries `isDefEq a b` with default transparency, but using
+at most `canonHeartbeats` heartbeats. It reports an issue if the threshold is reached.
+Remark: `parent` is use only to report an issue
+-/
+private def isDefEqBounded (a b : Expr) (parent : Expr) : GoalM Bool := do
+  withCurrHeartbeats do
+  let config ← getConfig
+  tryCatchRuntimeEx
+    (withTheReader Core.Context (fun ctx => { ctx with maxHeartbeats := config.canonHeartbeats }) do
+      withDefault <| isDefEq a b)
+    fun ex => do
+      if ex.isRuntime then
+        let curr := (← getConfig).canonHeartbeats
+        reportIssue m!"failed to show that{indentExpr a}\nis definitionally equal to{indentExpr b}\nwhile canonicalizing{indentExpr parent}\nusing `{curr}*1000` heartbeats, `(canonHeartbeats := {curr})`"
+        return false
+      else
+        throw ex
 
 /--
 Helper function for canonicalizing `e` occurring as the `i`th argument of an `f`-application.
-
-Thus, if diagnostics are enabled, we also re-check them using `TransparencyMode.default`. If the result is different
-we report to the user.
+If `useIsDefEqBounded` is `true`, we try `isDefEqBounded` before returning false
 -/
-def canonElemCore (f : Expr) (i : Nat) (e : Expr) (kind : CanonElemKind) : StateT State MetaM Expr := do
-  let s ← get
+def canonElemCore (parent : Expr) (f : Expr) (i : Nat) (e : Expr) (useIsDefEqBounded : Bool) : GoalM Expr := do
+  let s ← get'
   if let some c := s.canon.find? e then
     return c
   let key := (f, i)
@@ -85,20 +81,23 @@ def canonElemCore (f : Expr) (i : Nat) (e : Expr) (kind : CanonElemKind) : State
       -- We used to check `c.fvarsSubset e` because it is not
       -- in general safe to replace `e` with `c` if `c` has more free variables than `e`.
       -- However, we don't revert previously canonicalized elements in the `grind` tactic.
-      modify fun s => { s with canon := s.canon.insert e c }
-      trace[grind.debug.canon] "found {e} ===> {c}"
+      -- Moreover, we store the canonicalizer state in the `Goal` because we case-split
+      -- and different locals are added in different branches.
+      modify' fun s => { s with canon := s.canon.insert e c }
+      trace[grind.debugn.canon] "found {e} ===> {c}"
       return c
-    if kind != .type then
-      if (← isTracingEnabledFor `grind.issues <&&> (withDefault <| isDefEq e c)) then
-        -- TODO: consider storing this information in some structure that can be browsed later.
-        trace[grind.issues] "the following {kind.explain} are definitionally equal with `default` transparency but not with a more restrictive transparency{indentExpr e}\nand{indentExpr c}"
+    if useIsDefEqBounded then
+      if (← isDefEqBounded e c parent) then
+        modify' fun s => { s with canon := s.canon.insert e c }
+        trace[grind.debugn.canon] "found using `isDefEqBounded`: {e} ===> {c}"
+        return c
   trace[grind.debug.canon] "({f}, {i}) ↦ {e}"
-  modify fun s => { s with canon := s.canon.insert e e, argMap := s.argMap.insert key (e::cs) }
+  modify' fun s => { s with canon := s.canon.insert e e, argMap := s.argMap.insert key (e::cs) }
   return e
 
-abbrev canonType (f : Expr) (i : Nat) (e : Expr) := withDefault <| canonElemCore f i e .type
-abbrev canonInst (f : Expr) (i : Nat) (e : Expr) := withReducibleAndInstances <| canonElemCore f i e .instance
-abbrev canonImplicit (f : Expr) (i : Nat) (e : Expr) := withReducible <| canonElemCore f i e .implicit
+abbrev canonType (parent f : Expr) (i : Nat) (e : Expr) := withDefault <| canonElemCore parent f i e (useIsDefEqBounded := false)
+abbrev canonInst (parent f : Expr) (i : Nat) (e : Expr) := withReducibleAndInstances <| canonElemCore parent f i e (useIsDefEqBounded := true)
+abbrev canonImplicit (parent f : Expr) (i : Nat) (e : Expr) := withReducible <| canonElemCore parent f i e (useIsDefEqBounded := true)
 
 /--
 Return type for the `shouldCanon` function.
@@ -146,10 +145,10 @@ def shouldCanon (pinfos : Array ParamInfo) (i : Nat) (arg : Expr) : MetaM Should
   else
     return .visit
 
-unsafe def canonImpl (e : Expr) : StateT State MetaM Expr := do
+unsafe def canonImpl (e : Expr) : GoalM Expr := do
   visit e |>.run' mkPtrMap
 where
-  visit (e : Expr) : StateRefT (PtrMap Expr Expr) (StateT State MetaM) Expr := do
+  visit (e : Expr) : StateRefT (PtrMap Expr Expr) GoalM Expr := do
     unless e.isApp || e.isForall do return e
     -- Check whether it is cached
     if let some r := (← get).find? e then
@@ -159,11 +158,11 @@ where
         if f.isConstOf ``Lean.Grind.nestedProof && args.size == 2 then
           let prop := args[0]!
           let prop' ← visit prop
-          if let some r := (← getThe State).proofCanon.find? prop' then
+          if let some r := (← get').proofCanon.find? prop' then
             pure r
           else
             let e' := if ptrEq prop prop' then e else mkAppN f (args.set! 0 prop')
-            modifyThe State fun s => { s with proofCanon := s.proofCanon.insert prop' e' }
+            modify' fun s => { s with proofCanon := s.proofCanon.insert prop' e' }
             pure e'
         else
           let pinfos := (← getFunInfo f).paramInfo
@@ -173,9 +172,9 @@ where
             let arg := args[i]
             trace[grind.debug.canon] "[{repr (← shouldCanon pinfos i arg)}]: {arg} : {← inferType arg}"
             let arg' ← match (← shouldCanon pinfos i arg) with
-            | .canonType  => canonType f i arg
-            | .canonInst  => canonInst f i arg
-            | .canonImplicit => canonImplicit f i (← visit arg)
+            | .canonType  => canonType e f i arg
+            | .canonInst  => canonInst e f i arg
+            | .canonImplicit => canonImplicit e f i (← visit arg)
             | .visit      => visit arg
             unless ptrEq arg arg' do
               args := args.set i arg'
@@ -191,11 +190,11 @@ where
     modify fun s => s.insert e e'
     return e'
 
-/-- Canonicalizes nested types, type formers, and instances in `e`. -/
-def canon (e : Expr) : StateT State MetaM Expr := do
-  trace[grind.debug.canon] "{e}"
-  unsafe canonImpl e
-
 end Canon
 
+/-- Canonicalizes nested types, type formers, and instances in `e`. -/
+def canon (e : Expr) : GoalM Expr := do
+  trace[grind.debug.canon] "{e}"
+  unsafe Canon.canonImpl e
+
 end Lean.Meta.Grind

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

@@ -10,6 +10,8 @@ import Lean.Meta.Tactic.Grind.Types
 import Lean.Meta.Tactic.Grind.Inv
 import Lean.Meta.Tactic.Grind.PP
 import Lean.Meta.Tactic.Grind.Ctor
+import Lean.Meta.Tactic.Grind.Util
+import Lean.Meta.Tactic.Grind.Beta
 import Lean.Meta.Tactic.Grind.Internalize
 
 namespace Lean.Meta.Grind
@@ -39,7 +41,7 @@ Remove `root` parents from the congruence table.
 This is an auxiliary function performed while merging equivalence classes.
 -/
 private def removeParents (root : Expr) : GoalM ParentSet := do
-  let parents ← getParentsAndReset root
+  let parents ← getParents root
   for parent in parents do
     -- Recall that we may have `Expr.forallE` in `parents` because of `ForallProp.lean`
     if (← pure parent.isApp <&&> isCongrRoot parent) then
@@ -86,6 +88,51 @@ private partial def updateMT (root : Expr) : GoalM Unit := do
       setENode parent { node with mt := gmt }
       updateMT parent
 
+/--
+Helper function for combining `ENode.offset?` fields and propagating an equality
+to the offset constraint module.
+-/
+private def propagateOffsetEq (rhsRoot lhsRoot : ENode) : GoalM Unit := do
+  match lhsRoot.offset? with
+  | some lhsOffset =>
+    if let some rhsOffset := rhsRoot.offset? then
+      Arith.processNewOffsetEq lhsOffset rhsOffset
+    else if isNatNum rhsRoot.self then
+      Arith.processNewOffsetEqLit lhsOffset rhsRoot.self
+    else
+      -- We have to retrieve the node because other fields have been updated
+      let rhsRoot ← getENode rhsRoot.self
+      setENode rhsRoot.self { rhsRoot with offset? := lhsOffset }
+  | none =>
+    if isNatNum lhsRoot.self then
+    if let some rhsOffset := rhsRoot.offset? then
+      Arith.processNewOffsetEqLit rhsOffset lhsRoot.self
+
+/--
+Tries to apply beta-reductiong using the parent applications of the functions in `fns` with
+the lambda expressions in `lams`.
+-/
+def propagateBeta (lams : Array Expr) (fns : Array Expr) : GoalM Unit := do
+  if lams.isEmpty then return ()
+  let lamRoot ← getRoot lams.back!
+  trace[grind.debug.beta] "fns: {fns}, lams: {lams}"
+  for fn in fns do
+    trace[grind.debug.beta] "fn: {fn}, parents: {(← getParents fn).toArray}"
+    for parent in (← getParents fn) do
+      let mut args := #[]
+      let mut curr := parent
+      trace[grind.debug.beta] "parent: {parent}"
+      repeat
+        trace[grind.debug.beta] "curr: {curr}"
+        if (← isEqv curr lamRoot) then
+          propagateBetaEqs lams curr args.reverse
+        let .app f arg := curr
+          | break
+        -- Remark: recall that we do not eagerly internalize partial applications.
+        internalize curr (← getGeneration parent)
+        args := args.push arg
+        curr := f
+
 private partial def addEqStep (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit := do
   let lhsNode ← getENode lhs
   let rhsNode ← getENode rhs
@@ -118,7 +165,7 @@ private partial def addEqStep (lhs rhs proof : Expr) (isHEq : Bool) : GoalM Unit
   unless (← isInconsistent) do
     if valueInconsistency then
       closeGoalWithValuesEq lhsRoot.self rhsRoot.self
-  trace_goal[grind.debug] "after addEqStep, {← ppState}"
+  trace_goal[grind.debug] "after addEqStep, {← (← get).ppState}"
   checkInvariants
 where
   go (lhs rhs : Expr) (lhsNode rhsNode lhsRoot rhsRoot : ENode) (flipped : Bool) : GoalM Unit := do
@@ -137,35 +184,43 @@ where
       proof?  := proof
       flipped
     }
+    let lams₁ ← getEqcLambdas lhsRoot
+    let lams₂ ← getEqcLambdas rhsRoot
+    let fns₁  ← if lams₁.isEmpty then pure #[] else getFnRoots rhsRoot.self
+    let fns₂  ← if lams₂.isEmpty then pure #[] else getFnRoots lhsRoot.self
     let parents ← removeParents lhsRoot.self
     updateRoots lhs rhsNode.root
     trace_goal[grind.debug] "{← ppENodeRef lhs} new root {← ppENodeRef rhsNode.root}, {← ppENodeRef (← getRoot lhs)}"
     reinsertParents parents
+    propagateEqcDown lhs
     setENode lhsNode.root { (← getENode lhsRoot.self) with -- We must retrieve `lhsRoot` since it was updated.
       next := rhsRoot.next
     }
     setENode rhsNode.root { rhsRoot with
-      next := lhsRoot.next
-      size := rhsRoot.size + lhsRoot.size
+      next       := lhsRoot.next
+      size       := rhsRoot.size + lhsRoot.size
       hasLambdas := rhsRoot.hasLambdas || lhsRoot.hasLambdas
       heqProofs  := isHEq || rhsRoot.heqProofs || lhsRoot.heqProofs
     }
+    propagateBeta lams₁ fns₁
+    propagateBeta lams₂ fns₂
+    resetParentsOf lhsRoot.self
     copyParentsTo parents rhsNode.root
+    unless (← isInconsistent) do
+      updateMT rhsRoot.self
+    propagateOffsetEq rhsRoot lhsRoot
     unless (← isInconsistent) do
       for parent in parents do
         propagateUp parent
-    unless (← isInconsistent) do
-      updateMT rhsRoot.self
 
   updateRoots (lhs : Expr) (rootNew : Expr) : GoalM Unit := do
-    let rec loop (e : Expr) : GoalM Unit := do
-      let n ← getENode e
-      setENode e { n with root := rootNew }
+    traverseEqc lhs fun n =>
+      setENode n.self { n with root := rootNew }
+
+  propagateEqcDown (lhs : Expr) : GoalM Unit := do
+    traverseEqc lhs fun n =>
       unless (← isInconsistent) do
-        propagateDown e
-      if isSameExpr lhs n.next then return ()
-      loop n.next
-    loop lhs
+        propagateDown n.self
 
 /-- Ensures collection of equations to be processed is empty. -/
 private def resetNewEqs : GoalM Unit :=
@@ -192,22 +247,28 @@ where
     processTodo
 
 /-- Adds a new equality `lhs = rhs`. It assumes `lhs` and `rhs` have already been internalized. -/
-def addEq (lhs rhs proof : Expr) : GoalM Unit := do
+private def addEq (lhs rhs proof : Expr) : GoalM Unit := do
   addEqCore lhs rhs proof false
 
-
 /-- Adds a new heterogeneous equality `HEq lhs rhs`. It assumes `lhs` and `rhs` have already been internalized. -/
-def addHEq (lhs rhs proof : Expr) : GoalM Unit := do
+private def addHEq (lhs rhs proof : Expr) : GoalM Unit := do
   addEqCore lhs rhs proof true
 
+/-- Save asserted facts for pretty printing goal. -/
+private def storeFact (fact : Expr) : GoalM Unit := do
+  modify fun s => { s with facts := s.facts.push fact }
+
 /-- Internalizes `lhs` and `rhs`, and then adds equality `lhs = rhs`. -/
 def addNewEq (lhs rhs proof : Expr) (generation : Nat) : GoalM Unit := do
-  internalize lhs generation
-  internalize rhs generation
+  let eq ← mkEq lhs rhs
+  storeFact eq
+  internalize lhs generation eq
+  internalize rhs generation eq
   addEq lhs rhs proof
 
 /-- Adds a new `fact` justified by the given proof and using the given generation. -/
 def add (fact : Expr) (proof : Expr) (generation := 0) : GoalM Unit := do
+  storeFact fact
   trace_goal[grind.assert] "{fact}"
   if (← isInconsistent) then return ()
   resetNewEqs
@@ -217,22 +278,30 @@ def add (fact : Expr) (proof : Expr) (generation := 0) : GoalM Unit := do
 where
   go (p : Expr) (isNeg : Bool) : GoalM Unit := do
     match_expr p with
-    | Eq _ lhs rhs => goEq p lhs rhs isNeg false
-    | HEq _ lhs _ rhs => goEq p lhs rhs isNeg true
-    | _ =>
-      internalize p generation
-      if isNeg then
-        addEq p (← getFalseExpr) (← mkEqFalse proof)
+    | Eq α lhs rhs =>
+      if α.isProp then
+        -- It is morally an iff.
+        -- We do not use the `goEq` optimization because we want to register `p` as a case-split
+        goFact p isNeg
       else
-        addEq p (← getTrueExpr) (← mkEqTrue proof)
+        goEq p lhs rhs isNeg false
+    | HEq _ lhs _ rhs => goEq p lhs rhs isNeg true
+    | _ => goFact p isNeg
+
+  goFact (p : Expr) (isNeg : Bool) : GoalM Unit := do
+    internalize p generation
+    if isNeg then
+      addEq p (← getFalseExpr) (← mkEqFalse proof)
+    else
+      addEq p (← getTrueExpr) (← mkEqTrue proof)
 
   goEq (p : Expr) (lhs rhs : Expr) (isNeg : Bool) (isHEq : Bool) : GoalM Unit := do
     if isNeg then
       internalize p generation
       addEq p (← getFalseExpr) (← mkEqFalse proof)
     else
-      internalize lhs generation
-      internalize rhs generation
+      internalize lhs generation p
+      internalize rhs generation p
       addEqCore lhs rhs proof isHEq
 
 /-- Adds a new hypothesis. -/

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

@@ -20,7 +20,7 @@ private partial def propagateInjEqs (eqs : Expr) (proof : Expr) : GoalM Unit :=
   | HEq _ lhs _ rhs =>
     pushHEq (← shareCommon lhs) (← shareCommon rhs) proof
   | _ =>
-   trace_goal[grind.issues] "unexpected injectivity theorem result type{indentExpr eqs}"
+   reportIssue m!"unexpected injectivity theorem result type{indentExpr eqs}"
    return ()
 
 /--

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

@@ -129,6 +129,16 @@ private partial def matchArgs? (c : Choice) (p : Expr) (e : Expr) : OptionT Goal
   let c ← matchArg? c pArg eArg
   matchArgs? c p.appFn! e.appFn!
 
+/-- Similar to `matchArgs?` but if `p` has fewer arguments than `e`, we match `p` with a prefix of `e`. -/
+private partial def matchArgsPrefix? (c : Choice) (p : Expr) (e : Expr) : OptionT GoalM Choice := do
+  let pn := p.getAppNumArgs
+  let en := e.getAppNumArgs
+  guard (pn <= en)
+  if pn == en then
+    matchArgs? c p e
+  else
+    matchArgs? c p (e.getAppPrefix pn)
+
 /--
 Matches pattern `p` with term `e` with respect to choice `c`.
 We traverse the equivalence class of `e` looking for applications compatible with `p`.
@@ -194,7 +204,7 @@ private def processContinue (c : Choice) (p : Expr) : M Unit := do
     let n ← getENode app
     if n.generation < maxGeneration
        && (n.heqProofs || n.isCongrRoot) then
-      if let some c ← matchArgs? c p app |>.run then
+      if let some c ← matchArgsPrefix? c p app |>.run then
         let gen := n.generation
         let c := { c with gen := Nat.max gen c.gen }
         modify fun s => { s with choiceStack := c :: s.choiceStack }
@@ -240,7 +250,7 @@ private partial def instantiateTheorem (c : Choice) : M Unit := withDefault do w
   assert! c.assignment.size == numParams
   let (mvars, bis, _) ← forallMetaBoundedTelescope (← inferType proof) numParams
   if mvars.size != thm.numParams then
-    trace_goal[grind.issues] "unexpected number of parameters at {← thm.origin.pp}"
+    reportIssue m!"unexpected number of parameters at {← thm.origin.pp}"
     return ()
   -- Apply assignment
   for h : i in [:mvars.size] do
@@ -250,14 +260,14 @@ private partial def instantiateTheorem (c : Choice) : M Unit := withDefault do w
       let mvarIdType ← mvarId.getType
       let vType ← inferType v
       unless (← isDefEq mvarIdType vType <&&> mvarId.checkedAssign v) do
-        trace_goal[grind.issues] "type error constructing proof for {← thm.origin.pp}\nwhen assigning metavariable {mvars[i]} with {indentExpr v}\n{← mkHasTypeButIsExpectedMsg vType mvarIdType}"
+        reportIssue m!"type error constructing proof for {← thm.origin.pp}\nwhen assigning metavariable {mvars[i]} with {indentExpr v}\n{← mkHasTypeButIsExpectedMsg vType mvarIdType}"
         return ()
   -- Synthesize instances
   for mvar in mvars, bi in bis do
     if bi.isInstImplicit && !(← mvar.mvarId!.isAssigned) then
       let type ← inferType mvar
-      unless (← synthesizeInstance mvar type) do
-        trace_goal[grind.issues] "failed to synthesize instance when instantiating {← thm.origin.pp}{indentExpr type}"
+      unless (← synthesizeInstanceAndAssign mvar type) do
+        reportIssue m!"failed to synthesize instance when instantiating {← thm.origin.pp}{indentExpr type}"
         return ()
   let proof := mkAppN proof mvars
   if (← mvars.allM (·.mvarId!.isAssigned)) then
@@ -265,13 +275,9 @@ private partial def instantiateTheorem (c : Choice) : M Unit := withDefault do w
   else
     let mvars ← mvars.filterM fun mvar => return !(← mvar.mvarId!.isAssigned)
     if let some mvarBad ← mvars.findM? fun mvar => return !(← isProof mvar) then
-      trace_goal[grind.issues] "failed to instantiate {← thm.origin.pp}, failed to instantiate non propositional argument with type{indentExpr (← inferType mvarBad)}"
+      reportIssue m!"failed to instantiate {← thm.origin.pp}, failed to instantiate non propositional argument with type{indentExpr (← inferType mvarBad)}"
     let proof ← mkLambdaFVars (binderInfoForMVars := .default) mvars (← instantiateMVars proof)
     addNewInstance thm.origin proof c.gen
-where
-  synthesizeInstance (x type : Expr) : MetaM Bool := do
-    let .some val ← trySynthInstance type | return false
-    isDefEq x val
 
 /-- Process choice stack until we don't have more choices to be processed. -/
 private def processChoices : M Unit := do
@@ -300,7 +306,7 @@ private def main (p : Expr) (cnstrs : List Cnstr) : M Unit := do
     if (n.heqProofs || n.isCongrRoot) &&
        (!useMT || n.mt == gmt) then
       withInitApp app do
-        if let some c ← matchArgs? { cnstrs, assignment, gen := n.generation } p app |>.run then
+        if let some c ← matchArgsPrefix? { cnstrs, assignment, gen := n.generation } p app |>.run then
           modify fun s => { s with choiceStack := [c] }
           processChoices
 
@@ -360,7 +366,4 @@ def ematchAndAssert : GrindTactic := fun goal => do
     return none
   assertAll goal
 
-def ematchStar : GrindTactic :=
-  ematchAndAssert.iterate
-
 end Lean.Meta.Grind

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

@@ -170,11 +170,43 @@ private builtin_initialize ematchTheoremsExt : SimpleScopedEnvExtension EMatchTh
     initial  := {}
   }
 
+/--
+Symbols with built-in support in `grind` are unsuitable as pattern candidates for E-matching.
+This is because `grind` performs normalization operations and uses specialized data structures
+to implement these symbols, which may interfere with E-matching behavior.
+-/
 -- TODO: create attribute?
 private def forbiddenDeclNames := #[``Eq, ``HEq, ``Iff, ``And, ``Or, ``Not]
 
 private def isForbidden (declName : Name) := forbiddenDeclNames.contains declName
 
+/--
+Auxiliary function to expand a pattern containing forbidden application symbols
+into a multi-pattern.
+
+This function enhances the usability of the `[grind =]` attribute by automatically handling
+forbidden pattern symbols. For example, consider the following theorem tagged with this attribute:
+```
+getLast?_eq_some_iff {xs : List α} {a : α} : xs.getLast? = some a ↔ ∃ ys, xs = ys ++ [a]
+```
+Here, the selected pattern is `xs.getLast? = some a`, but `Eq` is a forbidden pattern symbol.
+Instead of producing an error, this function converts the pattern into a multi-pattern,
+allowing the attribute to be used conveniently.
+
+The function recursively expands patterns with forbidden symbols by splitting them
+into their sub-components. If the pattern does not contain forbidden symbols,
+it is returned as-is.
+-/
+partial def splitWhileForbidden (pat : Expr) : List Expr :=
+  match_expr pat with
+  | Not p => splitWhileForbidden p
+  | And p₁ p₂ => splitWhileForbidden p₁ ++ splitWhileForbidden p₂
+  | Or p₁ p₂ => splitWhileForbidden p₁ ++ splitWhileForbidden p₂
+  | Eq _ lhs rhs => splitWhileForbidden lhs ++ splitWhileForbidden rhs
+  | Iff lhs rhs => splitWhileForbidden lhs ++ splitWhileForbidden rhs
+  | HEq _ lhs _ rhs => splitWhileForbidden lhs ++ splitWhileForbidden rhs
+  | _ => [pat]
+
 private def dontCare := mkConst (Name.mkSimple "[grind_dontcare]")
 
 def mkGroundPattern (e : Expr) : Expr :=
@@ -237,19 +269,36 @@ private def getPatternFn? (pattern : Expr) : Option Expr :=
 
 /--
 Returns a bit-mask `mask` s.t. `mask[i]` is true if the corresponding argument is
-- a type (that is not a proposition) or type former, or
+- a type (that is not a proposition) or type former (which has forward dependencies) or
 - a proof, or
 - an instance implicit argument
 
 When `mask[i]`, we say the corresponding argument is a "support" argument.
 -/
 def getPatternSupportMask (f : Expr) (numArgs : Nat) : MetaM (Array Bool) := do
+  let pinfos := (← getFunInfoNArgs f numArgs).paramInfo
   forallBoundedTelescope (← inferType f) numArgs fun xs _ => do
-    xs.mapM fun x => do
+    xs.mapIdxM fun idx x => do
       if (← isProp x) then
         return false
-      else if (← isTypeFormer x <||> isProof x) then
+      else if (← isProof x) then
         return true
+      else if (← isTypeFormer x) then
+        if h : idx < pinfos.size then
+          /-
+          We originally wanted to ignore types and type formers in `grind` and treat them as supporting elements.
+          Thus, we would always return `true`. However, we changed our heuristic because of the following example:
+          ```
+          example {α} (f : α → Type) (a : α) (h : ∀ x, Nonempty (f x)) : Nonempty (f a) := by
+            grind
+          ```
+          In this example, we are reasoning about types. Therefore, we adjusted the heuristic as follows:
+          a type or type former is considered a supporting element only if it has forward dependencies.
+          Note that this is not the case for `Nonempty`.
+          -/
+          return pinfos[idx].hasFwdDeps
+        else
+          return true
       else
         return (← x.fvarId!.getDecl).binderInfo matches .instImplicit
 
@@ -467,8 +516,11 @@ def mkEMatchEqTheoremCore (origin : Origin) (levelParams : Array Name) (proof :
       | HEq _ lhs _ rhs => pure (lhs, rhs)
       | _ => throwError "invalid E-matching equality theorem, conclusion must be an equality{indentExpr type}"
     let pat := if useLhs then lhs else rhs
+    trace[grind.debug.ematch.pattern] "mkEMatchEqTheoremCore: origin: {← origin.pp}, pat: {pat}, useLhs: {useLhs}"
     let pat ← preprocessPattern pat normalizePattern
-    return (xs.size, [pat.abstract xs])
+    trace[grind.debug.ematch.pattern] "mkEMatchEqTheoremCore: after preprocessing: {pat}, {← normalize pat}"
+    let pats := splitWhileForbidden (pat.abstract xs)
+    return (xs.size, pats)
   mkEMatchTheoremCore origin levelParams numParams proof patterns
 
 /--
@@ -501,7 +553,7 @@ def getEMatchTheorems : CoreM EMatchTheorems :=
 
 inductive TheoremKind where
   | eqLhs | eqRhs | eqBoth | fwd | bwd | default
-  deriving Inhabited, BEq
+  deriving Inhabited, BEq, Repr
 
 private def TheoremKind.toAttribute : TheoremKind → String
   | .eqLhs   => "[grind =]"
@@ -601,9 +653,9 @@ private def collectPatterns? (proof : Expr) (xs : Array Expr) (searchPlaces : Ar
 
 def mkEMatchTheoremWithKind? (origin : Origin) (levelParams : Array Name) (proof : Expr) (kind : TheoremKind) : MetaM (Option EMatchTheorem) := do
   if kind == .eqLhs then
-    return (← mkEMatchEqTheoremCore origin levelParams proof (normalizePattern := false) (useLhs := true))
+    return (← mkEMatchEqTheoremCore origin levelParams proof (normalizePattern := true) (useLhs := true))
   else if kind == .eqRhs then
-    return (← mkEMatchEqTheoremCore origin levelParams proof (normalizePattern := false) (useLhs := false))
+    return (← mkEMatchEqTheoremCore origin levelParams proof (normalizePattern := true) (useLhs := false))
   let type ← inferType proof
   forallTelescopeReducing type fun xs type => do
     let searchPlaces ← match kind with
@@ -627,28 +679,40 @@ where
       levelParams, origin
     }
 
-private def getKind (stx : Syntax) : TheoremKind :=
+/-- Return theorem kind for `stx` of the form `Attr.grindThmMod` -/
+def getTheoremKindCore (stx : Syntax) : CoreM TheoremKind := do
+  match stx with
+  | `(Parser.Attr.grindThmMod| =) => return .eqLhs
+  | `(Parser.Attr.grindThmMod| →) => return .fwd
+  | `(Parser.Attr.grindThmMod| ←) => return .bwd
+  | `(Parser.Attr.grindThmMod| =_) => return .eqRhs
+  | `(Parser.Attr.grindThmMod| _=_) => return .eqBoth
+  | _ => throwError "unexpected `grind` theorem kind: `{stx}`"
+
+/-- Return theorem kind for `stx` of the form `(Attr.grindThmMod)?` -/
+def getTheoremKindFromOpt (stx : Syntax) : CoreM TheoremKind := do
   if stx[1].isNone then
-    .default
-  else if stx[1][0].getKind == ``Parser.Attr.grindEq then
-    .eqLhs
-  else if stx[1][0].getKind == ``Parser.Attr.grindFwd then
-    .fwd
-  else if stx[1][0].getKind == ``Parser.Attr.grindEqRhs then
-    .eqRhs
-  else if stx[1][0].getKind == ``Parser.Attr.grindEqBoth then
-    .eqBoth
+    return .default
   else
-    .bwd
+    getTheoremKindCore stx[1][0]
+
+def mkEMatchTheoremForDecl (declName : Name) (thmKind : TheoremKind) : MetaM EMatchTheorem := do
+  let some thm ← mkEMatchTheoremWithKind? (.decl declName) #[] (← getProofFor declName) thmKind
+    | throwError "`@{thmKind.toAttribute} theorem {declName}` {thmKind.explainFailure}, consider using different options or the `grind_pattern` command"
+  return thm
+
+def mkEMatchEqTheoremsForDef? (declName : Name) : MetaM (Option (Array EMatchTheorem)) := do
+  let some eqns ← getEqnsFor? declName | return none
+  eqns.mapM fun eqn => do
+    mkEMatchEqTheorem eqn (normalizePattern := true)
 
 private def addGrindEqAttr (declName : Name) (attrKind : AttributeKind) (thmKind : TheoremKind) (useLhs := true) : MetaM Unit := do
   if (← getConstInfo declName).isTheorem then
     ematchTheoremsExt.add (← mkEMatchEqTheorem declName (normalizePattern := true) (useLhs := useLhs)) attrKind
-  else if let some eqns ← getEqnsFor? declName then
+  else if let some thms ← mkEMatchEqTheoremsForDef? declName then
     unless useLhs do
       throwError "`{declName}` is a definition, you must only use the left-hand side for extracting patterns"
-    for eqn in eqns do
-      ematchTheoremsExt.add (← mkEMatchEqTheorem eqn) attrKind
+    thms.forM (ematchTheoremsExt.add · attrKind)
   else
     throwError s!"`{thmKind.toAttribute}` attribute can only be applied to equational theorems or function definitions"
 
@@ -663,10 +727,26 @@ private def addGrindAttr (declName : Name) (attrKind : AttributeKind) (thmKind :
   else if !(← getConstInfo declName).isTheorem then
     addGrindEqAttr declName attrKind thmKind
   else
-    let some thm ← mkEMatchTheoremWithKind? (.decl declName) #[] (← getProofFor declName) thmKind
-      | throwError "`@{thmKind.toAttribute} theorem {declName}` {thmKind.explainFailure}, consider using different options or the `grind_pattern` command"
+    let thm ← mkEMatchTheoremForDecl declName thmKind
     ematchTheoremsExt.add thm attrKind
 
+def EMatchTheorems.eraseDecl (s : EMatchTheorems) (declName : Name) : MetaM EMatchTheorems := do
+  let throwErr {α} : MetaM α :=
+    throwError "`{declName}` is not marked with the `[grind]` attribute"
+  let info ← getConstInfo declName
+  if !info.isTheorem then
+    if let some eqns ← getEqnsFor? declName then
+       let s := ematchTheoremsExt.getState (← getEnv)
+       unless eqns.all fun eqn => s.contains (.decl eqn) do
+         throwErr
+       return eqns.foldl (init := s) fun s eqn => s.erase (.decl eqn)
+    else
+      throwErr
+  else
+    unless ematchTheoremsExt.getState (← getEnv) |>.contains (.decl declName) do
+      throwErr
+    return s.erase <| .decl declName
+
 builtin_initialize
   registerBuiltinAttribute {
     name := `grind
@@ -689,7 +769,7 @@ builtin_initialize
       `grind` will add an instance of this theorem to the local context whenever it encounters the pattern `foo (foo x)`."
     applicationTime := .afterCompilation
     add := fun declName stx attrKind => do
-      addGrindAttr declName attrKind (getKind stx) |>.run' {}
+      addGrindAttr declName attrKind (← getTheoremKindFromOpt stx) |>.run' {}
     erase := fun declName => MetaM.run' do
       /-
       Remark: consider the following example
@@ -705,21 +785,9 @@ builtin_initialize
       attribute [-grind] foo  -- ok
       ```
       -/
-      let throwErr := throwError "`{declName}` is not marked with the `[grind]` attribute"
-      let info ← getConstInfo declName
-      if !info.isTheorem then
-        if let some eqns ← getEqnsFor? declName then
-           let s := ematchTheoremsExt.getState (← getEnv)
-           unless eqns.all fun eqn => s.contains (.decl eqn) do
-             throwErr
-           modifyEnv fun env => ematchTheoremsExt.modifyState env fun s =>
-             eqns.foldl (init := s) fun s eqn => s.erase (.decl eqn)
-        else
-          throwErr
-      else
-        unless ematchTheoremsExt.getState (← getEnv) |>.contains (.decl declName) do
-          throwErr
-        modifyEnv fun env => ematchTheoremsExt.modifyState env fun s => s.erase (.decl declName)
+      let s := ematchTheoremsExt.getState (← getEnv)
+      let s ← s.eraseDecl declName
+      modifyEnv fun env => ematchTheoremsExt.modifyState env fun _ => s
   }
 
 end Lean.Meta.Grind

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

@@ -0,0 +1,30 @@
+/-
+Copyright (c) 2025 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.Expr
+
+namespace Lean.Meta.Grind
+
+@[inline] def isSameExpr (a b : Expr) : Bool :=
+  -- It is safe to use pointer equality because we hashcons all expressions
+  -- inserted into the E-graph
+  unsafe ptrEq a b
+
+/--
+Key for the `ENodeMap` and `ParentMap` map.
+We use pointer addresses and rely on the fact all internalized expressions
+have been hash-consed, i.e., we have applied `shareCommon`.
+-/
+structure ENodeKey where
+  expr : Expr
+
+instance : Hashable ENodeKey where
+  hash k := unsafe (ptrAddrUnsafe k.expr).toUInt64
+
+instance : BEq ENodeKey where
+  beq k₁ k₂ := isSameExpr k₁.expr k₂.expr
+
+end Lean.Meta.Grind