chore: upstream List.modify, add lemmas, relate to Array.modify

This also requires us to expand the theory of `Int.bmod`.

---------

Co-authored-by: Alex Keizer <alex@keizer.dev>

.github/workflows/check-prelude.yml

@@ -11,7 +11,9 @@ jobs:
         with:
           # the default is to use a virtual merge commit between the PR and master: just use the PR
           ref: ${{ github.event.pull_request.head.sha }}
-          sparse-checkout: src/Lean
+          sparse-checkout: |
+            src/Lean
+            src/Std
       - name: Check Prelude
         run: |
           failed_files=""
@@ -19,8 +21,8 @@ jobs:
             if ! grep -q "^prelude$" "$file"; then
               failed_files="$failed_files$file\n"
             fi
-          done < <(find src/Lean -name '*.lean' -print0)
+          done < <(find src/Lean src/Std -name '*.lean' -print0)
           if [ -n "$failed_files" ]; then
             echo -e "The following files should use 'prelude':\n$failed_files"
             exit 1
-          fi
+          fi

.github/workflows/ci.yml

@@ -257,7 +257,7 @@ jobs:
                 "cross": true,
                 "shell": "bash -euxo pipefail {0}",
                 // Just a few selected tests because wasm is slow
-                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean|leanruntest_libuv\\.lean\""
+                "CTEST_OPTIONS": "-R \"leantest_1007\\.lean|leantest_Format\\.lean|leanruntest\\_1037.lean|leanruntest_ac_rfl\\.lean|leanruntest_tempfile.lean\\.|leanruntest_libuv\\.lean\""
               }
             ];
             console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
@@ -452,7 +452,7 @@ jobs:
         run: ccache -s
 
   # This job collects results from all the matrix jobs
-  # This can be made the “required” job, instead of listing each
+  # This can be made the "required" job, instead of listing each
   # matrix job separately
   all-done:
     name: Build matrix complete

.github/workflows/pr-release.yml

@@ -340,7 +340,7 @@ jobs:
             # (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
             git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
             lake update batteries
-            get add lake-manifest.json
+            git add lake-manifest.json
             git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
           fi
 

CODEOWNERS

@@ -4,14 +4,14 @@
 # Listed persons will automatically be asked by GitHub to review a PR touching these paths.
 # If multiple names are listed, a review by any of them is considered sufficient by default.
 
-/.github/ @Kha @semorrison
-/RELEASES.md @semorrison
+/.github/ @Kha @kim-em
+/RELEASES.md @kim-em
 /src/kernel/ @leodemoura
 /src/lake/ @tydeu
 /src/Lean/Compiler/ @leodemoura
 /src/Lean/Data/Lsp/ @mhuisi
-/src/Lean/Elab/Deriving/ @semorrison
-/src/Lean/Elab/Tactic/ @semorrison
+/src/Lean/Elab/Deriving/ @kim-em
+/src/Lean/Elab/Tactic/ @kim-em
 /src/Lean/Language/ @Kha
 /src/Lean/Meta/Tactic/ @leodemoura
 /src/Lean/Parser/ @Kha
@@ -19,7 +19,7 @@
 /src/Lean/PrettyPrinter/Delaborator/ @kmill
 /src/Lean/Server/ @mhuisi
 /src/Lean/Widget/ @Vtec234
-/src/Init/Data/ @semorrison
+/src/Init/Data/ @kim-em
 /src/Init/Data/Array/Lemmas.lean @digama0
 /src/Init/Data/List/Lemmas.lean @digama0
 /src/Init/Data/List/BasicAux.lean @digama0
@@ -45,3 +45,4 @@
 /src/Std/ @TwoFX
 /src/Std/Tactic/BVDecide/ @hargoniX
 /src/Lean/Elab/Tactic/BVDecide/ @hargoniX
+/src/Std/Sat/ @hargoniX

RELEASES.md

@@ -181,7 +181,7 @@ v4.12.0
   * [#4953](https://github.com/leanprover/lean4/pull/4953) defines "and-inverter graphs" (AIGs) as described in section 3 of [Davis-Swords 2013](https://arxiv.org/pdf/1304.7861.pdf).
 
 * **Parsec**
-  * [#4774](https://github.com/leanprover/lean4/pull/4774) generalizes the `Parsec` library, allowing parsing of iterable data beyong `String` such as `ByteArray`. (See breaking changes.)
+  * [#4774](https://github.com/leanprover/lean4/pull/4774) generalizes the `Parsec` library, allowing parsing of iterable data beyond `String` such as `ByteArray`. (See breaking changes.)
   * [#5115](https://github.com/leanprover/lean4/pull/5115) moves `Lean.Data.Parsec` to `Std.Internal.Parsec` for bootstrappng reasons.
 
 * `Thunk`

doc/make/msys2.md

@@ -18,14 +18,14 @@ the stdlib.
 ## Installing dependencies
 
 [The official webpage of MSYS2][msys2] provides one-click installers.
-Once installed, you should run the "MSYS2 MinGW 64-bit shell" from the start menu (the one that runs `mingw64.exe`).
-Do not run "MSYS2 MSYS" instead!
-MSYS2 has a package management system, [pacman][pacman], which is used in Arch Linux.
+Once installed, you should run the "MSYS2 CLANG64" shell from the start menu (the one that runs `clang64.exe`).
+Do not run "MSYS2 MSYS" or "MSYS2 MINGW64" instead!
+MSYS2 has a package management system, [pacman][pacman].
 
 Here are the commands to install all dependencies needed to compile Lean on your machine.
 
 ```bash
-pacman -S make python mingw-w64-x86_64-cmake mingw-w64-x86_64-clang mingw-w64-x86_64-ccache mingw-w64-x86_64-libuv mingw-w64-x86_64-gmp git unzip diffutils binutils
+pacman -S make python mingw-w64-clang-x86_64-cmake mingw-w64-clang-x86_64-clang mingw-w64-clang-x86_64-ccache mingw-w64-clang-x86_64-libuv mingw-w64-clang-x86_64-gmp git unzip diffutils binutils
 ```
 
 You should now be able to run these commands:
@@ -61,8 +61,7 @@ If you want a version that can run independently of your MSYS install
 then you need to copy the following dependent DLL's from where ever
 they are installed in your MSYS setup:
 
-- libgcc_s_seh-1.dll
-- libstdc++-6.dll
+- libc++.dll
 - libgmp-10.dll
 - libuv-1.dll
 - libwinpthread-1.dll
@@ -82,6 +81,6 @@ version clang to your path.
 
 **-bash: gcc: command not found**
 
-Make sure `/mingw64/bin` is in your PATH environment.  If it is not then
-check you launched the MSYS2 MinGW 64-bit shell from the start menu.
-(The one that runs `mingw64.exe`).
+Make sure `/clang64/bin` is in your PATH environment.  If it is not then
+check you launched the MSYS2 CLANG64 shell from the start menu.
+(The one that runs `clang64.exe`).

flake.nix

@@ -39,7 +39,19 @@
           CTEST_OUTPUT_ON_FAILURE = 1;
         } // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
           GMP = pkgsDist.gmp.override { withStatic = true; };
-          LIBUV = pkgsDist.libuv.overrideAttrs (attrs: { configureFlags = ["--enable-static"]; });
+          LIBUV = pkgsDist.libuv.overrideAttrs (attrs: {
+            configureFlags = ["--enable-static"];
+            hardeningDisable = [ "stackprotector" ];
+            # Sync version with CMakeLists.txt
+            version = "1.48.0";
+            src = pkgs.fetchFromGitHub {
+              owner = "libuv";
+              repo = "libuv";
+              rev = "v1.48.0";
+              sha256 = "100nj16fg8922qg4m2hdjh62zv4p32wyrllsvqr659hdhjc03bsk";
+            };
+            doCheck = false;
+          });
           GLIBC = pkgsDist.glibc;
           GLIBC_DEV = pkgsDist.glibc.dev;
           GCC_LIB = pkgsDist.gcc.cc.lib;

script/prepare-llvm-linux.sh

@@ -48,6 +48,8 @@ $CP llvm-host/lib/*/lib{c++,c++abi,unwind}.* llvm-host/lib/
 $CP -r llvm/include/*-*-* llvm-host/include/
 # glibc: use for linking (so Lean programs don't embed newer symbol versions), but not for running (because libc.so, librt.so, and ld.so must be compatible)!
 $CP $GLIBC/lib/libc_nonshared.a stage1/lib/glibc
+# libpthread_nonshared.a must be linked in order to be able to use `pthread_atfork(3)`. LibUV uses this function.
+$CP $GLIBC/lib/libpthread_nonshared.a stage1/lib/glibc
 for f in $GLIBC/lib/lib{c,dl,m,rt,pthread}-*; do b=$(basename $f); cp $f stage1/lib/glibc/${b%-*}.so; done
 OPTIONS=()
 echo -n " -DLEAN_STANDALONE=ON"
@@ -62,8 +64,8 @@ fi
 # use `-nostdinc` to make sure headers are not visible by default (in particular, not to `#include_next` in the clang headers),
 # but do not change sysroot so users can still link against system libs
 echo -n " -DLEANC_INTERNAL_FLAGS='-nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -L ROOT/lib/glibc ROOT/lib/glibc/libc_nonshared.a ROOT/lib/glibc/libpthread_nonshared.a -Wl,--as-needed -Wl,-Bstatic -lgmp -lunwind -luv -lpthread -ldl -lrt -Wl,-Bdynamic -Wl,--no-as-needed -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual
-echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-Wl,--as-needed -lgmp -luv -Wl,--no-as-needed'"
+echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-Wl,--as-needed -lgmp -luv -lpthread -ldl -lrt -Wl,--no-as-needed'"
 # do not set `LEAN_CC` for tests
 echo -n " -DLEAN_TEST_VARS=''"

script/prepare-llvm-mingw.sh

@@ -31,15 +31,15 @@ cp /clang64/lib/{crtbegin,crtend,crt2,dllcrt2}.o stage1/lib/
 # runtime
 (cd llvm; cp --parents lib/clang/*/lib/*/libclang_rt.builtins* ../stage1)
 # further dependencies
-cp /clang64/lib/lib{m,bcrypt,mingw32,moldname,mingwex,msvcrt,pthread,advapi32,shell32,user32,kernel32,ucrtbase}.* /clang64/lib/libgmp.a /clang64/lib/libuv.a llvm/lib/lib{c++,c++abi,unwind}.a stage1/lib/
+cp /clang64/lib/lib{m,bcrypt,mingw32,moldname,mingwex,msvcrt,pthread,advapi32,shell32,user32,kernel32,ucrtbase,psapi,iphlpapi,userenv,ws2_32,dbghelp,ole32}.* /clang64/lib/libgmp.a /clang64/lib/libuv.a llvm/lib/lib{c++,c++abi,unwind}.a stage1/lib/
 echo -n " -DLEAN_STANDALONE=ON"
 echo -n " -DCMAKE_C_COMPILER=$PWD/stage1/bin/clang.exe -DCMAKE_C_COMPILER_WORKS=1 -DCMAKE_CXX_COMPILER=$PWD/llvm/bin/clang++.exe -DCMAKE_CXX_COMPILER_WORKS=1 -DLEAN_CXX_STDLIB='-lc++ -lc++abi'"
 echo -n " -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_CXX_COMPILER=clang++"
 echo -n " -DLEAN_EXTRA_CXX_FLAGS='--sysroot $PWD/llvm -idirafter /clang64/include/'"
 echo -n " -DLEANC_INTERNAL_FLAGS='--sysroot ROOT -nostdinc -isystem ROOT/include/clang' -DLEANC_CC=ROOT/bin/clang.exe"
-echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -static-libgcc -Wl,-Bstatic -lgmp -luv -lunwind -Wl,-Bdynamic -fuse-ld=lld'"
+echo -n " -DLEANC_INTERNAL_LINKER_FLAGS='-L ROOT/lib -static-libgcc -Wl,-Bstatic -lgmp $(pkg-config --static --libs libuv) -lunwind -Wl,-Bdynamic -fuse-ld=lld'"
 # when not using the above flags, link GMP dynamically/as usual
-echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp -luv -lucrtbase'"
+echo -n " -DLEAN_EXTRA_LINKER_FLAGS='-lgmp $(pkg-config --libs libuv) -lucrtbase'"
 # do not set `LEAN_CC` for tests
 echo -n " -DAUTO_THREAD_FINALIZATION=OFF -DSTAGE0_AUTO_THREAD_FINALIZATION=OFF"
 echo -n " -DLEAN_TEST_VARS=''"

src/CMakeLists.txt

@@ -243,11 +243,56 @@ if("${USE_GMP}" MATCHES "ON")
   endif()
 endif()
 
-if(NOT "${CMAKE_SYSTEM_NAME}" MATCHES "Emscripten")
-  # LibUV
+# LibUV
+if("${CMAKE_SYSTEM_NAME}" MATCHES "Emscripten")
+  # Only on WebAssembly we compile LibUV ourselves
+  set(LIBUV_EMSCRIPTEN_FLAGS "${EMSCRIPTEN_SETTINGS}")
+
+  # LibUV does not compile on WebAssembly without modifications because
+  # building LibUV on a platform requires including stub implementations
+  # for features not present on the target platform. This patch includes
+  # the minimum amount of stub implementations needed for successfully
+  # running Lean on WebAssembly and using LibUV's temporary file support.
+  # It still leaves several symbols completely undefined: uv__fs_event_close,
+  # uv__hrtime, uv__io_check_fd, uv__io_fork, uv__io_poll, uv__platform_invalidate_fd
+  # uv__platform_loop_delete, uv__platform_loop_init. Making additional
+  # LibUV features available on WebAssembly might require adapting the
+  # patch to include additional LibUV source files.
+  set(LIBUV_PATCH_IN "
+diff --git a/CMakeLists.txt b/CMakeLists.txt
+index 5e8e0166..f3b29134 100644
+--- a/CMakeLists.txt
++++ b/CMakeLists.txt
+@@ -317,6 +317,11 @@ if(CMAKE_SYSTEM_NAME STREQUAL \"GNU\")
+        src/unix/hurd.c)
+ endif()
+
++if(CMAKE_SYSTEM_NAME STREQUAL \"Emscripten\")
++  list(APPEND uv_sources
++       src/unix/no-proctitle.c)
++endif()
++
+ if(CMAKE_SYSTEM_NAME STREQUAL \"Linux\")
+   list(APPEND uv_defines _GNU_SOURCE _POSIX_C_SOURCE=200112)
+   list(APPEND uv_libraries dl rt)
+")
+  string(REPLACE "\n" "\\n" LIBUV_PATCH ${LIBUV_PATCH_IN})
+
+  ExternalProject_add(libuv
+    PREFIX libuv
+    GIT_REPOSITORY https://github.com/libuv/libuv
+    # Sync version with flake.nix
+    GIT_TAG v1.48.0
+    CMAKE_ARGS -DCMAKE_BUILD_TYPE=Release -DLIBUV_BUILD_TESTS=OFF -DLIBUV_BUILD_SHARED=OFF -DCMAKE_AR=${CMAKE_AR} -DCMAKE_TOOLCHAIN_FILE=${CMAKE_TOOLCHAIN_FILE} -DCMAKE_POSITION_INDEPENDENT_CODE=ON -DCMAKE_C_FLAGS=${LIBUV_EMSCRIPTEN_FLAGS}
+	  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 "${CMAKE_BINARY_DIR}/libuv/src/libuv/libuv.a")
+else()
   find_package(LibUV 1.0.0 REQUIRED)
-  include_directories(${LIBUV_INCLUDE_DIR})
 endif()
+include_directories(${LIBUV_INCLUDE_DIR})
 if(NOT LEAN_STANDALONE)
   string(APPEND LEAN_EXTRA_LINKER_FLAGS " ${LIBUV_LIBRARIES}")
 endif()
@@ -522,6 +567,10 @@ if(${STAGE} GREATER 1)
   endif()
 else()
   add_subdirectory(runtime)
+  if("${CMAKE_SYSTEM_NAME}" MATCHES "Emscripten")
+    add_dependencies(leanrt libuv)
+    add_dependencies(leanrt_initial-exec libuv)
+  endif()
 
   add_subdirectory(util)
   set(LEAN_OBJS ${LEAN_OBJS} $<TARGET_OBJECTS:util>)
@@ -562,7 +611,10 @@ if (${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
   # simple. (And we are not interested in `Lake` anyway.) To use dynamic
   # linking, we would probably have to set MAIN_MODULE=2 on `leanshared`,
   # SIDE_MODULE=2 on `lean`, and set CMAKE_SHARED_LIBRARY_SUFFIX to ".js".
-  string(APPEND LEAN_EXE_LINKER_FLAGS " ${LIB}/temp/libleanshell.a ${TOOLCHAIN_STATIC_LINKER_FLAGS} ${EMSCRIPTEN_SETTINGS} -lnodefs.js -s EXIT_RUNTIME=1 -s MAIN_MODULE=1 -s LINKABLE=1 -s EXPORT_ALL=1")
+  # We set `ERROR_ON_UNDEFINED_SYMBOLS=0` because our build of LibUV does not
+  # define all symbols, see the comment about LibUV on WebAssembly further up
+  # in this file.
+  string(APPEND LEAN_EXE_LINKER_FLAGS " ${LIB}/temp/libleanshell.a ${TOOLCHAIN_STATIC_LINKER_FLAGS} ${EMSCRIPTEN_SETTINGS} -lnodefs.js -s EXIT_RUNTIME=1 -s MAIN_MODULE=1 -s LINKABLE=1 -s EXPORT_ALL=1 -s ERROR_ON_UNDEFINED_SYMBOLS=0")
 endif()
 
 # Build the compiler using the bootstrapped C sources for stage0, and use

src/Init.lean

@@ -35,3 +35,4 @@ import Init.Ext
 import Init.Omega
 import Init.MacroTrace
 import Init.Grind
+import Init.While

src/Init/Core.lean

@@ -1385,6 +1385,7 @@ gen_injective_theorems% Except
 gen_injective_theorems% EStateM.Result
 gen_injective_theorems% Lean.Name
 gen_injective_theorems% Lean.Syntax
+gen_injective_theorems% BitVec
 
 theorem Nat.succ.inj {m n : Nat} : m.succ = n.succ → m = n :=
   fun x => Nat.noConfusion x id
@@ -1864,7 +1865,8 @@ section
 variable {α : Type u}
 variable (r : α → α → Prop)
 
-instance {α : Sort u} {s : Setoid α} [d : ∀ (a b : α), Decidable (a ≈ b)] : DecidableEq (Quotient s) :=
+instance Quotient.decidableEq {α : Sort u} {s : Setoid α} [d : ∀ (a b : α), Decidable (a ≈ b)]
+    : DecidableEq (Quotient s) :=
   fun (q₁ q₂ : Quotient s) =>
     Quotient.recOnSubsingleton₂ q₁ q₂
       fun a₁ a₂ =>
@@ -1935,15 +1937,6 @@ instance : Subsingleton (Squash α) where
     apply Quot.sound
     trivial
 
-/-! # Relations -/
-
-/--
-`Antisymm (·≤·)` says that `(·≤·)` is antisymmetric, that is, `a ≤ b → b ≤ a → a = b`.
--/
-class Antisymm {α : Sort u} (r : α → α → Prop) : Prop where
-  /-- An antisymmetric relation `(·≤·)` satisfies `a ≤ b → b ≤ a → a = b`. -/
-  antisymm {a b : α} : r a b → r b a → a = b
-
 namespace Lean
 /-! # Kernel reduction hints -/
 
@@ -2119,4 +2112,14 @@ instance : Commutative Or := ⟨fun _ _ => propext or_comm⟩
 instance : Commutative And := ⟨fun _ _ => propext and_comm⟩
 instance : Commutative Iff := ⟨fun _ _ => propext iff_comm⟩
 
+/--
+`Antisymm (·≤·)` says that `(·≤·)` is antisymmetric, that is, `a ≤ b → b ≤ a → a = b`.
+-/
+class Antisymm (r : α → α → Prop) : Prop where
+  /-- An antisymmetric relation `(·≤·)` satisfies `a ≤ b → b ≤ a → a = b`. -/
+  antisymm {a b : α} : r a b → r b a → a = b
+
+@[deprecated Antisymm (since := "2024-10-16"), inherit_doc Antisymm]
+abbrev _root_.Antisymm (r : α → α → Prop) : Prop := Std.Antisymm r
+
 end Std

src/Init/Data.lean

@@ -40,3 +40,4 @@ import Init.Data.ULift
 import Init.Data.PLift
 import Init.Data.Zero
 import Init.Data.NeZero
+import Init.Data.Function

src/Init/Data/Array.lean

@@ -16,3 +16,4 @@ import Init.Data.Array.Lemmas
 import Init.Data.Array.TakeDrop
 import Init.Data.Array.Bootstrap
 import Init.Data.Array.GetLit
+import Init.Data.Array.MapIdx

src/Init/Data/Array/Attach.lean

@@ -5,6 +5,7 @@ Authors: Joachim Breitner, Mario Carneiro
 -/
 prelude
 import Init.Data.Array.Mem
+import Init.Data.Array.Lemmas
 import Init.Data.List.Attach
 
 namespace Array
@@ -26,4 +27,152 @@ Unsafe implementation of `attachWith`, taking advantage of the fact that the rep
   with the same elements but in the type `{x // x ∈ xs}`. -/
 @[inline] def attach (xs : Array α) : Array {x // x ∈ xs} := xs.attachWith _ fun _ => id
 
+@[simp] theorem _root_.List.attachWith_toArray {l : List α} {P : α → Prop} {H : ∀ x ∈ l.toArray, P x} :
+    l.toArray.attachWith P H = (l.attachWith P (by simpa using H)).toArray := by
+  simp [attachWith]
+
+@[simp] theorem _root_.List.attach_toArray {l : List α} :
+    l.toArray.attach = (l.attachWith (· ∈ l.toArray) (by simp)).toArray := by
+  simp [attach]
+
+@[simp] theorem toList_attachWith {l : Array α} {P : α → Prop} {H : ∀ x ∈ l, P x} :
+   (l.attachWith P H).toList = l.toList.attachWith P (by simpa [mem_toList] using H) := by
+  simp [attachWith]
+
+@[simp] theorem toList_attach {α : Type _} {l : Array α} :
+    l.attach.toList = l.toList.attachWith (· ∈ l) (by simp [mem_toList]) := by
+  simp [attach]
+
+/-! ## unattach
+
+`Array.unattach` is the (one-sided) inverse of `Array.attach`. It is a synonym for `Array.map Subtype.val`.
+
+We use it by providing a simp lemma `l.attach.unattach = l`, and simp lemmas which recognize higher order
+functions applied to `l : Array { x // p x }` which only depend on the value, not the predicate, and rewrite these
+in terms of a simpler function applied to `l.unattach`.
+
+Further, we provide simp lemmas that push `unattach` inwards.
+-/
+
+/--
+A synonym for `l.map (·.val)`. Mostly this should not be needed by users.
+It is introduced as in intermediate step by lemmas such as `map_subtype`,
+and is ideally subsequently simplified away by `unattach_attach`.
+
+If not, usually the right approach is `simp [Array.unattach, -Array.map_subtype]` to unfold.
+-/
+def unattach {α : Type _} {p : α → Prop} (l : Array { x // p x }) := l.map (·.val)
+
+@[simp] theorem unattach_nil {p : α → Prop} : (#[] : Array { x // p x }).unattach = #[] := rfl
+@[simp] theorem unattach_push {p : α → Prop} {a : { x // p x }} {l : Array { x // p x }} :
+    (l.push a).unattach = l.unattach.push a.1 := by
+  simp only [unattach, Array.map_push]
+
+@[simp] theorem size_unattach {p : α → Prop} {l : Array { x // p x }} :
+    l.unattach.size = l.size := by
+  unfold unattach
+  simp
+
+@[simp] theorem _root_.List.unattach_toArray {p : α → Prop} {l : List { x // p x }} :
+    l.toArray.unattach = l.unattach.toArray := by
+  simp only [unattach, List.map_toArray, List.unattach]
+
+@[simp] theorem toList_unattach {p : α → Prop} {l : Array { x // p x }} :
+    l.unattach.toList = l.toList.unattach := by
+  simp only [unattach, toList_map, List.unattach]
+
+@[simp] theorem unattach_attach {l : Array α} : l.attach.unattach = l := by
+  cases l
+  simp
+
+@[simp] theorem unattach_attachWith {p : α → Prop} {l : Array α}
+    {H : ∀ a ∈ l, p a} :
+    (l.attachWith p H).unattach = l := by
+  cases l
+  simp
+
+/-! ### Recognizing higher order functions using a function that only depends on the value. -/
+
+/--
+This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+theorem foldl_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : β → { x // p x } → β} {g : β → α → β} {x : β}
+    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} :
+    l.foldl f x = l.unattach.foldl g x := by
+  cases l
+  simp only [List.foldl_toArray', List.unattach_toArray]
+  rw [List.foldl_subtype] -- Why can't simp do this?
+  simp [hf]
+
+/-- Variant of `foldl_subtype` with side condition to check `stop = l.size`. -/
+@[simp] theorem foldl_subtype' {p : α → Prop} {l : Array { x // p x }}
+    {f : β → { x // p x } → β} {g : β → α → β} {x : β}
+    {hf : ∀ b x h, f b ⟨x, h⟩ = g b x} (h : stop = l.size) :
+    l.foldl f x 0 stop = l.unattach.foldl g x := by
+  subst h
+  rwa [foldl_subtype]
+
+/--
+This lemma identifies folds over arrays of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+theorem foldr_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → β → β} {g : α → β → β} {x : β}
+    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} :
+    l.foldr f x = l.unattach.foldr g x := by
+  cases l
+  simp only [List.foldr_toArray', List.unattach_toArray]
+  rw [List.foldr_subtype]
+  simp [hf]
+
+/-- Variant of `foldr_subtype` with side condition to check `stop = l.size`. -/
+@[simp] theorem foldr_subtype' {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → β → β} {g : α → β → β} {x : β}
+    {hf : ∀ x h b, f ⟨x, h⟩ b = g x b} (h : start = l.size) :
+    l.foldr f x start 0 = l.unattach.foldr g x := by
+  subst h
+  rwa [foldr_subtype]
+
+/--
+This lemma identifies maps over arrays of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem map_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → β} {g : α → β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    l.map f = l.unattach.map g := by
+  cases l
+  simp only [List.map_toArray, List.unattach_toArray]
+  rw [List.map_subtype]
+  simp [hf]
+
+@[simp] theorem filterMap_subtype {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → Option β} {g : α → Option β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    l.filterMap f = l.unattach.filterMap g := by
+  cases l
+  simp only [size_toArray, List.filterMap_toArray', List.unattach_toArray, List.length_unattach,
+    mk.injEq]
+  rw [List.filterMap_subtype]
+  simp [hf]
+
+@[simp] theorem unattach_filter {p : α → Prop} {l : Array { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    (l.filter f).unattach = l.unattach.filter g := by
+  cases l
+  simp [hf]
+
+/-! ### Simp lemmas pushing `unattach` inwards. -/
+
+@[simp] theorem unattach_reverse {p : α → Prop} {l : Array { x // p x }} :
+    l.reverse.unattach = l.unattach.reverse := by
+  cases l
+  simp
+
+@[simp] theorem unattach_append {p : α → Prop} {l₁ l₂ : Array { x // p x }} :
+    (l₁ ++ l₂).unattach = l₁.unattach ++ l₂.unattach := by
+  cases l₁
+  cases l₂
+  simp
+
 end Array

src/Init/Data/Array/Basic.lean

@@ -7,10 +7,11 @@ prelude
 import Init.WFTactics
 import Init.Data.Nat.Basic
 import Init.Data.Fin.Basic
-import Init.Data.UInt.Basic
+import Init.Data.UInt.BasicAux
 import Init.Data.Repr
 import Init.Data.ToString.Basic
 import Init.GetElem
+import Init.Data.List.ToArray
 universe u v w
 
 /-! ### Array literal syntax -/
@@ -24,6 +25,8 @@ variable {α : Type u}
 
 namespace Array
 
+@[deprecated size (since := "2024-10-13")] abbrev data := @toList
+
 /-! ### Preliminary theorems -/
 
 @[simp] theorem size_set (a : Array α) (i : Fin a.size) (v : α) : (set a i v).size = a.size :=
@@ -77,6 +80,26 @@ theorem ext' {as bs : Array α} (h : as.toList = bs.toList) : as = bs := by
 
 @[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
 
+@[simp] theorem getElem_toList {a : Array α} {i : Nat} (h : i < a.size) : a.toList[i] = a[i] := rfl
+
+end Array
+
+namespace List
+
+@[simp] theorem toArray_toList (a : Array α) : a.toList.toArray = a := rfl
+
+@[simp] theorem getElem_toArray {a : List α} {i : Nat} (h : i < a.toArray.size) :
+    a.toArray[i] = a[i]'(by simpa using h) := rfl
+
+@[simp] theorem getElem?_toArray {a : List α} {i : Nat} : a.toArray[i]? = a[i]? := rfl
+
+@[simp] theorem getElem!_toArray [Inhabited α] {a : List α} {i : Nat} :
+    a.toArray[i]! = a[i]! := rfl
+
+end List
+
+namespace Array
+
 @[deprecated toList_toArray (since := "2024-09-09")] abbrev data_toArray := @toList_toArray
 
 @[deprecated Array.toList (since := "2024-09-10")] abbrev Array.data := @Array.toList
@@ -215,7 +238,7 @@ def swapAt! (a : Array α) (i : Nat) (v : α) : α × Array α :=
   if h : i < a.size then
     swapAt a ⟨i, h⟩ v
   else
-    have : Inhabited α := ⟨v⟩
+    have : Inhabited (α × Array α) := ⟨(v, a)⟩
     panic! ("index " ++ toString i ++ " out of bounds")
 
 def shrink (a : Array α) (n : Nat) : Array α :=
@@ -395,20 +418,25 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
   decreasing_by simp_wf; decreasing_trivial_pre_omega
   map 0 (mkEmpty as.size)
 
+/-- Variant of `mapIdxM` which receives the index as a `Fin as.size`. -/
 @[inline]
-def mapIdxM {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) :=
+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) :=
   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
     | i+1, inv =>
-      have : j < as.size := by
+      have j_lt : j < as.size := by
         rw [← inv, Nat.add_assoc, Nat.add_comm 1 j, Nat.add_comm]
         apply Nat.le_add_right
-      let idx : Fin as.size := ⟨j, this⟩
       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 idx (as.get idx)))
+      map i (j+1) this (bs.push (← f ⟨j, j_lt⟩ (as.get ⟨j, 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] (as : Array α) (f : Nat → α → m β) : m (Array β) :=
+  as.mapFinIdxM fun i a => f i a
+
 @[inline]
 def findSomeM? {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (as : Array α) (f : α → m (Option β)) : m (Option β) := do
   for a in as do
@@ -514,8 +542,13 @@ def foldr {α : Type u} {β : Type v} (f : α → β → β) (init : β) (as : A
 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 mapIdx {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 : Fin as.size → α → β) : Array β :=
+  Id.run <| as.mapFinIdxM f
+
+@[inline]
+def mapIdx {α : Type u} {β : Type v} (as : Array α) (f : Nat → α → β) : Array β :=
   Id.run <| as.mapIdxM f
 
 /-- Turns `#[a, b]` into `#[(a, 0), (b, 1)]`. -/
@@ -606,13 +639,17 @@ protected def appendList (as : Array α) (bs : List α) : Array α :=
 instance : HAppend (Array α) (List α) (Array α) := ⟨Array.appendList⟩
 
 @[inline]
-def concatMapM [Monad m] (f : α → m (Array β)) (as : Array α) : m (Array β) :=
+def flatMapM [Monad m] (f : α → m (Array β)) (as : Array α) : m (Array β) :=
   as.foldlM (init := empty) fun bs a => do return bs ++ (← f a)
 
+@[deprecated concatMapM (since := "2024-10-16")] abbrev concatMapM := @flatMapM
+
 @[inline]
-def concatMap (f : α → Array β) (as : Array α) : Array β :=
+def flatMap (f : α → Array β) (as : Array α) : Array β :=
   as.foldl (init := empty) fun bs a => bs ++ f a
 
+@[deprecated flatMap (since := "2024-10-16")] abbrev concatMap := @flatMap
+
 /-- Joins array of array into a single array.
 
 `flatten #[#[a₁, a₂, ⋯], #[b₁, b₂, ⋯], ⋯]` = `#[a₁, a₂, ⋯, b₁, b₂, ⋯]`
@@ -812,9 +849,15 @@ def split (as : Array α) (p : α → Bool) : Array α × Array α :=
 
 /-! ## Auxiliary functions used in metaprogramming.
 
-We do not intend to provide verification theorems for these functions.
+We do not currently intend to provide verification theorems for these functions.
 -/
 
+/- ### reduceOption -/
+
+/-- Drop `none`s from a Array, and replace each remaining `some a` with `a`. -/
+@[inline] def reduceOption (as : Array (Option α)) : Array α :=
+  as.filterMap id
+
 /-! ### eraseReps -/
 
 /--

src/Init/Data/Array/Bootstrap.lean

@@ -42,7 +42,7 @@ theorem foldrM_eq_reverse_foldlM_toList.aux [Monad m]
   unfold foldrM.fold
   match i with
   | 0 => simp [List.foldlM, List.take]
-  | i+1 => rw [← List.take_concat_get _ _ h]; simp [← (aux f arr · i)]; rfl
+  | i+1 => rw [← List.take_concat_get _ _ h]; simp [← (aux f arr · i)]
 
 theorem foldrM_eq_reverse_foldlM_toList [Monad m] (f : α → β → m β) (init : β) (arr : Array α) :
     arr.foldrM f init = arr.toList.reverse.foldlM (fun x y => f y x) init := by

src/Init/Data/Array/DecidableEq.lean

@@ -6,6 +6,8 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.Basic
 import Init.Data.BEq
+import Init.Data.Nat.Lemmas
+import Init.Data.List.Nat.BEq
 import Init.ByCases
 
 namespace Array
@@ -26,6 +28,14 @@ theorem rel_of_isEqvAux
       subst hj'
       exact heqv.left
 
+theorem isEqvAux_of_rel (r : α → α → Bool) (a b : Array α) (hsz : a.size = b.size) (i : Nat) (hi : i ≤ a.size)
+    (w : ∀ j, (hj : j < i) → r (a[j]'(Nat.lt_of_lt_of_le hj hi)) (b[j]'(Nat.lt_of_lt_of_le hj (hsz ▸ hi)))) : Array.isEqvAux a b hsz r i hi := by
+  induction i with
+  | zero => simp [Array.isEqvAux]
+  | succ i ih =>
+    simp only [isEqvAux, Bool.and_eq_true]
+    exact ⟨w i (Nat.lt_add_one i), ih _ fun j hj => w j (Nat.lt_add_right 1 hj)⟩
+
 theorem rel_of_isEqv (r : α → α → Bool) (a b : Array α) :
     Array.isEqv a b r → ∃ h : a.size = b.size, ∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h')) := by
   simp only [isEqv]
@@ -33,6 +43,29 @@ theorem rel_of_isEqv (r : α → α → Bool) (a b : Array α) :
   · exact fun h' => ⟨h, rel_of_isEqvAux r a b h a.size (Nat.le_refl ..) h'⟩
   · intro; contradiction
 
+theorem isEqv_iff_rel (a b : Array α) (r) :
+    Array.isEqv a b r ↔ ∃ h : a.size = b.size, ∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h')) :=
+  ⟨rel_of_isEqv r a b, fun ⟨h, w⟩ => by
+    simp only [isEqv, ← h, ↓reduceDIte]
+    exact isEqvAux_of_rel r a b h a.size (by simp [h]) w⟩
+
+theorem isEqv_eq_decide (a b : Array α) (r) :
+    Array.isEqv a b r =
+      if h : a.size = b.size then decide (∀ (i : Nat) (h' : i < a.size), r (a[i]) (b[i]'(h ▸ h'))) else false := by
+  by_cases h : Array.isEqv a b r
+  · simp only [h, Bool.true_eq]
+    simp only [isEqv_iff_rel] at h
+    obtain ⟨h, w⟩ := h
+    simp [h, w]
+  · let h' := h
+    simp only [Bool.not_eq_true] at h
+    simp only [h, Bool.false_eq, dite_eq_right_iff, decide_eq_false_iff_not, Classical.not_forall,
+      Bool.not_eq_true]
+    simpa [isEqv_iff_rel] using h'
+
+@[simp] theorem isEqv_toList [BEq α] (a b : Array α) : (a.toList.isEqv b.toList r) = (a.isEqv b r) := by
+  simp [isEqv_eq_decide, List.isEqv_eq_decide]
+
 theorem eq_of_isEqv [DecidableEq α] (a b : Array α) (h : Array.isEqv a b (fun x y => x = y)) : a = b := by
   have ⟨h, h'⟩ := rel_of_isEqv (fun x y => x = y) a b h
   exact ext _ _ h (fun i lt _ => by simpa using h' i lt)
@@ -56,4 +89,22 @@ instance [DecidableEq α] : DecidableEq (Array α) :=
     | true  => isTrue (eq_of_isEqv a b h)
     | false => isFalse fun h' => by subst h'; rw [isEqv_self] at h; contradiction
 
+theorem beq_eq_decide [BEq α] (a b : Array α) :
+    (a == b) = if h : a.size = b.size then
+      decide (∀ (i : Nat) (h' : i < a.size), a[i] == b[i]'(h ▸ h')) else false := by
+  simp [BEq.beq, isEqv_eq_decide]
+
+@[simp] theorem beq_toList [BEq α] (a b : Array α) : (a.toList == b.toList) = (a == b) := by
+  simp [beq_eq_decide, List.beq_eq_decide]
+
 end Array
+
+namespace List
+
+@[simp] theorem isEqv_toArray [BEq α] (a b : List α) : (a.toArray.isEqv b.toArray r) = (a.isEqv b r) := by
+  simp [isEqv_eq_decide, Array.isEqv_eq_decide]
+
+@[simp] theorem beq_toArray [BEq α] (a b : List α) : (a.toArray == b.toArray) = (a == b) := by
+  simp [beq_eq_decide, Array.beq_eq_decide]
+
+end List

src/Init/Data/Array/GetLit.lean

@@ -41,6 +41,6 @@ where
   getLit_eq (as : Array α) (i : Nat) (h₁ : as.size = n) (h₂ : i < n) : as.getLit i h₁ h₂ = getElem as.toList i ((id (α := as.toList.length = n) h₁) ▸ h₂) :=
     rfl
   go (i : Nat) (hi : i ≤ as.size) : toListLitAux as n hsz i hi (as.toList.drop i) = as.toList := by
-    induction i <;> simp [getLit_eq, List.get_drop_eq_drop, toListLitAux, List.drop, *]
+    induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.get_drop_eq_drop, *]
 
 end Array

src/Init/Data/Array/MapIdx.lean

@@ -0,0 +1,92 @@
+/-
+Copyright (c) 2022 Mario Carneiro. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Mario Carneiro, Kim Morrison
+-/
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.MapIdx
+
+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)
+    (motive : Nat → Prop) (h0 : motive 0)
+    (p : Fin as.size → β → Prop)
+    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
+    motive as.size ∧ ∃ eq : (Array.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) :
+    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
+    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)
+      · 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
+  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])) :
+    ∃ 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
+
+@[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_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)
+    (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 _
+
+@[simp] theorem getElem?_mapFinIdx (a : Array α) (f : Fin a.size → α → β) (i : Nat) :
+    (a.mapFinIdx f)[i]? =
+      a[i]?.pbind fun b h => f ⟨i, (getElem?_eq_some_iff.1 h).1⟩ b := by
+  simp only [getElem?_def, size_mapFinIdx, getElem_mapFinIdx]
+  split <;> simp_all
+
+/-! ### mapIdx -/
+
+theorem mapIdx_induction (as : Array α) (f : Nat → α → β)
+    (motive : Nat → Prop) (h0 : motive 0)
+    (p : Fin as.size → β → Prop)
+    (hs : ∀ i, motive i.1 → p i (f i as[i]) ∧ motive (i + 1)) :
+    motive as.size ∧ ∃ eq : (Array.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
+  mapFinIdx_induction as (fun i a => f i a) motive h0 p hs
+
+theorem mapIdx_spec (as : Array α) (f : Nat → α → β)
+    (p : Fin as.size → β → Prop) (hs : ∀ i, p i (f i as[i])) :
+    ∃ eq : (Array.mapIdx as f).size = as.size,
+      ∀ i h, p ⟨i, h⟩ ((Array.mapIdx as f)[i]) :=
+  (mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => ⟨hs .., trivial⟩).2
+
+@[simp] theorem size_mapIdx (a : Array α) (f : Nat → α → β) : (a.mapIdx f).size = a.size :=
+  (mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
+
+@[simp] theorem getElem_mapIdx (a : Array α) (f : Nat → α → β) (i : Nat)
+    (h : i < (mapIdx a f).size) :
+    (a.mapIdx f)[i] = f i (a[i]'(by simp_all)) :=
+  (mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i (by simp_all)
+
+@[simp] theorem getElem?_mapIdx (a : Array α) (f : Nat → α → β) (i : Nat) :
+    (a.mapIdx f)[i]? =
+      a[i]?.map (f i) := by
+  simp [getElem?_def, size_mapIdx, getElem_mapIdx]
+
+end Array

src/Init/Data/BitVec/Basic.lean

@@ -1,19 +1,20 @@
 /-
 Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed
+Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed, Siddharth Bhat
 -/
 prelude
 import Init.Data.Fin.Basic
 import Init.Data.Nat.Bitwise.Lemmas
 import Init.Data.Nat.Power2
 import Init.Data.Int.Bitwise
+import Init.Data.BitVec.BasicAux
 
 /-!
-We define bitvectors. We choose the `Fin` representation over others for its relative efficiency
-(Lean has special support for `Nat`), alignment with `UIntXY` types which are also represented
-with `Fin`, and the fact that bitwise operations on `Fin` are already defined. Some other possible
-representations are `List Bool`, `{ l : List Bool // l.length = w }`, `Fin w → Bool`.
+We define the basic algebraic structure of bitvectors. We choose the `Fin` representation over
+others for its relative efficiency (Lean has special support for `Nat`),  and the fact that bitwise
+operations on `Fin` are already defined. Some other possible representations are `List Bool`,
+`{ l : List Bool // l.length = w }`, `Fin w → Bool`.
 
 We define many of the bitvector operations from the
 [`QF_BV` logic](https://smtlib.cs.uiowa.edu/logics-all.shtml#QF_BV).
@@ -22,60 +23,12 @@ of SMT-LIBv2.
 
 set_option linter.missingDocs true
 
-/--
-A bitvector of the specified width.
-
-This is represented as the underlying `Nat` number in both the runtime
-and the kernel, inheriting all the special support for `Nat`.
--/
-structure BitVec (w : Nat) where
-  /-- Construct a `BitVec w` from a number less than `2^w`.
-  O(1), because we use `Fin` as the internal representation of a bitvector. -/
-  ofFin ::
-  /-- Interpret a bitvector as a number less than `2^w`.
-  O(1), because we use `Fin` as the internal representation of a bitvector. -/
-  toFin : Fin (2^w)
-
-/--
-Bitvectors have decidable equality. This should be used via the instance `DecidableEq (BitVec n)`.
--/
--- We manually derive the `DecidableEq` instances for `BitVec` because
--- we want to have builtin support for bit-vector literals, and we
--- need a name for this function to implement `canUnfoldAtMatcher` at `WHNF.lean`.
-def BitVec.decEq (x y : BitVec n) : Decidable (x = y) :=
-  match x, y with
-  | ⟨n⟩, ⟨m⟩ =>
-    if h : n = m then
-      isTrue (h ▸ rfl)
-    else
-      isFalse (fun h' => BitVec.noConfusion h' (fun h' => absurd h' h))
-
-instance : DecidableEq (BitVec n) := BitVec.decEq
-
 namespace BitVec
 
 section Nat
 
-/-- The `BitVec` with value `i`, given a proof that `i < 2^n`. -/
-@[match_pattern]
-protected def ofNatLt {n : Nat} (i : Nat) (p : i < 2^n) : BitVec n where
-  toFin := ⟨i, p⟩
-
-/-- The `BitVec` with value `i mod 2^n`. -/
-@[match_pattern]
-protected def ofNat (n : Nat) (i : Nat) : BitVec n where
-  toFin := Fin.ofNat' (2^n) i
-
-instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
 instance natCastInst : NatCast (BitVec w) := ⟨BitVec.ofNat w⟩
 
-/-- Given a bitvector `x`, return the underlying `Nat`. This is O(1) because `BitVec` is a
-(zero-cost) wrapper around a `Nat`. -/
-protected def toNat (x : BitVec n) : Nat := x.toFin.val
-
-/-- Return the bound in terms of toNat. -/
-theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
-
 @[deprecated isLt (since := "2024-03-12")]
 theorem toNat_lt (x : BitVec n) : x.toNat < 2^n := x.isLt
 
@@ -238,22 +191,6 @@ end repr_toString
 
 section arithmetic
 
-/--
-Addition for bit vectors. This can be interpreted as either signed or unsigned addition
-modulo `2^n`.
-
-SMT-Lib name: `bvadd`.
--/
-protected def add (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + y.toNat)
-instance : Add (BitVec n) := ⟨BitVec.add⟩
-
-/--
-Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
-modulo `2^n`.
--/
-protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
-instance : Sub (BitVec n) := ⟨BitVec.sub⟩
-
 /--
 Negation for bit vectors. This can be interpreted as either signed or unsigned negation
 modulo `2^n`.
@@ -387,10 +324,6 @@ SMT-Lib name: `bvult`.
 -/
 protected def ult (x y : BitVec n) : Bool := x.toNat < y.toNat
 
-instance : LT (BitVec n) where lt := (·.toNat < ·.toNat)
-instance (x y : BitVec n) : Decidable (x < y) :=
-  inferInstanceAs (Decidable (x.toNat < y.toNat))
-
 /--
 Unsigned less-than-or-equal-to for bit vectors.
 
@@ -398,10 +331,6 @@ SMT-Lib name: `bvule`.
 -/
 protected def ule (x y : BitVec n) : Bool := x.toNat ≤ y.toNat
 
-instance : LE (BitVec n) where le := (·.toNat ≤ ·.toNat)
-instance (x y : BitVec n) : Decidable (x ≤ y) :=
-  inferInstanceAs (Decidable (x.toNat ≤ y.toNat))
-
 /--
 Signed less-than for bit vectors.
 
@@ -718,6 +647,8 @@ section normalization_eqs
 @[simp] theorem add_eq (x y : BitVec w)                   : BitVec.add x y = x + y            := rfl
 @[simp] theorem sub_eq (x y : BitVec w)                   : BitVec.sub x y = x - y            := rfl
 @[simp] theorem mul_eq (x y : BitVec w)                   : BitVec.mul x y = x * y            := rfl
+@[simp] theorem udiv_eq (x y : BitVec w)                  : BitVec.udiv x y = x / y           := rfl
+@[simp] theorem umod_eq (x y : BitVec w)                  : BitVec.umod x y = x % y           := rfl
 @[simp] theorem zero_eq                                   : BitVec.zero n = 0#n               := rfl
 end normalization_eqs
 

src/Init/Data/BitVec/BasicAux.lean

@@ -0,0 +1,52 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed
+-/
+prelude
+import Init.Data.Fin.Basic
+
+set_option linter.missingDocs true
+
+/-!
+This module exists to provide the very basic `BitVec` definitions required for
+`Init.Data.UInt.BasicAux`.
+-/
+
+namespace BitVec
+
+section Nat
+
+/-- The `BitVec` with value `i mod 2^n`. -/
+@[match_pattern]
+protected def ofNat (n : Nat) (i : Nat) : BitVec n where
+  toFin := Fin.ofNat' (2^n) i
+
+instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
+
+/-- Return the bound in terms of toNat. -/
+theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
+
+end Nat
+
+section arithmetic
+
+/--
+Addition for bit vectors. This can be interpreted as either signed or unsigned addition
+modulo `2^n`.
+
+SMT-Lib name: `bvadd`.
+-/
+protected def add (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + y.toNat)
+instance : Add (BitVec n) := ⟨BitVec.add⟩
+
+/--
+Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
+modulo `2^n`.
+-/
+protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
+instance : Sub (BitVec n) := ⟨BitVec.sub⟩
+
+end arithmetic
+
+end BitVec

src/Init/Data/BitVec/Bitblast.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix
+Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
 -/
 prelude
 import Init.Data.BitVec.Folds
@@ -18,6 +18,80 @@ as vectors of bits into proofs about Lean `BitVec` values.
 The module is named for the bit-blasting operation in an SMT solver that converts bitvector
 expressions into expressions about individual bits in each vector.
 
+### Example: How bitblasting works for multiplication
+
+We explain how the lemmas here are used for bitblasting,
+by using multiplication as a prototypical example.
+Other bitblasters for other operations follow the same pattern.
+To bitblast a multiplication of the form `x * y`,
+we must unfold the above into a form that the SAT solver understands.
+
+We assume that the solver already knows how to bitblast addition.
+This is known to `bv_decide`, by exploiting the lemma `add_eq_adc`,
+which says that `x + y : BitVec w` equals `(adc x y false).2`,
+where `adc` builds an add-carry circuit in terms of the primitive operations
+(bitwise and, bitwise or, bitwise xor) that bv_decide already understands.
+In this way, we layer bitblasters on top of each other,
+by reducing the multiplication bitblaster to an addition operation.
+
+The core lemma is given by `getLsbD_mul`:
+
+```lean
+ x y : BitVec w ⊢ (x * y).getLsbD i = (mulRec x y w).getLsbD i
+```
+
+Which says that the `i`th bit of `x * y` can be obtained by
+evaluating the `i`th bit of `(mulRec x y w)`.
+Once again, we assume that `bv_decide` knows how to implement `getLsbD`,
+given that `mulRec` can be understood by `bv_decide`.
+
+We write two lemmas to enable `bv_decide` to unfold `(mulRec x y w)`
+into a complete circuit, **when `w` is a known constant**`.
+This is given by two recurrence lemmas, `mulRec_zero_eq` and `mulRec_succ_eq`,
+which are applied repeatedly when the width is `0` and when the width is `w' + 1`:
+
+```lean
+mulRec_zero_eq :
+    mulRec x y 0 =
+      if y.getLsbD 0 then x else 0
+
+mulRec_succ_eq
+    mulRec x y (s + 1) =
+      mulRec x y s +
+      if y.getLsbD (s + 1) then (x <<< (s + 1)) else 0 := rfl
+```
+
+By repeatedly applying the lemmas `mulRec_zero_eq` and `mulRec_succ_eq`,
+one obtains a circuit for multiplication.
+Note that this circuit uses `BitVec.add`, `BitVec.getLsbD`, `BitVec.shiftLeft`.
+Here, `BitVec.add` and `BitVec.shiftLeft` are (recursively) bitblasted by `bv_decide`,
+using the lemmas `add_eq_adc` and `shiftLeft_eq_shiftLeftRec`,
+and `BitVec.getLsbD` is a primitive that `bv_decide` knows how to reduce to SAT.
+
+The two lemmas, `mulRec_zero_eq`, and `mulRec_succ_eq`,
+are used in `Std.Tactic.BVDecide.BVExpr.bitblast.blastMul`
+to prove the correctness of the circuit that is built by `bv_decide`.
+
+```lean
+def blastMul (aig : AIG BVBit) (input : AIG.BinaryRefVec aig w) : AIG.RefVecEntry BVBit w
+theorem denote_blastMul (aig : AIG BVBit) (lhs rhs : BitVec w) (assign : Assignment) :
+   ...
+   ⟦(blastMul aig input).aig, (blastMul aig input).vec.get idx hidx, assign.toAIGAssignment⟧
+     =
+   (lhs * rhs).getLsbD idx
+```
+
+The definition and theorem above are internal to `bv_decide`,
+and use `mulRec_{zero,succ}_eq` to prove that the circuit built by `bv_decide`
+computes the correct value for multiplication.
+
+To zoom out, therefore, we follow two steps:
+First, we prove bitvector lemmas to unfold a high-level operation (such as multiplication)
+into already bitblastable operations (such as addition and left shift).
+We then use these lemmas to prove the correctness of the circuit that `bv_decide` builds.
+
+We use this workflow to implement bitblasting for all SMT-LIB2 operations.
+
 ## Main results
 * `x + y : BitVec w` is `(adc x y false).2`.
 
@@ -193,6 +267,21 @@ theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := b
 
 /-! ### add -/
 
+theorem getMsbD_add {i : Nat} {i_lt : i < w} {x y : BitVec w} :
+    getMsbD (x + y) i =
+      Bool.xor (getMsbD x i) (Bool.xor (getMsbD y i) (carry (w - 1 - i) x y false)) := by
+  simp [getMsbD, getLsbD_add, i_lt, show w - 1 - i < w by omega]
+
+theorem msb_add {w : Nat} {x y: BitVec w} :
+    (x + y).msb =
+      Bool.xor x.msb (Bool.xor y.msb (carry (w - 1) x y false)) := by
+  simp only [BitVec.msb, BitVec.getMsbD]
+  by_cases h : w ≤ 0
+  · simp [h, show w = 0 by omega]
+  · rw [getLsbD_add (x := x)]
+    simp [show w > 0 by omega]
+    omega
+
 /-- Adding a bitvector to its own complement yields the all ones bitpattern -/
 @[simp] theorem add_not_self (x : BitVec w) : x + ~~~x = allOnes w := by
   rw [add_eq_adc, adc, iunfoldr_replace (fun _ => false) (allOnes w)]
@@ -218,6 +307,26 @@ theorem add_eq_or_of_and_eq_zero {w : Nat} (x y : BitVec w)
       simp_all [hx]
     · by_cases hx : x.getLsbD i <;> simp_all [hx]
 
+/-! ### Sub-/
+
+theorem getLsbD_sub {i : Nat} {i_lt : i < w} {x y : BitVec w} :
+    (x - y).getLsbD i
+      = (x.getLsbD i ^^ ((~~~y + 1#w).getLsbD i ^^ carry i x (~~~y + 1#w) false)) := by
+  rw [sub_toAdd, BitVec.neg_eq_not_add, getLsbD_add]
+  omega
+
+theorem getMsbD_sub {i : Nat} {i_lt : i < w} {x y : BitVec w} :
+    (x - y).getMsbD i =
+      (x.getMsbD i ^^ ((~~~y + 1).getMsbD i ^^ carry (w - 1 - i) x (~~~y + 1) false)) := by
+  rw [sub_toAdd, neg_eq_not_add, getMsbD_add]
+  · rfl
+  · omega
+
+theorem msb_sub {x y: BitVec w} :
+    (x - y).msb
+      = (x.msb ^^ ((~~~y + 1#w).msb ^^ carry (w - 1 - 0) x (~~~y + 1#w) false)) := by
+  simp [sub_toAdd, BitVec.neg_eq_not_add, msb_add]
+
 /-! ### Negation -/
 
 theorem bit_not_testBit (x : BitVec w) (i : Fin w) :
@@ -497,7 +606,7 @@ then `n.udiv d = q`. -/
 theorem udiv_eq_of_mul_add_toNat {d n q r : BitVec w} (hd : 0 < d)
     (hrd : r < d)
     (hdqnr : d.toNat * q.toNat + r.toNat = n.toNat) :
-    n.udiv d = q := by
+    n / d = q := by
   apply BitVec.eq_of_toNat_eq
   rw [toNat_udiv]
   replace hdqnr : (d.toNat * q.toNat + r.toNat) / d.toNat = n.toNat / d.toNat := by
@@ -513,7 +622,7 @@ theorem udiv_eq_of_mul_add_toNat {d n q r : BitVec w} (hd : 0 < d)
 then `n.umod d = r`. -/
 theorem umod_eq_of_mul_add_toNat {d n q r : BitVec w} (hrd : r < d)
     (hdqnr : d.toNat * q.toNat + r.toNat = n.toNat) :
-    n.umod d = r := by
+    n % d = r := by
   apply BitVec.eq_of_toNat_eq
   rw [toNat_umod]
   replace hdqnr : (d.toNat * q.toNat + r.toNat) % d.toNat = n.toNat % d.toNat := by
@@ -614,7 +723,7 @@ quotient has been correctly computed.
 theorem DivModState.udiv_eq_of_lawful {n d : BitVec w} {qr : DivModState w}
     (h_lawful : DivModState.Lawful {n, d} qr)
     (h_final  : qr.wn = 0) :
-    n.udiv d = qr.q := by
+    n / d = qr.q := by
   apply udiv_eq_of_mul_add_toNat h_lawful.hdPos h_lawful.hrLtDivisor
   have hdiv := h_lawful.hdiv
   simp only [h_final] at *
@@ -627,7 +736,7 @@ remainder has been correctly computed.
 theorem DivModState.umod_eq_of_lawful {qr : DivModState w}
     (h : DivModState.Lawful {n, d} qr)
     (h_final  : qr.wn = 0) :
-    n.umod d = qr.r := by
+    n % d = qr.r := by
   apply umod_eq_of_mul_add_toNat h.hrLtDivisor
   have hdiv := h.hdiv
   simp only [shiftRight_zero] at hdiv
@@ -693,7 +802,7 @@ theorem DivModState.toNat_shiftRight_sub_one_eq
     omega
 
 /--
-This is used when proving the correctness of the divison algorithm,
+This is used when proving the correctness of the division algorithm,
 where we know that `r < d`.
 We then want to show that `((r.shiftConcat b) - d) < d` as the loop invariant.
 In arithmetic, this is the same as showing that
@@ -801,7 +910,7 @@ theorem wn_divRec (args : DivModArgs w) (qr : DivModState w) :
 /-- The result of `udiv` agrees with the result of the division recurrence. -/
 theorem udiv_eq_divRec (hd : 0#w < d) :
     let out := divRec w {n, d} (DivModState.init w)
-    n.udiv d = out.q := by
+    n / d = out.q := by
   have := DivModState.lawful_init {n, d} hd
   have := lawful_divRec this
   apply DivModState.udiv_eq_of_lawful this (wn_divRec ..)
@@ -809,7 +918,7 @@ theorem udiv_eq_divRec (hd : 0#w < d) :
 /-- The result of `umod` agrees with the result of the division recurrence. -/
 theorem umod_eq_divRec (hd : 0#w < d) :
     let out := divRec w {n, d} (DivModState.init w)
-    n.umod d = out.r := by
+    n % d = out.r := by
   have := DivModState.lawful_init {n, d} hd
   have := lawful_divRec this
   apply DivModState.umod_eq_of_lawful this (wn_divRec ..)

src/Init/Data/BitVec/Lemmas.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed,
+Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth Bhat
 
 -/
 prelude
@@ -219,9 +219,25 @@ theorem getMsbD_of_zero_length (h : w = 0) (x : BitVec w) : x.getMsbD i = false
 theorem msb_of_zero_length (h : w = 0) (x : BitVec w) : x.msb = false := by
   subst h; simp [msb_zero_length]
 
+theorem ofFin_ofNat (n : Nat) :
+    ofFin (no_index (OfNat.ofNat n : Fin (2^w))) = OfNat.ofNat n := by
+  simp only [OfNat.ofNat, Fin.ofNat', BitVec.ofNat, Nat.and_pow_two_sub_one_eq_mod]
+
 theorem eq_of_toFin_eq : ∀ {x y : BitVec w}, x.toFin = y.toFin → x = y
   | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
 
+theorem toFin_inj {x y : BitVec w} : x.toFin = y.toFin ↔ x = y := by
+  apply Iff.intro
+  case mp =>
+    exact @eq_of_toFin_eq w x y
+  case mpr =>
+    intro h
+    simp [toFin, h]
+
+theorem toFin_zero : toFin (0 : BitVec w) = 0 := rfl
+theorem toFin_one  : toFin (1 : BitVec w) = 1 := by
+  rw [toFin_inj]; simp only [ofNat_eq_ofNat, ofFin_ofNat]
+
 @[simp] theorem toNat_ofBool (b : Bool) : (ofBool b).toNat = b.toNat := by
   cases b <;> rfl
 
@@ -270,6 +286,19 @@ theorem getLsbD_ofNat (n : Nat) (x : Nat) (i : Nat) :
 
 @[simp] theorem getMsbD_zero : (0#w).getMsbD i = false := by simp [getMsbD]
 
+@[simp] theorem getLsbD_one : (1#w).getLsbD i = (decide (0 < w) && decide (i = 0)) := by
+  simp only [getLsbD, toNat_ofNat, Nat.testBit_mod_two_pow]
+  by_cases h : i = 0
+    <;> simp [h, Nat.testBit_to_div_mod, Nat.div_eq_of_lt]
+
+@[simp] theorem getElem_one (h : i < w) : (1#w)[i] = decide (i = 0) := by
+  simp [← getLsbD_eq_getElem, getLsbD_one, h, show 0 < w by omega]
+
+/-- The msb at index `w-1` is the least significant bit, and is true when the width is nonzero. -/
+@[simp] theorem getMsbD_one : (1#w).getMsbD i = (decide (i = w - 1) && decide (0 < w)) := by
+  simp only [getMsbD]
+  by_cases h : 0 < w <;> by_cases h' : i = w - 1 <;> simp [h, h'] <;> omega
+
 @[simp] theorem toNat_mod_cancel (x : BitVec n) : x.toNat % (2^n) = x.toNat :=
   Nat.mod_eq_of_lt x.isLt
 
@@ -287,6 +316,12 @@ theorem getLsbD_ofNat (n : Nat) (x : Nat) (i : Nat) :
   simp [Nat.sub_sub_eq_min, Nat.min_eq_right]
   omega
 
+@[simp] theorem sub_add_bmod_cancel {x y : BitVec w} :
+    ((((2 ^ w : Nat) - y.toNat) : Int) + x.toNat).bmod (2 ^ w) =
+      ((x.toNat : Int) - y.toNat).bmod (2 ^ w) := by
+  rw [Int.sub_eq_add_neg, Int.add_assoc, Int.add_comm, Int.bmod_add_cancel, Int.add_comm,
+    Int.sub_eq_add_neg]
+
 private theorem lt_two_pow_of_le {x m n : Nat} (lt : x < 2 ^ m) (le : m ≤ n) : x < 2 ^ n :=
   Nat.lt_of_lt_of_le lt (Nat.pow_le_pow_of_le_right (by trivial : 0 < 2) le)
 
@@ -331,6 +366,10 @@ theorem getElem_ofBool {b : Bool} {i : Nat} : (ofBool b)[0] = b := by
 
 @[simp] theorem msb_zero : (0#w).msb = false := by simp [BitVec.msb, getMsbD]
 
+@[simp] theorem msb_one : (1#w).msb = decide (w = 1) := by
+  simp [BitVec.msb, getMsbD_one, ← Bool.decide_and]
+  omega
+
 theorem msb_eq_getLsbD_last (x : BitVec w) :
     x.msb = x.getLsbD (w - 1) := by
   simp only [BitVec.msb, getMsbD]
@@ -434,7 +473,7 @@ theorem toInt_inj {x y : BitVec n} : x.toInt = y.toInt ↔ x = y :=
 theorem toInt_ne {x y : BitVec n} : x.toInt ≠ y.toInt ↔ x ≠ y  := by
   rw [Ne, toInt_inj]
 
-@[simp] theorem toNat_ofInt {n : Nat} (i : Int) :
+@[simp, bv_toNat] theorem toNat_ofInt {n : Nat} (i : Int) :
   (BitVec.ofInt n i).toNat = (i % (2^n : Nat)).toNat := by
   unfold BitVec.ofInt
   simp
@@ -919,6 +958,21 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
           _ ≤ 2 ^ i := Nat.pow_le_pow_of_le_right Nat.zero_lt_two w
       · simp
 
+@[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
+    BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
+  simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLt, toNat_not,
+    toNat_ofNat]
+  cases h : Int.negSucc n % ((2 ^ w : Nat) : Int)
+  case ofNat =>
+    rw [Int.ofNat_eq_coe, Int.negSucc_emod] at h
+    · dsimp only
+      omega
+    · omega
+  case negSucc a =>
+    have neg := Int.negSucc_lt_zero a
+    have _ : 0 ≤ Int.negSucc n % ((2 ^ w : Nat) : Int) := Int.emod_nonneg _ (by omega)
+    omega
+
 @[simp] theorem toFin_not (x : BitVec w) :
     (~~~x).toFin = x.toFin.rev := by
   apply Fin.val_inj.mp
@@ -961,6 +1015,15 @@ theorem not_not {b : BitVec w} : ~~~(~~~b) = b := by
   ext i
   simp
 
+theorem not_eq_comm {x y : BitVec w} : ~~~ x = y ↔ x = ~~~ y := by
+  constructor
+  · intro h
+    rw [← h]
+    simp
+  · intro h
+    rw [h]
+    simp
+
 @[simp] theorem getMsb_not {x : BitVec w} :
     (~~~x).getMsbD i = (decide (i < w) && !(x.getMsbD i)) := by
   simp only [getMsbD]
@@ -1183,6 +1246,28 @@ theorem toNat_ushiftRight_lt (x : BitVec w) (n : Nat) (hn : n ≤ w) :
     · apply hn
   · apply Nat.pow_pos (by decide)
 
+@[simp]
+theorem getMsbD_ushiftRight {x : BitVec w} {i n : Nat} :
+    (x >>> n).getMsbD i = (decide (i < w) && (!decide (i < n) && x.getMsbD (i - n))) := by
+  simp only [getMsbD, getLsbD_ushiftRight]
+  by_cases h : i < n
+  · simp [getLsbD_ge, show w ≤ (n + (w - 1 - i)) by omega]
+    omega
+  · by_cases h₁ : i < w
+    · simp only [h, ushiftRight_eq, getLsbD_ushiftRight, show i - n < w by omega]
+      congr
+      omega
+    · simp [h, h₁]
+
+@[simp]
+theorem msb_ushiftRight {x : BitVec w} {n : Nat} :
+    (x >>> n).msb = (!decide (0 < n) && x.msb) := by
+  induction n
+  case zero =>
+    simp
+  case succ nn ih =>
+    simp [BitVec.ushiftRight_eq, getMsbD_ushiftRight, BitVec.msb, ih, show nn + 1 > 0 by omega]
+
 /-! ### ushiftRight reductions from BitVec to Nat -/
 
 @[simp]
@@ -1287,7 +1372,8 @@ theorem sshiftRight_or_distrib (x y : BitVec w) (n : Nat) :
     <;> simp [*]
 
 /-- The msb after arithmetic shifting right equals the original msb. -/
-theorem sshiftRight_msb_eq_msb {n : Nat} {x : BitVec w} :
+@[simp]
+theorem msb_sshiftRight {n : Nat} {x : BitVec w} :
     (x.sshiftRight n).msb = x.msb := by
   rw [msb_eq_getLsbD_last, getLsbD_sshiftRight, msb_eq_getLsbD_last]
   by_cases hw₀ : w = 0
@@ -1314,7 +1400,7 @@ theorem sshiftRight_add {x : BitVec w} {m n : Nat} :
       by_cases h₃ : m + (n + ↑i) < w
       · simp [h₃]
         omega
-      · simp [h₃, sshiftRight_msb_eq_msb]
+      · simp [h₃, msb_sshiftRight]
 
 theorem not_sshiftRight {b : BitVec w} :
     ~~~b.sshiftRight n = (~~~b).sshiftRight n := by
@@ -1332,98 +1418,55 @@ theorem not_sshiftRight_not {x : BitVec w} {n : Nat} :
     ~~~((~~~x).sshiftRight n) = x.sshiftRight n := by
   simp [not_sshiftRight]
 
+@[simp]
+theorem getMsbD_sshiftRight {x : BitVec w} {i n : Nat} :
+    getMsbD (x.sshiftRight n) i = (decide (i < w) && if i < n then x.msb else getMsbD x (i - n)) := by
+  simp only [getMsbD, BitVec.getLsbD_sshiftRight]
+  by_cases h : i < w
+  · simp only [h, decide_True, Bool.true_and]
+    by_cases h₁ : w ≤ w - 1 - i
+    · simp [h₁]
+      omega
+    · simp only [h₁, decide_False, Bool.not_false, Bool.true_and]
+      by_cases h₂ : i < n
+      · simp only [h₂, ↓reduceIte, ite_eq_right_iff]
+        omega
+      · simp only [show i - n < w by omega, h₂, ↓reduceIte, decide_True, Bool.true_and]
+        by_cases h₄ : n + (w - 1 - i) < w <;> (simp only [h₄, ↓reduceIte]; congr; omega)
+  · simp [h]
+
 /-! ### sshiftRight reductions from BitVec to Nat -/
 
 @[simp]
 theorem sshiftRight_eq' (x : BitVec w) : x.sshiftRight' y = x.sshiftRight y.toNat := rfl
 
-/-! ### udiv -/
+@[simp]
+theorem getLsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
+    getLsbD (x.sshiftRight' y) i =
+      (!decide (w ≤ i) && if y.toNat + i < w then x.getLsbD (y.toNat + i) else x.msb) := by
+  simp only [BitVec.sshiftRight', BitVec.getLsbD_sshiftRight]
 
-theorem udiv_eq {x y : BitVec n} : x.udiv y = BitVec.ofNat n (x.toNat / y.toNat) := by
-  have h : x.toNat / y.toNat < 2 ^ n := Nat.lt_of_le_of_lt (Nat.div_le_self ..) (by omega)
-  simp [udiv, bv_toNat, h, Nat.mod_eq_of_lt]
-
-@[simp, bv_toNat]
-theorem toNat_udiv {x y : BitVec n} : (x.udiv y).toNat = x.toNat / y.toNat := by
-  simp only [udiv_eq]
-  by_cases h : y = 0
+@[simp]
+theorem getMsbD_sshiftRight' {x y: BitVec w} {i : Nat} :
+    (x.sshiftRight y.toNat).getMsbD i = (decide (i < w) && if i < y.toNat then x.msb else x.getMsbD (i - y.toNat)) := by
+  simp only [BitVec.sshiftRight', getMsbD, BitVec.getLsbD_sshiftRight]
+  by_cases h : i < w
+  · simp only [h, decide_True, Bool.true_and]
+    by_cases h₁ : w ≤ w - 1 - i
+    · simp [h₁]
+      omega
+    · simp only [h₁, decide_False, Bool.not_false, Bool.true_and]
+      by_cases h₂ : i < y.toNat
+      · simp only [h₂, ↓reduceIte, ite_eq_right_iff]
+        omega
+      · simp only [show i - y.toNat < w by omega, h₂, ↓reduceIte, decide_True, Bool.true_and]
+        by_cases h₄ : y.toNat + (w - 1 - i) < w <;> (simp only [h₄, ↓reduceIte]; congr; omega)
   · simp [h]
-  · rw [toNat_ofNat, Nat.mod_eq_of_lt]
-    exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) (by omega)
 
-/-! ### umod -/
-
-theorem umod_eq {x y : BitVec n} :
-    x.umod y = BitVec.ofNat n (x.toNat % y.toNat) := by
-  have h : x.toNat % y.toNat < 2 ^ n := Nat.lt_of_le_of_lt (Nat.mod_le _ _) x.isLt
-  simp [umod, bv_toNat, Nat.mod_eq_of_lt h]
-
-@[simp, bv_toNat]
-theorem toNat_umod {x y : BitVec n} :
-    (x.umod y).toNat = x.toNat % y.toNat := rfl
-
-/-! ### sdiv -/
-
-/-- Equation theorem for `sdiv` in terms of `udiv`. -/
-theorem sdiv_eq (x y : BitVec w) : x.sdiv y =
-  match x.msb, y.msb with
-  | false, false => udiv x y
-  | false, true  =>  - (x.udiv (- y))
-  | true,  false => - ((- x).udiv y)
-  | true,  true  => (- x).udiv (- y) := by
-  rw [BitVec.sdiv]
-  rcases x.msb <;> rcases y.msb <;> simp
-
-@[bv_toNat]
-theorem toNat_sdiv {x y : BitVec w} : (x.sdiv y).toNat =
-    match x.msb, y.msb with
-    | false, false => (udiv x y).toNat
-    | false, true  =>  (- (x.udiv (- y))).toNat
-    | true,  false => (- ((- x).udiv y)).toNat
-    | true,  true  => ((- x).udiv (- y)).toNat := by
-  simp only [sdiv_eq, toNat_udiv]
-  by_cases h : x.msb <;> by_cases h' : y.msb <;> simp [h, h']
-
-theorem sdiv_eq_and (x y : BitVec 1) : x.sdiv y = x &&& y := by
-  have hx : x = 0#1 ∨ x = 1#1 := by bv_omega
-  have hy : y = 0#1 ∨ y = 1#1 := by bv_omega
-  rcases hx with rfl | rfl <;>
-    rcases hy with rfl | rfl <;>
-      rfl
-
-/-! ### smod -/
-
-/-- Equation theorem for `smod` in terms of `umod`. -/
-theorem smod_eq (x y : BitVec w) : x.smod y =
-  match x.msb, y.msb with
-  | false, false => x.umod y
-  | false, true =>
-    let u := x.umod (- y)
-    (if u = 0#w then u else u + y)
-  | true, false =>
-    let u := umod (- x) y
-    (if u = 0#w then u else y - u)
-  | true, true => - ((- x).umod (- y)) := by
-  rw [BitVec.smod]
-  rcases x.msb <;> rcases y.msb <;> simp
-
-@[bv_toNat]
-theorem toNat_smod {x y : BitVec w} : (x.smod y).toNat =
-    match x.msb, y.msb with
-    | false, false => (x.umod y).toNat
-    | false, true =>
-      let u := x.umod (- y)
-      (if u = 0#w then u.toNat else (u + y).toNat)
-    | true, false =>
-      let u := (-x).umod y
-      (if u = 0#w then u.toNat else (y - u).toNat)
-    | true, true => (- ((- x).umod (- y))).toNat := by
-  simp only [smod_eq, toNat_umod]
-  by_cases h : x.msb <;> by_cases h' : y.msb
-  <;> by_cases h'' : (-x).umod y = 0#w <;> by_cases h''' : x.umod (-y) = 0#w
-  <;> simp only [h, h', h'', h''']
-  <;> simp only [umod, toNat_eq, toNat_ofNatLt, toNat_ofNat, Nat.zero_mod] at h'' h'''
-  <;> simp [h'', h''']
+@[simp]
+theorem msb_sshiftRight' {x y: BitVec w} :
+    (x.sshiftRight' y).msb = x.msb := by
+  simp [BitVec.sshiftRight', BitVec.msb_sshiftRight]
 
 /-! ### signExtend -/
 
@@ -1640,6 +1683,11 @@ theorem shiftLeft_ushiftRight {x : BitVec w} {n : Nat}:
       · simp [hi₂]
       · simp [Nat.lt_one_iff, hi₂, show 1 + (i.val - 1) = i by omega]
 
+@[simp]
+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
@@ -1932,6 +1980,10 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n ((2^n - y.toNat) + x.toN
 @[simp] theorem toNat_sub {n} (x y : BitVec n) :
     (x - y).toNat = (((2^n - y.toNat) + x.toNat) % 2^n) := rfl
 
+@[simp, bv_toNat] theorem toInt_sub {x y : BitVec w} :
+    (x - y).toInt = (x.toInt - y.toInt).bmod (2 ^ w) := by
+  simp [toInt_eq_toNat_bmod, @Int.ofNat_sub y.toNat (2 ^ w) (by omega)]
+
 -- We prefer this lemma to `toNat_sub` for the `bv_toNat` simp set.
 -- For reasons we don't yet understand, unfolding via `toNat_sub` sometimes
 -- results in `omega` generating proof terms that are very slow in the kernel.
@@ -1954,6 +2006,8 @@ theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y =
 
 @[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp
 
+@[simp] protected theorem zero_sub (x : BitVec n) : 0#n - x = -x := rfl
+
 @[simp] protected theorem sub_self (x : BitVec n) : x - x = 0#n := by
   apply eq_of_toNat_eq
   simp only [toNat_sub]
@@ -1966,18 +2020,8 @@ theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y =
 
 theorem toInt_neg {x : BitVec w} :
     (-x).toInt = (-x.toInt).bmod (2 ^ w) := by
-  simp only [toInt_eq_toNat_bmod, toNat_neg, Int.ofNat_emod, Int.emod_bmod_congr]
-  rw [← Int.subNatNat_of_le (by omega), Int.subNatNat_eq_coe, Int.sub_eq_add_neg, Int.add_comm,
-    Int.bmod_add_cancel]
-  by_cases h : x.toNat < ((2 ^ w) + 1) / 2
-  · rw [Int.bmod_pos (x := x.toNat)]
-    all_goals simp only [toNat_mod_cancel']
-    norm_cast
-  · rw [Int.bmod_neg (x := x.toNat)]
-    · simp only [toNat_mod_cancel']
-      rw_mod_cast [Int.neg_sub, Int.sub_eq_add_neg, Int.add_comm, Int.bmod_add_cancel]
-    · norm_cast
-      simp_all
+  rw [← BitVec.zero_sub, toInt_sub]
+  simp [BitVec.toInt_ofNat]
 
 @[simp] theorem toFin_neg (x : BitVec n) :
     (-x).toFin = Fin.ofNat' (2^n) (2^n - x.toNat) :=
@@ -2014,7 +2058,7 @@ theorem negOne_eq_allOnes : -1#w = allOnes w := by
     have r : (2^w - 1) < 2^w := by omega
     simp [Nat.mod_eq_of_lt q, Nat.mod_eq_of_lt r]
 
-theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1 := by
+theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1#w := by
   apply eq_of_toNat_eq
   simp only [toNat_neg, ofNat_eq_ofNat, toNat_add, toNat_not, toNat_ofNat, Nat.add_mod_mod]
   congr
@@ -2034,11 +2078,41 @@ theorem neg_ne_iff_ne_neg {x y : BitVec w} : -x ≠ y ↔ x ≠ -y := by
     subst h'
     simp at h
 
+@[simp]
+theorem neg_eq_zero_iff {x : BitVec w} : -x = 0#w ↔ x = 0#w := by
+  constructor
+  · intro h
+    have : - (- x) = - 0 := by simp [h]
+    simpa using this
+  · intro h
+    simp [h]
+
 theorem sub_eq_xor {a b : BitVec 1} : a - b = a ^^^ b := by
   have ha : a = 0 ∨ a = 1 := eq_zero_or_eq_one _
   have hb : b = 0 ∨ b = 1 := eq_zero_or_eq_one _
   rcases ha with h | h <;> (rcases hb with h' | h' <;> (simp [h, h']))
 
+@[simp]
+theorem sub_eq_self {x : BitVec 1} : -x = x := by
+  have ha : x = 0 ∨ x = 1 := eq_zero_or_eq_one _
+  rcases ha with h | h <;> simp [h]
+
+theorem not_neg (x : BitVec w) : ~~~(-x) = x + -1#w := by
+  rcases w with _ | w
+  · apply Subsingleton.elim
+  · rw [BitVec.not_eq_comm]
+    apply BitVec.eq_of_toNat_eq
+    simp only [BitVec.toNat_neg, BitVec.toNat_not, BitVec.toNat_add, BitVec.toNat_ofNat,
+      Nat.add_mod_mod]
+    by_cases hx : x.toNat = 0
+    · simp [hx]
+    · rw [show (_ - 1 % _) = _ by rw [Nat.mod_eq_of_lt (by omega)],
+        show _ + (_ - 1) = (x.toNat - 1) + 2^(w + 1) by omega,
+        Nat.add_mod_right,
+        show (x.toNat - 1) % _ = _ by rw [Nat.mod_eq_of_lt (by omega)],
+        show (_ - x.toNat) % _ = _ by rw [Nat.mod_eq_of_lt (by omega)]]
+      omega
+
 /-! ### abs -/
 
 @[simp, bv_toNat]
@@ -2173,7 +2247,7 @@ protected theorem ne_of_lt {x y : BitVec n} : x < y → x ≠ y := by
   simp only [lt_def, ne_eq, toNat_eq]
   apply Nat.ne_of_lt
 
-protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x.umod y < y := by
+protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x % y < y := by
   simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod, umod, toNat_ofNatLt]
   apply Nat.mod_lt
 
@@ -2181,6 +2255,191 @@ theorem not_lt_iff_le {x y : BitVec w} : (¬ x < y) ↔ y ≤ x := by
   constructor <;>
     (intro h; simp only [lt_def, Nat.not_lt, le_def] at h ⊢; omega)
 
+/-! ### udiv -/
+
+theorem udiv_def {x y : BitVec n} : x / y = BitVec.ofNat n (x.toNat / y.toNat) := by
+  have h : x.toNat / y.toNat < 2 ^ n := Nat.lt_of_le_of_lt (Nat.div_le_self ..) (by omega)
+  rw [← udiv_eq]
+  simp [udiv, bv_toNat, h, Nat.mod_eq_of_lt]
+
+@[simp, bv_toNat]
+theorem toNat_udiv {x y : BitVec n} : (x / y).toNat = x.toNat / y.toNat := by
+  rw [udiv_def]
+  by_cases h : y = 0
+  · simp [h]
+  · rw [toNat_ofNat, Nat.mod_eq_of_lt]
+    exact Nat.lt_of_le_of_lt (Nat.div_le_self ..) (by omega)
+
+@[simp]
+theorem zero_udiv {x : BitVec w} : (0#w) / x = 0#w := by
+  simp [bv_toNat]
+
+@[simp]
+theorem udiv_zero {x : BitVec n} : x / 0#n = 0#n := by
+  simp [udiv_def]
+
+@[simp]
+theorem udiv_one {x : BitVec w} : x / 1#w = x := by
+  simp only [udiv_eq, toNat_eq, toNat_udiv, toNat_ofNat]
+  cases w
+  · simp [eq_nil x]
+  · simp
+
+@[simp]
+theorem udiv_eq_and {x y : BitVec 1} :
+    x / y = (x &&& y) := by
+  have hx : x = 0#1 ∨ x = 1#1 := by bv_omega
+  have hy : y = 0#1 ∨ y = 1#1 := by bv_omega
+  rcases hx with rfl | rfl <;>
+    rcases hy with rfl | rfl <;>
+      rfl
+
+@[simp]
+theorem udiv_self {x : BitVec w} :
+    x / x = if x == 0#w then 0#w else 1#w := by
+  by_cases h : x = 0#w
+  · simp [h]
+  · simp only [toNat_eq, toNat_ofNat, Nat.zero_mod] at h
+    simp only [udiv_eq, beq_iff_eq, toNat_eq, toNat_ofNat, Nat.zero_mod, h,
+      ↓reduceIte, toNat_udiv]
+    rw [Nat.div_self (by omega), Nat.mod_eq_of_lt (by omega)]
+
+/-! ### umod -/
+
+theorem umod_def {x y : BitVec n} :
+    x % y = BitVec.ofNat n (x.toNat % y.toNat) := by
+  rw [← umod_eq]
+  have h : x.toNat % y.toNat < 2 ^ n := Nat.lt_of_le_of_lt (Nat.mod_le _ _) x.isLt
+  simp [umod, bv_toNat, Nat.mod_eq_of_lt h]
+
+@[simp, bv_toNat]
+theorem toNat_umod {x y : BitVec n} :
+    (x % y).toNat = x.toNat % y.toNat := rfl
+
+@[simp]
+theorem umod_zero {x : BitVec n} : x % 0#n = x := by
+  simp [umod_def]
+
+@[simp]
+theorem zero_umod {x : BitVec w} : (0#w) % x = 0#w := by
+  simp [bv_toNat]
+
+@[simp]
+theorem umod_one {x : BitVec w} : x % (1#w) = 0#w := by
+  simp only [toNat_eq, toNat_umod, toNat_ofNat, Nat.zero_mod]
+  cases w
+  · simp [eq_nil x]
+  · simp [Nat.mod_one]
+
+@[simp]
+theorem umod_self {x : BitVec w} : x % x = 0#w := by
+  simp [bv_toNat]
+
+@[simp]
+theorem umod_eq_and {x y : BitVec 1} : x % y = x &&& (~~~y) := by
+  have hx : x = 0#1 ∨ x = 1#1 := by bv_omega
+  have hy : y = 0#1 ∨ y = 1#1 := by bv_omega
+  rcases hx with rfl | rfl <;>
+    rcases hy with rfl | rfl <;>
+      rfl
+
+/-! ### sdiv -/
+
+/-- Equation theorem for `sdiv` in terms of `udiv`. -/
+theorem sdiv_eq (x y : BitVec w) : x.sdiv y =
+  match x.msb, y.msb with
+  | false, false => udiv x y
+  | false, true  =>  - (x.udiv (- y))
+  | true,  false => - ((- x).udiv y)
+  | true,  true  => (- x).udiv (- y) := by
+  rw [BitVec.sdiv]
+  rcases x.msb <;> rcases y.msb <;> simp
+
+@[bv_toNat]
+theorem toNat_sdiv {x y : BitVec w} : (x.sdiv y).toNat =
+    match x.msb, y.msb with
+    | false, false => (udiv x y).toNat
+    | false, true  =>  (- (x.udiv (- y))).toNat
+    | true,  false => (- ((- x).udiv y)).toNat
+    | true,  true  => ((- x).udiv (- y)).toNat := by
+  simp only [sdiv_eq, toNat_udiv]
+  by_cases h : x.msb <;> by_cases h' : y.msb <;> simp [h, h']
+
+@[simp]
+theorem zero_sdiv {x : BitVec w} : (0#w).sdiv x = 0#w := by
+  simp only [sdiv_eq]
+  rcases x.msb with msb | msb <;> simp
+
+@[simp]
+theorem sdiv_zero {x : BitVec n} : x.sdiv 0#n = 0#n := by
+  simp only [sdiv_eq, msb_zero]
+  rcases x.msb with msb | msb <;> apply eq_of_toNat_eq <;> simp
+
+@[simp]
+theorem sdiv_one {x : BitVec w} : x.sdiv 1#w = x := by
+  simp only [sdiv_eq]
+  · by_cases h : w = 1
+    · subst h
+      rcases x.msb with msb | msb <;> simp
+    · rcases x.msb with msb | msb <;> simp [h]
+
+theorem sdiv_eq_and (x y : BitVec 1) : x.sdiv y = x &&& y := by
+  have hx : x = 0#1 ∨ x = 1#1 := by bv_omega
+  have hy : y = 0#1 ∨ y = 1#1 := by bv_omega
+  rcases hx with rfl | rfl <;>
+    rcases hy with rfl | rfl <;>
+      rfl
+
+@[simp]
+theorem sdiv_self {x : BitVec w} :
+    x.sdiv x = if x == 0#w then 0#w else 1#w := by
+  simp [sdiv_eq]
+  · by_cases h : w = 1
+    · subst h
+      rcases x.msb with msb | msb <;> simp
+    · rcases x.msb with msb | msb <;> simp [h]
+
+/-! ### smod -/
+
+/-- Equation theorem for `smod` in terms of `umod`. -/
+theorem smod_eq (x y : BitVec w) : x.smod y =
+  match x.msb, y.msb with
+  | false, false => x.umod y
+  | false, true =>
+    let u := x.umod (- y)
+    (if u = 0#w then u else u + y)
+  | true, false =>
+    let u := umod (- x) y
+    (if u = 0#w then u else y - u)
+  | true, true => - ((- x).umod (- y)) := by
+  rw [BitVec.smod]
+  rcases x.msb <;> rcases y.msb <;> simp
+
+@[bv_toNat]
+theorem toNat_smod {x y : BitVec w} : (x.smod y).toNat =
+    match x.msb, y.msb with
+    | false, false => (x.umod y).toNat
+    | false, true =>
+      let u := x.umod (- y)
+      (if u = 0#w then u.toNat else (u + y).toNat)
+    | true, false =>
+      let u := (-x).umod y
+      (if u = 0#w then u.toNat else (y - u).toNat)
+    | true, true => (- ((- x).umod (- y))).toNat := by
+  simp only [smod_eq, toNat_umod]
+  by_cases h : x.msb <;> by_cases h' : y.msb
+  <;> by_cases h'' : (-x).umod y = 0#w <;> by_cases h''' : x.umod (-y) = 0#w
+  <;> simp only [h, h', h'', h''']
+  <;> simp only [umod, toNat_eq, toNat_ofNatLt, toNat_ofNat, Nat.zero_mod] at h'' h'''
+  <;> simp [h'', h''']
+
+@[simp]
+theorem smod_zero {x : BitVec n} : x.smod 0#n = x := by
+  simp only [smod_eq, msb_zero]
+  rcases x.msb with msb | msb <;> apply eq_of_toNat_eq
+  · simp
+  · by_cases h : x = 0#n <;> simp [h]
+
 /-! ### ofBoolList -/
 
 @[simp] theorem getMsbD_ofBoolListBE : (ofBoolListBE bs).getMsbD i = bs.getD i false := by
@@ -2440,14 +2699,6 @@ theorem twoPow_zero {w : Nat} : twoPow w 0 = 1#w := by
   apply eq_of_toNat_eq
   simp
 
-@[simp]
-theorem getLsbD_one {w i : Nat} : (1#w).getLsbD i = (decide (0 < w) && decide (0 = i)) := by
-  rw [← twoPow_zero, getLsbD_twoPow]
-
-@[simp]
-theorem getElem_one {w i : Nat} (h : i < w) : (1#w)[i] = decide (i = 0) := by
-  rw [← twoPow_zero, getElem_twoPow]
-
 theorem shiftLeft_eq_mul_twoPow (x : BitVec w) (n : Nat) :
     x <<< n = x * (BitVec.twoPow w n) := by
   ext i
@@ -2467,7 +2718,6 @@ theorem shiftLeft_eq_mul_twoPow (x : BitVec w) (n : Nat) :
 @[simp] theorem zero_concat_true : concat 0#w true = 1#(w + 1) := by
   ext
   simp [getLsbD_concat]
-  omega
 
 /- ### setWidth, setWidth, and bitwise operations -/
 
@@ -2508,7 +2758,7 @@ theorem and_one_eq_setWidth_ofBool_getLsbD {x : BitVec w} :
   ext i
   simp only [getLsbD_and, getLsbD_one, getLsbD_setWidth, Fin.is_lt, decide_True, getLsbD_ofBool,
     Bool.true_and]
-  by_cases h : (0 = (i : Nat)) <;> simp [h] <;> omega
+  by_cases h : ((i : Nat) = 0) <;> simp [h] <;> omega
 
 @[simp]
 theorem replicate_zero_eq {x : BitVec w} : x.replicate 0 = 0#0 := by
@@ -2680,6 +2930,31 @@ theorem toNat_mul_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_mul, Nat.mod_eq_of_lt h]
 
+
+/--
+`x ≤ y + z` if and only if `x - z ≤ y`
+when `x - z` and `y + z` do not overflow.
+-/
+theorem le_add_iff_sub_le {x y z : BitVec w}
+    (hxz : z ≤ x) (hbz : y.toNat + z.toNat < 2^w) :
+      x ≤ y + z ↔ x - z ≤ y := by
+  simp_all only [BitVec.le_def]
+  rw [BitVec.toNat_sub_of_le (by rw [BitVec.le_def]; omega),
+    BitVec.toNat_add_of_lt (by omega)]
+  omega
+
+/--
+`x - z ≤ y - z` if and only if `x ≤ y`
+when `x - z` and `y - z` do not overflow.
+-/
+theorem sub_le_sub_iff_le {x y z : BitVec w} (hxz : z ≤ x) (hyz : z ≤ y) :
+    (x - z ≤ y - z) ↔ x ≤ y := by
+  simp_all only [BitVec.le_def]
+  rw [BitVec.toNat_sub_of_le (by rw [BitVec.le_def]; omega),
+    BitVec.toNat_sub_of_le (by rw [BitVec.le_def]; omega)]
+  omega
+
+
 /-! ### Decidable quantifiers -/
 
 theorem forall_zero_iff {P : BitVec 0 → Prop} :
@@ -2884,4 +3159,7 @@ abbrev zeroExtend_truncate_succ_eq_zeroExtend_truncate_or_twoPow_of_getLsbD_true
 @[deprecated and_one_eq_setWidth_ofBool_getLsbD (since := "2024-09-18")]
 abbrev and_one_eq_zeroExtend_ofBool_getLsbD := @and_one_eq_setWidth_ofBool_getLsbD
 
+@[deprecated msb_sshiftRight (since := "2024-10-03")]
+abbrev sshiftRight_msb_eq_msb := @msb_sshiftRight
+
 end BitVec

src/Init/Data/Char/Basic.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 -/
 prelude
-import Init.Data.UInt.Basic
+import Init.Data.UInt.BasicAux
 
 /-- Determines if the given integer is a valid [Unicode scalar value](https://www.unicode.org/glossary/#unicode_scalar_value).
 
@@ -42,8 +42,10 @@ theorem isValidUInt32 (n : Nat) (h : isValidCharNat n) : n < UInt32.size := by
 
 theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
   match h with
-  | Or.inl h        => Or.inl h
-  | Or.inr ⟨h₁, h₂⟩ => Or.inr ⟨h₁, h₂⟩
+  | Or.inl h =>
+    Or.inl (UInt32.ofNat'_lt_of_lt _ (by decide) h)
+  | Or.inr ⟨h₁, h₂⟩ =>
+    Or.inr ⟨UInt32.lt_ofNat'_of_lt _ (by decide) h₁, UInt32.ofNat'_lt_of_lt _ (by decide) h₂⟩
 
 theorem isValidChar_zero : isValidChar 0 :=
   Or.inl (by decide)
@@ -57,7 +59,7 @@ theorem isValidChar_zero : isValidChar 0 :=
   c.val.toUInt8
 
 /-- The numbers from 0 to 256 are all valid UTF-8 characters, so we can embed one in the other. -/
-def ofUInt8 (n : UInt8) : Char := ⟨n.toUInt32, .inl (Nat.lt_trans n.1.2 (by decide))⟩
+def ofUInt8 (n : UInt8) : Char := ⟨n.toUInt32, .inl (Nat.lt_trans n.toBitVec.isLt (by decide))⟩
 
 instance : Inhabited Char where
   default := 'A'

src/Init/Data/Fin/Lemmas.lean

@@ -244,9 +244,13 @@ theorem add_def (a b : Fin n) : a + b = Fin.mk ((a + b) % n) (Nat.mod_lt _ a.siz
 
 theorem val_add (a b : Fin n) : (a + b).val = (a.val + b.val) % n := rfl
 
-@[simp] protected theorem zero_add {n : Nat} [NeZero n] (i : Fin n) : (0 : Fin n) + i = i := by
+@[simp] protected theorem zero_add [NeZero n] (k : Fin n) : (0 : Fin n) + k = k := by
   ext
-  simp [Fin.add_def, Nat.mod_eq_of_lt i.2]
+  simp [Fin.add_def, Nat.mod_eq_of_lt k.2]
+
+@[simp] protected theorem add_zero [NeZero n] (k : Fin n) : k + 0 = k := by
+  ext
+  simp [add_def, Nat.mod_eq_of_lt k.2]
 
 theorem val_add_one_of_lt {n : Nat} {i : Fin n.succ} (h : i < last _) : (i + 1).1 = i + 1 := by
   match n with

src/Init/Data/Function.lean

@@ -0,0 +1,35 @@
+/-
+Copyright (c) 2024 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+
+prelude
+import Init.Core
+
+namespace Function
+
+@[inline]
+def curry : (α × β → φ) → α → β → φ := fun f a b => f (a, b)
+
+/-- Interpret a function with two arguments as a function on `α × β` -/
+@[inline]
+def uncurry : (α → β → φ) → α × β → φ := fun f a => f a.1 a.2
+
+@[simp]
+theorem curry_uncurry (f : α → β → φ) : curry (uncurry f) = f :=
+  rfl
+
+@[simp]
+theorem uncurry_curry (f : α × β → φ) : uncurry (curry f) = f :=
+  funext fun ⟨_a, _b⟩ => rfl
+
+@[simp]
+theorem uncurry_apply_pair {α β γ} (f : α → β → γ) (x : α) (y : β) : uncurry f (x, y) = f x y :=
+  rfl
+
+@[simp]
+theorem curry_apply {α β γ} (f : α × β → γ) (x : α) (y : β) : curry f x y = f (x, y) :=
+  rfl
+
+end Function

src/Init/Data/Hashable.lean

@@ -51,6 +51,9 @@ instance : Hashable USize where
 instance : Hashable (Fin n) where
   hash v := v.val.toUInt64
 
+instance : Hashable Char where
+  hash c := c.val.toUInt64
+
 instance : Hashable Int where
   hash
     | Int.ofNat n => UInt64.ofNat (2 * n)

src/Init/Data/Int/DivModLemmas.lean

@@ -1125,6 +1125,17 @@ theorem emod_add_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n + y) n = Int.bmo
   simp [Int.emod_def, Int.sub_eq_add_neg]
   rw [←Int.mul_neg, Int.add_right_comm,  Int.bmod_add_mul_cancel]
 
+@[simp]
+theorem emod_sub_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n - y) n = Int.bmod (x - y) n := by
+  simp only [emod_def, Int.sub_eq_add_neg]
+  rw [←Int.mul_neg, Int.add_right_comm,  Int.bmod_add_mul_cancel]
+
+@[simp]
+theorem sub_emod_bmod_congr (x : Int) (n : Nat) : Int.bmod (x - y%n) n = Int.bmod (x - y) n := by
+  simp only [emod_def]
+  rw [Int.sub_eq_add_neg, Int.neg_sub, Int.sub_eq_add_neg, ← Int.add_assoc, Int.add_right_comm,
+    Int.bmod_add_mul_cancel, Int.sub_eq_add_neg]
+
 @[simp]
 theorem emod_mul_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n * y) n = Int.bmod (x * y) n := by
   simp [Int.emod_def, Int.sub_eq_add_neg]
@@ -1140,9 +1151,28 @@ theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n
     rw [Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg]
     simp
 
+@[simp]
+theorem bmod_sub_bmod_congr : Int.bmod (Int.bmod x n - y) n = Int.bmod (x - y) n := by
+  rw [Int.bmod_def x n]
+  split
+  next p =>
+    simp only [emod_sub_bmod_congr]
+  next p =>
+    rw [Int.sub_eq_add_neg, Int.sub_eq_add_neg, Int.add_right_comm, ←Int.sub_eq_add_neg, ← Int.sub_eq_add_neg]
+    simp [emod_sub_bmod_congr]
+
 @[simp] theorem add_bmod_bmod : Int.bmod (x + Int.bmod y n) n = Int.bmod (x + y) n := by
   rw [Int.add_comm x, Int.bmod_add_bmod_congr, Int.add_comm y]
 
+@[simp] theorem sub_bmod_bmod : Int.bmod (x - Int.bmod y n) n = Int.bmod (x - y) n := by
+  rw [Int.bmod_def y n]
+  split
+  next p =>
+    simp [sub_emod_bmod_congr]
+  next p =>
+    rw [Int.sub_eq_add_neg, Int.sub_eq_add_neg, Int.neg_add, Int.neg_neg, ← Int.add_assoc, ← Int.sub_eq_add_neg]
+    simp [sub_emod_bmod_congr]
+
 @[simp]
 theorem bmod_mul_bmod : Int.bmod (Int.bmod x n * y) n = Int.bmod (x * y) n := by
   rw [bmod_def x n]

src/Init/Data/List.lean

@@ -23,3 +23,5 @@ import Init.Data.List.TakeDrop
 import Init.Data.List.Zip
 import Init.Data.List.Perm
 import Init.Data.List.Sort
+import Init.Data.List.ToArray
+import Init.Data.List.MapIdx

src/Init/Data/List/Attach.lean

@@ -568,22 +568,22 @@ If not, usually the right approach is `simp [List.unattach, -List.map_subtype]`
 -/
 def unattach {α : Type _} {p : α → Prop} (l : List { x // p x }) := l.map (·.val)
 
-@[simp] theorem unattach_nil {α : Type _} {p : α → Prop} : ([] : List { x // p x }).unattach = [] := rfl
-@[simp] theorem unattach_cons {α : Type _} {p : α → Prop} {a : { x // p x }} {l : List { x // p x }} :
+@[simp] theorem unattach_nil {p : α → Prop} : ([] : List { x // p x }).unattach = [] := rfl
+@[simp] theorem unattach_cons {p : α → Prop} {a : { x // p x }} {l : List { x // p x }} :
   (a :: l).unattach = a.val :: l.unattach := rfl
 
-@[simp] theorem length_unattach {α : Type _} {p : α → Prop} {l : List { x // p x }} :
+@[simp] theorem length_unattach {p : α → Prop} {l : List { x // p x }} :
     l.unattach.length = l.length := by
   unfold unattach
   simp
 
-@[simp] theorem unattach_attach {α : Type _} (l : List α) : l.attach.unattach = l := by
+@[simp] theorem unattach_attach {l : List α} : l.attach.unattach = l := by
   unfold unattach
   induction l with
   | nil => simp
   | cons a l ih => simp [ih, Function.comp_def]
 
-@[simp] theorem unattach_attachWith {α : Type _} {p : α → Prop} {l : List α}
+@[simp] theorem unattach_attachWith {p : α → Prop} {l : List α}
     {H : ∀ a ∈ l, p a} :
     (l.attachWith p H).unattach = l := by
   unfold unattach
@@ -639,15 +639,17 @@ and simplifies these to the function directly taking the value.
   | nil => simp
   | cons a l ih => simp [ih, hf, filterMap_cons]
 
-@[simp] theorem bind_subtype {p : α → Prop} {l : List { x // p x }}
+@[simp] theorem flatMap_subtype {p : α → Prop} {l : List { x // p x }}
     {f : { x // p x } → List β} {g : α → List β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
-    (l.bind f) = l.unattach.bind g := by
+    (l.flatMap f) = l.unattach.flatMap g := by
   unfold unattach
   induction l with
   | nil => simp
   | cons a l ih => simp [ih, hf]
 
-@[simp] theorem filter_unattach {p : α → Prop} {l : List { x // p x }}
+@[deprecated flatMap_subtype (since := "2024-10-16")] abbrev bind_subtype := @flatMap_subtype
+
+@[simp] theorem unattach_filter {p : α → Prop} {l : List { x // p x }}
     {f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
     (l.filter f).unattach = l.unattach.filter g := by
   induction l with
@@ -658,20 +660,22 @@ and simplifies these to the function directly taking the value.
 
 /-! ### Simp lemmas pushing `unattach` inwards. -/
 
-@[simp] theorem reverse_unattach {p : α → Prop} {l : List { x // p x }} :
+@[simp] theorem unattach_reverse {p : α → Prop} {l : List { x // p x }} :
     l.reverse.unattach = l.unattach.reverse := by
   simp [unattach, -map_subtype]
 
-@[simp] theorem append_unattach {p : α → Prop} {l₁ l₂ : List { x // p x }} :
+@[simp] theorem unattach_append {p : α → Prop} {l₁ l₂ : List { x // p x }} :
     (l₁ ++ l₂).unattach = l₁.unattach ++ l₂.unattach := by
   simp [unattach, -map_subtype]
 
-@[simp] theorem join_unattach {p : α → Prop} {l : List (List { x // p x })} :
-    l.join.unattach = (l.map unattach).join := by
+@[simp] theorem unattach_flatten {p : α → Prop} {l : List (List { x // p x })} :
+    l.flatten.unattach = (l.map unattach).flatten := by
   unfold unattach
   induction l <;> simp_all
 
-@[simp] theorem replicate_unattach {p : α → Prop} {n : Nat} {x : { x // p x }} :
+@[deprecated unattach_flatten (since := "2024-10-14")] abbrev unattach_join := @unattach_flatten
+
+@[simp] theorem unattach_replicate {p : α → Prop} {n : Nat} {x : { x // p x }} :
     (List.replicate n x).unattach = List.replicate n x.1 := by
   simp [unattach, -map_subtype]
 

src/Init/Data/List/Basic.lean

@@ -29,15 +29,16 @@ The operations are organized as follow:
 * Lexicographic ordering: `lt`, `le`, and instances.
 * Head and tail operators: `head`, `head?`, `headD?`, `tail`, `tail?`, `tailD`.
 * Basic operations:
-  `map`, `filter`, `filterMap`, `foldr`, `append`, `join`, `pure`, `bind`, `replicate`, and
+  `map`, `filter`, `filterMap`, `foldr`, `append`, `flatten`, `pure`, `bind`, `replicate`, and
   `reverse`.
 * Additional functions defined in terms of these: `leftpad`, `rightPad`, and `reduceOption`.
+* Operations using indexes: `mapIdx`.
 * List membership: `isEmpty`, `elem`, `contains`, `mem` (and the `∈` notation),
   and decidability for predicates quantifying over membership in a `List`.
 * Sublists: `take`, `drop`, `takeWhile`, `dropWhile`, `partition`, `dropLast`,
   `isPrefixOf`, `isPrefixOf?`, `isSuffixOf`, `isSuffixOf?`, `Subset`, `Sublist`,
   `rotateLeft` and `rotateRight`.
-* Manipulating elements: `replace`, `insert`, `erase`, `eraseP`, `eraseIdx`.
+* Manipulating elements: `replace`, `insert`, `modify`, `erase`, `eraseP`, `eraseIdx`.
 * Finding elements: `find?`, `findSome?`, `findIdx`, `indexOf`, `findIdx?`, `indexOf?`,
  `countP`, `count`, and `lookup`.
 * Logic: `any`, `all`, `or`, and `and`.
@@ -121,6 +122,11 @@ protected def beq [BEq α] : List α → List α → Bool
   | a::as, b::bs => a == b && List.beq as bs
   | _,     _     => false
 
+@[simp] theorem beq_nil_nil [BEq α] : List.beq ([] : List α) ([] : List α) = true := rfl
+@[simp] theorem beq_cons_nil [BEq α] (a : α) (as : List α) : List.beq (a::as) [] = false := rfl
+@[simp] theorem beq_nil_cons [BEq α] (a : α) (as : List α) : List.beq [] (a::as) = false := rfl
+theorem beq_cons₂ [BEq α] (a b : α) (as bs : List α) : List.beq (a::as) (b::bs) = (a == b && List.beq as bs) := rfl
+
 instance [BEq α] : BEq (List α) := ⟨List.beq⟩
 
 instance [BEq α] [LawfulBEq α] : LawfulBEq (List α) where
@@ -368,7 +374,7 @@ def tailD (list fallback : List α) : List α :=
 /-! ## Basic `List` operations.
 
 We define the basic functional programming operations on `List`:
-`map`, `filter`, `filterMap`, `foldr`, `append`, `join`, `pure`, `bind`, `replicate`, and `reverse`.
+`map`, `filter`, `filterMap`, `foldr`, `append`, `flatten`, `pure`, `bind`, `replicate`, and `reverse`.
 -/
 
 /-! ### map -/
@@ -542,41 +548,53 @@ theorem reverseAux_eq_append (as bs : List α) : reverseAux as bs = reverseAux a
   simp [reverse, reverseAux]
   rw [← reverseAux_eq_append]
 
-/-! ### join -/
+/-! ### flatten -/
 
 /--
-`O(|join L|)`. `join L` concatenates all the lists in `L` into one list.
-* `join [[a], [], [b, c], [d, e, f]] = [a, b, c, d, e, f]`
+`O(|flatten L|)`. `join L` concatenates all the lists in `L` into one list.
+* `flatten [[a], [], [b, c], [d, e, f]] = [a, b, c, d, e, f]`
 -/
-def join : List (List α) → List α
+def flatten : List (List α) → List α
   | []      => []
-  | a :: as => a ++ join as
+  | a :: as => a ++ flatten as
 
-@[simp] theorem join_nil : List.join ([] : List (List α)) = [] := rfl
-@[simp] theorem join_cons : (l :: ls).join = l ++ ls.join := rfl
+@[simp] theorem flatten_nil : List.flatten ([] : List (List α)) = [] := rfl
+@[simp] theorem flatten_cons : (l :: ls).flatten = l ++ ls.flatten := rfl
 
-/-! ### pure -/
+@[deprecated flatten (since := "2024-10-14"), inherit_doc flatten] abbrev join := @flatten
 
-/-- `pure x = [x]` is the `pure` operation of the list monad. -/
-@[inline] protected def pure {α : Type u} (a : α) : List α := [a]
+/-! ### singleton -/
 
-/-! ### bind -/
+/-- `singleton x = [x]`. -/
+@[inline] protected def singleton {α : Type u} (a : α) : List α := [a]
+
+set_option linter.missingDocs false in
+@[deprecated singleton (since := "2024-10-16")] protected abbrev pure := @singleton
+
+/-! ### flatMap -/
 
 /--
-`bind xs f` is the bind operation of the list monad. It applies `f` to each element of `xs`
+`flatMap xs f` applies `f` to each element of `xs`
 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] protected def bind {α : Type u} {β : Type v} (a : List α) (b : α → List β) : List β := join (map b a)
+@[inline] def flatMap {α : Type u} {β : Type v} (a : List α) (b : α → List β) : List β := flatten (map b a)
 
-@[simp] theorem bind_nil (f : α → List β) : List.bind [] f = [] := by simp [join, List.bind]
-@[simp] theorem bind_cons x xs (f : α → List β) :
-  List.bind (x :: xs) f = f x ++ List.bind xs f := by simp [join, List.bind]
+@[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]
 
 set_option linter.missingDocs false in
-@[deprecated bind_nil (since := "2024-06-15")] abbrev nil_bind := @bind_nil
+@[deprecated flatMap (since := "2024-10-16")] abbrev bind := @flatMap
 set_option linter.missingDocs false in
-@[deprecated bind_cons (since := "2024-06-15")] abbrev cons_bind := @bind_cons
+@[deprecated flatMap_nil (since := "2024-10-16")] abbrev nil_flatMap := @flatMap_nil
+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 -/
 
@@ -1101,6 +1119,35 @@ theorem replace_cons [BEq α] {a : α} :
 @[inline] protected def insert [BEq α] (a : α) (l : List α) : List α :=
   if l.elem a then l else a :: l
 
+/-! ### modify -/
+
+/--
+Apply a function to the nth tail of `l`. Returns the input without
+using `f` if the index is larger than the length of the List.
+```
+modifyTailIdx f 2 [a, b, c] = [a, b] ++ f [c]
+```
+-/
+@[simp] def modifyTailIdx (f : List α → List α) : Nat → List α → List α
+  | 0, l => f l
+  | _+1, [] => []
+  | n+1, a :: l => a :: modifyTailIdx f n l
+
+/-- Apply `f` to the head of the list, if it exists. -/
+@[inline] def modifyHead (f : α → α) : List α → List α
+  | [] => []
+  | a :: l => f a :: l
+
+@[simp] theorem modifyHead_nil (f : α → α) : [].modifyHead f = [] := by rw [modifyHead]
+@[simp] theorem modifyHead_cons (a : α) (l : List α) (f : α → α) :
+    (a :: l).modifyHead f = f a :: l := by rw [modifyHead]
+
+/--
+Apply `f` to the nth element of the list, if it exists, replacing that element with the result.
+-/
+def modify (f : α → α) : Nat → List α → List α :=
+  modifyTailIdx (modifyHead f)
+
 /-! ### erase -/
 
 /--
@@ -1395,12 +1442,25 @@ def unzip : List (α × β) → List α × List β
 
 /-! ## Ranges and enumeration -/
 
+/-- Sum of a list.
+
+`List.sum [a, b, c] = a + (b + (c + 0))` -/
+def sum {α} [Add α] [Zero α] : List α → α :=
+  foldr (· + ·) 0
+
+@[simp] theorem sum_nil [Add α] [Zero α] : ([] : List α).sum = 0 := rfl
+@[simp] theorem sum_cons [Add α] [Zero α] {a : α} {l : List α} : (a::l).sum = a + l.sum := rfl
+
 /-- Sum of a list of natural numbers. -/
--- This is not in the `List` namespace as later `List.sum` will be defined polymorphically.
+@[deprecated List.sum (since := "2024-10-17")]
 protected def _root_.Nat.sum (l : List Nat) : Nat := l.foldr (·+·) 0
 
-@[simp] theorem _root_.Nat.sum_nil : Nat.sum ([] : List Nat) = 0 := rfl
-@[simp] theorem _root_.Nat.sum_cons (a : Nat) (l : List Nat) :
+set_option linter.deprecated false in
+@[simp, deprecated sum_nil (since := "2024-10-17")]
+theorem _root_.Nat.sum_nil : Nat.sum ([] : List Nat) = 0 := rfl
+set_option linter.deprecated false in
+@[simp, deprecated sum_cons (since := "2024-10-17")]
+theorem _root_.Nat.sum_cons (a : Nat) (l : List Nat) :
     Nat.sum (a::l) = a + Nat.sum l := rfl
 
 /-! ### range -/
@@ -1527,7 +1587,7 @@ def intersperse (sep : α) : List α → List α
 * `intercalate sep [a, b, c] = a ++ sep ++ b ++ sep ++ c`
 -/
 def intercalate (sep : List α) (xs : List (List α)) : List α :=
-  join (intersperse sep xs)
+  (intersperse sep xs).flatten
 
 /-! ### eraseDups -/
 

src/Init/Data/List/BasicAux.lean

@@ -232,7 +232,8 @@ theorem sizeOf_get [SizeOf α] (as : List α) (i : Fin as.length) : sizeOf (as.g
     apply Nat.lt_trans ih
     simp_arith
 
-theorem le_antisymm [LT α] [s : Antisymm (¬ · < · : α → α → Prop)] {as bs : List α} (h₁ : as ≤ bs) (h₂ : bs ≤ as) : as = bs :=
+theorem le_antisymm [LT α] [s : Std.Antisymm (¬ · < · : α → α → Prop)]
+    {as bs : List α} (h₁ : as ≤ bs) (h₂ : bs ≤ as) : as = bs :=
   match as, bs with
   | [],    []    => rfl
   | [],    _::_ => False.elim <| h₂ (List.lt.nil ..)
@@ -248,7 +249,8 @@ theorem le_antisymm [LT α] [s : Antisymm (¬ · < · : α → α → Prop)] {as
         have : a = b := s.antisymm hab hba
         simp [this, ih]
 
-instance [LT α] [Antisymm (¬ · < · : α → α → Prop)] : Antisymm (· ≤ · : List α → List α → Prop) where
+instance [LT α] [Std.Antisymm (¬ · < · : α → α → Prop)] :
+    Std.Antisymm (· ≤ · : List α → List α → Prop) where
   antisymm h₁ h₂ := le_antisymm h₁ h₂
 
 end List

src/Init/Data/List/Count.lean

@@ -153,13 +153,15 @@ theorem countP_filterMap (p : β → Bool) (f : α → Option β) (l : List α)
   simp only [length_filterMap_eq_countP]
   congr
   ext a
-  simp (config := { contextual := true }) [Option.getD_eq_iff]
+  simp (config := { contextual := true }) [Option.getD_eq_iff, Option.isSome_eq_isSome]
 
-@[simp] theorem countP_join (l : List (List α)) :
-    countP p l.join = Nat.sum (l.map (countP p)) := by
-  simp only [countP_eq_length_filter, filter_join]
+@[simp] theorem countP_flatten (l : List (List α)) :
+    countP p l.flatten = (l.map (countP p)).sum := by
+  simp only [countP_eq_length_filter, filter_flatten]
   simp [countP_eq_length_filter']
 
+@[deprecated countP_flatten (since := "2024-10-14")] abbrev countP_join := @countP_flatten
+
 @[simp] theorem countP_reverse (l : List α) : countP p l.reverse = countP p l := by
   simp [countP_eq_length_filter, filter_reverse]
 
@@ -230,8 +232,10 @@ theorem count_singleton (a b : α) : count a [b] = if b == a then 1 else 0 := by
 @[simp] theorem count_append (a : α) : ∀ l₁ l₂, count a (l₁ ++ l₂) = count a l₁ + count a l₂ :=
   countP_append _
 
-theorem count_join (a : α) (l : List (List α)) : count a l.join = Nat.sum (l.map (count a)) := by
-  simp only [count_eq_countP, countP_join, count_eq_countP']
+theorem count_flatten (a : α) (l : List (List α)) : count a l.flatten = (l.map (count a)).sum := by
+  simp only [count_eq_countP, countP_flatten, count_eq_countP']
+
+@[deprecated count_flatten (since := "2024-10-14")] abbrev count_join := @count_flatten
 
 @[simp] theorem count_reverse (a : α) (l : List α) : count a l.reverse = count a l := by
   simp only [count_eq_countP, countP_eq_length_filter, filter_reverse, length_reverse]

src/Init/Data/List/Find.lean

@@ -132,14 +132,14 @@ theorem findSome?_append {l₁ l₂ : List α} : (l₁ ++ l₂).findSome? f = (l
     simp only [cons_append, findSome?]
     split <;> simp_all
 
-theorem head_join {L : List (List α)} (h : ∃ l, l ∈ L ∧ l ≠ []) :
-    (join L).head (by simpa using h) = (L.findSome? fun l => l.head?).get (by simpa using h) := by
-  simp [head_eq_iff_head?_eq_some, head?_join]
+theorem head_flatten {L : List (List α)} (h : ∃ l, l ∈ L ∧ l ≠ []) :
+    (flatten L).head (by simpa using h) = (L.findSome? fun l => l.head?).get (by simpa using h) := by
+  simp [head_eq_iff_head?_eq_some, head?_flatten]
 
-theorem getLast_join {L : List (List α)} (h : ∃ l, l ∈ L ∧ l ≠ []) :
-    (join L).getLast (by simpa using h) =
+theorem getLast_flatten {L : List (List α)} (h : ∃ l, l ∈ L ∧ l ≠ []) :
+    (flatten L).getLast (by simpa using h) =
       (L.reverse.findSome? fun l => l.getLast?).get (by simpa using h) := by
-  simp [getLast_eq_iff_getLast_eq_some, getLast?_join]
+  simp [getLast_eq_iff_getLast_eq_some, getLast?_flatten]
 
 theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
   cases n with
@@ -326,35 +326,35 @@ theorem get_find?_mem (xs : List α) (p : α → Bool) (h) : (xs.find? p).get h
     simp only [cons_append, find?]
     by_cases h : p x <;> simp [h, ih]
 
-@[simp] theorem find?_join (xs : List (List α)) (p : α → Bool) :
-    xs.join.find? p = xs.findSome? (·.find? p) := by
+@[simp] theorem find?_flatten (xs : List (List α)) (p : α → Bool) :
+    xs.flatten.find? p = xs.findSome? (·.find? p) := by
   induction xs with
   | nil => simp
   | cons x xs ih =>
-    simp only [join_cons, find?_append, findSome?_cons, ih]
+    simp only [flatten_cons, find?_append, findSome?_cons, ih]
     split <;> simp [*]
 
-theorem find?_join_eq_none {xs : List (List α)} {p : α → Bool} :
-    xs.join.find? p = none ↔ ∀ ys ∈ xs, ∀ x ∈ ys, !p x := by
+theorem find?_flatten_eq_none {xs : List (List α)} {p : α → Bool} :
+    xs.flatten.find? p = none ↔ ∀ ys ∈ xs, ∀ x ∈ ys, !p x := by
   simp
 
 /--
-If `find? p` returns `some a` from `xs.join`, then `p a` holds, and
+If `find? p` returns `some a` from `xs.flatten`, then `p a` holds, and
 some list in `xs` contains `a`, and no earlier element of that list satisfies `p`.
 Moreover, no earlier list in `xs` has an element satisfying `p`.
 -/
-theorem find?_join_eq_some {xs : List (List α)} {p : α → Bool} {a : α} :
-    xs.join.find? p = some a ↔
+theorem find?_flatten_eq_some {xs : List (List α)} {p : α → Bool} {a : α} :
+    xs.flatten.find? p = some a ↔
       p a ∧ ∃ as ys zs bs, xs = as ++ (ys ++ a :: zs) :: bs ∧
         (∀ a ∈ as, ∀ x ∈ a, !p x) ∧ (∀ x ∈ ys, !p x) := by
   rw [find?_eq_some]
   constructor
   · rintro ⟨h, ⟨ys, zs, h₁, h₂⟩⟩
     refine ⟨h, ?_⟩
-    rw [join_eq_append_iff] at h₁
+    rw [flatten_eq_append_iff] at h₁
     obtain (⟨as, bs, rfl, rfl, h₁⟩ | ⟨as, bs, c, cs, ds, rfl, rfl, h₁⟩) := h₁
     · replace h₁ := h₁.symm
-      rw [join_eq_cons_iff] at h₁
+      rw [flatten_eq_cons_iff] at h₁
       obtain ⟨bs, cs, ds, rfl, h₁, rfl⟩ := h₁
       refine ⟨as ++ bs, [], cs, ds, by simp, ?_⟩
       simp
@@ -371,21 +371,25 @@ theorem find?_join_eq_some {xs : List (List α)} {p : α → Bool} {a : α} :
       · intro x m
         simpa using h₂ x (by simpa using .inr m)
   · rintro ⟨h, ⟨as, ys, zs, bs, rfl, h₁, h₂⟩⟩
-    refine ⟨h, as.join ++ ys, zs ++ bs.join, by simp, ?_⟩
+    refine ⟨h, as.flatten ++ ys, zs ++ bs.flatten, by simp, ?_⟩
     intro a m
     simp at m
     obtain ⟨l, ml, m⟩ | m := m
     · exact h₁ l ml a m
     · exact h₂ a m
 
-@[simp] theorem find?_bind (xs : List α) (f : α → List β) (p : β → Bool) :
-    (xs.bind f).find? p = xs.findSome? (fun x => (f x).find? p) := by
-  simp [bind_def, findSome?_map]; rfl
+@[simp] theorem find?_flatMap (xs : List α) (f : α → List β) (p : β → Bool) :
+    (xs.flatMap f).find? p = xs.findSome? (fun x => (f x).find? p) := by
+  simp [flatMap_def, findSome?_map]; rfl
 
-theorem find?_bind_eq_none {xs : List α} {f : α → List β} {p : β → Bool} :
-    (xs.bind f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
+@[deprecated find?_flatMap (since := "2024-10-16")] abbrev find?_bind := @find?_flatMap
+
+theorem find?_flatMap_eq_none {xs : List α} {f : α → List β} {p : β → Bool} :
+    (xs.flatMap f).find? p = none ↔ ∀ x ∈ xs, ∀ y ∈ f x, !p y := by
   simp
 
+@[deprecated find?_flatMap_eq_none (since := "2024-10-16")] abbrev find?_bind_eq_none := @find?_flatMap_eq_none
+
 theorem find?_replicate : find? p (replicate n a) = if n = 0 then none else if p a then some a else none := by
   cases n
   · simp
@@ -786,15 +790,15 @@ theorem findIdx?_of_eq_none {xs : List α} {p : α → Bool} (w : xs.findIdx? p
   induction xs with simp
   | cons _ _ _ => split <;> simp_all [Option.map_or', Option.map_map]; rfl
 
-theorem findIdx?_join {l : List (List α)} {p : α → Bool} :
-    l.join.findIdx? p =
+theorem findIdx?_flatten {l : List (List α)} {p : α → Bool} :
+    l.flatten.findIdx? p =
       (l.findIdx? (·.any p)).map
-        fun i => Nat.sum ((l.take i).map List.length) +
+        fun i => ((l.take i).map List.length).sum +
           (l[i]?.map fun xs => xs.findIdx p).getD 0 := by
   induction l with
   | nil => simp
   | cons xs l ih =>
-    simp only [join, findIdx?_append, map_take, map_cons, findIdx?, any_eq_true, Nat.zero_add,
+    simp only [flatten, findIdx?_append, map_take, map_cons, findIdx?, any_eq_true, Nat.zero_add,
       findIdx?_succ]
     split
     · simp only [Option.map_some', take_zero, sum_nil, length_cons, zero_lt_succ,
@@ -976,4 +980,13 @@ theorem IsInfix.lookup_eq_none {l₁ l₂ : List (α × β)} (h : l₁ <:+: l₂
 
 end lookup
 
+/-! ### Deprecations -/
+
+@[deprecated head_flatten (since := "2024-10-14")] abbrev head_join := @head_flatten
+@[deprecated getLast_flatten (since := "2024-10-14")] abbrev getLast_join := @getLast_flatten
+@[deprecated find?_flatten (since := "2024-10-14")] abbrev find?_join := @find?_flatten
+@[deprecated find?_flatten_eq_none (since := "2024-10-14")] abbrev find?_join_eq_none := @find?_flatten_eq_none
+@[deprecated find?_flatten_eq_some (since := "2024-10-14")] abbrev find?_join_eq_some := @find?_flatten_eq_some
+@[deprecated findIdx?_flatten (since := "2024-10-14")] abbrev findIdx?_join := @findIdx?_flatten
+
 end List

src/Init/Data/List/Impl.lean

@@ -38,7 +38,7 @@ The following operations were already given `@[csimp]` replacements in `Init/Dat
 
 The following operations are given `@[csimp]` replacements below:
 `set`, `filterMap`, `foldr`, `append`, `bind`, `join`,
-`take`, `takeWhile`, `dropLast`, `replace`, `erase`, `eraseIdx`, `zipWith`,
+`take`, `takeWhile`, `dropLast`, `replace`, `modify`, `erase`, `eraseIdx`, `zipWith`,
 `enumFrom`, and `intercalate`.
 
 -/
@@ -93,29 +93,29 @@ The following operations are given `@[csimp]` replacements below:
 @[csimp] theorem foldr_eq_foldrTR : @foldr = @foldrTR := by
   funext α β f init l; simp [foldrTR, Array.foldr_eq_foldr_toList, -Array.size_toArray]
 
-/-! ### bind  -/
+/-! ### flatMap  -/
 
-/-- Tail recursive version of `List.bind`. -/
-@[inline] def bindTR (as : List α) (f : α → List β) : List β := go as #[] where
-  /-- Auxiliary for `bind`: `bind.go f as = acc.toList ++ bind f as` -/
+/-- Tail recursive version of `List.flatMap`. -/
+@[inline] def flatMapTR (as : List α) (f : α → List β) : 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 bind_eq_bindTR : @List.bind = @bindTR := by
+@[csimp] theorem flatMap_eq_flatMapTR : @List.flatMap = @flatMapTR := by
   funext α β as f
-  let rec go : ∀ as acc, bindTR.go f as acc = acc.toList ++ as.bind f
-    | [], acc => by simp [bindTR.go, bind]
-    | x::xs, acc => by simp [bindTR.go, bind, go xs]
+  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]
   exact (go as #[]).symm
 
-/-! ### join -/
+/-! ### flatten -/
 
-/-- Tail recursive version of `List.join`. -/
-@[inline] def joinTR (l : List (List α)) : List α := bindTR l id
+/-- Tail recursive version of `List.flatten`. -/
+@[inline] def flattenTR (l : List (List α)) : List α := flatMapTR l id
 
-@[csimp] theorem join_eq_joinTR : @join = @joinTR := by
-  funext α l; rw [← List.bind_id, List.bind_eq_bindTR]; rfl
+@[csimp] theorem flatten_eq_flattenTR : @flatten = @flattenTR := by
+  funext α l; rw [← List.flatMap_id, List.flatMap_eq_flatMapTR]; rfl
 
 /-! ## Sublists -/
 
@@ -197,6 +197,24 @@ The following operations are given `@[csimp]` replacements below:
     · simp [*]
     · intro h; rw [IH] <;> simp_all
 
+/-! ### modify -/
+
+/-- Tail-recursive version of `modify`. -/
+def modifyTR (f : α → α) (n : Nat) (l : List α) : List α := go l n #[] where
+  /-- Auxiliary for `modifyTR`: `modifyTR.go f l n acc = acc.toList ++ modify f n l`. -/
+  go : List α → Nat → Array α → List α
+  | [], _, acc => acc.toList
+  | a :: l, 0, acc => acc.toListAppend (f a :: l)
+  | a :: l, n+1, acc => go l n (acc.push a)
+
+theorem modifyTR_go_eq : ∀ l n, modifyTR.go f l n acc = acc.toList ++ modify f n l
+  | [], n => by cases n <;> simp [modifyTR.go, modify]
+  | a :: l, 0 => by simp [modifyTR.go, modify]
+  | a :: l, n+1 => by simp [modifyTR.go, modify, modifyTR_go_eq l]
+
+@[csimp] theorem modify_eq_modifyTR : @modify = @modifyTR := by
+  funext α f n l; simp [modifyTR, modifyTR_go_eq]
+
 /-! ### erase -/
 
 /-- Tail recursive version of `List.erase`. -/
@@ -322,7 +340,7 @@ where
   | [_] => simp
   | x::y::xs =>
     let rec go {acc x} : ∀ xs,
-      intercalateTR.go sep.toArray x xs acc = acc.toList ++ join (intersperse sep (x::xs))
+      intercalateTR.go sep.toArray x xs acc = acc.toList ++ flatten (intersperse sep (x::xs))
     | [] => by simp [intercalateTR.go]
     | _::_ => by simp [intercalateTR.go, go]
     simp [intersperse, go]

src/Init/Data/List/Lemmas.lean

@@ -1047,9 +1047,6 @@ theorem get_cons_length (x : α) (xs : List α) (n : Nat) (h : n = xs.length) :
 
 @[simp] theorem getLast?_singleton (a : α) : getLast? [a] = a := rfl
 
-theorem getLast!_of_getLast? [Inhabited α] : ∀ {l : List α}, getLast? l = some a → getLast! l = a
-  | _ :: _, rfl => rfl
-
 theorem getLast?_eq_getLast : ∀ l h, @getLast? α l = some (getLast l h)
   | [], h => nomatch h rfl
   | _ :: _, _ => rfl
@@ -1083,6 +1080,21 @@ theorem getLast?_concat (l : List α) : getLast? (l ++ [a]) = some a := by
 theorem getLastD_concat (a b l) : @getLastD α (l ++ [b]) a = b := by
   rw [getLastD_eq_getLast?, getLast?_concat]; rfl
 
+/-! ### getLast! -/
+
+@[simp] theorem getLast!_nil [Inhabited α] : ([] : List α).getLast! = default := rfl
+
+theorem getLast!_of_getLast? [Inhabited α] : ∀ {l : List α}, getLast? l = some a → getLast! l = a
+  | _ :: _, rfl => rfl
+
+theorem getLast!_eq_getElem! [Inhabited α] {l : List α} : l.getLast! = l[l.length - 1]! := by
+  cases l with
+  | nil => simp
+  | cons _ _ =>
+    apply getLast!_of_getLast?
+    rw [getElem!_pos, getElem_cons_length (h := by simp)]
+    rfl
+
 /-! ## Head and tail -/
 
 /-! ### head -/
@@ -1343,12 +1355,12 @@ theorem set_map {f : α → β} {l : List α} {n : Nat} {a : α} :
   simp
 
 @[simp] theorem head_map (f : α → β) (l : List α) (w) :
-    head (map f l) w = f (head l (by simpa using w)) := by
+    (map f l).head w = f (l.head (by simpa using w)) := by
   cases l
   · simp at w
   · simp_all
 
-@[simp] theorem head?_map (f : α → β) (l : List α) : head? (map f l) = (head? l).map f := by
+@[simp] theorem head?_map (f : α → β) (l : List α) : (map f l).head? = l.head?.map f := by
   cases l <;> rfl
 
 @[simp] theorem map_tail? (f : α → β) (l : List α) : (tail? l).map (map f) = tail? (map f l) := by
@@ -2068,106 +2080,97 @@ theorem eq_nil_or_concat : ∀ l : List α, l = [] ∨ ∃ L b, l = concat L b
     | _, .inl rfl => .inr ⟨[], a, rfl⟩
     | _, .inr ⟨L, b, rfl⟩ => .inr ⟨a::L, b, rfl⟩
 
-/-! ### join -/
+/-! ### flatten -/
 
-@[simp] theorem length_join (L : List (List α)) : (join L).length = Nat.sum (L.map length) := by
+@[simp] theorem length_flatten (L : List (List α)) : (flatten L).length = (L.map length).sum := by
   induction L with
   | nil => rfl
   | cons =>
-    simp [join, length_append, *]
+    simp [flatten, length_append, *]
 
-theorem join_singleton (l : List α) : [l].join = l := by simp
+theorem flatten_singleton (l : List α) : [l].flatten = l := by simp
 
-@[simp] theorem mem_join : ∀ {L : List (List α)}, a ∈ L.join ↔ ∃ l, l ∈ L ∧ a ∈ l
+@[simp] theorem mem_flatten : ∀ {L : List (List α)}, a ∈ L.flatten ↔ ∃ l, l ∈ L ∧ a ∈ l
   | [] => by simp
-  | b :: l => by simp [mem_join, or_and_right, exists_or]
+  | b :: l => by simp [mem_flatten, or_and_right, exists_or]
 
-@[simp] theorem join_eq_nil_iff {L : List (List α)} : L.join = [] ↔ ∀ l ∈ L, l = [] := by
+@[simp] theorem flatten_eq_nil_iff {L : List (List α)} : L.flatten = [] ↔ ∀ l ∈ L, l = [] := by
   induction L <;> simp_all
 
-@[deprecated join_eq_nil_iff (since := "2024-09-05")] abbrev join_eq_nil := @join_eq_nil_iff
-
-theorem join_ne_nil_iff {xs : List (List α)} : xs.join ≠ [] ↔ ∃ x, x ∈ xs ∧ x ≠ [] := by
+theorem flatten_ne_nil_iff {xs : List (List α)} : xs.flatten ≠ [] ↔ ∃ x, x ∈ xs ∧ x ≠ [] := by
   simp
 
-@[deprecated join_ne_nil_iff (since := "2024-09-05")] abbrev join_ne_nil := @join_ne_nil_iff
+theorem exists_of_mem_flatten : a ∈ flatten L → ∃ l, l ∈ L ∧ a ∈ l := mem_flatten.1
 
-theorem exists_of_mem_join : a ∈ join L → ∃ l, l ∈ L ∧ a ∈ l := mem_join.1
+theorem mem_flatten_of_mem (lL : l ∈ L) (al : a ∈ l) : a ∈ flatten L := mem_flatten.2 ⟨l, lL, al⟩
 
-theorem mem_join_of_mem (lL : l ∈ L) (al : a ∈ l) : a ∈ join L := mem_join.2 ⟨l, lL, al⟩
-
-theorem forall_mem_join {p : α → Prop} {L : List (List α)} :
-    (∀ (x) (_ : x ∈ join L), p x) ↔ ∀ (l) (_ : l ∈ L) (x) (_ : x ∈ l), p x := by
-  simp only [mem_join, forall_exists_index, and_imp]
+theorem forall_mem_flatten {p : α → Prop} {L : List (List α)} :
+    (∀ (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)
 
-theorem join_eq_bind {L : List (List α)} : join L = L.bind id := by
-  induction L <;> simp [List.bind]
+theorem flatten_eq_flatMap {L : List (List α)} : flatten L = L.flatMap id := by
+  induction L <;> simp [List.flatMap]
 
-theorem head?_join {L : List (List α)} : (join L).head? = L.findSome? fun l => l.head? := by
+theorem head?_flatten {L : List (List α)} : (flatten L).head? = L.findSome? fun l => l.head? := by
   induction L with
   | nil => rfl
   | cons =>
     simp only [findSome?_cons]
     split <;> simp_all
 
--- `getLast?_join` is proved later, after the `reverse` section.
--- `head_join` and `getLast_join` are proved in `Init.Data.List.Find`.
+-- `getLast?_flatten` is proved later, after the `reverse` section.
+-- `head_flatten` and `getLast_flatten` are proved in `Init.Data.List.Find`.
 
-theorem foldl_join (f : β → α → β) (b : β) (L : List (List α)) :
-    (join L).foldl f b = L.foldl (fun b l => l.foldl f b) b := by
+theorem foldl_flatten (f : β → α → β) (b : β) (L : List (List α)) :
+    (flatten L).foldl f b = L.foldl (fun b l => l.foldl f b) b := by
   induction L generalizing b <;> simp_all
 
-theorem foldr_join (f : α → β → β) (b : β) (L : List (List α)) :
-    (join L).foldr f b = L.foldr (fun l b => l.foldr f b) b := by
+theorem foldr_flatten (f : α → β → β) (b : β) (L : List (List α)) :
+    (flatten L).foldr f b = L.foldr (fun l b => l.foldr f b) b := by
   induction L <;> simp_all
 
-@[simp] theorem map_join (f : α → β) (L : List (List α)) : map f (join L) = join (map (map f) L) := by
+@[simp] theorem map_flatten (f : α → β) (L : List (List α)) : map f (flatten L) = flatten (map (map f) L) := by
   induction L <;> simp_all
 
-@[simp] theorem filterMap_join (f : α → Option β) (L : List (List α)) :
-    filterMap f (join L) = join (map (filterMap f) L) := by
+@[simp] theorem filterMap_flatten (f : α → Option β) (L : List (List α)) :
+    filterMap f (flatten L) = flatten (map (filterMap f) L) := by
   induction L <;> simp [*, filterMap_append]
 
-@[simp] theorem filter_join (p : α → Bool) (L : List (List α)) :
-    filter p (join L) = join (map (filter p) L) := by
+@[simp] theorem filter_flatten (p : α → Bool) (L : List (List α)) :
+    filter p (flatten L) = flatten (map (filter p) L) := by
   induction L <;> simp [*, filter_append]
 
-theorem join_filter_not_isEmpty  :
-    ∀ {L : List (List α)}, join (L.filter fun l => !l.isEmpty) = L.join
+theorem flatten_filter_not_isEmpty  :
+    ∀ {L : List (List α)}, flatten (L.filter fun l => !l.isEmpty) = L.flatten
   | [] => rfl
   | [] :: L
   | (a :: l) :: L => by
-      simp [join_filter_not_isEmpty (L := L)]
+      simp [flatten_filter_not_isEmpty (L := L)]
 
-theorem join_filter_ne_nil [DecidablePred fun l : List α => l ≠ []] {L : List (List α)} :
-    join (L.filter fun l => l ≠ []) = L.join := by
+theorem flatten_filter_ne_nil [DecidablePred fun l : List α => l ≠ []] {L : List (List α)} :
+    flatten (L.filter fun l => l ≠ []) = L.flatten := by
   simp only [ne_eq, ← isEmpty_iff, Bool.not_eq_true, Bool.decide_eq_false,
-    join_filter_not_isEmpty]
+    flatten_filter_not_isEmpty]
 
-@[deprecated filter_join (since := "2024-08-26")]
-theorem join_map_filter (p : α → Bool) (l : List (List α)) :
-    (l.map (filter p)).join = (l.join).filter p := by
-  rw [filter_join]
-
-@[simp] theorem join_append (L₁ L₂ : List (List α)) : join (L₁ ++ L₂) = join L₁ ++ join L₂ := by
+@[simp] theorem flatten_append (L₁ L₂ : List (List α)) : flatten (L₁ ++ L₂) = flatten L₁ ++ flatten L₂ := by
   induction L₁ <;> simp_all
 
-theorem join_concat (L : List (List α)) (l : List α) : join (L ++ [l]) = join L ++ l := by
+theorem flatten_concat (L : List (List α)) (l : List α) : flatten (L ++ [l]) = flatten L ++ l := by
   simp
 
-theorem join_join {L : List (List (List α))} : join (join L) = join (map join L) := by
+theorem flatten_flatten {L : List (List (List α))} : flatten (flatten L) = flatten (map flatten L) := by
   induction L <;> simp_all
 
-theorem join_eq_cons_iff {xs : List (List α)} {y : α} {ys : List α} :
-    xs.join = y :: ys ↔
-      ∃ as bs cs, xs = as ++ (y :: bs) :: cs ∧ (∀ l, l ∈ as → l = []) ∧ ys = bs ++ cs.join := by
+theorem flatten_eq_cons_iff {xs : List (List α)} {y : α} {ys : List α} :
+    xs.flatten = y :: ys ↔
+      ∃ as bs cs, xs = as ++ (y :: bs) :: cs ∧ (∀ l, l ∈ as → l = []) ∧ ys = bs ++ cs.flatten := by
   constructor
   · induction xs with
     | nil => simp
     | cons x xs ih =>
       intro h
-      simp only [join_cons] at h
+      simp only [flatten_cons] at h
       replace h := h.symm
       rw [cons_eq_append_iff] at h
       obtain (⟨rfl, h⟩ | ⟨z⟩) := h
@@ -2178,23 +2181,23 @@ theorem join_eq_cons_iff {xs : List (List α)} {y : α} {ys : List α} :
         refine ⟨[], a', xs, ?_⟩
         simp
   · rintro ⟨as, bs, cs, rfl, h₁, rfl⟩
-    simp [join_eq_nil_iff.mpr h₁]
+    simp [flatten_eq_nil_iff.mpr h₁]
 
-theorem join_eq_append_iff {xs : List (List α)} {ys zs : List α} :
-    xs.join = ys ++ zs ↔
-      (∃ as bs, xs = as ++ bs ∧ ys = as.join ∧ zs = bs.join) ∨
-        ∃ as bs c cs ds, xs = as ++ (bs ++ c :: cs) :: ds ∧ ys = as.join ++ bs ∧
-          zs = c :: cs ++ ds.join := by
+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) ∨
+        ∃ as bs c cs ds, xs = as ++ (bs ++ c :: cs) :: ds ∧ ys = as.flatten ++ bs ∧
+          zs = c :: cs ++ ds.flatten := by
   constructor
   · induction xs generalizing ys with
     | nil =>
-      simp only [join_nil, nil_eq, append_eq_nil, and_false, cons_append, false_and, exists_const,
+      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]
       rintro rfl rfl
       exact ⟨[], [], by simp⟩
     | cons x xs ih =>
       intro h
-      simp only [join_cons] at h
+      simp only [flatten_cons] at h
       rw [append_eq_append_iff] at h
       obtain (⟨ys, rfl, h⟩ | ⟨c', rfl, h⟩) := h
       · obtain (⟨as, bs, rfl, rfl, rfl⟩ | ⟨as, bs, c, cs, ds, rfl, rfl, rfl⟩) := ih h
@@ -2208,18 +2211,15 @@ theorem join_eq_append_iff {xs : List (List α)} {ys zs : List α} :
     · simp
     · simp
 
-@[deprecated join_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons := @join_eq_cons_iff
-@[deprecated join_eq_append_iff (since := "2024-09-05")] abbrev join_eq_append := @join_eq_append_iff
-
-/-- Two lists of sublists are equal iff their joins coincide, as well as the lengths of the
+/-- Two lists of sublists are equal iff their flattens coincide, as well as the lengths of the
 sublists. -/
-theorem eq_iff_join_eq : ∀ {L L' : List (List α)},
-    L = L' ↔ L.join = L'.join ∧ map length L = map length L'
+theorem eq_iff_flatten_eq : ∀ {L L' : List (List α)},
+    L = L' ↔ L.flatten = L'.flatten ∧ map length L = map length L'
   | _, [] => by simp_all
   | [], x' :: L' => by simp_all
   | x :: L, x' :: L' => by
     simp
-    rw [eq_iff_join_eq]
+    rw [eq_iff_flatten_eq]
     constructor
     · rintro ⟨rfl, h₁, h₂⟩
       simp_all
@@ -2227,86 +2227,86 @@ theorem eq_iff_join_eq : ∀ {L L' : List (List α)},
       obtain ⟨rfl, h⟩ := append_inj h₁ h₂
       exact ⟨rfl, h, h₃⟩
 
-/-! ### bind -/
+/-! ### flatMap -/
 
-theorem bind_def (l : List α) (f : α → List β) : l.bind f = join (map f l) := by rfl
+theorem flatMap_def (l : List α) (f : α → List β) : l.flatMap f = flatten (map f l) := by rfl
 
-@[simp] theorem bind_id (l : List (List α)) : List.bind l id = l.join := by simp [bind_def]
+@[simp] theorem flatMap_id (l : List (List α)) : List.flatMap l id = l.flatten := by simp [flatMap_def]
 
-@[simp] theorem mem_bind {f : α → List β} {b} {l : List α} : b ∈ l.bind f ↔ ∃ a, a ∈ l ∧ b ∈ f a := by
-  simp [bind_def, mem_join]
+@[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]
   exact ⟨fun ⟨_, ⟨a, h₁, rfl⟩, h₂⟩ => ⟨a, h₁, h₂⟩, fun ⟨a, h₁, h₂⟩ => ⟨_, ⟨a, h₁, rfl⟩, h₂⟩⟩
 
-theorem exists_of_mem_bind {b : β} {l : List α} {f : α → List β} :
-    b ∈ l.bind f → ∃ a, a ∈ l ∧ b ∈ f a := mem_bind.1
+theorem exists_of_mem_flatMap {b : β} {l : List α} {f : α → List β} :
+    b ∈ l.flatMap f → ∃ a, a ∈ l ∧ b ∈ f a := mem_flatMap.1
 
-theorem mem_bind_of_mem {b : β} {l : List α} {f : α → List β} {a} (al : a ∈ l) (h : b ∈ f a) :
-    b ∈ l.bind f := mem_bind.2 ⟨a, al, h⟩
+theorem mem_flatMap_of_mem {b : β} {l : List α} {f : α → List β} {a} (al : a ∈ l) (h : b ∈ f a) :
+    b ∈ l.flatMap f := mem_flatMap.2 ⟨a, al, h⟩
 
 @[simp]
-theorem bind_eq_nil_iff {l : List α} {f : α → List β} : List.bind l f = [] ↔ ∀ x ∈ l, f x = [] :=
-  join_eq_nil_iff.trans <| by
+theorem flatMap_eq_nil_iff {l : List α} {f : α → List β} : List.flatMap l 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]
 
-@[deprecated bind_eq_nil_iff (since := "2024-09-05")] abbrev bind_eq_nil := @bind_eq_nil_iff
+@[deprecated flatMap_eq_nil_iff (since := "2024-09-05")] abbrev bind_eq_nil := @flatMap_eq_nil_iff
 
-theorem forall_mem_bind {p : β → Prop} {l : List α} {f : α → List β} :
-    (∀ (x) (_ : x ∈ l.bind f), p x) ↔ ∀ (a) (_ : a ∈ l) (b) (_ : b ∈ f a), p b := by
-  simp only [mem_bind, forall_exists_index, and_imp]
+theorem forall_mem_flatMap {p : β → Prop} {l : List α} {f : α → List β} :
+    (∀ (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 bind_singleton (f : α → List β) (x : α) : [x].bind f = f x :=
+theorem flatMap_singleton (f : α → List β) (x : α) : [x].flatMap f = f x :=
   append_nil (f x)
 
-@[simp] theorem bind_singleton' (l : List α) : (l.bind fun x => [x]) = l := by
+@[simp] theorem flatMap_singleton' (l : List α) : (l.flatMap fun x => [x]) = l := by
   induction l <;> simp [*]
 
-theorem head?_bind {l : List α} {f : α → List β} :
-    (l.bind f).head? = l.findSome? fun a => (f a).head? := by
+theorem head?_flatMap {l : List α} {f : α → List β} :
+    (l.flatMap f).head? = l.findSome? fun a => (f a).head? := by
   induction l with
   | nil => rfl
   | cons =>
     simp only [findSome?_cons]
     split <;> simp_all
 
-@[simp] theorem bind_append (xs ys : List α) (f : α → List β) :
-    (xs ++ ys).bind f = xs.bind f ++ ys.bind f := by
-  induction xs; {rfl}; simp_all [bind_cons, append_assoc]
+@[simp] theorem flatMap_append (xs ys : List α) (f : α → List β) :
+    (xs ++ ys).flatMap f = xs.flatMap f ++ ys.flatMap f := by
+  induction xs; {rfl}; simp_all [flatMap_cons, append_assoc]
 
-@[deprecated bind_append (since := "2024-07-24")] abbrev append_bind := @bind_append
+@[deprecated flatMap_append (since := "2024-07-24")] abbrev append_bind := @flatMap_append
 
-theorem bind_assoc {α β} (l : List α) (f : α → List β) (g : β → List γ) :
-    (l.bind f).bind g = l.bind fun x => (f x).bind g := by
+theorem flatMap_assoc {α β} (l : List α) (f : α → List β) (g : β → List γ) :
+    (l.flatMap f).flatMap g = l.flatMap fun x => (f x).flatMap g := by
   induction l <;> simp [*]
 
-theorem map_bind (f : β → γ) (g : α → List β) :
-    ∀ l : List α, (l.bind g).map f = l.bind fun a => (g a).map f
+theorem map_flatMap (f : β → γ) (g : α → List β) :
+    ∀ l : List α, (l.flatMap g).map f = l.flatMap fun a => (g a).map f
   | [] => rfl
-  | a::l => by simp only [bind_cons, map_append, map_bind _ _ l]
+  | a::l => by simp only [flatMap_cons, map_append, map_flatMap _ _ l]
 
-theorem bind_map (f : α → β) (g : β → List γ) (l : List α) :
-    (map f l).bind g = l.bind (fun a => g (f a)) := by
-  induction l <;> simp [bind_cons, *]
+theorem flatMap_map (f : α → β) (g : β → List γ) (l : List α) :
+    (map f l).flatMap g = l.flatMap (fun a => g (f a)) := by
+  induction l <;> simp [flatMap_cons, *]
 
-theorem map_eq_bind {α β} (f : α → β) (l : List α) : map f l = l.bind fun x => [f x] := by
+theorem map_eq_flatMap {α β} (f : α → β) (l : List α) : map f l = l.flatMap fun x => [f x] := by
   simp only [← map_singleton]
-  rw [← bind_singleton' l, map_bind, bind_singleton']
+  rw [← flatMap_singleton' l, map_flatMap, flatMap_singleton']
 
-theorem filterMap_bind {β γ} (l : List α) (g : α → List β) (f : β → Option γ) :
-    (l.bind g).filterMap f = l.bind fun a => (g a).filterMap f := by
+theorem filterMap_flatMap {β γ} (l : List α) (g : α → List β) (f : β → Option γ) :
+    (l.flatMap g).filterMap f = l.flatMap fun a => (g a).filterMap f := by
   induction l <;> simp [*]
 
-theorem filter_bind (l : List α) (g : α → List β) (f : β → Bool) :
-    (l.bind g).filter f = l.bind fun a => (g a).filter f := by
+theorem filter_flatMap (l : List α) (g : α → List β) (f : β → Bool) :
+    (l.flatMap g).filter f = l.flatMap fun a => (g a).filter f := by
   induction l <;> simp [*]
 
-theorem bind_eq_foldl (f : α → List β) (l : List α) :
-    l.bind f = l.foldl (fun acc a => acc ++ f a) [] := by
-  suffices ∀ l', l' ++ l.bind f = l.foldl (fun acc a => acc ++ f a) l' by simpa using this []
+theorem flatMap_eq_foldl (f : α → List β) (l : List α) :
+    l.flatMap f = l.foldl (fun acc a => acc ++ f a) [] := by
+  suffices ∀ l', l' ++ l.flatMap f = l.foldl (fun acc a => acc ++ f a) l' by simpa using this []
   intro l'
   induction l generalizing l'
   · simp
-  · next ih => rw [bind_cons, ← append_assoc, ih, foldl_cons]
+  · next ih => rw [flatMap_cons, ← append_assoc, ih, foldl_cons]
 
 /-! ### replicate -/
 
@@ -2483,23 +2483,23 @@ theorem filterMap_replicate_of_some {f : α → Option β} (h : f a = some b) :
     (replicate n a).filterMap f = [] := by
   simp [filterMap_replicate, h]
 
-@[simp] theorem join_replicate_nil : (replicate n ([] : List α)).join = [] := by
+@[simp] theorem flatten_replicate_nil : (replicate n ([] : List α)).flatten = [] := by
   induction n <;> simp_all [replicate_succ]
 
-@[simp] theorem join_replicate_singleton : (replicate n [a]).join = replicate n a := by
+@[simp] theorem flatten_replicate_singleton : (replicate n [a]).flatten = replicate n a := by
   induction n <;> simp_all [replicate_succ]
 
-@[simp] theorem join_replicate_replicate : (replicate n (replicate m a)).join = replicate (n * m) a := by
+@[simp] theorem flatten_replicate_replicate : (replicate n (replicate m a)).flatten = replicate (n * m) a := by
   induction n with
   | zero => simp
   | succ n ih =>
-    simp only [replicate_succ, join_cons, ih, append_replicate_replicate, replicate_inj, or_true,
+    simp only [replicate_succ, flatten_cons, ih, append_replicate_replicate, replicate_inj, or_true,
       and_true, add_one_mul, Nat.add_comm]
 
-theorem bind_replicate {β} (f : α → List β) : (replicate n a).bind f = (replicate n (f a)).join := by
+theorem flatMap_replicate {β} (f : α → List β) : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
   induction n with
   | zero => simp
-  | succ n ih => simp only [replicate_succ, bind_cons, ih, join_cons]
+  | succ n ih => simp only [replicate_succ, flatMap_cons, ih, flatten_cons]
 
 @[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
   cases n <;> simp [replicate_succ]
@@ -2674,20 +2674,20 @@ theorem reverse_eq_concat {xs ys : List α} {a : α} :
     xs.reverse = ys ++ [a] ↔ xs = a :: ys.reverse := by
   rw [reverse_eq_iff, reverse_concat]
 
-/-- Reversing a join is the same as reversing the order of parts and reversing all parts. -/
-theorem reverse_join (L : List (List α)) :
-    L.join.reverse = (L.map reverse).reverse.join := by
+/-- Reversing a flatten is the same as reversing the order of parts and reversing all parts. -/
+theorem reverse_flatten (L : List (List α)) :
+    L.flatten.reverse = (L.map reverse).reverse.flatten := by
   induction L <;> simp_all
 
-/-- Joining a reverse is the same as reversing all parts and reversing the joined result. -/
-theorem join_reverse (L : List (List α)) :
-    L.reverse.join = (L.map reverse).join.reverse := by
+/-- Flattening a reverse is the same as reversing all parts and reversing the flattened result. -/
+theorem flatten_reverse (L : List (List α)) :
+    L.reverse.flatten = (L.map reverse).flatten.reverse := by
   induction L <;> simp_all
 
-theorem reverse_bind {β} (l : List α) (f : α → List β) : (l.bind f).reverse = l.reverse.bind (reverse ∘ f) := by
+theorem reverse_flatMap {β} (l : List α) (f : α → List β) : (l.flatMap f).reverse = l.reverse.flatMap (reverse ∘ f) := by
   induction l <;> simp_all
 
-theorem bind_reverse {β} (l : List α) (f : α → List β) : (l.reverse.bind f) = (l.bind (reverse ∘ f)).reverse := by
+theorem flatMap_reverse {β} (l : List α) (f : α → List β) : (l.reverse.flatMap f) = (l.flatMap (reverse ∘ f)).reverse := by
   induction l <;> simp_all
 
 @[simp] theorem reverseAux_eq (as bs : List α) : reverseAux as bs = reverse as ++ bs :=
@@ -2795,15 +2795,15 @@ theorem getLast_filterMap_of_eq_some {f : α → Option β} {l : List α} {w : l
   rw [head_filterMap_of_eq_some (by simp_all)]
   simp_all
 
-theorem getLast?_bind {L : List α} {f : α → List β} :
-    (L.bind f).getLast? = L.reverse.findSome? fun a => (f a).getLast? := by
-  simp only [← head?_reverse, reverse_bind]
-  rw [head?_bind]
+theorem getLast?_flatMap {L : List α} {f : α → List β} :
+    (L.flatMap f).getLast? = L.reverse.findSome? fun a => (f a).getLast? := by
+  simp only [← head?_reverse, reverse_flatMap]
+  rw [head?_flatMap]
   rfl
 
-theorem getLast?_join {L : List (List α)} :
-    (join L).getLast? = L.reverse.findSome? fun l => l.getLast? := by
-  simp [← bind_id, getLast?_bind]
+theorem getLast?_flatten {L : List (List α)} :
+    (flatten L).getLast? = L.reverse.findSome? fun l => l.getLast? := by
+  simp [← flatMap_id, getLast?_flatMap]
 
 theorem getLast?_replicate (a : α) (n : Nat) : (replicate n a).getLast? = if n = 0 then none else some a := by
   simp only [← head?_reverse, reverse_replicate, head?_replicate]
@@ -3302,18 +3302,22 @@ theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!
   | nil => rfl
   | cons h t ih => simp_all [Bool.and_assoc]
 
-@[simp] theorem any_join {l : List (List α)} : l.join.any f = l.any (any · f) := by
+@[simp] theorem any_flatten {l : List (List α)} : l.flatten.any f = l.any (any · f) := by
   induction l <;> simp_all
 
-@[simp] theorem all_join {l : List (List α)} : l.join.all f = l.all (all · f) := by
+@[deprecated any_flatten (since := "2024-10-14")] abbrev any_join := @any_flatten
+
+@[simp] theorem all_flatten {l : List (List α)} : l.flatten.all f = l.all (all · f) := by
   induction l <;> simp_all
 
-@[simp] theorem any_bind {l : List α} {f : α → List β} :
-    (l.bind f).any p = l.any fun a => (f a).any p := by
+@[deprecated all_flatten (since := "2024-10-14")] abbrev all_join := @all_flatten
+
+@[simp] theorem any_flatMap {l : List α} {f : α → List β} :
+    (l.flatMap f).any p = l.any fun a => (f a).any p := by
   induction l <;> simp_all
 
-@[simp] theorem all_bind {l : List α} {f : α → List β} :
-    (l.bind f).all p = l.all fun a => (f a).all p := by
+@[simp] theorem all_flatMap {l : List α} {f : α → List β} :
+    (l.flatMap f).all p = l.all fun a => (f a).all p := by
   induction l <;> simp_all
 
 @[simp] theorem any_reverse {l : List α} : l.reverse.any f = l.any f := by
@@ -3338,4 +3342,72 @@ theorem all_eq_not_any_not (l : List α) (p : α → Bool) : l.all p = !l.any (!
     (l.insert a).all f = (f a && l.all f) := by
   simp [all_eq]
 
+/-! ### Deprecations -/
+
+
+@[deprecated flatten_nil (since := "2024-10-14")] abbrev join_nil := @flatten_nil
+@[deprecated flatten_cons (since := "2024-10-14")] abbrev join_cons := @flatten_cons
+@[deprecated length_flatten (since := "2024-10-14")] abbrev length_join := @length_flatten
+@[deprecated flatten_singleton (since := "2024-10-14")] abbrev join_singleton := @flatten_singleton
+@[deprecated mem_flatten (since := "2024-10-14")] abbrev mem_join := @mem_flatten
+@[deprecated flatten_eq_nil_iff (since := "2024-09-05")] abbrev join_eq_nil := @flatten_eq_nil_iff
+@[deprecated flatten_eq_nil_iff (since := "2024-10-14")] abbrev join_eq_nil_iff := @flatten_eq_nil_iff
+@[deprecated flatten_ne_nil_iff (since := "2024-09-05")] abbrev join_ne_nil := @flatten_ne_nil_iff
+@[deprecated flatten_ne_nil_iff (since := "2024-10-14")] abbrev join_ne_nil_iff := @flatten_ne_nil_iff
+@[deprecated exists_of_mem_flatten (since := "2024-10-14")] abbrev exists_of_mem_join := @exists_of_mem_flatten
+@[deprecated mem_flatten_of_mem (since := "2024-10-14")] abbrev mem_join_of_mem := @mem_flatten_of_mem
+@[deprecated forall_mem_flatten (since := "2024-10-14")] abbrev forall_mem_join := @forall_mem_flatten
+@[deprecated flatten_eq_flatMap (since := "2024-10-14")] abbrev join_eq_bind := @flatten_eq_flatMap
+@[deprecated head?_flatten (since := "2024-10-14")] abbrev head?_join := @head?_flatten
+@[deprecated foldl_flatten (since := "2024-10-14")] abbrev foldl_join := @foldl_flatten
+@[deprecated foldr_flatten (since := "2024-10-14")] abbrev foldr_join := @foldr_flatten
+@[deprecated map_flatten (since := "2024-10-14")] abbrev map_join := @map_flatten
+@[deprecated filterMap_flatten (since := "2024-10-14")] abbrev filterMap_join := @filterMap_flatten
+@[deprecated filter_flatten (since := "2024-10-14")] abbrev filter_join := @filter_flatten
+@[deprecated flatten_filter_not_isEmpty (since := "2024-10-14")] abbrev join_filter_not_isEmpty := @flatten_filter_not_isEmpty
+@[deprecated flatten_filter_ne_nil (since := "2024-10-14")] abbrev join_filter_ne_nil := @flatten_filter_ne_nil
+@[deprecated filter_flatten (since := "2024-08-26")]
+theorem join_map_filter (p : α → Bool) (l : List (List α)) :
+    (l.map (filter p)).flatten = (l.flatten).filter p := by
+  rw [filter_flatten]
+@[deprecated flatten_append (since := "2024-10-14")] abbrev join_append := @flatten_append
+@[deprecated flatten_concat (since := "2024-10-14")] abbrev join_concat := @flatten_concat
+@[deprecated flatten_flatten (since := "2024-10-14")] abbrev join_join := @flatten_flatten
+@[deprecated flatten_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons_iff := @flatten_eq_cons_iff
+@[deprecated flatten_eq_cons_iff (since := "2024-09-05")] abbrev join_eq_cons := @flatten_eq_cons_iff
+@[deprecated flatten_eq_append_iff (since := "2024-09-05")] abbrev join_eq_append := @flatten_eq_append_iff
+@[deprecated flatten_eq_append_iff (since := "2024-10-14")] abbrev join_eq_append_iff := @flatten_eq_append_iff
+@[deprecated eq_iff_flatten_eq (since := "2024-10-14")] abbrev eq_iff_join_eq := @eq_iff_flatten_eq
+@[deprecated flatten_replicate_nil (since := "2024-10-14")] abbrev join_replicate_nil := @flatten_replicate_nil
+@[deprecated flatten_replicate_singleton (since := "2024-10-14")] abbrev join_replicate_singleton := @flatten_replicate_singleton
+@[deprecated flatten_replicate_replicate (since := "2024-10-14")] abbrev join_replicate_replicate := @flatten_replicate_replicate
+@[deprecated reverse_flatten (since := "2024-10-14")] abbrev reverse_join := @reverse_flatten
+@[deprecated flatten_reverse (since := "2024-10-14")] abbrev join_reverse := @flatten_reverse
+@[deprecated getLast?_flatten (since := "2024-10-14")] abbrev getLast?_join := @getLast?_flatten
+@[deprecated flatten_eq_flatMap (since := "2024-10-16")] abbrev flatten_eq_bind := @flatten_eq_flatMap
+@[deprecated flatMap_def (since := "2024-10-16")] abbrev bind_def := @flatMap_def
+@[deprecated flatMap_id (since := "2024-10-16")] abbrev bind_id := @flatMap_id
+@[deprecated mem_flatMap (since := "2024-10-16")] abbrev mem_bind := @mem_flatMap
+@[deprecated exists_of_mem_flatMap (since := "2024-10-16")] abbrev exists_of_mem_bind := @exists_of_mem_flatMap
+@[deprecated mem_flatMap_of_mem (since := "2024-10-16")] abbrev mem_bind_of_mem := @mem_flatMap_of_mem
+@[deprecated flatMap_eq_nil_iff (since := "2024-10-16")] abbrev bind_eq_nil_iff := @flatMap_eq_nil_iff
+@[deprecated forall_mem_flatMap (since := "2024-10-16")] abbrev forall_mem_bind := @forall_mem_flatMap
+@[deprecated flatMap_singleton (since := "2024-10-16")] abbrev bind_singleton := @flatMap_singleton
+@[deprecated flatMap_singleton' (since := "2024-10-16")] abbrev bind_singleton' := @flatMap_singleton'
+@[deprecated head?_flatMap (since := "2024-10-16")] abbrev head_bind := @head?_flatMap
+@[deprecated flatMap_append (since := "2024-10-16")] abbrev bind_append := @flatMap_append
+@[deprecated flatMap_assoc (since := "2024-10-16")] abbrev bind_assoc := @flatMap_assoc
+@[deprecated map_flatMap (since := "2024-10-16")] abbrev map_bind := @map_flatMap
+@[deprecated flatMap_map (since := "2024-10-16")] abbrev bind_map := @flatMap_map
+@[deprecated map_eq_flatMap (since := "2024-10-16")] abbrev map_eq_bind := @map_eq_flatMap
+@[deprecated filterMap_flatMap (since := "2024-10-16")] abbrev filterMap_bind := @filterMap_flatMap
+@[deprecated filter_flatMap (since := "2024-10-16")] abbrev filter_bind := @filter_flatMap
+@[deprecated flatMap_eq_foldl (since := "2024-10-16")] abbrev bind_eq_foldl := @flatMap_eq_foldl
+@[deprecated flatMap_replicate (since := "2024-10-16")] abbrev bind_replicate := @flatMap_replicate
+@[deprecated reverse_flatMap (since := "2024-10-16")] abbrev reverse_bind := @reverse_flatMap
+@[deprecated flatMap_reverse (since := "2024-10-16")] abbrev bind_reverse := @flatMap_reverse
+@[deprecated getLast?_flatMap (since := "2024-10-16")] abbrev getLast?_bind := @getLast?_flatMap
+@[deprecated any_flatMap (since := "2024-10-16")] abbrev any_bind := @any_flatMap
+@[deprecated all_flatMap (since := "2024-10-16")] abbrev all_bind := @all_flatMap
+
 end List

src/Init/Data/List/MapIdx.lean

@@ -0,0 +1,248 @@
+/-
+Copyright (c) 2024 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison, Mario Carneiro
+-/
+
+prelude
+import Init.Data.Array.Lemmas
+import Init.Data.List.Nat.Range
+
+namespace List
+
+/-! ## Operations using indexes -/
+
+/-! ### mapIdx -/
+
+/--
+Given a function `f : Nat → α → β` and `as : list α`, `as = [a₀, a₁, ...]`, returns the list
+`[f 0 a₀, f 1 a₁, ...]`.
+-/
+@[inline] def mapIdx (f : Nat → α → β) (as : List α) : List β := go as #[] where
+  /-- Auxiliary for `mapIdx`:
+  `mapIdx.go [a₀, a₁, ...] acc = acc.toList ++ [f acc.size a₀, f (acc.size + 1) a₁, ...]` -/
+  @[specialize] go : List α → Array β → List β
+  | [], acc => acc.toList
+  | a :: as, acc => go as (acc.push (f acc.size a))
+
+@[simp]
+theorem mapIdx_nil {f : Nat → α → β} : mapIdx f [] = [] :=
+  rfl
+
+theorem mapIdx_go_append  {l₁ l₂ : List α} {arr : Array β} :
+    mapIdx.go f (l₁ ++ l₂) arr = mapIdx.go f l₂ (List.toArray (mapIdx.go f l₁ arr)) := by
+  generalize h : (l₁ ++ l₂).length = len
+  induction len generalizing l₁ arr with
+  | zero =>
+    have l₁_nil : l₁ = [] := by
+      cases l₁
+      · rfl
+      · contradiction
+    have l₂_nil : l₂ = [] := by
+      cases l₂
+      · rfl
+      · rw [List.length_append] at h; contradiction
+    rw [l₁_nil, l₂_nil]; simp only [mapIdx.go, List.toArray_toList]
+  | succ len ih =>
+    cases l₁ with
+    | nil =>
+      simp only [mapIdx.go, nil_append, List.toArray_toList]
+    | cons head tail =>
+      simp only [mapIdx.go, List.append_eq]
+      rw [ih]
+      · simp only [cons_append, length_cons, length_append, Nat.succ.injEq] at h
+        simp only [length_append, h]
+
+theorem mapIdx_go_length {arr : Array β} :
+    length (mapIdx.go f l arr) = length l + arr.size := by
+  induction l generalizing arr with
+  | nil => simp only [mapIdx.go, length_nil, Nat.zero_add]
+  | cons _ _ ih =>
+    simp only [mapIdx.go, ih, Array.size_push, Nat.add_succ, length_cons, Nat.add_comm]
+
+@[simp] theorem mapIdx_concat {l : List α} {e : α} :
+    mapIdx f (l ++ [e]) = mapIdx f l ++ [f l.length e] := by
+  unfold mapIdx
+  rw [mapIdx_go_append]
+  simp only [mapIdx.go, Array.size_toArray, mapIdx_go_length, length_nil, Nat.add_zero,
+    Array.push_toList]
+
+@[simp] theorem mapIdx_singleton {a : α} : mapIdx f [a] = [f 0 a] := by
+  simpa using mapIdx_concat (l := [])
+
+theorem length_mapIdx_go : ∀ {l : List α} {arr : Array β},
+    (mapIdx.go f l arr).length = l.length + arr.size
+  | [], _ => by simp [mapIdx.go]
+  | a :: l, _ => by
+    simp only [mapIdx.go, length_cons]
+    rw [length_mapIdx_go]
+    simp
+    omega
+
+@[simp] theorem length_mapIdx {l : List α} : (l.mapIdx f).length = l.length := by
+  simp [mapIdx, length_mapIdx_go]
+
+theorem getElem?_mapIdx_go : ∀ {l : List α} {arr : Array β} {i : Nat},
+    (mapIdx.go f l arr)[i]? =
+      if h : i < arr.size then some arr[i] else Option.map (f i) l[i - arr.size]?
+  | [], arr, i => by
+    simp only [mapIdx.go, Array.toListImpl_eq, getElem?_eq, Array.length_toList,
+      Array.getElem_eq_getElem_toList, length_nil, Nat.not_lt_zero, ↓reduceDIte, Option.map_none']
+  | a :: l, arr, i => by
+    rw [mapIdx.go, getElem?_mapIdx_go]
+    simp only [Array.size_push]
+    split <;> split
+    · simp only [Option.some.injEq]
+      rw [Array.getElem_eq_getElem_toList]
+      simp only [Array.push_toList]
+      rw [getElem_append_left, Array.getElem_eq_getElem_toList]
+    · have : i = arr.size := by omega
+      simp_all
+    · omega
+    · have : i - arr.size = i - (arr.size + 1) + 1 := by omega
+      simp_all
+
+@[simp] theorem getElem?_mapIdx {l : List α} {i : Nat} :
+    (l.mapIdx f)[i]? = Option.map (f i) l[i]? := by
+  simp [mapIdx, getElem?_mapIdx_go]
+
+@[simp] theorem getElem_mapIdx {l : List α} {f : Nat → α → β} {i : Nat} {h : i < (l.mapIdx f).length} :
+    (l.mapIdx f)[i] = f i (l[i]'(by simpa using h)) := by
+  apply Option.some_inj.mp
+  rw [← getElem?_eq_getElem, getElem?_mapIdx, getElem?_eq_getElem (by simpa using h)]
+  simp
+
+theorem mapIdx_eq_enum_map {l : List α} :
+    l.mapIdx f = l.enum.map (Function.uncurry f) := by
+  ext1 i
+  simp only [getElem?_mapIdx, Option.map, getElem?_map, getElem?_enum]
+  split <;> simp
+
+@[simp]
+theorem mapIdx_cons {l : List α} {a : α} :
+    mapIdx f (a :: l) = f 0 a :: mapIdx (fun i => f (i + 1)) l := by
+  simp [mapIdx_eq_enum_map, enum_eq_zip_range, map_uncurry_zip_eq_zipWith,
+    range_succ_eq_map, zipWith_map_left]
+
+theorem mapIdx_append {K L : List α} :
+    (K ++ L).mapIdx f = K.mapIdx f ++ L.mapIdx fun i => f (i + K.length) := by
+  induction K generalizing f with
+  | nil => rfl
+  | cons _ _ ih => simp [ih (f := fun i => f (i + 1)), Nat.add_assoc]
+
+@[simp]
+theorem mapIdx_eq_nil_iff {l : List α} : List.mapIdx f l = [] ↔ l = [] := by
+  rw [List.mapIdx_eq_enum_map, List.map_eq_nil_iff, List.enum_eq_nil]
+
+theorem mapIdx_ne_nil_iff {l : List α} :
+    List.mapIdx f l ≠ [] ↔ l ≠ [] := by
+  simp
+
+theorem exists_of_mem_mapIdx {b : β} {l : List α}
+    (h : b ∈ mapIdx f l) : ∃ (i : Nat) (h : i < l.length), f i l[i] = b := by
+  rw [mapIdx_eq_enum_map] at h
+  replace h := exists_of_mem_map h
+  simp only [Prod.exists, mk_mem_enum_iff_getElem?, Function.uncurry_apply_pair] at h
+  obtain ⟨i, b, h, rfl⟩ := h
+  rw [getElem?_eq_some_iff] at h
+  obtain ⟨h, rfl⟩ := h
+  exact ⟨i, h, rfl⟩
+
+@[simp] theorem mem_mapIdx {b : β} {l : List α} :
+    b ∈ mapIdx f l ↔ ∃ (i : Nat) (h : i < l.length), f i l[i] = b := by
+  constructor
+  · intro h
+    exact exists_of_mem_mapIdx h
+  · rintro ⟨i, h, rfl⟩
+    rw [mem_iff_getElem]
+    exact ⟨i, by simpa using h, by simp⟩
+
+theorem mapIdx_eq_cons_iff {l : List α} {b : β} :
+    mapIdx f l = b :: l₂ ↔
+      ∃ (a : α) (l₁ : List α), l = a :: l₁ ∧ f 0 a = b ∧ mapIdx (fun i => f (i + 1)) l₁ = l₂ := by
+  cases l <;> simp [and_assoc]
+
+theorem mapIdx_eq_cons_iff' {l : List α} {b : β} :
+    mapIdx f l = b :: l₂ ↔
+      l.head?.map (f 0) = some b ∧ l.tail?.map (mapIdx fun i => f (i + 1)) = some l₂ := by
+  cases l <;> simp
+
+theorem mapIdx_eq_iff {l : List α} : mapIdx f l = l' ↔ ∀ i : Nat, l'[i]? = l[i]?.map (f i) := by
+  constructor
+  · intro w i
+    simpa using congrArg (fun l => l[i]?) w.symm
+  · intro w
+    ext1 i
+    simp [w]
+
+theorem mapIdx_eq_mapIdx_iff {l : List α} :
+    mapIdx f l = mapIdx g l ↔ ∀ i : Nat, (h : i < l.length) → f i l[i] = g i l[i] := by
+  constructor
+  · intro w i h
+    simpa [h] using congrArg (fun l => l[i]?) w
+  · intro w
+    apply ext_getElem
+    · simp
+    · intro i h₁ h₂
+      simp [w]
+
+@[simp] theorem mapIdx_set {l : List α} {i : Nat} {a : α} :
+    (l.set i a).mapIdx f = (l.mapIdx f).set i (f i a) := by
+  simp only [mapIdx_eq_iff, getElem?_set, length_mapIdx, getElem?_mapIdx]
+  intro i
+  split
+  · split <;> simp_all
+  · rfl
+
+@[simp] theorem head_mapIdx {l : List α} {f : Nat → α → β} {w : mapIdx f l ≠ []} :
+    (mapIdx f l).head w = f 0 (l.head (by simpa using w)) := by
+  cases l with
+  | nil => simp at w
+  | cons _ _ => simp
+
+@[simp] theorem head?_mapIdx {l : List α} {f : Nat → α → β} : (mapIdx f l).head? = l.head?.map (f 0) := by
+  cases l <;> simp
+
+@[simp] theorem getLast_mapIdx {l : List α} {f : Nat → α → β} {h} :
+    (mapIdx f l).getLast h = f (l.length - 1) (l.getLast (by simpa using h)) := by
+  cases l with
+  | nil => simp at h
+  | cons _ _ =>
+    simp only [← getElem_cons_length _ _ _ rfl]
+    simp only [mapIdx_cons]
+    simp only [← getElem_cons_length _ _ _ rfl]
+    simp only [← mapIdx_cons, getElem_mapIdx]
+    simp
+
+@[simp] theorem getLast?_mapIdx {l : List α} {f : Nat → α → β} :
+    (mapIdx f l).getLast? = (getLast? l).map (f (l.length - 1)) := by
+  cases l
+  · simp
+  · rw [getLast?_eq_getLast, getLast?_eq_getLast, getLast_mapIdx] <;> simp
+
+@[simp] theorem mapIdx_mapIdx {l : List α} {f : Nat → α → β} {g : Nat → β → γ} :
+    (l.mapIdx f).mapIdx g = l.mapIdx (fun i => g i ∘ f i) := by
+  simp [mapIdx_eq_iff]
+
+theorem mapIdx_eq_replicate_iff {l : List α} {f : Nat → α → β} {b : β} :
+    mapIdx f l = replicate l.length b ↔ ∀ (i : Nat) (h : i < l.length), f i l[i] = b := by
+  simp only [eq_replicate_iff, length_mapIdx, mem_mapIdx, forall_exists_index, true_and]
+  constructor
+  · intro w i h
+    apply w _ _ _ rfl
+  · rintro w _ i h rfl
+    exact w i h
+
+@[simp] theorem mapIdx_reverse {l : List α} {f : Nat → α → β} :
+    l.reverse.mapIdx f = (mapIdx (fun i => f (l.length - 1 - i)) l).reverse := by
+  simp [mapIdx_eq_iff]
+  intro i
+  by_cases h : i < l.length
+  · simp [getElem?_reverse, h]
+    congr
+    omega
+  · simp at h
+    rw [getElem?_eq_none (by simp [h]), getElem?_eq_none (by simp [h])]
+    simp
+
+end List

src/Init/Data/List/MinMax.lean

@@ -20,20 +20,28 @@ open Nat
 
 @[simp] theorem min?_nil [Min α] : ([] : List α).min? = none := rfl
 
--- We don't put `@[simp]` on `min?_cons`,
+-- We don't put `@[simp]` on `min?_cons'`,
 -- because the definition in terms of `foldl` is not useful for proofs.
-theorem min?_cons [Min α] {xs : List α} : (x :: xs).min? = foldl min x xs := rfl
+theorem min?_cons' [Min α] {xs : List α} : (x :: xs).min? = foldl min x xs := rfl
+
+@[simp] theorem min?_cons [Min α] [Std.Associative (min : α → α → α)] {xs : List α} :
+    (x :: xs).min? = some (xs.min?.elim x (min x)) := by
+  cases xs <;> simp [min?_cons', foldl_assoc]
 
 @[simp] theorem min?_eq_none_iff {xs : List α} [Min α] : xs.min? = none ↔ xs = [] := by
   cases xs <;> simp [min?]
 
+theorem isSome_min?_of_mem {l : List α} [Min α] {a : α} (h : a ∈ l) :
+    l.min?.isSome := by
+  cases l <;> simp_all [List.min?_cons']
+
 theorem min?_mem [Min α] (min_eq_or : ∀ a b : α, min a b = a ∨ min a b = b) :
     {xs : List α} → xs.min? = some a → a ∈ xs := by
   intro xs
   match xs with
   | nil => simp
   | x :: xs =>
-    simp only [min?_cons, Option.some.injEq, List.mem_cons]
+    simp only [min?_cons', Option.some.injEq, List.mem_cons]
     intro eq
     induction xs generalizing x with
     | nil =>
@@ -67,7 +75,7 @@ theorem le_min?_iff [Min α] [LE α]
 
 -- This could be refactored by designing appropriate typeclasses to replace `le_refl`, `min_eq_or`,
 -- and `le_min_iff`.
-theorem min?_eq_some_iff [Min α] [LE α] [anti : Antisymm ((· : α) ≤ ·)]
+theorem min?_eq_some_iff [Min α] [LE α] [anti : Std.Antisymm ((· : α) ≤ ·)]
     (le_refl : ∀ a : α, a ≤ a)
     (min_eq_or : ∀ a b : α, min a b = a ∨ min a b = b)
     (le_min_iff : ∀ a b c : α, a ≤ min b c ↔ a ≤ b ∧ a ≤ c) {xs : List α} :
@@ -85,23 +93,35 @@ theorem min?_replicate [Min α] {n : Nat} {a : α} (w : min a a = a) :
     (replicate n a).min? = if n = 0 then none else some a := by
   induction n with
   | zero => rfl
-  | succ n ih => cases n <;> simp_all [replicate_succ, min?_cons]
+  | succ n ih => cases n <;> simp_all [replicate_succ, min?_cons']
 
 @[simp] theorem min?_replicate_of_pos [Min α] {n : Nat} {a : α} (w : min a a = a) (h : 0 < n) :
     (replicate n a).min? = some a := by
   simp [min?_replicate, Nat.ne_of_gt h, w]
 
+theorem foldl_min [Min α] [Std.IdempotentOp (min : α → α → α)] [Std.Associative (min : α → α → α)]
+    {l : List α} {a : α} : l.foldl (init := a) min = min a (l.min?.getD a) := by
+  cases l <;> simp [min?, foldl_assoc, Std.IdempotentOp.idempotent]
+
 /-! ### max? -/
 
 @[simp] theorem max?_nil [Max α] : ([] : List α).max? = none := rfl
 
--- We don't put `@[simp]` on `max?_cons`,
+-- We don't put `@[simp]` on `max?_cons'`,
 -- because the definition in terms of `foldl` is not useful for proofs.
-theorem max?_cons [Max α] {xs : List α} : (x :: xs).max? = foldl max x xs := rfl
+theorem max?_cons' [Max α] {xs : List α} : (x :: xs).max? = foldl max x xs := rfl
+
+@[simp] theorem max?_cons [Max α] [Std.Associative (max : α → α → α)] {xs : List α} :
+    (x :: xs).max? = some (xs.max?.elim x (max x)) := by
+  cases xs <;> simp [max?_cons', foldl_assoc]
 
 @[simp] theorem max?_eq_none_iff {xs : List α} [Max α] : xs.max? = none ↔ xs = [] := by
   cases xs <;> simp [max?]
 
+theorem isSome_max?_of_mem {l : List α} [Max α] {a : α} (h : a ∈ l) :
+    l.max?.isSome := by
+  cases l <;> simp_all [List.max?_cons']
+
 theorem max?_mem [Max α] (min_eq_or : ∀ a b : α, max a b = a ∨ max a b = b) :
     {xs : List α} → xs.max? = some a → a ∈ xs
   | nil => by simp
@@ -126,7 +146,7 @@ theorem max?_le_iff [Max α] [LE α]
 
 -- This could be refactored by designing appropriate typeclasses to replace `le_refl`, `max_eq_or`,
 -- and `le_min_iff`.
-theorem max?_eq_some_iff [Max α] [LE α] [anti : Antisymm ((· : α) ≤ ·)]
+theorem max?_eq_some_iff [Max α] [LE α] [anti : Std.Antisymm ((· : α) ≤ ·)]
     (le_refl : ∀ a : α, a ≤ a)
     (max_eq_or : ∀ a b : α, max a b = a ∨ max a b = b)
     (max_le_iff : ∀ a b c : α, max b c ≤ a ↔ b ≤ a ∧ c ≤ a) {xs : List α} :
@@ -144,12 +164,16 @@ theorem max?_replicate [Max α] {n : Nat} {a : α} (w : max a a = a) :
     (replicate n a).max? = if n = 0 then none else some a := by
   induction n with
   | zero => rfl
-  | succ n ih => cases n <;> simp_all [replicate_succ, max?_cons]
+  | succ n ih => cases n <;> simp_all [replicate_succ, max?_cons']
 
 @[simp] theorem max?_replicate_of_pos [Max α] {n : Nat} {a : α} (w : max a a = a) (h : 0 < n) :
     (replicate n a).max? = some a := by
   simp [max?_replicate, Nat.ne_of_gt h, w]
 
+theorem foldl_max [Max α] [Std.IdempotentOp (max : α → α → α)] [Std.Associative (max : α → α → α)]
+    {l : List α} {a : α} : l.foldl (init := a) max = max a (l.max?.getD a) := by
+  cases l <;> simp [max?, foldl_assoc, Std.IdempotentOp.idempotent]
+
 @[deprecated min?_nil (since := "2024-09-29")] abbrev minimum?_nil := @min?_nil
 @[deprecated min?_cons (since := "2024-09-29")] abbrev minimum?_cons := @min?_cons
 @[deprecated min?_eq_none_iff (since := "2024-09-29")] abbrev mininmum?_eq_none_iff := @min?_eq_none_iff

src/Init/Data/List/Monadic.lean

@@ -99,4 +99,14 @@ theorem allM_eq_not_anyM_not [Monad m] [LawfulMonad m] (p : α → m Bool) (as :
     funext b
     split <;> simp_all
 
+/-! ### foldlM and foldrM -/
+
+theorem foldlM_map [Monad m] (f : β₁ → β₂) (g : α → β₂ → m α) (l : List β₁) (init : α) :
+    (l.map f).foldlM g init = l.foldlM (fun x y => g x (f y)) init := by
+  induction l generalizing g init <;> simp [*]
+
+theorem foldrM_map [Monad m] [LawfulMonad m] (f : β₁ → β₂) (g : β₂ → α → m α) (l : List β₁)
+    (init : α) : (l.map f).foldrM g init = l.foldrM (fun x y => g (f x) y) init := by
+  induction l generalizing g init <;> simp [*]
+
 end List

src/Init/Data/List/Nat.lean

@@ -12,3 +12,5 @@ import Init.Data.List.Nat.TakeDrop
 import Init.Data.List.Nat.Count
 import Init.Data.List.Nat.Erase
 import Init.Data.List.Nat.Find
+import Init.Data.List.Nat.BEq
+import Init.Data.List.Nat.Modify

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

@@ -0,0 +1,47 @@
+/-
+Copyright (c) 2024 Lean FRO All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kim Morrison
+-/
+prelude
+import Init.Data.Nat.Lemmas
+import Init.Data.List.Basic
+
+namespace List
+
+/-! ### isEqv-/
+
+theorem isEqv_eq_decide (a b : List α) (r) :
+    isEqv a b r = if h : a.length = b.length then
+      decide (∀ (i : Nat) (h' : i < a.length), r (a[i]'(h ▸ h')) (b[i]'(h ▸ h'))) else false := by
+  induction a generalizing b with
+  | nil =>
+    cases b <;> simp
+  | cons a as ih =>
+    cases b with
+    | nil => simp
+    | cons b bs =>
+      simp only [isEqv, ih, length_cons, Nat.add_right_cancel_iff]
+      split <;> simp [Nat.forall_lt_succ_left']
+
+/-! ### beq -/
+
+theorem beq_eq_isEqv [BEq α] (a b : List α) : a.beq b = isEqv a b (· == ·) := by
+  induction a generalizing b with
+  | nil =>
+    cases b <;> simp
+  | cons a as ih =>
+    cases b with
+    | nil => simp
+    | cons b bs =>
+      simp only [beq_cons₂, ih, isEqv_eq_decide, length_cons, Nat.add_right_cancel_iff,
+        Nat.forall_lt_succ_left', getElem_cons_zero, getElem_cons_succ, Bool.decide_and,
+        Bool.decide_eq_true]
+      split <;> simp
+
+theorem beq_eq_decide [BEq α] (a b : List α) :
+    (a == b) = if h : a.length = b.length then
+      decide (∀ (i : Nat) (h' : i < a.length), a[i] == b[i]'(h ▸ h')) else false := by
+  simp [BEq.beq, beq_eq_isEqv, isEqv_eq_decide]
+
+end List

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

@@ -96,75 +96,22 @@ theorem min?_eq_some_iff' {xs : List Nat} :
     (min_eq_or := fun _ _ => Nat.min_def .. ▸ by split <;> simp)
     (le_min_iff := fun _ _ _ => Nat.le_min)
 
--- This could be generalized,
--- but will first require further work on order typeclasses in the core repository.
-theorem min?_cons' {a : Nat} {l : List Nat} :
-    (a :: l).min? = some (match l.min? with
-    | none => a
-    | some m => min a m) := by
-  rw [min?_eq_some_iff']
-  split <;> rename_i h m
-  · simp_all
-  · rw [min?_eq_some_iff'] at m
-    obtain ⟨m, le⟩ := m
-    rw [Nat.min_def]
-    constructor
-    · split
-      · exact mem_cons_self a l
-      · exact mem_cons_of_mem a m
-    · intro b m
-      cases List.mem_cons.1 m with
-      | inl => split <;> omega
-      | inr h =>
-        specialize le b h
-        split <;> omega
-
-theorem foldl_min
-    {α : Type _} [Min α] [Std.IdempotentOp (min : α → α → α)] [Std.Associative (min : α → α → α)]
-    {l : List α} {a : α} :
-    l.foldl (init := a) min = min a (l.min?.getD a) := by
-  cases l with
-  | nil => simp [Std.IdempotentOp.idempotent]
-  | cons b l =>
-    simp only [min?]
-    induction l generalizing a b with
-    | nil => simp
-    | cons c l ih => simp [ih, Std.Associative.assoc]
-
-theorem foldl_min_right {α β : Type _}
-    [Min β] [Std.IdempotentOp (min : β → β → β)] [Std.Associative (min : β → β → β)]
-    {l : List α} {b : β} {f : α → β} :
-    (l.foldl (init := b) fun acc a => min acc (f a)) = min b ((l.map f).min?.getD b) := by
-  rw [← foldl_map, foldl_min]
-
-theorem foldl_min_le {l : List Nat} {a : Nat} : l.foldl (init := a) min ≤ a := by
-  induction l generalizing a with
-  | nil => simp
-  | cons c l ih =>
-    simp only [foldl_cons]
-    exact Nat.le_trans ih (Nat.min_le_left _ _)
-
-theorem foldl_min_min_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
-    l.foldl (init := a) min ≤ b :=
-  Nat.le_trans (foldl_min_le) h
-
-theorem min?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
-    l.min?.getD k ≤ a := by
-  cases l with
+theorem min?_get_le_of_mem {l : List Nat} {a : Nat} (h : a ∈ l) :
+    l.min?.get (isSome_min?_of_mem h) ≤ a := by
+  induction l with
   | nil => simp at h
-  | cons b l =>
-    simp [min?_cons]
-    simp at h
-    rcases h with (rfl | h)
-    · exact foldl_min_le
-    · induction l generalizing b with
-      | nil => simp_all
-      | cons c l ih =>
-        simp only [foldl_cons]
-        simp at h
-        rcases h with (rfl | h)
-        · exact foldl_min_min_of_le (Nat.min_le_right _ _)
-        · exact ih _ h
+  | cons b t ih =>
+    simp only [min?_cons, Option.get_some] at ih ⊢
+    rcases mem_cons.1 h with (rfl|h)
+    · cases t.min? with
+      | none => simp
+      | some b => simpa using Nat.min_le_left _ _
+    · obtain ⟨q, hq⟩ := Option.isSome_iff_exists.1 (isSome_min?_of_mem h)
+      simp only [hq, Option.elim_some] at ih ⊢
+      exact Nat.le_trans (Nat.min_le_right _ _) (ih h)
+
+theorem min?_getD_le_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) : l.min?.getD k ≤ a :=
+  Option.get_eq_getD _ ▸ min?_get_le_of_mem h
 
 /-! ### max? -/
 
@@ -176,75 +123,23 @@ theorem max?_eq_some_iff' {xs : List Nat} :
     (max_eq_or := fun _ _ => Nat.max_def .. ▸ by split <;> simp)
     (max_le_iff := fun _ _ _ => Nat.max_le)
 
--- This could be generalized,
--- but will first require further work on order typeclasses in the core repository.
-theorem max?_cons' {a : Nat} {l : List Nat} :
-    (a :: l).max? = some (match l.max? with
-    | none => a
-    | some m => max a m) := by
-  rw [max?_eq_some_iff']
-  split <;> rename_i h m
-  · simp_all
-  · rw [max?_eq_some_iff'] at m
-    obtain ⟨m, le⟩ := m
-    rw [Nat.max_def]
-    constructor
-    · split
-      · exact mem_cons_of_mem a m
-      · exact mem_cons_self a l
-    · intro b m
-      cases List.mem_cons.1 m with
-      | inl => split <;> omega
-      | inr h =>
-        specialize le b h
-        split <;> omega
-
-theorem foldl_max
-    {α : Type _} [Max α] [Std.IdempotentOp (max : α → α → α)] [Std.Associative (max : α → α → α)]
-    {l : List α} {a : α} :
-    l.foldl (init := a) max = max a (l.max?.getD a) := by
-  cases l with
-  | nil => simp [Std.IdempotentOp.idempotent]
-  | cons b l =>
-    simp only [max?]
-    induction l generalizing a b with
-    | nil => simp
-    | cons c l ih => simp [ih, Std.Associative.assoc]
-
-theorem foldl_max_right {α β : Type _}
-    [Max β] [Std.IdempotentOp (max : β → β → β)] [Std.Associative (max : β → β → β)]
-    {l : List α} {b : β} {f : α → β} :
-    (l.foldl (init := b) fun acc a => max acc (f a)) = max b ((l.map f).max?.getD b) := by
-  rw [← foldl_map, foldl_max]
-
-theorem le_foldl_max {l : List Nat} {a : Nat} : a ≤ l.foldl (init := a) max := by
-  induction l generalizing a with
-  | nil => simp
-  | cons c l ih =>
-    simp only [foldl_cons]
-    exact Nat.le_trans (Nat.le_max_left _ _) ih
-
-theorem le_foldl_max_of_le {l : List Nat} {a b : Nat} (h : a ≤ b) :
-    a ≤ l.foldl (init := b) max :=
-  Nat.le_trans h (le_foldl_max)
+theorem le_max?_get_of_mem {l : List Nat} {a : Nat} (h : a ∈ l) :
+    a ≤ l.max?.get (isSome_max?_of_mem h) := by
+  induction l with
+  | nil => simp at h
+  | cons b t ih =>
+    simp only [max?_cons, Option.get_some] at ih ⊢
+    rcases mem_cons.1 h with (rfl|h)
+    · cases t.max? with
+      | none => simp
+      | some b => simpa using Nat.le_max_left _ _
+    · obtain ⟨q, hq⟩ := Option.isSome_iff_exists.1 (isSome_max?_of_mem h)
+      simp only [hq, Option.elim_some] at ih ⊢
+      exact Nat.le_trans (ih h) (Nat.le_max_right _ _)
 
 theorem le_max?_getD_of_mem {l : List Nat} {a k : Nat} (h : a ∈ l) :
-    a ≤ l.max?.getD k := by
-  cases l with
-  | nil => simp at h
-  | cons b l =>
-    simp [max?_cons]
-    simp at h
-    rcases h with (rfl | h)
-    · exact le_foldl_max
-    · induction l generalizing b with
-      | nil => simp_all
-      | cons c l ih =>
-        simp only [foldl_cons]
-        simp at h
-        rcases h with (rfl | h)
-        · exact le_foldl_max_of_le (Nat.le_max_right b a)
-        · exact ih _ h
+    a ≤ l.max?.getD k :=
+  Option.get_eq_getD _ ▸ le_max?_get_of_mem h
 
 @[deprecated min?_eq_some_iff' (since := "2024-09-29")] abbrev minimum?_eq_some_iff' := @min?_eq_some_iff'
 @[deprecated min?_cons' (since := "2024-09-29")] abbrev minimum?_cons' := @min?_cons'

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

@@ -0,0 +1,102 @@
+/-
+Copyright (c) 2014 Parikshit Khanna. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, Mario Carneiro
+-/
+
+prelude
+import Init.Data.List.Nat.TakeDrop
+
+namespace List
+
+/-! ### modifyHead -/
+
+@[simp] theorem modifyHead_modifyHead (l : List α) (f g : α → α) :
+    (l.modifyHead f).modifyHead g = l.modifyHead (g ∘ f) := by cases l <;> simp [modifyHead]
+
+/-! ### modify -/
+
+@[simp] theorem modify_nil (f : α → α) (n) : [].modify f n = [] := by cases n <;> rfl
+
+@[simp] theorem modify_zero_cons (f : α → α) (a : α) (l : List α) :
+    (a :: l).modify f 0 = f a :: l := rfl
+
+@[simp] theorem modify_succ_cons (f : α → α) (a : α) (l : List α) (n) :
+    (a :: l).modify f (n + 1) = a :: l.modify f n := by rfl
+
+theorem modifyTailIdx_id : ∀ n (l : List α), l.modifyTailIdx id n = l
+  | 0, _ => rfl
+  | _+1, [] => rfl
+  | n+1, a :: l => congrArg (cons a) (modifyTailIdx_id n l)
+
+theorem eraseIdx_eq_modifyTailIdx : ∀ n (l : List α), eraseIdx l n = modifyTailIdx tail n l
+  | 0, l => by cases l <;> rfl
+  | _+1, [] => rfl
+  | _+1, _ :: _ => congrArg (cons _) (eraseIdx_eq_modifyTailIdx _ _)
+
+theorem getElem?_modify (f : α → α) :
+    ∀ n (l : List α) m, (modify f n l)[m]? = (fun a => if n = m then f a else a) <$> l[m]?
+  | n, l, 0 => by cases l <;> cases n <;> simp
+  | n, [], _+1 => by cases n <;> rfl
+  | 0, _ :: l, m+1 => by cases h : l[m]? <;> simp [h, modify, m.succ_ne_zero.symm]
+  | n+1, a :: l, m+1 => by
+    simp only [modify_succ_cons, getElem?_cons_succ, Nat.reduceEqDiff, Option.map_eq_map]
+    refine (getElem?_modify f n l m).trans ?_
+    cases h' : l[m]? <;> by_cases h : n = m <;>
+      simp [h, if_pos, if_neg, Option.map, mt Nat.succ.inj, not_false_iff, h']
+
+@[simp] theorem length_modifyTailIdx (f : List α → List α) (H : ∀ l, length (f l) = length l) :
+    ∀ n l, length (modifyTailIdx f n l) = length l
+  | 0, _ => H _
+  | _+1, [] => rfl
+  | _+1, _ :: _ => congrArg (·+1) (length_modifyTailIdx _ H _ _)
+
+theorem modifyTailIdx_add (f : List α → List α) (n) (l₁ l₂ : List α) :
+    modifyTailIdx f (l₁.length + n) (l₁ ++ l₂) = l₁ ++ modifyTailIdx f n l₂ := by
+  induction l₁ <;> simp [*, Nat.succ_add]
+
+@[simp] theorem length_modify (f : α → α) : ∀ n l, length (modify f n l) = length l :=
+  length_modifyTailIdx _ fun l => by cases l <;> rfl
+
+@[simp] theorem getElem?_modify_eq (f : α → α) (n) (l : List α) :
+    (modify f n l)[n]? = f <$> l[n]? := by
+  simp only [getElem?_modify, if_pos]
+
+@[simp] theorem getElem?_modify_ne (f : α → α) {m n} (l : List α) (h : m ≠ n) :
+    (modify f m l)[n]? = l[n]? := by
+  simp only [getElem?_modify, if_neg h, id_map']
+
+theorem getElem_modify (f : α → α) (n) (l : List α) (m) (h : m < (modify f n l).length) :
+    (modify f n l)[m] =
+      if n = m then f (l[m]'(by simp at h; omega)) else l[m]'(by simp at h; omega) := by
+  rw [getElem_eq_iff, getElem?_modify]
+  simp at h
+  simp [h]
+
+theorem modifyTailIdx_eq_take_drop (f : List α → List α) (H : f [] = []) :
+    ∀ n l, modifyTailIdx f n l = take n l ++ f (drop n l)
+  | 0, _ => rfl
+  | _ + 1, [] => H.symm
+  | n + 1, b :: l => congrArg (cons b) (modifyTailIdx_eq_take_drop f H n l)
+
+theorem modify_eq_take_drop (f : α → α) :
+    ∀ n l, modify f n l = take n l ++ modifyHead f (drop n l) :=
+  modifyTailIdx_eq_take_drop _ rfl
+
+theorem modify_eq_take_cons_drop (f : α → α) {n l} (h : n < length l) :
+    modify f n l = take n l ++ f l[n] :: drop (n + 1) l := by
+  rw [modify_eq_take_drop, drop_eq_getElem_cons h]; rfl
+
+theorem exists_of_modifyTailIdx (f : List α → List α) {n} {l : List α} (h : n ≤ l.length) :
+    ∃ l₁ l₂, l = l₁ ++ l₂ ∧ l₁.length = n ∧ modifyTailIdx f n l = l₁ ++ f l₂ :=
+  have ⟨_, _, eq, hl⟩ : ∃ l₁ l₂, l = l₁ ++ l₂ ∧ l₁.length = n :=
+    ⟨_, _, (take_append_drop n l).symm, length_take_of_le h⟩
+  ⟨_, _, eq, hl, hl ▸ eq ▸ modifyTailIdx_add (n := 0) ..⟩
+
+theorem exists_of_modify (f : α → α) {n} {l : List α} (h : n < l.length) :
+    ∃ l₁ a l₂, l = l₁ ++ a :: l₂ ∧ l₁.length = n ∧ modify f n l = l₁ ++ f a :: l₂ :=
+  match exists_of_modifyTailIdx _ (Nat.le_of_lt h) with
+  | ⟨_, _::_, eq, hl, H⟩ => ⟨_, _, _, eq, hl, H⟩
+  | ⟨_, [], eq, hl, _⟩ => nomatch Nat.ne_of_gt h (eq ▸ append_nil _ ▸ hl)
+
+end List

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

@@ -500,4 +500,13 @@ theorem enum_eq_zip_range (l : List α) : l.enum = (range l.length).zip l :=
 theorem unzip_enum_eq_prod (l : List α) : l.enum.unzip = (range l.length, l) := by
   simp only [enum_eq_zip_range, unzip_zip, length_range]
 
+theorem enum_eq_cons_iff {l : List α} :
+    l.enum = x :: l' ↔ ∃ a as, l = a :: as ∧ x = (0, a) ∧ l' = enumFrom 1 as := by
+  rw [enum, enumFrom_eq_cons_iff]
+
+theorem enum_eq_append_iff {l : List α} :
+    l.enum = l₁ ++ l₂ ↔
+      ∃ l₁' l₂', l = l₁' ++ l₂' ∧ l₁ = l₁'.enum ∧ l₂ = l₂'.enumFrom l₁'.length := by
+  simp [enum, enumFrom_eq_append_iff]
+
 end List

src/Init/Data/List/Pairwise.lean

@@ -160,21 +160,25 @@ theorem pairwise_middle {R : α → α → Prop} (s : ∀ {x y}, R x y → R y x
   rw [← append_assoc, pairwise_append, @pairwise_append _ _ ([a] ++ l₁), pairwise_append_comm s]
   simp only [mem_append, or_comm]
 
-theorem pairwise_join {L : List (List α)} :
-    Pairwise R (join L) ↔
+theorem pairwise_flatten {L : List (List α)} :
+    Pairwise R (flatten L) ↔
       (∀ l ∈ L, Pairwise R l) ∧ Pairwise (fun l₁ l₂ => ∀ x ∈ l₁, ∀ y ∈ l₂, R x y) L := by
   induction L with
   | nil => simp
   | cons l L IH =>
-    simp only [join, pairwise_append, IH, mem_join, exists_imp, and_imp, forall_mem_cons,
+    simp only [flatten, pairwise_append, IH, mem_flatten, exists_imp, and_imp, forall_mem_cons,
       pairwise_cons, and_assoc, and_congr_right_iff]
     rw [and_comm, and_congr_left_iff]
     intros; exact ⟨fun h a b c d e => h c d e a b, fun h c d e a b => h a b c d e⟩
 
-theorem pairwise_bind {R : β → β → Prop} {l : List α} {f : α → List β} :
-    List.Pairwise R (l.bind f) ↔
+@[deprecated pairwise_flatten (since := "2024-10-14")] abbrev pairwise_join := @pairwise_flatten
+
+theorem pairwise_flatMap {R : β → β → Prop} {l : List α} {f : α → List β} :
+    List.Pairwise R (l.flatMap f) ↔
       (∀ a ∈ l, Pairwise R (f a)) ∧ Pairwise (fun a₁ a₂ => ∀ x ∈ f a₁, ∀ y ∈ f a₂, R x y) l := by
-  simp [List.bind, pairwise_join, pairwise_map]
+  simp [List.flatMap, pairwise_flatten, pairwise_map]
+
+@[deprecated pairwise_flatMap (since := "2024-10-14")] abbrev pairwise_bind := @pairwise_flatMap
 
 theorem pairwise_reverse {l : List α} :
     l.reverse.Pairwise R ↔ l.Pairwise (fun a b => R b a) := by

src/Init/Data/List/Perm.lean

@@ -461,15 +461,19 @@ theorem Perm.nodup {l l' : List α} (hl : l ~ l') (hR : l.Nodup) : l'.Nodup := h
 theorem Perm.nodup_iff {l₁ l₂ : List α} : l₁ ~ l₂ → (Nodup l₁ ↔ Nodup l₂) :=
   Perm.pairwise_iff <| @Ne.symm α
 
-theorem Perm.join {l₁ l₂ : List (List α)} (h : l₁ ~ l₂) : l₁.join ~ l₂.join := by
+theorem Perm.flatten {l₁ l₂ : List (List α)} (h : l₁ ~ l₂) : l₁.flatten ~ l₂.flatten := by
   induction h with
   | nil => rfl
-  | cons _ _ ih => simp only [join_cons, perm_append_left_iff, ih]
-  | swap => simp only [join_cons, ← append_assoc, perm_append_right_iff]; exact perm_append_comm ..
+  | cons _ _ ih => simp only [flatten_cons, perm_append_left_iff, ih]
+  | swap => simp only [flatten_cons, ← append_assoc, perm_append_right_iff]; exact perm_append_comm ..
   | trans _ _ ih₁ ih₂ => exact trans ih₁ ih₂
 
-theorem Perm.bind_right {l₁ l₂ : List α} (f : α → List β) (p : l₁ ~ l₂) : l₁.bind f ~ l₂.bind f :=
-  (p.map _).join
+@[deprecated Perm.flatten (since := "2024-10-14")] abbrev Perm.join := @Perm.flatten
+
+theorem Perm.flatMap_right {l₁ l₂ : List α} (f : α → List β) (p : l₁ ~ l₂) : l₁.flatMap f ~ l₂.flatMap f :=
+  (p.map _).flatten
+
+@[deprecated Perm.flatMap_right (since := "2024-10-16")] abbrev Perm.bind_right := @Perm.flatMap_right
 
 theorem Perm.eraseP (f : α → Bool) {l₁ l₂ : List α}
     (H : Pairwise (fun a b => f a → f b → False) l₁) (p : l₁ ~ l₂) : eraseP f l₁ ~ eraseP f l₂ := by

src/Init/Data/List/Range.lean

@@ -20,7 +20,6 @@ open Nat
 
 /-! ## Ranges and enumeration -/
 
-
 /-! ### range' -/
 
 theorem range'_succ (s n step) : range' s (n + 1) step = s :: range' (s + step) n step := by

src/Init/Data/List/Sublist.lean

@@ -483,30 +483,30 @@ theorem sublist_replicate_iff : l <+ replicate m a ↔ ∃ n, n ≤ m ∧ l = re
       rw [w]
       exact (replicate_sublist_replicate a).2 le
 
-theorem sublist_join_of_mem {L : List (List α)} {l} (h : l ∈ L) : l <+ L.join := by
+theorem sublist_flatten_of_mem {L : List (List α)} {l} (h : l ∈ L) : l <+ L.flatten := by
   induction L with
   | nil => cases h
   | cons l' L ih =>
     rcases mem_cons.1 h with (rfl | h)
     · simp [h]
-    · simp [ih h, join_cons, sublist_append_of_sublist_right]
+    · simp [ih h, flatten_cons, sublist_append_of_sublist_right]
 
-theorem sublist_join_iff {L : List (List α)} {l} :
-    l <+ L.join ↔
-      ∃ L' : List (List α), l = L'.join ∧ ∀ i (_ : i < L'.length), L'[i] <+ L[i]?.getD [] := by
+theorem sublist_flatten_iff {L : List (List α)} {l} :
+    l <+ L.flatten ↔
+      ∃ L' : List (List α), l = L'.flatten ∧ ∀ i (_ : i < L'.length), L'[i] <+ L[i]?.getD [] := by
   induction L generalizing l with
   | nil =>
     constructor
     · intro w
-      simp only [join_nil, sublist_nil] at w
+      simp only [flatten_nil, sublist_nil] at w
       subst w
       exact ⟨[], by simp, fun i x => by cases x⟩
     · rintro ⟨L', rfl, h⟩
-      simp only [join_nil, sublist_nil, join_eq_nil_iff]
+      simp only [flatten_nil, sublist_nil, flatten_eq_nil_iff]
       simp only [getElem?_nil, Option.getD_none, sublist_nil] at h
       exact (forall_getElem (p := (· = []))).1 h
   | cons l' L ih =>
-    simp only [join_cons, sublist_append_iff, ih]
+    simp only [flatten_cons, sublist_append_iff, ih]
     constructor
     · rintro ⟨l₁, l₂, rfl, s, L', rfl, h⟩
       refine ⟨l₁ :: L', by simp, ?_⟩
@@ -517,21 +517,21 @@ theorem sublist_join_iff {L : List (List α)} {l} :
       | nil =>
         exact ⟨[], [], by simp, by simp, [], by simp, fun i x => by cases x⟩
       | cons l₁ L' =>
-        exact ⟨l₁, L'.join, by simp, by simpa using h 0 (by simp), L', rfl,
+        exact ⟨l₁, L'.flatten, by simp, by simpa using h 0 (by simp), L', rfl,
           fun i lt => by simpa using h (i+1) (Nat.add_lt_add_right lt 1)⟩
 
-theorem join_sublist_iff {L : List (List α)} {l} :
-    L.join <+ l ↔
-      ∃ L' : List (List α), l = L'.join ∧ ∀ i (_ : i < L.length), L[i] <+ L'[i]?.getD [] := by
+theorem flatten_sublist_iff {L : List (List α)} {l} :
+    L.flatten <+ l ↔
+      ∃ L' : List (List α), l = L'.flatten ∧ ∀ i (_ : i < L.length), L[i] <+ L'[i]?.getD [] := by
   induction L generalizing l with
   | nil =>
     constructor
     · intro _
       exact ⟨[l], by simp, fun i x => by cases x⟩
     · rintro ⟨L', rfl, _⟩
-      simp only [join_nil, nil_sublist]
+      simp only [flatten_nil, nil_sublist]
   | cons l' L ih =>
-    simp only [join_cons, append_sublist_iff, ih]
+    simp only [flatten_cons, append_sublist_iff, ih]
     constructor
     · rintro ⟨l₁, l₂, rfl, s, L', rfl, h⟩
       refine ⟨l₁ :: L', by simp, ?_⟩
@@ -543,7 +543,7 @@ theorem join_sublist_iff {L : List (List α)} {l} :
         exact ⟨[], [], by simp, by simpa using h 0 (by simp), [], by simp,
           fun i x => by simpa using h (i+1) (Nat.add_lt_add_right x 1)⟩
       | cons l₁ L' =>
-        exact ⟨l₁, L'.join, by simp, by simpa using h 0 (by simp), L', rfl,
+        exact ⟨l₁, L'.flatten, by simp, by simpa using h 0 (by simp), L', rfl,
           fun i lt => by simpa using h (i+1) (Nat.add_lt_add_right lt 1)⟩
 
 @[simp] theorem isSublist_iff_sublist [BEq α] [LawfulBEq α] {l₁ l₂ : List α} :
@@ -938,14 +938,14 @@ theorem isInfix_replicate_iff {n} {a : α} {l : List α} :
     · simpa using Nat.sub_add_cancel h
     · simpa using w
 
-theorem infix_of_mem_join : ∀ {L : List (List α)}, l ∈ L → l <:+: join L
+theorem infix_of_mem_flatten : ∀ {L : List (List α)}, l ∈ L → l <:+: flatten L
   | l' :: _, h =>
     match h with
     | List.Mem.head .. => infix_append [] _ _
     | List.Mem.tail _ hlMemL =>
-      IsInfix.trans (infix_of_mem_join hlMemL) <| (suffix_append _ _).isInfix
+      IsInfix.trans (infix_of_mem_flatten hlMemL) <| (suffix_append _ _).isInfix
 
-theorem prefix_append_right_inj (l) : l ++ l₁ <+: l ++ l₂ ↔ l₁ <+: l₂ :=
+@[simp] theorem prefix_append_right_inj (l) : l ++ l₁ <+: l ++ l₂ ↔ l₁ <+: l₂ :=
   exists_congr fun r => by rw [append_assoc, append_right_inj]
 
 theorem prefix_cons_inj (a) : a :: l₁ <+: a :: l₂ ↔ l₁ <+: l₂ :=
@@ -976,7 +976,7 @@ theorem mem_of_mem_drop {n} {l : List α} (h : a ∈ l.drop n) : a ∈ l :=
   drop_subset _ _ h
 
 theorem drop_suffix_drop_left (l : List α) {m n : Nat} (h : m ≤ n) : drop n l <:+ drop m l := by
-  rw [← Nat.sub_add_cancel h, ← drop_drop]
+  rw [← Nat.sub_add_cancel h, Nat.add_comm, ← drop_drop]
   apply drop_suffix
 
 -- See `Init.Data.List.Nat.TakeDrop` for `take_prefix_take_left`.
@@ -1087,4 +1087,11 @@ theorem prefix_iff_eq_take : l₁ <+: l₂ ↔ l₁ = take (length l₁) l₂ :=
 
 -- See `Init.Data.List.Nat.Sublist` for `suffix_iff_eq_append`, `prefix_take_iff`, and `suffix_iff_eq_drop`.
 
+/-! ### Deprecations -/
+
+@[deprecated sublist_flatten_of_mem (since := "2024-10-14")] abbrev sublist_join_of_mem := @sublist_flatten_of_mem
+@[deprecated sublist_flatten_iff (since := "2024-10-14")] abbrev sublist_join_iff := @sublist_flatten_iff
+@[deprecated flatten_sublist_iff (since := "2024-10-14")] abbrev flatten_join_iff := @flatten_sublist_iff
+@[deprecated infix_of_mem_flatten (since := "2024-10-14")] abbrev infix_of_mem_join := @infix_of_mem_flatten
+
 end List

src/Init/Data/List/TakeDrop.lean

@@ -97,14 +97,14 @@ theorem get?_take {l : List α} {n m : Nat} (h : m < n) : (l.take n).get? m = l.
 
 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 (n + m) l
+@[simp] theorem drop_drop (n : Nat) : ∀ (m) (l : List α), drop n (drop m l) = drop (m + n) l
   | m, [] => by simp
   | 0, l => by simp
   | m + 1, a :: l =>
     calc
       drop n (drop (m + 1) (a :: l)) = drop n (drop m l) := rfl
-      _ = drop (n + m) l := drop_drop n m l
-      _ = drop (n + (m + 1)) (a :: l) := rfl
+      _ = drop (m + n) l := drop_drop n m l
+      _ = drop ((m + 1) + n) (a :: l) := by rw [Nat.add_right_comm]; rfl
 
 theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (take (m + n) l)
   | 0, _, _ => by simp
@@ -112,7 +112,7 @@ theorem take_drop : ∀ (m n : Nat) (l : List α), take n (drop m l) = drop m (t
   | _+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 m (drop n l) := by
+theorem drop_add (m n) (l : List α) : drop (m + n) l = drop n (drop m l) := by
   simp [drop_drop]
 
 @[simp]
@@ -126,7 +126,7 @@ theorem tail_drop (l : List α) (n : Nat) : (l.drop n).tail = l.drop (n + 1) :=
 
 @[simp]
 theorem drop_tail (l : List α) (n : Nat) : l.tail.drop n = l.drop (n + 1) := by
-  rw [← drop_drop, drop_one]
+  rw [Nat.add_comm, ← drop_drop, drop_one]
 
 @[simp]
 theorem drop_eq_nil_iff {l : List α} {k : Nat} : l.drop k = [] ↔ l.length ≤ k := by

src/Init/Data/List/ToArray.lean

@@ -0,0 +1,23 @@
+/-
+Copyright (c) 2024 Lean FRO. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Henrik Böving
+-/
+prelude
+import Init.Data.List.Basic
+
+/--
+Auxiliary definition for `List.toArray`.
+`List.toArrayAux as r = r ++ as.toArray`
+-/
+@[inline_if_reduce]
+def List.toArrayAux : List α → Array α → Array α
+  | nil,       r => r
+  | cons a as, r => toArrayAux as (r.push a)
+
+/-- Convert a `List α` into an `Array α`. This is O(n) in the length of the list.  -/
+-- This function is exported to C, where it is called by `Array.mk`
+-- (the constructor) to implement this functionality.
+@[inline, match_pattern, pp_nodot, export lean_list_to_array]
+def List.toArrayImpl (as : List α) : Array α :=
+  as.toArrayAux (Array.mkEmpty as.length)

src/Init/Data/List/Zip.lean

@@ -5,6 +5,7 @@ Authors: Parikshit Khanna, Jeremy Avigad, Leonardo de Moura, Floris van Doorn, M
 -/
 prelude
 import Init.Data.List.TakeDrop
+import Init.Data.Function
 
 /-!
 # Lemmas about `List.zip`, `List.zipWith`, `List.zipWithAll`, and `List.unzip`.
@@ -238,6 +239,14 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {l₁ : List α} {l₂ : Li
   | zero => rfl
   | succ n ih => simp [replicate_succ, ih]
 
+theorem map_uncurry_zip_eq_zipWith (f : α → β → γ) (l : List α) (l' : List β) :
+    map (Function.uncurry f) (l.zip l') = zipWith f l l' := by
+  rw [zip]
+  induction l generalizing l' with
+  | nil => simp
+  | cons hl tl ih =>
+    cases l' <;> simp [ih]
+
 /-! ### zip -/
 
 theorem zip_eq_zipWith : ∀ (l₁ : List α) (l₂ : List β), zip l₁ l₂ = zipWith Prod.mk l₁ l₂

src/Init/Data/Nat/Basic.lean

@@ -131,7 +131,7 @@ theorem or_exists_add_one : p 0 ∨ (Exists fun n => p (n + 1)) ↔ Exists p :=
 @[simp] theorem blt_eq : (Nat.blt x y = true) = (x < y) := propext <| Iff.intro Nat.le_of_ble_eq_true Nat.ble_eq_true_of_le
 
 instance : LawfulBEq Nat where
-  eq_of_beq h := Nat.eq_of_beq_eq_true h
+  eq_of_beq h := by simpa using h
   rfl := by simp [BEq.beq]
 
 theorem beq_eq_true_eq (a b : Nat) : ((a == b) = true) = (a = b) := by simp
@@ -490,10 +490,10 @@ protected theorem le_antisymm_iff {a b : Nat} : a = b ↔ a ≤ b ∧ b ≤ a :=
             (fun ⟨hle, hge⟩ => Nat.le_antisymm hle hge)
 protected theorem eq_iff_le_and_ge : ∀{a b : Nat}, a = b ↔ a ≤ b ∧ b ≤ a := @Nat.le_antisymm_iff
 
-instance : Antisymm ( . ≤ . : Nat → Nat → Prop) where
+instance : Std.Antisymm ( . ≤ . : Nat → Nat → Prop) where
   antisymm h₁ h₂ := Nat.le_antisymm h₁ h₂
 
-instance : Antisymm (¬ . < . : Nat → Nat → Prop) where
+instance : Std.Antisymm (¬ . < . : Nat → Nat → Prop) where
   antisymm h₁ h₂ := Nat.le_antisymm (Nat.ge_of_not_lt h₂) (Nat.ge_of_not_lt h₁)
 
 protected theorem add_le_add_left {n m : Nat} (h : n ≤ m) (k : Nat) : k + n ≤ k + m :=
@@ -796,6 +796,8 @@ theorem pos_pow_of_pos {n : Nat} (m : Nat) (h : 0 < n) : 0 < n^m :=
   | zero => cases h
   | succ n => simp [Nat.pow_succ]
 
+protected theorem two_pow_pos (w : Nat) : 0 < 2^w := Nat.pos_pow_of_pos _ (by decide)
+
 instance {n m : Nat} [NeZero n] : NeZero (n^m) :=
   ⟨Nat.ne_zero_iff_zero_lt.mpr (Nat.pos_pow_of_pos m (pos_of_neZero _))⟩
 

src/Init/Data/Nat/Lemmas.lean

@@ -32,6 +32,77 @@ namespace Nat
 @[simp] theorem exists_add_one_eq : (∃ n, n + 1 = a) ↔ 0 < a :=
   ⟨fun ⟨n, h⟩ => by omega, fun h => ⟨a - 1, by omega⟩⟩
 
+/-- Dependent variant of `forall_lt_succ_right`. -/
+theorem forall_lt_succ_right' {p : (m : Nat) → (m < n + 1) → Prop} :
+    (∀ m (h : m < n + 1), p m h) ↔ (∀ m (h : m < n), p m (by omega)) ∧ p n (by omega) := by
+  simp only [Nat.lt_succ_iff, Nat.le_iff_lt_or_eq]
+  constructor
+  · intro w
+    constructor
+    · intro m h
+      exact w _ (.inl h)
+    · exact w _ (.inr rfl)
+  · rintro w m (h|rfl)
+    · exact w.1 _ h
+    · exact w.2
+
+/-- See `forall_lt_succ_right'` for a variant where `p` takes the bound as an argument. -/
+theorem forall_lt_succ_right {p : Nat → Prop} :
+    (∀ m, m < n + 1 → p m) ↔ (∀ m, m < n → p m) ∧ p n := by
+  simpa using forall_lt_succ_right' (p := fun m _ => p m)
+
+/-- Dependent variant of `forall_lt_succ_left`. -/
+theorem forall_lt_succ_left' {p : (m : Nat) → (m < n + 1) → Prop} :
+    (∀ m (h : m < n + 1), p m h) ↔ p 0 (by omega) ∧ (∀ m (h : m < n), p (m + 1) (by omega)) := by
+  constructor
+  · intro w
+    constructor
+    · exact w 0 (by omega)
+    · intro m h
+      exact w (m + 1) (by omega)
+  · rintro ⟨h₀, h₁⟩ m h
+    cases m with
+    | zero => exact h₀
+    | succ m => exact h₁ m (by omega)
+
+/-- See `forall_lt_succ_left'` for a variant where `p` takes the bound as an argument. -/
+theorem forall_lt_succ_left {p : Nat → Prop} :
+    (∀ m, m < n + 1 → p m) ↔ p 0 ∧ (∀ m, m < n → p (m + 1)) := by
+  simpa using forall_lt_succ_left' (p := fun m _ => p m)
+
+/-- Dependent variant of `exists_lt_succ_right`. -/
+theorem exists_lt_succ_right' {p : (m : Nat) → (m < n + 1) → Prop} :
+    (∃ m, ∃ (h : m < n + 1), p m h) ↔ (∃ m, ∃ (h : m < n), p m (by omega)) ∨ p n (by omega) := by
+  simp only [Nat.lt_succ_iff, Nat.le_iff_lt_or_eq]
+  constructor
+  · rintro ⟨m, (h|rfl), w⟩
+    · exact .inl ⟨m, h, w⟩
+    · exact .inr w
+  · rintro (⟨m, h, w⟩ | w)
+    · exact ⟨m, by omega, w⟩
+    · exact ⟨n, by omega, w⟩
+
+/-- See `exists_lt_succ_right'` for a variant where `p` takes the bound as an argument. -/
+theorem exists_lt_succ_right {p : Nat → Prop} :
+    (∃ m, m < n + 1 ∧ p m) ↔ (∃ m, m < n ∧ p m) ∨ p n := by
+  simpa using exists_lt_succ_right' (p := fun m _ => p m)
+
+/-- Dependent variant of `exists_lt_succ_left`. -/
+theorem exists_lt_succ_left' {p : (m : Nat) → (m < n + 1) → Prop} :
+    (∃ m, ∃ (h : m < n + 1), p m h) ↔ p 0 (by omega) ∨ (∃ m, ∃ (h : m < n), p (m + 1) (by omega)) := by
+  constructor
+  · rintro ⟨_|m, h, w⟩
+    · exact .inl w
+    · exact .inr ⟨m, by omega, w⟩
+  · rintro (w|⟨m, h, w⟩)
+    · exact ⟨0, by omega, w⟩
+    · exact ⟨m + 1, by omega, w⟩
+
+/-- See `exists_lt_succ_left'` for a variant where `p` takes the bound as an argument. -/
+theorem exists_lt_succ_left {p : Nat → Prop} :
+    (∃ m, m < n + 1 ∧ p m) ↔ p 0 ∨ (∃ m, m < n ∧ p (m + 1)) := by
+  simpa using exists_lt_succ_left' (p := fun m _ => p m)
+
 /-! ## add -/
 
 protected theorem add_add_add_comm (a b c d : Nat) : (a + b) + (c + d) = (a + c) + (b + d) := by

src/Init/Data/Nat/Power2.lean

@@ -8,8 +8,6 @@ import Init.Data.Nat.Linear
 
 namespace Nat
 
-protected theorem two_pow_pos (w : Nat) : 0 < 2^w := Nat.pos_pow_of_pos _ (by decide)
-
 theorem nextPowerOfTwo_dec {n power : Nat} (h₁ : power > 0) (h₂ : power < n) : n - power * 2 < n - power := by
   have : power * 2 = power + power := by simp_arith
   rw [this, Nat.sub_add_eq]

src/Init/Data/OfScientific.lean

@@ -10,8 +10,10 @@ import Init.Data.Nat.Log2
 
 /-- For decimal and scientific numbers (e.g., `1.23`, `3.12e10`).
    Examples:
-   - `OfScientific.ofScientific 123 true 2`    represents `1.23`
-   - `OfScientific.ofScientific 121 false 100` represents `121e100`
+   - `1.23` is syntax for `OfScientific.ofScientific (nat_lit 123) true (nat_lit 2)`
+   - `121e100` is syntax for `OfScientific.ofScientific (nat_lit 121) false (nat_lit 100)`
+
+   Note the use of `nat_lit`; there is no wrapping `OfNat.ofNat` in the resulting term.
 -/
 class OfScientific (α : Type u) where
   ofScientific (mantissa : Nat) (exponentSign : Bool) (decimalExponent : Nat) : α

src/Init/Data/Option/Attach.lean

@@ -44,7 +44,7 @@ theorem attach_congr {o₁ o₂ : Option α} (h : o₁ = o₂) :
   simp
 
 theorem attachWith_congr {o₁ o₂ : Option α} (w : o₁ = o₂) {P : α → Prop} {H : ∀ x ∈ o₁, P x} :
-    o₁.attachWith P H = o₂.attachWith P fun x h => H _ (w ▸ h) := by
+    o₁.attachWith P H = o₂.attachWith P fun _ h => H _ (w ▸ h) := by
   subst w
   simp
 
@@ -128,12 +128,12 @@ theorem attach_map {o : Option α} (f : α → β) :
   cases o <;> simp
 
 theorem attachWith_map {o : Option α} (f : α → β) {P : β → Prop} {H : ∀ (b : β), b ∈ o.map f → P b} :
-    (o.map f).attachWith P H = (o.attachWith (P ∘ f) (fun a h => H _ (mem_map_of_mem f h))).map
+    (o.map f).attachWith P H = (o.attachWith (P ∘ f) (fun _ h => H _ (mem_map_of_mem f h))).map
       fun ⟨x, h⟩ => ⟨f x, h⟩ := by
   cases o <;> simp
 
 theorem map_attach {o : Option α} (f : { x // x ∈ o } → β) :
-    o.attach.map f = o.pmap (fun a (h : a ∈ o) => f ⟨a, h⟩) (fun a h => h) := by
+    o.attach.map f = o.pmap (fun a (h : a ∈ o) => f ⟨a, h⟩) (fun _ h => h) := by
   cases o <;> simp
 
 theorem map_attachWith {o : Option α} {P : α → Prop} {H : ∀ (a : α), a ∈ o → P a}
@@ -175,4 +175,68 @@ theorem filter_attach {o : Option α} {p : {x // x ∈ o} → Bool} :
     o.attach.filter p = o.pbind fun a h => if p ⟨a, h⟩ then some ⟨a, h⟩ else none := by
   cases o <;> simp [filter_some]
 
+/-! ## unattach
+
+`Option.unattach` is the (one-sided) inverse of `Option.attach`. It is a synonym for `Option.map Subtype.val`.
+
+We use it by providing a simp lemma `l.attach.unattach = l`, and simp lemmas which recognize higher order
+functions applied to `l : Option { x // p x }` which only depend on the value, not the predicate, and rewrite these
+in terms of a simpler function applied to `l.unattach`.
+
+Further, we provide simp lemmas that push `unattach` inwards.
+-/
+
+/--
+A synonym for `l.map (·.val)`. Mostly this should not be needed by users.
+It is introduced as an intermediate step by lemmas such as `map_subtype`,
+and is ideally subsequently simplified away by `unattach_attach`.
+
+If not, usually the right approach is `simp [Option.unattach, -Option.map_subtype]` to unfold.
+-/
+def unattach {α : Type _} {p : α → Prop} (o : Option { x // p x }) := o.map (·.val)
+
+@[simp] theorem unattach_none {p : α → Prop} : (none : Option { x // p x }).unattach = none := rfl
+@[simp] theorem unattach_some {p : α → Prop} {a : { x // p x }} :
+  (some a).unattach = a.val := rfl
+
+@[simp] theorem isSome_unattach {p : α → Prop} {o : Option { x // p x }} :
+    o.unattach.isSome = o.isSome := by
+  simp [unattach]
+
+@[simp] theorem isNone_unattach {p : α → Prop} {o : Option { x // p x }} :
+    o.unattach.isNone = o.isNone := by
+  simp [unattach]
+
+@[simp] theorem unattach_attach (o : Option α) : o.attach.unattach = o := by
+  cases o <;> simp
+
+@[simp] theorem unattach_attachWith {p : α → Prop} {o : Option α}
+    {H : ∀ a ∈ o, p a} :
+    (o.attachWith p H).unattach = o := by
+  cases o <;> simp
+
+/-! ### Recognizing higher order functions on subtypes using a function that only depends on the value. -/
+
+/--
+This lemma identifies maps over lists of subtypes, where the function only depends on the value, not the proposition,
+and simplifies these to the function directly taking the value.
+-/
+@[simp] theorem map_subtype {p : α → Prop} {o : Option { x // p x }}
+    {f : { x // p x } → β} {g : α → β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    o.map f = o.unattach.map g := by
+  cases o <;> simp [hf]
+
+@[simp] theorem bind_subtype {p : α → Prop} {o : Option { x // p x }}
+    {f : { x // p x } → Option β} {g : α → Option β} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    (o.bind f) = o.unattach.bind g := by
+  cases o <;> simp [hf]
+
+@[simp] theorem unattach_filter {p : α → Prop} {o : Option { x // p x }}
+    {f : { x // p x } → Bool} {g : α → Bool} {hf : ∀ x h, f ⟨x, h⟩ = g x} :
+    (o.filter f).unattach = o.unattach.filter g := by
+  cases o
+  · simp
+  · simp only [filter_some, hf, unattach_some]
+    split <;> simp
+
 end Option

src/Init/Data/Option/Lemmas.lean

@@ -79,7 +79,7 @@ theorem eq_none_iff_forall_not_mem : o = none ↔ ∀ a, a ∉ o :=
 
 theorem isSome_iff_exists : isSome x ↔ ∃ a, x = some a := by cases x <;> simp [isSome]
 
-@[simp] theorem isSome_eq_isSome : (isSome x = isSome y) ↔ (x = none ↔ y = none) := by
+theorem isSome_eq_isSome : (isSome x = isSome y) ↔ (x = none ↔ y = none) := by
   cases x <;> cases y <;> simp
 
 @[simp] theorem isNone_none : @isNone α none = true := rfl

src/Init/Data/Prod.lean

@@ -7,6 +7,8 @@ prelude
 import Init.SimpLemmas
 import Init.NotationExtra
 
+namespace Prod
+
 instance [BEq α] [BEq β] [LawfulBEq α] [LawfulBEq β] : LawfulBEq (α × β) where
   eq_of_beq {a b} (h : a.1 == b.1 && a.2 == b.2) := by
     cases a; cases b
@@ -14,9 +16,65 @@ instance [BEq α] [BEq β] [LawfulBEq α] [LawfulBEq β] : LawfulBEq (α × β)
   rfl {a} := by cases a; simp [BEq.beq, LawfulBEq.rfl]
 
 @[simp]
-protected theorem Prod.forall {p : α × β → Prop} : (∀ x, p x) ↔ ∀ a b, p (a, b) :=
+protected theorem «forall» {p : α × β → Prop} : (∀ x, p x) ↔ ∀ a b, p (a, b) :=
   ⟨fun h a b ↦ h (a, b), fun h ⟨a, b⟩ ↦ h a b⟩
 
 @[simp]
-protected theorem Prod.exists {p : α × β → Prop} : (∃ x, p x) ↔ ∃ a b, p (a, b) :=
+protected theorem «exists» {p : α × β → Prop} : (∃ x, p x) ↔ ∃ a b, p (a, b) :=
   ⟨fun ⟨⟨a, b⟩, h⟩ ↦ ⟨a, b, h⟩, fun ⟨a, b, h⟩ ↦ ⟨⟨a, b⟩, h⟩⟩
+
+@[simp] theorem map_id : Prod.map (@id α) (@id β) = id := rfl
+
+@[simp] theorem map_id' : Prod.map (fun a : α => a) (fun b : β => b) = fun x ↦ x := rfl
+
+/--
+Composing a `Prod.map` with another `Prod.map` is equal to
+a single `Prod.map` of composed functions.
+-/
+theorem map_comp_map (f : α → β) (f' : γ → δ) (g : β → ε) (g' : δ → ζ) :
+    Prod.map g g' ∘ Prod.map f f' = Prod.map (g ∘ f) (g' ∘ f') :=
+  rfl
+
+/--
+Composing a `Prod.map` with another `Prod.map` is equal to
+a single `Prod.map` of composed functions, fully applied.
+-/
+theorem map_map (f : α → β) (f' : γ → δ) (g : β → ε) (g' : δ → ζ) (x : α × γ) :
+    Prod.map g g' (Prod.map f f' x) = Prod.map (g ∘ f) (g' ∘ f') x :=
+  rfl
+
+/-- Swap the factors of a product. `swap (a, b) = (b, a)` -/
+def swap : α × β → β × α := fun p => (p.2, p.1)
+
+@[simp]
+theorem swap_swap : ∀ x : α × β, swap (swap x) = x
+  | ⟨_, _⟩ => rfl
+
+@[simp]
+theorem fst_swap {p : α × β} : (swap p).1 = p.2 :=
+  rfl
+
+@[simp]
+theorem snd_swap {p : α × β} : (swap p).2 = p.1 :=
+  rfl
+
+@[simp]
+theorem swap_prod_mk {a : α} {b : β} : swap (a, b) = (b, a) :=
+  rfl
+
+@[simp]
+theorem swap_swap_eq : swap ∘ swap = @id (α × β) :=
+  funext swap_swap
+
+@[simp]
+theorem swap_inj {p q : α × β} : swap p = swap q ↔ p = q := by
+  cases p; cases q; simp [and_comm]
+
+/--
+For two functions `f` and `g`, the composition of `Prod.map f g` with `Prod.swap`
+is equal to the composition of `Prod.swap` with `Prod.map g f`.
+-/
+theorem map_comp_swap (f : α → β) (g : γ → δ) :
+    Prod.map f g ∘ Prod.swap = Prod.swap ∘ Prod.map g f := rfl
+
+end Prod

src/Init/Data/Repr.lean

@@ -7,7 +7,7 @@ prelude
 import Init.Data.Format.Basic
 import Init.Data.Int.Basic
 import Init.Data.Nat.Div
-import Init.Data.UInt.Basic
+import Init.Data.UInt.BasicAux
 import Init.Control.Id
 open Sum Subtype Nat
 

src/Init/Data/String/Basic.lean

@@ -317,6 +317,9 @@ theorem _root_.Char.utf8Size_le_four (c : Char) : c.utf8Size ≤ 4 := by
 
 @[simp] theorem pos_add_char (p : Pos) (c : Char) : (p + c).byteIdx = p.byteIdx + c.utf8Size := rfl
 
+protected theorem Pos.ne_zero_of_lt : {a b : Pos} → a < b → b ≠ 0
+  | _, _, hlt, rfl => Nat.not_lt_zero _ hlt
+
 theorem lt_next (s : String) (i : Pos) : i.1 < (s.next i).1 :=
   Nat.add_lt_add_left (Char.utf8Size_pos _) _
 
@@ -1021,6 +1024,66 @@ instance hasBeq : BEq Substring := ⟨beq⟩
 def sameAs (ss1 ss2 : Substring) : Bool :=
   ss1.startPos == ss2.startPos && ss1 == ss2
 
+/--
+Returns the longest common prefix of two substrings.
+The returned substring will use the same underlying string as `s`.
+-/
+def commonPrefix (s t : Substring) : Substring :=
+  { s with stopPos := loop s.startPos t.startPos }
+where
+  /-- Returns the ending position of the common prefix, working up from `spos, tpos`. -/
+  loop spos tpos :=
+    if h : spos < s.stopPos ∧ tpos < t.stopPos then
+      if s.str.get spos == t.str.get tpos then
+        have := Nat.sub_lt_sub_left h.1 (s.str.lt_next spos)
+        loop (s.str.next spos) (t.str.next tpos)
+      else
+        spos
+    else
+      spos
+  termination_by s.stopPos.byteIdx - spos.byteIdx
+
+/--
+Returns the longest common suffix of two substrings.
+The returned substring will use the same underlying string as `s`.
+-/
+def commonSuffix (s t : Substring) : Substring :=
+  { s with startPos := loop s.stopPos t.stopPos }
+where
+  /-- Returns the starting position of the common prefix, working down from `spos, tpos`. -/
+  loop spos tpos :=
+    if h : s.startPos < spos ∧ t.startPos < tpos then
+      let spos' := s.str.prev spos
+      let tpos' := t.str.prev tpos
+      if s.str.get spos' == t.str.get tpos' then
+        have : spos' < spos := s.str.prev_lt_of_pos spos (String.Pos.ne_zero_of_lt h.1)
+        loop spos' tpos'
+      else
+        spos
+    else
+      spos
+  termination_by spos.byteIdx
+
+/--
+If `pre` is a prefix of `s`, i.e. `s = pre ++ t`, returns the remainder `t`.
+-/
+def dropPrefix? (s : Substring) (pre : Substring) : Option Substring :=
+  let t := s.commonPrefix pre
+  if t.bsize = pre.bsize then
+    some { s with startPos := t.stopPos }
+  else
+    none
+
+/--
+If `suff` is a suffix of `s`, i.e. `s = t ++ suff`, returns the remainder `t`.
+-/
+def dropSuffix? (s : Substring) (suff : Substring) : Option Substring :=
+  let t := s.commonSuffix suff
+  if t.bsize = suff.bsize then
+    some { s with stopPos := t.startPos }
+  else
+    none
+
 end Substring
 
 namespace String
@@ -1082,6 +1145,28 @@ namespace String
 @[inline] def decapitalize (s : String) :=
   s.set 0 <| s.get 0 |>.toLower
 
+/--
+If `pre` is a prefix of `s`, i.e. `s = pre ++ t`, returns the remainder `t`.
+-/
+def dropPrefix? (s : String) (pre : String) : Option Substring :=
+  s.toSubstring.dropPrefix? pre.toSubstring
+
+/--
+If `suff` is a suffix of `s`, i.e. `s = t ++ suff`, returns the remainder `t`.
+-/
+def dropSuffix? (s : String) (suff : String) : Option Substring :=
+  s.toSubstring.dropSuffix? suff.toSubstring
+
+/-- `s.stripPrefix pre` will remove `pre` from the beginning of `s` if it occurs there,
+or otherwise return `s`. -/
+def stripPrefix (s : String) (pre : String) : String :=
+  s.dropPrefix? pre |>.map Substring.toString |>.getD s
+
+/-- `s.stripSuffix suff` will remove `suff` from the end of `s` if it occurs there,
+or otherwise return `s`. -/
+def stripSuffix (s : String) (suff : String) : String :=
+  s.dropSuffix? suff |>.map Substring.toString |>.getD s
+
 end String
 
 namespace Char

src/Init/Data/String/Extra.lean

@@ -5,6 +5,7 @@ Author: Leonardo de Moura
 -/
 prelude
 import Init.Data.ByteArray
+import Init.Data.UInt.Lemmas
 
 namespace String
 
@@ -20,14 +21,14 @@ def toNat! (s : String) : Nat :=
 def utf8DecodeChar? (a : ByteArray) (i : Nat) : Option Char := do
   let c ← a[i]?
   if c &&& 0x80 == 0 then
-    some ⟨c.toUInt32, .inl (Nat.lt_trans c.1.2 (by decide))⟩
+    some ⟨c.toUInt32, .inl (Nat.lt_trans c.toBitVec.isLt (by decide))⟩
   else if c &&& 0xe0 == 0xc0 then
     let c1 ← a[i+1]?
     guard (c1 &&& 0xc0 == 0x80)
     let r := ((c &&& 0x1f).toUInt32 <<< 6) ||| (c1 &&& 0x3f).toUInt32
     guard (0x80 ≤ r)
     -- TODO: Prove h from the definition of r once we have the necessary lemmas
-    if h : r < 0xd800 then some ⟨r, .inl h⟩ else none
+    if h : r < 0xd800 then some ⟨r, .inl (UInt32.toNat_lt_of_lt (by decide) h)⟩ else none
   else if c &&& 0xf0 == 0xe0 then
     let c1 ← a[i+1]?
     let c2 ← a[i+2]?
@@ -38,7 +39,14 @@ def utf8DecodeChar? (a : ByteArray) (i : Nat) : Option Char := do
       (c2 &&& 0x3f).toUInt32
     guard (0x800 ≤ r)
     -- TODO: Prove `r < 0x110000` from the definition of r once we have the necessary lemmas
-    if h : r < 0xd800 ∨ 0xdfff < r ∧ r < 0x110000 then some ⟨r, h⟩ else none
+    if h : r < 0xd800 ∨ 0xdfff < r ∧ r < 0x110000 then
+      have :=
+        match h with
+        | .inl h => Or.inl (UInt32.toNat_lt_of_lt (by decide) h)
+        | .inr h => Or.inr ⟨UInt32.lt_toNat_of_lt (by decide) h.left, UInt32.toNat_lt_of_lt (by decide) h.right⟩
+      some ⟨r, this⟩
+    else
+      none
   else if c &&& 0xf8 == 0xf0 then
     let c1 ← a[i+1]?
     let c2 ← a[i+2]?
@@ -50,7 +58,7 @@ def utf8DecodeChar? (a : ByteArray) (i : Nat) : Option Char := do
       ((c2 &&& 0x3f).toUInt32 <<< 6) |||
       (c3 &&& 0x3f).toUInt32
     if h : 0x10000 ≤ r ∧ r < 0x110000 then
-      some ⟨r, .inr ⟨Nat.lt_of_lt_of_le (by decide) h.1, h.2⟩⟩
+      some ⟨r, .inr ⟨Nat.lt_of_lt_of_le (by decide) (UInt32.le_toNat_of_le (by decide) h.left), UInt32.toNat_lt_of_lt (by decide) h.right⟩⟩
     else none
   else
     none
@@ -117,11 +125,11 @@ def utf8EncodeChar (c : Char) : List UInt8 :=
 /-- Converts the given `String` to a [UTF-8](https://en.wikipedia.org/wiki/UTF-8) encoded byte array. -/
 @[extern "lean_string_to_utf8"]
 def toUTF8 (a : @& String) : ByteArray :=
-  ⟨⟨a.data.bind utf8EncodeChar⟩⟩
+  ⟨⟨a.data.flatMap utf8EncodeChar⟩⟩
 
 @[simp] theorem size_toUTF8 (s : String) : s.toUTF8.size = s.utf8ByteSize := by
-  simp [toUTF8, ByteArray.size, Array.size, utf8ByteSize, List.bind]
-  induction s.data <;> simp [List.map, List.join, utf8ByteSize.go, Nat.add_comm, *]
+  simp [toUTF8, ByteArray.size, Array.size, utf8ByteSize, List.flatMap]
+  induction s.data <;> simp [List.map, List.flatten, utf8ByteSize.go, Nat.add_comm, *]
 
 /-- Accesses a byte in the UTF-8 encoding of the `String`. O(1) -/
 @[extern "lean_string_get_byte_fast"]

src/Init/Data/Sum.lean

@@ -4,21 +4,5 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Yury G. Kudryashov
 -/
 prelude
-import Init.Core
-
-namespace Sum
-
-deriving instance DecidableEq for Sum
-deriving instance BEq for Sum
-
-/-- Check if a sum is `inl` and if so, retrieve its contents. -/
-def getLeft? : α ⊕ β → Option α
-  | inl a => some a
-  | inr _ => none
-
-/-- Check if a sum is `inr` and if so, retrieve its contents. -/
-def getRight? : α ⊕ β → Option β
-  | inr b => some b
-  | inl _ => none
-
-end Sum
+import Init.Data.Sum.Basic
+import Init.Data.Sum.Lemmas

src/Init/Data/Sum/Basic.lean

@@ -0,0 +1,178 @@
+/-
+Copyright (c) 2017 Mario Carneiro. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Mario Carneiro, Yury G. Kudryashov
+-/
+prelude
+import Init.PropLemmas
+
+/-!
+# Disjoint union of types
+
+This file defines basic operations on the the sum type `α ⊕ β`.
+
+`α ⊕ β` is the type made of a copy of `α` and a copy of `β`. It is also called *disjoint union*.
+
+## Main declarations
+
+* `Sum.isLeft`: Returns whether `x : α ⊕ β` comes from the left component or not.
+* `Sum.isRight`: Returns whether `x : α ⊕ β` comes from the right component or not.
+* `Sum.getLeft`: Retrieves the left content of a `x : α ⊕ β` that is known to come from the left.
+* `Sum.getRight`: Retrieves the right content of `x : α ⊕ β` that is known to come from the right.
+* `Sum.getLeft?`: Retrieves the left content of `x : α ⊕ β` as an option type or returns `none`
+  if it's coming from the right.
+* `Sum.getRight?`: Retrieves the right content of `x : α ⊕ β` as an option type or returns `none`
+  if it's coming from the left.
+* `Sum.map`: Maps `α ⊕ β` to `γ ⊕ δ` component-wise.
+* `Sum.elim`: Nondependent eliminator/induction principle for `α ⊕ β`.
+* `Sum.swap`: Maps `α ⊕ β` to `β ⊕ α` by swapping components.
+* `Sum.LiftRel`: The disjoint union of two relations.
+* `Sum.Lex`: Lexicographic order on `α ⊕ β` induced by a relation on `α` and a relation on `β`.
+
+## Further material
+
+See `Batteries.Data.Sum.Lemmas` for theorems about these definitions.
+
+## Notes
+
+The definition of `Sum` takes values in `Type _`. This effectively forbids `Prop`- valued sum types.
+To this effect, we have `PSum`, which takes value in `Sort _` and carries a more complicated
+universe signature in consequence. The `Prop` version is `Or`.
+-/
+
+namespace Sum
+
+deriving instance DecidableEq for Sum
+deriving instance BEq for Sum
+
+section get
+
+/-- Check if a sum is `inl`. -/
+def isLeft : α ⊕ β → Bool
+  | inl _ => true
+  | inr _ => false
+
+/-- Check if a sum is `inr`. -/
+def isRight : α ⊕ β → Bool
+  | inl _ => false
+  | inr _ => true
+
+/-- Retrieve the contents from a sum known to be `inl`.-/
+def getLeft : (ab : α ⊕ β) → ab.isLeft → α
+  | inl a, _ => a
+
+/-- Retrieve the contents from a sum known to be `inr`.-/
+def getRight : (ab : α ⊕ β) → ab.isRight → β
+  | inr b, _ => b
+
+/-- Check if a sum is `inl` and if so, retrieve its contents. -/
+def getLeft? : α ⊕ β → Option α
+  | inl a => some a
+  | inr _ => none
+
+/-- Check if a sum is `inr` and if so, retrieve its contents. -/
+def getRight? : α ⊕ β → Option β
+  | inr b => some b
+  | inl _ => none
+
+@[simp] theorem isLeft_inl : (inl x : α ⊕ β).isLeft = true := rfl
+@[simp] theorem isLeft_inr : (inr x : α ⊕ β).isLeft = false := rfl
+@[simp] theorem isRight_inl : (inl x : α ⊕ β).isRight = false := rfl
+@[simp] theorem isRight_inr : (inr x : α ⊕ β).isRight = true := rfl
+
+@[simp] theorem getLeft_inl (h : (inl x : α ⊕ β).isLeft) : (inl x).getLeft h = x := rfl
+@[simp] theorem getRight_inr (h : (inr x : α ⊕ β).isRight) : (inr x).getRight h = x := rfl
+
+@[simp] theorem getLeft?_inl : (inl x : α ⊕ β).getLeft? = some x := rfl
+@[simp] theorem getLeft?_inr : (inr x : α ⊕ β).getLeft? = none := rfl
+@[simp] theorem getRight?_inl : (inl x : α ⊕ β).getRight? = none := rfl
+@[simp] theorem getRight?_inr : (inr x : α ⊕ β).getRight? = some x := rfl
+
+end get
+
+/-- Define a function on `α ⊕ β` by giving separate definitions on `α` and `β`. -/
+protected def elim {α β γ} (f : α → γ) (g : β → γ) : α ⊕ β → γ :=
+  fun x => Sum.casesOn x f g
+
+@[simp] theorem elim_inl (f : α → γ) (g : β → γ) (x : α) :
+    Sum.elim f g (inl x) = f x := rfl
+
+@[simp] theorem elim_inr (f : α → γ) (g : β → γ) (x : β) :
+    Sum.elim f g (inr x) = g x := rfl
+
+/-- Map `α ⊕ β` to `α' ⊕ β'` sending `α` to `α'` and `β` to `β'`. -/
+protected def map (f : α → α') (g : β → β') : α ⊕ β → α' ⊕ β' :=
+  Sum.elim (inl ∘ f) (inr ∘ g)
+
+@[simp] theorem map_inl (f : α → α') (g : β → β') (x : α) : (inl x).map f g = inl (f x) := rfl
+
+@[simp] theorem map_inr (f : α → α') (g : β → β') (x : β) : (inr x).map f g = inr (g x) := rfl
+
+/-- Swap the factors of a sum type -/
+def swap : α ⊕ β → β ⊕ α := Sum.elim inr inl
+
+@[simp] theorem swap_inl : swap (inl x : α ⊕ β) = inr x := rfl
+
+@[simp] theorem swap_inr : swap (inr x : α ⊕ β) = inl x := rfl
+
+section LiftRel
+
+/-- Lifts pointwise two relations between `α` and `γ` and between `β` and `δ` to a relation between
+`α ⊕ β` and `γ ⊕ δ`. -/
+inductive LiftRel (r : α → γ → Prop) (s : β → δ → Prop) : α ⊕ β → γ ⊕ δ → Prop
+  /-- `inl a` and `inl c` are related via `LiftRel r s` if `a` and `c` are related via `r`. -/
+  | protected inl {a c} : r a c → LiftRel r s (inl a) (inl c)
+  /-- `inr b` and `inr d` are related via `LiftRel r s` if `b` and `d` are related via `s`. -/
+  | protected inr {b d} : s b d → LiftRel r s (inr b) (inr d)
+
+@[simp] theorem liftRel_inl_inl : LiftRel r s (inl a) (inl c) ↔ r a c :=
+  ⟨fun h => by cases h; assumption, LiftRel.inl⟩
+
+@[simp] theorem not_liftRel_inl_inr : ¬LiftRel r s (inl a) (inr d) := nofun
+
+@[simp] theorem not_liftRel_inr_inl : ¬LiftRel r s (inr b) (inl c) := nofun
+
+@[simp] theorem liftRel_inr_inr : LiftRel r s (inr b) (inr d) ↔ s b d :=
+  ⟨fun h => by cases h; assumption, LiftRel.inr⟩
+
+instance {r : α → γ → Prop} {s : β → δ → Prop}
+    [∀ a c, Decidable (r a c)] [∀ b d, Decidable (s b d)] :
+    ∀ (ab : α ⊕ β) (cd : γ ⊕ δ), Decidable (LiftRel r s ab cd)
+  | inl _, inl _ => decidable_of_iff' _ liftRel_inl_inl
+  | inl _, inr _ => Decidable.isFalse not_liftRel_inl_inr
+  | inr _, inl _ => Decidable.isFalse not_liftRel_inr_inl
+  | inr _, inr _ => decidable_of_iff' _ liftRel_inr_inr
+
+end LiftRel
+
+section Lex
+
+/-- Lexicographic order for sum. Sort all the `inl a` before the `inr b`, otherwise use the
+respective order on `α` or `β`. -/
+inductive Lex (r : α → α → Prop) (s : β → β → Prop) : α ⊕ β → α ⊕ β → Prop
+  /-- `inl a₁` and `inl a₂` are related via `Lex r s` if `a₁` and `a₂` are related via `r`. -/
+  | protected inl {a₁ a₂} (h : r a₁ a₂) : Lex r s (inl a₁) (inl a₂)
+  /-- `inr b₁` and `inr b₂` are related via `Lex r s` if `b₁` and `b₂` are related via `s`. -/
+  | protected inr {b₁ b₂} (h : s b₁ b₂) : Lex r s (inr b₁) (inr b₂)
+  /-- `inl a` and `inr b` are always related via `Lex r s`. -/
+  | sep (a b) : Lex r s (inl a) (inr b)
+
+attribute [simp] Lex.sep
+
+@[simp] theorem lex_inl_inl : Lex r s (inl a₁) (inl a₂) ↔ r a₁ a₂ :=
+  ⟨fun h => by cases h; assumption, Lex.inl⟩
+
+@[simp] theorem lex_inr_inr : Lex r s (inr b₁) (inr b₂) ↔ s b₁ b₂ :=
+  ⟨fun h => by cases h; assumption, Lex.inr⟩
+
+@[simp] theorem lex_inr_inl : ¬Lex r s (inr b) (inl a) := nofun
+
+instance instDecidableRelSumLex [DecidableRel r] [DecidableRel s] : DecidableRel (Lex r s)
+  | inl _, inl _ => decidable_of_iff' _ lex_inl_inl
+  | inl _, inr _ => Decidable.isTrue (Lex.sep _ _)
+  | inr _, inl _ => Decidable.isFalse lex_inr_inl
+  | inr _, inr _ => decidable_of_iff' _ lex_inr_inr
+
+end Lex
+
+end Sum

src/Init/Data/Sum/Lemmas.lean

@@ -0,0 +1,251 @@
+/-
+Copyright (c) 2017 Mario Carneiro. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Mario Carneiro, Yury G. Kudryashov
+-/
+prelude
+import Init.Data.Sum.Basic
+import Init.Ext
+
+/-!
+# Disjoint union of types
+
+Theorems about the definitions introduced in `Init.Data.Sum.Basic`.
+-/
+
+open Function
+
+namespace Sum
+
+@[simp] protected theorem «forall» {p : α ⊕ β → Prop} :
+    (∀ x, p x) ↔ (∀ a, p (inl a)) ∧ ∀ b, p (inr b) :=
+  ⟨fun h => ⟨fun _ => h _, fun _ => h _⟩, fun ⟨h₁, h₂⟩ => Sum.rec h₁ h₂⟩
+
+@[simp] protected theorem «exists» {p : α ⊕ β → Prop} :
+    (∃ x, p x) ↔ (∃ a, p (inl a)) ∨ ∃ b, p (inr b) :=
+  ⟨ fun
+    | ⟨inl a, h⟩ => Or.inl ⟨a, h⟩
+    | ⟨inr b, h⟩ => Or.inr ⟨b, h⟩,
+    fun
+    | Or.inl ⟨a, h⟩ => ⟨inl a, h⟩
+    | Or.inr ⟨b, h⟩ => ⟨inr b, h⟩⟩
+
+theorem forall_sum {γ : α ⊕ β → Sort _} (p : (∀ ab, γ ab) → Prop) :
+    (∀ fab, p fab) ↔ (∀ fa fb, p (Sum.rec fa fb)) := by
+  refine ⟨fun h fa fb => h _, fun h fab => ?_⟩
+  have h1 : fab = Sum.rec (fun a => fab (Sum.inl a)) (fun b => fab (Sum.inr b)) := by
+    apply funext
+    rintro (_ | _) <;> rfl
+  rw [h1]; exact h _ _
+
+section get
+
+@[simp] theorem inl_getLeft : ∀ (x : α ⊕ β) (h : x.isLeft), inl (x.getLeft h) = x
+  | inl _, _ => rfl
+@[simp] theorem inr_getRight : ∀ (x : α ⊕ β) (h : x.isRight), inr (x.getRight h) = x
+  | inr _, _ => rfl
+
+@[simp] theorem getLeft?_eq_none_iff {x : α ⊕ β} : x.getLeft? = none ↔ x.isRight := by
+  cases x <;> simp only [getLeft?, isRight, eq_self_iff_true, reduceCtorEq]
+
+@[simp] theorem getRight?_eq_none_iff {x : α ⊕ β} : x.getRight? = none ↔ x.isLeft := by
+  cases x <;> simp only [getRight?, isLeft, eq_self_iff_true, reduceCtorEq]
+
+theorem eq_left_getLeft_of_isLeft : ∀ {x : α ⊕ β} (h : x.isLeft), x = inl (x.getLeft h)
+  | inl _, _ => rfl
+
+@[simp] theorem getLeft_eq_iff (h : x.isLeft) : x.getLeft h = a ↔ x = inl a := by
+  cases x <;> simp at h ⊢
+
+theorem eq_right_getRight_of_isRight : ∀ {x : α ⊕ β} (h : x.isRight), x = inr (x.getRight h)
+  | inr _, _ => rfl
+
+@[simp] theorem getRight_eq_iff (h : x.isRight) : x.getRight h = b ↔ x = inr b := by
+  cases x <;> simp at h ⊢
+
+@[simp] theorem getLeft?_eq_some_iff : x.getLeft? = some a ↔ x = inl a := by
+  cases x <;> simp only [getLeft?, Option.some.injEq, inl.injEq, reduceCtorEq]
+
+@[simp] theorem getRight?_eq_some_iff : x.getRight? = some b ↔ x = inr b := by
+  cases x <;> simp only [getRight?, Option.some.injEq, inr.injEq, reduceCtorEq]
+
+@[simp] theorem bnot_isLeft (x : α ⊕ β) : !x.isLeft = x.isRight := by cases x <;> rfl
+
+@[simp] theorem isLeft_eq_false {x : α ⊕ β} : x.isLeft = false ↔ x.isRight := by cases x <;> simp
+
+theorem not_isLeft {x : α ⊕ β} : ¬x.isLeft ↔ x.isRight := by simp
+
+@[simp] theorem bnot_isRight (x : α ⊕ β) : !x.isRight = x.isLeft := by cases x <;> rfl
+
+@[simp] theorem isRight_eq_false {x : α ⊕ β} : x.isRight = false ↔ x.isLeft := by cases x <;> simp
+
+theorem not_isRight {x : α ⊕ β} : ¬x.isRight ↔ x.isLeft := by simp
+
+theorem isLeft_iff : x.isLeft ↔ ∃ y, x = Sum.inl y := by cases x <;> simp
+
+theorem isRight_iff : x.isRight ↔ ∃ y, x = Sum.inr y := by cases x <;> simp
+
+end get
+
+theorem inl.inj_iff : (inl a : α ⊕ β) = inl b ↔ a = b := ⟨inl.inj, congrArg _⟩
+
+theorem inr.inj_iff : (inr a : α ⊕ β) = inr b ↔ a = b := ⟨inr.inj, congrArg _⟩
+
+theorem inl_ne_inr : inl a ≠ inr b := nofun
+
+theorem inr_ne_inl : inr b ≠ inl a := nofun
+
+/-! ### `Sum.elim` -/
+
+@[simp] theorem elim_comp_inl (f : α → γ) (g : β → γ) : Sum.elim f g ∘ inl = f :=
+  rfl
+
+@[simp] theorem elim_comp_inr (f : α → γ) (g : β → γ) : Sum.elim f g ∘ inr = g :=
+  rfl
+
+@[simp] theorem elim_inl_inr : @Sum.elim α β _ inl inr = id :=
+  funext fun x => Sum.casesOn x (fun _ => rfl) fun _ => rfl
+
+theorem comp_elim (f : γ → δ) (g : α → γ) (h : β → γ) :
+    f ∘ Sum.elim g h = Sum.elim (f ∘ g) (f ∘ h) :=
+  funext fun x => Sum.casesOn x (fun _ => rfl) fun _ => rfl
+
+@[simp] theorem elim_comp_inl_inr (f : α ⊕ β → γ) :
+    Sum.elim (f ∘ inl) (f ∘ inr) = f :=
+  funext fun x => Sum.casesOn x (fun _ => rfl) fun _ => rfl
+
+theorem elim_eq_iff {u u' : α → γ} {v v' : β → γ} :
+    Sum.elim u v = Sum.elim u' v' ↔ u = u' ∧ v = v' := by
+  simp [funext_iff]
+
+/-! ### `Sum.map` -/
+
+@[simp] theorem map_map (f' : α' → α'') (g' : β' → β'') (f : α → α') (g : β → β') :
+    ∀ x : Sum α β, (x.map f g).map f' g' = x.map (f' ∘ f) (g' ∘ g)
+  | inl _ => rfl
+  | inr _ => rfl
+
+@[simp] theorem map_comp_map (f' : α' → α'') (g' : β' → β'') (f : α → α') (g : β → β') :
+    Sum.map f' g' ∘ Sum.map f g = Sum.map (f' ∘ f) (g' ∘ g) :=
+  funext <| map_map f' g' f g
+
+@[simp] theorem map_id_id : Sum.map (@id α) (@id β) = id :=
+  funext fun x => Sum.recOn x (fun _ => rfl) fun _ => rfl
+
+theorem elim_map {f₁ : α → β} {f₂ : β → ε} {g₁ : γ → δ} {g₂ : δ → ε} {x} :
+    Sum.elim f₂ g₂ (Sum.map f₁ g₁ x) = Sum.elim (f₂ ∘ f₁) (g₂ ∘ g₁) x := by
+  cases x <;> rfl
+
+theorem elim_comp_map {f₁ : α → β} {f₂ : β → ε} {g₁ : γ → δ} {g₂ : δ → ε} :
+    Sum.elim f₂ g₂ ∘ Sum.map f₁ g₁ = Sum.elim (f₂ ∘ f₁) (g₂ ∘ g₁) :=
+  funext fun _ => elim_map
+
+@[simp] theorem isLeft_map (f : α → β) (g : γ → δ) (x : α ⊕ γ) :
+    isLeft (x.map f g) = isLeft x := by
+  cases x <;> rfl
+
+@[simp] theorem isRight_map (f : α → β) (g : γ → δ) (x : α ⊕ γ) :
+    isRight (x.map f g) = isRight x := by
+  cases x <;> rfl
+
+@[simp] theorem getLeft?_map (f : α → β) (g : γ → δ) (x : α ⊕ γ) :
+    (x.map f g).getLeft? = x.getLeft?.map f := by
+  cases x <;> rfl
+
+@[simp] theorem getRight?_map (f : α → β) (g : γ → δ) (x : α ⊕ γ) :
+    (x.map f g).getRight? = x.getRight?.map g := by cases x <;> rfl
+
+/-! ### `Sum.swap` -/
+
+@[simp] theorem swap_swap (x : α ⊕ β) : swap (swap x) = x := by cases x <;> rfl
+
+@[simp] theorem swap_swap_eq : swap ∘ swap = @id (α ⊕ β) := funext <| swap_swap
+
+@[simp] theorem isLeft_swap (x : α ⊕ β) : x.swap.isLeft = x.isRight := by cases x <;> rfl
+
+@[simp] theorem isRight_swap (x : α ⊕ β) : x.swap.isRight = x.isLeft := by cases x <;> rfl
+
+@[simp] theorem getLeft?_swap (x : α ⊕ β) : x.swap.getLeft? = x.getRight? := by cases x <;> rfl
+
+@[simp] theorem getRight?_swap (x : α ⊕ β) : x.swap.getRight? = x.getLeft? := by cases x <;> rfl
+
+section LiftRel
+
+theorem LiftRel.mono (hr : ∀ a b, r₁ a b → r₂ a b) (hs : ∀ a b, s₁ a b → s₂ a b)
+  (h : LiftRel r₁ s₁ x y) : LiftRel r₂ s₂ x y := by
+  cases h
+  · exact LiftRel.inl (hr _ _ ‹_›)
+  · exact LiftRel.inr (hs _ _ ‹_›)
+
+theorem LiftRel.mono_left (hr : ∀ a b, r₁ a b → r₂ a b) (h : LiftRel r₁ s x y) :
+    LiftRel r₂ s x y :=
+  (h.mono hr) fun _ _ => id
+
+theorem LiftRel.mono_right (hs : ∀ a b, s₁ a b → s₂ a b) (h : LiftRel r s₁ x y) :
+    LiftRel r s₂ x y :=
+  h.mono (fun _ _ => id) hs
+
+protected theorem LiftRel.swap (h : LiftRel r s x y) : LiftRel s r x.swap y.swap := by
+  cases h
+  · exact LiftRel.inr ‹_›
+  · exact LiftRel.inl ‹_›
+
+@[simp] theorem liftRel_swap_iff : LiftRel s r x.swap y.swap ↔ LiftRel r s x y :=
+  ⟨fun h => by rw [← swap_swap x, ← swap_swap y]; exact h.swap, LiftRel.swap⟩
+
+end LiftRel
+
+section Lex
+
+protected theorem LiftRel.lex {a b : α ⊕ β} (h : LiftRel r s a b) : Lex r s a b := by
+  cases h
+  · exact Lex.inl ‹_›
+  · exact Lex.inr ‹_›
+
+theorem liftRel_subrelation_lex : Subrelation (LiftRel r s) (Lex r s) := LiftRel.lex
+
+theorem Lex.mono (hr : ∀ a b, r₁ a b → r₂ a b) (hs : ∀ a b, s₁ a b → s₂ a b) (h : Lex r₁ s₁ x y) :
+    Lex r₂ s₂ x y := by
+  cases h
+  · exact Lex.inl (hr _ _ ‹_›)
+  · exact Lex.inr (hs _ _ ‹_›)
+  · exact Lex.sep _ _
+
+theorem Lex.mono_left (hr : ∀ a b, r₁ a b → r₂ a b) (h : Lex r₁ s x y) : Lex r₂ s x y :=
+  (h.mono hr) fun _ _ => id
+
+theorem Lex.mono_right (hs : ∀ a b, s₁ a b → s₂ a b) (h : Lex r s₁ x y) : Lex r s₂ x y :=
+  h.mono (fun _ _ => id) hs
+
+theorem lex_acc_inl (aca : Acc r a) : Acc (Lex r s) (inl a) := by
+  induction aca with
+  | intro _ _ IH =>
+    constructor
+    intro y h
+    cases h with
+    | inl h' => exact IH _ h'
+
+theorem lex_acc_inr (aca : ∀ a, Acc (Lex r s) (inl a)) {b} (acb : Acc s b) :
+    Acc (Lex r s) (inr b) := by
+  induction acb with
+  | intro _ _ IH =>
+    constructor
+    intro y h
+    cases h with
+    | inr h' => exact IH _ h'
+    | sep => exact aca _
+
+theorem lex_wf (ha : WellFounded r) (hb : WellFounded s) : WellFounded (Lex r s) :=
+  have aca : ∀ a, Acc (Lex r s) (inl a) := fun a => lex_acc_inl (ha.apply a)
+  ⟨fun x => Sum.recOn x aca fun b => lex_acc_inr aca (hb.apply b)⟩
+
+end Lex
+
+theorem elim_const_const (c : γ) :
+    Sum.elim (const _ c : α → γ) (const _ c : β → γ) = const _ c := by
+  apply funext
+  rintro (_ | _) <;> rfl
+
+@[simp] theorem elim_lam_const_lam_const (c : γ) :
+    Sum.elim (fun _ : α => c) (fun _ : β => c) = fun _ => c :=
+  Sum.elim_const_const c

src/Init/Data/ToString/Basic.lean

@@ -5,7 +5,7 @@ Author: Leonardo de Moura
 -/
 prelude
 import Init.Data.String.Basic
-import Init.Data.UInt.Basic
+import Init.Data.UInt.BasicAux
 import Init.Data.Nat.Div
 import Init.Data.Repr
 import Init.Data.Int.Basic

src/Init/Data/UInt.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Henrik Böving
 -/
 prelude
+import Init.Data.UInt.BasicAux
 import Init.Data.UInt.Basic
 import Init.Data.UInt.Log2
 import Init.Data.UInt.Lemmas

src/Init/Data/UInt/Basic.lean

@@ -4,52 +4,50 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Leonardo de Moura
 -/
 prelude
-import Init.Data.Fin.Basic
+import Init.Data.UInt.BasicAux
+import Init.Data.BitVec.Basic
 
 open Nat
 
-@[extern "lean_uint8_of_nat"]
-def UInt8.ofNat (n : @& Nat) : UInt8 := ⟨Fin.ofNat n⟩
-abbrev Nat.toUInt8 := UInt8.ofNat
-@[extern "lean_uint8_to_nat"]
-def UInt8.toNat (n : UInt8) : Nat := n.val.val
 @[extern "lean_uint8_add"]
-def UInt8.add (a b : UInt8) : UInt8 := ⟨a.val + b.val⟩
+def UInt8.add (a b : UInt8) : UInt8 := ⟨a.toBitVec + b.toBitVec⟩
 @[extern "lean_uint8_sub"]
-def UInt8.sub (a b : UInt8) : UInt8 := ⟨a.val - b.val⟩
+def UInt8.sub (a b : UInt8) : UInt8 := ⟨a.toBitVec - b.toBitVec⟩
 @[extern "lean_uint8_mul"]
-def UInt8.mul (a b : UInt8) : UInt8 := ⟨a.val * b.val⟩
+def UInt8.mul (a b : UInt8) : UInt8 := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_uint8_div"]
-def UInt8.div (a b : UInt8) : UInt8 := ⟨a.val / b.val⟩
+def UInt8.div (a b : UInt8) : UInt8 := ⟨BitVec.udiv a.toBitVec b.toBitVec⟩
 @[extern "lean_uint8_mod"]
-def UInt8.mod (a b : UInt8) : UInt8 := ⟨a.val % b.val⟩
-@[extern "lean_uint8_modn"]
+def UInt8.mod (a b : UInt8) : UInt8 := ⟨BitVec.umod a.toBitVec b.toBitVec⟩
+@[extern "lean_uint8_modn", deprecated UInt8.mod (since := "2024-09-23")]
 def UInt8.modn (a : UInt8) (n : @& Nat) : UInt8 := ⟨Fin.modn a.val n⟩
 @[extern "lean_uint8_land"]
-def UInt8.land (a b : UInt8) : UInt8 := ⟨Fin.land a.val b.val⟩
+def UInt8.land (a b : UInt8) : UInt8 := ⟨a.toBitVec &&& b.toBitVec⟩
 @[extern "lean_uint8_lor"]
-def UInt8.lor (a b : UInt8) : UInt8 := ⟨Fin.lor a.val b.val⟩
+def UInt8.lor (a b : UInt8) : UInt8 := ⟨a.toBitVec ||| b.toBitVec⟩
 @[extern "lean_uint8_xor"]
-def UInt8.xor (a b : UInt8) : UInt8 := ⟨Fin.xor a.val b.val⟩
+def UInt8.xor (a b : UInt8) : UInt8 := ⟨a.toBitVec ^^^ b.toBitVec⟩
 @[extern "lean_uint8_shift_left"]
-def UInt8.shiftLeft (a b : UInt8) : UInt8 := ⟨a.val <<< (modn b 8).val⟩
+def UInt8.shiftLeft (a b : UInt8) : UInt8 := ⟨a.toBitVec <<< (mod b 8).toBitVec⟩
 @[extern "lean_uint8_shift_right"]
-def UInt8.shiftRight (a b : UInt8) : UInt8 := ⟨a.val >>> (modn b 8).val⟩
-def UInt8.lt (a b : UInt8) : Prop := a.val < b.val
-def UInt8.le (a b : UInt8) : Prop := a.val ≤ b.val
+def UInt8.shiftRight (a b : UInt8) : UInt8 := ⟨a.toBitVec >>> (mod b 8).toBitVec⟩
+def UInt8.lt (a b : UInt8) : Prop := a.toBitVec < b.toBitVec
+def UInt8.le (a b : UInt8) : Prop := a.toBitVec ≤ b.toBitVec
 
-instance UInt8.instOfNat : OfNat UInt8 n := ⟨UInt8.ofNat n⟩
 instance : Add UInt8       := ⟨UInt8.add⟩
 instance : Sub UInt8       := ⟨UInt8.sub⟩
 instance : Mul UInt8       := ⟨UInt8.mul⟩
 instance : Mod UInt8       := ⟨UInt8.mod⟩
+
+set_option linter.deprecated false in
 instance : HMod UInt8 Nat UInt8 := ⟨UInt8.modn⟩
+
 instance : Div UInt8       := ⟨UInt8.div⟩
 instance : LT UInt8        := ⟨UInt8.lt⟩
 instance : LE UInt8        := ⟨UInt8.le⟩
 
 @[extern "lean_uint8_complement"]
-def UInt8.complement (a:UInt8) : UInt8 := 0-(a+1)
+def UInt8.complement (a : UInt8) : UInt8 := ⟨~~~a.toBitVec⟩
 
 instance : Complement UInt8 := ⟨UInt8.complement⟩
 instance : AndOp UInt8     := ⟨UInt8.land⟩
@@ -58,69 +56,58 @@ instance : Xor UInt8       := ⟨UInt8.xor⟩
 instance : ShiftLeft UInt8  := ⟨UInt8.shiftLeft⟩
 instance : ShiftRight UInt8 := ⟨UInt8.shiftRight⟩
 
-set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint8_dec_lt"]
 def UInt8.decLt (a b : UInt8) : Decidable (a < b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n < m))
+  inferInstanceAs (Decidable (a.toBitVec < b.toBitVec))
 
-set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint8_dec_le"]
 def UInt8.decLe (a b : UInt8) : Decidable (a ≤ b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
+  inferInstanceAs (Decidable (a.toBitVec ≤ b.toBitVec))
 
 instance (a b : UInt8) : Decidable (a < b) := UInt8.decLt a b
 instance (a b : UInt8) : Decidable (a ≤ b) := UInt8.decLe a b
 instance : Max UInt8 := maxOfLe
 instance : Min UInt8 := minOfLe
 
-@[extern "lean_uint16_of_nat"]
-def UInt16.ofNat (n : @& Nat) : UInt16 := ⟨Fin.ofNat n⟩
-abbrev Nat.toUInt16 := UInt16.ofNat
-@[extern "lean_uint16_to_nat"]
-def UInt16.toNat (n : UInt16) : Nat := n.val.val
 @[extern "lean_uint16_add"]
-def UInt16.add (a b : UInt16) : UInt16 := ⟨a.val + b.val⟩
+def UInt16.add (a b : UInt16) : UInt16 := ⟨a.toBitVec + b.toBitVec⟩
 @[extern "lean_uint16_sub"]
-def UInt16.sub (a b : UInt16) : UInt16 := ⟨a.val - b.val⟩
+def UInt16.sub (a b : UInt16) : UInt16 := ⟨a.toBitVec - b.toBitVec⟩
 @[extern "lean_uint16_mul"]
-def UInt16.mul (a b : UInt16) : UInt16 := ⟨a.val * b.val⟩
+def UInt16.mul (a b : UInt16) : UInt16 := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_uint16_div"]
-def UInt16.div (a b : UInt16) : UInt16 := ⟨a.val / b.val⟩
+def UInt16.div (a b : UInt16) : UInt16 := ⟨BitVec.udiv a.toBitVec b.toBitVec⟩
 @[extern "lean_uint16_mod"]
-def UInt16.mod (a b : UInt16) : UInt16 := ⟨a.val % b.val⟩
-@[extern "lean_uint16_modn"]
+def UInt16.mod (a b : UInt16) : UInt16 := ⟨BitVec.umod a.toBitVec b.toBitVec⟩
+@[extern "lean_uint16_modn", deprecated UInt16.mod (since := "2024-09-23")]
 def UInt16.modn (a : UInt16) (n : @& Nat) : UInt16 := ⟨Fin.modn a.val n⟩
 @[extern "lean_uint16_land"]
-def UInt16.land (a b : UInt16) : UInt16 := ⟨Fin.land a.val b.val⟩
+def UInt16.land (a b : UInt16) : UInt16 := ⟨a.toBitVec &&& b.toBitVec⟩
 @[extern "lean_uint16_lor"]
-def UInt16.lor (a b : UInt16) : UInt16 := ⟨Fin.lor a.val b.val⟩
+def UInt16.lor (a b : UInt16) : UInt16 := ⟨a.toBitVec ||| b.toBitVec⟩
 @[extern "lean_uint16_xor"]
-def UInt16.xor (a b : UInt16) : UInt16 := ⟨Fin.xor a.val b.val⟩
+def UInt16.xor (a b : UInt16) : UInt16 := ⟨a.toBitVec ^^^ b.toBitVec⟩
 @[extern "lean_uint16_shift_left"]
-def UInt16.shiftLeft (a b : UInt16) : UInt16 := ⟨a.val <<< (modn b 16).val⟩
-@[extern "lean_uint16_to_uint8"]
-def UInt16.toUInt8 (a : UInt16) : UInt8 := a.toNat.toUInt8
-@[extern "lean_uint8_to_uint16"]
-def UInt8.toUInt16 (a : UInt8) : UInt16 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
+def UInt16.shiftLeft (a b : UInt16) : UInt16 := ⟨a.toBitVec <<< (mod b 16).toBitVec⟩
 @[extern "lean_uint16_shift_right"]
-def UInt16.shiftRight (a b : UInt16) : UInt16 := ⟨a.val >>> (modn b 16).val⟩
-def UInt16.lt (a b : UInt16) : Prop := a.val < b.val
-def UInt16.le (a b : UInt16) : Prop := a.val ≤ b.val
+def UInt16.shiftRight (a b : UInt16) : UInt16 := ⟨a.toBitVec >>> (mod b 16).toBitVec⟩
+def UInt16.lt (a b : UInt16) : Prop := a.toBitVec < b.toBitVec
+def UInt16.le (a b : UInt16) : Prop := a.toBitVec ≤ b.toBitVec
 
-instance UInt16.instOfNat : OfNat UInt16 n := ⟨UInt16.ofNat n⟩
 instance : Add UInt16       := ⟨UInt16.add⟩
 instance : Sub UInt16       := ⟨UInt16.sub⟩
 instance : Mul UInt16       := ⟨UInt16.mul⟩
 instance : Mod UInt16       := ⟨UInt16.mod⟩
+
+set_option linter.deprecated false in
 instance : HMod UInt16 Nat UInt16 := ⟨UInt16.modn⟩
+
 instance : Div UInt16       := ⟨UInt16.div⟩
 instance : LT UInt16        := ⟨UInt16.lt⟩
 instance : LE UInt16        := ⟨UInt16.le⟩
 
 @[extern "lean_uint16_complement"]
-def UInt16.complement (a:UInt16) : UInt16 := 0-(a+1)
+def UInt16.complement (a : UInt16) : UInt16 := ⟨~~~a.toBitVec⟩
 
 instance : Complement UInt16 := ⟨UInt16.complement⟩
 instance : AndOp UInt16     := ⟨UInt16.land⟩
@@ -132,74 +119,53 @@ instance : ShiftRight UInt16 := ⟨UInt16.shiftRight⟩
 set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint16_dec_lt"]
 def UInt16.decLt (a b : UInt16) : Decidable (a < b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n < m))
+  inferInstanceAs (Decidable (a.toBitVec < b.toBitVec))
 
 set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint16_dec_le"]
 def UInt16.decLe (a b : UInt16) : Decidable (a ≤ b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
+  inferInstanceAs (Decidable (a.toBitVec ≤ b.toBitVec))
 
 instance (a b : UInt16) : Decidable (a < b) := UInt16.decLt a b
 instance (a b : UInt16) : Decidable (a ≤ b) := UInt16.decLe a b
 instance : Max UInt16 := maxOfLe
 instance : Min UInt16 := minOfLe
 
-@[extern "lean_uint32_of_nat"]
-def UInt32.ofNat (n : @& Nat) : UInt32 := ⟨Fin.ofNat n⟩
-@[extern "lean_uint32_of_nat"]
-def UInt32.ofNat' (n : Nat) (h : n < UInt32.size) : UInt32 := ⟨⟨n, h⟩⟩
-/--
-Converts the given natural number to `UInt32`, but returns `2^32 - 1` for natural numbers `>= 2^32`.
--/
-def UInt32.ofNatTruncate (n : Nat) : UInt32 :=
-  if h : n < UInt32.size then
-    UInt32.ofNat' n h
-  else
-    UInt32.ofNat' (UInt32.size - 1) (by decide)
-abbrev Nat.toUInt32 := UInt32.ofNat
 @[extern "lean_uint32_add"]
-def UInt32.add (a b : UInt32) : UInt32 := ⟨a.val + b.val⟩
+def UInt32.add (a b : UInt32) : UInt32 := ⟨a.toBitVec + b.toBitVec⟩
 @[extern "lean_uint32_sub"]
-def UInt32.sub (a b : UInt32) : UInt32 := ⟨a.val - b.val⟩
+def UInt32.sub (a b : UInt32) : UInt32 := ⟨a.toBitVec - b.toBitVec⟩
 @[extern "lean_uint32_mul"]
-def UInt32.mul (a b : UInt32) : UInt32 := ⟨a.val * b.val⟩
+def UInt32.mul (a b : UInt32) : UInt32 := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_uint32_div"]
-def UInt32.div (a b : UInt32) : UInt32 := ⟨a.val / b.val⟩
+def UInt32.div (a b : UInt32) : UInt32 := ⟨BitVec.udiv a.toBitVec b.toBitVec⟩
 @[extern "lean_uint32_mod"]
-def UInt32.mod (a b : UInt32) : UInt32 := ⟨a.val % b.val⟩
-@[extern "lean_uint32_modn"]
+def UInt32.mod (a b : UInt32) : UInt32 := ⟨BitVec.umod a.toBitVec b.toBitVec⟩
+@[extern "lean_uint32_modn", deprecated UInt32.mod (since := "2024-09-23")]
 def UInt32.modn (a : UInt32) (n : @& Nat) : UInt32 := ⟨Fin.modn a.val n⟩
 @[extern "lean_uint32_land"]
-def UInt32.land (a b : UInt32) : UInt32 := ⟨Fin.land a.val b.val⟩
+def UInt32.land (a b : UInt32) : UInt32 := ⟨a.toBitVec &&& b.toBitVec⟩
 @[extern "lean_uint32_lor"]
-def UInt32.lor (a b : UInt32) : UInt32 := ⟨Fin.lor a.val b.val⟩
+def UInt32.lor (a b : UInt32) : UInt32 := ⟨a.toBitVec ||| b.toBitVec⟩
 @[extern "lean_uint32_xor"]
-def UInt32.xor (a b : UInt32) : UInt32 := ⟨Fin.xor a.val b.val⟩
+def UInt32.xor (a b : UInt32) : UInt32 := ⟨a.toBitVec ^^^ b.toBitVec⟩
 @[extern "lean_uint32_shift_left"]
-def UInt32.shiftLeft (a b : UInt32) : UInt32 := ⟨a.val <<< (modn b 32).val⟩
+def UInt32.shiftLeft (a b : UInt32) : UInt32 := ⟨a.toBitVec <<< (mod b 32).toBitVec⟩
 @[extern "lean_uint32_shift_right"]
-def UInt32.shiftRight (a b : UInt32) : UInt32 := ⟨a.val >>> (modn b 32).val⟩
-@[extern "lean_uint32_to_uint8"]
-def UInt32.toUInt8 (a : UInt32) : UInt8 := a.toNat.toUInt8
-@[extern "lean_uint32_to_uint16"]
-def UInt32.toUInt16 (a : UInt32) : UInt16 := a.toNat.toUInt16
-@[extern "lean_uint8_to_uint32"]
-def UInt8.toUInt32 (a : UInt8) : UInt32 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
-@[extern "lean_uint16_to_uint32"]
-def UInt16.toUInt32 (a : UInt16) : UInt32 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
+def UInt32.shiftRight (a b : UInt32) : UInt32 := ⟨a.toBitVec >>> (mod b 32).toBitVec⟩
 
-instance UInt32.instOfNat : OfNat UInt32 n := ⟨UInt32.ofNat n⟩
 instance : Add UInt32       := ⟨UInt32.add⟩
 instance : Sub UInt32       := ⟨UInt32.sub⟩
 instance : Mul UInt32       := ⟨UInt32.mul⟩
 instance : Mod UInt32       := ⟨UInt32.mod⟩
+
+set_option linter.deprecated false in
 instance : HMod UInt32 Nat UInt32 := ⟨UInt32.modn⟩
+
 instance : Div UInt32       := ⟨UInt32.div⟩
 
 @[extern "lean_uint32_complement"]
-def UInt32.complement (a:UInt32) : UInt32 := 0-(a+1)
+def UInt32.complement (a : UInt32) : UInt32 := ⟨~~~a.toBitVec⟩
 
 instance : Complement UInt32 := ⟨UInt32.complement⟩
 instance : AndOp UInt32     := ⟨UInt32.land⟩
@@ -208,60 +174,45 @@ instance : Xor UInt32       := ⟨UInt32.xor⟩
 instance : ShiftLeft UInt32  := ⟨UInt32.shiftLeft⟩
 instance : ShiftRight UInt32 := ⟨UInt32.shiftRight⟩
 
-@[extern "lean_uint64_of_nat"]
-def UInt64.ofNat (n : @& Nat) : UInt64 := ⟨Fin.ofNat n⟩
-abbrev Nat.toUInt64 := UInt64.ofNat
-@[extern "lean_uint64_to_nat"]
-def UInt64.toNat (n : UInt64) : Nat := n.val.val
 @[extern "lean_uint64_add"]
-def UInt64.add (a b : UInt64) : UInt64 := ⟨a.val + b.val⟩
+def UInt64.add (a b : UInt64) : UInt64 := ⟨a.toBitVec + b.toBitVec⟩
 @[extern "lean_uint64_sub"]
-def UInt64.sub (a b : UInt64) : UInt64 := ⟨a.val - b.val⟩
+def UInt64.sub (a b : UInt64) : UInt64 := ⟨a.toBitVec - b.toBitVec⟩
 @[extern "lean_uint64_mul"]
-def UInt64.mul (a b : UInt64) : UInt64 := ⟨a.val * b.val⟩
+def UInt64.mul (a b : UInt64) : UInt64 := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_uint64_div"]
-def UInt64.div (a b : UInt64) : UInt64 := ⟨a.val / b.val⟩
+def UInt64.div (a b : UInt64) : UInt64 := ⟨BitVec.udiv a.toBitVec b.toBitVec⟩
 @[extern "lean_uint64_mod"]
-def UInt64.mod (a b : UInt64) : UInt64 := ⟨a.val % b.val⟩
-@[extern "lean_uint64_modn"]
+def UInt64.mod (a b : UInt64) : UInt64 := ⟨BitVec.umod a.toBitVec b.toBitVec⟩
+@[extern "lean_uint64_modn", deprecated UInt64.mod (since := "2024-09-23")]
 def UInt64.modn (a : UInt64) (n : @& Nat) : UInt64 := ⟨Fin.modn a.val n⟩
 @[extern "lean_uint64_land"]
-def UInt64.land (a b : UInt64) : UInt64 := ⟨Fin.land a.val b.val⟩
+def UInt64.land (a b : UInt64) : UInt64 := ⟨a.toBitVec &&& b.toBitVec⟩
 @[extern "lean_uint64_lor"]
-def UInt64.lor (a b : UInt64) : UInt64 := ⟨Fin.lor a.val b.val⟩
+def UInt64.lor (a b : UInt64) : UInt64 := ⟨a.toBitVec ||| b.toBitVec⟩
 @[extern "lean_uint64_xor"]
-def UInt64.xor (a b : UInt64) : UInt64 := ⟨Fin.xor a.val b.val⟩
+def UInt64.xor (a b : UInt64) : UInt64 := ⟨a.toBitVec ^^^ b.toBitVec⟩
 @[extern "lean_uint64_shift_left"]
-def UInt64.shiftLeft (a b : UInt64) : UInt64 := ⟨a.val <<< (modn b 64).val⟩
+def UInt64.shiftLeft (a b : UInt64) : UInt64 := ⟨a.toBitVec <<< (mod b 64).toBitVec⟩
 @[extern "lean_uint64_shift_right"]
-def UInt64.shiftRight (a b : UInt64) : UInt64 := ⟨a.val >>> (modn b 64).val⟩
-def UInt64.lt (a b : UInt64) : Prop := a.val < b.val
-def UInt64.le (a b : UInt64) : Prop := a.val ≤ b.val
-@[extern "lean_uint64_to_uint8"]
-def UInt64.toUInt8 (a : UInt64) : UInt8 := a.toNat.toUInt8
-@[extern "lean_uint64_to_uint16"]
-def UInt64.toUInt16 (a : UInt64) : UInt16 := a.toNat.toUInt16
-@[extern "lean_uint64_to_uint32"]
-def UInt64.toUInt32 (a : UInt64) : UInt32 := a.toNat.toUInt32
-@[extern "lean_uint8_to_uint64"]
-def UInt8.toUInt64 (a : UInt8) : UInt64 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
-@[extern "lean_uint16_to_uint64"]
-def UInt16.toUInt64 (a : UInt16) : UInt64 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
-@[extern "lean_uint32_to_uint64"]
-def UInt32.toUInt64 (a : UInt32) : UInt64 := ⟨a.val, Nat.lt_trans a.1.2 (by decide)⟩
+def UInt64.shiftRight (a b : UInt64) : UInt64 := ⟨a.toBitVec >>> (mod b 64).toBitVec⟩
+def UInt64.lt (a b : UInt64) : Prop := a.toBitVec < b.toBitVec
+def UInt64.le (a b : UInt64) : Prop := a.toBitVec ≤ b.toBitVec
 
-instance UInt64.instOfNat : OfNat UInt64 n := ⟨UInt64.ofNat n⟩
 instance : Add UInt64       := ⟨UInt64.add⟩
 instance : Sub UInt64       := ⟨UInt64.sub⟩
 instance : Mul UInt64       := ⟨UInt64.mul⟩
 instance : Mod UInt64       := ⟨UInt64.mod⟩
+
+set_option linter.deprecated false in
 instance : HMod UInt64 Nat UInt64 := ⟨UInt64.modn⟩
+
 instance : Div UInt64       := ⟨UInt64.div⟩
 instance : LT UInt64        := ⟨UInt64.lt⟩
 instance : LE UInt64        := ⟨UInt64.le⟩
 
 @[extern "lean_uint64_complement"]
-def UInt64.complement (a:UInt64) : UInt64 := 0-(a+1)
+def UInt64.complement (a : UInt64) : UInt64 := ⟨~~~a.toBitVec⟩
 
 instance : Complement UInt64 := ⟨UInt64.complement⟩
 instance : AndOp UInt64     := ⟨UInt64.land⟩
@@ -273,79 +224,52 @@ instance : ShiftRight UInt64 := ⟨UInt64.shiftRight⟩
 @[extern "lean_bool_to_uint64"]
 def Bool.toUInt64 (b : Bool) : UInt64 := if b then 1 else 0
 
-set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint64_dec_lt"]
 def UInt64.decLt (a b : UInt64) : Decidable (a < b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n < m))
+  inferInstanceAs (Decidable (a.toBitVec < b.toBitVec))
 
-set_option bootstrap.genMatcherCode false in
 @[extern "lean_uint64_dec_le"]
 def UInt64.decLe (a b : UInt64) : Decidable (a ≤ b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
+  inferInstanceAs (Decidable (a.toBitVec ≤ b.toBitVec))
 
 instance (a b : UInt64) : Decidable (a < b) := UInt64.decLt a b
 instance (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
 instance : Max UInt64 := maxOfLe
 instance : Min UInt64 := minOfLe
 
--- This instance would interfere with the global instance `NeZero (n + 1)`,
--- so we only enable it locally.
-@[local instance]
-private def instNeZeroUSizeSize : NeZero USize.size := ⟨add_one_ne_zero _⟩
-
-@[deprecated (since := "2024-09-16")]
-theorem usize_size_gt_zero : USize.size > 0 :=
-  Nat.zero_lt_succ ..
-
-@[extern "lean_usize_of_nat"]
-def USize.ofNat (n : @& Nat) : USize := ⟨Fin.ofNat'  _ n⟩
-abbrev Nat.toUSize := USize.ofNat
-@[extern "lean_usize_to_nat"]
-def USize.toNat (n : USize) : Nat := n.val.val
-@[extern "lean_usize_add"]
-def USize.add (a b : USize) : USize := ⟨a.val + b.val⟩
-@[extern "lean_usize_sub"]
-def USize.sub (a b : USize) : USize := ⟨a.val - b.val⟩
 @[extern "lean_usize_mul"]
-def USize.mul (a b : USize) : USize := ⟨a.val * b.val⟩
+def USize.mul (a b : USize) : USize := ⟨a.toBitVec * b.toBitVec⟩
 @[extern "lean_usize_div"]
-def USize.div (a b : USize) : USize := ⟨a.val / b.val⟩
+def USize.div (a b : USize) : USize := ⟨a.toBitVec / b.toBitVec⟩
 @[extern "lean_usize_mod"]
-def USize.mod (a b : USize) : USize := ⟨a.val % b.val⟩
-@[extern "lean_usize_modn"]
+def USize.mod (a b : USize) : USize := ⟨a.toBitVec % b.toBitVec⟩
+@[extern "lean_usize_modn", deprecated USize.mod (since := "2024-09-23")]
 def USize.modn (a : USize) (n : @& Nat) : USize := ⟨Fin.modn a.val n⟩
 @[extern "lean_usize_land"]
-def USize.land (a b : USize) : USize := ⟨Fin.land a.val b.val⟩
+def USize.land (a b : USize) : USize := ⟨a.toBitVec &&& b.toBitVec⟩
 @[extern "lean_usize_lor"]
-def USize.lor (a b : USize) : USize := ⟨Fin.lor a.val b.val⟩
+def USize.lor (a b : USize) : USize := ⟨a.toBitVec ||| b.toBitVec⟩
 @[extern "lean_usize_xor"]
-def USize.xor (a b : USize) : USize := ⟨Fin.xor a.val b.val⟩
+def USize.xor (a b : USize) : USize := ⟨a.toBitVec ^^^ b.toBitVec⟩
 @[extern "lean_usize_shift_left"]
-def USize.shiftLeft (a b : USize) : USize := ⟨a.val <<< (modn b System.Platform.numBits).val⟩
+def USize.shiftLeft (a b : USize) : USize := ⟨a.toBitVec <<< (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
 @[extern "lean_usize_shift_right"]
-def USize.shiftRight (a b : USize) : USize := ⟨a.val >>> (modn b System.Platform.numBits).val⟩
+def USize.shiftRight (a b : USize) : USize := ⟨a.toBitVec >>> (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
 @[extern "lean_uint32_to_usize"]
-def UInt32.toUSize (a : UInt32) : USize := USize.ofNat32 a.val a.1.2
+def UInt32.toUSize (a : UInt32) : USize := USize.ofNat32 a.toBitVec.toNat a.toBitVec.isLt
 @[extern "lean_usize_to_uint32"]
 def USize.toUInt32 (a : USize) : UInt32 := a.toNat.toUInt32
 
-def USize.lt (a b : USize) : Prop := a.val < b.val
-def USize.le (a b : USize) : Prop := a.val ≤ b.val
-
-instance USize.instOfNat : OfNat USize n := ⟨USize.ofNat n⟩
-instance : Add USize       := ⟨USize.add⟩
-instance : Sub USize       := ⟨USize.sub⟩
 instance : Mul USize       := ⟨USize.mul⟩
 instance : Mod USize       := ⟨USize.mod⟩
+
+set_option linter.deprecated false in
 instance : HMod USize Nat USize := ⟨USize.modn⟩
+
 instance : Div USize       := ⟨USize.div⟩
-instance : LT USize        := ⟨USize.lt⟩
-instance : LE USize        := ⟨USize.le⟩
 
 @[extern "lean_usize_complement"]
-def USize.complement (a:USize) : USize := 0-(a+1)
+def USize.complement (a : USize) : USize := ⟨~~~a.toBitVec⟩
 
 instance : Complement USize := ⟨USize.complement⟩
 instance : AndOp USize      := ⟨USize.land⟩
@@ -354,19 +278,5 @@ instance : Xor USize        := ⟨USize.xor⟩
 instance : ShiftLeft USize  := ⟨USize.shiftLeft⟩
 instance : ShiftRight USize := ⟨USize.shiftRight⟩
 
-set_option bootstrap.genMatcherCode false in
-@[extern "lean_usize_dec_lt"]
-def USize.decLt (a b : USize) : Decidable (a < b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n < m))
-
-set_option bootstrap.genMatcherCode false in
-@[extern "lean_usize_dec_le"]
-def USize.decLe (a b : USize) : Decidable (a ≤ b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (n <= m))
-
-instance (a b : USize) : Decidable (a < b) := USize.decLt a b
-instance (a b : USize) : Decidable (a ≤ b) := USize.decLe a b
 instance : Max USize := maxOfLe
 instance : Min USize := minOfLe

src/Init/Data/UInt/BasicAux.lean

@@ -0,0 +1,132 @@
+/-
+Copyright (c) 2018 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Data.Fin.Basic
+import Init.Data.BitVec.BasicAux
+
+/-!
+This module exists to provide the very basic `UInt8` etc. definitions required for
+`Init.Data.Char.Basic` and `Init.Data.Array.Basic`. These are very important as they are used in
+meta code that is then (transitively) used in `Init.Data.UInt.Basic` and `Init.Data.BitVec.Basic`.
+This file thus breaks the import cycle that would be created by this dependency.
+-/
+
+open Nat
+
+def UInt8.val (x : UInt8) : Fin UInt8.size := x.toBitVec.toFin
+@[extern "lean_uint8_of_nat"]
+def UInt8.ofNat (n : @& Nat) : UInt8 := ⟨BitVec.ofNat 8 n⟩
+abbrev Nat.toUInt8 := UInt8.ofNat
+@[extern "lean_uint8_to_nat"]
+def UInt8.toNat (n : UInt8) : Nat := n.toBitVec.toNat
+
+instance UInt8.instOfNat : OfNat UInt8 n := ⟨UInt8.ofNat n⟩
+
+def UInt16.val (x : UInt16) : Fin UInt16.size := x.toBitVec.toFin
+@[extern "lean_uint16_of_nat"]
+def UInt16.ofNat (n : @& Nat) : UInt16 := ⟨BitVec.ofNat 16 n⟩
+abbrev Nat.toUInt16 := UInt16.ofNat
+@[extern "lean_uint16_to_nat"]
+def UInt16.toNat (n : UInt16) : Nat := n.toBitVec.toNat
+@[extern "lean_uint16_to_uint8"]
+def UInt16.toUInt8 (a : UInt16) : UInt8 := a.toNat.toUInt8
+@[extern "lean_uint8_to_uint16"]
+def UInt8.toUInt16 (a : UInt8) : UInt16 := ⟨⟨a.toNat, Nat.lt_trans a.toBitVec.isLt (by decide)⟩⟩
+
+instance UInt16.instOfNat : OfNat UInt16 n := ⟨UInt16.ofNat n⟩
+
+def UInt32.val (x : UInt32) : Fin UInt32.size := x.toBitVec.toFin
+@[extern "lean_uint32_of_nat"]
+def UInt32.ofNat (n : @& Nat) : UInt32 := ⟨BitVec.ofNat 32 n⟩
+@[extern "lean_uint32_of_nat"]
+def UInt32.ofNat' (n : Nat) (h : n < UInt32.size) : UInt32 := ⟨BitVec.ofNatLt n h⟩
+/--
+Converts the given natural number to `UInt32`, but returns `2^32 - 1` for natural numbers `>= 2^32`.
+-/
+def UInt32.ofNatTruncate (n : Nat) : UInt32 :=
+  if h : n < UInt32.size then
+    UInt32.ofNat' n h
+  else
+    UInt32.ofNat' (UInt32.size - 1) (by decide)
+abbrev Nat.toUInt32 := UInt32.ofNat
+@[extern "lean_uint32_to_uint8"]
+def UInt32.toUInt8 (a : UInt32) : UInt8 := a.toNat.toUInt8
+@[extern "lean_uint32_to_uint16"]
+def UInt32.toUInt16 (a : UInt32) : UInt16 := a.toNat.toUInt16
+@[extern "lean_uint8_to_uint32"]
+def UInt8.toUInt32 (a : UInt8) : UInt32 := ⟨⟨a.toNat, Nat.lt_trans a.toBitVec.isLt (by decide)⟩⟩
+@[extern "lean_uint16_to_uint32"]
+def UInt16.toUInt32 (a : UInt16) : UInt32 := ⟨⟨a.toNat, Nat.lt_trans a.toBitVec.isLt (by decide)⟩⟩
+
+instance UInt32.instOfNat : OfNat UInt32 n := ⟨UInt32.ofNat n⟩
+
+theorem UInt32.ofNat'_lt_of_lt {n m : Nat} (h1 : n < UInt32.size) (h2 : m < UInt32.size) :
+     n < m → UInt32.ofNat' n h1 < UInt32.ofNat m := by
+  simp only [(· < ·), BitVec.toNat, ofNat', BitVec.ofNatLt, ofNat, BitVec.ofNat, Fin.ofNat',
+    Nat.mod_eq_of_lt h2, imp_self]
+
+theorem UInt32.lt_ofNat'_of_lt {n m : Nat} (h1 : n < UInt32.size) (h2 : m < UInt32.size) :
+     m < n → UInt32.ofNat m < UInt32.ofNat' n h1  := by
+  simp only [(· < ·), BitVec.toNat, ofNat', BitVec.ofNatLt, ofNat, BitVec.ofNat, Fin.ofNat',
+    Nat.mod_eq_of_lt h2, imp_self]
+
+def UInt64.val (x : UInt64) : Fin UInt64.size := x.toBitVec.toFin
+@[extern "lean_uint64_of_nat"]
+def UInt64.ofNat (n : @& Nat) : UInt64 := ⟨BitVec.ofNat 64 n⟩
+abbrev Nat.toUInt64 := UInt64.ofNat
+@[extern "lean_uint64_to_nat"]
+def UInt64.toNat (n : UInt64) : Nat := n.toBitVec.toNat
+@[extern "lean_uint64_to_uint8"]
+def UInt64.toUInt8 (a : UInt64) : UInt8 := a.toNat.toUInt8
+@[extern "lean_uint64_to_uint16"]
+def UInt64.toUInt16 (a : UInt64) : UInt16 := a.toNat.toUInt16
+@[extern "lean_uint64_to_uint32"]
+def UInt64.toUInt32 (a : UInt64) : UInt32 := a.toNat.toUInt32
+@[extern "lean_uint8_to_uint64"]
+def UInt8.toUInt64 (a : UInt8) : UInt64 := ⟨⟨a.toNat, Nat.lt_trans a.toBitVec.isLt (by decide)⟩⟩
+@[extern "lean_uint16_to_uint64"]
+def UInt16.toUInt64 (a : UInt16) : UInt64 := ⟨⟨a.toNat, Nat.lt_trans a.toBitVec.isLt (by decide)⟩⟩
+@[extern "lean_uint32_to_uint64"]
+def UInt32.toUInt64 (a : UInt32) : UInt64 := ⟨⟨a.toNat, Nat.lt_trans a.toBitVec.isLt (by decide)⟩⟩
+
+instance UInt64.instOfNat : OfNat UInt64 n := ⟨UInt64.ofNat n⟩
+
+theorem usize_size_gt_zero : USize.size > 0 := by
+  cases usize_size_eq with
+  | inl h => rw [h]; decide
+  | inr h => rw [h]; decide
+
+def USize.val (x : USize) : Fin USize.size := x.toBitVec.toFin
+@[extern "lean_usize_of_nat"]
+def USize.ofNat (n : @& Nat) : USize := ⟨BitVec.ofNat _ n⟩
+abbrev Nat.toUSize := USize.ofNat
+@[extern "lean_usize_to_nat"]
+def USize.toNat (n : USize) : Nat := n.toBitVec.toNat
+@[extern "lean_usize_add"]
+def USize.add (a b : USize) : USize := ⟨a.toBitVec + b.toBitVec⟩
+@[extern "lean_usize_sub"]
+def USize.sub (a b : USize) : USize := ⟨a.toBitVec - b.toBitVec⟩
+
+def USize.lt (a b : USize) : Prop := a.toBitVec < b.toBitVec
+def USize.le (a b : USize) : Prop := a.toBitVec ≤ b.toBitVec
+
+instance USize.instOfNat : OfNat USize n := ⟨USize.ofNat n⟩
+
+instance : Add USize       := ⟨USize.add⟩
+instance : Sub USize       := ⟨USize.sub⟩
+instance : LT USize        := ⟨USize.lt⟩
+instance : LE USize        := ⟨USize.le⟩
+
+@[extern "lean_usize_dec_lt"]
+def USize.decLt (a b : USize) : Decidable (a < b) :=
+  inferInstanceAs (Decidable (a.toBitVec < b.toBitVec))
+
+@[extern "lean_usize_dec_le"]
+def USize.decLe (a b : USize) : Decidable (a ≤ b) :=
+  inferInstanceAs (Decidable (a.toBitVec ≤ b.toBitVec))
+
+instance (a b : USize) : Decidable (a < b) := USize.decLt a b
+instance (a b : USize) : Decidable (a ≤ b) := USize.decLe a b

src/Init/Data/UInt/Bitwise.lean

@@ -6,13 +6,14 @@ Authors: Markus Himmel
 prelude
 import Init.Data.UInt.Basic
 import Init.Data.Fin.Bitwise
+import Init.Data.BitVec.Lemmas
 
 set_option hygiene false in
 macro "declare_bitwise_uint_theorems" typeName:ident : command =>
 `(
 namespace $typeName
 
-@[simp] protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := Fin.and_val ..
+@[simp] protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
 
 end $typeName
 )

src/Init/Data/UInt/Lemmas.lean

@@ -6,6 +6,8 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.UInt.Basic
 import Init.Data.Fin.Lemmas
+import Init.Data.BitVec.Lemmas
+import Init.Data.BitVec.Bitblast
 
 set_option hygiene false in
 macro "declare_uint_theorems" typeName:ident : command =>
@@ -17,50 +19,111 @@ instance : Inhabited $typeName where
 
 theorem zero_def : (0 : $typeName) = ⟨0⟩ := rfl
 theorem one_def : (1 : $typeName) = ⟨1⟩ := rfl
-theorem sub_def (a b : $typeName) : a - b = ⟨a.val - b.val⟩ := rfl
-theorem mul_def (a b : $typeName) : a * b = ⟨a.val * b.val⟩ := rfl
-theorem mod_def (a b : $typeName) : a % b = ⟨a.val % b.val⟩ := rfl
-theorem add_def (a b : $typeName) : a + b = ⟨a.val + b.val⟩ := rfl
+theorem sub_def (a b : $typeName) : a - b = ⟨a.toBitVec - b.toBitVec⟩ := rfl
+theorem mul_def (a b : $typeName) : a * b = ⟨a.toBitVec * b.toBitVec⟩ := rfl
+theorem mod_def (a b : $typeName) : a % b = ⟨a.toBitVec % b.toBitVec⟩ := rfl
+theorem add_def (a b : $typeName) : a + b = ⟨a.toBitVec + b.toBitVec⟩ := rfl
 
-@[simp] theorem mk_val_eq : ∀ (a : $typeName), mk a.val = a
+@[simp] theorem mk_toBitVec_eq : ∀ (a : $typeName), mk a.toBitVec = a
   | ⟨_, _⟩ => rfl
-theorem val_eq_of_lt {a : Nat} : a < size → ((ofNat a).val : Nat) = a :=
-  Nat.mod_eq_of_lt
-theorem toNat_ofNat_of_lt {n : Nat} (h : n < size) : (ofNat n).toNat = n := by
-  rw [toNat, val_eq_of_lt h]
 
-theorem le_def {a b : $typeName} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
-theorem lt_def {a b : $typeName} : a < b ↔ a.1 < b.1 := .rfl
-theorem lt_iff_val_lt_val {a b : $typeName} : a < b ↔ a.val < b.val := .rfl
-@[simp] protected theorem not_le {a b : $typeName} : ¬ a ≤ b ↔ b < a := Fin.not_le
-@[simp] protected theorem not_lt {a b : $typeName} : ¬ a < b ↔ b ≤ a := Fin.not_lt
+theorem toBitVec_eq_of_lt {a : Nat} : a < size → (ofNat a).toBitVec.toNat = a :=
+  Nat.mod_eq_of_lt
+
+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
+
+theorem lt_def {a b : $typeName} : a < b ↔ a.toBitVec < b.toBitVec := .rfl
+
+@[simp] protected theorem not_le {a b : $typeName} : ¬ a ≤ b ↔ b < a := by simp [le_def, lt_def]
+
+@[simp] protected theorem not_lt {a b : $typeName} : ¬ a < b ↔ b ≤ a := by simp [le_def, lt_def]
+
 @[simp] protected theorem le_refl (a : $typeName) : a ≤ a := by simp [le_def]
+
 @[simp] protected theorem lt_irrefl (a : $typeName) : ¬ a < a := by simp
-protected theorem le_trans {a b c : $typeName} : a ≤ b → b ≤ c → a ≤ c := Fin.le_trans
-protected theorem lt_trans {a b c : $typeName} : a < b → b < c → a < c := Fin.lt_trans
-protected theorem le_total (a b : $typeName) : a ≤ b ∨ b ≤ a := Fin.le_total a.1 b.1
-protected theorem lt_asymm {a b : $typeName} (h : a < b) : ¬ b < a := Fin.lt_asymm h
-protected theorem val_eq_of_eq {a b : $typeName} (h : a = b) : a.val = b.val := h ▸ rfl
-protected theorem eq_of_val_eq {a b : $typeName} (h : a.val = b.val) : a = b := by cases a; cases b; simp at h; simp [h]
-open $typeName (val_eq_of_eq) in
-protected theorem ne_of_val_ne {a b : $typeName} (h : a.val ≠ b.val) : a ≠ b := fun h' => absurd (val_eq_of_eq h') h
-open $typeName (ne_of_val_ne) in
-protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := ne_of_val_ne (Fin.ne_of_lt h)
+
+protected theorem le_trans {a b c : $typeName} : a ≤ b → b ≤ c → a ≤ c := BitVec.le_trans
+
+protected theorem lt_trans {a b c : $typeName} : a < b → b < c → a < c := BitVec.lt_trans
+
+protected theorem le_total (a b : $typeName) : a ≤ b ∨ b ≤ a := BitVec.le_total ..
+
+protected theorem lt_asymm {a b : $typeName} : a < b → ¬ b < a := BitVec.lt_asymm
+
+protected theorem toBitVec_eq_of_eq {a b : $typeName} (h : a = b) : a.toBitVec = b.toBitVec := h ▸ rfl
+
+protected theorem eq_of_toBitVec_eq {a b : $typeName} (h : a.toBitVec = b.toBitVec) : a = b := by
+  cases a; cases b; simp_all
+
+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]
+
+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) in
+protected theorem ne_of_lt {a b : $typeName} (h : a < b) : a ≠ b := by
+  apply ne_of_toBitVec_ne
+  apply BitVec.ne_of_lt
+  simpa [lt_def] using h
 
 @[simp] protected theorem toNat_zero : (0 : $typeName).toNat = 0 := Nat.zero_mod _
-@[simp] protected theorem toNat_mod (a b : $typeName) : (a % b).toNat = a.toNat % b.toNat := Fin.mod_val ..
-@[simp] protected theorem toNat_div (a b : $typeName) : (a / b).toNat = a.toNat / b.toNat := Fin.div_val ..
-@[simp] protected theorem toNat_sub_of_le (a b : $typeName) : b ≤ a → (a - b).toNat = a.toNat - b.toNat := Fin.sub_val_of_le
-@[simp] protected theorem toNat_modn (a : $typeName) (b : Nat) : (a.modn b).toNat = a.toNat % b := Fin.modn_val ..
-protected theorem modn_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % m) < m
-  | ⟨u⟩, h => Fin.modn_lt u h
-open $typeName (modn_lt) in
-protected theorem mod_lt (a b : $typeName) (h : 0 < b) : a % b < b := modn_lt _ (by simp [lt_def] at h; exact h)
+
+@[simp] protected theorem toNat_mod (a b : $typeName) : (a % b).toNat = a.toNat % b.toNat := BitVec.toNat_umod ..
+
+@[simp] protected theorem toNat_div (a b : $typeName) : (a / b).toNat = a.toNat / b.toNat := BitVec.toNat_udiv  ..
+
+@[simp] protected theorem toNat_sub_of_le (a b : $typeName) : b ≤ a → (a - b).toNat = a.toNat - b.toNat := BitVec.toNat_sub_of_le
+
+protected theorem toNat_lt_size (a : $typeName) : a.toNat < size := a.toBitVec.isLt
+
+open $typeName (toNat_mod toNat_lt_size) in
+protected theorem toNat_mod_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % ofNat m) < m := by
+  intro u h1
+  by_cases h2 : m < size
+  · rw [toNat_mod, toNat_ofNat_of_lt h2]
+    apply Nat.mod_lt _ h1
+  · apply Nat.lt_of_lt_of_le
+    · apply toNat_lt_size
+    · simpa using h2
+
+open $typeName (toNat_mod_lt) in
+set_option linter.deprecated false in
+@[deprecated toNat_mod_lt (since := "2024-09-24")]
+protected theorem modn_lt {m : Nat} : ∀ (u : $typeName), m > 0 → toNat (u % m) < m := by
+  intro u
+  simp only [(· % ·)]
+  simp only [gt_iff_lt, toNat, modn, Fin.modn_val, BitVec.natCast_eq_ofNat, BitVec.toNat_ofNat,
+    Nat.reducePow]
+  rw [Nat.mod_eq_of_lt]
+  · apply Nat.mod_lt
+  · apply Nat.lt_of_le_of_lt
+    · apply Nat.mod_le
+    · apply Fin.is_lt
+
+protected theorem mod_lt (a : $typeName) {b : $typeName} : 0 < b → a % b < b := by
+  simp only [lt_def, mod_def]
+  apply BitVec.umod_lt
+
 protected theorem toNat.inj : ∀ {a b : $typeName}, a.toNat = b.toNat → a = b
   | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
-protected theorem toNat_lt_size (a : $typeName) : a.toNat < size := a.1.2
+
 @[simp] protected theorem ofNat_one : ofNat 1 = 1 := rfl
 
+@[simp]
+theorem val_ofNat (n : Nat) : val (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
+
+@[simp]
+theorem toBitVec_ofNat (n : Nat) : toBitVec (no_index (OfNat.ofNat n)) = BitVec.ofNat _ n := rfl
+
+@[simp]
+theorem mk_ofNat (n : Nat) : mk (BitVec.ofNat _ n) = OfNat.ofNat n := rfl
+
 end $typeName
 )
 
@@ -70,27 +133,34 @@ declare_uint_theorems UInt32
 declare_uint_theorems UInt64
 declare_uint_theorems USize
 
+theorem UInt32.toNat_lt_of_lt {n : UInt32} {m : Nat} (h : m < size) : n < ofNat m → n.toNat < m := by
+  simp [lt_def, BitVec.lt_def, UInt32.toNat, toBitVec_eq_of_lt h]
+
+theorem UInt32.lt_toNat_of_lt {n : UInt32} {m : Nat} (h : m < size) : ofNat m < n → m < n.toNat := by
+  simp [lt_def, BitVec.lt_def, UInt32.toNat, toBitVec_eq_of_lt h]
+
+theorem UInt32.toNat_le_of_le {n : UInt32} {m : Nat} (h : m < size) : n ≤ ofNat m → n.toNat ≤ m := by
+  simp [le_def, BitVec.le_def, UInt32.toNat, toBitVec_eq_of_lt h]
+
+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 (since := "2024-06-23")] protected abbrev UInt8.zero_toNat := @UInt8.toNat_zero
 @[deprecated (since := "2024-06-23")] protected abbrev UInt8.div_toNat := @UInt8.toNat_div
 @[deprecated (since := "2024-06-23")] protected abbrev UInt8.mod_toNat := @UInt8.toNat_mod
-@[deprecated (since := "2024-06-23")] protected abbrev UInt8.modn_toNat := @UInt8.toNat_modn
 
 @[deprecated (since := "2024-06-23")] protected abbrev UInt16.zero_toNat := @UInt16.toNat_zero
 @[deprecated (since := "2024-06-23")] protected abbrev UInt16.div_toNat := @UInt16.toNat_div
 @[deprecated (since := "2024-06-23")] protected abbrev UInt16.mod_toNat := @UInt16.toNat_mod
-@[deprecated (since := "2024-06-23")] protected abbrev UInt16.modn_toNat := @UInt16.toNat_modn
 
 @[deprecated (since := "2024-06-23")] protected abbrev UInt32.zero_toNat := @UInt32.toNat_zero
 @[deprecated (since := "2024-06-23")] protected abbrev UInt32.div_toNat := @UInt32.toNat_div
 @[deprecated (since := "2024-06-23")] protected abbrev UInt32.mod_toNat := @UInt32.toNat_mod
-@[deprecated (since := "2024-06-23")] protected abbrev UInt32.modn_toNat := @UInt32.toNat_modn
 
 @[deprecated (since := "2024-06-23")] protected abbrev UInt64.zero_toNat := @UInt64.toNat_zero
 @[deprecated (since := "2024-06-23")] protected abbrev UInt64.div_toNat := @UInt64.toNat_div
 @[deprecated (since := "2024-06-23")] protected abbrev UInt64.mod_toNat := @UInt64.toNat_mod
-@[deprecated (since := "2024-06-23")] protected abbrev UInt64.modn_toNat := @UInt64.toNat_modn
 
 @[deprecated (since := "2024-06-23")] protected abbrev USize.zero_toNat := @USize.toNat_zero
 @[deprecated (since := "2024-06-23")] protected abbrev USize.div_toNat := @USize.toNat_div
 @[deprecated (since := "2024-06-23")] protected abbrev USize.mod_toNat := @USize.toNat_mod
-@[deprecated (since := "2024-06-23")] protected abbrev USize.modn_toNat := @USize.toNat_modn

src/Init/Data/UInt/Log2.lean

@@ -7,16 +7,16 @@ prelude
 import Init.Data.Fin.Log2
 
 @[extern "lean_uint8_log2"]
-def UInt8.log2 (a : UInt8) : UInt8 := ⟨Fin.log2 a.val⟩
+def UInt8.log2 (a : UInt8) : UInt8 := ⟨⟨Fin.log2 a.val⟩⟩
 
 @[extern "lean_uint16_log2"]
-def UInt16.log2 (a : UInt16) : UInt16 := ⟨Fin.log2 a.val⟩
+def UInt16.log2 (a : UInt16) : UInt16 := ⟨⟨Fin.log2 a.val⟩⟩
 
 @[extern "lean_uint32_log2"]
-def UInt32.log2 (a : UInt32) : UInt32 := ⟨Fin.log2 a.val⟩
+def UInt32.log2 (a : UInt32) : UInt32 := ⟨⟨Fin.log2 a.val⟩⟩
 
 @[extern "lean_uint64_log2"]
-def UInt64.log2 (a : UInt64) : UInt64 := ⟨Fin.log2 a.val⟩
+def UInt64.log2 (a : UInt64) : UInt64 := ⟨⟨Fin.log2 a.val⟩⟩
 
 @[extern "lean_usize_log2"]
-def USize.log2 (a : USize) : USize := ⟨Fin.log2 a.val⟩
+def USize.log2 (a : USize) : USize := ⟨⟨Fin.log2 a.val⟩⟩

src/Init/MetaTypes.lean

@@ -224,11 +224,7 @@ structure Config where
   -/
   index             : Bool := true
   /--
-  When `true` (default: `true`), `simp` will **not** create a proof for a rewriting rule associated
-  with an `rfl`-theorem.
-  Rewriting rules are provided by users by annotating theorems with the attribute `@[simp]`.
-  If the proof of the theorem is just `rfl` (reflexivity), and `implicitDefEqProofs := true`, `simp`
-  will **not** create a proof term which is an application of the annotated theorem.
+  This option does not have any effect (yet).
   -/
   implicitDefEqProofs : Bool := true
   deriving Inhabited, BEq

src/Init/Notation.lean

@@ -535,24 +535,21 @@ syntax (name := includeStr) "include_str " term : term
 
 /--
 The `run_cmd doSeq` command executes code in `CommandElabM Unit`.
-This is almost the same as `#eval show CommandElabM Unit from do doSeq`,
-except that it doesn't print an empty diagnostic.
+This is the same as `#eval show CommandElabM Unit from discard do doSeq`.
 -/
 syntax (name := runCmd) "run_cmd " doSeq : command
 
 /--
 The `run_elab doSeq` command executes code in `TermElabM Unit`.
-This is almost the same as `#eval show TermElabM Unit from do doSeq`,
-except that it doesn't print an empty diagnostic.
+This is the same as `#eval show TermElabM Unit from discard do doSeq`.
 -/
 syntax (name := runElab) "run_elab " doSeq : command
 
 /--
 The `run_meta doSeq` command executes code in `MetaM Unit`.
-This is almost the same as `#eval show MetaM Unit from do doSeq`,
-except that it doesn't print an empty diagnostic.
+This is the same as `#eval show MetaM Unit from do discard doSeq`.
 
-(This is effectively a synonym for `run_elab`.)
+(This is effectively a synonym for `run_elab` since `MetaM` lifts to `TermElabM`.)
 -/
 syntax (name := runMeta) "run_meta " doSeq : command
 
@@ -675,6 +672,13 @@ Message ordering:
 
 For example, `#guard_msgs (error, drop all) in cmd` means to check warnings and drop
 everything else.
+
+The command elaborator has special support for `#guard_msgs` for linting.
+The `#guard_msgs` itself wants to capture linter warnings,
+so it elaborates the command it is attached to as if it were a top-level command.
+However, the command elaborator runs linters for *all* top-level commands,
+which would include `#guard_msgs` itself, and would cause duplicate and/or uncaptured linter warnings.
+The top-level command elaborator only runs the linters if `#guard_msgs` is not present.
 -/
 syntax (name := guardMsgsCmd)
   (docComment)? "#guard_msgs" (ppSpace guardMsgsSpec)? " in" ppLine command : command

src/Init/NotationExtra.lean

@@ -10,6 +10,7 @@ import Init.Data.ToString.Basic
 import Init.Data.Array.Subarray
 import Init.Conv
 import Init.Meta
+import Init.While
 
 namespace Lean
 
@@ -168,9 +169,9 @@ end Lean
   | _                => throw ()
 
 @[app_unexpander sorryAx] def unexpandSorryAx : Lean.PrettyPrinter.Unexpander
-  | `($(_) _)   => `(sorry)
-  | `($(_) _ _) => `(sorry)
-  | _           => throw ()
+  | `($(_) $_)    => `(sorry)
+  | `($(_) $_ $_) => `(sorry)
+  | _             => throw ()
 
 @[app_unexpander Eq.ndrec] def unexpandEqNDRec : Lean.PrettyPrinter.Unexpander
   | `($(_) $m $h) => `($h ▸ $m)
@@ -223,38 +224,6 @@ end Lean
   | `($_ $array $index) => `($array[$index]?)
   | _ => throw ()
 
-@[app_unexpander Name.mkStr1] def unexpandMkStr1 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++  a.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr2] def unexpandMkStr2 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr3] def unexpandMkStr3 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr4] def unexpandMkStr4 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr5] def unexpandMkStr5 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr6] def unexpandMkStr6 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString ++ "." ++ a6.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr7] def unexpandMkStr7 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str $a7:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString ++ "." ++ a6.getString ++ "." ++ a7.getString)]
-  | _  => throw ()
-
-@[app_unexpander Name.mkStr8] def unexpandMkStr8 : Lean.PrettyPrinter.Unexpander
-  | `($(_) $a1:str $a2:str $a3:str $a4:str $a5:str $a6:str $a7:str $a8:str) => return mkNode `Lean.Parser.Term.quotedName #[Syntax.mkNameLit ("`" ++ a1.getString ++ "." ++ a2.getString ++ "." ++ a3.getString ++ "." ++ a4.getString ++ "." ++ a5.getString ++ "." ++ a6.getString ++ "." ++ a7.getString ++ "." ++ a8.getString)]
-  | _  => throw ()
-
 @[app_unexpander Array.empty] def unexpandArrayEmpty : Lean.PrettyPrinter.Unexpander
   | _ => `(#[])
 
@@ -376,42 +345,6 @@ syntax (name := solveTactic) "solve" withPosition((ppDedent(ppLine) colGe "| " t
 macro_rules
   | `(tactic| solve $[| $ts]* ) => `(tactic| focus first $[| ($ts); done]*)
 
-/-! # `repeat` and `while` notation -/
-
-inductive Loop where
-  | mk
-
-@[inline]
-partial def Loop.forIn {β : Type u} {m : Type u → Type v} [Monad m] (_ : Loop) (init : β) (f : Unit → β → m (ForInStep β)) : m β :=
-  let rec @[specialize] loop (b : β) : m β := do
-    match ← f () b with
-      | ForInStep.done b  => pure b
-      | ForInStep.yield b => loop b
-  loop init
-
-instance : ForIn m Loop Unit where
-  forIn := Loop.forIn
-
-syntax "repeat " doSeq : doElem
-
-macro_rules
-  | `(doElem| repeat $seq) => `(doElem| for _ in Loop.mk do $seq)
-
-syntax "while " ident " : " termBeforeDo " do " doSeq : doElem
-
-macro_rules
-  | `(doElem| while $h : $cond do $seq) => `(doElem| repeat if $h : $cond then $seq else break)
-
-syntax "while " termBeforeDo " do " doSeq : doElem
-
-macro_rules
-  | `(doElem| while $cond do $seq) => `(doElem| repeat if $cond then $seq else break)
-
-syntax "repeat " doSeq ppDedent(ppLine) "until " term : doElem
-
-macro_rules
-  | `(doElem| repeat $seq until $cond) => `(doElem| repeat do $seq:doSeq; if $cond then break)
-
 macro:50 e:term:51 " matches " p:sepBy1(term:51, " | ") : term =>
   `(((match $e:term with | $[$p:term]|* => true | _ => false) : Bool))
 

src/Init/Prelude.lean

@@ -1592,9 +1592,6 @@ def Nat.beq : (@& Nat) → (@& Nat) → Bool
   | succ _, zero   => false
   | succ n, succ m => beq n m
 
-instance : BEq Nat where
-  beq := Nat.beq
-
 theorem Nat.eq_of_beq_eq_true : {n m : Nat} → Eq (beq n m) true → Eq n m
   | zero,   zero,   _ => rfl
   | zero,   succ _, h => Bool.noConfusion h
@@ -1869,6 +1866,52 @@ instance {n} : LE (Fin n) where
 instance Fin.decLt {n} (a b : Fin n) : Decidable (LT.lt a b) := Nat.decLt ..
 instance Fin.decLe {n} (a b : Fin n) : Decidable (LE.le a b) := Nat.decLe ..
 
+/--
+A bitvector of the specified width.
+
+This is represented as the underlying `Nat` number in both the runtime
+and the kernel, inheriting all the special support for `Nat`.
+-/
+structure BitVec (w : Nat) where
+  /-- Construct a `BitVec w` from a number less than `2^w`.
+  O(1), because we use `Fin` as the internal representation of a bitvector. -/
+  ofFin ::
+  /-- Interpret a bitvector as a number less than `2^w`.
+  O(1), because we use `Fin` as the internal representation of a bitvector. -/
+  toFin : Fin (hPow 2 w)
+
+/--
+Bitvectors have decidable equality. This should be used via the instance `DecidableEq (BitVec n)`.
+-/
+-- We manually derive the `DecidableEq` instances for `BitVec` because
+-- we want to have builtin support for bit-vector literals, and we
+-- need a name for this function to implement `canUnfoldAtMatcher` at `WHNF.lean`.
+def BitVec.decEq (x y : BitVec n) : Decidable (Eq x y) :=
+  match x, y with
+  | ⟨n⟩, ⟨m⟩ =>
+    dite (Eq n m)
+      (fun h => isTrue (h ▸ rfl))
+      (fun h => isFalse (fun h' => BitVec.noConfusion h' (fun h' => absurd h' h)))
+
+instance : DecidableEq (BitVec n) := BitVec.decEq
+
+/-- The `BitVec` with value `i`, given a proof that `i < 2^n`. -/
+@[match_pattern]
+protected def BitVec.ofNatLt {n : Nat} (i : Nat) (p : LT.lt i (hPow 2 n)) : BitVec n where
+  toFin := ⟨i, p⟩
+
+/-- Given a bitvector `x`, return the underlying `Nat`. This is O(1) because `BitVec` is a
+(zero-cost) wrapper around a `Nat`. -/
+protected def BitVec.toNat (x : BitVec n) : Nat := x.toFin.val
+
+instance : LT (BitVec n) where lt := (LT.lt ·.toNat ·.toNat)
+instance (x y : BitVec n) : Decidable (LT.lt x y) :=
+  inferInstanceAs (Decidable (LT.lt x.toNat y.toNat))
+
+instance : LE (BitVec n) where le := (LE.le ·.toNat ·.toNat)
+instance (x y : BitVec n) : Decidable (LE.le x y) :=
+  inferInstanceAs (Decidable (LE.le x.toNat y.toNat))
+
 /-- The size of type `UInt8`, that is, `2^8 = 256`. -/
 abbrev UInt8.size : Nat := 256
 
@@ -1877,12 +1920,12 @@ The type of unsigned 8-bit integers. This type has special support in the
 compiler to make it actually 8 bits rather than wrapping a `Nat`.
 -/
 structure UInt8 where
-  /-- Unpack a `UInt8` as a `Nat` less than `2^8`.
+  /-- Unpack a `UInt8` as a `BitVec 8`.
   This function is overridden with a native implementation. -/
-  val : Fin UInt8.size
+  toBitVec : BitVec 8
 
 attribute [extern "lean_uint8_of_nat_mk"] UInt8.mk
-attribute [extern "lean_uint8_to_nat"] UInt8.val
+attribute [extern "lean_uint8_to_nat"] UInt8.toBitVec
 
 /--
 Pack a `Nat` less than `2^8` into a `UInt8`.
@@ -1890,7 +1933,7 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_uint8_of_nat"]
 def UInt8.ofNatCore (n : @& Nat) (h : LT.lt n UInt8.size) : UInt8 where
-  val := { val := n, isLt := h }
+  toBitVec := BitVec.ofNatLt n h
 
 set_option bootstrap.genMatcherCode false in
 /--
@@ -1901,7 +1944,9 @@ This function is overridden with a native implementation.
 def UInt8.decEq (a b : UInt8) : Decidable (Eq a b) :=
   match a, b with
   | ⟨n⟩, ⟨m⟩ =>
-    dite (Eq n m) (fun h => isTrue (h ▸ rfl)) (fun h => isFalse (fun h' => UInt8.noConfusion h' (fun h' => absurd h' h)))
+    dite (Eq n m)
+      (fun h => isTrue (h ▸ rfl))
+      (fun h => isFalse (fun h' => UInt8.noConfusion h' (fun h' => absurd h' h)))
 
 instance : DecidableEq UInt8 := UInt8.decEq
 
@@ -1916,12 +1961,12 @@ The type of unsigned 16-bit integers. This type has special support in the
 compiler to make it actually 16 bits rather than wrapping a `Nat`.
 -/
 structure UInt16 where
-  /-- Unpack a `UInt16` as a `Nat` less than `2^16`.
+  /-- Unpack a `UInt16` as a `BitVec 16`.
   This function is overridden with a native implementation. -/
-  val : Fin UInt16.size
+  toBitVec : BitVec 16
 
 attribute [extern "lean_uint16_of_nat_mk"] UInt16.mk
-attribute [extern "lean_uint16_to_nat"] UInt16.val
+attribute [extern "lean_uint16_to_nat"] UInt16.toBitVec
 
 /--
 Pack a `Nat` less than `2^16` into a `UInt16`.
@@ -1929,7 +1974,7 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_uint16_of_nat"]
 def UInt16.ofNatCore (n : @& Nat) (h : LT.lt n UInt16.size) : UInt16 where
-  val := { val := n, isLt := h }
+  toBitVec := BitVec.ofNatLt n h
 
 set_option bootstrap.genMatcherCode false in
 /--
@@ -1940,7 +1985,9 @@ This function is overridden with a native implementation.
 def UInt16.decEq (a b : UInt16) : Decidable (Eq a b) :=
   match a, b with
   | ⟨n⟩, ⟨m⟩ =>
-    dite (Eq n m) (fun h => isTrue (h ▸ rfl)) (fun h => isFalse (fun h' => UInt16.noConfusion h' (fun h' => absurd h' h)))
+    dite (Eq n m)
+      (fun h => isTrue (h ▸ rfl))
+      (fun h => isFalse (fun h' => UInt16.noConfusion h' (fun h' => absurd h' h)))
 
 instance : DecidableEq UInt16 := UInt16.decEq
 
@@ -1955,12 +2002,12 @@ The type of unsigned 32-bit integers. This type has special support in the
 compiler to make it actually 32 bits rather than wrapping a `Nat`.
 -/
 structure UInt32 where
-  /-- Unpack a `UInt32` as a `Nat` less than `2^32`.
+  /-- Unpack a `UInt32` as a `BitVec 32.
   This function is overridden with a native implementation. -/
-  val : Fin UInt32.size
+  toBitVec : BitVec 32
 
 attribute [extern "lean_uint32_of_nat_mk"] UInt32.mk
-attribute [extern "lean_uint32_to_nat"] UInt32.val
+attribute [extern "lean_uint32_to_nat"] UInt32.toBitVec
 
 /--
 Pack a `Nat` less than `2^32` into a `UInt32`.
@@ -1968,14 +2015,14 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_uint32_of_nat"]
 def UInt32.ofNatCore (n : @& Nat) (h : LT.lt n UInt32.size) : UInt32 where
-  val := { val := n, isLt := h }
+  toBitVec := BitVec.ofNatLt n h
 
 /--
 Unpack a `UInt32` as a `Nat`.
 This function is overridden with a native implementation.
 -/
 @[extern "lean_uint32_to_nat"]
-def UInt32.toNat (n : UInt32) : Nat := n.val.val
+def UInt32.toNat (n : UInt32) : Nat := n.toBitVec.toNat
 
 set_option bootstrap.genMatcherCode false in
 /--
@@ -1994,30 +2041,26 @@ instance : Inhabited UInt32 where
   default := UInt32.ofNatCore 0 (by decide)
 
 instance : LT UInt32 where
-  lt a b := LT.lt a.val b.val
+  lt a b := LT.lt a.toBitVec b.toBitVec
 
 instance : LE UInt32 where
-  le a b := LE.le a.val b.val
+  le a b := LE.le a.toBitVec b.toBitVec
 
-set_option bootstrap.genMatcherCode false in
 /--
 Decides less-equal on `UInt32`.
 This function is overridden with a native implementation.
 -/
 @[extern "lean_uint32_dec_lt"]
 def UInt32.decLt (a b : UInt32) : Decidable (LT.lt a b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (LT.lt n m))
+  inferInstanceAs (Decidable (LT.lt a.toBitVec b.toBitVec))
 
-set_option bootstrap.genMatcherCode false in
 /--
 Decides less-than on `UInt32`.
 This function is overridden with a native implementation.
 -/
 @[extern "lean_uint32_dec_le"]
 def UInt32.decLe (a b : UInt32) : Decidable (LE.le a b) :=
-  match a, b with
-  | ⟨n⟩, ⟨m⟩ => inferInstanceAs (Decidable (LE.le n m))
+  inferInstanceAs (Decidable (LE.le a.toBitVec b.toBitVec))
 
 instance (a b : UInt32) : Decidable (LT.lt a b) := UInt32.decLt a b
 instance (a b : UInt32) : Decidable (LE.le a b) := UInt32.decLe a b
@@ -2031,12 +2074,12 @@ The type of unsigned 64-bit integers. This type has special support in the
 compiler to make it actually 64 bits rather than wrapping a `Nat`.
 -/
 structure UInt64 where
-  /-- Unpack a `UInt64` as a `Nat` less than `2^64`.
+  /-- Unpack a `UInt64` as a `BitVec 64`.
   This function is overridden with a native implementation. -/
-  val : Fin UInt64.size
+  toBitVec: BitVec 64
 
 attribute [extern "lean_uint64_of_nat_mk"] UInt64.mk
-attribute [extern "lean_uint64_to_nat"] UInt64.val
+attribute [extern "lean_uint64_to_nat"] UInt64.toBitVec
 
 /--
 Pack a `Nat` less than `2^64` into a `UInt64`.
@@ -2044,7 +2087,7 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_uint64_of_nat"]
 def UInt64.ofNatCore (n : @& Nat) (h : LT.lt n UInt64.size) : UInt64 where
-  val := { val := n, isLt := h }
+  toBitVec := BitVec.ofNatLt n h
 
 set_option bootstrap.genMatcherCode false in
 /--
@@ -2055,36 +2098,20 @@ This function is overridden with a native implementation.
 def UInt64.decEq (a b : UInt64) : Decidable (Eq a b) :=
   match a, b with
   | ⟨n⟩, ⟨m⟩ =>
-    dite (Eq n m) (fun h => isTrue (h ▸ rfl)) (fun h => isFalse (fun h' => UInt64.noConfusion h' (fun h' => absurd h' h)))
+    dite (Eq n m)
+      (fun h => isTrue (h ▸ rfl))
+      (fun h => isFalse (fun h' => UInt64.noConfusion h' (fun h' => absurd h' h)))
 
 instance : DecidableEq UInt64 := UInt64.decEq
 
 instance : Inhabited UInt64 where
   default := UInt64.ofNatCore 0 (by decide)
 
-/--
-The size of type `USize`, that is, `2^System.Platform.numBits`, which may
-be either `2^32` or `2^64` depending on the platform's architecture.
-
-Remark: we define `USize.size` using `(2^numBits - 1) + 1` to ensure the
-Lean unifier can solve constraints such as `?m + 1 = USize.size`. Recall that
-`numBits` does not reduce to a numeral in the Lean kernel since it is platform
-specific. Without this trick, the following definition would be rejected by the
-Lean type checker.
-```
-def one: Fin USize.size := 1
-```
-Because Lean would fail to synthesize instance `OfNat (Fin USize.size) 1`.
-Recall that the `OfNat` instance for `Fin` is
-```
-instance : OfNat (Fin (n+1)) i where
-  ofNat := Fin.ofNat i
-```
--/
-abbrev USize.size : Nat := hAdd (hSub (hPow 2 System.Platform.numBits) 1) 1
+/-- The size of type `USize`, that is, `2^System.Platform.numBits`. -/
+abbrev USize.size : Nat := (hPow 2 System.Platform.numBits)
 
 theorem usize_size_eq : Or (Eq USize.size 4294967296) (Eq USize.size 18446744073709551616) :=
-  show Or (Eq (Nat.succ (Nat.sub (hPow 2 System.Platform.numBits) 1)) 4294967296) (Eq (Nat.succ (Nat.sub (hPow 2 System.Platform.numBits) 1)) 18446744073709551616) from
+  show Or (Eq (hPow 2 System.Platform.numBits) 4294967296) (Eq (hPow 2 System.Platform.numBits) 18446744073709551616) from
   match System.Platform.numBits, System.Platform.numBits_eq with
   | _, Or.inl rfl => Or.inl (by decide)
   | _, Or.inr rfl => Or.inr (by decide)
@@ -2097,21 +2124,20 @@ For example, if running on a 32-bit machine, USize is equivalent to UInt32.
 Or on a 64-bit machine, UInt64.
 -/
 structure USize where
-  /-- Unpack a `USize` as a `Nat` less than `USize.size`.
+  /-- Unpack a `USize` as a `BitVec System.Platform.numBits`.
   This function is overridden with a native implementation. -/
-  val : Fin USize.size
+  toBitVec : BitVec System.Platform.numBits
 
 attribute [extern "lean_usize_of_nat_mk"] USize.mk
-attribute [extern "lean_usize_to_nat"] USize.val
+attribute [extern "lean_usize_to_nat"] USize.toBitVec
 
 /--
 Pack a `Nat` less than `USize.size` into a `USize`.
 This function is overridden with a native implementation.
 -/
 @[extern "lean_usize_of_nat"]
-def USize.ofNatCore (n : @& Nat) (h : LT.lt n USize.size) : USize := {
-  val := { val := n, isLt := h }
-}
+def USize.ofNatCore (n : @& Nat) (h : LT.lt n USize.size) : USize where
+  toBitVec := BitVec.ofNatLt n h
 
 set_option bootstrap.genMatcherCode false in
 /--
@@ -2122,7 +2148,9 @@ This function is overridden with a native implementation.
 def USize.decEq (a b : USize) : Decidable (Eq a b) :=
   match a, b with
   | ⟨n⟩, ⟨m⟩ =>
-    dite (Eq n m) (fun h =>isTrue (h ▸ rfl)) (fun h => isFalse (fun h' => USize.noConfusion h' (fun h' => absurd h' h)))
+    dite (Eq n m)
+      (fun h => isTrue (h ▸ rfl))
+      (fun h => isFalse (fun h' => USize.noConfusion h' (fun h' => absurd h' h)))
 
 instance : DecidableEq USize := USize.decEq
 
@@ -2138,12 +2166,12 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_usize_of_nat"]
 def USize.ofNat32 (n : @& Nat) (h : LT.lt n 4294967296) : USize where
-  val := {
-    val  := n
-    isLt := match USize.size, usize_size_eq with
+  toBitVec :=
+    BitVec.ofNatLt n (
+      match System.Platform.numBits, System.Platform.numBits_eq with
       | _, Or.inl rfl => h
       | _, Or.inr rfl => Nat.lt_trans h (by decide)
-  }
+    )
 
 /--
 A `Nat` denotes a valid unicode codepoint if it is less than `0x110000`, and
@@ -2178,7 +2206,7 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_uint32_of_nat"]
 def Char.ofNatAux (n : @& Nat) (h : n.isValidChar) : Char :=
-  { val := ⟨{ val := n, isLt := isValidChar_UInt32 h }⟩, valid := h }
+  { val := ⟨BitVec.ofNatLt n (isValidChar_UInt32 h)⟩, valid := h }
 
 /--
 Convert a `Nat` into a `Char`. If the `Nat` does not encode a valid unicode scalar value,
@@ -2188,7 +2216,7 @@ Convert a `Nat` into a `Char`. If the `Nat` does not encode a valid unicode scal
 def Char.ofNat (n : Nat) : Char :=
   dite (n.isValidChar)
     (fun h => Char.ofNatAux n h)
-    (fun _ => { val := ⟨{ val := 0, isLt := by decide }⟩, valid := Or.inl (by decide) })
+    (fun _ => { val := ⟨BitVec.ofNatLt 0 (by decide)⟩, valid := Or.inl (by decide) })
 
 theorem Char.eq_of_val_eq : ∀ {c d : Char}, Eq c.val d.val → Eq c d
   | ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
@@ -2716,28 +2744,6 @@ def Array.extract (as : Array α) (start stop : Nat) : Array α :=
   let sz' := Nat.sub (min stop as.size) start
   loop sz' start (mkEmpty sz')
 
-/--
-Auxiliary definition for `List.toArray`.
-`List.toArrayAux as r = r ++ as.toArray`
--/
-@[inline_if_reduce]
-def List.toArrayAux : List α → Array α → Array α
-  | nil,       r => r
-  | cons a as, r => toArrayAux as (r.push a)
-
-/-- A non-tail-recursive version of `List.length`, used for `List.toArray`. -/
-@[inline_if_reduce]
-def List.redLength : List α → Nat
-  | nil       => 0
-  | cons _ as => as.redLength.succ
-
-/-- Convert a `List α` into an `Array α`. This is O(n) in the length of the list.  -/
--- This function is exported to C, where it is called by `Array.mk`
--- (the constructor) to implement this functionality.
-@[inline, match_pattern, pp_nodot, export lean_list_to_array]
-def List.toArrayImpl (as : List α) : Array α :=
-  as.toArrayAux (Array.mkEmpty as.redLength)
-
 /-- The typeclass which supplies the `>>=` "bind" function. See `Monad`. -/
 class Bind (m : Type u → Type v) where
   /-- If `x : m α` and `f : α → m β`, then `x >>= f : m β` represents the
@@ -2891,6 +2897,32 @@ instance (m n o) [MonadLift n o] [MonadLiftT m n] : MonadLiftT m o where
 instance (m) : MonadLiftT m m where
   monadLift x := x
 
+/--
+Typeclass used for adapting monads. This is similar to `MonadLift`, but instances are allowed to
+make use of default state for the purpose of synthesizing such an instance, if necessary.
+Every `MonadLift` instance gives a `MonadEval` instance.
+
+The purpose of this class is for the `#eval` command,
+which looks for a `MonadEval m CommandElabM` or `MonadEval m IO` instance.
+-/
+class MonadEval (m : semiOutParam (Type u → Type v)) (n : Type u → Type w) where
+  /-- Evaluates a value from monad `m` into monad `n`. -/
+  monadEval : {α : Type u} → m α → n α
+
+instance [MonadLift m n] : MonadEval m n where
+  monadEval := MonadLift.monadLift
+
+/-- The transitive closure of `MonadEval`. -/
+class MonadEvalT (m : Type u → Type v) (n : Type u → Type w) where
+  /-- Evaluates a value from monad `m` into monad `n`. -/
+  monadEval : {α : Type u} → m α → n α
+
+instance (m n o) [MonadEval n o] [MonadEvalT m n] : MonadEvalT m o where
+  monadEval x := MonadEval.monadEval (m := n) (MonadEvalT.monadEval x)
+
+instance (m) : MonadEvalT m m where
+  monadEval x := x
+
 /--
 A functor in the category of monads. Can be used to lift monad-transforming functions.
 Based on [`MFunctor`] from the `pipes` Haskell package, but not restricted to
@@ -3444,15 +3476,13 @@ This function is overridden with a native implementation.
 -/
 @[extern "lean_usize_to_uint64"]
 def USize.toUInt64 (u : USize) : UInt64 where
-  val := {
-    val  := u.val.val
-    isLt :=
-      let ⟨n, h⟩ := u
-      show LT.lt n _ from
-      match USize.size, usize_size_eq, h with
-      | _, Or.inl rfl, h => Nat.lt_trans h (by decide)
-      | _, Or.inr rfl, h => h
-  }
+  toBitVec := BitVec.ofNatLt u.toBitVec.toNat (
+        let ⟨⟨n, h⟩⟩ := u
+        show LT.lt n _ from
+        match System.Platform.numBits, System.Platform.numBits_eq, h with
+        | _, Or.inl rfl, h => Nat.lt_trans h (by decide)
+        | _, Or.inr rfl, h => h
+      )
 
 /-- An opaque hash mixing operation, used to implement hashing for tuples. -/
 @[extern "lean_uint64_mix_hash"]

src/Init/PropLemmas.lean

@@ -135,6 +135,10 @@ Both reduce to `b = false ∧ c = false` via `not_or`.
 
 theorem not_and_of_not_or_not (h : ¬a ∨ ¬b) : ¬(a ∧ b) := h.elim (mt (·.1)) (mt (·.2))
 
+/-! ## not equal -/
+
+theorem ne_of_apply_ne {α β : Sort _} (f : α → β) {x y : α} : f x ≠ f y → x ≠ y :=
+  mt <| congrArg _
 
 /-! ## Ite -/
 
@@ -384,6 +388,17 @@ theorem forall_prop_of_false {p : Prop} {q : p → Prop} (hn : ¬p) : (∀ h' :
 
 end quantifiers
 
+/-! ## membership -/
+
+section Mem
+variable [Membership α β] {s t : β} {a b : α}
+
+theorem ne_of_mem_of_not_mem (h : a ∈ s) : b ∉ s → a ≠ b := mt fun e => e ▸ h
+
+theorem ne_of_mem_of_not_mem' (h : a ∈ s) : a ∉ t → s ≠ t := mt fun e => e ▸ h
+
+end Mem
+
 /-! ## Nonempty -/
 
 @[simp] theorem nonempty_prop {p : Prop} : Nonempty p ↔ p :=

src/Init/SizeOf.lean

@@ -67,6 +67,7 @@ deriving instance SizeOf for PLift
 deriving instance SizeOf for ULift
 deriving instance SizeOf for Decidable
 deriving instance SizeOf for Fin
+deriving instance SizeOf for BitVec
 deriving instance SizeOf for UInt8
 deriving instance SizeOf for UInt16
 deriving instance SizeOf for UInt32

src/Init/SizeOfLemmas.lean

@@ -11,22 +11,25 @@ import Init.Data.Nat.Linear
 @[simp] protected theorem Fin.sizeOf (a : Fin n) : sizeOf a = a.val + 1 := by
   cases a; simp_arith
 
-@[simp] protected theorem UInt8.sizeOf (a : UInt8) : sizeOf a = a.toNat + 2 := by
-  cases a; simp_arith [UInt8.toNat]
+@[simp] protected theorem BitVec.sizeOf (a : BitVec w) : sizeOf a = sizeOf a.toFin + 1 := by
+  cases a; simp_arith
 
-@[simp] protected theorem UInt16.sizeOf (a : UInt16) : sizeOf a = a.toNat + 2 := by
-  cases a; simp_arith [UInt16.toNat]
+@[simp] protected theorem UInt8.sizeOf (a : UInt8) : sizeOf a = a.toNat + 3 := by
+  cases a; simp_arith [UInt8.toNat, BitVec.toNat]
 
-@[simp] protected theorem UInt32.sizeOf (a : UInt32) : sizeOf a = a.toNat + 2 := by
-  cases a; simp_arith [UInt32.toNat]
+@[simp] protected theorem UInt16.sizeOf (a : UInt16) : sizeOf a = a.toNat + 3 := by
+  cases a; simp_arith [UInt16.toNat, BitVec.toNat]
 
-@[simp] protected theorem UInt64.sizeOf (a : UInt64) : sizeOf a = a.toNat + 2 := by
-  cases a; simp_arith [UInt64.toNat]
+@[simp] protected theorem UInt32.sizeOf (a : UInt32) : sizeOf a = a.toNat + 3 := by
+  cases a; simp_arith [UInt32.toNat, BitVec.toNat]
 
-@[simp] protected theorem USize.sizeOf (a : USize) : sizeOf a = a.toNat + 2 := by
-  cases a; simp_arith [USize.toNat]
+@[simp] protected theorem UInt64.sizeOf (a : UInt64) : sizeOf a = a.toNat + 3 := by
+  cases a; simp_arith [UInt64.toNat, BitVec.toNat]
 
-@[simp] protected theorem Char.sizeOf (a : Char) : sizeOf a = a.toNat + 3 := by
+@[simp] protected theorem USize.sizeOf (a : USize) : sizeOf a = a.toNat + 3 := by
+  cases a; simp_arith [USize.toNat, BitVec.toNat]
+
+@[simp] protected theorem Char.sizeOf (a : Char) : sizeOf a = a.toNat + 4 := by
   cases a; simp_arith [Char.toNat]
 
 @[simp] protected theorem Subtype.sizeOf {α : Sort u_1} {p : α → Prop} (s : Subtype p) : sizeOf s = sizeOf s.val + 1 := by

src/Init/System/IO.lean

@@ -928,41 +928,6 @@ def withIsolatedStreams [Monad m] [MonadFinally m] [MonadLiftT BaseIO m] (x : m
 end FS
 end IO
 
-universe u
-
-namespace Lean
-
-/-- Typeclass used for presenting the output of an `#eval` command. -/
-class Eval (α : Type u) where
-  -- We default `hideUnit` to `true`, but set it to `false` in the direct call from `#eval`
-  -- so that `()` output is hidden in chained instances such as for some `IO Unit`.
-  -- We take `Unit → α` instead of `α` because ‵α` may contain effectful debugging primitives (e.g., `dbg_trace`)
-  eval : (Unit → α) → (hideUnit : Bool := true) → IO Unit
-
-instance instEval [ToString α] : Eval α where
-  eval a _ := IO.println (toString (a ()))
-
-instance [Repr α] : Eval α where
-  eval a _ := IO.println (repr (a ()))
-
-instance : Eval Unit where
-  eval u hideUnit := if hideUnit then pure () else IO.println (repr (u ()))
-
-instance [Eval α] : Eval (IO α) where
-  eval x _ := do
-    let a ← x ()
-    Eval.eval fun _ => a
-
-instance [Eval α] : Eval (BaseIO α) where
-  eval x _ := do
-    let a ← x ()
-    Eval.eval fun _ => a
-
-def runEval [Eval α] (a : Unit → α) : IO (String × Except IO.Error Unit) :=
-  IO.FS.withIsolatedStreams (Eval.eval a false |>.toBaseIO)
-
-end Lean
-
 syntax "println! " (interpolatedStr(term) <|> term) : term
 
 macro_rules

src/Init/Tactics.lean

@@ -268,9 +268,9 @@ syntax (name := case') "case' " sepBy1(caseArg, " | ") " => " tacticSeq : tactic
 `next x₁ ... xₙ => tac` additionally renames the `n` most recent hypotheses with
 inaccessible names to the given names.
 -/
-macro "next " args:binderIdent* arrowTk:" => " tac:tacticSeq : tactic =>
+macro nextTk:"next " args:binderIdent* arrowTk:" => " tac:tacticSeq : tactic =>
   -- Limit ref variability for incrementality; see Note [Incremental Macros]
-  withRef arrowTk `(tactic| case _ $args* =>%$arrowTk $tac)
+  withRef arrowTk `(tactic| case%$nextTk _ $args* =>%$arrowTk $tac)
 
 /-- `all_goals tac` runs `tac` on each goal, concatenating the resulting goals, if any. -/
 syntax (name := allGoals) "all_goals " tacticSeq : tactic
@@ -375,12 +375,12 @@ The same as `rfl`, but without trying `eq_refl` at the end.
 -/
 syntax (name := applyRfl) "apply_rfl" : tactic
 
--- We try `apply_rfl` first, beause it produces a nice error message
+-- We try `apply_rfl` first, because it produces a nice error message
 macro_rules | `(tactic| rfl) => `(tactic| apply_rfl)
 
 -- But, mostly for backward compatibility, we try `eq_refl` too (reduces more aggressively)
 macro_rules | `(tactic| rfl) => `(tactic| eq_refl)
--- Als for backward compatibility, because `exact` can trigger the implicit lambda feature (see #5366)
+-- Also for backward compatibility, because `exact` can trigger the implicit lambda feature (see #5366)
 macro_rules | `(tactic| rfl) => `(tactic| exact HEq.rfl)
 /--
 `rfl'` is similar to `rfl`, but disables smart unfolding and unfolds all kinds of definitions,
@@ -399,19 +399,6 @@ example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by ac_rfl
 -/
 syntax (name := acRfl) "ac_rfl" : tactic
 
-/--
-`ac_nf` normalizes equalities up to application of an associative and commutative operator.
-```
-instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
-instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
-
-example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
- ac_nf
- -- goal: a + (b + (c + d)) = a + (b + (c + d))
-```
--/
-syntax (name := acNf) "ac_nf" : tactic
-
 /--
 The `sorry` tactic closes the goal using `sorryAx`. This is intended for stubbing out incomplete
 parts of a proof while still having a syntactically correct proof skeleton. Lean will give
@@ -923,6 +910,15 @@ macro_rules | `(tactic| trivial) => `(tactic| simp)
 -/
 syntax "trivial" : tactic
 
+/--
+`classical tacs` runs `tacs` in a scope where `Classical.propDecidable` is a low priority
+local instance.
+
+Note that `classical` is a scoping tactic: it adds the instance only within the
+scope of the tactic.
+-/
+syntax (name := classical) "classical" ppDedent(tacticSeq) : tactic
+
 /--
 The `split` tactic is useful for breaking nested if-then-else and `match` expressions into separate cases.
 For a `match` expression with `n` cases, the `split` tactic generates at most `n` subgoals.
@@ -1172,6 +1168,9 @@ Currently the preprocessor is implemented as `try simp only [bv_toNat] at *`.
 -/
 macro "bv_omega" : tactic => `(tactic| (try simp only [bv_toNat] at *) <;> omega)
 
+/-- Implementation of `ac_nf` (the full `ac_nf` calls `trivial` afterwards). -/
+syntax (name := acNf0) "ac_nf0" (location)? : tactic
+
 /-- Implementation of `norm_cast` (the full `norm_cast` calls `trivial` afterwards). -/
 syntax (name := normCast0) "norm_cast0" (location)? : tactic
 
@@ -1222,6 +1221,24 @@ See also `push_cast`, which moves casts inwards rather than lifting them outward
 macro "norm_cast" loc:(location)? : tactic =>
   `(tactic| norm_cast0 $[$loc]? <;> try trivial)
 
+/--
+`ac_nf` normalizes equalities up to application of an associative and commutative operator.
+- `ac_nf` normalizes all hypotheses and the goal target of the goal.
+- `ac_nf at l` normalizes at location(s) `l`, where `l` is either `*` or a
+  list of hypotheses in the local context. In the latter case, a turnstile `⊢` or `|-`
+  can also be used, to signify the target of the goal.
+```
+instance : Associative (α := Nat) (.+.) := ⟨Nat.add_assoc⟩
+instance : Commutative (α := Nat) (.+.) := ⟨Nat.add_comm⟩
+
+example (a b c d : Nat) : a + b + c + d = d + (b + c) + a := by
+ ac_nf
+ -- goal: a + (b + (c + d)) = a + (b + (c + d))
+```
+-/
+macro "ac_nf" loc:(location)? : tactic =>
+  `(tactic| ac_nf0 $[$loc]? <;> try trivial)
+
 /--
 `push_cast` rewrites the goal to move certain coercions (*casts*) inward, toward the leaf nodes.
 This uses `norm_cast` lemmas in the forward direction.

src/Init/While.lean

@@ -0,0 +1,51 @@
+/-
+Copyright (c) 2020 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Leonardo de Moura
+-/
+prelude
+import Init.Core
+
+/-!
+# Notation for `while` and `repeat` loops.
+-/
+
+namespace Lean
+
+/-! # `repeat` and `while` notation -/
+
+inductive Loop where
+  | mk
+
+@[inline]
+partial def Loop.forIn {β : Type u} {m : Type u → Type v} [Monad m] (_ : Loop) (init : β) (f : Unit → β → m (ForInStep β)) : m β :=
+  let rec @[specialize] loop (b : β) : m β := do
+    match ← f () b with
+      | ForInStep.done b  => pure b
+      | ForInStep.yield b => loop b
+  loop init
+
+instance : ForIn m Loop Unit where
+  forIn := Loop.forIn
+
+syntax "repeat " doSeq : doElem
+
+macro_rules
+  | `(doElem| repeat $seq) => `(doElem| for _ in Loop.mk do $seq)
+
+syntax "while " ident " : " termBeforeDo " do " doSeq : doElem
+
+macro_rules
+  | `(doElem| while $h : $cond do $seq) => `(doElem| repeat if $h : $cond then $seq else break)
+
+syntax "while " termBeforeDo " do " doSeq : doElem
+
+macro_rules
+  | `(doElem| while $cond do $seq) => `(doElem| repeat if $cond then $seq else break)
+
+syntax "repeat " doSeq ppDedent(ppLine) "until " term : doElem
+
+macro_rules
+  | `(doElem| repeat $seq until $cond) => `(doElem| repeat do $seq:doSeq; if $cond then break)
+
+end Lean

src/Lean.lean

@@ -20,7 +20,6 @@ import Lean.MetavarContext
 import Lean.AuxRecursor
 import Lean.Meta
 import Lean.Util
-import Lean.Eval
 import Lean.Structure
 import Lean.PrettyPrinter
 import Lean.CoreM
@@ -30,7 +29,6 @@ import Lean.Server
 import Lean.ScopedEnvExtension
 import Lean.DocString
 import Lean.DeclarationRange
-import Lean.LazyInitExtension
 import Lean.LoadDynlib
 import Lean.Widget
 import Lean.Log
@@ -38,3 +36,4 @@ import Lean.Linter
 import Lean.SubExpr
 import Lean.LabelAttribute
 import Lean.AddDecl
+import Lean.Replay

src/Lean/CoreM.lean

@@ -7,7 +7,6 @@ prelude
 import Lean.Util.RecDepth
 import Lean.Util.Trace
 import Lean.Log
-import Lean.Eval
 import Lean.ResolveName
 import Lean.Elab.InfoTree.Types
 import Lean.MonadEnv
@@ -277,12 +276,6 @@ def mkFreshUserName (n : Name) : CoreM Name :=
   | Except.error (Exception.internal id _) => throw <| IO.userError <| "internal exception #" ++ toString id.idx
   | Except.ok a                            => return a
 
-instance [MetaEval α] : MetaEval (CoreM α) where
-  eval env opts x _ := do
-    let x : CoreM α := do try x finally printTraces
-    let (a, s) ← (withConsistentCtx x).toIO { fileName := "<CoreM>", fileMap := default, options := opts } { env := env }
-    MetaEval.eval s.env opts a (hideUnit := true)
-
 -- withIncRecDepth for a monad `m` such that `[MonadControlT CoreM n]`
 protected def withIncRecDepth [Monad m] [MonadControlT CoreM m] (x : m α) : m α :=
   controlAt CoreM fun runInBase => withIncRecDepth (runInBase x)
@@ -309,7 +302,7 @@ register_builtin_option debug.moduleNameAtTimeout : Bool := {
 def throwMaxHeartbeat (moduleName : Name) (optionName : Name) (max : Nat) : CoreM Unit := do
   let includeModuleName := debug.moduleNameAtTimeout.get (← getOptions)
   let atModuleName := if includeModuleName then s!" at `{moduleName}`" else ""
-  throw <| Exception.error (← getRef) m!"\
+  throw <| Exception.error (← getRef) <| .tagged `runtime.maxHeartbeats m!"\
     (deterministic) timeout{atModuleName}, maximum number of heartbeats ({max/1000}) has been reached\n\
     Use `set_option {optionName} <num>` to set the limit.\
     {useDiagnosticMsg}"
@@ -395,10 +388,7 @@ export Core (CoreM mkFreshUserName checkSystem withCurrHeartbeats)
   This function is a bit hackish. The heartbeat exception should probably be an internal exception.
   We used a similar hack at `Exception.isMaxRecDepth` -/
 def Exception.isMaxHeartbeat (ex : Exception) : Bool :=
-  match ex with
-  | Exception.error _ (MessageData.ofFormatWithInfos ⟨Std.Format.text msg, _⟩) =>
-    "(deterministic) timeout".isPrefixOf msg
-  | _ => false
+  ex matches Exception.error _ (.tagged `runtime.maxHeartbeats _)
 
 /-- Creates the expression `d → b` -/
 def mkArrow (d b : Expr) : CoreM Expr :=

src/Lean/Data/HashMap.lean

@@ -46,7 +46,7 @@ private def mkIdx {sz : Nat} (hash : UInt64) (h : sz.isPowerOfTwo) : { u : USize
   if h' : u.toNat < sz then
     ⟨u, h'⟩
   else
-    ⟨0, by simp [USize.toNat, OfNat.ofNat, USize.ofNat]; apply Nat.pos_of_isPowerOfTwo h⟩
+    ⟨0, by simp; apply Nat.pos_of_isPowerOfTwo h⟩
 
 @[inline] def reinsertAux (hashFn : α → UInt64) (data : HashMapBucket α β) (a : α) (b : β) : HashMapBucket α β :=
   let ⟨i, h⟩ := mkIdx (hashFn a) data.property

src/Lean/Data/HashSet.lean

@@ -42,7 +42,7 @@ private def mkIdx {sz : Nat} (hash : UInt64) (h : sz.isPowerOfTwo) : { u : USize
   if h' : u.toNat < sz then
     ⟨u, h'⟩
   else
-    ⟨0, by simp [USize.toNat, OfNat.ofNat, USize.ofNat]; apply Nat.pos_of_isPowerOfTwo h⟩
+    ⟨0, by simp; apply Nat.pos_of_isPowerOfTwo h⟩
 
 @[inline] def reinsertAux (hashFn : α → UInt64) (data : HashSetBucket α) (a : α) : HashSetBucket α :=
   let ⟨i, h⟩ := mkIdx (hashFn a) data.property

src/Lean/Data/Lsp/Capabilities.lean

@@ -54,7 +54,7 @@ structure WorkspaceEditClientCapabilities where
   deriving ToJson, FromJson
 
 structure WorkspaceClientCapabilities where
-  applyEdit: Bool
+  applyEdit? : Option Bool := none
   workspaceEdit? : Option WorkspaceEditClientCapabilities := none
   deriving ToJson, FromJson
 

src/Lean/Data/Lsp/LanguageFeatures.lean

@@ -41,6 +41,18 @@ structure InsertReplaceEdit where
   replace : Range
   deriving FromJson, ToJson
 
+inductive CompletionItemTag where
+  | deprecated
+  deriving Inhabited, DecidableEq, Repr
+
+instance : ToJson CompletionItemTag where
+  toJson t := toJson (t.toCtorIdx + 1)
+
+instance : FromJson CompletionItemTag where
+  fromJson? v := do
+    let i : Nat ← fromJson? v
+    return CompletionItemTag.ofNat (i-1)
+
 structure CompletionItem where
   label          : String
   detail?        : Option String := none
@@ -49,8 +61,8 @@ structure CompletionItem where
   textEdit?      : Option InsertReplaceEdit := none
   sortText?      : Option String := none
   data?          : Option Json := none
+  tags?          : Option (Array CompletionItemTag) := none
   /-
-  tags? : CompletionItemTag[]
   deprecated? : boolean
   preselect? : boolean
   filterText? : string
@@ -59,7 +71,8 @@ structure CompletionItem where
   insertTextMode? : InsertTextMode
   additionalTextEdits? : TextEdit[]
   commitCharacters? : string[]
-  command? : Command -/
+  command? : Command
+  -/
   deriving FromJson, ToJson, Inhabited
 
 structure CompletionList where

src/Lean/Data/PersistentArray.lean

@@ -7,6 +7,7 @@ prelude
 import Init.Data.Array.Basic
 import Init.NotationExtra
 import Init.Data.ToString.Macro
+import Init.Data.UInt.Basic
 
 universe u v w
 

src/Lean/Data/PersistentHashMap.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Init.Data.Array.BasicAux
 import Init.Data.ToString.Macro
+import Init.Data.UInt.Basic
 
 namespace Lean
 universe u v w w'

src/Lean/Data/Trie.lean

@@ -76,7 +76,7 @@ partial def upsert (t : Trie α) (s : String) (f : Option α → α) : Trie α :
         let c := s.getUtf8Byte i h
         if c == c'
         then node1 v c' (loop (i + 1) t')
-        else 
+        else
           let t := insertEmpty (i + 1)
           node v (.mk #[c, c']) #[t, t']
       else
@@ -190,7 +190,7 @@ private partial def toStringAux {α : Type} : Trie α → List Format
   | node1 _ c t =>
     [ format (repr c), Format.group $ Format.nest 4 $ flip Format.joinSep Format.line $ toStringAux t ]
   | node _ cs ts =>
-    List.join $ List.zipWith (fun c t =>
+    List.flatten $ List.zipWith (fun c t =>
       [ format (repr c), (Format.group $ Format.nest 4 $ flip Format.joinSep Format.line $ toStringAux t) ]
     ) cs.toList ts.toList
 

src/Lean/Data/Xml/Parser.lean

@@ -459,7 +459,7 @@ mutual
 
       let z ← optional (Content.Character <$> CharData)
       pure #[y, z]
-    let xs := #[x] ++ xs.concatMap id |>.filterMap id
+    let xs := #[x] ++ xs.flatMap id |>.filterMap id
     let mut res := #[]
     for x in xs do
       if res.size > 0 then

src/Lean/Declaration.lean

@@ -369,8 +369,13 @@ def RecursorVal.getFirstIndexIdx (v : RecursorVal) : Nat :=
 def RecursorVal.getFirstMinorIdx (v : RecursorVal) : Nat :=
   v.numParams + v.numMotives
 
-def RecursorVal.getInduct (v : RecursorVal) : Name :=
-  v.name.getPrefix
+/-- The inductive type of the major argument of the recursor. -/
+def RecursorVal.getMajorInduct (v : RecursorVal) : Name :=
+  go v.getMajorIdx v.type
+where
+  go
+  | 0, e => e.bindingDomain!.getAppFn.constName!
+  | n+1, e => go n e.bindingBody!
 
 inductive QuotKind where
   | type  -- `Quot`

src/Lean/DeclarationRange.lean

@@ -42,8 +42,9 @@ builtin_initialize declRangeExt : MapDeclarationExtension DeclarationRanges ←
 def addBuiltinDeclarationRanges (declName : Name) (declRanges : DeclarationRanges) : IO Unit :=
   builtinDeclRanges.modify (·.insert declName declRanges)
 
-def addDeclarationRanges [MonadEnv m] (declName : Name) (declRanges : DeclarationRanges) : m Unit :=
-  modifyEnv fun env => declRangeExt.insert env declName declRanges
+def addDeclarationRanges [Monad m] [MonadEnv m] (declName : Name) (declRanges : DeclarationRanges) : m Unit := do
+  unless declRangeExt.contains (← getEnv) declName do
+    modifyEnv fun env => declRangeExt.insert env declName declRanges
 
 def findDeclarationRangesCore? [Monad m] [MonadEnv m] (declName : Name) : m (Option DeclarationRanges) :=
   return declRangeExt.find? (← getEnv) declName

src/Lean/DocString/Extension.lean

@@ -16,7 +16,7 @@ import Init.Data.String.Extra
 namespace Lean
 
 private builtin_initialize builtinDocStrings : IO.Ref (NameMap String) ← IO.mkRef {}
-private builtin_initialize docStringExt : MapDeclarationExtension String ← mkMapDeclarationExtension
+builtin_initialize docStringExt : MapDeclarationExtension String ← mkMapDeclarationExtension
 
 def addBuiltinDocString (declName : Name) (docString : String) : IO Unit :=
   builtinDocStrings.modify (·.insert declName docString.removeLeadingSpaces)

src/Lean/Elab.lean

@@ -42,6 +42,7 @@ import Lean.Elab.Notation
 import Lean.Elab.Mixfix
 import Lean.Elab.MacroRules
 import Lean.Elab.BuiltinCommand
+import Lean.Elab.BuiltinEvalCommand
 import Lean.Elab.RecAppSyntax
 import Lean.Elab.Eval
 import Lean.Elab.Calc

src/Lean/Elab/App.lean

@@ -528,7 +528,7 @@ mutual
       main
 
   /--
-  Create a fresh metavariable for the implicit argument, add it to `f`, and thn execute the main loop.
+  Create a fresh metavariable for the implicit argument, add it to `f`, and then execute the main loop.
   -/
   private partial def addImplicitArg (argName : Name) : M Expr := do
     let argType ← getArgExpectedType
@@ -777,7 +777,7 @@ def getElabElimExprInfo (elimExpr : Expr) : MetaM ElabElimInfo := do
   forallTelescopeReducing elimType fun xs type => do
     let motive  := type.getAppFn
     let motiveArgs := type.getAppArgs
-    unless motive.isFVar do
+    unless motive.isFVar && motiveArgs.size > 0 do
       throwError "unexpected eliminator resulting type{indentExpr type}"
     let motiveType ← inferType motive
     forallTelescopeReducing motiveType fun motiveParams motiveResultType => do
@@ -1118,9 +1118,17 @@ where
 
 /-- Auxiliary inductive datatype that represents the resolution of an `LVal`. -/
 inductive LValResolution where
+  /-- When applied to `f`, effectively expands to `BaseStruct.fieldName (self := Struct.toBase f)`.
+  This is a special named argument where it suppresses any explicit arguments depending on it so that type parameters don't need to be supplied. -/
   | projFn   (baseStructName : Name) (structName : Name) (fieldName : Name)
+  /-- Similar to `projFn`, but for extracting field indexed by `idx`. Works for structure-like inductive types in general. -/
   | projIdx  (structName : Name) (idx : Nat)
+  /-- When applied to `f`, effectively expands to `constName ... (Struct.toBase f)`, with the argument placed in the correct
+  positional argument if possible, or otherwise as a named argument. The `Struct.toBase` is not present if `baseStructName == structName`,
+  in which case these do not need to be structures. Supports generalized field notation. -/
   | const    (baseStructName : Name) (structName : Name) (constName : Name)
+  /-- Like `const`, but with `fvar` instead of `constName`.
+  The `fullName` is the name of the recursive function, and `baseName` is the base name of the type to search for in the parameter list. -/
   | localRec (baseName : Name) (fullName : Name) (fvar : Expr)
 
 private def throwLValError (e : Expr) (eType : Expr) (msg : MessageData) : TermElabM α :=
@@ -1290,45 +1298,70 @@ private def typeMatchesBaseName (type : Expr) (baseName : Name) : MetaM Bool :=
   else
     return (← whnfR type).isAppOf baseName
 
-/-- Auxiliary method for field notation. It tries to add `e` as a new argument to `args` or `namedArgs`.
-   This method first finds the parameter with a type of the form `(baseName ...)`.
-   When the parameter is found, if it an explicit one and `args` is big enough, we add `e` to `args`.
-   Otherwise, if there isn't another parameter with the same name, we add `e` to `namedArgs`.
+/--
+Auxiliary method for field notation. Tries to add `e` as a new argument to `args` or `namedArgs`.
+This method first finds the parameter with a type of the form `(baseName ...)`.
+When the parameter is found, if it an explicit one and `args` is big enough, we add `e` to `args`.
+Otherwise, if there isn't another parameter with the same name, we add `e` to `namedArgs`.
 
-   Remark: `fullName` is the name of the resolved "field" access function. It is used for reporting errors -/
-private def addLValArg (baseName : Name) (fullName : Name) (e : Expr) (args : Array Arg) (namedArgs : Array NamedArg) (fType : Expr)
-    : TermElabM (Array Arg × Array NamedArg) :=
-  forallTelescopeReducing fType fun xs _ => do
-    let mut argIdx := 0 -- position of the next explicit argument
-    let mut remainingNamedArgs := namedArgs
-    for h : i in [:xs.size] do
-      let x := xs[i]
-      let xDecl ← x.fvarId!.getDecl
-      /- If there is named argument with name `xDecl.userName`, then we skip it. -/
-      match remainingNamedArgs.findIdx? (fun namedArg => namedArg.name == xDecl.userName) with
-      | some idx =>
+Remark: `fullName` is the name of the resolved "field" access function. It is used for reporting errors
+-/
+private partial def addLValArg (baseName : Name) (fullName : Name) (e : Expr) (args : Array Arg) (namedArgs : Array NamedArg) (f : Expr) :
+    MetaM (Array Arg × Array NamedArg) := do
+  withoutModifyingState <| go f (← inferType f) 0 namedArgs (namedArgs.map (·.name)) true
+where
+  /--
+  * `argIdx` is the position into `args` for the next place an explicit argument can be inserted.
+  * `remainingNamedArgs` keeps track of named arguments that haven't been visited yet,
+    for handling the case where multiple parameters have the same name.
+  * `unusableNamedArgs` keeps track of names that can't be used as named arguments. This is initialized with user-provided named arguments.
+  * `allowNamed` is whether or not to allow using named arguments.
+    Disabled after using `CoeFun` since those parameter names unlikely to be meaningful,
+    and otherwise whether dot notation works or not could feel random.
+  -/
+  go (f fType : Expr) (argIdx : Nat) (remainingNamedArgs : Array NamedArg) (unusableNamedArgs : Array Name) (allowNamed : Bool) := withIncRecDepth do
+    /- Use metavariables (rather than `forallTelescope`) to prevent `coerceToFunction?` from succeeding when multiple instances could apply -/
+    let (xs, bInfos, fType') ← forallMetaTelescope fType
+    let mut argIdx := argIdx
+    let mut remainingNamedArgs := remainingNamedArgs
+    let mut unusableNamedArgs := unusableNamedArgs
+    for x in xs, bInfo in bInfos do
+      let xDecl ← x.mvarId!.getDecl
+      if let some idx := remainingNamedArgs.findIdx? (·.name == xDecl.userName) then
+        /- If there is named argument with name `xDecl.userName`, then it is accounted for and we can't make use of it. -/
         remainingNamedArgs := remainingNamedArgs.eraseIdx idx
-      | none =>
-        let type := xDecl.type
-        if (← typeMatchesBaseName type baseName) then
+      else
+        if (← typeMatchesBaseName xDecl.type baseName) then
           /- We found a type of the form (baseName ...).
              First, we check if the current argument is an explicit one,
-             and the current explicit position "fits" at `args` (i.e., it must be ≤ arg.size) -/
-          if argIdx ≤ args.size && xDecl.binderInfo.isExplicit then
-            /- We insert `e` as an explicit argument -/
+             and if the current explicit position "fits" at `args` (i.e., it must be ≤ arg.size) -/
+          if argIdx ≤ args.size && bInfo.isExplicit then
+            /- We can insert `e` as an explicit argument -/
             return (args.insertAt! argIdx (Arg.expr e), namedArgs)
-          /- If we can't add `e` to `args`, we try to add it using a named argument, but this is only possible
-             if there isn't an argument with the same name occurring before it. -/
-          for j in [:i] do
-            let prev := xs[j]!
-            let prevDecl ← prev.fvarId!.getDecl
-            if prevDecl.userName == xDecl.userName then
-              throwError "invalid field notation, function '{fullName}' has argument with the expected type{indentExpr type}\nbut it cannot be used"
-          return (args, namedArgs.push { name := xDecl.userName, val := Arg.expr e })
-        if xDecl.binderInfo.isExplicit then
-          -- advance explicit argument position
+          else
+            /- If we can't add `e` to `args`, we try to add it using a named argument, but this is only possible
+               if there isn't an argument with the same name occurring before it. -/
+            if !allowNamed || unusableNamedArgs.contains xDecl.userName then
+              throwError "\
+                invalid field notation, function '{fullName}' has argument with the expected type\
+                {indentExpr xDecl.type}\n\
+                but it cannot be used"
+            else
+              return (args, namedArgs.push { name := xDecl.userName, val := Arg.expr e })
+        /- Advance `argIdx` and update seen named arguments. -/
+        if bInfo.isExplicit then
           argIdx := argIdx + 1
-    throwError "invalid field notation, function '{fullName}' does not have argument with type ({baseName} ...) that can be used, it must be explicit or implicit with a unique name"
+        unusableNamedArgs := unusableNamedArgs.push xDecl.userName
+    /- If named arguments aren't allowed, then it must still be possible to pass the value as an explicit argument.
+       Otherwise, we can abort now. -/
+    if allowNamed || argIdx ≤ args.size then
+      if let fType'@(.forallE ..) ← whnf fType' then
+        return ← go (mkAppN f xs) fType' argIdx remainingNamedArgs unusableNamedArgs allowNamed
+      if let some f' ← coerceToFunction? (mkAppN f xs) then
+        return ← go f' (← inferType f') argIdx remainingNamedArgs unusableNamedArgs false
+    throwError "\
+      invalid field notation, function '{fullName}' does not have argument with type ({baseName} ...) that can be used, \
+      it must be explicit or implicit with a unique name"
 
 /-- Adds the `TermInfo` for the field of a projection. See `Lean.Parser.Term.identProjKind`. -/
 private def addProjTermInfo
@@ -1375,8 +1408,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
       let projFn ← mkConst constName
       let projFn ← addProjTermInfo lval.getRef projFn
       if lvals.isEmpty then
-        let projFnType ← inferType projFn
-        let (args, namedArgs) ← addLValArg baseStructName constName f args namedArgs projFnType
+        let (args, namedArgs) ← addLValArg baseStructName constName f args namedArgs projFn
         elabAppArgs projFn namedArgs args expectedType? explicit ellipsis
       else
         let f ← elabAppArgs projFn #[] #[Arg.expr f] (expectedType? := none) (explicit := false) (ellipsis := false)
@@ -1384,8 +1416,7 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
     | LValResolution.localRec baseName fullName fvar =>
       let fvar ← addProjTermInfo lval.getRef fvar
       if lvals.isEmpty then
-        let fvarType ← inferType fvar
-        let (args, namedArgs) ← addLValArg baseName fullName f args namedArgs fvarType
+        let (args, namedArgs) ← addLValArg baseName fullName f args namedArgs fvar
         elabAppArgs fvar namedArgs args expectedType? explicit ellipsis
       else
         let f ← elabAppArgs fvar #[] #[Arg.expr f] (expectedType? := none) (explicit := false) (ellipsis := false)
@@ -1394,8 +1425,6 @@ private def elabAppLValsAux (namedArgs : Array NamedArg) (args : Array Arg) (exp
 
 private def elabAppLVals (f : Expr) (lvals : List LVal) (namedArgs : Array NamedArg) (args : Array Arg)
     (expectedType? : Option Expr) (explicit ellipsis : Bool) : TermElabM Expr := do
-  if !lvals.isEmpty && explicit then
-    throwError "invalid use of field notation with `@` modifier"
   elabAppLValsAux namedArgs args expectedType? explicit ellipsis f lvals
 
 def elabExplicitUnivs (lvls : Array Syntax) : TermElabM (List Level) := do
@@ -1494,19 +1523,21 @@ private partial def elabAppFn (f : Syntax) (lvals : List LVal) (namedArgs : Arra
     withReader (fun ctx => { ctx with errToSorry := false }) do
       f.getArgs.foldlM (init := acc) fun acc f => elabAppFn f lvals namedArgs args expectedType? explicit ellipsis true acc
   else
-    let elabFieldName (e field : Syntax) := do
+    let elabFieldName (e field : Syntax) (explicit : Bool) := do
       let newLVals := field.identComponents.map fun comp =>
         -- We use `none` in `suffix?` since `field` can't be part of a composite name
         LVal.fieldName comp comp.getId.getString! none f
       elabAppFn e (newLVals ++ lvals) namedArgs args expectedType? explicit ellipsis overloaded acc
-    let elabFieldIdx (e idxStx : Syntax) := do
+    let elabFieldIdx (e idxStx : Syntax) (explicit : Bool) := do
       let some idx := idxStx.isFieldIdx? | throwError "invalid field index"
       elabAppFn e (LVal.fieldIdx idxStx idx :: lvals) namedArgs args expectedType? explicit ellipsis overloaded acc
     match f with
-    | `($(e).$idx:fieldIdx) => elabFieldIdx e idx
-    | `($e |>.$idx:fieldIdx) => elabFieldIdx e idx
-    | `($(e).$field:ident) => elabFieldName e field
-    | `($e |>.$field:ident) => elabFieldName e field
+    | `($(e).$idx:fieldIdx) => elabFieldIdx e idx explicit
+    | `($e |>.$idx:fieldIdx) => elabFieldIdx e idx explicit
+    | `($(e).$field:ident) => elabFieldName e field explicit
+    | `($e |>.$field:ident) => elabFieldName e field explicit
+    | `(@$(e).$idx:fieldIdx) => elabFieldIdx e idx (explicit := true)
+    | `(@$(e).$field:ident) => elabFieldName e field (explicit := true)
     | `($_:ident@$_:term) =>
       throwError "unexpected occurrence of named pattern"
     | `($id:ident) => do
@@ -1663,8 +1694,10 @@ private def elabAtom : TermElab := fun stx expectedType? => do
 
 @[builtin_term_elab explicit] def elabExplicit : TermElab := fun stx expectedType? =>
   match stx with
-  | `(@$_:ident)         => elabAtom stx expectedType?  -- Recall that `elabApp` also has support for `@`
+  | `(@$_:ident)          => elabAtom stx expectedType?  -- Recall that `elabApp` also has support for `@`
   | `(@$_:ident.{$_us,*}) => elabAtom stx expectedType?
+  | `(@$(_).$_:fieldIdx)  => elabAtom stx expectedType?
+  | `(@$(_).$_:ident)     => elabAtom stx expectedType?
   | `(@($t))             => elabTerm t expectedType? (implicitLambda := false)    -- `@` is being used just to disable implicit lambdas
   | `(@$t)               => elabTerm t expectedType? (implicitLambda := false)   -- `@` is being used just to disable implicit lambdas
   | _                    => throwUnsupportedSyntax

src/Lean/Elab/BuiltinCommand.lean

@@ -12,16 +12,18 @@ import Lean.Elab.Eval
 import Lean.Elab.Command
 import Lean.Elab.Open
 import Lean.Elab.SetOption
+import Init.System.Platform
 
 namespace Lean.Elab.Command
 
 @[builtin_command_elab moduleDoc] def elabModuleDoc : CommandElab := fun stx => do
-   match stx[1] with
-   | Syntax.atom _ val =>
-     let doc := val.extract 0 (val.endPos - ⟨2⟩)
-     let range ← Elab.getDeclarationRange stx
-     modifyEnv fun env => addMainModuleDoc env ⟨doc, range⟩
-   | _ => throwErrorAt stx "unexpected module doc string{indentD stx[1]}"
+  match stx[1] with
+  | Syntax.atom _ val =>
+    let doc := val.extract 0 (val.endPos - ⟨2⟩)
+    let some range ← Elab.getDeclarationRange? stx
+      | return  -- must be from partial syntax, ignore
+    modifyEnv fun env => addMainModuleDoc env ⟨doc, range⟩
+  | _ => throwErrorAt stx "unexpected module doc string{indentD stx[1]}"
 
 private def addScope (isNewNamespace : Bool) (isNoncomputable : Bool) (header : String) (newNamespace : Name) : CommandElabM Unit := do
   modify fun s => { s with
@@ -229,7 +231,7 @@ private def replaceBinderAnnotation (binder : TSyntax ``Parser.Term.bracketedBin
 
 @[builtin_command_elab «variable»] def elabVariable : CommandElab
   | `(variable $binders*) => do
-    let binders ← binders.concatMapM replaceBinderAnnotation
+    let binders ← binders.flatMapM replaceBinderAnnotation
     -- Try to elaborate `binders` for sanity checking
     runTermElabM fun _ => Term.withSynthesize <| Term.withAutoBoundImplicit <|
       Term.elabBinders binders fun _ => pure ()
@@ -311,167 +313,6 @@ def failIfSucceeds (x : CommandElabM Unit) : CommandElabM Unit := do
     failIfSucceeds <| elabCheckCore (ignoreStuckTC := false) (← `(#check $term))
   | _ => throwUnsupportedSyntax
 
-private def mkEvalInstCore (evalClassName : Name) (e : Expr) : MetaM Expr := do
-  let α    ← inferType e
-  let u    ← getDecLevel α
-  let inst := mkApp (Lean.mkConst evalClassName [u]) α
-  try
-    synthInstance inst
-  catch _ =>
-    -- Put `α` in WHNF and try again
-    try
-      let α ← whnf α
-      synthInstance (mkApp (Lean.mkConst evalClassName [u]) α)
-    catch _ =>
-      -- Fully reduce `α` and try again
-      try
-        let α ← reduce (skipTypes := false) α
-        synthInstance (mkApp (Lean.mkConst evalClassName [u]) α)
-      catch _ =>
-        throwError "expression{indentExpr e}\nhas type{indentExpr α}\nbut instance{indentExpr inst}\nfailed to be synthesized, this instance instructs Lean on how to display the resulting value, recall that any type implementing the `Repr` class also implements the `{evalClassName}` class"
-
-private def mkRunMetaEval (e : Expr) : MetaM Expr :=
-  withLocalDeclD `env (mkConst ``Lean.Environment) fun env =>
-  withLocalDeclD `opts (mkConst ``Lean.Options) fun opts => do
-    let α ← inferType e
-    let u ← getDecLevel α
-    let instVal ← mkEvalInstCore ``Lean.MetaEval e
-    let e := mkAppN (mkConst ``Lean.runMetaEval [u]) #[α, instVal, env, opts, e]
-    instantiateMVars (← mkLambdaFVars #[env, opts] e)
-
-private def mkRunEval (e : Expr) : MetaM Expr := do
-  let α ← inferType e
-  let u ← getDecLevel α
-  let instVal ← mkEvalInstCore ``Lean.Eval e
-  instantiateMVars (mkAppN (mkConst ``Lean.runEval [u]) #[α, instVal, mkSimpleThunk e])
-
-unsafe def elabEvalCoreUnsafe (bang : Bool) (tk term : Syntax): CommandElabM Unit := do
-    let declName := `_eval
-    let addAndCompile (value : Expr) : TermElabM Unit := do
-      let value ← Term.levelMVarToParam (← instantiateMVars value)
-      let type ← inferType value
-      let us := collectLevelParams {} value |>.params
-      let value ← instantiateMVars value
-      let decl := Declaration.defnDecl {
-        name        := declName
-        levelParams := us.toList
-        type        := type
-        value       := value
-        hints       := ReducibilityHints.opaque
-        safety      := DefinitionSafety.unsafe
-      }
-      Term.ensureNoUnassignedMVars decl
-      addAndCompile decl
-    -- Check for sorry axioms
-    let checkSorry (declName : Name) : MetaM Unit := do
-      unless bang do
-        let axioms ← collectAxioms declName
-        if axioms.contains ``sorryAx then
-          throwError ("cannot evaluate expression that depends on the `sorry` axiom.\nUse `#eval!` to " ++
-            "evaluate nevertheless (which may cause lean to crash).")
-    -- Elaborate `term`
-    let elabEvalTerm : TermElabM Expr := do
-      let e ← Term.elabTerm term none
-      Term.synthesizeSyntheticMVarsNoPostponing
-      if (← Term.logUnassignedUsingErrorInfos (← getMVars e)) then throwAbortTerm
-      if (← isProp e) then
-        mkDecide e
-      else
-        return e
-    -- Evaluate using term using `MetaEval` class.
-    let elabMetaEval : CommandElabM Unit := do
-      -- Generate an action without executing it. We use `withoutModifyingEnv` to ensure
-      -- we don't pollute the environment with auxliary declarations.
-      -- We have special support for `CommandElabM` to ensure `#eval` can be used to execute commands
-      -- that modify `CommandElabM` state not just the `Environment`.
-      let act : Sum (CommandElabM Unit) (Environment → Options → IO (String × Except IO.Error Environment)) ←
-        runTermElabM fun _ => Term.withDeclName declName do withoutModifyingEnv do
-          let e ← elabEvalTerm
-          let eType ← instantiateMVars (← inferType e)
-          if eType.isAppOfArity ``CommandElabM 1 then
-            let mut stx ← Term.exprToSyntax e
-            unless (← isDefEq eType.appArg! (mkConst ``Unit)) do
-              stx ← `($stx >>= fun v => IO.println (repr v))
-            let act ← Lean.Elab.Term.evalTerm (CommandElabM Unit) (mkApp (mkConst ``CommandElabM) (mkConst ``Unit)) stx
-            pure <| Sum.inl act
-          else
-            let e ← mkRunMetaEval e
-            addAndCompile e
-            checkSorry declName
-            let act ← evalConst (Environment → Options → IO (String × Except IO.Error Environment)) declName
-            pure <| Sum.inr act
-      match act with
-      | .inl act => act
-      | .inr act =>
-        let (out, res) ← act (← getEnv) (← getOptions)
-        logInfoAt tk out
-        match res with
-        | Except.error e => throwError e.toString
-        | Except.ok env  => setEnv env; pure ()
-    -- Evaluate using term using `Eval` class.
-    let elabEval : CommandElabM Unit := runTermElabM fun _ => Term.withDeclName declName do withoutModifyingEnv do
-      -- fall back to non-meta eval if MetaEval hasn't been defined yet
-      -- modify e to `runEval e`
-      let e ← mkRunEval (← elabEvalTerm)
-      addAndCompile e
-      checkSorry declName
-      let act ← evalConst (IO (String × Except IO.Error Unit)) declName
-      let (out, res) ← liftM (m := IO) act
-      logInfoAt tk out
-      match res with
-      | Except.error e => throwError e.toString
-      | Except.ok _    => pure ()
-    if (← getEnv).contains ``Lean.MetaEval then do
-      elabMetaEval
-    else
-      elabEval
-
-@[implemented_by elabEvalCoreUnsafe]
-opaque elabEvalCore (bang : Bool) (tk term : Syntax): CommandElabM Unit
-
-@[builtin_command_elab «eval»]
-def elabEval : CommandElab
-  | `(#eval%$tk $term) => elabEvalCore false tk term
-  | _ => throwUnsupportedSyntax
-
-@[builtin_command_elab evalBang]
-def elabEvalBang : CommandElab
-  | `(Parser.Command.evalBang|#eval!%$tk $term) => elabEvalCore true tk term
-  | _ => throwUnsupportedSyntax
-
-private def checkImportsForRunCmds : CommandElabM Unit := do
-  unless (← getEnv).contains ``CommandElabM do
-    throwError "to use this command, include `import Lean.Elab.Command`"
-
-@[builtin_command_elab runCmd]
-def elabRunCmd : CommandElab
-  | `(run_cmd $elems:doSeq) => do
-    checkImportsForRunCmds
-    (← liftTermElabM <| Term.withDeclName `_run_cmd <|
-      unsafe Term.evalTerm (CommandElabM Unit)
-        (mkApp (mkConst ``CommandElabM) (mkConst ``Unit))
-        (← `(discard do $elems)))
-  | _ => throwUnsupportedSyntax
-
-@[builtin_command_elab runElab]
-def elabRunElab : CommandElab
-  | `(run_elab $elems:doSeq) => do
-    checkImportsForRunCmds
-    (← liftTermElabM <| Term.withDeclName `_run_elab <|
-      unsafe Term.evalTerm (CommandElabM Unit)
-        (mkApp (mkConst ``CommandElabM) (mkConst ``Unit))
-        (← `(Command.liftTermElabM <| discard do $elems)))
-  | _ => throwUnsupportedSyntax
-
-@[builtin_command_elab runMeta]
-def elabRunMeta : CommandElab := fun stx =>
-  match stx with
-  | `(run_meta $elems:doSeq) => do
-     checkImportsForRunCmds
-     let stxNew ← `(command| run_elab (show Lean.Meta.MetaM Unit from do $elems))
-     withMacroExpansion stx stxNew do elabCommand stxNew
-  | _ => throwUnsupportedSyntax
-
 @[builtin_command_elab «synth»] def elabSynth : CommandElab := fun stx => do
   let term := stx[1]
   withoutModifyingEnv <| runTermElabM fun _ => Term.withDeclName `_synth_cmd do
@@ -509,7 +350,7 @@ def elabRunMeta : CommandElab := fun stx =>
 @[builtin_command_elab Lean.Parser.Command.include] def elabInclude : CommandElab
   | `(Lean.Parser.Command.include| include $ids*) => do
     let sc ← getScope
-    let vars ← sc.varDecls.concatMapM getBracketedBinderIds
+    let vars ← sc.varDecls.flatMapM getBracketedBinderIds
     let mut uids := #[]
     for id in ids do
       if let some idx := vars.findIdx? (· == id.getId) then
@@ -564,6 +405,16 @@ def elabRunMeta : CommandElab := fun stx =>
       includedVars := sc.includedVars.filter (!omittedVars.contains ·) }
   | _ => throwUnsupportedSyntax
 
+@[builtin_command_elab version] def elabVersion : CommandElab := fun _ => do
+  let mut target := System.Platform.target
+  if target.isEmpty then target := "unknown"
+  -- Only one should be set, but good to know if multiple are set in error.
+  let platforms :=
+    (if System.Platform.isWindows then [" Windows"] else [])
+    ++ (if System.Platform.isOSX then [" macOS"] else [])
+    ++ (if System.Platform.isEmscripten then [" Emscripten"] else [])
+  logInfo m!"Lean {Lean.versionString}\nTarget: {target}{String.join platforms}"
+
 @[builtin_command_elab Parser.Command.exit] def elabExit : CommandElab := fun _ =>
   logWarning "using 'exit' to interrupt Lean"
 

src/Lean/Elab/BuiltinEvalCommand.lean

@@ -0,0 +1,277 @@
+/-
+Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Kyle Miller
+-/
+prelude
+import Lean.Util.CollectAxioms
+import Lean.Elab.Deriving.Basic
+import Lean.Elab.MutualDef
+
+/-!
+# Implementation of `#eval` command
+-/
+
+namespace Lean.Elab.Command
+open Meta
+
+register_builtin_option eval.pp : Bool := {
+  defValue := true
+  descr    := "('#eval' command) enables using 'ToExpr' instances to pretty print the result, \
+               otherwise uses 'Repr' or 'ToString' instances"
+}
+
+register_builtin_option eval.type : Bool := {
+  defValue := false -- TODO: set to 'true'
+  descr    := "('#eval' command) enables pretty printing the type of the result"
+}
+
+register_builtin_option eval.derive.repr : Bool := {
+  defValue := true
+  descr    := "('#eval' command) enables auto-deriving 'Repr' instances as a fallback"
+}
+
+builtin_initialize
+  registerTraceClass `Elab.eval
+
+/--
+Elaborates the term, ensuring the result has no expression metavariables.
+If there would be unsolved-for metavariables, tries hinting that the resulting type
+is a monadic value with the `CommandElabM`, `TermElabM`, or `IO` monads.
+Throws errors if the term is a proof or a type, but lifts props to `Bool` using `mkDecide`.
+-/
+private def elabTermForEval (term : Syntax) (expectedType? : Option Expr) : TermElabM Expr := do
+  let ty ← expectedType?.getDM mkFreshTypeMVar
+  let e ← Term.elabTermEnsuringType term ty
+  synthesizeWithHinting ty
+  let e ← instantiateMVars e
+  if (← Term.logUnassignedUsingErrorInfos (← getMVars e)) then throwAbortTerm
+  if ← isProof e then
+    throwError m!"cannot evaluate, proofs are not computationally relevant"
+  let e ← if (← isProp e) then mkDecide e else pure e
+  if ← isType e then
+    throwError m!"cannot evaluate, types are not computationally relevant"
+  trace[Elab.eval] "elaborated term:{indentExpr e}"
+  return e
+where
+  /-- Try different strategies to make `Term.synthesizeSyntheticMVarsNoPostponing` succeed. -/
+  synthesizeWithHinting (ty : Expr) : TermElabM Unit := do
+    Term.synthesizeSyntheticMVarsUsingDefault
+    let s ← saveState
+    try
+      Term.synthesizeSyntheticMVarsNoPostponing
+    catch ex =>
+      let exS ← saveState
+      -- Try hinting that `ty` is a monad application.
+      for m in #[``CommandElabM, ``TermElabM, ``IO] do
+        s.restore true
+        try
+          if ← isDefEq ty (← mkFreshMonadApp m) then
+            Term.synthesizeSyntheticMVarsNoPostponing
+            return
+        catch _ => pure ()
+      -- None of the hints worked, so throw the original error.
+      exS.restore true
+      throw ex
+  mkFreshMonadApp (n : Name) : MetaM Expr := do
+    let m ← mkConstWithFreshMVarLevels n
+    let (args, _, _) ← forallMetaBoundedTelescope (← inferType m) 1
+    return mkAppN m args
+
+private def addAndCompileExprForEval (declName : Name) (value : Expr) (allowSorry := false) : TermElabM Unit := do
+  -- Use the `elabMutualDef` machinery to be able to support `let rec`.
+  -- Hack: since we are using the `TermElabM` version, we can insert the `value` as a metavariable via `exprToSyntax`.
+  -- An alternative design would be to make `elabTermForEval` into a term elaborator and elaborate the command all at once
+  -- with `unsafe def _eval := term_for_eval% $t`, which we did try, but unwanted error messages
+  -- such as "failed to infer definition type" can surface.
+  let defView := mkDefViewOfDef { isUnsafe := true, stx := ⟨.missing⟩ }
+    (← `(Parser.Command.definition|
+          def $(mkIdent <| `_root_ ++ declName) := $(← Term.exprToSyntax value)))
+  Term.elabMutualDef #[] { header := "" } #[defView]
+  unless allowSorry do
+    let axioms ← collectAxioms declName
+    if axioms.contains ``sorryAx then
+      throwError "\
+        aborting evaluation since the expression depends on the 'sorry' axiom, \
+        which can lead to runtime instability and crashes.\n\n\
+        To attempt to evaluate anyway despite the risks, use the '#eval!' command."
+
+/--
+Try to make a `@projFn ty inst e` application, even if it takes unfolding the type `ty` of `e` to synthesize the instance `inst`.
+-/
+private partial def mkDeltaInstProj (inst projFn : Name) (e : Expr) (ty? : Option Expr := none) (tryReduce : Bool := true) : MetaM Expr := do
+  let ty ← ty?.getDM (inferType e)
+  if let .some inst ← trySynthInstance (← mkAppM inst #[ty]) then
+    mkAppOptM projFn #[ty, inst, e]
+  else
+    let ty ← whnfCore ty
+    let some ty ← unfoldDefinition? ty
+      | guard tryReduce
+        -- Reducing the type is a strategy `#eval` used before the refactor of #5627.
+        -- The test lean/run/hlistOverload.lean depends on it, so we preserve the behavior.
+        let ty ← reduce (skipTypes := false) ty
+        mkDeltaInstProj inst projFn e ty (tryReduce := false)
+    mkDeltaInstProj inst projFn e ty tryReduce
+
+/-- Try to make a `toString e` application, even if it takes unfolding the type of `e` to find a `ToString` instance. -/
+private def mkToString (e : Expr) (ty? : Option Expr := none) : MetaM Expr := do
+  mkDeltaInstProj ``ToString ``toString e ty?
+
+/-- Try to make a `repr e` application, even if it takes unfolding the type of `e` to find a `Repr` instance. -/
+private def mkRepr (e : Expr) (ty? : Option Expr := none) : MetaM Expr := do
+  mkDeltaInstProj ``Repr ``repr e ty?
+
+/-- Try to make a `toExpr e` application, even if it takes unfolding the type of `e` to find a `ToExpr` instance. -/
+private def mkToExpr (e : Expr) (ty? : Option Expr := none) : MetaM Expr := do
+  mkDeltaInstProj ``ToExpr ``toExpr e ty?
+
+/--
+Returns a representation of `e` using `Format`, or else fails.
+If the `eval.derive.repr` option is true, then tries automatically deriving a `Repr` instance first.
+Currently auto-derivation does not attempt to derive recursively.
+-/
+private def mkFormat (e : Expr) : MetaM Expr := do
+  mkRepr e <|> (do mkAppM ``Std.Format.text #[← mkToString e])
+  <|> do
+    if eval.derive.repr.get (← getOptions) then
+      if let .const name _ := (← whnf (← inferType e)).getAppFn then
+        try
+          trace[Elab.eval] "Attempting to derive a 'Repr' instance for '{MessageData.ofConstName name}'"
+          liftCommandElabM do applyDerivingHandlers ``Repr #[name] none
+          resetSynthInstanceCache
+          return ← mkRepr e
+        catch ex =>
+          trace[Elab.eval] "Failed to use derived 'Repr' instance. Exception: {ex.toMessageData}"
+    throwError m!"could not synthesize a 'Repr' or 'ToString' instance for type{indentExpr (← inferType e)}"
+
+/--
+Returns a representation of `e` using `MessageData`, or else fails.
+Tries `mkFormat` if a `ToExpr` instance can't be synthesized.
+-/
+private def mkMessageData (e : Expr) : MetaM Expr := do
+  (do guard <| eval.pp.get (← getOptions); mkAppM ``MessageData.ofExpr #[← mkToExpr e])
+  <|> (return mkApp (mkConst ``MessageData.ofFormat) (← mkFormat e))
+  <|> do throwError m!"could not synthesize a 'ToExpr', 'Repr', or 'ToString' instance for type{indentExpr (← inferType e)}"
+
+private structure EvalAction where
+  eval : CommandElabM MessageData
+  /-- Whether to print the result of evaluation.
+  If `some`, the expression is what type to use for the type ascription when `pp.type` is true. -/
+  printVal : Option Expr
+
+unsafe def elabEvalCoreUnsafe (bang : Bool) (tk term : Syntax) (expectedType? : Option Expr) : CommandElabM Unit := withRef tk do
+  let declName := `_eval
+  -- `t` is either `MessageData` or `Format`, and `mkT` is for synthesizing an expression that yields a `t`.
+  -- The `toMessageData` function adapts `t` to `MessageData`.
+  let mkAct {t : Type} [Inhabited t] (toMessageData : t → MessageData) (mkT : Expr → MetaM Expr) (e : Expr) : TermElabM EvalAction := do
+    -- Create a monadic action given the name of the monad `mc`, the monad `m` itself,
+    -- and an expression `e` to evaluate in this monad.
+    -- A trick here is that `mkMAct?` makes use of `MonadEval` instances are currently available in this stage,
+    -- and we do not need them to be available in the target environment.
+    let mkMAct? (mc : Name) (m : Type → Type) [Monad m] [MonadEvalT m CommandElabM] (e : Expr) : TermElabM (Option EvalAction) := do
+      let some e ← observing? (mkAppOptM ``MonadEvalT.monadEval #[none, mkConst mc, none, none, e])
+        | return none
+      let eType := e.appFn!.appArg!
+      if ← isDefEq eType (mkConst ``Unit) then
+        addAndCompileExprForEval declName e (allowSorry := bang)
+        let mf : m Unit ← evalConst (m Unit) declName
+        return some { eval := do MonadEvalT.monadEval mf; pure "", printVal := none }
+      else
+        let rf ← withLocalDeclD `x eType fun x => do mkLambdaFVars #[x] (← mkT x)
+        let r ← mkAppM ``Functor.map #[rf, e]
+        addAndCompileExprForEval declName r (allowSorry := bang)
+        let mf : m t ← evalConst (m t) declName
+        return some { eval := toMessageData <$> MonadEvalT.monadEval mf, printVal := some eType }
+    if let some act ← mkMAct? ``CommandElabM CommandElabM e
+                    -- Fallbacks in case we are in the Lean package but don't have `CommandElabM` yet
+                    <||> mkMAct? ``TermElabM TermElabM e <||> mkMAct? ``MetaM MetaM e <||> mkMAct? ``CoreM CoreM e
+                    -- Fallback in case nothing is imported
+                    <||> mkMAct? ``IO IO e then
+      return act
+    else
+      -- Otherwise, assume this is a pure value.
+      -- There is no need to adapt pure values to `CommandElabM`.
+      -- This enables `#eval` to work on pure values even when `CommandElabM` is not available.
+      let r ← try mkT e catch ex => do
+        -- Diagnose whether the value is monadic for a representable value, since it's better to mention `MonadEval` in that case.
+        try
+          let some (m, ty) ← isTypeApp? (← inferType e) | failure
+          guard <| (← isMonad? m).isSome
+          -- Verify that there is a way to form some representation:
+          discard <| withLocalDeclD `x ty fun x => mkT x
+        catch _ =>
+          throw ex
+        throwError m!"unable to synthesize '{MessageData.ofConstName ``MonadEval}' instance \
+          to adapt{indentExpr (← inferType e)}\n\
+          to '{MessageData.ofConstName ``IO}' or '{MessageData.ofConstName ``CommandElabM}'."
+      addAndCompileExprForEval declName r (allowSorry := bang)
+      -- `evalConst` may emit IO, but this is collected by `withIsolatedStreams` below.
+      let r ← toMessageData <$> evalConst t declName
+      return { eval := pure r, printVal := some (← inferType e) }
+  let (output, exOrRes) ← IO.FS.withIsolatedStreams do
+    try
+      -- Generate an action without executing it. We use `withoutModifyingEnv` to ensure
+      -- we don't pollute the environment with auxiliary declarations.
+      let act : EvalAction ← liftTermElabM do Term.withDeclName declName do withoutModifyingEnv do
+        let e ← elabTermForEval term expectedType?
+        -- If there is an elaboration error, don't evaluate!
+        if e.hasSyntheticSorry then throwAbortTerm
+        -- We want `#eval` to work even in the core library, so if `ofFormat` isn't available,
+        -- we fall back on a `Format`-based approach.
+        if (← getEnv).contains ``Lean.MessageData.ofFormat then
+          mkAct id (mkMessageData ·) e
+        else
+          mkAct Lean.MessageData.ofFormat (mkFormat ·) e
+      let res ← act.eval
+      return Sum.inr (res, act.printVal)
+    catch ex =>
+      return Sum.inl ex
+  if !output.isEmpty then logInfoAt tk output
+  match exOrRes with
+  | .inl ex => logException ex
+  | .inr (_, none) => pure ()
+  | .inr (res, some type) =>
+    if eval.type.get (← getOptions) then
+      logInfo m!"{res} : {type}"
+    else
+      logInfo res
+
+@[implemented_by elabEvalCoreUnsafe]
+opaque elabEvalCore (bang : Bool) (tk term : Syntax) (expectedType? : Option Expr) : CommandElabM Unit
+
+@[builtin_command_elab «eval»]
+def elabEval : CommandElab
+  | `(#eval%$tk $term) => elabEvalCore false tk term none
+  | _ => throwUnsupportedSyntax
+
+@[builtin_command_elab evalBang]
+def elabEvalBang : CommandElab
+  | `(#eval!%$tk $term) => elabEvalCore true tk term none
+  | _ => throwUnsupportedSyntax
+
+@[builtin_command_elab runCmd]
+def elabRunCmd : CommandElab
+  | `(run_cmd%$tk $elems:doSeq) => do
+    unless (← getEnv).contains ``CommandElabM do
+      throwError "to use this command, include `import Lean.Elab.Command`"
+    elabEvalCore false tk (← `(discard do $elems)) (mkApp (mkConst ``CommandElabM) (mkConst ``Unit))
+  | _ => throwUnsupportedSyntax
+
+@[builtin_command_elab runElab]
+def elabRunElab : CommandElab
+  | `(run_elab%$tk $elems:doSeq) => do
+    unless (← getEnv).contains ``TermElabM do
+      throwError "to use this command, include `import Lean.Elab.Term`"
+    elabEvalCore false tk (← `(discard do $elems)) (mkApp (mkConst ``TermElabM) (mkConst ``Unit))
+  | _ => throwUnsupportedSyntax
+
+@[builtin_command_elab runMeta]
+def elabRunMeta : CommandElab := fun stx =>
+  match stx with
+  | `(run_meta%$tk $elems:doSeq) => do
+    unless (← getEnv).contains ``MetaM do
+      throwError "to use this command, include `import Lean.Meta.Basic`"
+    elabEvalCore false tk (← `(discard do $elems)) (mkApp (mkConst ``MetaM) (mkConst ``Unit))
+  | _ => throwUnsupportedSyntax
+
+end Lean.Elab.Command