chore: rename List.bind and Array.concatMap to flatMap

fix

.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
 

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/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/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

@@ -11,6 +11,7 @@ import Init.Data.UInt.Basic
 import Init.Data.Repr
 import Init.Data.ToString.Basic
 import Init.GetElem
+import Init.Data.List.ToArray
 universe u v w
 
 /-! ### Array literal syntax -/
@@ -215,7 +216,7 @@ 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 :=
@@ -606,13 +607,17 @@ 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, ⋯]`

src/Init/Data/Array/Lemmas.lean

@@ -108,23 +108,52 @@ theorem toArray_concat {as : List α} {x : α} :
   funext a
   simp
 
-@[simp] theorem foldrM_toArray [Monad m] (f : α → β → m β) (init : β) (l : List α) :
+theorem foldrM_toArray [Monad m] (f : α → β → m β) (init : β) (l : List α) :
     l.toArray.foldrM f init = l.foldrM f init := by
   rw [foldrM_eq_reverse_foldlM_toList]
   simp
 
-@[simp] theorem foldlM_toArray [Monad m] (f : β → α → m β) (init : β) (l : List α) :
+theorem foldlM_toArray [Monad m] (f : β → α → m β) (init : β) (l : List α) :
     l.toArray.foldlM f init = l.foldlM f init := by
   rw [foldlM_eq_foldlM_toList]
 
-@[simp] theorem foldr_toArray (f : α → β → β) (init : β) (l : List α) :
+theorem foldr_toArray (f : α → β → β) (init : β) (l : List α) :
     l.toArray.foldr f init = l.foldr f init := by
   rw [foldr_eq_foldr_toList]
 
-@[simp] theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
+theorem foldl_toArray (f : β → α → β) (init : β) (l : List α) :
     l.toArray.foldl f init = l.foldl f init := by
   rw [foldl_eq_foldl_toList]
 
+/-- Variant of `foldrM_toArray` with a side condition for the `start` argument. -/
+@[simp] theorem foldrM_toArray' [Monad m] (f : α → β → m β) (init : β) (l : List α)
+    (h : start = l.toArray.size) :
+    l.toArray.foldrM f init start 0 = l.foldrM f init := by
+  subst h
+  rw [foldrM_eq_reverse_foldlM_toList]
+  simp
+
+/-- Variant of `foldlM_toArray` with a side condition for the `stop` argument. -/
+@[simp] theorem foldlM_toArray' [Monad m] (f : β → α → m β) (init : β) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.foldlM f init 0 stop = l.foldlM f init := by
+  subst h
+  rw [foldlM_eq_foldlM_toList]
+
+/-- Variant of `foldr_toArray` with a side condition for the `start` argument. -/
+@[simp] theorem foldr_toArray' (f : α → β → β) (init : β) (l : List α)
+    (h : start = l.toArray.size) :
+    l.toArray.foldr f init start 0 = l.foldr f init := by
+  subst h
+  rw [foldr_eq_foldr_toList]
+
+/-- Variant of `foldl_toArray` with a side condition for the `stop` argument. -/
+@[simp] theorem foldl_toArray' (f : β → α → β) (init : β) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.foldl f init 0 stop = l.foldl f init := by
+  subst h
+  rw [foldl_eq_foldl_toList]
+
 @[simp] theorem append_toArray (l₁ l₂ : List α) :
     l₁.toArray ++ l₂.toArray = (l₁ ++ l₂).toArray := by
   apply ext'
@@ -213,14 +242,17 @@ abbrev map_data := @toList_map
   cases arr
   simp
 
-theorem foldl_toList_eq_bind (l : List α) (acc : Array β)
+theorem foldl_toList_eq_flatMap (l : List α) (acc : Array β)
     (F : Array β → α → Array β) (G : α → List β)
     (H : ∀ acc a, (F acc a).toList = acc.toList ++ G a) :
-    (l.foldl F acc).toList = acc.toList ++ l.bind G := by
-  induction l generalizing acc <;> simp [*, List.bind]
+    (l.foldl F acc).toList = acc.toList ++ l.flatMap G := by
+  induction l generalizing acc <;> simp [*, List.flatMap]
 
-@[deprecated foldl_toList_eq_bind (since := "2024-09-09")]
-abbrev foldl_data_eq_bind := @foldl_toList_eq_bind
+@[deprecated foldl_toList_eq_flatMap (since := "2024-10-16")]
+abbrev foldl_toList_eq_bind := @foldl_toList_eq_flatMap
+
+@[deprecated foldl_toList_eq_flatMap (since := "2024-10-16")]
+abbrev foldl_data_eq_bind := @foldl_toList_eq_flatMap
 
 theorem foldl_toList_eq_map (l : List α) (acc : Array β) (G : α → β) :
     (l.foldl (fun acc a => acc.push (G a)) acc).toList = acc.toList ++ l.map G := by
@@ -553,6 +585,13 @@ theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]?
 theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
     a.swapAt! i v = (a[i], a.set ⟨i, h⟩ v) := by simp [swapAt!, h]
 
+@[simp] theorem size_swapAt! (a : Array α) (i : Nat) (v : α) :
+    (a.swapAt! i v).2.size = a.size := by
+  simp only [swapAt!]
+  split
+  · simp
+  · rfl
+
 @[simp] theorem toList_pop (a : Array α) : a.pop.toList = a.toList.dropLast := by simp [pop]
 
 @[deprecated toList_pop (since := "2024-09-09")]
@@ -730,6 +769,18 @@ theorem foldr_induction
   simp [foldr, foldrM]; split; {exact go _ h0}
   · next h => exact (Nat.eq_zero_of_not_pos h ▸ h0)
 
+@[congr]
+theorem foldl_congr {as bs : Array α} (h₀ : as = bs) {f g : β → α → β} (h₁ : f = g)
+     {a b : β} (h₂ : a = b) {start start' stop stop' : Nat} (h₃ : start = start') (h₄ : stop = stop') :
+    as.foldl f a start stop = bs.foldl g b start' stop' := by
+  congr
+
+@[congr]
+theorem foldr_congr {as bs : Array α} (h₀ : as = bs) {f g : α → β → β} (h₁ : f = g)
+     {a b : β} (h₂ : a = b) {start start' stop stop' : Nat} (h₃ : start = start') (h₄ : stop = stop') :
+    as.foldr f a start stop = bs.foldr g b start' stop' := by
+  congr
+
 /-! ### map -/
 
 @[simp] theorem mem_map {f : α → β} {l : Array α} : b ∈ l.map f ↔ ∃ a, a ∈ l ∧ f a = b := by
@@ -814,6 +865,13 @@ theorem map_spec (as : Array α) (f : α → β) (p : Fin as.size → β → Pro
     (as.map f)[i]? = as[i]?.map f := by
   simp [getElem?_def]
 
+@[simp] theorem map_push {f : α → β} {as : Array α} {x : α} :
+    (as.push x).map f = (as.map f).push (f x) := by
+  ext
+  · simp
+  · simp only [getElem_map, get_push, size_map]
+    split <;> rfl
+
 /-! ### mapIdx -/
 
 -- This could also be proved from `SatisfiesM_mapIdxM` in Batteries.
@@ -920,6 +978,13 @@ abbrev filter_data := @toList_filter
 theorem mem_of_mem_filter {a : α} {l} (h : a ∈ filter p l) : a ∈ l :=
   (mem_filter.mp h).1
 
+@[congr]
+theorem filter_congr {as bs : Array α} (h : as = bs)
+    {f : α → Bool} {g : α → Bool} (h' : f = g) {start stop start' stop' : Nat}
+    (h₁ : start = start') (h₂ : stop = stop') :
+    filter f as start stop = filter g bs start' stop' := by
+  congr
+
 /-! ### filterMap -/
 
 @[simp] theorem toList_filterMap (f : α → Option β) (l : Array α) :
@@ -942,6 +1007,13 @@ abbrev filterMap_data := @toList_filterMap
     b ∈ filterMap f l ↔ ∃ a, a ∈ l ∧ f a = some b := by
   simp only [mem_def, toList_filterMap, List.mem_filterMap]
 
+@[congr]
+theorem filterMap_congr {as bs : Array α} (h : as = bs)
+    {f : α → Option β} {g : α → Option β} (h' : f = g) {start stop start' stop' : Nat}
+    (h₁ : start = start') (h₂ : stop = stop') :
+    filterMap f as start stop = filterMap g bs start' stop' := by
+  congr
+
 /-! ### empty -/
 
 theorem size_empty : (#[] : Array α).size = 0 := rfl
@@ -998,7 +1070,7 @@ theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) :
 
 /-! ### flatten -/
 
-@[simp] theorem toList_flatten {l : Array (Array α)} : l.flatten.toList = (l.toList.map toList).join := by
+@[simp] theorem toList_flatten {l : Array (Array α)} : l.flatten.toList = (l.toList.map toList).flatten := by
   dsimp [flatten]
   simp only [foldl_eq_foldl_toList]
   generalize l.toList = l
@@ -1009,7 +1081,7 @@ theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) :
   | cons h => induction h.toList <;> simp [*]
 
 theorem mem_flatten : ∀ {L : Array (Array α)}, a ∈ L.flatten ↔ ∃ l, l ∈ L ∧ a ∈ l := by
-  simp only [mem_def, toList_flatten, List.mem_join, List.mem_map]
+  simp only [mem_def, toList_flatten, List.mem_flatten, List.mem_map]
   intro l
   constructor
   · rintro ⟨_, ⟨s, m, rfl⟩, h⟩
@@ -1432,18 +1504,44 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   · simp
   · simp_all [List.set_eq_of_length_le]
 
-@[simp] theorem anyM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
+theorem anyM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
     l.toArray.anyM p = l.anyM p := by
   rw [← anyM_toList]
 
-@[simp] theorem any_toArray (p : α → Bool) (l : List α) : l.toArray.any p = l.any p := by
+theorem any_toArray (p : α → Bool) (l : List α) : l.toArray.any p = l.any p := by
   rw [any_toList]
 
-@[simp] theorem allM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
+theorem allM_toArray [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α) :
     l.toArray.allM p = l.allM p := by
   rw [← allM_toList]
 
-@[simp] theorem all_toArray (p : α → Bool) (l : List α) : l.toArray.all p = l.all p := by
+theorem all_toArray (p : α → Bool) (l : List α) : l.toArray.all p = l.all p := by
+  rw [all_toList]
+
+/-- Variant of `anyM_toArray` with a side condition on `stop`. -/
+@[simp] theorem anyM_toArray' [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.anyM p 0 stop = l.anyM p := by
+  subst h
+  rw [← anyM_toList]
+
+/-- Variant of `any_toArray` with a side condition on `stop`. -/
+@[simp] theorem any_toArray' (p : α → Bool) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.any p 0 stop = l.any p := by
+  subst h
+  rw [any_toList]
+
+/-- Variant of `allM_toArray` with a side condition on `stop`. -/
+@[simp] theorem allM_toArray' [Monad m] [LawfulMonad m] (p : α → m Bool) (l : List α)
+    (h : stop = l.toArray.size) :
+    l.toArray.allM p 0 stop = l.allM p := by
+  subst h
+  rw [← allM_toList]
+
+/-- Variant of `all_toArray` with a side condition on `stop`. -/
+@[simp] theorem all_toArray' (p : α → Bool) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.all p 0 stop = l.all p := by
+  subst h
   rw [all_toList]
 
 @[simp] theorem swap_toArray (l : List α) (i j : Fin l.toArray.size) :
@@ -1459,17 +1557,27 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
   apply ext'
   simp
 
-@[simp] theorem filter_toArray (p : α → Bool) (l : List α) :
+@[simp] theorem filter_toArray' (p : α → Bool) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.filter p 0 stop = (l.filter p).toArray := by
+  subst h
+  apply ext'
+  rw [toList_filter]
+
+@[simp] theorem filterMap_toArray' (f : α → Option β) (l : List α) (h : stop = l.toArray.size) :
+    l.toArray.filterMap f 0 stop = (l.filterMap f).toArray := by
+  subst h
+  apply ext'
+  rw [toList_filterMap]
+
+theorem filter_toArray (p : α → Bool) (l : List α) :
     l.toArray.filter p = (l.filter p).toArray := by
-  apply ext'
-  erw [toList_filter] -- `erw` required to unify `l.length` with `l.toArray.size`.
+  simp
 
-@[simp] theorem filterMap_toArray (f : α → Option β) (l : List α) :
+theorem filterMap_toArray (f : α → Option β) (l : List α) :
     l.toArray.filterMap f = (l.filterMap f).toArray := by
-  apply ext'
-  erw [toList_filterMap] -- `erw` required to unify `l.length` with `l.toArray.size`.
+  simp
 
-@[simp] theorem flatten_toArray (l : List (List α)) : (l.toArray.map List.toArray).flatten = l.join.toArray := by
+@[simp] theorem flatten_toArray (l : List (List α)) : (l.toArray.map List.toArray).flatten = l.flatten.toArray := by
   apply ext'
   simp [Function.comp_def]
 

src/Init/Data/BitVec/Basic.lean

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, 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
@@ -718,6 +718,8 @@ 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/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`.
 
@@ -497,7 +571,7 @@ 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 +587,7 @@ 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 +688,7 @@ 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 +701,7 @@ 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 +767,7 @@ 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 +875,7 @@ 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 +883,7 @@ 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
 
@@ -434,7 +450,7 @@ 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 +935,21 @@ 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 +992,15 @@ 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 +1223,28 @@ 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 +1349,8 @@ 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 +1377,7 @@ 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 +1395,55 @@ 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 +1660,11 @@ 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
@@ -2014,7 +2039,7 @@ 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 +2059,36 @@ 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']))
 
+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 +2223,7 @@ 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 +2231,169 @@ 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']
+
+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_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
+
+/-! ### 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
@@ -2680,6 +2893,31 @@ 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 +3122,7 @@ 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/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/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

@@ -29,9 +29,10 @@ 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`,
@@ -368,7 +369,7 @@ 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 +543,50 @@ 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
+
+@[deprecated flatten (since := "2024-10-14"), inherit_doc flatten] abbrev join := @flatten
 
 /-! ### pure -/
 
 /-- `pure x = [x]` is the `pure` operation of the list monad. -/
 @[inline] protected def pure {α : Type u} (a : α) : List α := [a]
 
-/-! ### bind -/
+/-! ### 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 -/
 
@@ -1527,7 +1537,7 @@ 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/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 = Nat.sum (l.map (countP p)) := 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 = Nat.sum (l.map (count a)) := 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) +
           (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

@@ -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 -/
 
@@ -322,7 +322,7 @@ 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

@@ -1343,12 +1343,12 @@ 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 +2068,98 @@ 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 = Nat.sum (L.map length) := 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 +2170,23 @@ 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 +2200,15 @@ 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 +2216,86 @@ 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 +2472,23 @@ 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 +2663,20 @@ 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 +2784,15 @@ 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 +3291,22 @@ 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 +3331,72 @@ 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 =>
@@ -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
@@ -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/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/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/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 :=
@@ -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/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/Option/Attach.lean

@@ -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/String/Extra.lean

@@ -117,11 +117,11 @@ 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/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

@@ -223,38 +223,6 @@ 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
   | _ => `(#[])
 

src/Init/Prelude.lean

@@ -2716,28 +2716,6 @@ 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 +2869,32 @@ 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

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

@@ -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
@@ -1172,6 +1159,9 @@ 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 +1212,24 @@ 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/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
@@ -38,3 +37,4 @@ 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/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/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/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

@@ -229,7 +229,7 @@ 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 +311,6 @@ 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 +348,7 @@ 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

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 }
+    (← `(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

src/Lean/Elab/BuiltinTerm.lean

@@ -103,9 +103,11 @@ private def elabOptLevel (stx : Syntax) : TermElabM Level :=
 @[builtin_term_elab Lean.Parser.Term.omission] def elabOmission : TermElab := fun stx expectedType? => do
   logWarning m!"\
     The '⋯' token is used by the pretty printer to indicate omitted terms, and it should not be used directly. \
-    It logs this warning and then elaborates like `_`.\
-    \n\nThe presence of `⋯` in pretty printing output is controlled by the 'pp.deepTerms' and `pp.proofs` options. \
-    These options can be further adjusted using `pp.deepTerms.threshold` and `pp.proofs.threshold`."
+    It logs this warning and then elaborates like '_'.\
+    \n\n\
+    The presence of '⋯' in pretty printing output is controlled by the 'pp.maxSteps', 'pp.deepTerms' and 'pp.proofs' options. \
+    These options can be further adjusted using 'pp.deepTerms.threshold' and 'pp.proofs.threshold'. \
+    If this '⋯' was copied from the Infoview, the hover there for the original '⋯' explains which of these options led to the omission."
   elabHole stx expectedType?
 
 @[builtin_term_elab «letMVar»] def elabLetMVar : TermElab := fun stx expectedType? => do

src/Lean/Elab/Command.lean

@@ -520,8 +520,12 @@ def elabCommandTopLevel (stx : Syntax) : CommandElabM Unit := withRef stx do pro
     -- recovery more coarse. In particular, If `c` in `set_option ... in $c` fails, the remaining
     -- `end` command of the `in` macro would be skipped and the option would be leaked to the outside!
     elabCommand stx
-    withLogging do
-      runLinters stx
+    -- Run the linters, unless `#guard_msgs` is present, which is special and runs `elabCommandTopLevel` itself,
+    -- so it is a "super-top-level" command. This is the only command that does this, so we just special case it here
+    -- rather than engineer a general solution.
+    unless (stx.find? (·.isOfKind ``Lean.guardMsgsCmd)).isSome do
+      withLogging do
+        runLinters stx
   finally
     -- note the order: first process current messages & info trees, then add back old messages & trees,
     -- then convert new traces to messages
@@ -567,7 +571,7 @@ def getBracketedBinderIds : Syntax → CommandElabM (Array Name)
 private def mkTermContext (ctx : Context) (s : State) : CommandElabM Term.Context := do
   let scope      := s.scopes.head!
   let mut sectionVars := {}
-  for id in (← scope.varDecls.concatMapM getBracketedBinderIds), uid in scope.varUIds do
+  for id in (← scope.varDecls.flatMapM getBracketedBinderIds), uid in scope.varUIds do
     sectionVars := sectionVars.insert id uid
   return {
     macroStack             := ctx.macroStack
@@ -615,6 +619,9 @@ def liftTermElabM (x : TermElabM α) : CommandElabM α := do
   let ((ea, _), _) ← runCore x
   MonadExcept.ofExcept ea
 
+instance : MonadEval TermElabM CommandElabM where
+  monadEval := liftTermElabM
+
 /--
 Execute the monadic action `elabFn xs` as a `CommandElabM` monadic action, where `xs` are free variables
 corresponding to all active scoped variables declared using the `variable` command.
@@ -707,7 +714,7 @@ def expandDeclId (declId : Syntax) (modifiers : Modifiers) : CommandElabM Expand
   let currNamespace ← getCurrNamespace
   let currLevelNames ← getLevelNames
   let r ← Elab.expandDeclId currNamespace currLevelNames declId modifiers
-  for id in (← (← getScope).varDecls.concatMapM getBracketedBinderIds) do
+  for id in (← (← getScope).varDecls.flatMapM getBracketedBinderIds) do
     if id == r.shortName then
       throwError "invalid declaration name '{r.shortName}', there is a section variable with the same name"
   return r
@@ -723,6 +730,12 @@ Commands that modify the processing of subsequent commands,
 such as `open` and `namespace` commands,
 only have an effect for the remainder of the `CommandElabM` computation passed here,
 and do not affect subsequent commands.
+
+*Warning:* when using this from `MetaM` monads, the caches are *not* reset.
+If the command defines new instances for example, you should use `Lean.Meta.resetSynthInstanceCache`
+to reset the instance cache.
+While the `modifyEnv` function for `MetaM` clears its caches entirely,
+`liftCommandElabM` has no way to reset these caches.
 -/
 def liftCommandElabM (cmd : CommandElabM α) : CoreM α := do
   let (a, commandState) ←

src/Lean/Elab/Declaration.lean

@@ -136,8 +136,8 @@ def elabAxiom (modifiers : Modifiers) (stx : Syntax) : CommandElabM Unit := do
         Term.applyAttributesAt declName modifiers.attrs AttributeApplicationTime.afterCompilation
 
 /-
-leading_parser "inductive " >> declId >> optDeclSig >> optional ":=" >> many ctor
-leading_parser atomic (group ("class " >> "inductive ")) >> declId >> optDeclSig >> optional ":=" >> many ctor >> optDeriving
+leading_parser "inductive " >> declId >> optDeclSig >> optional ("where" <|> ":=") >> many ctor
+leading_parser atomic (group ("class " >> "inductive ")) >> declId >> optDeclSig >> optional ("where" <|> ":=") >> many ctor >> optDeriving
 -/
 private def inductiveSyntaxToView (modifiers : Modifiers) (decl : Syntax) : CommandElabM InductiveView := do
   checkValidInductiveModifier modifiers
@@ -167,6 +167,10 @@ private def inductiveSyntaxToView (modifiers : Modifiers) (decl : Syntax) : Comm
   let computedFields ← (decl[5].getOptional?.map (·[1].getArgs) |>.getD #[]).mapM fun cf => withRef cf do
     return { ref := cf, modifiers := cf[0], fieldId := cf[1].getId, type := ⟨cf[3]⟩, matchAlts := ⟨cf[4]⟩ }
   let classes ← liftCoreM <| getOptDerivingClasses decl[6]
+  if decl[3][0].isToken ":=" then
+    -- https://github.com/leanprover/lean4/issues/5236
+    withRef decl[0] <| Linter.logLintIf Linter.linter.deprecated decl[3]
+      "'inductive ... :=' has been deprecated in favor of 'inductive ... where'."
   return {
     ref             := decl
     shortDeclName   := name
@@ -382,19 +386,28 @@ def elabMutual : CommandElab := fun stx => do
     for attrName in toErase do
       Attribute.erase declName attrName
 
-@[builtin_macro Lean.Parser.Command.«initialize»] def expandInitialize : Macro
+@[builtin_command_elab Lean.Parser.Command.«initialize»] def elabInitialize : CommandElab
   | stx@`($declModifiers:declModifiers $kw:initializeKeyword $[$id? : $type? ←]? $doSeq) => do
     let attrId := mkIdentFrom stx <| if kw.raw[0].isToken "initialize" then `init else `builtin_init
     if let (some id, some type) := (id?, type?) then
       let `(Parser.Command.declModifiersT| $[$doc?:docComment]? $[@[$attrs?,*]]? $(vis?)? $[unsafe%$unsafe?]?) := stx[0]
-        | Macro.throwErrorAt declModifiers "invalid initialization command, unexpected modifiers"
-      `($[unsafe%$unsafe?]? def initFn : IO $type := with_decl_name% ?$id do $doSeq
-        $[$doc?:docComment]? @[$attrId:ident initFn, $(attrs?.getD ∅),*] $(vis?)? opaque $id : $type)
+        | throwErrorAt declModifiers "invalid initialization command, unexpected modifiers"
+      let defStx ← `($[$doc?:docComment]? @[$attrId:ident initFn, $(attrs?.getD ∅),*] $(vis?)? opaque $id : $type)
+      let mut fullId := (← getCurrNamespace) ++ id.getId
+      if vis?.any (·.raw.isOfKind ``Parser.Command.private) then
+        fullId := mkPrivateName (← getEnv) fullId
+      -- We need to add `id`'s ranges *before* elaborating `initFn` (and then `id` itself) as
+      -- otherwise the info context created by `with_decl_name` will be incomplete and break the
+      -- call hierarchy
+      addDeclarationRanges fullId defStx
+      elabCommand (← `(
+        $[unsafe%$unsafe?]? def initFn : IO $type := with_decl_name% $(mkIdent fullId) do $doSeq
+        $defStx:command))
     else
       let `(Parser.Command.declModifiersT| $[$doc?:docComment]? ) := declModifiers
-        | Macro.throwErrorAt declModifiers "invalid initialization command, unexpected modifiers"
-      `($[$doc?:docComment]? @[$attrId:ident] def initFn : IO Unit := do $doSeq)
-  | _ => Macro.throwUnsupported
+        | throwErrorAt declModifiers "invalid initialization command, unexpected modifiers"
+      elabCommand (← `($[$doc?:docComment]? @[$attrId:ident] def initFn : IO Unit := do $doSeq))
+  | _ => throwUnsupportedSyntax
 
 builtin_initialize
   registerTraceClass `Elab.axiom

src/Lean/Elab/Deriving/FromToJson.lean

@@ -36,7 +36,7 @@ def mkToJsonBodyForStruct (header : Header) (indName : Name) : TermElabM Term :=
     let target := mkIdent header.targetNames[0]!
     if isOptField then ``(opt $nm $target.$(mkIdent field))
     else ``([($nm, toJson ($target).$(mkIdent field))])
-  `(mkObj <| List.join [$fields,*])
+  `(mkObj <| List.flatten [$fields,*])
 
 def mkToJsonBodyForInduct (ctx : Context) (header : Header) (indName : Name) : TermElabM Term := do
   let indVal ← getConstInfoInduct indName

src/Lean/Elab/Frontend.lean

@@ -151,7 +151,7 @@ def runFrontend
   snaps.runAndReport opts jsonOutput
 
   if let some ileanFileName := ileanFileName? then
-    let trees := snaps.getAll.concatMap (match ·.infoTree? with | some t => #[t] | _ => #[])
+    let trees := snaps.getAll.flatMap (match ·.infoTree? with | some t => #[t] | _ => #[])
     let references := Lean.Server.findModuleRefs inputCtx.fileMap trees (localVars := false)
     let ilean := { module := mainModuleName, references := ← references.toLspModuleRefs : Lean.Server.Ilean }
     IO.FS.writeFile ileanFileName $ Json.compress $ toJson ilean

src/Lean/Elab/GuardMsgs.lean

@@ -140,6 +140,7 @@ def MessageOrdering.apply (mode : MessageOrdering) (msgs : List String) : List S
         |>.trim |> removeTrailingWhitespaceMarker
     let (whitespace, ordering, specFn) ← parseGuardMsgsSpec spec?
     let initMsgs ← modifyGet fun st => (st.messages, { st with messages := {} })
+    -- The `#guard_msgs` command is special-cased in `elabCommandTopLevel` to ensure linters only run once.
     elabCommandTopLevel cmd
     let msgs := (← get).messages
     let mut toCheck : MessageLog := .empty

src/Lean/Elab/Inductive.lean

@@ -425,9 +425,9 @@ where
   levelMVarToParam' (type : Expr) : TermElabM Expr := do
     Term.levelMVarToParam type (except := fun mvarId => univToInfer? == some mvarId)
 
-def mkResultUniverse (us : Array Level) (rOffset : Nat) : Level :=
+def mkResultUniverse (us : Array Level) (rOffset : Nat) (preferProp : Bool) : Level :=
   if us.isEmpty && rOffset == 0 then
-    levelOne
+    if preferProp then levelZero else levelOne
   else
     let r := Level.mkNaryMax us.toList
     if rOffset == 0 && !r.isZero && !r.isNeverZero then
@@ -512,6 +512,31 @@ where
           for ctorParam in ctorParams[numParams:] do
             accLevelAtCtor ctor ctorParam r rOffset
 
+/--
+Decides whether the inductive type should be `Prop`-valued when the universe is not given
+and when the universe inference algorithm `collectUniverses` determines
+that the inductive type could naturally be `Prop`-valued.
+Recall: the natural universe level is the mimimum universe level for all the types of all the constructor parameters.
+
+Heuristic:
+- We want `Prop` when each inductive type is a syntactic subsingleton.
+  That's to say, when each inductive type has at most one constructor.
+  Such types carry no data anyway.
+- Exception: if no inductive type has any constructors, these are likely stubbed-out declarations,
+  so we prefer `Type` instead.
+- Exception: if each constructor has no parameters, then these are likely partially-written enumerations,
+  so we prefer `Type` instead.
+-/
+private def isPropCandidate (numParams : Nat) (indTypes : List InductiveType) : MetaM Bool := do
+  unless indTypes.foldl (fun n indType => max n indType.ctors.length) 0 == 1 do
+    return false
+  for indType in indTypes do
+    for ctor in indType.ctors do
+      let cparams ← forallTelescopeReducing ctor.type fun ctorParams _ => pure (ctorParams.size - numParams)
+      unless cparams == 0 do
+        return true
+  return false
+
 private def updateResultingUniverse (views : Array InductiveView) (numParams : Nat) (indTypes : List InductiveType) : TermElabM (List InductiveType) := do
   let r ← getResultingUniverse indTypes
   let rOffset : Nat   := r.getOffset
@@ -520,7 +545,7 @@ private def updateResultingUniverse (views : Array InductiveView) (numParams : N
     throwError "failed to compute resulting universe level of inductive datatype, provide universe explicitly: {r}"
   let us ← collectUniverses views r rOffset numParams indTypes
   trace[Elab.inductive] "updateResultingUniverse us: {us}, r: {r}, rOffset: {rOffset}"
-  let rNew := mkResultUniverse us rOffset
+  let rNew := mkResultUniverse us rOffset (← isPropCandidate numParams indTypes)
   assignLevelMVar r.mvarId! rNew
   indTypes.mapM fun indType => do
     let type ← instantiateMVars indType.type
@@ -745,7 +770,7 @@ private partial def fixedIndicesToParams (numParams : Nat) (indTypes : Array Ind
   forallBoundedTelescope indTypes[0]!.type numParams fun params type => do
     let otherTypes ← indTypes[1:].toArray.mapM fun indType => do whnfD (← instantiateForall indType.type params)
     let ctorTypes ← indTypes.toList.mapM fun indType => indType.ctors.mapM fun ctor => do whnfD (← instantiateForall ctor.type params)
-    let typesToCheck := otherTypes.toList ++ ctorTypes.join
+    let typesToCheck := otherTypes.toList ++ ctorTypes.flatten
     let rec go (i : Nat) (type : Expr) (typesToCheck : List Expr) : MetaM Nat := do
       if i < mask.size then
         if !masks.all fun mask => i < mask.size && mask[i]! then

src/Lean/Elab/InfoTree/Types.lean

@@ -83,7 +83,7 @@ inductive CompletionInfo where
   | namespaceId (stx : Syntax)
   | option (stx : Syntax)
   | endSection (stx : Syntax) (scopeNames : List String)
-  | tactic (stx : Syntax) (goals : List MVarId)
+  | tactic (stx : Syntax)
   -- TODO `import`
 
 /-- Info for an option reference (e.g. in `set_option`). -/

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

@@ -226,7 +226,7 @@ def allCombinations (xss : Array (Array α)) : Option (Array (Array α)) :=
   else
     let rec go i acc : Array (Array α):=
       if h : i < xss.size then
-        xss[i].concatMap fun x => go (i + 1) (acc.push x)
+        xss[i].flatMap fun x => go (i + 1) (acc.push x)
       else
         #[acc]
     some (go 0 #[])

src/Lean/Elab/StructInst.lean

@@ -473,7 +473,10 @@ private def getFieldIdx (structName : Name) (fieldNames : Array Name) (fieldName
 def mkProjStx? (s : Syntax) (structName : Name) (fieldName : Name) : TermElabM (Option Syntax) := do
   if (findField? (← getEnv) structName fieldName).isNone then
     return none
-  return some <| mkNode ``Parser.Term.proj #[s, mkAtomFrom s ".", mkIdentFrom s fieldName]
+  return some <|
+    mkNode ``Parser.Term.explicit
+      #[mkAtomFrom s "@",
+        mkNode ``Parser.Term.proj #[s, mkAtomFrom s ".", mkIdentFrom s fieldName]]
 
 def findField? (fields : Fields) (fieldName : Name) : Option (Field Struct) :=
   fields.find? fun field =>
@@ -685,7 +688,7 @@ private partial def elabStruct (s : Struct) (expectedType? : Option Expr) : Term
               let type := (d.getArg! 0).consumeTypeAnnotations
               let mvar ← mkTacticMVar type stx (.fieldAutoParam fieldName s.structName)
               -- Note(kmill): We are adding terminfo to simulate a previous implementation that elaborated `tacticBlock`.
-              -- (See the aformentioned `processExplicitArg` for a comment about this.)
+              -- (See the aforementioned `processExplicitArg` for a comment about this.)
               addTermInfo' stx mvar
               cont mvar field
           | _ =>

src/Lean/Elab/Structure.lean

@@ -137,7 +137,12 @@ def structSimpleBinder   := leading_parser atomic (declModifiers true >> ident)
 def structFields         := leading_parser many (structExplicitBinder <|> structImplicitBinder <|> structInstBinder)
 ```
 -/
-private def expandFields (structStx : Syntax) (structModifiers : Modifiers) (structDeclName : Name) : TermElabM (Array StructFieldView) :=
+private def expandFields (structStx : Syntax) (structModifiers : Modifiers) (structDeclName : Name) : TermElabM (Array StructFieldView) := do
+  if structStx[5][0].isToken ":=" then
+    -- https://github.com/leanprover/lean4/issues/5236
+    let cmd := if structStx[0].getKind == ``Parser.Command.classTk then "class" else "structure"
+    withRef structStx[0] <| Linter.logLintIf Linter.linter.deprecated structStx[5][0]
+      s!"{cmd} ... :=' has been deprecated in favor of '{cmd} ... where'."
   let fieldBinders := if structStx[5].isNone then #[] else structStx[5][2][0].getArgs
   fieldBinders.foldlM (init := #[]) fun (views : Array StructFieldView) fieldBinder => withRef fieldBinder do
     let mut fieldBinder := fieldBinder
@@ -632,6 +637,19 @@ where
           msg := msg ++ "\nrecall that Lean only infers the resulting universe level automatically when there is a unique solution for the universe level constraints, consider explicitly providing the structure resulting universe level"
         throwError msg
 
+/--
+Decides whether the structure should be `Prop`-valued when the universe is not given
+and when the universe inference algorithm `collectUniversesFromFields` determines
+that the inductive type could naturally be `Prop`-valued.
+
+See `Lean.Elab.Command.isPropCandidate` for an explanation.
+Specialized to structures, the heuristic is that we prefer a `Prop` instead of a `Type` structure
+when it could be a syntactic subsingleton.
+Exception: no-field structures are `Type` since they are likely stubbed-out declarations.
+-/
+private def isPropCandidate (fieldInfos : Array StructFieldInfo) : Bool :=
+  !fieldInfos.isEmpty
+
 private def updateResultingUniverse (fieldInfos : Array StructFieldInfo) (type : Expr) : TermElabM Expr := do
   let r ← getResultUniverse type
   let rOffset : Nat   := r.getOffset
@@ -639,7 +657,7 @@ private def updateResultingUniverse (fieldInfos : Array StructFieldInfo) (type :
   match r with
   | Level.mvar mvarId =>
     let us ← collectUniversesFromFields r rOffset fieldInfos
-    let rNew := mkResultUniverse us rOffset
+    let rNew := mkResultUniverse us rOffset (isPropCandidate fieldInfos)
     assignLevelMVar mvarId rNew
     instantiateMVars type
   | _ => throwError "failed to compute resulting universe level of structure, provide universe explicitly"
@@ -866,7 +884,8 @@ private def elabStructureView (view : StructView) : TermElabM Unit := do
         addDefaults lctx defaultAuxDecls
 
 /-
-leading_parser (structureTk <|> classTk) >> declId >> many Term.bracketedBinder >> optional «extends» >> Term.optType >> " := " >> optional structCtor >> structFields >> optDeriving
+leading_parser (structureTk <|> classTk) >> declId >> many Term.bracketedBinder >> optional «extends» >> Term.optType >>
+  optional (("where" <|> ":=") >> optional structCtor >> structFields) >> optDeriving
 
 where
 def «extends» := leading_parser " extends " >> sepBy1 termParser ", "

src/Lean/Elab/Tactic/BVDecide/External.lean

@@ -169,8 +169,9 @@ def satQuery (solverPath : System.FilePath) (problemPath : System.FilePath) (pro
   let out? ← runInterruptible timeout { cmd, args, stdin := .piped, stdout := .piped, stderr := .null }
   match out? with
   | .timeout =>
-    let mut err := "The SAT solver timed out while solving the problem."
-    err := err ++ "\nConsider increasing the timeout with `set_option sat.timeout <sec>`"
+    let mut err := "The SAT solver timed out while solving the problem.\n"
+    err := err ++ "Consider increasing the timeout with `set_option sat.timeout <sec>`.\n"
+    err := err ++ "If solving your problem relies inherently on using associativity or commutativity, consider enabling the `bv.ac_nf` option."
     throwError err
   | .success { exitCode := exitCode, stdout := stdout, stderr := stderr} =>
     if exitCode == 255 then

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

@@ -52,6 +52,11 @@ register_builtin_option debug.bv.graphviz : Bool := {
   descr := "Output the AIG of bv_decide as graphviz into a file called aig.gv in the working directory of the Lean process."
 }
 
+register_builtin_option bv.ac_nf : Bool := {
+  defValue := false
+  descr := "Canonicalize with respect to associativity and commutativitiy."
+}
+
 builtin_initialize bvNormalizeExt : Meta.SimpExtension ←
   Meta.registerSimpAttr `bv_normalize "simp theorems used by bv_normalize"
 

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

@@ -41,7 +41,7 @@ def lratChecker (cfg : TacticContext) (bvExpr : BVLogicalExpr) : MetaM Expr := d
 
 @[inherit_doc Lean.Parser.Tactic.bvCheck]
 def bvCheck (g : MVarId) (cfg : TacticContext) : MetaM Unit := do
-  let unsatProver : UnsatProver := fun reflectionResult _ => do
+  let unsatProver : UnsatProver := fun _ reflectionResult _ => do
     withTraceNode `sat (fun _ => return "Preparing LRAT reflection term") do
       let proof ← lratChecker cfg reflectionResult.bvExpr
       return .ok ⟨proof, ""⟩
@@ -60,8 +60,8 @@ def evalBvCheck : Tactic := fun
       | some g' => bvCheck g' cfg
       | none =>
         let bvNormalizeStx ← `(tactic| bv_normalize)
+        logWarning m!"This goal can be closed by only applying bv_normalize, no need to keep the LRAT proof around."
         TryThis.addSuggestion tk bvNormalizeStx (origSpan? := ← getRef)
-        throwError m!"This goal can be closed by only applying bv_normalize, no need to keep the LRAT proof around."
   | _ => throwUnsupportedSyntax
 
 end Frontend.BVCheck

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

@@ -83,6 +83,10 @@ structure ReflectionResult where
 A counter example generated from the bitblaster.
 -/
 structure CounterExample where
+  /--
+  The goal in which to interpret this counter example.
+  -/
+  goal : MVarId
   /--
   The set of unused but potentially relevant hypotheses. Useful for diagnosing spurious counter
   examples.
@@ -97,7 +101,7 @@ structure UnsatProver.Result where
   proof : Expr
   lratCert : LratCert
 
-abbrev UnsatProver := ReflectionResult → Std.HashMap Nat (Nat × Expr) →
+abbrev UnsatProver := MVarId → ReflectionResult → Std.HashMap Nat (Nat × Expr) →
     MetaM (Except CounterExample UnsatProver.Result)
 
 /--
@@ -112,8 +116,9 @@ abbrev DiagnosisM : Type → Type := ReaderT CounterExample <| StateRefT Diagnos
 namespace DiagnosisM
 
 def run (x : DiagnosisM Unit) (counterExample : CounterExample) : MetaM Diagnosis := do
-  let (_, issues) ← ReaderT.run x counterExample |>.run {}
-  return issues
+  counterExample.goal.withContext do
+    let (_, issues) ← ReaderT.run x counterExample |>.run {}
+    return issues
 
 def unusedHyps : DiagnosisM (Std.HashSet FVarId) := do
   return (← read).unusedHypotheses
@@ -177,7 +182,7 @@ def explainCounterExampleQuality (counterExample : CounterExample) : MetaM Messa
     err := err ++ m!"Consider the following assignment:\n"
     return err
 
-def lratBitblaster (cfg : TacticContext) (reflectionResult : ReflectionResult)
+def lratBitblaster (goal : MVarId) (cfg : TacticContext) (reflectionResult : ReflectionResult)
     (atomsAssignment : Std.HashMap Nat (Nat × Expr)) :
     MetaM (Except CounterExample UnsatProver.Result) := do
   let bvExpr := reflectionResult.bvExpr
@@ -206,11 +211,13 @@ def lratBitblaster (cfg : TacticContext) (reflectionResult : ReflectionResult)
 
   match res with
   | .ok cert =>
+    trace[Meta.Tactic.sat] "SAT solver found a proof."
     let proof ← cert.toReflectionProof cfg bvExpr ``verifyBVExpr ``unsat_of_verifyBVExpr_eq_true
     return .ok ⟨proof, cert⟩
   | .error assignment =>
+    trace[Meta.Tactic.sat] "SAT solver found a counter example."
     let equations := reconstructCounterExample map assignment aigSize atomsAssignment
-    return .error { unusedHypotheses := reflectionResult.unusedHypotheses, equations }
+    return .error { goal, unusedHypotheses := reflectionResult.unusedHypotheses, equations }
 
 
 def reflectBV (g : MVarId) : M ReflectionResult := g.withContext do
@@ -248,7 +255,7 @@ def closeWithBVReflection (g : MVarId) (unsatProver : UnsatProver) :
 
     let atomsPairs := (← getThe State).atoms.toList.map (fun (expr, ⟨width, ident⟩) => (ident, (width, expr)))
     let atomsAssignment := Std.HashMap.ofList atomsPairs
-    match ← unsatProver reflectionResult atomsAssignment with
+    match ← unsatProver g reflectionResult atomsAssignment with
     | .ok ⟨bvExprUnsat, cert⟩ =>
       let proveFalse ← reflectionResult.proveFalse bvExprUnsat
       g.assign proveFalse
@@ -256,9 +263,9 @@ def closeWithBVReflection (g : MVarId) (unsatProver : UnsatProver) :
     | .error counterExample => return .error counterExample
 
 def bvUnsat (g : MVarId) (cfg : TacticContext) : MetaM (Except CounterExample LratCert) := M.run do
-  let unsatProver : UnsatProver := fun reflectionResult atomsAssignment => do
+  let unsatProver : UnsatProver := fun g reflectionResult atomsAssignment => do
     withTraceNode `bv (fun _ => return "Preparing LRAT reflection term") do
-      lratBitblaster cfg reflectionResult atomsAssignment
+      lratBitblaster g cfg reflectionResult atomsAssignment
   closeWithBVReflection g unsatProver
 
 /--
@@ -289,9 +296,11 @@ def bvDecide (g : MVarId) (cfg : TacticContext) : MetaM Result := do
   match ← bvDecide' g cfg with
   | .ok result => return result
   | .error counterExample =>
-    let error ← explainCounterExampleQuality counterExample
-    let folder := fun error (var, value) => error ++ m!"{var} = {value.bv}\n"
-    throwError counterExample.equations.foldl (init := error) folder
+    counterExample.goal.withContext do
+      let error ← explainCounterExampleQuality counterExample
+      let folder := fun error (var, value) => error ++ m!"{var} = {value.bv}\n"
+      let errorMessage := counterExample.equations.foldl (init := error) folder
+      throwError (← addMessageContextFull errorMessage)
 
 @[builtin_tactic Lean.Parser.Tactic.bvDecide]
 def evalBvTrace : Tactic := fun

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

@@ -27,6 +27,8 @@ instance : ToExpr BVBinOp where
     | .xor => mkConst ``BVBinOp.xor
     | .add => mkConst ``BVBinOp.add
     | .mul => mkConst ``BVBinOp.mul
+    | .udiv => mkConst ``BVBinOp.udiv
+    | .umod => mkConst ``BVBinOp.umod
   toTypeExpr := mkConst ``BVBinOp
 
 instance : ToExpr BVUnOp where

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

@@ -80,6 +80,10 @@ partial def of (x : Expr) : M (Option ReifiedBVExpr) := do
     binaryReflection lhsExpr rhsExpr .add ``Std.Tactic.BVDecide.Reflect.BitVec.add_congr
   | HMul.hMul _ _ _ _ lhsExpr rhsExpr =>
     binaryReflection lhsExpr rhsExpr .mul ``Std.Tactic.BVDecide.Reflect.BitVec.mul_congr
+  | HDiv.hDiv _ _ _ _ lhsExpr rhsExpr =>
+    binaryReflection lhsExpr rhsExpr .udiv ``Std.Tactic.BVDecide.Reflect.BitVec.udiv_congr
+  | HMod.hMod _ _ _ _ lhsExpr rhsExpr =>
+    binaryReflection lhsExpr rhsExpr .umod ``Std.Tactic.BVDecide.Reflect.BitVec.umod_congr
   | Complement.complement _ _ innerExpr =>
     unaryReflection innerExpr .not ``Std.Tactic.BVDecide.Reflect.BitVec.not_congr
   | HShiftLeft.hShiftLeft _ β _ _ innerExpr distanceExpr =>

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

@@ -105,7 +105,7 @@ instance : ToExpr LRAT.IntAction where
       mkApp3 (mkConst ``LRAT.Action.del [.zero, .zero]) beta alpha (toExpr ids)
   toTypeExpr := mkConst ``LRAT.IntAction
 
-def LratCert.ofFile (lratPath : System.FilePath) (trimProofs : Bool) : MetaM LratCert := do
+def LratCert.ofFile (lratPath : System.FilePath) (trimProofs : Bool) : CoreM LratCert := do
   let proofInput ← IO.FS.readBinFile lratPath
   let proof ←
     withTraceNode `sat (fun _ => return s!"Parsing LRAT file") do
@@ -139,8 +139,8 @@ Run an external SAT solver on the `CNF` to obtain an LRAT proof.
 This will obtain an `LratCert` if the formula is UNSAT and throw errors otherwise.
 -/
 def runExternal (cnf : CNF Nat) (solver : System.FilePath) (lratPath : System.FilePath)
-    (trimProofs : Bool) (timeout : Nat) (binaryProofs : Bool)
-    : MetaM (Except (Array (Bool × Nat)) LratCert) := do
+    (trimProofs : Bool) (timeout : Nat) (binaryProofs : Bool) :
+    CoreM (Except (Array (Bool × Nat)) LratCert) := do
   IO.FS.withTempFile fun cnfHandle cnfPath => do
     withTraceNode `sat (fun _ => return "Serializing SAT problem to DIMACS file") do
       -- lazyPure to prevent compiler lifting
@@ -162,7 +162,7 @@ def runExternal (cnf : CNF Nat) (solver : System.FilePath) (lratPath : System.Fi
 /--
 Add an auxiliary declaration. Only used to create constants that appear in our reflection proof.
 -/
-def mkAuxDecl (name : Name) (value type : Expr) : MetaM Unit :=
+def mkAuxDecl (name : Name) (value type : Expr) : CoreM Unit :=
   addAndCompile <| .defnDecl {
     name := name,
     levelParams := [],
@@ -181,8 +181,7 @@ function together with a correctness theorem for it.
   `∀ (b : α) (c : LratCert), verifier b c = true → unsat b`
 -/
 def LratCert.toReflectionProof [ToExpr α] (cert : LratCert) (cfg : TacticContext) (reflected : α)
-    (verifier : Name) (unsat_of_verifier_eq_true : Name) : 
-    MetaM Expr := do
+    (verifier : Name) (unsat_of_verifier_eq_true : Name) : MetaM Expr := do
   withTraceNode `sat (fun _ => return "Compiling expr term") do
     mkAuxDecl cfg.exprDef (toExpr reflected) (toTypeExpr α)
 
@@ -198,13 +197,20 @@ def LratCert.toReflectionProof [ToExpr α] (cert : LratCert) (cfg : TacticContex
     let auxValue := mkApp2 (mkConst verifier) reflectedExpr certExpr
     mkAuxDecl cfg.reflectionDef auxValue (mkConst ``Bool)
 
-  let nativeProof :=
+  let auxType ← mkEq (mkConst cfg.reflectionDef) (toExpr true)
+  let auxProof :=
     mkApp3
       (mkConst ``Lean.ofReduceBool)
       (mkConst cfg.reflectionDef)
       (toExpr true)
       (← mkEqRefl (toExpr true))
-  return mkApp3 (mkConst unsat_of_verifier_eq_true) reflectedExpr certExpr nativeProof
+  try
+    let auxLemma ←
+      withTraceNode `sat (fun _ => return "Verifying LRAT certificate") do
+        mkAuxLemma [] auxType auxProof
+    return mkApp3 (mkConst unsat_of_verifier_eq_true) reflectedExpr certExpr (mkConst auxLemma)
+  catch e =>
+    throwError m!"Failed to check the LRAT certificate in the kernel:\n{e.toMessageData}"
 
 
 end Frontend

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

@@ -5,6 +5,7 @@ Authors: Henrik Böving
 -/
 prelude
 import Lean.Meta.AppBuilder
+import Lean.Meta.Tactic.AC.Main
 import Lean.Elab.Tactic.Simp
 import Lean.Elab.Tactic.FalseOrByContra
 import Lean.Elab.Tactic.BVDecide.Frontend.Attr
@@ -64,6 +65,69 @@ builtin_simproc [bv_normalize] maxUlt (BitVec.ult (_ : BitVec _) (_ : BitVec _))
   else
     return .continue
 
+-- A specialised version of BitVec.neg_eq_not_add so it doesn't trigger on -constant
+builtin_simproc [bv_normalize] neg_eq_not_add (-(_ : BitVec _)) := fun e => do
+  let_expr Neg.neg typ _ val := e | return .continue
+  let_expr BitVec widthExpr := typ | return .continue
+  let some w ← getNatValue? widthExpr | return .continue
+  match ← getBitVecValue? val with
+  | some _ => return .continue
+  | none =>
+    let proof := mkApp2 (mkConst ``BitVec.neg_eq_not_add) (toExpr w) val
+    let expr ← mkAppM ``HAdd.hAdd #[← mkAppM ``Complement.complement #[val], (toExpr 1#w)]
+    return .visit { expr := expr, proof? := some proof }
+
+builtin_simproc [bv_normalize] bv_add_const ((_ : BitVec _) + ((_ : BitVec _) + (_ : BitVec _))) :=
+  fun e => do
+    let_expr HAdd.hAdd _ _ _ _ exp1 rhs := e | return .continue
+    let_expr HAdd.hAdd _ _ _ _ exp2 exp3 := rhs | return .continue
+    let some ⟨w, exp1Val⟩ ←  getBitVecValue? exp1 | return .continue
+    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
+    match ← getBitVecValue? exp2 with
+    | some ⟨w', exp2Val⟩ =>
+      if h : w = w' then
+        let newLhs := exp1Val + h ▸ exp2Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp3]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+    | none =>
+      let some ⟨w', exp3Val⟩ ← getBitVecValue? exp3 | return .continue
+      if h : w = w' then
+        let newLhs := exp1Val + h ▸ exp3Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+
+builtin_simproc [bv_normalize] bv_add_const' (((_ : BitVec _) + (_ : BitVec _)) + (_ : BitVec _)) :=
+  fun e => do
+    let_expr HAdd.hAdd _ _ _ _ lhs exp3 := e | return .continue
+    let_expr HAdd.hAdd _ _ _ _ exp1 exp2 := lhs | return .continue
+    let some ⟨w, exp3Val⟩ ←  getBitVecValue? exp3 | return .continue
+    let proofBuilder thm := mkApp4 (mkConst thm) (toExpr w) exp1 exp2 exp3
+    match ← getBitVecValue? exp1 with
+    | some ⟨w', exp1Val⟩ =>
+      if h : w = w' then
+        let newLhs := exp3Val + h ▸ exp1Val
+        -- TODO
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp2]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_left'
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+    | none =>
+      let some ⟨w', exp2Val⟩ ← getBitVecValue? exp2 | return .continue
+      if h : w = w' then
+        let newLhs := exp3Val + h ▸ exp2Val
+        let expr ← mkAppM ``HAdd.hAdd #[toExpr newLhs, exp1]
+        let proof := proofBuilder ``Std.Tactic.BVDecide.Normalize.BitVec.add_const_right'
+        return .visit { expr := expr, proof? := some proof }
+      else
+        return .continue
+
 /--
 A pass in the normalization pipeline. Takes the current goal and produces a refined one or closes
 the goal fully, indicated by returning `none`.
@@ -112,11 +176,36 @@ def rewriteRulesPass : Pass := fun goal => do
   let some (_, newGoal) := result? | return none
   return newGoal
 
+/--
+Normalize with respect to Associativity and Commutativity.
+-/
+def acNormalizePass : Pass := fun goal => do
+  let mut newGoal := goal
+  for hyp in (← goal.getNondepPropHyps) do
+    let result ← Lean.Meta.AC.acNfHypMeta newGoal hyp
+
+    if let .some nextGoal := result then
+      newGoal := nextGoal
+    else
+      return none
+
+  return newGoal
+
 /--
 The normalization passes used by `bv_normalize` and thus `bv_decide`.
 -/
 def defaultPipeline : List Pass := [rewriteRulesPass]
 
+def passPipeline : MetaM (List Pass) := do
+  let opts ← getOptions
+
+  let mut passPipeline := defaultPipeline
+
+  if bv.ac_nf.get opts then
+    passPipeline := passPipeline ++ [acNormalizePass]
+
+  return passPipeline
+
 end Pass
 
 def bvNormalize (g : MVarId) : MetaM (Option MVarId) := do
@@ -124,7 +213,7 @@ def bvNormalize (g : MVarId) : MetaM (Option MVarId) := do
     -- Contradiction proof
     let some g ← g.falseOrByContra | return none
     trace[Meta.Tactic.bv] m!"Running preprocessing pipeline on:\n{g}"
-    Pass.fixpointPipeline Pass.defaultPipeline g
+    Pass.fixpointPipeline (← Pass.passPipeline) g
 
 @[builtin_tactic Lean.Parser.Tactic.bvNormalize]
 def evalBVNormalize : Tactic := fun
@@ -137,5 +226,3 @@ def evalBVNormalize : Tactic := fun
 
 end Frontend.Normalize
 end Lean.Elab.Tactic.BVDecide
-
-

src/Lean/Elab/Tactic/BuiltinTactic.lean

@@ -313,7 +313,7 @@ partial def evalChoiceAux (tactics : Array Syntax) (i : Nat) : TacticM Unit :=
 @[builtin_tactic skip] def evalSkip : Tactic := fun _ => pure ()
 
 @[builtin_tactic unknown] def evalUnknown : Tactic := fun stx => do
-  addCompletionInfo <| CompletionInfo.tactic stx (← getGoals)
+  addCompletionInfo <| CompletionInfo.tactic stx
 
 @[builtin_tactic failIfSuccess] def evalFailIfSuccess : Tactic := fun stx =>
   Term.withoutErrToSorry <| withoutRecover do

src/Lean/Elab/Tactic/ElabTerm.lean

@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
 prelude
 import Lean.Meta.Tactic.Constructor
 import Lean.Meta.Tactic.Assert
+import Lean.Meta.Tactic.AuxLemma
 import Lean.Meta.Tactic.Clear
 import Lean.Meta.Tactic.Rename
 import Lean.Elab.Tactic.Basic
@@ -375,7 +376,7 @@ private def preprocessPropToDecide (expectedType : Expr) : TermElabM Expr := do
 Given the decidable instance `inst`, reduces it and returns a decidable instance expression
 in whnf that can be regarded as the reason for the failure of `inst` to fully reduce.
 -/
-private partial def blameDecideReductionFailure (inst : Expr) : MetaM Expr := do
+private partial def blameDecideReductionFailure (inst : Expr) : MetaM Expr := withIncRecDepth do
   let inst ← whnf inst
   -- If it's the Decidable recursor, then blame the major premise.
   if inst.isAppOfArity ``Decidable.rec 5 then
@@ -393,74 +394,100 @@ private partial def blameDecideReductionFailure (inst : Expr) : MetaM Expr := do
               return ← blameDecideReductionFailure inst''
   return inst
 
-@[builtin_tactic Lean.Parser.Tactic.decide] def evalDecide : Tactic := fun _ =>
-  closeMainGoalUsing `decide fun expectedType => do
+def evalDecideCore (tacticName : Name) (kernelOnly : Bool) : TacticM Unit :=
+  closeMainGoalUsing tacticName fun expectedType => do
     let expectedType ← preprocessPropToDecide expectedType
-    let d ← mkDecide expectedType
-    let d ← instantiateMVars d
-    -- Get instance from `d`
-    let s := d.appArg!
-    -- Reduce the instance rather than `d` itself for diagnostics purposes.
-    let r ← withAtLeastTransparency .default <| whnf s
-    if r.isAppOf ``isTrue then
-      -- Success!
-      -- While we have a proof from reduction, we do not embed it in the proof term,
-      -- and instead we let the kernel recompute it during type checking from the following more
-      -- efficient term. The kernel handles the unification `e =?= true` specially.
-      let rflPrf ← mkEqRefl (toExpr true)
-      return mkApp3 (Lean.mkConst ``of_decide_eq_true) expectedType s rflPrf
+    let pf ← mkDecideProof expectedType
+    -- Get instance from `pf`
+    let s := pf.appFn!.appArg!
+    if kernelOnly then
+      -- Reduce the decidable instance to (hopefully!) `isTrue` by passing `pf` to the kernel.
+      -- The `mkAuxLemma` function caches the result in two ways:
+      -- 1. First, the function makes use of a `type`-indexed cache per module.
+      -- 2. Second, once the proof is added to the environment, the kernel doesn't need to check the proof again.
+      let levelsInType := (collectLevelParams {} expectedType).params
+      -- Level variables occurring in `expectedType`, in ambient order
+      let lemmaLevels := (← Term.getLevelNames).reverse.filter levelsInType.contains
+      try
+        let lemmaName ← mkAuxLemma lemmaLevels expectedType pf
+        return mkConst lemmaName (lemmaLevels.map .param)
+      catch _ =>
+        diagnose expectedType s none
     else
-      -- Diagnose the failure, lazily so that there is no performance impact if `decide` isn't being used interactively.
-      throwError MessageData.ofLazyM (es := #[expectedType]) do
-        if r.isAppOf ``isFalse then
-          return m!"\
-          tactic 'decide' proved that the proposition\
+      let r ← withAtLeastTransparency .default <| whnf s
+      if r.isAppOf ``isTrue then
+        -- Success!
+        -- While we have a proof from reduction, we do not embed it in the proof term,
+        -- and instead we let the kernel recompute it during type checking from the following more
+        -- efficient term. The kernel handles the unification `e =?= true` specially.
+        return pf
+      else
+        diagnose expectedType s r
+where
+  diagnose {α : Type} (expectedType s : Expr) (r? : Option Expr) : TacticM α :=
+    -- Diagnose the failure, lazily so that there is no performance impact if `decide` isn't being used interactively.
+    throwError MessageData.ofLazyM (es := #[expectedType]) do
+      let r ← r?.getDM (withAtLeastTransparency .default <| whnf s)
+      if r.isAppOf ``isTrue then
+        return m!"\
+          tactic '{tacticName}' failed. internal error: the elaborator is able to reduce the \
+          '{MessageData.ofConstName ``Decidable}' instance, but the kernel is not able to"
+      else if r.isAppOf ``isFalse then
+        return m!"\
+          tactic '{tacticName}' proved that the proposition\
           {indentExpr expectedType}\n\
           is false"
-        -- Re-reduce the instance and collect diagnostics, to get all unfolded Decidable instances
-        let (reason, unfoldedInsts) ← withoutModifyingState <| withOptions (fun opt => diagnostics.set opt true) do
-          modifyDiag (fun _ => {})
-          let reason ← withAtLeastTransparency .default <| blameDecideReductionFailure s
-          let unfolded := (← get).diag.unfoldCounter.foldl (init := #[]) fun cs n _ => cs.push n
-          let unfoldedInsts ← unfolded |>.qsort Name.lt |>.filterMapM fun n => do
-            let e ← mkConstWithLevelParams n
-            if (← Meta.isClass? (← inferType e)) == ``Decidable then
-              return m!"'{MessageData.ofConst e}'"
-            else
-              return none
-          return (reason, unfoldedInsts)
-        let stuckMsg :=
-          if unfoldedInsts.isEmpty then
-            m!"Reduction got stuck at the '{MessageData.ofConstName ``Decidable}' instance{indentExpr reason}"
+      -- Re-reduce the instance and collect diagnostics, to get all unfolded Decidable instances
+      let (reason, unfoldedInsts) ← withoutModifyingState <| withOptions (fun opt => diagnostics.set opt true) do
+        modifyDiag (fun _ => {})
+        let reason ← withAtLeastTransparency .default <| blameDecideReductionFailure s
+        let unfolded := (← get).diag.unfoldCounter.foldl (init := #[]) fun cs n _ => cs.push n
+        let unfoldedInsts ← unfolded |>.qsort Name.lt |>.filterMapM fun n => do
+          let e ← mkConstWithLevelParams n
+          if (← Meta.isClass? (← inferType e)) == ``Decidable then
+            return m!"'{MessageData.ofConst e}'"
           else
-            let instances := if unfoldedInsts.size == 1 then "instance" else "instances"
-            m!"After unfolding the {instances} {MessageData.andList unfoldedInsts.toList}, \
-            reduction got stuck at the '{MessageData.ofConstName ``Decidable}' instance{indentExpr reason}"
-        let hint :=
-          if reason.isAppOf ``Eq.rec then
-            m!"\n\n\
-            Hint: Reduction got stuck on '▸' ({MessageData.ofConstName ``Eq.rec}), \
-            which suggests that one of the '{MessageData.ofConstName ``Decidable}' instances is defined using tactics such as 'rw' or 'simp'. \
-            To avoid tactics, make use of functions such as \
-            '{MessageData.ofConstName ``inferInstanceAs}' or '{MessageData.ofConstName ``decidable_of_decidable_of_iff}' \
-            to alter a proposition."
-          else if reason.isAppOf ``Classical.choice then
-            m!"\n\n\
-            Hint: Reduction got stuck on '{MessageData.ofConstName ``Classical.choice}', \
-            which indicates that a '{MessageData.ofConstName ``Decidable}' instance \
-            is defined using classical reasoning, proving an instance exists rather than giving a concrete construction. \
-            The 'decide' tactic works by evaluating a decision procedure via reduction, and it cannot make progress with such instances. \
-            This can occur due to the 'opened scoped Classical' command, which enables the instance \
-            '{MessageData.ofConstName ``Classical.propDecidable}'."
-          else
-            MessageData.nil
-        return m!"\
-          tactic 'decide' failed for proposition\
-          {indentExpr expectedType}\n\
-          since its '{MessageData.ofConstName ``Decidable}' instance\
-          {indentExpr s}\n\
-          did not reduce to '{MessageData.ofConstName ``isTrue}' or '{MessageData.ofConstName ``isFalse}'.\n\n\
-          {stuckMsg}{hint}"
+            return none
+        return (reason, unfoldedInsts)
+      let stuckMsg :=
+        if unfoldedInsts.isEmpty then
+          m!"Reduction got stuck at the '{MessageData.ofConstName ``Decidable}' instance{indentExpr reason}"
+        else
+          let instances := if unfoldedInsts.size == 1 then "instance" else "instances"
+          m!"After unfolding the {instances} {MessageData.andList unfoldedInsts.toList}, \
+          reduction got stuck at the '{MessageData.ofConstName ``Decidable}' instance{indentExpr reason}"
+      let hint :=
+        if reason.isAppOf ``Eq.rec then
+          m!"\n\n\
+          Hint: Reduction got stuck on '▸' ({MessageData.ofConstName ``Eq.rec}), \
+          which suggests that one of the '{MessageData.ofConstName ``Decidable}' instances is defined using tactics such as 'rw' or 'simp'. \
+          To avoid tactics, make use of functions such as \
+          '{MessageData.ofConstName ``inferInstanceAs}' or '{MessageData.ofConstName ``decidable_of_decidable_of_iff}' \
+          to alter a proposition."
+        else if reason.isAppOf ``Classical.choice then
+          m!"\n\n\
+          Hint: Reduction got stuck on '{MessageData.ofConstName ``Classical.choice}', \
+          which indicates that a '{MessageData.ofConstName ``Decidable}' instance \
+          is defined using classical reasoning, proving an instance exists rather than giving a concrete construction. \
+          The '{tacticName}' tactic works by evaluating a decision procedure via reduction, \
+          and it cannot make progress with such instances. \
+          This can occur due to the 'opened scoped Classical' command, which enables the instance \
+          '{MessageData.ofConstName ``Classical.propDecidable}'."
+        else
+          MessageData.nil
+      return m!"\
+        tactic '{tacticName}' failed for proposition\
+        {indentExpr expectedType}\n\
+        since its '{MessageData.ofConstName ``Decidable}' instance\
+        {indentExpr s}\n\
+        did not reduce to '{MessageData.ofConstName ``isTrue}' or '{MessageData.ofConstName ``isFalse}'.\n\n\
+        {stuckMsg}{hint}"
+
+@[builtin_tactic Lean.Parser.Tactic.decide] def evalDecide : Tactic := fun _ =>
+  evalDecideCore `decide false
+
+@[builtin_tactic Lean.Parser.Tactic.decideBang] def evalDecideBang : Tactic := fun _ =>
+  evalDecideCore `decide! true
 
 private def mkNativeAuxDecl (baseName : Name) (type value : Expr) : TermElabM Name := do
   let auxName ← Term.mkAuxName baseName

src/Lean/Elab/Tactic/Simpa.lean

@@ -7,6 +7,7 @@ prelude
 import Lean.Meta.Tactic.Assumption
 import Lean.Meta.Tactic.TryThis
 import Lean.Elab.Tactic.Simp
+import Lean.Elab.App
 import Lean.Linter.Basic
 
 /--
@@ -46,27 +47,43 @@ deriving instance Repr for UseImplicitLambdaResult
           return {}
       g.withContext do
       let stats ← if let some stx := usingArg then
-        setGoals [g]
-        g.withContext do
+        let mvarCounterSaved := (← getMCtx).mvarCounter
         let e ← Tactic.elabTerm stx none (mayPostpone := true)
-        let (h, g) ← if let .fvar h ← instantiateMVars e then
-          pure (h, g)
-        else
-          (← g.assert `h (← inferType e) e).intro1
-        let (result?, stats) ← simpGoal g ctx (simprocs := simprocs) (fvarIdsToSimp := #[h])
+        unless ← occursCheck g e do
+          throwError "occurs check failed, expression{indentExpr e}\ncontains the goal {Expr.mvar g}"
+        -- Copy the goal. We want to defer assigning `g := g'` to prevent `MVarId.note` from
+        -- partially assigning the goal in case we need to log unassigned metavariables.
+        -- Without deferring, this can cause `logUnassignedAndAbort` to report that `g` could not
+        -- be synthesized; recall that this function reports that a metavariable could not be
+        -- synthesized if, after mvar instantiation, it contains one of the provided mvars.
+        let gCopy ← mkFreshExprSyntheticOpaqueMVar (← g.getType) (← g.getTag)
+        let (h, g') ← gCopy.mvarId!.note `h e
+        let (result?, stats) ← simpGoal g' ctx (simprocs := simprocs) (fvarIdsToSimp := #[h])
           (simplifyTarget := false) (stats := stats) (discharge? := discharge?)
         match result? with
-        | some (xs, g) =>
-          let h := match xs with | #[h] | #[] => h | _ => unreachable!
-          let name ← mkFreshBinderNameForTactic `h
-          let g ← g.rename h name
-          g.assign <|← g.withContext do
-            Tactic.elabTermEnsuringType (mkIdent name) (← g.getType)
+        | some (xs, g') =>
+          let h := xs[0]?.getD h
+          let name ← mkFreshUserName `h
+          let g' ← g'.rename h name
+          setGoals [g']
+          g'.withContext do
+            let gType ← g'.getType
+            let h ← Term.elabTerm (mkIdent name) gType
+            Term.synthesizeSyntheticMVarsNoPostponing
+            let hType ← inferType h
+            unless (← withAssignableSyntheticOpaque <| isDefEq gType hType) do
+              -- `e` still is valid in this new local context
+              Term.throwTypeMismatchError gType hType h
+                (header? := some m!"type mismatch, term{indentExpr e}\nafter simplification")
+            logUnassignedAndAbort (← filterOldMVars (← getMVars e) mvarCounterSaved)
+            closeMainGoal `simpa (checkUnassigned := false) h
         | none =>
           if getLinterUnnecessarySimpa (← getOptions) then
-            if (← getLCtx).getRoundtrippingUserName? h |>.isSome then
-              logLint linter.unnecessarySimpa (← getRef)
-                m!"try 'simp at {Expr.fvar h}' instead of 'simpa using {Expr.fvar h}'"
+            if let .fvar h := e then
+              if (← getLCtx).getRoundtrippingUserName? h |>.isSome then
+                logLint linter.unnecessarySimpa (← getRef)
+                  m!"try 'simp at {Expr.fvar h}' instead of 'simpa using {Expr.fvar h}'"
+        g.assign gCopy
         pure stats
       else if let some ldecl := (← getLCtx).findFromUserName? `this then
         if let (some (_, g), stats) ← simpGoal g ctx (simprocs := simprocs)

src/Lean/Elab/Term.lean

@@ -80,8 +80,9 @@ structure SyntheticMVarDecl where
   We have three different kinds of error context.
 -/
 inductive MVarErrorKind where
-  /-- Metavariable for implicit arguments. `ctx` is the parent application. -/
-  | implicitArg (ctx : Expr)
+  /-- Metavariable for implicit arguments. `ctx` is the parent application,
+  `lctx` is a local context where it is valid (necessary for eta feature for named arguments). -/
+  | implicitArg (lctx : LocalContext) (ctx : Expr)
   /-- Metavariable for explicit holes provided by the user (e.g., `_` and `?m`) -/
   | hole
   /-- "Custom", `msgData` stores the additional error messages. -/
@@ -90,7 +91,7 @@ inductive MVarErrorKind where
 
 instance : ToString MVarErrorKind where
   toString
-    | .implicitArg _   => "implicitArg"
+    | .implicitArg _ _ => "implicitArg"
     | .hole            => "hole"
     | .custom _        => "custom"
 
@@ -735,7 +736,7 @@ def registerMVarErrorHoleInfo (mvarId : MVarId) (ref : Syntax) : TermElabM Unit
   registerMVarErrorInfo { mvarId, ref, kind := .hole }
 
 def registerMVarErrorImplicitArgInfo (mvarId : MVarId) (ref : Syntax) (app : Expr) : TermElabM Unit := do
-  registerMVarErrorInfo { mvarId, ref, kind := .implicitArg app }
+  registerMVarErrorInfo { mvarId, ref, kind := .implicitArg (← getLCtx) app }
 
 def registerMVarErrorCustomInfo (mvarId : MVarId) (ref : Syntax) (msgData : MessageData) : TermElabM Unit := do
   registerMVarErrorInfo { mvarId, ref, kind := .custom msgData }
@@ -761,7 +762,7 @@ def throwMVarError (m : MessageData) : TermElabM α := do
 
 def MVarErrorInfo.logError (mvarErrorInfo : MVarErrorInfo) (extraMsg? : Option MessageData) : TermElabM Unit := do
   match mvarErrorInfo.kind with
-  | MVarErrorKind.implicitArg app => do
+  | MVarErrorKind.implicitArg lctx app => withLCtx lctx {} do
     let app ← instantiateMVars app
     let msg ← addArgName "don't know how to synthesize implicit argument"
     let msg := msg ++ m!"{indentExpr app.setAppPPExplicitForExposingMVars}" ++ Format.line ++ "context:" ++ Format.line ++ MessageData.ofGoal mvarErrorInfo.mvarId
@@ -946,13 +947,13 @@ def applyAttributesAt (declName : Name) (attrs : Array Attribute) (applicationTi
 def applyAttributes (declName : Name) (attrs : Array Attribute) : TermElabM Unit :=
   applyAttributesCore declName attrs none
 
-def mkTypeMismatchError (header? : Option String) (e : Expr) (eType : Expr) (expectedType : Expr) : TermElabM MessageData := do
+def mkTypeMismatchError (header? : Option MessageData) (e : Expr) (eType : Expr) (expectedType : Expr) : TermElabM MessageData := do
   let header : MessageData := match header? with
     | some header => m!"{header} "
     | none        => m!"type mismatch{indentExpr e}\n"
   return m!"{header}{← mkHasTypeButIsExpectedMsg eType expectedType}"
 
-def throwTypeMismatchError (header? : Option String) (expectedType : Expr) (eType : Expr) (e : Expr)
+def throwTypeMismatchError (header? : Option MessageData) (expectedType : Expr) (eType : Expr) (e : Expr)
     (f? : Option Expr := none) (_extraMsg? : Option MessageData := none) : TermElabM α := do
   /-
     We ignore `extraMsg?` for now. In all our tests, it contained no useful information. It was
@@ -2047,13 +2048,6 @@ def TermElabM.toIO (x : TermElabM α)
   let ((a, s), sCore, sMeta) ← (x.run ctx s).toIO ctxCore sCore ctxMeta sMeta
   return (a, sCore, sMeta, s)
 
-instance [MetaEval α] : MetaEval (TermElabM α) where
-  eval env opts x _ := do
-    let x : TermElabM α := do
-      try x finally
-        (← Core.getMessageLog).forM fun msg => do IO.println (← msg.toString)
-    MetaEval.eval env opts (hideUnit := true) <| x.run' {}
-
 /--
   Execute `x` and then tries to solve pending universe constraints.
   Note that, stuck constraints will not be discarded.

src/Lean/Eval.lean

@@ -1,27 +0,0 @@
-/-
-Copyright (c) 2019 Microsoft Corporation. All rights reserved.
-Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Leonardo de Moura, Sebastian Ullrich
--/
-prelude
-import Lean.Environment
-
-namespace Lean
-
-universe u
-
-/--
-`Eval` extension that gives access to the current environment & options.
-The basic `Eval` class is in the prelude and should not depend on these
-types.
--/
-class MetaEval (α : Type u) where
-  eval : Environment → Options → α → (hideUnit : Bool) → IO Environment
-
-instance {α : Type u} [Eval α] : MetaEval α :=
-  ⟨fun env _ a hideUnit => do Eval.eval (fun _ => a) hideUnit; pure env⟩
-
-def runMetaEval {α : Type u} [MetaEval α] (env : Environment) (opts : Options) (a : α) : IO (String × Except IO.Error Environment) :=
-  IO.FS.withIsolatedStreams (MetaEval.eval env opts a false |>.toBaseIO)
-
-end Lean

src/Lean/Exception.lean

@@ -120,7 +120,7 @@ instance [BEq α] [Hashable α] [Monad m] [STWorld ω m] [MonadRecDepth m] : Mon
 Throw a "maximum recursion depth has been reached" exception using the given reference syntax.
 -/
 def throwMaxRecDepthAt [MonadError m] (ref : Syntax) : m α :=
-  throw <| .error ref (MessageData.ofFormat (Std.Format.text maxRecDepthErrorMessage))
+  throw <| .error ref (.tagged `runtime.maxRecDepth <| MessageData.ofFormat (Std.Format.text maxRecDepthErrorMessage))
 
 /--
 Return true if `ex` was generated by `throwMaxRecDepthAt`.
@@ -129,9 +129,7 @@ but it is also produced by `MacroM` which implemented in the prelude, and intern
 been defined yet.
 -/
 def Exception.isMaxRecDepth (ex : Exception) : Bool :=
-  match ex with
-  | error _ (MessageData.ofFormatWithInfos ⟨Std.Format.text msg, _⟩) => msg == maxRecDepthErrorMessage
-  | _ => false
+  ex matches error _ (.tagged `runtime.maxRecDepth _)
 
 /--
 Increment the current recursion depth and then execute `x`.

src/Lean/Linter/Basic.lean

@@ -23,8 +23,14 @@ def logLint [Monad m] [MonadLog m] [AddMessageContext m] [MonadOptions m]
   let disable := m!"note: this linter can be disabled with `set_option {linterOption.name} false`"
   logWarningAt stx (.tagged linterOption.name m!"{msg}\n{disable}")
 
-/-- If `linterOption` is true, print a linter warning message at the position determined by `stx`.
+/--
+If `linterOption` is enabled, print a linter warning message at the position determined by `stx`.
+
+Whether a linter option is enabled or not is determined by the following sequence:
+1. If it is set, then the value determines whether or not it is enabled.
+2. Otherwise, if `linter.all` is set, then its value determines whether or not the option is enabled.
+3. Otherwise, the default value determines whether or not it is enabled.
 -/
 def logLintIf [Monad m] [MonadLog m] [AddMessageContext m] [MonadOptions m]
     (linterOption : Lean.Option Bool) (stx : Syntax) (msg : MessageData) : m Unit := do
-  if linterOption.get (← getOptions) then logLint linterOption stx msg
+  if getLinterValue linterOption (← getOptions) then logLint linterOption stx msg

src/Lean/Linter/UnusedVariables.lean

@@ -255,10 +255,6 @@ builtin_initialize addBuiltinUnusedVariablesIgnoreFn (fun _ stack opts =>
     (stx.isOfKind ``Lean.Parser.Term.matchAlt && pos == 1) ||
     (stx.isOfKind ``Lean.Parser.Tactic.inductionAltLHS && pos == 2))
 
-/-- `#guard_msgs in cmd` itself runs linters in `cmd` (via `elabCommandTopLevel`), so do not run them again. -/
-builtin_initialize addBuiltinUnusedVariablesIgnoreFn (fun _ stack _ =>
-    stack.any fun (stx, _) => stx.isOfKind ``Lean.guardMsgsCmd)
-
 /-- Get the current list of `IgnoreFunction`s. -/
 def getUnusedVariablesIgnoreFns : CommandElabM (Array IgnoreFunction) := do
   return (unusedVariablesIgnoreFnsExt.getState (← getEnv)).2

src/Lean/Meta/Basic.lean

@@ -246,12 +246,20 @@ structure DefEqCache where
   all       : PersistentHashMap (Expr × Expr) Bool := {}
   deriving Inhabited
 
+/--
+  A cache for `inferType` at transparency levels `.default` an `.all`.
+-/
+structure InferTypeCaches where
+  default   : InferTypeCache
+  all       : InferTypeCache
+  deriving Inhabited
+
 /--
   Cache datastructures for type inference, type class resolution, whnf, and definitional equality.
 -/
 structure Cache where
-  inferType      : InferTypeCache := {}
-  funInfo        : FunInfoCache   := {}
+  inferType      : InferTypeCaches := ⟨{}, {}⟩
+  funInfo        : FunInfoCache := {}
   synthInstance  : SynthInstanceCache := {}
   whnfDefault    : WhnfCache := {} -- cache for closed terms and `TransparencyMode.default`
   whnfAll        : WhnfCache := {} -- cache for closed terms and `TransparencyMode.all`
@@ -448,9 +456,6 @@ instance : MonadBacktrack SavedState MetaM where
   let ((a, s), sCore) ← (x.run ctx s).toIO ctxCore sCore
   pure (a, sCore, s)
 
-instance [MetaEval α] : MetaEval (MetaM α) :=
-  ⟨fun env opts x _ => MetaEval.eval env opts x.run' true⟩
-
 protected def throwIsDefEqStuck : MetaM α :=
   throw <| Exception.internal isDefEqStuckExceptionId
 
@@ -478,8 +483,11 @@ variable [MonadControlT MetaM n] [Monad n]
 @[inline] def modifyCache (f : Cache → Cache) : MetaM Unit :=
   modify fun { mctx, cache, zetaDeltaFVarIds, postponed, diag } => { mctx, cache := f cache, zetaDeltaFVarIds, postponed, diag }
 
-@[inline] def modifyInferTypeCache (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
-  modifyCache fun ⟨ic, c1, c2, c3, c4, c5, c6⟩ => ⟨f ic, c1, c2, c3, c4, c5, c6⟩
+@[inline] def modifyInferTypeCacheDefault (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
+  modifyCache fun ⟨⟨icd, ica⟩, c1, c2, c3, c4, c5, c6⟩ => ⟨⟨f icd, ica⟩, c1, c2, c3, c4, c5, c6⟩
+
+@[inline] def modifyInferTypeCacheAll (f : InferTypeCache → InferTypeCache) : MetaM Unit :=
+  modifyCache fun ⟨⟨icd, ica⟩, c1, c2, c3, c4, c5, c6⟩ => ⟨⟨icd, f ica⟩, c1, c2, c3, c4, c5, c6⟩
 
 @[inline] def modifyDefEqTransientCache (f : DefEqCache → DefEqCache) : MetaM Unit :=
   modifyCache fun ⟨c1, c2, c3, c4, c5, defeqTrans, c6⟩ => ⟨c1, c2, c3, c4, c5, f defeqTrans, c6⟩
@@ -490,6 +498,9 @@ variable [MonadControlT MetaM n] [Monad n]
 @[inline] def resetDefEqPermCaches : MetaM Unit :=
   modifyDefEqPermCache fun _ => {}
 
+@[inline] def resetSynthInstanceCache : MetaM Unit :=
+  modifyCache fun c => {c with synthInstance := {}}
+
 @[inline] def modifyDiag (f : Diagnostics → Diagnostics) : MetaM Unit := do
   if (← isDiagnosticsEnabled) then
     modify fun { mctx, cache, zetaDeltaFVarIds, postponed, diag } => { mctx, cache, zetaDeltaFVarIds, postponed, diag := f diag }

src/Lean/Meta/FunInfo.lean

@@ -55,7 +55,7 @@ private def updateHasFwdDeps (pinfo : Array ParamInfo) (backDeps : Array Nat) :
 private def getFunInfoAux (fn : Expr) (maxArgs? : Option Nat) : MetaM FunInfo :=
   checkFunInfoCache fn maxArgs? do
     let fnType ← inferType fn
-    withTransparency TransparencyMode.default do
+    withAtLeastTransparency TransparencyMode.default do
       forallBoundedTelescope fnType maxArgs? fun fvars type => do
         let mut paramInfo := #[]
         let mut higherOrderOutParams : FVarIdSet := {}

src/Lean/Meta/InferType.lean

@@ -166,13 +166,24 @@ private def inferFVarType (fvarId : FVarId) : MetaM Expr := do
   | none   => fvarId.throwUnknown
 
 @[inline] private def checkInferTypeCache (e : Expr) (inferType : MetaM Expr) : MetaM Expr := do
-  match (← get).cache.inferType.find? e with
-  | some type => return type
-  | none =>
-    let type ← inferType
-    unless e.hasMVar || type.hasMVar do
-      modifyInferTypeCache fun c => c.insert e type
-    return type
+  match (← getTransparency) with
+  | .default =>
+    match (← get).cache.inferType.default.find? e with
+    | some type => return type
+    | none =>
+      let type ← inferType
+      unless e.hasMVar || type.hasMVar do
+        modifyInferTypeCacheDefault fun c => c.insert e type
+      return type
+  | .all =>
+    match (← get).cache.inferType.all.find? e with
+    | some type => return type
+    | none =>
+      let type ← inferType
+      unless e.hasMVar || type.hasMVar do
+        modifyInferTypeCacheAll fun c => c.insert e type
+      return type
+  | _ => panic! "checkInferTypeCache: transparency mode not default or all"
 
 @[export lean_infer_type]
 def inferTypeImp (e : Expr) : MetaM Expr :=
@@ -191,7 +202,7 @@ def inferTypeImp (e : Expr) : MetaM Expr :=
     | .forallE ..    => checkInferTypeCache e (inferForallType e)
     | .lam ..        => checkInferTypeCache e (inferLambdaType e)
     | .letE ..       => checkInferTypeCache e (inferLambdaType e)
-  withIncRecDepth <| withTransparency TransparencyMode.default (infer e)
+  withIncRecDepth <| withAtLeastTransparency TransparencyMode.default (infer e)
 
 /--
   Return `LBool.true` if given level is always equivalent to universe level zero.

src/Lean/Meta/Instances.lean

@@ -208,7 +208,9 @@ private partial def computeSynthOrder (inst : Expr) (projInfo? : Option Projecti
           let typeLines := ("" : MessageData).joinSep <| Array.toList <| ← toSynth.mapM fun i => do
             let ty ← instantiateMVars (← inferType argMVars[i]!)
             return indentExpr (ty.setPPExplicit true)
-          logError m!"cannot find synthesization order for instance {inst} with type{indentExpr instTy}\nall remaining arguments have metavariables:{typeLines}"
+          throwError m!"\
+            cannot find synthesization order for instance {inst} with type{indentExpr instTy}\n\
+            all remaining arguments have metavariables:{typeLines}"
         pure toSynth[0]!
     synthed := synthed.push next
     toSynth := toSynth.filter (· != next)
@@ -218,9 +220,10 @@ private partial def computeSynthOrder (inst : Expr) (projInfo? : Option Projecti
   if synthInstance.checkSynthOrder.get (← getOptions) then
     let ty ← instantiateMVars ty
     if ty.hasExprMVar then
-      logError m!"instance does not provide concrete values for (semi-)out-params{indentExpr (ty.setPPExplicit true)}"
+      throwError m!"instance does not provide concrete values for (semi-)out-params{indentExpr (ty.setPPExplicit true)}"
 
-  trace[Meta.synthOrder] "synthesizing the arguments of {inst} in the order {synthed}:{("" : MessageData).joinSep (← synthed.mapM fun i => return indentExpr (← inferType argVars[i]!)).toList}"
+  trace[Meta.synthOrder] "synthesizing the arguments of {inst} in the order {synthed}:\
+    {("" : MessageData).joinSep (← synthed.mapM fun i => return indentExpr (← inferType argVars[i]!)).toList}"
 
   return synthed
 

src/Lean/Meta/PPGoal.lean

@@ -33,7 +33,7 @@ register_builtin_option pp.showLetValues : Bool := {
 }
 
 private def addLine (fmt : Format) : Format :=
-  if fmt.isNil then fmt else fmt ++ Format.line
+  if fmt.isNil then fmt else fmt ++ "\n"
 
 def getGoalPrefix (mvarDecl : MetavarDecl) : String :=
   if isLHSGoal? mvarDecl.type |>.isSome then
@@ -99,6 +99,6 @@ def ppGoal (mvarId : MVarId) : MetaM Format := do
       let fmt := fmt ++ getGoalPrefix mvarDecl ++ Format.nest indent typeFmt
       match mvarDecl.userName with
       | Name.anonymous => return fmt
-      | name           => return "case " ++ format name.eraseMacroScopes ++ Format.line ++ fmt
+      | name           => return "case " ++ format name.eraseMacroScopes ++ "\n" ++ fmt
 
 end Lean.Meta

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

@@ -140,6 +140,25 @@ where
     | .op l r => mkApp2 preContext.op (convertTarget vars l) (convertTarget vars r)
     | .var x => vars[x]!
 
+def post (e : Expr) : SimpM Simp.Step := do
+  let ctx ← Simp.getContext
+  match e, ctx.parent? with
+  | bin op₁ l r, some (bin op₂ _ _) =>
+    if ←isDefEq op₁ op₂ then
+      return Simp.Step.done { expr := e }
+    match ←preContext op₁ with
+    | some pc =>
+      let (proof, newTgt) ← buildNormProof pc l r
+      return Simp.Step.done { expr := newTgt, proof? := proof }
+    | none => return Simp.Step.done { expr := e }
+  | bin op l r, _ =>
+    match ←preContext op with
+    | some pc =>
+      let (proof, newTgt) ← buildNormProof pc l r
+      return Simp.Step.done { expr := newTgt, proof? := proof }
+    | none => return Simp.Step.done { expr := e }
+  | e, _ => return Simp.Step.done { expr := e }
+
 def rewriteUnnormalized (mvarId : MVarId) : MetaM MVarId := do
   let simpCtx :=
     {
@@ -150,41 +169,48 @@ def rewriteUnnormalized (mvarId : MVarId) : MetaM MVarId := do
   let tgt ← instantiateMVars (← mvarId.getType)
   let (res, _) ← Simp.main tgt simpCtx (methods := { post })
   applySimpResultToTarget mvarId tgt res
-where
-  post (e : Expr) : SimpM Simp.Step := do
-    let ctx ← Simp.getContext
-    match e, ctx.parent? with
-    | bin op₁ l r, some (bin op₂ _ _) =>
-      if ←isDefEq op₁ op₂ then
-        return Simp.Step.done { expr := e }
-      match ←preContext op₁ with
-      | some pc =>
-        let (proof, newTgt) ← buildNormProof pc l r
-        return Simp.Step.done { expr := newTgt, proof? := proof }
-      | none => return Simp.Step.done { expr := e }
-    | bin op l r, _ =>
-      match ←preContext op with
-      | some pc =>
-        let (proof, newTgt) ← buildNormProof pc l r
-        return Simp.Step.done { expr := newTgt, proof? := proof }
-      | none => return Simp.Step.done { expr := e }
-    | e, _ => return Simp.Step.done { expr := e }
 
 def rewriteUnnormalizedRefl (goal : MVarId) : MetaM Unit := do
-  let newGoal ← rewriteUnnormalized goal
-  newGoal.refl
-
-def rewriteUnnormalizedNormalForm (goal : MVarId) : TacticM Unit := do
-  let newGoal ← rewriteUnnormalized goal
-  replaceMainGoal [newGoal]
+  (← rewriteUnnormalized goal).refl
 
 @[builtin_tactic acRfl] def acRflTactic : Lean.Elab.Tactic.Tactic := fun _ => do
   let goal ← getMainGoal
   goal.withContext <| rewriteUnnormalizedRefl goal
 
-@[builtin_tactic acNf] def acNfTactic : Lean.Elab.Tactic.Tactic := fun _ => do
-  let goal ← getMainGoal
-  goal.withContext <| rewriteUnnormalizedNormalForm goal
+def acNfHypMeta (goal : MVarId) (fvarId : FVarId) : MetaM (Option MVarId) := do
+  goal.withContext do
+    let simpCtx :=
+    {
+      simpTheorems  := {}
+      congrTheorems := (← getSimpCongrTheorems)
+      config        := Simp.neutralConfig
+    }
+    let tgt ← instantiateMVars (← fvarId.getType)
+    let (res, _) ← Simp.main tgt simpCtx (methods := { post })
+    return (← applySimpResultToLocalDecl goal fvarId res false).map (·.snd)
+
+/-- Implementation of the `ac_nf` tactic when operating on the main goal. -/
+def acNfTargetTactic : TacticM Unit :=
+  liftMetaTactic1 fun goal => rewriteUnnormalized goal
+
+/-- Implementation of the `ac_nf` tactic when operating on a hypothesis. -/
+def acNfHypTactic (fvarId : FVarId) : TacticM Unit :=
+  liftMetaTactic1 fun goal => acNfHypMeta goal fvarId
+
+@[builtin_tactic acNf0]
+def evalNf0 : Tactic := fun stx => do
+  match stx with
+  | `(tactic| ac_nf0 $[$loc?]?) =>
+    let loc := if let some loc := loc? then expandLocation loc else Location.targets #[] true
+    withMainContext do
+      match loc with
+      | Location.targets hyps target =>
+        if target then acNfTargetTactic
+        (← getFVarIds hyps).forM acNfHypTactic
+      | Location.wildcard =>
+        acNfTargetTactic
+        (← (← getMainGoal).getNondepPropHyps).forM acNfHypTactic
+  | _ => Lean.Elab.throwUnsupportedSyntax
 
 builtin_initialize
   registerTraceClass `Meta.AC

src/Lean/Meta/Tactic/Assert.lean

@@ -82,6 +82,10 @@ structure Hypothesis where
   userName : Name
   type     : Expr
   value    : Expr
+  /-- The hypothesis' `BinderInfo` -/
+  binderInfo : BinderInfo := .default
+  /-- The hypothesis' `LocalDeclKind` -/
+  kind : LocalDeclKind := .default
 
 /--
   Convert the given goal `Ctx |- target` into `Ctx, (hs[0].userName : hs[0].type) ... |-target`.
@@ -94,11 +98,19 @@ def _root_.Lean.MVarId.assertHypotheses (mvarId : MVarId) (hs : Array Hypothesis
     let tag    ← mvarId.getTag
     let target ← mvarId.getType
     let targetNew := hs.foldr (init := target) fun h targetNew =>
-      mkForall h.userName BinderInfo.default h.type targetNew
+      .forallE h.userName h.type targetNew h.binderInfo
     let mvarNew ← mkFreshExprSyntheticOpaqueMVar targetNew tag
-    let val := hs.foldl (init := mvarNew) fun val h => mkApp val h.value
+    let val := hs.foldl (init := mvarNew) fun val h => .app val h.value
     mvarId.assign val
-    mvarNew.mvarId!.introNP hs.size
+    let (fvarIds, mvarId) ← mvarNew.mvarId!.introNP hs.size
+    mvarId.modifyLCtx fun lctx => Id.run do
+      let mut lctx := lctx
+      for h : i in [:hs.size] do
+        let h := hs[i]
+        if h.kind != .default then
+          lctx := lctx.setKind fvarIds[i]! h.kind
+      pure lctx
+    return (fvarIds, mvarId)
 
 /--
 Replace hypothesis `hyp` in goal `g` with `proof : typeNew`.

src/Lean/Meta/Tactic/Backtrack.lean

@@ -167,7 +167,7 @@ private partial def processIndependentGoals (orig : List MVarId) (goals remainin
     -- and the new subgoals generated from goals on which it is successful.
     let (failed, newSubgoals') ← tryAllM igs fun g =>
       run cfg trace next orig cfg.maxDepth [g] []
-    let newSubgoals := newSubgoals'.join
+    let newSubgoals := newSubgoals'.flatten
     withTraceNode trace
       (fun _ => return m!"failed: {← ppMVarIds failed}, new: {← ppMVarIds newSubgoals}") do
     -- Update the list of goals with respect to which we need to check independence.

src/Lean/Meta/Tactic/Clear.lean

@@ -43,9 +43,31 @@ def _root_.Lean.MVarId.tryClear (mvarId : MVarId) (fvarId : FVarId) : MetaM MVar
   mvarId.clear fvarId <|> pure mvarId
 
 /--
-Try to erase the given free variables from the goal `mvarId`.
+Try to clear the given fvars from the local context.
+
+The fvars must be given in the order they appear in the local context.
+
+See also `tryClearMany'` which takes care of reordering internally,
+and returns the cleared hypotheses along with the new goal.
 -/
 def _root_.Lean.MVarId.tryClearMany (mvarId : MVarId) (fvarIds : Array FVarId) : MetaM MVarId := do
   fvarIds.foldrM (init := mvarId) fun fvarId mvarId => mvarId.tryClear fvarId
 
+/--
+Try to clear the given fvars from the local context. Returns the new goal and
+the hypotheses that were cleared.
+
+Does not require the `hyps` to be given in the order in which they
+appear in the local context.
+-/
+def _root_.Lean.MVarId.tryClearMany' (goal : MVarId) (fvarIds : Array FVarId) :
+    MetaM (MVarId × Array FVarId) :=
+  goal.withContext do
+    let fvarIds := (← getLCtx).sortFVarsByContextOrder fvarIds
+    fvarIds.foldrM (init := (goal, Array.mkEmpty fvarIds.size))
+      fun h (goal, cleared) => do
+        let goal' ← goal.tryClear h
+        let cleared := if goal == goal' then cleared else cleared.push h
+        return (goal', cleared)
+
 end Lean.Meta

src/Lean/Meta/Tactic/FunInd.lean

@@ -662,8 +662,16 @@ def deriveUnaryInduction (name : Name) : MetaM Name := do
   let varNames ← forallTelescope info.type fun xs _ => xs.mapM (·.fvarId!.getUserName)
 
   -- Uses of WellFounded.fix can be partially applied. Here we eta-expand the body
-  -- to avoid dealing with this
-  let e ← lambdaTelescope info.value fun params body => do mkLambdaFVars params (← etaExpand body)
+  -- to make sure that `target` indeed the last parameter
+  let e := info.value
+  let e ← lambdaTelescope e fun params body => do
+    if body.isAppOfArity ``WellFounded.fix 5 then
+      forallBoundedTelescope (← inferType body) (some 1) fun xs _ => do
+        unless xs.size = 1 do
+          throwError "functional induction: Failed to eta-expand{indentExpr e}"
+        mkLambdaFVars (params ++ xs) (mkAppN body xs)
+    else
+      pure e
   let e' ← lambdaTelescope e fun params funBody => MatcherApp.withUserNames params varNames do
     match_expr funBody with
     | fix@WellFounded.fix α _motive rel wf body target =>
@@ -710,7 +718,11 @@ def deriveUnaryInduction (name : Name) : MetaM Name := do
         -- So for now lets just keep them around.
         let e' ← mkLambdaFVars (binderInfoForMVars := .default) fixedParams e'
         instantiateMVars e'
-    | _ => throwError "Function {name} not defined via WellFounded.fix:{indentExpr funBody}"
+    | _ =>
+      if funBody.isAppOf ``WellFounded.fix then
+        throwError "Function {name} defined via WellFounded.fix with unexpected arity {funBody.getAppNumArgs}:{indentExpr funBody}"
+      else
+        throwError "Function {name} not defined via WellFounded.fix:{indentExpr funBody}"
 
   unless (← isTypeCorrect e') do
     logError m!"failed to derive a type-correct induction principle:{indentExpr e'}"

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

@@ -575,7 +575,7 @@ where
 
 /--
 Discharges assumptions of the form `∀ …, a = b` using `rfl`. This is particularly useful for higher
-order assumptions of the form `∀ …, e = ?g x y` to instaniate  a paramter `g` even if that does not
+order assumptions of the form `∀ …, e = ?g x y` to instaniate  a parameter `g` even if that does not
 appear on the lhs of the rule.
 -/
 def dischargeRfl (e : Expr) : SimpM (Option Expr) := do

src/Lean/Meta/Tactic/TryThis.lean

@@ -135,16 +135,9 @@ def getIndentAndColumn (map : FileMap) (range : String.Range) : Nat × Nat :=
   let body := map.source.findAux (· ≠ ' ') range.start start
   ((body - start).1, (range.start - start).1)
 
-/-- Replace subexpressions like `?m.1234` with `?_` so it can be copy-pasted. -/
-partial def replaceMVarsByUnderscores [Monad m] [MonadQuotation m]
-    (s : Syntax) : m Syntax :=
-  s.replaceM fun s => do
-    let `(?$id:ident) := s | pure none
-    if id.getId.hasNum || id.getId.isInternal then `(?_) else pure none
-
 /-- Delaborate `e` into syntax suitable for use by `refine`. -/
 def delabToRefinableSyntax (e : Expr) : MetaM Term :=
-  return ⟨← replaceMVarsByUnderscores (← delab e)⟩
+  withOptions (pp.mvars.anonymous.set · false) do delab e
 
 /--
 An option allowing the user to customize the ideal input width. Defaults to 100.

src/Lean/Meta/Transform.lean

@@ -145,7 +145,7 @@ def zetaReduce (e : Expr) : MetaM Expr := do
       | none => return TransformStep.done e
       | some localDecl =>
         if let some value := localDecl.value? then
-          return TransformStep.visit value
+          return TransformStep.visit (← instantiateMVars value)
         else
           return TransformStep.done e
     | _ => return .continue

src/Lean/Parser/Command.lean

@@ -462,9 +462,33 @@ structure Pair (α : Type u) (β : Type v) : Type (max u v) where
   "#check " >> termParser
 @[builtin_command_parser] def check_failure  := leading_parser
   "#check_failure " >> termParser -- Like `#check`, but succeeds only if term does not type check
-@[builtin_command_parser] def eval           := leading_parser
+/--
+`#eval e` evaluates the expression `e` by compiling and evaluating it.
+
+* The command attempts to use `ToExpr`, `Repr`, or `ToString` instances to print the result.
+* If `e` is a monadic value of type `m ty`, then the command tries to adapt the monad `m`
+  to one of the monads that `#eval` supports, which include `IO`, `CoreM`, `MetaM`, `TermElabM`, and `CommandElabM`.
+  Users can define `MonadEval` instances to extend the list of supported monads.
+
+The `#eval` command gracefully degrades in capability depending on what is imported.
+Importing the `Lean.Elab.Command` module provides full capabilities.
+
+Due to unsoundness, `#eval` refuses to evaluate expressions that depend on `sorry`, even indirectly,
+since the presence of `sorry` can lead to runtime instability and crashes.
+This check can be overridden with the `#eval! e` command.
+
+Options:
+* If `eval.pp` is true (default: true) then tries to use `ToExpr` instances to make use of the
+  usual pretty printer. Otherwise, only tries using `Repr` and `ToString` instances.
+* If `eval.type` is true (default: false) then pretty prints the type of the evaluated value.
+* If `eval.derive.repr` is true (default: true) then attempts to auto-derive a `Repr` instance
+  when there is no other way to print the result.
+
+See also: `#reduce e` for evaluation by term reduction.
+-/
+@[builtin_command_parser, builtin_doc] def eval := leading_parser
   "#eval " >> termParser
-@[builtin_command_parser] def evalBang       := leading_parser
+@[builtin_command_parser, inherit_doc eval] def evalBang := leading_parser
   "#eval! " >> termParser
 @[builtin_command_parser] def synth          := leading_parser
   "#synth " >> termParser

src/Lean/Parser/Tactic.lean

@@ -125,6 +125,16 @@ example : 1 + 1 = 2 := by rfl
 @[builtin_tactic_parser] def decide := leading_parser
   nonReservedSymbol "decide"
 
+/--
+`decide!` is a variant of the `decide` tactic that uses kernel reduction to prove the goal.
+It has the following properties:
+- Since it uses kernel reduction instead of elaborator reduction, it ignores transparency and can unfold everything.
+- While `decide` needs to reduce the `Decidable` instance twice (once during elaboration to verify whether the tactic succeeds,
+  and once during kernel type checking), the `decide!` tactic reduces it exactly once.
+-/
+@[builtin_tactic_parser] def decideBang := leading_parser
+  nonReservedSymbol "decide!"
+
 /-- `native_decide` will attempt to prove a goal of type `p` by synthesizing an instance
 of `Decidable p` and then evaluating it to `isTrue ..`. Unlike `decide`, this
 uses `#eval` to evaluate the decidability instance.

src/Lean/Parser/Term.lean

@@ -140,11 +140,68 @@ def optSemicolon (p : Parser) : Parser :=
 /-- The universe of propositions. `Prop ≡ Sort 0`. -/
 @[builtin_term_parser] def prop := leading_parser
   "Prop"
-/-- A placeholder term, to be synthesized by unification. -/
+/--
+A *hole* (or *placeholder term*), which stands for an unknown term that is expected to be inferred based on context.
+For example, in `@id _ Nat.zero`, the `_` must be the type of `Nat.zero`, which is `Nat`.
+
+The way this works is that holes create fresh metavariables.
+The elaborator is allowed to assign terms to metavariables while it is checking definitional equalities.
+This is often known as *unification*.
+
+Normally, all holes must be solved for. However, there are a few contexts where this is not necessary:
+* In `match` patterns, holes are catch-all patterns.
+* In some tactics, such as `refine'` and `apply`, unsolved-for placeholders become new goals.
+
+Related concept: implicit parameters are automatically filled in with holes during the elaboration process.
+
+See also `?m` syntax (synthetic holes).
+-/
 @[builtin_term_parser] def hole := leading_parser
   "_"
-/-- Parses a "synthetic hole", that is, `?foo` or `?_`.
-This syntax is used to construct named metavariables. -/
+/--
+A *synthetic hole* (or *synthetic placeholder*), which stands for an unknown term that should be synthesized using tactics.
+- `?_` creates a fresh metavariable with an auto-generated name.
+- `?m` either refers to a pre-existing metavariable named `m` or creates a fresh metavariable with that name.
+
+In particular, the synthetic hole syntax creates "synthetic opaque metavariables",
+the same kind of metavariable used to represent goals in the tactic state.
+
+Synthetic holes are similar to holes in that `_` also creates metavariables,
+but synthetic opaque metavariables have some different properties:
+- In tactics such as `refine`, only synthetic holes yield new goals.
+- During elaboration, unification will not solve for synthetic opaque metavariables, they are "opaque".
+  This is to prevent counterintuitive behavior such as disappearing goals.
+- When synthetic holes appear under binders, they capture local variables using a more complicated mechanism known as delayed assignment.
+
+## Delayed assigned metavariables
+
+This section gives an overview of some technical details of synthetic holes, which you should feel free to skip.
+Understanding delayed assignments is mainly useful for those who are working on tactics and other metaprogramming.
+It is included here until there is a suitable place for it in the reference manual.
+
+When a synthetic hole appears under a binding construct, such as for example `fun (x : α) (y : β) => ?s`,
+the system creates a *delayed assignment*. This consists of
+1. A metavariable `?m` of type `(x : α) → (y : β) → γ x y` whose local context is the local context outside the `fun`,
+  where `γ x y` is the type of `?s`. Recall that `x` and `y` appear in the local context of `?s`.
+2. A delayed assigment record associating `?m` to `?s` and the variables `#[x, y]` in the local context of `?s`
+
+Then, this function elaborates as `fun (x : α) (y : β) => ?m x y`, where one should understand `x` and `y` here
+as being De Bruijn indexes, since Lean uses the locally nameless encoding of lambda calculus.
+
+Once `?s` is fully solved for, in the sense that after metavariable instantiation it is a metavariable-free term `e`,
+then we can make the assignment `?m := fun (x' : α) (y' : β) => e[x := x', y := y']`.
+(Implementation note: Lean only instantiates full applications `?m x' y'` of delayed assigned metavariables, to skip forming this function.)
+This delayed assignment mechanism is essential to the operation of basic tactics like `intro`,
+and a good mental model is that it is a way to "apply" the metavariable `?s` by substituting values in for some of its local variables.
+While it would be easier to immediately assign `?s := ?m x y`,
+delayed assigment preserves `?s` as an unsolved-for metavariable with a local context that still contains `x` and `y`,
+which is exactly what tactics like `intro` need.
+
+By default, delayed assigned metavariables pretty print with what they are delayed assigned to.
+The delayed assigned metavariables themselves can be pretty printed using `set_option pp.mvars.delayed true`.
+
+For more information, see the "Gruesome details" module docstrings in `Lean.MetavarContext`.
+-/
 @[builtin_term_parser] def syntheticHole := leading_parser
   "?" >> (ident <|> "_")
 /--
@@ -451,7 +508,7 @@ def withAnonymousAntiquot := leading_parser
 @[builtin_term_parser] def «trailing_parser» := leading_parser:leadPrec
   "trailing_parser" >> optExprPrecedence >> optExprPrecedence >> ppSpace >> termParser
 
-/-- 
+/--
 Indicates that an argument to a function marked `@[extern]` is borrowed.
 
 Being borrowed only affects the ABI and runtime behavior of the function when compiled or interpreted. From the perspective of Lean's type system, this annotation has no effect. It similarly has no effect on functions not marked `@[extern]`.

src/Lean/PrettyPrinter.lean

@@ -105,7 +105,7 @@ builtin_initialize
   ppFnsRef.set {
     ppExprWithInfos := fun ctx e => ctx.runMetaM <| withoutContext <| ppExprWithInfos e,
     ppTerm := fun ctx stx => ctx.runCoreM <| withoutContext <| ppTerm stx,
-    ppLevel := fun ctx l => return l.format (mvars := getPPMVars ctx.opts),
+    ppLevel := fun ctx l => return l.format (mvars := getPPMVarsLevels ctx.opts),
     ppGoal := fun ctx mvarId => ctx.runMetaM <| withoutContext <| Meta.ppGoal mvarId
   }
 

src/Lean/PrettyPrinter/Delaborator/Builtins.lean

@@ -51,19 +51,25 @@ def delabBVar : Delab := do
   let Expr.bvar idx ← getExpr | unreachable!
   pure $ mkIdent $ Name.mkSimple $ "#" ++ toString idx
 
+def delabMVarAux (m : MVarId) : DelabM Term := do
+  let mkMVarPlaceholder : DelabM Term := `(?_)
+  let mkMVar (n : Name) : DelabM Term := `(?$(mkIdent n))
+  withTypeAscription (cond := ← getPPOption getPPMVarsWithType) do
+    if ← getPPOption getPPMVars then
+      match (← m.getDecl).userName with
+      | .anonymous =>
+        if ← getPPOption getPPMVarsAnonymous then
+          mkMVar <| m.name.replacePrefix `_uniq `m
+        else
+          mkMVarPlaceholder
+      | n => mkMVar n
+    else
+      mkMVarPlaceholder
+
 @[builtin_delab mvar]
 def delabMVar : Delab := do
   let Expr.mvar n ← getExpr | unreachable!
-  withTypeAscription (cond := ← getPPOption getPPMVarsWithType) do
-    if ← getPPOption getPPMVars then
-      let mvarDecl ← n.getDecl
-      let n :=
-        match mvarDecl.userName with
-        | .anonymous => n.name.replacePrefix `_uniq `m
-        | n => n
-      `(?$(mkIdent n))
-    else
-      `(?_)
+  delabMVarAux n
 
 @[builtin_delab sort]
 def delabSort : Delab := do
@@ -72,7 +78,7 @@ def delabSort : Delab := do
   | Level.zero => `(Prop)
   | Level.succ .zero => `(Type)
   | _ =>
-    let mvars ← getPPOption getPPMVars
+    let mvars ← getPPOption getPPMVarsLevels
     match l.dec with
     | some l' => `(Type $(Level.quote l' (prec := max_prec) (mvars := mvars)))
     | none    => `(Sort $(Level.quote l (prec := max_prec) (mvars := mvars)))
@@ -98,7 +104,7 @@ def delabConst : Delab := do
         c := c₀
     pure <| mkIdent c
   else
-    let mvars ← getPPOption getPPMVars
+    let mvars ← getPPOption getPPMVarsLevels
     `($(mkIdent c).{$[$(ls.toArray.map (Level.quote · (prec := 0) (mvars := mvars)))],*})
 
   let stx ← maybeAddBlockImplicit stx
@@ -570,6 +576,16 @@ def withOverApp (arity : Nat) (x : Delab) : Delab := do
       withAnnotateTermInfo x
     delabAppCore (n - arity) delabHead (unexpand := false)
 
+@[builtin_delab app]
+def delabDelayedAssignedMVar : Delab := whenNotPPOption getPPMVarsDelayed do
+  let .mvar mvarId := (← getExpr).getAppFn | failure
+  let some decl ← getDelayedMVarAssignment? mvarId | failure
+  withOverApp decl.fvars.size do
+    let args := (← getExpr).getAppArgs
+    -- Only delaborate using decl.mvarIdPending if the delayed mvar is applied to fvars
+    guard <| args.all Expr.isFVar
+    delabMVarAux decl.mvarIdPending
+
 /-- State for `delabAppMatch` and helpers. -/
 structure AppMatchState where
   info        : MatcherInfo
@@ -1200,12 +1216,29 @@ def delabDo : Delab := whenPPOption getPPNotation do
   `(do $items:doSeqItem*)
 
 def reifyName : Expr → DelabM Name
-  | .const ``Lean.Name.anonymous .. => return Name.anonymous
-  | .app (.app (.const ``Lean.Name.str ..) n) (.lit (.strVal s)) => return (← reifyName n).mkStr s
-  | .app (.app (.const ``Lean.Name.num ..) n) (.lit (.natVal i)) => return (← reifyName n).mkNum i
+  | .const ``Lean.Name.anonymous _ => return Name.anonymous
+  | mkApp2 (.const ``Lean.Name.str _) n (.lit (.strVal s)) => return (← reifyName n).mkStr s
+  | mkApp2 (.const ``Lean.Name.num _) n (.lit (.natVal i)) => return (← reifyName n).mkNum i
+  | mkApp (.const ``Lean.Name.mkStr1 _) (.lit (.strVal a)) => return Lean.Name.mkStr1 a
+  | mkApp2 (.const ``Lean.Name.mkStr2 _) (.lit (.strVal a1)) (.lit (.strVal a2)) =>
+    return Lean.Name.mkStr2 a1 a2
+  | mkApp3 (.const ``Lean.Name.mkStr3 _) (.lit (.strVal a1)) (.lit (.strVal a2)) (.lit (.strVal a3)) =>
+    return Lean.Name.mkStr3 a1 a2 a3
+  | mkApp4 (.const ``Lean.Name.mkStr4 _) (.lit (.strVal a1)) (.lit (.strVal a2)) (.lit (.strVal a3)) (.lit (.strVal a4)) =>
+    return Lean.Name.mkStr4 a1 a2 a3 a4
+  | mkApp5 (.const ``Lean.Name.mkStr5 _) (.lit (.strVal a1)) (.lit (.strVal a2)) (.lit (.strVal a3)) (.lit (.strVal a4)) (.lit (.strVal a5)) =>
+    return Lean.Name.mkStr5 a1 a2 a3 a4 a5
+  | mkApp6 (.const ``Lean.Name.mkStr6 _) (.lit (.strVal a1)) (.lit (.strVal a2)) (.lit (.strVal a3)) (.lit (.strVal a4)) (.lit (.strVal a5)) (.lit (.strVal a6)) =>
+    return Lean.Name.mkStr6 a1 a2 a3 a4 a5 a6
+  | mkApp7 (.const ``Lean.Name.mkStr7 _) (.lit (.strVal a1)) (.lit (.strVal a2)) (.lit (.strVal a3)) (.lit (.strVal a4)) (.lit (.strVal a5)) (.lit (.strVal a6)) (.lit (.strVal a7)) =>
+    return Lean.Name.mkStr7 a1 a2 a3 a4 a5 a6 a7
+  | mkApp8 (.const ``Lean.Name.mkStr8 _) (.lit (.strVal a1)) (.lit (.strVal a2)) (.lit (.strVal a3)) (.lit (.strVal a4)) (.lit (.strVal a5)) (.lit (.strVal a6)) (.lit (.strVal a7)) (.lit (.strVal a8)) =>
+    return Lean.Name.mkStr8 a1 a2 a3 a4 a5 a6 a7 a8
   | _ => failure
 
-@[builtin_delab app.Lean.Name.str]
+@[builtin_delab app.Lean.Name.str,
+  builtin_delab app.Lean.Name.mkStr1, builtin_delab app.Lean.Name.mkStr2, builtin_delab app.Lean.Name.mkStr3, builtin_delab app.Lean.Name.mkStr4,
+  builtin_delab app.Lean.Name.mkStr5, builtin_delab app.Lean.Name.mkStr6, builtin_delab app.Lean.Name.mkStr7, builtin_delab app.Lean.Name.mkStr8]
 def delabNameMkStr : Delab := whenPPOption getPPNotation do
   let n ← reifyName (← getExpr)
   -- not guaranteed to be a syntactically valid name, but usually more helpful than the explicit version

src/Lean/PrettyPrinter/Delaborator/Options.lean

@@ -90,11 +90,29 @@ register_builtin_option pp.mvars : Bool := {
   descr    := "(pretty printer) display names of metavariables when true, \
     and otherwise display them as '?_' (for expression metavariables) and as '_' (for universe level metavariables)"
 }
+register_builtin_option pp.mvars.levels : Bool := {
+  defValue := true
+  group    := "pp"
+  descr    := "(pretty printer) display universe level metavariables as `?u.22` when true, and otherwise display them as '_'. \
+    When either 'pp.mvars' or 'pp.mvars.anonymous' is false, this is 'false' as well."
+}
+register_builtin_option pp.mvars.anonymous : Bool := {
+  defValue := true
+  group    := "pp"
+  descr    := "(pretty printer) display names for auto-generated metavariables such as `?m.22` when true, \
+    and otherwise display them as '?_' (for expression metavariables) and as '_' (for universe level metavariables). \
+    When 'pp.mvars' is false, this is 'false' as well."
+}
 register_builtin_option pp.mvars.withType : Bool := {
   defValue := false
   group    := "pp"
   descr    := "(pretty printer) display metavariables with a type ascription"
 }
+register_builtin_option pp.mvars.delayed : Bool := {
+  defValue := false
+  group    := "pp"
+  descr    := "(pretty printer) display delayed assigned metavariables when true, otherwise display what they are assigned to"
+}
 register_builtin_option pp.beta : Bool := {
   defValue := false
   group    := "pp"
@@ -243,7 +261,10 @@ def getPPFullNames (o : Options) : Bool := o.get pp.fullNames.name (getPPAll o)
 def getPPPrivateNames (o : Options) : Bool := o.get pp.privateNames.name (getPPAll o)
 def getPPInstantiateMVars (o : Options) : Bool := o.get pp.instantiateMVars.name pp.instantiateMVars.defValue
 def getPPMVars (o : Options) : Bool := o.get pp.mvars.name pp.mvars.defValue
+def getPPMVarsAnonymous (o : Options) : Bool := o.get pp.mvars.anonymous.name (pp.mvars.anonymous.defValue && getPPMVars o)
+def getPPMVarsLevels (o : Options) : Bool := o.get pp.mvars.levels.name (pp.mvars.levels.defValue && getPPMVarsAnonymous o)
 def getPPMVarsWithType (o : Options) : Bool := o.get pp.mvars.withType.name pp.mvars.withType.defValue
+def getPPMVarsDelayed (o : Options) : Bool := o.get pp.mvars.delayed.name (pp.mvars.delayed.defValue || getPPAll o)
 def getPPBeta (o : Options) : Bool := o.get pp.beta.name pp.beta.defValue
 def getPPSafeShadowing (o : Options) : Bool := o.get pp.safeShadowing.name pp.safeShadowing.defValue
 def getPPProofs (o : Options) : Bool := o.get pp.proofs.name (pp.proofs.defValue || getPPAll o)

src/Lean/Server/CodeActions/Basic.lean

@@ -124,7 +124,7 @@ def handleCodeAction (params : CodeActionParams) : RequestM (RequestTask (Array
         let names := codeActionProviderExt.getState env |>.toArray
         let caps ← names.mapM evalCodeActionProvider
         return (← builtinCodeActionProviders.get).toList.toArray ++ Array.zip names caps
-      caps.concatMapM fun (providerName, cap) => do
+      caps.flatMapM fun (providerName, cap) => do
         let cas ← cap params snap
         cas.mapIdxM fun i lca => do
           if lca.lazy?.isNone then return lca.eager

src/Lean/Server/CodeActions/Provider.lean

@@ -38,7 +38,7 @@ A code action which calls all `@[hole_code_action]` code actions on each hole
     unless head ≤ endPos && startPos ≤ tail do return result
     result.push (ctx, info)
   let #[(ctx, info)] := holes | return #[]
-  (holeCodeActionExt.getState snap.env).2.concatMapM (· params snap ctx info)
+  (holeCodeActionExt.getState snap.env).2.flatMapM (· params snap ctx info)
 
 /--
 The return value of `findTactic?`.