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3 Commits

Author SHA1 Message Date
Scott Morrison
0faf31008f cleanup 2024-03-06 09:17:05 +11:00
Scott Morrison
1f9f87d2f5 better unrolling 2024-03-06 09:09:06 +11:00
Scott Morrison
ae4123d9c0 feat: refactor of BitVec/Bitblast.lean 2024-03-05 22:37:10 +11:00
3334 changed files with 17477 additions and 85022 deletions

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@@ -9,15 +9,9 @@ assignees: ''
### Prerequisites
Please put an X between the brackets as you perform the following steps:
* [ ] Check that your issue is not already filed:
https://github.com/leanprover/lean4/issues
* [ ] Reduce the issue to a minimal, self-contained, reproducible test case.
Avoid dependencies to Mathlib or Batteries.
* [ ] Test your test case against the latest nightly release, for example on
https://live.lean-lang.org/#project=lean-nightly
(You can also use the settings there to switch to “Lean nightly”)
* [ ] Put an X between the brackets on this line if you have done all of the following:
* Check that your issue is not already [filed](https://github.com/leanprover/lean4/issues).
* Reduce the issue to a minimal, self-contained, reproducible test case. Avoid dependencies to mathlib4 or std4.
### Description
@@ -39,8 +33,8 @@ Please put an X between the brackets as you perform the following steps:
### Versions
[Output of `#eval Lean.versionString`]
[OS version, if not using live.lean-lang.org.]
[Output of `#eval Lean.versionString` or of `lean --version` in the folder that the issue occured in]
[OS version]
### Additional Information

View File

@@ -15,7 +15,7 @@ jobs:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v4
uses: actions/checkout@v3
- name: actionlint
uses: raven-actions/actionlint@v1
with:

View File

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

View File

@@ -6,20 +6,10 @@ on:
tags:
- '*'
pull_request:
types: [opened, synchronize, reopened, labeled]
merge_group:
schedule:
- cron: '0 7 * * *' # 8AM CET/11PM PT
# for manual re-release of a nightly
workflow_dispatch:
inputs:
action:
description: 'Action'
required: true
default: 'release nightly'
type: choice
options:
- release nightly
concurrency:
group: ${{ github.workflow }}-${{ github.ref }}-${{ github.event_name }}
@@ -31,10 +21,8 @@ jobs:
configure:
runs-on: ubuntu-latest
outputs:
# 0: PRs without special label
# 1: PRs with `merge-ci` label, merge queue checks, master commits
# 2: PRs with `release-ci` label, releases (incl. nightlies)
check-level: ${{ steps.set-level.outputs.check-level }}
# Should we run only a quick CI? Yes on a pull request without the full-ci label
quick: ${{ steps.set-quick.outputs.quick }}
# The build matrix, dynamically generated here
matrix: ${{ steps.set-matrix.outputs.result }}
# Should we make a nightly release? If so, this output contains the lean version string, else it is empty
@@ -51,12 +39,163 @@ jobs:
RELEASE_TAG: ${{ steps.set-release.outputs.RELEASE_TAG }}
steps:
- name: Run quick CI?
id: set-quick
env:
quick: ${{
github.event_name == 'pull_request' && !contains( github.event.pull_request.labels.*.name, 'full-ci')
}}
run: |
echo "quick=${{env.quick}}" >> "$GITHUB_OUTPUT"
- name: Configure build matrix
id: set-matrix
uses: actions/github-script@v7
with:
script: |
const quick = ${{ steps.set-quick.outputs.quick }};
console.log(`quick: ${quick}`)
let matrix = [
{
// portable release build: use channel with older glibc (2.27)
"name": "Linux LLVM",
"os": "ubuntu-latest",
"release": false,
"quick": false,
"shell": "nix-shell --arg pkgsDist \"import (fetchTarball \\\"channel:nixos-19.03\\\") {{}}\" --run \"bash -euxo pipefail {0}\"",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
"binary-check": "ldd -v",
// foreign code may be linked against more recent glibc
// reverse-ffi needs to be updated to link to LLVM libraries
"CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
"CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
},
{
"name": "Linux release",
"os": "ubuntu-latest",
"release": true,
"quick": true,
"shell": "nix-shell --arg pkgsDist \"import (fetchTarball \\\"channel:nixos-19.03\\\") {{}}\" --run \"bash -euxo pipefail {0}\"",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
"binary-check": "ldd -v",
// foreign code may be linked against more recent glibc
"CTEST_OPTIONS": "-E 'foreign'"
},
{
"name": "Linux",
"os": "ubuntu-latest",
"check-stage3": true,
"test-speedcenter": true,
"quick": false,
},
{
"name": "Linux Debug",
"os": "ubuntu-latest",
"quick": false,
"CMAKE_OPTIONS": "-DCMAKE_BUILD_TYPE=Debug",
// exclude seriously slow tests
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
},
{
"name": "Linux fsanitize",
"os": "ubuntu-latest",
"quick": false,
// turn off custom allocator & symbolic functions to make LSAN do its magic
"CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-fsanitize=address,undefined -DLEANC_EXTRA_FLAGS='-fsanitize=address,undefined -fsanitize-link-c++-runtime' -DSMALL_ALLOCATOR=OFF -DBSYMBOLIC=OFF",
// exclude seriously slow/problematic tests (laketests crash)
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
},
{
"name": "macOS",
"os": "macos-latest",
"release": true,
"quick": false,
"shell": "bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
"binary-check": "otool -L",
"tar": "gtar" // https://github.com/actions/runner-images/issues/2619
},
{
"name": "macOS aarch64",
"os": "macos-latest",
"release": true,
"quick": false,
"cross": true,
"cross_target": "aarch64-apple-darwin",
"shell": "bash -euxo pipefail {0}",
"CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm-aarch64-* lean-llvm-x86_64-*",
"binary-check": "otool -L",
"tar": "gtar" // https://github.com/actions/runner-images/issues/2619
},
{
"name": "Windows",
"os": "windows-2022",
"release": true,
"quick": false,
"shell": "msys2 {0}",
"CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
// for reasons unknown, interactivetests are flaky on Windows
"CTEST_OPTIONS": "--repeat until-pass:2",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
"binary-check": "ldd"
},
{
"name": "Linux aarch64",
"os": "ubuntu-latest",
"CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
"release": true,
"quick": false,
"cross": true,
"cross_target": "aarch64-unknown-linux-gnu",
"shell": "nix-shell --arg pkgsDist \"import (fetchTarball \\\"channel:nixos-19.03\\\") {{ localSystem.config = \\\"aarch64-unknown-linux-gnu\\\"; }}\" --run \"bash -euxo pipefail {0}\"",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
},
{
"name": "Linux 32bit",
"os": "ubuntu-latest",
// Use 32bit on stage0 and stage1 to keep oleans compatible
"CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86",
"cmultilib": true,
"release": true,
"quick": false,
"cross": true,
"shell": "bash -euxo pipefail {0}"
},
{
"name": "Web Assembly",
"os": "ubuntu-latest",
// Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
"CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
"wasm": true,
"cmultilib": true,
"release": true,
"quick": false,
"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\""
}
];
console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
if (quick) {
return matrix.filter((job) => job.quick)
} else {
return matrix
}
- name: Checkout
uses: actions/checkout@v4
uses: actions/checkout@v3
# don't schedule nightlies on forks
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4'
- name: Set Nightly
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4'
id: set-nightly
run: |
if [[ -n '${{ secrets.PUSH_NIGHTLY_TOKEN }}' ]]; then
@@ -101,170 +240,6 @@ jobs:
echo "Tag ${TAG_NAME} did not match SemVer regex."
fi
- name: Set check level
id: set-level
# We do not use github.event.pull_request.labels.*.name here because
# re-running a run does not update that list, and we do want to be able to
# rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
run: |
check_level=0
if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" ]]; then
check_level=2
elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
check_level=1
else
labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }}) --jq '.labels'"
if echo "$labels" | grep -q "release-ci"; then
check_level=2
elif echo "$labels" | grep -q "merge-ci"; then
check_level=1
fi
fi
echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
env:
GH_TOKEN: ${{ github.token }}
- name: Configure build matrix
id: set-matrix
uses: actions/github-script@v7
with:
script: |
const level = ${{ steps.set-level.outputs.check-level }};
console.log(`level: ${level}`);
// use large runners where available (original repo)
let large = ${{ github.repository == 'leanprover/lean4' }};
let matrix = [
{
// portable release build: use channel with older glibc (2.27)
"name": "Linux LLVM",
"os": "ubuntu-latest",
"release": false,
"check-level": 2,
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
"binary-check": "ldd -v",
// foreign code may be linked against more recent glibc
// reverse-ffi needs to be updated to link to LLVM libraries
"CTEST_OPTIONS": "-E 'foreign|leanlaketest_reverse-ffi'",
"CMAKE_OPTIONS": "-DLLVM=ON -DLLVM_CONFIG=${GITHUB_WORKSPACE}/build/llvm-host/bin/llvm-config"
},
{
"name": "Linux release",
"os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
"release": true,
"check-level": 0,
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
"binary-check": "ldd -v",
// foreign code may be linked against more recent glibc
"CTEST_OPTIONS": "-E 'foreign'"
},
{
"name": "Linux",
"os": large ? "nscloud-ubuntu-22.04-amd64-4x8" : "ubuntu-latest",
"check-stage3": level >= 2,
"test-speedcenter": level >= 2,
"check-level": 1,
},
{
"name": "Linux Debug",
"os": "ubuntu-latest",
"check-level": 2,
"CMAKE_PRESET": "debug",
// exclude seriously slow tests
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
},
// TODO: suddenly started failing in CI
/*{
"name": "Linux fsanitize",
"os": "ubuntu-latest",
"check-level": 2,
// turn off custom allocator & symbolic functions to make LSAN do its magic
"CMAKE_PRESET": "sanitize",
// exclude seriously slow/problematic tests (laketests crash)
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
},*/
{
"name": "macOS",
"os": "macos-13",
"release": true,
"check-level": 2,
"shell": "bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-apple-darwin.tar.zst",
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
"binary-check": "otool -L",
"tar": "gtar" // https://github.com/actions/runner-images/issues/2619
},
{
"name": "macOS aarch64",
"os": "macos-14",
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
"release": true,
"check-level": 1,
"shell": "bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-apple-darwin.tar.zst",
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
"binary-check": "otool -L",
"tar": "gtar" // https://github.com/actions/runner-images/issues/2619
},
{
"name": "Windows",
"os": "windows-2022",
"release": true,
"check-level": 2,
"shell": "msys2 {0}",
"CMAKE_OPTIONS": "-G \"Unix Makefiles\" -DUSE_GMP=OFF",
// for reasons unknown, interactivetests are flaky on Windows
"CTEST_OPTIONS": "--repeat until-pass:2",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-mingw.sh lean-llvm*",
"binary-check": "ldd"
},
{
"name": "Linux aarch64",
"os": "ubuntu-latest",
"CMAKE_OPTIONS": "-DUSE_GMP=OFF -DLEAN_INSTALL_SUFFIX=-linux_aarch64",
"release": true,
"check-level": 2,
"cross": true,
"cross_target": "aarch64-unknown-linux-gnu",
"shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-x86_64-linux-gnu.tar.zst https://github.com/leanprover/lean-llvm/releases/download/15.0.1/lean-llvm-aarch64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm-aarch64-* lean-llvm-x86_64-*"
},
{
"name": "Linux 32bit",
"os": "ubuntu-latest",
// Use 32bit on stage0 and stage1 to keep oleans compatible
"CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86",
"cmultilib": true,
"release": true,
"check-level": 2,
"cross": true,
"shell": "bash -euxo pipefail {0}"
},
{
"name": "Web Assembly",
"os": "ubuntu-latest",
// Build a native 32bit binary in stage0 and use it to compile the oleans and the wasm build
"CMAKE_OPTIONS": "-DCMAKE_C_COMPILER_WORKS=1 -DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_CMAKE_CXX_COMPILER=clang++ -DSTAGE0_CMAKE_C_COMPILER=clang -DSTAGE0_CMAKE_EXECUTABLE_SUFFIX=\"\" -DUSE_GMP=OFF -DMMAP=OFF -DSTAGE0_MMAP=OFF -DCMAKE_AR=../emsdk/emsdk-main/upstream/emscripten/emar -DCMAKE_TOOLCHAIN_FILE=../emsdk/emsdk-main/upstream/emscripten/cmake/Modules/Platform/Emscripten.cmake -DLEAN_INSTALL_SUFFIX=-linux_wasm32",
"wasm": true,
"cmultilib": true,
"release": true,
"check-level": 2,
"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\""
}
];
console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`)
return matrix.filter((job) => level >= job["check-level"])
build:
needs: [configure]
if: github.event_name != 'schedule' || github.repository == 'leanprover/lean4'
@@ -276,7 +251,7 @@ jobs:
runs-on: ${{ matrix.os }}
defaults:
run:
shell: ${{ matrix.shell || 'nix develop -c bash -euxo pipefail {0}' }}
shell: ${{ matrix.shell || 'nix-shell --run "bash -euxo pipefail {0}"' }}
name: ${{ matrix.name }}
env:
# must be inside workspace
@@ -291,34 +266,28 @@ jobs:
CXX: c++
MACOSX_DEPLOYMENT_TARGET: 10.15
steps:
- name: Checkout
uses: actions/checkout@v3
with:
submodules: true
# the default is to use a virtual merge commit between the PR and master: just use the PR
ref: ${{ github.event.pull_request.head.sha }}
- name: Install Nix
uses: DeterminateSystems/nix-installer-action@main
if: runner.os == 'Linux' && !matrix.cmultilib
uses: cachix/install-nix-action@v18
with:
install_url: https://releases.nixos.org/nix/nix-2.12.0/install
if: matrix.os == 'ubuntu-latest' && !matrix.cmultilib
- name: Install MSYS2
uses: msys2/setup-msys2@v2
with:
msystem: clang64
# `:p` means prefix with appropriate msystem prefix
pacboy: "make python cmake:p clang:p ccache:p gmp:p git zip unzip diffutils binutils tree zstd:p tar"
if: runner.os == 'Windows'
if: matrix.os == 'windows-2022'
- name: Install Brew Packages
run: |
brew install ccache tree zstd coreutils gmp
if: runner.os == 'macOS'
- name: Checkout
uses: actions/checkout@v4
with:
# the default is to use a virtual merge commit between the PR and master: just use the PR
ref: ${{ github.event.pull_request.head.sha }}
# Do check out some CI-relevant files from virtual merge commit to accommodate CI changes on
# master (as the workflow files themselves are always taken from the merge)
# (needs to be after "Install *" to use the right shell)
- name: CI Merge Checkout
run: |
git fetch --depth=1 origin ${{ github.sha }}
git checkout FETCH_HEAD flake.nix flake.lock
if: github.event_name == 'pull_request'
# (needs to be after "Checkout" so files don't get overriden)
if: matrix.os == 'macos-latest'
- name: Setup emsdk
uses: mymindstorm/setup-emsdk@v12
with:
@@ -334,22 +303,26 @@ jobs:
uses: actions/cache@v3
with:
path: .ccache
key: ${{ matrix.name }}-build-v3-${{ github.event.pull_request.head.sha }}
key: ${{ matrix.name }}-build-v3-${{ github.sha }}
# fall back to (latest) previous cache
restore-keys: |
${{ matrix.name }}-build-v3
# open nix-shell once for initial setup
- name: Setup
run: |
ccache --zero-stats
if: runner.os == 'Linux'
- name: Set up NPROC
# open nix-shell once for initial setup
true
if: matrix.os == 'ubuntu-latest'
- name: Set up core dumps
run: |
echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
mkdir -p $PWD/coredumps
# store in current directory, for easy uploading together with binary
echo $PWD/coredumps/%e.%p.%t | sudo tee /proc/sys/kernel/core_pattern
if: matrix.os == 'ubuntu-latest'
- name: Build
run: |
mkdir build
cd build
ulimit -c unlimited # coredumps
# arguments passed to `cmake`
# this also enables githash embedding into stage 1 library
OPTIONS=(-DCHECK_OLEAN_VERSION=ON)
@@ -375,11 +348,9 @@ jobs:
OPTIONS+=(-DLEAN_SPECIAL_VERSION_DESC=${{ needs.configure.outputs.LEAN_SPECIAL_VERSION_DESC }})
fi
# contortion to support empty OPTIONS with old macOS bash
cmake .. --preset ${{ matrix.CMAKE_PRESET || 'release' }} -B . ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
time make -j$NPROC
- name: Install
run: |
make -C build install
cmake .. ${{ matrix.CMAKE_OPTIONS }} ${OPTIONS[@]+"${OPTIONS[@]}"} -DLEAN_INSTALL_PREFIX=$PWD/..
make -j4
make install
- name: Check Binaries
run: ${{ matrix.binary-check }} lean-*/bin/* || true
- name: List Install Tree
@@ -397,7 +368,7 @@ jobs:
else
${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
fi
- uses: actions/upload-artifact@v4
- uses: actions/upload-artifact@v3
if: matrix.release
with:
name: build-${{ matrix.name }}
@@ -407,43 +378,65 @@ jobs:
build/stage1/bin/lean --stats src/Lean.lean
if: ${{ !matrix.cross }}
- name: Test
id: test
run: |
time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/stage1 -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.check-level >= 1
- name: Test Summary
uses: test-summary/action@v2
with:
paths: build/stage1/test-results.xml
# prefix `if` above with `always` so it's run even if tests failed
if: always() && steps.test.conclusion != 'skipped'
cd build/stage1
ulimit -c unlimited # coredumps
# exclude nonreproducible test
ctest -j4 --output-on-failure ${{ matrix.CTEST_OPTIONS }} < /dev/null
if: (matrix.wasm || !matrix.cross) && needs.configure.outputs.quick == 'false'
- name: Check Test Binary
run: ${{ matrix.binary-check }} tests/compiler/534.lean.out
if: (!matrix.cross) && steps.test.conclusion != 'skipped'
if: ${{ !matrix.cross && needs.configure.outputs.quick == 'false' }}
- name: Build Stage 2
run: |
make -C build -j$NPROC stage2
cd build
ulimit -c unlimited # coredumps
make -j4 stage2
if: matrix.test-speedcenter
- name: Check Stage 3
run: |
make -C build -j$NPROC stage3
cd build
ulimit -c unlimited # coredumps
make -j4 check-stage3
if: matrix.test-speedcenter
- name: Test Speedcenter Benchmarks
run: |
# Necessary for some timing metrics but does not work on Namespace runners
# and we just want to test that the benchmarks run at all here
#echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
echo -1 | sudo tee /proc/sys/kernel/perf_event_paranoid
export BUILD=$PWD/build PATH=$PWD/build/stage1/bin:$PATH
cd tests/bench
nix shell .#temci -c temci exec --config speedcenter.yaml --included_blocks fast --runs 1
if: matrix.test-speedcenter
- name: Check rebootstrap
run: |
cd build
ulimit -c unlimited # coredumps
# clean rebuild in case of Makefile changes
make -C build update-stage0 && rm -rf build/stage* && make -C build -j$NPROC
if: matrix.name == 'Linux' && needs.configure.outputs.check-level >= 1
make update-stage0 && rm -rf ./stage* && make -j4
if: matrix.name == 'Linux' && needs.configure.outputs.quick == 'false'
- name: CCache stats
run: ccache -s
- name: Show stacktrace for coredumps
if: ${{ failure() && matrix.os == 'ubuntu-latest' }}
run: |
for c in coredumps/*; do
progbin="$(file $c | sed "s/.*execfn: '\([^']*\)'.*/\1/")"
echo bt | $GDB/bin/gdb -q $progbin $c || true
done
# has not been used in a long while, would need to be adapted to new
# shared libs
#- name: Upload coredumps
# uses: actions/upload-artifact@v3
# if: ${{ failure() && matrix.os == 'ubuntu-latest' }}
# with:
# name: coredumps-${{ matrix.name }}
# path: |
# ./coredumps
# ./build/stage0/bin/lean
# ./build/stage0/lib/lean/libleanshared.so
# ./build/stage1/bin/lean
# ./build/stage1/lib/lean/libleanshared.so
# ./build/stage2/bin/lean
# ./build/stage2/lib/lean/libleanshared.so
# This job collects results from all the matrix jobs
# This can be made the “required” job, instead of listing each
@@ -452,10 +445,9 @@ jobs:
name: Build matrix complete
runs-on: ubuntu-latest
needs: build
# mark as merely cancelled not failed if builds are cancelled
if: ${{ !cancelled() }}
if: ${{ always() }}
steps:
- if: contains(needs.*.result, 'failure')
- if: contains(needs.*.result, 'failure') || contains(needs.*.result, 'cancelled')
uses: actions/github-script@v7
with:
script: |
@@ -470,7 +462,7 @@ jobs:
runs-on: ubuntu-latest
needs: build
steps:
- uses: actions/download-artifact@v4
- uses: actions/download-artifact@v3
with:
path: artifacts
- name: Release
@@ -478,14 +470,8 @@ jobs:
with:
files: artifacts/*/*
fail_on_unmatched_files: true
prerelease: ${{ !startsWith(github.ref, 'refs/tags/v') || contains(github.ref, '-rc') }}
env:
GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
- name: Update release.lean-lang.org
run: |
gh workflow -R leanprover/release-index run update-index.yml
env:
GITHUB_TOKEN: ${{ secrets.RELEASE_INDEX_TOKEN }}
# This job creates nightly releases during the cron job.
# It is responsible for creating the tag, and automatically generating a changelog.
@@ -495,12 +481,12 @@ jobs:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v4
uses: actions/checkout@v3
with:
# needed for tagging
fetch-depth: 0
token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
- uses: actions/download-artifact@v4
- uses: actions/download-artifact@v3
with:
path: artifacts
- name: Prepare Nightly Release
@@ -528,8 +514,3 @@ jobs:
repository: ${{ github.repository_owner }}/lean4-nightly
env:
GITHUB_TOKEN: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
- name: Update release.lean-lang.org
run: |
gh workflow -R leanprover/release-index run update-index.yml
env:
GITHUB_TOKEN: ${{ secrets.RELEASE_INDEX_TOKEN }}

View File

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

View File

@@ -6,6 +6,7 @@ on:
tags:
- '*'
pull_request:
types: [opened, synchronize, reopened, labeled]
merge_group:
concurrency:
@@ -13,36 +14,18 @@ concurrency:
cancel-in-progress: true
jobs:
# see ci.yml
configure:
runs-on: ubuntu-latest
outputs:
matrix: ${{ steps.set-matrix.outputs.result }}
steps:
- name: Configure build matrix
id: set-matrix
uses: actions/github-script@v7
with:
script: |
let large = ${{ github.repository == 'leanprover/lean4' }};
let matrix = [
{
"name": "Nix Linux",
"os": large ? "nscloud-ubuntu-22.04-amd64-8x8" : "ubuntu-latest",
}
];
console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
return matrix;
Build:
needs: [configure]
runs-on: ${{ matrix.os }}
defaults:
run:
shell: nix run .#ciShell -- bash -euxo pipefail {0}
strategy:
matrix:
include: ${{fromJson(needs.configure.outputs.matrix)}}
include:
- name: Nix Linux
os: ubuntu-latest
#- name: Nix macOS
# os: macos-latest
# complete all jobs
fail-fast: false
name: ${{ matrix.name }}
@@ -50,7 +33,7 @@ jobs:
NIX_BUILD_ARGS: --print-build-logs --fallback
steps:
- name: Checkout
uses: actions/checkout@v4
uses: actions/checkout@v3
with:
# the default is to use a virtual merge commit between the PR and master: just use the PR
ref: ${{ github.event.pull_request.head.sha }}
@@ -94,13 +77,7 @@ jobs:
nix build $NIX_BUILD_ARGS .#cacheRoots -o push-build
- name: Test
run: |
nix build --keep-failed $NIX_BUILD_ARGS .#test -o push-test || (ln -s /tmp/nix-build-*/source/src/build/ ./push-test; false)
- name: Test Summary
uses: test-summary/action@v2
with:
paths: push-test/test-results.xml
if: always()
continue-on-error: true
nix build $NIX_BUILD_ARGS .#test -o push-test
- name: Build manual
run: |
nix build $NIX_BUILD_ARGS --update-input lean --no-write-lock-file ./doc#{lean-mdbook,leanInk,alectryon,test,inked} -o push-doc

View File

@@ -126,22 +126,24 @@ jobs:
if [ "$NIGHTLY_SHA" = "$MERGE_BASE_SHA" ]; then
echo "The merge base of this PR coincides with the nightly release"
BATTERIES_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/batteries.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
MATHLIB_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/mathlib4.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
if [[ -n "$BATTERIES_REMOTE_TAGS" ]]; then
echo "... and Batteries has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
if [[ -n "$MATHLIB_REMOTE_TAGS" ]]; then
echo "... and Mathlib has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE=""
if [[ -n "$MATHLIB_REMOTE_TAGS" ]]; then
echo "... and Mathlib has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
else
echo "... but Mathlib does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Mathlib CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Mathlib CI should run now."
fi
else
echo "... but Batteries does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Batteries CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Batteries CI should run now."
echo "... but Mathlib does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Mathlib CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Mathlib CI should run now."
fi
STD_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover/std4.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
if [[ -n "$STD_REMOTE_TAGS" ]]; then
echo "... and Std has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE=""
else
echo "... but Std does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Std CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Std CI should run now."
fi
else
@@ -149,9 +151,7 @@ jobs:
echo "but 'git merge-base origin/master HEAD' reported: $MERGE_BASE_SHA"
git -C lean4.git log -10 origin/master
git -C lean4.git fetch origin nightly-with-mathlib
NIGHTLY_WITH_MATHLIB_SHA="$(git -C lean4.git rev-parse "origin/nightly-with-mathlib")"
MESSAGE="- ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_WITH_MATHLIB_SHA\`."
MESSAGE="- ❗ Std/Mathlib CI will not be attempted unless your PR branches off the \`nightly-with-mathlib\` branch. Try \`git rebase $MERGE_BASE_SHA --onto $NIGHTLY_SHA\`."
fi
if [[ -n "$MESSAGE" ]]; then
@@ -223,27 +223,27 @@ jobs:
description: description,
});
# We next automatically create a Batteries branch using this toolchain.
# Batteries doesn't itself have a mechanism to report results of CI from this branch back to Lean
# Instead this is taken care of by Mathlib CI, which will fail if Batteries fails.
# We next automatically create a Std branch using this toolchain.
# Std doesn't itself have a mechanism to report results of CI from this branch back to Lean
# Instead this is taken care of by Mathlib CI, which will fail if Std fails.
- name: Cleanup workspace
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
run: |
sudo rm -rf ./*
# Checkout the Batteries repository with all branches
- name: Checkout Batteries repository
# Checkout the Std repository with all branches
- name: Checkout Std repository
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
uses: actions/checkout@v4
uses: actions/checkout@v3
with:
repository: leanprover-community/batteries
repository: leanprover/std4
token: ${{ secrets.MATHLIB4_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
- name: Check if tag exists
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
id: check_batteries_tag
id: check_std_tag
run: |
git config user.name "leanprover-community-mathlib4-bot"
git config user.email "leanprover-community-mathlib4-bot@users.noreply.github.com"
@@ -251,7 +251,7 @@ jobs:
if git ls-remote --heads --tags --exit-code origin "nightly-testing-${MOST_RECENT_NIGHTLY}" >/dev/null; then
BASE="nightly-testing-${MOST_RECENT_NIGHTLY}"
else
echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Batteries. Falling back to 'nightly-testing'."
echo "This shouldn't be possible: couldn't find a 'nightly-testing-${MOST_RECENT_NIGHTLY}' tag at Std. Falling back to 'nightly-testing'."
BASE=nightly-testing
fi
@@ -268,7 +268,7 @@ jobs:
else
echo "Branch already exists, pushing an empty commit."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
# The Batteries `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
# The Std `nightly-testing` or `nightly-testing-YYYY-MM-DD` branch may have moved since this branch was created, so merge their changes.
# (This should no longer be possible once `nightly-testing-YYYY-MM-DD` is a tag, but it is still safe to merge.)
git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
git commit --allow-empty -m "Trigger CI for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
@@ -291,20 +291,13 @@ jobs:
# Checkout the mathlib4 repository with all branches
- name: Checkout mathlib4 repository
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
uses: actions/checkout@v4
uses: actions/checkout@v3
with:
repository: leanprover-community/mathlib4
token: ${{ secrets.MATHLIB4_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
- name: install elan
run: |
set -o pipefail
curl -sSfL https://github.com/leanprover/elan/releases/download/v3.0.0/elan-x86_64-unknown-linux-gnu.tar.gz | tar xz
./elan-init -y --default-toolchain none
echo "$HOME/.elan/bin" >> "${GITHUB_PATH}"
- name: Check if tag exists
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
id: check_mathlib_tag
@@ -328,9 +321,8 @@ jobs:
git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}" > lean-toolchain
git add lean-toolchain
sed -i 's,require "leanprover-community" / "batteries" @ ".\+",require "leanprover-community" / "batteries" @ "git#nightly-testing-'"${MOST_RECENT_NIGHTLY}"'",' lakefile.lean
lake update batteries
git add lakefile.lean lake-manifest.json
sed -i "s/require std from git \"https:\/\/github.com\/leanprover\/std4\" @ \".\+\"/require std from git \"https:\/\/github.com\/leanprover\/std4\" @ \"nightly-testing-${MOST_RECENT_NIGHTLY}\"/" lakefile.lean
git add lakefile.lean
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, pushing an empty commit."

View File

@@ -1,33 +0,0 @@
name: Restart by label
on:
pull_request_target:
types:
- unlabeled
- labeled
jobs:
restart-on-label:
runs-on: ubuntu-latest
if: contains(github.event.label.name, 'merge-ci') || contains(github.event.label.name, 'release-ci')
steps:
- run: |
# Finding latest CI workflow run on current pull request
# (unfortunately cannot search by PR number, only base branch,
# and that is't even unique given PRs from forks, but the risk
# of confusion is low and the danger is mild)
run_id=$(gh run list -e pull_request -b "$head_ref" --workflow 'CI' --limit 1 \
--limit 1 --json databaseId --jq '.[0].databaseId')
echo "Run id: ${run_id}"
gh run view "$run_id"
echo "Cancelling (just in case)"
gh run cancel "$run_id" || echo "(failed)"
echo "Waiting for 30s"
sleep 30
gh run view "$run_id"
echo "Rerunning"
gh run rerun "$run_id"
gh run view "$run_id"
shell: bash
env:
head_ref: ${{ github.head_ref }}
GH_TOKEN: ${{ github.token }}
GH_REPO: ${{ github.repository }}

View File

@@ -23,7 +23,7 @@ jobs:
# This action should push to an otherwise protected branch, so it
# uses a deploy key with write permissions, as suggested at
# https://stackoverflow.com/a/76135647/946226
- uses: actions/checkout@v4
- uses: actions/checkout@v3
with:
ssh-key: ${{secrets.STAGE0_SSH_KEY}}
- run: echo "should_update_stage0=yes" >> "$GITHUB_ENV"

6
.gitignore vendored
View File

@@ -4,10 +4,8 @@
*.lock
.lake
lake-manifest.json
/build
/src/lakefile.toml
/tests/lakefile.toml
/lakefile.toml
build
!/src/lake/Lake/Build
GPATH
GRTAGS
GSYMS

View File

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

View File

@@ -1,83 +0,0 @@
{
"version": 2,
"cmakeMinimumRequired": {
"major": 3,
"minor": 10,
"patch": 0
},
"configurePresets": [
{
"name": "release",
"displayName": "Default development optimized build config",
"generator": "Unix Makefiles",
"binaryDir": "${sourceDir}/build/release"
},
{
"name": "debug",
"displayName": "Debug build config",
"cacheVariables": {
"CMAKE_BUILD_TYPE": "Debug"
},
"generator": "Unix Makefiles",
"binaryDir": "${sourceDir}/build/debug"
},
{
"name": "sanitize",
"displayName": "Sanitize build config",
"cacheVariables": {
"LEAN_EXTRA_CXX_FLAGS": "-fsanitize=address,undefined",
"LEANC_EXTRA_FLAGS": "-fsanitize=address,undefined -fsanitize-link-c++-runtime",
"SMALL_ALLOCATOR": "OFF",
"BSYMBOLIC": "OFF"
},
"generator": "Unix Makefiles",
"binaryDir": "${sourceDir}/build/sanitize"
},
{
"name": "sandebug",
"inherits": ["debug", "sanitize"],
"displayName": "Sanitize+debug build config",
"binaryDir": "${sourceDir}/build/sandebug"
}
],
"buildPresets": [
{
"name": "release",
"configurePreset": "release"
},
{
"name": "debug",
"configurePreset": "debug"
},
{
"name": "sanitize",
"configurePreset": "sanitize"
},
{
"name": "sandebug",
"configurePreset": "sandebug"
}
],
"testPresets": [
{
"name": "release",
"configurePreset": "release",
"output": {"outputOnFailure": true, "shortProgress": true}
},
{
"name": "debug",
"configurePreset": "debug",
"inherits": "release"
},
{
"name": "sanitize",
"configurePreset": "sanitize",
"inherits": "release"
},
{
"name": "sandebug",
"configurePreset": "sandebug",
"inherits": "release"
}
]
}

View File

@@ -6,40 +6,17 @@
/.github/ @Kha @semorrison
/RELEASES.md @semorrison
/src/Init/IO.lean @joehendrix
/src/kernel/ @leodemoura
/src/lake/ @tydeu
/src/Lean/Compiler/ @leodemoura
/src/Lean/Data/Lsp/ @mhuisi
/src/Lean/Elab/Deriving/ @semorrison
/src/Lean/Elab/Tactic/ @semorrison
/src/Lean/Language/ @Kha
/src/Lean/Meta/Tactic/ @leodemoura
/src/Lean/Parser/ @Kha
/src/Lean/PrettyPrinter/ @Kha
/src/Lean/PrettyPrinter/Delaborator/ @kmill
/src/Lean/Server/ @mhuisi
/src/Lean/Widget/ @Vtec234
/src/Init/Data/ @semorrison
/src/Init/Data/Array/Lemmas.lean @digama0
/src/Init/Data/List/Lemmas.lean @digama0
/src/Init/Data/List/BasicAux.lean @digama0
/src/Init/Data/Array/Subarray.lean @david-christiansen
/src/Lean/Elab/Tactic/RCases.lean @digama0
/src/Init/RCases.lean @digama0
/src/Lean/Elab/Tactic/Ext.lean @digama0
/src/Init/Ext.lean @digama0
/src/Lean/Elab/Tactic/Simpa.lean @digama0
/src/Lean/Elab/Tactic/NormCast.lean @digama0
/src/Lean/Meta/Tactic/NormCast.lean @digama0
/src/Lean/Meta/Tactic/TryThis.lean @digama0
/src/Lean/Elab/Tactic/SimpTrace.lean @digama0
/src/Lean/Elab/Tactic/NoMatch.lean @digama0
/src/Lean/Elab/Tactic/ShowTerm.lean @digama0
/src/Lean/Elab/Tactic/Repeat.lean @digama0
/src/Lean/Meta/Tactic/Repeat.lean @digama0
/src/Lean/Meta/CoeAttr.lean @digama0
/src/Lean/Elab/GuardMsgs.lean @digama0
/src/Lean/Elab/Tactic/Guard.lean @digama0
/src/Init/Guard.lean @digama0
/src/Lean/Server/CodeActions/ @digama0
/src/Std/ @TwoFX
/src/runtime/io.cpp @joehendrix

View File

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

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@@ -8,822 +8,9 @@ This file contains work-in-progress notes for the upcoming release, as well as p
Please check the [releases](https://github.com/leanprover/lean4/releases) page for the current status
of each version.
v4.11.0
----------
Development in progress.
v4.10.0
----------
Release candidate, release notes will be copied from branch `releases/v4.10.0` once completed.
v4.9.0
----------
### Language features, tactics, and metaprograms
* **Definition transparency**
* [#4053](https://github.com/leanprover/lean4/pull/4053) adds the `seal` and `unseal` commands, which make definitions locally be irreducible or semireducible.
* [#4061](https://github.com/leanprover/lean4/pull/4061) marks functions defined by well-founded recursion with `@[irreducible]` by default,
which should prevent the expensive and often unfruitful unfolding of such definitions (see breaking changes below).
* **Incrementality**
* [#3940](https://github.com/leanprover/lean4/pull/3940) extends incremental elaboration into various steps inside of declarations:
definition headers, bodies, and tactics.
![Recording 2024-05-10](https://github.com/leanprover/lean4/assets/109126/c9d67b6f-c131-4bc3-a0de-7d63eaf1bfc9).
* [250994](https://github.com/leanprover/lean4/commit/250994166ce036ab8644e459129f51ea79c1c2d2)
and [67338b](https://github.com/leanprover/lean4/commit/67338bac2333fa39a8656e8f90574784e4c23d3d)
add `@[incremental]` attribute to mark an elaborator as supporting incremental elaboration.
* [#4259](https://github.com/leanprover/lean4/pull/4259) improves resilience by ensuring incremental commands and tactics are reached only in supported ways.
* [#4268](https://github.com/leanprover/lean4/pull/4268) adds special handling for `:= by` so that stray tokens in tactic blocks do not inhibit incrementality.
* [#4308](https://github.com/leanprover/lean4/pull/4308) adds incremental `have` tactic.
* [#4340](https://github.com/leanprover/lean4/pull/4340) fixes incorrect info tree reuse.
* [#4364](https://github.com/leanprover/lean4/pull/4364) adds incrementality for careful command macros such as `set_option in theorem`, `theorem foo.bar`, and `lemma`.
* [#4395](https://github.com/leanprover/lean4/pull/4395) adds conservative fix for whitespace handling to avoid incremental reuse leading to goals in front of the text cursor being shown.
* [#4407](https://github.com/leanprover/lean4/pull/4407) fixes non-incremental commands in macros blocking further incremental reporting.
* [#4436](https://github.com/leanprover/lean4/pull/4436) fixes incremental reporting when there are nested tactics in terms.
* **Functional induction**
* [#4135](https://github.com/leanprover/lean4/pull/4135) ensures that the names used for functional induction are reserved.
* [#4327](https://github.com/leanprover/lean4/pull/4327) adds support for structural recursion on reflexive types.
For example,
```lean4
inductive Many (α : Type u) where
| none : Many α
| more : α → (Unit → Many α) → Many α
def Many.map {α β : Type u} (f : α → β) : Many α → Many β
| .none => .none
| .more x xs => .more (f x) (fun _ => (xs ()).map f)
#check Many.map.induct
/-
Many.map.induct {α β : Type u} (f : α → β) (motive : Many α → Prop)
(case1 : motive Many.none)
(case2 : ∀ (x : α) (xs : Unit → Many α), motive (xs ()) → motive (Many.more x xs)) :
∀ (a : Many α), motive a
-/
```
* [#3903](https://github.com/leanprover/lean4/pull/3903) makes the Lean frontend normalize all line endings to LF before processing.
This lets Lean be insensitive to CRLF vs LF line endings, improving the cross-platform experience and making Lake hashes be faithful to what Lean processes.
* [#4130](https://github.com/leanprover/lean4/pull/4130) makes the tactic framework be able to recover from runtime errors (for example, deterministic timeouts or maximum recursion depth errors).
* `split` tactic
* [#4211](https://github.com/leanprover/lean4/pull/4211) fixes `split at h` when `h` has forward dependencies.
* [#4349](https://github.com/leanprover/lean4/pull/4349) allows `split` for `if`-expressions to work on non-propositional goals.
* `apply` tactic
* [#3929](https://github.com/leanprover/lean4/pull/3929) makes error message for `apply` show implicit arguments in unification errors as needed.
Modifies `MessageData` type (see breaking changes below).
* `cases` tactic
* [#4224](https://github.com/leanprover/lean4/pull/4224) adds support for unification of offsets such as `x + 20000 = 20001` in `cases` tactic.
* `omega` tactic
* [#4073](https://github.com/leanprover/lean4/pull/4073) lets `omega` fall back to using classical `Decidable` instances when setting up contradiction proofs.
* [#4141](https://github.com/leanprover/lean4/pull/4141) and [#4184](https://github.com/leanprover/lean4/pull/4184) fix bugs.
* [#4264](https://github.com/leanprover/lean4/pull/4264) improves `omega` error message if no facts found in local context.
* [#4358](https://github.com/leanprover/lean4/pull/4358) improves expression matching in `omega` by using `match_expr`.
* `simp` tactic
* [#4176](https://github.com/leanprover/lean4/pull/4176) makes names of erased lemmas clickable.
* [#4208](https://github.com/leanprover/lean4/pull/4208) adds a pretty printer for discrimination tree keys.
* [#4202](https://github.com/leanprover/lean4/pull/4202) adds `Simp.Config.index` configuration option,
which controls whether to use the full discrimination tree when selecting candidate simp lemmas.
When `index := false`, only the head function is taken into account, like in Lean 3.
This feature can help users diagnose tricky simp failures or issues in code from libraries
developed using Lean 3 and then ported to Lean 4.
In the following example, it will report that `foo` is a problematic theorem.
```lean
opaque f : Nat → Nat → Nat
@[simp] theorem foo : f x (x, y).2 = y := by sorry
example : f a b ≤ b := by
set_option diagnostics true in
simp (config := { index := false })
/-
[simp] theorems with bad keys
foo, key: f _ (@Prod.mk _ _).2
-/
```
With the information above, users can annotate theorems such as `foo` using `no_index` for problematic subterms. Example:
```lean
opaque f : Nat → Nat → Nat
@[simp] theorem foo : f x (no_index (x, y).2) = y := by sorry
example : f a b ≤ b := by
simp -- `foo` is still applied with `index := true`
```
* [#4274](https://github.com/leanprover/lean4/pull/4274) prevents internal `match` equational theorems from appearing in simp trace.
* [#4177](https://github.com/leanprover/lean4/pull/4177) and [#4359](https://github.com/leanprover/lean4/pull/4359) make `simp` continue even if a simp lemma does not elaborate, if the tactic state is in recovery mode.
* [#4341](https://github.com/leanprover/lean4/pull/4341) fixes panic when applying `@[simp]` to malformed theorem syntax.
* [#4345](https://github.com/leanprover/lean4/pull/4345) fixes `simp` so that it does not use the forward version of a user-specified backward theorem.
* [#4352](https://github.com/leanprover/lean4/pull/4352) adds missing `dsimp` simplifications for fixed parameters of generated congruence theorems.
* [#4362](https://github.com/leanprover/lean4/pull/4362) improves trace messages for `simp` so that constants are hoverable.
* **Elaboration**
* [#4046](https://github.com/leanprover/lean4/pull/4046) makes subst notation (`he ▸ h`) try rewriting in both directions even when there is no expected type available.
* [#3328](https://github.com/leanprover/lean4/pull/3328) adds support for identifiers in autoparams (for example, `rfl` in `(h : x = y := by exact rfl)`).
* [#4096](https://github.com/leanprover/lean4/pull/4096) changes how the type in `let` and `have` is elaborated, requiring that any tactics in the type be evaluated before proceeding, improving performance.
* [#4215](https://github.com/leanprover/lean4/pull/4215) ensures the expression tree elaborator commits to the computed "max type" for the entire arithmetic expression.
* [#4267](https://github.com/leanprover/lean4/pull/4267) cases signature elaboration errors to show even if there are parse errors in the body.
* [#4368](https://github.com/leanprover/lean4/pull/4368) improves error messages when numeric literals fail to synthesize an `OfNat` instance,
including special messages warning when the expected type of the numeral can be a proposition.
* **Metaprogramming**
* [#4167](https://github.com/leanprover/lean4/pull/4167) adds `Lean.MVarId.revertAll` to revert all free variables.
* [#4169](https://github.com/leanprover/lean4/pull/4169) adds `Lean.MVarId.ensureNoMVar` to ensure the goal's target contains no expression metavariables.
* [#4180](https://github.com/leanprover/lean4/pull/4180) adds `cleanupAnnotations` parameter to `forallTelescope` methods.
* [#4307](https://github.com/leanprover/lean4/pull/4307) adds support for parser aliases in syntax quotations.
* Work toward implementing `grind` tactic
* [0a515e](https://github.com/leanprover/lean4/commit/0a515e2ec939519dafb4b99daa81d6bf3c411404)
and [#4164](https://github.com/leanprover/lean4/pull/4164)
add `grind_norm` and `grind_norm_proc` attributes and `@[grind_norm]` theorems.
* [#4170](https://github.com/leanprover/lean4/pull/4170), [#4221](https://github.com/leanprover/lean4/pull/4221),
and [#4249](https://github.com/leanprover/lean4/pull/4249) create `grind` preprocessor and core module.
* [#4235](https://github.com/leanprover/lean4/pull/4235) and [d6709e](https://github.com/leanprover/lean4/commit/d6709eb1576c5d40fc80462637dc041f970e4d9f)
add special `cases` tactic to `grind` along with `@[grind_cases]` attribute to mark types that this `cases` tactic should automatically apply to.
* [#4243](https://github.com/leanprover/lean4/pull/4243) adds special `injection?` tactic to `grind`.
* **Other fixes or improvements**
* [#4065](https://github.com/leanprover/lean4/pull/4065) fixes a bug in the `Nat.reduceLeDiff` simproc.
* [#3969](https://github.com/leanprover/lean4/pull/3969) makes deprecation warnings activate even for generalized field notation ("dot notation").
* [#4132](https://github.com/leanprover/lean4/pull/4132) fixes the `sorry` term so that it does not activate the implicit lambda feature
* [9803c5](https://github.com/leanprover/lean4/commit/9803c5dd63dc993628287d5f998525e74af03839)
and [47c8e3](https://github.com/leanprover/lean4/commit/47c8e340d65b01f4d9f011686e3dda0d4bb30a20)
move `cdot` and `calc` parsers to `Lean` namespace.
* [#4252](https://github.com/leanprover/lean4/pull/4252) fixes the `case` tactic so that it is usable in macros by having it erase macro scopes from the tag.
* [26b671](https://github.com/leanprover/lean4/commit/26b67184222e75529e1b166db050aaebee323d2d)
and [cc33c3](https://github.com/leanprover/lean4/commit/cc33c39cb022d8a3166b1e89677c78835ead1fc7)
extract `haveId` syntax.
* [#4335](https://github.com/leanprover/lean4/pull/4335) fixes bugs in partial `calc` tactic when there is mdata or metavariables.
* [#4329](https://github.com/leanprover/lean4/pull/4329) makes `termination_by?` report unused each unused parameter as `_`.
* **Docs:** [#4238](https://github.com/leanprover/lean4/pull/4238), [#4294](https://github.com/leanprover/lean4/pull/4294),
[#4338](https://github.com/leanprover/lean4/pull/4338).
### Language server, widgets, and IDE extensions
* [#4066](https://github.com/leanprover/lean4/pull/4066) fixes features like "Find References" when browsing core Lean sources.
* [#4254](https://github.com/leanprover/lean4/pull/4254) allows embedding user widgets in structured messages.
Companion PR is [vscode-lean4#449](https://github.com/leanprover/vscode-lean4/pull/449).
* [#4445](https://github.com/leanprover/lean4/pull/4445) makes watchdog more resilient against badly behaving clients.
### Library
* [#4059](https://github.com/leanprover/lean4/pull/4059) upstreams many `List` and `Array` operations and theorems from Batteries.
* [#4055](https://github.com/leanprover/lean4/pull/4055) removes the unused `Inhabited` instance for `Subtype`.
* [#3967](https://github.com/leanprover/lean4/pull/3967) adds dates in existing `@[deprecated]` attributes.
* [#4231](https://github.com/leanprover/lean4/pull/4231) adds boilerplate `Char`, `UInt`, and `Fin` theorems.
* [#4205](https://github.com/leanprover/lean4/pull/4205) fixes the `MonadStore` type classes to use `semiOutParam`.
* [#4350](https://github.com/leanprover/lean4/pull/4350) renames `IsLawfulSingleton` to `LawfulSingleton`.
* `Nat`
* [#4094](https://github.com/leanprover/lean4/pull/4094) swaps `Nat.zero_or` and `Nat.or_zero`.
* [#4098](https://github.com/leanprover/lean4/pull/4098) and [#4145](https://github.com/leanprover/lean4/pull/4145)
change the definition of `Nat.mod` so that `n % (m + n)` reduces when `n` is literal without relying on well-founded recursion,
which becomes irreducible by default in [#4061](https://github.com/leanprover/lean4/pull/4061).
* [#4188](https://github.com/leanprover/lean4/pull/4188) redefines `Nat.testBit` to be more performant.
* Theorems: [#4199](https://github.com/leanprover/lean4/pull/4199).
* `Array`
* [#4074](https://github.com/leanprover/lean4/pull/4074) improves the functional induction principle `Array.feraseIdx.induct`.
* `List`
* [#4172](https://github.com/leanprover/lean4/pull/4172) removes `@[simp]` from `List.length_pos`.
* `Option`
* [#4037](https://github.com/leanprover/lean4/pull/4037) adds theorems to simplify `Option`-valued dependent if-then-else.
* [#4314](https://github.com/leanprover/lean4/pull/4314) removes `@[simp]` from `Option.bind_eq_some`.
* `BitVec`
* Theorems: [#3920](https://github.com/leanprover/lean4/pull/3920), [#4095](https://github.com/leanprover/lean4/pull/4095),
[#4075](https://github.com/leanprover/lean4/pull/4075), [#4148](https://github.com/leanprover/lean4/pull/4148),
[#4165](https://github.com/leanprover/lean4/pull/4165), [#4178](https://github.com/leanprover/lean4/pull/4178),
[#4200](https://github.com/leanprover/lean4/pull/4200), [#4201](https://github.com/leanprover/lean4/pull/4201),
[#4298](https://github.com/leanprover/lean4/pull/4298), [#4299](https://github.com/leanprover/lean4/pull/4299),
[#4257](https://github.com/leanprover/lean4/pull/4257), [#4179](https://github.com/leanprover/lean4/pull/4179),
[#4321](https://github.com/leanprover/lean4/pull/4321), [#4187](https://github.com/leanprover/lean4/pull/4187).
* [#4193](https://github.com/leanprover/lean4/pull/4193) adds simprocs for reducing `x >>> i` and `x <<< i` where `i` is a bitvector literal.
* [#4194](https://github.com/leanprover/lean4/pull/4194) adds simprocs for reducing `(x <<< i) <<< j` and `(x >>> i) >>> j` where `i` and `j` are natural number literals.
* [#4229](https://github.com/leanprover/lean4/pull/4229) redefines `rotateLeft`/`rotateRight` to use modulo reduction of shift offset.
* [0d3051](https://github.com/leanprover/lean4/commit/0d30517dca094a07bcb462252f718e713b93ffba) makes `<num>#<term>` bitvector literal notation global.
* `Char`/`String`
* [#4143](https://github.com/leanprover/lean4/pull/4143) modifies `String.substrEq` to avoid linter warnings in downstream code.
* [#4233](https://github.com/leanprover/lean4/pull/4233) adds simprocs for `Char` and `String` inequalities.
* [#4348](https://github.com/leanprover/lean4/pull/4348) upstreams Mathlib lemmas.
* [#4354](https://github.com/leanprover/lean4/pull/4354) upstreams basic `String` lemmas.
* `HashMap`
* [#4248](https://github.com/leanprover/lean4/pull/4248) fixes implicitness of typeclass arguments in `HashMap.ofList`.
* `IO`
* [#4036](https://github.com/leanprover/lean4/pull/4036) adds `IO.Process.getCurrentDir` and `IO.Process.setCurrentDir` for adjusting the current process's working directory.
* **Cleanup:** [#4077](https://github.com/leanprover/lean4/pull/4077), [#4189](https://github.com/leanprover/lean4/pull/4189),
[#4304](https://github.com/leanprover/lean4/pull/4304).
* **Docs:** [#4001](https://github.com/leanprover/lean4/pull/4001), [#4166](https://github.com/leanprover/lean4/pull/4166),
[#4332](https://github.com/leanprover/lean4/pull/4332).
### Lean internals
* **Defeq and WHNF algorithms**
* [#4029](https://github.com/leanprover/lean4/pull/4029) remove unnecessary `checkpointDefEq`
* [#4206](https://github.com/leanprover/lean4/pull/4206) fixes `isReadOnlyOrSyntheticOpaque` to respect metavariable depth.
* [#4217](https://github.com/leanprover/lean4/pull/4217) fixes missing occurs check for delayed assignments.
* **Definition transparency**
* [#4052](https://github.com/leanprover/lean4/pull/4052) adds validation to application of `@[reducible]`/`@[semireducible]`/`@[irreducible]` attributes (with `local`/`scoped` modifiers as well).
Setting `set_option allowUnsafeReductibility true` turns this validation off.
* **Inductive types**
* [#3591](https://github.com/leanprover/lean4/pull/3591) fixes a bug where indices could be incorrectly promoted to parameters.
* [#3398](https://github.com/leanprover/lean4/pull/3398) fixes a bug in the injectivity theorem generator.
* [#4342](https://github.com/leanprover/lean4/pull/4342) fixes elaboration of mutual inductives with instance parameters.
* **Diagnostics and profiling**
* [#3986](https://github.com/leanprover/lean4/pull/3986) adds option `trace.profiler.useHeartbeats` to switch `trace.profiler.threshold` to being in terms of heartbeats instead of milliseconds.
* [#4082](https://github.com/leanprover/lean4/pull/4082) makes `set_option diagnostics true` report kernel diagnostic information.
* **Typeclass resolution**
* [#4119](https://github.com/leanprover/lean4/pull/4119) fixes multiple issues with TC caching interacting with `synthPendingDepth`, adds `maxSynthPendingDepth` option with default value `1`.
* [#4210](https://github.com/leanprover/lean4/pull/4210) ensures local instance cache does not contain multiple copies of the same instance.
* [#4216](https://github.com/leanprover/lean4/pull/4216) fix handling of metavariables, to avoid needing to set the option `backward.synthInstance.canonInstances` to `false`.
* **Other fixes or improvements**
* [#4080](https://github.com/leanprover/lean4/pull/4080) fixes propagation of state for `Lean.Elab.Command.liftCoreM` and `Lean.Elab.Command.liftTermElabM`.
* [#3944](https://github.com/leanprover/lean4/pull/3944) makes the `Repr` deriving handler be consistent between `structure` and `inductive` for how types and proofs are erased.
* [#4113](https://github.com/leanprover/lean4/pull/4113) propagates `maxHeartbeats` to kernel to control "(kernel) deterministic timeout" error.
* [#4125](https://github.com/leanprover/lean4/pull/4125) reverts [#3970](https://github.com/leanprover/lean4/pull/3970) (monadic generalization of `FindExpr`).
* [#4128](https://github.com/leanprover/lean4/pull/4128) catches stack overflow in auto-bound implicits feature.
* [#4129](https://github.com/leanprover/lean4/pull/4129) adds `tryCatchRuntimeEx` combinator to replace `catchRuntimeEx` reader state.
* [#4155](https://github.com/leanprover/lean4/pull/4155) simplifies the expression canonicalizer.
* [#4151](https://github.com/leanprover/lean4/pull/4151) and [#4369](https://github.com/leanprover/lean4/pull/4369)
add many missing trace classes.
* [#4185](https://github.com/leanprover/lean4/pull/4185) makes congruence theorem generators clean up type annotations of argument types.
* [#4192](https://github.com/leanprover/lean4/pull/4192) fixes restoration of infotrees when auto-bound implicit feature is activated,
fixing a pretty printing error in hovers and strengthening the unused variable linter.
* [dfb496](https://github.com/leanprover/lean4/commit/dfb496a27123c3864571aec72f6278e2dad1cecf) fixes `declareBuiltin` to allow it to be called multiple times per declaration.
* Cleanup: [#4112](https://github.com/leanprover/lean4/pull/4112), [#4126](https://github.com/leanprover/lean4/pull/4126), [#4091](https://github.com/leanprover/lean4/pull/4091), [#4139](https://github.com/leanprover/lean4/pull/4139), [#4153](https://github.com/leanprover/lean4/pull/4153).
* Tests: [030406](https://github.com/leanprover/lean4/commit/03040618b8f9b35b7b757858483e57340900cdc4), [#4133](https://github.com/leanprover/lean4/pull/4133).
### Compiler, runtime, and FFI
* [#4100](https://github.com/leanprover/lean4/pull/4100) improves reset/reuse algorithm; it now runs a second pass relaxing the constraint that reused memory cells must only be for the exact same constructor.
* [#2903](https://github.com/leanprover/lean4/pull/2903) fixes segfault in old compiler from mishandling `noConfusion` applications.
* [#4311](https://github.com/leanprover/lean4/pull/4311) fixes bug in constant folding.
* [#3915](https://github.com/leanprover/lean4/pull/3915) documents the runtime memory layout for inductive types.
### Lake
* [#4057](https://github.com/leanprover/lean4/pull/4057) adds support for docstrings on `require` commands.
* [#4088](https://github.com/leanprover/lean4/pull/4088) improves hovers for `family_def` and `library_data` commands.
* [#4147](https://github.com/leanprover/lean4/pull/4147) adds default `README.md` to package templates
* [#4261](https://github.com/leanprover/lean4/pull/4261) extends `lake test` help page, adds help page for `lake check-test`,
adds `lake lint` and tag `@[lint_driver]`, adds support for specifying test and lint drivers from dependencies,
adds `testDriverArgs` and `lintDriverArgs` options, adds support for library test drivers,
makes `lake check-test` and `lake check-lint` only load the package without dependencies.
* [#4270](https://github.com/leanprover/lean4/pull/4270) adds `lake pack` and `lake unpack` for packing and unpacking Lake build artifacts from an archive.
* [#4083](https://github.com/leanprover/lean4/pull/4083)
Switches the manifest format to use `major.minor.patch` semantic
versions. Major version increments indicate breaking changes (e.g., new
required fields and semantic changes to existing fields). Minor version
increments (after `0.x`) indicate backwards-compatible extensions (e.g.,
adding optional fields, removing fields). This change is backwards
compatible. Lake will still successfully read old manifests with numeric
versions. It will treat the numeric version `N` as semantic version
`0.N.0`. Lake will also accept manifest versions with `-` suffixes
(e.g., `x.y.z-foo`) and then ignore the suffix.
* [#4273](https://github.com/leanprover/lean4/pull/4273) adds a lift from `JobM` to `FetchM` for backwards compatibility reasons.
* [#4351](https://github.com/leanprover/lean4/pull/4351) fixes `LogIO`-to-`CliM`-lifting performance issues.
* [#4343](https://github.com/leanprover/lean4/pull/4343) make Lake store the dependency trace for a build in
the cached build long and then verifies that it matches the trace of the current build before replaying the log.
* [#4402](https://github.com/leanprover/lean4/pull/4402) moves the cached log into the trace file (no more `.log.json`).
This means logs are no longer cached on fatal errors and this ensures that an out-of-date log is not associated with an up-to-date trace.
Separately, `.hash` file generation was changed to be more reliable as well.
The `.hash` files are deleted as part of the build and always regenerate with `--rehash`.
* **Other fixes or improvements**
* [#4056](https://github.com/leanprover/lean4/pull/4056) cleans up tests
* [#4244](https://github.com/leanprover/lean4/pull/4244) fixes `noRelease` test when Lean repo is tagged
* [#4346](https://github.com/leanprover/lean4/pull/4346) improves `tests/serve`
* [#4356](https://github.com/leanprover/lean4/pull/4356) adds build log path to the warning for a missing or invalid build log.
### DevOps
* [#3984](https://github.com/leanprover/lean4/pull/3984) adds a script (`script/rebase-stage0.sh`) for `git rebase -i` that automatically updates each stage0.
* [#4108](https://github.com/leanprover/lean4/pull/4108) finishes renamings from transition to Std to Batteries.
* [#4109](https://github.com/leanprover/lean4/pull/4109) adjusts the Github bug template to mention testing using [live.lean-lang.org](https://live.lean-lang.org).
* [#4136](https://github.com/leanprover/lean4/pull/4136) makes CI rerun only when `full-ci` label is added or removed.
* [#4175](https://github.com/leanprover/lean4/pull/4175) and [72b345](https://github.com/leanprover/lean4/commit/72b345c621a9a06d3a5a656da2b793a5eea5f168)
switch to using `#guard_msgs` to run tests as much as possible.
* [#3125](https://github.com/leanprover/lean4/pull/3125) explains the Lean4 `pygments` lexer.
* [#4247](https://github.com/leanprover/lean4/pull/4247) sets up a procedure for preparing release notes.
* [#4032](https://github.com/leanprover/lean4/pull/4032) modernizes build instructions and workflows.
* [#4255](https://github.com/leanprover/lean4/pull/4255) moves some expensive checks from merge queue to releases.
* [#4265](https://github.com/leanprover/lean4/pull/4265) adds aarch64 macOS as native compilation target for CI.
* [f05a82](https://github.com/leanprover/lean4/commit/f05a82799a01569edeb5e2594cd7d56282320f9e) restores macOS aarch64 install suffix in CI
* [#4317](https://github.com/leanprover/lean4/pull/4317) updates build instructions for macOS.
* [#4333](https://github.com/leanprover/lean4/pull/4333) adjusts workflow to update Batteries in manifest when creating `lean-pr-testing-NNNN` Mathlib branches.
* [#4355](https://github.com/leanprover/lean4/pull/4355) simplifies `lean4checker` step of release checklist.
* [#4361](https://github.com/leanprover/lean4/pull/4361) adds installing elan to `pr-release` CI step.
### Breaking changes
While most changes could be considered to be a breaking change, this section makes special note of API changes.
* `Nat.zero_or` and `Nat.or_zero` have been swapped ([#4094](https://github.com/leanprover/lean4/pull/4094)).
* `IsLawfulSingleton` is now `LawfulSingleton` ([#4350](https://github.com/leanprover/lean4/pull/4350)).
* `BitVec.rotateLeft` and `BitVec.rotateRight` now take the shift modulo the bitwidth ([#4229](https://github.com/leanprover/lean4/pull/4229)).
* These are no longer simp lemmas:
`List.length_pos` ([#4172](https://github.com/leanprover/lean4/pull/4172)),
`Option.bind_eq_some` ([#4314](https://github.com/leanprover/lean4/pull/4314)).
* Types in `let` and `have` (both the expressions and tactics) may fail to elaborate due to new restrictions on what sorts of elaboration problems may be postponed ([#4096](https://github.com/leanprover/lean4/pull/4096)).
In particular, tactics embedded in the type will no longer make use of the type of `value` in expressions such as `let x : type := value; body`.
* Now functions defined by well-founded recursion are marked with `@[irreducible]` by default ([#4061](https://github.com/leanprover/lean4/pull/4061)).
Existing proofs that hold by definitional equality (e.g. `rfl`) can be
rewritten to explictly unfold the function definition (using `simp`,
`unfold`, `rw`), or the recursive function can be temporarily made
semireducible (using `unseal f in` before the command), or the function
definition itself can be marked as `@[semireducible]` to get the previous
behavior.
* Due to [#3929](https://github.com/leanprover/lean4/pull/3929):
* The `MessageData.ofPPFormat` constructor has been removed.
Its functionality has been split into two:
- for lazy structured messages, please use `MessageData.lazy`;
- for embedding `Format` or `FormatWithInfos`, use `MessageData.ofFormatWithInfos`.
An example migration can be found in [#3929](https://github.com/leanprover/lean4/pull/3929/files#diff-5910592ab7452a0e1b2616c62d22202d2291a9ebb463145f198685aed6299867L109).
* The `MessageData.ofFormat` constructor has been turned into a function.
If you need to inspect `MessageData`, you can pattern-match on `MessageData.ofFormatWithInfos`.
v4.8.0
v4.8.0 (development in progress)
---------
### Language features, tactics, and metaprograms
* **Functional induction principles.**
[#3432](https://github.com/leanprover/lean4/pull/3432), [#3620](https://github.com/leanprover/lean4/pull/3620),
[#3754](https://github.com/leanprover/lean4/pull/3754), [#3762](https://github.com/leanprover/lean4/pull/3762),
[#3738](https://github.com/leanprover/lean4/pull/3738), [#3776](https://github.com/leanprover/lean4/pull/3776),
[#3898](https://github.com/leanprover/lean4/pull/3898).
Derived from the definition of a (possibly mutually) recursive function,
a **functional induction principle** is created that is tailored to proofs about that function.
For example from:
```
def ackermann : Nat → Nat → Nat
| 0, m => m + 1
| n+1, 0 => ackermann n 1
| n+1, m+1 => ackermann n (ackermann (n + 1) m)
```
we get
```
ackermann.induct (motive : Nat → Nat → Prop) (case1 : ∀ (m : Nat), motive 0 m)
(case2 : ∀ (n : Nat), motive n 1 → motive (Nat.succ n) 0)
(case3 : ∀ (n m : Nat), motive (n + 1) m → motive n (ackermann (n + 1) m) → motive (Nat.succ n) (Nat.succ m))
(x x : Nat) : motive x x
```
It can be used in the `induction` tactic using the `using` syntax:
```
induction n, m using ackermann.induct
```
* The termination checker now recognizes more recursion patterns without an
explicit `termination_by`. In particular the idiom of counting up to an upper
bound, as in
```
def Array.sum (arr : Array Nat) (i acc : Nat) : Nat :=
if _ : i < arr.size then
Array.sum arr (i+1) (acc + arr[i])
else
acc
```
is recognized without having to say `termination_by arr.size - i`.
* [#3630](https://github.com/leanprover/lean4/pull/3630) makes `termination_by?` not use `sizeOf` when not needed
* [#3652](https://github.com/leanprover/lean4/pull/3652) improves the `termination_by` syntax.
* [#3658](https://github.com/leanprover/lean4/pull/3658) changes how termination arguments are elaborated.
* [#3665](https://github.com/leanprover/lean4/pull/3665) refactors GuessLex to allow inferring more complex termination arguments
* [#3666](https://github.com/leanprover/lean4/pull/3666) infers termination arguments such as `xs.size - i`
* [#3629](https://github.com/leanprover/lean4/pull/3629),
[#3655](https://github.com/leanprover/lean4/pull/3655),
[#3747](https://github.com/leanprover/lean4/pull/3747):
Adds `@[induction_eliminator]` and `@[cases_eliminator]` attributes to be able to define custom eliminators
for the `induction` and `cases` tactics, replacing the `@[eliminator]` attribute.
Gives custom eliminators for `Nat` so that `induction` and `cases` put goal states into terms of `0` and `n + 1`
rather than `Nat.zero` and `Nat.succ n`.
Added option `tactic.customEliminators` to control whether to use custom eliminators.
Added a hack for `rcases`/`rintro`/`obtain` to use the custom eliminator for `Nat`.
* **Shorter instances names.** There is a new algorithm for generating names for anonymous instances.
Across Std and Mathlib, the median ratio between lengths of new names and of old names is about 72%.
With the old algorithm, the longest name was 1660 characters, and now the longest name is 202 characters.
The new algorithm's 95th percentile name length is 67 characters, versus 278 for the old algorithm.
While the new algorithm produces names that are 1.2% less unique,
it avoids cross-project collisions by adding a module-based suffix
when it does not refer to declarations from the same "project" (modules that share the same root).
[#3089](https://github.com/leanprover/lean4/pull/3089)
and [#3934](https://github.com/leanprover/lean4/pull/3934).
* [8d2adf](https://github.com/leanprover/lean4/commit/8d2adf521d2b7636347a5b01bfe473bf0fcfaf31)
Importing two different files containing proofs of the same theorem is no longer considered an error.
This feature is particularly useful for theorems that are automatically generated on demand (e.g., equational theorems).
* [84b091](https://github.com/leanprover/lean4/commit/84b0919a116e9be12f933e764474f45d964ce85c)
Lean now generates an error if the type of a theorem is **not** a proposition.
* **Definition transparency.** [47a343](https://github.com/leanprover/lean4/commit/47a34316fc03ce936fddd2d3dce44784c5bcdfa9). `@[reducible]`, `@[semireducible]`, and `@[irreducible]` are now scoped and able to be set for imported declarations.
* `simp`/`dsimp`
* [#3607](https://github.com/leanprover/lean4/pull/3607) enables kernel projection reduction in `dsimp`
* [b24fbf](https://github.com/leanprover/lean4/commit/b24fbf44f3aaa112f5d799ef2a341772d1eb222d)
and [acdb00](https://github.com/leanprover/lean4/commit/acdb0054d5a0efa724cff596ac26852fad5724c4):
`dsimproc` command
to define defeq-preserving simplification procedures.
* [#3624](https://github.com/leanprover/lean4/pull/3624) makes `dsimp` normalize raw nat literals as `OfNat.ofNat` applications.
* [#3628](https://github.com/leanprover/lean4/pull/3628) makes `simp` correctly handle `OfScientific.ofScientific` literals.
* [#3654](https://github.com/leanprover/lean4/pull/3654) makes `dsimp?` report used simprocs.
* [dee074](https://github.com/leanprover/lean4/commit/dee074dcde03a37b7895a4901df2e4fa490c73c7) fixes equation theorem
handling in `simp` for non-recursive definitions.
* [#3819](https://github.com/leanprover/lean4/pull/3819) improved performance when simp encounters a loop.
* [#3821](https://github.com/leanprover/lean4/pull/3821) fixes discharger/cache interaction.
* [#3824](https://github.com/leanprover/lean4/pull/3824) keeps `simp` from breaking `Char` literals.
* [#3838](https://github.com/leanprover/lean4/pull/3838) allows `Nat` instances matching to be more lenient.
* [#3870](https://github.com/leanprover/lean4/pull/3870) documentation for `simp` configuration options.
* [#3972](https://github.com/leanprover/lean4/pull/3972) fixes simp caching.
* [#4044](https://github.com/leanprover/lean4/pull/4044) improves cache behavior for "well-behaved" dischargers.
* `omega`
* [#3639](https://github.com/leanprover/lean4/pull/3639), [#3766](https://github.com/leanprover/lean4/pull/3766),
[#3853](https://github.com/leanprover/lean4/pull/3853), [#3875](https://github.com/leanprover/lean4/pull/3875):
introduces a term canonicalizer.
* [#3736](https://github.com/leanprover/lean4/pull/3736) improves handling of positivity for the modulo operator for `Int`.
* [#3828](https://github.com/leanprover/lean4/pull/3828) makes it work as a `simp` discharger.
* [#3847](https://github.com/leanprover/lean4/pull/3847) adds helpful error messages.
* `rfl`
* [#3671](https://github.com/leanprover/lean4/pull/3671), [#3708](https://github.com/leanprover/lean4/pull/3708): upstreams the `@[refl]` attribute and the `rfl` tactic.
* [#3751](https://github.com/leanprover/lean4/pull/3751) makes `apply_rfl` not operate on `Eq` itself.
* [#4067](https://github.com/leanprover/lean4/pull/4067) improves error message when there are no goals.
* [#3719](https://github.com/leanprover/lean4/pull/3719) upstreams the `rw?` tactic, with fixes and improvements in
[#3783](https://github.com/leanprover/lean4/pull/3783), [#3794](https://github.com/leanprover/lean4/pull/3794),
[#3911](https://github.com/leanprover/lean4/pull/3911).
* `conv`
* [#3659](https://github.com/leanprover/lean4/pull/3659) adds a `conv` version of the `calc` tactic.
* [#3763](https://github.com/leanprover/lean4/pull/3763) makes `conv` clean up using `try with_reducible rfl` instead of `try rfl`.
* `#guard_msgs`
* [#3617](https://github.com/leanprover/lean4/pull/3617) introduces whitespace protection using the `` character.
* [#3883](https://github.com/leanprover/lean4/pull/3883):
The `#guard_msgs` command now has options to change whitespace normalization and sensitivity to message ordering.
For example, `#guard_msgs (whitespace := lax) in cmd` collapses whitespace before checking messages,
and `#guard_msgs (ordering := sorted) in cmd` sorts the messages in lexicographic order before checking.
* [#3931](https://github.com/leanprover/lean4/pull/3931) adds an unused variables ignore function for `#guard_msgs`.
* [#3912](https://github.com/leanprover/lean4/pull/3912) adds a diff between the expected and actual outputs. This feature is currently
disabled by default, but can be enabled with `set_option guard_msgs.diff true`.
Depending on user feedback, this option may default to `true` in a future version of Lean.
* `do` **notation**
* [#3820](https://github.com/leanprover/lean4/pull/3820) makes it an error to lift `(<- ...)` out of a pure `if ... then ... else ...`
* **Lazy discrimination trees**
* [#3610](https://github.com/leanprover/lean4/pull/3610) fixes a name collision for `LazyDiscrTree` that could lead to cache poisoning.
* [#3677](https://github.com/leanprover/lean4/pull/3677) simplifies and fixes `LazyDiscrTree` handling for `exact?`/`apply?`.
* [#3685](https://github.com/leanprover/lean4/pull/3685) moves general `exact?`/`apply?` functionality into `LazyDiscrTree`.
* [#3769](https://github.com/leanprover/lean4/pull/3769) has lemma selection improvements for `rw?` and `LazyDiscrTree`.
* [#3818](https://github.com/leanprover/lean4/pull/3818) improves ordering of matches.
* [#3590](https://github.com/leanprover/lean4/pull/3590) adds `inductive.autoPromoteIndices` option to be able to disable auto promotion of indices in the `inductive` command.
* **Miscellaneous bug fixes and improvements**
* [#3606](https://github.com/leanprover/lean4/pull/3606) preserves `cache` and `dischargeDepth` fields in `Lean.Meta.Simp.Result.mkEqSymm`.
* [#3633](https://github.com/leanprover/lean4/pull/3633) makes `elabTermEnsuringType` respect `errToSorry`, improving error recovery of the `have` tactic.
* [#3647](https://github.com/leanprover/lean4/pull/3647) enables `noncomputable unsafe` definitions, for deferring implementations until later.
* [#3672](https://github.com/leanprover/lean4/pull/3672) adjust namespaces of tactics.
* [#3725](https://github.com/leanprover/lean4/pull/3725) fixes `Ord` derive handler for indexed inductive types with unused alternatives.
* [#3893](https://github.com/leanprover/lean4/pull/3893) improves performance of derived `Ord` instances.
* [#3771](https://github.com/leanprover/lean4/pull/3771) changes error reporting for failing tactic macros. Improves `rfl` error message.
* [#3745](https://github.com/leanprover/lean4/pull/3745) fixes elaboration of generalized field notation if the object of the notation is an optional parameter.
* [#3799](https://github.com/leanprover/lean4/pull/3799) makes commands such as `universe`, `variable`, `namespace`, etc. require that their argument appear in a later column.
Commands that can optionally parse an `ident` or parse any number of `ident`s generally should require
that the `ident` use `colGt`. This keeps typos in commands from being interpreted as identifiers.
* [#3815](https://github.com/leanprover/lean4/pull/3815) lets the `split` tactic be used for writing code.
* [#3822](https://github.com/leanprover/lean4/pull/3822) adds missing info in `induction` tactic for `with` clauses of the form `| cstr a b c => ?_`.
* [#3806](https://github.com/leanprover/lean4/pull/3806) fixes `withSetOptionIn` combinator.
* [#3844](https://github.com/leanprover/lean4/pull/3844) removes unused `trace.Elab.syntax` option.
* [#3896](https://github.com/leanprover/lean4/pull/3896) improves hover and go-to-def for `attribute` command.
* [#3989](https://github.com/leanprover/lean4/pull/3989) makes linter options more discoverable.
* [#3916](https://github.com/leanprover/lean4/pull/3916) fixes go-to-def for syntax defined with `@[builtin_term_parser]`.
* [#3962](https://github.com/leanprover/lean4/pull/3962) fixes how `solveByElim` handles `symm` lemmas, making `exact?`/`apply?` usable again.
* [#3968](https://github.com/leanprover/lean4/pull/3968) improves the `@[deprecated]` attribute, adding `(since := "<date>")` field.
* [#3768](https://github.com/leanprover/lean4/pull/3768) makes `#print` command show structure fields.
* [#3974](https://github.com/leanprover/lean4/pull/3974) makes `exact?%` behave like `by exact?` rather than `by apply?`.
* [#3994](https://github.com/leanprover/lean4/pull/3994) makes elaboration of `he ▸ h` notation more predictable.
* [#3991](https://github.com/leanprover/lean4/pull/3991) adjusts transparency for `decreasing_trivial` macros.
* [#4092](https://github.com/leanprover/lean4/pull/4092) improves performance of `binop%` and `binrel%` expression tree elaborators.
* **Docs:** [#3748](https://github.com/leanprover/lean4/pull/3748), [#3796](https://github.com/leanprover/lean4/pull/3796),
[#3800](https://github.com/leanprover/lean4/pull/3800), [#3874](https://github.com/leanprover/lean4/pull/3874),
[#3863](https://github.com/leanprover/lean4/pull/3863), [#3862](https://github.com/leanprover/lean4/pull/3862),
[#3891](https://github.com/leanprover/lean4/pull/3891), [#3873](https://github.com/leanprover/lean4/pull/3873),
[#3908](https://github.com/leanprover/lean4/pull/3908), [#3872](https://github.com/leanprover/lean4/pull/3872).
### Language server and IDE extensions
* [#3602](https://github.com/leanprover/lean4/pull/3602) enables `import` auto-completions.
* [#3608](https://github.com/leanprover/lean4/pull/3608) fixes issue [leanprover/vscode-lean4#392](https://github.com/leanprover/vscode-lean4/issues/392).
Diagnostic ranges had an off-by-one error that would misplace goal states for example.
* [#3014](https://github.com/leanprover/lean4/pull/3014) introduces snapshot trees, foundational work for incremental tactics and parallelism.
[#3849](https://github.com/leanprover/lean4/pull/3849) adds basic incrementality API.
* [#3271](https://github.com/leanprover/lean4/pull/3271) adds support for server-to-client requests.
* [#3656](https://github.com/leanprover/lean4/pull/3656) fixes jump to definition when there are conflicting names from different files.
Fixes issue [#1170](https://github.com/leanprover/lean4/issues/1170).
* [#3691](https://github.com/leanprover/lean4/pull/3691), [#3925](https://github.com/leanprover/lean4/pull/3925),
[#3932](https://github.com/leanprover/lean4/pull/3932) keep semantic tokens synchronized (used for semantic highlighting), with performance improvements.
* [#3247](https://github.com/leanprover/lean4/pull/3247) and [#3730](https://github.com/leanprover/lean4/pull/3730)
add diagnostics to run "Restart File" when a file dependency is saved.
* [#3722](https://github.com/leanprover/lean4/pull/3722) uses the correct module names when displaying references.
* [#3728](https://github.com/leanprover/lean4/pull/3728) makes errors in header reliably appear and makes the "Import out of date" warning be at "hint" severity.
[#3739](https://github.com/leanprover/lean4/pull/3739) simplifies the text of this warning.
* [#3778](https://github.com/leanprover/lean4/pull/3778) fixes [#3462](https://github.com/leanprover/lean4/issues/3462),
where info nodes from before the cursor would be used for computing completions.
* [#3985](https://github.com/leanprover/lean4/pull/3985) makes trace timings appear in Infoview.
### Pretty printing
* [#3797](https://github.com/leanprover/lean4/pull/3797) fixes the hovers over binders so that they show their types.
* [#3640](https://github.com/leanprover/lean4/pull/3640) and [#3735](https://github.com/leanprover/lean4/pull/3735): Adds attribute `@[pp_using_anonymous_constructor]` to make structures pretty print as `⟨x, y, z⟩`
rather than as `{a := x, b := y, c := z}`.
This attribute is applied to `Sigma`, `PSigma`, `PProd`, `Subtype`, `And`, and `Fin`.
* [#3749](https://github.com/leanprover/lean4/pull/3749)
Now structure instances pretty print with parent structures' fields inlined.
That is, if `B` extends `A`, then `{ toA := { x := 1 }, y := 2 }` now pretty prints as `{ x := 1, y := 2 }`.
Setting option `pp.structureInstances.flatten` to false turns this off.
* [#3737](https://github.com/leanprover/lean4/pull/3737), [#3744](https://github.com/leanprover/lean4/pull/3744)
and [#3750](https://github.com/leanprover/lean4/pull/3750):
Option `pp.structureProjections` is renamed to `pp.fieldNotation`, and there is now a suboption `pp.fieldNotation.generalized`
to enable pretty printing function applications using generalized field notation (defaults to true).
Field notation can be disabled on a function-by-function basis using the `@[pp_nodot]` attribute.
The notation is not used for theorems.
* [#4071](https://github.com/leanprover/lean4/pull/4071) fixes interaction between app unexpanders and `pp.fieldNotation.generalized`
* [#3625](https://github.com/leanprover/lean4/pull/3625) makes `delabConstWithSignature` (used by `#check`) have the ability to put arguments "after the colon"
to avoid printing inaccessible names.
* [#3798](https://github.com/leanprover/lean4/pull/3798),
[#3978](https://github.com/leanprover/lean4/pull/3978),
[#3798](https://github.com/leanprover/lean4/pull/3980):
Adds options `pp.mvars` (default: true) and `pp.mvars.withType` (default: false).
When `pp.mvars` is false, expression metavariables pretty print as `?_` and universe metavariables pretty print as `_`.
When `pp.mvars.withType` is true, expression metavariables pretty print with a type ascription.
These can be set when using `#guard_msgs` to make tests not depend on the particular names of metavariables.
* [#3917](https://github.com/leanprover/lean4/pull/3917) makes binders hoverable and gives them docstrings.
* [#4034](https://github.com/leanprover/lean4/pull/4034) makes hovers for RHS terms in `match` expressions in the Infoview reliably show the correct term.
### Library
* `Bool`/`Prop`
* [#3508](https://github.com/leanprover/lean4/pull/3508) improves `simp` confluence for `Bool` and `Prop` terms.
* Theorems: [#3604](https://github.com/leanprover/lean4/pull/3604)
* `Nat`
* [#3579](https://github.com/leanprover/lean4/pull/3579) makes `Nat.succ_eq_add_one` be a simp lemma, now that `induction`/`cases` uses `n + 1` instead of `Nat.succ n`.
* [#3808](https://github.com/leanprover/lean4/pull/3808) replaces `Nat.succ` simp rules with simprocs.
* [#3876](https://github.com/leanprover/lean4/pull/3876) adds faster `Nat.repr` implementation in C.
* `Int`
* Theorems: [#3890](https://github.com/leanprover/lean4/pull/3890)
* `UInt`s
* [#3960](https://github.com/leanprover/lean4/pull/3960) improves performance of upcasting.
* `Array` and `Subarray`
* [#3676](https://github.com/leanprover/lean4/pull/3676) removes `Array.eraseIdxAux`, `Array.eraseIdxSzAux`, and `Array.eraseIdx'`.
* [#3648](https://github.com/leanprover/lean4/pull/3648) simplifies `Array.findIdx?`.
* [#3851](https://github.com/leanprover/lean4/pull/3851) renames fields of `Subarray`.
* `List`
* [#3785](https://github.com/leanprover/lean4/pull/3785) upstreams tail-recursive List operations and `@[csimp]` lemmas.
* `BitVec`
* Theorems: [#3593](https://github.com/leanprover/lean4/pull/3593),
[#3593](https://github.com/leanprover/lean4/pull/3593), [#3597](https://github.com/leanprover/lean4/pull/3597),
[#3598](https://github.com/leanprover/lean4/pull/3598), [#3721](https://github.com/leanprover/lean4/pull/3721),
[#3729](https://github.com/leanprover/lean4/pull/3729), [#3880](https://github.com/leanprover/lean4/pull/3880),
[#4039](https://github.com/leanprover/lean4/pull/4039).
* [#3884](https://github.com/leanprover/lean4/pull/3884) protects `Std.BitVec`.
* `String`
* [#3832](https://github.com/leanprover/lean4/pull/3832) fixes `String.splitOn`.
* [#3959](https://github.com/leanprover/lean4/pull/3959) adds `String.Pos.isValid`.
* [#3959](https://github.com/leanprover/lean4/pull/3959) UTF-8 string validation.
* [#3961](https://github.com/leanprover/lean4/pull/3961) adds a model implementation for UTF-8 encoding and decoding.
* `IO`
* [#4097](https://github.com/leanprover/lean4/pull/4097) adds `IO.getTaskState` which returns whether a task is finished, actively running, or waiting on other Tasks to finish.
* **Refactors**
* [#3605](https://github.com/leanprover/lean4/pull/3605) reduces imports for `Init.Data.Nat` and `Init.Data.Int`.
* [#3613](https://github.com/leanprover/lean4/pull/3613) reduces imports for `Init.Omega.Int`.
* [#3634](https://github.com/leanprover/lean4/pull/3634) upstreams `Std.Data.Nat`
and [#3635](https://github.com/leanprover/lean4/pull/3635) upstreams `Std.Data.Int`.
* [#3790](https://github.com/leanprover/lean4/pull/3790) reduces more imports for `omega`.
* [#3694](https://github.com/leanprover/lean4/pull/3694) extends `GetElem` interface with `getElem!` and `getElem?` to simplify containers like `RBMap`.
* [#3865](https://github.com/leanprover/lean4/pull/3865) renames `Option.toMonad` (see breaking changes below).
* [#3882](https://github.com/leanprover/lean4/pull/3882) unifies `lexOrd` with `compareLex`.
* **Other fixes or improvements**
* [#3765](https://github.com/leanprover/lean4/pull/3765) makes `Quotient.sound` be a `theorem`.
* [#3645](https://github.com/leanprover/lean4/pull/3645) fixes `System.FilePath.parent` in the case of absolute paths.
* [#3660](https://github.com/leanprover/lean4/pull/3660) `ByteArray.toUInt64LE!` and `ByteArray.toUInt64BE!` were swapped.
* [#3881](https://github.com/leanprover/lean4/pull/3881), [#3887](https://github.com/leanprover/lean4/pull/3887) fix linearity issues in `HashMap.insertIfNew`, `HashSet.erase`, and `HashMap.erase`.
The `HashMap.insertIfNew` fix improves `import` performance.
* [#3830](https://github.com/leanprover/lean4/pull/3830) ensures linearity in `Parsec.many*Core`.
* [#3930](https://github.com/leanprover/lean4/pull/3930) adds `FS.Stream.isTty` field.
* [#3866](https://github.com/leanprover/lean4/pull/3866) deprecates `Option.toBool` in favor of `Option.isSome`.
* [#3975](https://github.com/leanprover/lean4/pull/3975) upstreams `Data.List.Init` and `Data.Array.Init` material from Std.
* [#3942](https://github.com/leanprover/lean4/pull/3942) adds instances that make `ac_rfl` work without Mathlib.
* [#4010](https://github.com/leanprover/lean4/pull/4010) changes `Fin.induction` to use structural induction.
* [02753f](https://github.com/leanprover/lean4/commit/02753f6e4c510c385efcbf71fa9a6bec50fce9ab)
fixes bug in `reduceLeDiff` simproc.
* [#4097](https://github.com/leanprover/lean4/pull/4097)
adds `IO.TaskState` and `IO.getTaskState` to get the task from the Lean runtime's task manager.
* **Docs:** [#3615](https://github.com/leanprover/lean4/pull/3615), [#3664](https://github.com/leanprover/lean4/pull/3664),
[#3707](https://github.com/leanprover/lean4/pull/3707), [#3734](https://github.com/leanprover/lean4/pull/3734),
[#3868](https://github.com/leanprover/lean4/pull/3868), [#3861](https://github.com/leanprover/lean4/pull/3861),
[#3869](https://github.com/leanprover/lean4/pull/3869), [#3858](https://github.com/leanprover/lean4/pull/3858),
[#3856](https://github.com/leanprover/lean4/pull/3856), [#3857](https://github.com/leanprover/lean4/pull/3857),
[#3867](https://github.com/leanprover/lean4/pull/3867), [#3864](https://github.com/leanprover/lean4/pull/3864),
[#3860](https://github.com/leanprover/lean4/pull/3860), [#3859](https://github.com/leanprover/lean4/pull/3859),
[#3871](https://github.com/leanprover/lean4/pull/3871), [#3919](https://github.com/leanprover/lean4/pull/3919).
### Lean internals
* **Defeq and WHNF algorithms**
* [#3616](https://github.com/leanprover/lean4/pull/3616) gives better support for reducing `Nat.rec` expressions.
* [#3774](https://github.com/leanprover/lean4/pull/3774) add tracing for "non-easy" WHNF cases.
* [#3807](https://github.com/leanprover/lean4/pull/3807) fixes an `isDefEq` performance issue, now trying structure eta *after* lazy delta reduction.
* [#3816](https://github.com/leanprover/lean4/pull/3816) fixes `.yesWithDeltaI` behavior to prevent increasing transparency level when reducing projections.
* [#3837](https://github.com/leanprover/lean4/pull/3837) improves heuristic at `isDefEq`.
* [#3965](https://github.com/leanprover/lean4/pull/3965) improves `isDefEq` for constraints of the form `t.i =?= s.i`.
* [#3977](https://github.com/leanprover/lean4/pull/3977) improves `isDefEqProj`.
* [#3981](https://github.com/leanprover/lean4/pull/3981) adds universe constraint approximations to be able to solve `u =?= max u ?v` using `?v = u`.
These approximations are only applied when universe constraints cannot be postponed anymore.
* [#4004](https://github.com/leanprover/lean4/pull/4004) improves `isDefEqProj` during typeclass resolution.
* [#4012](https://github.com/leanprover/lean4/pull/4012) adds `backward.isDefEq.lazyProjDelta` and `backward.isDefEq.lazyWhnfCore` backwards compatibility flags.
* **Kernel**
* [#3966](https://github.com/leanprover/lean4/pull/3966) removes dead code.
* [#4035](https://github.com/leanprover/lean4/pull/4035) fixes mismatch for `TheoremVal` between Lean and C++.
* **Discrimination trees**
* [423fed](https://github.com/leanprover/lean4/commit/423fed79a9de75705f34b3e8648db7e076c688d7)
and [3218b2](https://github.com/leanprover/lean4/commit/3218b25974d33e92807af3ce42198911c256ff1d):
simplify handling of dependent/non-dependent pi types.
* **Typeclass instance synthesis**
* [#3638](https://github.com/leanprover/lean4/pull/3638) eta-reduces synthesized instances
* [ce350f](https://github.com/leanprover/lean4/commit/ce350f348161e63fccde6c4a5fe1fd2070e7ce0f) fixes a linearity issue
* [917a31](https://github.com/leanprover/lean4/commit/917a31f694f0db44d6907cc2b1485459afe74d49)
improves performance by considering at most one answer for subgoals not containing metavariables.
[#4008](https://github.com/leanprover/lean4/pull/4008) adds `backward.synthInstance.canonInstances` backward compatibility flag.
* **Definition processing**
* [#3661](https://github.com/leanprover/lean4/pull/3661), [#3767](https://github.com/leanprover/lean4/pull/3767) changes automatically generated equational theorems to be named
using suffix `.eq_<idx>` instead of `._eq_<idx>`, and `.eq_def` instead of `._unfold`. (See breaking changes below.)
[#3675](https://github.com/leanprover/lean4/pull/3675) adds a mechanism to reserve names.
[#3803](https://github.com/leanprover/lean4/pull/3803) fixes reserved name resolution inside namespaces and fixes handling of `match`er declarations and equation lemmas.
* [#3662](https://github.com/leanprover/lean4/pull/3662) causes auxiliary definitions nested inside theorems to become `def`s if they are not proofs.
* [#4006](https://github.com/leanprover/lean4/pull/4006) makes proposition fields of `structure`s be theorems.
* [#4018](https://github.com/leanprover/lean4/pull/4018) makes it an error for a theorem to be `extern`.
* [#4047](https://github.com/leanprover/lean4/pull/4047) improves performance making equations for well-founded recursive definitions.
* **Refactors**
* [#3614](https://github.com/leanprover/lean4/pull/3614) avoids unfolding in `Lean.Meta.evalNat`.
* [#3621](https://github.com/leanprover/lean4/pull/3621) centralizes functionality for `Fix`/`GuessLex`/`FunInd` in the `ArgsPacker` module.
* [#3186](https://github.com/leanprover/lean4/pull/3186) rewrites the UnusedVariable linter to be more performant.
* [#3589](https://github.com/leanprover/lean4/pull/3589) removes coercion from `String` to `Name` (see breaking changes below).
* [#3237](https://github.com/leanprover/lean4/pull/3237) removes the `lines` field from `FileMap`.
* [#3951](https://github.com/leanprover/lean4/pull/3951) makes msg parameter to `throwTacticEx` optional.
* **Diagnostics**
* [#4016](https://github.com/leanprover/lean4/pull/4016), [#4019](https://github.com/leanprover/lean4/pull/4019),
[#4020](https://github.com/leanprover/lean4/pull/4020), [#4030](https://github.com/leanprover/lean4/pull/4030),
[#4031](https://github.com/leanprover/lean4/pull/4031),
[c3714b](https://github.com/leanprover/lean4/commit/c3714bdc6d46845c0428735b283c5b48b23cbcf7),
[#4049](https://github.com/leanprover/lean4/pull/4049) adds `set_option diagnostics true` for diagnostic counters.
Tracks number of unfolded declarations, instances, reducible declarations, used instances, recursor reductions,
`isDefEq` heuristic applications, among others.
This option is suggested in exceptional situations, such as at deterministic timeout and maximum recursion depth.
* [283587](https://github.com/leanprover/lean4/commit/283587987ab2eb3b56fbc3a19d5f33ab9e04a2ef)
adds diagnostic information for `simp`.
* [#4043](https://github.com/leanprover/lean4/pull/4043) adds diagnostic information for congruence theorems.
* [#4048](https://github.com/leanprover/lean4/pull/4048) display diagnostic information
for `set_option diagnostics true in <tactic>` and `set_option diagnostics true in <term>`.
* **Other features**
* [#3800](https://github.com/leanprover/lean4/pull/3800) adds environment extension to record which definitions use structural or well-founded recursion.
* [#3801](https://github.com/leanprover/lean4/pull/3801) `trace.profiler` can now export to Firefox Profiler.
* [#3918](https://github.com/leanprover/lean4/pull/3918), [#3953](https://github.com/leanprover/lean4/pull/3953) adds `@[builtin_doc]` attribute to make docs and location of a declaration available as a builtin.
* [#3939](https://github.com/leanprover/lean4/pull/3939) adds the `lean --json` CLI option to print messages as JSON.
* [#3075](https://github.com/leanprover/lean4/pull/3075) improves `test_extern` command.
* [#3970](https://github.com/leanprover/lean4/pull/3970) gives monadic generalization of `FindExpr`.
* **Docs:** [#3743](https://github.com/leanprover/lean4/pull/3743), [#3921](https://github.com/leanprover/lean4/pull/3921),
[#3954](https://github.com/leanprover/lean4/pull/3954).
* **Other fixes:** [#3622](https://github.com/leanprover/lean4/pull/3622),
[#3726](https://github.com/leanprover/lean4/pull/3726), [#3823](https://github.com/leanprover/lean4/pull/3823),
[#3897](https://github.com/leanprover/lean4/pull/3897), [#3964](https://github.com/leanprover/lean4/pull/3964),
[#3946](https://github.com/leanprover/lean4/pull/3946), [#4007](https://github.com/leanprover/lean4/pull/4007),
[#4026](https://github.com/leanprover/lean4/pull/4026).
### Compiler, runtime, and FFI
* [#3632](https://github.com/leanprover/lean4/pull/3632) makes it possible to allocate and free thread-local runtime resources for threads not started by Lean itself.
* [#3627](https://github.com/leanprover/lean4/pull/3627) improves error message about compacting closures.
* [#3692](https://github.com/leanprover/lean4/pull/3692) fixes deadlock in `IO.Promise.resolve`.
* [#3753](https://github.com/leanprover/lean4/pull/3753) catches error code from `MoveFileEx` on Windows.
* [#4028](https://github.com/leanprover/lean4/pull/4028) fixes a double `reset` bug in `ResetReuse` transformation.
* [6e731b](https://github.com/leanprover/lean4/commit/6e731b4370000a8e7a5cfb675a7f3d7635d21f58)
removes `interpreter` copy constructor to avoid potential memory safety issues.
### Lake
* **TOML Lake configurations**. [#3298](https://github.com/leanprover/lean4/pull/3298), [#4104](https://github.com/leanprover/lean4/pull/4104).
Lake packages can now use TOML as a alternative configuration file format instead of Lean. If the default `lakefile.lean` is missing, Lake will also look for a `lakefile.toml`. The TOML version of the configuration supports a restricted set of the Lake configuration options, only including those which can easily mapped to a TOML data structure. The TOML syntax itself fully compiles with the TOML v1.0.0 specification.
As part of the introduction of this new feature, we have been helping maintainers of some major packages within the ecosystem switch to this format. For example, the following is Aesop's new `lakefile.toml`:
**[leanprover-community/aesop/lakefile.toml](https://raw.githubusercontent.com/leanprover-community/aesop/de11e0ecf372976e6d627c210573146153090d2d/lakefile.toml)**
```toml
name = "aesop"
defaultTargets = ["Aesop"]
testRunner = "test"
precompileModules = false
[[require]]
name = "batteries"
git = "https://github.com/leanprover-community/batteries"
rev = "main"
[[lean_lib]]
name = "Aesop"
[[lean_lib]]
name = "AesopTest"
globs = ["AesopTest.+"]
leanOptions = {linter.unusedVariables = false}
[[lean_exe]]
name = "test"
srcDir = "scripts"
```
To assist users who wish to transition their packages between configuration file formats, there is also a new `lake translate-config` command for migrating to/from TOML.
Running `lake translate-config toml` will produce a `lakefile.toml` version of a package's `lakefile.lean`. Any configuration options unsupported by the TOML format will be discarded during translation, but the original `lakefile.lean` will remain so that you can verify the translation looks good before deleting it.
* **Build progress overhaul.** [#3835](https://github.com/leanprover/lean4/pull/3835), [#4115](https://github.com/leanprover/lean4/pull/4115), [#4127](https://github.com/leanprover/lean4/pull/4127), [#4220](https://github.com/leanprover/lean4/pull/4220), [#4232](https://github.com/leanprover/lean4/pull/4232), [#4236](https://github.com/leanprover/lean4/pull/4236).
Builds are now managed by a top-level Lake build monitor, this makes the output of Lake builds more standardized and enables producing prettier and more configurable progress reports.
As part of this change, job isolation has improved. Stray I/O and other build related errors in custom targets are now properly isolated and caught as part of their job. Import errors no longer cause Lake to abort the entire build and are instead localized to the build jobs of the modules in question.
Lake also now uses ANSI escape sequences to add color and produce progress lines that update in-place; this can be toggled on and off using `--ansi` / `--no-ansi`.
`--wfail` and `--iofail` options have been added that causes a build to fail if any of the jobs log a warning (`--wfail`) or produce any output or log information messages (`--iofail`). Unlike some other build systems, these options do **NOT** convert these logs into errors, and Lake does not abort jobs on such a log (i.e., dependent jobs will still continue unimpeded).
* `lake test`. [#3779](https://github.com/leanprover/lean4/pull/3779).
Lake now has a built-in `test` command which will run a script or executable labelled `@[test_runner]` (in Lean) or defined as the `testRunner` (in TOML) in the root package.
Lake also provides a `lake check-test` command which will exit with code `0` if the package has a properly configured test runner or error with `1` otherwise.
* `lake lean`. [#3793](https://github.com/leanprover/lean4/pull/3793).
The new command `lake lean <file> [-- <args...>]` functions like `lake env lean <file> <args...>`, except that it builds the imports of `file` before running `lean`. This makes it very useful for running test or example code that imports modules that are not guaranteed to have been built beforehand.
* **Miscellaneous bug fixes and improvements**
* [#3609](https://github.com/leanprover/lean4/pull/3609) `LEAN_GITHASH` environment variable to override the detected Git hash for Lean when computing traces, useful for testing custom builds of Lean.
* [#3795](https://github.com/leanprover/lean4/pull/3795) improves relative package directory path normalization in the pre-rename check.
* [#3957](https://github.com/leanprover/lean4/pull/3957) fixes handling of packages that appear multiple times in a dependency tree.
* [#3999](https://github.com/leanprover/lean4/pull/3999) makes it an error for there to be a mismatch between a package name and what it is required as. Also adds a special message for the `std`-to-`batteries` rename.
* [#4033](https://github.com/leanprover/lean4/pull/4033) fixes quiet mode.
* **Docs:** [#3704](https://github.com/leanprover/lean4/pull/3704).
### DevOps
* [#3536](https://github.com/leanprover/lean4/pull/3536) and [#3833](https://github.com/leanprover/lean4/pull/3833)
add a checklist for the release process.
* [#3600](https://github.com/leanprover/lean4/pull/3600) runs nix-ci more uniformly.
* [#3612](https://github.com/leanprover/lean4/pull/3612) avoids argument limits when building on Windows.
* [#3682](https://github.com/leanprover/lean4/pull/3682) builds Lean's `.o` files in parallel to rest of core.
* [#3601](https://github.com/leanprover/lean4/pull/3601)
changes the way Lean is built on Windows (see breaking changes below).
As a result, Lake now dynamically links executables with `supportInterpreter := true` on Windows
to `libleanshared.dll` and `libInit_shared.dll`. Therefore, such executables will not run
unless those shared libraries are co-located with the executables or part of `PATH`.
Running the executable via `lake exe` will ensure these libraries are part of `PATH`.
In a related change, the signature of the `nativeFacets` Lake configuration options has changed
from a static `Array` to a function `(shouldExport : Bool) → Array`.
See its docstring or Lake's [README](src/lake/README.md) for further details on the changed option.
* [#3690](https://github.com/leanprover/lean4/pull/3690) marks "Build matrix complete" as canceled if the build is canceled.
* [#3700](https://github.com/leanprover/lean4/pull/3700), [#3702](https://github.com/leanprover/lean4/pull/3702),
[#3701](https://github.com/leanprover/lean4/pull/3701), [#3834](https://github.com/leanprover/lean4/pull/3834),
[#3923](https://github.com/leanprover/lean4/pull/3923): fixes and improvements for std and mathlib CI.
* [#3712](https://github.com/leanprover/lean4/pull/3712) fixes `nix build .` on macOS.
* [#3717](https://github.com/leanprover/lean4/pull/3717) replaces `shell.nix` in devShell with `flake.nix`.
* [#3715](https://github.com/leanprover/lean4/pull/3715) and [#3790](https://github.com/leanprover/lean4/pull/3790) add test result summaries.
* [#3971](https://github.com/leanprover/lean4/pull/3971) prevents stage0 changes via the merge queue.
* [#3979](https://github.com/leanprover/lean4/pull/3979) adds handling for `changes-stage0` label.
* [#3952](https://github.com/leanprover/lean4/pull/3952) adds a script to summarize GitHub issues.
* [18a699](https://github.com/leanprover/lean4/commit/18a69914da53dbe37c91bc2b9ce65e1dc01752b6)
fixes asan linking
### Breaking changes
* Due to the major Lake build refactor, code using the affected parts of the Lake API or relying on the previous output format of Lake builds is likely to have been broken. We have tried to minimize the breakages and, where possible, old definitions have been marked `@[deprecated]` with a reference to the new alternative.
* Executables configured with `supportInterpreter := true` on Windows should now be run via `lake exe` to function properly.
* Automatically generated equational theorems are now named using suffix `.eq_<idx>` instead of `._eq_<idx>`, and `.eq_def` instead of `._unfold`. Example:
```
def fact : Nat → Nat
| 0 => 1
| n+1 => (n+1) * fact n
theorem ex : fact 0 = 1 := by unfold fact; decide
#check fact.eq_1
-- fact.eq_1 : fact 0 = 1
#check fact.eq_2
-- fact.eq_2 (n : Nat) : fact (Nat.succ n) = (n + 1) * fact n
#check fact.eq_def
/-
fact.eq_def :
∀ (x : Nat),
fact x =
match x with
| 0 => 1
| Nat.succ n => (n + 1) * fact n
-/
```
* The coercion from `String` to `Name` was removed. Previously, it was `Name.mkSimple`, which does not separate strings at dots, but experience showed that this is not always the desired coercion. For the previous behavior, manually insert a call to `Name.mkSimple`.
* The `Subarray` fields `as`, `h₁` and `h₂` have been renamed to `array`, `start_le_stop`, and `stop_le_array_size`, respectively. This more closely follows standard Lean conventions. Deprecated aliases for the field projections were added; these will be removed in a future release.
* The change to the instance name algorithm (described above) can break projects that made use of the auto-generated names.
* `Option.toMonad` has been renamed to `Option.getM` and the unneeded `[Monad m]` instance argument has been removed.
v4.7.0
---------

9
default.nix Normal file
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@@ -0,0 +1,9 @@
# used for `nix-shell https://github.com/leanprover/lean4/archive/master.tar.gz -A nix`
{ nix = (import ./shell.nix {}).nix; } //
(import (
fetchTarball {
url = "https://github.com/edolstra/flake-compat/archive/c75e76f80c57784a6734356315b306140646ee84.tar.gz";
sha256 = "071aal00zp2m9knnhddgr2wqzlx6i6qa1263lv1y7bdn2w20h10h"; }
) {
src = ./.;
}).defaultNix

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@@ -1,4 +1,4 @@
open Batteries
open Std
open Lean
inductive BoolExpr where

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@@ -1,11 +1 @@
# Characters
A value of type `Char`, also known as a character, is a [Unicode scalar value](https://www.unicode.org/glossary/#unicode_scalar_value). It is represented using an unsigned 32-bit integer and is statically guaranteed to be a valid Unicode scalar value.
Syntactically, character literals are enclosed in single quotes.
```lean
#eval 'a' -- 'a'
#eval '' -- '∀'
```
Characters are ordered and can be decidably compared using the relational operators `=`, `<`, `≤`, `>`, `≥`.

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@@ -75,28 +75,26 @@ The github repository will automatically update stage0 on `master` once
If you have write access to the lean4 repository, you can also also manually
trigger that process, for example to be able to use new features in the compiler itself.
You can do that on <https://github.com/leanprover/lean4/actions/workflows/update-stage0.yml>
You can do that on <https://github.com/nomeata/lean4/actions/workflows/update-stage0.yml>
or using Github CLI with
```
gh workflow run update-stage0.yml
```
Leaving stage0 updates to the CI automation is preferable, but should you need
to do it locally, you can use `make update-stage0-commit` in `build/release` to
update `stage0` from `stage1` or `make -C stageN update-stage0-commit` to
update from another stage. This command will automatically stage the updated files
and introduce a commit,so make sure to commit your work before that.
If you rebased the branch (either onto a newer version of `master`, or fixing
up some commits prior to the stage0 update, recreate the stage0 update commits.
The script `script/rebase-stage0.sh` can be used for that.
The CI should prevent PRs with changes to stage0 (besides `stdlib_flags.h`)
from entering `master` through the (squashing!) merge queue, and label such PRs
with the `changes-stage0` label. Such PRs should have a cleaned up history,
with separate stage0 update commits; then coordinate with the admins to merge
your PR using rebase merge, bypassing the merge queue.
Leaving stage0 updates to the CI automation is preferrable, but should you need
to do it locally, you can use `make update-stage0` in `build/release`, to
update `stage0` from `stage1`, `make -C stageN update-stage0` to update from
another stage, or `nix run .#update-stage0-commit` to update using nix.
Updates to `stage0` should be their own commits in the Git history. So should
you have to include the stage0 update in your PR (rather than using above
automation after merging changes), commit your work before running `make
update-stage0`, commit the updated `stage0` compiler code with the commit
message:
```
chore: update stage0
```
and coordinate with the admins to not squash your PR.
## Further Bootstrapping Complications

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@@ -53,59 +53,10 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
Its runtime value is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number (`lean_box`/`lean_unbox`).
* A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
* Any other type is represented by `lean_object *`.
Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
Its runtime value is a pointer to an object of a subtype of `lean_object` (see respective declarations in `lean.h`) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
Example: the runtime value of `u : Unit` is always `lean_box(0)`.
#### Inductive types
For inductive types which are in the fallback `lean_object *` case above and not trivial constructors, the type is stored as a `lean_ctor_object`, and `lean_is_ctor` will return true. A `lean_ctor_object` stores the constructor index in the header, and the fields are stored in the `m_objs` portion of the object.
The memory order of the fields is derived from the types and order of the fields in the declaration. They are ordered as follows:
* Non-scalar fields stored as `lean_object *`
* Fields of type `USize`
* Other scalar fields, in decreasing order by size
Within each group the fields are ordered in declaration order. **Warning**: Trivial wrapper types still count toward a field being treated as non-scalar for this purpose.
* To access fields of the first kind, use `lean_ctor_get(val, i)` to get the `i`th non-scalar field.
* To access `USize` fields, use `lean_ctor_get_usize(val, n+i)` to get the `i`th usize field and `n` is the total number of fields of the first kind.
* To access other scalar fields, use `lean_ctor_get_uintN(val, off)` or `lean_ctor_get_usize(val, off)` as appropriate. Here `off` is the byte offset of the field in the structure, starting at `n*sizeof(void*)` where `n` is the number of fields of the first two kinds.
For example, a structure such as
```lean
structure S where
ptr_1 : Array Nat
usize_1 : USize
sc64_1 : UInt64
ptr_2 : { x : UInt64 // x > 0 } -- wrappers don't count as scalars
sc64_2 : Float -- `Float` is 64 bit
sc8_1 : Bool
sc16_1 : UInt16
sc8_2 : UInt8
sc64_3 : UInt64
usize_2 : USize
ptr_3 : Char -- trivial wrapper around `UInt32`
sc32_1 : UInt32
sc16_2 : UInt16
```
would get re-sorted into the following memory order:
* `S.ptr_1` - `lean_ctor_get(val, 0)`
* `S.ptr_2` - `lean_ctor_get(val, 1)`
* `S.ptr_3` - `lean_ctor_get(val, 2)`
* `S.usize_1` - `lean_ctor_get_usize(val, 3)`
* `S.usize_2` - `lean_ctor_get_usize(val, 4)`
* `S.sc64_1` - `lean_ctor_get_uint64(val, sizeof(void*)*5)`
* `S.sc64_2` - `lean_ctor_get_float(val, sizeof(void*)*5 + 8)`
* `S.sc64_3` - `lean_ctor_get_uint64(val, sizeof(void*)*5 + 16)`
* `S.sc32_1` - `lean_ctor_get_uint32(val, sizeof(void*)*5 + 24)`
* `S.sc16_1` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 28)`
* `S.sc16_2` - `lean_ctor_get_uint16(val, sizeof(void*)*5 + 30)`
* `S.sc8_1` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 32)`
* `S.sc8_2` - `lean_ctor_get_uint8(val, sizeof(void*)*5 + 33)`
### Borrowing
By default, all `lean_object *` parameters of an `@[extern]` function are considered *owned*, i.e. the external code is passed a "virtual RC token" and is responsible for passing this token along to another consuming function (exactly once) or freeing it via `lean_dec`.
@@ -160,15 +111,6 @@ if (lean_io_result_is_ok(res)) {
lean_io_mark_end_initialization();
```
In addition, any other thread not spawned by the Lean runtime itself must be initialized for Lean use by calling
```c
void lean_initialize_thread();
```
and should be finalized in order to free all thread-local resources by calling
```c
void lean_finalize_thread();
```
## `@[extern]` in the Interpreter
The interpreter can run Lean declarations for which symbols are available in loaded shared libraries, which includes `@[extern]` declarations.

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@@ -5,8 +5,7 @@ See below for the checklist for release candidates.
We'll use `v4.6.0` as the intended release version as a running example.
- One week before the planned release, ensure that (1) someone has written the release notes and (2) someone has written the first draft of the release blog post.
If there is any material in `./releases_drafts/`, then the release notes are not done. (See the section "Writing the release notes".)
- One week before the planned release, ensure that someone has written the first draft of the release blog post
- `git checkout releases/v4.6.0`
(This branch should already exist, from the release candidates.)
- `git pull`
@@ -14,8 +13,15 @@ We'll use `v4.6.0` as the intended release version as a running example.
- `set(LEAN_VERSION_MINOR 6)` (for whichever `6` is appropriate)
- `set(LEAN_VERSION_IS_RELEASE 1)`
- (both of these should already be in place from the release candidates)
- It is possible that the `v4.6.0` section of `RELEASES.md` is out of sync between
`releases/v4.6.0` and `master`. This should be reconciled:
- Run `git diff master RELEASES.md`.
- You should expect to see additons on `master` in the `v4.7.0-rc1` section; ignore these.
(i.e. the new release notes for the upcoming release candidate).
- Reconcile discrepancies in the `v4.6.0` section,
usually via copy and paste and a commit to `releases/v4.6.0`.
- `git tag v4.6.0`
- `git push $REMOTE v4.6.0`, where `$REMOTE` is the upstream Lean repository (e.g., `origin`, `upstream`)
- `git push origin v4.6.0`
- Now wait, while CI runs.
- You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`,
looking for the `v4.6.0` tag.
@@ -24,85 +30,56 @@ We'll use `v4.6.0` as the intended release version as a running example.
you may want to start on the release candidate checklist now.
- Go to https://github.com/leanprover/lean4/releases and verify that the `v4.6.0` release appears.
- Edit the release notes on Github to select the "Set as the latest release".
- Follow the instructions in creating a release candidate for the "GitHub release notes" step,
now that we have a written `RELEASES.md` section.
Do a quick sanity check.
- Copy and paste the Github release notes from the previous releases candidate for this version
(e.g. `v4.6.0-rc1`), and quickly sanity check.
- Next, we will move a curated list of downstream repos to the latest stable release.
- For each of the repositories listed below:
- Make a PR to `master`/`main` changing the toolchain to `v4.6.0`
- Update the toolchain file
- In the Lakefile, if there are dependencies on specific version tags of dependencies that you've already pushed as part of this process, update them to the new tag.
If they depend on `main` or `master`, don't change this; you've just updated the dependency, so it will work and be saved in the manifest
- Run `lake update`
- The PR title should be "chore: bump toolchain to v4.6.0".
- Merge the PR once CI completes.
- Create the tag `v4.6.0` from `master`/`main` and push it.
- Merge the tag `v4.6.0` into the `stable` branch and push it.
- Make a PR to `master`/`main` changing the toolchain to `v4.6.0`.
The PR title should be "chore: bump toolchain to v4.6.0".
Since the `v4.6.0` release should be functionally identical to the last release candidate,
which the repository should already be on, this PR is a no-op besides changing the toolchain.
- Once this is merged, create the tag `v4.6.0` from `master`/`main` and push it.
- Merge the tag `v4.6.0` into the stable branch.
- We do this for the repositories:
- [lean4checker](https://github.com/leanprover/lean4checker)
- No dependencies
- Toolchain bump PR
- Create and push the tag
- Merge the tag into `stable`
- [Batteries](https://github.com/leanprover-community/batteries)
- No dependencies
- Toolchain bump PR
- Create and push the tag
- Merge the tag into `stable`
- `lean4checker` uses a different version tagging scheme: use `toolchain/v4.6.0` rather than `v4.6.0`.
- [Std](https://github.com/leanprover-community/repl)
- [ProofWidgets4](https://github.com/leanprover-community/ProofWidgets4)
- Dependencies: `Batteries`
- Note on versions and branches:
- `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
which does not refer to the toolchain being used.
- Make a new release in this sequence after merging the toolchain bump PR.
- `ProofWidgets` does not maintain a `stable` branch.
- Toolchain bump PR
- Create and push the tag, following the version convention of the repository
- `ProofWidgets` uses a sequential version tagging scheme, e.g. `v0.0.29`,
which does not refer to the toolchain being used.
- Make a new release in this sequence after merging the toolchain bump PR.
- `ProofWidgets` does not maintain a `stable` branch.
- [Aesop](https://github.com/leanprover-community/aesop)
- Dependencies: `Batteries`
- Toolchain bump PR including updated Lake manifest
- Create and push the tag
- Merge the tag into `stable`
- [doc-gen4](https://github.com/leanprover/doc-gen4)
- Dependencies: exist, but they're not part of the release workflow
- Toolchain bump PR including updated Lake manifest
- Create and push the tag
- There is no `stable` branch; skip this step
- [import-graph](https://github.com/leanprover-community/import-graph)
- Toolchain bump PR including updated Lake manifest
- Create and push the tag
- There is no `stable` branch; skip this step
- [Mathlib](https://github.com/leanprover-community/mathlib4)
- Dependencies: `Aesop`, `ProofWidgets4`, `lean4checker`, `Batteries`, `doc-gen4`, `import-graph`
- Toolchain bump PR notes:
- In addition to updating the `lean-toolchain` and `lakefile.lean`,
in `.github/workflows/lean4checker.yml` update the line
`git checkout v4.6.0` to the appropriate tag.
- Push the PR branch to the main Mathlib repository rather than a fork, or CI may not work reliably
- Create and push the tag
- Create a new branch from the tag, push it, and open a pull request against `stable`.
Coordinate with a Mathlib maintainer to get this merged.
- In addition to updating the `lean-toolchain` and `lakefile.lean`,
in `.github/workflows/build.yml.in` in the `lean4checker` section update the line
`git checkout toolchain/v4.6.0` to the appropriate tag,
and then run `.github/workflows/mk_build_yml.sh`.
- [REPL](https://github.com/leanprover-community/repl)
- Dependencies: `Mathlib` (for test code)
- Note that there are two copies of `lean-toolchain`/`lakefile.lean`:
in the root, and in `test/Mathlib/`. Edit both, and run `lake update` in both directories.
- Toolchain bump PR including updated Lake manifest
- Create and push the tag
- Merge the tag into `stable`
- The `v4.6.0` section of `RELEASES.md` is out of sync between
`releases/v4.6.0` and `master`. This should be reconciled:
- Replace the `v4.6.0` section on `master` with the `v4.6.0` section on `releases/v4.6.0`
and commit this to `master`.
in the root, and in `test/Mathlib/`.
- Note that there are dependencies between these packages:
you should update the lakefile so that you are using the `v4.6.0` tag of upstream repositories
(or the sequential tag for `ProofWidgets4`), and run `lake update` before committing.
- This means that this process is sequential; each repository must have its bump PR merged,
and the new tag pushed, before you can make the PR for the downstream repositories.
- `lean4checker` has no dependencies
- `Std` has no dependencies
- `Aesop` depends on `Std`
- `ProofWidgets4` depends on `Std`
- `Mathlib` depends on `Aesop`, `ProofWidgets4`, and `lean4checker` (and transitively on `Std`)
- `REPL` depends on `Mathlib` (this dependency is only for testing).
- Merge the release announcement PR for the Lean website - it will be deployed automatically
- Finally, make an announcement!
This should go in https://leanprover.zulipchat.com/#narrow/stream/113486-announce, with topic `v4.6.0`.
Please see previous announcements for suggested language.
You will want a few bullet points for main topics from the release notes.
Link to the blog post from the Zulip announcement.
- Make sure that whoever is handling social media knows the release is out.
Please also make sure that whoever is handling social media knows the release is out.
## Optimistic(?) time estimates:
- Initial checks and push the tag: 30 minutes.
- Note that if `RELEASES.md` has discrepancies this could take longer!
- Waiting for the release: 60 minutes.
- Fixing release notes: 10 minutes.
- Bumping toolchains in downstream repositories, up to creating the Mathlib PR: 30 minutes.
@@ -118,8 +95,8 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
- Decide which nightly release you want to turn into a release candidate.
We will use `nightly-2024-02-29` in this example.
- It is essential that Batteries and Mathlib already have reviewed branches compatible with this nightly.
- Check that both Batteries and Mathlib's `bump/v4.7.0` branch contain `nightly-2024-02-29`
- It is essential that Std and Mathlib already have reviewed branches compatible with this nightly.
- Check that both Std and Mathlib's `bump/v4.7.0` branch contain `nightly-2024-02-29`
in their `lean-toolchain`.
- The steps required to reach that state are beyond the scope of this checklist, but see below!
- Create the release branch from this nightly tag:
@@ -129,26 +106,29 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
git checkout nightly-2024-02-29
git checkout -b releases/v4.7.0
```
- In `RELEASES.md` replace `Development in progress` in the `v4.7.0` section with `Release notes to be written.`
- We will rely on automatically generated release notes for release candidates,
and the written release notes will be used for stable versions only.
It is essential to choose the nightly that will become the release candidate as early as possible, to avoid confusion.
- In `RELEASES.md` remove `(development in progress)` from the `v4.7.0` section header.
- Our current goal is to have written release notes only about major language features or breaking changes,
and to rely on automatically generated release notes for bugfixes and minor changes.
- Do not wait on `RELEASES.md` being perfect before creating the `release/v4.7.0` branch. It is essential to choose the nightly which will become the release candidate as early as possible, to avoid confusion.
- If there are major changes not reflected in `RELEASES.md` already, you may need to solicit help from the authors.
- Minor changes and bug fixes do not need to be documented in `RELEASES.md`: they will be added automatically on the Github release page.
- Commit your changes to `RELEASES.md`, and push.
- Remember that changes to `RELEASES.md` after you have branched `releases/v4.7.0` should also be cherry-picked back to `master`.
- In `src/CMakeLists.txt`,
- verify that you see `set(LEAN_VERSION_MINOR 7)` (for whichever `7` is appropriate); this should already have been updated when the development cycle began.
- `set(LEAN_VERSION_IS_RELEASE 1)` (this should be a change; on `master` and nightly releases it is always `0`).
- Commit your changes to `src/CMakeLists.txt`, and push.
- `git tag v4.7.0-rc1`
- `git push origin v4.7.0-rc1`
- Ping the FRO Zulip that release notes need to be written. The release notes do not block completing the rest of this checklist.
- Now wait, while CI runs.
- You can monitor this at `https://github.com/leanprover/lean4/actions/workflows/ci.yml`, looking for the `v4.7.0-rc1` tag.
- This step can take up to an hour.
- (GitHub release notes) Once the release appears at https://github.com/leanprover/lean4/releases/
- Once the release appears at https://github.com/leanprover/lean4/releases/
- Edit the release notes on Github to select the "Set as a pre-release box".
- If release notes have been written already, copy the section of `RELEASES.md` for this version into the Github release notes
and use the title "Changes since v4.6.0 (from RELEASES.md)".
- Otherwise, in the "previous tag" dropdown, select `v4.6.0`, and click "Generate release notes".
This will add a list of all the commits since the last stable version.
- Copy the section of `RELEASES.md` for this version into the Github release notes.
- Use the title "Changes since v4.6.0 (from RELEASES.md)"
- Then in the "previous tag" dropdown, select `v4.6.0`, and click "Generate release notes".
- This will add a list of all the commits since the last stable version.
- Delete anything already mentioned in the hand-written release notes above.
- Delete "update stage0" commits, and anything with a completely inscrutable commit message.
- Briefly rearrange the remaining items by category (e.g. `simp`, `lake`, `bug fixes`),
@@ -174,10 +154,7 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
- We do this for the same list of repositories as for stable releases, see above.
As above, there are dependencies between these, and so the process above is iterative.
It greatly helps if you can merge the `bump/v4.7.0` PRs yourself!
It is essential for Mathlib CI that you then create the next `bump/v4.8.0` branch
for the next development cycle.
Set the `lean-toolchain` file on this branch to same `nightly` you used for this release.
- For Batteries/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
- For Std/Aesop/Mathlib, which maintain a `nightly-testing` branch, make sure there is a tag
`nightly-testing-2024-02-29` with date corresponding to the nightly used for the release
(create it if not), and then on the `nightly-testing` branch `git reset --hard master`, and force push.
- Make an announcement!
@@ -187,17 +164,8 @@ We'll use `v4.7.0-rc1` as the intended release version in this example.
Please also make sure that whoever is handling social media knows the release is out.
- Begin the next development cycle (i.e. for `v4.8.0`) on the Lean repository, by making a PR that:
- Updates `src/CMakeLists.txt` to say `set(LEAN_VERSION_MINOR 8)`
- Replaces the "development in progress" in the `v4.7.0` section of `RELEASES.md` with
```
Release candidate, release notes will be copied from `branch releases/v4.7.0` once completed.
```
and inserts the following section before that section:
```
v4.8.0
----------
Development in progress.
```
- Removes all the entries from the `./releases_drafts/` folder.
- Removes `(in development)` from the section heading in `RELEASES.md` for `v4.7.0`,
and creates a new `v4.8.0 (in development)` section heading.
## Time estimates:
Slightly longer than the corresponding steps for a stable release.
@@ -208,7 +176,7 @@ In particular, updating the downstream repositories is significantly more work
# Preparing `bump/v4.7.0` branches
While not part of the release process per se,
this is a brief summary of the work that goes into updating Batteries/Aesop/Mathlib to new versions.
this is a brief summary of the work that goes into updating Std/Aesop/Mathlib to new versions.
Please read https://leanprover-community.github.io/contribute/tags_and_branches.html
@@ -231,18 +199,3 @@ Please read https://leanprover-community.github.io/contribute/tags_and_branches.
* It is always okay to merge in the following directions:
`master` -> `bump/v4.7.0` -> `bump/nightly-2024-02-15` -> `nightly-testing`.
Please remember to push any merges you make to intermediate steps!
# Writing the release notes
We are currently trying a system where release notes are compiled all at once from someone looking through the commit history.
The exact steps are a work in progress.
Here is the general idea:
* The work is done right on the `releases/v4.6.0` branch sometime after it is created but before the stable release is made.
The release notes for `v4.6.0` will be copied to `master`.
* There can be material for release notes entries in commit messages.
* There can also be pre-written entries in `./releases_drafts`, which should be all incorporated in the release notes and then deleted from the branch.
See `./releases_drafts/README.md` for more information.
* The release notes should be written from a downstream expert user's point of view.
This section will be updated when the next release notes are written (for `v4.10.0`).

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

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

View File

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

View File

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

View File

@@ -1 +0,0 @@
build

View File

@@ -1,4 +1,4 @@
#!/usr/bin/env bash
source ../../tests/common.sh
exec_check lean -Dlinter.all=false "$f"
exec_check lean -j 0 -Dlinter.all=false "$f"

View File

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

100
doc/latex/lean4.py Normal file
View File

@@ -0,0 +1,100 @@
# -*- coding: utf-8 -*-
"""
pygments.lexers.theorem
~~~~~~~~~~~~~~~~~~~~~~~
Lexers for theorem-proving languages.
:copyright: Copyright 2006-2017 by the Pygments team, see AUTHORS.
:license: BSD, see LICENSE for details.
"""
import re
from pygments.lexer import RegexLexer, default, words
from pygments.token import Text, Comment, Operator, Keyword, Name, String, \
Number, Punctuation, Generic
__all__ = ['Lean4Lexer']
class Lean4Lexer(RegexLexer):
"""
For the `Lean 4 <https://github.com/leanprover/lean4>`_
theorem prover.
.. versionadded:: 2.0
"""
name = 'Lean4'
aliases = ['lean4']
filenames = ['*.lean']
mimetypes = ['text/x-lean']
flags = re.MULTILINE | re.UNICODE
keywords1 = (
'import', 'abbreviation', 'opaque_hint', 'tactic_hint', 'definition',
'renaming', 'inline', 'hiding', 'parameter', 'lemma', 'variable',
'theorem', 'axiom', 'inductive', 'structure', 'universe', 'alias',
'help', 'options', 'precedence', 'postfix', 'prefix',
'infix', 'infixl', 'infixr', 'notation', '#eval',
'#check', '#reduce', '#exit', 'coercion', 'end', 'private', 'using', 'namespace',
'including', 'instance', 'section', 'context', 'protected', 'expose',
'export', 'set_option', 'extends', 'open', 'example',
'constant', 'constants', 'print', 'opaque', 'reducible', 'irreducible',
'def', 'macro', 'elab', 'syntax', 'macro_rules', 'reduce', 'where',
'abbrev', 'noncomputable', 'class', 'attribute', 'synth', 'mutual',
)
keywords2 = (
'forall', 'fun', 'Pi', 'obtain', 'from', 'have', 'show', 'assume',
'take', 'let', 'if', 'else', 'then', 'by', 'in', 'with', 'begin',
'proof', 'qed', 'calc', 'match', 'nomatch', 'do', 'at',
)
keywords3 = (
# Sorts
'Type', 'Prop', 'Sort',
)
operators = (
u'!=', u'#', u'&', u'&&', u'*', u'+', u'-', u'/', u'@', u'!', u'`',
u'-.', u'->', u'.', u'..', u'...', u'::', u':>', u';', u';;', u'<',
u'<-', u'=', u'==', u'>', u'_', u'|', u'||', u'~', u'=>', u'<=', u'>=',
u'/\\', u'\\/', u'', u'Π', u'λ', u'', u'', u'', u'', u'', u'',
u'¬', u'⁻¹', u'', u'', u'', u'', u'', u'', u'', u'×', u'',
u'', u'', u'', u'',
)
punctuation = (u'(', u')', u':', u'{', u'}', u'[', u']', u'', u'',
u':=', u',')
tokens = {
'root': [
(r'\s+', Text),
(r'/-', Comment, 'comment'),
(r'--.*?$', Comment.Single),
(words(keywords1, prefix=r'\b', suffix=r'\b'), Keyword.Namespace),
(words(keywords2, prefix=r'\b', suffix=r'\b'), Keyword),
(words(keywords3, prefix=r'\b', suffix=r'\b'), Keyword.Type),
(words(operators), Name.Builtin.Pseudo),
(words(punctuation), Operator),
(u"[A-Za-z_\u03b1-\u03ba\u03bc-\u03fb\u1f00-\u1ffe\u2100-\u214f]"
u"[A-Za-z_'\u03b1-\u03ba\u03bc-\u03fb\u1f00-\u1ffe\u2070-\u2079"
u"\u207f-\u2089\u2090-\u209c\u2100-\u214f0-9]*", Name),
(r'\d+', Number.Integer),
(r'"', String.Double, 'string'),
(r'[~?][a-z][\w\']*:', Name.Variable)
],
'comment': [
# Multiline Comments
(r'[^/-]', Comment.Multiline),
(r'/-', Comment.Multiline, '#push'),
(r'-/', Comment.Multiline, '#pop'),
(r'[/-]', Comment.Multiline)
],
'string': [
(r'[^\\"]+', String.Double),
(r'\\[n"\\]', String.Escape),
('"', String.Double, '#pop'),
],
}

View File

@@ -1,7 +1,3 @@
These are instructions to set up a working development environment for those who wish to make changes to Lean itself. It is part of the [Development Guide](doc/dev/index.md).
We strongly suggest that new users instead follow the [Quickstart](doc/quickstart.md) to get started using Lean, since this sets up an environment that can automatically manage multiple Lean toolchain versions, which is necessary when working within the Lean ecosystem.
Requirements
------------
@@ -16,32 +12,44 @@ Platform-Specific Setup
- [Windows (msys2)](msys2.md)
- [Windows (WSL)](wsl.md)
- [macOS (homebrew)](osx-10.9.md)
- Linux/macOS/WSL via [Nix](https://nixos.org/nix/): Call `nix develop` in the project root. That's it.
- Linux/macOS/WSL via [Nix](https://nixos.org/nix/): Call `nix-shell` in the project root. That's it.
Generic Build Instructions
--------------------------
Setting up a basic parallelized release build:
Setting up a basic release build:
```bash
git clone https://github.com/leanprover/lean4
git clone https://github.com/leanprover/lean4 --recurse-submodules
cd lean4
cmake --preset release
make -C build/release -j$(nproc) # see below for macOS
mkdir -p build/release
cd build/release
cmake ../..
make
```
You can replace `$(nproc)`, which is not available on macOS and some alternative shells, with the desired parallelism amount.
For regular development, we recommend running
```bash
git config submodule.recurse true
```
in the checkout so that `--recurse-submodules` doesn't have to be
specified with `git pull/checkout/...`.
The above commands will compile the Lean library and binaries into the
`stage1` subfolder; see below for details.
`stage1` subfolder; see below for details. Add `-j N` for an
appropriate `N` to `make` for a parallel build.
You should not usually run `cmake --install` after a successful build.
For example, on an AMD Ryzen 9 `make` takes 00:04:55, whereas `make -j 10`
takes 00:01:38. Your results may vary depending on the speed of your hard
drive.
You should not usually run `make install` after a successful build.
See [Dev setup using elan](../dev/index.md#dev-setup-using-elan) on how to properly set up your editor to use the correct stage depending on the source directory.
Useful CMake Configuration Settings
-----------------------------------
Pass these along with the `cmake --preset release` command.
There are also two alternative presets that combine some of these options you can use instead of `release`: `debug` and `sandebug` (sanitize + debug).
Pass these along with the `cmake ../..` command.
* `-D CMAKE_BUILD_TYPE=`\
Select the build type. Valid values are `RELEASE` (default), `DEBUG`,

39
doc/make/msvc.md Normal file
View File

@@ -0,0 +1,39 @@
# Compiling Lean with Visual Studio
WARNING: Compiling Lean with Visual Studio doesn't currently work.
There's an ongoing effort to port Lean to Visual Studio.
The instructions below are for VS 2017.
In the meantime you can use [MSYS2](msys2.md) or [WSL](wsl.md).
## Installing dependencies
First, install `vcpkg` from https://github.com/Microsoft/vcpkg if you haven't
done so already.
Then, open a console in the directory you cloned `vcpkg` to, and type:
`vcpkg install mpir` for the 32-bit library or
`vcpkg install mpir:x64-windows` for the x64 one.
In Visual Studio, use the "open folder" feature and open the Lean directory.
Go to the `CMake->Change CMake Settings` menu. File `CMakeSettings.json` opens.
In each of the targets, add the following snippet (i.e., after every
`ctestCommandArgs`):
```json
"variables": [
{
"name": "CMAKE_TOOLCHAIN_FILE",
"value": "C:\\path\\to\\vcpkg\\scripts\\buildsystems\\vcpkg.cmake"
}
]
```
## Enable Intellisense
In Visual Studio, press Ctrl+Q and type `CppProperties.json` and press Enter.
Ensure `includePath` variables include `"${workspaceRoot}\\src"`.
## Build Lean
Press F7.

View File

@@ -38,9 +38,10 @@ cmake --version
Then follow the [generic build instructions](index.md) in the MSYS2
MinGW shell, using:
```
cmake --preset release -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
cmake ../.. -G "Unix Makefiles" -DCMAKE_C_COMPILER=clang -DCMAKE_CXX_COMPILER=clang++
```
instead of `cmake --preset release`. This will use the clang compiler instead of gcc, which is required with msys2.
instead of `cmake ../..`. This ensures that cmake will call `sh` instead of `cmd.exe`
for script tasks and it will use the clang compiler instead of gcc, which is required.
## Install lean

View File

@@ -1,4 +1,4 @@
# Install Packages on OS X 14.5
# Install Packages on OS X 10.9
We assume that you are using [homebrew][homebrew] as a package manager.
@@ -22,7 +22,7 @@ brew install gcc
```
To install clang++-3.5 via homebrew, please execute:
```bash
brew install llvm
brew install llvm --with-clang --with-asan
```
To use compilers other than the default one (Apple's clang++), you
need to use `-DCMAKE_CXX_COMPILER` option to specify the compiler

View File

@@ -15,7 +15,7 @@ data type containing several important pieces of information. First and foremost
current player, and it has a random generator.
-/
open Batteries (HashMap)
open Std (HashMap)
abbrev TileIndex := Nat × Nat -- a 2D index
inductive TileState where

View File

@@ -6,7 +6,6 @@ Platforms built & tested by our CI, available as binary releases via elan (see b
* x86-64 Linux with glibc 2.27+
* x86-64 macOS 10.15+
* aarch64 (Apple Silicon) macOS 10.15+
* x86-64 Windows 10+
### Tier 2
@@ -17,6 +16,7 @@ Releases may be silently broken due to the lack of automated testing.
Issue reports and fixes are welcome.
* aarch64 Linux with glibc 2.27+
* aarch64 (Apple Silicon) macOS
* x86 (32-bit) Linux
* Emscripten Web Assembly

View File

@@ -43,8 +43,7 @@ $ pdflatex test.tex
## Example with `minted`
First [install Pygments](https://pygments.org/download/) (version 2.18 or newer).
Then save the following sample LaTeX file `test.tex` into the same directory:
First [install Pygments](https://pygments.org/download/). Then save [`lean4.py`](https://raw.githubusercontent.com/leanprover/lean4/master/doc/latex/lean4.py), which contains an version of the Lean highlighter updated for Lean 4, and the following sample LaTeX file `test.tex` into the same directory:
```latex
\documentclass{article}
@@ -52,8 +51,9 @@ Then save the following sample LaTeX file `test.tex` into the same directory:
% switch to a monospace font supporting more Unicode characters
\setmonofont{FreeMono}
\usepackage{minted}
\newmintinline[lean]{lean4}{bgcolor=white}
\newminted[leancode]{lean4}{fontsize=\footnotesize}
% instruct minted to use our local theorem.py
\newmintinline[lean]{lean4.py:Lean4Lexer -x}{bgcolor=white}
\newminted[leancode]{lean4.py:Lean4Lexer -x}{fontsize=\footnotesize}
\usemintedstyle{tango} % a nice, colorful theme
\begin{document}
@@ -67,6 +67,9 @@ theorem funext {f₁ f₂ : ∀ (x : α), β x} (h : ∀ x, f₁ x = f₂ x) : f
\end{document}
```
If your version of `minted` is v2.7 or newer, but before v3.0,
you will additionally need to follow the workaround described in https://github.com/gpoore/minted/issues/360.
You can then compile `test.tex` by executing the following command:
```bash
@@ -78,14 +81,11 @@ Some remarks:
- either `xelatex` or `lualatex` is required to handle Unicode characters in the code.
- `--shell-escape` is needed to allow `xelatex` to execute `pygmentize` in a shell.
- If the chosen monospace font is missing some Unicode symbols, you can direct them to be displayed using a fallback font or other replacement LaTeX code.
``` latex
\usepackage{newunicodechar}
\newfontfamily{\freeserif}{DejaVu Sans}
\newunicodechar{✝}{\freeserif{✝}}
\newunicodechar{𝓞}{\ensuremath{\mathcal{O}}}
```
- If you are using an old version of Pygments, you can copy
[`lean.py`](https://raw.githubusercontent.com/pygments/pygments/master/pygments/lexers/lean.py) into your working directory,
and use `lean4.py:Lean4Lexer -x` instead of `lean4` above.
If your version of `minted` is v2.7 or newer, but before v3.0,
you will additionally need to follow the workaround described in https://github.com/gpoore/minted/issues/360.
``` latex
\usepackage{newunicodechar}
\newfontfamily{\freeserif}{DejaVu Sans}
\newunicodechar{✝}{\freeserif{✝}}
\newunicodechar{𝓞}{\ensuremath{\mathcal{O}}}
```
- minted has a "helpful" feature that draws red boxes around characters the chosen lexer doesn't recognize.
Since the Lean lexer cannot encompass all user-defined syntax, it is advisable to [work around](https://tex.stackexchange.com/a/343506/14563) this feature.

105
flake.lock generated
View File

@@ -1,31 +1,12 @@
{
"nodes": {
"flake-compat": {
"flake": false,
"locked": {
"lastModified": 1673956053,
"narHash": "sha256-4gtG9iQuiKITOjNQQeQIpoIB6b16fm+504Ch3sNKLd8=",
"owner": "edolstra",
"repo": "flake-compat",
"rev": "35bb57c0c8d8b62bbfd284272c928ceb64ddbde9",
"type": "github"
},
"original": {
"owner": "edolstra",
"repo": "flake-compat",
"type": "github"
}
},
"flake-utils": {
"inputs": {
"systems": "systems"
},
"locked": {
"lastModified": 1710146030,
"narHash": "sha256-SZ5L6eA7HJ/nmkzGG7/ISclqe6oZdOZTNoesiInkXPQ=",
"lastModified": 1656928814,
"narHash": "sha256-RIFfgBuKz6Hp89yRr7+NR5tzIAbn52h8vT6vXkYjZoM=",
"owner": "numtide",
"repo": "flake-utils",
"rev": "b1d9ab70662946ef0850d488da1c9019f3a9752a",
"rev": "7e2a3b3dfd9af950a856d66b0a7d01e3c18aa249",
"type": "github"
},
"original": {
@@ -37,11 +18,11 @@
"lean4-mode": {
"flake": false,
"locked": {
"lastModified": 1709737301,
"narHash": "sha256-uT9JN2kLNKJK9c/S/WxLjiHmwijq49EgLb+gJUSDpz0=",
"lastModified": 1676498134,
"narHash": "sha256-u3WvyKxOViZG53hkb8wd2/Og6muTecbh+NdflIgVeyk=",
"owner": "leanprover",
"repo": "lean4-mode",
"rev": "f1f24c15134dee3754b82c9d9924866fe6bc6b9f",
"rev": "2c6ef33f476fdf5eb5e4fa4fa023ba8b11372440",
"type": "github"
},
"original": {
@@ -50,35 +31,34 @@
"type": "github"
}
},
"libgit2": {
"lowdown-src": {
"flake": false,
"locked": {
"lastModified": 1697646580,
"narHash": "sha256-oX4Z3S9WtJlwvj0uH9HlYcWv+x1hqp8mhXl7HsLu2f0=",
"owner": "libgit2",
"repo": "libgit2",
"rev": "45fd9ed7ae1a9b74b957ef4f337bc3c8b3df01b5",
"lastModified": 1633514407,
"narHash": "sha256-Dw32tiMjdK9t3ETl5fzGrutQTzh2rufgZV4A/BbxuD4=",
"owner": "kristapsdz",
"repo": "lowdown",
"rev": "d2c2b44ff6c27b936ec27358a2653caaef8f73b8",
"type": "github"
},
"original": {
"owner": "libgit2",
"repo": "libgit2",
"owner": "kristapsdz",
"repo": "lowdown",
"type": "github"
}
},
"nix": {
"inputs": {
"flake-compat": "flake-compat",
"libgit2": "libgit2",
"lowdown-src": "lowdown-src",
"nixpkgs": "nixpkgs",
"nixpkgs-regression": "nixpkgs-regression"
},
"locked": {
"lastModified": 1711102798,
"narHash": "sha256-CXOIJr8byjolqG7eqCLa+Wfi7rah62VmLoqSXENaZnw=",
"lastModified": 1657097207,
"narHash": "sha256-SmeGmjWM3fEed3kQjqIAO8VpGmkC2sL1aPE7kKpK650=",
"owner": "NixOS",
"repo": "nix",
"rev": "a22328066416650471c3545b0b138669ea212ab4",
"rev": "f6316b49a0c37172bca87ede6ea8144d7d89832f",
"type": "github"
},
"original": {
@@ -89,33 +69,16 @@
},
"nixpkgs": {
"locked": {
"lastModified": 1709083642,
"narHash": "sha256-7kkJQd4rZ+vFrzWu8sTRtta5D1kBG0LSRYAfhtmMlSo=",
"lastModified": 1653988320,
"narHash": "sha256-ZaqFFsSDipZ6KVqriwM34T739+KLYJvNmCWzErjAg7c=",
"owner": "NixOS",
"repo": "nixpkgs",
"rev": "b550fe4b4776908ac2a861124307045f8e717c8e",
"rev": "2fa57ed190fd6c7c746319444f34b5917666e5c1",
"type": "github"
},
"original": {
"owner": "NixOS",
"ref": "release-23.11",
"repo": "nixpkgs",
"type": "github"
}
},
"nixpkgs-old": {
"flake": false,
"locked": {
"lastModified": 1581379743,
"narHash": "sha256-i1XCn9rKuLjvCdu2UeXKzGLF6IuQePQKFt4hEKRU5oc=",
"owner": "NixOS",
"repo": "nixpkgs",
"rev": "34c7eb7545d155cc5b6f499b23a7cb1c96ab4d59",
"type": "github"
},
"original": {
"owner": "NixOS",
"ref": "nixos-19.03",
"ref": "nixos-22.05-small",
"repo": "nixpkgs",
"type": "github"
}
@@ -138,11 +101,11 @@
},
"nixpkgs_2": {
"locked": {
"lastModified": 1710889954,
"narHash": "sha256-Pr6F5Pmd7JnNEMHHmspZ0qVqIBVxyZ13ik1pJtm2QXk=",
"lastModified": 1686089707,
"narHash": "sha256-LTNlJcru2qJ0XhlhG9Acp5KyjB774Pza3tRH0pKIb3o=",
"owner": "NixOS",
"repo": "nixpkgs",
"rev": "7872526e9c5332274ea5932a0c3270d6e4724f3b",
"rev": "af21c31b2a1ec5d361ed8050edd0303c31306397",
"type": "github"
},
"original": {
@@ -157,23 +120,7 @@
"flake-utils": "flake-utils",
"lean4-mode": "lean4-mode",
"nix": "nix",
"nixpkgs": "nixpkgs_2",
"nixpkgs-old": "nixpkgs-old"
}
},
"systems": {
"locked": {
"lastModified": 1681028828,
"narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
"owner": "nix-systems",
"repo": "default",
"rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
"type": "github"
},
"original": {
"owner": "nix-systems",
"repo": "default",
"type": "github"
"nixpkgs": "nixpkgs_2"
}
}
},

View File

@@ -2,9 +2,6 @@
description = "Lean interactive theorem prover";
inputs.nixpkgs.url = "github:NixOS/nixpkgs/nixpkgs-unstable";
# old nixpkgs used for portable release with older glibc (2.27)
inputs.nixpkgs-old.url = "github:NixOS/nixpkgs/nixos-19.03";
inputs.nixpkgs-old.flake = false;
inputs.flake-utils.url = "github:numtide/flake-utils";
inputs.nix.url = "github:NixOS/nix";
inputs.lean4-mode = {
@@ -20,43 +17,14 @@
# inputs.lean4-mode.follows = "lean4-mode";
#};
outputs = { self, nixpkgs, nixpkgs-old, flake-utils, nix, lean4-mode, ... }@inputs: flake-utils.lib.eachDefaultSystem (system:
outputs = { self, nixpkgs, flake-utils, nix, lean4-mode, ... }@inputs: flake-utils.lib.eachDefaultSystem (system:
let
pkgs = import nixpkgs {
inherit system;
# for `vscode-with-extensions`
config.allowUnfree = true;
};
# An old nixpkgs for creating releases with an old glibc
pkgsDist-old = import nixpkgs-old { inherit system; };
# An old nixpkgs for creating releases with an old glibc
pkgsDist-old-aarch = import nixpkgs-old { localSystem.config = "aarch64-unknown-linux-gnu"; };
lean-packages = pkgs.callPackage (./nix/packages.nix) { src = ./.; inherit nix lean4-mode; };
devShellWithDist = pkgsDist: pkgs.mkShell.override {
stdenv = pkgs.overrideCC pkgs.stdenv lean-packages.llvmPackages.clang;
} ({
buildInputs = with pkgs; [
cmake gmp ccache
lean-packages.llvmPackages.llvm # llvm-symbolizer for asan/lsan
gdb
# TODO: only add when proven to not affect the flakification
#pkgs.python3
tree # for CI
];
# https://github.com/NixOS/nixpkgs/issues/60919
hardeningDisable = [ "all" ];
# more convenient `ctest` output
CTEST_OUTPUT_ON_FAILURE = 1;
} // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
GMP = pkgsDist.gmp.override { withStatic = true; };
GLIBC = pkgsDist.glibc;
GLIBC_DEV = pkgsDist.glibc.dev;
GCC_LIB = pkgsDist.gcc.cc.lib;
ZLIB = pkgsDist.zlib;
GDB = pkgsDist.gdb;
});
in {
packages = lean-packages // rec {
debug = lean-packages.override { debug = true; };
@@ -81,10 +49,7 @@
};
defaultPackage = lean-packages.lean-all;
# The default development shell for working on lean itself
devShells.default = devShellWithDist pkgs;
devShells.oldGlibc = devShellWithDist pkgsDist-old;
devShells.oldGlibcAArch = devShellWithDist pkgsDist-old-aarch;
inherit (lean-packages) devShell;
checks.lean = lean-packages.test;
}) // rec {

View File

@@ -65,7 +65,7 @@ rec {
installPhase = ''
mkdir -p $out/bin $out/lib/lean
mv bin/lean $out/bin/
mv lib/lean/*.{so,dylib} $out/lib/lean
mv lib/lean/*.so $out/lib/lean
'';
meta.mainProgram = "lean";
});
@@ -87,8 +87,7 @@ rec {
leanFlags = [ "-DwarningAsError=true" ];
} // args);
Init' = build { name = "Init"; deps = []; };
Std' = build { name = "Std"; deps = [ Init' ]; };
Lean' = build { name = "Lean"; deps = [ Std' ]; };
Lean' = build { name = "Lean"; deps = [ Init' ]; };
attachSharedLib = sharedLib: pkg: pkg // {
inherit sharedLib;
mods = mapAttrs (_: m: m // { inherit sharedLib; propagatedLoadDynlibs = []; }) pkg.mods;
@@ -96,8 +95,7 @@ rec {
in (all: all // all.lean) rec {
inherit (Lean) emacs-dev emacs-package vscode-dev vscode-package;
Init = attachSharedLib leanshared Init';
Std = attachSharedLib leanshared Std' // { allExternalDeps = [ Init ]; };
Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Std ]; };
Lean = attachSharedLib leanshared Lean' // { allExternalDeps = [ Init ]; };
Lake = build {
name = "Lake";
src = src + "/src/lake";
@@ -111,24 +109,23 @@ rec {
linkFlags = lib.optional stdenv.isLinux "-rdynamic";
src = src + "/src/lake";
};
stdlib = [ Init Std Lean Lake ];
stdlib = [ Init Lean Lake ];
modDepsFiles = symlinkJoin { name = "modDepsFiles"; paths = map (l: l.modDepsFile) (stdlib ++ [ Leanc ]); };
depRoots = symlinkJoin { name = "depRoots"; paths = map (l: l.depRoots) stdlib; };
iTree = symlinkJoin { name = "ileans"; paths = map (l: l.iTree) stdlib; };
Leanc = build { name = "Leanc"; src = lean-bin-tools-unwrapped.leanc_src; deps = stdlib; roots = [ "Leanc" ]; };
stdlibLinkFlags = "${lib.concatMapStringsSep " " (l: "-L${l.staticLib}") stdlib} -L${leancpp}/lib/lean";
stdlibLinkFlags = "-L${Init.staticLib} -L${Lean.staticLib} -L${Lake.staticLib} -L${leancpp}/lib/lean";
libInit_shared = runCommand "libInit_shared" { buildInputs = [ stdenv.cc ]; libName = "libInit_shared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
mkdir $out
touch empty.c
${stdenv.cc}/bin/cc -shared -o $out/$libName empty.c
LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared -Wl,-Bsymbolic \
-Wl,--whole-archive -lInit ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++ -lm ${stdlibLinkFlags} \
$(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
-o $out/$libName
'';
leanshared = runCommand "leanshared" { buildInputs = [ stdenv.cc ]; libName = "libleanshared${stdenv.hostPlatform.extensions.sharedLibrary}"; } ''
mkdir $out
LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared ${lib.optionalString stdenv.isLinux "-Wl,-Bsymbolic"} \
${if stdenv.isDarwin
then "-Wl,-force_load,${Init.staticLib}/libInit.a -Wl,-force_load,${Std.staticLib}/libStd.a -Wl,-force_load,${Lean.staticLib}/libLean.a -Wl,-force_load,${leancpp}/lib/lean/libleancpp.a ${leancpp}/lib/libleanrt_initial-exec.a -lc++"
else "-Wl,--whole-archive -lInit -lStd -lLean -lleancpp ${leancpp}/lib/libleanrt_initial-exec.a -Wl,--no-whole-archive -lstdc++"} \
-lm ${stdlibLinkFlags} \
LEAN_CC=${stdenv.cc}/bin/cc ${lean-bin-tools-unwrapped}/bin/leanc -shared -Wl,-Bsymbolic \
${libInit_shared}/* -Wl,--whole-archive -lLean -lleancpp -Wl,--no-whole-archive -lstdc++ -lm ${stdlibLinkFlags} \
$(${llvmPackages.libllvm.dev}/bin/llvm-config --ldflags --libs) \
-o $out/$libName
'';
@@ -154,9 +151,11 @@ rec {
'';
meta.mainProgram = "lean";
};
cacheRoots = linkFarmFromDrvs "cacheRoots" ([
cacheRoots = linkFarmFromDrvs "cacheRoots" [
stage0 lean leanc lean-all iTree modDepsFiles depRoots Leanc.src
] ++ map (lib: lib.oTree) stdlib);
# .o files are not a runtime dependency on macOS because of lack of thin archives
Lean.oTree Lake.oTree
];
test = buildCMake {
name = "lean-test-${desc}";
realSrc = lib.sourceByRegex src [ "src.*" "tests.*" ];
@@ -171,17 +170,16 @@ rec {
ln -sf ${lean-all}/* .
'';
buildPhase = ''
ctest --output-junit test-results.xml --output-on-failure -E 'leancomptest_(doc_example|foreign)' -j$NIX_BUILD_CORES
ctest --output-on-failure -E 'leancomptest_(doc_example|foreign)' -j$NIX_BUILD_CORES
'';
installPhase = ''
mkdir $out
mv test-results.xml $out
touch $out
'';
};
update-stage0 =
let cTree = symlinkJoin { name = "cs"; paths = map (lib: lib.cTree) stdlib; }; in
let cTree = symlinkJoin { name = "cs"; paths = [ Init.cTree Lean.cTree ]; }; in
writeShellScriptBin "update-stage0" ''
CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/lib/update-stage0"}
CSRCS=${cTree} CP_C_PARAMS="--dereference --no-preserve=all" ${src + "/script/update-stage0"}
'';
update-stage0-commit = writeShellScriptBin "update-stage0-commit" ''
set -euo pipefail

View File

@@ -5,7 +5,7 @@ let lean-final' = lean-final; in
lib.makeOverridable (
{ name, src, fullSrc ? src, srcPrefix ? "", srcPath ? "$PWD/${srcPrefix}",
# Lean dependencies. Each entry should be an output of buildLeanPackage.
deps ? [ lean.Init lean.Std lean.Lean ],
deps ? [ lean.Lean ],
# Static library dependencies. Each derivation `static` should contain a static library in the directory `${static}`.
staticLibDeps ? [],
# Whether to wrap static library inputs in a -Wl,--start-group [...] -Wl,--end-group to ensure dependencies are resolved.
@@ -176,7 +176,7 @@ with builtins; let
# make local "copy" so `drv`'s Nix store path doesn't end up in ccache's hash
ln -s ${drv.c}/${drv.cPath} src.c
# on the other hand, a debug build is pretty fast anyway, so preserve the path for gdb
leanc -c -o $out/$oPath $leancFlags -fPIC ${if debug then "${drv.c}/${drv.cPath} -g" else "src.c -O3 -DNDEBUG -DLEAN_EXPORTING"}
leanc -c -o $out/$oPath $leancFlags -fPIC ${if debug then "${drv.c}/${drv.cPath} -g" else "src.c -O3 -DNDEBUG"}
'';
};
mkMod = mod: deps:
@@ -224,8 +224,7 @@ with builtins; let
allLinkFlags = lib.foldr (shared: acc: acc ++ [ "-L${shared}" "-l${shared.linkName or shared.name}" ]) linkFlags allNativeSharedLibs;
objects = mapAttrs (_: m: m.obj) mods';
bintools = if stdenv.isDarwin then darwin.cctools else stdenv.cc.bintools.bintools;
staticLib = runCommand "${name}-lib" { buildInputs = [ bintools ]; } ''
staticLib = runCommand "${name}-lib" { buildInputs = [ stdenv.cc.bintools.bintools ]; } ''
mkdir -p $out
ar Trcs $out/lib${libName}.a ${lib.concatStringsSep " " (map (drv: "${drv}/${drv.oPath}") (attrValues objects))};
'';
@@ -250,7 +249,7 @@ in rec {
${if stdenv.isDarwin then "-Wl,-force_load,${staticLib}/lib${libName}.a" else "-Wl,--whole-archive ${staticLib}/lib${libName}.a -Wl,--no-whole-archive"} \
${lib.concatStringsSep " " (map (d: "${d.sharedLib}/*") deps)}'';
executable = lib.makeOverridable ({ withSharedStdlib ? true }: let
objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.leanshared}/*";
objPaths = map (drv: "${drv}/${drv.oPath}") (attrValues objects) ++ lib.optional withSharedStdlib "${lean-final.libInit_shared}/* ${lean-final.leanshared}/*";
in runCommand executableName { buildInputs = [ stdenv.cc leanc ]; } ''
mkdir -p $out/bin
leanc ${staticLibLinkWrapper (lib.concatStringsSep " " (objPaths ++ map (d: "${d}/*.a") allStaticLibDeps))} \

View File

@@ -1,22 +0,0 @@
Draft release notes
-------------------
This folder contains drafts of release notes for inclusion in `RELEASES.md`.
During the process to create a release candidate, we look through all the commits that make up the release
to prepare the release notes, and in that process we take these drafts into account.
Guidelines:
- You should prefer adding release notes to commit messages over adding anything to this folder.
A release note should briefly explain the impact of a change from a user's point of view.
Please mark these parts out with words such as **release notes** and/or **breaking changes**.
- It is not necessary to add anything to this folder. It is meant for larger features that span multiple PRs,
or for anything that would be helpful when preparing the release notes that might be missed
by someone reading through the change log.
- If the PR that adds a feature simultaneously adds a draft release note, including the PR number is not required
since it can be obtained from the git history for the file.
When release notes are prepared, all the draft release notes are deleted from this folder.
For release candidates beyond the first one, you can either update `RELEASE.md` directly
or continue to add drafts.
When a release is finalized, we will copy the completed release notes from `RELEASE.md` to the `master` branch.

View File

@@ -1,45 +0,0 @@
A new linter flags situations where a local variable's name is one of
the argumentless constructors of its type. This can arise when a user either
doesn't open a namespace or doesn't add a dot or leading qualifier, as
in the following:
````
inductive Tree (α : Type) where
| leaf
| branch (left : Tree α) (val : α) (right : Tree α)
def depth : Tree α → Nat
| leaf => 0
````
With this linter, the `leaf` pattern is highlighted as a local
variable whose name overlaps with the constructor `Tree.leaf`.
The linter can be disabled with `set_option linter.constructorNameAsVariable false`.
Additionally, the error message that occurs when a name in a pattern that takes arguments isn't valid now suggests similar names that would be valid. This means that the following definition:
```
def length (list : List α) : Nat :=
match list with
| nil => 0
| cons x xs => length xs + 1
```
now results in the following warning:
```
warning: Local variable 'nil' resembles constructor 'List.nil' - write '.nil' (with a dot) or 'List.nil' to use the constructor.
note: this linter can be disabled with `set_option linter.constructorNameAsVariable false`
```
and error:
```
invalid pattern, constructor or constant marked with '[match_pattern]' expected
Suggestion: 'List.cons' is similar
```
#4301

View File

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

View File

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

View File

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

View File

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

View File

@@ -1,33 +0,0 @@
#!/usr/bin/env bash
set -euo pipefail
rm -r stage0 || true
# don't copy untracked files
# `:!` is git glob flavor for exclude patterns
for f in $(git ls-files src ':!:src/lake/*' ':!:src/Leanc.lean'); do
if [[ $f == *.lean ]]; then
f=${f#src/}
f=${f%.lean}.c
mkdir -p $(dirname stage0/stdlib/$f)
cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
else
mkdir -p $(dirname stage0/$f)
cp $f stage0/$f
fi
done
# special handling for Lake files due to its nested directory
# copy the README to ensure the `stage0/src/lake` directory is comitted
for f in $(git ls-files 'src/lake/Lake/*' src/lake/Lake.lean src/lake/README.md ':!:src/lakefile.toml'); do
if [[ $f == *.lean ]]; then
f=${f#src/lake}
f=${f%.lean}.c
mkdir -p $(dirname stage0/stdlib/$f)
cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
else
mkdir -p $(dirname stage0/$f)
cp $f stage0/$f
fi
done
git add stage0

View File

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

18
script/update-stage0 Executable file
View File

@@ -0,0 +1,18 @@
#!/usr/bin/env bash
set -euo pipefail
rm -r stage0 || true
# don't copy untracked files
# `:!` is git glob flavor for exclude patterns
for f in $(git ls-files src ':!:src/lake/*' ':!:src/Leanc.lean'); do
if [[ $f == *.lean ]]; then
f=${f#src/}
f=${f%.lean}.c
mkdir -p $(dirname stage0/stdlib/$f)
cp ${CP_C_PARAMS:-} $CSRCS/$f stage0/stdlib/$f
else
mkdir -p $(dirname stage0/$f)
cp $f stage0/$f
fi
done
git add stage0

27
shell.nix Normal file
View File

@@ -0,0 +1,27 @@
let
flake = (import ./default.nix);
flakePkgs = flake.packages.${builtins.currentSystem};
in { pkgs ? flakePkgs.nixpkgs, pkgsDist ? pkgs }:
# use `shell` as default
(attribs: attribs.shell // attribs) rec {
shell = pkgs.mkShell.override {
stdenv = pkgs.overrideCC pkgs.stdenv flakePkgs.llvmPackages.clang;
} (rec {
buildInputs = with pkgs; [
cmake gmp ccache
flakePkgs.llvmPackages.llvm # llvm-symbolizer for asan/lsan
];
# https://github.com/NixOS/nixpkgs/issues/60919
hardeningDisable = [ "all" ];
# more convenient `ctest` output
CTEST_OUTPUT_ON_FAILURE = 1;
} // pkgs.lib.optionalAttrs pkgs.stdenv.isLinux {
GMP = pkgsDist.gmp.override { withStatic = true; };
GLIBC = pkgsDist.glibc;
GLIBC_DEV = pkgsDist.glibc.dev;
GCC_LIB = pkgsDist.gcc.cc.lib;
ZLIB = pkgsDist.zlib;
GDB = pkgsDist.gdb;
});
nix = flake.devShell.${builtins.currentSystem};
}

View File

@@ -9,7 +9,7 @@ endif()
include(ExternalProject)
project(LEAN CXX C)
set(LEAN_VERSION_MAJOR 4)
set(LEAN_VERSION_MINOR 11)
set(LEAN_VERSION_MINOR 8)
set(LEAN_VERSION_PATCH 0)
set(LEAN_VERSION_IS_RELEASE 0) # This number is 1 in the release revision, and 0 otherwise.
set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
@@ -73,7 +73,6 @@ option(USE_GMP "USE_GMP" ON)
# development-specific options
option(CHECK_OLEAN_VERSION "Only load .olean files compiled with the current version of Lean" OFF)
option(USE_LAKE "Use Lake instead of lean.mk for building core libs from language server" OFF)
set(LEAN_EXTRA_MAKE_OPTS "" CACHE STRING "extra options to lean --make")
set(LEANC_CC ${CMAKE_C_COMPILER} CACHE STRING "C compiler to use in `leanc`")
@@ -300,11 +299,11 @@ if(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
cmake_path(GET ZLIB_LIBRARY PARENT_PATH ZLIB_LIBRARY_PARENT_PATH)
string(APPEND LEANSHARED_LINKER_FLAGS " -L ${ZLIB_LIBRARY_PARENT_PATH}")
endif()
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lStd -lLean -lleanrt")
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lLean -lleanrt")
elseif(${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lStd -lLean -lnodefs.js -lleanrt")
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -lleancpp -lInit -lLean -lnodefs.js -lleanrt")
else()
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -Wl,--start-group -lleancpp -lLean -Wl,--end-group -lStd -Wl,--start-group -lInit -lleanrt -Wl,--end-group")
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " -Wl,--start-group -lleancpp -lLean -Wl,--end-group -Wl,--start-group -lInit -lleanrt -Wl,--end-group")
endif()
set(LEAN_CXX_STDLIB "-lstdc++" CACHE STRING "C++ stdlib linker flags")
@@ -316,12 +315,6 @@ endif()
string(APPEND TOOLCHAIN_STATIC_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
string(APPEND TOOLCHAIN_SHARED_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
# in local builds, link executables and not just dynlibs against C++ stdlib as well,
# which is required for e.g. asan
if(NOT LEAN_STANDALONE)
string(APPEND CMAKE_EXE_LINKER_FLAGS " ${LEAN_CXX_STDLIB}")
endif()
# flags for user binaries = flags for toolchain binaries + Lake
string(APPEND LEANC_STATIC_LINKER_FLAGS " ${TOOLCHAIN_STATIC_LINKER_FLAGS} -lLake")
@@ -510,15 +503,15 @@ file(RELATIVE_PATH LIB ${LEAN_SOURCE_DIR} ${CMAKE_BINARY_DIR}/lib)
# set up libInit_shared only on Windows; see also stdlib.make.in
if(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
set(INIT_SHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libInit.a.export ${CMAKE_BINARY_DIR}/lib/temp/libStd.a.export ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a -Wl,--no-whole-archive -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libInit_shared.dll.a")
set(INIT_SHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a -Wl,--no-whole-archive -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libInit_shared.dll.a")
endif()
if(${CMAKE_SYSTEM_NAME} MATCHES "Darwin")
set(LEANSHARED_LINKER_FLAGS "-Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libInit.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libStd.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLean.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libleancpp.a ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
set(LEANSHARED_LINKER_FLAGS "-Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libInit.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libLean.a -Wl,-force_load,${CMAKE_BINARY_DIR}/lib/lean/libleancpp.a ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
elseif(${CMAKE_SYSTEM_NAME} MATCHES "Windows")
set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive ${CMAKE_BINARY_DIR}/lib/temp/libLean.a.export -lleancpp -Wl,--no-whole-archive -lInit_shared -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libleanshared.dll.a")
set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lLean -lleancpp -Wl,--no-whole-archive -lInit_shared -Wl,--out-implib,${CMAKE_BINARY_DIR}/lib/lean/libleanshared.dll.a")
else()
set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit -lStd -lLean -lleancpp -Wl,--no-whole-archive ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
set(LEANSHARED_LINKER_FLAGS "-Wl,--whole-archive -lInit -lLean -lleancpp -Wl,--no-whole-archive ${CMAKE_BINARY_DIR}/runtime/libleanrt_initial-exec.a ${LEANSHARED_LINKER_FLAGS}")
endif()
if (${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
@@ -540,7 +533,7 @@ add_custom_target(make_stdlib ALL
# The actual rule is in a separate makefile because we want to prefix it with '+' to use the Make job server
# for a parallelized nested build, but CMake doesn't let us do that.
# We use `lean` from the previous stage, but `leanc`, headers, etc. from the current stage
COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Std Lean
COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make Init Lean
VERBATIM)
# if we have LLVM enabled, then build `lean.h.bc` which has the LLVM bitcode
@@ -578,7 +571,11 @@ else()
string(APPEND CMAKE_EXE_LINKER_FLAGS " -lInit_shared -lleanshared")
endif()
if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
if(${STAGE} GREATER 0 AND NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
if(NOT EXISTS ${LEAN_SOURCE_DIR}/lake/Lake.lean)
message(FATAL_ERROR "src/lake does not exist. Please check out the Lake submodule using `git submodule update --init src/lake`.")
endif()
add_custom_target(lake ALL
WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
DEPENDS leanshared
@@ -588,13 +585,9 @@ endif()
if(PREV_STAGE)
add_custom_target(update-stage0
COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/lib/update-stage0'
COMMAND bash -c 'CSRCS=${CMAKE_BINARY_DIR}/lib/temp script/update-stage0'
DEPENDS make_stdlib
WORKING_DIRECTORY "${LEAN_SOURCE_DIR}/..")
add_custom_target(update-stage0-commit
COMMAND git commit -m "chore: update stage0"
DEPENDS update-stage0)
endif()
# use Bash version for building, use Lean version in bin/ for tests & distribution
@@ -655,9 +648,3 @@ endif()
string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE "${CMAKE_EXE_LINKER_FLAGS}")
string(REPLACE "$" "$$" CMAKE_EXE_LINKER_FLAGS_MAKE_MAKE "${CMAKE_EXE_LINKER_FLAGS_MAKE}")
configure_file(${LEAN_SOURCE_DIR}/stdlib.make.in ${CMAKE_BINARY_DIR}/stdlib.make)
if(USE_LAKE AND STAGE EQUAL 1)
configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/lakefile.toml)
configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../tests/lakefile.toml)
configure_file(${LEAN_SOURCE_DIR}/lakefile.toml.in ${LEAN_SOURCE_DIR}/../lakefile.toml)
endif()

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@@ -33,5 +33,3 @@ import Init.SizeOfLemmas
import Init.BinderPredicates
import Init.Ext
import Init.Omega
import Init.MacroTrace
import Init.Grind

View File

@@ -21,9 +21,9 @@ macro_rules
/-! ## if-then-else -/
@[simp] theorem if_true {_ : Decidable True} (t e : α) : ite True t e = t := if_pos trivial
@[simp] theorem if_true {h : Decidable True} (t e : α) : ite True t e = t := if_pos trivial
@[simp] theorem if_false {_ : Decidable False} (t e : α) : ite False t e = e := if_neg id
@[simp] theorem if_false {h : Decidable False} (t e : α) : ite False t e = e := if_neg id
theorem ite_id [Decidable c] {α} (t : α) : (if c then t else t) = t := by split <;> rfl
@@ -63,16 +63,3 @@ theorem ite_some_none_eq_none [Decidable P] :
@[simp] theorem ite_some_none_eq_some [Decidable P] :
(if P then some x else none) = some y P x = y := by
split <;> simp_all
-- This is not marked as `simp` as it is already handled by `dite_eq_right_iff`.
theorem dite_some_none_eq_none [Decidable P] {x : P α} :
(if h : P then some (x h) else none) = none ¬P := by
simp only [dite_eq_right_iff]
rfl
@[simp] theorem dite_some_none_eq_some [Decidable P] {x : P α} {y : α} :
(if h : P then some (x h) else none) = some y h : P, x h = y := by
by_cases h : P <;> simp only [h, dite_cond_eq_true, dite_cond_eq_false, Option.some.injEq,
false_iff, not_exists]
case pos => exact fun h_eq Exists.intro h h_eq, fun h_exists => h_exists.2
case neg => exact fun h_false _ h_false

View File

@@ -15,13 +15,6 @@ namespace Classical
noncomputable def indefiniteDescription {α : Sort u} (p : α Prop) (h : x, p x) : {x // p x} :=
choice <| let x, px := h; x, px
/--
Given that there exists an element satisfying `p`, returns one such element.
This is a straightforward consequence of, and equivalent to, `Classical.choice`.
See also `choose_spec`, which asserts that the returned value has property `p`.
-/
noncomputable def choose {α : Sort u} {p : α Prop} (h : x, p x) : α :=
(indefiniteDescription p h).val

View File

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

View File

@@ -131,7 +131,7 @@ protected def adapt {ε' α : Type u} (f : ε → ε') : ExceptT ε m α → Exc
end ExceptT
@[always_inline]
instance (m : Type u Type v) (ε₁ : Type u) (ε₂ : Type u) [MonadExceptOf ε₁ m] : MonadExceptOf ε₁ (ExceptT ε₂ m) where
instance (m : Type u Type v) (ε₁ : Type u) (ε₂ : Type u) [Monad m] [MonadExceptOf ε₁ m] : MonadExceptOf ε₁ (ExceptT ε₂ m) where
throw e := ExceptT.mk <| throwThe ε₁ e
tryCatch x handle := ExceptT.mk <| tryCatchThe ε₁ x handle

View File

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Control.Lawful.Basic
import Init.Control.Lawful
/-!
The Exception monad transformer using CPS style.
@@ -18,7 +18,6 @@ namespace ExceptCpsT
def run {ε α : Type u} [Monad m] (x : ExceptCpsT ε m α) : m (Except ε α) :=
x _ (fun a => pure (Except.ok a)) (fun e => pure (Except.error e))
set_option linter.unusedVariables false in -- `s` unused
@[always_inline, inline]
def runK {ε α : Type u} (x : ExceptCpsT ε m α) (s : ε) (ok : α m β) (error : ε m β) : m β :=
x _ ok error

View File

@@ -4,5 +4,373 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich, Leonardo de Moura, Mario Carneiro
-/
prelude
import Init.Control.Lawful.Basic
import Init.Control.Lawful.Instances
import Init.SimpLemmas
import Init.Control.Except
import Init.Control.StateRef
open Function
@[simp] theorem monadLift_self [Monad m] (x : m α) : monadLift x = x :=
rfl
class LawfulFunctor (f : Type u Type v) [Functor f] : Prop where
map_const : (Functor.mapConst : α f β f α) = Functor.map const β
id_map (x : f α) : id <$> x = x
comp_map (g : α β) (h : β γ) (x : f α) : (h g) <$> x = h <$> g <$> x
export LawfulFunctor (map_const id_map comp_map)
attribute [simp] id_map
@[simp] theorem id_map' [Functor m] [LawfulFunctor m] (x : m α) : (fun a => a) <$> x = x :=
id_map x
class LawfulApplicative (f : Type u Type v) [Applicative f] extends LawfulFunctor f : Prop where
seqLeft_eq (x : f α) (y : f β) : x <* y = const β <$> x <*> y
seqRight_eq (x : f α) (y : f β) : x *> y = const α id <$> x <*> y
pure_seq (g : α β) (x : f α) : pure g <*> x = g <$> x
map_pure (g : α β) (x : α) : g <$> (pure x : f α) = pure (g x)
seq_pure {α β : Type u} (g : f (α β)) (x : α) : g <*> pure x = (fun h => h x) <$> g
seq_assoc {α β γ : Type u} (x : f α) (g : f (α β)) (h : f (β γ)) : h <*> (g <*> x) = ((@comp α β γ) <$> h) <*> g <*> x
comp_map g h x := (by
repeat rw [ pure_seq]
simp [seq_assoc, map_pure, seq_pure])
export LawfulApplicative (seqLeft_eq seqRight_eq pure_seq map_pure seq_pure seq_assoc)
attribute [simp] map_pure seq_pure
@[simp] theorem pure_id_seq [Applicative f] [LawfulApplicative f] (x : f α) : pure id <*> x = x := by
simp [pure_seq]
class LawfulMonad (m : Type u Type v) [Monad m] extends LawfulApplicative m : Prop where
bind_pure_comp (f : α β) (x : m α) : x >>= (fun a => pure (f a)) = f <$> x
bind_map {α β : Type u} (f : m (α β)) (x : m α) : f >>= (. <$> x) = f <*> x
pure_bind (x : α) (f : α m β) : pure x >>= f = f x
bind_assoc (x : m α) (f : α m β) (g : β m γ) : x >>= f >>= g = x >>= fun x => f x >>= g
map_pure g x := (by rw [ bind_pure_comp, pure_bind])
seq_pure g x := (by rw [ bind_map]; simp [map_pure, bind_pure_comp])
seq_assoc x g h := (by simp [ bind_pure_comp, bind_map, bind_assoc, pure_bind])
export LawfulMonad (bind_pure_comp bind_map pure_bind bind_assoc)
attribute [simp] pure_bind bind_assoc
@[simp] theorem bind_pure [Monad m] [LawfulMonad m] (x : m α) : x >>= pure = x := by
show x >>= (fun a => pure (id a)) = x
rw [bind_pure_comp, id_map]
theorem map_eq_pure_bind [Monad m] [LawfulMonad m] (f : α β) (x : m α) : f <$> x = x >>= fun a => pure (f a) := by
rw [ bind_pure_comp]
theorem seq_eq_bind_map {α β : Type u} [Monad m] [LawfulMonad m] (f : m (α β)) (x : m α) : f <*> x = f >>= (. <$> x) := by
rw [ bind_map]
theorem bind_congr [Bind m] {x : m α} {f g : α m β} (h : a, f a = g a) : x >>= f = x >>= g := by
simp [funext h]
@[simp] theorem bind_pure_unit [Monad m] [LawfulMonad m] {x : m PUnit} : (x >>= fun _ => pure ) = x := by
rw [bind_pure]
theorem map_congr [Functor m] {x : m α} {f g : α β} (h : a, f a = g a) : (f <$> x : m β) = g <$> x := by
simp [funext h]
theorem seq_eq_bind {α β : Type u} [Monad m] [LawfulMonad m] (mf : m (α β)) (x : m α) : mf <*> x = mf >>= fun f => f <$> x := by
rw [bind_map]
theorem seqRight_eq_bind [Monad m] [LawfulMonad m] (x : m α) (y : m β) : x *> y = x >>= fun _ => y := by
rw [seqRight_eq]
simp [map_eq_pure_bind, seq_eq_bind_map, const]
theorem seqLeft_eq_bind [Monad m] [LawfulMonad m] (x : m α) (y : m β) : x <* y = x >>= fun a => y >>= fun _ => pure a := by
rw [seqLeft_eq]; simp [map_eq_pure_bind, seq_eq_bind_map]
/--
An alternative constructor for `LawfulMonad` which has more
defaultable fields in the common case.
-/
theorem LawfulMonad.mk' (m : Type u Type v) [Monad m]
(id_map : {α} (x : m α), id <$> x = x)
(pure_bind : {α β} (x : α) (f : α m β), pure x >>= f = f x)
(bind_assoc : {α β γ} (x : m α) (f : α m β) (g : β m γ),
x >>= f >>= g = x >>= fun x => f x >>= g)
(map_const : {α β} (x : α) (y : m β),
Functor.mapConst x y = Function.const β x <$> y := by intros; rfl)
(seqLeft_eq : {α β} (x : m α) (y : m β),
x <* y = (x >>= fun a => y >>= fun _ => pure a) := by intros; rfl)
(seqRight_eq : {α β} (x : m α) (y : m β), x *> y = (x >>= fun _ => y) := by intros; rfl)
(bind_pure_comp : {α β} (f : α β) (x : m α),
x >>= (fun y => pure (f y)) = f <$> x := by intros; rfl)
(bind_map : {α β} (f : m (α β)) (x : m α), f >>= (. <$> x) = f <*> x := by intros; rfl)
: LawfulMonad m :=
have map_pure {α β} (g : α β) (x : α) : g <$> (pure x : m α) = pure (g x) := by
rw [ bind_pure_comp]; simp [pure_bind]
{ id_map, bind_pure_comp, bind_map, pure_bind, bind_assoc, map_pure,
comp_map := by simp [ bind_pure_comp, bind_assoc, pure_bind]
pure_seq := by intros; rw [ bind_map]; simp [pure_bind]
seq_pure := by intros; rw [ bind_map]; simp [map_pure, bind_pure_comp]
seq_assoc := by simp [ bind_pure_comp, bind_map, bind_assoc, pure_bind]
map_const := funext fun x => funext (map_const x)
seqLeft_eq := by simp [seqLeft_eq, bind_map, bind_pure_comp, pure_bind, bind_assoc]
seqRight_eq := fun x y => by
rw [seqRight_eq, bind_map, bind_pure_comp, bind_assoc]; simp [pure_bind, id_map] }
/-! # Id -/
namespace Id
@[simp] theorem map_eq (x : Id α) (f : α β) : f <$> x = f x := rfl
@[simp] theorem bind_eq (x : Id α) (f : α id β) : x >>= f = f x := rfl
@[simp] theorem pure_eq (a : α) : (pure a : Id α) = a := rfl
instance : LawfulMonad Id := by
refine' { .. } <;> intros <;> rfl
end Id
/-! # ExceptT -/
namespace ExceptT
theorem ext [Monad m] {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
simp [run] at h
assumption
@[simp] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
@[simp] theorem run_lift [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
@[simp] theorem run_throw [Monad m] : run (throw e : ExceptT ε m β) = pure (Except.error e) := rfl
@[simp] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α ExceptT ε m β) : run (ExceptT.lift x >>= f : ExceptT ε m β) = x >>= fun a => run (f a) := by
simp[ExceptT.run, ExceptT.lift, bind, ExceptT.bind, ExceptT.mk, ExceptT.bindCont, map_eq_pure_bind]
@[simp] theorem bind_throw [Monad m] [LawfulMonad m] (f : α ExceptT ε m β) : (throw e >>= f) = throw e := by
simp [throw, throwThe, MonadExceptOf.throw, bind, ExceptT.bind, ExceptT.bindCont, ExceptT.mk]
theorem run_bind [Monad m] (x : ExceptT ε m α)
: run (x >>= f : ExceptT ε m β)
=
run x >>= fun
| Except.ok x => run (f x)
| Except.error e => pure (Except.error e) :=
rfl
@[simp] theorem lift_pure [Monad m] [LawfulMonad m] (a : α) : ExceptT.lift (pure a) = (pure a : ExceptT ε m α) := by
simp [ExceptT.lift, pure, ExceptT.pure]
@[simp] theorem run_map [Monad m] [LawfulMonad m] (f : α β) (x : ExceptT ε m α)
: (f <$> x).run = Except.map f <$> x.run := by
simp [Functor.map, ExceptT.map, map_eq_pure_bind]
apply bind_congr
intro a; cases a <;> simp [Except.map]
protected theorem seq_eq {α β ε : Type u} [Monad m] (mf : ExceptT ε m (α β)) (x : ExceptT ε m α) : mf <*> x = mf >>= fun f => f <$> x :=
rfl
protected theorem bind_pure_comp [Monad m] [LawfulMonad m] (f : α β) (x : ExceptT ε m α) : x >>= pure f = f <$> x := by
intros; rfl
protected theorem seqLeft_eq {α β ε : Type u} {m : Type u Type v} [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x <* y = const β <$> x <*> y := by
show (x >>= fun a => y >>= fun _ => pure a) = (const (α := α) β <$> x) >>= fun f => f <$> y
rw [ ExceptT.bind_pure_comp]
apply ext
simp [run_bind]
apply bind_congr
intro
| Except.error _ => simp
| Except.ok _ =>
simp [map_eq_pure_bind]; apply bind_congr; intro b;
cases b <;> simp [comp, Except.map, const]
protected theorem seqRight_eq [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x *> y = const α id <$> x <*> y := by
show (x >>= fun _ => y) = (const α id <$> x) >>= fun f => f <$> y
rw [ ExceptT.bind_pure_comp]
apply ext
simp [run_bind]
apply bind_congr
intro a; cases a <;> simp
instance [Monad m] [LawfulMonad m] : LawfulMonad (ExceptT ε m) where
id_map := by intros; apply ext; simp
map_const := by intros; rfl
seqLeft_eq := ExceptT.seqLeft_eq
seqRight_eq := ExceptT.seqRight_eq
pure_seq := by intros; apply ext; simp [ExceptT.seq_eq, run_bind]
bind_pure_comp := ExceptT.bind_pure_comp
bind_map := by intros; rfl
pure_bind := by intros; apply ext; simp [run_bind]
bind_assoc := by intros; apply ext; simp [run_bind]; apply bind_congr; intro a; cases a <;> simp
end ExceptT
/-! # Except -/
instance : LawfulMonad (Except ε) := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun a f => rfl)
(bind_assoc := fun a f g => by cases a <;> rfl)
instance : LawfulApplicative (Except ε) := inferInstance
instance : LawfulFunctor (Except ε) := inferInstance
/-! # ReaderT -/
namespace ReaderT
theorem ext {x y : ReaderT ρ m α} (h : ctx, x.run ctx = y.run ctx) : x = y := by
simp [run] at h
exact funext h
@[simp] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
@[simp] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α ReaderT ρ m β) (ctx : ρ)
: (x >>= f).run ctx = x.run ctx >>= λ a => (f a).run ctx := rfl
@[simp] theorem run_mapConst [Monad m] (a : α) (x : ReaderT ρ m β) (ctx : ρ)
: (Functor.mapConst a x).run ctx = Functor.mapConst a (x.run ctx) := rfl
@[simp] theorem run_map [Monad m] (f : α β) (x : ReaderT ρ m α) (ctx : ρ)
: (f <$> x).run ctx = f <$> x.run ctx := rfl
@[simp] theorem run_monadLift [MonadLiftT n m] (x : n α) (ctx : ρ)
: (monadLift x : ReaderT ρ m α).run ctx = (monadLift x : m α) := rfl
@[simp] theorem run_monadMap [MonadFunctor n m] (f : {β : Type u} n β n β) (x : ReaderT ρ m α) (ctx : ρ)
: (monadMap @f x : ReaderT ρ m α).run ctx = monadMap @f (x.run ctx) := rfl
@[simp] theorem run_read [Monad m] (ctx : ρ) : (ReaderT.read : ReaderT ρ m ρ).run ctx = pure ctx := rfl
@[simp] theorem run_seq {α β : Type u} [Monad m] (f : ReaderT ρ m (α β)) (x : ReaderT ρ m α) (ctx : ρ)
: (f <*> x).run ctx = (f.run ctx <*> x.run ctx) := rfl
@[simp] theorem run_seqRight [Monad m] (x : ReaderT ρ m α) (y : ReaderT ρ m β) (ctx : ρ)
: (x *> y).run ctx = (x.run ctx *> y.run ctx) := rfl
@[simp] theorem run_seqLeft [Monad m] (x : ReaderT ρ m α) (y : ReaderT ρ m β) (ctx : ρ)
: (x <* y).run ctx = (x.run ctx <* y.run ctx) := rfl
instance [Monad m] [LawfulFunctor m] : LawfulFunctor (ReaderT ρ m) where
id_map := by intros; apply ext; simp
map_const := by intros; funext a b; apply ext; intros; simp [map_const]
comp_map := by intros; apply ext; intros; simp [comp_map]
instance [Monad m] [LawfulApplicative m] : LawfulApplicative (ReaderT ρ m) where
seqLeft_eq := by intros; apply ext; intros; simp [seqLeft_eq]
seqRight_eq := by intros; apply ext; intros; simp [seqRight_eq]
pure_seq := by intros; apply ext; intros; simp [pure_seq]
map_pure := by intros; apply ext; intros; simp [map_pure]
seq_pure := by intros; apply ext; intros; simp [seq_pure]
seq_assoc := by intros; apply ext; intros; simp [seq_assoc]
instance [Monad m] [LawfulMonad m] : LawfulMonad (ReaderT ρ m) where
bind_pure_comp := by intros; apply ext; intros; simp [LawfulMonad.bind_pure_comp]
bind_map := by intros; apply ext; intros; simp [bind_map]
pure_bind := by intros; apply ext; intros; simp
bind_assoc := by intros; apply ext; intros; simp
end ReaderT
/-! # StateRefT -/
instance [Monad m] [LawfulMonad m] : LawfulMonad (StateRefT' ω σ m) :=
inferInstanceAs (LawfulMonad (ReaderT (ST.Ref ω σ) m))
/-! # StateT -/
namespace StateT
theorem ext {x y : StateT σ m α} (h : s, x.run s = y.run s) : x = y :=
funext h
@[simp] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
rfl
@[simp] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
@[simp] theorem run_bind [Monad m] (x : StateT σ m α) (f : α StateT σ m β) (s : σ)
: (x >>= f).run s = x.run s >>= λ p => (f p.1).run p.2 := by
simp [bind, StateT.bind, run]
@[simp] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
simp [Functor.map, StateT.map, run, map_eq_pure_bind]
@[simp] theorem run_get [Monad m] (s : σ) : (get : StateT σ m σ).run s = pure (s, s) := rfl
@[simp] theorem run_set [Monad m] (s s' : σ) : (set s' : StateT σ m PUnit).run s = pure (, s') := rfl
@[simp] theorem run_modify [Monad m] (f : σ σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (, f s) := rfl
@[simp] theorem run_modifyGet [Monad m] (f : σ α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
simp [modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, run]
@[simp] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
@[simp] theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
simp [StateT.lift, StateT.run, bind, StateT.bind]
@[simp] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
@[simp] theorem run_monadMap [Monad m] [MonadFunctor n m] (f : {β : Type u} n β n β) (x : StateT σ m α) (s : σ)
: (monadMap @f x : StateT σ m α).run s = monadMap @f (x.run s) := rfl
@[simp] theorem run_seq {α β σ : Type u} [Monad m] [LawfulMonad m] (f : StateT σ m (α β)) (x : StateT σ m α) (s : σ) : (f <*> x).run s = (f.run s >>= fun fs => (fun (p : α × σ) => (fs.1 p.1, p.2)) <$> x.run fs.2) := by
show (f >>= fun g => g <$> x).run s = _
simp
@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x *> y).run s = (x.run s >>= fun p => y.run p.2) := by
show (x >>= fun _ => y).run s = _
simp
@[simp] theorem run_seqLeft {α β σ : Type u} [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x <* y).run s = (x.run s >>= fun p => y.run p.2 >>= fun p' => pure (p.1, p'.2)) := by
show (x >>= fun a => y >>= fun _ => pure a).run s = _
simp
theorem seqRight_eq [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) : x *> y = const α id <$> x <*> y := by
apply ext; intro s
simp [map_eq_pure_bind, const]
apply bind_congr; intro p; cases p
simp [Prod.eta]
theorem seqLeft_eq [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) : x <* y = const β <$> x <*> y := by
apply ext; intro s
simp [map_eq_pure_bind]
instance [Monad m] [LawfulMonad m] : LawfulMonad (StateT σ m) where
id_map := by intros; apply ext; intros; simp[Prod.eta]
map_const := by intros; rfl
seqLeft_eq := seqLeft_eq
seqRight_eq := seqRight_eq
pure_seq := by intros; apply ext; intros; simp
bind_pure_comp := by intros; apply ext; intros; simp; apply LawfulMonad.bind_pure_comp
bind_map := by intros; rfl
pure_bind := by intros; apply ext; intros; simp
bind_assoc := by intros; apply ext; intros; simp
end StateT
/-! # EStateM -/
instance : LawfulMonad (EStateM ε σ) := .mk'
(id_map := fun x => funext <| fun s => by
dsimp only [EStateM.instMonadEStateM, EStateM.map]
match x s with
| .ok _ _ => rfl
| .error _ _ => rfl)
(pure_bind := fun _ _ => rfl)
(bind_assoc := fun x _ _ => funext <| fun s => by
dsimp only [EStateM.instMonadEStateM, EStateM.bind]
match x s with
| .ok _ _ => rfl
| .error _ _ => rfl)
(map_const := fun _ _ => rfl)
/-! # Option -/
instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun x f => rfl)
(bind_assoc := fun x f g => by cases x <;> rfl)
(bind_pure_comp := fun f x => by cases x <;> rfl)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance

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/-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich, Leonardo de Moura, Mario Carneiro
-/
prelude
import Init.SimpLemmas
import Init.Meta
open Function
@[simp] theorem monadLift_self {m : Type u Type v} (x : m α) : monadLift x = x :=
rfl
/--
The `Functor` typeclass only contains the operations of a functor.
`LawfulFunctor` further asserts that these operations satisfy the laws of a functor,
including the preservation of the identity and composition laws:
```
id <$> x = x
(h ∘ g) <$> x = h <$> g <$> x
```
-/
class LawfulFunctor (f : Type u Type v) [Functor f] : Prop where
map_const : (Functor.mapConst : α f β f α) = Functor.map const β
id_map (x : f α) : id <$> x = x
comp_map (g : α β) (h : β γ) (x : f α) : (h g) <$> x = h <$> g <$> x
export LawfulFunctor (map_const id_map comp_map)
attribute [simp] id_map
@[simp] theorem id_map' [Functor m] [LawfulFunctor m] (x : m α) : (fun a => a) <$> x = x :=
id_map x
/--
The `Applicative` typeclass only contains the operations of an applicative functor.
`LawfulApplicative` further asserts that these operations satisfy the laws of an applicative functor:
```
pure id <*> v = v
pure (·∘·) <*> u <*> v <*> w = u <*> (v <*> w)
pure f <*> pure x = pure (f x)
u <*> pure y = pure (· y) <*> u
```
-/
class LawfulApplicative (f : Type u Type v) [Applicative f] extends LawfulFunctor f : Prop where
seqLeft_eq (x : f α) (y : f β) : x <* y = const β <$> x <*> y
seqRight_eq (x : f α) (y : f β) : x *> y = const α id <$> x <*> y
pure_seq (g : α β) (x : f α) : pure g <*> x = g <$> x
map_pure (g : α β) (x : α) : g <$> (pure x : f α) = pure (g x)
seq_pure {α β : Type u} (g : f (α β)) (x : α) : g <*> pure x = (fun h => h x) <$> g
seq_assoc {α β γ : Type u} (x : f α) (g : f (α β)) (h : f (β γ)) : h <*> (g <*> x) = ((@comp α β γ) <$> h) <*> g <*> x
comp_map g h x := (by
repeat rw [ pure_seq]
simp [seq_assoc, map_pure, seq_pure])
export LawfulApplicative (seqLeft_eq seqRight_eq pure_seq map_pure seq_pure seq_assoc)
attribute [simp] map_pure seq_pure
@[simp] theorem pure_id_seq [Applicative f] [LawfulApplicative f] (x : f α) : pure id <*> x = x := by
simp [pure_seq]
/--
The `Monad` typeclass only contains the operations of a monad.
`LawfulMonad` further asserts that these operations satisfy the laws of a monad,
including associativity and identity laws for `bind`:
```
pure x >>= f = f x
x >>= pure = x
x >>= f >>= g = x >>= (fun x => f x >>= g)
```
`LawfulMonad.mk'` is an alternative constructor containing useful defaults for many fields.
-/
class LawfulMonad (m : Type u Type v) [Monad m] extends LawfulApplicative m : Prop where
bind_pure_comp (f : α β) (x : m α) : x >>= (fun a => pure (f a)) = f <$> x
bind_map {α β : Type u} (f : m (α β)) (x : m α) : f >>= (. <$> x) = f <*> x
pure_bind (x : α) (f : α m β) : pure x >>= f = f x
bind_assoc (x : m α) (f : α m β) (g : β m γ) : x >>= f >>= g = x >>= fun x => f x >>= g
map_pure g x := (by rw [ bind_pure_comp, pure_bind])
seq_pure g x := (by rw [ bind_map]; simp [map_pure, bind_pure_comp])
seq_assoc x g h := (by simp [ bind_pure_comp, bind_map, bind_assoc, pure_bind])
export LawfulMonad (bind_pure_comp bind_map pure_bind bind_assoc)
attribute [simp] pure_bind bind_assoc
@[simp] theorem bind_pure [Monad m] [LawfulMonad m] (x : m α) : x >>= pure = x := by
show x >>= (fun a => pure (id a)) = x
rw [bind_pure_comp, id_map]
theorem map_eq_pure_bind [Monad m] [LawfulMonad m] (f : α β) (x : m α) : f <$> x = x >>= fun a => pure (f a) := by
rw [ bind_pure_comp]
theorem seq_eq_bind_map {α β : Type u} [Monad m] [LawfulMonad m] (f : m (α β)) (x : m α) : f <*> x = f >>= (. <$> x) := by
rw [ bind_map]
theorem bind_congr [Bind m] {x : m α} {f g : α m β} (h : a, f a = g a) : x >>= f = x >>= g := by
simp [funext h]
@[simp] theorem bind_pure_unit [Monad m] [LawfulMonad m] {x : m PUnit} : (x >>= fun _ => pure ) = x := by
rw [bind_pure]
theorem map_congr [Functor m] {x : m α} {f g : α β} (h : a, f a = g a) : (f <$> x : m β) = g <$> x := by
simp [funext h]
theorem seq_eq_bind {α β : Type u} [Monad m] [LawfulMonad m] (mf : m (α β)) (x : m α) : mf <*> x = mf >>= fun f => f <$> x := by
rw [bind_map]
theorem seqRight_eq_bind [Monad m] [LawfulMonad m] (x : m α) (y : m β) : x *> y = x >>= fun _ => y := by
rw [seqRight_eq]
simp [map_eq_pure_bind, seq_eq_bind_map, const]
theorem seqLeft_eq_bind [Monad m] [LawfulMonad m] (x : m α) (y : m β) : x <* y = x >>= fun a => y >>= fun _ => pure a := by
rw [seqLeft_eq]; simp [map_eq_pure_bind, seq_eq_bind_map]
/--
An alternative constructor for `LawfulMonad` which has more
defaultable fields in the common case.
-/
theorem LawfulMonad.mk' (m : Type u Type v) [Monad m]
(id_map : {α} (x : m α), id <$> x = x)
(pure_bind : {α β} (x : α) (f : α m β), pure x >>= f = f x)
(bind_assoc : {α β γ} (x : m α) (f : α m β) (g : β m γ),
x >>= f >>= g = x >>= fun x => f x >>= g)
(map_const : {α β} (x : α) (y : m β),
Functor.mapConst x y = Function.const β x <$> y := by intros; rfl)
(seqLeft_eq : {α β} (x : m α) (y : m β),
x <* y = (x >>= fun a => y >>= fun _ => pure a) := by intros; rfl)
(seqRight_eq : {α β} (x : m α) (y : m β), x *> y = (x >>= fun _ => y) := by intros; rfl)
(bind_pure_comp : {α β} (f : α β) (x : m α),
x >>= (fun y => pure (f y)) = f <$> x := by intros; rfl)
(bind_map : {α β} (f : m (α β)) (x : m α), f >>= (. <$> x) = f <*> x := by intros; rfl)
: LawfulMonad m :=
have map_pure {α β} (g : α β) (x : α) : g <$> (pure x : m α) = pure (g x) := by
rw [ bind_pure_comp]; simp [pure_bind]
{ id_map, bind_pure_comp, bind_map, pure_bind, bind_assoc, map_pure,
comp_map := by simp [ bind_pure_comp, bind_assoc, pure_bind]
pure_seq := by intros; rw [ bind_map]; simp [pure_bind]
seq_pure := by intros; rw [ bind_map]; simp [map_pure, bind_pure_comp]
seq_assoc := by simp [ bind_pure_comp, bind_map, bind_assoc, pure_bind]
map_const := funext fun x => funext (map_const x)
seqLeft_eq := by simp [seqLeft_eq, bind_map, bind_pure_comp, pure_bind, bind_assoc]
seqRight_eq := fun x y => by
rw [seqRight_eq, bind_map, bind_pure_comp, bind_assoc]; simp [pure_bind, id_map] }
/-! # Id -/
namespace Id
@[simp] theorem map_eq (x : Id α) (f : α β) : f <$> x = f x := rfl
@[simp] theorem bind_eq (x : Id α) (f : α id β) : x >>= f = f x := rfl
@[simp] theorem pure_eq (a : α) : (pure a : Id α) = a := rfl
instance : LawfulMonad Id := by
refine' { .. } <;> intros <;> rfl
end Id
/-! # Option -/
instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun x f => rfl)
(bind_assoc := fun x f g => by cases x <;> rfl)
(bind_pure_comp := fun f x => by cases x <;> rfl)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance

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/-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Ullrich, Leonardo de Moura, Mario Carneiro
-/
prelude
import Init.Control.Lawful.Basic
import Init.Control.Except
import Init.Control.StateRef
open Function
/-! # ExceptT -/
namespace ExceptT
theorem ext {x y : ExceptT ε m α} (h : x.run = y.run) : x = y := by
simp [run] at h
assumption
@[simp] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
@[simp] theorem run_lift [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
@[simp] theorem run_throw [Monad m] : run (throw e : ExceptT ε m β) = pure (Except.error e) := rfl
@[simp] theorem run_bind_lift [Monad m] [LawfulMonad m] (x : m α) (f : α ExceptT ε m β) : run (ExceptT.lift x >>= f : ExceptT ε m β) = x >>= fun a => run (f a) := by
simp[ExceptT.run, ExceptT.lift, bind, ExceptT.bind, ExceptT.mk, ExceptT.bindCont, map_eq_pure_bind]
@[simp] theorem bind_throw [Monad m] [LawfulMonad m] (f : α ExceptT ε m β) : (throw e >>= f) = throw e := by
simp [throw, throwThe, MonadExceptOf.throw, bind, ExceptT.bind, ExceptT.bindCont, ExceptT.mk]
theorem run_bind [Monad m] (x : ExceptT ε m α)
: run (x >>= f : ExceptT ε m β)
=
run x >>= fun
| Except.ok x => run (f x)
| Except.error e => pure (Except.error e) :=
rfl
@[simp] theorem lift_pure [Monad m] [LawfulMonad m] (a : α) : ExceptT.lift (pure a) = (pure a : ExceptT ε m α) := by
simp [ExceptT.lift, pure, ExceptT.pure]
@[simp] theorem run_map [Monad m] [LawfulMonad m] (f : α β) (x : ExceptT ε m α)
: (f <$> x).run = Except.map f <$> x.run := by
simp [Functor.map, ExceptT.map, map_eq_pure_bind]
apply bind_congr
intro a; cases a <;> simp [Except.map]
protected theorem seq_eq {α β ε : Type u} [Monad m] (mf : ExceptT ε m (α β)) (x : ExceptT ε m α) : mf <*> x = mf >>= fun f => f <$> x :=
rfl
protected theorem bind_pure_comp [Monad m] (f : α β) (x : ExceptT ε m α) : x >>= pure f = f <$> x := by
intros; rfl
protected theorem seqLeft_eq {α β ε : Type u} {m : Type u Type v} [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x <* y = const β <$> x <*> y := by
show (x >>= fun a => y >>= fun _ => pure a) = (const (α := α) β <$> x) >>= fun f => f <$> y
rw [ ExceptT.bind_pure_comp]
apply ext
simp [run_bind]
apply bind_congr
intro
| Except.error _ => simp
| Except.ok _ =>
simp [map_eq_pure_bind]; apply bind_congr; intro b;
cases b <;> simp [comp, Except.map, const]
protected theorem seqRight_eq [Monad m] [LawfulMonad m] (x : ExceptT ε m α) (y : ExceptT ε m β) : x *> y = const α id <$> x <*> y := by
show (x >>= fun _ => y) = (const α id <$> x) >>= fun f => f <$> y
rw [ ExceptT.bind_pure_comp]
apply ext
simp [run_bind]
apply bind_congr
intro a; cases a <;> simp
instance [Monad m] [LawfulMonad m] : LawfulMonad (ExceptT ε m) where
id_map := by intros; apply ext; simp
map_const := by intros; rfl
seqLeft_eq := ExceptT.seqLeft_eq
seqRight_eq := ExceptT.seqRight_eq
pure_seq := by intros; apply ext; simp [ExceptT.seq_eq, run_bind]
bind_pure_comp := ExceptT.bind_pure_comp
bind_map := by intros; rfl
pure_bind := by intros; apply ext; simp [run_bind]
bind_assoc := by intros; apply ext; simp [run_bind]; apply bind_congr; intro a; cases a <;> simp
end ExceptT
/-! # Except -/
instance : LawfulMonad (Except ε) := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun a f => rfl)
(bind_assoc := fun a f g => by cases a <;> rfl)
instance : LawfulApplicative (Except ε) := inferInstance
instance : LawfulFunctor (Except ε) := inferInstance
/-! # ReaderT -/
namespace ReaderT
theorem ext {x y : ReaderT ρ m α} (h : ctx, x.run ctx = y.run ctx) : x = y := by
simp [run] at h
exact funext h
@[simp] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
@[simp] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α ReaderT ρ m β) (ctx : ρ)
: (x >>= f).run ctx = x.run ctx >>= λ a => (f a).run ctx := rfl
@[simp] theorem run_mapConst [Monad m] (a : α) (x : ReaderT ρ m β) (ctx : ρ)
: (Functor.mapConst a x).run ctx = Functor.mapConst a (x.run ctx) := rfl
@[simp] theorem run_map [Monad m] (f : α β) (x : ReaderT ρ m α) (ctx : ρ)
: (f <$> x).run ctx = f <$> x.run ctx := rfl
@[simp] theorem run_monadLift [MonadLiftT n m] (x : n α) (ctx : ρ)
: (monadLift x : ReaderT ρ m α).run ctx = (monadLift x : m α) := rfl
@[simp] theorem run_monadMap [MonadFunctor n m] (f : {β : Type u} n β n β) (x : ReaderT ρ m α) (ctx : ρ)
: (monadMap @f x : ReaderT ρ m α).run ctx = monadMap @f (x.run ctx) := rfl
@[simp] theorem run_read [Monad m] (ctx : ρ) : (ReaderT.read : ReaderT ρ m ρ).run ctx = pure ctx := rfl
@[simp] theorem run_seq {α β : Type u} [Monad m] (f : ReaderT ρ m (α β)) (x : ReaderT ρ m α) (ctx : ρ)
: (f <*> x).run ctx = (f.run ctx <*> x.run ctx) := rfl
@[simp] theorem run_seqRight [Monad m] (x : ReaderT ρ m α) (y : ReaderT ρ m β) (ctx : ρ)
: (x *> y).run ctx = (x.run ctx *> y.run ctx) := rfl
@[simp] theorem run_seqLeft [Monad m] (x : ReaderT ρ m α) (y : ReaderT ρ m β) (ctx : ρ)
: (x <* y).run ctx = (x.run ctx <* y.run ctx) := rfl
instance [Monad m] [LawfulFunctor m] : LawfulFunctor (ReaderT ρ m) where
id_map := by intros; apply ext; simp
map_const := by intros; funext a b; apply ext; intros; simp [map_const]
comp_map := by intros; apply ext; intros; simp [comp_map]
instance [Monad m] [LawfulApplicative m] : LawfulApplicative (ReaderT ρ m) where
seqLeft_eq := by intros; apply ext; intros; simp [seqLeft_eq]
seqRight_eq := by intros; apply ext; intros; simp [seqRight_eq]
pure_seq := by intros; apply ext; intros; simp [pure_seq]
map_pure := by intros; apply ext; intros; simp [map_pure]
seq_pure := by intros; apply ext; intros; simp [seq_pure]
seq_assoc := by intros; apply ext; intros; simp [seq_assoc]
instance [Monad m] [LawfulMonad m] : LawfulMonad (ReaderT ρ m) where
bind_pure_comp := by intros; apply ext; intros; simp [LawfulMonad.bind_pure_comp]
bind_map := by intros; apply ext; intros; simp [bind_map]
pure_bind := by intros; apply ext; intros; simp
bind_assoc := by intros; apply ext; intros; simp
end ReaderT
/-! # StateRefT -/
instance [Monad m] [LawfulMonad m] : LawfulMonad (StateRefT' ω σ m) :=
inferInstanceAs (LawfulMonad (ReaderT (ST.Ref ω σ) m))
/-! # StateT -/
namespace StateT
theorem ext {x y : StateT σ m α} (h : s, x.run s = y.run s) : x = y :=
funext h
@[simp] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
rfl
@[simp] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
@[simp] theorem run_bind [Monad m] (x : StateT σ m α) (f : α StateT σ m β) (s : σ)
: (x >>= f).run s = x.run s >>= λ p => (f p.1).run p.2 := by
simp [bind, StateT.bind, run]
@[simp] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
simp [Functor.map, StateT.map, run, map_eq_pure_bind]
@[simp] theorem run_get [Monad m] (s : σ) : (get : StateT σ m σ).run s = pure (s, s) := rfl
@[simp] theorem run_set [Monad m] (s s' : σ) : (set s' : StateT σ m PUnit).run s = pure (, s') := rfl
@[simp] theorem run_modify [Monad m] (f : σ σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (, f s) := rfl
@[simp] theorem run_modifyGet [Monad m] (f : σ α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
simp [modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, run]
@[simp] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
simp [StateT.lift, StateT.run, bind, StateT.bind]
@[simp] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
@[simp] theorem run_monadMap [MonadFunctor n m] (f : {β : Type u} n β n β) (x : StateT σ m α) (s : σ) :
(monadMap @f x : StateT σ m α).run s = monadMap @f (x.run s) := rfl
@[simp] theorem run_seq {α β σ : Type u} [Monad m] [LawfulMonad m] (f : StateT σ m (α β)) (x : StateT σ m α) (s : σ) : (f <*> x).run s = (f.run s >>= fun fs => (fun (p : α × σ) => (fs.1 p.1, p.2)) <$> x.run fs.2) := by
show (f >>= fun g => g <$> x).run s = _
simp
@[simp] theorem run_seqRight [Monad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x *> y).run s = (x.run s >>= fun p => y.run p.2) := by
show (x >>= fun _ => y).run s = _
simp
@[simp] theorem run_seqLeft {α β σ : Type u} [Monad m] (x : StateT σ m α) (y : StateT σ m β) (s : σ) : (x <* y).run s = (x.run s >>= fun p => y.run p.2 >>= fun p' => pure (p.1, p'.2)) := by
show (x >>= fun a => y >>= fun _ => pure a).run s = _
simp
theorem seqRight_eq [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) : x *> y = const α id <$> x <*> y := by
apply ext; intro s
simp [map_eq_pure_bind, const]
apply bind_congr; intro p; cases p
simp [Prod.eta]
theorem seqLeft_eq [Monad m] [LawfulMonad m] (x : StateT σ m α) (y : StateT σ m β) : x <* y = const β <$> x <*> y := by
apply ext; intro s
simp [map_eq_pure_bind]
instance [Monad m] [LawfulMonad m] : LawfulMonad (StateT σ m) where
id_map := by intros; apply ext; intros; simp[Prod.eta]
map_const := by intros; rfl
seqLeft_eq := seqLeft_eq
seqRight_eq := seqRight_eq
pure_seq := by intros; apply ext; intros; simp
bind_pure_comp := by intros; apply ext; intros; simp; apply LawfulMonad.bind_pure_comp
bind_map := by intros; rfl
pure_bind := by intros; apply ext; intros; simp
bind_assoc := by intros; apply ext; intros; simp
end StateT
/-! # EStateM -/
instance : LawfulMonad (EStateM ε σ) := .mk'
(id_map := fun x => funext <| fun s => by
dsimp only [EStateM.instMonad, EStateM.map]
match x s with
| .ok _ _ => rfl
| .error _ _ => rfl)
(pure_bind := fun _ _ => rfl)
(bind_assoc := fun x _ _ => funext <| fun s => by
dsimp only [EStateM.instMonad, EStateM.bind]
match x s with
| .ok _ _ => rfl
| .error _ _ => rfl)
(map_const := fun _ _ => rfl)

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@@ -10,7 +10,7 @@ import Init.Control.Except
universe u v
instance : ToBool (Option α) := Option.isSome
instance : ToBool (Option α) := Option.toBool
def OptionT (m : Type u Type v) (α : Type u) : Type v :=
m (Option α)
@@ -67,7 +67,7 @@ instance : MonadExceptOf Unit (OptionT m) where
throw := fun _ => OptionT.fail
tryCatch := OptionT.tryCatch
instance (ε : Type u) [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
instance (ε : Type u) [Monad m] [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
throw e := OptionT.mk <| throwThe ε e
tryCatch x handle := OptionT.mk <| tryCatchThe ε x handle

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@@ -32,7 +32,7 @@ instance : MonadControl m (ReaderT ρ m) where
restoreM x _ := x
@[always_inline]
instance ReaderT.tryFinally [MonadFinally m] : MonadFinally (ReaderT ρ m) where
instance ReaderT.tryFinally [MonadFinally m] [Monad m] : MonadFinally (ReaderT ρ m) where
tryFinally' x h ctx := tryFinally' (x ctx) (fun a? => h a? ctx)
@[reducible] def ReaderM (ρ : Type u) := ReaderT ρ Id

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@@ -87,7 +87,7 @@ protected def lift {α : Type u} (t : m α) : StateT σ m α :=
instance : MonadLift m (StateT σ m) := StateT.lift
@[always_inline]
instance (σ m) : MonadFunctor m (StateT σ m) := fun f x s => f (x s)
instance (σ m) [Monad m] : MonadFunctor m (StateT σ m) := fun f x s => f (x s)
@[always_inline]
instance (ε) [MonadExceptOf ε m] : MonadExceptOf ε (StateT σ m) := {

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@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Control.Lawful.Basic
import Init.Control.Lawful
/-!
The State monad transformer using CPS style.
@@ -14,18 +14,16 @@ def StateCpsT (σ : Type u) (m : Type u → Type v) (α : Type u) := (δ : Type
namespace StateCpsT
variable {α σ : Type u} {m : Type u Type v}
@[always_inline, inline]
def runK (x : StateCpsT σ m α) (s : σ) (k : α σ m β) : m β :=
def runK {α σ : Type u} {m : Type u Type v} (x : StateCpsT σ m α) (s : σ) (k : α σ m β) : m β :=
x _ s k
@[always_inline, inline]
def run [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
def run {α σ : Type u} {m : Type u Type v} [Monad m] (x : StateCpsT σ m α) (s : σ) : m (α × σ) :=
runK x s (fun a s => pure (a, s))
@[always_inline, inline]
def run' [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
def run' {α σ : Type u} {m : Type u Type v} [Monad m] (x : StateCpsT σ m α) (s : σ) : m α :=
runK x s (fun a _ => pure a)
@[always_inline]
@@ -50,29 +48,29 @@ protected def lift [Monad m] (x : m α) : StateCpsT σ m α :=
instance [Monad m] : MonadLift m (StateCpsT σ m) where
monadLift := StateCpsT.lift
@[simp] theorem runK_pure (a : α) (s : σ) (k : α σ m β) : (pure a : StateCpsT σ m α).runK s k = k a s := rfl
@[simp] theorem runK_pure {m : Type u Type v} (a : α) (s : σ) (k : α σ m β) : (pure a : StateCpsT σ m α).runK s k = k a s := rfl
@[simp] theorem runK_get (s : σ) (k : σ σ m β) : (get : StateCpsT σ m σ).runK s k = k s s := rfl
@[simp] theorem runK_get {m : Type u Type v} (s : σ) (k : σ σ m β) : (get : StateCpsT σ m σ).runK s k = k s s := rfl
@[simp] theorem runK_set (s s' : σ) (k : PUnit σ m β) : (set s' : StateCpsT σ m PUnit).runK s k = k s' := rfl
@[simp] theorem runK_set {m : Type u Type v} (s s' : σ) (k : PUnit σ m β) : (set s' : StateCpsT σ m PUnit).runK s k = k s' := rfl
@[simp] theorem runK_modify (f : σ σ) (s : σ) (k : PUnit σ m β) : (modify f : StateCpsT σ m PUnit).runK s k = k (f s) := rfl
@[simp] theorem runK_modify {m : Type u Type v} (f : σ σ) (s : σ) (k : PUnit σ m β) : (modify f : StateCpsT σ m PUnit).runK s k = k (f s) := rfl
@[simp] theorem runK_lift [Monad m] (x : m α) (s : σ) (k : α σ m β) : (StateCpsT.lift x : StateCpsT σ m α).runK s k = x >>= (k . s) := rfl
@[simp] theorem runK_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) (k : α σ m β) : (StateCpsT.lift x : StateCpsT σ m α).runK s k = x >>= (k . s) := rfl
@[simp] theorem runK_monadLift [Monad m] [MonadLiftT n m] (x : n α) (s : σ) (k : α σ m β)
@[simp] theorem runK_monadLift {σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) (k : α σ m β)
: (monadLift x : StateCpsT σ m α).runK s k = (monadLift x : m α) >>= (k . s) := rfl
@[simp] theorem runK_bind_pure (a : α) (f : α StateCpsT σ m β) (s : σ) (k : β σ m γ) : (pure a >>= f).runK s k = (f a).runK s k := rfl
@[simp] theorem runK_bind_pure {α σ : Type u} [Monad m] (a : α) (f : α StateCpsT σ m β) (s : σ) (k : β σ m γ) : (pure a >>= f).runK s k = (f a).runK s k := rfl
@[simp] theorem runK_bind_lift [Monad m] (x : m α) (f : α StateCpsT σ m β) (s : σ) (k : β σ m γ)
@[simp] theorem runK_bind_lift {α σ : Type u} [Monad m] (x : m α) (f : α StateCpsT σ m β) (s : σ) (k : β σ m γ)
: (StateCpsT.lift x >>= f).runK s k = x >>= fun a => (f a).runK s k := rfl
@[simp] theorem runK_bind_get (f : σ StateCpsT σ m β) (s : σ) (k : β σ m γ) : (get >>= f).runK s k = (f s).runK s k := rfl
@[simp] theorem runK_bind_get {σ : Type u} [Monad m] (f : σ StateCpsT σ m β) (s : σ) (k : β σ m γ) : (get >>= f).runK s k = (f s).runK s k := rfl
@[simp] theorem runK_bind_set (f : PUnit StateCpsT σ m β) (s s' : σ) (k : β σ m γ) : (set s' >>= f).runK s k = (f ).runK s' k := rfl
@[simp] theorem runK_bind_set {σ : Type u} [Monad m] (f : PUnit StateCpsT σ m β) (s s' : σ) (k : β σ m γ) : (set s' >>= f).runK s k = (f ).runK s' k := rfl
@[simp] theorem runK_bind_modify (f : σ σ) (g : PUnit StateCpsT σ m β) (s : σ) (k : β σ m γ) : (modify f >>= g).runK s k = (g ).runK (f s) k := rfl
@[simp] theorem runK_bind_modify {σ : Type u} [Monad m] (f : σ σ) (g : PUnit StateCpsT σ m β) (s : σ) (k : β σ m γ) : (modify f >>= g).runK s k = (g ).runK (f s) k := rfl
@[simp] theorem run_eq [Monad m] (x : StateCpsT σ m α) (s : σ) : x.run s = x.runK s (fun a s => pure (a, s)) := rfl

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@@ -34,22 +34,22 @@ protected def lift (x : m α) : StateRefT' ω σ m α :=
instance [Monad m] : Monad (StateRefT' ω σ m) := inferInstanceAs (Monad (ReaderT _ _))
instance : MonadLift m (StateRefT' ω σ m) := StateRefT'.lift
instance (σ m) : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
instance (σ m) [Monad m] : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
instance [Alternative m] [Monad m] : Alternative (StateRefT' ω σ m) := inferInstanceAs (Alternative (ReaderT _ _))
@[inline]
protected def get [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
protected def get [Monad m] [MonadLiftT (ST ω) m] : StateRefT' ω σ m σ :=
fun ref => ref.get
@[inline]
protected def set [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
protected def set [Monad m] [MonadLiftT (ST ω) m] (s : σ) : StateRefT' ω σ m PUnit :=
fun ref => ref.set s
@[inline]
protected def modifyGet [MonadLiftT (ST ω) m] (f : σ α × σ) : StateRefT' ω σ m α :=
protected def modifyGet [Monad m] [MonadLiftT (ST ω) m] (f : σ α × σ) : StateRefT' ω σ m α :=
fun ref => ref.modifyGet f
instance [MonadLiftT (ST ω) m] : MonadStateOf σ (StateRefT' ω σ m) where
instance [MonadLiftT (ST ω) m] [Monad m] : MonadStateOf σ (StateRefT' ω σ m) where
get := StateRefT'.get
set := StateRefT'.set
modifyGet := StateRefT'.modifyGet
@@ -64,5 +64,5 @@ end StateRefT'
instance (ω σ : Type) (m : Type Type) : MonadControl m (StateRefT' ω σ m) :=
inferInstanceAs (MonadControl m (ReaderT _ _))
instance {m : Type Type} {ω σ : Type} [MonadFinally m] : MonadFinally (StateRefT' ω σ m) :=
instance {m : Type Type} {ω σ : Type} [MonadFinally m] [Monad m] : MonadFinally (StateRefT' ω σ m) :=
inferInstanceAs (MonadFinally (ReaderT _ _))

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@@ -6,7 +6,7 @@ Authors: Leonardo de Moura
Notation for operators defined at Prelude.lean
-/
prelude
import Init.Tactics
import Init.Meta
namespace Lean.Parser.Tactic.Conv
@@ -156,6 +156,7 @@ match [a, b] with
simplifies to `a`. -/
syntax (name := simpMatch) "simp_match" : conv
/-- Executes the given tactic block without converting `conv` goal into a regular goal. -/
syntax (name := nestedTacticCore) "tactic'" " => " tacticSeq : conv
@@ -201,7 +202,7 @@ macro (name := anyGoals) tk:"any_goals " s:convSeq : conv =>
with inaccessible names to the given names.
* `case tag₁ | tag₂ => tac` is equivalent to `(case tag₁ => tac); (case tag₂ => tac)`.
-/
macro (name := case) tk:"case " args:sepBy1(caseArg, "|") arr:" => " s:convSeq : conv =>
macro (name := case) tk:"case " args:sepBy1(caseArg, " | ") arr:" => " s:convSeq : conv =>
`(conv| tactic' => case%$tk $args|* =>%$arr conv' => ($s); all_goals rfl)
/--
@@ -210,7 +211,7 @@ has been solved after applying `tac`, nor admits the goal if `tac` failed.
Recall that `case` closes the goal using `sorry` when `tac` fails, and
the tactic execution is not interrupted.
-/
macro (name := case') tk:"case' " args:sepBy1(caseArg, "|") arr:" => " s:convSeq : conv =>
macro (name := case') tk:"case' " args:sepBy1(caseArg, " | ") arr:" => " s:convSeq : conv =>
`(conv| tactic' => case'%$tk $args|* =>%$arr conv' => $s)
/--

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@@ -19,7 +19,7 @@ which applies to all applications of the function).
-/
@[simp] def inline {α : Sort u} (a : α) : α := a
theorem id_def {α : Sort u} (a : α) : id a = a := rfl
theorem id.def {α : Sort u} (a : α) : id a = a := rfl
/--
`flip f a b` is `f b a`. It is useful for "point-free" programming,
@@ -165,7 +165,6 @@ whose first component is `a : α` and whose second component is `b : β a`
It is sometimes known as the dependent sum type, since it is the type level version
of an indexed summation.
-/
@[pp_using_anonymous_constructor]
structure Sigma {α : Type u} (β : α Type v) where
/-- Constructor for a dependent pair. If `a : α` and `b : β a` then `⟨a, b⟩ : Sigma β`.
(This will usually require a type ascription to determine `β`
@@ -191,7 +190,6 @@ which can cause problems for universe level unification,
because the equation `max 1 u v = ?u + 1` has no solution in level arithmetic.
`PSigma` is usually only used in automation that constructs pairs of arbitrary types.
-/
@[pp_using_anonymous_constructor]
structure PSigma {α : Sort u} (β : α Sort v) where
/-- Constructor for a dependent pair. If `a : α` and `b : β a` then `⟨a, b⟩ : PSigma β`.
(This will usually require a type ascription to determine `β`
@@ -468,11 +466,11 @@ class Singleton (α : outParam <| Type u) (β : Type v) where
export Singleton (singleton)
/-- `insert x ∅ = {x}` -/
class LawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
class IsLawfulSingleton (α : Type u) (β : Type v) [EmptyCollection β] [Insert α β] [Singleton α β] :
Prop where
/-- `insert x ∅ = {x}` -/
insert_emptyc_eq (x : α) : (insert x : β) = singleton x
export LawfulSingleton (insert_emptyc_eq)
export IsLawfulSingleton (insert_emptyc_eq)
/-- Type class used to implement the notation `{ a ∈ c | p a }` -/
class Sep (α : outParam <| Type u) (γ : Type v) where
@@ -642,7 +640,7 @@ instance : LawfulBEq String := inferInstance
/-! # Logical connectives and equality -/
@[inherit_doc True.intro] theorem trivial : True :=
@[inherit_doc True.intro] def trivial : True :=
theorem mt {a b : Prop} (h₁ : a b) (h₂ : ¬b) : ¬a :=
fun ha => h₂ (h₁ ha)
@@ -739,16 +737,13 @@ theorem beq_false_of_ne [BEq α] [LawfulBEq α] {a b : α} (h : a ≠ b) : (a ==
section
variable {α β φ : Sort u} {a a' : α} {b b' : β} {c : φ}
/-- Non-dependent recursor for `HEq` -/
noncomputable def HEq.ndrec.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} β Sort u1} (m : motive a) {β : Sort u2} {b : β} (h : HEq a b) : motive b :=
theorem HEq.ndrec.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} β Sort u1} (m : motive a) {β : Sort u2} {b : β} (h : HEq a b) : motive b :=
h.rec m
/-- `HEq.ndrec` variant -/
noncomputable def HEq.ndrecOn.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} β Sort u1} {β : Sort u2} {b : β} (h : HEq a b) (m : motive a) : motive b :=
theorem HEq.ndrecOn.{u1, u2} {α : Sort u2} {a : α} {motive : {β : Sort u2} β Sort u1} {β : Sort u2} {b : β} (h : HEq a b) (m : motive a) : motive b :=
h.rec m
/-- `HEq.ndrec` variant -/
noncomputable def HEq.elim {α : Sort u} {a : α} {p : α Sort v} {b : α} (h₁ : HEq a b) (h₂ : p a) : p b :=
theorem HEq.elim {α : Sort u} {a : α} {p : α Sort v} {b : α} (h₁ : HEq a b) (h₂ : p a) : p b :=
eq_of_heq h₁ h₂
theorem HEq.subst {p : (T : Sort u) T Prop} (h₁ : HEq a b) (h₂ : p α a) : p β b :=
@@ -1089,18 +1084,15 @@ def InvImage {α : Sort u} {β : Sort v} (r : β → β → Prop) (f : α → β
fun a₁ a₂ => r (f a₁) (f a₂)
/--
The transitive closure `TransGen r` of a relation `r` is the smallest relation which is
transitive and contains `r`. `TransGen r a z` if and only if there exists a sequence
The transitive closure `r` of a relation `r` is the smallest relation which is
transitive and contains `r`. `r a z` if and only if there exists a sequence
`a r b r ... r z` of length at least 1 connecting `a` to `z`.
-/
inductive Relation.TransGen {α : Sort u} (r : α α Prop) : α α Prop
/-- If `r a b` then `TransGen r a b`. This is the base case of the transitive closure. -/
| single {a b} : r a b TransGen r a b
inductive TC {α : Sort u} (r : α α Prop) : α α Prop where
/-- If `r a b` then `r a b`. This is the base case of the transitive closure. -/
| base : a b, r a b TC r a b
/-- The transitive closure is transitive. -/
| tail {a b c} : TransGen r a b r b c TransGen r a c
/-- Deprecated synonym for `Relation.TransGen`. -/
@[deprecated Relation.TransGen (since := "2024-07-16")] abbrev TC := @Relation.TransGen
| trans : a b c, TC r a b TC r b c TC r a c
/-! # Subtype -/
@@ -1117,6 +1109,9 @@ theorem eta (a : {x // p x}) (h : p (val a)) : mk (val a) h = a := by
cases a
exact rfl
instance {α : Type u} {p : α Prop} {a : α} (h : p a) : Inhabited {x // p x} where
default := a, h
instance {α : Type u} {p : α Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
fun a, h₁ b, h₂ =>
if h : a = b then isTrue (by subst h; exact rfl)
@@ -1176,7 +1171,7 @@ def Prod.lexLt [LT α] [LT β] (s : α × β) (t : α × β) : Prop :=
s.1 < t.1 (s.1 = t.1 s.2 < t.2)
instance Prod.lexLtDec
[LT α] [LT β] [DecidableEq α]
[LT α] [LT β] [DecidableEq α] [DecidableEq β]
[(a b : α) Decidable (a < b)] [(a b : β) Decidable (a < b)]
: (s t : α × β) Decidable (Prod.lexLt s t) :=
fun _ _ => inferInstanceAs (Decidable (_ _))
@@ -1194,11 +1189,6 @@ def Prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂
(f : α₁ α₂) (g : β₁ β₂) : α₁ × β₁ α₂ × β₂
| (a, b) => (f a, g b)
@[simp] theorem Prod.map_apply (f : α β) (g : γ δ) (x) (y) :
Prod.map f g (x, y) = (f x, g y) := rfl
@[simp] theorem Prod.map_fst (f : α β) (g : γ δ) (x) : (Prod.map f g x).1 = f x.1 := rfl
@[simp] theorem Prod.map_snd (f : α β) (g : γ δ) (x) : (Prod.map f g x).2 = g x.2 := rfl
/-! # Dependent products -/
theorem ex_of_PSigma {α : Type u} {p : α Prop} : (PSigma (fun x => p x)) Exists (fun x => p x)
@@ -1313,6 +1303,7 @@ gen_injective_theorems% Fin
gen_injective_theorems% Array
gen_injective_theorems% Sum
gen_injective_theorems% PSum
gen_injective_theorems% Nat
gen_injective_theorems% Option
gen_injective_theorems% List
gen_injective_theorems% Except
@@ -1320,12 +1311,6 @@ gen_injective_theorems% EStateM.Result
gen_injective_theorems% Lean.Name
gen_injective_theorems% Lean.Syntax
theorem Nat.succ.inj {m n : Nat} : m.succ = n.succ m = n :=
fun x => Nat.noConfusion x id
theorem Nat.succ.injEq (u v : Nat) : (u.succ = v.succ) = (u = v) :=
Eq.propIntro Nat.succ.inj (congrArg Nat.succ)
@[simp] theorem beq_iff_eq [BEq α] [LawfulBEq α] (a b : α) : a == b a = b :=
eq_of_beq, by intro h; subst h; exact LawfulBEq.rfl
@@ -1365,9 +1350,6 @@ theorem iff_false_right (ha : ¬a) : (b ↔ a) ↔ ¬b := Iff.comm.trans (iff_fa
theorem of_iff_true (h : a True) : a := h.mpr trivial
theorem iff_true_intro (h : a) : a True := iff_of_true h trivial
theorem eq_iff_true_of_subsingleton [Subsingleton α] (x y : α) : x = y True :=
iff_true_intro (Subsingleton.elim ..)
theorem not_of_iff_false : (p False) ¬p := Iff.mp
theorem iff_false_intro (h : ¬a) : a False := iff_of_false h id
@@ -1609,7 +1591,7 @@ protected def mk' {α : Sort u} [s : Setoid α] (a : α) : Quotient s :=
The analogue of `Quot.sound`: If `a` and `b` are related by the equivalence relation,
then they have equal equivalence classes.
-/
theorem sound {α : Sort u} {s : Setoid α} {a b : α} : a b Quotient.mk s a = Quotient.mk s b :=
def sound {α : Sort u} {s : Setoid α} {a b : α} : a b Quotient.mk s a = Quotient.mk s b :=
Quot.sound
/--
@@ -1873,7 +1855,7 @@ instance : Subsingleton (Squash α) where
/--
`Antisymm (·≤·)` says that `(·≤·)` is antisymmetric, that is, `a ≤ b → b ≤ a → a = b`.
-/
class Antisymm {α : Sort u} (r : α α Prop) : Prop where
class Antisymm {α : Sort u} (r : α α Prop) where
/-- An antisymmetric relation `(·≤·)` satisfies `a ≤ b → b ≤ a → a = b`. -/
antisymm {a b : α} : r a b r b a a = b
@@ -2048,8 +2030,4 @@ class LawfulCommIdentity (op : ααα) (o : outParam α) [hc : Commuta
left_id a := Eq.trans (hc.comm o a) (right_id a)
right_id a := Eq.trans (hc.comm a o) (left_id a)
instance : Commutative Or := fun _ _ => propext or_comm
instance : Commutative And := fun _ _ => propext and_comm
instance : Commutative Iff := fun _ _ => propext iff_comm
end Std

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@@ -14,7 +14,6 @@ import Init.Data.String
import Init.Data.List
import Init.Data.Int
import Init.Data.Array
import Init.Data.Array.Subarray.Split
import Init.Data.ByteArray
import Init.Data.FloatArray
import Init.Data.Fin
@@ -35,4 +34,3 @@ import Init.Data.Queue
import Init.Data.Channel
import Init.Data.Cast
import Init.Data.Sum
import Init.Data.BEq

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@@ -106,7 +106,7 @@ def norm [info : ContextInformation α] (ctx : α) (e : Expr) : List Nat :=
let xs := if info.isComm ctx then sort xs else xs
if info.isIdem ctx then mergeIdem xs else xs
noncomputable def List.two_step_induction
theorem List.two_step_induction
{motive : List Nat Sort u}
(l : List Nat)
(empty : motive [])
@@ -146,8 +146,8 @@ theorem Context.evalList_mergeIdem (ctx : Context α) (h : ContextInformation.is
| nil =>
simp [mergeIdem, mergeIdem.loop]
split
next h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
next => rfl
case inl h₂ => simp [evalList, h₂, h.1, EvalInformation.evalOp]
rfl
| cons z zs =>
by_cases h₂ : x = y
case pos =>
@@ -191,11 +191,11 @@ theorem Context.evalList_insert
. simp [evalList, h.1, EvalInformation.evalOp]
| step y z zs ih =>
simp [insert] at *; split
next => rfl
next =>
case inl => rfl
case inr =>
split
next => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
next => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
case inl => simp [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
case inr => simp_all [evalList, EvalInformation.evalOp]; rw [h.1, ctx.assoc.1, h.1 (evalList _ _ _)]
theorem Context.evalList_sort_congr
(ctx : Context α)

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@@ -10,7 +10,5 @@ import Init.Data.Array.BinSearch
import Init.Data.Array.InsertionSort
import Init.Data.Array.DecidableEq
import Init.Data.Array.Mem
import Init.Data.Array.Attach
import Init.Data.Array.BasicAux
import Init.Data.Array.Lemmas
import Init.Data.Array.TakeDrop

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@@ -1,29 +0,0 @@
/-
Copyright (c) 2021 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner, Mario Carneiro
-/
prelude
import Init.Data.Array.Mem
import Init.Data.List.Attach
namespace Array
/--
Unsafe implementation of `attachWith`, taking advantage of the fact that the representation of
`Array {x // P x}` is the same as the input `Array α`.
-/
@[inline] private unsafe def attachWithImpl
(xs : Array α) (P : α Prop) (_ : x xs, P x) : Array {x // P x} := unsafeCast xs
/-- `O(1)`. "Attach" a proof `P x` that holds for all the elements of `xs` to produce a new array
with the same elements but in the type `{x // P x}`. -/
@[implemented_by attachWithImpl] def attachWith
(xs : Array α) (P : α Prop) (H : x xs, P x) : Array {x // P x} :=
xs.data.attachWith P fun x h => H x (Array.Mem.mk h)
/-- `O(1)`. "Attach" the proof that the elements of `xs` are in `xs` to produce a new array
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
end Array

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@@ -10,7 +10,7 @@ import Init.Data.Fin.Basic
import Init.Data.UInt.Basic
import Init.Data.Repr
import Init.Data.ToString.Basic
import Init.GetElem
import Init.Util
universe u v w
namespace Array
@@ -31,7 +31,6 @@ def ofFn {n} (f : Fin n → α) : Array α := go 0 (mkEmpty n) where
go (i : Nat) (acc : Array α) : Array α :=
if h : i < n then go (i+1) (acc.push (f i, h)) else acc
termination_by n - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
/-- The array `#[0, 1, ..., n - 1]`. -/
def range (n : Nat) : Array Nat :=
@@ -44,7 +43,7 @@ instance : EmptyCollection (Array α) := ⟨Array.empty⟩
instance : Inhabited (Array α) where
default := Array.empty
@[simp] def isEmpty (a : Array α) : Bool :=
def isEmpty (a : Array α) : Bool :=
a.size = 0
def singleton (v : α) : Array α :=
@@ -53,7 +52,7 @@ def singleton (v : α) : Array α :=
/-- Low-level version of `fget` which is as fast as a C array read.
`Fin` values are represented as tag pointers in the Lean runtime. Thus,
`fget` may be slightly slower than `uget`. -/
@[extern "lean_array_uget", simp]
@[extern "lean_array_uget"]
def uget (a : @& Array α) (i : USize) (h : i.toNat < a.size) : α :=
a[i.toNat]
@@ -305,7 +304,6 @@ def mapM {α : Type u} {β : Type v} {m : Type v → Type w} [Monad m] (f : α
else
pure r
termination_by as.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
map 0 (mkEmpty as.size)
@[inline]
@@ -378,7 +376,6 @@ def anyM {α : Type u} {m : Type → Type w} [Monad m] (p : α → m Bool) (as :
else
pure false
termination_by stop - j
decreasing_by simp_wf; decreasing_trivial_pre_omega
loop start
if h : stop as.size then
any stop h
@@ -459,13 +456,24 @@ def findRev? {α : Type} (as : Array α) (p : α → Bool) : Option α :=
@[inline]
def findIdx? {α : Type u} (as : Array α) (p : α Bool) : Option Nat :=
let rec loop (j : Nat) :=
if h : j < as.size then
if p as[j] then some j else loop (j + 1)
else none
termination_by as.size - j
decreasing_by simp_wf; decreasing_trivial_pre_omega
loop 0
let rec loop (i : Nat) (j : Nat) (inv : i + j = as.size) : Option Nat :=
if hlt : j < as.size then
match i, inv with
| 0, inv => by
apply False.elim
rw [Nat.zero_add] at inv
rw [inv] at hlt
exact absurd hlt (Nat.lt_irrefl _)
| i+1, inv =>
if p as[j] then
some j
else
have : i + (j+1) = as.size := by
rw [ inv, Nat.add_comm j 1, Nat.add_assoc]
loop i (j+1) this
else
none
loop as.size 0 rfl
def getIdx? [BEq α] (a : Array α) (v : α) : Option Nat :=
a.findIdx? fun a => a == v
@@ -479,7 +487,7 @@ def all (as : Array α) (p : α → Bool) (start := 0) (stop := as.size) : Bool
Id.run <| as.allM p start stop
def contains [BEq α] (as : Array α) (a : α) : Bool :=
as.any (· == a)
as.any fun b => a == b
def elem [BEq α] (a : α) (as : Array α) : Bool :=
as.contains a
@@ -559,7 +567,6 @@ def isEqvAux (a b : Array α) (hsz : a.size = b.size) (p : αα → Bool) (
else
true
termination_by a.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
@[inline] def isEqv (a b : Array α) (p : α α Bool) : Bool :=
if h : a.size = b.size then
@@ -664,7 +671,6 @@ def indexOfAux [BEq α] (a : Array α) (v : α) (i : Nat) : Option (Fin a.size)
else indexOfAux a v (i+1)
else none
termination_by a.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
def indexOf? [BEq α] (a : Array α) (v : α) : Option (Fin a.size) :=
indexOfAux a v 0
@@ -707,7 +713,6 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
else
as
termination_by as.size
decreasing_by simp_wf; decreasing_trivial_pre_omega
def takeWhile (p : α Bool) (as : Array α) : Array α :=
let rec go (i : Nat) (r : Array α) : Array α :=
@@ -720,38 +725,35 @@ def takeWhile (p : α → Bool) (as : Array α) : Array α :=
else
r
termination_by as.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
go 0 #[]
/-- Remove the element at a given index from an array without bounds checks, using a `Fin` index.
This function takes worst case O(n) time because
it has to backshift all elements at positions greater than `i`.-/
def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
if h : i.val + 1 < a.size then
let a' := a.swap i.val + 1, h i
let i' : Fin a'.size := i.val + 1, by simp [a', h]
a'.feraseIdx i'
def eraseIdxAux (i : Nat) (a : Array α) : Array α :=
if h : i < a.size then
let idx : Fin a.size := i, h;
let idx1 : Fin a.size := i - 1, by exact Nat.lt_of_le_of_lt (Nat.pred_le i) h;
let a' := a.swap idx idx1
eraseIdxAux (i+1) a'
else
a.pop
termination_by a.size - i.val
decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ i.isLt
termination_by a.size - i
theorem size_feraseIdx (a : Array α) (i : Fin a.size) : (a.feraseIdx i).size = a.size - 1 := by
induction a, i using Array.feraseIdx.induct with
| @case1 a i h a' _ ih =>
unfold feraseIdx
simp [h, a', ih]
| case2 a i h =>
unfold feraseIdx
simp [h]
def feraseIdx (a : Array α) (i : Fin a.size) : Array α :=
eraseIdxAux (i.val + 1) a
/-- Remove the element at a given index from an array, or do nothing if the index is out of bounds.
This function takes worst case O(n) time because
it has to backshift all elements at positions greater than `i`.-/
def eraseIdx (a : Array α) (i : Nat) : Array α :=
if h : i < a.size then a.feraseIdx i, h else a
if i < a.size then eraseIdxAux (i+1) a else a
def eraseIdxSzAux (a : Array α) (i : Nat) (r : Array α) (heq : r.size = a.size) : { r : Array α // r.size = a.size - 1 } :=
if h : i < r.size then
let idx : Fin r.size := i, h;
let idx1 : Fin r.size := i - 1, by exact Nat.lt_of_le_of_lt (Nat.pred_le i) h;
eraseIdxSzAux a (i+1) (r.swap idx idx1) ((size_swap r idx idx1).trans heq)
else
r.pop, (size_pop r).trans (heq rfl)
termination_by r.size - i
def eraseIdx' (a : Array α) (i : Fin a.size) : { r : Array α // r.size = a.size - 1 } :=
eraseIdxSzAux a (i.val + 1) a rfl
def erase [BEq α] (as : Array α) (a : α) : Array α :=
match as.indexOf? a with
@@ -768,7 +770,6 @@ def erase [BEq α] (as : Array α) (a : α) : Array α :=
else
as
termination_by j.1
decreasing_by simp_wf; decreasing_trivial_pre_omega
let j := as.size
let as := as.push a
loop as j, size_push .. j.lt_succ_self
@@ -789,11 +790,11 @@ def toArrayLit (a : Array α) (n : Nat) (hsz : a.size = n) : Array α :=
theorem ext' {as bs : Array α} (h : as.data = bs.data) : as = bs := by
cases as; cases bs; simp at h; rw [h]
@[simp] theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
theorem toArrayAux_eq (as : List α) (acc : Array α) : (as.toArrayAux acc).data = acc.data ++ as := by
induction as generalizing acc <;> simp [*, List.toArrayAux, Array.push, List.append_assoc, List.concat_eq_append]
theorem data_toArray (as : List α) : as.toArray.data = as := by
simp [List.toArray, Array.mkEmpty]
simp [List.toArray, toArrayAux_eq, Array.mkEmpty]
theorem toArrayLit_eq (as : Array α) (n : Nat) (hsz : as.size = n) : as = toArrayLit as n hsz := by
apply ext'
@@ -808,7 +809,7 @@ where
rfl
go (i : Nat) (hi : i as.size) : toListLitAux as n hsz i hi (as.data.drop i) = as.data := by
induction i <;> simp [getLit_eq, List.get_drop_eq_drop, toListLitAux, List.drop, *]
cases i <;> simp [getLit_eq, List.get_drop_eq_drop, toListLitAux, List.drop, go]
def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size bs.size) (i : Nat) : Bool :=
if h : i < as.size then
@@ -822,7 +823,6 @@ def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size ≤ bs.size) (i : N
else
true
termination_by as.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
/-- Return true iff `as` is a prefix of `bs`.
That is, `bs = as ++ t` for some `t : List α`.-/
@@ -844,7 +844,6 @@ private def allDiffAux [BEq α] (as : Array α) (i : Nat) : Bool :=
else
true
termination_by as.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
def allDiff [BEq α] (as : Array α) : Bool :=
allDiffAux as 0
@@ -860,7 +859,6 @@ def allDiff [BEq α] (as : Array α) : Bool :=
else
cs
termination_by as.size - i
decreasing_by simp_wf; decreasing_trivial_pre_omega
@[inline] def zipWith (as : Array α) (bs : Array β) (f : α β γ) : Array γ :=
zipWithAux f as bs 0 #[]

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@@ -9,7 +9,7 @@ import Init.Data.Nat.Linear
import Init.NotationExtra
theorem Array.of_push_eq_push {as bs : Array α} (h : as.push a = bs.push b) : as = bs a = b := by
simp only [push, mk.injEq] at h
simp [push] at h
have h₁, h₂ := List.of_concat_eq_concat h
cases as; cases bs
simp_all
@@ -48,7 +48,6 @@ where
let b f as[i]
go (i+1) acc.val.push b, by simp [acc.property] hlt
termination_by as.size - i
decreasing_by decreasing_trivial_pre_omega
@[inline] private unsafe def mapMonoMImp [Monad m] (as : Array α) (f : α m α) : m (Array α) :=
go 0 as

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@@ -21,25 +21,22 @@ theorem eq_of_isEqvAux [DecidableEq α] (a b : Array α) (hsz : a.size = b.size)
subst heq
exact absurd (Nat.lt_of_lt_of_le high low) (Nat.lt_irrefl j)
termination_by a.size - i
decreasing_by decreasing_trivial_pre_omega
theorem eq_of_isEqv [DecidableEq α] (a b : Array α) : Array.isEqv a b (fun x y => x = y) a = b := by
simp [Array.isEqv]
split
next hsz =>
case inr => intro; contradiction
case inl hsz =>
intro h
have aux := eq_of_isEqvAux a b hsz 0 (Nat.zero_le ..) h
exact ext a b hsz fun i h _ => aux i (Nat.zero_le ..) _
next => intro; contradiction
theorem isEqvAux_self [DecidableEq α] (a : Array α) (i : Nat) : Array.isEqvAux a a rfl (fun x y => x = y) i = true := by
unfold Array.isEqvAux
split
next h => simp [h, isEqvAux_self a (i+1)]
next h => simp [h]
case inl h => simp [h, isEqvAux_self a (i+1)]
case inr h => simp [h]
termination_by a.size - i
decreasing_by decreasing_trivial_pre_omega
theorem isEqv_self [DecidableEq α] (a : Array α) : Array.isEqv a a (fun x y => x = y) = true := by
simp [isEqv, isEqvAux_self]

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@@ -5,41 +5,28 @@ Authors: Mario Carneiro
-/
prelude
import Init.Data.Nat.MinMax
import Init.Data.Nat.Lemmas
import Init.Data.List.Lemmas
import Init.Data.Fin.Basic
import Init.Data.Array.Mem
import Init.TacticsExtra
/-!
## Bootstrapping theorems about arrays
This file contains some theorems about `Array` and `List` needed for `Init.Data.List.Impl`.
This file contains some theorems about `Array` and `List` needed for `Std.List.Basic`.
-/
namespace Array
attribute [simp] data_toArray uset
@[simp] theorem singleton_def (v : α) : singleton v = #[v] := rfl
@[simp] theorem toArray_data : (a : Array α) a.data.toArray = a
| l => ext' (data_toArray l)
@[simp] theorem data_length {l : Array α} : l.data.length = l.size := rfl
@[simp] theorem mkEmpty_eq (α n) : @mkEmpty α n = #[] := rfl
@[simp] theorem size_toArray (as : List α) : as.toArray.size = as.length := by simp [size]
@[simp] theorem size_mk (as : List α) : (Array.mk as).size = as.length := by simp [size]
theorem getElem_eq_data_getElem (a : Array α) (h : i < a.size) : a[i] = a.data[i] := by
by_cases i < a.size <;> (try simp [*]) <;> rfl
@[deprecated getElem_eq_data_getElem (since := "2024-06-12")]
theorem getElem_eq_data_get (a : Array α) (h : i < a.size) : a[i] = a.data.get i, h := by
simp [getElem_eq_data_getElem]
by_cases i < a.size <;> (try simp [*]) <;> rfl
theorem foldlM_eq_foldlM_data.aux [Monad m]
(f : β α m β) (arr : Array α) (i j) (H : arr.size i + j) (b) :
@@ -51,7 +38,7 @@ theorem foldlM_eq_foldlM_data.aux [Monad m]
simp [foldlM_eq_foldlM_data.aux f arr i (j+1) H]
rw (config := {occs := .pos [2]}) [ List.get_drop_eq_drop _ _ _]
rfl
· rw [List.drop_of_length_le (Nat.ge_of_not_lt _)]; rfl
· rw [List.drop_length_le (Nat.ge_of_not_lt _)]; rfl
theorem foldlM_eq_foldlM_data [Monad m]
(f : β α m β) (init : β) (arr : Array α) :
@@ -118,11 +105,11 @@ theorem foldr_push (f : α → β → β) (init : β) (arr : Array α) (a : α)
theorem get_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
have : i < (a.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
(a.push x)[i] = a[i] := by
simp only [push, getElem_eq_data_getElem, List.concat_eq_append, List.getElem_append_left, h]
simp only [push, getElem_eq_data_get, List.concat_eq_append, List.get_append_left, h]
@[simp] theorem get_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
simp only [push, getElem_eq_data_getElem, List.concat_eq_append]
rw [List.getElem_append_right] <;> simp [getElem_eq_data_getElem, Nat.zero_lt_one]
simp only [push, getElem_eq_data_get, List.concat_eq_append]
rw [List.get_append_right] <;> simp [getElem_eq_data_get, Nat.zero_lt_one]
theorem get_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size) :
(a.push x)[i] = if h : i < a.size then a[i] else x := by
@@ -139,11 +126,9 @@ where
mapM.map f arr i r = (arr.data.drop i).foldlM (fun bs a => bs.push <$> f a) r := by
unfold mapM.map; split
· rw [ List.get_drop_eq_drop _ i _]
simp only [aux (i + 1), map_eq_pure_bind, data_length, List.foldlM_cons, bind_assoc, pure_bind]
rfl
· rw [List.drop_of_length_le (Nat.ge_of_not_lt _)]; rfl
simp [aux (i+1), map_eq_pure_bind]; rfl
· rw [List.drop_length_le (Nat.ge_of_not_lt _)]; rfl
termination_by arr.size - i
decreasing_by decreasing_trivial_pre_omega
@[simp] theorem map_data (f : α β) (arr : Array α) : (arr.map f).data = arr.data.map f := by
rw [map, mapM_eq_foldlM]
@@ -153,8 +138,7 @@ where
simp [H]
@[simp] theorem size_map (f : α β) (arr : Array α) : (arr.map f).size = arr.size := by
simp only [ data_length]
simp
simp [size]
@[simp] theorem pop_data (arr : Array α) : arr.pop.data = arr.data.dropLast := rfl
@@ -202,8 +186,7 @@ theorem anyM_stop_le_start [Monad m] (p : α → m Bool) (as : Array α) (start
theorem mem_def (a : α) (as : Array α) : a as a as.data :=
fun | .mk h => h, Array.Mem.mk
/-! # get -/
/-- # get -/
@[simp] theorem get_eq_getElem (a : Array α) (i : Fin _) : a.get i = a[i.1] := rfl
theorem getElem?_lt
@@ -220,7 +203,7 @@ theorem getElem?_len_le (a : Array α) {i : Nat} (h : a.size ≤ i) : a[i]? = no
theorem getD_get? (a : Array α) (i : Nat) (d : α) :
Option.getD a[i]? d = if p : i < a.size then a[i]'p else d := by
if h : i < a.size then
simp [setD, h, getElem?_def]
simp [setD, h, getElem?]
else
have p : i a.size := Nat.le_of_not_gt h
simp [setD, getElem?_len_le _ p, h]
@@ -233,16 +216,16 @@ theorem get!_eq_getD [Inhabited α] (a : Array α) : a.get! n = a.getD n default
@[simp] theorem get!_eq_getElem? [Inhabited α] (a : Array α) (i : Nat) : a.get! i = (a.get? i).getD default := by
by_cases p : i < a.size <;> simp [getD_get?, get!_eq_getD, p]
/-! # set -/
/-- # set -/
@[simp] theorem getElem_set_eq (a : Array α) (i : Fin a.size) (v : α) {j : Nat}
(eq : i.val = j) (p : j < (a.set i v).size) :
(a.set i v)[j]'p = v := by
simp [set, getElem_eq_data_getElem, eq]
simp [set, getElem_eq_data_get, eq]
@[simp] theorem getElem_set_ne (a : Array α) (i : Fin a.size) (v : α) {j : Nat} (pj : j < (a.set i v).size)
(h : i.val j) : (a.set i v)[j]'pj = a[j]'(size_set a i v pj) := by
simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]
simp only [set, getElem_eq_data_get, List.get_set_ne _ h]
theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
(h : j < (a.set i v).size) :
@@ -256,7 +239,7 @@ theorem getElem_set (a : Array α) (i : Fin a.size) (v : α) (j : Nat)
(ne : i.val j) : (a.set i v)[j]? = a[j]? := by
by_cases h : j < a.size <;> simp [getElem?_lt, getElem?_ge, Nat.ge_of_not_lt, ne, h]
/-! # setD -/
/- # setD -/
@[simp] theorem set!_is_setD : @set! = @setD := rfl
@@ -282,793 +265,4 @@ theorem getElem?_setD_eq (a : Array α) {i : Nat} (p : i < a.size) (v : α) : (a
by_cases h : i < a.size <;>
simp [setD, Nat.not_lt_of_le, h, getD_get?]
/-! # ofFn -/
@[simp] theorem size_ofFn_go {n} (f : Fin n α) (i acc) :
(ofFn.go f i acc).size = acc.size + (n - i) := by
if hin : i < n then
unfold ofFn.go
have : 1 + (n - (i + 1)) = n - i :=
Nat.sub_sub .. Nat.add_sub_cancel' (Nat.le_sub_of_add_le (Nat.add_comm .. hin))
rw [dif_pos hin, size_ofFn_go f (i+1), size_push, Nat.add_assoc, this]
else
have : n - i = 0 := Nat.sub_eq_zero_of_le (Nat.le_of_not_lt hin)
unfold ofFn.go
simp [hin, this]
termination_by n - i
@[simp] theorem size_ofFn (f : Fin n α) : (ofFn f).size = n := by simp [ofFn]
theorem getElem_ofFn_go (f : Fin n α) (i) {acc k}
(hki : k < n) (hin : i n) (hi : i = acc.size)
(hacc : j, hj : j < acc.size, acc[j] = f j, Nat.lt_of_lt_of_le hj (hi hin)) :
haveI : acc.size + (n - acc.size) = n := Nat.add_sub_cancel' (hi hin)
(ofFn.go f i acc)[k]'(by simp [*]) = f k, hki := by
unfold ofFn.go
if hin : i < n then
have : 1 + (n - (i + 1)) = n - i :=
Nat.sub_sub .. Nat.add_sub_cancel' (Nat.le_sub_of_add_le (Nat.add_comm .. hin))
simp only [dif_pos hin]
rw [getElem_ofFn_go f (i+1) _ hin (by simp [*]) (fun j hj => ?hacc)]
cases (Nat.lt_or_eq_of_le <| Nat.le_of_lt_succ (by simpa using hj)) with
| inl hj => simp [get_push, hj, hacc j hj]
| inr hj => simp [get_push, *]
else
simp [hin, hacc k (Nat.lt_of_lt_of_le hki (Nat.le_of_not_lt (hi hin)))]
termination_by n - i
@[simp] theorem getElem_ofFn (f : Fin n α) (i : Nat) (h) :
(ofFn f)[i] = f i, size_ofFn f h :=
getElem_ofFn_go _ _ _ (by simp) (by simp) nofun
/-- # mkArray -/
@[simp] theorem mkArray_data (n : Nat) (v : α) : (mkArray n v).data = List.replicate n v := rfl
@[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
(mkArray n v)[i] = v := by simp [Array.getElem_eq_data_getElem]
/-- # mem -/
theorem mem_data {a : α} {l : Array α} : a l.data a l := (mem_def _ _).symm
theorem not_mem_nil (a : α) : ¬ a #[] := nofun
/-- # get lemmas -/
theorem getElem?_mem {l : Array α} {i : Fin l.size} : l[i] l := by
erw [Array.mem_def, getElem_eq_data_getElem]
apply List.get_mem
theorem getElem_fin_eq_data_get (a : Array α) (i : Fin _) : a[i] = a.data.get i := rfl
@[simp] theorem ugetElem_eq_getElem (a : Array α) {i : USize} (h : i.toNat < a.size) :
a[i] = a[i.toNat] := rfl
theorem getElem?_eq_getElem (a : Array α) (i : Nat) (h : i < a.size) : a[i]? = a[i] :=
getElem?_pos ..
theorem get?_len_le (a : Array α) (i : Nat) (h : a.size i) : a[i]? = none := by
simp [getElem?_neg, h]
theorem getElem_mem_data (a : Array α) (h : i < a.size) : a[i] a.data := by
simp only [getElem_eq_data_getElem, List.getElem_mem]
theorem getElem?_eq_data_get? (a : Array α) (i : Nat) : a[i]? = a.data.get? i := by
by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]; rfl
theorem get?_eq_data_get? (a : Array α) (i : Nat) : a.get? i = a.data.get? i :=
getElem?_eq_data_get? ..
theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
simp [get!_eq_getD]
@[simp] theorem back_eq_back? [Inhabited α] (a : Array α) : a.back = a.back?.getD default := by
simp [back, back?]
@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
simp [back?, getElem?_eq_data_get?]
theorem back_push [Inhabited α] (a : Array α) : (a.push x).back = x := by simp
theorem get?_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
(a.push x)[i]? = some a[i] := by
rw [getElem?_pos, get_push_lt]
theorem get?_push_eq (a : Array α) (x : α) : (a.push x)[a.size]? = some x := by
rw [getElem?_pos, get_push_eq]
theorem get?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x else a[i]? := by
match Nat.lt_trichotomy i a.size with
| Or.inl g =>
have h1 : i < a.size + 1 := by omega
have h2 : i a.size := by omega
simp [getElem?_def, size_push, g, h1, h2, get_push_lt]
| Or.inr (Or.inl heq) =>
simp [heq, getElem?_pos, get_push_eq]
| Or.inr (Or.inr g) =>
simp only [getElem?_def, size_push]
have h1 : ¬ (i < a.size) := by omega
have h2 : ¬ (i < a.size + 1) := by omega
have h3 : i a.size := by omega
simp [h1, h2, h3]
@[simp] theorem get?_size {a : Array α} : a[a.size]? = none := by
simp only [getElem?_def, Nat.lt_irrefl, dite_false]
@[simp] theorem data_set (a : Array α) (i v) : (a.set i v).data = a.data.set i.1 v := rfl
theorem get_set_eq (a : Array α) (i : Fin a.size) (v : α) :
(a.set i v)[i.1] = v := by
simp only [set, getElem_eq_data_getElem, List.getElem_set_eq]
theorem get?_set_eq (a : Array α) (i : Fin a.size) (v : α) :
(a.set i v)[i.1]? = v := by simp [getElem?_pos, i.2]
@[simp] theorem get?_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α)
(h : i.1 j) : (a.set i v)[j]? = a[j]? := by
by_cases j < a.size <;> simp [getElem?_pos, getElem?_neg, *]
theorem get?_set (a : Array α) (i : Fin a.size) (j : Nat) (v : α) :
(a.set i v)[j]? = if i.1 = j then some v else a[j]? := by
if h : i.1 = j then subst j; simp [*] else simp [*]
theorem get_set (a : Array α) (i : Fin a.size) (j : Nat) (hj : j < a.size) (v : α) :
(a.set i v)[j]'(by simp [*]) = if i = j then v else a[j] := by
if h : i.1 = j then subst j; simp [*] else simp [*]
@[simp] theorem get_set_ne (a : Array α) (i : Fin a.size) {j : Nat} (v : α) (hj : j < a.size)
(h : i.1 j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
simp only [set, getElem_eq_data_getElem, List.getElem_set_ne h]
theorem getElem_setD (a : Array α) (i : Nat) (v : α) (h : i < (setD a i v).size) :
(setD a i v)[i] = v := by
simp at h
simp only [setD, h, dite_true, get_set, ite_true]
theorem set_set (a : Array α) (i : Fin a.size) (v v' : α) :
(a.set i v).set i, by simp [i.2] v' = a.set i v' := by simp [set, List.set_set]
private theorem fin_cast_val (e : n = n') (i : Fin n) : e i = i.1, e i.2 := by cases e; rfl
theorem swap_def (a : Array α) (i j : Fin a.size) :
a.swap i j = (a.set i (a.get j)).set j.1, by simp [j.2] (a.get i) := by
simp [swap, fin_cast_val]
theorem data_swap (a : Array α) (i j : Fin a.size) :
(a.swap i j).data = (a.data.set i (a.get j)).set j (a.get i) := by simp [swap_def]
theorem get?_swap (a : Array α) (i j : Fin a.size) (k : Nat) : (a.swap i j)[k]? =
if j = k then some a[i.1] else if i = k then some a[j.1] else a[k]? := by
simp [swap_def, get?_set, getElem_fin_eq_data_get]
@[simp] theorem swapAt_def (a : Array α) (i : Fin a.size) (v : α) :
a.swapAt i v = (a[i.1], a.set i v) := rfl
-- @[simp] -- FIXME: gives a weird linter error
theorem swapAt!_def (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
a.swapAt! i v = (a[i], a.set i, h v) := by simp [swapAt!, h]
@[simp] theorem data_pop (a : Array α) : a.pop.data = a.data.dropLast := by simp [pop]
@[simp] theorem pop_empty : (#[] : Array α).pop = #[] := rfl
@[simp] theorem pop_push (a : Array α) : (a.push x).pop = a := by simp [pop]
@[simp] theorem getElem_pop (a : Array α) (i : Nat) (hi : i < a.pop.size) :
a.pop[i] = a[i]'(Nat.lt_of_lt_of_le (a.size_pop hi) (Nat.sub_le _ _)) :=
List.getElem_dropLast ..
theorem eq_empty_of_size_eq_zero {as : Array α} (h : as.size = 0) : as = #[] := by
apply ext
· simp [h]
· intros; contradiction
theorem eq_push_pop_back_of_size_ne_zero [Inhabited α] {as : Array α} (h : as.size 0) :
as = as.pop.push as.back := by
apply ext
· simp [Nat.sub_add_cancel (Nat.zero_lt_of_ne_zero h)]
· intros i h h'
if hlt : i < as.pop.size then
rw [get_push_lt (h:=hlt), getElem_pop]
else
have heq : i = as.pop.size :=
Nat.le_antisymm (size_pop .. Nat.le_pred_of_lt h) (Nat.le_of_not_gt hlt)
cases heq; rw [get_push_eq, back, size_pop, get!_eq_getD, getD, dif_pos h]; rfl
theorem eq_push_of_size_ne_zero {as : Array α} (h : as.size 0) :
(bs : Array α) (c : α), as = bs.push c :=
let _ : Inhabited α := as[0]
as.pop, as.back, eq_push_pop_back_of_size_ne_zero h
theorem size_eq_length_data (as : Array α) : as.size = as.data.length := rfl
@[simp] theorem size_swap! (a : Array α) (i j) :
(a.swap! i j).size = a.size := by unfold swap!; split <;> (try split) <;> simp [size_swap]
@[simp] theorem size_reverse (a : Array α) : a.reverse.size = a.size := by
let rec go (as : Array α) (i j) : (reverse.loop as i j).size = as.size := by
rw [reverse.loop]
if h : i < j then
have := reverse.termination h
simp [(go · (i+1) j-1, ·), h]
else simp [h]
termination_by j - i
simp only [reverse]; split <;> simp [go]
@[simp] theorem size_range {n : Nat} : (range n).size = n := by
unfold range
induction n with
| zero => simp [Nat.fold]
| succ k ih =>
rw [Nat.fold, flip]
simp only [mkEmpty_eq, size_push] at *
omega
set_option linter.deprecated false in
@[simp] theorem reverse_data (a : Array α) : a.reverse.data = a.data.reverse := by
let rec go (as : Array α) (i j hj)
(h : i + j + 1 = a.size) (h₂ : as.size = a.size)
(H : k, as.data.get? k = if i k k j then a.data.get? k else a.data.reverse.get? k)
(k) : (reverse.loop as i j, hj).data.get? k = a.data.reverse.get? k := by
rw [reverse.loop]; dsimp; split <;> rename_i h₁
· have p := reverse.termination h₁
match j with | j+1 => ?_
simp only [Nat.add_sub_cancel] at p
rw [(go · (i+1) j)]
· rwa [Nat.add_right_comm i]
· simp [size_swap, h₂]
· intro k
rw [ getElem?_eq_data_get?, get?_swap]
simp only [H, getElem_eq_data_get, List.get?_eq_get, Nat.le_of_lt h₁, getElem?_eq_data_get?]
split <;> rename_i h₂
· simp only [ h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
exact (List.get?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
split <;> rename_i h₃
· simp only [ h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
exact (List.get?_reverse' i (j+1) (Eq.trans (by simp_arith) h)).symm
simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
· rw [H]; split <;> rename_i h₂
· cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
cases Nat.le_antisymm h₂.1 h₂.2
exact (List.get?_reverse' _ _ h).symm
· rfl
termination_by j - i
simp only [reverse]
split
· match a with | [] | [_] => rfl
· have := Nat.sub_add_cancel (Nat.le_of_not_le _)
refine List.ext_get? <| go _ _ _ _ (by simp [this]) rfl fun k => ?_
split
· rfl
· rename_i h
simp only [ show k < _ + 1 _ from Nat.lt_succ (n := a.size - 1), this, Nat.zero_le,
true_and, Nat.not_lt] at h
rw [List.get?_eq_none.2 _, List.get?_eq_none.2 (a.data.length_reverse _)]
/-! ### foldl / foldr -/
-- This proof is the pure version of `Array.SatisfiesM_foldlM`,
-- reproduced to avoid a dependency on `SatisfiesM`.
theorem foldl_induction
{as : Array α} (motive : Nat β Prop) {init : β} (h0 : motive 0 init) {f : β α β}
(hf : i : Fin as.size, b, motive i.1 b motive (i.1 + 1) (f b as[i])) :
motive as.size (as.foldl f init) := by
let rec go {i j b} (h₁ : j as.size) (h₂ : as.size i + j) (H : motive j b) :
(motive as.size) (foldlM.loop (m := Id) f as as.size (Nat.le_refl _) i j b) := by
unfold foldlM.loop; split
· next hj =>
split
· cases Nat.not_le_of_gt (by simp [hj]) h₂
· exact go hj (by rwa [Nat.succ_add] at h₂) (hf j, hj b H)
· next hj => exact Nat.le_antisymm h₁ (Nat.ge_of_not_lt hj) H
simpa [foldl, foldlM] using go (Nat.zero_le _) (Nat.le_refl _) h0
-- This proof is the pure version of `Array.SatisfiesM_foldrM`,
-- reproduced to avoid a dependency on `SatisfiesM`.
theorem foldr_induction
{as : Array α} (motive : Nat β Prop) {init : β} (h0 : motive as.size init) {f : α β β}
(hf : i : Fin as.size, b, motive (i.1 + 1) b motive i.1 (f as[i] b)) :
motive 0 (as.foldr f init) := by
let rec go {i b} (hi : i as.size) (H : motive i b) :
(motive 0) (foldrM.fold (m := Id) f as 0 i hi b) := by
unfold foldrM.fold; simp; split
· next hi => exact (hi H)
· next hi =>
split; {simp at hi}
· next i hi' =>
exact go _ (hf i, hi' b H)
simp [foldr, foldrM]; split; {exact go _ h0}
· next h => exact (Nat.eq_zero_of_not_pos h h0)
/-! ### map -/
@[simp] theorem mem_map {f : α β} {l : Array α} : b l.map f a, a l f a = b := by
simp only [mem_def, map_data, List.mem_map]
theorem mapM_eq_mapM_data [Monad m] [LawfulMonad m] (f : α m β) (arr : Array α) :
arr.mapM f = return mk ( arr.data.mapM f) := by
rw [mapM_eq_foldlM, foldlM_eq_foldlM_data, List.foldrM_reverse]
conv => rhs; rw [ List.reverse_reverse arr.data]
induction arr.data.reverse with
| nil => simp; rfl
| cons a l ih => simp [ih]; simp [map_eq_pure_bind, push]
theorem mapM_map_eq_foldl (as : Array α) (f : α β) (i) :
mapM.map (m := Id) f as i b = as.foldl (start := i) (fun r a => r.push (f a)) b := by
unfold mapM.map
split <;> rename_i h
· simp only [Id.bind_eq]
dsimp [foldl, Id.run, foldlM]
rw [mapM_map_eq_foldl, dif_pos (by omega), foldlM.loop, dif_pos h]
-- Calling `split` here gives a bad goal.
have : size as - i = Nat.succ (size as - i - 1) := by omega
rw [this]
simp [foldl, foldlM, Id.run, Nat.sub_add_eq]
· dsimp [foldl, Id.run, foldlM]
rw [dif_pos (by omega), foldlM.loop, dif_neg h]
rfl
termination_by as.size - i
theorem map_eq_foldl (as : Array α) (f : α β) :
as.map f = as.foldl (fun r a => r.push (f a)) #[] :=
mapM_map_eq_foldl _ _ _
theorem map_induction (as : Array α) (f : α β) (motive : Nat Prop) (h0 : motive 0)
(p : Fin as.size β Prop) (hs : i, motive i.1 p i (f as[i]) motive (i+1)) :
motive as.size
eq : (as.map f).size = as.size, i h, p i, h ((as.map f)[i]) := by
have t := foldl_induction (as := as) (β := Array β)
(motive := fun i arr => motive i arr.size = i i h2, p i arr[i.1])
(init := #[]) (f := fun r a => r.push (f a)) ?_ ?_
obtain m, eq, w := t
· refine m, by simpa [map_eq_foldl] using eq, ?_
intro i h
simp [eq] at w
specialize w i, h h
simpa [map_eq_foldl] using w
· exact h0, rfl, nofun
· intro i b m, eq, w
refine ?_, ?_, ?_
· exact (hs _ m).2
· simp_all
· intro j h
simp at h
by_cases h' : j < size b
· rw [get_push]
simp_all
· rw [get_push, dif_neg h']
simp only [show j = i by omega]
exact (hs _ m).1
theorem map_spec (as : Array α) (f : α β) (p : Fin as.size β Prop)
(hs : i, p i (f as[i])) :
eq : (as.map f).size = as.size, i h, p i, h ((as.map f)[i]) := by
simpa using map_induction as f (fun _ => True) trivial p (by simp_all)
@[simp] theorem getElem_map (f : α β) (as : Array α) (i : Nat) (h) :
((as.map f)[i]) = f (as[i]'(size_map .. h)) := by
have := map_spec as f (fun i b => b = f (as[i]))
simp only [implies_true, true_implies] at this
obtain eq, w := this
apply w
simp_all
/-! ### mapIdx -/
-- This could also be prove from `SatisfiesM_mapIdxM`.
theorem mapIdx_induction (as : Array α) (f : Fin as.size α β)
(motive : Nat Prop) (h0 : motive 0)
(p : Fin as.size β Prop)
(hs : i, motive i.1 p i (f i as[i]) motive (i + 1)) :
motive as.size eq : (Array.mapIdx as f).size = as.size,
i h, p i, h ((Array.mapIdx as f)[i]) := by
let rec go {bs i j h} (h₁ : j = bs.size) (h₂ : i h h', p i, h bs[i]) (hm : motive j) :
let arr : Array β := Array.mapIdxM.map (m := Id) as f i j h bs
motive as.size eq : arr.size = as.size, i h, p i, h arr[i] := by
induction i generalizing j bs with simp [mapIdxM.map]
| zero =>
have := (Nat.zero_add _).symm.trans h
exact this hm, h₁ this, fun _ _ => h₂ ..
| succ i ih =>
apply @ih (bs.push (f j, by omega as[j])) (j + 1) (by omega) (by simp; omega)
· intro i i_lt h'
rw [get_push]
split
· apply h₂
· simp only [size_push] at h'
obtain rfl : i = j := by omega
apply (hs i, by omega hm).1
· exact (hs j, by omega hm).2
simp [mapIdx, mapIdxM]; exact go rfl nofun h0
theorem mapIdx_spec (as : Array α) (f : Fin as.size α β)
(p : Fin as.size β Prop) (hs : i, p i (f i as[i])) :
eq : (Array.mapIdx as f).size = as.size,
i h, p i, h ((Array.mapIdx as f)[i]) :=
(mapIdx_induction _ _ (fun _ => True) trivial p fun _ _ => hs .., trivial).2
@[simp] theorem size_mapIdx (a : Array α) (f : Fin a.size α β) : (a.mapIdx f).size = a.size :=
(mapIdx_spec (p := fun _ _ => True) (hs := fun _ => trivial)).1
@[simp] theorem size_zipWithIndex (as : Array α) : as.zipWithIndex.size = as.size :=
Array.size_mapIdx _ _
@[simp] theorem getElem_mapIdx (a : Array α) (f : Fin a.size α β) (i : Nat)
(h : i < (mapIdx a f).size) :
haveI : i < a.size := by simp_all
(a.mapIdx f)[i] = f i, this a[i] :=
(mapIdx_spec _ _ (fun i b => b = f i a[i]) fun _ => rfl).2 i _
/-! ### modify -/
@[simp] theorem size_modify (a : Array α) (i : Nat) (f : α α) : (a.modify i f).size = a.size := by
unfold modify modifyM Id.run
split <;> simp
theorem get_modify {arr : Array α} {x i} (h : i < arr.size) :
(arr.modify x f).get i, by simp [h] =
if x = i then f (arr.get i, h) else arr.get i, h := by
simp [modify, modifyM, Id.run]; split
· simp [get_set _ _ _ h]; split <;> simp [*]
· rw [if_neg (mt (by rintro rfl; exact h) _)]
/-! ### filter -/
@[simp] theorem filter_data (p : α Bool) (l : Array α) :
(l.filter p).data = l.data.filter p := by
dsimp only [filter]
rw [foldl_eq_foldl_data]
generalize l.data = l
suffices a, (List.foldl (fun r a => if p a = true then push r a else r) a l).data =
a.data ++ List.filter p l by
simpa using this #[]
induction l with simp
| cons => split <;> simp [*]
@[simp] theorem filter_filter (q) (l : Array α) :
filter p (filter q l) = filter (fun a => p a q a) l := by
apply ext'
simp only [filter_data, List.filter_filter]
@[simp] theorem mem_filter : x filter p as x as p x := by
simp only [mem_def, filter_data, List.mem_filter]
theorem mem_of_mem_filter {a : α} {l} (h : a filter p l) : a l :=
(mem_filter.mp h).1
/-! ### filterMap -/
@[simp] theorem filterMap_data (f : α Option β) (l : Array α) :
(l.filterMap f).data = l.data.filterMap f := by
dsimp only [filterMap, filterMapM]
rw [foldlM_eq_foldlM_data]
generalize l.data = l
have this : a : Array β, (Id.run (List.foldlM (m := Id) ?_ a l)).data =
a.data ++ List.filterMap f l := ?_
exact this #[]
induction l
· simp_all [Id.run]
· simp_all [Id.run, List.filterMap_cons]
split <;> simp_all
@[simp] theorem mem_filterMap (f : α Option β) (l : Array α) {b : β} :
b filterMap f l a, a l f a = some b := by
simp only [mem_def, filterMap_data, List.mem_filterMap]
/-! ### empty -/
theorem size_empty : (#[] : Array α).size = 0 := rfl
theorem empty_data : (#[] : Array α).data = [] := rfl
/-! ### append -/
theorem push_eq_append_singleton (as : Array α) (x) : as.push x = as ++ #[x] := rfl
@[simp] theorem mem_append {a : α} {s t : Array α} : a s ++ t a s a t := by
simp only [mem_def, append_data, List.mem_append]
theorem size_append (as bs : Array α) : (as ++ bs).size = as.size + bs.size := by
simp only [size, append_data, List.length_append]
theorem get_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
(as ++ bs)[i] = as[i] := by
simp only [getElem_eq_data_getElem]
have h' : i < (as.data ++ bs.data).length := by rwa [ data_length, append_data] at h
conv => rhs; rw [ List.getElem_append_left (bs := bs.data) (h' := h')]
apply List.get_of_eq; rw [append_data]
theorem get_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size i)
(hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. h)) :
(as ++ bs)[i] = bs[i - as.size] := by
simp only [getElem_eq_data_getElem]
have h' : i < (as.data ++ bs.data).length := by rwa [ data_length, append_data] at h
conv => rhs; rw [ List.getElem_append_right (h' := h') (h := Nat.not_lt_of_ge hle)]
apply List.get_of_eq; rw [append_data]
@[simp] theorem append_nil (as : Array α) : as ++ #[] = as := by
apply ext'; simp only [append_data, empty_data, List.append_nil]
@[simp] theorem nil_append (as : Array α) : #[] ++ as = as := by
apply ext'; simp only [append_data, empty_data, List.nil_append]
theorem append_assoc (as bs cs : Array α) : as ++ bs ++ cs = as ++ (bs ++ cs) := by
apply ext'; simp only [append_data, List.append_assoc]
/-! ### extract -/
theorem extract_loop_zero (as bs : Array α) (start : Nat) : extract.loop as 0 start bs = bs := by
rw [extract.loop]; split <;> rfl
theorem extract_loop_succ (as bs : Array α) (size start : Nat) (h : start < as.size) :
extract.loop as (size+1) start bs = extract.loop as size (start+1) (bs.push as[start]) := by
rw [extract.loop, dif_pos h]; rfl
theorem extract_loop_of_ge (as bs : Array α) (size start : Nat) (h : start as.size) :
extract.loop as size start bs = bs := by
rw [extract.loop, dif_neg (Nat.not_lt_of_ge h)]
theorem extract_loop_eq_aux (as bs : Array α) (size start : Nat) :
extract.loop as size start bs = bs ++ extract.loop as size start #[] := by
induction size using Nat.recAux generalizing start bs with
| zero => rw [extract_loop_zero, extract_loop_zero, append_nil]
| succ size ih =>
if h : start < as.size then
rw [extract_loop_succ (h:=h), ih (bs.push _), push_eq_append_singleton]
rw [extract_loop_succ (h:=h), ih (#[].push _), push_eq_append_singleton, nil_append]
rw [append_assoc]
else
rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
rw [extract_loop_of_ge (h:=Nat.le_of_not_lt h)]
rw [append_nil]
theorem extract_loop_eq (as bs : Array α) (size start : Nat) (h : start + size as.size) :
extract.loop as size start bs = bs ++ as.extract start (start + size) := by
simp [extract]; rw [extract_loop_eq_aux, Nat.min_eq_left h, Nat.add_sub_cancel_left]
theorem size_extract_loop (as bs : Array α) (size start : Nat) :
(extract.loop as size start bs).size = bs.size + min size (as.size - start) := by
induction size using Nat.recAux generalizing start bs with
| zero => rw [extract_loop_zero, Nat.zero_min, Nat.add_zero]
| succ size ih =>
if h : start < as.size then
rw [extract_loop_succ (h:=h), ih, size_push, Nat.add_assoc, Nat.add_min_add_left,
Nat.sub_succ, Nat.one_add, Nat.one_add, Nat.succ_pred_eq_of_pos (Nat.sub_pos_of_lt h)]
else
have h := Nat.le_of_not_gt h
rw [extract_loop_of_ge (h:=h), Nat.sub_eq_zero_of_le h, Nat.min_zero, Nat.add_zero]
@[simp] theorem size_extract (as : Array α) (start stop : Nat) :
(as.extract start stop).size = min stop as.size - start := by
simp [extract]; rw [size_extract_loop, size_empty, Nat.zero_add, Nat.sub_min_sub_right,
Nat.min_assoc, Nat.min_self]
theorem get_extract_loop_lt_aux (as bs : Array α) (size start : Nat) (hlt : i < bs.size) :
i < (extract.loop as size start bs).size := by
rw [size_extract_loop]
apply Nat.lt_of_lt_of_le hlt
exact Nat.le_add_right ..
theorem get_extract_loop_lt (as bs : Array α) (size start : Nat) (hlt : i < bs.size)
(h := get_extract_loop_lt_aux as bs size start hlt) :
(extract.loop as size start bs)[i] = bs[i] := by
apply Eq.trans _ (get_append_left (bs:=extract.loop as size start #[]) hlt)
· rw [size_append]; exact Nat.lt_of_lt_of_le hlt (Nat.le_add_right ..)
· congr; rw [extract_loop_eq_aux]
theorem get_extract_loop_ge_aux (as bs : Array α) (size start : Nat) (hge : i bs.size)
(h : i < (extract.loop as size start bs).size) : start + i - bs.size < as.size := by
have h : i < bs.size + (as.size - start) := by
apply Nat.lt_of_lt_of_le h
rw [size_extract_loop]
apply Nat.add_le_add_left
exact Nat.min_le_right ..
rw [Nat.add_sub_assoc hge]
apply Nat.add_lt_of_lt_sub'
exact Nat.sub_lt_left_of_lt_add hge h
theorem get_extract_loop_ge (as bs : Array α) (size start : Nat) (hge : i bs.size)
(h : i < (extract.loop as size start bs).size)
(h' := get_extract_loop_ge_aux as bs size start hge h) :
(extract.loop as size start bs)[i] = as[start + i - bs.size] := by
induction size using Nat.recAux generalizing start bs with
| zero =>
rw [size_extract_loop, Nat.zero_min, Nat.add_zero] at h
omega
| succ size ih =>
have : start < as.size := by
apply Nat.lt_of_le_of_lt (Nat.le_add_right start (i - bs.size))
rwa [ Nat.add_sub_assoc hge]
have : i < (extract.loop as size (start+1) (bs.push as[start])).size := by
rwa [ extract_loop_succ]
have heq : (extract.loop as (size+1) start bs)[i] =
(extract.loop as size (start+1) (bs.push as[start]))[i] := by
congr 1; rw [extract_loop_succ]
rw [heq]
if hi : bs.size = i then
cases hi
have h₁ : bs.size < (bs.push as[start]).size := by rw [size_push]; exact Nat.lt_succ_self ..
have h₂ : bs.size < (extract.loop as size (start+1) (bs.push as[start])).size := by
rw [size_extract_loop]; apply Nat.lt_of_lt_of_le h₁; exact Nat.le_add_right ..
have h : (extract.loop as size (start + 1) (push bs as[start]))[bs.size] = as[start] := by
rw [get_extract_loop_lt as (bs.push as[start]) size (start+1) h₁ h₂, get_push_eq]
rw [h]; congr; rw [Nat.add_sub_cancel]
else
have hge : bs.size + 1 i := Nat.lt_of_le_of_ne hge hi
rw [ih (bs.push as[start]) (start+1) ((size_push ..).symm hge)]
congr 1; rw [size_push, Nat.add_right_comm, Nat.add_sub_add_right]
theorem get_extract_aux {as : Array α} {start stop : Nat} (h : i < (as.extract start stop).size) :
start + i < as.size := by
rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
apply Nat.sub_le_sub_right; apply Nat.min_le_right
@[simp] theorem get_extract {as : Array α} {start stop : Nat}
(h : i < (as.extract start stop).size) :
(as.extract start stop)[i] = as[start + i]'(get_extract_aux h) :=
show (extract.loop as (min stop as.size - start) start #[])[i]
= as[start + i]'(get_extract_aux h) by rw [get_extract_loop_ge]; rfl; exact Nat.zero_le _
@[simp] theorem extract_all (as : Array α) : as.extract 0 as.size = as := by
apply ext
· rw [size_extract, Nat.min_self, Nat.sub_zero]
· intros; rw [get_extract]; congr; rw [Nat.zero_add]
theorem extract_empty_of_stop_le_start (as : Array α) {start stop : Nat} (h : stop start) :
as.extract start stop = #[] := by
simp [extract]; rw [Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.zero_min,
extract_loop_zero]
theorem extract_empty_of_size_le_start (as : Array α) {start stop : Nat} (h : as.size start) :
as.extract start stop = #[] := by
simp [extract]; rw [Nat.sub_min_sub_right, Nat.sub_eq_zero_of_le h, Nat.min_zero,
extract_loop_zero]
@[simp] theorem extract_empty (start stop : Nat) : (#[] : Array α).extract start stop = #[] :=
extract_empty_of_size_le_start _ (Nat.zero_le _)
/-! ### any -/
-- Auxiliary for `any_iff_exists`.
theorem anyM_loop_iff_exists (p : α Bool) (as : Array α) (start stop) (h : stop as.size) :
anyM.loop (m := Id) p as stop h start = true
i : Fin as.size, start i i < stop p as[i] = true := by
unfold anyM.loop
split <;> rename_i h₁
· dsimp
split <;> rename_i h₂
· simp only [true_iff]
refine start, by omega, by dsimp; omega, by dsimp; omega, h₂
· rw [anyM_loop_iff_exists]
constructor
· rintro i, ge, lt, h
have : start i := by rintro rfl; omega
exact i, by omega, lt, h
· rintro i, ge, lt, h
have : start i := by rintro rfl; erw [h] at h₂; simp_all
exact i, by omega, lt, h
· simp
omega
termination_by stop - start
-- This could also be proved from `SatisfiesM_anyM_iff_exists` in `Batteries.Data.Array.Init.Monadic`
theorem any_iff_exists (p : α Bool) (as : Array α) (start stop) :
any as p start stop i : Fin as.size, start i.1 i.1 < stop p as[i] := by
dsimp [any, anyM, Id.run]
split
· rw [anyM_loop_iff_exists]; rfl
· rw [anyM_loop_iff_exists]
constructor
· rintro i, ge, _, h
exact i, by omega, by omega, h
· rintro i, ge, _, h
exact i, by omega, by omega, h
theorem any_eq_true (p : α Bool) (as : Array α) :
any as p i : Fin as.size, p as[i] := by simp [any_iff_exists, Fin.isLt]
theorem any_def {p : α Bool} (as : Array α) : as.any p = as.data.any p := by
rw [Bool.eq_iff_iff, any_eq_true, List.any_eq_true]; simp only [List.mem_iff_get]
exact fun i, h => _, i, rfl, h, fun _, i, rfl, h => i, h
/-! ### all -/
theorem all_eq_not_any_not (p : α Bool) (as : Array α) (start stop) :
all as p start stop = !(any as (!p ·) start stop) := by
dsimp [all, allM]
rfl
theorem all_iff_forall (p : α Bool) (as : Array α) (start stop) :
all as p start stop i : Fin as.size, start i.1 i.1 < stop p as[i] := by
rw [all_eq_not_any_not]
suffices ¬(any as (!p ·) start stop = true)
i : Fin as.size, start i.1 i.1 < stop p as[i] by
simp_all
rw [any_iff_exists]
simp
theorem all_eq_true (p : α Bool) (as : Array α) : all as p i : Fin as.size, p as[i] := by
simp [all_iff_forall, Fin.isLt]
theorem all_def {p : α Bool} (as : Array α) : as.all p = as.data.all p := by
rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_getElem]
constructor
· rintro w x r, h, rfl
rw [ getElem_eq_data_getElem]
exact w r, h
· intro w i
exact w as[i] i, i.2, (getElem_eq_data_getElem as i.2).symm
theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p x, x l p x := by
simp only [all_def, List.all_eq_true, mem_def]
/-! ### contains -/
theorem contains_def [DecidableEq α] {a : α} {as : Array α} : as.contains a a as := by
rw [mem_def, contains, any_def, List.any_eq_true]; simp [and_comm]
instance [DecidableEq α] (a : α) (as : Array α) : Decidable (a as) :=
decidable_of_iff _ contains_def
/-! ### swap -/
open Fin
@[simp] theorem get_swap_right (a : Array α) {i j : Fin a.size} : (a.swap i j)[j.val] = a[i] :=
by simp only [swap, fin_cast_val, get_eq_getElem, getElem_set_eq, getElem_fin]
@[simp] theorem get_swap_left (a : Array α) {i j : Fin a.size} : (a.swap i j)[i.val] = a[j] :=
if he : ((Array.size_set _ _ _).symm j).val = i.val then by
simp only [he, fin_cast_val, get_swap_right, getElem_fin]
else by
apply Eq.trans
· apply Array.get_set_ne
· simp only [size_set, Fin.isLt]
· assumption
· simp [get_set_ne]
@[simp] theorem get_swap_of_ne (a : Array α) {i j : Fin a.size} (hp : p < a.size)
(hi : p i) (hj : p j) : (a.swap i j)[p]'(a.size_swap .. |>.symm hp) = a[p] := by
apply Eq.trans
· have : ((a.size_set i (a.get j)).symm j).val = j.val := by simp only [fin_cast_val]
apply Array.get_set_ne
· simp only [this]
apply Ne.symm
· assumption
· apply Array.get_set_ne
· apply Ne.symm
· assumption
theorem get_swap (a : Array α) (i j : Fin a.size) (k : Nat) (hk: k < a.size) :
(a.swap i j)[k]'(by simp_all) = if k = i then a[j] else if k = j then a[i] else a[k] := by
split
· simp_all only [get_swap_left]
· split <;> simp_all
theorem get_swap' (a : Array α) (i j : Fin a.size) (k : Nat) (hk' : k < (a.swap i j).size) :
(a.swap i j)[k] = if k = i then a[j] else if k = j then a[i] else a[k]'(by simp_all) := by
apply get_swap
@[simp] theorem swap_swap (a : Array α) {i j : Fin a.size} :
(a.swap i j).swap i.1, (a.size_swap ..).symm i.2 j.1, (a.size_swap ..).symm j.2 = a := by
apply ext
· simp only [size_swap]
· intros
simp only [get_swap']
split
· simp_all
· split <;> simp_all
theorem swap_comm (a : Array α) {i j : Fin a.size} : a.swap i j = a.swap j i := by
apply ext
· simp only [size_swap]
· intros
simp only [get_swap']
split
· split <;> simp_all
· split <;> simp_all
end Array

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@@ -23,24 +23,17 @@ theorem sizeOf_lt_of_mem [SizeOf α] {as : Array α} (h : a ∈ as) : sizeOf a <
cases as with | _ as =>
exact Nat.lt_trans (List.sizeOf_lt_of_mem h.val) (by simp_arith)
theorem sizeOf_get [SizeOf α] (as : Array α) (i : Fin as.size) : sizeOf (as.get i) < sizeOf as := by
@[simp] theorem sizeOf_get [SizeOf α] (as : Array α) (i : Fin as.size) : sizeOf (as.get i) < sizeOf as := by
cases as with | _ as =>
exact Nat.lt_trans (List.sizeOf_get ..) (by simp_arith)
@[simp] theorem sizeOf_getElem [SizeOf α] (as : Array α) (i : Nat) (h : i < as.size) :
sizeOf (as[i]'h) < sizeOf as := sizeOf_get _ _
/-- This tactic, added to the `decreasing_trivial` toolbox, proves that
`sizeOf arr[i] < sizeOf arr`, which is useful for well founded recursions
over a nested inductive like `inductive T | mk : Array T → T`. -/
macro "array_get_dec" : tactic =>
`(tactic| first
-- subsumed by simp
-- | with_reducible apply sizeOf_get
-- | with_reducible apply sizeOf_getElem
| (with_reducible apply Nat.lt_trans (sizeOf_get ..)); simp_arith
| (with_reducible apply Nat.lt_trans (sizeOf_getElem ..)); simp_arith
)
| apply sizeOf_get
| apply Nat.lt_trans (sizeOf_get ..); simp_arith)
macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_get_dec)
@@ -50,10 +43,9 @@ provided that `a ∈ arr` which is useful for well founded recursions over a nes
-- NB: This is analogue to tactic `sizeOf_list_dec`
macro "array_mem_dec" : tactic =>
`(tactic| first
| with_reducible apply Array.sizeOf_lt_of_mem; assumption; done
| with_reducible
apply Nat.lt_trans (Array.sizeOf_lt_of_mem ?h)
case' h => assumption
| apply Array.sizeOf_lt_of_mem; assumption; done
| apply Nat.lt_trans (Array.sizeOf_lt_of_mem ?h)
case' h => assumption
simp_arith)
macro_rules | `(tactic| decreasing_trivial) => `(tactic| array_mem_dec)

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@@ -10,7 +10,7 @@ namespace Array
-- TODO: remove the [Inhabited α] parameters as soon as we have the tactic framework for automating proof generation and using Array.fget
def qpartition (as : Array α) (lt : α α Bool) (lo hi : Nat) : Nat × Array α :=
if h : as.size = 0 then (0, as) else have : Inhabited α := as[0]'(by revert h; cases as.size <;> simp) -- TODO: remove
if h : as.size = 0 then (0, as) else have : Inhabited α := as[0]'(by revert h; cases as.size <;> simp [Nat.zero_lt_succ]) -- TODO: remove
let mid := (lo + hi) / 2
let as := if lt (as.get! mid) (as.get! lo) then as.swap! lo mid else as
let as := if lt (as.get! hi) (as.get! lo) then as.swap! lo hi else as
@@ -27,7 +27,6 @@ def qpartition (as : Array α) (lt : αα → Bool) (lo hi : Nat) : Nat ×
let as := as.swap! i hi
(i, as)
termination_by hi - j
decreasing_by all_goals simp_wf; decreasing_trivial_pre_omega
loop as lo lo
@[inline] partial def qsort (as : Array α) (lt : α α Bool) (low := 0) (high := as.size - 1) : Array α :=

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@@ -9,40 +9,25 @@ import Init.Data.Array.Basic
universe u v w
structure Subarray (α : Type u) where
array : Array α
as : Array α
start : Nat
stop : Nat
start_le_stop : start stop
stop_le_array_size : stop array.size
@[deprecated Subarray.array (since := "2024-04-13")]
abbrev Subarray.as (s : Subarray α) : Array α := s.array
@[deprecated Subarray.start_le_stop (since := "2024-04-13")]
theorem Subarray.h₁ (s : Subarray α) : s.start s.stop := s.start_le_stop
@[deprecated Subarray.stop_le_array_size (since := "2024-04-13")]
theorem Subarray.h₂ (s : Subarray α) : s.stop s.array.size := s.stop_le_array_size
h₁ : start stop
h₂ : stop as.size
namespace Subarray
def size (s : Subarray α) : Nat :=
s.stop - s.start
theorem size_le_array_size {s : Subarray α} : s.size s.array.size := by
let {array, start, stop, start_le_stop, stop_le_array_size} := s
simp [size]
apply Nat.le_trans (Nat.sub_le stop start)
assumption
def get (s : Subarray α) (i : Fin s.size) : α :=
have : s.start + i.val < s.array.size := by
apply Nat.lt_of_lt_of_le _ s.stop_le_array_size
have : s.start + i.val < s.as.size := by
apply Nat.lt_of_lt_of_le _ s.h₂
have := i.isLt
simp [size] at this
rw [Nat.add_comm]
exact Nat.add_lt_of_lt_sub this
s.array[s.start + i.val]
s.as[s.start + i.val]
instance : GetElem (Subarray α) Nat α fun xs i => i < xs.size where
getElem xs i h := xs.get i, h
@@ -55,7 +40,7 @@ abbrev get! [Inhabited α] (s : Subarray α) (i : Nat) : α :=
def popFront (s : Subarray α) : Subarray α :=
if h : s.start < s.stop then
{ s with start := s.start + 1, start_le_stop := Nat.le_of_lt_succ (Nat.add_lt_add_right h 1) }
{ s with start := s.start + 1, h₁ := Nat.le_of_lt_succ (Nat.add_lt_add_right h 1) }
else
s
@@ -63,7 +48,7 @@ def popFront (s : Subarray α) : Subarray α :=
let sz := USize.ofNat s.stop
let rec @[specialize] loop (i : USize) (b : β) : m β := do
if i < sz then
let a := s.array.uget i lcProof
let a := s.as.uget i lcProof
match ( f a b) with
| ForInStep.done b => pure b
| ForInStep.yield b => loop (i+1) b
@@ -81,27 +66,27 @@ instance : ForIn m (Subarray α) α where
@[inline]
def foldlM {α : Type u} {β : Type v} {m : Type v Type w} [Monad m] (f : β α m β) (init : β) (as : Subarray α) : m β :=
as.array.foldlM f (init := init) (start := as.start) (stop := as.stop)
as.as.foldlM f (init := init) (start := as.start) (stop := as.stop)
@[inline]
def foldrM {α : Type u} {β : Type v} {m : Type v Type w} [Monad m] (f : α β m β) (init : β) (as : Subarray α) : m β :=
as.array.foldrM f (init := init) (start := as.stop) (stop := as.start)
as.as.foldrM f (init := init) (start := as.stop) (stop := as.start)
@[inline]
def anyM {α : Type u} {m : Type Type w} [Monad m] (p : α m Bool) (as : Subarray α) : m Bool :=
as.array.anyM p (start := as.start) (stop := as.stop)
as.as.anyM p (start := as.start) (stop := as.stop)
@[inline]
def allM {α : Type u} {m : Type Type w} [Monad m] (p : α m Bool) (as : Subarray α) : m Bool :=
as.array.allM p (start := as.start) (stop := as.stop)
as.as.allM p (start := as.start) (stop := as.stop)
@[inline]
def forM {α : Type u} {m : Type v Type w} [Monad m] (f : α m PUnit) (as : Subarray α) : m PUnit :=
as.array.forM f (start := as.start) (stop := as.stop)
as.as.forM f (start := as.start) (stop := as.stop)
@[inline]
def forRevM {α : Type u} {m : Type v Type w} [Monad m] (f : α m PUnit) (as : Subarray α) : m PUnit :=
as.array.forRevM f (start := as.stop) (stop := as.start)
as.as.forRevM f (start := as.stop) (stop := as.start)
@[inline]
def foldl {α : Type u} {β : Type v} (f : β α β) (init : β) (as : Subarray α) : β :=
@@ -148,25 +133,15 @@ variable {α : Type u}
def toSubarray (as : Array α) (start : Nat := 0) (stop : Nat := as.size) : Subarray α :=
if h₂ : stop as.size then
if h₁ : start stop then
{ array := as, start := start, stop := stop,
start_le_stop := h₁, stop_le_array_size := h₂ }
else
{ array := as, start := stop, stop := stop,
start_le_stop := Nat.le_refl _, stop_le_array_size := h₂ }
if h₁ : start stop then
{ as := as, start := start, stop := stop, h₁ := h₁, h₂ := h₂ }
else
{ as := as, start := stop, stop := stop, h₁ := Nat.le_refl _, h₂ := h₂ }
else
if h₁ : start as.size then
{ array := as,
start := start,
stop := as.size,
start_le_stop := h₁,
stop_le_array_size := Nat.le_refl _ }
else
{ array := as,
start := as.size,
stop := as.size,
start_le_stop := Nat.le_refl _,
stop_le_array_size := Nat.le_refl _ }
if h₁ : start as.size then
{ as := as, start := start, stop := as.size, h₁ := h₁, h₂ := Nat.le_refl _ }
else
{ as := as, start := as.size, stop := as.size, h₁ := Nat.le_refl _, h₂ := Nat.le_refl _ }
@[coe]
def ofSubarray (s : Subarray α) : Array α := Id.run do

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

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@@ -1,17 +0,0 @@
/-
Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
prelude
import Init.Data.Array.Lemmas
import Init.Data.List.TakeDrop
namespace Array
theorem exists_of_uset (self : Array α) (i d h) :
l₁ l₂, self.data = l₁ ++ self[i] :: l₂ List.length l₁ = i.toNat
(self.uset i d h).data = l₁ ++ d :: l₂ := by
simpa [Array.getElem_eq_data_getElem] using List.exists_of_set _
end Array

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@@ -1,60 +0,0 @@
/-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Markus Himmel
-/
prelude
import Init.Data.Bool
set_option linter.missingDocs true
/-- `PartialEquivBEq α` says that the `BEq` implementation is a
partial equivalence relation, that is:
* it is symmetric: `a == b → b == a`
* it is transitive: `a == b → b == c → a == c`.
-/
class PartialEquivBEq (α) [BEq α] : Prop where
/-- Symmetry for `BEq`. If `a == b` then `b == a`. -/
symm : (a : α) == b b == a
/-- Transitivity for `BEq`. If `a == b` and `b == c` then `a == c`. -/
trans : (a : α) == b b == c a == c
/-- `ReflBEq α` says that the `BEq` implementation is reflexive. -/
class ReflBEq (α) [BEq α] : Prop where
/-- Reflexivity for `BEq`. -/
refl : (a : α) == a
/-- `EquivBEq` says that the `BEq` implementation is an equivalence relation. -/
class EquivBEq (α) [BEq α] extends PartialEquivBEq α, ReflBEq α : Prop
@[simp]
theorem BEq.refl [BEq α] [ReflBEq α] {a : α} : a == a :=
ReflBEq.refl
theorem beq_of_eq [BEq α] [ReflBEq α] {a b : α} : a = b a == b
| rfl => BEq.refl
theorem BEq.symm [BEq α] [PartialEquivBEq α] {a b : α} : a == b b == a :=
PartialEquivBEq.symm
theorem BEq.comm [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = (b == a) :=
Bool.eq_iff_iff.2 BEq.symm, BEq.symm
theorem BEq.symm_false [BEq α] [PartialEquivBEq α] {a b : α} : (a == b) = false (b == a) = false :=
BEq.comm (α := α) id
theorem BEq.trans [BEq α] [PartialEquivBEq α] {a b c : α} : a == b b == c a == c :=
PartialEquivBEq.trans
theorem BEq.neq_of_neq_of_beq [BEq α] [PartialEquivBEq α] {a b c : α} :
(a == b) = false b == c (a == c) = false :=
fun h₁ h₂ => Bool.eq_false_iff.2 fun h₃ => Bool.eq_false_iff.1 h₁ (BEq.trans h₃ (BEq.symm h₂))
theorem BEq.neq_of_beq_of_neq [BEq α] [PartialEquivBEq α] {a b c : α} :
a == b (b == c) = false (a == c) = false :=
fun h₁ h₂ => Bool.eq_false_iff.2 fun h₃ => Bool.eq_false_iff.1 h₂ (BEq.trans (BEq.symm h₁) h₃)
instance (priority := low) [BEq α] [LawfulBEq α] : EquivBEq α where
refl := LawfulBEq.rfl
symm h := (beq_iff_eq _ _).2 <| Eq.symm <| (beq_iff_eq _ _).1 h
trans hab hbc := (beq_iff_eq _ _).2 <| ((beq_iff_eq _ _).1 hab).trans <| (beq_iff_eq _ _).1 hbc

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@@ -1,13 +1,12 @@
/-
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
-/
prelude
import Init.Data.Fin.Basic
import Init.Data.Nat.Bitwise.Lemmas
import Init.Data.Nat.Power2
import Init.Data.Int.Bitwise
/-!
We define bitvectors. We choose the `Fin` representation over others for its relative efficiency
@@ -34,8 +33,7 @@ structure BitVec (w : Nat) where
O(1), because we use `Fin` as the internal representation of a bitvector. -/
toFin : Fin (2^w)
@[deprecated (since := "2024-04-12")]
protected abbrev Std.BitVec := _root_.BitVec
@[deprecated] abbrev Std.BitVec := _root_.BitVec
-- We manually derive the `DecidableEq` instances for `BitVec` because
-- we want to have builtin support for bit-vector literals, and we
@@ -74,9 +72,6 @@ protected def toNat (a : BitVec n) : Nat := a.toFin.val
/-- Return the bound in terms of toNat. -/
theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
@[deprecated isLt (since := "2024-03-12")]
theorem toNat_lt (x : BitVec n) : x.toNat < 2^n := x.isLt
/-- Theorem for normalizing the bit vector literal representation. -/
-- TODO: This needs more usage data to assess which direction the simp should go.
@[simp, bv_toNat] theorem ofNat_eq_ofNat : @OfNat.ofNat (BitVec n) i _ = .ofNat n i := rfl
@@ -151,12 +146,12 @@ end Int
section Syntax
/-- Notation for bit vector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
syntax:max num noWs "#" noWs term:max : term
macro_rules | `($i:num#$n) => `(BitVec.ofNat $n $i)
scoped syntax:max term:max noWs "#" noWs term:max : term
macro_rules | `($i#$n) => `(BitVec.ofNat $n $i)
/-- Unexpander for bit vector literals. -/
@[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
| `($(_) $n $i:num) => `($i:num#$n)
| `($(_) $n $i) => `($i#$n)
| _ => throw ()
/-- Notation for bit vector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLt i lt`. -/
@@ -198,7 +193,7 @@ instance : Add (BitVec n) := ⟨BitVec.add⟩
Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
modulo `2^n`.
-/
protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
protected def sub (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + (2^n - y.toNat))
instance : Sub (BitVec n) := BitVec.sub
/--
@@ -504,7 +499,7 @@ equivalent to `a * 2^s`, modulo `2^n`.
SMT-Lib name: `bvshl` except this operator uses a `Nat` shift value.
-/
protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (a.toNat <<< s)
protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := (a.toNat <<< s)#n
instance : HShiftLeft (BitVec w) Nat (BitVec w) := .shiftLeft
/--
@@ -534,11 +529,6 @@ def sshiftRight (a : BitVec n) (s : Nat) : BitVec n := .ofInt n (a.toInt >>> s)
instance {n} : HShiftLeft (BitVec m) (BitVec n) (BitVec m) := fun x y => x <<< y.toNat
instance {n} : HShiftRight (BitVec m) (BitVec n) (BitVec m) := fun x y => x >>> y.toNat
/-- Auxiliary function for `rotateLeft`, which does not take into account the case where
the rotation amount is greater than the bitvector width. -/
def rotateLeftAux (x : BitVec w) (n : Nat) : BitVec w :=
x <<< n ||| x >>> (w - n)
/--
Rotate left for bit vectors. All the bits of `x` are shifted to higher positions, with the top `n`
bits wrapping around to fill the low bits.
@@ -548,15 +538,7 @@ rotateLeft 0b0011#4 3 = 0b1001
```
SMT-Lib name: `rotate_left` except this operator uses a `Nat` shift amount.
-/
def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := rotateLeftAux x (n % w)
/--
Auxiliary function for `rotateRight`, which does not take into account the case where
the rotation amount is greater than the bitvector width.
-/
def rotateRightAux (x : BitVec w) (n : Nat) : BitVec w :=
x >>> n ||| x <<< (w - n)
def rotateLeft (x : BitVec w) (n : Nat) : BitVec w := x <<< n ||| x >>> (w - n)
/--
Rotate right for bit vectors. All the bits of `x` are shifted to lower positions, with the
@@ -567,7 +549,7 @@ rotateRight 0b01001#5 1 = 0b10100
```
SMT-Lib name: `rotate_right` except this operator uses a `Nat` shift amount.
-/
def rotateRight (x : BitVec w) (n : Nat) : BitVec w := rotateRightAux x (n % w)
def rotateRight (x : BitVec w) (n : Nat) : BitVec w := x >>> n ||| x <<< (w - n)
/--
Concatenation of bitvectors. This uses the "big endian" convention that the more significant
@@ -614,13 +596,6 @@ theorem ofBool_append (msb : Bool) (lsbs : BitVec w) :
ofBool msb ++ lsbs = (cons msb lsbs).cast (Nat.add_comm ..) :=
rfl
/--
`twoPow w i` is the bitvector `2^i` if `i < w`, and `0` otherwise.
That is, 2 to the power `i`.
For the bitwise point of view, it has the `i`th bit as `1` and all other bits as `0`.
-/
def twoPow (w : Nat) (i : Nat) : BitVec w := 1#w <<< i
end bitwise
section normalization_eqs
@@ -639,14 +614,4 @@ section normalization_eqs
@[simp] theorem zero_eq : BitVec.zero n = 0#n := rfl
end normalization_eqs
/-- Converts a list of `Bool`s to a big-endian `BitVec`. -/
def ofBoolListBE : (bs : List Bool) BitVec bs.length
| [] => 0#0
| b :: bs => cons b (ofBoolListBE bs)
/-- Converts a list of `Bool`s to a little-endian `BitVec`. -/
def ofBoolListLE : (bs : List Bool) BitVec bs.length
| [] => 0#0
| b :: bs => concat (ofBoolListLE bs) b
end BitVec

View File

@@ -98,6 +98,128 @@ theorem carry_succ (i : Nat) (x y : BitVec w) (c : Bool) :
exact mod_two_pow_add_mod_two_pow_add_bool_lt_two_pow_succ ..
cases x.toNat.testBit i <;> cases y.toNat.testBit i <;> (simp; omega)
/--
Does the addition of two `BitVec`s overflow?
The nice feature of this definition is that
it can be unfolded recursively to a circuit:
```
example (x y : BitVec 4) :
addOverflow x y =
atLeastTwo (x.getLsb 3) (y.getLsb 3) (atLeastTwo (x.getLsb 2) (y.getLsb 2)
(atLeastTwo (x.getLsb 1) (y.getLsb 1) (x.getLsb 0 && y.getLsb 0))) := by
simp [addOverflow, msb_truncate, BitVec.msb, getMsb]
```
-/
def addOverflow (x y : BitVec w) (c : Bool := false) : Bool :=
match w with
| 0 => c
| (w + 1) => atLeastTwo x.msb y.msb (addOverflow (x.truncate w) (y.truncate w) c)
@[simp] theorem addOverflow_length_zero {x y : BitVec 0} : addOverflow x y c = c := rfl
theorem addOverflow_length_succ {x y : BitVec (w+1)} :
addOverflow x y c = atLeastTwo x.msb y.msb (addOverflow (x.truncate w) (y.truncate w) c) :=
rfl
@[simp] theorem addOverflow_zero_left_succ :
addOverflow 0#(w+1) y c = (y.msb && addOverflow 0#w (y.truncate w) c) := by
simp [addOverflow]
@[simp] theorem addOverflow_zero_right_succ {x : BitVec (w+1)} :
addOverflow x 0#(w+1) c = (x.msb && addOverflow (x.truncate w) 0#w c) := by
simp [addOverflow]
@[simp] theorem addOverflow_zero_zero :
addOverflow 0#i 0#i c = (decide (i = 0) && c) := by
cases i <;> simp
theorem carry_eq_addOverflow (i) (x y : BitVec w) (c) :
carry i x y c = addOverflow (x.truncate i) (y.truncate i) c := by
match i with
| 0 => simp
| (i + 1) =>
rw [addOverflow_length_succ, carry_succ, carry_eq_addOverflow]
simp [msb_zeroExtend, Nat.le_succ]
theorem addOverflow_eq_carry {x y : BitVec w} :
addOverflow x y c = carry w x y c := by
have := carry_eq_addOverflow w x y c
simpa using this.symm
theorem addOverflow_cons_cons :
addOverflow (cons a x) (cons b y) = atLeastTwo a b (addOverflow x y) := by
simp [addOverflow]
theorem add_cons_cons (w) (x y : BitVec w) :
(cons a x) + (cons b y) = cons (Bool.xor a (Bool.xor b (addOverflow x y))) (x + y) := by
have pos : 0 < 2^w := Nat.pow_pos Nat.zero_lt_two
apply eq_of_toNat_eq
simp only [toNat_add, toNat_cons']
rw [addOverflow_eq_carry, carry]
simp [Nat.mod_pow_succ]
by_cases h : 2 ^ w x.toNat + y.toNat
· simp [h]
have p : (x.toNat + y.toNat) / 2 ^ w = 1 := by
apply Nat.div_eq_of_lt_le <;> omega
cases a <;> cases b
<;> simp [Nat.one_shiftLeft, Nat.add_left_comm x.toNat, Nat.add_assoc, p, pos]
<;> simp [Nat.add_comm]
· simp [h]
have p : (x.toNat + y.toNat) / 2 ^ w = 0 := by
apply Nat.div_eq_of_lt_le <;> omega
cases a <;> cases b
<;> simp [Nat.one_shiftLeft, Nat.add_left_comm x.toNat, Nat.add_assoc, p, pos]
<;> simp [Nat.add_comm]
theorem msb_add (x y : BitVec w) :
(x + y).msb =
Bool.xor x.msb (Bool.xor y.msb (addOverflow (x.truncate (w-1)) (y.truncate (w-1)))) := by
cases w with
| zero => simp
| succ w =>
conv =>
lhs
rw [eq_msb_cons_truncate x, eq_msb_cons_truncate y, add_cons_cons]
simp [succ_eq_add_one, Nat.add_one_sub_one]
/--
Variant of `getLsb_add` in terms of `addOverflow` rather than `carry`.
-/
theorem getLsb_add' (i : Nat) (x y : BitVec w) :
getLsb (x + y) i = (decide (i < w) && Bool.xor (x.getLsb i)
(Bool.xor (y.getLsb i) (addOverflow (x.truncate i) (y.truncate i)))) := by
by_cases h : i < w
· rw [ msb_truncate (x + y), truncate_add, msb_add, msb_truncate, msb_truncate]
rw [Nat.add_one_sub_one, truncate_truncate_of_le, truncate_truncate_of_le]
simp [h]
all_goals omega
· simp [h]
simp at h
simp [h]
theorem addOverflow_eq_false_of_and_eq_zero {x y : BitVec w} (h : x &&& y = 0#w) :
addOverflow x y = false := by
induction w with
| zero => rfl
| succ w ih =>
have h₁ := congrArg BitVec.msb h
have h₂ := congrArg (·.truncate w) h
simp at h₁ h₂
simp_all [addOverflow_length_succ]
theorem or_eq_add_of_and_eq_zero (x y : BitVec w) (h : x &&& y = 0) :
x ||| y = x + y := by
ext i
have h₁ := congrArg (getLsb · i) h
have h₂ := congrArg (truncate i) h
simp at h₁ h₂
simp only [getLsb_add', getLsb_or]
rw [addOverflow_eq_false_of_and_eq_zero h₂]
-- sat
revert h₁
cases x.getLsb i <;> cases y.getLsb i <;> simp
/-- Carry function for bitwise addition. -/
def adcb (x y c : Bool) : Bool × Bool := (atLeastTwo x y c, Bool.xor x (Bool.xor y c))
@@ -159,171 +281,4 @@ theorem add_eq_adc (w : Nat) (x y : BitVec w) : x + y = (adc x y false).snd := b
theorem allOnes_sub_eq_not (x : BitVec w) : allOnes w - x = ~~~x := by
rw [ add_not_self x, BitVec.add_comm, add_sub_cancel]
/-- Addition of bitvectors is the same as bitwise or, if bitwise and is zero. -/
theorem add_eq_or_of_and_eq_zero {w : Nat} (x y : BitVec w)
(h : x &&& y = 0#w) : x + y = x ||| y := by
rw [add_eq_adc, adc, iunfoldr_replace (fun _ => false) (x ||| y)]
· rfl
· simp only [adcb, atLeastTwo, Bool.and_false, Bool.or_false, bne_false, getLsb_or,
Prod.mk.injEq, and_eq_false_imp]
intros i
replace h : (x &&& y).getLsb i = (0#w).getLsb i := by rw [h]
simp only [getLsb_and, getLsb_zero, and_eq_false_imp] at h
constructor
· intros hx
simp_all [hx]
· by_cases hx : x.getLsb i <;> simp_all [hx]
/-! ### Negation -/
theorem bit_not_testBit (x : BitVec w) (i : Fin w) :
getLsb (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) i.val = !(getLsb x i.val) := by
apply iunfoldr_getLsb (fun _ => ()) i (by simp)
theorem bit_not_add_self (x : BitVec w) :
((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd + x = -1 := by
simp only [add_eq_adc]
apply iunfoldr_replace_snd (fun _ => false) (-1) false rfl
intro i; simp only [ BitVec.not, adcb, testBit_toNat]
rw [iunfoldr_replace_snd (fun _ => ()) (((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd)]
<;> simp [bit_not_testBit, negOne_eq_allOnes, getLsb_allOnes]
theorem bit_not_eq_not (x : BitVec w) :
((iunfoldr (fun i c => (c, !(x.getLsb i)))) ()).snd = ~~~ x := by
simp [allOnes_sub_eq_not, BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), negOne_eq_allOnes]
theorem bit_neg_eq_neg (x : BitVec w) : -x = (adc (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) (BitVec.ofNat w 1) false).snd:= by
simp only [ add_eq_adc]
rw [iunfoldr_replace_snd ((fun _ => ())) (((iunfoldr (fun (i : Fin w) c => (c, !(x.getLsb i)))) ()).snd) _ rfl]
· rw [BitVec.eq_sub_iff_add_eq.mpr (bit_not_add_self x), sub_toAdd, BitVec.add_comm _ (-x)]
simp [ sub_toAdd, BitVec.sub_add_cancel]
· simp [bit_not_testBit x _]
/-! ### Inequalities (le / lt) -/
theorem ult_eq_not_carry (x y : BitVec w) : x.ult y = !carry w x (~~~y) true := by
simp only [BitVec.ult, carry, toNat_mod_cancel, toNat_not, toNat_true, ge_iff_le, decide_not,
Nat.not_le, decide_eq_decide]
rw [Nat.mod_eq_of_lt (by omega)]
omega
theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
simp [BitVec.ule, BitVec.ult, decide_not]
theorem ule_eq_carry (x y : BitVec w) : x.ule y = carry w y (~~~x) true := by
simp [ule_eq_not_ult, ult_eq_not_carry]
/-- If two bitvectors have the same `msb`, then signed and unsigned comparisons coincide -/
theorem slt_eq_ult_of_msb_eq {x y : BitVec w} (h : x.msb = y.msb) :
x.slt y = x.ult y := by
simp only [BitVec.slt, toInt_eq_msb_cond, BitVec.ult, decide_eq_decide, h]
cases y.msb <;> simp
/-- If two bitvectors have different `msb`s, then unsigned comparison is determined by this bit -/
theorem ult_eq_msb_of_msb_neq {x y : BitVec w} (h : x.msb y.msb) :
x.ult y = y.msb := by
simp only [BitVec.ult, msb_eq_decide, ne_eq, decide_eq_decide] at *
omega
/-- If two bitvectors have different `msb`s, then signed and unsigned comparisons are opposites -/
theorem slt_eq_not_ult_of_msb_neq {x y : BitVec w} (h : x.msb y.msb) :
x.slt y = !x.ult y := by
simp only [BitVec.slt, toInt_eq_msb_cond, Bool.eq_not_of_ne h, ult_eq_msb_of_msb_neq h]
cases y.msb <;> (simp; omega)
theorem slt_eq_ult (x y : BitVec w) :
x.slt y = (x.msb != y.msb).xor (x.ult y) := by
by_cases h : x.msb = y.msb
· simp [h, slt_eq_ult_of_msb_eq]
· have h' : x.msb != y.msb := by simp_all
simp [slt_eq_not_ult_of_msb_neq h, h']
theorem slt_eq_not_carry (x y : BitVec w) :
x.slt y = (x.msb == y.msb).xor (carry w x (~~~y) true) := by
simp only [slt_eq_ult, bne, ult_eq_not_carry]
cases x.msb == y.msb <;> simp
theorem sle_eq_not_slt (x y : BitVec w) : x.sle y = !y.slt x := by
simp only [BitVec.sle, BitVec.slt, decide_not, decide_eq_decide]; omega
theorem sle_eq_carry (x y : BitVec w) :
x.sle y = !((x.msb == y.msb).xor (carry w y (~~~x) true)) := by
rw [sle_eq_not_slt, slt_eq_not_carry, beq_comm]
/-! ### mul recurrence for bitblasting -/
/--
A recurrence that describes multiplication as repeated addition.
Is useful for bitblasting multiplication.
-/
def mulRec (l r : BitVec w) (s : Nat) : BitVec w :=
let cur := if r.getLsb s then (l <<< s) else 0
match s with
| 0 => cur
| s + 1 => mulRec l r s + cur
theorem mulRec_zero_eq (l r : BitVec w) :
mulRec l r 0 = if r.getLsb 0 then l else 0 := by
simp [mulRec]
theorem mulRec_succ_eq (l r : BitVec w) (s : Nat) :
mulRec l r (s + 1) = mulRec l r s + if r.getLsb (s + 1) then (l <<< (s + 1)) else 0 := rfl
/--
Recurrence lemma: truncating to `i+1` bits and then zero extending to `w`
equals truncating upto `i` bits `[0..i-1]`, and then adding the `i`th bit of `x`.
-/
theorem zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow (x : BitVec w) (i : Nat) :
zeroExtend w (x.truncate (i + 1)) =
zeroExtend w (x.truncate i) + (x &&& twoPow w i) := by
rw [add_eq_or_of_and_eq_zero]
· ext k
simp only [getLsb_zeroExtend, Fin.is_lt, decide_True, Bool.true_and, getLsb_or, getLsb_and]
by_cases hik : i = k
· subst hik
simp
· simp only [getLsb_twoPow, hik, decide_False, Bool.and_false, Bool.or_false]
by_cases hik' : k < (i + 1)
· have hik'' : k < i := by omega
simp [hik', hik'']
· have hik'' : ¬ (k < i) := by omega
simp [hik', hik'']
· ext k
simp
omega
/--
Recurrence lemma: multiplying `l` with the first `s` bits of `r` is the
same as truncating `r` to `s` bits, then zero extending to the original length,
and performing the multplication. -/
theorem mulRec_eq_mul_signExtend_truncate (l r : BitVec w) (s : Nat) :
mulRec l r s = l * ((r.truncate (s + 1)).zeroExtend w) := by
induction s
case zero =>
simp only [mulRec_zero_eq, ofNat_eq_ofNat, Nat.reduceAdd]
by_cases r.getLsb 0
case pos hr =>
simp only [hr, reduceIte, truncate, zeroExtend_one_eq_ofBool_getLsb_zero,
hr, ofBool_true, ofNat_eq_ofNat]
rw [zeroExtend_ofNat_one_eq_ofNat_one_of_lt (by omega)]
simp
case neg hr =>
simp [hr, zeroExtend_one_eq_ofBool_getLsb_zero]
case succ s' hs =>
rw [mulRec_succ_eq, hs]
have heq :
(if r.getLsb (s' + 1) = true then l <<< (s' + 1) else 0) =
(l * (r &&& (BitVec.twoPow w (s' + 1)))) := by
simp only [ofNat_eq_ofNat, and_twoPow_eq]
by_cases hr : r.getLsb (s' + 1) <;> simp [hr]
rw [heq, BitVec.mul_add, zeroExtend_truncate_succ_eq_zeroExtend_truncate_add_twoPow]
theorem getLsb_mul (x y : BitVec w) (i : Nat) :
(x * y).getLsb i = (mulRec x y w).getLsb i := by
simp only [mulRec_eq_mul_signExtend_truncate]
rw [truncate, truncate_eq_zeroExtend, truncate_eq_zeroExtend,
truncate_truncate_of_le]
· simp
· omega
end BitVec

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

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@@ -52,8 +52,8 @@ theorem eq_iff_iff {a b : Bool} : a = b ↔ (a ↔ b) := by cases b <;> simp
@[simp] theorem decide_eq_true {b : Bool} [Decidable (b = true)] : decide (b = true) = b := by cases b <;> simp
@[simp] theorem decide_eq_false {b : Bool} [Decidable (b = false)] : decide (b = false) = !b := by cases b <;> simp
theorem decide_true_eq {b : Bool} [Decidable (true = b)] : decide (true = b) = b := by cases b <;> simp
theorem decide_false_eq {b : Bool} [Decidable (false = b)] : decide (false = b) = !b := by cases b <;> simp
@[simp] theorem decide_true_eq {b : Bool} [Decidable (true = b)] : decide (true = b) = b := by cases b <;> simp
@[simp] theorem decide_false_eq {b : Bool} [Decidable (false = b)] : decide (false = b) = !b := by cases b <;> simp
/-! ### and -/
@@ -74,7 +74,6 @@ Added for confluence with `not_and_self` `and_not_self` on term
@[simp] theorem eq_false_and_eq_true_self : (b : Bool), (b = false b = true) False := by decide
theorem and_comm : (x y : Bool), (x && y) = (y && x) := by decide
instance : Std.Commutative (· && ·) := and_comm
theorem and_left_comm : (x y z : Bool), (x && (y && z)) = (y && (x && z)) := by decide
theorem and_right_comm : (x y z : Bool), ((x && y) && z) = ((x && z) && y) := by decide
@@ -121,7 +120,6 @@ Needed for confluence of term `(a || b) ↔ a` which reduces to `(a || b) = a` v
@[simp] theorem iff_or_self : (a b : Bool), (b = (a || b)) (a b) := by decide
theorem or_comm : (x y : Bool), (x || y) = (y || x) := by decide
instance : Std.Commutative (· || ·) := or_comm
theorem or_left_comm : (x y z : Bool), (x || (y || z)) = (y || (x || z)) := by decide
theorem or_right_comm : (x y z : Bool), ((x || y) || z) = ((x || z) || y) := by decide
@@ -134,9 +132,6 @@ theorem and_or_distrib_right : ∀ (x y z : Bool), ((x || y) && z) = (x && z ||
theorem or_and_distrib_left : (x y z : Bool), (x || y && z) = ((x || y) && (x || z)) := by decide
theorem or_and_distrib_right : (x y z : Bool), (x && y || z) = ((x || z) && (y || z)) := by decide
theorem and_xor_distrib_left : (x y z : Bool), (x && xor y z) = xor (x && y) (x && z) := by decide
theorem and_xor_distrib_right : (x y z : Bool), (xor x y && z) = xor (x && z) (y && z) := by decide
/-- De Morgan's law for boolean and -/
@[simp] theorem not_and : (x y : Bool), (!(x && y)) = (!x || !y) := by decide
@@ -163,7 +158,7 @@ Consider the term: `¬((b && c) = true)`:
-/
@[simp] theorem and_eq_false_imp : (x y : Bool), (x && y) = false (x = true y = false) := by decide
theorem or_eq_true_iff : (x y : Bool), (x || y) = true x = true y = true := by simp
@[simp] theorem or_eq_true_iff : (x y : Bool), (x || y) = true x = true y = true := by decide
@[simp] theorem or_eq_false_iff : (x y : Bool), (x || y) = false x = false y = false := by decide
@@ -187,17 +182,13 @@ in false_eq and true_eq.
@[simp] theorem true_beq : b, (true == b) = b := by decide
@[simp] theorem false_beq : b, (false == b) = !b := by decide
instance : Std.LawfulIdentity (· == ·) true where
left_id := true_beq
right_id := beq_true
@[simp] theorem beq_true : b, (b == true) = b := by decide
@[simp] theorem beq_false : b, (b == false) = !b := by decide
@[simp] theorem true_bne : (b : Bool), (true != b) = !b := by decide
@[simp] theorem false_bne : (b : Bool), (false != b) = b := by decide
@[simp] theorem bne_true : (b : Bool), (b != true) = !b := by decide
@[simp] theorem bne_false : (b : Bool), (b != false) = b := by decide
instance : Std.LawfulIdentity (· != ·) false where
left_id := false_bne
right_id := bne_false
@[simp] theorem not_beq_self : (x : Bool), ((!x) == x) = false := by decide
@[simp] theorem beq_not_self : (x : Bool), (x == !x) = false := by decide
@@ -220,21 +211,12 @@ due to `beq_iff_eq`.
@[simp] theorem not_bne_not : (x y : Bool), ((!x) != (!y)) = (x != y) := by decide
@[simp] theorem bne_assoc : (x y z : Bool), ((x != y) != z) = (x != (y != z)) := by decide
instance : Std.Associative (· != ·) := bne_assoc
@[simp] theorem bne_left_inj : (x y z : Bool), (x != y) = (x != z) y = z := by decide
@[simp] theorem bne_right_inj : (x y z : Bool), (x != z) = (y != z) x = y := by decide
theorem eq_not_of_ne : {x y : Bool}, x y x = !y := by decide
/-! ### coercision related normal forms -/
theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
(a == b) = decide (a = b) := by
cases h : a == b
· simp [ne_of_beq_false h]
· simp [eq_of_beq h]
@[simp] theorem not_eq_not : {a b : Bool}, ¬a = !b a = b := by decide
@[simp] theorem not_not_eq : {a b : Bool}, ¬(!a) = b a = b := by decide
@@ -245,11 +227,6 @@ theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
@[simp] theorem coe_false_iff_true : (a b : Bool), (a = false b) (!a) = b := by decide
@[simp] theorem coe_false_iff_false : (a b : Bool), (a = false b = false) (!a) = (!b) := by decide
/-! ### beq properties -/
theorem beq_comm {α} [BEq α] [LawfulBEq α] {a b : α} : (a == b) = (b == a) :=
(Bool.coe_iff_coe (a == b) (b == a)).mp (by simp [@eq_comm α])
/-! ### xor -/
theorem false_xor : (x : Bool), xor false x = x := false_bne
@@ -351,7 +328,7 @@ theorem and_or_inj_left_iff :
/-! ## toNat -/
/-- convert a `Bool` to a `Nat`, `false -> 0`, `true -> 1` -/
def toNat (b : Bool) : Nat := cond b 1 0
def toNat (b:Bool) : Nat := cond b 1 0
@[simp] theorem toNat_false : false.toNat = 0 := rfl
@@ -360,8 +337,7 @@ def toNat (b : Bool) : Nat := cond b 1 0
theorem toNat_le (c : Bool) : c.toNat 1 := by
cases c <;> trivial
@[deprecated toNat_le (since := "2024-02-23")]
abbrev toNat_le_one := toNat_le
@[deprecated toNat_le] abbrev toNat_le_one := toNat_le
theorem toNat_lt (b : Bool) : b.toNat < 2 :=
Nat.lt_succ_of_le (toNat_le _)
@@ -452,17 +428,12 @@ theorem cond_eq_if : (bif b then x else y) = (if b then x else y) := cond_eq_ite
@[simp] theorem cond_self (c : Bool) (t : α) : cond c t t = t := by cases c <;> rfl
/-
This is a simp rule in Mathlib, but results in non-confluence that is difficult
to fix as decide distributes over propositions. As an example, observe that
`cond (decide (p ∧ q)) t f` could simplify to either:
This is a simp rule in Mathlib, but results in non-confluence that is
difficult to fix as decide distributes over propositions.
* `if p ∧ q then t else f` via `Bool.cond_decide` or
* `cond (decide p && decide q) t f` via `Bool.decide_and`.
A possible approach to improve normalization between `cond` and `ite` would be
to completely simplify away `cond` by making `cond_eq_ite` a `simp` rule, but
that has not been taken since it could surprise users to migrate pure `Bool`
operations like `cond` to a mix of `Prop` and `Bool`.
A possible fix would be to completely simplify away `cond`, but that
is not taken since it could result in major rewriting of code that is
otherwise purely about `Bool`.
-/
theorem cond_decide {α} (p : Prop) [Decidable p] (t e : α) :
cond (decide p) t e = if p then t else e := by
@@ -494,16 +465,6 @@ protected theorem cond_false {α : Type u} {a b : α} : cond false a b = b := co
@[simp] theorem cond_true_same : (c b : Bool), cond c c b = (c || b) := by decide
@[simp] theorem cond_false_same : (c b : Bool), cond c b c = (c && b) := by decide
theorem cond_pos {b : Bool} {a a' : α} (h : b = true) : (bif b then a else a') = a := by
rw [h, cond_true]
theorem cond_neg {b : Bool} {a a' : α} (h : b = false) : (bif b then a else a') = a' := by
rw [h, cond_false]
theorem apply_cond (f : α β) {b : Bool} {a a' : α} :
f (bif b then a else a') = bif b then f a else f a' := by
cases b <;> simp
/-# decidability -/
protected theorem decide_coe (b : Bool) [Decidable (b = true)] : decide (b = true) = b := decide_eq_true

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@@ -92,24 +92,20 @@ protected def append (a : ByteArray) (b : ByteArray) : ByteArray :=
instance : Append ByteArray := ByteArray.append
def toList (bs : ByteArray) : List UInt8 :=
partial def toList (bs : ByteArray) : List UInt8 :=
let rec loop (i : Nat) (r : List UInt8) :=
if i < bs.size then
loop (i+1) (bs.get! i :: r)
else
r.reverse
termination_by bs.size - i
decreasing_by decreasing_trivial_pre_omega
loop 0 []
@[inline] def findIdx? (a : ByteArray) (p : UInt8 Bool) (start := 0) : Option Nat :=
@[inline] partial def findIdx? (a : ByteArray) (p : UInt8 Bool) (start := 0) : Option Nat :=
let rec @[specialize] loop (i : Nat) :=
if i < a.size then
if p (a.get! i) then some i else loop (i+1)
else
none
termination_by a.size - i
decreasing_by decreasing_trivial_pre_omega
loop start
/--
@@ -199,18 +195,6 @@ instance : ToString ByteArray := ⟨fun bs => bs.toList.toString⟩
/-- Interpret a `ByteArray` of size 8 as a little-endian `UInt64`. -/
def ByteArray.toUInt64LE! (bs : ByteArray) : UInt64 :=
assert! bs.size == 8
(bs.get! 7).toUInt64 <<< 0x38 |||
(bs.get! 6).toUInt64 <<< 0x30 |||
(bs.get! 5).toUInt64 <<< 0x28 |||
(bs.get! 4).toUInt64 <<< 0x20 |||
(bs.get! 3).toUInt64 <<< 0x18 |||
(bs.get! 2).toUInt64 <<< 0x10 |||
(bs.get! 1).toUInt64 <<< 0x8 |||
(bs.get! 0).toUInt64
/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
assert! bs.size == 8
(bs.get! 0).toUInt64 <<< 0x38 |||
(bs.get! 1).toUInt64 <<< 0x30 |||
@@ -220,3 +204,15 @@ def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
(bs.get! 5).toUInt64 <<< 0x10 |||
(bs.get! 6).toUInt64 <<< 0x8 |||
(bs.get! 7).toUInt64
/-- Interpret a `ByteArray` of size 8 as a big-endian `UInt64`. -/
def ByteArray.toUInt64BE! (bs : ByteArray) : UInt64 :=
assert! bs.size == 8
(bs.get! 7).toUInt64 <<< 0x38 |||
(bs.get! 6).toUInt64 <<< 0x30 |||
(bs.get! 5).toUInt64 <<< 0x28 |||
(bs.get! 4).toUInt64 <<< 0x20 |||
(bs.get! 3).toUInt64 <<< 0x18 |||
(bs.get! 2).toUInt64 <<< 0x10 |||
(bs.get! 1).toUInt64 <<< 0x8 |||
(bs.get! 0).toUInt64

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@@ -41,7 +41,7 @@ Sends a message on an `Channel`.
This function does not block.
-/
def Channel.send (ch : Channel α) (v : α) : BaseIO Unit :=
def Channel.send (v : α) (ch : Channel α) : BaseIO Unit :=
ch.atomically do
let st get
if st.closed then return

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@@ -5,4 +5,3 @@ Authors: Leonardo de Moura
-/
prelude
import Init.Data.Char.Basic
import Init.Data.Char.Lemmas

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@@ -40,7 +40,7 @@ theorem isValidUInt32 (n : Nat) (h : isValidCharNat n) : n < UInt32.size := by
apply Nat.lt_trans h₂
decide
theorem isValidChar_of_isValidCharNat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
theorem isValidChar_of_isValidChar_Nat (n : Nat) (h : isValidCharNat n) : isValidChar (UInt32.ofNat' n (isValidUInt32 n h)) :=
match h with
| Or.inl h => Or.inl h
| Or.inr h₁, h₂ => Or.inr h₁, h₂
@@ -52,13 +52,6 @@ theorem isValidChar_zero : isValidChar 0 :=
@[inline] def toNat (c : Char) : Nat :=
c.val.toNat
/-- Convert a character into a `UInt8`, by truncating (reducing modulo 256) if necessary. -/
@[inline] def toUInt8 (c : Char) : UInt8 :=
c.val.toUInt8
/-- The numbers from 0 to 256 are all valid UTF-8 characters, so we can embed one in the other. -/
def ofUInt8 (n : UInt8) : Char := n.toUInt32, .inl (Nat.lt_trans n.1.2 (by decide))
instance : Inhabited Char where
default := 'A'

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@@ -1,39 +0,0 @@
/-
Copyright (c) 2024 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import Init.Data.Char.Basic
import Init.Data.UInt.Lemmas
namespace Char
theorem le_def {a b : Char} : a b a.1 b.1 := .rfl
theorem lt_def {a b : Char} : a < b a.1 < b.1 := .rfl
theorem lt_iff_val_lt_val {a b : Char} : a < b a.val < b.val := Iff.rfl
@[simp] protected theorem not_le {a b : Char} : ¬ a b b < a := UInt32.not_le
@[simp] protected theorem not_lt {a b : Char} : ¬ a < b b a := UInt32.not_lt
@[simp] protected theorem le_refl (a : Char) : a a := by simp [le_def]
@[simp] protected theorem lt_irrefl (a : Char) : ¬ a < a := by simp
protected theorem le_trans {a b c : Char} : a b b c a c := UInt32.le_trans
protected theorem lt_trans {a b c : Char} : a < b b < c a < c := UInt32.lt_trans
protected theorem le_total (a b : Char) : a b b a := UInt32.le_total a.1 b.1
protected theorem lt_asymm {a b : Char} (h : a < b) : ¬ b < a := UInt32.lt_asymm h
protected theorem ne_of_lt {a b : Char} (h : a < b) : a b := Char.ne_of_val_ne (UInt32.ne_of_lt h)
theorem utf8Size_eq (c : Char) : c.utf8Size = 1 c.utf8Size = 2 c.utf8Size = 3 c.utf8Size = 4 := by
have := c.utf8Size_pos
have := c.utf8Size_le_four
omega
@[simp] theorem ofNat_toNat (c : Char) : Char.ofNat c.toNat = c := by
rw [Char.ofNat, dif_pos]
rfl
@[ext] protected theorem ext : {a b : Char} a.val = b.val a = b
| _,_, _,_, rfl => rfl
end Char
@[deprecated Char.utf8Size (since := "2024-06-04")] abbrev String.csize := Char.utf8Size

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@@ -4,7 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Robert Y. Lewis, Keeley Hoek, Mario Carneiro
-/
prelude
import Init.Data.Nat.Div
import Init.Data.Nat.Bitwise.Basic
import Init.Coe
open Nat
@@ -13,40 +15,17 @@ namespace Fin
instance coeToNat : CoeOut (Fin n) Nat :=
fun v => v.val
/--
From the empty type `Fin 0`, any desired result `α` can be derived. This is simlar to `Empty.elim`.
-/
def elim0.{u} {α : Sort u} : Fin 0 α
| _, h => absurd h (not_lt_zero _)
/--
Returns the successor of the argument.
The bound in the result type is increased:
```
(2 : Fin 3).succ = (3 : Fin 4)
```
This differs from addition, which wraps around:
```
(2 : Fin 3) + 1 = (0 : Fin 3)
```
-/
def succ : Fin n Fin n.succ
| i, h => i+1, Nat.succ_lt_succ h
variable {n : Nat}
/--
Returns `a` modulo `n + 1` as a `Fin n.succ`.
-/
protected def ofNat {n : Nat} (a : Nat) : Fin n.succ :=
a % (n+1), Nat.mod_lt _ (Nat.zero_lt_succ _)
/--
Returns `a` modulo `n` as a `Fin n`.
The assumption `n > 0` ensures that `Fin n` is nonempty.
-/
protected def ofNat' {n : Nat} (a : Nat) (h : n > 0) : Fin n :=
a % n, Nat.mod_lt _ h
@@ -56,34 +35,14 @@ private theorem mlt {b : Nat} : {a : Nat} → a < n → b % n < n
have : n > 0 := Nat.lt_trans (Nat.zero_lt_succ _) h;
Nat.mod_lt _ this
/-- Addition modulo `n` -/
protected def add : Fin n Fin n Fin n
| a, h, b, _ => (a + b) % n, mlt h
/-- Multiplication modulo `n` -/
protected def mul : Fin n Fin n Fin n
| a, h, b, _ => (a * b) % n, mlt h
/-- Subtraction modulo `n` -/
protected def sub : Fin n Fin n Fin n
/-
The definition of `Fin.sub` has been updated to improve performance.
The right-hand-side of the following `match` was originally
```
⟨(a + (n - b)) % n, mlt h⟩
```
This caused significant performance issues when testing definitional equality,
such as `x =?= x - 1` where `x : Fin n` and `n` is a big number,
as Lean spent a long time reducing
```
((n - 1) + x.val) % n
```
For example, this was an issue for `Fin 2^64` (i.e., `UInt64`).
This change improves performance by leveraging the fact that `Nat.add` is defined
using recursion on the second argument.
See issue #4413.
-/
| a, h, b, _ => ((n - b) + a) % n, mlt h
| a, h, b, _ => (a + (n - b)) % n, mlt h
/-!
Remark: land/lor can be defined without using (% n), but
@@ -210,7 +169,10 @@ theorem val_add_one_le_of_lt {n : Nat} {a b : Fin n} (h : a < b) : (a : Nat) + 1
theorem val_add_one_le_of_gt {n : Nat} {a b : Fin n} (h : a > b) : (b : Nat) + 1 (a : Nat) := h
theorem exists_iff {p : Fin n Prop} : (Exists fun i => p i) Exists fun i => Exists fun h => p i, h :=
fun i, hi, hpi => i, hi, hpi, fun i, hi, hpi => i, hi, hpi
end Fin
instance [GetElem cont Nat elem dom] : GetElem cont (Fin n) elem fun xs i => dom xs i where
getElem xs i h := getElem xs i.1 h
macro_rules
| `(tactic| get_elem_tactic_trivial) => `(tactic| apply Fin.val_lt_of_le; get_elem_tactic_trivial; done)

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@@ -1,15 +0,0 @@
/-
Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
prelude
import Init.Data.Nat.Bitwise
import Init.Data.Fin.Basic
namespace Fin
@[simp] theorem and_val (a b : Fin n) : (a &&& b).val = a.val &&& b.val :=
Nat.mod_eq_of_lt (Nat.lt_of_le_of_lt Nat.and_le_left a.isLt)
end Fin

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@@ -6,15 +6,12 @@ Authors: François G. Dorais
prelude
import Init.Data.Nat.Linear
namespace Fin
/-- Folds over `Fin n` from the left: `foldl 3 f x = f (f (f x 0) 1) 2`. -/
@[inline] def foldl (n) (f : α Fin n α) (init : α) : α := loop init 0 where
/-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)` -/
loop (x : α) (i : Nat) : α :=
if h : i < n then loop (f x i, h) (i+1) else x
termination_by n - i
decreasing_by decreasing_trivial_pre_omega
/-- Folds over `Fin n` from the right: `foldr 3 f x = f 0 (f 1 (f 2 x))`. -/
@[inline] def foldr (n) (f : Fin n α α) (init : α) : α := loop n, Nat.le_refl n init where
@@ -22,5 +19,3 @@ namespace Fin
loop : {i // i n} α α
| 0, _, x => x
| i+1, h, x => loop i, Nat.le_of_lt h (f i, h x)
end Fin

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

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@@ -1,7 +1,7 @@
/-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Leonardo de Moura
Authors: Mario Carneiro
-/
prelude
import Init.Data.Fin.Basic
@@ -11,9 +11,6 @@ import Init.ByCases
import Init.Conv
import Init.Omega
-- Remove after the next stage0 update
set_option allowUnsafeReducibility true
namespace Fin
/-- If you actually have an element of `Fin n`, then the `n` is always positive -/
@@ -24,7 +21,7 @@ theorem mod_def (a m : Fin n) : a % m = Fin.mk (a % m) (Nat.lt_of_le_of_lt (Nat.
theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a * b) % n) (Nat.mod_lt _ a.size_pos) := rfl
theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b) + a) % n) (Nat.mod_lt _ a.size_pos) := rfl
theorem sub_def (a b : Fin n) : a - b = Fin.mk ((a + (n - b)) % n) (Nat.mod_lt _ a.size_pos) := rfl
theorem size_pos' : [Nonempty (Fin n)], 0 < n | i => i.size_pos
@@ -37,28 +34,32 @@ theorem pos_iff_nonempty {n : Nat} : 0 < n ↔ Nonempty (Fin n) :=
@[simp] protected theorem eta (a : Fin n) (h : a < n) : (a, h : Fin n) = a := rfl
@[ext] protected theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
@[ext] theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
theorem ext_iff {a b : Fin n} : a = b a.1 = b.1 := val_inj.symm
theorem val_ne_iff {a b : Fin n} : a.1 b.1 a b := not_congr val_inj
theorem exists_iff {p : Fin n Prop} : ( i, p i) i h, p i, h :=
fun i, hi, hpi => i, hi, hpi, fun i, hi, hpi => i, hi, hpi
theorem forall_iff {p : Fin n Prop} : ( i, p i) i h, p i, h :=
fun h i hi => h i, hi, fun h i, hi => h i hi
protected theorem mk.inj_iff {n a b : Nat} {ha : a < n} {hb : b < n} :
(a, ha : Fin n) = b, hb a = b := Fin.ext_iff
(a, ha : Fin n) = b, hb a = b := ext_iff
theorem val_mk {m n : Nat} (h : m < n) : (m, h : Fin n).val = m := rfl
theorem eq_mk_iff_val_eq {a : Fin n} {k : Nat} {hk : k < n} :
a = k, hk (a : Nat) = k := Fin.ext_iff
a = k, hk (a : Nat) = k := ext_iff
theorem mk_val (i : Fin n) : (i, i.isLt : Fin n) = i := Fin.eta ..
@[simp] theorem val_ofNat' (a : Nat) (is_pos : n > 0) :
(Fin.ofNat' a is_pos).val = a % n := rfl
@[deprecated ofNat'_zero_val (since := "2024-02-22")]
theorem ofNat'_zero_val : (Fin.ofNat' 0 h).val = 0 := Nat.zero_mod _
@[deprecated ofNat'_zero_val] theorem ofNat'_zero_val : (Fin.ofNat' 0 h).val = 0 := Nat.zero_mod _
@[simp] theorem mod_val (a b : Fin n) : (a % b).val = a.val % b.val :=
rfl
@@ -89,18 +90,6 @@ theorem lt_iff_val_lt_val {a b : Fin n} : a < b ↔ a.val < b.val := Iff.rfl
@[simp] protected theorem not_lt {a b : Fin n} : ¬ a < b b a := Nat.not_lt
@[simp] protected theorem le_refl (a : Fin n) : a a := by simp [le_def]
@[simp] protected theorem lt_irrefl (a : Fin n) : ¬ a < a := by simp
protected theorem le_trans {a b c : Fin n} : a b b c a c := Nat.le_trans
protected theorem lt_trans {a b c : Fin n} : a < b b < c a < c := Nat.lt_trans
protected theorem le_total (a b : Fin n) : a b b a := Nat.le_total a b
protected theorem lt_asymm {a b : Fin n} (h : a < b) : ¬ b < a := Nat.lt_asymm h
protected theorem ne_of_lt {a b : Fin n} (h : a < b) : a b := Fin.ne_of_val_ne (Nat.ne_of_lt h)
protected theorem ne_of_gt {a b : Fin n} (h : a < b) : b a := Fin.ne_of_val_ne (Nat.ne_of_gt h)
@@ -143,7 +132,7 @@ theorem eq_succ_of_ne_zero {n : Nat} {i : Fin (n + 1)} (hi : i ≠ 0) : ∃ j :
@[simp] theorem val_rev (i : Fin n) : rev i = n - (i + 1) := rfl
@[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := Fin.ext <| by
@[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := ext <| by
rw [val_rev, val_rev, Nat.sub_sub, Nat.sub_sub_self (by exact i.2), Nat.add_sub_cancel]
@[simp] theorem rev_le_rev {i j : Fin n} : rev i rev j j i := by
@@ -169,12 +158,12 @@ theorem le_last (i : Fin (n + 1)) : i ≤ last n := Nat.le_of_lt_succ i.is_lt
theorem last_pos : (0 : Fin (n + 2)) < last (n + 1) := Nat.succ_pos _
theorem eq_last_of_not_lt {i : Fin (n + 1)} (h : ¬(i : Nat) < n) : i = last n :=
Fin.ext <| Nat.le_antisymm (le_last i) (Nat.not_lt.1 h)
ext <| Nat.le_antisymm (le_last i) (Nat.not_lt.1 h)
theorem val_lt_last {i : Fin (n + 1)} : i last n (i : Nat) < n :=
Decidable.not_imp_comm.1 eq_last_of_not_lt
@[simp] theorem rev_last (n : Nat) : rev (last n) = 0 := Fin.ext <| by simp
@[simp] theorem rev_last (n : Nat) : rev (last n) = 0 := ext <| by simp
@[simp] theorem rev_zero (n : Nat) : rev 0 = last n := by
rw [ rev_rev (last _), rev_last]
@@ -242,11 +231,11 @@ theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 := Fin.ne_of_lt one_pos
@[simp] theorem succ_lt_succ_iff {a b : Fin n} : a.succ < b.succ a < b := Nat.succ_lt_succ_iff
@[simp] theorem succ_inj {a b : Fin n} : a.succ = b.succ a = b := by
refine fun h => Fin.ext ?_, congrArg _
refine fun h => ext ?_, congrArg _
apply Nat.le_antisymm <;> exact succ_le_succ_iff.1 (h Nat.le_refl _)
theorem succ_ne_zero {n} : k : Fin n, Fin.succ k 0
| k, _, heq => Nat.succ_ne_zero k <| congrArg Fin.val heq
| k, _, heq => Nat.succ_ne_zero k <| ext_iff.1 heq
@[simp] theorem succ_zero_eq_one : Fin.succ (0 : Fin (n + 1)) = 1 := rfl
@@ -265,7 +254,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
rw [ succ_zero_eq_one, succ_lt_succ_iff]; exact succ_pos a
@[simp] theorem add_one_lt_iff {n : Nat} {k : Fin (n + 2)} : k + 1 < k k = last _ := by
simp only [lt_def, val_add, val_last, Fin.ext_iff]
simp only [lt_def, val_add, val_last, ext_iff]
let k, hk := k
match Nat.eq_or_lt_of_le (Nat.le_of_lt_succ hk) with
| .inl h => cases h; simp [Nat.succ_pos]
@@ -283,7 +272,7 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
split <;> simp [*, (Nat.succ_ne_zero _).symm, Nat.ne_of_gt (Nat.lt_succ_self _)]
@[simp] theorem last_le_iff {n : Nat} {k : Fin (n + 1)} : last n k k = last n := by
rw [Fin.ext_iff, Nat.le_antisymm_iff, le_def, and_iff_right (by apply le_last)]
rw [ext_iff, Nat.le_antisymm_iff, le_def, and_iff_right (by apply le_last)]
@[simp] theorem lt_add_one_iff {n : Nat} {k : Fin (n + 1)} : k < k + 1 k < last n := by
rw [ Decidable.not_iff_not]; simp
@@ -304,10 +293,10 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
@[simp] theorem castLE_mk (i n m : Nat) (hn : i < n) (h : n m) :
castLE h i, hn = i, Nat.lt_of_lt_of_le hn h := rfl
@[simp] theorem castLE_zero {n m : Nat} (h : n.succ m.succ) : castLE h 0 = 0 := by simp [Fin.ext_iff]
@[simp] theorem castLE_zero {n m : Nat} (h : n.succ m.succ) : castLE h 0 = 0 := by simp [ext_iff]
@[simp] theorem castLE_succ {m n : Nat} (h : m + 1 n + 1) (i : Fin m) :
castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [Fin.ext_iff]
castLE h i.succ = (castLE (Nat.succ_le_succ_iff.mp h) i).succ := by simp [ext_iff]
@[simp] theorem castLE_castLE {k m n} (km : k m) (mn : m n) (i : Fin k) :
Fin.castLE mn (Fin.castLE km i) = Fin.castLE (Nat.le_trans km mn) i :=
@@ -320,7 +309,7 @@ theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
@[simp] theorem coe_cast (h : n = m) (i : Fin n) : (cast h i : Nat) = i := rfl
@[simp] theorem cast_last {n' : Nat} {h : n + 1 = n' + 1} : cast h (last n) = last n' :=
Fin.ext (by rw [coe_cast, val_last, val_last, Nat.succ.inj h])
ext (by rw [coe_cast, val_last, val_last, Nat.succ.inj h])
@[simp] theorem cast_mk (h : n = m) (i : Nat) (hn : i < n) : cast h i, hn = i, h hn := rfl
@@ -346,7 +335,7 @@ theorem castAdd_lt {m : Nat} (n : Nat) (i : Fin m) : (castAdd n i : Nat) < m :=
/-- For rewriting in the reverse direction, see `Fin.cast_castAdd_left`. -/
theorem castAdd_cast {n n' : Nat} (m : Nat) (i : Fin n') (h : n' = n) :
castAdd m (Fin.cast h i) = Fin.cast (congrArg (. + m) h) (castAdd m i) := Fin.ext rfl
castAdd m (Fin.cast h i) = Fin.cast (congrArg (. + m) h) (castAdd m i) := ext rfl
theorem cast_castAdd_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
cast h (castAdd m i) = castAdd m (cast (Nat.add_right_cancel h) i) := rfl
@@ -376,7 +365,7 @@ theorem castSucc_lt_succ (i : Fin n) : Fin.castSucc i < i.succ :=
lt_def.2 <| by simp only [coe_castSucc, val_succ, Nat.lt_succ_self]
theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i Fin.castSucc j i < j.succ := by
simpa only [lt_def, le_def] using Nat.add_one_le_add_one_iff.symm
simpa [lt_def, le_def] using Nat.succ_le_succ_iff.symm
theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
Fin.castSucc i < j i.succ j := .rfl
@@ -395,7 +384,7 @@ theorem castSucc_lt_iff_succ_le {n : Nat} {i : Fin n} {j : Fin (n + 1)} :
@[simp] theorem castSucc_lt_castSucc_iff {a b : Fin n} :
Fin.castSucc a < Fin.castSucc b a < b := .rfl
theorem castSucc_inj {a b : Fin n} : castSucc a = castSucc b a = b := by simp [Fin.ext_iff]
theorem castSucc_inj {a b : Fin n} : castSucc a = castSucc b a = b := by simp [ext_iff]
theorem castSucc_lt_last (a : Fin n) : castSucc a < last n := a.is_lt
@@ -407,7 +396,7 @@ theorem castSucc_lt_last (a : Fin n) : castSucc a < last n := a.is_lt
theorem castSucc_pos {i : Fin (n + 1)} (h : 0 < i) : 0 < castSucc i := by
simpa [lt_def] using h
@[simp] theorem castSucc_eq_zero_iff (a : Fin (n + 1)) : castSucc a = 0 a = 0 := by simp [Fin.ext_iff]
@[simp] theorem castSucc_eq_zero_iff (a : Fin (n + 1)) : castSucc a = 0 a = 0 := by simp [ext_iff]
theorem castSucc_ne_zero_iff (a : Fin (n + 1)) : castSucc a 0 a 0 :=
not_congr <| castSucc_eq_zero_iff a
@@ -419,7 +408,7 @@ theorem castSucc_fin_succ (n : Nat) (j : Fin n) :
theorem coeSucc_eq_succ {a : Fin n} : castSucc a + 1 = a.succ := by
cases n
· exact a.elim0
· simp [Fin.ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
· simp [ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
theorem lt_succ {a : Fin n} : castSucc a < a.succ := by
rw [castSucc, lt_def, coe_castAdd, val_succ]; exact Nat.lt_succ_self a.val
@@ -452,7 +441,7 @@ theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
@[simp] theorem cast_addNat_right {n m m' : Nat} (i : Fin n) (h : n + m' = n + m) :
cast h (addNat i m') = addNat i m :=
Fin.ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
@[simp] theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
@@ -472,7 +461,7 @@ theorem cast_natAdd_right {n n' m : Nat} (i : Fin n') (h : m + n' = m + n) :
@[simp] theorem cast_natAdd_left {n m m' : Nat} (i : Fin n) (h : m' + n = m + n) :
cast h (natAdd m' i) = natAdd m i :=
Fin.ext <| (congrArg (· + (i : Nat)) (Nat.add_right_cancel h) : _)
ext <| (congrArg (· + (i : Nat)) (Nat.add_right_cancel h) : _)
theorem castAdd_natAdd (p m : Nat) {n : Nat} (i : Fin n) :
castAdd p (natAdd m i) = cast (Nat.add_assoc ..).symm (natAdd m (castAdd p i)) := rfl
@@ -482,27 +471,27 @@ theorem natAdd_castAdd (p m : Nat) {n : Nat} (i : Fin n) :
theorem natAdd_natAdd (m n : Nat) {p : Nat} (i : Fin p) :
natAdd m (natAdd n i) = cast (Nat.add_assoc ..) (natAdd (m + n) i) :=
Fin.ext <| (Nat.add_assoc ..).symm
ext <| (Nat.add_assoc ..).symm
@[simp]
theorem cast_natAdd_zero {n n' : Nat} (i : Fin n) (h : 0 + n = n') :
cast h (natAdd 0 i) = cast ((Nat.zero_add _).symm.trans h) i :=
Fin.ext <| Nat.zero_add _
ext <| Nat.zero_add _
@[simp]
theorem cast_natAdd (n : Nat) {m : Nat} (i : Fin m) :
cast (Nat.add_comm ..) (natAdd n i) = addNat i n := Fin.ext <| Nat.add_comm ..
cast (Nat.add_comm ..) (natAdd n i) = addNat i n := ext <| Nat.add_comm ..
@[simp]
theorem cast_addNat {n : Nat} (m : Nat) (i : Fin n) :
cast (Nat.add_comm ..) (addNat i m) = natAdd m i := Fin.ext <| Nat.add_comm ..
cast (Nat.add_comm ..) (addNat i m) = natAdd m i := ext <| Nat.add_comm ..
@[simp] theorem natAdd_last {m n : Nat} : natAdd n (last m) = last (n + m) := rfl
theorem natAdd_castSucc {m n : Nat} {i : Fin m} : natAdd n (castSucc i) = castSucc (natAdd n i) :=
rfl
theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := Fin.ext <| by
theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := ext <| by
rw [val_rev, coe_castAdd, coe_addNat, val_rev, Nat.sub_add_comm (Nat.succ_le_of_lt k.is_lt)]
theorem rev_addNat (k : Fin n) (m : Nat) : rev (addNat k m) = castAdd m (rev k) := by
@@ -532,7 +521,7 @@ theorem pred_eq_iff_eq_succ {n : Nat} (i : Fin (n + 1)) (hi : i ≠ 0) (j : Fin
theorem pred_mk_succ (i : Nat) (h : i < n + 1) :
Fin.pred i + 1, Nat.add_lt_add_right h 1 (ne_of_val_ne (Nat.ne_of_gt (mk_succ_pos i h))) =
i, h := by
simp only [Fin.ext_iff, coe_pred, Nat.add_sub_cancel]
simp only [ext_iff, coe_pred, Nat.add_sub_cancel]
@[simp] theorem pred_mk_succ' (i : Nat) (h₁ : i + 1 < n + 1 + 1) (h₂) :
Fin.pred i + 1, h₁ h₂ = i, Nat.lt_of_succ_lt_succ h₁ := pred_mk_succ i _
@@ -552,14 +541,14 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
{a b : Fin (n + 1)} {ha : a 0} {hb : b 0}, a.pred ha = b.pred hb a = b
| 0, _, _, ha, _ => by simp only [mk_zero, ne_eq, not_true] at ha
| i + 1, _, 0, _, _, hb => by simp only [mk_zero, ne_eq, not_true] at hb
| i + 1, hi, j + 1, hj, ha, hb => by simp [Fin.ext_iff, Nat.succ.injEq]
| i + 1, hi, j + 1, hj, ha, hb => by simp [ext_iff]
@[simp] theorem pred_one {n : Nat} :
Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
pred (i + 1) (Fin.ne_of_gt (add_one_pos _ (lt_def.2 h))) = castLT i h := by
rw [Fin.ext_iff, coe_pred, coe_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
rw [ext_iff, coe_pred, coe_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
exact Nat.add_lt_add_right h 1
@[simp] theorem coe_subNat (i : Fin (n + m)) (h : m i) : (i.subNat m h : Nat) = i - m := rfl
@@ -571,10 +560,10 @@ theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
pred (castSucc i.succ) (Fin.ne_of_gt (castSucc_pos i.succ_pos)) = castSucc i := rfl
@[simp] theorem addNat_subNat {i : Fin (n + m)} (h : m i) : addNat (subNat m i h) m = i :=
Fin.ext <| Nat.sub_add_cancel h
ext <| Nat.sub_add_cancel h
@[simp] theorem subNat_addNat (i : Fin n) (m : Nat) (h : m addNat i m := le_coe_addNat m i) :
subNat m (addNat i m) h = i := Fin.ext <| Nat.add_sub_cancel i m
subNat m (addNat i m) h = i := ext <| Nat.add_sub_cancel i m
@[simp] theorem natAdd_subNat_cast {i : Fin (n + m)} (h : n i) :
natAdd n (subNat n (cast (Nat.add_comm ..) i) h) = i := by simp [ cast_addNat]; rfl
@@ -613,7 +602,6 @@ A version of `Fin.succRec` taking `i : Fin n` as the first argument. -/
@Fin.succRecOn (n + 1) i.succ motive zero succ = succ n i (Fin.succRecOn i zero succ) := by
cases i; rfl
/-- Define `motive i` by induction on `i : Fin (n + 1)` via induction on the underlying `Nat` value.
This function has two arguments: `zero` handles the base case on `motive 0`,
and `succ` defines the inductive step using `motive i.castSucc`.
@@ -622,12 +610,8 @@ and `succ` defines the inductive step using `motive i.castSucc`.
@[elab_as_elim] def induction {motive : Fin (n + 1) Sort _} (zero : motive 0)
(succ : i : Fin n, motive (castSucc i) motive i.succ) :
i : Fin (n + 1), motive i
| i, hi => go i hi
where
-- Use a curried function so that this is structurally recursive
go : (i : Nat) (hi : i < n + 1), motive i, hi
| 0, hi => by rwa [Fin.mk_zero]
| i+1, hi => succ i, Nat.lt_of_succ_lt_succ hi (go i (Nat.lt_of_succ_lt hi))
| 0, hi => by rwa [Fin.mk_zero]
| i+1, hi => succ i, Nat.lt_of_succ_lt_succ hi (induction zero succ i, Nat.lt_of_succ_lt hi)
@[simp] theorem induction_zero {motive : Fin (n + 1) Sort _} (zero : motive 0)
(hs : i : Fin n, motive (castSucc i) motive i.succ) :
@@ -699,7 +683,6 @@ and `cast` defines the inductive step using `motive i.succ`, inducting downwards
termination_by n + 1 - i
decreasing_by decreasing_with
-- FIXME: we put the proof down here to avoid getting a dummy `have` in the definition
try simp only [Nat.succ_sub_succ_eq_sub]
exact Nat.add_sub_add_right .. Nat.sub_lt_sub_left i.2 (Nat.lt_succ_self i)
@[simp] theorem reverseInduction_last {n : Nat} {motive : Fin (n + 1) Sort _} {zero succ} :
@@ -757,16 +740,16 @@ theorem addCases_right {m n : Nat} {motive : Fin (m + n) → Sort _} {left right
/-! ### sub -/
protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = (a + (n - b)) % n := by
cases a; cases b; rfl
@[simp] theorem ofNat'_sub (x : Nat) (lt : 0 < n) (y : Fin n) :
Fin.ofNat' x lt - y = Fin.ofNat' ((n - y.val) + x) lt := by
Fin.ofNat' x lt - y = Fin.ofNat' (x + (n - y.val)) lt := by
apply Fin.eq_of_val_eq
simp [Fin.ofNat', Fin.sub_def]
@[simp] theorem sub_ofNat' (x : Fin n) (y : Nat) (lt : 0 < n) :
x - Fin.ofNat' y lt = Fin.ofNat' ((n - y % n) + x.val) lt := by
x - Fin.ofNat' y lt = Fin.ofNat' (x.val + (n - y % n)) lt := by
apply Fin.eq_of_val_eq
simp [Fin.ofNat', Fin.sub_def]
@@ -777,20 +760,17 @@ private theorem _root_.Nat.mod_eq_sub_of_lt_two_mul {x n} (h₁ : n ≤ x) (h₂
theorem coe_sub_iff_le {a b : Fin n} : ((a - b) : Nat) = a - b b a := by
rw [sub_def, le_def]
dsimp only
if h : n (n - b) + a then
if h : n a + (n - b) then
rw [Nat.mod_eq_sub_of_lt_two_mul h]
all_goals omega
else
rw [Nat.mod_eq_of_lt]
all_goals omega
theorem sub_val_of_le {a b : Fin n} : b a (a - b).val = a.val - b.val :=
coe_sub_iff_le.2
theorem coe_sub_iff_lt {a b : Fin n} : ((a - b) : Nat) = n + a - b a < b := by
rw [sub_def, lt_def]
dsimp only
if h : n (n - b) + a then
if h : n a + (n - b) then
rw [Nat.mod_eq_sub_of_lt_two_mul h]
all_goals omega
else
@@ -808,28 +788,47 @@ theorem coe_mul {n : Nat} : ∀ a b : Fin n, ((a * b : Fin n) : Nat) = a * b % n
protected theorem mul_one (k : Fin (n + 1)) : k * 1 = k := by
match n with
| 0 => exact Subsingleton.elim (α := Fin 1) ..
| n+1 => simp [Fin.ext_iff, mul_def, Nat.mod_eq_of_lt (is_lt k)]
| n+1 => simp [ext_iff, mul_def, Nat.mod_eq_of_lt (is_lt k)]
protected theorem mul_comm (a b : Fin n) : a * b = b * a :=
Fin.ext <| by rw [mul_def, mul_def, Nat.mul_comm]
instance : Std.Commutative (α := Fin n) (· * ·) := Fin.mul_comm
ext <| by rw [mul_def, mul_def, Nat.mul_comm]
protected theorem mul_assoc (a b c : Fin n) : a * b * c = a * (b * c) := by
apply eq_of_val_eq
simp only [val_mul]
rw [ Nat.mod_eq_of_lt a.isLt, Nat.mod_eq_of_lt b.isLt, Nat.mod_eq_of_lt c.isLt]
simp only [ Nat.mul_mod, Nat.mul_assoc]
instance : Std.Associative (α := Fin n) (· * ·) := Fin.mul_assoc
protected theorem one_mul (k : Fin (n + 1)) : (1 : Fin (n + 1)) * k = k := by
rw [Fin.mul_comm, Fin.mul_one]
instance : Std.LawfulIdentity (α := Fin (n + 1)) (· * ·) 1 where
left_id := Fin.one_mul
right_id := Fin.mul_one
protected theorem mul_zero (k : Fin (n + 1)) : k * 0 = 0 := by simp [Fin.ext_iff, mul_def]
protected theorem mul_zero (k : Fin (n + 1)) : k * 0 = 0 := by simp [ext_iff, mul_def]
protected theorem zero_mul (k : Fin (n + 1)) : (0 : Fin (n + 1)) * k = 0 := by
simp [Fin.ext_iff, mul_def]
simp [ext_iff, mul_def]
end Fin
namespace USize
@[simp] theorem lt_def {a b : USize} : a < b a.toNat < b.toNat := .rfl
@[simp] theorem le_def {a b : USize} : a b a.toNat b.toNat := .rfl
@[simp] theorem zero_toNat : (0 : USize).toNat = 0 := Nat.zero_mod _
@[simp] theorem mod_toNat (a b : USize) : (a % b).toNat = a.toNat % b.toNat :=
Fin.mod_val ..
@[simp] theorem div_toNat (a b : USize) : (a / b).toNat = a.toNat / b.toNat :=
Fin.div_val ..
@[simp] theorem modn_toNat (a : USize) (b : Nat) : (a.modn b).toNat = a.toNat % b :=
Fin.modn_val ..
theorem mod_lt (a b : USize) (h : 0 < b) : a % b < b := USize.modn_lt _ (by simp at h; exact h)
theorem toNat.inj : {a b : USize}, a.toNat = b.toNat a = b
| _, _, _, _, rfl => rfl
end USize

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@@ -101,13 +101,13 @@ Returns an undefined value if `x` is not finite.
instance : ToString Float where
toString := Float.toString
@[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float
instance : Repr Float where
reprPrec n prec := if n < UInt64.toFloat 0 then Repr.addAppParen (toString n) prec else toString n
reprPrec n _ := Float.toString n
instance : ReprAtom Float :=
@[extern "lean_uint64_to_float"] opaque UInt64.toFloat (n : UInt64) : Float
@[extern "sin"] opaque Float.sin : Float Float
@[extern "cos"] opaque Float.cos : Float Float
@[extern "tan"] opaque Float.tan : Float Float

View File

@@ -20,27 +20,24 @@ private def formatInfo (showInfo : Bool) (info : SourceInfo) (f : Format) : Form
| true, SourceInfo.synthetic pos endPos false => f!"{pos}:{f}:{endPos}"
| _, _ => f
partial def formatStxAux (maxDepth : Option Nat) (showInfo : Bool) (depth : Nat) : Syntax Format
| atom info val => formatInfo showInfo info <| format (repr val)
| ident info _ val _ => formatInfo showInfo info <| format "`" ++ format val
| missing => "<missing>"
| node info kind args =>
partial def formatStxAux (maxDepth : Option Nat) (showInfo : Bool) : Nat Syntax Format
| _, atom info val => formatInfo showInfo info $ format (repr val)
| _, ident info _ val _ => formatInfo showInfo info $ format "`" ++ format val
| _, missing => "<missing>"
| depth, node _ kind args =>
let depth := depth + 1;
if kind == nullKind then
sbracket <|
sbracket $
if args.size > 0 && depth > maxDepth.getD depth then
".."
else
joinSep (args.toList.map (formatStxAux maxDepth showInfo depth)) line
else
let shorterName := kind.replacePrefix `Lean.Parser Name.anonymous
let header := formatInfo showInfo info <| format shorterName
let shorterName := kind.replacePrefix `Lean.Parser Name.anonymous;
let header := format shorterName;
let body : List Format :=
if args.size > 0 && depth > maxDepth.getD depth then
[".."]
else
args.toList.map (formatStxAux maxDepth showInfo depth)
paren <| joinSep (header :: body) line
if args.size > 0 && depth > maxDepth.getD depth then [".."] else args.toList.map (formatStxAux maxDepth showInfo depth);
paren $ joinSep (header :: body) line
/-- Pretty print the given syntax `stx` as a `Format`.
Nodes deeper than `maxDepth` are omitted.

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@@ -62,16 +62,3 @@ instance (P : Prop) : Hashable P where
/-- An opaque (low-level) hash operation used to implement hashing for pointers. -/
@[always_inline, inline] def hash64 (u : UInt64) : UInt64 :=
mixHash u 11
/-- `LawfulHashable α` says that the `BEq α` and `Hashable α` instances on `α` are compatible, i.e.,
that `a == b` implies `hash a = hash b`. This is automatic if the `BEq` instance is lawful.
-/
class LawfulHashable (α : Type u) [BEq α] [Hashable α] where
/-- If `a == b`, then `hash a = hash b`. -/
hash_eq (a b : α) : a == b hash a = hash b
theorem hash_eq [BEq α] [Hashable α] [LawfulHashable α] {a b : α} : a == b hash a = hash b :=
LawfulHashable.hash_eq a b
instance (priority := low) [BEq α] [Hashable α] [LawfulBEq α] : LawfulHashable α where
hash_eq _ _ h := eq_of_beq h rfl

View File

@@ -11,4 +11,3 @@ import Init.Data.Int.DivModLemmas
import Init.Data.Int.Gcd
import Init.Data.Int.Lemmas
import Init.Data.Int.Order
import Init.Data.Int.Pow

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