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Author SHA1 Message Date
Kim Morrison
703b963b09 chore: make some extCore and customEliminators public for Batteries 2025-10-16 09:51:34 +11:00
3992 changed files with 22708 additions and 66879 deletions

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@@ -1,34 +0,0 @@
To build Lean you should use `make -j -C build/release`.
To run a test you should use `cd tests/lean/run && ./test_single.sh example_test.lean`.
## New features
When asked to implement new features:
* begin by reviewing existing relevant code and tests
* write comprehensive tests first (expecting that these will initially fail)
* and then iterate on the implementation until the tests pass.
All new tests should go in `tests/lean/run/`. These tests don't have expected output; we just check there are no errors. You should use `#guard_msgs` to check for specific messages.
## Success Criteria
*Never* report success on a task unless you have verified both a clean build without errors, and that the relevant tests pass.
## Build System Safety
**NEVER manually delete build directories** (build/, stage0/, stage1/, etc.) even when builds fail.
- ONLY use the project's documented build command: `make -j -C build/release`
- If a build is broken, ask the user before attempting any manual cleanup
## LSP and IDE Diagnostics
After rebuilding, LSP diagnostics may be stale until the user interacts with files. Trust command-line test results over IDE diagnostics.
## Update prompting when the user is frustrated
If the user expresses frustration with you, stop and ask them to help update this `.claude/CLAUDE.md` file with missing guidance.
## Creating pull requests.
All PRs must have a first paragraph starting with "This PR". This paragraph is automatically incorporated into release notes. Read `lean4/doc/dev/commit_convention.md` when making PRs.

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@@ -16,26 +16,14 @@ These comments explain the scripts' behavior, which repositories get special han
## Process
1. Run `script/release_checklist.py {version}` to check the current status
2. **CRITICAL: If preliminary lean4 checks fail, STOP immediately and alert the user**
- Check for: release branch exists, CMake version correct, tag exists, release page exists, release notes exist
- **IMPORTANT**: The release page is created AUTOMATICALLY by CI after pushing the tag - DO NOT create it manually
- Do NOT create any PRs or proceed with repository updates if these checks fail
3. Create a todo list tracking all repositories that need updates
4. **CRITICAL RULE: You can ONLY run `release_steps.py` for a repository if `release_checklist.py` explicitly says to do so**
- The checklist output will say "Run `script/release_steps.py {version} {repo_name}` to create it"
- If a repository shows "🟡 Dependencies not ready", you CANNOT create a PR for it yet
- You MUST rerun `release_checklist.py` before attempting to create PRs for any new repositories
5. For each repository that the checklist says needs updating:
2. Create a todo list tracking all repositories that need updates
3. For each repository that needs updating:
- Run `script/release_steps.py {version} {repo_name}` to create the PR
- Mark it complete when the PR is created
6. After creating PRs, notify the user which PRs need review and merging
7. **MANDATORY: Rerun `release_checklist.py` to check current status**
- Do this after creating each batch of PRs
- Do this after the user reports PRs have been merged
- NEVER assume a repository is ready without checking the checklist output
8. As PRs are merged and tagged, dependent repositories will become ready
9. Continue the cycle: run checklist → create PRs for ready repos → wait for merges → repeat
10. Continue until all repositories are updated and the release is complete
4. After creating PRs, notify the user which PRs need review and merging
5. Continuously rerun `script/release_checklist.py {version}` to check progress
6. As PRs are merged, dependent repositories will become ready - create PRs for those as well
7. Continue until all repositories are updated and the release is complete
## Important Notes

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@@ -3,6 +3,9 @@ name: build-template
on:
workflow_call:
inputs:
check-level:
type: string
required: true
config:
type: string
required: true
@@ -213,7 +216,7 @@ jobs:
else
${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
fi
- uses: actions/upload-artifact@v5
- uses: actions/upload-artifact@v4
if: matrix.release
with:
name: build-${{ matrix.name }}
@@ -227,7 +230,7 @@ jobs:
run: |
ulimit -c unlimited # coredumps
time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
if: matrix.test
if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.test)
- name: Test Summary
uses: test-summary/action@v2
with:

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@@ -11,8 +11,8 @@ jobs:
- uses: actions/checkout@v5
with:
ref: ${{ github.event.pull_request.head.sha }}
filter: blob:none
fetch-depth: 0
filter: tree:0
- name: Find base commit
if: github.event_name == 'pull_request'

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@@ -31,6 +31,10 @@ 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 }}
# The build matrix, dynamically generated here
matrix: ${{ steps.set-matrix.outputs.matrix }}
# secondary build jobs that should not block the CI success/merge queue
@@ -106,54 +110,6 @@ jobs:
TAG_NAME="${GITHUB_REF##*/}"
echo "RELEASE_TAG=$TAG_NAME" >> "$GITHUB_OUTPUT"
- name: Validate CMakeLists.txt version matches tag
if: steps.set-release.outputs.RELEASE_TAG != ''
run: |
echo "Validating CMakeLists.txt version matches tag ${{ steps.set-release.outputs.RELEASE_TAG }}"
# Extract version values from CMakeLists.txt
CMAKE_MAJOR=$(grep -E "^set\(LEAN_VERSION_MAJOR " src/CMakeLists.txt | grep -oE '[0-9]+')
CMAKE_MINOR=$(grep -E "^set\(LEAN_VERSION_MINOR " src/CMakeLists.txt | grep -oE '[0-9]+')
CMAKE_PATCH=$(grep -E "^set\(LEAN_VERSION_PATCH " src/CMakeLists.txt | grep -oE '[0-9]+')
CMAKE_IS_RELEASE=$(grep -E "^set\(LEAN_VERSION_IS_RELEASE " src/CMakeLists.txt | grep -oE '[0-9]+')
# Expected values from tag parsing
TAG_MAJOR="${{ steps.set-release.outputs.LEAN_VERSION_MAJOR }}"
TAG_MINOR="${{ steps.set-release.outputs.LEAN_VERSION_MINOR }}"
TAG_PATCH="${{ steps.set-release.outputs.LEAN_VERSION_PATCH }}"
ERRORS=""
if [[ "$CMAKE_MAJOR" != "$TAG_MAJOR" ]]; then
ERRORS+="LEAN_VERSION_MAJOR: expected $TAG_MAJOR, found $CMAKE_MAJOR\n"
fi
if [[ "$CMAKE_MINOR" != "$TAG_MINOR" ]]; then
ERRORS+="LEAN_VERSION_MINOR: expected $TAG_MINOR, found $CMAKE_MINOR\n"
fi
if [[ "$CMAKE_PATCH" != "$TAG_PATCH" ]]; then
ERRORS+="LEAN_VERSION_PATCH: expected $TAG_PATCH, found $CMAKE_PATCH\n"
fi
if [[ "$CMAKE_IS_RELEASE" != "1" ]]; then
ERRORS+="LEAN_VERSION_IS_RELEASE: expected 1, found $CMAKE_IS_RELEASE\n"
fi
if [[ -n "$ERRORS" ]]; then
echo "::error::Version mismatch between tag and src/CMakeLists.txt"
echo ""
echo "Tag ${{ steps.set-release.outputs.RELEASE_TAG }} expects version $TAG_MAJOR.$TAG_MINOR.$TAG_PATCH"
echo "But src/CMakeLists.txt has mismatched values:"
echo -e "$ERRORS"
echo ""
echo "Fix src/CMakeLists.txt, delete the tag, and re-tag."
exit 1
fi
echo "Version validation passed: $TAG_MAJOR.$TAG_MINOR.$TAG_PATCH"
# 0: PRs without special label
# 1: PRs with `merge-ci` label, merge queue checks, master commits
# 2: nightlies
# 3: PRs with `release-ci` label, full releases
- name: Set check level
id: set-level
# We do not use github.event.pull_request.labels.*.name here because
@@ -161,28 +117,21 @@ jobs:
# rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
run: |
check_level=0
fast=false
if [[ -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
check_level=3
elif [[ -n "${{ steps.set-nightly.outputs.nightly }}" ]]; then
if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
check_level=2
elif [[ "${{ 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 "$labels" | grep -q "release-ci"; then
check_level=3
check_level=2
elif echo "$labels" | grep -q "merge-ci"; then
check_level=1
fi
if echo "$labels" | grep -q "fast-ci"; then
fast=true
fi
fi
echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
echo "fast=$fast" >> "$GITHUB_OUTPUT"
env:
GH_TOKEN: ${{ github.token }}
@@ -192,8 +141,7 @@ jobs:
with:
script: |
const level = ${{ steps.set-level.outputs.check-level }};
const fast = ${{ steps.set-level.outputs.fast }};
console.log(`level: ${level}, fast: ${fast}`);
console.log(`level: ${level}`);
// use large runners where available (original repo)
let large = ${{ github.repository == 'leanprover/lean4' }};
const isPr = "${{ github.event_name }}" == "pull_request";
@@ -204,8 +152,7 @@ jobs:
"name": "Linux LLVM",
"os": "ubuntu-latest",
"release": false,
"enabled": level >= 2,
"test": true,
"check-level": 2,
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -218,19 +165,17 @@ jobs:
{
// portable release build: use channel with older glibc (2.26)
"name": "Linux release",
// usually not a bottleneck so make exclusive to `fast-ci`
"os": large && fast ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
"os": "ubuntu-latest",
"release": true,
// Special handling for release jobs. We want:
// 1. To run it in PRs so developers get PR toolchains (so secondary without tests is sufficient)
// 1. To run it in PRs so developers get PR toolchains (so secondary is sufficient)
// 2. To skip it in merge queues as it takes longer than the
// Linux lake build and adds little value in the merge queue
// 3. To run it in release (obviously)
// 4. To run it for pushes to master so that pushes to master have a Linux toolchain
// available as an artifact for Grove to use.
"enabled": isPr || level != 1 || isPushToMaster,
"test": level >= 1,
"secondary": level == 0,
"check-level": (isPr || isPushToMaster) ? 0 : 2,
"secondary": isPr,
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -241,44 +186,38 @@ jobs:
{
"name": "Linux Lake",
"os": large ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
"enabled": true,
"check-level": 0,
"check-rebootstrap": level >= 1,
"check-stage3": level >= 2,
// only check-level >= 1 opts into tests implicitly. TODO: Clean up this logic.
"test": true,
// NOTE: `test-speedcenter` currently seems to be broken on `ubuntu-latest`
"test-speedcenter": large && level >= 2,
// We are not warning-free yet on all platforms, start here
"CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-Werror",
// made explicit until it can be assumed to have propagated to PRs
"CMAKE_OPTIONS": "-DUSE_LAKE=ON",
},
{
"name": "Linux Reldebug",
"os": "ubuntu-latest",
"enabled": level >= 2,
"test": true,
"check-level": 2,
"CMAKE_PRESET": "reldebug",
},
{
// TODO: suddenly started failing in CI
/*{
"name": "Linux fsanitize",
// Always run on large if available, more reliable regarding timeouts
"os": large ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
"enabled": level >= 2,
// do not fail nightlies on this for now
"secondary": level <= 2,
"test": true,
"os": "ubuntu-latest",
"check-level": 2,
// turn off custom allocator & symbolic functions to make LSAN do its magic
"CMAKE_PRESET": "sanitize",
// `StackOverflow*` correctly triggers ubsan
// `reverse-ffi` fails to link in sanitizers
// `interactive` and `async_select_channel` fail nondeterministically, would need to
// be investigated.
"CTEST_OPTIONS": "-E 'StackOverflow|reverse-ffi|interactive|async_select_channel'"
},
// exclude seriously slow/problematic tests (laketests crash)
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
},*/
{
"name": "macOS",
"os": "macos-15-intel",
"release": true,
"test": false, // Tier 2 platform
"enabled": level >= 2,
"check-level": 2,
"shell": "bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-apple-darwin.tar.zst",
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
@@ -289,7 +228,7 @@ jobs:
{
"name": "macOS aarch64",
// standard GH runner only comes with 7GB so use large runner if possible when running tests
"os": large && (fast || level >= 1) ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
"os": large && !isPr ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
"release": true,
"shell": "bash -euxo pipefail {0}",
@@ -298,16 +237,14 @@ jobs:
"binary-check": "otool -L",
"tar": "gtar", // https://github.com/actions/runner-images/issues/2619
// See "Linux release" for release job levels; Grove is not a concern here
"enabled": isPr || level != 1,
"test": level >= 1,
"secondary": level == 0,
"check-level": isPr ? 0 : 2,
"secondary": isPr,
},
{
"name": "Windows",
"os": large && (fast || level >= 2) ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
"os": large && level == 2 ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
"release": true,
"enabled": level >= 2,
"test": true,
"check-level": 2,
"shell": "msys2 {0}",
"CMAKE_OPTIONS": "-G \"Unix Makefiles\"",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
@@ -319,8 +256,7 @@ jobs:
"os": "nscloud-ubuntu-22.04-arm64-4x16",
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-linux_aarch64",
"release": true,
"enabled": level >= 2,
"test": true,
"check-level": 2,
"shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-aarch64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -333,7 +269,7 @@ jobs:
// "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DPKG_CONFIG_EXECUTABLE=/usr/bin/i386-linux-gnu-pkg-config",
// "cmultilib": true,
// "release": true,
// "enabled": level >= 2,
// "check-level": 2,
// "cross": true,
// "shell": "bash -euxo pipefail {0}"
//}
@@ -345,7 +281,7 @@ jobs:
// "wasm": true,
// "cmultilib": true,
// "release": true,
// "enabled": level >= 2,
// "check-level": 2,
// "cross": true,
// "shell": "bash -euxo pipefail {0}",
// // Just a few selected tests because wasm is slow
@@ -359,7 +295,7 @@ jobs:
}
}
console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
matrix = matrix.filter((job) => job["enabled"]);
matrix = matrix.filter((job) => level >= job["check-level"]);
core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));
core.setOutput('matrix-secondary', matrix.filter((job) => job["secondary"]));
@@ -369,6 +305,7 @@ jobs:
uses: ./.github/workflows/build-template.yml
with:
config: ${{needs.configure.outputs.matrix}}
check-level: ${{ needs.configure.outputs.check-level }}
nightly: ${{ needs.configure.outputs.nightly }}
LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
@@ -384,6 +321,7 @@ jobs:
uses: ./.github/workflows/build-template.yml
with:
config: ${{needs.configure.outputs.matrix-secondary}}
check-level: ${{ needs.configure.outputs.check-level }}
nightly: ${{ needs.configure.outputs.nightly }}
LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
@@ -427,11 +365,11 @@ jobs:
runs-on: ubuntu-latest
needs: build
steps:
- uses: actions/download-artifact@v6
- uses: actions/download-artifact@v5
with:
path: artifacts
- name: Release
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
with:
files: artifacts/*/*
fail_on_unmatched_files: true
@@ -456,10 +394,8 @@ jobs:
with:
# needed for tagging
fetch-depth: 0
# Doesn't seem to be working when additionally fetching from lean4-nightly
#filter: tree:0
token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
- uses: actions/download-artifact@v6
- uses: actions/download-artifact@v5
with:
path: artifacts
- name: Prepare Nightly Release
@@ -477,7 +413,7 @@ jobs:
echo -e "\n*Full commit log*\n" >> diff.md
git log --oneline "$last_tag"..HEAD | sed 's/^/* /' >> diff.md
- name: Release Nightly
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
with:
body_path: diff.md
prerelease: true

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@@ -48,17 +48,17 @@ jobs:
git -C lean4.git remote add origin https://github.com/${{ github.repository_owner }}/lean4.git
git -C lean4.git fetch -n origin master
git -C lean4.git fetch -n origin "${{ steps.workflow-info.outputs.sourceHeadSha }}"
# Create both the original tag and the SHA-suffixed tag
SHORT_SHA="${{ steps.workflow-info.outputs.sourceHeadSha }}"
SHORT_SHA="${SHORT_SHA:0:7}"
# Export the short SHA for use in subsequent steps
echo "SHORT_SHA=${SHORT_SHA}" >> "$GITHUB_ENV"
git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }} "${{ steps.workflow-info.outputs.sourceHeadSha }}"
git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}" "${{ steps.workflow-info.outputs.sourceHeadSha }}"
git -C lean4.git remote add pr-releases https://foo:'${{ secrets.PR_RELEASES_TOKEN }}'@github.com/${{ github.repository_owner }}/lean4-pr-releases.git
git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}
git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}"
@@ -71,7 +71,7 @@ jobs:
GH_TOKEN: ${{ secrets.PR_RELEASES_TOKEN }}
- name: Release (short format)
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
with:
name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }}
# There are coredumps files here as well, but all in deeper subdirectories.
@@ -86,7 +86,7 @@ jobs:
- name: Release (SHA-suffixed format)
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
with:
name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }} (${{ steps.workflow-info.outputs.sourceHeadSha }})
# There are coredumps files here as well, but all in deeper subdirectories.
@@ -200,7 +200,7 @@ jobs:
-H "Accept: application/vnd.github.v3+json" \
"https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
| jq -r '.[].name')"
if echo "$LABELS" | grep -q "^force-mathlib-ci$"; then
echo "force-mathlib-ci label detected, forcing CI despite issues"
MESSAGE="Forcing Mathlib CI because the \`force-mathlib-ci\` label is present, despite problem: $MESSAGE"
@@ -301,7 +301,7 @@ jobs:
-H "Accept: application/vnd.github.v3+json" \
"https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
| jq -r '.[].name')"
if echo "$LABELS" | grep -q "^force-manual-ci$"; then
echo "force-manual-ci label detected, forcing CI despite issues"
MESSAGE="Forcing reference manual CI because the \`force-manual-ci\` label is present, despite problem: $MESSAGE"
@@ -401,7 +401,6 @@ jobs:
token: ${{ secrets.MATHLIB4_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
filter: tree:0
- name: Check if tag exists
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
@@ -426,7 +425,7 @@ jobs:
git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, updating lean-toolchain."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -435,7 +434,7 @@ jobs:
git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes
@@ -461,7 +460,6 @@ jobs:
token: ${{ secrets.MATHLIB4_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
filter: tree:0
- name: install elan
run: |
@@ -496,7 +494,7 @@ jobs:
sed -i 's,require "leanprover-community" / "batteries" @ git ".\+",require "leanprover-community" / "batteries" @ git "lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}",' lakefile.lean
lake update batteries
git add lakefile.lean lake-manifest.json
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, updating lean-toolchain and bumping Batteries."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -507,7 +505,7 @@ jobs:
git add lean-toolchain
lake update batteries
git add lake-manifest.json
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes
@@ -532,7 +530,6 @@ jobs:
token: ${{ secrets.MANUAL_PR_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
filter: tree:0
- name: Check if tag in reference manual exists
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.reference-manual-ready.outputs.manual_ready == 'true'
@@ -558,7 +555,7 @@ jobs:
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git add lakefile.lean lake-manifest.json
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, updating lean-toolchain."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -568,7 +565,7 @@ jobs:
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git add lake-manifest.json
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes

View File

@@ -15,6 +15,6 @@ jobs:
script: |
const msg = context.payload.pull_request? context.payload.pull_request.title : context.payload.merge_group.head_commit.message;
console.log(`Message: ${msg}`)
if (!/^(feat|fix|doc|style|refactor|test|chore|perf): (?![A-Z][a-z]).*[^.]($|\n\n)/.test(msg)) {
if (!/^(feat|fix|doc|style|refactor|test|chore|perf): .*[^.]($|\n\n)/.test(msg)) {
core.setFailed('PR title does not follow the Commit Convention (https://leanprover.github.io/lean4/doc/dev/commit_convention.html).');
}

1
.gitignore vendored
View File

@@ -20,6 +20,7 @@ tasks.json
settings.json
.gdb_history
.vscode/*
!.vscode/settings.json
script/__pycache__
*.produced.out
CMakeSettings.json

View File

@@ -41,7 +41,7 @@
"SMALL_ALLOCATOR": "OFF",
"USE_MIMALLOC": "OFF",
"BSYMBOLIC": "OFF",
"LEAN_TEST_VARS": "MAIN_STACK_SIZE=16000 LSAN_OPTIONS=max_leaks=10"
"LEAN_TEST_VARS": "MAIN_STACK_SIZE=16000"
},
"generator": "Unix Makefiles",
"binaryDir": "${sourceDir}/build/sanitize"

View File

@@ -72,9 +72,6 @@ update the archived C source code of the stage 0 compiler in `stage0/src`.
The github repository will automatically update stage0 on `master` once
`src/stdlib_flags.h` and `stage0/src/stdlib_flags.h` are out of sync.
To trigger this, modify `stage0/src/stdlib_flags.h` (e.g., by adding or changing
a comment). When `update-stage0` runs, it will overwrite `stage0/src/stdlib_flags.h`
with the contents of `src/stdlib_flags.h`, bringing them back in sync.
NOTE: A full rebuild of stage 1 will only be triggered when the *committed* contents of `stage0/` are changed.
Thus if you change files in it manually instead of through `update-stage0-commit` (see below) or fetching updates from git, you either need to commit those changes first or run `make -C build/release clean-stdlib`.

View File

@@ -52,7 +52,7 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
Similarly, the signed integer types `Int8`, ..., `Int64`, `ISize` are also represented by the unsigned C types `uint8_t`, ..., `uint64_t`, `size_t`, respectively, because they have a trivial structure.
* `Nat` and `Int` are represented by `lean_object *`.
Their runtime values 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 or integer (`lean_box`/`lean_unbox`).
* A universe `Sort u`, type constructor `... → Sort u`, `Void α` 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)`
* 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.
@@ -129,7 +129,8 @@ For all other modules imported by `lean`, the initializer is run without `builti
Thus `[init]` functions are run iff their module is imported, regardless of whether they have native code available or not, while `[builtin_init]` functions are only run for native executable or plugins, regardless of whether their module is imported or not.
`lean` uses built-in initializers for e.g. registering basic parsers that should be available even without importing their module (which is necessary for bootstrapping).
The initializer for module `A.B` in a package `foo` is called `initialize_foo_A_B`. For modules in the Lean core (e.g., `Init.Prelude`), the initializer is called `initialize_Init_Prelude`. Module initializers will automatically initialize any imported modules. They are also idempotent (when run with the same `builtin` flag), but not thread-safe.
The initializer for module `A.B` is called `initialize_A_B` and will automatically initialize any imported modules.
Module initializers are idempotent (when run with the same `builtin` flag), but not thread-safe.
**Important for process-related functionality**: If your application needs to use process-related functions from libuv, such as `Std.Internal.IO.Process.getProcessTitle` and `Std.Internal.IO.Process.setProcessTitle`, you must call `lean_setup_args(argc, argv)` (which returns a potentially modified `argv` that must be used in place of the original) **before** calling `lean_initialize()` or `lean_initialize_runtime_module()`. This sets up process handling capabilities correctly, which is essential for certain system-level operations that Lean's runtime may depend on.
@@ -140,8 +141,8 @@ void lean_initialize_runtime_module();
void lean_initialize();
char ** lean_setup_args(int argc, char ** argv);
lean_object * initialize_A_B(uint8_t builtin);
lean_object * initialize_C(uint8_t builtin);
lean_object * initialize_A_B(uint8_t builtin, lean_object *);
lean_object * initialize_C(uint8_t builtin, lean_object *);
...
argv = lean_setup_args(argc, argv); // if using process-related functionality
@@ -151,7 +152,7 @@ lean_initialize_runtime_module();
lean_object * res;
// use same default as for Lean executables
uint8_t builtin = 1;
res = initialize_A_B(builtin);
res = initialize_A_B(builtin, lean_io_mk_world());
if (lean_io_result_is_ok(res)) {
lean_dec_ref(res);
} else {
@@ -159,7 +160,7 @@ if (lean_io_result_is_ok(res)) {
lean_dec(res);
return ...; // do not access Lean declarations if initialization failed
}
res = initialize_C(builtin);
res = initialize_C(builtin, lean_io_mk_world());
if (lean_io_result_is_ok(res)) {
...

View File

@@ -94,8 +94,10 @@ theorem List.palindrome_of_eq_reverse (h : as.reverse = as) : Palindrome as := b
next => exact Palindrome.nil
next a => exact Palindrome.single a
next a b as ih =>
obtain rfl, h, - := by simpa using h
exact Palindrome.sandwich b (ih h)
have : a = b := by simp_all
subst this
have : as.reverse = as := by simp_all
exact Palindrome.sandwich a (ih this)
/-!
We now define a function that returns `true` iff `as` is a palindrome.

View File

@@ -15,8 +15,7 @@
],
"settings": {
// Open terminal at root, not current workspace folder
// (there is not way to directly refer to the root folder included as `.` above)
"terminal.integrated.cwd": "${workspaceFolder:src}/..",
"terminal.integrated.cwd": "${workspaceFolder:.}",
"files.insertFinalNewline": true,
"files.trimTrailingWhitespace": true,
"cmake.buildDirectory": "${workspaceFolder}/build/release",

View File

@@ -1,54 +0,0 @@
This release introduces the Lean module system, which allows files to
control the visibility of their contents for other files. In previous
releases, this feature was available as a preview when the option
`experimental.module` was set to `true`; it is now a fully supported
feature of Lean.
# Benefits
Because modules reduce the amount of information exposed to other
code, they speed up rebuilds because irrelevant changes can be
ignored, they make it possible to be deliberate about API evolution by
hiding details that may change from clients, they help proofs be
checked faster by avoiding accidentally unfolding definitions, and
they lead to smaller executable files through improved dead code
elimination.
# Visibility
A source file is a module if it begins with the `module` keyword. By
default, declarations in a module are private; the `public` modifier
exports them. Proofs of theorems and bodies of definitions are private
by default even when their signatures are public; the bodies of
definitions can be made public by adding the `@[expose]`
attribute. Theorems and opaque constants never expose their bodies.
`public section` and `@[expose] section` change the default visibility
of declarations in the section.
# Imports
Modules may only import other modules. By default, `import` adds the
public information of the imported module to the private scope of the
current module. Adding the `public` modifier to an import places the
imported modules's public information in the public scope of the
current module, exposing it in turn to the current module's clients.
Within a package, `import all` can be used to import another module's
private scope into the current module; this can be used to separate
lemmas or tests from definition modules without exposing details to
downstream clients.
# Meta Code
Code used in metaprograms must be marked `meta`. This ensures that the
code is compiled and available for execution when it is needed during
elaboration. Meta code may only reference other meta code. A whole
module can be made available in the meta phase using `meta import`;
this allows code to be shared across phases by importing the module in
each phase. Code that is reachable from public metaprograms must be
imported via `public meta import`, while local metaprograms can use
plain `meta import` for their dependencies.
The module system is described in detail in [the Lean language reference](https://lean-reference-manual-review.netlify.app/find/?domain=Verso.Genre.Manual.section&name=files).

View File

@@ -0,0 +1,132 @@
/-
Copyright (c) 2025 Amazon.com, Inc. or its affiliates. All Rights Reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean
namespace Lean.Meta.Grind.Analyzer
/-!
A simple E-matching annotation analyzer.
For each theorem annotated as an E-matching candidate, it creates an artificial goal, executes `grind` and shows the
number of instances created.
For a theorem of the form `params -> type`, the artificial goal is of the form `params -> type -> False`.
-/
/--
`grind` configuration for the analyzer. We disable case-splits and lookahead,
increase the number of generations, and limit the number of instances generated.
-/
def config : Grind.Config := {
splits := 0
lookahead := false
mbtc := false
ematch := 20
instances := 100
gen := 10
}
structure Config where
/-- Minimum number of instantiations to trigger summary report -/
min : Nat := 10
/-- Minimum number of instantiations to trigger detailed report -/
detailed : Nat := 50
def mkParams : MetaM Params := do
let params Grind.mkParams config
let ematch getEMatchTheorems
let casesTypes Grind.getCasesTypes
return { params with ematch, casesTypes }
/-- Returns the total number of generated instances. -/
private def sum (cs : PHashMap Origin Nat) : Nat := Id.run do
let mut r := 0
for (_, c) in cs do
r := r + c
return r
private def thmsToMessageData (thms : PHashMap Origin Nat) : MetaM MessageData := do
let data := thms.toArray.filterMap fun (origin, c) =>
match origin with
| .decl declName => some (declName, c)
| _ => none
let data := data.qsort fun (d₁, c₁) (d₂, c₂) => if c₁ == c₂ then Name.lt d₁ d₂ else c₁ > c₂
let data data.mapM fun (declName, counter) =>
return .trace { cls := `thm } m!"{.ofConst (← mkConstWithLevelParams declName)} ↦ {counter}" #[]
return .trace { cls := `thm } "instances" data
/--
Analyzes theorem `declName`. That is, creates the artificial goal based on `declName` type,
and invokes `grind` on it.
-/
def analyzeEMatchTheorem (declName : Name) (c : Config) : MetaM Unit := do
let info getConstInfo declName
let mvarId forallTelescope info.type fun _ type => do
withLocalDeclD `h type fun _ => do
return ( mkFreshExprMVar (mkConst ``False)).mvarId!
let result Grind.main mvarId ( mkParams) (pure ())
let thms := result.counters.thm
let s := sum thms
if s > c.min then
IO.println s!"{declName} : {s}"
if s > c.detailed then
logInfo m!"{declName}\n{← thmsToMessageData thms}"
-- Not sure why this is failing: `down_pure` perhaps has an unnecessary universe parameter?
run_meta analyzeEMatchTheorem ``Std.Do.SPred.down_pure {}
/-- Analyzes all theorems in the standard library marked as E-matching theorems. -/
def analyzeEMatchTheorems (c : Config := {}) : MetaM Unit := do
let origins := ( getEMatchTheorems).getOrigins
let decls := origins.filterMap fun | .decl declName => some declName | _ => none
for declName in decls.mergeSort Name.lt do
try
analyzeEMatchTheorem declName c
catch e =>
logError m!"{declName} failed with {e.toMessageData}"
logInfo m!"Finished analyzing {decls.length} theorems"
/-- Macro for analyzing E-match theorems with unlimited heartbeats -/
macro "#analyzeEMatchTheorems" : command => `(
set_option maxHeartbeats 0 in
run_meta analyzeEMatchTheorems
)
#analyzeEMatchTheorems
-- -- We can analyze specific theorems using commands such as
set_option trace.grind.ematch.instance true
-- 1. grind immediately sees `(#[] : Array α) = ([] : List α).toArray` but probably this should be hidden.
-- 2. `Vector.toArray_empty` keys on `Array.mk []` rather than `#v[].toArray`
-- I guess we could add `(#[].extract _ _).extract _ _` as a stop pattern.
run_meta analyzeEMatchTheorem ``Array.extract_empty {}
-- Neither `Option.bind_some` nor `Option.bind_fun_some` fire, because the terms appear inside
-- lambdas. So we get crazy things like:
-- `fun x => ((some x).bind some).bind fun x => (some x).bind fun x => (some x).bind some`
-- We could consider replacing `filterMap_some` with
-- `filterMap g (filterMap f xs) = filterMap (f >=> g) xs`
-- to avoid the lambda that `grind` struggles with, but this would require more API around the fish.
run_meta analyzeEMatchTheorem ``Array.filterMap_some {}
-- Not entirely certain what is wrong here, but certainly
-- `eq_empty_of_append_eq_empty` is firing too often.
-- Ideally we could instantiate this is we fine `xs ++ ys` in the same equivalence class,
-- note just as soon as we see `xs ++ ys`.
-- I've tried removing this in https://github.com/leanprover/lean4/pull/10162
run_meta analyzeEMatchTheorem ``Array.range'_succ {}
-- Perhaps the same story here.
run_meta analyzeEMatchTheorem ``Array.range_succ {}
-- `zip_map_left` and `zip_map_right` are bad grind lemmas,
-- checking if they can be removed in https://github.com/leanprover/lean4/pull/10163
run_meta analyzeEMatchTheorem ``Array.zip_map {}
-- It seems crazy to me that as soon as we have `0 >>> n = 0`, we instantiate based on the
-- pattern `0 >>> n >>> m` by substituting `0` into `0 >>> n` to produce the `0 >>> n >>> n`.
-- I don't think any forbidden subterms can help us here. I don't know what to do. :-(
run_meta analyzeEMatchTheorem ``Int.zero_shiftRight {}

View File

@@ -57,19 +57,19 @@ def main (args : List String) : IO Unit := do
sec := "\n\n" ++ sec
if insertPos?.isNone then
sec := sec ++ "\n\n"
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.rawEndPos
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.endPos
-- prepend each import with `public `
for imp in imps.reverse do
let insertPos := imp.raw.getPos?.get!
let prfx := if doMeta then "public meta " else "public "
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.rawEndPos
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.endPos
-- insert `module` header
let mut initText := text.extract 0 startPos
if !initText.trim.isEmpty then
-- If there is a header comment, preserve it and put `module` in the line after
initText := initText.trimRight ++ "\n"
text := initText ++ "module\n\n" ++ text.extract startPos text.rawEndPos
text := initText ++ "module\n\n" ++ text.extract startPos text.endPos
IO.FS.writeFile path text

View File

@@ -131,11 +131,10 @@ structure State where
`transDeps[i]` is the (non-reflexive) transitive closure of `mods[i].imports`. More specifically,
* `j ∈ transDeps[i].pub` if `i -(public import)->+ j`
* `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
* `j ∈ transDeps[i].priv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].pub/priv`
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(import ...)-> i'` and `j ∈ transDeps[i'].metaPub`
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].metaPub/metaPriv`
* `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
-/
transDeps : Array Needs := #[]
/--
@@ -163,10 +162,10 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
-- `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
transImps := transImps.union .priv {j} |>.union .priv (impTransImps.get .pub)
if imp.importAll then
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].pub/priv`
transImps := transImps.union .priv (impTransImps.get .pub impTransImps.get .priv)
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
transImps := transImps.union .priv (impTransImps.get .pub)
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import)->* j`
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
if imp.isExported then
transImps := transImps.union .metaPub (impTransImps.get .metaPub)
if imp.isMeta then
@@ -174,13 +173,10 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
if !imp.isExported then
if imp.isMeta then
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import)->* j`
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
transImps := transImps.union .metaPriv {j} |>.union .metaPriv (impTransImps.get .pub impTransImps.get .metaPub)
if imp.importAll then
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].metaPub/metaPriv`
transImps := transImps.union .metaPriv (impTransImps.get .metaPub impTransImps.get .metaPriv)
else
-- `j ∈ transDeps[i].metaPriv` if `i -(import ...)-> i'` and `j ∈ transDeps[i'].metaPub`
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
transImps := transImps.union .metaPriv (impTransImps.get .metaPub)
transImps
@@ -189,8 +185,7 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
def calcNeeds (env : Environment) (i : ModuleIdx) : Needs := Id.run do
let mut needs := default
for ci in env.header.moduleData[i]!.constants do
-- Added guard for cases like `structure` that are still exported even if private
let pubCI? := guard (!isPrivateName ci.name) *> (env.setExporting true).find? ci.name
let pubCI? := env.setExporting true |>.find? ci.name
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
needs := visitExpr k ci.type needs
if let some e := ci.value? (allowOpaque := true) then
@@ -221,8 +216,7 @@ def getExplanations (env : Environment) (i : ModuleIdx) :
Std.HashMap (ModuleIdx × NeedsKind) (Option (Name × Name)) := Id.run do
let mut deps := default
for ci in env.header.moduleData[i]!.constants do
-- Added guard for cases like `structure` that are still exported even if private
let pubCI? := guard (!isPrivateName ci.name) *> (env.setExporting true).find? ci.name
let pubCI? := env.setExporting true |>.find? ci.name
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
deps := visitExpr k ci.name ci.type deps
if let some e := ci.value? (allowOpaque := true) then
@@ -292,7 +286,7 @@ and `endPos` is the position of the end of the header.
-/
def parseHeaderFromString (text path : String) :
IO (System.FilePath × Parser.InputContext ×
TSyntax ``Parser.Module.header × String.Pos.Raw) := do
TSyntaxArray ``Parser.Module.import × String.Pos) := do
let inputCtx := Parser.mkInputContext text path
let (header, parserState, msgs) Parser.parseHeader inputCtx
if !msgs.toList.isEmpty then -- skip this file if there are parse errors
@@ -300,8 +294,8 @@ def parseHeaderFromString (text path : String) :
throw <| .userError "parse errors in file"
-- the insertion point for `add` is the first newline after the imports
let insertion := header.raw.getTailPos?.getD parserState.pos
let insertion := text.findAux (· == '\n') text.rawEndPos insertion + '\n'
pure (path, inputCtx, header, insertion)
let insertion := text.findAux (· == '\n') text.endPos insertion + 1
pure (path, inputCtx, .mk header.raw[2].getArgs, insertion)
/-- Parse a source file to extract the location of the import lines, for edits and error messages.
@@ -310,18 +304,13 @@ and `endPos` is the position of the end of the header.
-/
def parseHeader (srcSearchPath : SearchPath) (mod : Name) :
IO (System.FilePath × Parser.InputContext ×
TSyntax ``Parser.Module.header × String.Pos.Raw) := do
TSyntaxArray ``Parser.Module.import × String.Pos) := do
-- Parse the input file
let some path srcSearchPath.findModuleWithExt "lean" mod
| throw <| .userError s!"error: failed to find source file for {mod}"
let text IO.FS.readFile path
parseHeaderFromString text path.toString
def decodeHeader : TSyntax ``Parser.Module.header Option (TSyntax `module) × Option (TSyntax `prelude) × TSyntaxArray ``Parser.Module.import
| `(Parser.Module.header| $[module%$moduleTk?]? $[prelude%$preludeTk?]? $imports*) =>
(moduleTk?.map .mk, preludeTk?.map .mk, imports)
| _ => unreachable!
def decodeImport : TSyntax ``Parser.Module.import Import
| `(Parser.Module.import| $[public%$pubTk?]? $[meta%$metaTk?]? import $[all%$allTk?]? $id) =>
{ module := id.getId, isExported := pubTk?.isSome, isMeta := metaTk?.isSome, importAll := allTk?.isSome }
@@ -337,20 +326,11 @@ def decodeImport : TSyntax ``Parser.Module.import → Import
* `addOnly`: if true, only add missing imports, do not remove unused ones
-/
def visitModule (srcSearchPath : SearchPath)
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits) (headerStx : TSyntax ``Parser.Module.header)
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits)
(addOnly := false) (githubStyle := false) (explain := false) : StateT State IO Edits := do
let s get
-- Do transitive reduction of `needs` in `deps`.
let mut deps := needs
let (_, prelude?, imports) := decodeHeader headerStx
if prelude?.isNone then
deps := deps.union .pub {s.env.getModuleIdx? `Init |>.get!}
for imp in imports do
if addOnly || imp.raw.getTrailing?.any (·.toString.toSlice.contains "shake: keep") then
let imp := decodeImport imp
let j := s.env.getModuleIdx? imp.module |>.get!
let k := NeedsKind.ofImport imp
deps := deps.union k {j}
for j in [0:s.mods.size] do
let transDeps := s.transDeps[j]!
for k in NeedsKind.all do
@@ -374,8 +354,7 @@ def visitModule (srcSearchPath : SearchPath)
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
else
let k := NeedsKind.ofImport imp
-- A private import should also be removed if the public version is needed
if !deps.has k j || !k.isExported && deps.has { k with isExported := true } j then
if !addOnly && !deps.has k j && !deps.has { k with isExported := false } j then
toRemove := toRemove.push imp
else
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
@@ -406,8 +385,7 @@ def visitModule (srcSearchPath : SearchPath)
if githubStyle then
try
let (path, inputCtx, stx, endHeader) parseHeader srcSearchPath s.modNames[i]!
let (_, _, imports) := decodeHeader stx
let (path, inputCtx, imports, endHeader) parseHeader srcSearchPath s.modNames[i]!
for stx in imports do
if toRemove.any fun imp => imp == decodeImport stx then
let pos := inputCtx.fileMap.toPosition stx.raw.getPos?.get!
@@ -551,61 +529,51 @@ def main (args : List String) : IO UInt32 := do
let needs := s.mods.mapIdx fun i _ =>
Task.spawn fun _ => calcNeeds s.env i
-- Parse headers in parallel
let headers s.mods.mapIdxM fun i _ =>
BaseIO.asTask (parseHeader srcSearchPath s.modNames[i]! |>.toBaseIO)
if args.fix then
println! "The following changes will be made automatically:"
-- Check all selected modules
let mut edits : Edits :=
let mut revNeeds : Needs := default
for i in [0:s.mods.size], t in needs, header in headers do
match header.get with
| .ok (_, _, stx, _) =>
edits visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!)
srcSearchPath i t.get revNeeds edits stx args.githubStyle args.explain
if isExtraRevModUse s.env i then
revNeeds := revNeeds.union .priv {i}
| .error e =>
println! e.toString
for i in [0:s.mods.size], t in needs do
edits visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!) srcSearchPath i t.get revNeeds edits args.githubStyle args.explain
if isExtraRevModUse s.env i then
revNeeds := revNeeds.union .priv {i}
if !args.fix then
-- return error if any issues were found
return if edits.isEmpty then 0 else 1
-- Apply the edits to existing files
let mut count := 0
for mod in s.modNames, header? in headers do
let some (remove, add) := edits[mod]? | continue
let count edits.foldM (init := 0) fun count mod (remove, add) => do
let add : Array Import := add.qsortOrd
-- Parse the input file
let .ok (path, inputCtx, stx, insertion) := header?.get | continue
let (_, _, imports) := decodeHeader stx
let (path, inputCtx, imports, insertion)
try parseHeader srcSearchPath mod
catch e => println! e.toString; return count
let text := inputCtx.fileMap.source
-- Calculate the edit result
let mut pos : String.Pos.Raw := 0
let mut pos : String.Pos := 0
let mut out : String := ""
let mut seen : Std.HashSet Import := {}
for stx in imports do
let mod := decodeImport stx
if remove.contains mod || seen.contains mod then
out := out ++ String.Pos.Raw.extract text pos stx.raw.getPos?.get!
out := out ++ text.extract pos stx.raw.getPos?.get!
-- We use the end position of the syntax, but include whitespace up to the first newline
pos := text.findAux (· == '\n') text.rawEndPos stx.raw.getTailPos?.get! + '\n'
pos := text.findAux (· == '\n') text.endPos stx.raw.getTailPos?.get! + 1
seen := seen.insert mod
out := out ++ String.Pos.Raw.extract text pos insertion
out := out ++ text.extract pos insertion
for mod in add do
if !seen.contains mod then
seen := seen.insert mod
out := out ++ s!"{mod}\n"
out := out ++ String.Pos.Raw.extract text insertion text.rawEndPos
out := out ++ text.extract insertion text.endPos
IO.FS.writeFile path out
count := count + 1
return count + 1
-- Since we throw an error upon encountering issues, we can be sure that everything worked
-- if we reach this point of the script.

View File

@@ -60,7 +60,7 @@ if (arity == fixed + {n}) \{
for j in [n:max + 1] do
let fs := mkFsArgs (j - n)
let sep := if j = n then "" else ", "
emit s!" case {j}: \{ obj* r = FN{j}(f)({fs}{sep}{args}); lean_free_object(f); return r; }\n"
emit s!" case {j}: \{ obj* r = FN{j}(f)({fs}{sep}{args}); lean_free_small_object(f); return r; }\n"
emit " }
}
switch (arity) {\n"
@@ -162,7 +162,7 @@ static obj* fix_args(obj* f, unsigned n, obj*const* as) {
for (unsigned i = 0; i < fixed; i++, source++, target++) {
*target = *source;
}
lean_free_object(f);
lean_free_small_object(f);
}
for (unsigned i = 0; i < n; i++, as++, target++) {
*target = *as;

96
script/bench.sh Executable file
View File

@@ -0,0 +1,96 @@
#!/usr/bin/env bash
set -euxo pipefail
cmake --preset release 1>&2
# We benchmark against stage2/bin to test new optimizations.
timeout -s KILL 1h time make -C build/release -j$(nproc) stage3 1>&2
export PATH=$PWD/build/release/stage2/bin:$PATH
# The extra opts used to be passed to the Makefile during benchmarking only but with Lake it is
# easier to configure them statically.
cmake -B build/release/stage3 -S src -DLEAN_EXTRA_LAKEFILE_TOML='weakLeanArgs=["-Dprofiler=true", "-Dprofiler.threshold=9999999", "--stats"]' 1>&2
(
cd tests/bench
timeout -s KILL 1h time temci exec --config speedcenter.yaml --in speedcenter.exec.velcom.yaml 1>&2
temci report run_output.yaml --reporter codespeed2
)
if [ -d .git ]; then
DIR="$(git rev-parse @)"
BASE_URL="https://speed.lean-lang.org/lean4-out/$DIR"
{
cat <<'EOF'
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>Lakeprof Report</title>
</head>
<h1>Lakeprof Report</h1>
<button type="button" id="btn_fetch">View build trace in Perfetto</button>
<script type="text/javascript">
const ORIGIN = 'https://ui.perfetto.dev';
const btnFetch = document.getElementById('btn_fetch');
async function fetchAndOpen(traceUrl) {
const resp = await fetch(traceUrl);
// Error checking is left as an exercise to the reader.
const blob = await resp.blob();
const arrayBuffer = await blob.arrayBuffer();
openTrace(arrayBuffer, traceUrl);
}
function openTrace(arrayBuffer, traceUrl) {
const win = window.open(ORIGIN);
if (!win) {
btnFetch.style.background = '#f3ca63';
btnFetch.onclick = () => openTrace(arrayBuffer);
btnFetch.innerText = 'Popups blocked, click here to open the trace file';
return;
}
const timer = setInterval(() => win.postMessage('PING', ORIGIN), 50);
const onMessageHandler = (evt) => {
if (evt.data !== 'PONG') return;
// We got a PONG, the UI is ready.
window.clearInterval(timer);
window.removeEventListener('message', onMessageHandler);
const reopenUrl = new URL(location.href);
reopenUrl.hash = `#reopen=${traceUrl}`;
win.postMessage({
perfetto: {
buffer: arrayBuffer,
title: 'Lake Build Trace',
url: reopenUrl.toString(),
}}, ORIGIN);
};
window.addEventListener('message', onMessageHandler);
}
// This is triggered when following the link from the Perfetto UI's sidebar.
if (location.hash.startsWith('#reopen=')) {
const traceUrl = location.hash.substr(8);
fetchAndOpen(traceUrl);
}
EOF
cat <<EOF
btnFetch.onclick = () => fetchAndOpen("$BASE_URL/lakeprof.trace_event");
</script>
EOF
echo "<pre><code>"
(cd src; lakeprof report -prc)
echo "</code></pre>"
echo "</body></html>"
} | tee index.html
curl -T index.html $BASE_URL/index.html
curl -T src/lakeprof.log $BASE_URL/lakeprof.log
curl -T src/lakeprof.trace_event $BASE_URL/lakeprof.trace_event
fi

View File

@@ -10,16 +10,6 @@ Tests language server memory use by repeatedly re-elaborate a given file.
NOTE: only works on Linux for now.
-/
def determineRSS (pid : UInt32) : IO Nat := do
let status IO.FS.readFile s!"/proc/{pid}/smaps_rollup"
let some rssLine := status.splitOn "\n" |>.find? (·.startsWith "Rss:")
| throw <| IO.userError "No RSS in proc status"
let rssLine := rssLine.dropPrefix "Rss:"
let rssLine := rssLine.dropWhile Char.isWhitespace
let some rssInKB := rssLine.takeWhile Char.isDigit |>.toNat?
| throw <| IO.userError "Cannot parse RSS"
return rssInKB
def main (args : List String) : IO Unit := do
let leanCmd :: file :: iters :: args := args | panic! "usage: script <lean> <file> <#iterations> <server-args>..."
let file IO.FS.realPath file
@@ -44,14 +34,11 @@ def main (args : List String) : IO Unit := do
let text IO.FS.readFile file
let (_, headerEndPos, _) Elab.parseImports text
let headerEndPos := FileMap.ofString text |>.leanPosToLspPos headerEndPos
let n := iters.toNat!
let mut lastRSS? : Option Nat := none
let mut totalRSSDelta : Int := 0
let mut requestNo : Nat := 1
let mut versionNo : Nat := 1
Ipc.writeNotification "textDocument/didOpen", {
textDocument := { uri := uri, languageId := "lean", version := 1, text := text } : DidOpenTextDocumentParams }
for i in [0:n] do
for i in [0:iters.toNat!] do
if i > 0 then
versionNo := versionNo + 1
let params : DidChangeTextDocumentParams := {
@@ -74,16 +61,9 @@ def main (args : List String) : IO Unit := do
IO.eprintln diag.message
requestNo := requestNo + 1
let rss determineRSS ( read).pid
-- The first `didChange` usually results in a significantly higher RSS increase than
-- the others, so we ignore it.
if i > 1 then
if let some lastRSS := lastRSS? then
totalRSSDelta := totalRSSDelta + ((rss : Int) - (lastRSS : Int))
lastRSS? := some rss
let avgRSSDelta := totalRSSDelta / (n - 2)
IO.println s!"avg-reelab-rss-delta: {avgRSSDelta}"
let status IO.FS.readFile s!"/proc/{(← read).pid}/status"
for line in status.splitOn "\n" |>.filter (·.startsWith "RssAnon") do
IO.eprintln line
let _ Ipc.collectDiagnostics requestNo uri versionNo
( Ipc.stdin).writeLspMessage (Message.notification "exit" none)

View File

@@ -1,89 +0,0 @@
import Lean.Data.Lsp
import Lean.Elab.Import
open Lean
open Lean.Lsp
open Lean.JsonRpc
/-!
Tests watchdog memory use by repeatedly re-elaborate a given file.
NOTE: only works on Linux for now.
-/
def determineRSS (pid : UInt32) : IO Nat := do
let status IO.FS.readFile s!"/proc/{pid}/smaps_rollup"
let some rssLine := status.splitOn "\n" |>.find? (·.startsWith "Rss:")
| throw <| IO.userError "No RSS in proc status"
let rssLine := rssLine.dropPrefix "Rss:"
let rssLine := rssLine.dropWhile Char.isWhitespace
let some rssInKB := rssLine.takeWhile Char.isDigit |>.toNat?
| throw <| IO.userError "Cannot parse RSS"
return rssInKB
def main (args : List String) : IO Unit := do
let leanCmd :: file :: iters :: args := args | panic! "usage: script <lean> <file> <#iterations> <server-args>..."
let file IO.FS.realPath file
let uri := s!"file://{file}"
Ipc.runWith leanCmd (#["--server", "-DstderrAsMessages=false"] ++ args ++ #[uri]) do
let capabilities := {
textDocument? := some {
completion? := some {
completionItem? := some {
insertReplaceSupport? := true
}
}
}
}
Ipc.writeRequest 0, "initialize", { capabilities : InitializeParams }
discard <| Ipc.readResponseAs 0 InitializeResult
Ipc.writeNotification "initialized", InitializedParams.mk
let text IO.FS.readFile file
let (_, headerEndPos, _) Elab.parseImports text
let headerEndPos := FileMap.ofString text |>.leanPosToLspPos headerEndPos
let n := iters.toNat!
let mut lastRSS? : Option Nat := none
let mut totalRSSDelta : Int := 0
let mut requestNo : Nat := 1
let mut versionNo : Nat := 1
Ipc.writeNotification "textDocument/didOpen", {
textDocument := { uri := uri, languageId := "lean", version := 1, text := text } : DidOpenTextDocumentParams }
for i in [0:iters.toNat!] do
if i > 0 then
versionNo := versionNo + 1
let params : DidChangeTextDocumentParams := {
textDocument := {
uri := uri
version? := versionNo
}
contentChanges := #[TextDocumentContentChangeEvent.rangeChange {
start := headerEndPos
«end» := headerEndPos
} " "]
}
let params := toJson params
Ipc.writeNotification "textDocument/didChange", params
requestNo := requestNo + 1
let diags Ipc.collectDiagnostics requestNo uri versionNo
if let some diags := diags then
for diag in diags.param.diagnostics do
IO.eprintln diag.message
requestNo := requestNo + 1
Ipc.waitForILeans requestNo uri versionNo
let rss determineRSS ( read).pid
-- The first `didChange` usually results in a significantly higher RSS increase than
-- the others, so we ignore it.
if i > 1 then
if let some lastRSS := lastRSS? then
totalRSSDelta := totalRSSDelta + ((rss : Int) - (lastRSS : Int))
lastRSS? := some rss
let avgRSSDelta := totalRSSDelta / (n - 2)
IO.println s!"avg-reelab-rss-delta: {avgRSSDelta}"
let _ Ipc.collectDiagnostics requestNo uri versionNo
Ipc.shutdown requestNo
discard <| Ipc.waitForExit

View File

@@ -58,11 +58,7 @@ OPTIONS=()
# We build cadical using the custom toolchain on Linux to avoid glibc versioning issues
echo -n " -DLEAN_STANDALONE=ON -DCADICAL_USE_CUSTOM_CXX=ON"
echo -n " -DCMAKE_CXX_COMPILER=$PWD/llvm-host/bin/clang++ -DLEAN_CXX_STDLIB='-Wl,-Bstatic -lc++ -lc++abi -Wl,-Bdynamic'"
# these should also be used for cadical, so do not use `LEAN_EXTRA_CXX_FLAGS` here
echo -n " -DCMAKE_CXX_FLAGS='--sysroot $PWD/llvm -idirafter $GLIBC_DEV/include ${EXTRA_FLAGS:-}'"
# the above does not include linker flags which will be added below based on context, so skip the
# generic check by cmake
echo -n " -DCMAKE_C_COMPILER_WORKS=1 -DCMAKE_CXX_COMPILER_WORKS=1"
echo -n " -DLEAN_EXTRA_CXX_FLAGS='--sysroot $PWD/llvm -idirafter $GLIBC_DEV/include ${EXTRA_FLAGS:-}'"
# use target compiler directly when not cross-compiling
if [[ -L llvm-host ]]; then
echo -n " -DCMAKE_C_COMPILER=$PWD/stage1/bin/clang"

View File

@@ -13,15 +13,8 @@ What this script does:
- Checks that the release branch (releases/vX.Y.0) exists
- Verifies CMake version settings are correct
- Confirms the release tag exists
- Validates the release page exists on GitHub (created automatically by CI after tag push)
- Checks the release notes page on lean-lang.org (updated while bumping the `reference-manual` repository)
**IMPORTANT: If the release page doesn't exist, the script will skip checking
downstream repositories and the master branch configuration. The preliminary
infrastructure must be in place before the release process can proceed.**
**NOTE: The GitHub release page is created AUTOMATICALLY by CI after the tag is pushed.
DO NOT create it manually. Wait for CI to complete after pushing the tag.**
- Validates the release page exists on GitHub
- Checks the release notes page on lean-lang.org
2. For each downstream repository (batteries, mathlib4, etc.):
- Checks if dependencies are ready (e.g., mathlib4 depends on batteries)
@@ -31,8 +24,6 @@ What this script does:
- Ensures tags are merged into stable branches (for non-RC releases)
- Verifies bump branches exist and are configured correctly
- Special handling for ProofWidgets4 release tags
- For mathlib4: runs verify_version_tags.py to validate the release tag
(checks git/GitHub consistency, toolchain, elan, cache, and build)
3. Optionally automates missing steps (when not in --dry-run mode):
- Creates missing release tags using push_repo_release_tag.py
@@ -131,39 +122,6 @@ def release_page_exists(repo_url, tag_name, github_token):
response = requests.get(api_url, headers=headers)
return response.status_code == 200
def get_tag_workflow_status(repo_url, tag_name, github_token):
"""Get the status of CI workflows running for a specific tag."""
api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
headers = {'Authorization': f'token {github_token}'} if github_token else {}
# Get workflow runs for the tag
# GitHub's workflow runs API uses the branch/tag name in the 'head_branch' field
api_url = f"{api_base}/actions/runs?event=push&head_branch={tag_name}"
response = requests.get(api_url, headers=headers)
if response.status_code != 200:
return None
data = response.json()
workflow_runs = data.get('workflow_runs', [])
if not workflow_runs:
return None
# Get the most recent workflow run for this tag
run = workflow_runs[0]
status = run.get('status')
conclusion = run.get('conclusion')
workflow_name = run.get('name', 'CI')
run_id = run.get('id')
return {
'status': status,
'conclusion': conclusion,
'workflow_name': workflow_name,
'run_id': run_id
}
def get_release_notes(tag_name):
"""Fetch release notes page title from lean-lang.org."""
# Strip -rcX suffix if present for the URL
@@ -172,17 +130,20 @@ def get_release_notes(tag_name):
try:
response = requests.get(reference_url)
response.raise_for_status() # Raise HTTPError for bad responses (4xx or 5xx)
# Extract title using regex
match = re.search(r"<title>(.*?)</title>", response.text, re.IGNORECASE | re.DOTALL)
if match:
return match.group(1).strip()
else:
print(f" ⚠️ Could not find <title> tag in {reference_url}")
return None
except requests.exceptions.RequestException:
except requests.exceptions.RequestException as e:
print(f" ❌ Error fetching release notes from {reference_url}: {e}")
return None
except Exception:
except Exception as e:
print(f" ❌ An unexpected error occurred while processing release notes: {e}")
return None
def get_branch_content(repo_url, branch, file_path, github_token):
@@ -501,57 +462,6 @@ def check_proofwidgets4_release(repo_url, target_toolchain, github_token):
print(f" You will need to create and push a tag v0.0.{next_version}")
return False
def run_mathlib_verify_version_tags(toolchain, verbose=False):
"""Run mathlib4's verify_version_tags.py script to validate the release tag.
This clones mathlib4 to a temp directory and runs the verification script.
Returns True if verification passes, False otherwise.
"""
import tempfile
print(f" ... Running mathlib4 verify_version_tags.py {toolchain}")
with tempfile.TemporaryDirectory() as tmpdir:
# Clone mathlib4 (shallow clone is sufficient for running the script)
clone_result = subprocess.run(
['git', 'clone', '--depth', '1', 'https://github.com/leanprover-community/mathlib4.git', tmpdir],
capture_output=True,
text=True
)
if clone_result.returncode != 0:
print(f" ❌ Failed to clone mathlib4: {clone_result.stderr.strip()[:200]}")
return False
# Run the verification script
script_path = os.path.join(tmpdir, 'scripts', 'verify_version_tags.py')
if not os.path.exists(script_path):
print(f" ❌ verify_version_tags.py not found in mathlib4 (expected at scripts/verify_version_tags.py)")
return False
# Run from the mathlib4 directory so git operations work
result = subprocess.run(
['python3', script_path, toolchain],
cwd=tmpdir,
capture_output=True,
text=True,
timeout=900 # 15 minutes timeout for cache download etc.
)
# Print output with indentation
if result.stdout:
for line in result.stdout.strip().split('\n'):
print(f" {line}")
if result.stderr:
for line in result.stderr.strip().split('\n'):
print(f" {line}")
if result.returncode != 0:
print(f" ❌ mathlib4 verify_version_tags.py failed")
return False
print(f" ✅ mathlib4 verify_version_tags.py passed")
return True
def main():
parser = argparse.ArgumentParser(description="Check release status of Lean4 repositories")
parser.add_argument("toolchain", help="The toolchain version to check (e.g., v4.6.0)")
@@ -602,57 +512,30 @@ def main():
print(f" ❌ Short commit hash {commit_hash[:SHORT_HASH_LENGTH]} is numeric and starts with 0, causing issues for version parsing. Try regenerating the last commit to get a new hash.")
lean4_success = False
release_page_ready = release_page_exists(lean_repo_url, toolchain, github_token)
if not release_page_ready:
print(f" ❌ Release page for {toolchain} does not exist (This will be created by CI.)")
# Check CI workflow status
workflow_status = get_tag_workflow_status(lean_repo_url, toolchain, github_token)
if workflow_status:
status = workflow_status['status']
conclusion = workflow_status['conclusion']
workflow_name = workflow_status['workflow_name']
run_id = workflow_status['run_id']
workflow_url = f"{lean_repo_url}/actions/runs/{run_id}"
if status == 'in_progress' or status == 'queued':
print(f" 🔄 {workflow_name} workflow is {status}: {workflow_url}")
elif status == 'completed':
if conclusion == 'success':
print(f"{workflow_name} workflow completed successfully: {workflow_url}")
elif conclusion == 'failure':
print(f"{workflow_name} workflow failed: {workflow_url}")
else:
print(f" ⚠️ {workflow_name} workflow completed with status: {conclusion}: {workflow_url}")
else:
print(f" {workflow_name} workflow status: {status}: {workflow_url}")
if not release_page_exists(lean_repo_url, toolchain, github_token):
print(f" ❌ Release page for {toolchain} does not exist")
lean4_success = False
else:
print(f" ✅ Release page for {toolchain} exists")
# Check the actual release notes page title (informational only - does not block)
# Check the actual release notes page title
actual_title = get_release_notes(toolchain)
expected_title_prefix = f"Lean {toolchain.lstrip('v')}" # e.g., "Lean 4.19.0" or "Lean 4.19.0-rc1"
base_tag = toolchain.split('-')[0]
release_notes_url = f"https://lean-lang.org/doc/reference/latest/releases/{base_tag}/"
if actual_title is None:
print(f" ⚠️ Release notes not found at {release_notes_url} (this will be fixed while updating the reference-manual repository)")
# Error already printed by get_release_notes
lean4_success = False
elif not actual_title.startswith(expected_title_prefix):
print(f" ⚠️ Release notes page title mismatch. Expected prefix '{expected_title_prefix}', got '{actual_title}'. Check {release_notes_url}")
# Construct URL for the error message (using the base tag)
base_tag = toolchain.split('-')[0]
check_url = f"https://lean-lang.org/doc/reference/latest/releases/{base_tag}/"
print(f" ❌ Release notes page title mismatch. Expected prefix '{expected_title_prefix}', got '{actual_title}'. Check {check_url}")
lean4_success = False
else:
print(f" ✅ Release notes page title looks good ('{actual_title}').")
repo_status["lean4"] = lean4_success
# If the release page doesn't exist, skip repository checks and master branch checks
# The preliminary infrastructure must be in place first
if not release_page_exists(lean_repo_url, toolchain, github_token):
print("\n⚠️ Release process blocked: preliminary Lean4 infrastructure incomplete.")
print(" Complete the steps above, then rerun this script to proceed with downstream repositories.")
return
# Load repositories and perform further checks
print("\nChecking repositories...")
@@ -816,12 +699,6 @@ def main():
repo_status[name] = False
continue
# For mathlib4, run verify_version_tags.py to validate the release tag
if name == "mathlib4":
if not run_mathlib_verify_version_tags(toolchain, verbose):
repo_status[name] = False
continue
repo_status[name] = success
# Final check for lean4 master branch

View File

@@ -589,19 +589,8 @@ def execute_release_steps(repo, version, config):
# Clean lake cache for a fresh build
print(blue("Cleaning lake cache..."))
run_command("lake clean", cwd=repo_path)
# Check if downstream of Mathlib and get cache if so
mathlib_package_dir = repo_path / ".lake" / "packages" / "mathlib"
if mathlib_package_dir.exists():
print(blue("Project is downstream of Mathlib, fetching cache..."))
try:
run_command("lake exe cache get", cwd=repo_path, stream_output=True)
print(green("Cache fetched successfully"))
except subprocess.CalledProcessError as e:
print(yellow("Failed to fetch cache, continuing anyway..."))
print(yellow(f"Cache fetch error: {e}"))
run_command("rm -rf .lake", cwd=repo_path)
try:
run_command("lake build", cwd=repo_path, stream_output=True)
print(green("Build completed successfully"))

View File

@@ -10,7 +10,7 @@ endif()
include(ExternalProject)
project(LEAN CXX C)
set(LEAN_VERSION_MAJOR 4)
set(LEAN_VERSION_MINOR 27)
set(LEAN_VERSION_MINOR 25)
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'")
@@ -42,7 +42,7 @@ if(LLD_PATH)
endif()
set(LEAN_EXTRA_LINKER_FLAGS ${LEAN_EXTRA_LINKER_FLAGS_DEFAULT} CACHE STRING "Additional flags used by the linker")
set(LEAN_EXTRA_CXX_FLAGS "" CACHE STRING "Additional flags used by the C++ compiler. Unlike `CMAKE_CXX_FLAGS`, these will not be used to build e.g. cadical.")
set(LEAN_EXTRA_CXX_FLAGS "" CACHE STRING "Additional flags used by the C++ compiler")
set(LEAN_TEST_VARS "LEAN_CC=${CMAKE_C_COMPILER}" CACHE STRING "Additional environment variables used when running tests")
if (NOT CMAKE_BUILD_TYPE)
@@ -191,7 +191,7 @@ endif()
set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${CMAKE_SOURCE_DIR}/cmake/Modules")
# Initialize CXXFLAGS.
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${LEAN_EXTRA_CXX_FLAGS} -DLEAN_BUILD_TYPE=\"${CMAKE_BUILD_TYPE}\" -DLEAN_EXPORTING")
set(CMAKE_CXX_FLAGS "${LEAN_EXTRA_CXX_FLAGS} -DLEAN_BUILD_TYPE=\"${CMAKE_BUILD_TYPE}\" -DLEAN_EXPORTING")
set(CMAKE_CXX_FLAGS_DEBUG "-DLEAN_DEBUG")
set(CMAKE_CXX_FLAGS_MINSIZEREL "-DNDEBUG")
set(CMAKE_CXX_FLAGS_RELEASE "-DNDEBUG")

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@@ -14,6 +14,7 @@ public import Init.ByCases
public import Init.RCases
public import Init.Core
public import Init.Control
public import Init.Data.Basic
public import Init.WF
public import Init.WFTactics
public import Init.Data

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@@ -7,6 +7,7 @@ Authors: Joachim Breitner
module
prelude
public import Init.Prelude
public import Init.Tactics
public section

View File

@@ -44,10 +44,3 @@ theorem apply_ite (f : α → β) (P : Prop) [Decidable P] (x y : α) :
/-- A `dite` whose results do not actually depend on the condition may be reduced to an `ite`. -/
@[simp] theorem dite_eq_ite [Decidable P] :
(dite P (fun _ => a) (fun _ => b)) = ite P a b := rfl
-- Remark: dite and ite are "defally equal" when we ignore the proofs.
@[deprecated dite_eq_ite (since := "2025-10-29")]
theorem dif_eq_if (c : Prop) {h : Decidable c} {α : Sort u} (t : α) (e : α) : dite c (fun _ => t) (fun _ => e) = ite c t e :=
match h with
| isTrue _ => rfl
| isFalse _ => rfl

View File

@@ -181,6 +181,9 @@ theorem not_imp_iff_and_not : ¬(a → b) ↔ a ∧ ¬b := Decidable.not_imp_iff
theorem not_and_iff_not_or_not : ¬(a b) ¬a ¬b := Decidable.not_and_iff_not_or_not
@[deprecated not_and_iff_not_or_not (since := "2025-03-18")]
abbrev not_and_iff_or_not_not := @not_and_iff_not_or_not
theorem not_iff : ¬(a b) (¬a b) := Decidable.not_iff
@[simp] theorem imp_iff_left_iff : (b a b) a b := Decidable.imp_iff_left_iff
@@ -205,5 +208,3 @@ export Classical (imp_iff_right_iff imp_and_neg_imp_iff and_or_imp not_imp)
/-- Show that an element extracted from `P : ∃ a, p a` using `P.choose` satisfies `p`. -/
theorem Exists.choose_spec {p : α Prop} (P : a, p a) : p P.choose := Classical.choose_spec P
grind_pattern Exists.choose_spec => P.choose

View File

@@ -25,7 +25,7 @@ instances are provided for the same type.
instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α where
forIn x b f := forIn' x b fun a _ => f a
@[simp] theorem forIn'_eq_forIn [d : Membership α ρ] [ForIn' m ρ α d] {β} (x : ρ) (b : β)
@[simp] theorem forIn'_eq_forIn [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m] (x : ρ) (b : β)
(f : (a : α) a x β m (ForInStep β)) (g : (a : α) β m (ForInStep β))
(h : a m b, f a m b = g a b) :
forIn' x b f = forIn x b g := by
@@ -40,11 +40,14 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
simp [h]
rfl
@[wf_preprocess] theorem forIn_eq_forIn' [d : Membership α ρ] [ForIn' m ρ α d] {β}
@[wf_preprocess] theorem forIn_eq_forIn' [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m]
(x : ρ) (b : β) (f : (a : α) β m (ForInStep β)) :
forIn x b f = forIn' x b (fun x h => binderNameHint x f <| binderNameHint h () <| f x) := by
rfl
@[deprecated forIn_eq_forIn' (since := "2025-04-04")]
abbrev forIn_eq_forin' := @forIn_eq_forIn'
/--
Extracts the value from a `ForInStep`, ignoring whether it is `ForInStep.done` or `ForInStep.yield`.
-/
@@ -403,7 +406,7 @@ class ForM (m : Type u → Type v) (γ : Type w₁) (α : outParam (Type w₂))
/--
Runs the monadic action `f` on each element of the collection `coll`.
-/
forM (coll : γ) (f : α m PUnit) : m PUnit
forM [Monad m] (coll : γ) (f : α m PUnit) : m PUnit
export ForM (forM)

View File

@@ -6,6 +6,8 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Control.State
public import Init.Control.Except
public import Init.Data.ToString.Basic
public section

View File

@@ -10,6 +10,7 @@ module
prelude
public import Init.Control.Basic
public import Init.Control.Id
public import Init.Coe
@[expose] public section
@@ -148,23 +149,6 @@ This is the inverse of `ExceptT.mk`.
@[always_inline, inline, expose]
def ExceptT.run {ε : Type u} {m : Type u Type v} {α : Type u} (x : ExceptT ε m α) : m (Except ε α) := x
/--
Use a monadic action that may throw an exception by providing explicit success and failure
continuations.
-/
@[always_inline, inline, expose]
def ExceptT.runK [Monad m] (x : ExceptT ε m α) (ok : α m β) (error : ε m β) : m β :=
x.run >>= (·.casesOn error ok)
/--
Returns the value of a computation, forgetting whether it was an exception or a success.
This corresponds to early return.
-/
@[always_inline, inline, expose]
def ExceptT.runCatch [Monad m] (x : ExceptT α m α) : m α :=
x.runK pure pure
namespace ExceptT
variable {ε : Type u} {m : Type u Type v} [Monad m]

View File

@@ -7,6 +7,8 @@ module
prelude
public import Init.Ext
public import Init.SimpLemmas
public import Init.Meta
public section
@@ -170,7 +172,6 @@ theorem bind_pure_unit [Monad m] [LawfulMonad m] {x : m PUnit} : (x >>= fun _ =>
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]
@[deprecated seq_eq_bind_map (since := "2025-10-26")]
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 <$> x := by
rw [bind_map]
@@ -256,4 +257,20 @@ instance : LawfulMonad Id := by
@[simp] theorem run_seqLeft (x y : Id α) : (x <* y).run = x.run := rfl
@[simp] theorem run_seq (f : Id (α β)) (x : Id α) : (f <*> x).run = f.run x.run := rfl
-- These lemmas are bad as they abuse the defeq of `Id α` and `α`
@[deprecated run_map (since := "2025-03-05")] theorem map_eq (x : Id α) (f : α β) : f <$> x = f x := rfl
@[deprecated run_bind (since := "2025-03-05")] theorem bind_eq (x : Id α) (f : α id β) : x >>= f = f x := rfl
@[deprecated run_pure (since := "2025-03-05")] theorem pure_eq (a : α) : (pure a : Id α) = a := rfl
end Id
/-! # Option -/
instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun _ _ => rfl)
(bind_assoc := fun x _ _ => by cases x <;> rfl)
(bind_pure_comp := fun _ x => by cases x <;> rfl)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance

View File

@@ -7,11 +7,14 @@ module
prelude
public import Init.Control.Lawful.Basic
public import Init.Control.Except
import all Init.Control.Except
public import Init.Control.Option
import all Init.Control.Option
public import Init.Control.State
import all Init.Control.State
public import Init.Control.StateRef
public import Init.Ext
public section
@@ -189,12 +192,12 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (OptionT m) where
@[simp] theorem run_seq [Monad m] [LawfulMonad m] (f : OptionT m (α β)) (x : OptionT m α) :
(f <*> x).run = Option.elimM f.run (pure none) (fun f => Option.map f <$> x.run) := by
simp [seq_eq_bind_map, Option.elimM, Option.elim]
simp [seq_eq_bind, Option.elimM, Option.elim]
@[simp] theorem run_seqLeft [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
(x <* y).run = Option.elimM x.run (pure none)
(fun x => Option.map (Function.const β x) <$> y.run) := by
simp [seqLeft_eq, seq_eq_bind_map, Option.elimM, OptionT.run_bind]
simp [seqLeft_eq, seq_eq_bind, Option.elimM, OptionT.run_bind]
@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
(x *> y).run = Option.elimM x.run (pure none) (Function.const α y.run) := by
@@ -219,7 +222,7 @@ instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun _ _ => by rfl)
(bind_assoc := fun a _ _ => by cases a <;> rfl)
(bind_pure_comp := fun _ x => by cases x <;> rfl)
(bind_pure_comp := bind_pure_comp)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance

View File

@@ -7,6 +7,7 @@ module
prelude
public import Init.Control.Lawful.Basic
public import Init.RCases
public import Init.ByCases
public section

View File

@@ -6,13 +6,17 @@ Authors: Quang Dao, Paul Reichert
module
prelude
public import Init.Control.Option
import all Init.Control.Option
public import Init.Control.Except
import all Init.Control.Except
public import Init.Control.ExceptCps
import all Init.Control.ExceptCps
public import Init.Control.StateRef
import all Init.Control.StateRef
public import Init.Control.StateCps
import all Init.Control.StateCps
public import Init.Control.Id
import all Init.Control.Id
public import Init.Control.Lawful.MonadLift.Lemmas
public import Init.Control.Lawful.Instances

View File

@@ -23,7 +23,7 @@ theorem monadLift_map [LawfulMonad m] [LawfulMonad n] (f : α → β) (ma : m α
theorem monadLift_seq [LawfulMonad m] [LawfulMonad n] (mf : m (α β)) (ma : m α) :
monadLift (mf <*> ma) = monadLift mf <*> (monadLift ma : n α) := by
simp only [seq_eq_bind_map, monadLift_map, monadLift_bind]
simp only [seq_eq_bind, monadLift_map, monadLift_bind]
theorem monadLift_seqLeft [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
monadLift (x <* y) = (monadLift x : n α) <* (monadLift y : n β) := by

View File

@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.Option.Basic
public import Init.Control.Basic
public import Init.Control.Except
public section
@@ -27,7 +28,7 @@ failure occurred.
/--
Executes an action that might fail in the underlying monad `m`, returning `none` in case of failure.
-/
@[always_inline, inline, expose]
@[always_inline, inline]
def OptionT.run {m : Type u Type v} {α : Type u} (x : OptionT m α) : m (Option α) :=
x
@@ -69,7 +70,7 @@ instance {m : Type u → Type v} [Pure m] : Inhabited (OptionT m α) where
/--
Recovers from failures. Typically used via the `<|>` operator.
-/
@[always_inline, inline, expose] protected def orElse (x : OptionT m α) (y : Unit OptionT m α) : OptionT m α := OptionT.mk do
@[always_inline, inline] protected def orElse (x : OptionT m α) (y : Unit OptionT m α) : OptionT m α := OptionT.mk do
match ( x) with
| some a => pure (some a)
| _ => y ()
@@ -77,7 +78,7 @@ Recovers from failures. Typically used via the `<|>` operator.
/--
A recoverable failure.
-/
@[always_inline, inline, expose] protected def fail : OptionT m α := OptionT.mk do
@[always_inline, inline] protected def fail : OptionT m α := OptionT.mk do
pure none
instance : Alternative (OptionT m) where
@@ -90,7 +91,7 @@ Converts a computation from the underlying monad into one that could fail, even
This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
lifting](lean-manual://section/monad-lifting).
-/
@[always_inline, inline, expose] protected def lift (x : m α) : OptionT m α := OptionT.mk do
@[always_inline, inline] protected def lift (x : m α) : OptionT m α := OptionT.mk do
return some ( x)
instance : MonadLift m (OptionT m) := OptionT.lift
@@ -100,11 +101,11 @@ instance : MonadFunctor m (OptionT m) := ⟨fun f x => f x⟩
/--
Handles failures by treating them as exceptions of type `Unit`.
-/
@[always_inline, inline, expose] protected def tryCatch (x : OptionT m α) (handle : PUnit OptionT m α) : OptionT m α := OptionT.mk do
let some a x | handle
@[always_inline, inline] protected def tryCatch (x : OptionT m α) (handle : Unit OptionT m α) : OptionT m α := OptionT.mk do
let some a x | handle ()
pure <| some a
instance : MonadExceptOf PUnit (OptionT m) where
instance : MonadExceptOf Unit (OptionT m) where
throw := fun _ => OptionT.fail
tryCatch := OptionT.tryCatch

View File

@@ -8,6 +8,8 @@ The Reader monad transformer for passing immutable State.
module
prelude
public import Init.Control.Basic
public import Init.Control.Id
public import Init.Control.Except
public section

View File

@@ -8,6 +8,8 @@ The State monad transformer.
module
prelude
public import Init.Control.Basic
public import Init.Control.Id
public import Init.Control.Except
public section

View File

@@ -8,6 +8,7 @@ notation, basic datatypes and type classes
module
prelude
public meta import Init.Prelude
public import Init.SizeOf
public section
@@ -377,7 +378,7 @@ class ForIn (m : Type u₁ → Type u₂) (ρ : Type u) (α : outParam (Type v))
More information about the translation of `for` loops into `ForIn.forIn` is available in [the Lean
reference manual](lean-manual://section/monad-iteration-syntax).
-/
forIn {β} (xs : ρ) (b : β) (f : α β m (ForInStep β)) : m β
forIn {β} [Monad m] (xs : ρ) (b : β) (f : α β m (ForInStep β)) : m β
export ForIn (forIn)
@@ -405,7 +406,7 @@ class ForIn' (m : Type u₁ → Type u₂) (ρ : Type u) (α : outParam (Type v)
More information about the translation of `for` loops into `ForIn'.forIn'` is available in [the
Lean reference manual](lean-manual://section/monad-iteration-syntax).
-/
forIn' {β} (x : ρ) (b : β) (f : (a : α) a x β m (ForInStep β)) : m β
forIn' {β} [Monad m] (x : ρ) (b : β) (f : (a : α) a x β m (ForInStep β)) : m β
export ForIn' (forIn')
@@ -600,6 +601,17 @@ export LawfulSingleton (insert_empty_eq)
attribute [simp] insert_empty_eq
@[deprecated insert_empty_eq (since := "2025-03-12")]
theorem insert_emptyc_eq [EmptyCollection β] [Insert α β] [Singleton α β]
[LawfulSingleton α β] (x : α) : (insert x : β) = singleton x :=
insert_empty_eq _
@[deprecated insert_empty_eq (since := "2025-03-12")]
theorem LawfulSingleton.insert_emptyc_eq [EmptyCollection β] [Insert α β] [Singleton α β]
[LawfulSingleton α β] (x : α) : (insert x : β) = singleton x :=
insert_empty_eq _
/-- Type class used to implement the notation `{ a ∈ c | p a }` -/
class Sep (α : outParam <| Type u) (γ : Type v) where
/-- Computes `{ a ∈ c | p a }`. -/
@@ -1084,6 +1096,14 @@ theorem of_toBoolUsing_eq_true {p : Prop} {d : Decidable p} (h : toBoolUsing d =
theorem of_toBoolUsing_eq_false {p : Prop} {d : Decidable p} (h : toBoolUsing d = false) : ¬p :=
of_decide_eq_false h
set_option linter.missingDocs false in
@[deprecated of_toBoolUsing_eq_true (since := "2025-04-04")]
abbrev ofBoolUsing_eq_true := @of_toBoolUsing_eq_true
set_option linter.missingDocs false in
@[deprecated of_toBoolUsing_eq_false (since := "2025-04-04")]
abbrev ofBoolUsing_eq_false := @of_toBoolUsing_eq_false
instance : Decidable True :=
isTrue trivial
@@ -1146,7 +1166,6 @@ end
else isFalse (fun h => absurd (h hp) hq)
else isTrue (fun h => absurd h hp)
@[inline]
instance {p q} [Decidable p] [Decidable q] : Decidable (p q) :=
if hp : p then
if hq : q then
@@ -1188,13 +1207,17 @@ theorem dif_neg {c : Prop} {h : Decidable c} (hnc : ¬c) {α : Sort u} {t : c
| isTrue hc => absurd hc hnc
| isFalse _ => rfl
@[macro_inline]
-- Remark: dite and ite are "defally equal" when we ignore the proofs.
theorem dif_eq_if (c : Prop) {h : Decidable c} {α : Sort u} (t : α) (e : α) : dite c (fun _ => t) (fun _ => e) = ite c t e :=
match h with
| isTrue _ => rfl
| isFalse _ => rfl
instance {c t e : Prop} [dC : Decidable c] [dT : Decidable t] [dE : Decidable e] : Decidable (if c then t else e) :=
match dC with
| isTrue _ => dT
| isFalse _ => dE
@[inline]
instance {c : Prop} {t : c Prop} {e : ¬c Prop} [dC : Decidable c] [dT : h, Decidable (t h)] [dE : h, Decidable (e h)] : Decidable (if h : c then t h else e h) :=
match dC with
| isTrue hc => dT hc
@@ -1345,12 +1368,12 @@ namespace Subtype
theorem exists_of_subtype {α : Type u} {p : α Prop} : { x // p x } Exists (fun x => p x)
| a, h => a, h
variable {α : Sort u} {p : α Prop}
set_option linter.missingDocs false in
@[deprecated exists_of_subtype (since := "2025-04-04")]
abbrev existsOfSubtype := @exists_of_subtype
protected theorem ext : {a1 a2 : {x // p x}}, val a1 = val a2 a1 = a2
| _, _, _, _, rfl => rfl
variable {α : Type u} {p : α Prop}
@[deprecated Subtype.ext (since := "2025-10-26")]
protected theorem eq : {a1 a2 : {x // p x}}, val a1 = val a2 a1 = a2
| _, _, _, _, rfl => rfl
@@ -1365,9 +1388,9 @@ instance {α : Type u} {p : α → Prop} [BEq α] [ReflBEq α] : ReflBEq {x : α
rfl {x} := BEq.refl x.1
instance {α : Type u} {p : α Prop} [BEq α] [LawfulBEq α] : LawfulBEq {x : α // p x} where
eq_of_beq h := Subtype.ext (eq_of_beq h)
eq_of_beq h := Subtype.eq (eq_of_beq h)
instance {α : Sort u} {p : α Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
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)
else isFalse (fun h' => Subtype.noConfusion h' (fun h' => absurd h' h))
@@ -1468,8 +1491,6 @@ def Prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂
@[simp] theorem Prod.map_apply (f : α β) (g : γ δ) (x) (y) :
Prod.map f g (x, y) = (f x, g y) := rfl
-- We add `@[grind =]` to these in `Init.Data.Prod`.
@[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
@@ -1486,24 +1507,20 @@ protected theorem PSigma.eta {α : Sort u} {β : α → Sort v} {a₁ a₂ : α}
/-! # Universe polymorphic unit -/
theorem PUnit.ext (a b : PUnit) : a = b := by
cases a; cases b; exact rfl
@[deprecated PUnit.ext (since := "2025-10-26")]
theorem PUnit.subsingleton (a b : PUnit) : a = b := by
cases a; cases b; exact rfl
theorem PUnit.eq_punit (a : PUnit) : a = :=
PUnit.ext a
PUnit.subsingleton a
instance : Subsingleton PUnit :=
Subsingleton.intro PUnit.ext
Subsingleton.intro PUnit.subsingleton
instance : Inhabited PUnit where
default :=
instance : DecidableEq PUnit :=
fun a b => isTrue (PUnit.ext a b)
fun a b => isTrue (PUnit.subsingleton a b)
/-! # Setoid -/
@@ -1590,7 +1607,7 @@ gen_injective_theorems% PSum
gen_injective_theorems% Sigma
gen_injective_theorems% String
gen_injective_theorems% String.Pos.Raw
gen_injective_theorems% Substring.Raw
gen_injective_theorems% Substring
gen_injective_theorems% Subtype
gen_injective_theorems% Sum
gen_injective_theorems% Task
@@ -2507,7 +2524,8 @@ class Antisymm (r : αα → Prop) : Prop where
/-- An antisymmetric relation `r` satisfies `r a b → r b a → a = b`. -/
antisymm (a b : α) : r a b r b a a = b
/-- `Asymm r` means that the binary relation `r` is asymmetric, that is, `r a b → ¬ r b a`. -/
/-- `Asymm r` means that the binary relation `r` is asymmetric, that is,
`r a b → ¬ r b a`. -/
class Asymm (r : α α Prop) : Prop where
/-- An asymmetric relation satisfies `r a b → ¬ r b a`. -/
asymm : a b, r a b ¬r b a
@@ -2517,19 +2535,16 @@ class Symm (r : αα → Prop) : Prop where
/-- A symmetric relation satisfies `r a b → r b a`. -/
symm : a b, r a b r b a
/-- `Total X r` means that the binary relation `r` on `X` is total, that is, `r a b` or `r b a`. -/
/-- `Total X r` means that the binary relation `r` on `X` is total, that is, that for any
`x y : X` we have `r x y` or `r y x`. -/
class Total (r : α α Prop) : Prop where
/-- A total relation satisfies `r a b` or `r b a`. -/
/-- A total relation satisfies `r a b r b a`. -/
total : a b, r a b r b a
/-- `Irrefl r` means the binary relation `r` is irreflexive, that is, `r x x` never holds. -/
/-- `Irrefl r` means the binary relation `r` is irreflexive, that is, `r x x` never
holds. -/
class Irrefl (r : α α Prop) : Prop where
/-- An irreflexive relation satisfies `¬ r a a`. -/
irrefl : a, ¬r a a
/-- `Trichotomous r` says that `r` is trichotomous, that is, `¬ r a b → ¬ r b a → a = b`. -/
class Trichotomous (r : α α Prop) : Prop where
/-- An trichotomous relation `r` satisfies `¬ r a b → ¬ r b a → a = b`. -/
trichotomous (a b : α) : ¬ r a b ¬ r b a a = b
end Std

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@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Basic
public import Init.Data.Nat
public import Init.Data.Bool
public import Init.Data.BitVec

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@@ -7,6 +7,7 @@ Authors: Dany Fabian
module
prelude
public import Init.Classical
public import Init.ByCases
@[expose] public section

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@@ -6,7 +6,10 @@ Authors: Joachim Breitner, Mario Carneiro
module
prelude
public import Init.Data.Array.Mem
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Count
public import Init.Data.List.Attach
import all Init.Data.List.Attach
public section
@@ -749,6 +752,9 @@ and simplifies these to the function directly taking the value.
(Array.replicate n x).unattach = Array.replicate n x.1 := by
simp [unattach]
@[deprecated unattach_replicate (since := "2025-03-18")]
abbrev unattach_mkArray := @unattach_replicate
/-! ### Well-founded recursion preprocessing setup -/
@[wf_preprocess] theorem map_wfParam {xs : Array α} {f : α β} :

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@@ -6,6 +6,10 @@ Authors: Leonardo de Moura
module
prelude
public import Init.WFTactics
public import Init.Data.Nat.Basic
public import Init.Data.Fin.Basic
public import Init.Data.UInt.BasicAux
public import Init.GetElem
public import Init.Data.List.ToArrayImpl
import all Init.Data.List.ToArrayImpl
@@ -209,6 +213,20 @@ Examples:
def replicate {α : Type u} (n : Nat) (v : α) : Array α where
toList := List.replicate n v
/--
Creates an array that contains `n` repetitions of `v`.
The corresponding `List` function is `List.replicate`.
Examples:
* `Array.mkArray 2 true = #[true, true]`
* `Array.mkArray 3 () = #[(), (), ()]`
* `Array.mkArray 0 "anything" = #[]`
-/
@[extern "lean_mk_array", deprecated replicate (since := "2025-03-18")]
def mkArray {α : Type u} (n : Nat) (v : α) : Array α where
toList := List.replicate n v
/--
Swaps two elements of an array. The modification is performed in-place when the reference to the
array is unique.
@@ -226,7 +244,7 @@ def swap (xs : Array α) (i j : @& Nat) (hi : i < xs.size := by get_elem_tactic)
let xs' := xs.set i v₂
xs'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set _).symm)
@[simp, grind =] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
@[simp] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
change ((xs.set i xs[j]).set j xs[i]
(Nat.lt_of_lt_of_eq hj (size_set _).symm)).size = xs.size
rw [size_set, size_set]
@@ -242,7 +260,7 @@ Examples:
* `#["red", "green", "blue", "brown"].swapIfInBounds 0 4 = #["red", "green", "blue", "brown"]`
* `#["red", "green", "blue", "brown"].swapIfInBounds 9 2 = #["red", "green", "blue", "brown"]`
-/
@[extern "lean_array_swap", expose]
@[extern "lean_array_swap", grind]
def swapIfInBounds (xs : Array α) (i j : @& Nat) : Array α :=
if h₁ : i < xs.size then
if h₂ : j < xs.size then swap xs i j
@@ -448,7 +466,7 @@ Examples:
-/
abbrev take (xs : Array α) (i : Nat) : Array α := extract xs 0 i
@[simp, grind =] theorem take_eq_extract {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i := rfl
@[simp] theorem take_eq_extract {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i := rfl
/--
Removes the first `i` elements of `xs`. If `xs` has fewer than `i` elements, the new array is empty.
@@ -462,7 +480,7 @@ Examples:
-/
abbrev drop (xs : Array α) (i : Nat) : Array α := extract xs i xs.size
@[simp, grind =] theorem drop_eq_extract {xs : Array α} {i : Nat} : xs.drop i = xs.extract i xs.size := rfl
@[simp] theorem drop_eq_extract {xs : Array α} {i : Nat} : xs.drop i = xs.extract i xs.size := rfl
@[inline]
unsafe def modifyMUnsafe [Monad m] (xs : Array α) (i : Nat) (f : α m α) : m (Array α) := do
@@ -570,7 +588,7 @@ protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad
| ForInStep.yield b => loop i (Nat.le_of_lt h') b
loop as.size (Nat.le_refl _) b
instance [Monad m] : ForIn' m (Array α) α inferInstance where
instance : ForIn' m (Array α) α inferInstance where
forIn' := Array.forIn'
-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
@@ -1001,7 +1019,7 @@ unless `start < stop`. By default, the entire array is used.
protected def forM {α : Type u} {m : Type v Type w} [Monad m] (f : α m PUnit) (as : Array α) (start := 0) (stop := as.size) : m PUnit :=
as.foldlM (fun _ => f) start stop
instance [Monad m] : ForM m (Array α) α where
instance : ForM m (Array α) α where
forM xs f := Array.forM f xs
-- We simplify `Array.forM` to `forM`.
@@ -1295,7 +1313,7 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
/--
Returns the index of the first element equal to `a`, or `none` if no element is equal
Returns the index of the first element equal to `a`, or the size of the array if no element is equal
to `a`. The index is returned as a `Fin`, which guarantees that it is in bounds.
Examples:
@@ -1704,7 +1722,7 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
as
decreasing_by simp_wf; decreasing_trivial_pre_omega
@[simp, grind =] theorem popWhile_empty {p : α Bool} :
@[simp] theorem popWhile_empty {p : α Bool} :
popWhile p #[] = #[] := by
simp [popWhile]
@@ -1751,8 +1769,7 @@ termination_by xs.size - i
decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
-- This is required in `Lean.Data.PersistentHashMap`.
@[simp, grind =]
theorem size_eraseIdx {xs : Array α} (i : Nat) (h) : (xs.eraseIdx i h).size = xs.size - 1 := by
@[simp] theorem size_eraseIdx {xs : Array α} (i : Nat) (h) : (xs.eraseIdx i h).size = xs.size - 1 := by
induction xs, i, h using Array.eraseIdx.induct with
| @case1 xs i h h' xs' ih =>
unfold eraseIdx
@@ -2134,3 +2151,5 @@ instance [ToString α] : ToString (Array α) where
toString xs := String.Internal.append "#" (toString xs.toList)
end Array
export Array (mkArray)

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@@ -6,8 +6,10 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Nat.Linear
public import Init.NotationExtra
public section

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@@ -6,7 +6,9 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Int.DivMod.Lemmas
public import Init.Omega
public section
universe u v

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@@ -8,6 +8,7 @@ module
prelude
public import Init.Data.List.TakeDrop
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public section
@@ -31,7 +32,7 @@ theorem foldlM_toList.aux [Monad m]
· cases Nat.not_le_of_gt _ (Nat.zero_add _ H)
· rename_i i; rw [Nat.succ_add] at H
simp [foldlM_toList.aux (j := j+1) H]
rw (occs := [2]) [ List.getElem_cons_drop _]
rw (occs := [2]) [ List.getElem_cons_drop_succ_eq_drop _]
simp
· rw [List.drop_of_length_le (Nat.ge_of_not_lt _)]; simp
@@ -100,15 +101,9 @@ abbrev push_toList := @toList_push
@[simp, grind =] theorem empty_append {xs : Array α} : #[] ++ xs = xs := by
apply ext'; simp only [toList_append, List.nil_append]
@[simp] theorem append_assoc {xs ys zs : Array α} : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
@[simp, grind _=_] theorem append_assoc {xs ys zs : Array α} : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
apply ext'; simp only [toList_append, List.append_assoc]
grind_pattern append_assoc => (xs ++ ys) ++ zs where
xs =/= #[]; ys =/= #[]; zs =/= #[]
grind_pattern append_assoc => xs ++ (ys ++ zs) where
xs =/= #[]; ys =/= #[]; zs =/= #[]
@[simp] theorem appendList_eq_append {xs : Array α} {l : List α} : xs.appendList l = xs ++ l := rfl
@[simp, grind =] theorem toList_appendList {xs : Array α} {l : List α} :
@@ -116,4 +111,6 @@ grind_pattern append_assoc => xs ++ (ys ++ zs) where
rw [ appendList_eq_append]; unfold Array.appendList
induction l generalizing xs <;> simp [*]
end Array

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@@ -6,6 +6,7 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.Count
@@ -99,6 +100,9 @@ theorem countP_le_size : countP p xs ≤ xs.size := by
theorem countP_replicate {a : α} {n : Nat} : countP p (replicate n a) = if p a then n else 0 := by
simp [ List.toArray_replicate, List.countP_replicate]
@[deprecated countP_replicate (since := "2025-03-18")]
abbrev countP_mkArray := @countP_replicate
theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
(if p xs[i] then 1 else 0) xs.countP p := by
rcases xs with xs
@@ -259,9 +263,15 @@ theorem count_eq_size {xs : Array α} : count a xs = xs.size ↔ ∀ b ∈ xs, a
@[simp] theorem count_replicate_self {a : α} {n : Nat} : count a (replicate n a) = n := by
simp [ List.toArray_replicate]
@[deprecated count_replicate_self (since := "2025-03-18")]
abbrev count_mkArray_self := @count_replicate_self
theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
simp [ List.toArray_replicate, List.count_replicate]
@[deprecated count_replicate (since := "2025-03-18")]
abbrev count_mkArray := @count_replicate
theorem filter_beq {xs : Array α} (a : α) : xs.filter (· == a) = replicate (count a xs) a := by
rcases xs with xs
simp [List.filter_beq]
@@ -275,6 +285,9 @@ theorem replicate_count_eq_of_count_eq_size {xs : Array α} (h : count a xs = xs
rw [ toList_inj]
simp [List.replicate_count_eq_of_count_eq_length (by simpa using h)]
@[deprecated replicate_count_eq_of_count_eq_size (since := "2025-03-18")]
abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
@[simp] theorem count_filter {xs : Array α} (h : p a) : count a (filter p xs) = count a xs := by
rcases xs with xs
simp [List.count_filter, h]

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@@ -6,9 +6,11 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.BEq
public import Init.Data.List.Nat.BEq
public import Init.ByCases
public section
@@ -89,41 +91,11 @@ theorem isEqv_self_beq [BEq α] [ReflBEq α] (xs : Array α) : Array.isEqv xs xs
theorem isEqv_self [DecidableEq α] (xs : Array α) : Array.isEqv xs xs (· = ·) = true := by
simp [isEqv, isEqvAux_self]
def instDecidableEqImpl [DecidableEq α] : DecidableEq (Array α) := fun xs ys =>
match h:isEqv xs ys (fun a b => a = b) with
| true => isTrue (eq_of_isEqv xs ys h)
| false => isFalse (by subst ·; rw [isEqv_self] at h; contradiction)
instance instDecidableEq [DecidableEq α] : DecidableEq (Array α) := fun xs ys =>
match xs with
| [] =>
match ys with
| [] => isTrue rfl
| _ :: _ => isFalse (Array.noConfusion · (List.noConfusion ·))
| a :: as =>
match ys with
| [] => isFalse (Array.noConfusion · (List.noConfusion ·))
| b :: bs => instDecidableEqImpl a :: as b :: bs
@[csimp]
theorem instDecidableEq_csimp : @instDecidableEq = @instDecidableEqImpl :=
Subsingleton.allEq _ _
/--
Equality with `#[]` is decidable even if the underlying type does not have decidable equality.
-/
instance instDecidableEqEmp (xs : Array α) : Decidable (xs = #[]) :=
match xs with
| [] => isTrue rfl
| _ :: _ => isFalse (Array.noConfusion · (List.noConfusion ·))
/--
Equality with `#[]` is decidable even if the underlying type does not have decidable equality.
-/
instance instDecidableEmpEq (ys : Array α) : Decidable (#[] = ys) :=
match ys with
| [] => isTrue rfl
| _ :: _ => isFalse (Array.noConfusion · (List.noConfusion ·))
instance [DecidableEq α] : DecidableEq (Array α) :=
fun xs ys =>
match h:isEqv xs ys (fun a b => a = b) with
| true => isTrue (eq_of_isEqv xs ys h)
| false => isFalse fun h' => by subst h'; rw [isEqv_self] at h; contradiction
theorem beq_eq_decide [BEq α] (xs ys : Array α) :
(xs == ys) = if h : xs.size = ys.size then

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@@ -6,8 +6,11 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.Erase
public import Init.Data.List.Nat.Basic
public section
@@ -139,16 +142,25 @@ theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
simp only [ List.toArray_replicate, List.eraseP_toArray, List.eraseP_replicate]
split <;> simp
@[deprecated eraseP_replicate (since := "2025-03-18")]
abbrev eraseP_mkArray := @eraseP_replicate
@[simp] theorem eraseP_replicate_of_pos {n : Nat} {a : α} (h : p a) :
(replicate n a).eraseP p = replicate (n - 1) a := by
simp only [ List.toArray_replicate, List.eraseP_toArray]
simp [h]
@[deprecated eraseP_replicate_of_pos (since := "2025-03-18")]
abbrev eraseP_mkArray_of_pos := @eraseP_replicate_of_pos
@[simp] theorem eraseP_replicate_of_neg {n : Nat} {a : α} (h : ¬p a) :
(replicate n a).eraseP p = replicate n a := by
simp only [ List.toArray_replicate, List.eraseP_toArray]
simp [h]
@[deprecated eraseP_replicate_of_neg (since := "2025-03-18")]
abbrev eraseP_mkArray_of_neg := @eraseP_replicate_of_neg
theorem eraseP_eq_iff {p} {xs : Array α} :
xs.eraseP p = ys
(( a xs, ¬ p a) xs = ys)
@@ -269,6 +281,9 @@ theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
simp only [List.erase_replicate, beq_iff_eq, List.toArray_replicate]
split <;> simp
@[deprecated erase_replicate (since := "2025-03-18")]
abbrev erase_mkArray := @erase_replicate
-- The arguments `a b` are explicit,
-- so they can be specified to prevent `simp` repeatedly applying the lemma.
@[grind =]
@@ -296,11 +311,17 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
simp only [ List.toArray_replicate, List.erase_toArray]
simp
@[deprecated erase_replicate_self (since := "2025-03-18")]
abbrev erase_mkArray_self := @erase_replicate_self
@[simp] theorem erase_replicate_ne [LawfulBEq α] {a b : α} (h : !b == a) :
(replicate n a).erase b = replicate n a := by
rw [erase_of_not_mem]
simp_all
@[deprecated erase_replicate_ne (since := "2025-03-18")]
abbrev erase_mkArray_ne := @erase_replicate_ne
end erase
/-! ### eraseIdxIfInBounds -/
@@ -411,6 +432,9 @@ theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} {h} :
simp only [ List.toArray_replicate, List.eraseIdx_toArray]
simp [List.eraseIdx_replicate, h]
@[deprecated eraseIdx_replicate (since := "2025-03-18")]
abbrev eraseIdx_mkArray := @eraseIdx_replicate
theorem mem_eraseIdx_iff_getElem {x : α} {xs : Array α} {k} {h} : x xs.eraseIdx k h i w, i k xs[i]'w = x := by
rcases xs with xs
simp [List.mem_eraseIdx_iff_getElem, *]

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@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.TakeDrop
public section
@@ -200,7 +201,7 @@ theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
simp [getElem?_extract]
omega
@[simp] theorem extract_extract {as : Array α} {i j k l : Nat} :
@[simp, grind =] theorem extract_extract {as : Array α} {i j k l : Nat} :
(as.extract i j).extract k l = as.extract (i + k) (min (i + l) j) := by
ext m h₁ h₂
· simp
@@ -208,9 +209,6 @@ theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
· simp only [size_extract] at h₁ h₂
simp [Nat.add_assoc]
grind_pattern extract_extract => (as.extract i j).extract k l where
as =/= #[]
theorem extract_eq_empty_of_eq_empty {as : Array α} {i j : Nat} (h : as = #[]) :
as.extract i j = #[] := by
simp [h]
@@ -292,6 +290,9 @@ theorem extract_append_right {as bs : Array α} :
· simp only [size_extract, size_replicate] at h₁ h₂
simp only [getElem_extract, getElem_replicate]
@[deprecated extract_replicate (since := "2025-03-18")]
abbrev extract_mkArray := @extract_replicate
theorem extract_eq_extract_right {as : Array α} {i j j' : Nat} :
as.extract i j = as.extract i j' min (j - i) (as.size - i) = min (j' - i) (as.size - i) := by
rcases as with as
@@ -409,6 +410,8 @@ theorem popWhile_append {xs ys : Array α} :
rcases ys with ys
simp only [List.append_toArray, List.popWhile_toArray, List.reverse_append, List.dropWhile_append,
List.isEmpty_iff, List.isEmpty_toArray, List.isEmpty_reverse]
-- Why do these not fire with `simp`?
rw [List.popWhile_toArray, List.isEmpty_toArray, List.isEmpty_reverse]
split
· rfl
· simp
@@ -427,20 +430,32 @@ theorem popWhile_append {xs ys : Array α} :
(replicate n a).takeWhile p = (replicate n a).filter p := by
simp [ List.toArray_replicate]
@[deprecated takeWhile_replicate_eq_filter (since := "2025-03-18")]
abbrev takeWhile_mkArray_eq_filter := @takeWhile_replicate_eq_filter
theorem takeWhile_replicate {p : α Bool} :
(replicate n a).takeWhile p = if p a then replicate n a else #[] := by
simp [takeWhile_replicate_eq_filter, filter_replicate]
@[deprecated takeWhile_replicate (since := "2025-03-18")]
abbrev takeWhile_mkArray := @takeWhile_replicate
@[simp] theorem popWhile_replicate_eq_filter_not {p : α Bool} :
(replicate n a).popWhile p = (replicate n a).filter (fun a => !p a) := by
simp [ List.toArray_replicate, List.filter_reverse]
@[deprecated popWhile_replicate_eq_filter_not (since := "2025-03-18")]
abbrev popWhile_mkArray_eq_filter_not := @popWhile_replicate_eq_filter_not
theorem popWhile_replicate {p : α Bool} :
(replicate n a).popWhile p = if p a then #[] else replicate n a := by
simp only [popWhile_replicate_eq_filter_not, size_replicate, filter_replicate, Bool.not_eq_eq_eq_not,
Bool.not_true]
split <;> simp_all
@[deprecated popWhile_replicate (since := "2025-03-18")]
abbrev popWhile_mkArray := @popWhile_replicate
theorem extract_takeWhile {as : Array α} {i : Nat} :
(as.takeWhile p).extract 0 i = (as.extract 0 i).takeWhile p := by
rcases as with as

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@@ -6,6 +6,7 @@ Authors: François G. Dorais
module
prelude
public import Init.Data.List.FinRange
public import Init.Data.Array.OfFn
public section

View File

@@ -7,7 +7,10 @@ module
prelude
public import Init.Data.List.Nat.Find
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Attach
public import Init.Data.Array.Range
public section
@@ -129,19 +132,31 @@ theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
simp [ List.toArray_replicate, List.findSome?_replicate]
@[deprecated findSome?_replicate (since := "2025-03-18")]
abbrev findSome?_mkArray := @findSome?_replicate
@[simp] theorem findSome?_replicate_of_pos (h : 0 < n) : findSome? f (replicate n a) = f a := by
simp [findSome?_replicate, Nat.ne_of_gt h]
@[deprecated findSome?_replicate_of_pos (since := "2025-03-18")]
abbrev findSome?_mkArray_of_pos := @findSome?_replicate_of_pos
-- Argument is unused, but used to decide whether `simp` should unfold.
@[simp] theorem findSome?_replicate_of_isSome (_ : (f a).isSome) :
findSome? f (replicate n a) = if n = 0 then none else f a := by
simp [findSome?_replicate]
@[deprecated findSome?_replicate_of_isSome (since := "2025-03-18")]
abbrev findSome?_mkArray_of_isSome := @findSome?_replicate_of_isSome
@[simp] theorem findSome?_replicate_of_isNone (h : (f a).isNone) :
findSome? f (replicate n a) = none := by
rw [Option.isNone_iff_eq_none] at h
simp [findSome?_replicate, h]
@[deprecated findSome?_replicate_of_isNone (since := "2025-03-18")]
abbrev findSome?_mkArray_of_isNone := @findSome?_replicate_of_isNone
/-! ### find? -/
@[simp, grind =] theorem find?_empty : find? p #[] = none := rfl
@@ -306,10 +321,16 @@ theorem find?_replicate :
find? p (replicate n a) = if p a then some a else none := by
simp [find?_replicate, Nat.ne_of_gt h]
@[deprecated find?_replicate_of_size_pos (since := "2025-03-18")]
abbrev find?_mkArray_of_length_pos := @find?_replicate_of_size_pos
@[simp] theorem find?_replicate_of_pos (h : p a) :
find? p (replicate n a) = if n = 0 then none else some a := by
simp [find?_replicate, h]
@[deprecated find?_replicate_of_pos (since := "2025-03-18")]
abbrev find?_mkArray_of_pos := @find?_replicate_of_pos
@[simp] theorem find?_replicate_of_neg (h : ¬ p a) : find? p (replicate n a) = none := by
simp [find?_replicate, h]
@@ -565,6 +586,9 @@ theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
simp only [List.findIdx?_toArray]
simp
@[deprecated findIdx?_replicate (since := "2025-03-18")]
abbrev findIdx?_mkArray := @findIdx?_replicate
theorem findIdx?_eq_findSome?_zipIdx {xs : Array α} {p : α Bool} :
xs.findIdx? p = xs.zipIdx.findSome? fun a, i => if p a then some i else none := by
rcases xs with xs

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@@ -50,6 +50,6 @@ where
getLit_eq (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : xs.getLit i h₁ h₂ = getElem xs.toList i ((id (α := xs.toList.length = n) h₁) h₂) :=
rfl
go (i : Nat) (hi : i xs.size) : toListLitAux xs n hsz i hi (xs.toList.drop i) = xs.toList := by
induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop, *]
induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop_succ_eq_drop, *]
end Array

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@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.InsertIdx
public section

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@@ -6,10 +6,17 @@ Authors: Mario Carneiro, Kim Morrison
module
prelude
public import Init.Data.Nat.Lemmas
public import Init.Data.List.Range
public import Init.Data.List.Nat.TakeDrop
public import Init.Data.List.Nat.Modify
public import Init.Data.List.Nat.Basic
public import Init.Data.List.Monadic
public import Init.Data.List.OfFn
public import Init.Data.Array.Mem
public import Init.Data.Array.DecidableEq
public import Init.Data.Range.Lemmas
public import Init.TacticsExtra
public import Init.Data.List.ToArray
import all Init.Data.List.Control
import all Init.Data.Array.Basic
@@ -245,13 +252,12 @@ theorem back_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.pus
replace h := List.append_inj_right' h (by simp)
simpa using h
theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b a = b xs = ys := by
theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys := by
cases xs
cases ys
simp [And.comm]
theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys :=
(push_eq_push.1 h).2
simp at h
replace h := List.append_inj_left' h (by simp)
simp [h]
theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a xs = ys :=
pop_eq_of_push_eq, fun h => by simp [h]
@@ -259,6 +265,15 @@ theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a ↔ xs
theorem push_inj_right {a b : α} {xs : Array α} : xs.push a = xs.push b a = b :=
back_eq_of_push_eq, fun h => by simp [h]
theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b a = b xs = ys := by
constructor
· intro h
exact back_eq_of_push_eq h, pop_eq_of_push_eq h
· rintro rfl, rfl
rfl
theorem push_eq_append_singleton {as : Array α} {x : α} : as.push x = as ++ #[x] := rfl
theorem exists_push_of_ne_empty {xs : Array α} (h : xs #[]) :
(ys : Array α) (a : α), xs = ys.push a := by
rcases xs with xs
@@ -309,23 +324,41 @@ theorem singleton_inj : #[a] = #[b] ↔ a = b := by
@[simp, grind =] theorem size_replicate {n : Nat} {v : α} : (replicate n v).size = n :=
List.length_replicate ..
@[deprecated size_replicate (since := "2025-03-18")]
abbrev size_mkArray := @size_replicate
@[simp] theorem toList_replicate : (replicate n a).toList = List.replicate n a := by
simp only [replicate]
@[deprecated toList_replicate (since := "2025-03-18")]
abbrev toList_mkArray := @toList_replicate
@[simp, grind =] theorem replicate_zero : replicate 0 a = #[] := rfl
@[deprecated replicate_zero (since := "2025-03-18")]
abbrev mkArray_zero := @replicate_zero
@[grind =]
theorem replicate_succ : replicate (n + 1) a = (replicate n a).push a := by
apply toList_inj.1
simp [List.replicate_succ']
@[deprecated replicate_succ (since := "2025-03-18")]
abbrev mkArray_succ := @replicate_succ
@[simp, grind =] theorem getElem_replicate {n : Nat} {v : α} {i : Nat} (h : i < (replicate n v).size) :
(replicate n v)[i] = v := by simp [ getElem_toList]
@[deprecated getElem_replicate (since := "2025-03-18")]
abbrev getElem_mkArray := @getElem_replicate
@[grind =] theorem getElem?_replicate {n : Nat} {v : α} {i : Nat} :
(replicate n v)[i]? = if i < n then some v else none := by
simp [getElem?_def]
@[deprecated getElem?_replicate (since := "2025-03-18")]
abbrev getElem?_mkArray := @getElem?_replicate
/-! ### mem -/
@[grind ]
@@ -809,11 +842,6 @@ theorem contains_eq_true_of_mem [BEq α] [ReflBEq α] {a : α} {as : Array α} (
theorem elem_iff [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
elem a xs = true a xs := mem_of_contains_eq_true, contains_eq_true_of_mem
@[grind =]
theorem contains_iff_mem [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
xs.contains a = true a xs := mem_of_contains_eq_true, contains_eq_true_of_mem
@[deprecated contains_iff_mem (since := "2025-10-26")]
theorem contains_iff [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
xs.contains a = true a xs := mem_of_contains_eq_true, contains_eq_true_of_mem
@@ -1053,6 +1081,12 @@ theorem mem_or_eq_of_mem_setIfInBounds
cases xs
simp
@[deprecated beq_empty_eq (since := "2025-04-04")]
abbrev beq_empty_iff := @beq_empty_eq
@[deprecated empty_beq_eq (since := "2025-04-04")]
abbrev empty_beq_iff := @empty_beq_eq
@[simp, grind =] theorem push_beq_push [BEq α] {a b : α} {xs ys : Array α} :
(xs.push a == ys.push b) = (xs == ys && a == b) := by
cases xs
@@ -1073,6 +1107,9 @@ theorem size_eq_of_beq [BEq α] {xs ys : Array α} (h : xs == ys) : xs.size = ys
rw [Bool.eq_iff_iff]
simp +contextual
@[deprecated replicate_beq_replicate (since := "2025-03-18")]
abbrev mkArray_beq_mkArray := @replicate_beq_replicate
private theorem beq_of_beq_singleton [BEq α] {a b : α} : #[a] == #[b] a == b := by
intro h
have : isEqv #[a] #[b] BEq.beq = true := h
@@ -1136,7 +1173,7 @@ where
aux (i bs) :
mapM.map f xs i bs = (xs.toList.drop i).foldlM (fun bs a => bs.push <$> f a) bs := by
unfold mapM.map; split
· rw [ List.getElem_cons_drop _]
· rw [ List.getElem_cons_drop_succ_eq_drop _]
simp only [aux (i + 1), map_eq_pure_bind, List.foldlM_cons, bind_assoc,
pure_bind]
rfl
@@ -1628,15 +1665,12 @@ theorem filterMap_eq_filter {p : α → Bool} (w : stop = as.size) :
cases as
simp
@[grind =]
theorem filterMap_filterMap {f : α Option β} {g : β Option γ} {xs : Array α} :
filterMap g (filterMap f xs) = filterMap (fun x => (f x).bind g) xs := by
cases xs
simp [List.filterMap_filterMap]
grind_pattern filterMap_filterMap => filterMap g (filterMap f xs) where
f =/= some
g =/= some
@[grind =]
theorem map_filterMap {f : α Option β} {g : β γ} {xs : Array α} :
map g (filterMap f xs) = filterMap (fun x => (f x).map g) xs := by
@@ -1691,6 +1725,9 @@ theorem forall_none_of_filterMap_eq_empty (h : filterMap f xs = #[]) : ∀ x ∈
cases xs
simp
@[deprecated filterMap_eq_empty_iff (since := "2025-04-04")]
abbrev filterMap_eq_nil_iff := @filterMap_eq_empty_iff
theorem filterMap_eq_push_iff {f : α Option β} {xs : Array α} {ys : Array β} {b : β} :
filterMap f xs = ys.push b as a bs,
xs = as.push a ++ bs filterMap f as = ys f a = some b ( x, x bs f x = none) := by
@@ -1853,9 +1890,6 @@ theorem getElem_of_append {xs ys zs : Array α} (eq : xs = ys.push a ++ zs) (h :
theorem push_eq_append {a : α} {as : Array α} : as.push a = as ++ #[a] := rfl
@[deprecated push_eq_append (since := "2025-10-26")]
theorem push_eq_append_singleton {as : Array α} {x : α} : as.push x = as ++ #[x] := rfl
theorem append_inj {xs₁ xs₂ ys₁ ys₂ : Array α} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) :
xs₁ = xs₂ ys₁ = ys₂ := by
rcases xs₁ with s₁
@@ -2056,22 +2090,11 @@ theorem append_eq_map_iff {f : α → β} :
| nil => simp
| cons as => induction as.toList <;> simp [*]
@[simp] theorem flatten_toArray_map_toArray {L : List (List α)} :
@[simp] theorem flatten_toArray_map {L : List (List α)} :
(L.map List.toArray).toArray.flatten = L.flatten.toArray := by
apply ext'
simp [Function.comp_def]
@[deprecated flatten_toArray_map_toArray (since := "2025-10-26")]
theorem flatten_toArray_map {L : List (List α)} :
(L.map List.toArray).toArray.flatten = L.flatten.toArray := by
simp
@[grind =]
theorem flatten_map_toArray_toArray {L : List (List α)} :
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
simp
@[deprecated flatten_map_toArray_toArray (since := "2025-10-26")]
theorem flatten_map_toArray {L : List (List α)} :
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
simp
@@ -2118,33 +2141,32 @@ theorem forall_mem_flatten {p : α → Prop} {xss : Array (Array α)} :
theorem flatten_eq_flatMap {xss : Array (Array α)} : flatten xss = xss.flatMap id := by
induction xss using array₂_induction
rw [flatten_toArray_map_toArray, List.flatten_eq_flatMap]
rw [flatten_toArray_map, List.flatten_eq_flatMap]
simp [List.flatMap_map]
@[simp, grind _=_] theorem map_flatten {f : α β} {xss : Array (Array α)} :
(flatten xss).map f = (map (map f) xss).flatten := by
induction xss using array₂_induction with
| of xss =>
simp only [flatten_toArray_map_toArray, List.map_toArray, List.map_flatten, List.map_map,
simp only [flatten_toArray_map, List.map_toArray, List.map_flatten, List.map_map,
Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map_toArray]
rw [ Function.comp_def, List.map_map, flatten_toArray_map]
@[simp, grind =] theorem filterMap_flatten {f : α Option β} {xss : Array (Array α)} {stop : Nat} (w : stop = xss.flatten.size) :
filterMap f (flatten xss) 0 stop = flatten (map (filterMap f) xss) := by
subst w
induction xss using array₂_induction
simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
List.filterMap_toArray', List.filterMap_flatten, List.map_toArray, List.map_map,
Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map_toArray]
simp only [flatten_toArray_map, List.size_toArray, List.length_flatten, List.filterMap_toArray',
List.filterMap_flatten, List.map_toArray, List.map_map, Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map]
@[simp, grind =] theorem filter_flatten {p : α Bool} {xss : Array (Array α)} {stop : Nat} (w : stop = xss.flatten.size) :
filter p (flatten xss) 0 stop = flatten (map (filter p) xss) := by
subst w
induction xss using array₂_induction
simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
List.filter_toArray', List.filter_flatten, List.map_toArray, List.map_map, Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map_toArray]
simp only [flatten_toArray_map, List.size_toArray, List.length_flatten, List.filter_toArray',
List.filter_flatten, List.map_toArray, List.map_map, Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map]
theorem flatten_filter_not_isEmpty {xss : Array (Array α)} :
flatten (xss.filter fun xs => !xs.isEmpty) = xss.flatten := by
@@ -2167,23 +2189,23 @@ theorem flatten_filter_ne_empty [DecidablePred fun xs : Array α => xs ≠ #[]]
induction xss using array₂_induction
rcases xs with l
have this : [l.toArray] = [l].map List.toArray := by simp
simp only [List.push_toArray, flatten_toArray_map_toArray, List.append_toArray]
rw [this, List.map_append, flatten_toArray_map_toArray]
simp only [List.push_toArray, flatten_toArray_map, List.append_toArray]
rw [this, List.map_append, flatten_toArray_map]
simp
theorem flatten_flatten {xss : Array (Array (Array α))} : flatten (flatten xss) = flatten (map flatten xss) := by
induction xss using array₃_induction with
| of xss =>
rw [flatten_toArray_map_toArray]
rw [flatten_toArray_map]
have : (xss.map (fun xs => xs.map List.toArray)).flatten = xss.flatten.map List.toArray := by
induction xss with
| nil => simp
| cons xs xss ih =>
simp only [List.map_cons, List.flatten_cons, ih, List.map_append]
rw [this, flatten_toArray_map_toArray, List.flatten_flatten, List.map_toArray, Array.map_map,
rw [this, flatten_toArray_map, List.flatten_flatten, List.map_toArray, Array.map_map,
List.map_toArray, map_map, Function.comp_def]
simp only [Function.comp_apply, flatten_toArray_map_toArray]
rw [List.map_toArray, Function.comp_def, List.map_map, flatten_toArray_map_toArray]
simp only [Function.comp_apply, flatten_toArray_map]
rw [List.map_toArray, Function.comp_def, List.map_map, flatten_toArray_map]
theorem flatten_eq_push_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
xss.flatten = ys.push y
@@ -2192,13 +2214,13 @@ theorem flatten_eq_push_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
induction xss using array₂_induction with
| of xs =>
rcases ys with ys
rw [flatten_toArray_map_toArray, List.push_toArray, mk.injEq, List.flatten_eq_append_iff]
rw [flatten_toArray_map, List.push_toArray, mk.injEq, List.flatten_eq_append_iff]
constructor
· rintro (as, bs, rfl, rfl, h | as, bs, c, cs, ds, rfl, rfl, h)
· rw [List.singleton_eq_flatten_iff] at h
obtain xs, ys, rfl, h₁, h₂ := h
exact ((as ++ xs).map List.toArray).toArray, #[], (ys.map List.toArray).toArray, by simp,
by simpa using h₂, by rw [flatten_toArray_map_toArray]; simpa
by simpa using h₂, by rw [flatten_toArray_map]; simpa
· rw [List.singleton_eq_append_iff] at h
obtain (h₁, h₂ | h₁, h₂) := h
· simp at h₁
@@ -2231,8 +2253,8 @@ theorem push_eq_flatten_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
-- zs = cs ++ ds.flatten := by sorry
/-- Two arrays of arrays are equal iff their flattens coincide, as well as the sizes of the
arrays. -/
/-- Two arrays of subarrays are equal iff their flattens coincide, as well as the sizes of the
subarrays. -/
theorem eq_iff_flatten_eq {xss₁ xss₂ : Array (Array α)} :
xss₁ = xss₂ xss₁.flatten = xss₂.flatten map size xss₁ = map size xss₂ := by
cases xss₁ using array₂_induction with
@@ -2243,12 +2265,18 @@ theorem eq_iff_flatten_eq {xss₁ xss₂ : Array (Array α)} :
rw [List.map_inj_right]
simp +contextual
theorem flatten_toArray_map_toArray {xss : List (List α)} :
(xss.map List.toArray).toArray.flatten = xss.flatten.toArray := by
simp
/-! ### flatMap -/
theorem flatMap_def {xs : Array α} {f : α Array β} : xs.flatMap f = flatten (map f xs) := by
rcases xs with l
simp [flatten_toArray, Function.comp_def, List.flatMap_def]
@[simp, grind =] theorem flatMap_empty {β} {f : α Array β} : (#[] : Array α).flatMap f = #[] := rfl
theorem flatMap_toList {xs : Array α} {f : α List β} :
xs.toList.flatMap f = (xs.flatMap (fun a => (f a).toArray)).toList := by
rcases xs with l
@@ -2259,7 +2287,6 @@ theorem flatMap_toList {xs : Array α} {f : α → List β} :
rcases xs with l
simp
@[deprecated List.flatMap_toArray_cons (since := "2025-10-29")]
theorem flatMap_toArray_cons {β} {f : α Array β} {a : α} {as : List α} :
(a :: as).toArray.flatMap f = f a ++ as.toArray.flatMap f := by
simp [flatMap]
@@ -2270,7 +2297,6 @@ theorem flatMap_toArray_cons {β} {f : α → Array β} {a : α} {as : List α}
intro cs
induction as generalizing cs <;> simp_all
@[deprecated List.flatMap_toArray (since := "2025-10-29")]
theorem flatMap_toArray {β} {f : α Array β} {as : List α} :
as.toArray.flatMap f = (as.flatMap (fun a => (f a).toList)).toArray := by
simp
@@ -2371,44 +2397,77 @@ theorem flatMap_eq_foldl {f : α → Array β} {xs : Array α} :
@[simp] theorem replicate_one : replicate 1 a = #[a] := rfl
@[deprecated replicate_one (since := "2025-03-18")]
abbrev mkArray_one := @replicate_one
/-- Variant of `replicate_succ` that prepends `a` at the beginning of the array. -/
theorem replicate_succ' : replicate (n + 1) a = #[a] ++ replicate n a := by
apply Array.ext'
simp [List.replicate_succ]
@[deprecated replicate_succ' (since := "2025-03-18")]
abbrev mkArray_succ' := @replicate_succ'
@[simp, grind =] theorem mem_replicate {a b : α} {n} : b replicate n a n 0 b = a := by
unfold replicate
simp only [List.mem_toArray, List.mem_replicate]
@[deprecated mem_replicate (since := "2025-03-18")]
abbrev mem_mkArray := @mem_replicate
@[grind ] theorem eq_of_mem_replicate {a b : α} {n} (h : b replicate n a) : b = a := (mem_replicate.1 h).2
@[deprecated eq_of_mem_mkArray (since := "2025-03-18")]
abbrev eq_of_mem_mkArray := @eq_of_mem_replicate
theorem forall_mem_replicate {p : α Prop} {a : α} {n} :
( b, b replicate n a p b) n = 0 p a := by
cases n <;> simp [mem_replicate]
@[deprecated forall_mem_replicate (since := "2025-03-18")]
abbrev forall_mem_mkArray := @forall_mem_replicate
@[simp] theorem replicate_succ_ne_empty {n : Nat} {a : α} : replicate (n+1) a #[] := by
simp [replicate_succ]
@[deprecated replicate_succ_ne_empty (since := "2025-03-18")]
abbrev mkArray_succ_ne_empty := @replicate_succ_ne_empty
@[simp] theorem replicate_eq_empty_iff {n : Nat} {a : α} : replicate n a = #[] n = 0 := by
cases n <;> simp
@[deprecated replicate_eq_empty_iff (since := "2025-03-18")]
abbrev mkArray_eq_empty_iff := @replicate_eq_empty_iff
@[simp] theorem replicate_inj : replicate n a = replicate m b n = m (n = 0 a = b) := by
rw [ toList_inj]
simp
@[deprecated replicate_inj (since := "2025-03-18")]
abbrev mkArray_inj := @replicate_inj
theorem eq_replicate_of_mem {a : α} {xs : Array α} (h : (b) (_ : b xs), b = a) : xs = replicate xs.size a := by
rw [ toList_inj]
simpa using List.eq_replicate_of_mem (by simpa using h)
@[deprecated eq_replicate_of_mem (since := "2025-03-18")]
abbrev eq_mkArray_of_mem := @eq_replicate_of_mem
theorem eq_replicate_iff {a : α} {n} {xs : Array α} :
xs = replicate n a xs.size = n (b) (_ : b xs), b = a := by
rw [ toList_inj]
simpa using List.eq_replicate_iff (l := xs.toList)
@[deprecated eq_replicate_iff (since := "2025-03-18")]
abbrev eq_mkArray_iff := @eq_replicate_iff
theorem map_eq_replicate_iff {xs : Array α} {f : α β} {b : β} :
xs.map f = replicate xs.size b x xs, f x = b := by
simp [eq_replicate_iff]
@[deprecated map_eq_replicate_iff (since := "2025-03-18")]
abbrev map_eq_mkArray_iff := @map_eq_replicate_iff
@[simp] theorem map_const {xs : Array α} {b : β} : map (Function.const α b) xs = replicate xs.size b :=
map_eq_replicate_iff.mpr fun _ _ => rfl
@@ -2425,86 +2484,143 @@ theorem map_const' {xs : Array α} {b : β} : map (fun _ => b) xs = replicate xs
apply Array.ext'
simp
@[deprecated set_replicate_self (since := "2025-03-18")]
abbrev set_mkArray_self := @set_replicate_self
@[simp] theorem setIfInBounds_replicate_self : (replicate n a).setIfInBounds i a = replicate n a := by
apply Array.ext'
simp
@[deprecated setIfInBounds_replicate_self (since := "2025-03-18")]
abbrev setIfInBounds_mkArray_self := @setIfInBounds_replicate_self
@[simp] theorem replicate_append_replicate : replicate n a ++ replicate m a = replicate (n + m) a := by
apply Array.ext'
simp
@[deprecated replicate_append_replicate (since := "2025-03-18")]
abbrev mkArray_append_mkArray := @replicate_append_replicate
theorem append_eq_replicate_iff {xs ys : Array α} {a : α} :
xs ++ ys = replicate n a
xs.size + ys.size = n xs = replicate xs.size a ys = replicate ys.size a := by
simp [ toList_inj, List.append_eq_replicate_iff]
@[deprecated append_eq_replicate_iff (since := "2025-03-18")]
abbrev append_eq_mkArray_iff := @append_eq_replicate_iff
theorem replicate_eq_append_iff {xs ys : Array α} {a : α} :
replicate n a = xs ++ ys
xs.size + ys.size = n xs = replicate xs.size a ys = replicate ys.size a := by
rw [eq_comm, append_eq_replicate_iff]
@[deprecated replicate_eq_append_iff (since := "2025-03-18")]
abbrev replicate_eq_mkArray_iff := @replicate_eq_append_iff
@[simp] theorem map_replicate : (replicate n a).map f = replicate n (f a) := by
apply Array.ext'
simp
@[deprecated map_replicate (since := "2025-03-18")]
abbrev map_mkArray := @map_replicate
@[grind =] theorem filter_replicate (w : stop = n) :
(replicate n a).filter p 0 stop = if p a then replicate n a else #[] := by
apply Array.ext'
simp only [w]
split <;> simp_all
@[deprecated filter_replicate (since := "2025-03-18")]
abbrev filter_mkArray := @filter_replicate
@[simp] theorem filter_replicate_of_pos (w : stop = n) (h : p a) :
(replicate n a).filter p 0 stop = replicate n a := by
simp [filter_replicate, h, w]
@[deprecated filter_replicate_of_pos (since := "2025-03-18")]
abbrev filter_mkArray_of_pos := @filter_replicate_of_pos
@[simp] theorem filter_replicate_of_neg (w : stop = n) (h : ¬ p a) :
(replicate n a).filter p 0 stop = #[] := by
simp [filter_replicate, h, w]
@[deprecated filter_replicate_of_neg (since := "2025-03-18")]
abbrev filter_mkArray_of_neg := @filter_replicate_of_neg
theorem filterMap_replicate {f : α Option β} (w : stop = n := by simp) :
(replicate n a).filterMap f 0 stop = match f a with | none => #[] | .some b => replicate n b := by
apply Array.ext'
simp only [w, size_replicate, toList_filterMap', toList_replicate, List.filterMap_replicate]
split <;> simp_all
@[deprecated filterMap_replicate (since := "2025-03-18")]
abbrev filterMap_mkArray := @filterMap_replicate
-- This is not a useful `simp` lemma because `b` is unknown.
theorem filterMap_replicate_of_some {f : α Option β} (h : f a = some b) :
(replicate n a).filterMap f = replicate n b := by
simp [filterMap_replicate, h]
@[deprecated filterMap_replicate_of_some (since := "2025-03-18")]
abbrev filterMap_mkArray_of_some := @filterMap_replicate_of_some
@[simp] theorem filterMap_replicate_of_isSome {f : α Option β} (h : (f a).isSome) :
(replicate n a).filterMap f = replicate n (Option.get _ h) := by
match w : f a, h with
| some b, _ => simp [filterMap_replicate, w]
@[deprecated filterMap_replicate_of_isSome (since := "2025-03-18")]
abbrev filterMap_mkArray_of_isSome := @filterMap_replicate_of_isSome
@[simp] theorem filterMap_replicate_of_none {f : α Option β} (h : f a = none) :
(replicate n a).filterMap f = #[] := by
simp [filterMap_replicate, h]
@[deprecated filterMap_replicate_of_none (since := "2025-03-18")]
abbrev filterMap_mkArray_of_none := @filterMap_replicate_of_none
@[simp] theorem flatten_replicate_empty : (replicate n (#[] : Array α)).flatten = #[] := by
rw [ toList_inj]
simp
@[deprecated flatten_replicate_empty (since := "2025-03-18")]
abbrev flatten_mkArray_empty := @flatten_replicate_empty
@[simp] theorem flatten_replicate_singleton : (replicate n #[a]).flatten = replicate n a := by
rw [ toList_inj]
simp
@[deprecated flatten_replicate_singleton (since := "2025-03-18")]
abbrev flatten_mkArray_singleton := @flatten_replicate_singleton
@[simp] theorem flatten_replicate_replicate : (replicate n (replicate m a)).flatten = replicate (n * m) a := by
rw [ toList_inj]
simp
@[deprecated flatten_replicate_replicate (since := "2025-03-18")]
abbrev flatten_mkArray_replicate := @flatten_replicate_replicate
theorem flatMap_replicate {f : α Array β} : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
rw [ toList_inj]
simp [List.flatMap_replicate]
@[deprecated flatMap_replicate (since := "2025-03-18")]
abbrev flatMap_mkArray := @flatMap_replicate
@[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
rw [ List.toArray_replicate, List.isEmpty_toArray]
simp
@[deprecated isEmpty_replicate (since := "2025-03-18")]
abbrev isEmpty_mkArray := @isEmpty_replicate
@[simp] theorem sum_replicate_nat {n : Nat} {a : Nat} : (replicate n a).sum = n * a := by
rw [ List.toArray_replicate, List.sum_toArray]
simp
@[deprecated sum_replicate_nat (since := "2025-03-18")]
abbrev sum_mkArray_nat := @sum_replicate_nat
/-! ### Preliminaries about `swap` needed for `reverse`. -/
@[grind =]
@@ -2546,8 +2662,8 @@ theorem getElem?_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} : (xs.swap i
split <;> rename_i h₃
· simp only [ h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
exact (List.getElem?_reverse' (Eq.trans (by simp +arith) h)).symm
simp only [Nat.succ_le_iff, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
Nat.lt_succ_iff.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
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
@@ -2562,7 +2678,7 @@ theorem getElem?_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} : (xs.swap i
split
· rfl
· rename_i h
simp only [ show k < _ + 1 _ from Nat.lt_succ_iff (n := xs.size - 1), this, Nat.zero_le,
simp only [ show k < _ + 1 _ from Nat.lt_succ (n := xs.size - 1), this, Nat.zero_le,
true_and, Nat.not_lt] at h
rw [List.getElem?_eq_none_iff.2 _, List.getElem?_eq_none_iff.2 (xs.toList.length_reverse _)]
@@ -2691,6 +2807,9 @@ theorem flatten_reverse {xss : Array (Array α)} :
rw [ toList_inj]
simp
@[deprecated reverse_replicate (since := "2025-03-18")]
abbrev reverse_mkArray := @reverse_replicate
/-! ### extract -/
theorem extract_loop_zero {xs ys : Array α} {start : Nat} : extract.loop xs 0 start ys = ys := by
@@ -2710,8 +2829,8 @@ theorem extract_loop_eq_aux {xs ys : Array α} {size start : Nat} :
| zero => rw [extract_loop_zero, extract_loop_zero, append_empty]
| succ size ih =>
if h : start < xs.size then
rw [extract_loop_succ (h := h), ih, push_eq_append]
rw [extract_loop_succ (h := h), ih (ys := #[].push _), push_eq_append, empty_append]
rw [extract_loop_succ (h := h), ih, push_eq_append_singleton]
rw [extract_loop_succ (h := h), ih (ys := #[].push _), push_eq_append_singleton, empty_append]
rw [append_assoc]
else
rw [extract_loop_of_ge (h := Nat.le_of_not_lt h)]
@@ -3328,16 +3447,6 @@ theorem foldr_filterMap {f : α → Option β} {g : β → γγ} {xs : Arra
(xs.filterMap f).foldr g init = xs.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
simp [foldr_filterMap']
theorem foldl_flatMap {f : α Array β} {g : γ β γ} {xs : Array α} {init : γ} :
(xs.flatMap f).foldl g init = xs.foldl (fun acc x => (f x).foldl g acc) init := by
rcases xs with l
simp [List.foldl_flatMap]
theorem foldr_flatMap {f : α Array β} {g : β γ γ} {xs : Array α} {init : γ} :
(xs.flatMap f).foldr g init = xs.foldr (fun x acc => (f x).foldr g acc) init := by
rcases xs with l
simp [List.foldr_flatMap]
theorem foldl_map_hom' {g : α β} {f : α α α} {f' : β β β} {a : α} {xs : Array α}
{stop : Nat} (h : x y, f' (g x) (g y) = g (f x y)) (w : stop = xs.size) :
(xs.map g).foldl f' (g a) 0 stop = g (xs.foldl f a) := by
@@ -3555,6 +3664,11 @@ theorem mem_of_back? {xs : Array α} {a : α} (h : xs.back? = some a) : a ∈ xs
rcases ys with ys
simp only [List.append_toArray, List.back_toArray, List.getLast_append, List.isEmpty_iff,
List.isEmpty_toArray]
split
· rw [dif_pos]
simpa only [List.isEmpty_toArray]
· rw [dif_neg]
simpa only [List.isEmpty_toArray]
theorem back_append_right {xs ys : Array α} (h : 0 < ys.size) :
(xs ++ ys).back (by simp; omega) = ys.back h := by
@@ -3605,9 +3719,15 @@ theorem back?_replicate {a : α} {n : Nat} :
rw [replicate_eq_toArray_replicate]
simp only [List.back?_toArray, List.getLast?_replicate]
@[deprecated back?_replicate (since := "2025-03-18")]
abbrev back?_mkArray := @back?_replicate
@[simp] theorem back_replicate {xs : Array α} (w : 0 < n) : (replicate n xs).back (by simpa using w) = xs := by
simp [back_eq_getElem]
@[deprecated back_replicate (since := "2025-03-18")]
abbrev back_mkArray := @back_replicate
/-! ## Additional operations -/
/-! ### leftpad -/
@@ -3625,6 +3745,9 @@ theorem size_rightpad {n : Nat} {a : α} {xs : Array α} :
theorem elem_push_self [BEq α] [LawfulBEq α] {xs : Array α} {a : α} : (xs.push a).elem a = true := by simp
@[deprecated elem_push_self (since := "2025-04-04")]
abbrev elem_cons_self := @elem_push_self
theorem contains_eq_any_beq [BEq α] {xs : Array α} {a : α} : xs.contains a = xs.any (a == ·) := by
rcases xs with xs
simp [List.contains_eq_any_beq]
@@ -3638,6 +3761,11 @@ theorem contains_iff_exists_mem_beq [BEq α] {xs : Array α} {a : α} :
-- With `LawfulBEq α`, it would be better to use `contains_iff_mem` directly.
grind_pattern contains_iff_exists_mem_beq => xs.contains a
@[grind _=_]
theorem contains_iff_mem [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
xs.contains a a xs := by
simp
@[simp, grind =]
theorem contains_toList [BEq α] {xs : Array α} {x : α} :
xs.toList.contains x = xs.contains x := by
@@ -3697,6 +3825,9 @@ theorem pop_append {xs ys : Array α} :
@[simp, grind =] theorem pop_replicate {n : Nat} {a : α} : (replicate n a).pop = replicate (n - 1) a := by
ext <;> simp
@[deprecated pop_replicate (since := "2025-03-18")]
abbrev pop_mkArray := @pop_replicate
/-! ## Logic -/
/-! ### any / all -/
@@ -3926,10 +4057,16 @@ theorem all_filterMap {xs : Array α} {f : α → Option β} {p : β → Bool} :
(replicate n a).any f = if n = 0 then false else f a := by
induction n <;> simp_all [replicate_succ']
@[deprecated any_replicate (since := "2025-03-18")]
abbrev any_mkArray := @any_replicate
@[simp] theorem all_replicate {n : Nat} {a : α} :
(replicate n a).all f = if n = 0 then true else f a := by
induction n <;> simp_all +contextual [replicate_succ']
@[deprecated all_replicate (since := "2025-03-18")]
abbrev all_mkArray := @all_replicate
/-! ### modify -/
@[simp, grind =] theorem size_modify {xs : Array α} {i : Nat} {f : α α} : (xs.modify i f).size = xs.size := by
@@ -3966,29 +4103,28 @@ theorem getElem_modify_of_ne {xs : Array α} {i : Nat} (h : i ≠ j)
/-! ### swap -/
@[grind =]
theorem getElem_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} (hk : k < (xs.swap i j hi hj).size) :
(xs.swap i j hi hj)[k] = if k = i then xs[j] else if k = j then xs[i] else xs[k]'(by simp_all) := by
simp only [swap_def, getElem_set, eq_comm (a := k)]
split <;> split <;> simp_all
@[simp] theorem getElem_swap_right {xs : Array α} {i j : Nat} {hi hj} :
(xs.swap i j hi hj)[j]'(by simpa using hj) = xs[i] := by
simp +contextual [getElem_swap]
simp [swap_def]
@[simp] theorem getElem_swap_left {xs : Array α} {i j : Nat} {hi hj} :
(xs.swap i j hi hj)[i]'(by simpa using hi) = xs[j] := by
simp [getElem_swap]
simp +contextual [swap_def, getElem_set]
@[simp] theorem getElem_swap_of_ne {xs : Array α} {i j : Nat} {hi hj}
{h : k < (xs.swap i j hi hj).size} (hi' : k i) (hj' : k j) :
(xs.swap i j hi hj)[k] = xs[k]'(by simp_all) := by
simp [getElem_swap, hi', hj']
@[simp] theorem getElem_swap_of_ne {xs : Array α} {i j : Nat} {hi hj} (hp : k < xs.size)
(hi' : k i) (hj' : k j) : (xs.swap i j hi hj)[k]'(xs.size_swap .. |>.symm hp) = xs[k] := by
simp [swap_def, getElem_set, hi'.symm, hj'.symm]
@[deprecated getElem_swap (since := "2025-10-10")]
theorem getElem_swap' {xs : Array α} {i j : Nat} {hi hj} {k : Nat} (hk : k < xs.size) :
(xs.swap i j hi hj)[k]'(by simp_all) = if k = i then xs[j] else if k = j then xs[i] else xs[k] :=
getElem_swap _ _ _
(xs.swap i j hi hj)[k]'(by simp_all) = if k = i then xs[j] else if k = j then xs[i] else xs[k] := by
split
· simp_all only [getElem_swap_left]
· split <;> simp_all
@[grind =]
theorem getElem_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} (hk : k < (xs.swap i j hi hj).size) :
(xs.swap i j hi hj)[k] = if k = i then xs[j] else if k = j then xs[i] else xs[k]'(by simp_all) := by
apply getElem_swap'
@[simp] theorem swap_swap {xs : Array α} {i j : Nat} (hi hj) :
(xs.swap i j hi hj).swap i j ((xs.size_swap ..).symm hi) ((xs.size_swap ..).symm hj) = xs := by
@@ -4009,66 +4145,8 @@ theorem swap_comm {xs : Array α} {i j : Nat} (hi hj) : xs.swap i j hi hj = xs.s
· split <;> simp_all
· split <;> simp_all
/-! ### swapIfInBounds -/
@[grind =] theorem swapIfInBounds_def {xs : Array α} {i j : Nat} :
xs.swapIfInBounds i j = if h₁ : i < xs.size then
if h₂ : j < xs.size then swap xs i j else xs else xs := rfl
@[simp, grind =] theorem size_swapIfInBounds {xs : Array α} {i j : Nat} :
(xs.swapIfInBounds i j).size = xs.size := by
unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
@[grind =] theorem getElem_swapIfInBounds {xs : Array α} {i j k : Nat}
(hk : k < (xs.swapIfInBounds i j).size) :
(xs.swapIfInBounds i j)[k] =
if h₁ : k = i j < xs.size then xs[j]'h₁.2 else if h₂ : k = j i < xs.size then xs[i]'h₂.2
else xs[k]'(by simp_all) := by
rw [size_swapIfInBounds] at hk
unfold swapIfInBounds
split <;> rename_i hi
· split <;> rename_i hj
· simp only [hi, hj, and_true]
exact getElem_swap _ _ _
· simp only [hi, hj, and_true, and_false, dite_false]
split <;> simp_all
· simp only [hi, and_false, dite_false]
split <;> simp_all
@[simp]
theorem getElem_swapIfInBounds_of_size_le_left {xs : Array α} {i j k : Nat} (hi : xs.size i)
(hk : k < (xs.swapIfInBounds i j).size) :
(xs.swapIfInBounds i j)[k] = xs[k]'(Nat.lt_of_lt_of_eq hk size_swapIfInBounds) := by
have h₁ : k i := Nat.ne_of_lt <| Nat.lt_of_lt_of_le hk <|
Nat.le_trans (Nat.le_of_eq (size_swapIfInBounds)) hi
have h₂ : ¬ (i < xs.size) := Nat.not_lt_of_le hi
simp [getElem_swapIfInBounds, h₁, h₂]
@[simp]
theorem getElem_swapIfInBounds_of_size_le_right {xs : Array α} {i j k : Nat} (hj : xs.size j)
(hk : k < (xs.swapIfInBounds i j).size) :
(xs.swapIfInBounds i j)[k] = xs[k]'(Nat.lt_of_lt_of_eq hk size_swapIfInBounds) := by
have h₁ : ¬ (j < xs.size) := Nat.not_lt_of_le hj
have h₂ : k j := Nat.ne_of_lt <| Nat.lt_of_lt_of_le hk <|
Nat.le_trans (Nat.le_of_eq (size_swapIfInBounds)) hj
simp [getElem_swapIfInBounds, h₁, h₂]
@[simp]
theorem getElem_swapIfInBounds_left {xs : Array α} {i j : Nat} (hj : j < xs.size)
(hi : i < (xs.swapIfInBounds i j).size) : (xs.swapIfInBounds i j)[i] = xs[j] := by
simp [getElem_swapIfInBounds, hj]
@[simp]
theorem getElem_swapIfInBounds_right {xs : Array α} {i j : Nat} (hi : i < xs.size)
(hj : j < (xs.swapIfInBounds i j).size) :
(xs.swapIfInBounds i j)[j] = xs[i] := by
simp +contextual [getElem_swapIfInBounds, hi]
@[simp]
theorem getElem_swapIfInBounds_of_ne_of_ne {xs : Array α} {i j k : Nat} (hi : k i) (hj : k j)
(hk : k < (xs.swapIfInBounds i j).size) :
(xs.swapIfInBounds i j)[k] = xs[k]'(Nat.lt_of_lt_of_eq hk size_swapIfInBounds) := by
simp [getElem_swapIfInBounds, hi, hj]
(xs.swapIfInBounds i j).size = xs.size := by unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
/-! ### swapAt -/
@@ -4163,11 +4241,17 @@ theorem replace_extract {xs : Array α} {i : Nat} :
(replicate n a).replace a b = #[b] ++ replicate (n - 1) a := by
cases n <;> simp_all [replicate_succ', replace_append]
@[deprecated replace_replicate_self (since := "2025-03-18")]
abbrev replace_mkArray_self := @replace_replicate_self
@[simp] theorem replace_replicate_ne {a b c : α} (h : !b == a) :
(replicate n a).replace b c = replicate n a := by
rw [replace_of_not_mem]
simp_all
@[deprecated replace_replicate_ne (since := "2025-03-18")]
abbrev replace_mkArray_ne := @replace_replicate_ne
end replace
/-! ### toListRev -/
@@ -4330,15 +4414,14 @@ theorem size_uset {xs : Array α} {v : α} {i : USize} (h : i.toNat < xs.size) :
theorem getElem!_eq_getD [Inhabited α] {xs : Array α} {i} : xs[i]! = xs.getD i default := by
rfl
theorem getElem_eq_getD {xs : Array α} {i} {h : i < xs.size} (fallback : α) :
xs[i]'h = xs.getD i fallback := by
rw [getD_eq_getD_getElem?, getElem_eq_getElem?_get, Option.get_eq_getD]
/-! # mem -/
@[deprecated mem_toList_iff (since := "2025-05-26")]
theorem mem_toList {a : α} {xs : Array α} : a xs.toList a xs := mem_def.symm
@[deprecated not_mem_empty (since := "2025-03-25")]
theorem not_mem_nil (a : α) : ¬ a #[] := nofun
/-! # get lemmas -/
theorem lt_of_getElem {x : α} {xs : Array α} {i : Nat} {hidx : i < xs.size} (_ : xs[i] = x) :
@@ -4350,7 +4433,6 @@ theorem getElem_fin_eq_getElem_toList {xs : Array α} {i : Fin xs.size} : xs[i]
@[simp] theorem ugetElem_eq_getElem {xs : Array α} {i : USize} (h : i.toNat < xs.size) :
xs[i] = xs[i.toNat] := rfl
@[deprecated getElem?_eq_none (since := "2025-10-26")]
theorem getElem?_size_le {xs : Array α} {i : Nat} (h : xs.size i) : xs[i]? = none := by
simp [getElem?_neg, h]
@@ -4370,7 +4452,6 @@ theorem getElem?_push_lt {xs : Array α} {x : α} {i : Nat} (h : i < xs.size) :
(xs.push x)[i]? = some xs[i] := by
rw [getElem?_pos (xs.push x) i (size_push _ Nat.lt_succ_of_lt h), getElem_push_lt]
@[deprecated getElem?_push_size (since := "2025-10-26")]
theorem getElem?_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size]? = some x := by
rw [getElem?_pos (xs.push x) xs.size (size_push _ Nat.lt_succ_self xs.size), getElem_push_eq]
@@ -4389,6 +4470,12 @@ theorem getElem?_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size]? = some
cases xs
simp
/-! ### contains -/
@[deprecated contains_iff (since := "2025-04-07")]
abbrev contains_def [DecidableEq α] {a : α} {xs : Array α} : xs.contains a a xs :=
contains_iff
/-! ### isPrefixOf -/
@[simp, grind =] theorem isPrefixOf_toList [BEq α] {xs ys : Array α} :
@@ -4502,8 +4589,7 @@ theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray
apply ext'
simp
@[deprecated Array.flatten_map_toArray_toArray (since := "2025-10-26")]
theorem flatten_toArray {L : List (List α)} :
@[simp, grind =] theorem flatten_toArray {L : List (List α)} :
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
apply ext'
simp

View File

@@ -6,6 +6,9 @@ Author: Kim Morrison
module
prelude
public import Init.Core
import Init.Data.Array.Basic
import Init.Data.Nat.Lemmas
public import Init.Data.Range.Polymorphic.Iterators
public import Init.Data.Range.Polymorphic.Nat
import Init.Data.Iterators.Consumers

View File

@@ -10,7 +10,9 @@ import all Init.Data.Array.Lex.Basic
public import Init.Data.Array.Lex.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Lex
import Init.Data.Range.Polymorphic.Lemmas
import Init.Data.Range.Polymorphic.NatLemmas
import Init.Data.Order.Lemmas
public section
@@ -34,18 +36,7 @@ grind_pattern _root_.List.le_toArray => l₁.toArray ≤ l₂.toArray
grind_pattern lt_toList => xs.toList < ys.toList
grind_pattern le_toList => xs.toList ys.toList
@[simp]
protected theorem not_lt [LT α] {xs ys : Array α} : ¬ xs < ys ys xs := Iff.rfl
@[deprecated Array.not_lt (since := "2025-10-26")]
protected theorem not_lt_iff_ge [LT α] {xs ys : Array α} : ¬ xs < ys ys xs := Iff.rfl
@[simp]
protected theorem not_le [LT α] {xs ys : Array α} :
¬ xs ys ys < xs :=
Classical.not_not
@[deprecated Array.not_le (since := "2025-10-26")]
protected theorem not_le_iff_gt [LT α] {xs ys : Array α} :
¬ xs ys ys < xs :=
Classical.not_not
@@ -75,11 +66,11 @@ private theorem cons_lex_cons [BEq α] {lt : αα → Bool} {a b : α} {xs
Nat.add_min_add_left, Nat.add_lt_add_iff_left, Std.Rco.forIn'_eq_forIn'_toList]
conv =>
lhs; congr; congr
rw [cons_lex_cons.forIn'_congr_aux Std.Rco.toList_eq_if_roo rfl (fun _ _ _ => rfl)]
rw [cons_lex_cons.forIn'_congr_aux Std.Rco.toList_eq_if rfl (fun _ _ _ => rfl)]
simp only [bind_pure_comp, map_pure]
rw [cons_lex_cons.forIn'_congr_aux (if_pos (by omega)) rfl (fun _ _ _ => rfl)]
simp only [Std.toList_roo_eq_toList_rco_of_isSome_succ? (lo := 0) (h := rfl),
Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_rco_succ_succ,
simp only [Std.toList_Roo_eq_toList_Rco_of_isSome_succ? (lo := 0) (h := rfl),
Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_Rco_succ_succ,
Option.get_some, List.forIn'_cons, List.size_toArray, List.length_cons, List.length_nil,
Nat.lt_add_one, getElem_append_left, List.getElem_toArray, List.getElem_cons_zero]
cases lt a b
@@ -151,7 +142,7 @@ protected theorem lt_of_le_of_lt [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrd
@[deprecated Array.lt_of_le_of_lt (since := "2025-08-01")]
protected theorem lt_of_le_of_lt' [LT α]
[i₁ : Std.Asymm (· < · : α α Prop)]
[i₂ : Std.Trichotomous (· < · : α α Prop)]
[i₂ : Std.Antisymm (¬ · < · : α α Prop)]
[i₃ : Trans (¬ · < · : α α Prop) (¬ · < ·) (¬ · < ·)]
{xs ys zs : Array α} (h₁ : xs ys) (h₂ : ys < zs) : xs < zs :=
letI := LE.ofLT α
@@ -165,7 +156,7 @@ protected theorem le_trans [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α]
@[deprecated Array.le_trans (since := "2025-08-01")]
protected theorem le_trans' [LT α]
[i₁ : Std.Asymm (· < · : α α Prop)]
[i₂ : Std.Trichotomous (· < · : α α Prop)]
[i₂ : Std.Antisymm (¬ · < · : α α Prop)]
[i₃ : Trans (¬ · < · : α α Prop) (¬ · < ·) (¬ · < ·)]
{xs ys zs : Array α} (h₁ : xs ys) (h₂ : ys zs) : xs zs :=
letI := LE.ofLT α
@@ -189,6 +180,12 @@ protected theorem le_total [LT α]
[i : Std.Asymm (· < · : α α Prop)] (xs ys : Array α) : xs ys ys xs :=
List.le_total xs.toList ys.toList
@[simp] protected theorem not_lt [LT α]
{xs ys : Array α} : ¬ xs < ys ys xs := Iff.rfl
@[simp] protected theorem not_le [LT α]
{xs ys : Array α} : ¬ ys xs xs < ys := Classical.not_not
protected theorem le_of_lt [LT α]
[i : Std.Asymm (· < · : α α Prop)]
{xs ys : Array α} (h : xs < ys) : xs ys :=
@@ -196,7 +193,7 @@ protected theorem le_of_lt [LT α]
protected theorem le_iff_lt_or_eq [LT α]
[Std.Irrefl (· < · : α α Prop)]
[Std.Trichotomous (· < · : α α Prop)]
[Std.Antisymm (¬ · < · : α α Prop)]
[Std.Asymm (· < · : α α Prop)]
{xs ys : Array α} : xs ys xs < ys xs = ys := by
simpa using List.le_iff_lt_or_eq (l₁ := xs.toList) (l₂ := ys.toList)
@@ -285,7 +282,7 @@ protected theorem lt_iff_exists [LT α] {xs ys : Array α} :
protected theorem le_iff_exists [LT α]
[Std.Asymm (· < · : α α Prop)]
[Std.Trichotomous (· < · : α α Prop)] {xs ys : Array α} :
[Std.Antisymm (¬ · < · : α α Prop)] {xs ys : Array α} :
xs ys
(xs = ys.take xs.size)
( (i : Nat) (h₁ : i < xs.size) (h₂ : i < ys.size),
@@ -304,7 +301,7 @@ theorem append_left_lt [LT α] {xs ys zs : Array α} (h : ys < zs) :
theorem append_left_le [LT α]
[Std.Asymm (· < · : α α Prop)]
[Std.Trichotomous (· < · : α α Prop)]
[Std.Antisymm (¬ · < · : α α Prop)]
{xs ys zs : Array α} (h : ys zs) :
xs ++ ys xs ++ zs := by
cases xs
@@ -327,9 +324,9 @@ protected theorem map_lt [LT α] [LT β]
protected theorem map_le [LT α] [LT β]
[Std.Asymm (· < · : α α Prop)]
[Std.Trichotomous (· < · : α α Prop)]
[Std.Antisymm (¬ · < · : α α Prop)]
[Std.Asymm (· < · : β β Prop)]
[Std.Trichotomous (· < · : β β Prop)]
[Std.Antisymm (¬ · < · : β β Prop)]
{xs ys : Array α} {f : α β} (w : x y, x < y f x < f y) (h : xs ys) :
map f xs map f ys := by
cases xs

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@@ -6,7 +6,10 @@ Authors: Mario Carneiro, Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Attach
public import Init.Data.Array.OfFn
public import Init.Data.List.MapIdx
import all Init.Data.List.MapIdx
@@ -296,6 +299,9 @@ theorem mapFinIdx_eq_replicate_iff {xs : Array α} {f : (i : Nat) → α → (h
rw [ toList_inj]
simp [List.mapFinIdx_eq_replicate_iff]
@[deprecated mapFinIdx_eq_replicate_iff (since := "2025-03-18")]
abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
@[simp, grind =] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) α (h : i < xs.reverse.size) β} :
xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
rcases xs with l
@@ -435,6 +441,9 @@ theorem mapIdx_eq_replicate_iff {xs : Array α} {f : Nat → α → β} {b : β}
rw [ toList_inj]
simp [List.mapIdx_eq_replicate_iff]
@[deprecated mapIdx_eq_replicate_iff (since := "2025-03-18")]
abbrev mapIdx_eq_mkArray_iff := @mapIdx_eq_replicate_iff
@[simp, grind =] theorem mapIdx_reverse {xs : Array α} {f : Nat α β} :
xs.reverse.mapIdx f = (mapIdx (fun i => f (xs.size - 1 - i)) xs).reverse := by
rcases xs with xs

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@@ -6,6 +6,8 @@ Authors: Leonardo de Moura, Joachim Breitner
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Nat.Linear
public import Init.Data.List.BasicAux
public section

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@@ -6,9 +6,13 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.List.Control
import all Init.Data.List.Control
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Attach
public import Init.Data.List.Monadic
public section

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@@ -6,8 +6,11 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Monadic
public import Init.Data.List.OfFn
public import Init.Data.List.FinRange
public section

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@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.List.Nat.Perm
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
@@ -84,6 +85,9 @@ theorem Perm.size_eq {xs ys : Array α} (p : xs ~ ys) : xs.size = ys.size := by
simp only [perm_iff_toList_perm] at p
simpa using p.length_eq
@[deprecated Perm.size_eq (since := "2025-04-17")]
abbrev Perm.length_eq := @Perm.size_eq
theorem Perm.mem_iff {a : α} {xs ys : Array α} (p : xs ~ ys) : a xs a ys := by
rcases xs with xs
rcases ys with ys
@@ -104,7 +108,7 @@ grind_pattern Perm.append => xs ~ ys, as ~ bs, ys ++ bs
theorem Perm.push (x : α) {xs ys : Array α} (p : xs ~ ys) :
xs.push x ~ ys.push x := by
rw [push_eq_append]
rw [push_eq_append_singleton]
exact p.append .rfl
grind_pattern Perm.push => xs ~ ys, xs.push x

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@@ -6,10 +6,14 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.OfFn
import all Init.Data.Array.OfFn
public import Init.Data.Array.MapIdx
public import Init.Data.Array.Zip
public import Init.Data.List.Nat.Range
public section

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@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
module
prelude
public import Init.GetElem
public import Init.Data.Array.Basic
import Init.Data.Array.GetLit
public import Init.Data.Slice.Basic

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@@ -7,6 +7,7 @@ Authors: David Thrane Christiansen
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Array.Subarray
import all Init.Data.Array.Subarray
public import Init.Omega

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@@ -6,8 +6,10 @@ Authors: Markus Himmel
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.TakeDrop
public section

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@@ -6,8 +6,10 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.TakeDrop
public import Init.Data.List.Zip
public section
@@ -166,6 +168,9 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {as : Array α} {bs : Array
zipWith f (replicate m a) (replicate n b) = replicate (min m n) (f a b) := by
simp [ List.toArray_replicate]
@[deprecated zipWith_replicate (since := "2025-03-18")]
abbrev zipWith_mkArray := @zipWith_replicate
theorem map_uncurry_zip_eq_zipWith {f : α β γ} {as : Array α} {bs : Array β} :
map (Function.uncurry f) (as.zip bs) = zipWith f as bs := by
cases as
@@ -291,6 +296,9 @@ theorem zip_eq_append_iff {as : Array α} {bs : Array β} :
zip (replicate m a) (replicate n b) = replicate (min m n) (a, b) := by
simp [ List.toArray_replicate]
@[deprecated zip_replicate (since := "2025-03-18")]
abbrev zip_mkArray := @zip_replicate
theorem zip_eq_zip_take_min {as : Array α} {bs : Array β} :
zip as bs = zip (as.take (min as.size bs.size)) (bs.take (min as.size bs.size)) := by
cases as
@@ -342,6 +350,9 @@ theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option
zipWithAll f (replicate n a) (replicate n b) = replicate n (f (some a) (some b)) := by
simp [ List.toArray_replicate]
@[deprecated zipWithAll_replicate (since := "2025-03-18")]
abbrev zipWithAll_mkArray := @zipWithAll_replicate
/-! ### zipWithM -/
@[simp, grind =]
@@ -399,4 +410,7 @@ theorem zip_of_prod {as : Array α} {bs : Array β} {xs : Array (α × β)} (hl
unzip (replicate n (a, b)) = (replicate n a, replicate n b) := by
ext1 <;> simp
@[deprecated unzip_replicate (since := "2025-03-18")]
abbrev unzip_mkArray := @unzip_replicate
end Array

18
src/Init/Data/Basic.lean Normal file
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@@ -0,0 +1,18 @@
/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Data.Nat.Basic
public import Init.Data.Fin.Basic
public import Init.Data.List.Basic
public import Init.Data.Char.Basic
public import Init.Data.String.Basic
public import Init.Data.Option.Basic
public import Init.Data.UInt
public import Init.Data.Repr
public import Init.Data.ToString.Basic
public import Init.Data.String.Extra

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@@ -6,8 +6,11 @@ Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex
module
prelude
public import Init.Data.Fin.Basic
public import Init.Data.Nat.Bitwise.Lemmas
public import Init.Data.Nat.Power2
public import Init.Data.Int.Bitwise.Basic
public import Init.Data.BitVec.BasicAux
@[expose] public section
@@ -203,8 +206,8 @@ If `n` is `0`, then one digit is returned. Otherwise, `⌊(n + 3) / 4⌋` digits
-- `Internal` string functions by moving this definition out to a separate file that can live
-- downstream of `Init.Data.String.Basic`.
protected def toHex {n : Nat} (x : BitVec n) : String :=
let s := String.ofList (Nat.toDigits 16 x.toNat)
let t := String.ofList (List.replicate ((n+3) / 4 - String.Internal.length s) '0')
let s := (Nat.toDigits 16 x.toNat).asString
let t := (List.replicate ((n+3) / 4 - String.Internal.length s) '0').asString
String.Internal.append t s
/-- `BitVec` representation. -/

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@@ -6,11 +6,16 @@ Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
module
prelude
public import Init.Data.Nat.Bitwise.Basic
import all Init.Data.Nat.Bitwise.Basic
public import Init.Data.Nat.Mod
public import Init.Data.Int.DivMod
import all Init.Data.Int.DivMod
public import Init.Data.Int.LemmasAux
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.Decidable
public import Init.Data.BitVec.Lemmas
public import Init.Data.BitVec.Folds
import Init.BinderPredicates
@@ -635,11 +640,12 @@ theorem mulRec_eq_mul_signExtend_setWidth (x y : BitVec w) (s : Nat) :
simp only [mulRec_zero_eq, ofNat_eq_ofNat, Nat.reduceAdd]
by_cases y.getLsbD 0
case pos hy =>
simp only [hy, reduceIte, setWidth_one, ofBool_true, ofNat_eq_ofNat]
simp only [hy, reduceIte, setWidth_one_eq_ofBool_getLsb_zero,
ofBool_true, ofNat_eq_ofNat]
rw [setWidth_ofNat_one_eq_ofNat_one_of_lt (by omega)]
simp
case neg hy =>
simp [hy, setWidth_one]
simp [hy, setWidth_one_eq_ofBool_getLsb_zero]
case succ s' hs =>
rw [mulRec_succ_eq, hs]
have heq :
@@ -1024,7 +1030,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
case neg.hrWidth =>
simp only
have hdr' : d (qr.r.shiftConcat (n.getLsbD (qr.wn - 1))) :=
BitVec.not_lt.mp rltd
BitVec.not_lt_iff_le.mp rltd
have hr' : ((qr.r.shiftConcat (n.getLsbD (qr.wn - 1)))).toNat < 2 ^ (qr.wr + 1) := by
apply toNat_shiftConcat_lt_of_lt <;> bv_omega
rw [BitVec.toNat_sub_of_le hdr']
@@ -1032,7 +1038,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
case neg.hqWidth =>
apply toNat_shiftConcat_lt_of_lt <;> omega
case neg.hdiv =>
have rltd' := (BitVec.not_lt.mp rltd)
have rltd' := (BitVec.not_lt_iff_le.mp rltd)
simp only [qr.toNat_shiftRight_sub_one_eq h,
BitVec.toNat_sub_of_le rltd',
toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hrWidth]
@@ -1406,7 +1412,7 @@ theorem eq_iff_eq_of_inv (f : α → BitVec w) (g : BitVec w → α) (h : ∀ x,
have := congrArg g h'
simpa [h] using this
@[deprecated BitVec.ne_intMin_of_msb_eq_false (since := "2025-10-26")]
@[simp]
theorem ne_intMin_of_lt_of_msb_false {x : BitVec w} (hw : 0 < w) (hx : x.msb = false) :
x intMin w := by
have := toNat_lt_of_msb_false hx
@@ -1511,7 +1517,7 @@ theorem sdiv_ne_intMin_of_ne_intMin {x y : BitVec w} (h : x ≠ intMin w) :
by_cases hx : x.msb <;> by_cases hy : y.msb
<;> simp only [hx, hy, neg_ne_intMin_inj]
<;> simp only [Bool.not_eq_true] at hx hy
<;> apply ne_intMin_of_msb_eq_false (by omega)
<;> apply ne_intMin_of_lt_of_msb_false (by omega)
<;> rw [msb_udiv]
<;> try simp only [hx, Bool.false_and]
· simp [h, ne_zero_of_msb_true, hx]
@@ -1623,7 +1629,7 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w b ≠ -1
· have ry := (intMin_udiv_eq_intMin_iff b).mp
simp only [hb1, imp_false] at ry
simp [msb_udiv, ha_intMin, hb1, ry, intMin_udiv_ne_zero_of_ne_zero, hb, hb0]
· have := @BitVec.ne_intMin_of_msb_eq_false w wpos ((-a) / b) (by simp [ha, ha0, ha_intMin])
· have := @BitVec.ne_intMin_of_lt_of_msb_false w ((-a) / b) wpos (by simp [ha, ha0, ha_intMin])
simp [msb_neg, h', this, ha, ha_intMin]
rw [toInt_eq_toNat_of_msb hb, toInt_eq_neg_toNat_neg_of_msb_true ha, Int.neg_tdiv,
Int.tdiv_eq_ediv_of_nonneg (by omega), sdiv_toInt_of_msb_true_of_msb_false]
@@ -1634,7 +1640,7 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w b ≠ -1
rw [toInt_udiv_of_msb ha, toInt_eq_toNat_of_msb ha]
rw [toInt_eq_neg_toNat_neg_of_msb_true hb, Int.tdiv_neg, Int.tdiv_eq_ediv_of_nonneg (by omega)]
· apply sdiv_ne_intMin_of_ne_intMin
apply ne_intMin_of_msb_eq_false (by omega) ha
apply ne_intMin_of_lt_of_msb_false (by omega) ha
· rw [sdiv, Int.tdiv_cases, udiv_eq, neg_eq, if_pos (toInt_nonneg_of_msb_false ha),
if_pos (toInt_nonneg_of_msb_false hb), ha, hb, toInt_udiv_of_msb ha,
toInt_eq_toNat_of_msb ha, toInt_eq_toNat_of_msb hb]
@@ -1926,7 +1932,7 @@ theorem toInt_sub_neg_umod {x y : BitVec w} (hxmsb : x.msb = true) (hymsb : y.ms
rw [Int.bmod_eq_of_le (by omega) (by omega)]
simp only [toInt_eq_toNat_of_msb hymsb, BitVec.toInt_eq_neg_toNat_neg_of_msb_true hxmsb,
Int.dvd_neg] at hdvd
simp only [hdvd, reduceIte, Int.natAbs_natCast]
simp only [hdvd, reduceIte, Int.natAbs_cast]
theorem srem_zero_of_dvd {x y : BitVec w} (h : y.toInt x.toInt) :
x.srem y = 0#w := by

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@@ -6,8 +6,10 @@ Authors: Joe Hendrix, Harun Khan
module
prelude
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.Lemmas
public import Init.Data.Nat.Lemmas
public import Init.Data.Fin.Iterate
public section
@@ -82,7 +84,7 @@ theorem iunfoldr_getLsbD' {f : Fin w → αα × Bool} (state : Nat → α)
intro i
simp only [getLsbD_cons]
have hj2 : j.val w := by simp
cases (Nat.lt_or_eq_of_le (Nat.lt_succ_iff.mp i.isLt)) with
cases (Nat.lt_or_eq_of_le (Nat.lt_succ.mp i.isLt)) with
| inl h3 => simp [(Nat.ne_of_lt h3)]
exact (ih hj2).1 i.val, h3
| inr h3 => simp [h3]

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@@ -6,14 +6,25 @@ Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth B
module
prelude
public import Init.Data.Bool
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.BasicAux
import all Init.Data.BitVec.BasicAux
public import Init.Data.Fin.Lemmas
public import Init.Data.Nat.Lemmas
public import Init.Data.Nat.Div.Lemmas
public import Init.Data.Nat.Mod
public import Init.Data.Nat.Div.Lemmas
public import Init.Data.Int.Bitwise.Lemmas
public import Init.Data.Int.LemmasAux
public import Init.Data.Int.Pow
public import Init.Data.Int.LemmasAux
public import Init.Data.BitVec.Bootstrap
public import Init.Data.Order.Factories
public import Init.Data.List.BasicAux
import Init.Data.List.Lemmas
import Init.Data.BEq
public section
@@ -34,6 +45,14 @@ namespace BitVec
simp only [Bool.and_eq_false_imp, decide_eq_true_eq]
omega
set_option linter.missingDocs false in
@[deprecated getLsbD_of_ge (since := "2025-04-04")]
abbrev getLsbD_ge := @getLsbD_of_ge
set_option linter.missingDocs false in
@[deprecated getMsbD_of_ge (since := "2025-04-04")]
abbrev getMsbD_ge := @getMsbD_of_ge
theorem lt_of_getLsbD {x : BitVec w} {i : Nat} : getLsbD x i = true i < w := by
if h : i < w then
simp [h]
@@ -64,7 +83,6 @@ theorem getElem?_eq_none_iff {l : BitVec w} : l[n]? = none ↔ w ≤ n := by
theorem none_eq_getElem?_iff {l : BitVec w} : none = l[n]? w n := by
simp
@[simp]
theorem getElem?_eq_none {l : BitVec w} (h : w n) : l[n]? = none := getElem?_eq_none_iff.mpr h
theorem getElem?_eq (l : BitVec w) (i : Nat) :
@@ -133,6 +151,9 @@ theorem two_pow_le_toNat_of_getElem_eq_true {i : Nat} {x : BitVec w}
rw [ getElem_eq_testBit_toNat x i hi]
exact hx
@[grind =] theorem msb_eq_getMsbD (x : BitVec w) : x.msb = x.getMsbD 0 := by
simp [BitVec.msb]
@[grind =] theorem getMsb_eq_getLsb (x : BitVec w) (i : Fin w) :
x.getMsb i = x.getLsb w - 1 - i, by omega := by
simp only [getMsb, getLsb]
@@ -159,13 +180,18 @@ theorem getLsbD_eq_getMsbD (x : BitVec w) (i : Nat) : x.getLsbD i = (decide (i <
apply getLsbD_of_ge
omega
@[deprecated getElem?_eq_none (since := "2025-10-29")]
theorem getElem?_of_ge (x : BitVec w) (i : Nat) (ge : w i) : x[i]? = none := by
@[simp] theorem getElem?_of_ge (x : BitVec w) (i : Nat) (ge : w i) : x[i]? = none := by
simp [ge]
@[simp] theorem getMsb?_of_ge (x : BitVec w) (i : Nat) (ge : w i) : getMsb? x i = none := by
simp [getMsb?_eq_getLsb?]; omega
set_option linter.missingDocs false in
@[deprecated getElem?_of_ge (since := "2025-04-04")] abbrev getLsb?_ge := @getElem?_of_ge
set_option linter.missingDocs false in
@[deprecated getMsb?_of_ge (since := "2025-04-04")] abbrev getMsb?_ge := @getMsb?_of_ge
theorem lt_of_getElem?_eq_some (x : BitVec w) (i : Nat) : x[i]? = some b i < w := by
cases h : x[i]? with
| none => simp
@@ -188,6 +214,18 @@ theorem lt_of_isSome_getMsb? (x : BitVec w) (i : Nat) : (getMsb? x i).isSome →
else
simp [Nat.ge_of_not_lt h]
set_option linter.missingDocs false in
@[deprecated lt_of_getElem?_eq_some (since := "2025-04-04")]
abbrev lt_of_getLsb?_eq_some := @lt_of_getElem?_eq_some
set_option linter.missingDocs false in
@[deprecated lt_of_isSome_getElem? (since := "2025-04-04")]
abbrev lt_of_getLsb?_isSome := @lt_of_isSome_getElem?
set_option linter.missingDocs false in
@[deprecated lt_of_isSome_getMsb? (since := "2025-04-04")]
abbrev lt_of_getMsb?_isSome := @lt_of_isSome_getMsb?
theorem getMsbD_eq_getMsb?_getD (x : BitVec w) (i : Nat) :
x.getMsbD i = (x.getMsb? i).getD false := by
rw [getMsbD_eq_getLsbD]
@@ -417,18 +455,12 @@ theorem getElem?_zero_ofNat_one : (BitVec.ofNat (w+1) 1)[0]? = some true := by
-- This does not need to be a `@[simp]` theorem as it is already handled by `getElem?_eq_getElem`.
theorem getElem?_zero_ofBool (b : Bool) : (ofBool b)[0]? = some b := by
simp only [ofBool, ofNat_eq_ofNat, cond_eq_ite]
simp only [ofBool, ofNat_eq_ofNat, cond_eq_if]
split <;> simp_all
@[simp, grind =]
theorem getElem_ofBool_zero {b : Bool} : (ofBool b)[0] = b := by
@[simp, grind =] theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
rw [getElem_eq_iff, getElem?_zero_ofBool]
@[deprecated getElem_ofBool_zero (since := "2025-10-29")]
theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
simp
theorem getElem?_succ_ofBool (b : Bool) (i : Nat) : (ofBool b)[i + 1]? = none := by
simp
@@ -439,6 +471,8 @@ theorem getLsbD_ofBool (b : Bool) (i : Nat) : (ofBool b).getLsbD i = ((i = 0) &&
· simp only [ofBool, ofNat_eq_ofNat, cond_true, getLsbD_ofNat, Bool.and_true]
by_cases hi : i = 0 <;> simp [hi] <;> omega
theorem getElem_ofBool_zero {b : Bool} : (ofBool b)[0] = b := by simp
@[simp]
theorem getElem_ofBool {b : Bool} {h : i < 1}: (ofBool b)[i] = b := by
simp [ getLsbD_eq_getElem]
@@ -521,10 +555,6 @@ theorem toNat_ge_of_msb_true {x : BitVec n} (p : BitVec.msb x = true) : x.toNat
@[grind _=_] theorem msb_eq_getMsbD_zero (x : BitVec w) : x.msb = x.getMsbD 0 := by
cases w <;> simp [getMsbD_eq_getLsbD, msb_eq_getLsbD_last]
@[deprecated msb_eq_getMsbD_zero (since := "2025-10-26")]
theorem msb_eq_getMsbD (x : BitVec w) : x.msb = x.getMsbD 0 := by
simp [BitVec.msb]
/-! ### cast -/
@[simp, grind =] theorem toFin_cast (h : w = v) (x : BitVec w) :
@@ -586,7 +616,7 @@ theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) :=
simp only [toInt_eq_toNat_cond]
split
next g =>
rw [Int.bmod_eq_emod_of_lt] <;> simp only [Int.natCast_emod, toNat_mod_cancel]
rw [Int.bmod_pos] <;> simp only [Int.natCast_emod, toNat_mod_cancel]
omega
next g =>
rw [Int.bmod_neg] <;> simp only [Int.natCast_emod, toNat_mod_cancel]
@@ -994,14 +1024,7 @@ theorem msb_setWidth' (x : BitVec w) (h : w ≤ v) : (x.setWidth' h).msb = (deci
theorem msb_setWidth'' (x : BitVec w) : (x.setWidth (k + 1)).msb = x.getLsbD k := by
simp [BitVec.msb, getMsbD]
/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
theorem setWidth_one {x : BitVec w} :
x.setWidth 1 = ofBool (x.getLsbD 0) := by
ext i
simp [show i = 0 by omega]
/-- zero extending a bitvector to width 1 equals the boolean of the lsb. -/
@[deprecated setWidth_one (since := "2025-10-29")]
theorem setWidth_one_eq_ofBool_getLsb_zero (x : BitVec w) :
x.setWidth 1 = BitVec.ofBool (x.getLsbD 0) := by
ext i h
@@ -1017,6 +1040,12 @@ theorem setWidth_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
have hv := (@Nat.testBit_one_eq_true_iff_self_eq_zero i)
by_cases h : Nat.testBit 1 i = true <;> simp_all
/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
theorem setWidth_one {x : BitVec w} :
x.setWidth 1 = ofBool (x.getLsbD 0) := by
ext i
simp [show i = 0 by omega]
@[simp, grind =] theorem setWidth_ofNat_of_le (h : v w) (x : Nat) : setWidth v (BitVec.ofNat w x) = BitVec.ofNat v x := by
apply BitVec.eq_of_toNat_eq
simp only [toNat_setWidth, toNat_ofNat]
@@ -1056,7 +1085,7 @@ theorem toInt_setWidth' {m n : Nat} (p : m ≤ n) {x : BitVec m} :
@[simp, grind =] theorem toFin_setWidth' {m n : Nat} (p : m n) (x : BitVec m) :
(setWidth' p x).toFin = x.toFin.castLE (Nat.pow_le_pow_right (by omega) (by omega)) := by
ext
rw [setWidth'_eq, toFin_setWidth, Fin.val_ofNat, Fin.val_castLE, val_toFin,
rw [setWidth'_eq, toFin_setWidth, Fin.val_ofNat, Fin.coe_castLE, val_toFin,
Nat.mod_eq_of_lt (by apply BitVec.toNat_lt_twoPow_of_le p)]
theorem toNat_setWidth_of_le {w w' : Nat} {b : BitVec w} (h : w w') : (b.setWidth w').toNat = b.toNat := by
@@ -1190,7 +1219,7 @@ let x' = x.extractLsb' 7 5 = _ _ 9 8 7
@[simp] theorem getLsbD_extract (hi lo : Nat) (x : BitVec n) (i : Nat) :
getLsbD (extractLsb hi lo x) i = (i (hi-lo) && getLsbD x (lo+i)) := by
simp [getLsbD, Nat.lt_succ_iff]
simp [getLsbD, Nat.lt_succ]
@[simp] theorem getLsbD_extractLsb {hi lo : Nat} {x : BitVec n} {i : Nat} :
(extractLsb hi lo x).getLsbD i = (decide (i < hi - lo + 1) && x.getLsbD (lo + i)) := by
@@ -1646,11 +1675,11 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
@[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_natCast, toNat_eq, toNat_ofNatLT, toNat_not,
simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLT, toNat_not,
toNat_ofNat]
cases h : Int.negSucc n % ((2 ^ w : Nat) : Int)
case ofNat =>
rw [Int.ofNat_eq_natCast, Int.negSucc_emod] at h
rw [Int.ofNat_eq_coe, Int.negSucc_emod] at h
· dsimp only
omega
· omega
@@ -1732,6 +1761,9 @@ theorem not_eq_comm {x y : BitVec w} : ~~~ x = y ↔ x = ~~~ y := by
rw [h]
simp
set_option linter.missingDocs false in
@[deprecated getMsbD_not (since := "2025-04-04")] abbrev getMsb_not := @getMsbD_not
@[simp] theorem msb_not {x : BitVec w} : (~~~x).msb = (decide (0 < w) && !x.msb) := by
simp [BitVec.msb]
@@ -2551,6 +2583,10 @@ theorem signExtend_eq_setWidth_of_le (x : BitVec w) {v : Nat} (hv : v ≤ w) :
ext i h
simp [getElem_signExtend, show i < w by omega]
@[deprecated signExtend_eq_setWidth_of_le (since := "2025-03-07")]
theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v w) :
x.signExtend v = x.setWidth v := signExtend_eq_setWidth_of_le x hv
/-- Sign extending to the same bitwidth is a no op. -/
@[simp] theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
rw [signExtend_eq_setWidth_of_le _ (Nat.le_refl _), setWidth_eq]
@@ -3610,6 +3646,9 @@ theorem sub_eq_add_neg {n} (x y : BitVec n) : x - y = x + - y := by
simp only [toNat_sub, toNat_add, toNat_neg, Nat.add_mod_mod]
rw [Nat.add_comm]
set_option linter.missingDocs false in
@[deprecated sub_eq_add_neg (since := "2025-04-04")] abbrev sub_toAdd := @sub_eq_add_neg
theorem add_left_neg (x : BitVec w) : -x + x = 0#w := by
apply toInt_inj.mp
simp [toInt_neg, Int.add_left_neg]
@@ -3649,6 +3688,10 @@ theorem neg_one_eq_allOnes : -1#w = allOnes w := by
have r : (2^w - 1) < 2^w := by omega
simp [Nat.mod_eq_of_lt q, Nat.mod_eq_of_lt r]
set_option linter.missingDocs false in
@[deprecated neg_one_eq_allOnes (since := "2025-04-04")]
abbrev negOne_eq_allOnes := @neg_one_eq_allOnes
theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1#w := by
apply eq_of_toNat_eq
simp only [toNat_neg, toNat_add, toNat_not, toNat_ofNat, Nat.add_mod_mod]
@@ -4065,7 +4108,6 @@ protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x % y < y :=
simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod]
apply Nat.mod_lt
@[deprecated BitVec.not_lt (since := "2025-10-26")]
theorem not_lt_iff_le {x y : BitVec w} : (¬ x < y) y x := by
constructor <;>
(intro h; simp only [lt_def, Nat.not_lt, le_def] at h ; omega)
@@ -4082,7 +4124,7 @@ theorem not_lt_zero {x : BitVec w} : ¬x < 0#w := of_decide_eq_false rfl
theorem le_zero_iff {x : BitVec w} : x 0#w x = 0#w := by
constructor
· intro h
have : x 0 := BitVec.not_lt.mp not_lt_zero
have : x 0 := not_lt_iff_le.mp not_lt_zero
exact Eq.symm (BitVec.le_antisymm this h)
· simp_all
@@ -4105,7 +4147,7 @@ theorem not_allOnes_lt {x : BitVec w} : ¬allOnes w < x := by
theorem allOnes_le_iff {x : BitVec w} : allOnes w x x = allOnes w := by
constructor
· intro h
have : x allOnes w := BitVec.not_lt.mp not_allOnes_lt
have : x allOnes w := not_lt_iff_le.mp not_allOnes_lt
exact Eq.symm (BitVec.le_antisymm h this)
· simp_all
@@ -4651,6 +4693,9 @@ theorem zero_smod {x : BitVec w} : (0#w).smod x = 0#w := by
@[simp, grind =] theorem getLsbD_ofBoolListLE : (ofBoolListLE bs).getLsbD i = bs.getD i false := by
induction bs generalizing i <;> cases i <;> simp_all [ofBoolListLE]
set_option linter.missingDocs false in
@[deprecated getLsbD_ofBoolListLE (since := "2025-04-04")] abbrev getLsb_ofBoolListLE := @getLsbD_ofBoolListLE
@[simp, grind =] theorem getMsbD_ofBoolListLE :
(ofBoolListLE bs).getMsbD i = (decide (i < bs.length) && bs.getD (bs.length - 1 - i) false) := by
simp [getMsbD_eq_getLsbD]
@@ -4721,6 +4766,14 @@ theorem getLsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
apply getLsbD_of_ge
omega
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateLeftAux_of_lt (since := "2025-04-04")]
abbrev getLsbD_rotateLeftAux_of_le := @getLsbD_rotateLeftAux_of_lt
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateLeftAux_of_ge (since := "2025-04-04")]
abbrev getLsbD_rotateLeftAux_of_geq := @getLsbD_rotateLeftAux_of_ge
/-- When `r < w`, we give a formula for `(x.rotateLeft r).getLsbD i`. -/
theorem getLsbD_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
(x.rotateLeft r).getLsbD i =
@@ -4877,6 +4930,14 @@ theorem getLsbD_rotateRightAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
apply getLsbD_of_ge
omega
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateRightAux_of_lt (since := "2025-04-04")]
abbrev getLsbD_rotateRightAux_of_le := @getLsbD_rotateRightAux_of_lt
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateRightAux_of_ge (since := "2025-04-04")]
abbrev getLsbD_rotateRightAux_of_geq := @getLsbD_rotateRightAux_of_ge
/-- `rotateRight` equals the bit fiddling definition of `rotateRightAux` when the rotation amount is
smaller than the bitwidth. -/
theorem rotateRight_eq_rotateRightAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :

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@@ -111,11 +111,35 @@ Needed for confluence of term `(a && b) ↔ a` which reduces to `(a && b) = a` v
@[simp] theorem eq_self_and : {a b : Bool}, (a = (a && b)) (a b) := by decide
@[simp] theorem eq_and_self : {a b : Bool}, (b = (a && b)) (b a) := by decide
@[deprecated and_eq_left_iff_imp (since := "2025-04-04")]
abbrev and_iff_left_iff_imp := @and_eq_left_iff_imp
@[deprecated and_eq_right_iff_imp (since := "2025-04-04")]
abbrev and_iff_right_iff_imp := @and_eq_right_iff_imp
@[deprecated eq_self_and (since := "2025-04-04")]
abbrev iff_self_and := @eq_self_and
@[deprecated eq_and_self (since := "2025-04-04")]
abbrev iff_and_self := @eq_and_self
@[simp] theorem not_and_eq_left_iff_and : {a b : Bool}, ((!a && b) = a) !a !b := by decide
@[simp] theorem and_not_eq_right_iff_and : {a b : Bool}, ((a && !b) = b) !a !b := by decide
@[simp] theorem eq_not_self_and : {a b : Bool}, (a = (!a && b)) !a !b := by decide
@[simp] theorem eq_and_not_self : {a b : Bool}, (b = (a && !b)) !a !b := by decide
@[deprecated not_and_eq_left_iff_and (since := "2025-04-04")]
abbrev not_and_iff_left_iff_imp := @not_and_eq_left_iff_and
@[deprecated and_not_eq_right_iff_and (since := "2025-04-04")]
abbrev and_not_iff_right_iff_imp := @and_not_eq_right_iff_and
@[deprecated eq_not_self_and (since := "2025-04-04")]
abbrev iff_not_self_and := @eq_not_self_and
@[deprecated eq_and_not_self (since := "2025-04-04")]
abbrev iff_and_not_self := @eq_and_not_self
/-! ### or -/
@[simp] theorem or_self_left : (a b : Bool), (a || (a || b)) = (a || b) := by decide
@@ -145,11 +169,35 @@ Needed for confluence of term `(a || b) ↔ a` which reduces to `(a || b) = a` v
@[simp] theorem eq_self_or : {a b : Bool}, (a = (a || b)) (b a) := by decide
@[simp] theorem eq_or_self : {a b : Bool}, (b = (a || b)) (a b) := by decide
@[deprecated or_eq_left_iff_imp (since := "2025-04-04")]
abbrev or_iff_left_iff_imp := @or_eq_left_iff_imp
@[deprecated or_eq_right_iff_imp (since := "2025-04-04")]
abbrev or_iff_right_iff_imp := @or_eq_right_iff_imp
@[deprecated eq_self_or (since := "2025-04-04")]
abbrev iff_self_or := @eq_self_or
@[deprecated eq_or_self (since := "2025-04-04")]
abbrev iff_or_self := @eq_or_self
@[simp] theorem not_or_eq_left_iff_and : {a b : Bool}, ((!a || b) = a) a b := by decide
@[simp] theorem or_not_eq_right_iff_and : {a b : Bool}, ((a || !b) = b) a b := by decide
@[simp] theorem eq_not_self_or : {a b : Bool}, (a = (!a || b)) a b := by decide
@[simp] theorem eq_or_not_self : {a b : Bool}, (b = (a || !b)) a b := by decide
@[deprecated not_or_eq_left_iff_and (since := "2025-04-04")]
abbrev not_or_iff_left_iff_imp := @not_or_eq_left_iff_and
@[deprecated or_not_eq_right_iff_and (since := "2025-04-04")]
abbrev or_not_iff_right_iff_imp := @or_not_eq_right_iff_and
@[deprecated eq_not_self_or (since := "2025-04-04")]
abbrev iff_not_self_or := @eq_not_self_or
@[deprecated eq_or_not_self (since := "2025-04-04")]
abbrev iff_or_not_self := @eq_or_not_self
theorem or_comm : (x y : Bool), (x || y) = (y || x) := by decide
instance : Std.Commutative (· || ·) := or_comm
@@ -514,7 +562,6 @@ theorem exists_bool {p : Bool → Prop} : (∃ b, p b) ↔ p false p true :=
theorem cond_eq_ite {α} (b : Bool) (t e : α) : cond b t e = if b then t else e := by
cases b <;> simp
@[deprecated cond_eq_ite (since := "2025-10-29")]
theorem cond_eq_if : (bif b then x else y) = (if b then x else y) := cond_eq_ite b x y
@[simp] theorem cond_not (b : Bool) (t e : α) : cond (!b) t e = cond b e t := by
@@ -574,6 +621,11 @@ protected theorem cond_false {α : Sort u} {a b : α} : cond false a b = b := co
@[simp] theorem cond_then_self : (c b : Bool), cond c c b = (c || b) := by decide
@[simp] theorem cond_else_self : (c b : Bool), cond c b c = (c && b) := by decide
@[deprecated cond_then_not_self (since := "2025-04-04")] abbrev cond_true_not_same := @cond_then_not_self
@[deprecated cond_else_not_self (since := "2025-04-04")] abbrev cond_false_not_same := @cond_else_not_self
@[deprecated cond_then_self (since := "2025-04-04")] abbrev cond_true_same := @cond_then_self
@[deprecated cond_else_self (since := "2025-04-04")] abbrev cond_false_same := @cond_else_self
theorem cond_pos {b : Bool} {a a' : α} (h : b = true) : (bif b then a else a') = a := by
rw [h, cond_true]
@@ -613,7 +665,7 @@ theorem decide_beq_decide (p q : Prop) [dpq : Decidable (p ↔ q)] [dp : Decidab
end Bool
export Bool (cond_eq_if cond_eq_ite xor and or not)
export Bool (cond_eq_if xor and or not)
/-! ### decide -/

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@@ -6,8 +6,11 @@ Author: Leonardo de Moura
module
prelude
public import Init.Data.Array.DecidableEq
public import Init.Data.UInt.Basic
public import Init.Data.UInt.BasicAux
import all Init.Data.UInt.BasicAux
public import Init.Data.Option.Basic
public import Init.Data.Array.Extract
set_option doc.verso true
@@ -24,6 +27,9 @@ attribute [ext] ByteArray
instance : DecidableEq ByteArray :=
fun _ _ => decidable_of_decidable_of_iff ByteArray.ext_iff.symm
@[deprecated emptyWithCapacity (since := "2025-03-12")]
abbrev mkEmpty := emptyWithCapacity
instance : Inhabited ByteArray where
default := empty
@@ -132,11 +138,6 @@ Copies the bytes with indices {name}`b` (inclusive) to {name}`e` (exclusive) to
def extract (a : ByteArray) (b e : Nat) : ByteArray :=
a.copySlice b empty 0 (e - b)
/--
Appends two byte arrays using fast array primitives instead of converting them into lists and back.
In compiled code, this function replaces calls to {name}`ByteArray.append`.
-/
@[inline]
protected def fastAppend (a : ByteArray) (b : ByteArray) : ByteArray :=
-- we assume that `append`s may be repeated, so use asymptotic growing; use `copySlice` directly to customize
@@ -248,7 +249,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : ByteAr
| ForInStep.yield b => loop i (Nat.le_of_lt h') b
loop as.size (Nat.le_refl _) b
instance [Monad m] : ForIn m ByteArray UInt8 where
instance : ForIn m ByteArray UInt8 where
forIn := ByteArray.forIn
/--

View File

@@ -6,6 +6,7 @@ Author: Markus Himmel
module
prelude
public import Init.Prelude
public import Init.Data.List.Basic
public section

View File

@@ -7,11 +7,10 @@ module
prelude
public import Init.Data.ByteArray.Basic
public import Init.Data.Array.Extract
public section
namespace ByteArray
-- At present the preferred normal form for empty byte arrays is `ByteArray.empty`
@[simp]
theorem emptyc_eq_empty : ( : ByteArray) = ByteArray.empty := rfl
@@ -20,10 +19,10 @@ theorem emptyc_eq_empty : (∅ : ByteArray) = ByteArray.empty := rfl
theorem emptyWithCapacity_eq_empty : ByteArray.emptyWithCapacity 0 = ByteArray.empty := rfl
@[simp]
theorem data_empty : ByteArray.empty.data = #[] := rfl
theorem ByteArray.data_empty : ByteArray.empty.data = #[] := rfl
@[simp]
theorem data_extract {a : ByteArray} {b e : Nat} :
theorem ByteArray.data_extract {a : ByteArray} {b e : Nat} :
(a.extract b e).data = a.data.extract b e := by
simp [extract, copySlice]
by_cases b e
@@ -31,39 +30,39 @@ theorem data_extract {a : ByteArray} {b e : Nat} :
· rw [Array.extract_eq_empty_of_le (by omega), Array.extract_eq_empty_of_le (by omega)]
@[simp]
theorem extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
theorem ByteArray.extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
ext1
simp
@[simp]
theorem extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
theorem ByteArray.extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
ext1
simp [Nat.min_le_left]
theorem fastAppend_eq_copySlice {a b : ByteArray} :
theorem ByteArray.fastAppend_eq_copySlice {a b : ByteArray} :
a.fastAppend b = b.copySlice 0 a a.size b.size false := rfl
@[simp]
theorem _root_.List.toByteArray_append {l l' : List UInt8} :
theorem List.toByteArray_append {l l' : List UInt8} :
(l ++ l').toByteArray = l.toByteArray ++ l'.toByteArray := by
simp [List.toByteArray_append']
@[simp]
theorem toList_data_append {l l' : ByteArray} :
theorem ByteArray.toList_data_append {l l' : ByteArray} :
(l ++ l').data.toList = l.data.toList ++ l'.data.toList := by
simp [ append_eq]
@[simp]
theorem data_append {l l' : ByteArray} :
theorem ByteArray.data_append {l l' : ByteArray} :
(l ++ l').data = l.data ++ l'.data := by
simp [ Array.toList_inj]
@[simp]
theorem size_empty : ByteArray.empty.size = 0 := by
theorem ByteArray.size_empty : ByteArray.empty.size = 0 := by
simp [ ByteArray.size_data]
@[simp]
theorem _root_.List.data_toByteArray {l : List UInt8} :
theorem List.data_toByteArray {l : List UInt8} :
l.toByteArray.data = l.toArray := by
rw [List.toByteArray]
suffices a b, (List.toByteArray.loop a b).data = b.data ++ a.toArray by
@@ -72,159 +71,153 @@ theorem _root_.List.data_toByteArray {l : List UInt8} :
fun_induction List.toByteArray.loop a b with simp_all
@[simp]
theorem _root_.List.size_toByteArray {l : List UInt8} :
theorem List.size_toByteArray {l : List UInt8} :
l.toByteArray.size = l.length := by
simp [ ByteArray.size_data]
@[simp]
theorem _root_.List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
theorem List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
@[simp]
theorem empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
theorem ByteArray.empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
ext1
simp
@[simp]
theorem append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
theorem ByteArray.append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
ext1
simp
@[simp, grind =]
theorem size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
theorem ByteArray.size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
simp [ size_data]
@[simp]
theorem size_eq_zero_iff {a : ByteArray} : a.size = 0 a = ByteArray.empty := by
theorem ByteArray.size_eq_zero_iff {a : ByteArray} : a.size = 0 a = ByteArray.empty := by
refine fun h => ?_, fun h => h ByteArray.size_empty
ext1
simp [ Array.size_eq_zero_iff, h]
theorem getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
theorem ByteArray.getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
a[i] = a.data[i]'(by simpa [ size_data]) := rfl
@[simp]
theorem getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
theorem ByteArray.getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
(hlt : i < a.size) : (a ++ b)[i] = a[i] := by
simp only [getElem_eq_getElem_data, data_append]
rw [Array.getElem_append_left (by simpa)]
theorem getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
theorem ByteArray.getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
(hle : a.size i) : (a ++ b)[i] = b[i - a.size]'(by simp_all; omega) := by
simp only [getElem_eq_getElem_data, data_append]
rw [Array.getElem_append_right (by simpa)]
simp
@[simp]
theorem _root_.List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
theorem List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
l.toByteArray[i]'h = l[i]'(by simp_all) := by
simp [ByteArray.getElem_eq_getElem_data]
theorem _root_.List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
theorem List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
l[i]'h = l.toByteArray[i]'(by simp_all) := by
simp
@[simp]
theorem size_extract {a : ByteArray} {b e : Nat} :
theorem ByteArray.size_extract {a : ByteArray} {b e : Nat} :
(a.extract b e).size = min e a.size - b := by
simp [ size_data]
@[simp]
theorem extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty min j b.size i := by
theorem ByteArray.extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty min j b.size i := by
rw [ size_eq_zero_iff, size_extract]
omega
@[simp]
theorem extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
theorem ByteArray.extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
simp only [extract_eq_empty_iff]
exact Nat.le_trans (Nat.min_le_left _ _) (by simp)
@[simp]
theorem append_eq_empty_iff {a b : ByteArray} :
theorem ByteArray.append_eq_empty_iff {a b : ByteArray} :
a ++ b = ByteArray.empty a = ByteArray.empty b = ByteArray.empty := by
simp [ size_eq_zero_iff, size_append]
@[simp]
theorem toByteArray_eq_empty {l : List UInt8} :
theorem List.toByteArray_eq_empty {l : List UInt8} :
l.toByteArray = ByteArray.empty l = [] := by
simp [ ByteArray.size_eq_zero_iff]
@[simp]
theorem append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
theorem ByteArray.append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
xs ++ ys₁ = xs ++ ys₂ ys₁ = ys₂ := by
simp [ByteArray.ext_iff, Array.append_right_inj]
@[simp]
theorem append_left_inj {xs₁ xs₂ : ByteArray} (ys : ByteArray) :
xs₁ ++ ys = xs₂ ++ ys xs₁ = xs₂ := by
simp [ByteArray.ext_iff, Array.append_left_inj]
@[simp]
theorem extract_append_extract {a : ByteArray} {i j k : Nat} :
theorem ByteArray.extract_append_extract {a : ByteArray} {i j k : Nat} :
a.extract i j ++ a.extract j k = a.extract (min i j) (max j k) := by
ext1
simp
theorem extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
theorem ByteArray.extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
(hi : i j) (hk : j k) :
a.extract i k = a.extract i j ++ a.extract j k := by
simp
rw [Nat.min_eq_left hi, Nat.max_eq_right hk]
theorem append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
theorem ByteArray.append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
simp only [ByteArray.ext_iff, ByteArray.size_data, ByteArray.data_append] at *
exact Array.append_inj_left h hl
theorem extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
theorem ByteArray.extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
(a ++ b).extract i j = b := by
subst hi hj
ext1
simp [ size_data]
theorem extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
theorem ByteArray.extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
(a ++ b).extract 0 i = a := by
subst hi
ext1
simp
theorem extract_append_size_left {a b : ByteArray} {i : Nat} :
theorem ByteArray.extract_append_size_left {a b : ByteArray} {i : Nat} :
(a ++ b).extract i a.size = a.extract i a.size := by
ext1
simp
theorem extract_append_size_add {a b : ByteArray} {i j : Nat} :
theorem ByteArray.extract_append_size_add {a b : ByteArray} {i j : Nat} :
(a ++ b).extract (a.size + i) (a.size + j) = b.extract i j := by
ext1
simp
theorem extract_append {as bs : ByteArray} {i j : Nat} :
theorem ByteArray.extract_append {as bs : ByteArray} {i j : Nat} :
(as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
ext1
simp
theorem extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
theorem ByteArray.extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
(a ++ b).extract (k + i) (k + j) = b.extract i j := by
cases h
rw [extract_append_size_add]
theorem extract_extract {a : ByteArray} {i j k l : Nat} :
theorem ByteArray.extract_extract {a : ByteArray} {i j k l : Nat} :
(a.extract i j).extract k l = a.extract (i + k) (min (i + l) j) := by
ext1
simp
theorem getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
theorem ByteArray.getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
start + i < xs.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
theorem getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
theorem ByteArray.getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
(h) : (b.extract start stop)[i]'h = b[start + i]'(getElem_extract_aux h) := by
simp [getElem_eq_getElem_data]
theorem extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
theorem ByteArray.extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
a.extract i j = a.extract i' j min j a.size - i = min j a.size - i' := by
simp [ByteArray.ext_iff, Array.extract_eq_extract_left]
theorem extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 a.size) :
theorem ByteArray.extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 a.size) :
a.extract i (i + 1) = [a[i]].toByteArray := by
ext
· simp
@@ -233,57 +226,34 @@ theorem extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 ≤ a.size) :
obtain rfl : j = 0 := by simpa using hj'
simp [ByteArray.getElem_eq_getElem_data]
theorem extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 a.size) :
theorem ByteArray.extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 a.size) :
a.extract i (i + 2) = [a[i], a[i + 1]].toByteArray := by
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
extract_add_one (by omega), extract_add_one (by omega)]
simp [ List.toByteArray_append]
theorem extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 a.size) :
theorem ByteArray.extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 a.size) :
a.extract i (i + 3) = [a[i], a[i + 1], a[i + 2]].toByteArray := by
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
extract_add_one (by omega), extract_add_two (by omega)]
simp [ List.toByteArray_append]
theorem extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 a.size) :
theorem ByteArray.extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 a.size) :
a.extract i (i + 4) = [a[i], a[i + 1], a[i + 2], a[i + 3]].toByteArray := by
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
extract_add_one (by omega), extract_add_three (by omega)]
simp [ List.toByteArray_append]
theorem append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
theorem ByteArray.append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
ext1
simp
@[simp]
theorem toList_empty : ByteArray.empty.toList = [] := by
theorem ByteArray.toList_empty : ByteArray.empty.toList = [] := by
simp [ByteArray.toList, ByteArray.toList.loop]
theorem copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
theorem ByteArray.copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
ByteArray.copySlice src srcOff dest destOff len exact =
dest.extract 0 destOff ++ src.extract srcOff (srcOff +len) ++ dest.extract (destOff + min len (src.data.size - srcOff)) dest.data.size := by
ext1
simp [copySlice]
@[simp]
theorem data_set {as : ByteArray} {i : Nat} {h : i < as.size} {a : UInt8} :
(as.set i a h).data = as.data.set i a (by simpa) := by
simp [set]
theorem set_eq_push_extract_append_extract {as : ByteArray} {i : Nat} (h : i < as.size) {a : UInt8} :
as.set i a h = (as.extract 0 i).push a ++ as.extract (i + 1) as.size := by
ext1
simpa using Array.set_eq_push_extract_append_extract _
@[simp]
theorem append_toByteArray_singleton {as : ByteArray} {a : UInt8} :
as ++ [a].toByteArray = as.push a := by
ext1
simp
@[simp]
theorem extract_zero_max_size {a : ByteArray} {i : Nat} : a.extract 0 (max i a.size) = a := by
ext1
simp [Nat.le_max_right]
end ByteArray

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@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Char.Basic
import all Init.Data.Char.Basic
public import Init.Data.UInt.Lemmas
@@ -13,16 +14,12 @@ public section
namespace Char
@[deprecated Char.ext (since := "2025-10-26")]
protected theorem eq_of_val_eq : {a b : Char} a.val = b.val a = b
@[ext] protected theorem ext : {a b : Char} a.val = b.val a = b
| _,_, _,_, rfl => rfl
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
@[deprecated lt_def (since := "2025-10-26")]
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]
@@ -55,12 +52,8 @@ instance leAntisymm : Std.Antisymm (· ≤ · : Char → Char → Prop) where
antisymm _ _ := Char.le_antisymm
-- This instance is useful while setting up instances for `String`.
instance ltTrichotomous : Std.Trichotomous (· < · : Char Char Prop) where
trichotomous _ _ h₁ h₂ := Char.le_antisymm (by simpa using h₂) (by simpa using h₁)
@[deprecated ltTrichotomous (since := "2025-10-27")]
def notLTAntisymm : Std.Antisymm (¬ · < · : Char Char Prop) where
antisymm := Char.ltTrichotomous.trichotomous
antisymm _ _ h₁ h₂ := Char.le_antisymm (by simpa using h₂) (by simpa using h₁)
instance ltAsymm : Std.Asymm (· < · : Char Char Prop) where
asymm _ _ := Char.lt_asymm
@@ -77,9 +70,4 @@ def notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
rw [Char.ofNat, dif_pos]
rfl
@[simp]
theorem toUInt8_val {c : Char} : c.val.toUInt8 = c.toUInt8 := rfl
theorem toString_eq_singleton {c : Char} : c.toString = String.singleton c := rfl
end Char

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@@ -8,6 +8,7 @@ module
prelude
public import Init.Data.Rat.Lemmas
import Init.Data.Int.Bitwise.Lemmas
import Init.Data.Int.DivMod.Lemmas
import Init.Hints
/-!
@@ -287,7 +288,7 @@ theorem toRat_add (x y : Dyadic) : toRat (x + y) = toRat x + toRat y := by
· rename_i h
cases Int.sub_eq_iff_eq_add.mp h
rw [toRat_ofOdd_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
simp only [succ_eq_add_one, Int.ofNat_eq_natCast, Int.add_shiftLeft, Int.shiftLeft_add,
simp only [succ_eq_add_one, Int.ofNat_eq_coe, Int.add_shiftLeft, Int.shiftLeft_add,
Int.natCast_mul, Int.natCast_shiftLeft, Int.shiftLeft_mul_shiftLeft, Int.add_mul]
congr 2 <;> omega
· rename_i h
@@ -438,13 +439,13 @@ theorem toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
rcases h : mkRat a b with n, d, hnz, hr
obtain m, hm, rfl, rfl := Rat.mkRat_num_den hb h
cases prec
· simp only [Rat.toDyadic, Int.ofNat_eq_natCast, Int.toNat_natCast, Int.toNat_neg_natCast,
· simp only [Rat.toDyadic, Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast,
shiftLeft_zero, Int.natCast_mul]
rw [Int.mul_comm d, Int.ediv_ediv_of_nonneg (by simp), Int.shiftLeft_mul,
rw [Int.mul_comm d, Int.ediv_ediv (by simp), Int.shiftLeft_mul,
Int.mul_ediv_cancel _ (by simpa using hm)]
· simp only [Rat.toDyadic, Int.natCast_shiftLeft, Int.negSucc_eq, Int.natCast_add_one,
Int.toNat_neg_natCast, Int.shiftLeft_zero, Int.neg_neg, Int.toNat_natCast, Int.natCast_mul]
rw [Int.mul_comm d, Int.mul_shiftLeft, Int.ediv_ediv_of_nonneg (by simp),
rw [Int.mul_comm d, Int.mul_shiftLeft, Int.ediv_ediv (by simp),
Int.mul_ediv_cancel _ (by simpa using hm)]
theorem toDyadic_eq_ofIntWithPrec (x : Rat) (prec : Int) :
@@ -463,7 +464,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
rw [Rat.floor_def, Int.shiftLeft_eq, Nat.shiftLeft_eq]
match prec with
| .ofNat prec =>
simp only [Int.ofNat_eq_natCast, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
simp only [Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
Nat.mul_one]
have : (2 ^ prec : Rat) = ((2 ^ prec : Nat) : Rat) := by simp
rw [Rat.zpow_natCast, this, Rat.mul_def']
@@ -472,7 +473,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
Rat.den_ofNat, Nat.one_pow, Nat.mul_one]
split
· simp_all
· rw [Int.ediv_ediv_of_nonneg (Int.natCast_nonneg _)]
· rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
congr 1
rw [Int.natCast_ediv, Int.mul_ediv_cancel']
rw [Int.natCast_dvd_natCast]
@@ -495,7 +496,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
simp only [this, Int.mul_one]
split
· simp_all
· rw [Int.ediv_ediv_of_nonneg (Int.natCast_nonneg _)]
· rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
congr 1
rw [Int.natCast_ediv, Int.mul_ediv_cancel']
· simp
@@ -682,11 +683,9 @@ instance : LE Dyadic where
instance : DecidableLT Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
instance : DecidableLE Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
@[simp]
theorem toRat_lt_toRat_iff {x y : Dyadic} : x.toRat < y.toRat x < y := blt_iff_toRat.symm
theorem lt_iff_toRat {x y : Dyadic} : x < y x.toRat < y.toRat := blt_iff_toRat
@[simp]
theorem toRat_le_toRat_iff {x y : Dyadic} : x.toRat y.toRat x y := ble_iff_toRat.symm
theorem le_iff_toRat {x y : Dyadic} : x y x.toRat y.toRat := ble_iff_toRat
@[simp]
protected theorem not_le {x y : Dyadic} : ¬x < y y x := by
@@ -698,20 +697,20 @@ protected theorem not_lt {x y : Dyadic} : ¬x ≤ y ↔ y < x := by
@[simp]
protected theorem le_refl (x : Dyadic) : x x := by
rw [ toRat_le_toRat_iff]
rw [le_iff_toRat]
exact Rat.le_refl
protected theorem le_trans {x y z : Dyadic} (h : x y) (h' : y z) : x z := by
rw [ toRat_le_toRat_iff] at h h'
rw [le_iff_toRat] at h h'
exact Rat.le_trans h h'
protected theorem le_antisymm {x y : Dyadic} (h : x y) (h' : y x) : x = y := by
rw [ toRat_le_toRat_iff] at h h'
rw [le_iff_toRat] at h h'
rw [ toRat_inj]
exact Rat.le_antisymm h h'
protected theorem le_total (x y : Dyadic) : x y y x := by
rw [ toRat_le_toRat_iff, toRat_le_toRat_iff]
rw [le_iff_toRat, le_iff_toRat]
exact Rat.le_total
instance : Std.LawfulOrderLT Dyadic where

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@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.Dyadic.Basic
public import Init.Grind.Ring.Basic
public import Init.Grind.Ordered.Ring
/-! # Internal `grind` algebra instances for `Dyadic`. -/
@@ -52,8 +53,8 @@ instance : NoNatZeroDivisors Dyadic where
instance : OrderedRing Dyadic where
zero_lt_one := by decide
add_le_left_iff _ := by simp [ toRat_le_toRat_iff, Rat.add_le_add_right]
mul_lt_mul_of_pos_left {_ _ _} := by simpa [ toRat_lt_toRat_iff] using Rat.mul_lt_mul_of_pos_left
mul_lt_mul_of_pos_right {_ _ _} := by simpa [ toRat_lt_toRat_iff] using Rat.mul_lt_mul_of_pos_right
add_le_left_iff _ := by simp [le_iff_toRat, Rat.add_le_add_right]
mul_lt_mul_of_pos_left {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_left
mul_lt_mul_of_pos_right {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_right
end Dyadic

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@@ -5,6 +5,7 @@ Authors: Kim Morrison
-/
module
prelude
import Init.Data.Dyadic.Basic
import Init.Data.Dyadic.Round
import Init.Grind.Ordered.Ring
@@ -27,7 +28,7 @@ def invAtPrec (x : Dyadic) (prec : Int) : Dyadic :=
/-- For a positive dyadic `x`, `invAtPrec x prec * x ≤ 1`. -/
theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
invAtPrec x prec * x 1 := by
rw [ toRat_le_toRat_iff]
rw [le_iff_toRat]
rw [toRat_mul]
rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
unfold invAtPrec
@@ -39,19 +40,19 @@ theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
simp only
have h_le : ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat (ofOdd n k hn).toRat.inv := Rat.toRat_toDyadic_le
have h_pos : 0 (ofOdd n k hn).toRat := by
rw [ toRat_lt_toRat_iff, toRat_zero] at hx
rw [lt_iff_toRat, toRat_zero] at hx
exact Rat.le_of_lt hx
calc ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat * (ofOdd n k hn).toRat
(ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := Rat.mul_le_mul_of_nonneg_right h_le h_pos
_ = 1 := by
apply Rat.inv_mul_cancel
rw [ toRat_lt_toRat_iff, toRat_zero] at hx
rw [lt_iff_toRat, toRat_zero] at hx
exact Rat.ne_of_gt hx
/-- For a positive dyadic `x`, `1 < (invAtPrec x prec + 2^(-prec)) * x`. -/
theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
1 < (invAtPrec x prec + ofIntWithPrec 1 prec) * x := by
rw [ toRat_lt_toRat_iff]
rw [lt_iff_toRat]
rw [toRat_mul]
rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
unfold invAtPrec
@@ -64,12 +65,12 @@ theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
have h_le : (ofOdd n k hn).toRat.inv < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat :=
Rat.lt_toRat_toDyadic_add
have h_pos : 0 < (ofOdd n k hn).toRat := by
rwa [ toRat_lt_toRat_iff, toRat_zero] at hx
rwa [lt_iff_toRat, toRat_zero] at hx
calc
1 = (ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := by
symm
apply Rat.inv_mul_cancel
rw [ toRat_lt_toRat_iff, toRat_zero] at hx
rw [lt_iff_toRat, toRat_zero] at hx
exact Rat.ne_of_gt hx
_ < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat * (ofOdd n k hn).toRat :=
Rat.mul_lt_mul_of_pos_right h_le h_pos

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@@ -8,6 +8,7 @@ module
prelude
public import Init.Data.Dyadic.Basic
import all Init.Data.Dyadic.Instances
import Init.Data.Int.Bitwise.Lemmas
import Init.Grind.Ordered.Rat
import Init.Grind.Ordered.Field
@@ -28,7 +29,7 @@ theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
match h : k - prec with
| .ofNat l =>
dsimp
rw [ofOdd_eq_ofIntWithPrec, toRat_le_toRat_iff]
rw [ofOdd_eq_ofIntWithPrec, le_iff_toRat]
replace h : k = Int.ofNat l + prec := by omega
subst h
simp only [toRat_ofIntWithPrec_eq_mul_two_pow]
@@ -36,7 +37,7 @@ theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
refine Lean.Grind.OrderedRing.mul_le_mul_of_nonneg_right ?_ (Rat.zpow_nonneg (by decide))
rw [Int.shiftRight_eq_div_pow]
rw [ Lean.Grind.Field.IsOrdered.mul_le_mul_iff_of_pos_right (c := 2^(Int.ofNat l)) (Rat.zpow_pos (by decide))]
simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_natCast]
simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_coe]
rw [Rat.mul_assoc, Rat.zpow_add (by decide), Int.add_left_neg, Rat.zpow_zero, Rat.mul_one]
have : (2 : Rat) ^ (l : Int) = (2 ^ l : Int) := by
rw [Rat.zpow_natCast, Rat.intCast_pow, Rat.intCast_ofNat]

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@@ -246,11 +246,6 @@ instance neg (n : Nat) : Neg (Fin n) :=
theorem neg_def (a : Fin n) : -a = (n - a) % n, Nat.mod_lt _ a.pos := rfl
-- Later we give another version called `Fin.val_neg` that splits on `a = 0`.
protected theorem val_neg' (a : Fin n) : ((-a : Fin n) : Nat) = (n - a) % n :=
rfl
@[deprecated Fin.val_neg' (since := "2025-11-21")]
protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : Nat) = (n - a) % n :=
rfl

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@@ -7,6 +7,7 @@ module
prelude
public import Init.Data.Nat.Bitwise
public import Init.Data.Fin.Basic
public section

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@@ -6,6 +6,7 @@ Authors: François G. Dorais
module
prelude
public import Init.Data.Nat.Linear
public import Init.Control.Lawful.Basic
public import Init.Data.Fin.Lemmas

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@@ -7,6 +7,7 @@ module
prelude
public import Init.PropLemmas
public import Init.Data.Fin.Basic
public section

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@@ -8,6 +8,10 @@ module
prelude
public import Init.Data.Nat.Lemmas
public import Init.Ext
public import Init.ByCases
public import Init.Conv
public import Init.Omega
public import Init.Data.Order.Factories
import Init.Data.Order.Lemmas
@[expose] public section
@@ -16,25 +20,17 @@ open Std
namespace Fin
@[simp, grind =] theorem ofNat_zero (n : Nat) [NeZero n] : Fin.ofNat n 0 = 0 := rfl
@[simp] theorem ofNat_zero (n : Nat) [NeZero n] : Fin.ofNat n 0 = 0 := rfl
@[deprecated ofNat_zero (since := "2025-05-28")] abbrev ofNat'_zero := @ofNat_zero
theorem mod_def (a m : Fin n) : a % m = Fin.mk (a.val % m.val) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
rfl
theorem val_mod (a m : Fin n) : (a % m).val = a.val % m.val := rfl
theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a.val * b.val) % n) (Nat.mod_lt _ a.pos) := rfl
theorem val_mul (a b : Fin n) : (a * b).val = (a.val * b.val) % n := rfl
theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b.val) + a.val) % n) (Nat.mod_lt _ a.pos) := rfl
@[grind =]
theorem val_sub (a b : Fin n) : (a - b).val = ((n - b.val) + a.val) % n := rfl
@[grind ]
theorem pos' : [Nonempty (Fin n)], 0 < n | i => i.pos
@[simp] theorem is_lt (a : Fin n) : (a : Nat) < n := a.2
@@ -46,8 +42,7 @@ 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, grind ext]
protected theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
@[ext] protected theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
theorem val_ne_iff {a b : Fin n} : a.1 b.1 a b := not_congr val_inj
@@ -78,7 +73,7 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
@[deprecated val_ofNat (since := "2025-05-28")] abbrev val_ofNat' := @val_ofNat
@[simp, grind =] theorem ofNat_self {n : Nat} [NeZero n] : Fin.ofNat n n = 0 := by
@[simp] theorem ofNat_self {n : Nat} [NeZero n] : Fin.ofNat n n = 0 := by
ext
simp
congr
@@ -98,7 +93,7 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
@[simp] theorem div_val (a b : Fin n) : (a / b).val = a.val / b.val :=
rfl
@[simp, grind =] theorem modn_val (a : Fin n) (b : Nat) : (a.modn b).val = a.val % b :=
@[simp] theorem modn_val (a : Fin n) (b : Nat) : (a.modn b).val = a.val % b :=
rfl
@[simp] theorem val_eq_zero (a : Fin 1) : a.val = 0 :=
@@ -166,7 +161,6 @@ theorem le_def {a b : Fin n} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
theorem lt_def {a b : Fin n} : a < b a.1 < b.1 := .rfl
@[deprecated lt_def (since := "2025-10-26")]
theorem lt_iff_val_lt_val {a b : Fin n} : a < b a.val < b.val := Iff.rfl
@[simp] protected theorem not_le {a b : Fin n} : ¬ a b b < a := Nat.not_le
@@ -268,15 +262,13 @@ instance : LawfulOrderLT (Fin n) where
lt_iff := by
simp [ Fin.not_le, Decidable.imp_iff_not_or, Std.Total.total]
@[simp] theorem val_rev (i : Fin n) : (rev i).val = n - (i + 1) := rfl
grind_pattern val_rev => i.rev
@[simp, grind =] theorem val_rev (i : Fin n) : (rev i).val = n - (i + 1) := rfl
@[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := Fin.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
simp only [le_def, val_rev, Nat.sub_le_sub_iff_left (Nat.succ_le_iff.2 j.is_lt)]
simp only [le_def, val_rev, Nat.sub_le_sub_iff_left (Nat.succ_le.2 j.is_lt)]
exact Nat.succ_le_succ_iff
@[simp] theorem rev_inj {i j : Fin n} : rev i = rev j i = j :=
@@ -295,8 +287,6 @@ theorem rev_eq {n a : Nat} (i : Fin (n + 1)) (h : n = a + i) :
@[simp] theorem val_last (n : Nat) : (last n).1 = n := rfl
grind_pattern val_last => last n
@[simp] theorem last_zero : (Fin.last 0 : Fin 1) = 0 := by
ext
simp
@@ -397,17 +387,14 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
rw [Fin.lt_def, val_add, val_zero, val_one, Nat.mod_eq_of_lt h]
exact Nat.zero_lt_succ _
@[deprecated zero_lt_one (since := "2025-10-26")]
theorem one_pos : (0 : Fin (n + 2)) < 1 := Nat.succ_pos 0
theorem zero_ne_one : (0 : Fin (n + 2)) 1 := Fin.ne_of_lt zero_lt_one
theorem zero_ne_one : (0 : Fin (n + 2)) 1 := Fin.ne_of_lt one_pos
/-! ### succ and casts into larger Fin types -/
@[simp] theorem val_succ (j : Fin n) : (j.succ : Nat) = j + 1 := rfl
grind_pattern val_succ => j.succ
@[simp] theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by
simp [Fin.lt_def]
@@ -468,18 +455,12 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) 1 :=
Fin.ne_of_gt (one_lt_succ_succ a)
@[simp, grind =] theorem val_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : Nat) = i := rfl
@[deprecated val_castLT (since := "2025-11-21")]
theorem coe_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : Nat) = i := rfl
@[simp] theorem coe_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : Nat) = i := rfl
@[simp] theorem castLT_mk (i n m : Nat) (hn : i < n) (hm : i < m) : castLT i, hn hm = i, hm :=
rfl
@[simp, grind =] theorem val_castLE (h : n m) (i : Fin n) : (castLE h i : Nat) = i := rfl
@[deprecated val_castLE (since := "2025-11-21")]
theorem coe_castLE (h : n m) (i : Fin n) : (castLE h i : Nat) = i := rfl
@[simp, grind =] theorem coe_castLE (h : n m) (i : Fin n) : (castLE h i : Nat) = i := rfl
@[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
@@ -491,16 +472,13 @@ theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : Nat) = i := rfl
@[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 :=
Fin.ext (by simp only [val_castLE])
Fin.ext (by simp only [coe_castLE])
@[simp] theorem castLE_comp_castLE {k m n} (km : k m) (mn : m n) :
Fin.castLE mn Fin.castLE km = Fin.castLE (Nat.le_trans km mn) :=
funext (castLE_castLE km mn)
@[simp, grind =] theorem val_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
@[deprecated val_cast (since := "2025-11-21")]
theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
@[simp] theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
@[simp] theorem cast_castLE {k m n} (km : k m) (mn : m = n) (i : Fin k) :
Fin.cast mn (i.castLE km) = i.castLE (mn km) :=
@@ -513,7 +491,7 @@ theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
@[simp] theorem cast_zero [NeZero n] [NeZero m] (h : n = m) : Fin.cast h 0 = 0 := rfl
@[simp] theorem cast_last {n' : Nat} {h : n + 1 = n' + 1} : (last n).cast h = last n' :=
Fin.ext (by rw [val_cast, val_last, val_last, Nat.succ.inj h])
Fin.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) : Fin.cast h i, hn = i, h hn := rfl
@@ -528,10 +506,7 @@ theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
theorem castLE_of_eq {m n : Nat} (h : m = n) {h' : m n} : castLE h' = Fin.cast h := rfl
@[simp, grind =] theorem val_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
@[deprecated val_castAdd (since := "2025-11-21")]
theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
@[simp] theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
@[simp] theorem castAdd_zero : (castAdd 0 : Fin n Fin (n + 0)) = Fin.cast rfl := rfl
@@ -567,18 +542,15 @@ the reverse direction. -/
theorem succ_cast_eq {n' : Nat} (i : Fin n) (h : n = n') :
(i.cast h).succ = i.succ.cast (by rw [h]) := rfl
@[simp, grind =] theorem val_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
@[simp] theorem coe_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
@[deprecated val_castSucc (since := "2025-11-21")]
theorem coe_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc i, h = i, Nat.lt_succ_of_lt h := rfl
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc i, h = i, Nat.lt.step h := rfl
@[simp] theorem cast_castSucc {n' : Nat} {h : n + 1 = n' + 1} {i : Fin n} :
i.castSucc.cast h = (i.cast (Nat.succ.inj h)).castSucc := rfl
theorem castSucc_lt_succ {i : Fin n} : i.castSucc < i.succ :=
lt_def.2 <| by simp only [val_castSucc, val_succ, Nat.lt_succ_self]
theorem castSucc_lt_succ (i : Fin n) : i.castSucc < 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 j.castSucc i < j.succ := by
simpa only [lt_def, le_def] using Nat.add_one_le_add_one_iff.symm
@@ -617,12 +589,8 @@ theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < i.castSucc := by
theorem castSucc_ne_zero_iff [NeZero n] {a : Fin n} : a.castSucc 0 a 0 :=
not_congr <| castSucc_eq_zero_iff
@[simp, grind _=_]
theorem castSucc_succ (i : Fin n) : i.succ.castSucc = i.castSucc.succ := rfl
@[deprecated castSucc_succ (since := "2025-10-29")]
theorem castSucc_fin_succ (n : Nat) (j : Fin n) :
j.succ.castSucc = (j.castSucc).succ := by simp
j.succ.castSucc = (j.castSucc).succ := by simp [Fin.ext_iff]
@[simp]
theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
@@ -630,9 +598,8 @@ theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
· exact a.elim0
· simp [Fin.ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
@[deprecated castSucc_lt_succ (since := "2025-10-29")]
theorem lt_succ {a : Fin n} : a.castSucc < a.succ := by
rw [castSucc, lt_def, val_castAdd, val_succ]; exact Nat.lt_succ_self a.val
rw [castSucc, lt_def, coe_castAdd, val_succ]; exact Nat.lt_succ_self a.val
theorem exists_castSucc_eq {n : Nat} {i : Fin (n + 1)} : ( j, castSucc j = i) i last n :=
fun j, hj => hj Fin.ne_of_lt j.castSucc_lt_last,
@@ -640,10 +607,7 @@ theorem exists_castSucc_eq {n : Nat} {i : Fin (n + 1)} : (∃ j, castSucc j = i)
theorem succ_castSucc {n : Nat} (i : Fin n) : i.castSucc.succ = i.succ.castSucc := rfl
@[simp, grind =] theorem val_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
@[deprecated val_addNat (since := "2025-11-21")]
theorem coe_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
@[simp] theorem coe_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
@[simp] theorem addNat_zero (n : Nat) (i : Fin n) : addNat i 0 = i := by
ext
@@ -671,10 +635,7 @@ theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
(addNat i m').cast h = addNat i m :=
Fin.ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
@[simp, grind =] theorem val_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
@[deprecated val_natAdd (since := "2025-11-21")]
theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
@[simp] theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
@[simp] theorem natAdd_mk (n i : Nat) (hi : i < m) :
natAdd n i, hi = n + i, Nat.add_lt_add_left hi n := rfl
@@ -731,7 +692,7 @@ theorem natAdd_castSucc {m n : Nat} {i : Fin m} : natAdd n (castSucc i) = castSu
omega
theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := Fin.ext <| by
rw [val_rev, val_castAdd, val_addNat, val_rev, Nat.sub_add_comm (Nat.succ_le_of_lt k.is_lt)]
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
rw [ rev_rev (castAdd ..), rev_castAdd, rev_rev]
@@ -740,6 +701,9 @@ theorem rev_castSucc (k : Fin n) : rev (castSucc k) = succ (rev k) := k.rev_cast
theorem rev_succ (k : Fin n) : rev (succ k) = castSucc (rev k) := k.rev_addNat 1
@[simp, grind _=_]
theorem castSucc_succ (i : Fin n) : i.succ.castSucc = i.castSucc.succ := rfl
@[simp, grind =]
theorem castLE_refl (h : n n) (i : Fin n) : i.castLE h = i := rfl
@@ -753,12 +717,7 @@ theorem castSucc_natAdd (n : Nat) (i : Fin k) :
/-! ### pred -/
@[simp] theorem val_pred (j : Fin (n + 1)) (h : j 0) : (j.pred h : Nat) = j - 1 := rfl
grind_pattern val_pred => j.pred h
@[deprecated val_pred (since := "2025-11-21")]
theorem coe_pred (j : Fin (n + 1)) (h : j 0) : (j.pred h : Nat) = j - 1 := rfl
@[simp] theorem coe_pred (j : Fin (n + 1)) (h : j 0) : (j.pred h : Nat) = j - 1 := rfl
@[simp] theorem succ_pred : (i : Fin (n + 1)) (h : i 0), (i.pred h).succ = i
| 0, _, hi => by simp only [mk_zero, ne_eq, not_true] at hi
@@ -776,7 +735,7 @@ 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, val_pred, Nat.add_sub_cancel]
simp only [Fin.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 _
@@ -799,17 +758,14 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
| i + 1, hi, j + 1, hj, ha, hb => by simp [Fin.ext_iff]
@[simp] theorem pred_one {n : Nat} :
Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt zero_lt_one)) = 0 := rfl
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, val_pred, val_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
rw [Fin.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, grind =] theorem val_subNat (i : Fin (n + m)) (h : m i) : (i.subNat m h : Nat) = i - m := rfl
@[deprecated val_subNat (since := "2025-11-21")]
theorem coe_subNat (i : Fin (n + m)) (h : m i) : (i.subNat m h : Nat) = i - m := rfl
@[simp] theorem coe_subNat (i : Fin (n + m)) (h : m i) : (i.subNat m h : Nat) = i - m := rfl
@[simp] theorem subNat_mk {i : Nat} (h₁ : i < n + m) (h₂ : m i) :
subNat m i, h₁ h₂ = i - m, Nat.sub_lt_right_of_lt_add h₂ h₁ := rfl
@@ -874,11 +830,11 @@ step. `Fin.succRec` is a version of this induction principle that takes the `Fin
(zero : n, motive (n + 1) 0) (succ : n i, motive n i motive (Nat.succ n) i.succ) :
motive n i := i.succRec zero succ
@[simp, grind =] theorem succRecOn_zero {motive : n, Fin n Sort _} {zero succ} (n) :
@[simp] theorem succRecOn_zero {motive : n, Fin n Sort _} {zero succ} (n) :
@Fin.succRecOn (n + 1) 0 motive zero succ = zero n := by
cases n <;> rfl
@[simp, grind =] theorem succRecOn_succ {motive : n, Fin n Sort _} {zero succ} {n} (i : Fin n) :
@[simp] theorem succRecOn_succ {motive : n, Fin n Sort _} {zero succ} {n} (i : Fin n) :
@Fin.succRecOn (n + 1) i.succ motive zero succ = succ n i (Fin.succRecOn i zero succ) := by
cases i; rfl
@@ -906,11 +862,11 @@ where
| 0, hi => by rwa [Fin.mk_zero]
| i+1, hi => succ i, Nat.lt_of_succ_lt_succ hi (go i (Nat.lt_of_succ_lt hi))
@[simp, grind =] theorem induction_zero {motive : Fin (n + 1) Sort _} (zero : motive 0)
@[simp] theorem induction_zero {motive : Fin (n + 1) Sort _} (zero : motive 0)
(hs : i : Fin n, motive (castSucc i) motive i.succ) :
(induction zero hs : i : Fin (n + 1), motive i) 0 = zero := rfl
@[simp, grind =] theorem induction_succ {motive : Fin (n + 1) Sort _} (zero : motive 0)
@[simp] theorem induction_succ {motive : Fin (n + 1) Sort _} (zero : motive 0)
(succ : i : Fin n, motive (castSucc i) motive i.succ) (i : Fin n) :
induction (motive := motive) zero succ i.succ = succ i (induction zero succ (castSucc i)) := rfl
@@ -942,13 +898,13 @@ The corresponding induction principle is `Fin.induction`.
(zero : motive 0) (succ : i : Fin n, motive i.succ) :
i : Fin (n + 1), motive i := induction zero fun i _ => succ i
@[simp, grind =] theorem cases_zero {n} {motive : Fin (n + 1) Sort _} {zero succ} :
@[simp] theorem cases_zero {n} {motive : Fin (n + 1) Sort _} {zero succ} :
@Fin.cases n motive zero succ 0 = zero := rfl
@[simp, grind =] theorem cases_succ {n} {motive : Fin (n + 1) Sort _} {zero succ} (i : Fin n) :
@[simp] theorem cases_succ {n} {motive : Fin (n + 1) Sort _} {zero succ} (i : Fin n) :
@Fin.cases n motive zero succ i.succ = succ i := rfl
@[simp, grind =] theorem cases_succ' {n} {motive : Fin (n + 1) Sort _} {zero succ}
@[simp] theorem cases_succ' {n} {motive : Fin (n + 1) Sort _} {zero succ}
{i : Nat} (h : i + 1 < n + 1) :
@Fin.cases n motive zero succ i.succ, h = succ i, Nat.lt_of_succ_lt_succ h := rfl
@@ -998,7 +954,7 @@ For the induction:
| j + 1 => go j (by omega) (by omega) (cast j, by omega x)
go _ _ (by omega) last
@[simp, grind =] theorem reverseInduction_last {n : Nat} {motive : Fin (n + 1) Sort _} {zero succ} :
@[simp] theorem reverseInduction_last {n : Nat} {motive : Fin (n + 1) Sort _} {zero succ} :
(reverseInduction zero succ (Fin.last n) : motive (Fin.last n)) = zero := by
rw [reverseInduction, reverseInduction.go]; simp
@@ -1015,7 +971,7 @@ private theorem reverseInduction_castSucc_aux {n : Nat} {motive : Fin (n + 1)
dsimp only
rw [ih _ _ (by omega), eq_comm, reverseInduction.go, dif_neg (by change i.1 + 1 _; omega)]
@[simp, grind =] theorem reverseInduction_castSucc {n : Nat} {motive : Fin (n + 1) Sort _} {zero succ}
@[simp] theorem reverseInduction_castSucc {n : Nat} {motive : Fin (n + 1) Sort _} {zero succ}
(i : Fin n) : reverseInduction (motive := motive) zero succ (castSucc i) =
succ i (reverseInduction zero succ i.succ) := by
rw [reverseInduction, reverseInduction_castSucc_aux _ _ _ i.isLt, reverseInduction]
@@ -1034,11 +990,11 @@ The corresponding induction principle is `Fin.reverseInduction`.
(cast : i : Fin n, motive (castSucc i)) (i : Fin (n + 1)) : motive i :=
reverseInduction last (fun i _ => cast i) i
@[simp, grind =] theorem lastCases_last {n : Nat} {motive : Fin (n + 1) Sort _} {last cast} :
@[simp] theorem lastCases_last {n : Nat} {motive : Fin (n + 1) Sort _} {last cast} :
(Fin.lastCases last cast (Fin.last n) : motive (Fin.last n)) = last :=
reverseInduction_last ..
@[simp, grind =] theorem lastCases_castSucc {n : Nat} {motive : Fin (n + 1) Sort _} {last cast}
@[simp] theorem lastCases_castSucc {n : Nat} {motive : Fin (n + 1) Sort _} {last cast}
(i : Fin n) : (Fin.lastCases last cast (Fin.castSucc i) : motive (Fin.castSucc i)) = cast i :=
reverseInduction_castSucc ..
@@ -1058,11 +1014,11 @@ as `Fin.natAdd m (j : Fin n)`.
if hi : (i : Nat) < m then (castAdd_castLT n i hi) (left (castLT i hi))
else (natAdd_subNat_cast (Nat.le_of_not_lt hi)) (right _)
@[simp, grind =] theorem addCases_left {m n : Nat} {motive : Fin (m + n) Sort _} {left right} (i : Fin m) :
@[simp] theorem addCases_left {m n : Nat} {motive : Fin (m + n) Sort _} {left right} (i : Fin m) :
addCases (motive := motive) left right (Fin.castAdd n i) = left i := by
rw [addCases, dif_pos (castAdd_lt _ _)]; rfl
@[simp, grind =]
@[simp]
theorem addCases_right {m n : Nat} {motive : Fin (m + n) Sort _} {left right} (i : Fin n) :
addCases (motive := motive) left right (natAdd m i) = right i := by
have : ¬(natAdd m i : Nat) < m := Nat.not_lt.2 (le_coe_natAdd ..)
@@ -1095,7 +1051,6 @@ theorem add_ofNat [NeZero n] (x : Fin n) (y : Nat) :
/-! ### sub -/
@[deprecated val_sub (since := "2025-11-21")]
protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
cases a; cases b; rfl
@@ -1147,7 +1102,6 @@ theorem coe_sub_iff_lt {a b : Fin n} : (↑(a - b) : Nat) = n + a - b ↔ a < b
/-! ### neg -/
@[grind =]
theorem val_neg {n : Nat} [NeZero n] (x : Fin n) :
(-x).val = if x = 0 then 0 else n - x.val := by
change (n - x) % n = _
@@ -1163,7 +1117,7 @@ protected theorem sub_eq_add_neg {n : Nat} (x y : Fin n) : x - y = x + -y := by
apply elim0 x
· replace h : NeZero n := h
ext
rw [Fin.val_sub, Fin.val_add, val_neg]
rw [Fin.coe_sub, Fin.val_add, val_neg]
split
· simp_all
· simp [Nat.add_comm]
@@ -1184,7 +1138,9 @@ theorem mul_ofNat [NeZero n] (x : Fin n) (y : Nat) :
@[deprecated mul_ofNat (since := "2025-05-28")] abbrev mul_ofNat' := @mul_ofNat
@[deprecated val_mul (since := "2025-10-26")]
theorem val_mul {n : Nat} : a b : Fin n, (a * b).val = a.val * b.val % n
| _, _, _, _ => rfl
theorem coe_mul {n : Nat} : a b : Fin n, ((a * b : Fin n) : Nat) = a * b % n
| _, _, _, _ => rfl

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@@ -6,6 +6,8 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Core
public import Init.Data.Int.Basic
public import Init.Data.ToString.Basic
public section

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@@ -6,6 +6,9 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Core
public import Init.Data.Int.Basic
public import Init.Data.ToString.Basic
public import Init.Data.Float
public section

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@@ -6,7 +6,9 @@ Author: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Float
public import Init.Data.Option.Basic
import Init.Ext
public import Init.Data.Array.DecidableEq
@@ -29,6 +31,9 @@ attribute [ext] FloatArray
def emptyWithCapacity (c : @& Nat) : FloatArray :=
{ data := #[] }
@[deprecated emptyWithCapacity (since := "2025-03-12")]
abbrev mkEmpty := emptyWithCapacity
def empty : FloatArray :=
emptyWithCapacity 0
@@ -129,7 +134,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : FloatA
| ForInStep.yield b => loop i (Nat.le_of_lt h') b
loop as.size (Nat.le_refl _) b
instance [Monad m] : ForIn m FloatArray Float where
instance : ForIn m FloatArray Float where
forIn := FloatArray.forIn
/-- See comment at `forInUnsafe` -/

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@@ -170,7 +170,7 @@ private def spaceUptoLine : Format → Bool → Int → Nat → SpaceResult
| text s, flatten, _, _ =>
let p := String.Internal.posOf s '\n'
let off := String.Internal.offsetOfPos s p
{ foundLine := p != s.rawEndPos, foundFlattenedHardLine := flatten && p != s.rawEndPos, space := off }
{ foundLine := p != s.endPos, foundFlattenedHardLine := flatten && p != s.endPos, space := off }
| append f₁ f₂, flatten, m, w => merge w (spaceUptoLine f₁ flatten m w) (spaceUptoLine f₂ flatten m)
| nest n f, flatten, m, w => spaceUptoLine f flatten (m - n) w
| group f _, _, m, w => spaceUptoLine f true m w
@@ -264,14 +264,14 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
| nest n f => be w (gs' ({ i with f, indent := i.indent + n }::is))
| text s =>
let p := String.Internal.posOf s '\n'
if p == s.rawEndPos then
if p == s.endPos then
pushOutput s
endTags i.activeTags
be w (gs' is)
else
pushOutput (String.Internal.extract s {} p)
pushNewline i.indent.toNat
let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.rawEndPos) }::is
let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.endPos) }::is
-- after a hard line break, re-evaluate whether to flatten the remaining group
-- note that we shouldn't start flattening after a hard break outside a group
if g.fla == .disallow then
@@ -411,6 +411,7 @@ Renders a `Format` to a string.
* `column`: begin the first line wrap `column` characters earlier than usual
(this is useful when the output String will be printed starting at `column`)
-/
@[export lean_format_pretty]
def pretty (f : Format) (width : Nat := defWidth) (indent : Nat := 0) (column := 0) : String :=
let act : StateM State Unit := prettyM f width indent
State.out <| act (State.mk "" column) |>.snd

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@@ -6,8 +6,10 @@ Author: Leonardo de Moura
module
prelude
public import Init.Data.Format.Basic
public import Init.Data.Array.Basic
import Init.Data.String.Search
public import Init.Data.ToString.Basic
import Init.Data.String.Basic
public section
@@ -47,7 +49,7 @@ Converts a string to a pretty-printer document, replacing newlines in the string
`Std.Format.line`.
-/
def String.toFormat (s : String) : Std.Format :=
Std.Format.joinSep (s.split '\n').toList Std.Format.line
Std.Format.joinSep (s.splitOn "\n") Std.Format.line
instance : ToFormat String.Pos.Raw where
format p := format p.byteIdx

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@@ -9,6 +9,7 @@ prelude
public import Init.Data.Format.Macro
public import Init.Data.Format.Instances
public import Init.Meta
import Init.Data.String.Basic
import Init.Data.ToString.Name
public section

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@@ -5,6 +5,7 @@ Authors: Kim Morrison
-/
module
prelude
public import Init.Core
public import Init.Grind.Tactics
public section
namespace Function

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@@ -6,7 +6,9 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.UInt.Basic
public import Init.Data.String.Basic
public import Init.Data.ByteArray.Basic
public section
universe u

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@@ -80,10 +80,7 @@ protected theorem zero_ne_one : (0 : Int) ≠ 1 := nofun
/-! ## Coercions -/
@[simp] theorem ofNat_eq_natCast (n : Nat) : Int.ofNat n = n := rfl
@[deprecated ofNat_eq_natCast (since := "2025-10-29")]
theorem ofNat_eq_coe : Int.ofNat n = Nat.cast n := rfl
@[simp] theorem ofNat_eq_coe : Int.ofNat n = Nat.cast n := rfl
@[simp] theorem ofNat_zero : ((0 : Nat) : Int) = 0 := rfl
@@ -316,7 +313,7 @@ the logical model.
Examples:
* `(7 : Int).natAbs = 7`
* `(0 : Int).natAbs = 0`
* `(-11 : Int).natAbs = 11`
* `((-11 : Int).natAbs = 11`
-/
@[extern "lean_nat_abs", expose]
def natAbs (m : @& Int) : Nat :=
@@ -372,6 +369,9 @@ def toNat? : Int → Option Nat
| (n : Nat) => some n
| -[_+1] => none
@[deprecated toNat? (since := "2025-03-11"), inherit_doc toNat?]
abbrev toNat' := toNat?
/-! ## divisibility -/
/--
@@ -392,9 +392,9 @@ Examples:
* `(0 : Int) ^ 10 = 0`
* `(-7 : Int) ^ 3 = -343`
-/
protected def pow : Int Nat Int
| (m : Nat), n => Int.ofNat (m ^ n)
| m@-[_+1], n => if n % 2 = 0 then Int.ofNat (m.natAbs ^ n) else - Int.ofNat (m.natAbs ^ n)
protected def pow (m : Int) : Nat Int
| 0 => 1
| succ n => Int.pow m n * m
instance : NatPow Int where
pow := Int.pow

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@@ -24,17 +24,12 @@ theorem natCast_shiftRight (n s : Nat) : n >>> s = (n : Int) >>> s := rfl
theorem negSucc_shiftRight (m n : Nat) :
-[m+1] >>> n = -[m >>>n +1] := rfl
@[grind _=_]
theorem shiftRight_add (i : Int) (m n : Nat) :
i >>> (m + n) = i >>> m >>> n := by
simp only [shiftRight_eq, Int.shiftRight]
cases i <;> simp [Nat.shiftRight_add]
grind_pattern shiftRight_add => i >>> (m + n) where
i =/= 0
grind_pattern shiftRight_add => i >>> m >>> n where
i =/= 0
theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
m >>> n = m / ((2 ^ n) : Nat) := by
simp only [shiftRight_eq, Int.shiftRight, Nat.shiftRight_eq_div_pow]
@@ -52,10 +47,10 @@ theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
simp [Int.shiftRight_eq_div_pow]
theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n 0) : n n >>> s := by
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_natCast]
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
split
case _ _ _ m =>
simp only [ofNat_eq_natCast] at h
simp only [ofNat_eq_coe] at h
by_cases hm : m = 0
· simp [hm]
· omega
@@ -66,14 +61,14 @@ theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : n ≤ n >>>
omega
theorem shiftRight_le_of_nonneg {n : Int} {s : Nat} (h : 0 n) : n >>> s n := by
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_natCast]
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
split
case _ _ _ m =>
simp only [Int.ofNat_eq_natCast] at h
simp only [Int.ofNat_eq_coe] at h
by_cases hm : m = 0
· simp [hm]
· have := Nat.shiftRight_le m s
rw [ofNat_eq_natCast]
rw [ofNat_eq_coe]
omega
case _ _ _ m =>
omega
@@ -113,7 +108,7 @@ theorem shiftLeft_succ (m : Int) (n : Nat) : m <<< (n + 1) = (m <<< n) * 2 := by
change Int.shiftLeft _ _ = Int.shiftLeft _ _ * 2
match m with
| (m : Nat) =>
dsimp only [Int.shiftLeft, Int.ofNat_eq_natCast]
dsimp only [Int.shiftLeft, Int.ofNat_eq_coe]
rw [Nat.shiftLeft_succ, Nat.mul_comm, natCast_mul, ofNat_two]
| Int.negSucc m =>
dsimp only [Int.shiftLeft]

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@@ -6,6 +6,7 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Int.DivMod.Lemmas
public import Init.Data.Int.Gcd
public section

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@@ -9,4 +9,3 @@ prelude
public import Init.Data.Int.DivMod.Basic
public import Init.Data.Int.DivMod.Bootstrap
public import Init.Data.Int.DivMod.Lemmas
public import Init.Data.Int.DivMod.Pow

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