Compare commits

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7 Commits

Author SHA1 Message Date
Leonardo de Moura
31cd6bac1b chore: update comments 2025-10-22 17:43:09 -07:00
Leonardo de Moura
e5c6459887 chore: add checkSystem 2025-10-22 17:34:16 -07:00
Leonardo de Moura
acedf24747 chore: missing file 2025-10-22 17:24:43 -07:00
Leonardo de Moura
12df6ce4a3 feat: use parameter optimizer at finish? 2025-10-22 17:23:49 -07:00
Leonardo de Moura
73f6c29d8b chore: 2025-10-22 16:30:03 -07:00
Leonardo de Moura
a93800ac19 chore: move 2025-10-22 16:30:03 -07:00
Leonardo de Moura
5642496dbe feat: simple parameter minimizer 2025-10-22 16:30:03 -07:00
4165 changed files with 30278 additions and 103173 deletions

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@@ -1,47 +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
Follow the commit convention in `doc/dev/commit_convention.md`.
**Title format:** `<type>: <subject>` where type is one of: `feat`, `fix`, `doc`, `style`, `refactor`, `test`, `chore`, `perf`.
Subject should use imperative present tense ("add" not "added"), no capitalization, no trailing period.
**Body format:** The first paragraph must start with "This PR". This paragraph is automatically incorporated into release notes. Use imperative present tense. Include motivation and contrast with previous behavior when relevant.
Example:
```
feat: add optional binder limit to `mkPatternFromTheorem`
This PR adds a `num?` parameter to `mkPatternFromTheorem` to control how many
leading quantifiers are stripped when creating a pattern.
```

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@@ -39,7 +39,6 @@ These comments explain the scripts' behavior, which repositories get special han
## Important Notes
- **NEVER merge PRs autonomously** - always wait for the user to merge PRs themselves
- The `release_steps.py` script is idempotent - it's safe to rerun
- The `release_checklist.py` script is idempotent - it's safe to rerun
- Some repositories depend on others (e.g., mathlib4 depends on batteries, aesop, etc.)

1
.gitattributes vendored
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@@ -4,7 +4,6 @@ RELEASES.md merge=union
stage0/** binary linguist-generated
# The following file is often manually edited, so do show it in diffs
stage0/src/stdlib_flags.h -binary -linguist-generated
doc/std/grove/GroveStdlib/Generated/** linguist-generated
# These files should not have line endings translated on Windows, because
# it throws off parser tests. Later lines override earlier ones, so the
# runner code is still treated as ordinary text.

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@@ -9,7 +9,7 @@ assignees: ''
### Prerequisites
<!-- Please put an X between the brackets as you perform the following steps: -->
Please put an X between the brackets as you perform the following steps:
* [ ] Check that your issue is not already filed:
https://github.com/leanprover/lean4/issues

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@@ -15,7 +15,7 @@ jobs:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v6
uses: actions/checkout@v5
- name: actionlint
uses: raven-actions/actionlint@v2
with:

View File

@@ -67,13 +67,13 @@ jobs:
if: runner.os == 'macOS'
- name: Checkout
if: (!endsWith(matrix.os, '-with-cache'))
uses: actions/checkout@v6
uses: actions/checkout@v5
with:
# the default is to use a virtual merge commit between the PR and master: just use the PR
ref: ${{ github.event.pull_request.head.sha }}
- name: Namespace Checkout
if: endsWith(matrix.os, '-with-cache')
uses: namespacelabs/nscloud-checkout-action@v8
uses: namespacelabs/nscloud-checkout-action@v7
with:
ref: ${{ github.event.pull_request.head.sha }}
- name: Open Nix shell once
@@ -213,14 +213,14 @@ 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-${{ matrix.name }}
path: pack/*
- name: Lean stats
run: |
build/$TARGET_STAGE/bin/lean --stats src/Lean.lean
build/$TARGET_STAGE/bin/lean --stats src/Lean.lean -Dexperimental.module=true
if: ${{ !matrix.cross }}
- name: Test
id: test

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@@ -7,7 +7,7 @@ jobs:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v6
uses: actions/checkout@v5
with:
# the default is to use a virtual merge commit between the PR and master: just use the PR
ref: ${{ github.event.pull_request.head.sha }}

View File

@@ -8,7 +8,7 @@ jobs:
check-stage0-on-queue:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v6
- uses: actions/checkout@v5
with:
ref: ${{ github.event.pull_request.head.sha }}
fetch-depth: 0

View File

@@ -1,57 +0,0 @@
name: Check stdlib_flags.h modifications
on:
pull_request:
types: [opened, synchronize, reopened, labeled, unlabeled]
jobs:
check-stdlib-flags:
runs-on: ubuntu-latest
steps:
- name: Check if stdlib_flags.h was modified
uses: actions/github-script@v8
with:
script: |
// Get the list of files changed in this PR
const files = await github.paginate(
github.rest.pulls.listFiles,
{
owner: context.repo.owner,
repo: context.repo.repo,
pull_number: context.payload.pull_request.number,
}
);
// Check if stdlib_flags.h was modified
const stdlibFlagsModified = files.some(file =>
file.filename === 'src/stdlib_flags.h'
);
if (stdlibFlagsModified) {
console.log('src/stdlib_flags.h was modified in this PR');
// Check if the unlock label is present
const { data: pr } = await github.rest.pulls.get({
owner: context.repo.owner,
repo: context.repo.repo,
pull_number: context.issue.number,
});
const hasUnlockLabel = pr.labels.some(label =>
label.name === 'unlock-upstream-stdlib-flags'
);
if (!hasUnlockLabel) {
core.setFailed(
'src/stdlib_flags.h was modified. This is likely a mistake. If you would like to change ' +
'bootstrapping settings or request a stage0 update, you should modify stage0/src/stdlib_flags.h. ' +
'If you really want to change src/stdlib_flags.h (which should be extremely rare), set the ' +
'unlock-upstream-stdlib-flags label.'
);
} else {
console.log('Found unlock-upstream-stdlib-flags');
}
} else {
console.log('src/stdlib_flags.h was not modified');
}

View File

@@ -50,9 +50,9 @@ jobs:
steps:
- name: Checkout
uses: actions/checkout@v6
uses: actions/checkout@v5
# don't schedule nightlies on forks
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly' || (startsWith(github.ref, 'refs/tags/') && github.repository == 'leanprover/lean4')
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
- name: Set Nightly
if: github.event_name == 'schedule' && github.repository == 'leanprover/lean4' || inputs.action == 'release nightly'
id: set-nightly
@@ -106,54 +106,9 @@ 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 -m 1 -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.$TAG_PATCH"
# 0: PRs without special label
# 1: PRs with `merge-ci` label, merge queue checks, master commits
# 2: nightlies
# 3: PRs with `release-ci` label, full releases
# 2: PRs with `release-ci` label, releases (incl. nightlies)
- name: Set check level
id: set-level
# We do not use github.event.pull_request.labels.*.name here because
@@ -163,16 +118,14 @@ jobs:
check_level=0
fast=false
if [[ -n "${{ 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
@@ -247,8 +200,8 @@ jobs:
"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",
@@ -257,25 +210,17 @@ jobs:
"test": true,
"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",
"os": "ubuntu-latest",
"enabled": level >= 2,
// do not fail nightlies on this for now
"secondary": level <= 2,
"test": true,
// 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..
// 9366 is too close to timeout.
// `bv_` sometimes times out calling into cadical even though we should be using the
// standard compile flags for it.
"CTEST_OPTIONS": "-E 'StackOverflow|reverse-ffi|interactive|async_select_channel|9366|run/bv_'"
},
// exclude seriously slow/problematic tests (laketests crash)
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
},*/
{
"name": "macOS",
"os": "macos-15-intel",
@@ -307,7 +252,7 @@ jobs:
},
{
"name": "Windows",
"os": large && (fast || level >= 2) ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
"os": large && (fast || level == 2) ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
"release": true,
"enabled": level >= 2,
"test": true,
@@ -430,11 +375,11 @@ 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@a06a81a03ee405af7f2048a818ed3f03bbf83c7b
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
with:
files: artifacts/*/*
fail_on_unmatched_files: true
@@ -455,14 +400,14 @@ jobs:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v6
uses: actions/checkout@v5
with:
# needed for tagging
fetch-depth: 0
# Doesn't seem to be working when additionally fetching from lean4-nightly
#filter: tree:0
token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
- uses: actions/download-artifact@v6
- uses: actions/download-artifact@v5
with:
path: artifacts
- name: Prepare Nightly Release
@@ -480,7 +425,7 @@ jobs:
echo -e "\n*Full commit log*\n" >> diff.md
git log --oneline "$last_tag"..HEAD | sed 's/^/* /' >> diff.md
- name: Release Nightly
uses: softprops/action-gh-release@a06a81a03ee405af7f2048a818ed3f03bbf83c7b
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
with:
body_path: diff.md
prerelease: true

View File

@@ -6,7 +6,7 @@ jobs:
check-lean-files:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v6
- uses: actions/checkout@v5
- name: Verify .lean files start with a copyright header.
run: |

View File

@@ -51,7 +51,7 @@ jobs:
- name: Fetch upstream invalidated facts
if: ${{ steps.should-run.outputs.should-run == 'true' && steps.workflow-info.outputs.pullRequestNumber != '' }}
id: fetch-upstream
uses: TwoFx/grove-action/fetch-upstream@v0.5
uses: TwoFx/grove-action/fetch-upstream@v0.4
with:
artifact-name: grove-invalidated-facts
base-ref: master
@@ -65,7 +65,6 @@ jobs:
workflow: ci.yml
path: artifacts
name: "build-Linux release"
allow_forks: true
name_is_regexp: true
- name: Unpack toolchain
@@ -96,7 +95,7 @@ jobs:
- name: Build
if: ${{ steps.should-run.outputs.should-run == 'true' }}
id: build
uses: TwoFx/grove-action/build@v0.5
uses: TwoFx/grove-action/build@v0.4
with:
project-path: doc/std/grove
script-name: grove-stdlib

View File

@@ -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@a06a81a03ee405af7f2048a818ed3f03bbf83c7b
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@a06a81a03ee405af7f2048a818ed3f03bbf83c7b
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.
@@ -127,7 +127,7 @@ jobs:
description: "${{ github.repository_owner }}/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}",
});
- name: Add toolchain-available label
- name: Add label
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
uses: actions/github-script@v8
with:
@@ -166,14 +166,22 @@ jobs:
if [ "$NIGHTLY_SHA" = "$MERGE_BASE_SHA" ]; then
echo "The merge base of this PR coincides with the nightly release"
BATTERIES_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/batteries.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
MATHLIB_REMOTE_TAGS="$(git ls-remote https://github.com/leanprover-community/mathlib4-nightly-testing.git nightly-testing-"$MOST_RECENT_NIGHTLY")"
if [[ -n "$MATHLIB_REMOTE_TAGS" ]]; then
echo "... and Mathlib has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
if [[ -n "$BATTERIES_REMOTE_TAGS" ]]; then
echo "... and Batteries has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE=""
if [[ -n "$MATHLIB_REMOTE_TAGS" ]]; then
echo "... and Mathlib has a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
else
echo "... but Mathlib does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Mathlib CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Mathlib CI should run now."
fi
else
echo "... but Mathlib does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Mathlib CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Mathlib CI should run now."
echo "... but Batteries does not yet have a 'nightly-testing-$MOST_RECENT_NIGHTLY' tag."
MESSAGE="- ❗ Batteries CI can not be attempted yet, as the \`nightly-testing-$MOST_RECENT_NIGHTLY\` tag does not exist there yet. We will retry when you push more commits. If you rebase your branch onto \`nightly-with-mathlib\`, Batteries CI should run now."
fi
else
echo "The most recently nightly tag on this branch has SHA: $NIGHTLY_SHA"
@@ -387,7 +395,7 @@ jobs:
# Checkout the Batteries repository with all branches
- name: Checkout Batteries repository
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
uses: actions/checkout@v6
uses: actions/checkout@v5
with:
repository: leanprover-community/batteries
token: ${{ secrets.MATHLIB4_BOT }}
@@ -418,7 +426,7 @@ jobs:
git switch -c lean-pr-testing-${{ 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 }}
@@ -427,7 +435,7 @@ 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
@@ -447,7 +455,7 @@ jobs:
# Checkout the mathlib4 repository with all branches
- name: Checkout mathlib4 repository
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
uses: actions/checkout@v6
uses: actions/checkout@v5
with:
repository: leanprover-community/mathlib4-nightly-testing
token: ${{ secrets.MATHLIB4_BOT }}
@@ -488,7 +496,7 @@ jobs:
sed -i 's,require "leanprover-community" / "batteries" @ git ".\+",require "leanprover-community" / "batteries" @ git "lean-pr-testing-${{ 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-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -499,7 +507,7 @@ jobs:
git add lean-toolchain
lake update batteries
git add lake-manifest.json
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes
@@ -507,18 +515,6 @@ jobs:
run: |
git push origin lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
- name: Add mathlib4-nightly-available label
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
uses: actions/github-script@v8
with:
script: |
await github.rest.issues.addLabels({
issue_number: ${{ steps.workflow-info.outputs.pullRequestNumber }},
owner: context.repo.owner,
repo: context.repo.repo,
labels: ['mathlib4-nightly-available']
})
# We next automatically create a reference manual branch using this toolchain.
# Reference manual CI will be responsible for reporting back success or failure
# to the PR comments asynchronously (and thus transitively SubVerso/Verso).
@@ -530,7 +526,7 @@ jobs:
# Checkout the reference manual repository with all branches
- name: Checkout mathlib4 repository
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.reference-manual-ready.outputs.manual_ready == 'true'
uses: actions/checkout@v6
uses: actions/checkout@v5
with:
repository: leanprover/reference-manual
token: ${{ secrets.MANUAL_PR_BOT }}
@@ -562,7 +558,7 @@ jobs:
echo "leanprover/lean4-pr-releases:pr-release-${{ 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 }}
@@ -572,7 +568,7 @@ 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).');
}

View File

@@ -27,7 +27,7 @@ jobs:
# This action should push to an otherwise protected branch, so it
# uses a deploy key with write permissions, as suggested at
# https://stackoverflow.com/a/76135647/946226
- uses: actions/checkout@v6
- uses: actions/checkout@v5
with:
ssh-key: ${{secrets.STAGE0_SSH_KEY}}
- run: echo "should_update_stage0=yes" >> "$GITHUB_ENV"

View File

@@ -44,9 +44,7 @@ if (NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
set(CADICAL_CXX c++)
if (CADICAL_USE_CUSTOM_CXX)
set(CADICAL_CXX ${CMAKE_CXX_COMPILER})
# Use same platform flags as for Lean executables, in particular from `prepare-llvm-linux.sh`,
# but not Lean-specific `LEAN_EXTRA_CXX_FLAGS` such as fsanitize.
set(CADICAL_CXXFLAGS "${CMAKE_CXX_FLAGS}")
set(CADICAL_CXXFLAGS "${LEAN_EXTRA_CXX_FLAGS}")
set(CADICAL_LDFLAGS "-Wl,-rpath=\\$$ORIGIN/../lib")
endif()
find_program(CCACHE ccache)

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

@@ -1,9 +1,190 @@
# Foreign Function Interface
The Lean FFI documentation is now part of the [Lean language reference](https://lean-lang.org/doc/reference/latest/).
NOTE: The current interface was designed for internal use in Lean and should be considered **unstable**.
It will be refined and extended in the future.
* [General FFI](https://lean-lang.org/doc/reference/latest/find/?domain=Verso.Genre.Manual.section&name=ffi)
* [Representation of inductive types](https://lean-lang.org/doc/reference/latest/find/?domain=Verso.Genre.Manual.section&name=inductive-types-ffi)
* [String](https://lean-lang.org/doc/reference/latest/find/?domain=Verso.Genre.Manual.section&name=string-ffi)
* [Array](https://lean-lang.org/doc/reference/latest/find/?domain=Verso.Genre.Manual.section&name=array-ffi)
As Lean is written partially in Lean itself and partially in C++, it offers efficient interoperability between the two languages (or rather, between Lean and any language supporting C interfaces).
This support is however currently limited to transferring Lean data types; in particular, it is not possible yet to pass or return compound data structures such as C `struct`s by value from or to Lean.
There are two primary attributes for interoperating with other languages:
* `@[extern "sym"] constant leanSym : ...` binds a Lean declaration to the external symbol `sym`.
It can also be used with `def` to provide an internal definition, but ensuring consistency of both definitions is up to the user.
* `@[export sym] def leanSym : ...` exports `leanSym` under the unmangled symbol name `sym`.
For simple examples of how to call foreign code from Lean and vice versa, see <https://github.com/leanprover/lean4/blob/master/src/lake/examples/ffi> and <https://github.com/leanprover/lean4/blob/master/src/lake/examples/reverse-ffi>, respectively.
## The Lean ABI
The Lean Application Binary Interface (ABI) describes how the signature of a Lean declaration is encoded as a native calling convention.
It is based on the standard C ABI and calling convention of the target platform.
For a Lean declaration marked with either `@[extern "sym"]` or `@[export sym]` for some symbol name `sym`, let `α₁ → ... → αₙ → β` be the normalized declaration's type.
If `n` is 0, the corresponding C declaration is
```c
extern s sym;
```
where `s` is the C translation of `β` as specified in the next section.
In the case of an `@[extern]` definition, the symbol's value is guaranteed to be initialized only after calling the Lean module's initializer or that of an importing module; see [Initialization](#initialization).
If `n` is greater than 0, the corresponding C declaration is
```c
s sym(t, ..., tₘ);
```
where the parameter types `tᵢ` are the C translation of the `αᵢ` as in the next section.
In the case of `@[extern]` all *irrelevant* types are removed first; see next section.
### Translating Types from Lean to C
* The integer types `UInt8`, ..., `UInt64`, `USize` are represented by the C types `uint8_t`, ..., `uint64_t`, `size_t`, respectively
* `Char` is represented by `uint32_t`
* `Float` is represented by `double`
* An *enum* inductive type of at least 2 and at most 2^32 constructors, each of which with no parameters, is represented by the first type of `uint8_t`, `uint16_t`, `uint32_t` that is sufficient to represent all constructor indices.
For example, the type `Bool` is represented as `uint8_t` with values `0` for `false` and `1` for `true`.
* `Decidable α` is represented the same way as `Bool`
* An inductive type with a *trivial structure*, that is,
* it is none of the types described above
* it is not marked `unsafe`
* it has a single constructor with a single parameter of *relevant* type
is represented by the representation of that parameter's type.
For example, `{ x : α // p }`, the `Subtype` structure of a value of type `α` and an irrelevant proof, is represented by the representation of `α`.
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)`
* 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.
Example: the runtime value of `u : Unit` is always `lean_box(0)`.
#### Inductive types
For inductive types which are in the fallback `lean_object *` case above and not trivial constructors, the type is stored as a `lean_ctor_object`, and `lean_is_ctor` will return true. A `lean_ctor_object` stores the constructor index in the header, and the fields are stored in the `m_objs` portion of the object.
The memory order of the fields is derived from the types and order of the fields in the declaration. They are ordered as follows:
* Non-scalar fields stored as `lean_object *`
* Fields of type `USize`
* Other scalar fields, in decreasing order by size
Within each group the fields are ordered in declaration order. Trivial wrapper types count as their underlying wrapped type for this purpose.
* To access fields of the first kind, use `lean_ctor_get(val, i)` to get the `i`th non-scalar field.
* To access `USize` fields, use `lean_ctor_get_usize(val, n+i)` to get the `i`th usize field and `n` is the total number of fields of the first kind.
* To access other scalar fields, use `lean_ctor_get_uintN(val, off)` or `lean_ctor_get_usize(val, off)` as appropriate. Here `off` is the byte offset of the field in the structure, starting at `n*sizeof(void*)` where `n` is the number of fields of the first two kinds.
For example, a structure such as
```lean
structure S where
ptr_1 : Array Nat
usize_1 : USize
sc64_1 : UInt64
sc64_2 : { x : UInt64 // x > 0 } -- wrappers of scalars count as scalars
sc64_3 : Float -- `Float` is 64 bit
sc8_1 : Bool
sc16_1 : UInt16
sc8_2 : UInt8
sc64_4 : UInt64
usize_2 : USize
sc32_1 : Char -- trivial wrapper around `UInt32`
sc32_2 : UInt32
sc16_2 : UInt16
```
would get re-sorted into the following memory order:
* `S.ptr_1` - `lean_ctor_get(val, 0)`
* `S.usize_1` - `lean_ctor_get_usize(val, 1)`
* `S.usize_2` - `lean_ctor_get_usize(val, 2)`
* `S.sc64_1` - `lean_ctor_get_uint64(val, sizeof(void*)*3)`
* `S.sc64_2` - `lean_ctor_get_uint64(val, sizeof(void*)*3 + 8)`
* `S.sc64_3` - `lean_ctor_get_float(val, sizeof(void*)*3 + 16)`
* `S.sc64_4` - `lean_ctor_get_uint64(val, sizeof(void*)*3 + 24)`
* `S.sc32_1` - `lean_ctor_get_uint32(val, sizeof(void*)*3 + 32)`
* `S.sc32_2` - `lean_ctor_get_uint32(val, sizeof(void*)*3 + 36)`
* `S.sc16_1` - `lean_ctor_get_uint16(val, sizeof(void*)*3 + 40)`
* `S.sc16_2` - `lean_ctor_get_uint16(val, sizeof(void*)*3 + 42)`
* `S.sc8_1` - `lean_ctor_get_uint8(val, sizeof(void*)*3 + 44)`
* `S.sc8_2` - `lean_ctor_get_uint8(val, sizeof(void*)*3 + 45)`
### Borrowing
By default, all `lean_object *` parameters of an `@[extern]` function are considered *owned*, i.e. the external code is passed a "virtual RC token" and is responsible for passing this token along to another consuming function (exactly once) or freeing it via `lean_dec`.
To reduce reference counting overhead, parameters can be marked as *borrowed* by prefixing their type with `@&`.
Borrowed objects must only be passed to other non-consuming functions (arbitrarily often) or converted to owned values using `lean_inc`.
In `lean.h`, the `lean_object *` aliases `lean_obj_arg` and `b_lean_obj_arg` are used to mark this difference on the C side.
Return values and `@[export]` parameters are always owned at the moment.
## Initialization
When including Lean code as part of a larger program, modules must be *initialized* before accessing any of their declarations.
Module initialization entails
* initialization of all "constants" (nullary functions), including closed terms lifted out of other functions
* execution of all `[init]` functions
* execution of all `[builtin_init]` functions, if the `builtin` parameter of the module initializer has been set
The module initializer is automatically run with the `builtin` flag for executables compiled from Lean code and for "plugins" loaded with `lean --plugin`.
For all other modules imported by `lean`, the initializer is run without `builtin`.
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` 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.
Together with initialization of the Lean runtime, you should execute code like the following exactly once before accessing any Lean declarations:
```c
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);
...
argv = lean_setup_args(argc, argv); // if using process-related functionality
lean_initialize_runtime_module();
//lean_initialize(); // necessary (and replaces `lean_initialize_runtime_module`) if you (indirectly) access the `Lean` package
lean_object * res;
// use same default as for Lean executables
uint8_t builtin = 1;
res = initialize_A_B(builtin);
if (lean_io_result_is_ok(res)) {
lean_dec_ref(res);
} else {
lean_io_result_show_error(res);
lean_dec(res);
return ...; // do not access Lean declarations if initialization failed
}
res = initialize_C(builtin);
if (lean_io_result_is_ok(res)) {
...
//lean_init_task_manager(); // necessary if you (indirectly) use `Task`
lean_io_mark_end_initialization();
```
In addition, any other thread not spawned by the Lean runtime itself must be initialized for Lean use by calling
```c
void lean_initialize_thread();
```
and should be finalized in order to free all thread-local resources by calling
```c
void lean_finalize_thread();
```
## `@[extern]` in the Interpreter
The interpreter can run Lean declarations for which symbols are available in loaded shared libraries, which includes `@[extern]` declarations.
Thus to e.g. run `#eval` on such a declaration, you need to
1. compile (at least) the module containing the declaration and its dependencies into a shared library, and then
1. pass this library to `lean --load-dynlib=` to run code `import`ing this module.
Note that it is not sufficient to load the foreign library containing the external symbol because the interpreter depends on code that is emitted for each `@[extern]` declaration.
Thus it is not possible to interpret an `@[extern]` declaration in the same file.
See [`tests/compiler/foreign`](https://github.com/leanprover/lean4/tree/master/tests/compiler/foreign/) for an example.

View File

@@ -69,10 +69,6 @@ We'll use `v4.6.0` as the intended release version as a running example.
- `repl`:
There are two copies of `lean-toolchain`/`lakefile.lean`:
in the root, and in `test/Mathlib/`. Edit both, and run `lake update` in both directories.
- `lean-fro.org`:
After updating the toolchains and running `lake update`, you must run `scripts/update.sh` to regenerate
the site content. This script updates generated files that depend on the Lean version.
The `release_steps.py` script handles this automatically.
- An awkward situation that sometimes occurs (e.g. with Verso) is that the `master`/`main` branch has already been moved
to a nightly toolchain that comes *after* the stable toolchain we are
targeting. In this case it is necessary to create a branch `releases/v4.6.0` from the last commit which was on

View File

@@ -51,10 +51,6 @@ All these tests are included by [src/shell/CMakeLists.txt](https://github.com/le
codes and do not check the expected output even though output is
produced, it is ignored.
**Note:** Tests in this directory run with `-Dlinter.all=false` to reduce noise.
If your test needs to verify linter behavior (e.g., deprecation warnings),
explicitly enable the relevant linter with `set_option linter.<name> true`.
- [`tests/lean/interactive`](https://github.com/leanprover/lean4/tree/master/tests/lean/interactive/): are designed to test server requests at a
given position in the input file. Each .lean file contains comments
that indicate how to simulate a client request at that position.

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

@@ -4,7 +4,6 @@ import GroveStdlib.Generated.«associative-creation-operations»
import GroveStdlib.Generated.«associative-modification-operations»
import GroveStdlib.Generated.«associative-create-then-query»
import GroveStdlib.Generated.«associative-all-operations-covered»
import GroveStdlib.Generated.«slice-producing»
/-
This file is autogenerated by grove. You can manually edit it, for example to resolve merge
@@ -21,4 +20,3 @@ def restoreState : RestoreStateM Unit := do
«associative-modification-operations».restoreState
«associative-create-then-query».restoreState
«associative-all-operations-covered».restoreState
«slice-producing».restoreState

View File

@@ -1,459 +0,0 @@
import Grove.Framework
/-
This file is autogenerated by grove. You can manually edit it, for example to resolve merge
conflicts, but be careful.
-/
open Grove.Framework Widget
namespace GroveStdlib.Generated.«slice-producing»
def «c8a13d6d-7ed6-4cd1-a386-23e2d55ce6f7» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "c8a13d6d-7ed6-4cd1-a386-23e2d55ce6f7"
rowId := "c8a13d6d-7ed6-4cd1-a386-23e2d55ce6f7"
rowState := #["String", "String.slice", Declaration.def {
name := `String.slice
renderedStatement := "String.slice (s : String) (startInclusive endExclusive : s.Pos)\n (h : startInclusive ≤ endExclusive) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.slice", Declaration.def {
name := `String.Slice.slice
renderedStatement := "String.Slice.slice (s : String.Slice) (newStart newEnd : s.Pos) (h : newStart ≤ newEnd) :\n String.Slice"
isDeprecated := false
}
,"string-pos-forwards", "String.Pos.slice", Declaration.def {
name := `String.Pos.slice
renderedStatement := "String.Pos.slice {s : String} (pos p₀ p₁ : s.Pos) (h₁ : p₀ ≤ pos) (h₂ : pos ≤ p₁) :\n (s.slice p₀ p₁ ⋯).Pos"
isDeprecated := false
}
,"string-pos-backwards", "String.Pos.ofSlice", Declaration.def {
name := `String.Pos.ofSlice
renderedStatement := "String.Pos.ofSlice {s : String} {p₀ p₁ : s.Pos} {h : p₀ ≤ p₁} (pos : (s.slice p₀ p₁ h).Pos) : s.Pos"
isDeprecated := false
}
,"string-slice-pos-forwards", "String.Slice.Pos.slice", Declaration.def {
name := `String.Slice.Pos.slice
renderedStatement := "String.Slice.Pos.slice {s : String.Slice} (pos p₀ p₁ : s.Pos) (h₁ : p₀ ≤ pos) (h₂ : pos ≤ p₁) :\n (s.slice p₀ p₁ ⋯).Pos"
isDeprecated := false
}
,"string-slice-pos-backwards", "String.Slice.Pos.ofSlice", Declaration.def {
name := `String.Slice.Pos.ofSlice
renderedStatement := "String.Slice.Pos.ofSlice {s : String.Slice} {p₀ p₁ : s.Pos} {h : p₀ ≤ p₁}\n (pos : (s.slice p₀ p₁ h).Pos) : s.Pos"
isDeprecated := false
}
,"string-pos-noproof", "String.Pos.sliceOrPanic", Declaration.def {
name := `String.Pos.sliceOrPanic
renderedStatement := "String.Pos.sliceOrPanic {s : String} (pos p₀ p₁ : s.Pos) {h : p₀ ≤ p₁} : (s.slice p₀ p₁ h).Pos"
isDeprecated := false
}
,"string-slice-pos-noproof", "String.Slice.Pos.sliceOrPanic", Declaration.def {
name := `String.Slice.Pos.sliceOrPanic
renderedStatement := "String.Slice.Pos.sliceOrPanic {s : String.Slice} (pos p₀ p₁ : s.Pos) {h : p₀ ≤ p₁} :\n (s.slice p₀ p₁ h).Pos"
isDeprecated := false
}
,]
metadata := {
status := .done
comment := ""
}
def «21b4fdfd-f8b3-44f5-a59e-57f1dc1d6819» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "21b4fdfd-f8b3-44f5-a59e-57f1dc1d6819"
rowId := "21b4fdfd-f8b3-44f5-a59e-57f1dc1d6819"
rowState := #["String", "String.slice?", Declaration.def {
name := `String.slice?
renderedStatement := "String.slice? (s : String) (startInclusive endExclusive : s.Pos) : Option String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.slice?", Declaration.def {
name := `String.Slice.slice?
renderedStatement := "String.Slice.slice? (s : String.Slice) (newStart newEnd : s.Pos) : Option String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .postponed
comment := "Would be good to have better support"
}
def «6f2b6ecb-2f0c-4e45-9da3-eb7f2e15eff0» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "6f2b6ecb-2f0c-4e45-9da3-eb7f2e15eff0"
rowId := "6f2b6ecb-2f0c-4e45-9da3-eb7f2e15eff0"
rowState := #["String", "String.slice!", Declaration.def {
name := `String.slice!
renderedStatement := "String.slice! (s : String) (p₁ p₂ : s.Pos) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.slice!", Declaration.def {
name := `String.Slice.slice!
renderedStatement := "String.Slice.slice! (s : String.Slice) (newStart newEnd : s.Pos) : String.Slice"
isDeprecated := false
}
,"string-pos-forwards", "String.Pos.slice!", Declaration.def {
name := `String.Pos.slice!
renderedStatement := "String.Pos.slice! {s : String} (pos p₀ p₁ : s.Pos) : (s.slice! p₀ p₁).Pos"
isDeprecated := false
}
,"string-pos-backwards", "String.Pos.ofSlice!", Declaration.def {
name := `String.Pos.ofSlice!
renderedStatement := "String.Pos.ofSlice! {s : String} {p₀ p₁ : s.Pos} (pos : (s.slice! p₀ p₁).Pos) : s.Pos"
isDeprecated := false
}
,"string-slice-pos-forwards", "String.Slice.Pos.slice!", Declaration.def {
name := `String.Slice.Pos.slice!
renderedStatement := "String.Slice.Pos.slice! {s : String.Slice} (pos p₀ p₁ : s.Pos) : (s.slice! p₀ p₁).Pos"
isDeprecated := false
}
,"string-slice-pos-backwards", "String.Slice.Pos.ofSlice!", Declaration.def {
name := `String.Slice.Pos.ofSlice!
renderedStatement := "String.Slice.Pos.ofSlice! {s : String.Slice} {p₀ p₁ : s.Pos} (pos : (s.slice! p₀ p₁).Pos) : s.Pos"
isDeprecated := false
}
,]
metadata := {
status := .done
comment := ""
}
def «a3bdf66d-bc11-4019-aee9-2f1c1701de52» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "a3bdf66d-bc11-4019-aee9-2f1c1701de52"
rowId := "a3bdf66d-bc11-4019-aee9-2f1c1701de52"
rowState := #["String", "String.trimAsciiStart", Declaration.def {
name := `String.trimAsciiStart
renderedStatement := "String.trimAsciiStart (s : String) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.trimAsciiStart", Declaration.def {
name := `String.Slice.trimAsciiStart
renderedStatement := "String.Slice.trimAsciiStart (s : String.Slice) : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing `of` version at least"
}
def «f12b2730-7a4d-465c-8a6d-9d051c300fd5» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "f12b2730-7a4d-465c-8a6d-9d051c300fd5"
rowId := "f12b2730-7a4d-465c-8a6d-9d051c300fd5"
rowState := #["String", "String.trimAsciiEnd", Declaration.def {
name := `String.trimAsciiEnd
renderedStatement := "String.trimAsciiEnd (s : String) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.trimAsciiEnd", Declaration.def {
name := `String.Slice.trimAsciiEnd
renderedStatement := "String.Slice.trimAsciiEnd (s : String.Slice) : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing `of` version at least"
}
def «32307b55-d6d1-4756-a947-dbe4dfde573c» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "32307b55-d6d1-4756-a947-dbe4dfde573c"
rowId := "32307b55-d6d1-4756-a947-dbe4dfde573c"
rowState := #["String", "String.trimAscii", Declaration.def {
name := `String.trimAscii
renderedStatement := "String.trimAscii (s : String) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.trimAscii", Declaration.def {
name := `String.Slice.trimAscii
renderedStatement := "String.Slice.trimAscii (s : String.Slice) : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing `of` version at least\n"
}
def «dce95a38-f55a-4d6a-ae79-078ffe4b5c15» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "dce95a38-f55a-4d6a-ae79-078ffe4b5c15"
rowId := "dce95a38-f55a-4d6a-ae79-078ffe4b5c15"
rowState := #["String", "String.toSlice", Declaration.def {
name := `String.toSlice
renderedStatement := "String.toSlice (s : String) : String.Slice"
isDeprecated := false
}
,"string-pos-forwards", "String.Pos.toSlice", Declaration.def {
name := `String.Pos.toSlice
renderedStatement := "String.Pos.toSlice {s : String} (pos : s.Pos) : s.toSlice.Pos"
isDeprecated := false
}
,"string-pos-backwards", "String.Pos.ofToSlice", Declaration.def {
name := `String.Pos.ofToSlice
renderedStatement := "String.Pos.ofToSlice {s : String} (pos : s.toSlice.Pos) : s.Pos"
isDeprecated := false
}
,]
metadata := {
status := .done
comment := ""
}
def «005a3f30-5dab-493f-b168-32c36a2bdf7c» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "005a3f30-5dab-493f-b168-32c36a2bdf7c"
rowId := "005a3f30-5dab-493f-b168-32c36a2bdf7c"
rowState := #["String.Slice", "String.Slice.str", Declaration.def {
name := `String.Slice.str
renderedStatement := "String.Slice.str (self : String.Slice) : String"
isDeprecated := false
}
,"string-slice-pos-forwards", "String.Slice.Pos.str", Declaration.def {
name := `String.Slice.Pos.str
renderedStatement := "String.Slice.Pos.str {s : String.Slice} (pos : s.Pos) : s.str.Pos"
isDeprecated := false
}
,"string-slice-pos-backwards", "String.Slice.Pos.ofStr", Declaration.def {
name := `String.Slice.Pos.ofStr
renderedStatement := "String.Slice.Pos.ofStr {s : String.Slice} (pos : s.str.Pos) (h₁ : s.startInclusive ≤ pos)\n (h₂ : pos ≤ s.endExclusive) : s.Pos"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing `no proof` version\n"
}
def «5f1a154c-ae2f-43a1-9409-2ce95b163ef3» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "5f1a154c-ae2f-43a1-9409-2ce95b163ef3"
rowId := "5f1a154c-ae2f-43a1-9409-2ce95b163ef3"
rowState := #["String", "String.drop", Declaration.def {
name := `String.drop
renderedStatement := "String.drop (s : String) (n : Nat) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.drop", Declaration.def {
name := `String.Slice.drop
renderedStatement := "String.Slice.drop (s : String.Slice) (n : Nat) : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «179518d1-ad07-4b2b-8ffe-3b7616e4c4ab» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "179518d1-ad07-4b2b-8ffe-3b7616e4c4ab"
rowId := "179518d1-ad07-4b2b-8ffe-3b7616e4c4ab"
rowState := #["String", "String.take", Declaration.def {
name := `String.take
renderedStatement := "String.take (s : String) (n : Nat) : String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.take", Declaration.def {
name := `String.Slice.take
renderedStatement := "String.Slice.take (s : String.Slice) (n : Nat) : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «55c587fd-a7a8-4633-a4ae-e2c4e768ad28» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "55c587fd-a7a8-4633-a4ae-e2c4e768ad28"
rowId := "55c587fd-a7a8-4633-a4ae-e2c4e768ad28"
rowState := #["String", "String.dropWhile", Declaration.def {
name := `String.dropWhile
renderedStatement := "String.dropWhile {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.ForwardPattern pat] :\n String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.dropWhile", Declaration.def {
name := `String.Slice.dropWhile
renderedStatement := "String.Slice.dropWhile {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.ForwardPattern pat] : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «d4444684-4279-4400-9be2-561a7cdb32c1» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "d4444684-4279-4400-9be2-561a7cdb32c1"
rowId := "d4444684-4279-4400-9be2-561a7cdb32c1"
rowState := #["String", "String.takeWhile", Declaration.def {
name := `String.takeWhile
renderedStatement := "String.takeWhile {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.ForwardPattern pat] :\n String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.takeWhile", Declaration.def {
name := `String.Slice.takeWhile
renderedStatement := "String.Slice.takeWhile {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.ForwardPattern pat] : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «1c9e6689-65a0-4d4b-b001-256e83917d98» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "1c9e6689-65a0-4d4b-b001-256e83917d98"
rowId := "1c9e6689-65a0-4d4b-b001-256e83917d98"
rowState := #["String", "String.dropEndWhile", Declaration.def {
name := `String.dropEndWhile
renderedStatement := "String.dropEndWhile {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.BackwardPattern pat] :\n String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.dropEndWhile", Declaration.def {
name := `String.Slice.dropEndWhile
renderedStatement := "String.Slice.dropEndWhile {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.BackwardPattern pat] : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «b836052b-3470-4a8e-8989-6951c898de37» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "b836052b-3470-4a8e-8989-6951c898de37"
rowId := "b836052b-3470-4a8e-8989-6951c898de37"
rowState := #["String", "String.takeEndWhile", Declaration.def {
name := `String.takeEndWhile
renderedStatement := "String.takeEndWhile {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.BackwardPattern pat] :\n String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.takeEndWhile", Declaration.def {
name := `String.Slice.takeEndWhile
renderedStatement := "String.Slice.takeEndWhile {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.BackwardPattern pat] : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «5aa777d8-9642-43d8-9e20-30400fb8bb9d» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "5aa777d8-9642-43d8-9e20-30400fb8bb9d"
rowId := "5aa777d8-9642-43d8-9e20-30400fb8bb9d"
rowState := #["String", "String.dropPrefix", Declaration.def {
name := `String.dropPrefix
renderedStatement := "String.dropPrefix {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.ForwardPattern pat] :\n String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.dropPrefix", Declaration.def {
name := `String.Slice.dropPrefix
renderedStatement := "String.Slice.dropPrefix {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.ForwardPattern pat] : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «80e3869d-fcfe-459d-8433-fe221f7b3c7a» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "80e3869d-fcfe-459d-8433-fe221f7b3c7a"
rowId := "80e3869d-fcfe-459d-8433-fe221f7b3c7a"
rowState := #["String", "String.dropSuffix", Declaration.def {
name := `String.dropSuffix
renderedStatement := "String.dropSuffix {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.BackwardPattern pat] :\n String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.dropSuffix", Declaration.def {
name := `String.Slice.dropSuffix
renderedStatement := "String.Slice.dropSuffix {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.BackwardPattern pat] : String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .bad
comment := "Missing position transformations"
}
def «4feda3e0-903b-4d52-b34e-0af70f7866e0» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "4feda3e0-903b-4d52-b34e-0af70f7866e0"
rowId := "4feda3e0-903b-4d52-b34e-0af70f7866e0"
rowState := #["String", "String.dropPrefix?", Declaration.def {
name := `String.dropPrefix?
renderedStatement := "String.dropPrefix? {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.ForwardPattern pat] :\n Option String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.dropPrefix?", Declaration.def {
name := `String.Slice.dropPrefix?
renderedStatement := "String.Slice.dropPrefix? {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.ForwardPattern pat] : Option String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .postponed
comment := "Missing position transformations"
}
def «45ca44c8-fbd5-4400-8297-a60778f302b0» : AssociationTable.Fact .declaration where
widgetId := "slice-producing"
factId := "45ca44c8-fbd5-4400-8297-a60778f302b0"
rowId := "45ca44c8-fbd5-4400-8297-a60778f302b0"
rowState := #["String", "String.dropSuffix?", Declaration.def {
name := `String.dropSuffix?
renderedStatement := "String.dropSuffix? {ρ : Type} (s : String) (pat : ρ) [String.Slice.Pattern.BackwardPattern pat] :\n Option String.Slice"
isDeprecated := false
}
,"String.Slice", "String.Slice.dropSuffix?", Declaration.def {
name := `String.Slice.dropSuffix?
renderedStatement := "String.Slice.dropSuffix? {ρ : Type} (s : String.Slice) (pat : ρ)\n [String.Slice.Pattern.BackwardPattern pat] : Option String.Slice"
isDeprecated := false
}
,]
metadata := {
status := .postponed
comment := "Missing position transformations"
}
def table : AssociationTable.Data .declaration where
widgetId := "slice-producing"
rows := #[
"c8a13d6d-7ed6-4cd1-a386-23e2d55ce6f7", "slice", #["String", "String.slice","String.Slice", "String.Slice.slice","string-pos-forwards", "String.Pos.slice","string-pos-backwards", "String.Pos.ofSlice","string-slice-pos-forwards", "String.Slice.Pos.slice","string-slice-pos-backwards", "String.Slice.Pos.ofSlice","string-pos-noproof", "String.Pos.sliceOrPanic","string-slice-pos-noproof", "String.Slice.Pos.sliceOrPanic",],
"21b4fdfd-f8b3-44f5-a59e-57f1dc1d6819", "slice?", #["String", "String.slice?","String.Slice", "String.Slice.slice?",],
"6f2b6ecb-2f0c-4e45-9da3-eb7f2e15eff0", "slice!", #["String", "String.slice!","String.Slice", "String.Slice.slice!","string-pos-forwards", "String.Pos.slice!","string-pos-backwards", "String.Pos.ofSlice!","string-slice-pos-forwards", "String.Slice.Pos.slice!","string-slice-pos-backwards", "String.Slice.Pos.ofSlice!",],
"a3bdf66d-bc11-4019-aee9-2f1c1701de52", "trimAsciiStart", #["String", "String.trimAsciiStart","String.Slice", "String.Slice.trimAsciiStart",],
"f12b2730-7a4d-465c-8a6d-9d051c300fd5", "trimAsciiEnd", #["String", "String.trimAsciiEnd","String.Slice", "String.Slice.trimAsciiEnd",],
"32307b55-d6d1-4756-a947-dbe4dfde573c", "trimAscii", #["String", "String.trimAscii","String.Slice", "String.Slice.trimAscii",],
"dce95a38-f55a-4d6a-ae79-078ffe4b5c15", "toSlice", #["String", "String.toSlice","string-pos-forwards", "String.Pos.toSlice","string-pos-backwards", "String.Pos.ofToSlice",],
"005a3f30-5dab-493f-b168-32c36a2bdf7c", "str", #["String.Slice", "String.Slice.str","string-slice-pos-forwards", "String.Slice.Pos.str","string-slice-pos-backwards", "String.Slice.Pos.ofStr",],
"5f1a154c-ae2f-43a1-9409-2ce95b163ef3", "drop", #["String", "String.drop","String.Slice", "String.Slice.drop",],
"179518d1-ad07-4b2b-8ffe-3b7616e4c4ab", "take", #["String", "String.take","String.Slice", "String.Slice.take",],
"55c587fd-a7a8-4633-a4ae-e2c4e768ad28", "dropWhile", #["String", "String.dropWhile","String.Slice", "String.Slice.dropWhile",],
"d4444684-4279-4400-9be2-561a7cdb32c1", "takeWhile", #["String", "String.takeWhile","String.Slice", "String.Slice.takeWhile",],
"1c9e6689-65a0-4d4b-b001-256e83917d98", "dropEndWhile", #["String", "String.dropEndWhile","String.Slice", "String.Slice.dropEndWhile",],
"b836052b-3470-4a8e-8989-6951c898de37", "takeEndWhile", #["String", "String.takeEndWhile","String.Slice", "String.Slice.takeEndWhile",],
"5aa777d8-9642-43d8-9e20-30400fb8bb9d", "dropPrefix", #["String", "String.dropPrefix","String.Slice", "String.Slice.dropPrefix",],
"80e3869d-fcfe-459d-8433-fe221f7b3c7a", "dropSuffix", #["String", "String.dropSuffix","String.Slice", "String.Slice.dropSuffix",],
"4feda3e0-903b-4d52-b34e-0af70f7866e0", "dropPrefix?", #["String", "String.dropPrefix?","String.Slice", "String.Slice.dropPrefix?",],
"45ca44c8-fbd5-4400-8297-a60778f302b0", "dropSuffix?", #["String", "String.dropSuffix?","String.Slice", "String.Slice.dropSuffix?",],
]
facts := #[
«c8a13d6d-7ed6-4cd1-a386-23e2d55ce6f7»,
«21b4fdfd-f8b3-44f5-a59e-57f1dc1d6819»,
«6f2b6ecb-2f0c-4e45-9da3-eb7f2e15eff0»,
«a3bdf66d-bc11-4019-aee9-2f1c1701de52»,
«f12b2730-7a4d-465c-8a6d-9d051c300fd5»,
«32307b55-d6d1-4756-a947-dbe4dfde573c»,
«dce95a38-f55a-4d6a-ae79-078ffe4b5c15»,
«005a3f30-5dab-493f-b168-32c36a2bdf7c»,
«5f1a154c-ae2f-43a1-9409-2ce95b163ef3»,
«179518d1-ad07-4b2b-8ffe-3b7616e4c4ab»,
«55c587fd-a7a8-4633-a4ae-e2c4e768ad28»,
«d4444684-4279-4400-9be2-561a7cdb32c1»,
«1c9e6689-65a0-4d4b-b001-256e83917d98»,
«b836052b-3470-4a8e-8989-6951c898de37»,
«5aa777d8-9642-43d8-9e20-30400fb8bb9d»,
«80e3869d-fcfe-459d-8433-fe221f7b3c7a»,
«4feda3e0-903b-4d52-b34e-0af70f7866e0»,
«45ca44c8-fbd5-4400-8297-a60778f302b0»,
]
def restoreState : RestoreStateM Unit := do
addAssociationTable table

View File

@@ -15,7 +15,7 @@ namespace GroveStdlib
namespace Std
def introduction : Node :=
.text "introduction", "Welcome to the interactive Lean standard library outline!"
.text "Welcome to the interactive Lean standard library outline!"
end Std

View File

@@ -11,87 +11,9 @@ namespace GroveStdlib.Std.CoreTypesAndOperations
namespace StringsAndFormatting
open Lean Meta
def introduction : Text where
id := "string-introduction"
content := Grove.Markdown.render [
.h1 "The Lean string library",
.text "The Lean standard library contains a fully-featured string library, centered around the types `String` and `String.Slice`.",
.text "`String` is defined as the subtype of `ByteArray` of valid UTF-8 strings. A `String.Slice` is a `String` together with a start and end position.",
.text "`String` is equivalent to `List Char`, but it has a more efficient runtime representation. While the logical model based on `ByteArray` is overwritten in the runtime, the runtime implementation is very similar to the logical model, with the main difference being that the length of a string in Unicode code points is cached in the runtime implementation.",
.text "We are considering removing this feature in the future (i.e., deprecating `String.length`), as the number of UTF-8 codepoints in a string is not particularly useful, and if needed it can be computed in linear time using `s.positions.count`."
]
def highLevelStringTypes : List Lean.Name :=
[`String, `String.Slice, `String.Pos, `String.Slice.Pos]
def creatingStringsAndSlices : Text where
id := "transforming-strings-and-slices"
content := Grove.Markdown.render [
.h2 "Transforming strings and slices",
.text "The Lean standard library contains a number of functions that take one or more strings and slices and return a string or a slice.",
.text "If possible, these functions should avoid allocating a new string, and return a slice of their input(s) instead.",
.text "Usually, for every operation `f`, there will be functions `String.f` and `String.Slice.f`, where `String.f s` is defined as `String.Slice.f s.toSlice`.",
.text "In particular, functions that transform strings and slices should live in the `String` and `String.Slice` namespaces even if they involve a `String.Pos`/`String.Slice.Pos` (like `String.sliceTo`), for reasons that will become clear shortly.",
.h3 "Transforming positions",
.text "Since positions on strings and slices are dependent on the string or slice, whenever users transform a string/slice, they will be interested in interpreting positions on the original string/slice as positions on the result, or vice versa.",
.text "Consequently, every operation that transforms a string or slice should come with a corresponding set of transformations between positions, usually in both directions, possibly with one of the directions being conditional.",
.text "For example, given a string `s` and a position `p` on `s`, we have the slice `s.sliceFrom p`, which is the slice from `p` to the end of `s`. A position on `s.sliceFrom p` can always be interpreted as a position on `s`. This is the \"backwards\" transformation. Conversely, a position `q` on `s` can be interpreted as a position on `s.sliceFrom p` as long as `p ≤ q`. This is the conditional forwards direction.",
.text "The convention for naming these transformations is that the forwards transformation should have the same name as the transformation on strings/slices, but it should be located in the `String.Pos` or `String.Slice.Pos` namespace, depending on the type of the starting position (so that dot notation is possible for the forward direction). The backwards transformation should have the same name as the operation on strings/slices, but with an `of` prefix, and live in the same namespace as the forwards transformation (so in general dot notation will not be available).",
.text "So, in the `sliceFrom` example, the forward direction would be called `String.Pos.sliceFrom`, while the backwards direction should be called `String.Pos.ofSliceFrom` (not `String.Slice.Pos.ofSliceFrom`).",
.text "If one of the directions is conditional, it should have a corresponding panicking operation that does not require a proof; in our example this would be `String.Pos.sliceFrom!`.",
.text "Sometimes there is a name clash for the panicking operations if the operation on strings is already panicking. For example, there are both `String.slice` and `String.slice!`. If the original operation is already panicking, we only provide panicking transformation operations. But now `String.Pos.slice!` could refer both to the panicking forwards transformation associated with `String.slice`, and also to the (only) forwards transformation associated with `String.slice!`. In this situation, we use an `orPanic` suffix to disambiguate. So the panicking forwards operation associated with `String.slice` is called `String.Pos.sliceOrPanic`, and the forwards operation associated with `String.slice!` is called `String.Pos.slice!`."
]
-- TODO: also include the `HAppend` instance(s)
def sliceProducing : AssociationTable (β := Alias Lean.Name) .declaration
[`String, `String.Slice,
Alias.mk `String.Pos "string-pos-forwards" "String.Pos (forwards)",
Alias.mk `String.Pos "string-pos-backwards" "String.Pos (backwards)",
Alias.mk `String.Pos "string-pos-noproof" "String.Pos (no proof)",
Alias.mk `String.Slice.Pos "string-slice-pos-forwards" "String.Slice.Pos (forwards)",
Alias.mk `String.Slice.Pos "string-slice-pos-backwards" "String.Slice.Pos (backwards)",
Alias.mk `String.Slice.Pos "string-slice-pos-noproof" "String.Slice.Pos (no proof)"] where
id := "slice-producing"
title := "String functions returning strings or slices"
description := "Operations on strings and string slices that themselves return a new string slice."
dataSources n := DataSource.definitionsInNamespace n.inner
def sliceProducingComplete : Assertion where
widgetId := "slice-producing-complete"
title := "Slice-producing table is complete"
description := "All functions in the `String.**` namespace that return a string or a slice are covered in the table"
check := do
let mut ans := #[]
let covered := Std.HashSet.ofArray ( valuesInAssociationTable sliceProducing)
let pred : DataSource.DeclarationPredicate :=
DataSource.DeclarationPredicate.all [.isDefinition, .not .isDeprecated,
.notInNamespace `String.Pos.Raw, .notInNamespace `String.Legacy,
.not .isInstance]
let env getEnv
for name in declarationsMatching `String pred do
let some c := env.find? name | continue
if c.type.getForallBody.getUsedConstants.any (fun n => n == ``String || n == ``String.Slice) then
let success : Bool := name.toString covered
ans := ans.push {
assertionId := name.toString
description := s!"`{name}` should appear in the table."
passed := success
message := s!"`{name}` was{if success then "" else " not"} found in the table."
}
return ans
end StringsAndFormatting
open StringsAndFormatting
def stringsAndFormatting : Node :=
.section "strings-and-formatting" "Strings and formatting"
#[.text introduction,
.text creatingStringsAndSlices,
.associationTable sliceProducing,
.assertion sliceProducingComplete]
.section "strings-and-formatting" "Strings and formatting" #[]
end GroveStdlib.Std.CoreTypesAndOperations
end GroveStdlib.Std.CoreTypesAndOperations

View File

@@ -5,7 +5,7 @@
"type": "git",
"subDir": "backend",
"scope": "",
"rev": "c580a425c9b7fa2aebaec2a1d8de16b2e2283c40",
"rev": "3e8aabdea58c11813c5d3b7eeb187ded44ee9a34",
"name": "grove",
"manifestFile": "lake-manifest.json",
"inputRev": "master",
@@ -15,10 +15,10 @@
"type": "git",
"subDir": null,
"scope": "leanprover",
"rev": "d9fc8ae23024be37424a189982c92356e37935c8",
"rev": "1604206fcd0462da9a241beeac0e2df471647435",
"name": "Cli",
"manifestFile": "lake-manifest.json",
"inputRev": "nightly-testing",
"inputRev": "main",
"inherited": true,
"configFile": "lakefile.toml"}],
"name": "grovestdlib",

View File

@@ -810,7 +810,7 @@ Docstrings for constants should have the following structure:
The **short summary** should be 13 sentences (ideally 1) and provide
enough information for most readers to quickly decide whether the
constant is relevant to their task. The first (or only) sentence of
docstring is relevant to their task. The first (or only) sentence of
the short summary should be a *sentence fragment* in which the subject
is implied to be the documented item, written in present tense
indicative, or a *noun phrase* that characterizes the documented
@@ -1123,110 +1123,6 @@ infix:50 " ⇔ " => Bijection
recommended_spelling "bij" for "⇔" in [Bijection, «term_⇔_»]
```
#### Tactics
Docstrings for tactics should have the following structure:
* Short summary
* Details
* Variants
* Examples
Sometimes more than one declaration is needed to implement what the user
sees as a single tactic. In that case, only one declaration should have
the associated docstring, and the others should have the `tactic_alt`
attribute to mark them as an implementation detail.
The **short summary** should be 13 sentences (ideally 1) and provide
enough information for most readers to quickly decide whether the
tactic is relevant to their task. The first (or only) sentence of
the short summary should be a full sentence in which the subject
is an example invocation of the tactic, written in present tense
indicative. If the example tactic invocation names parameters, then the
short summary may refer to them. For the example invocation, prefer the
simplest or most typical example. Explain more complicated forms in the
variants section. If needed, abbreviate the invocation by naming part of
the syntax and expanding it in the next sentence. The summary should be
written as a single paragraph.
**Details**, if needed, may be 1-3 paragraphs that describe further
relevant information. They may insert links as needed. This section
should fully explain the scope of the tactic: its syntax format,
on which goals it works and what the resulting goal(s) look like. It
should be clear whether the tactic fails if it does not close the main
goal and whether it creates any side goals. The details may include
explanatory examples that cant necessarily be machine checked and
dont fit the format.
If the tactic is extensible using `macro_rules`, mention this in the
details, with a link to `lean-manual://section/tactic-macro-extension`
and give a one-line example. If the tactic provides an attribute or a
command that allows the user to extend its behavior, the documentation
on how to extend the tactic belongs to that attribute or command. In the
tactic docstring, use a single sentence to refer the reader to this
further documentation.
**Variants**, if needed, should be a bulleted list describing different
options and forms of the same tactic. The reader should be able to parse
and understand the parts of a tactic invocation they are hovering over,
using this list. Each list item should describe an individual variant
and take one of two formats: the **short summary** as above, or a
**named list item**. A named list item consists of a title in bold
followed by an indented short paragraph.
Variants should be explained from the perspective of the tactic's users, not
their implementers. A tactic that is implemented as a single Lean parser may
have multiple variants from the perspective of users, while a tactic that is
implemented as multiple parsers may have no variants, but merely an optional
part of the syntax.
**Examples** should start with the line `Examples:` (or `Example:` if
theres exactly one). The section should consist of a sequence of code
blocks, each showing a Lean declaration (usually with the `example`
keyword) that invokes the tactic. When the effect of the tactic is not
clear from the code, you can use code comments to describe this. Do
not include text between examples, because it can be unclear whether
the text refers to the code before or after the example.
##### Example
````
`rw [e]` uses the expression `e` as a rewrite rule on the main goal,
then tries to close the goal by "cheap" (reducible) `rfl`.
If `e` is a defined constant, then the equational theorems associated with `e`
are used. This provides a convenient way to unfold `e`. If `e` has parameters,
the tactic will try to fill these in by unification with the matching part of
the target. Parameters are only filled in once per rule, restricting which
later rewrites can be found. Parameters that are not filled in after
unification will create side goals. If the `rfl` fails to close the main goal,
no error is raised.
`rw` may fail to rewrite terms "under binders", such as `∀ x, ...` or `∃ x,
...`. `rw` can also fail with a "motive is type incorrect" error in the context
of dependent types. In these cases, consider using `simp only`.
* `rw [e₁, ... eₙ]` applies the given rules sequentially.
* `rw [← e]` or `rw [<- e]` applies the rewrite in the reverse direction.
* `rw [e] at l` rewrites with `e` at location(s) `l`.
* `rw (occs := .pos L) [e]`, where `L` is a literal list of natural numbers,
only rewrites the given occurrences in the target. Occurrences count from 1.
* `rw (occs := .neg L) [e]`, where `L` is a literal list of natural numbers,
skips rewriting the given occurrences in the target. Occurrences count from 1.
Examples:
```lean
example {a b : Nat} (h : a + a = b) : (a + a) + (a + a) = b + b := by rw [h]
```
```lean
example {f : Nat -> Nat} (h : ∀ x, f x = 1) (a b : Nat) : f a = f b := by
rw [h] -- `rw` instantiates `h` only once, so this is equivalent to: `rw [h a]`
-- goal: ⊢ 1 = f b
rw [h] -- equivalent to: `rw [h b]`
```
````
## Dictionary

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

@@ -3,21 +3,16 @@ Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sebastian Ullrich
-/
module
import Lean.Environment
import Lake.CLI.Main
import Lean.ExtraModUses
import Lake.CLI.Main
import Lean.Parser.Module
import Lake.Load.Workspace
/-! # Shake: A Lean import minimizer
/-! # `lake exe shake` command
This command will check the current project (or a specified target module) and all dependencies for
unused imports. This works by looking at generated `.olean` files to deduce required imports and
ensuring that every import is used to contribute some constant or other elaboration dependency
recorded by `recordExtraModUse` and friends.
recorded by `recordExtraModUse`. Because recompilation is not needed this is quite fast (about 8
seconds to check `Mathlib` and all dependencies).
-/
/-- help string for the command line interface -/
@@ -33,83 +28,13 @@ Options:
--force
Skips the `lake build --no-build` sanity check
--keep-implied
Preserves existing imports that are implied by other imports and thus not technically needed
anymore
--keep-prefix
If an import `X` would be replaced in favor of a more specific import `X.Y...` it implies,
preserves the original import instead. More generally, prefers inserting `import X` even if it
was not part of the original imports as long as it was in the original transitive import closure
of the current module.
--keep-public
Preserves all `public` imports to avoid breaking changes for external downstream modules
--add-public
Adds new imports as `public` if they have been in the original public closure of that module.
In other words, public imports will not be removed from a module unless they are unused even
in the private scope, and those that are removed will be re-added as `public` in downstream
modules even if only needed in the private scope there. Unlike `--keep-public`, this may
introduce breaking changes but will still limit the number of inserted imports.
--explain
Gives constants explaining why each module is needed
--fix
Apply the suggested fixes directly. Make sure you have a clean checkout
before running this, so you can review the changes.
--gh-style
Outputs messages that can be parsed by `gh-problem-matcher-wrap`
Annotations:
The following annotations can be added to Lean files in order to configure the behavior of
`shake`. Only the substring `shake: ` directly followed by a directive is checked for, so multiple
directives can be mixed in one line such as `-- shake: keep-downstream, shake: keep-all`, and they
can be surrounded by arbitrary comments such as `-- shake: keep (metaprogram output dependency)`.
* `module -- shake: keep-downstream`:
Preserves this module in all (current) downstream modules, adding new imports of it if needed.
* `module -- shake: keep-all`:
Preserves all existing imports in this module as is. New imports now needed because of upstream
changes may still be added.
* `import X -- shake: keep`:
Preserves this specific import in the current module. The most common use case is to preserve a
public import that will be needed in downstream modules to make sense of the output of a
metaprogram defined in this module. For example, if a tactic is defined that may synthesize a
reference to a theorem when run, there is no way for `shake` to detect this by itself and the
module of that theorem should be publicly imported and annotated with `keep` in the tactic's
module.
```
public import X -- shake: keep (metaprogram output dependency)
...
elab \"my_tactic\" : tactic => do
... mkConst ``f -- `f`, defined in `X`, may appear in the output of this tactic
```
"
open Lean
/-- The parsed CLI arguments. See `help` for more information -/
structure Args where
help : Bool := false
keepImplied : Bool := false
keepPrefix : Bool := false
keepPublic : Bool := false
addPublic : Bool := false
force : Bool := false
githubStyle : Bool := false
explain : Bool := false
trace : Bool := false
fix : Bool := false
/-- `<MODULE>..`: the list of root modules to check -/
mods : Array Name := #[]
/-- We use `Nat` as a bitset for doing efficient set operations.
The bit indexes will usually be a module index. -/
structure Bitset where
@@ -163,7 +88,7 @@ def ofImport : Lean.Import → NeedsKind
end NeedsKind
/-- Logically, a map `NeedsKind → Set ModuleIdx`, or `Set Import`. -/
/-- Logically, a map `NeedsKind → Bitset`. -/
structure Needs where
pub : Bitset
priv : Bitset
@@ -199,20 +124,6 @@ def Needs.union (needs : Needs) (k : NeedsKind) (s : Bitset) : Needs :=
def Needs.sub (needs : Needs) (k : NeedsKind) (s : Bitset) : Needs :=
needs.modify k (fun s' => s' ^^^ (s' s))
instance : Union Needs where
union a b := {
pub := a.pub b.pub
priv := a.priv b.priv
metaPub := a.metaPub b.metaPub
metaPriv := a.metaPriv b.metaPriv }
/-- The list of edits that will be applied in `--fix`. `edits[i] = (removed, added)` where:
* If `j ∈ removed` then we want to delete module named `j` from the imports of `i`
* If `j ∈ added` then we want to add module index `j` to the imports of `i`.
-/
abbrev Edits := Std.HashMap Name (Array Import × Array Import)
/-- The main state of the checker, containing information on all loaded modules. -/
structure State where
env : Environment
@@ -220,11 +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 := #[]
/--
@@ -232,10 +142,6 @@ structure State where
changes to upstream headers.
-/
transDepsOrig : Array Needs := #[]
/-- Modules that should always be preserved downstream. -/
preserve : Needs := default
/-- Edits to be applied to the module imports. -/
edits : Edits := {}
def State.mods (s : State) := s.env.header.moduleData
def State.modNames (s : State) := s.env.header.moduleNames
@@ -256,10 +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
@@ -267,49 +173,20 @@ 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
def isDeclMeta' (env : Environment) (declName : Name) : Bool :=
-- Matchers are not compiled by themselves but inlined by the compiler, so there is no IR decl
-- to be tagged as `meta`.
-- TODO: It would be better to base the entire `meta` inference on the IR only and consider module
-- references from any other context as compatible with both phases.
let inferFor :=
if declName.isStr && (declName.getString!.startsWith "match_" || declName.getString! == "_unsafe_rec") then declName.getPrefix else declName
-- `isMarkedMeta` knows about non-defs such as `meta structure`, isDeclMeta knows about decls
-- implicitly marked meta
isMarkedMeta env inferFor || isDeclMeta env inferFor
/--
Given an `Expr` reference, returns the declaration name that should be considered the reference, if
any.
-/
def getDepConstName? (env : Environment) (ref : Name) : Option Name := do
-- Ignore references to reserved names, they can be re-generated in-place
guard <| !isReservedName env ref
-- `_simp_...` constants are similar, use base decl instead
return if ref.isStr && ref.getString!.startsWith "_simp_" then
ref.getPrefix
else
ref
/-- Calculates the needs for a given module `mod` from constants and recorded extra uses. -/
def calcNeeds (s : State) (i : ModuleIdx) : Needs := Id.run do
let env := s.env
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 k := { isExported := pubCI?.isSome, isMeta := isDeclMeta' env 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
-- type and value has identical visibility under `meta`
@@ -324,33 +201,23 @@ def calcNeeds (s : State) (i : ModuleIdx) : Needs := Id.run do
return needs
where
/-- Accumulate the results from expression `e` into `deps`. -/
visitExpr (k : NeedsKind) (e : Expr) (deps : Needs) : Needs :=
let env := s.env
Lean.Expr.foldConsts e deps fun c deps => Id.run do
let mut deps := deps
if let some c := getDepConstName? env c then
if let some j := env.getModuleIdxFor? c then
let k := { k with isMeta := k.isMeta && !isDeclMeta' env c }
if j != i then
deps := deps.union k {j}
for indMod in (indirectModUseExt.getState env)[c]?.getD #[] do
if s.transDeps[i]!.has k indMod then
deps := deps.union k {indMod}
return deps
abbrev Explanations := Std.HashMap (ModuleIdx × NeedsKind) (Option (Name × Name))
visitExpr (k : NeedsKind) e deps :=
Lean.Expr.foldConsts e deps fun c deps => match env.getModuleIdxFor? c with
| some j =>
let k := { k with isMeta := k.isMeta && !isMeta env c }
if j != i then deps.union k {j} else deps
| _ => deps
/--
Calculates the same as `calcNeeds` but tracing each module to a use-def declaration pair or
`none` if merely a recorded extra use.
-/
def getExplanations (s : State) (i : ModuleIdx) : Explanations := Id.run do
let env := s.env
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 k := { isExported := pubCI?.isSome, isMeta := isDeclMeta' env 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
let k := if k.isMeta then k else
@@ -366,25 +233,18 @@ def getExplanations (s : State) (i : ModuleIdx) : Explanations := Id.run do
where
/-- Accumulate the results from expression `e` into `deps`. -/
visitExpr (k : NeedsKind) name e deps :=
let env := s.env
Lean.Expr.foldConsts e deps fun c deps => Id.run do
let mut deps := deps
if let some c := getDepConstName? env c then
if let some j := env.getModuleIdxFor? c then
let k := { k with isMeta := k.isMeta && !isDeclMeta' env c }
deps := addExplanation j k name c deps
for indMod in (indirectModUseExt.getState env)[c]?.getD #[] do
if s.transDeps[i]!.has k indMod then
deps := addExplanation indMod k name (`_indirect ++ c) deps
return deps
addExplanation (j : ModuleIdx) (k : NeedsKind) (use def_ : Name) (deps : Explanations) : Explanations :=
if
if let some (some (name', _)) := deps[(j, k)]? then
decide (use.toString.length < name'.toString.length)
else true
then
deps.insert (j, k) (use, def_)
else deps
Lean.Expr.foldConsts e deps fun c deps => match env.getModuleIdxFor? c with
| some i =>
let k := { k with isMeta := k.isMeta && !isMeta env c }
if
if let some (some (name', _)) := deps[(i, k)]? then
decide (name.toString.length < name'.toString.length)
else true
then
deps.insert (i, k) (name, c)
else
deps
| _ => deps
partial def initStateFromEnv (env : Environment) : State := Id.run do
let mut s := { env }
@@ -400,6 +260,13 @@ partial def initStateFromEnv (env : Environment) : State := Id.run do
s := { s with transDepsOrig := s.transDeps }
return s
/-- The list of edits that will be applied in `--fix`. `edits[i] = (removed, added)` where:
* If `j ∈ removed` then we want to delete module named `j` from the imports of `i`
* If `j ∈ added` then we want to add module index `j` to the imports of `i`.
-/
abbrev Edits := Std.HashMap Name (Array Import × Array Import)
/-- Register that we want to remove `tgt` from the imports of `src`. -/
def Edits.remove (ed : Edits) (src : Name) (tgt : Import) : Edits :=
match ed.get? src with
@@ -418,8 +285,8 @@ Returns `(path, inputCtx, imports, endPos)` where `imports` is the `Lean.Parser.
and `endPos` is the position of the end of the header.
-/
def parseHeaderFromString (text path : String) :
IO (System.FilePath × (ictx : Parser.InputContext) ×
TSyntax ``Parser.Module.header × String.Pos ictx.fileMap.source) := do
IO (System.FilePath × Parser.InputContext ×
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
@@ -427,8 +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 := inputCtx.fileMap.source.pos! insertion |>.find (· == '\n') |>.next!
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.
@@ -436,19 +303,14 @@ Returns `(path, inputCtx, imports, endPos)` where `imports` is the `Lean.Parser.
and `endPos` is the position of the end of the header.
-/
def parseHeader (srcSearchPath : SearchPath) (mod : Name) :
IO (System.FilePath × (ictx : Parser.InputContext) ×
TSyntax ``Parser.Module.header × String.Pos ictx.fileMap.source) := do
IO (System.FilePath × Parser.InputContext ×
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)
| stx => panic! s!"unexpected header syntax {stx}"
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 }
@@ -456,174 +318,63 @@ def decodeImport : TSyntax ``Parser.Module.import → Import
/-- Analyze and report issues from module `i`. Arguments:
* `pkg`: the first component of the module name
* `srcSearchPath`: Used to find the path for error reporting purposes
* `i`: the module index
* `needs`: the module's calculated needs
* `pinned`: dependencies that should be preserved even if unused
* `edits`: accumulates the list of edits to apply if `--fix` is true
* `addOnly`: if true, only add missing imports, do not remove unused ones
-/
def visitModule (pkg : Name) (srcSearchPath : SearchPath)
(i : Nat) (needs : Needs) (headerStx : TSyntax ``Parser.Module.header) (args : Args)
(addOnly := false) : StateT State IO Unit := do
if isExtraRevModUse ( get).env i then
modify fun s => { s with preserve := s.preserve.union (if args.addPublic then .pub else .priv) {i} }
if args.trace then
IO.eprintln s!"Preserving `{(← get).modNames[i]!}` because of recorded extra rev use"
-- only process modules in the selected package
-- TODO: should be after `keep-downstream` but core headers are not found yet?
if !pkg.isPrefixOf ( get).modNames[i]! then
return
let (module?, prelude?, imports) := decodeHeader headerStx
if module?.any (·.raw.getTrailing?.any (·.toString.contains "shake: keep-downstream")) then
modify fun s => { s with preserve := s.preserve.union (if args.addPublic then .pub else .priv) {i} }
def visitModule (srcSearchPath : SearchPath)
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits)
(addOnly := false) (githubStyle := false) (explain := false) : StateT State IO Edits := do
let s get
let addOnly := addOnly || module?.any (·.raw.getTrailing?.any (·.toString.contains "shake: keep-all"))
-- Do transitive reduction of `needs` in `deps`.
let mut deps := needs
for j in [0:s.mods.size] do
let transDeps := s.transDeps[j]!
for k in NeedsKind.all do
if s.transDepsOrig[i]!.has k j && preserve.has k j then
deps := deps.union k {j}
if deps.has k j then
let transDeps := addTransitiveImps .empty { k with module := .anonymous } j transDeps
for k' in NeedsKind.all do
deps := deps.sub k' (transDeps.sub k' {j} |>.get k')
-- Add additional preserved imports
for impStx in imports do
let imp := decodeImport impStx
-- Any import which is not in `transDeps` was unused.
-- Also accumulate `newDeps` which is the transitive closure of the remaining imports
let mut toRemove : Array Import := #[]
let mut newDeps := Needs.empty
for imp in s.mods[i]!.imports do
let j := s.env.getModuleIdx? imp.module |>.get!
let k := NeedsKind.ofImport imp
if addOnly ||
args.keepPublic && imp.isExported ||
impStx.raw.getTrailing?.any (·.toString.contains "shake: keep") then
deps := deps.union k {j}
if args.trace then
IO.eprintln s!"Adding `{imp}` as additional dependency"
if
-- skip folder-nested imports
s.modNames[i]!.isPrefixOf imp.module ||
imp.importAll then
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
else
let k := NeedsKind.ofImport imp
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]!
-- If `newDeps` does not cover `deps`, then we have to add back some imports until it does.
-- To minimize new imports we pick only new imports which are not transitively implied by
-- another new import
let mut toAdd : Array Import := #[]
for j in [0:s.mods.size] do
for k in NeedsKind.all do
-- Remove `meta` while preserving, no use-case for preserving `meta` so far.
-- Downgrade to private unless `--add-public` is used.
if s.transDepsOrig[i]!.has k j &&
(s.preserve.has { k with isMeta := false, isExported := false } j ||
s.preserve.has { k with isMeta := false, isExported := true } j) then
deps := deps.union { k with isMeta := false, isExported := k.isExported && args.addPublic } {j}
-- Do transitive reduction of `needs` in `deps`.
if !addOnly then
for j in [0:s.mods.size] do
let transDeps := s.transDeps[j]!
for k in NeedsKind.all do
if deps.has k j then
let transDeps := addTransitiveImps .empty { k with module := .anonymous } j transDeps
for k' in NeedsKind.all do
deps := deps.sub k' (transDeps.sub k' {j} |>.get k')
if prelude?.isNone then
deps := deps.union .pub {s.env.getModuleIdx? `Init |>.get!}
-- Accumulate `transDeps` which is the non-reflexive transitive closure of the still-live imports
let mut transDeps := Needs.empty
let mut alwaysAdd : Array Import := #[] -- to be added even if implied by other imports
for imp in s.mods[i]!.imports do
let j := s.env.getModuleIdx? imp.module |>.get!
let k := NeedsKind.ofImport imp
if deps.has k j || imp.importAll then
transDeps := addTransitiveImps transDeps imp j s.transDeps[j]!
deps := deps.union k {j}
-- skip folder-nested `public (meta)? import`s but remove `meta`
else if s.modNames[i]!.isPrefixOf imp.module then
let imp := { imp with isMeta := false }
let k := { k with isMeta := false }
if args.trace then
IO.eprintln s!"`{imp}` is preserved as folder-nested import"
transDeps := addTransitiveImps transDeps imp j s.transDeps[j]!
deps := deps.union k {j}
if !s.mods[i]!.imports.contains imp then
alwaysAdd := alwaysAdd.push imp
-- If `transDeps` does not cover `deps`, then we have to add back some imports until it does.
-- To minimize new imports we pick only new imports which are not transitively implied by
-- another new import, so we visit module indices in descending order.
let mut keptPrefix := false
let mut newTransDeps := transDeps
let mut toAdd : Array Import := #[]
for j in (0...s.mods.size).toArray.reverse do
for k in NeedsKind.all do
if deps.has k j && !newTransDeps.has k j && !newTransDeps.has { k with isExported := true } j then
-- `add-public/keep-prefix` may change the import and even module we're considering
let mut k := k
let mut imp : Import := { k with module := s.modNames[j]! }
let mut j := j
if args.trace then
IO.eprintln s!"`{imp}` is needed{if needs.has k j then " (calculated)" else ""}"
if args.addPublic && !k.isExported &&
-- also add as public if previously `public meta`, which could be from automatic porting
(s.transDepsOrig[i]!.has { k with isExported := true } j || s.transDepsOrig[i]!.has { k with isExported := true, isMeta := true } j) then
k := { k with isExported := true }
imp := { imp with isExported := true }
if args.trace then
IO.eprintln s!"* upgrading to `{imp}` because of `--add-public`"
if args.keepPrefix then
let rec tryPrefix : Name Option ModuleIdx
| .str p _ => tryPrefix p <|> (do
let j' s.env.getModuleIdx? p
-- `j'` must be reachable from `i` (allow downgrading from `meta`)
guard <| s.transDepsOrig[i]!.has k j' || s.transDepsOrig[i]!.has { k with isMeta := true } j'
let j'transDeps := addTransitiveImps .empty p j' s.transDeps[j']!
-- `j` must be reachable from `j'` (now downgrading must be done in the other direction)
guard <| j'transDeps.has k j || j'transDeps.has { k with isMeta := false } j
return j')
| _ => none
if let some j' := tryPrefix imp.module then
imp := { imp with module := s.modNames[j']! }
j := j'
keptPrefix := true
if args.trace then
IO.eprintln s!"* upgrading to `{imp}` because of `--keep-prefix`"
if !s.mods[i]!.imports.contains imp then
toAdd := toAdd.push imp
deps := deps.union k {j}
newTransDeps := addTransitiveImps newTransDeps imp j s.transDeps[j]!
if keptPrefix then
-- if an import was replaced by `--keep-prefix`, we did not necessarily visit the modules in
-- dependency order anymore and so we have to redo the transitive closure checking
newTransDeps := transDeps
for j in (0...s.mods.size).toArray.reverse do
for k in NeedsKind.all do
if deps.has k j then
let mut imp : Import := { k with module := s.modNames[j]! }
if toAdd.contains imp && (newTransDeps.has k j || newTransDeps.has { k with isExported := true } j) then
if args.trace then
IO.eprintln s!"Removing `{imp}` from imports to be added because it is now implied"
toAdd := toAdd.erase imp
deps := deps.sub k {j}
else
newTransDeps := addTransitiveImps newTransDeps imp j s.transDeps[j]!
-- now that `toAdd` filtering is done, add `alwaysAdd`
toAdd := alwaysAdd ++ toAdd
-- Any import which is still not in `deps` was unused
let mut toRemove : Array Import := #[]
for imp in s.mods[i]!.imports do
let j := s.env.getModuleIdx? imp.module |>.get!
let k := NeedsKind.ofImport imp
if args.keepImplied && newTransDeps.has k j then
if args.trace && !deps.has k j then
IO.eprintln s!"`{imp}` is implied by other imports"
else if !deps.has k j then
if args.trace then
IO.eprintln s!"`{imp}` is now unused"
toRemove := toRemove.push imp
-- A private import should also be removed if the public version has been added
else if !k.isExported && !imp.importAll && newTransDeps.has { k with isExported := true } j then
if args.trace then
IO.eprintln s!"`{imp}` is already covered by `{ { imp with isExported := true } }`"
toRemove := toRemove.push imp
if deps.has k j && !newDeps.has k j && !newDeps.has { k with isExported := true } j then
let imp := { k with module := s.modNames[j]! }
toAdd := toAdd.push imp
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
-- mark and report the removals
modify fun s => { s with
edits := toRemove.foldl (init := s.edits) fun edits imp =>
edits.remove s.modNames[i]! imp }
let mut edits := toRemove.foldl (init := edits) fun edits imp =>
edits.remove s.modNames[i]! imp
if !toAdd.isEmpty || !toRemove.isEmpty || args.explain then
if !toAdd.isEmpty || !toRemove.isEmpty || explain then
if let some path srcSearchPath.findModuleWithExt "lean" s.modNames[i]! then
println! "{path}:"
else
@@ -632,10 +383,9 @@ def visitModule (pkg : Name) (srcSearchPath : SearchPath)
if !toRemove.isEmpty then
println! " remove {toRemove}"
if args.githubStyle then
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!
@@ -643,15 +393,14 @@ def visitModule (pkg : Name) (srcSearchPath : SearchPath)
(use `lake exe shake --fix` to fix this, or `lake exe shake --update` to ignore)"
if !toAdd.isEmpty then
-- we put the insert message on the beginning of the last import line
let pos := inputCtx.fileMap.toPosition endHeader.offset
let pos := inputCtx.fileMap.toPosition endHeader
println! "{path}:{pos.line-1}:1: warning: \
add {toAdd} instead"
catch _ => pure ()
-- mark and report the additions
modify fun s => { s with
edits := toAdd.foldl (init := s.edits) fun edits imp =>
edits.add s.modNames[i]! imp }
edits := toAdd.foldl (init := edits) fun edits imp =>
edits.add s.modNames[i]! imp
if !toAdd.isEmpty then
println! " add {toAdd}"
@@ -666,15 +415,14 @@ def visitModule (pkg : Name) (srcSearchPath : SearchPath)
let j := s.env.getModuleIdx? imp.module |>.get!
newTransDepsI := addTransitiveImps newTransDepsI imp j s.transDeps[j]!
modify fun s => { s with transDeps := s.transDeps.set! i newTransDepsI }
set { s with transDeps := s.transDeps.set! i newTransDepsI }
if args.explain then
let explanation := getExplanations s i
if explain then
let explanation := getExplanations s.env i
let sanitize n := if n.hasMacroScopes then (sanitizeName n).run' { options := {} } else n
let run (imp : Import) := do
let j := s.env.getModuleIdx? imp.module |>.get!
let mut k := NeedsKind.ofImport imp
if let some exp? := explanation[(j, k)]? <|> guard args.addPublic *> explanation[(j, { k with isExported := false})]? then
if let some exp? := explanation[(j, NeedsKind.ofImport imp)]? then
println! " note: `{imp}` required"
if let some (n, c) := exp? then
println! " because `{sanitize n}` refers to `{sanitize c}`"
@@ -685,6 +433,8 @@ def visitModule (pkg : Name) (srcSearchPath : SearchPath)
run j
for i in toAdd do run i
return edits
/-- Convert a list of module names to a bitset of module indexes -/
def toBitset (s : State) (ns : List Name) : Bitset :=
ns.foldl (init := ) fun c name =>
@@ -692,26 +442,40 @@ def toBitset (s : State) (ns : List Name) : Bitset :=
| some i => c {i}
| none => c
/-- The parsed CLI arguments. See `help` for more information -/
structure Args where
/-- `--help`: shows the help -/
help : Bool := false
/-- `--force`: skips the `lake build --no-build` sanity check -/
force : Bool := false
/-- `--gh-style`: output messages that can be parsed by `gh-problem-matcher-wrap` -/
githubStyle : Bool := false
/-- `--explain`: give constants explaining why each module is needed -/
explain : Bool := false
/-- `--fix`: apply the fixes directly -/
fix : Bool := false
/-- `<MODULE>..`: the list of root modules to check -/
mods : Array Name := #[]
local instance : Ord Import where
compare :=
let _ := @lexOrd
compareOn fun imp => (!imp.isExported, imp.module.toString)
compare a b :=
if a.isExported && !b.isExported then
Ordering.lt
else if !a.isExported && b.isExported then
Ordering.gt
else
a.module.cmp b.module
/-- The main entry point. See `help` for more information on arguments. -/
public def main (args : List String) : IO UInt32 := do
def main (args : List String) : IO UInt32 := do
initSearchPath ( findSysroot)
-- Parse the arguments
let rec parseArgs (args : Args) : List String Args
| [] => args
| "--help" :: rest => parseArgs { args with help := true } rest
| "--keep-implied" :: rest => parseArgs { args with keepImplied := true } rest
| "--keep-prefix" :: rest => parseArgs { args with keepPrefix := true } rest
| "--keep-public" :: rest => parseArgs { args with keepPublic := true } rest
| "--add-public" :: rest => parseArgs { args with addPublic := true } rest
| "--force" :: rest => parseArgs { args with force := true } rest
| "--fix" :: rest => parseArgs { args with fix := true } rest
| "--explain" :: rest => parseArgs { args with explain := true } rest
| "--trace" :: rest => parseArgs { args with trace := true } rest
| "--gh-style" :: rest => parseArgs { args with githubStyle := true } rest
| "--" :: rest => { args with mods := args.mods ++ rest.map (·.toName) }
| other :: rest => parseArgs { args with mods := args.mods.push other.toName } rest
@@ -754,72 +518,62 @@ public def main (args : List String) : IO UInt32 := do
let imps := mods.map ({ module := · })
let (_, s) importModulesCore imps (isExported := true) |>.run
let s := s.markAllExported
let mut env finalizeImport s (isModule := true) imps {} (leakEnv := false) (loadExts := false)
-- the one env ext we want to initialize
let is := indirectModUseExt.toEnvExtension.getState env
let newState indirectModUseExt.addImportedFn is.importedEntries { env := env, opts := {} }
env := indirectModUseExt.toEnvExtension.setState (asyncMode := .sync) env { is with state := newState }
let env finalizeImport s (isModule := true) imps {} (leakEnv := false) (loadExts := false)
StateT.run' (s := initStateFromEnv env) do
let s get
-- Parse the config file
-- Run the calculation of the `needs` array in parallel
let needs := s.mods.mapIdx fun i _ =>
Task.spawn fun _ => calcNeeds s i
-- Parse headers in parallel
let headers s.mods.mapIdxM fun i _ =>
if !pkg.isPrefixOf s.modNames[i]! then
pure <| Task.pure <| .ok default, default, default, default
else
BaseIO.asTask (parseHeader srcSearchPath s.modNames[i]! |>.toBaseIO)
Task.spawn fun _ => calcNeeds s.env i
if args.fix then
println! "The following changes will be made automatically:"
-- Check all selected modules
for i in [0:s.mods.size], t in needs, header in headers do
match header.get with
| .ok _, _, stx, _ =>
visitModule pkg srcSearchPath i t.get stx args
| .error e =>
println! e.toString
let mut edits : Edits :=
let mut revNeeds : Needs := default
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 ( get).edits.isEmpty then 0 else 1
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) := ( get).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 text := text.startPos
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 ++ text.extract pos (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.pos! stx.raw.getTailPos?.get! |>.find '\n' |>.next!
pos := text.findAux (· == '\n') text.rawEndPos stx.raw.getTailPos?.get! + 1
seen := seen.insert mod
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 ++ text.extract insertion text.endPos
out := out ++ text.extract insertion text.rawEndPos
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

@@ -1,441 +0,0 @@
#!/usr/bin/env python3
"""
build_artifact.py: Download pre-built CI artifacts for a Lean commit.
Usage:
build_artifact.py # Download artifact for current HEAD
build_artifact.py --sha abc1234 # Download artifact for specific commit
build_artifact.py --clear-cache # Clear artifact cache
This script downloads pre-built binaries from GitHub Actions CI runs,
which is much faster than building from source (~30s vs 2-5min).
Artifacts are cached in ~/.cache/lean_build_artifact/ for reuse.
"""
import argparse
import json
import os
import platform
import shutil
import subprocess
import sys
import urllib.request
import urllib.error
from pathlib import Path
from typing import Optional
# Constants
GITHUB_API_BASE = "https://api.github.com"
LEAN4_REPO = "leanprover/lean4"
# CI artifact cache
CACHE_DIR = Path.home() / '.cache' / 'lean_build_artifact'
ARTIFACT_CACHE = CACHE_DIR
# Sentinel value indicating CI failed (don't bother building locally)
CI_FAILED = object()
# ANSI colors for terminal output
class Colors:
RED = '\033[91m'
GREEN = '\033[92m'
YELLOW = '\033[93m'
BLUE = '\033[94m'
BOLD = '\033[1m'
RESET = '\033[0m'
def color(text: str, c: str) -> str:
"""Apply color to text if stdout is a tty."""
if sys.stdout.isatty():
return f"{c}{text}{Colors.RESET}"
return text
def error(msg: str) -> None:
"""Print error message and exit."""
print(color(f"Error: {msg}", Colors.RED), file=sys.stderr)
sys.exit(1)
def warn(msg: str) -> None:
"""Print warning message."""
print(color(f"Warning: {msg}", Colors.YELLOW), file=sys.stderr)
def info(msg: str) -> None:
"""Print info message."""
print(color(msg, Colors.BLUE), file=sys.stderr)
def success(msg: str) -> None:
"""Print success message."""
print(color(msg, Colors.GREEN), file=sys.stderr)
# -----------------------------------------------------------------------------
# Platform detection
# -----------------------------------------------------------------------------
def get_artifact_name() -> Optional[str]:
"""Get CI artifact name for current platform."""
system = platform.system()
machine = platform.machine()
if system == 'Darwin':
if machine == 'arm64':
return 'build-macOS aarch64'
return 'build-macOS' # Intel
elif system == 'Linux':
if machine == 'aarch64':
return 'build-Linux aarch64'
return 'build-Linux release'
# Windows not supported for CI artifact download
return None
# -----------------------------------------------------------------------------
# GitHub API helpers
# -----------------------------------------------------------------------------
_github_token_warning_shown = False
def get_github_token() -> Optional[str]:
"""Get GitHub token from environment or gh CLI."""
global _github_token_warning_shown
# Check environment variable first
token = os.environ.get('GITHUB_TOKEN')
if token:
return token
# Try to get token from gh CLI
try:
result = subprocess.run(
['gh', 'auth', 'token'],
capture_output=True,
text=True,
timeout=5
)
if result.returncode == 0 and result.stdout.strip():
return result.stdout.strip()
except (FileNotFoundError, subprocess.TimeoutExpired):
pass
# Warn once if no token available
if not _github_token_warning_shown:
_github_token_warning_shown = True
warn("No GitHub authentication found. API rate limits may apply.")
warn("Run 'gh auth login' or set GITHUB_TOKEN to avoid rate limiting.")
return None
def github_api_request(url: str) -> dict:
"""Make a GitHub API request and return JSON response."""
headers = {
'Accept': 'application/vnd.github.v3+json',
'User-Agent': 'build-artifact'
}
token = get_github_token()
if token:
headers['Authorization'] = f'token {token}'
req = urllib.request.Request(url, headers=headers)
try:
with urllib.request.urlopen(req, timeout=30) as response:
return json.loads(response.read().decode())
except urllib.error.HTTPError as e:
if e.code == 403:
error(f"GitHub API rate limit exceeded. Set GITHUB_TOKEN environment variable to increase limit.")
elif e.code == 404:
error(f"GitHub resource not found: {url}")
else:
error(f"GitHub API error: {e.code} {e.reason}")
except urllib.error.URLError as e:
error(f"Network error accessing GitHub API: {e.reason}")
# -----------------------------------------------------------------------------
# CI artifact cache functions
# -----------------------------------------------------------------------------
def get_cache_path(sha: str) -> Path:
"""Get cache directory for a commit's artifact."""
return ARTIFACT_CACHE / sha[:12]
def is_cached(sha: str) -> bool:
"""Check if artifact for this commit is already cached and valid."""
cache_path = get_cache_path(sha)
return cache_path.exists() and (cache_path / 'bin' / 'lean').exists()
def check_zstd_support() -> bool:
"""Check if tar supports zstd compression."""
try:
result = subprocess.run(
['tar', '--zstd', '--version'],
capture_output=True,
timeout=5
)
return result.returncode == 0
except (subprocess.TimeoutExpired, FileNotFoundError):
return False
def check_gh_available() -> bool:
"""Check if gh CLI is available and authenticated."""
try:
result = subprocess.run(
['gh', 'auth', 'status'],
capture_output=True,
timeout=10
)
return result.returncode == 0
except (subprocess.TimeoutExpired, FileNotFoundError):
return False
def download_ci_artifact(sha: str, quiet: bool = False):
"""
Try to download CI artifact for a commit.
Returns:
- Path to extracted toolchain directory if available
- CI_FAILED sentinel if CI run failed (don't bother building locally)
- None if no artifact available but local build might work
"""
# Check cache first
if is_cached(sha):
return get_cache_path(sha)
artifact_name = get_artifact_name()
if artifact_name is None:
return None # Unsupported platform
cache_path = get_cache_path(sha)
try:
# Query for CI workflow run for this commit, including status
# Note: Query parameters must be in the URL for GET requests
result = subprocess.run(
['gh', 'api', f'repos/{LEAN4_REPO}/actions/runs?head_sha={sha}&per_page=100',
'--jq', r'.workflow_runs[] | select(.name == "CI") | "\(.id) \(.conclusion // "null")"'],
capture_output=True,
text=True,
timeout=30
)
if result.returncode != 0 or not result.stdout.strip():
return None # No CI run found (old commit?)
# Parse "run_id conclusion" format
line = result.stdout.strip().split('\n')[0]
parts = line.split(' ', 1)
run_id = parts[0]
conclusion = parts[1] if len(parts) > 1 else "null"
# Check if the desired artifact exists for this run
result = subprocess.run(
['gh', 'api', f'repos/{LEAN4_REPO}/actions/runs/{run_id}/artifacts',
'--jq', f'.artifacts[] | select(.name == "{artifact_name}") | .id'],
capture_output=True,
text=True,
timeout=30
)
if result.returncode != 0 or not result.stdout.strip():
# No artifact available
# If CI failed and no artifact, the build itself likely failed - skip
if conclusion == "failure":
return CI_FAILED
# Otherwise (in progress, expired, etc.) - fall back to local build
return None
# Download artifact
cache_path.mkdir(parents=True, exist_ok=True)
if not quiet:
print("downloading CI artifact... ", end='', flush=True)
result = subprocess.run(
['gh', 'run', 'download', run_id,
'-n', artifact_name,
'-R', LEAN4_REPO,
'-D', str(cache_path)],
capture_output=True,
text=True,
timeout=600 # 10 minutes for large downloads
)
if result.returncode != 0:
shutil.rmtree(cache_path, ignore_errors=True)
return None
# Extract tar.zst - find the file (name varies by platform/version)
tar_files = list(cache_path.glob('*.tar.zst'))
if not tar_files:
shutil.rmtree(cache_path, ignore_errors=True)
return None
tar_file = tar_files[0]
if not quiet:
print("extracting... ", end='', flush=True)
result = subprocess.run(
['tar', '--zstd', '-xf', tar_file.name],
cwd=cache_path,
capture_output=True,
timeout=300
)
if result.returncode != 0:
shutil.rmtree(cache_path, ignore_errors=True)
return None
# Move contents up from lean-VERSION-PLATFORM/ to cache_path/
# The extracted directory name varies (e.g., lean-4.15.0-linux, lean-4.15.0-darwin_aarch64)
extracted_dirs = [d for d in cache_path.iterdir() if d.is_dir() and d.name.startswith('lean-')]
if extracted_dirs:
extracted = extracted_dirs[0]
for item in extracted.iterdir():
dest = cache_path / item.name
if dest.exists():
if dest.is_dir():
shutil.rmtree(dest)
else:
dest.unlink()
shutil.move(str(item), str(cache_path / item.name))
extracted.rmdir()
# Clean up tar file
tar_file.unlink()
# Verify the extraction worked
if not (cache_path / 'bin' / 'lean').exists():
shutil.rmtree(cache_path, ignore_errors=True)
return None
return cache_path
except (subprocess.TimeoutExpired, FileNotFoundError):
shutil.rmtree(cache_path, ignore_errors=True)
return None
# -----------------------------------------------------------------------------
# Git helpers
# -----------------------------------------------------------------------------
def get_current_commit() -> str:
"""Get the current git HEAD commit SHA."""
try:
result = subprocess.run(
['git', 'rev-parse', 'HEAD'],
capture_output=True,
text=True,
timeout=5
)
if result.returncode == 0:
return result.stdout.strip()
error(f"Failed to get current commit: {result.stderr.strip()}")
except subprocess.TimeoutExpired:
error("Timeout getting current commit")
except FileNotFoundError:
error("git not found")
def resolve_sha(short_sha: str) -> str:
"""Resolve a (possibly short) SHA to full 40-character SHA using git rev-parse."""
if len(short_sha) == 40:
return short_sha
try:
result = subprocess.run(
['git', 'rev-parse', short_sha],
capture_output=True,
text=True,
timeout=5
)
if result.returncode == 0:
full_sha = result.stdout.strip()
if len(full_sha) == 40:
return full_sha
error(f"Cannot resolve SHA '{short_sha}': {result.stderr.strip() or 'not found in repository'}")
except subprocess.TimeoutExpired:
error(f"Timeout resolving SHA '{short_sha}'")
except FileNotFoundError:
error("git not found - required for SHA resolution")
# -----------------------------------------------------------------------------
# Main
# -----------------------------------------------------------------------------
def main():
parser = argparse.ArgumentParser(
description='Download pre-built CI artifacts for a Lean commit.',
formatter_class=argparse.RawDescriptionHelpFormatter,
epilog="""
This script downloads pre-built binaries from GitHub Actions CI runs,
which is much faster than building from source (~30s vs 2-5min).
Artifacts are cached in ~/.cache/lean_build_artifact/ for reuse.
Examples:
build_artifact.py # Download for current HEAD
build_artifact.py --sha abc1234 # Download for specific commit
build_artifact.py --clear-cache # Clear cache to free disk space
"""
)
parser.add_argument('--sha', metavar='SHA',
help='Commit SHA to download artifact for (default: current HEAD)')
parser.add_argument('--clear-cache', action='store_true',
help='Clear artifact cache and exit')
parser.add_argument('--quiet', '-q', action='store_true',
help='Suppress progress messages (still prints result path)')
args = parser.parse_args()
# Handle cache clearing
if args.clear_cache:
if ARTIFACT_CACHE.exists():
size = sum(f.stat().st_size for f in ARTIFACT_CACHE.rglob('*') if f.is_file())
shutil.rmtree(ARTIFACT_CACHE)
info(f"Cleared cache at {ARTIFACT_CACHE} ({size / 1024 / 1024:.1f} MB)")
else:
info(f"Cache directory does not exist: {ARTIFACT_CACHE}")
return
# Get commit SHA
if args.sha:
sha = resolve_sha(args.sha)
else:
sha = get_current_commit()
if not args.quiet:
info(f"Commit: {sha[:12]}")
# Check prerequisites
if not check_gh_available():
error("gh CLI not available or not authenticated. Run 'gh auth login' first.")
if not check_zstd_support():
error("tar does not support zstd compression. Install zstd or a newer tar.")
artifact_name = get_artifact_name()
if artifact_name is None:
error(f"No CI artifacts available for this platform ({platform.system()} {platform.machine()})")
if not args.quiet:
info(f"Platform: {artifact_name}")
# Check cache
if is_cached(sha):
path = get_cache_path(sha)
if not args.quiet:
success("Using cached artifact")
print(path)
return
# Download artifact
result = download_ci_artifact(sha, quiet=args.quiet)
if result is CI_FAILED:
if not args.quiet:
print() # End the "downloading..." line
error(f"CI build failed for commit {sha[:12]}")
elif result is None:
if not args.quiet:
print() # End the "downloading..." line
error(f"No CI artifact available for commit {sha[:12]}")
else:
if not args.quiet:
print(color("done", Colors.GREEN))
print(result)
if __name__ == '__main__':
main()

View File

@@ -7,5 +7,3 @@ root = "Modulize"
[[lean_exe]]
name = "shake"
root = "Shake"
# needed by `Lake.loadWorkspace`
supportInterpreter = true

File diff suppressed because it is too large Load Diff

View File

@@ -1,307 +0,0 @@
/-
Copyright Strata Contributors
SPDX-License-Identifier: Apache-2.0 OR MIT
-/
namespace Strata
namespace Python
/-
Parser and translator for some basic regular expression patterns supported by
Python's `re` library
Ref.: https://docs.python.org/3/library/re.html
Also see
https://github.com/python/cpython/blob/759a048d4bea522fda2fe929be0fba1650c62b0e/Lib/re/_parser.py
for a reference implementation.
-/
-------------------------------------------------------------------------------
inductive ParseError where
/--
`patternError` is raised when Python's `re.patternError` exception is
raised.
[Reference: Python's re exceptions](https://docs.python.org/3/library/re.html#exceptions):
"Exception raised when a string passed to one of the functions here is not a
valid regular expression (for example, it might contain unmatched
parentheses) or when some other error occurs during compilation or matching.
It is never an error if a string contains no match for a pattern."
-/
| patternError (message : String) (pattern : String) (pos : String.Pos.Raw)
/--
`unimplemented` is raised whenever we don't support some regex operations
(e.g., lookahead assertions).
-/
| unimplemented (message : String) (pattern : String) (pos : String.Pos.Raw)
deriving Repr
def ParseError.toString : ParseError String
| .patternError msg pat pos => s!"Pattern error at position {pos.byteIdx}: {msg} in pattern '{pat}'"
| .unimplemented msg pat pos => s!"Unimplemented at position {pos.byteIdx}: {msg} in pattern '{pat}'"
instance : ToString ParseError where
toString := ParseError.toString
-------------------------------------------------------------------------------
/--
Regular Expression Nodes
-/
inductive RegexAST where
/-- Single literal character: `a` -/
| char : Char RegexAST
/-- Character range: `[a-z]` -/
| range : Char Char RegexAST
/-- Alternation: `a|b` -/
| union : RegexAST RegexAST RegexAST
/-- Concatenation: `ab` -/
| concat : RegexAST RegexAST RegexAST
/-- Any character: `.` -/
| anychar : RegexAST
/-- Zero or more: `a*` -/
| star : RegexAST RegexAST
/-- One or more: `a+` -/
| plus : RegexAST RegexAST
/-- Zero or one: `a?` -/
| optional : RegexAST RegexAST
/-- Bounded repetition: `a{n,m}` -/
| loop : RegexAST Nat Nat RegexAST
/-- Start of string: `^` -/
| anchor_start : RegexAST
/-- End of string: `$` -/
| anchor_end : RegexAST
/-- Grouping: `(abc)` -/
| group : RegexAST RegexAST
/-- Empty string: `()` or `""` -/
| empty : RegexAST
/-- Complement: `[^a-z]` -/
| complement : RegexAST RegexAST
deriving Inhabited, Repr
-------------------------------------------------------------------------------
/-- Parse character class like [a-z], [0-9], etc. into union of ranges and
chars. Note that this parses `|` as a character. -/
def parseCharClass (s : String) (pos : String.Pos.Raw) : Except ParseError (RegexAST × String.Pos.Raw) := do
if pos.get? s != some '[' then throw (.patternError "Expected '[' at start of character class" s pos)
let mut i := pos.next s
-- Check for complement (negation) with leading ^
let isComplement := !i.atEnd s && i.get? s == some '^'
if isComplement then
i := i.next s
let mut result : Option RegexAST := none
-- Process each element in the character class.
while !i.atEnd s && i.get? s != some ']' do
-- Uncommenting this makes the code stop
--dbg_trace "Working" (pure ())
let some c1 := i.get? s | throw (.patternError "Invalid character in class" s i)
let i1 := i.next s
-- Check for range pattern: c1-c2.
if !i1.atEnd s && i1.get? s == some '-' then
let i2 := i1.next s
if !i2.atEnd s && i2.get? s != some ']' then
let some c2 := i2.get? s | throw (.patternError "Invalid character in range" s i2)
if c1 > c2 then
throw (.patternError s!"Invalid character range [{c1}-{c2}]: \
start character '{c1}' is greater than end character '{c2}'" s i)
let r := RegexAST.range c1 c2
-- Union with previous elements.
result := some (match result with | none => r | some prev => RegexAST.union prev r)
i := i2.next s
continue
-- Single character.
let r := RegexAST.char c1
result := some (match result with | none => r | some prev => RegexAST.union prev r)
i := i.next s
let some ast := result | throw (.patternError "Unterminated character set" s pos)
let finalAst := if isComplement then RegexAST.complement ast else ast
pure (finalAst, i.next s)
-------------------------------------------------------------------------------
/-- Parse numeric repeats like `{10}` or `{1,10}` into min and max bounds. -/
def parseBounds (s : String) (pos : String.Pos.Raw) : Except ParseError (Nat × Nat × String.Pos.Raw) := do
if pos.get? s != some '{' then throw (.patternError "Expected '{' at start of bounds" s pos)
let mut i := pos.next s
let mut numStr := ""
-- Parse first number.
while !i.atEnd s && (i.get? s).any Char.isDigit do
numStr := numStr.push ((i.get? s).get!)
i := i.next s
let some n := numStr.toNat? | throw (.patternError "Invalid minimum bound" s pos)
-- Check for comma (range) or closing brace (exact count).
match i.get? s with
| some '}' => pure (n, n, i.next s) -- {n} means exactly n times.
| some ',' =>
i := i.next s
-- Parse maximum bound
numStr := ""
while !i.atEnd s && (i.get? s).any Char.isDigit do
numStr := numStr.push ((i.get? s).get!)
i := i.next s
let some max := numStr.toNat? | throw (.patternError "Invalid maximum bound" s i)
if i.get? s != some '}' then throw (.patternError "Expected '}' at end of bounds" s i)
-- Validate bounds order
if max < n then
throw (.patternError s!"Invalid repeat bounds \{{n},{max}}: \
maximum {max} is less than minimum {n}" s pos)
pure (n, max, i.next s)
| _ => throw (.patternError "Invalid bounds syntax" s i)
-------------------------------------------------------------------------------
mutual
/--
Parse atom: single element (char, class, anchor, group) with optional
quantifier. Stops at the first `|`.
-/
partial def parseAtom (s : String) (pos : String.Pos.Raw) : Except ParseError (RegexAST × String.Pos.Raw) := do
if pos.atEnd s then throw (.patternError "Unexpected end of regex" s pos)
let some c := pos.get? s | throw (.patternError "Invalid position" s pos)
-- Detect invalid quantifier at start
if c == '*' || c == '+' || c == '{' || c == '?' then
throw (.patternError s!"Quantifier '{c}' at position {pos} has nothing to quantify" s pos)
-- Detect unbalanced closing parenthesis
if c == ')' then
throw (.patternError "Unbalanced parenthesis" s pos)
-- Parse base element (anchor, char class, group, anychar, escape, or single char).
let (base, nextPos) match c with
| '^' => pure (RegexAST.anchor_start, pos.next s)
| '$' => pure (RegexAST.anchor_end, pos.next s)
| '[' => parseCharClass s pos
| '(' => parseExplicitGroup s pos
| '.' => pure (RegexAST.anychar, pos.next s)
| '\\' =>
-- Handle escape sequence.
-- Note: Python uses a single backslash as an escape character, but Lean
-- strings need to escape that. After DDMification, we will see two
-- backslashes in Strata for every Python backslash.
let nextPos := pos.next s
if nextPos.atEnd s then throw (.patternError "Incomplete escape sequence at end of regex" s pos)
let some escapedChar := nextPos.get? s | throw (.patternError "Invalid escape position" s nextPos)
-- Check for special sequences (unsupported right now).
match escapedChar with
| 'A' | 'b' | 'B' | 'd' | 'D' | 's' | 'S' | 'w' | 'W' | 'z' | 'Z' =>
throw (.unimplemented s!"Special sequence \\{escapedChar} is not supported" s pos)
| 'a' | 'f' | 'n' | 'N' | 'r' | 't' | 'u' | 'U' | 'v' | 'x' =>
throw (.unimplemented s!"Escape sequence \\{escapedChar} is not supported" s pos)
| c =>
if c.isDigit then
throw (.unimplemented s!"Backreference \\{c} is not supported" s pos)
else
pure (RegexAST.char escapedChar, nextPos.next s)
| _ => pure (RegexAST.char c, pos.next s)
-- Check for numeric repeat suffix on base element (but not on anchors)
match base with
| .anchor_start | .anchor_end => pure (base, nextPos)
| _ =>
if !nextPos.atEnd s then
match nextPos.get? s with
| some '{' =>
let (min, max, finalPos) parseBounds s nextPos
pure (RegexAST.loop base min max, finalPos)
| some '*' =>
let afterStar := nextPos.next s
if !afterStar.atEnd s then
match afterStar.get? s with
| some '?' => throw (.unimplemented "Non-greedy quantifier *? is not supported" s nextPos)
| some '+' => throw (.unimplemented "Possessive quantifier *+ is not supported" s nextPos)
| _ => pure (RegexAST.star base, afterStar)
else pure (RegexAST.star base, afterStar)
| some '+' =>
let afterPlus := nextPos.next s
if !afterPlus.atEnd s then
match afterPlus.get? s with
| some '?' => throw (.unimplemented "Non-greedy quantifier +? is not supported" s nextPos)
| some '+' => throw (.unimplemented "Possessive quantifier ++ is not supported" s nextPos)
| _ => pure (RegexAST.plus base, afterPlus)
else pure (RegexAST.plus base, afterPlus)
| some '?' =>
let afterQuestion := nextPos.next s
if !afterQuestion.atEnd s then
match afterQuestion.get? s with
| some '?' => throw (.unimplemented "Non-greedy quantifier ?? is not supported" s nextPos)
| some '+' => throw (.unimplemented "Possessive quantifier ?+ is not supported" s nextPos)
| _ => pure (RegexAST.optional base, afterQuestion)
else pure (RegexAST.optional base, afterQuestion)
| _ => pure (base, nextPos)
else
pure (base, nextPos)
/-- Parse explicit group with parentheses. -/
partial def parseExplicitGroup (s : String) (pos : String.Pos.Raw) : Except ParseError (RegexAST × String.Pos.Raw) := do
if pos.get? s != some '(' then throw (.patternError "Expected '(' at start of group" s pos)
let mut i := pos.next s
-- Check for extension notation (?...
if !i.atEnd s && i.get? s == some '?' then
let i1 := i.next s
if !i1.atEnd s then
match i1.get? s with
| some '=' => throw (.unimplemented "Positive lookahead (?=...) is not supported" s pos)
| some '!' => throw (.unimplemented "Negative lookahead (?!...) is not supported" s pos)
| _ => throw (.unimplemented "Extension notation (?...) is not supported" s pos)
let (inner, finalPos) parseGroup s i (some ')')
pure (.group inner, finalPos)
/-- Parse group: handles alternation and concatenation at current scope. -/
partial def parseGroup (s : String) (pos : String.Pos.Raw) (endChar : Option Char) :
Except ParseError (RegexAST × String.Pos.Raw) := do
let mut alternatives : List (List RegexAST) := [[]]
let mut i := pos
-- Parse until end of string or `endChar`.
while !i.atEnd s && (endChar.isNone || i.get? s != endChar) do
if i.get? s == some '|' then
-- Push a new scope to `alternatives`.
alternatives := [] :: alternatives
i := i.next s
else
let (ast, nextPos) parseAtom s i
alternatives := match alternatives with
| [] => [[ast]]
| head :: tail => (ast :: head) :: tail
i := nextPos
-- Check for expected end character.
if let some ec := endChar then
if i.get? s != some ec then
throw (.patternError s!"Expected '{ec}'" s i)
i := i.next s
-- Build result: concatenate each alternative, then union them.
let concatAlts := alternatives.reverse.filterMap fun alt =>
match alt.reverse with
| [] => -- Empty regex.
some (.empty)
| [single] => some single
| head :: tail => some (tail.foldl RegexAST.concat head)
match concatAlts with
| [] => pure (.empty, i)
| [single] => pure (single, i)
| head :: tail => pure (tail.foldl RegexAST.union head, i)
end
/-- info: Except.ok (Strata.Python.RegexAST.range 'A' 'z', { byteIdx := 5 }) -/
#guard_msgs in
#eval parseCharClass "[A-z]" 0
-- Test code: Print done
#print "Done!"

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

@@ -31,8 +31,6 @@ 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
@@ -501,57 +499,6 @@ 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)")
@@ -816,12 +763,6 @@ 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

@@ -50,26 +50,12 @@ repositories:
dependencies:
- lean4-cli
- name: lean4-unicode-basic
url: https://github.com/fgdorais/lean4-unicode-basic
toolchain-tag: true
stable-branch: false
branch: main
dependencies: []
- name: BibtexQuery
url: https://github.com/dupuisf/BibtexQuery
toolchain-tag: true
stable-branch: false
branch: master
dependencies: [lean4-unicode-basic]
- name: doc-gen4
url: https://github.com/leanprover/doc-gen4
toolchain-tag: true
stable-branch: false
branch: main
dependencies: [lean4-cli, BibtexQuery]
dependencies: [lean4-cli]
- name: reference-manual
url: https://github.com/leanprover/reference-manual
@@ -127,30 +113,10 @@ repositories:
dependencies:
- mathlib4
- name: verso-web-components
url: https://github.com/leanprover/verso-web-components
toolchain-tag: true
stable-branch: false
branch: main
dependencies:
- verso
- name: lean-fro.org
url: https://github.com/leanprover/lean-fro.org
toolchain-tag: false
stable-branch: false
branch: master
dependencies:
- verso-web-components
- name: comparator
url: https://github.com/leanprover/comparator
toolchain-tag: true
stable-branch: false
branch: master
- name: lean4export
url: https://github.com/leanprover/lean4export
toolchain-tag: true
stable-branch: false
branch: master
- verso

View File

@@ -23,7 +23,6 @@ What this script does:
- Special merging strategies for repositories with nightly-testing branches
- Safety checks for repositories using bump branches
- Custom build and test procedures
- lean-fro.org: runs scripts/update.sh to regenerate site content
6. Commits the changes with message "chore: bump toolchain to {version}"
@@ -413,14 +412,20 @@ def execute_release_steps(repo, version, config):
run_command("lake update", cwd=repo_path, stream_output=True)
print(blue("Running `lake update` in examples/hero..."))
run_command("lake update", cwd=repo_path / "examples" / "hero", stream_output=True)
# Run scripts/update.sh to regenerate content
print(blue("Running `scripts/update.sh` to regenerate content..."))
run_command("scripts/update.sh", cwd=repo_path, stream_output=True)
print(green("Content regenerated successfully"))
elif repo_name == "cslib":
print(blue("Updating lakefile.toml..."))
run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)
print(blue("Updating docs/lakefile.toml..."))
run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path / "docs")
# Update lean-toolchain in docs
print(blue("Updating docs/lean-toolchain..."))
docs_toolchain = repo_path / "docs" / "lean-toolchain"
with open(docs_toolchain, "w") as f:
f.write(f"leanprover/lean4:{version}\n")
print(green(f"Updated docs/lean-toolchain to leanprover/lean4:{version}"))
run_command("lake update", cwd=repo_path, stream_output=True)
elif dependencies:
run_command(f'perl -pi -e \'s/"v4\\.[0-9]+(\\.[0-9]+)?(-rc[0-9]+)?"/"' + version + '"/g\' lakefile.*', cwd=repo_path)

View File

@@ -10,7 +10,7 @@ endif()
include(ExternalProject)
project(LEAN CXX C)
set(LEAN_VERSION_MAJOR 4)
set(LEAN_VERSION_MINOR 28)
set(LEAN_VERSION_MINOR 26)
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")
@@ -448,8 +448,8 @@ if(LLVM AND ${STAGE} GREATER 0)
# - In particular, `host/bin/llvm-config` produces flags like `-Lllvm-host/lib/libLLVM`, while
# we need the path to be `-Lllvm/lib/libLLVM`. Thus, we perform this replacement here.
string(REPLACE "llvm-host" "llvm" LEANSHARED_LINKER_FLAGS ${LEANSHARED_LINKER_FLAGS})
string(REPLACE "llvm-host" "llvm" CMAKE_CXX_FLAGS ${CMAKE_CXX_FLAGS})
message(VERBOSE "leanshared linker flags: '${LEANSHARED_LINKER_FLAGS}' | lean extra cxx flags '${CMAKE_CXX_FLAGS}'")
string(REPLACE "llvm-host" "llvm" LEAN_EXTRA_CXX_FLAGS ${LEAN_EXTRA_CXX_FLAGS})
message(VERBOSE "leanshared linker flags: '${LEANSHARED_LINKER_FLAGS}' | lean extra cxx flags '${LEAN_EXTR_CXX_FLAGS}'")
endif()
# get rid of unused parts of C++ stdlib
@@ -695,7 +695,7 @@ endif()
set(STDLIBS Init Std Lean Leanc)
if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
list(APPEND STDLIBS Lake LeanChecker)
list(APPEND STDLIBS Lake)
endif()
add_custom_target(make_stdlib ALL
@@ -758,12 +758,6 @@ if(NOT ${CMAKE_SYSTEM_NAME} MATCHES "Emscripten")
DEPENDS lake_shared
COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make lake
VERBATIM)
add_custom_target(leanchecker ALL
WORKING_DIRECTORY ${LEAN_SOURCE_DIR}
DEPENDS lake_shared
COMMAND $(MAKE) -f ${CMAKE_BINARY_DIR}/stdlib.make leanchecker
VERBATIM)
endif()
if(PREV_STAGE)

View File

@@ -14,8 +14,8 @@ 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.WFComputable
public import Init.WFTactics
public import Init.Data
public import Init.System

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

@@ -102,7 +102,7 @@ noncomputable def strongIndefiniteDescription {α : Sort u} (p : α → Prop) (h
xp.val, fun _ => xp.property)
(fun hp => choice h, fun h => absurd h hp)
/-- The Hilbert epsilon function. -/
/-- the Hilbert epsilon Function -/
noncomputable def epsilon {α : Sort u} [h : Nonempty α] (p : α Prop) : α :=
(strongIndefiniteDescription p h).val
@@ -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

@@ -116,7 +116,7 @@ On top of these instances this file defines several auxiliary type classes:
* `CoeOTC := CoeOut* Coe*`
* `CoeHTC := CoeHead? CoeOut* Coe*`
* `CoeHTCT := CoeHead? CoeOut* Coe* CoeTail?`
* `CoeT := CoeHead? CoeOut* Coe* CoeTail? | CoeDep`
* `CoeDep := CoeHead? CoeOut* Coe* CoeTail? | CoeDep`
-/

View File

@@ -16,4 +16,3 @@ public import Init.Control.Option
public import Init.Control.Lawful
public import Init.Control.StateCps
public import Init.Control.ExceptCps
public import Init.Control.MonadAttach

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`.
-/
@@ -144,7 +147,7 @@ instance : ToBool Bool where
Converts the result of the monadic action `x` to a `Bool`. If it is `true`, returns it and ignores
`y`; otherwise, runs `y` and returns its result.
This is a monadic counterpart to the short-circuiting `||` operator, usually accessed via the `<||>`
This a monadic counterpart to the short-circuiting `||` operator, usually accessed via the `<||>`
operator.
-/
@[macro_inline] def orM {m : Type u Type v} {β : Type u} [Monad m] [ToBool β] (x y : m β) : m β := do
@@ -161,7 +164,7 @@ recommended_spelling "orM" for "<||>" in [orM, «term_<||>_»]
Converts the result of the monadic action `x` to a `Bool`. If it is `true`, returns `y`; otherwise,
returns the original result of `x`.
This is a monadic counterpart to the short-circuiting `&&` operator, usually accessed via the `<&&>`
This a monadic counterpart to the short-circuiting `&&` operator, usually accessed via the `<&&>`
operator.
-/
@[macro_inline] def andM {m : Type u Type v} {β : Type u} [Monad m] [ToBool β] (x y : m β) : m β := do
@@ -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)

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@@ -25,12 +25,6 @@ instance [Repr ε] [Repr α] : Repr (Result ε σ α) where
| Result.error e _, prec => Repr.addAppParen ("EStateM.Result.error " ++ reprArg e) prec
| Result.ok a _, prec => Repr.addAppParen ("EStateM.Result.ok " ++ reprArg a) prec
instance : MonadAttach (EStateM ε σ) where
CanReturn x a := Exists fun s => Exists fun s' => x.run s = .ok a s'
attach x s := match h : x s with
| .ok a s' => .ok a, s, s', h s'
| .error e s' => .error e s'
end EStateM
namespace EStateM

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@@ -148,23 +148,6 @@ 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]
@@ -329,8 +312,3 @@ instance ExceptT.finally {m : Type u → Type v} {ε : Type u} [MonadFinally m]
| (.ok a, .ok b) => pure (.ok (a, b))
| (_, .error e) => pure (.error e) -- second error has precedence
| (.error e, _) => pure (.error e)
instance [Monad m] [MonadAttach m] : MonadAttach (ExceptT ε m) where
CanReturn x a := MonadAttach.CanReturn (m := m) x (.ok a)
attach x := show m (Except ε _) from
(fun a, h => match a with | .ok a => .ok a, h | .error e => .error e) <$> MonadAttach.attach (m := m) x

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@@ -75,13 +75,6 @@ instance [Monad m] : MonadLift m (ExceptCpsT σ m) where
instance [Inhabited ε] : Inhabited (ExceptCpsT ε m α) where
default := fun _ _ k₂ => k₂ default
/--
For continuation monads, it is not possible to provide a computable `MonadAttach` instance that
actually adds information about the return value. Therefore, this instance always attaches a proof
of `True`.
-/
instance : MonadAttach (ExceptCpsT ε m) := .trivial
@[simp] theorem run_pure [Monad m] : run (pure x : ExceptCpsT ε m α) = pure (Except.ok x) := rfl
@[simp] theorem run_lift {α ε : Type u} [Monad m] (x : m α) : run (ExceptCpsT.lift x : ExceptCpsT ε m α) = (x >>= fun a => pure (Except.ok a) : m (Except ε α)) := rfl

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@@ -9,7 +9,6 @@ module
prelude
public import Init.Core
public import Init.Control.MonadAttach
public section
@@ -68,15 +67,4 @@ instance [OfNat α n] : OfNat (Id α) n :=
instance {m : Type u Type v} [Pure m] : MonadLiftT Id m where
monadLift x := pure x.run
instance : MonadAttach Id where
CanReturn x a := x.run = a
attach x := pure x.run, rfl
instance : LawfulMonadAttach Id where
map_attach := rfl
canReturn_map_imp := by
intro _ _ x _ h
cases h
exact x.run.2
end Id

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@@ -10,4 +10,3 @@ public import Init.Control.Lawful.Basic
public import Init.Control.Lawful.Instances
public import Init.Control.Lawful.Lemmas
public import Init.Control.Lawful.MonadLift
public import Init.Control.Lawful.MonadAttach

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@@ -170,7 +170,6 @@ 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 <$> x := by
rw [bind_map]
@@ -248,12 +247,28 @@ namespace Id
instance : LawfulMonad Id := by
refine LawfulMonad.mk' _ ?_ ?_ ?_ <;> intros <;> rfl
@[simp, grind =] theorem run_map (x : Id α) (f : α β) : (f <$> x).run = f x.run := rfl
@[simp, grind =] theorem run_bind (x : Id α) (f : α Id β) : (x >>= f).run = (f x.run).run := rfl
@[simp, grind =] theorem run_pure (a : α) : (pure a : Id α).run = a := rfl
@[simp, grind =] theorem pure_run (a : Id α) : pure a.run = a := rfl
@[simp] theorem run_map (x : Id α) (f : α β) : (f <$> x).run = f x.run := rfl
@[simp] theorem run_bind (x : Id α) (f : α Id β) : (x >>= f).run = (f x.run).run := rfl
@[simp] theorem run_pure (a : α) : (pure a : Id α).run = a := rfl
@[simp] theorem pure_run (a : Id α) : pure a.run = a := rfl
@[simp] theorem run_seqRight (x y : Id α) : (x *> y).run = y.run := rfl
@[simp] theorem run_seqLeft (x y : Id α) : (x <* y).run = x.run := rfl
@[simp] theorem run_seq (f : Id (α β)) (x : Id α) : (f <*> x).run = f.run x.run := rfl
-- These lemmas are bad as they abuse the defeq of `Id α` and `α`
@[deprecated run_map (since := "2025-03-05")] theorem map_eq (x : Id α) (f : α β) : f <$> 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

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@@ -17,9 +17,6 @@ public section
open Function
@[simp, grind =] theorem monadMap_refl {m : Type _ Type _} {α} (f : {α}, m α m α) :
monadMap @f = @f α := rfl
/-! # ExceptT -/
namespace ExceptT
@@ -28,8 +25,6 @@ namespace ExceptT
simp [run] at h
assumption
@[simp, grind =] theorem run_mk (x : m (Except ε α)) : run (mk x : ExceptT ε m α) = x := rfl
@[simp, grind =] theorem run_pure [Monad m] (x : α) : run (pure x : ExceptT ε m α) = pure (Except.ok x) := rfl
@[simp, grind =] theorem run_lift [Monad.{u, v} m] (x : m α) : run (ExceptT.lift x : ExceptT ε m α) = (Except.ok <$> x : m (Except ε α)) := rfl
@@ -60,9 +55,6 @@ theorem run_bind [Monad m] (x : ExceptT ε m α) (f : α → ExceptT ε m β)
apply bind_congr
intro a; cases a <;> simp [Except.map]
@[simp, grind =] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} n β n β) (x : ExceptT ε m α)
: (monadMap @f x : ExceptT ε m α).run = monadMap @f (x.run) := rfl
protected theorem seq_eq {α β ε : Type u} [Monad m] (mf : ExceptT ε m (α β)) (x : ExceptT ε m α) : mf <*> x = mf >>= fun f => f <$> x :=
rfl
@@ -105,22 +97,6 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (ExceptT ε m) where
simp only [ExceptT.instMonad, ExceptT.map, ExceptT.mk, throw, throwThe, MonadExceptOf.throw,
pure_bind]
/-! Note that the `MonadControl` instance for `ExceptT` is not monad-generic. -/
@[simp] theorem run_restoreM [Monad m] (x : stM m (ExceptT ε m) α) :
ExceptT.run (restoreM x) = pure x := rfl
@[simp] theorem run_liftWith [Monad m] (f : ({β : Type u} ExceptT ε m β m (stM m (ExceptT ε m) β)) m α) :
ExceptT.run (liftWith f) = Except.ok <$> (f fun x => x.run) :=
rfl
@[simp] theorem run_controlAt [Monad m] [LawfulMonad m] (f : ({β : Type u} ExceptT ε m β m (stM m (ExceptT ε m) β)) m (stM m (ExceptT ε m) α)) :
ExceptT.run (controlAt m f) = f fun x => x.run := by
simp [controlAt, run_bind, bind_map_left]
@[simp] theorem run_control [Monad m] [LawfulMonad m] (f : ({β : Type u} ExceptT ε m β m (stM m (ExceptT ε m) β)) m (stM m (ExceptT ε m) α)) :
ExceptT.run (control f) = f fun x => x.run := run_controlAt f
end ExceptT
/-! # Except -/
@@ -174,9 +150,6 @@ namespace OptionT
apply bind_congr
intro a; cases a <;> simp [OptionT.pure, OptionT.mk]
@[simp, grind =] theorem run_monadMap [MonadFunctorT n m] (f : {β : Type u} n β n β) (x : OptionT m α)
: (monadMap @f x : OptionT m α).run = monadMap @f (x.run) := rfl
protected theorem seq_eq {α β : Type u} [Monad m] (mf : OptionT m (α β)) (x : OptionT m α) : mf <*> x = mf >>= fun f => f <$> x :=
rfl
@@ -216,12 +189,12 @@ 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
@@ -238,24 +211,6 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (OptionT m) where
(x <|> y).run = Option.elimM x.run y.run (fun x => pure (some x)) :=
bind_congr fun | some _ => by rfl | none => by rfl
/-! Note that the `MonadControl` instance for `OptionT` is not monad-generic. -/
@[simp] theorem run_restoreM [Monad m] (x : stM m (OptionT m) α) :
OptionT.run (restoreM x) = pure x := rfl
@[simp] theorem run_liftWith [Monad m] [LawfulMonad m] (f : ({β : Type u} OptionT m β m (stM m (OptionT m) β)) m α) :
OptionT.run (liftWith f) = Option.some <$> (f fun x => x.run) := by
dsimp [liftWith]
rw [ bind_pure_comp]
rfl
@[simp] theorem run_controlAt [Monad m] [LawfulMonad m] (f : ({β : Type u} OptionT m β m (stM m (OptionT m) β)) m (stM m (OptionT m) α)) :
OptionT.run (controlAt m f) = f fun x => x.run := by
simp [controlAt, Option.elimM, Option.elim]
@[simp] theorem run_control [Monad m] [LawfulMonad m] (f : ({β : Type u} OptionT m β m (stM m (OptionT m) β)) m (stM m (OptionT m) α)) :
OptionT.run (control f) = f fun x => x.run := run_controlAt f
end OptionT
/-! # Option -/
@@ -264,7 +219,7 @@ 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
@@ -277,9 +232,6 @@ namespace ReaderT
simp [run] at h
exact funext h
@[simp, grind =] theorem run_mk (x : ρ m α) (ctx : ρ) : run (.mk x : ReaderT ρ m α) ctx = x ctx :=
rfl
@[simp, grind =] theorem run_pure [Monad m] (a : α) (ctx : ρ) : (pure a : ReaderT ρ m α).run ctx = pure a := rfl
@[simp, grind =] theorem run_bind [Monad m] (x : ReaderT ρ m α) (f : α ReaderT ρ m β) (ctx : ρ)
@@ -327,22 +279,6 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (ReaderT ρ m) where
pure_bind := by intros; apply ext; intros; simp
bind_assoc := by intros; apply ext; intros; simp
/-! Note that the `MonadControl` instance for `ReaderT` is not monad-generic. -/
@[simp] theorem run_restoreM [Monad m] (x : stM m (ReaderT ρ m) α) (ctx : ρ) :
ReaderT.run (restoreM x) ctx = pure x := rfl
@[simp] theorem run_liftWith [Monad m] (f : ({β : Type u} ReaderT ρ m β m (stM m (ReaderT ρ m) β)) m α) (ctx : ρ) :
ReaderT.run (liftWith f) ctx = (f fun x => x.run ctx) :=
rfl
@[simp] theorem run_controlAt [Monad m] [LawfulMonad m] (f : ({β : Type u} ReaderT ρ m β m (stM m (ReaderT ρ m) β)) m (stM m (ReaderT ρ m) α)) (ctx : ρ) :
ReaderT.run (controlAt m f) ctx = f fun x => x.run ctx := by
simp [controlAt]
@[simp] theorem run_control [Monad m] [LawfulMonad m] (f : ({β : Type u} ReaderT ρ m β m (stM m (ReaderT ρ m) β)) m (stM m (ReaderT ρ m) α)) (ctx : ρ) :
ReaderT.run (control f) ctx = f fun x => x.run ctx := run_controlAt f ctx
end ReaderT
/-! # StateRefT -/
@@ -357,20 +293,17 @@ namespace StateT
@[ext, grind ext] theorem ext {x y : StateT σ m α} (h : s, x.run s = y.run s) : x = y :=
funext h
@[simp, grind =] theorem run_mk [Monad m] (x : σ m (α × σ)) (s : σ) : run (.mk x) s = x s :=
rfl
@[simp, grind =] theorem run'_eq [Monad m] (x : StateT σ m α) (s : σ) : run' x s = (·.1) <$> run x s :=
rfl
@[simp, grind =] theorem run_pure [Monad m] (a : α) (s : σ) : (pure a : StateT σ m α).run s = pure (a, s) := rfl
@[simp, grind =] theorem run_bind [Monad m] (x : StateT σ m α) (f : α StateT σ m β) (s : σ)
: (x >>= f).run s = x.run s >>= λ p => (f p.1).run p.2 := rfl
: (x >>= f).run s = x.run s >>= λ p => (f p.1).run p.2 := by
simp [bind, StateT.bind, run]
@[simp, grind =] theorem run_map {α β σ : Type u} [Monad m] [LawfulMonad m] (f : α β) (x : StateT σ m α) (s : σ) : (f <$> x).run s = (fun (p : α × σ) => (f p.1, p.2)) <$> x.run s := by
rw [ bind_pure_comp (m := m)]
rfl
simp [Functor.map, StateT.map, run, bind_pure_comp]
@[simp, grind =] theorem run_get [Monad m] (s : σ) : (get : StateT σ m σ).run s = pure (s, s) := rfl
@@ -379,13 +312,13 @@ namespace StateT
@[simp, grind =] theorem run_modify [Monad m] (f : σ σ) (s : σ) : (modify f : StateT σ m PUnit).run s = pure (, f s) := rfl
@[simp, grind =] theorem run_modifyGet [Monad m] (f : σ α × σ) (s : σ) : (modifyGet f : StateT σ m α).run s = pure ((f s).1, (f s).2) := by
rfl
simp [modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, run]
@[simp, grind =] theorem run_lift {α σ : Type u} [Monad m] (x : m α) (s : σ) : (StateT.lift x : StateT σ m α).run s = x >>= fun a => pure (a, s) := rfl
@[grind =]
theorem run_bind_lift {α σ : Type u} [Monad m] [LawfulMonad m] (x : m α) (f : α StateT σ m β) (s : σ) : (StateT.lift x >>= f).run s = x >>= fun a => (f a).run s := by
simp
simp [StateT.lift, StateT.run, bind, StateT.bind]
@[simp, grind =] theorem run_monadLift {α σ : Type u} [Monad m] [MonadLiftT n m] (x : n α) (s : σ) : (monadLift x : StateT σ m α).run s = (monadLift x : m α) >>= fun a => pure (a, s) := rfl
@@ -425,48 +358,10 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (StateT σ m) where
pure_bind := by intros; apply ext; intros; simp
bind_assoc := by intros; apply ext; intros; simp
/-! Note that the `MonadControl` instance for `StateT` is not monad-generic. -/
@[simp] theorem run_restoreM [Monad m] [LawfulMonad m] (x : stM m (StateT σ m) α) (s : σ) :
StateT.run (restoreM x) s = pure x := by
simp [restoreM, MonadControl.restoreM]
rfl
@[simp] theorem run_liftWith [Monad m] [LawfulMonad m] (f : ({β : Type u} StateT σ m β m (stM m (StateT σ m) β)) m α) (s : σ) :
StateT.run (liftWith f) s = ((·, s) <$> f fun x => x.run s) := by
simp [liftWith, MonadControl.liftWith, Function.comp_def]
@[simp] theorem run_controlAt [Monad m] [LawfulMonad m] (f : ({β : Type u} StateT σ m β m (stM m (StateT σ m) β)) m (stM m (StateT σ m) α)) (s : σ) :
StateT.run (controlAt m f) s = f fun x => x.run s := by
simp [controlAt]
@[simp] theorem run_control [Monad m] [LawfulMonad m] (f : ({β : Type u} StateT σ m β m (stM m (StateT σ m) β)) m (stM m (StateT σ m) α)) (s : σ) :
StateT.run (control f) s = f fun x => x.run s := run_controlAt f s
end StateT
/-! # EStateM -/
namespace EStateM
@[simp, grind =] theorem run_pure (a : α) (s : σ) :
EStateM.run (pure a : EStateM ε σ α) s = .ok a s := rfl
@[simp, grind =] theorem run_get (s : σ) :
EStateM.run (get : EStateM ε σ σ) s = .ok s s := rfl
@[simp, grind =] theorem run_set (s₁ s₂ : σ) :
EStateM.run (set s₁ : EStateM ε σ PUnit) s₂ = .ok .unit s₁ := rfl
@[simp, grind =] theorem run_modify (f : σ σ) (s : σ) :
EStateM.run (modify f : EStateM ε σ PUnit) s = .ok .unit (f s) := rfl
@[simp, grind =] theorem run_modifyGet (f : σ α × σ) (s : σ) :
EStateM.run (modifyGet f : EStateM ε σ α) s = .ok (f s).1 (f s).2 := rfl
@[simp, grind =] theorem run_throw (e : ε) (s : σ):
EStateM.run (throw e : EStateM ε σ PUnit) s = .error e s := rfl
instance : LawfulMonad (EStateM ε σ) := .mk'
(id_map := fun x => funext <| fun s => by
dsimp only [EStateM.instMonad, EStateM.map]
@@ -480,5 +375,3 @@ instance : LawfulMonad (EStateM ε σ) := .mk'
| .ok _ _ => rfl
| .error _ _ => rfl)
(map_const := fun _ _ => rfl)
end EStateM

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@@ -1,10 +0,0 @@
/-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Control.Lawful.MonadAttach.Lemmas
public import Init.Control.Lawful.MonadAttach.Instances

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@@ -1,86 +0,0 @@
/-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Control.Reader
public import Init.Control.Lawful.Instances
import Init.Control.Lawful.MonadAttach.Lemmas
public instance [Monad m] [LawfulMonad m] [MonadAttach m] [WeaklyLawfulMonadAttach m] :
WeaklyLawfulMonadAttach (ReaderT ρ m) where
map_attach := by
simp only [Functor.map, MonadAttach.attach, Functor.map_map, WeaklyLawfulMonadAttach.map_attach]
intros; rfl
public instance [Monad m] [LawfulMonad m] [MonadAttach m] [LawfulMonadAttach m] :
LawfulMonadAttach (ReaderT ρ m) where
canReturn_map_imp := by
simp only [Functor.map, MonadAttach.CanReturn, ReaderT.run]
rintro _ _ x a r, h
apply LawfulMonadAttach.canReturn_map_imp h
public instance [Monad m] [LawfulMonad m] [MonadAttach m] [WeaklyLawfulMonadAttach m] :
WeaklyLawfulMonadAttach (StateT σ m) where
map_attach := by
intro α x
simp only [Functor.map, StateT, funext_iff, StateT.map, bind_pure_comp, MonadAttach.attach,
Functor.map_map]
exact fun s => WeaklyLawfulMonadAttach.map_attach
public instance [Monad m] [LawfulMonad m] [MonadAttach m] [LawfulMonadAttach m] :
LawfulMonadAttach (StateT σ m) where
canReturn_map_imp := by
simp only [Functor.map, MonadAttach.CanReturn, StateT.run, StateT.map, bind_pure_comp]
rintro _ _ x a s, s', h
obtain a, h, h' := LawfulMonadAttach.canReturn_map_imp' h
cases h'
exact a.1.2
public instance [Monad m] [LawfulMonad m] [MonadAttach m] [WeaklyLawfulMonadAttach m] :
WeaklyLawfulMonadAttach (ExceptT ε m) where
map_attach {α} x := by
simp only [Functor.map, MonadAttach.attach, ExceptT.map]
simp
conv => rhs; rw [ WeaklyLawfulMonadAttach.map_attach (m := m) (x := x)]
simp only [map_eq_pure_bind]
apply bind_congr; intro a
match a with
| .ok _, _ => simp
| .error _, _ => simp
public instance [Monad m] [LawfulMonad m] [MonadAttach m] [LawfulMonadAttach m] :
LawfulMonadAttach (ExceptT ε m) where
canReturn_map_imp {α P x a} := by
simp only [Functor.map, MonadAttach.CanReturn, ExceptT.map, ExceptT.mk]
let x' := (fun a => show Subtype (fun a : Except _ _ => match a with | .ok a => P a | .error e => True) from match a with | .ok a => .ok a.1 | .error e => .error e, by cases a <;> simp [Subtype.property]) <$> show m _ from x
have := LawfulMonadAttach.canReturn_map_imp (m := m) (x := x') (a := .ok a)
simp only at this
intro h
apply this
simp only [x', map_eq_pure_bind, bind_assoc]
refine cast ?_ h
congr 1
apply bind_congr; intro a
split <;> simp
public instance [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] :
WeaklyLawfulMonadAttach (StateRefT' ω σ m) :=
inferInstanceAs (WeaklyLawfulMonadAttach (ReaderT _ _))
public instance [Monad m] [MonadAttach m] [LawfulMonad m] [LawfulMonadAttach m] :
LawfulMonadAttach (StateRefT' ω σ m) :=
inferInstanceAs (LawfulMonadAttach (ReaderT _ _))
section
attribute [local instance] MonadAttach.trivial
public instance [Monad m] [LawfulMonad m] :
WeaklyLawfulMonadAttach m where
map_attach := by simp [MonadAttach.attach]
end

View File

@@ -1,90 +0,0 @@
/-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Control.MonadAttach
import all Init.Control.MonadAttach
public import Init.Control.Lawful.Lemmas
public import Init.Control.Lawful.MonadLift.Lemmas
public theorem LawfulMonadAttach.canReturn_bind_imp' [Monad m] [LawfulMonad m]
[MonadAttach m] [LawfulMonadAttach m]
{x : m α} {f : α m β} :
MonadAttach.CanReturn (x >>= f) b Exists fun a => MonadAttach.CanReturn x a MonadAttach.CanReturn (f a) b := by
intro h
let P (b : β) := Exists fun a => MonadAttach.CanReturn x a MonadAttach.CanReturn (f a) b
have h' : (x >>= f) = Subtype.val <$> (MonadAttach.attach x >>= (fun a => (do
let b MonadAttach.attach (f a)
return b.1, a.1, a.2, b.2 : m (Subtype P)))) := by
simp only [map_bind, map_pure]
simp only [bind_pure_comp, WeaklyLawfulMonadAttach.map_attach]
rw (occs := [1]) [ WeaklyLawfulMonadAttach.map_attach (x := x)]
simp
rw [h'] at h
have := LawfulMonadAttach.canReturn_map_imp h
exact this
public theorem LawfulMonadAttach.eq_of_canReturn_pure [Monad m] [MonadAttach m]
[LawfulMonad m] [LawfulMonadAttach m] {a b : α}
(h : MonadAttach.CanReturn (m := m) (pure a) b) :
a = b := by
let x : m (Subtype (a = ·)) := pure a, rfl
have : pure a = Subtype.val <$> x := by simp [x]
rw [this] at h
exact LawfulMonadAttach.canReturn_map_imp h
public theorem LawfulMonadAttach.canReturn_map_imp' [Monad m] [LawfulMonad m]
[MonadAttach m] [LawfulMonadAttach m]
{x : m α} {f : α β} :
MonadAttach.CanReturn (f <$> x) b Exists fun a => MonadAttach.CanReturn x a f a = b := by
rw [map_eq_pure_bind]
intro h
obtain a, h, h' := canReturn_bind_imp' h
exact a, h, eq_of_canReturn_pure h'
public theorem LawfulMonadAttach.canReturn_liftM_imp'
[Monad m] [MonadAttach m] [LawfulMonad m] [LawfulMonadAttach m]
[Monad n] [MonadAttach n] [LawfulMonad n] [LawfulMonadAttach n]
[MonadLiftT m n] [LawfulMonadLiftT m n] {x : m α} {a : α} :
MonadAttach.CanReturn (liftM (n := n) x) a MonadAttach.CanReturn x a := by
intro h
simp only [ WeaklyLawfulMonadAttach.map_attach (x := x), liftM_map] at h
exact canReturn_map_imp h
public theorem WeaklyLawfulMonadAttach.attach_bind_val
[Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m]
{x : m α} {f : α m β} :
MonadAttach.attach x >>= (fun a => f a.val) = x >>= f := by
conv => rhs; simp only [ map_attach (x := x), bind_map_left]
public theorem WeaklyLawfulMonadAttach.bind_attach_of_nonempty
[Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Nonempty (m β)]
{x : m α} {f : Subtype (MonadAttach.CanReturn x) m β} :
open scoped Classical in
MonadAttach.attach x >>= f = x >>= (fun a => if ha : MonadAttach.CanReturn x a then f a, ha else Classical.ofNonempty) := by
conv => rhs; simp +singlePass only [ map_attach (x := x)]
simp [Subtype.property]
public theorem MonadAttach.attach_bind_eq_pbind
[Monad m] [MonadAttach m]
{x : m α} {f : Subtype (MonadAttach.CanReturn x) m β} :
MonadAttach.attach x >>= f = MonadAttach.pbind x (fun a ha => f a, ha) := by
simp [MonadAttach.pbind]
public theorem WeaklyLawfulMonadAttach.pbind_eq_bind
[Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m]
{x : m α} {f : α m β} :
MonadAttach.pbind x (fun a _ => f a) = x >>= f := by
conv => rhs; rw [ map_attach (x := x)]
simp [MonadAttach.pbind]
public theorem WeaklyLawfulMonadAttach.pbind_eq_bind'
[Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m]
{x : m α} {f : α m β} :
MonadAttach.pbind x (fun a _ => f a) = x >>= f := by
conv => rhs; rw [ map_attach (x := x)]
simp [MonadAttach.pbind]

View File

@@ -6,7 +6,6 @@ Authors: Quang Dao
module
prelude
public import Init.Control.Id
public import Init.Control.Lawful.Basic
public import Init.Control.Lawful.MonadLift.Basic
@@ -14,14 +13,6 @@ public section
universe u v w
theorem instMonadLiftTOfMonadLift_instMonadLiftTOfPure [Monad m] [Monad n] {_ : MonadLift m n}
[LawfulMonadLift m n] : instMonadLiftTOfMonadLift Id m n = Id.instMonadLiftTOfPure := by
have hext {a b : MonadLiftT Id n} (h : @a.monadLift = @b.monadLift) : a = b := by
cases a <;> cases b <;> simp_all
apply hext
ext α x
simp [monadLift, LawfulMonadLift.monadLift_pure]
variable {m : Type u Type v} {n : Type u Type w} [Monad m] [Monad n] [MonadLiftT m n]
[LawfulMonadLiftT m n] {α β : Type u}
@@ -32,7 +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

@@ -1,126 +0,0 @@
/-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert
-/
module
prelude
public import Init.Control.Basic
set_option linter.all true
set_option doc.verso true
/-!
# {name (scope := "Init.Control.MonadAttach")}`MonadAttach`
This module provides a mechanism for attaching proofs to the return values of monadic computations,
producing a new monadic computation returning a {name}`Subtype`.
This function is primarily used to allow definitions by [well-founded
recursion](lean-manual://section/well-founded-recursion) that sequence computations using
{name}`Bind.bind` (`>>=`) to prove properties about the return values of prior computations when
a recursive call happens.
This allows the well-founded recursion mechanism to prove that the function terminates.
-/
-- verso docstring is added below
set_option linter.missingDocs false in
public class MonadAttach (m : Type u Type v) where
/--
A predicate that can be assumed to be true for all return values {name}`a` of actions {name}`x`
in {name}`m`, in all situations.
-/
CanReturn {α : Type u} : (x : m α) (a : α) Prop
/--
Attaches a proof of {name}`MonadAttach.CanReturn` to the return value of {name}`x`. This proof
can be used to prove the termination of well-founded recursive functions.
-/
attach {α : Type u} (x : m α) : m (Subtype (CanReturn x))
-- verso docstring is added below
set_option linter.missingDocs false in
public class WeaklyLawfulMonadAttach (m : Type u Type v) [Monad m] [MonadAttach m] where
map_attach {α : Type u} {x : m α} : Subtype.val <$> MonadAttach.attach x = x
/--
This type class ensures that {name}`MonadAttach.CanReturn` is the unique strongest possible
postcondition.
-/
public class LawfulMonadAttach (m : Type u Type v) [Monad m] [MonadAttach m] extends
WeaklyLawfulMonadAttach m where
canReturn_map_imp {α : Type u} {P : α Prop} {x : m (Subtype P)} {a : α} :
MonadAttach.CanReturn (Subtype.val <$> x) a P a
/--
Like {name}`Bind.bind`, {name}`pbind` sequences two computations {lean}`x : m α` and {lean}`f`,
allowing the second to depend on the value computed by the first.
But other than with {name}`Bind.bind`, the second computation can also depend on a proof that
the return value {given}`a` of {name}`x` satisfies {lean}`MonadAttach.CanReturn x a`.
-/
public def MonadAttach.pbind [Monad m] [MonadAttach m]
(x : m α) (f : (a : α) MonadAttach.CanReturn x a m β) : m β :=
MonadAttach.attach x >>= (fun a, ha => f a ha)
/--
A {lean}`MonadAttach` instance where all return values are possible and {name}`attach` adds no
information to the return value, except a trivial proof of {name}`True`.
This instance is used whenever no more useful {name}`MonadAttach` instance can be implemented.
It always has a {name}`WeaklyLawfulMonadAttach`, but usually no {name}`LawfulMonadAttach` instance.
-/
@[expose]
public protected def MonadAttach.trivial {m : Type u Type v} [Monad m] : MonadAttach m where
CanReturn _ _ := True
attach x := (·, .intro) <$> x
section
variable (α : Type u) [ m, Monad m] [ m, MonadAttach m]
set_option doc.verso true
/--
For every {given}`x : m α`, this type class provides a predicate {lean}`MonadAttach.CanReturn x`
and a way to attach a proof of this predicate to the return values of {name}`x` by providing
an element {lean}`MonadAttach.attach x` of {lean}`m { a : α // MonadAttach.CanReturn x a }`.
Instances should abide the law {lean}`Subtype.val <$> MonadAttach.attach x = x`, which is encoded by
the {name}`WeaklyLawfulMonadAttach` type class. The stronger type class {name}`LawfulMonadAttach`
ensures that {lean}`MonadAttach.CanReturn x` is the _unique_ strongest possible predicate.
Similarly to {name (scope := "Init.Data.List.Attach")}`List.attach`, the purpose of
{name}`MonadAttach` is to attach proof terms necessary for well-founded termination proofs.
The iterator library relies on {name}`MonadAttach` for combinators such as
{name (scope := "Init.Data.Iterators")}`Std.Iter.filterM` in order to automatically attach
information about the monadic predicate's behavior that could be relevant for the termination
behavior of the iterator.
*Limitations*:
For many monads, there is a strongly lawful {lean}`MonadAttach` instance, but there are exceptions.
For example, there is no way to provide a computable {lean}`MonadAttach` instance for the CPS monad
transformers
{name (scope := "Init.Control.StateCps")}`StateCpsT` and
{name (scope := "Init.Control.StateCps")}`ExceptCpsT` with a predicate that is not always
{name}`True`. Therefore, such CPS monads only provide the trivial {lean}`MonadAttach` instance
{lean}`MonadAttach.trivial` together with {name}`WeaklyLawfulMonadAttach`, but without
{name}`LawfulMonadAttach`.
For most monads with side effects, {lean}`MonadAttach` is too weak to fully capture the behavior of
computations because the postcondition represented by {name}`MonadAttach.CanReturn` neither depends
on the prior internal state of the monad, nor does it contain information about how the state of the
monad changes with the computation.
-/
add_decl_doc MonadAttach
/--
This type class ensures that every monadic action {given}`x : m α` can be recovered by stripping the
proof component from the subtypes returned by
{lean}`(MonadAttach.attach x) : m { a : α // MonadAttach.CanReturn x a }` . In other words,
the type class ensures that {lean}`Subtype.val <$> MonadAttach.attach x = x`.
-/
add_decl_doc WeaklyLawfulMonadAttach
end

View File

@@ -112,12 +112,6 @@ instance (ε : Type u) [MonadExceptOf ε m] : MonadExceptOf ε (OptionT m) where
throw e := OptionT.mk <| throwThe ε e
tryCatch x handle := OptionT.mk <| tryCatchThe ε x handle
instance [MonadAttach m] : MonadAttach (OptionT m) where
CanReturn x a := MonadAttach.CanReturn x.run (some a)
attach x := .mk ((fun
| some a, h => some a, h
| none, _ => none) <$> MonadAttach.attach x.run)
end OptionT
instance [Monad m] : MonadControl m (OptionT m) where

View File

@@ -51,7 +51,3 @@ A monad with access to a read-only value of type `ρ`. The value can be locally
`withReader`, but it cannot be mutated.
-/
abbrev ReaderM (ρ : Type u) := ReaderT ρ Id
instance [Monad m] [MonadAttach m] : MonadAttach (ReaderT ρ m) where
CanReturn x a := Exists (fun r => MonadAttach.CanReturn (x.run r) a)
attach x := fun r => (fun a, h => a, r, h) <$> MonadAttach.attach (x.run r)

View File

@@ -25,12 +25,6 @@ of a value and a state.
@[expose] def StateT (σ : Type u) (m : Type u Type v) (α : Type u) : Type (max u v) :=
σ m (α × σ)
/--
Interpret `σ → m (α × σ)` as an element of `StateT σ m α`.
-/
@[always_inline, inline, expose]
def StateT.mk {σ : Type u} {m : Type u Type v} {α : Type u} (x : σ m (α × σ)) : StateT σ m α := x
/--
Executes an action from a monad with added state in the underlying monad `m`. Given an initial
state, it returns a value paired with the final state.
@@ -204,7 +198,3 @@ instance StateT.tryFinally {m : Type u → Type v} {σ : Type u} [MonadFinally m
| some (a, s') => h (some a) s'
| none => h none s
pure ((a, b), s'')
instance [Monad m] [MonadAttach m] : MonadAttach (StateT σ m) where
CanReturn x a := Exists fun s => Exists fun s' => MonadAttach.CanReturn (x.run s) (a, s')
attach x := fun s => (fun a, s', h => a, s, s', h, s') <$> MonadAttach.attach (x.run s)

View File

@@ -68,13 +68,6 @@ instance : MonadStateOf σ (StateCpsT σ m) where
set s := fun _ _ k => k s
modifyGet f := fun _ s k => let (a, s) := f s; k a s
/--
For continuation monads, it is not possible to provide a computable `MonadAttach` instance that
actually adds information about the return value. Therefore, this instance always attaches a proof
of `True`.
-/
instance : MonadAttach (StateCpsT ε m) := .trivial
/--
Runs an action from the underlying monad in the monad with state. The state is not modified.

View File

@@ -64,7 +64,6 @@ instance [Monad m] : Monad (StateRefT' ω σ m) := inferInstanceAs (Monad (Reade
instance : MonadLift m (StateRefT' ω σ m) := StateRefT'.lift
instance (σ m) : MonadFunctor m (StateRefT' ω σ m) := inferInstanceAs (MonadFunctor m (ReaderT _ _))
instance [Alternative m] [Monad m] : Alternative (StateRefT' ω σ m) := inferInstanceAs (Alternative (ReaderT _ _))
instance [Monad m] [MonadAttach m] : MonadAttach (StateRefT' ω σ m) := inferInstanceAs (MonadAttach (ReaderT _ _))
/--
Retrieves the current value of the monad's mutable state.

View File

@@ -201,7 +201,6 @@ An element of `α ⊕ β` is either an `a : α` wrapped in `Sum.inl` or a `b :
indication of which of the two types was chosen. The union of a singleton set with itself contains
one element, while `Unit ⊕ Unit` contains distinct values `inl ()` and `inr ()`.
-/
@[suggest_for Either]
inductive Sum (α : Type u) (β : Type v) where
/-- Left injection into the sum type `α ⊕ β`. -/
| inl (val : α) : Sum α β
@@ -337,7 +336,7 @@ inductive Exists {α : Sort u} (p : α → Prop) : Prop where
An indication of whether a loop's body terminated early that's used to compile the `for x in xs`
notation.
A collection's `ForIn` or `ForIn'` instance describes how to iterate over its elements. The monadic
A collection's `ForIn` or `ForIn'` instance describe's how to iterate over its elements. The monadic
action that represents the body of the loop returns a `ForInStep α`, where `α` is the local state
used to implement features such as `let mut`.
-/
@@ -378,7 +377,7 @@ 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)
@@ -406,7 +405,7 @@ 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')
@@ -510,12 +509,12 @@ abbrev SSuperset [HasSSubset α] (a b : α) := SSubset b a
/-- Notation type class for the union operation ``. -/
class Union (α : Type u) where
/-- `a b` is the union of `a` and `b`. -/
/-- `a b` is the union of`a` and `b`. -/
union : α α α
/-- Notation type class for the intersection operation `∩`. -/
class Inter (α : Type u) where
/-- `a ∩ b` is the intersection of `a` and `b`. -/
/-- `a ∩ b` is the intersection of`a` and `b`. -/
inter : α α α
/-- Notation type class for the set difference `\`. -/
@@ -538,10 +537,10 @@ infix:50 " ⊇ " => Superset
/-- Strict superset relation: `a ⊃ b` -/
infix:50 "" => SSuperset
/-- `a b` is the union of `a` and `b`. -/
/-- `a b` is the union of`a` and `b`. -/
infixl:65 " " => Union.union
/-- `a ∩ b` is the intersection of `a` and `b`. -/
/-- `a ∩ b` is the intersection of`a` and `b`. -/
infixl:70 "" => Inter.inter
/--
@@ -601,6 +600,17 @@ 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 }`. -/
@@ -940,7 +950,9 @@ theorem HEq.subst {p : (T : Sort u) → T → Prop} (h₁ : a ≍ b) (h₂ : p
@[symm] theorem HEq.symm (h : a b) : b a :=
h.rec (HEq.refl a)
/-- Propositionally equal terms are also heterogeneously equal. -/
theorem heq_of_eq (h : a = a') : a a' :=
Eq.subst h (HEq.refl a)
/-- Heterogeneous equality is transitive. -/
theorem HEq.trans (h₁ : a b) (h₂ : b c) : a c :=
@@ -1083,6 +1095,14 @@ 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
@@ -1145,7 +1165,6 @@ 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
@@ -1187,13 +1206,17 @@ 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
@@ -1344,12 +1367,12 @@ 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
@@ -1364,12 +1387,12 @@ 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 rfl .rfl (heq_of_eq h') (fun h' => absurd (eq_of_heq h') h))
else isFalse (fun h' => Subtype.noConfusion h' (fun h' => absurd h' h))
end Subtype
@@ -1428,8 +1451,8 @@ instance [DecidableEq α] [DecidableEq β] : DecidableEq (α × β) :=
| isTrue e₁ =>
match decEq b b' with
| isTrue e₂ => isTrue (e₁ e₂ rfl)
| isFalse n₂ => isFalse fun h => Prod.noConfusion rfl rfl (heq_of_eq h) fun _ e₂' => absurd (eq_of_heq e₂') n₂
| isFalse n₁ => isFalse fun h => Prod.noConfusion rfl rfl (heq_of_eq h) fun e₁' _ => absurd (eq_of_heq e₁') n₁
| isFalse n₂ => isFalse fun h => Prod.noConfusion h fun _ e₂' => absurd e₂' n₂
| isFalse n₁ => isFalse fun h => Prod.noConfusion h fun e₁' _ => absurd e₁' n₁
instance [BEq α] [BEq β] : BEq (α × β) where
beq := fun (a₁, b₁) (a₂, b₂) => a₁ == a₂ && b₁ == b₂
@@ -1467,8 +1490,6 @@ 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
@@ -1485,24 +1506,20 @@ 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 -/
@@ -1589,7 +1606,7 @@ 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
@@ -2506,7 +2523,8 @@ 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
@@ -2516,19 +2534,16 @@ 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

View File

@@ -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

View File

@@ -572,6 +572,9 @@ def unattach {α : Type _} {p : α → Prop} (xs : Array { x // p x }) : Array
@[simp] theorem unattach_empty {p : α Prop} : (#[] : Array { x // p x }).unattach = #[] := by
simp [unattach]
@[deprecated unattach_empty (since := "2025-05-26")]
abbrev unattach_nil := @unattach_empty
@[simp] theorem unattach_push {p : α Prop} {a : { x // p x }} {xs : Array { x // p x }} :
(xs.push a).unattach = xs.unattach.push a.1 := by
simp only [unattach, Array.map_push]
@@ -746,6 +749,9 @@ 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} :

View File

@@ -209,6 +209,20 @@ 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 +240,7 @@ 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 +256,7 @@ 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 +462,7 @@ 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 +476,7 @@ 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 +584,7 @@ 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'`.
@@ -589,8 +603,6 @@ unsafe def foldlMUnsafe {α : Type u} {β : Type v} {m : Type v → Type w} [Mon
if start < stop then
if stop as.size then
fold (USize.ofNat start) (USize.ofNat stop) init
else if start < as.size then
fold (USize.ofNat start) (USize.ofNat as.size) init
else
pure init
else
@@ -1003,7 +1015,7 @@ 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`.
@@ -1297,7 +1309,7 @@ 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:
@@ -1350,7 +1362,7 @@ Examples:
* `#[2, 4, 5, 6].any (· % 2 = 0) = true`
* `#[2, 4, 5, 6].any (· % 2 = 1) = true`
-/
@[inline, expose, suggest_for Array.some]
@[inline, expose]
def any (as : Array α) (p : α Bool) (start := 0) (stop := as.size) : Bool :=
Id.run <| as.anyM (pure <| p ·) start stop
@@ -1368,7 +1380,7 @@ Examples:
* `#[2, 4, 6].all (· % 2 = 0) = true`
* `#[2, 4, 5, 6].all (· % 2 = 0) = false`
-/
@[inline, suggest_for Array.every]
@[inline]
def all (as : Array α) (p : α Bool) (start := 0) (stop := as.size) : Bool :=
Id.run <| as.allM (pure <| p ·) start stop
@@ -1706,7 +1718,7 @@ 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]
@@ -1753,8 +1765,7 @@ 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
@@ -2136,3 +2147,5 @@ instance [ToString α] : ToString (Array α) where
toString xs := String.Internal.append "#" (toString xs.toList)
end Array
export Array (mkArray)

View File

@@ -31,7 +31,7 @@ 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
@@ -73,6 +73,9 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init
rcases xs with xs
simp [push, List.concat_eq_append]
@[deprecated toList_push (since := "2025-05-26")]
abbrev push_toList := @toList_push
@[simp, grind =] theorem toListAppend_eq {xs : Array α} {l : List α} : xs.toListAppend l = xs.toList ++ l := by
simp [toListAppend, foldr_toList]
@@ -97,15 +100,9 @@ theorem foldrM_eq_reverse_foldlM_toList [Monad m] {f : α → β → m β} {init
@[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} :
@@ -113,4 +110,6 @@ 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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@@ -62,12 +62,12 @@ theorem size_eq_countP_add_countP {xs : Array α} : xs.size = countP p xs + coun
rcases xs with xs
simp [List.length_eq_countP_add_countP (p := p)]
@[grind =]
theorem countP_eq_size_filter {xs : Array α} : countP p xs = (filter p xs).size := by
rcases xs with xs
simp [List.countP_eq_length_filter]
grind_pattern countP_eq_size_filter => xs.countP p, xs.filter p
@[grind =]
theorem countP_eq_size_filter' : countP p = size filter p := by
funext xs
apply countP_eq_size_filter
@@ -99,6 +99,9 @@ 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 +262,15 @@ 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 +284,9 @@ 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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@@ -89,57 +89,11 @@ 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 (fun h => Array.noConfusion rfl (heq_of_eq h) (fun h => List.noConfusion rfl h))
| a :: as =>
match ys with
| [] => isFalse (fun h => Array.noConfusion rfl (heq_of_eq h) (fun h => List.noConfusion rfl h))
| 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 (fun h => Array.noConfusion rfl (heq_of_eq h) (fun h => List.noConfusion rfl h))
/--
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 (fun h => Array.noConfusion rfl (heq_of_eq h) (fun h => List.noConfusion rfl h))
@[inline]
def instDecidableEqEmpImpl (xs : Array α) : Decidable (xs = #[]) :=
decidable_of_iff xs.isEmpty <| by rcases xs with <;> simp [Array.isEmpty]
@[inline]
def instDecidableEmpEqImpl (xs : Array α) : Decidable (#[] = xs) :=
decidable_of_iff xs.isEmpty <| by rcases xs with <;> simp [Array.isEmpty]
@[csimp]
theorem instDecidableEqEmp_csimp : @instDecidableEqEmp = @instDecidableEqEmpImpl :=
Subsingleton.allEq _ _
@[csimp]
theorem instDecidableEmpEq_csimp : @instDecidableEmpEq = @instDecidableEmpEqImpl :=
Subsingleton.allEq _ _
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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@@ -139,16 +139,25 @@ 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 +278,9 @@ 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 +308,17 @@ 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 -/
@@ -389,6 +407,9 @@ theorem eraseIdx_append_of_size_le {xs : Array α} {k : Nat} (hk : xs.size ≤ k
simp at hk
simp [List.eraseIdx_append_of_length_le, *]
@[deprecated eraseIdx_append_of_size_le (since := "2025-06-11")]
abbrev eraseIdx_append_of_length_le := @eraseIdx_append_of_size_le
@[grind =]
theorem eraseIdx_append {xs ys : Array α} (h : k < (xs ++ ys).size) :
eraseIdx (xs ++ ys) k =
@@ -408,6 +429,9 @@ 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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@@ -200,7 +200,7 @@ 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 +208,6 @@ 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 +289,9 @@ 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 +409,8 @@ 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 +429,32 @@ 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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@@ -129,19 +129,31 @@ 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
@@ -159,6 +171,9 @@ theorem find?_singleton {a : α} {p : α → Bool} :
findRev? p (xs.push a) = findRev? p xs := by
cases xs; simp [h]
@[deprecated findRev?_push_of_neg (since := "2025-06-12")]
abbrev findRev?_cons_of_neg := @findRev?_push_of_neg
@[grind =]
theorem finRev?_push {xs : Array α} :
findRev? p (xs.push a) = (Option.guard p a).or (xs.findRev? p) := by
@@ -168,6 +183,9 @@ theorem finRev?_push {xs : Array α} :
· rw [findRev?_push_of_pos, Option.guard_eq_some_iff.mpr rfl, h]
all_goals simp [h]
@[deprecated finRev?_push (since := "2025-06-12")]
abbrev findRev?_cons := @finRev?_push
@[simp, grind =] theorem find?_eq_none : find? p xs = none x xs, ¬ p x := by
cases xs; simp
@@ -300,10 +318,16 @@ 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]
@@ -559,6 +583,9 @@ 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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@@ -53,6 +53,11 @@ theorem eraseIdx_insertIdx_self {i : Nat} {xs : Array α} (h : i ≤ xs.size) :
rcases xs with xs
simp_all
@[deprecated eraseIdx_insertIdx_self (since := "2025-06-15")]
theorem eraseIdx_insertIdx {i : Nat} {xs : Array α} (h : i xs.size) :
(xs.insertIdx i a).eraseIdx i (by simp; omega) = xs := by
simp [eraseIdx_insertIdx_self]
theorem insertIdx_eraseIdx_of_ge {as : Array α}
(w₁ : i < as.size) (w₂ : j (as.eraseIdx i).size) (h : i j) :
(as.eraseIdx i).insertIdx j a =

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@@ -62,9 +62,6 @@ theorem eq_empty_of_size_eq_zero (h : xs.size = 0) : xs = #[] := by
cases xs
simp_all
grind_pattern eq_empty_of_size_eq_zero => xs.size where
guard xs.size = 0
theorem ne_empty_of_size_eq_add_one (h : xs.size = n + 1) : xs #[] := by
cases xs
simpa using List.ne_nil_of_length_eq_add_one h
@@ -115,8 +112,7 @@ theorem none_eq_getElem?_iff {xs : Array α} {i : Nat} : none = xs[i]? ↔ xs.si
theorem getElem?_eq_none {xs : Array α} (h : xs.size i) : xs[i]? = none := by
simp [h]
grind_pattern Array.getElem?_eq_none => xs.size, xs[i]? where
guard xs.size i
grind_pattern Array.getElem?_eq_none => xs.size, xs[i]?
@[simp] theorem getElem?_eq_getElem {xs : Array α} {i : Nat} (h : i < xs.size) : xs[i]? = some xs[i] :=
getElem?_pos ..
@@ -249,13 +245,12 @@ 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]
@@ -263,6 +258,15 @@ 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
@@ -313,23 +317,41 @@ 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 ]
@@ -813,11 +835,6 @@ 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
@@ -1057,6 +1074,12 @@ 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
@@ -1077,6 +1100,9 @@ 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
@@ -1140,7 +1166,7 @@ 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
@@ -1632,15 +1658,12 @@ 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
@@ -1695,6 +1718,9 @@ 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
@@ -1762,6 +1788,11 @@ theorem toArray_append {xs : List α} {ys : Array α} :
theorem singleton_eq_toArray_singleton {a : α} : #[a] = [a].toArray := rfl
@[deprecated empty_append (since := "2025-05-26")]
theorem empty_append_fun : ((#[] : Array α) ++ ·) = id := by
funext l
simp
@[simp, grind =] theorem mem_append {a : α} {xs ys : Array α} : a xs ++ ys a xs a ys := by
simp only [mem_def, toList_append, List.mem_append]
@@ -1852,9 +1883,6 @@ 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
@@ -2055,22 +2083,11 @@ 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
@@ -2117,33 +2134,32 @@ 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
@@ -2166,23 +2182,23 @@ 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
@@ -2191,13 +2207,13 @@ 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
@@ -2230,8 +2246,8 @@ 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
@@ -2242,12 +2258,18 @@ 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
@@ -2258,7 +2280,6 @@ 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]
@@ -2269,7 +2290,6 @@ 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
@@ -2370,44 +2390,77 @@ 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
@@ -2424,86 +2477,143 @@ 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 =]
@@ -2545,8 +2655,8 @@ 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
@@ -2561,7 +2671,7 @@ 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 _)]
@@ -2690,6 +2800,9 @@ 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
@@ -2709,8 +2822,8 @@ 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)]
@@ -3247,6 +3360,14 @@ rather than `(arr.push a).size` as the argument.
l.foldl (fun xs x => xs.push x) xs = xs ++ l.toArray := by
simpa using List.foldl_push_eq_append (f := id)
@[deprecated _root_.List.foldl_push_eq_append' (since := "2025-05-18")]
theorem _root_.List.foldl_push {l : List α} {as : Array α} : l.foldl Array.push as = as ++ l.toArray := by
induction l generalizing as <;> simp [*]
@[deprecated _root_.List.foldr_push_eq_append' (since := "2025-05-18")]
theorem _root_.List.foldr_push {l : List α} {as : Array α} : l.foldr (fun a bs => push bs a) as = as ++ l.reverse.toArray := by
rw [List.foldr_eq_foldl_reverse, List.foldl_push_eq_append']
-- TODO: a multi-pattern is being selected there because E-matching does not go inside lambdas.
@[simp, grind! ] theorem foldr_append_eq_append {xs : Array α} {f : α Array β} {ys : Array β} :
xs.foldr (f · ++ ·) ys = (xs.map f).flatten ++ ys := by
@@ -3319,16 +3440,6 @@ 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
@@ -3546,6 +3657,11 @@ 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
@@ -3596,9 +3712,15 @@ 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 -/
@@ -3616,6 +3738,9 @@ 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]
@@ -3629,6 +3754,11 @@ 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
@@ -3688,6 +3818,9 @@ 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 -/
@@ -3917,10 +4050,16 @@ 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
@@ -3957,29 +4096,28 @@ 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
@@ -4000,66 +4138,8 @@ 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 -/
@@ -4154,11 +4234,17 @@ 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 -/
@@ -4321,9 +4407,13 @@ 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 -/
@@ -4336,7 +4426,6 @@ 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]
@@ -4356,7 +4445,6 @@ 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]
@@ -4375,6 +4463,12 @@ 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} :
@@ -4488,8 +4582,7 @@ 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

@@ -34,18 +34,7 @@ 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
@@ -73,11 +62,19 @@ private theorem cons_lex_cons [BEq α] {lt : αα → Bool} {a b : α} {xs
(lt a b || a == b && xs.lex ys lt) := by
simp only [lex, size_append, List.size_toArray, List.length_cons, List.length_nil, Nat.zero_add,
Nat.add_min_add_left, Nat.add_lt_add_iff_left, Std.Rco.forIn'_eq_forIn'_toList]
rw [cons_lex_cons.forIn'_congr_aux (Nat.toList_rco_eq_cons (by omega)) rfl (fun _ _ _ => rfl)]
simp only [bind_pure_comp, map_pure, Nat.toList_rco_succ_succ, Nat.add_comm 1]
cases h : lt a b
· cases h' : a == b <;> simp [bne, *]
· simp [*]
conv =>
lhs; congr; congr
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,
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
· rw [bne]
cases a == b <;> simp
· simp
@[simp, grind =] theorem _root_.List.lex_toArray [BEq α] {lt : α α Bool} {l₁ l₂ : List α} :
l₁.toArray.lex l₂.toArray lt = l₁.lex l₂ lt := by
@@ -143,7 +140,7 @@ 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
@@ -157,7 +154,7 @@ 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
@@ -181,6 +178,12 @@ 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 :=
@@ -188,7 +191,7 @@ 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)
@@ -277,7 +280,7 @@ 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),
@@ -296,7 +299,7 @@ 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
@@ -319,9 +322,9 @@ 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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@@ -296,6 +296,9 @@ 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 +438,9 @@ 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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@@ -39,6 +39,10 @@ theorem map_toList_inj [Monad m] [LawfulMonad m]
@[simp, grind =] theorem idRun_mapM {xs : Array α} {f : α Id β} : (xs.mapM f).run = xs.map (f · |>.run) :=
mapM_pure
@[deprecated idRun_mapM (since := "2025-05-21")]
theorem mapM_id {xs : Array α} {f : α Id β} : xs.mapM f = xs.map f :=
mapM_pure
@[simp, grind =] theorem mapM_map [Monad m] [LawfulMonad m] {f : α β} {g : β m γ} {xs : Array α} :
(xs.map f).mapM g = xs.mapM (g f) := by
rcases xs with xs
@@ -197,6 +201,13 @@ theorem idRun_forIn'_yield_eq_foldl
xs.attach.foldl (fun b a, h => f a h b |>.run) init := by
simp
@[deprecated idRun_forIn'_yield_eq_foldl (since := "2025-05-21")]
theorem forIn'_yield_eq_foldl
{xs : Array α} (f : (a : α) a xs β β) (init : β) :
forIn' (m := Id) xs init (fun a m b => .yield (f a m b)) =
xs.attach.foldl (fun b a, h => f a h b) init :=
forIn'_pure_yield_eq_foldl _ _
@[simp, grind =] theorem forIn'_map [Monad m] [LawfulMonad m]
{xs : Array α} (g : α β) (f : (b : β) b xs.map g γ m (ForInStep γ)) :
forIn' (xs.map g) init f = forIn' xs init fun a h y => f (g a) (mem_map_of_mem h) y := by
@@ -238,6 +249,13 @@ theorem idRun_forIn_yield_eq_foldl
xs.foldl (fun b a => f a b |>.run) init := by
simp
@[deprecated idRun_forIn_yield_eq_foldl (since := "2025-05-21")]
theorem forIn_yield_eq_foldl
{xs : Array α} (f : α β β) (init : β) :
forIn (m := Id) xs init (fun a b => .yield (f a b)) =
xs.foldl (fun b a => f a b) init :=
forIn_pure_yield_eq_foldl _ _
@[simp, grind =] theorem forIn_map [Monad m] [LawfulMonad m]
{xs : Array α} {g : α β} {f : β γ m (ForInStep γ)} :
forIn (xs.map g) init f = forIn xs init fun a y => f (g a) y := by

View File

@@ -84,6 +84,9 @@ 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 +107,7 @@ 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

View File

@@ -280,7 +280,7 @@ Checks whether any of the elements in a subarray satisfy a Boolean predicate.
The elements are tested starting at the lowest index and moving up. The search terminates as soon as
an element that satisfies the predicate is found.
-/
@[inline, suggest_for Subarray.some]
@[inline]
def any {α : Type u} (p : α Bool) (as : Subarray α) : Bool :=
Id.run <| as.anyM (pure <| p ·)
@@ -290,7 +290,7 @@ Checks whether all of the elements in a subarray satisfy a Boolean predicate.
The elements are tested starting at the lowest index and moving up. The search terminates as soon as
an element that does not satisfy the predicate is found.
-/
@[inline, suggest_for Subarray.every]
@[inline]
def all {α : Type u} (p : α Bool) (as : Subarray α) : Bool :=
Id.run <| as.allM (pure <| p ·)

View File

@@ -166,6 +166,9 @@ 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 +294,9 @@ 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 +348,9 @@ 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 =]
@@ -353,6 +362,14 @@ theorem zipWithM_eq_mapM_id_zipWith {m : Type v → Type w} [Monad m] [LawfulMon
/-! ### unzip -/
@[deprecated fst_unzip (since := "2025-05-26")]
theorem unzip_fst : (unzip l).fst = l.map Prod.fst := by
simp
@[deprecated snd_unzip (since := "2025-05-26")]
theorem unzip_snd : (unzip l).snd = l.map Prod.snd := by
simp
@[grind =]
theorem unzip_eq_map {xs : Array (α × β)} : unzip xs = (xs.map Prod.fst, xs.map Prod.snd) := by
cases xs
@@ -391,4 +408,7 @@ 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

10
src/Init/Data/Basic.lean Normal file
View File

@@ -0,0 +1,10 @@
/-
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.UInt
public import Init.Data.String.Extra

View File

@@ -77,6 +77,9 @@ Returns the `i`th least significant bit.
-/
@[inline, expose] def getLsb (x : BitVec w) (i : Fin w) : Bool := x.toNat.testBit i
@[deprecated getLsb (since := "2025-06-17"), inherit_doc getLsb]
abbrev getLsb' := @getLsb
/-- Returns the `i`th least significant bit, or `none` if `i ≥ w`. -/
@[inline, expose] def getLsb? (x : BitVec w) (i : Nat) : Option Bool :=
if h : i < w then some (getLsb x i, h) else none
@@ -86,6 +89,9 @@ Returns the `i`th most significant bit.
-/
@[inline] def getMsb (x : BitVec w) (i : Fin w) : Bool := x.getLsb w-1-i, by omega
@[deprecated getMsb (since := "2025-06-17"), inherit_doc getMsb]
abbrev getMsb' := @getMsb
/-- Returns the `i`th most significant bit or `none` if `i ≥ w`. -/
@[inline] def getMsb? (x : BitVec w) (i : Nat) : Option Bool :=
if h : i < w then some (getMsb x i, h) else none
@@ -197,8 +203,8 @@ 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. -/
@@ -290,7 +296,7 @@ Lean convention that division by zero returns zero.
Examples:
* `(7#4).sdiv 2 = 3#4`
* `(-8#4).sdiv 2 = -4#4`
* `(-9#4).sdiv 2 = -4#4`
* `(5#4).sdiv -2 = -2#4`
* `(-7#4).sdiv (-2) = 3#4`
-/
@@ -864,17 +870,4 @@ def clz (x : BitVec w) : BitVec w := clzAuxRec x (w - 1)
/-- Count the number of trailing zeros. -/
def ctz (x : BitVec w) : BitVec w := (x.reverse).clz
/-- Count the number of bits with value `1` downward from the `pos`-th bit to the
`0`-th bit of `x`, storing the result in `acc`. -/
def cpopNatRec (x : BitVec w) (pos acc : Nat) : Nat :=
match pos with
| 0 => acc
| n + 1 => x.cpopNatRec n (acc + (x.getLsbD n).toNat)
/-- Population count operation, to count the number of bits with value `1` in `x`.
Also known as `popcount`, `popcnt`.
-/
@[suggest_for BitVec.popcount BitVec.popcnt]
def cpop (x : BitVec w) : BitVec w := BitVec.ofNat w (cpopNatRec x w 0)
end BitVec

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@@ -635,11 +635,12 @@ 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 :
@@ -835,7 +836,7 @@ execution. -/
structure DivModArgs (w : Nat) where
/-- the numerator (aka, dividend) -/
n : BitVec w
/-- the denominator (aka, divisor)-/
/-- the denumerator (aka, divisor)-/
d : BitVec w
/-- A `DivModState` is lawful if the remainder width `wr` plus the numerator width `wn` equals `w`,
@@ -1024,7 +1025,7 @@ 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 +1033,7 @@ 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 +1407,7 @@ 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 +1512,7 @@ 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 +1624,7 @@ 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 +1635,7 @@ 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 +1927,7 @@ 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

View File

@@ -82,7 +82,7 @@ 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]

View File

@@ -34,6 +34,14 @@ 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]
@@ -64,12 +72,8 @@ 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
grind_pattern BitVec.getElem?_eq_none => l[n]? where
guard w n
theorem getElem?_eq (l : BitVec w) (i : Nat) :
l[i]? = if h : i < w then some l[i] else none := by
split <;> simp_all
@@ -136,6 +140,9 @@ 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]
@@ -148,6 +155,10 @@ theorem two_pow_le_toNat_of_getElem_eq_true {i : Nat} {x : BitVec w}
@[grind =] theorem getMsbD_eq_getLsbD (x : BitVec w) (i : Nat) : x.getMsbD i = (decide (i < w) && x.getLsbD (w - 1 - i)) := by
rw [getMsbD, getLsbD]
@[deprecated getMsb_eq_getLsb (since := "2025-06-17")]
theorem getMsb'_eq_getLsb' (x : BitVec w) (i : Nat) : x.getMsbD i = (decide (i < w) && x.getLsbD (w - 1 - i)) := by
rw [getMsbD, getLsbD]
theorem getLsbD_eq_getMsbD (x : BitVec w) (i : Nat) : x.getLsbD i = (decide (i < w) && x.getMsbD (w - 1 - i)) := by
rw [getMsbD]
by_cases h₁ : i < w <;> by_cases h₂ : w - 1 - i < w <;>
@@ -158,13 +169,18 @@ 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
@@ -187,6 +203,18 @@ 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]
@@ -416,18 +444,12 @@ 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
@@ -438,6 +460,8 @@ 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]
@@ -520,10 +544,6 @@ 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) :
@@ -585,7 +605,7 @@ 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]
@@ -993,14 +1013,7 @@ 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
@@ -1016,20 +1029,18 @@ 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]
rw [Nat.mod_mod_of_dvd]
exact Nat.pow_dvd_pow_iff_le_right'.mpr h
@[simp]
theorem setWidth_ofNat_of_le_of_lt {x : Nat} (h : w v) (h' : x < 2 ^ w) :
setWidth v (BitVec.ofNat w x) = BitVec.ofNat v x := by
apply BitVec.eq_of_toNat_eq
have := Nat.pow_le_pow_of_le (a := 2) (m := v) (n := w) (by omega) h
simp only [toNat_setWidth, toNat_ofNat]
rw [Nat.mod_eq_of_lt (by omega), Nat.mod_eq_of_lt (by omega), Nat.mod_eq_of_lt (by omega)]
/--
Iterated `setWidth` agrees with the second `setWidth`
except in the case the first `setWidth` is a non-trivial truncation,
@@ -1063,7 +1074,7 @@ 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
@@ -1197,7 +1208,7 @@ 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
@@ -1263,31 +1274,11 @@ theorem extractLsb'_setWidth_of_le {b : BitVec w} {start len w' : Nat} (h : star
simp
omega
@[simp]
theorem extractLsb_setWidth_of_lt {x : BitVec w} {hi lo v : Nat} (h : lo + hi < v) :
(x.setWidth v).extractLsb hi lo = x.extractLsb hi lo := by
simp only [BitVec.extractLsb]
ext k hk
simp
omega
theorem setWidth_extractLsb'_of_le {c : BitVec w} (h : len₁ len₂) :
(c.extractLsb' start len₂).setWidth len₁ = c.extractLsb' start len₁ := by
ext i hi
simp [show i < len₂ by omega]
theorem extractLsb'_cast {x : BitVec w} :
(x.cast hcast).extractLsb' start len = x.extractLsb' start len := by
ext k hk
simp
@[simp]
theorem extractLsb'_extractLsb'_of_le {x : BitVec w} (hlt : start + len len') :
(x.extractLsb' 0 len').extractLsb' start len = x.extractLsb' start len := by
ext k hk
simp
omega
/-! ### allOnes -/
@[simp, grind =] theorem toNat_allOnes : (allOnes v).toNat = 2^v - 1 := by
@@ -1673,11 +1664,11 @@ 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
@@ -1759,6 +1750,9 @@ 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]
@@ -2578,6 +2572,10 @@ 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]
@@ -2944,15 +2942,6 @@ theorem setWidth_eq_append {v : Nat} {x : BitVec v} {w : Nat} (h : v ≤ w) :
omega
· simp [hiv, getLsbD_of_ge x i (by omega)]
@[simp]
theorem extractLsb'_append_extractLsb' {x : BitVec (w + len)} :
(x.extractLsb' len w ++ x.extractLsb' 0 len) = x := by
ext i hi
simp only [getElem_append, getElem_extractLsb', Nat.zero_add, dite_eq_ite]
split
· rw [ getLsbD_eq_getElem]
· simp [show len + (i - len) = i by omega, getLsbD_eq_getElem]
theorem setWidth_eq_extractLsb' {v : Nat} {x : BitVec v} {w : Nat} (h : w v) :
x.setWidth w = x.extractLsb' 0 w := by
rw [setWidth_eq_append_extractLsb']
@@ -3250,11 +3239,6 @@ theorem cons_append_append (x : BitVec w₁) (y : BitVec w₂) (z : BitVec w₃)
· simp [h₂]; omega
· simp [h₂]; omega
@[simp]
theorem extractLsb'_cons {x : BitVec w} :
(x.cons y).extractLsb' 0 w = x := by
simp [BitVec.toNat_eq, Nat.or_mod_two_pow, Nat.shiftLeft_eq]
/-! ### concat -/
@[simp, grind =] theorem toNat_concat (x : BitVec w) (b : Bool) :
@@ -3353,15 +3337,6 @@ theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
ext
simp [getElem_concat]
theorem extractLsb'_concat {x : BitVec (w + 1)} {y : Bool} :
(x.concat y).extractLsb' 0 (t + 1) = (x.extractLsb' 0 t).concat y := by
ext i hi
simp only [ getLsbD_eq_getElem, getLsbD_extractLsb', hi, decide_true, Nat.zero_add,
getLsbD_concat, Bool.true_and]
split
· simp
· simp [show i - 1 < t by omega]
/-! ### shiftConcat -/
@[grind =]
@@ -3660,6 +3635,9 @@ 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]
@@ -3699,6 +3677,10 @@ 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]
@@ -4115,7 +4097,6 @@ 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)
@@ -4132,7 +4113,7 @@ 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
@@ -4155,7 +4136,7 @@ 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
@@ -4701,6 +4682,9 @@ 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]
@@ -4771,6 +4755,14 @@ 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 =
@@ -4927,6 +4919,14 @@ 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) :
@@ -5651,7 +5651,7 @@ theorem msb_eq_toNat {x : BitVec w}:
simp only [msb_eq_decide, ge_iff_le]
/-- Negating a bitvector created from a natural number equals
creating a bitvector from the negative of that number.
creating a bitvector from the the negative of that number.
-/
theorem neg_ofNat_eq_ofInt_neg {w : Nat} {x : Nat} :
- BitVec.ofNat w x = BitVec.ofInt w (- x) := by
@@ -5866,16 +5866,6 @@ theorem reverse_reverse_eq {x : BitVec w} :
ext k hk
rw [getElem_reverse, getMsbD_reverse, getLsbD_eq_getElem]
@[simp]
theorem concat_reverse_setWidth_msb_eq_reverse {x : BitVec (w + 1)} :
concat ((x.setWidth w).reverse) x.msb = x.reverse := by
ext i hi
simp only [getElem_reverse, BitVec.msb, getElem_concat, getMsbD_setWidth, Nat.le_add_right,
Nat.sub_eq_zero_of_le, Nat.zero_le, decide_true, Bool.true_and, dite_eq_ite]
by_cases hzero : i = 0
· simp [hzero]
· simp [hzero, show i - 1 + (w + 1) - w = i by omega]
/-! ### Inequalities (le / lt) -/
theorem ule_eq_not_ult (x y : BitVec w) : x.ule y = !y.ult x := by
@@ -6351,241 +6341,4 @@ theorem two_pow_ctz_le_toNat_of_ne_zero {x : BitVec w} (hx : x ≠ 0#w) :
have hclz := getLsbD_true_ctz_of_ne_zero (x := x) hx
exact Nat.ge_two_pow_of_testBit hclz
/-! ### Population Count -/
@[simp]
theorem cpopNatRec_zero_self {x : BitVec w} :
x.cpopNatRec 0 acc = acc := rfl
@[simp]
theorem cpopNatRec_succ {n : Nat} {x : BitVec w} :
x.cpopNatRec (n + 1) acc = x.cpopNatRec n (acc + (x.getLsbD n).toNat) := rfl
@[simp]
theorem cpopNatRec_zero :
(0#w).cpopNatRec n acc = acc := by
induction n
· case zero =>
simp
· case succ n ihn =>
simp [ihn]
theorem cpopNatRec_eq {x : BitVec w} {n : Nat} (acc : Nat):
x.cpopNatRec n acc = x.cpopNatRec n 0 + acc := by
induction n generalizing acc
· case zero =>
simp
· case succ n ihn =>
simp [ihn (acc := acc + (x.getLsbD n).toNat), ihn (acc := (x.getLsbD n).toNat)]
omega
theorem cpopNatRec_add {x : BitVec w} {acc n : Nat} :
x.cpopNatRec n (acc + acc') = x.cpopNatRec n acc + acc' := by
rw [cpopNatRec_eq (acc := acc + acc'), cpopNatRec_eq (acc := acc), Nat.add_assoc]
theorem cpopNatRec_le {x : BitVec w} (n : Nat) :
x.cpopNatRec n acc acc + n := by
induction n generalizing acc
· case zero =>
simp
· case succ n ihn =>
have : (x.getLsbD n).toNat 1 := by cases x.getLsbD n <;> simp
specialize ihn (acc := acc + (x.getLsbD n).toNat)
simp
omega
@[simp]
theorem cpopNatRec_of_le {x : BitVec w} (k n : Nat) (hn : w n) :
x.cpopNatRec (n + k) acc = x.cpopNatRec n acc := by
induction k
· case zero =>
simp
· case succ k ihk =>
simp [show n + (k + 1) = (n + k) + 1 by omega, ihk, show w n + k by omega]
theorem cpopNatRec_zero_le (x : BitVec w) (n : Nat) :
x.cpopNatRec n 0 w := by
induction n
· case zero =>
simp
· case succ n ihn =>
by_cases hle : n w
· by_cases hx : x.getLsbD n
· have := cpopNatRec_le (x := x) (acc := 1) (by omega)
have := lt_of_getLsbD hx
simp [hx]
omega
· have := cpopNatRec_le (x := x) (acc := 0) (by omega)
simp [hx]
omega
· simp [show w n by omega]
omega
@[simp]
theorem cpopNatRec_allOnes (h : n w) :
(allOnes w).cpopNatRec n acc = acc + n := by
induction n
· case zero =>
simp
· case succ n ihn =>
specialize ihn (by omega)
simp [show n < w by omega, ihn,
cpopNatRec_add (acc := acc) (acc' := 1)]
omega
@[simp]
theorem cpop_allOnes :
(allOnes w).cpop = BitVec.ofNat w w := by
simp [cpop, cpopNatRec_allOnes]
@[simp]
theorem cpop_zero :
(0#w).cpop = 0#w := by
simp [cpop]
theorem toNat_cpop_le (x : BitVec w) :
x.cpop.toNat w := by
have hlt := Nat.lt_two_pow_self (n := w)
have hle := cpopNatRec_zero_le (x := x) (n := w)
simp only [cpop, toNat_ofNat, ge_iff_le]
rw [Nat.mod_eq_of_lt (by omega)]
exact hle
@[simp]
theorem cpopNatRec_cons_of_le {x : BitVec w} {b : Bool} (hn : n w) :
(cons b x).cpopNatRec n acc = x.cpopNatRec n acc := by
induction n generalizing acc
· case zero =>
simp
· case succ n ihn =>
specialize ihn (acc := acc + ((cons b x).getLsbD n).toNat) (by omega)
rw [cpopNatRec_succ, ihn, getLsbD_cons]
simp [show ¬ n = w by omega]
@[simp]
theorem cpopNatRec_cons_of_lt {x : BitVec w} {b : Bool} (hn : w < n) :
(cons b x).cpopNatRec n acc = b.toNat + x.cpopNatRec n acc := by
induction n generalizing acc
· case zero =>
omega
· case succ n ihn =>
by_cases hlt : w < n
· rw [cpopNatRec_succ, ihn (acc := acc + ((cons b x).getLsbD n).toNat) (by omega)]
simp [getLsbD_cons, show ¬ n = w by omega]
· simp [show w = n by omega, getElem_cons,
cpopNatRec_add (acc := acc) (acc' := b.toNat), Nat.add_comm]
theorem cpopNatRec_concat_of_lt {x : BitVec w} {b : Bool} (hn : 0 < n) :
(concat x b).cpopNatRec n acc = b.toNat + x.cpopNatRec (n - 1) acc := by
induction n generalizing acc
· case zero =>
omega
· case succ n ihn =>
by_cases hn0 : 0 < n
· specialize ihn (acc := (acc + ((x.concat b).getLsbD n).toNat)) (by omega)
rw [cpopNatRec_succ, ihn, cpopNatRec_add (acc := acc)]
simp [getLsbD_concat, show ¬ n = 0 by omega, show n + 1 - 1 = n - 1 + 1 by omega, cpopNatRec_add]
· simp [show n = 0 by omega]
omega
theorem toNat_cpop (x : BitVec w) :
x.cpop.toNat = x.cpopNatRec w 0 := by
have := cpopNatRec_zero_le x w
have := toNat_cpop_le x
have := Nat.lt_two_pow_self (n := w)
rw [cpop, toNat_ofNat, Nat.mod_eq_of_lt]
omega
@[simp]
theorem toNat_cpop_cons {x : BitVec w} {b : Bool} :
(x.cons b).cpop.toNat = b.toNat + x.cpop.toNat := by
simp [toNat_cpop, getElem_cons, cpopNatRec_eq (acc := b.toNat), Nat.add_comm]
@[simp]
theorem cpopNatRec_setWidth_of_le (x : BitVec w) (h : pos v) :
(setWidth v x).cpopNatRec pos acc = x.cpopNatRec pos acc := by
induction pos generalizing acc
· case zero =>
simp
· case succ pos ih =>
simp only [cpopNatRec_succ, getLsbD_setWidth]
rw [ih]
· congr
by_cases h : pos < v
<;> simp [h]
omega
· omega
theorem cpop_cons {x : BitVec w} {b : Bool} :
(x.cons b).cpop = b.toNat + x.cpop.setWidth (w + 1) := by
have := toNat_cpop_le x
have := Bool.toNat_lt b
simp only [natCast_eq_ofNat, toNat_eq, toNat_add, toNat_ofNat, toNat_setWidth, Nat.lt_add_one,
toNat_mod_cancel_of_lt, Nat.mod_add_mod]
rw [toNat_cpop_cons, Nat.mod_eq_of_lt]
omega
theorem cpop_concat {x : BitVec w} {b : Bool} :
(x.concat b).cpop = b.toNat + x.cpop.setWidth (w + 1) := by
have := cpopNatRec_zero_le (x := x) (n := w)
have := Nat.lt_two_pow_self (n := w)
rw [cpop, cpop, cpopNatRec_concat_of_lt,
Nat.add_one_sub_one, natCast_eq_ofNat, ofNat_add]
congr
rw [setWidth_ofNat_of_le_of_lt (x := x.cpopNatRec w 0) (by omega) (by omega)]
omega
@[simp]
theorem toNat_cpop_concat {x : BitVec w} {b : Bool} :
(x.concat b).cpop.toNat = b.toNat + x.cpop.toNat := by
have := toNat_cpop_le (x := x)
have := Nat.lt_two_pow_self (n := w + 1)
simp only [cpop_concat, natCast_eq_ofNat, toNat_add, toNat_ofNat, toNat_setWidth, Nat.lt_add_one,
toNat_mod_cancel_of_lt, Nat.mod_add_mod]
rw [Nat.mod_eq_of_lt]
cases b <;> (simp; omega)
theorem cpop_cons_eq_cpop_concat (x : BitVec w) :
(x.cons y).cpop = (x.concat y).cpop := by
rw [cpop_cons, cpop_concat]
@[simp]
theorem cpop_reverse (x : BitVec w) :
x.reverse.cpop = x.cpop := by
induction w
· case zero =>
simp [cpop, reverse]
· case succ w ihw =>
rw [ concat_reverse_setWidth_msb_eq_reverse, cpop_concat, ihw, cpop_cons]
simp
@[simp]
theorem cpopNatRec_cast_eq_of_eq {x : BitVec w} (p : w = v) :
(x.cast p).cpopNatRec n = x.cpopNatRec n := by
subst p; simp
@[simp]
theorem cpop_cast (x : BitVec w) (h : w = v) :
(x.cast h).cpop = x.cpop.cast h := by
simp [cpop, cpopNatRec_cast_eq_of_eq, h]
@[simp]
theorem toNat_cpop_append {x : BitVec w} {y : BitVec u} :
(x ++ y).cpop.toNat = x.cpop.toNat + y.cpop.toNat := by
induction w generalizing u
· case zero =>
simp [cpop]
· case succ w ihw =>
rw [ cons_msb_setWidth x, toNat_cpop_cons, cons_append, cpop_cast, toNat_cast,
toNat_cpop_cons, ihw, Nat.add_assoc]
theorem cpop_append {x : BitVec w} {y : BitVec u} :
(x ++ y).cpop = x.cpop.setWidth (w + u) + y.cpop.setWidth (w + u) := by
apply eq_of_toNat_eq
have := toNat_cpop_le x
have := toNat_cpop_le y
have := Nat.lt_two_pow_self (n := w + u)
simp only [toNat_cpop_append, toNat_add, toNat_setWidth, Nat.add_mod_mod, Nat.mod_add_mod]
rw [Nat.mod_eq_of_lt (by omega)]
end BitVec

View File

@@ -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
@@ -260,7 +308,7 @@ instance : Std.Associative (· != ·) := ⟨bne_assoc⟩
theorem eq_not_of_ne : {x y : Bool}, x y x = !y := by decide
/-! ### coercion related normal forms -/
/-! ### coercision related normal forms -/
theorem beq_eq_decide_eq [BEq α] [LawfulBEq α] [DecidableEq α] (a b : α) :
(a == b) = decide (a = b) := by
@@ -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 -/

View File

@@ -24,6 +24,9 @@ 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 +135,6 @@ 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 +246,7 @@ 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
/--
@@ -269,8 +267,6 @@ unsafe def foldlMUnsafe {β : Type v} {m : Type v → Type w} [Monad m] (f : β
if start < stop then
if stop as.size then
fold (USize.ofNat start) (USize.ofNat stop) init
else if start < as.size then
fold (USize.ofNat start) (USize.ofNat as.size) init
else
pure init
else

View File

@@ -10,8 +10,6 @@ public import Init.Data.ByteArray.Basic
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 +18,10 @@ 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 +29,39 @@ 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 +70,153 @@ 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 +225,50 @@ 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} :
theorem ByteArray.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} :
theorem ByteArray.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} :
theorem ByteArray.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

View File

@@ -102,7 +102,7 @@ Returns `true` if the character is a uppercase ASCII letter.
The uppercase ASCII letters are the following: `ABCDEFGHIJKLMNOPQRSTUVWXYZ`.
-/
@[inline] def isUpper (c : Char) : Bool :=
c.val 'A'.val c.val 'Z'.val
c.val 65 && c.val 90
/--
Returns `true` if the character is a lowercase ASCII letter.
@@ -110,7 +110,7 @@ Returns `true` if the character is a lowercase ASCII letter.
The lowercase ASCII letters are the following: `abcdefghijklmnopqrstuvwxyz`.
-/
@[inline] def isLower (c : Char) : Bool :=
c.val 'a'.val && c.val 'z'.val
c.val 97 && c.val 122
/--
Returns `true` if the character is an ASCII letter.
@@ -126,7 +126,7 @@ Returns `true` if the character is an ASCII digit.
The ASCII digits are the following: `0123456789`.
-/
@[inline] def isDigit (c : Char) : Bool :=
c.val '0'.val && c.val '9'.val
c.val 48 && c.val 57
/--
Returns `true` if the character is an ASCII letter or digit.
@@ -143,16 +143,9 @@ alphabet are returned unchanged.
The uppercase ASCII letters are the following: `ABCDEFGHIJKLMNOPQRSTUVWXYZ`.
-/
@[inline]
def toLower (c : Char) : Char :=
if h : c.val 'A'.val c.val 'Z'.val then
c.val + ('a'.val - 'A'.val), ?_
else
c
where finally
have h : c.val.toBitVec.toNat + ('a'.val - 'A'.val).toBitVec.toNat < 0xd800 :=
Nat.add_lt_add_right (Nat.lt_of_le_of_lt h.2 (by decide)) _
exact .inl (lt_of_eq_of_lt (Nat.mod_eq_of_lt (Nat.lt_trans h (by decide))) h)
let n := toNat c;
if n >= 65 n <= 90 then ofNat (n + 32) else c
/--
Converts a lowercase ASCII letter to the corresponding uppercase letter. Letters outside the ASCII
@@ -160,20 +153,8 @@ alphabet are returned unchanged.
The lowercase ASCII letters are the following: `abcdefghijklmnopqrstuvwxyz`.
-/
@[inline]
def toUpper (c : Char) : Char :=
if h : c.val 'a'.val c.val 'z'.val then
c.val + ('A'.val - 'a'.val), ?_
else
c
where finally
have h₁ : 2^32 c.val.toNat + ('A'.val - 'a'.val).toNat :=
@Nat.add_le_add 'a'.val.toNat _ (2^32 - 'a'.val.toNat) _ h.1 (by decide)
have h₂ : c.val.toBitVec.toNat + ('A'.val - 'a'.val).toNat < 2^32 + 0xd800 :=
Nat.add_lt_add_right (Nat.lt_of_le_of_lt h.2 (by decide)) _
have add_eq {x y : UInt32} : (x + y).toNat = (x.toNat + y.toNat) % 2^32 := rfl
replace h₂ := Nat.sub_lt_left_of_lt_add h₁ h₂
exact .inl <| lt_of_eq_of_lt (add_eq.trans (Nat.mod_eq_sub_mod h₁) |>.trans
(Nat.mod_eq_of_lt (Nat.lt_trans h₂ (by decide)))) h₂
let n := toNat c;
if n >= 97 n <= 122 then ofNat (n - 32) else c
end Char

View File

@@ -13,16 +13,12 @@ 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 +51,8 @@ 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 +69,4 @@ 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

View File

@@ -287,7 +287,7 @@ 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 +438,13 @@ 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 +463,7 @@ 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 +472,7 @@ 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 +495,7 @@ 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 +682,9 @@ 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 +696,20 @@ 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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@@ -52,8 +52,8 @@ 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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@@ -27,7 +27,7 @@ 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 +39,19 @@ 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 +64,12 @@ 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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@@ -28,7 +28,7 @@ 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 +36,7 @@ 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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