mirror of
https://github.com/leanprover/lean4.git
synced 2026-03-20 20:04:23 +00:00
Compare commits
1 Commits
grind_patt
...
extCore_pu
| Author | SHA1 | Date | |
|---|---|---|---|
|
|
703b963b09 |
@@ -1,34 +0,0 @@
|
||||
To build Lean you should use `make -j -C build/release`.
|
||||
|
||||
To run a test you should use `cd tests/lean/run && ./test_single.sh example_test.lean`.
|
||||
|
||||
## New features
|
||||
|
||||
When asked to implement new features:
|
||||
* begin by reviewing existing relevant code and tests
|
||||
* write comprehensive tests first (expecting that these will initially fail)
|
||||
* and then iterate on the implementation until the tests pass.
|
||||
|
||||
All new tests should go in `tests/lean/run/`. These tests don't have expected output; we just check there are no errors. You should use `#guard_msgs` to check for specific messages.
|
||||
|
||||
## Success Criteria
|
||||
|
||||
*Never* report success on a task unless you have verified both a clean build without errors, and that the relevant tests pass.
|
||||
|
||||
## Build System Safety
|
||||
|
||||
**NEVER manually delete build directories** (build/, stage0/, stage1/, etc.) even when builds fail.
|
||||
- ONLY use the project's documented build command: `make -j -C build/release`
|
||||
- If a build is broken, ask the user before attempting any manual cleanup
|
||||
|
||||
## LSP and IDE Diagnostics
|
||||
|
||||
After rebuilding, LSP diagnostics may be stale until the user interacts with files. Trust command-line test results over IDE diagnostics.
|
||||
|
||||
## Update prompting when the user is frustrated
|
||||
|
||||
If the user expresses frustration with you, stop and ask them to help update this `.claude/CLAUDE.md` file with missing guidance.
|
||||
|
||||
## Creating pull requests.
|
||||
|
||||
All PRs must have a first paragraph starting with "This PR". This paragraph is automatically incorporated into release notes. Read `lean4/doc/dev/commit_convention.md` when making PRs.
|
||||
@@ -16,26 +16,14 @@ These comments explain the scripts' behavior, which repositories get special han
|
||||
## Process
|
||||
|
||||
1. Run `script/release_checklist.py {version}` to check the current status
|
||||
2. **CRITICAL: If preliminary lean4 checks fail, STOP immediately and alert the user**
|
||||
- Check for: release branch exists, CMake version correct, tag exists, release page exists, release notes exist
|
||||
- **IMPORTANT**: The release page is created AUTOMATICALLY by CI after pushing the tag - DO NOT create it manually
|
||||
- Do NOT create any PRs or proceed with repository updates if these checks fail
|
||||
3. Create a todo list tracking all repositories that need updates
|
||||
4. **CRITICAL RULE: You can ONLY run `release_steps.py` for a repository if `release_checklist.py` explicitly says to do so**
|
||||
- The checklist output will say "Run `script/release_steps.py {version} {repo_name}` to create it"
|
||||
- If a repository shows "🟡 Dependencies not ready", you CANNOT create a PR for it yet
|
||||
- You MUST rerun `release_checklist.py` before attempting to create PRs for any new repositories
|
||||
5. For each repository that the checklist says needs updating:
|
||||
2. Create a todo list tracking all repositories that need updates
|
||||
3. For each repository that needs updating:
|
||||
- Run `script/release_steps.py {version} {repo_name}` to create the PR
|
||||
- Mark it complete when the PR is created
|
||||
6. After creating PRs, notify the user which PRs need review and merging
|
||||
7. **MANDATORY: Rerun `release_checklist.py` to check current status**
|
||||
- Do this after creating each batch of PRs
|
||||
- Do this after the user reports PRs have been merged
|
||||
- NEVER assume a repository is ready without checking the checklist output
|
||||
8. As PRs are merged and tagged, dependent repositories will become ready
|
||||
9. Continue the cycle: run checklist → create PRs for ready repos → wait for merges → repeat
|
||||
10. Continue until all repositories are updated and the release is complete
|
||||
4. After creating PRs, notify the user which PRs need review and merging
|
||||
5. Continuously rerun `script/release_checklist.py {version}` to check progress
|
||||
6. As PRs are merged, dependent repositories will become ready - create PRs for those as well
|
||||
7. Continue until all repositories are updated and the release is complete
|
||||
|
||||
## Important Notes
|
||||
|
||||
|
||||
7
.github/workflows/build-template.yml
vendored
7
.github/workflows/build-template.yml
vendored
@@ -3,6 +3,9 @@ name: build-template
|
||||
on:
|
||||
workflow_call:
|
||||
inputs:
|
||||
check-level:
|
||||
type: string
|
||||
required: true
|
||||
config:
|
||||
type: string
|
||||
required: true
|
||||
@@ -213,7 +216,7 @@ jobs:
|
||||
else
|
||||
${{ matrix.tar || 'tar' }} cf - $dir | zstd -T0 --no-progress -o pack/$dir.tar.zst
|
||||
fi
|
||||
- uses: actions/upload-artifact@v5
|
||||
- uses: actions/upload-artifact@v4
|
||||
if: matrix.release
|
||||
with:
|
||||
name: build-${{ matrix.name }}
|
||||
@@ -227,7 +230,7 @@ jobs:
|
||||
run: |
|
||||
ulimit -c unlimited # coredumps
|
||||
time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
|
||||
if: matrix.test
|
||||
if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.test)
|
||||
- name: Test Summary
|
||||
uses: test-summary/action@v2
|
||||
with:
|
||||
|
||||
2
.github/workflows/check-stage0.yml
vendored
2
.github/workflows/check-stage0.yml
vendored
@@ -11,8 +11,8 @@ jobs:
|
||||
- uses: actions/checkout@v5
|
||||
with:
|
||||
ref: ${{ github.event.pull_request.head.sha }}
|
||||
filter: blob:none
|
||||
fetch-depth: 0
|
||||
filter: tree:0
|
||||
|
||||
- name: Find base commit
|
||||
if: github.event_name == 'pull_request'
|
||||
|
||||
144
.github/workflows/ci.yml
vendored
144
.github/workflows/ci.yml
vendored
@@ -31,6 +31,10 @@ jobs:
|
||||
configure:
|
||||
runs-on: ubuntu-latest
|
||||
outputs:
|
||||
# 0: PRs without special label
|
||||
# 1: PRs with `merge-ci` label, merge queue checks, master commits
|
||||
# 2: PRs with `release-ci` label, releases (incl. nightlies)
|
||||
check-level: ${{ steps.set-level.outputs.check-level }}
|
||||
# The build matrix, dynamically generated here
|
||||
matrix: ${{ steps.set-matrix.outputs.matrix }}
|
||||
# secondary build jobs that should not block the CI success/merge queue
|
||||
@@ -106,54 +110,6 @@ jobs:
|
||||
TAG_NAME="${GITHUB_REF##*/}"
|
||||
echo "RELEASE_TAG=$TAG_NAME" >> "$GITHUB_OUTPUT"
|
||||
|
||||
- name: Validate CMakeLists.txt version matches tag
|
||||
if: steps.set-release.outputs.RELEASE_TAG != ''
|
||||
run: |
|
||||
echo "Validating CMakeLists.txt version matches tag ${{ steps.set-release.outputs.RELEASE_TAG }}"
|
||||
|
||||
# Extract version values from CMakeLists.txt
|
||||
CMAKE_MAJOR=$(grep -E "^set\(LEAN_VERSION_MAJOR " src/CMakeLists.txt | grep -oE '[0-9]+')
|
||||
CMAKE_MINOR=$(grep -E "^set\(LEAN_VERSION_MINOR " src/CMakeLists.txt | grep -oE '[0-9]+')
|
||||
CMAKE_PATCH=$(grep -E "^set\(LEAN_VERSION_PATCH " src/CMakeLists.txt | grep -oE '[0-9]+')
|
||||
CMAKE_IS_RELEASE=$(grep -E "^set\(LEAN_VERSION_IS_RELEASE " src/CMakeLists.txt | grep -oE '[0-9]+')
|
||||
|
||||
# Expected values from tag parsing
|
||||
TAG_MAJOR="${{ steps.set-release.outputs.LEAN_VERSION_MAJOR }}"
|
||||
TAG_MINOR="${{ steps.set-release.outputs.LEAN_VERSION_MINOR }}"
|
||||
TAG_PATCH="${{ steps.set-release.outputs.LEAN_VERSION_PATCH }}"
|
||||
|
||||
ERRORS=""
|
||||
|
||||
if [[ "$CMAKE_MAJOR" != "$TAG_MAJOR" ]]; then
|
||||
ERRORS+="LEAN_VERSION_MAJOR: expected $TAG_MAJOR, found $CMAKE_MAJOR\n"
|
||||
fi
|
||||
if [[ "$CMAKE_MINOR" != "$TAG_MINOR" ]]; then
|
||||
ERRORS+="LEAN_VERSION_MINOR: expected $TAG_MINOR, found $CMAKE_MINOR\n"
|
||||
fi
|
||||
if [[ "$CMAKE_PATCH" != "$TAG_PATCH" ]]; then
|
||||
ERRORS+="LEAN_VERSION_PATCH: expected $TAG_PATCH, found $CMAKE_PATCH\n"
|
||||
fi
|
||||
if [[ "$CMAKE_IS_RELEASE" != "1" ]]; then
|
||||
ERRORS+="LEAN_VERSION_IS_RELEASE: expected 1, found $CMAKE_IS_RELEASE\n"
|
||||
fi
|
||||
|
||||
if [[ -n "$ERRORS" ]]; then
|
||||
echo "::error::Version mismatch between tag and src/CMakeLists.txt"
|
||||
echo ""
|
||||
echo "Tag ${{ steps.set-release.outputs.RELEASE_TAG }} expects version $TAG_MAJOR.$TAG_MINOR.$TAG_PATCH"
|
||||
echo "But src/CMakeLists.txt has mismatched values:"
|
||||
echo -e "$ERRORS"
|
||||
echo ""
|
||||
echo "Fix src/CMakeLists.txt, delete the tag, and re-tag."
|
||||
exit 1
|
||||
fi
|
||||
|
||||
echo "Version validation passed: $TAG_MAJOR.$TAG_MINOR.$TAG_PATCH"
|
||||
|
||||
# 0: PRs without special label
|
||||
# 1: PRs with `merge-ci` label, merge queue checks, master commits
|
||||
# 2: nightlies
|
||||
# 3: PRs with `release-ci` label, full releases
|
||||
- name: Set check level
|
||||
id: set-level
|
||||
# We do not use github.event.pull_request.labels.*.name here because
|
||||
@@ -161,28 +117,21 @@ jobs:
|
||||
# rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
|
||||
run: |
|
||||
check_level=0
|
||||
fast=false
|
||||
|
||||
if [[ -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
|
||||
check_level=3
|
||||
elif [[ -n "${{ steps.set-nightly.outputs.nightly }}" ]]; then
|
||||
if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
|
||||
check_level=2
|
||||
elif [[ "${{ github.event_name }}" != "pull_request" ]]; then
|
||||
check_level=1
|
||||
else
|
||||
labels="$(gh api repos/${{ github.repository_owner }}/${{ github.event.repository.name }}/pulls/${{ github.event.pull_request.number }} --jq '.labels')"
|
||||
if echo "$labels" | grep -q "release-ci"; then
|
||||
check_level=3
|
||||
check_level=2
|
||||
elif echo "$labels" | grep -q "merge-ci"; then
|
||||
check_level=1
|
||||
fi
|
||||
if echo "$labels" | grep -q "fast-ci"; then
|
||||
fast=true
|
||||
fi
|
||||
fi
|
||||
|
||||
echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
|
||||
echo "fast=$fast" >> "$GITHUB_OUTPUT"
|
||||
env:
|
||||
GH_TOKEN: ${{ github.token }}
|
||||
|
||||
@@ -192,8 +141,7 @@ jobs:
|
||||
with:
|
||||
script: |
|
||||
const level = ${{ steps.set-level.outputs.check-level }};
|
||||
const fast = ${{ steps.set-level.outputs.fast }};
|
||||
console.log(`level: ${level}, fast: ${fast}`);
|
||||
console.log(`level: ${level}`);
|
||||
// use large runners where available (original repo)
|
||||
let large = ${{ github.repository == 'leanprover/lean4' }};
|
||||
const isPr = "${{ github.event_name }}" == "pull_request";
|
||||
@@ -204,8 +152,7 @@ jobs:
|
||||
"name": "Linux LLVM",
|
||||
"os": "ubuntu-latest",
|
||||
"release": false,
|
||||
"enabled": level >= 2,
|
||||
"test": true,
|
||||
"check-level": 2,
|
||||
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
|
||||
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
|
||||
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
|
||||
@@ -218,19 +165,17 @@ jobs:
|
||||
{
|
||||
// portable release build: use channel with older glibc (2.26)
|
||||
"name": "Linux release",
|
||||
// usually not a bottleneck so make exclusive to `fast-ci`
|
||||
"os": large && fast ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
|
||||
"os": "ubuntu-latest",
|
||||
"release": true,
|
||||
// Special handling for release jobs. We want:
|
||||
// 1. To run it in PRs so developers get PR toolchains (so secondary without tests is sufficient)
|
||||
// 1. To run it in PRs so developers get PR toolchains (so secondary is sufficient)
|
||||
// 2. To skip it in merge queues as it takes longer than the
|
||||
// Linux lake build and adds little value in the merge queue
|
||||
// 3. To run it in release (obviously)
|
||||
// 4. To run it for pushes to master so that pushes to master have a Linux toolchain
|
||||
// available as an artifact for Grove to use.
|
||||
"enabled": isPr || level != 1 || isPushToMaster,
|
||||
"test": level >= 1,
|
||||
"secondary": level == 0,
|
||||
"check-level": (isPr || isPushToMaster) ? 0 : 2,
|
||||
"secondary": isPr,
|
||||
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
|
||||
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
|
||||
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
|
||||
@@ -241,44 +186,38 @@ jobs:
|
||||
{
|
||||
"name": "Linux Lake",
|
||||
"os": large ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
|
||||
"enabled": true,
|
||||
"check-level": 0,
|
||||
"check-rebootstrap": level >= 1,
|
||||
"check-stage3": level >= 2,
|
||||
// only check-level >= 1 opts into tests implicitly. TODO: Clean up this logic.
|
||||
"test": true,
|
||||
// NOTE: `test-speedcenter` currently seems to be broken on `ubuntu-latest`
|
||||
"test-speedcenter": large && level >= 2,
|
||||
// We are not warning-free yet on all platforms, start here
|
||||
"CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-Werror",
|
||||
// made explicit until it can be assumed to have propagated to PRs
|
||||
"CMAKE_OPTIONS": "-DUSE_LAKE=ON",
|
||||
},
|
||||
{
|
||||
"name": "Linux Reldebug",
|
||||
"os": "ubuntu-latest",
|
||||
"enabled": level >= 2,
|
||||
"test": true,
|
||||
"check-level": 2,
|
||||
"CMAKE_PRESET": "reldebug",
|
||||
},
|
||||
{
|
||||
// TODO: suddenly started failing in CI
|
||||
/*{
|
||||
"name": "Linux fsanitize",
|
||||
// Always run on large if available, more reliable regarding timeouts
|
||||
"os": large ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
|
||||
"enabled": level >= 2,
|
||||
// do not fail nightlies on this for now
|
||||
"secondary": level <= 2,
|
||||
"test": true,
|
||||
"os": "ubuntu-latest",
|
||||
"check-level": 2,
|
||||
// turn off custom allocator & symbolic functions to make LSAN do its magic
|
||||
"CMAKE_PRESET": "sanitize",
|
||||
// `StackOverflow*` correctly triggers ubsan
|
||||
// `reverse-ffi` fails to link in sanitizers
|
||||
// `interactive` and `async_select_channel` fail nondeterministically, would need to
|
||||
// be investigated.
|
||||
"CTEST_OPTIONS": "-E 'StackOverflow|reverse-ffi|interactive|async_select_channel'"
|
||||
},
|
||||
// exclude seriously slow/problematic tests (laketests crash)
|
||||
"CTEST_OPTIONS": "-E 'interactivetest|leanpkgtest|laketest|benchtest'"
|
||||
},*/
|
||||
{
|
||||
"name": "macOS",
|
||||
"os": "macos-15-intel",
|
||||
"release": true,
|
||||
"test": false, // Tier 2 platform
|
||||
"enabled": level >= 2,
|
||||
"check-level": 2,
|
||||
"shell": "bash -euxo pipefail {0}",
|
||||
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-apple-darwin.tar.zst",
|
||||
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
|
||||
@@ -289,7 +228,7 @@ jobs:
|
||||
{
|
||||
"name": "macOS aarch64",
|
||||
// standard GH runner only comes with 7GB so use large runner if possible when running tests
|
||||
"os": large && (fast || level >= 1) ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
|
||||
"os": large && !isPr ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
|
||||
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
|
||||
"release": true,
|
||||
"shell": "bash -euxo pipefail {0}",
|
||||
@@ -298,16 +237,14 @@ jobs:
|
||||
"binary-check": "otool -L",
|
||||
"tar": "gtar", // https://github.com/actions/runner-images/issues/2619
|
||||
// See "Linux release" for release job levels; Grove is not a concern here
|
||||
"enabled": isPr || level != 1,
|
||||
"test": level >= 1,
|
||||
"secondary": level == 0,
|
||||
"check-level": isPr ? 0 : 2,
|
||||
"secondary": isPr,
|
||||
},
|
||||
{
|
||||
"name": "Windows",
|
||||
"os": large && (fast || level >= 2) ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
|
||||
"os": large && level == 2 ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
|
||||
"release": true,
|
||||
"enabled": level >= 2,
|
||||
"test": true,
|
||||
"check-level": 2,
|
||||
"shell": "msys2 {0}",
|
||||
"CMAKE_OPTIONS": "-G \"Unix Makefiles\"",
|
||||
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
|
||||
@@ -319,8 +256,7 @@ jobs:
|
||||
"os": "nscloud-ubuntu-22.04-arm64-4x16",
|
||||
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-linux_aarch64",
|
||||
"release": true,
|
||||
"enabled": level >= 2,
|
||||
"test": true,
|
||||
"check-level": 2,
|
||||
"shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
|
||||
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-aarch64-linux-gnu.tar.zst",
|
||||
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
|
||||
@@ -333,7 +269,7 @@ jobs:
|
||||
// "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DPKG_CONFIG_EXECUTABLE=/usr/bin/i386-linux-gnu-pkg-config",
|
||||
// "cmultilib": true,
|
||||
// "release": true,
|
||||
// "enabled": level >= 2,
|
||||
// "check-level": 2,
|
||||
// "cross": true,
|
||||
// "shell": "bash -euxo pipefail {0}"
|
||||
//}
|
||||
@@ -345,7 +281,7 @@ jobs:
|
||||
// "wasm": true,
|
||||
// "cmultilib": true,
|
||||
// "release": true,
|
||||
// "enabled": level >= 2,
|
||||
// "check-level": 2,
|
||||
// "cross": true,
|
||||
// "shell": "bash -euxo pipefail {0}",
|
||||
// // Just a few selected tests because wasm is slow
|
||||
@@ -359,7 +295,7 @@ jobs:
|
||||
}
|
||||
}
|
||||
console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
|
||||
matrix = matrix.filter((job) => job["enabled"]);
|
||||
matrix = matrix.filter((job) => level >= job["check-level"]);
|
||||
core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));
|
||||
core.setOutput('matrix-secondary', matrix.filter((job) => job["secondary"]));
|
||||
|
||||
@@ -369,6 +305,7 @@ jobs:
|
||||
uses: ./.github/workflows/build-template.yml
|
||||
with:
|
||||
config: ${{needs.configure.outputs.matrix}}
|
||||
check-level: ${{ needs.configure.outputs.check-level }}
|
||||
nightly: ${{ needs.configure.outputs.nightly }}
|
||||
LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
|
||||
LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
|
||||
@@ -384,6 +321,7 @@ jobs:
|
||||
uses: ./.github/workflows/build-template.yml
|
||||
with:
|
||||
config: ${{needs.configure.outputs.matrix-secondary}}
|
||||
check-level: ${{ needs.configure.outputs.check-level }}
|
||||
nightly: ${{ needs.configure.outputs.nightly }}
|
||||
LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
|
||||
LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
|
||||
@@ -427,11 +365,11 @@ jobs:
|
||||
runs-on: ubuntu-latest
|
||||
needs: build
|
||||
steps:
|
||||
- uses: actions/download-artifact@v6
|
||||
- uses: actions/download-artifact@v5
|
||||
with:
|
||||
path: artifacts
|
||||
- name: Release
|
||||
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
|
||||
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
|
||||
with:
|
||||
files: artifacts/*/*
|
||||
fail_on_unmatched_files: true
|
||||
@@ -456,10 +394,8 @@ jobs:
|
||||
with:
|
||||
# needed for tagging
|
||||
fetch-depth: 0
|
||||
# Doesn't seem to be working when additionally fetching from lean4-nightly
|
||||
#filter: tree:0
|
||||
token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
|
||||
- uses: actions/download-artifact@v6
|
||||
- uses: actions/download-artifact@v5
|
||||
with:
|
||||
path: artifacts
|
||||
- name: Prepare Nightly Release
|
||||
@@ -477,7 +413,7 @@ jobs:
|
||||
echo -e "\n*Full commit log*\n" >> diff.md
|
||||
git log --oneline "$last_tag"..HEAD | sed 's/^/* /' >> diff.md
|
||||
- name: Release Nightly
|
||||
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
|
||||
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
|
||||
with:
|
||||
body_path: diff.md
|
||||
prerelease: true
|
||||
|
||||
29
.github/workflows/pr-release.yml
vendored
29
.github/workflows/pr-release.yml
vendored
@@ -48,17 +48,17 @@ jobs:
|
||||
git -C lean4.git remote add origin https://github.com/${{ github.repository_owner }}/lean4.git
|
||||
git -C lean4.git fetch -n origin master
|
||||
git -C lean4.git fetch -n origin "${{ steps.workflow-info.outputs.sourceHeadSha }}"
|
||||
|
||||
|
||||
# Create both the original tag and the SHA-suffixed tag
|
||||
SHORT_SHA="${{ steps.workflow-info.outputs.sourceHeadSha }}"
|
||||
SHORT_SHA="${SHORT_SHA:0:7}"
|
||||
|
||||
|
||||
# Export the short SHA for use in subsequent steps
|
||||
echo "SHORT_SHA=${SHORT_SHA}" >> "$GITHUB_ENV"
|
||||
|
||||
git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }} "${{ steps.workflow-info.outputs.sourceHeadSha }}"
|
||||
git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}" "${{ steps.workflow-info.outputs.sourceHeadSha }}"
|
||||
|
||||
|
||||
git -C lean4.git remote add pr-releases https://foo:'${{ secrets.PR_RELEASES_TOKEN }}'@github.com/${{ github.repository_owner }}/lean4-pr-releases.git
|
||||
git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}
|
||||
git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}"
|
||||
@@ -71,7 +71,7 @@ jobs:
|
||||
GH_TOKEN: ${{ secrets.PR_RELEASES_TOKEN }}
|
||||
- name: Release (short format)
|
||||
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
|
||||
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
|
||||
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
|
||||
with:
|
||||
name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }}
|
||||
# There are coredumps files here as well, but all in deeper subdirectories.
|
||||
@@ -86,7 +86,7 @@ jobs:
|
||||
|
||||
- name: Release (SHA-suffixed format)
|
||||
if: ${{ steps.workflow-info.outputs.pullRequestNumber != '' }}
|
||||
uses: softprops/action-gh-release@6da8fa9354ddfdc4aeace5fc48d7f679b5214090
|
||||
uses: softprops/action-gh-release@6cbd405e2c4e67a21c47fa9e383d020e4e28b836
|
||||
with:
|
||||
name: Release for PR ${{ steps.workflow-info.outputs.pullRequestNumber }} (${{ steps.workflow-info.outputs.sourceHeadSha }})
|
||||
# There are coredumps files here as well, but all in deeper subdirectories.
|
||||
@@ -200,7 +200,7 @@ jobs:
|
||||
-H "Accept: application/vnd.github.v3+json" \
|
||||
"https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
|
||||
| jq -r '.[].name')"
|
||||
|
||||
|
||||
if echo "$LABELS" | grep -q "^force-mathlib-ci$"; then
|
||||
echo "force-mathlib-ci label detected, forcing CI despite issues"
|
||||
MESSAGE="Forcing Mathlib CI because the \`force-mathlib-ci\` label is present, despite problem: $MESSAGE"
|
||||
@@ -301,7 +301,7 @@ jobs:
|
||||
-H "Accept: application/vnd.github.v3+json" \
|
||||
"https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
|
||||
| jq -r '.[].name')"
|
||||
|
||||
|
||||
if echo "$LABELS" | grep -q "^force-manual-ci$"; then
|
||||
echo "force-manual-ci label detected, forcing CI despite issues"
|
||||
MESSAGE="Forcing reference manual CI because the \`force-manual-ci\` label is present, despite problem: $MESSAGE"
|
||||
@@ -401,7 +401,6 @@ jobs:
|
||||
token: ${{ secrets.MATHLIB4_BOT }}
|
||||
ref: nightly-testing
|
||||
fetch-depth: 0 # This ensures we check out all tags and branches.
|
||||
filter: tree:0
|
||||
|
||||
- name: Check if tag exists
|
||||
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
|
||||
@@ -426,7 +425,7 @@ jobs:
|
||||
git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
|
||||
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
|
||||
git add lean-toolchain
|
||||
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
else
|
||||
echo "Branch already exists, updating lean-toolchain."
|
||||
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
|
||||
@@ -435,7 +434,7 @@ jobs:
|
||||
git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
|
||||
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
|
||||
git add lean-toolchain
|
||||
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
fi
|
||||
|
||||
- name: Push changes
|
||||
@@ -461,7 +460,6 @@ jobs:
|
||||
token: ${{ secrets.MATHLIB4_BOT }}
|
||||
ref: nightly-testing
|
||||
fetch-depth: 0 # This ensures we check out all tags and branches.
|
||||
filter: tree:0
|
||||
|
||||
- name: install elan
|
||||
run: |
|
||||
@@ -496,7 +494,7 @@ jobs:
|
||||
sed -i 's,require "leanprover-community" / "batteries" @ git ".\+",require "leanprover-community" / "batteries" @ git "lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}",' lakefile.lean
|
||||
lake update batteries
|
||||
git add lakefile.lean lake-manifest.json
|
||||
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
else
|
||||
echo "Branch already exists, updating lean-toolchain and bumping Batteries."
|
||||
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
|
||||
@@ -507,7 +505,7 @@ jobs:
|
||||
git add lean-toolchain
|
||||
lake update batteries
|
||||
git add lake-manifest.json
|
||||
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
fi
|
||||
|
||||
- name: Push changes
|
||||
@@ -532,7 +530,6 @@ jobs:
|
||||
token: ${{ secrets.MANUAL_PR_BOT }}
|
||||
ref: nightly-testing
|
||||
fetch-depth: 0 # This ensures we check out all tags and branches.
|
||||
filter: tree:0
|
||||
|
||||
- name: Check if tag in reference manual exists
|
||||
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.reference-manual-ready.outputs.manual_ready == 'true'
|
||||
@@ -558,7 +555,7 @@ jobs:
|
||||
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
|
||||
git add lean-toolchain
|
||||
git add lakefile.lean lake-manifest.json
|
||||
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
else
|
||||
echo "Branch already exists, updating lean-toolchain."
|
||||
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
|
||||
@@ -568,7 +565,7 @@ jobs:
|
||||
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
|
||||
git add lean-toolchain
|
||||
git add lake-manifest.json
|
||||
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
|
||||
fi
|
||||
|
||||
- name: Push changes
|
||||
|
||||
2
.github/workflows/pr-title.yml
vendored
2
.github/workflows/pr-title.yml
vendored
@@ -15,6 +15,6 @@ jobs:
|
||||
script: |
|
||||
const msg = context.payload.pull_request? context.payload.pull_request.title : context.payload.merge_group.head_commit.message;
|
||||
console.log(`Message: ${msg}`)
|
||||
if (!/^(feat|fix|doc|style|refactor|test|chore|perf): (?![A-Z][a-z]).*[^.]($|\n\n)/.test(msg)) {
|
||||
if (!/^(feat|fix|doc|style|refactor|test|chore|perf): .*[^.]($|\n\n)/.test(msg)) {
|
||||
core.setFailed('PR title does not follow the Commit Convention (https://leanprover.github.io/lean4/doc/dev/commit_convention.html).');
|
||||
}
|
||||
|
||||
1
.gitignore
vendored
1
.gitignore
vendored
@@ -20,6 +20,7 @@ tasks.json
|
||||
settings.json
|
||||
.gdb_history
|
||||
.vscode/*
|
||||
!.vscode/settings.json
|
||||
script/__pycache__
|
||||
*.produced.out
|
||||
CMakeSettings.json
|
||||
|
||||
@@ -41,7 +41,7 @@
|
||||
"SMALL_ALLOCATOR": "OFF",
|
||||
"USE_MIMALLOC": "OFF",
|
||||
"BSYMBOLIC": "OFF",
|
||||
"LEAN_TEST_VARS": "MAIN_STACK_SIZE=16000 LSAN_OPTIONS=max_leaks=10"
|
||||
"LEAN_TEST_VARS": "MAIN_STACK_SIZE=16000"
|
||||
},
|
||||
"generator": "Unix Makefiles",
|
||||
"binaryDir": "${sourceDir}/build/sanitize"
|
||||
|
||||
@@ -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`.
|
||||
|
||||
@@ -52,7 +52,7 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
|
||||
Similarly, the signed integer types `Int8`, ..., `Int64`, `ISize` are also represented by the unsigned C types `uint8_t`, ..., `uint64_t`, `size_t`, respectively, because they have a trivial structure.
|
||||
* `Nat` and `Int` are represented by `lean_object *`.
|
||||
Their runtime values is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number or integer (`lean_box`/`lean_unbox`).
|
||||
* A universe `Sort u`, type constructor `... → Sort u`, `Void α` or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
|
||||
* A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
|
||||
* Any other type is represented by `lean_object *`.
|
||||
Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
|
||||
|
||||
@@ -129,7 +129,8 @@ For all other modules imported by `lean`, the initializer is run without `builti
|
||||
Thus `[init]` functions are run iff their module is imported, regardless of whether they have native code available or not, while `[builtin_init]` functions are only run for native executable or plugins, regardless of whether their module is imported or not.
|
||||
`lean` uses built-in initializers for e.g. registering basic parsers that should be available even without importing their module (which is necessary for bootstrapping).
|
||||
|
||||
The initializer for module `A.B` in a package `foo` is called `initialize_foo_A_B`. For modules in the Lean core (e.g., `Init.Prelude`), the initializer is called `initialize_Init_Prelude`. Module initializers will automatically initialize any imported modules. They are also idempotent (when run with the same `builtin` flag), but not thread-safe.
|
||||
The initializer for module `A.B` is called `initialize_A_B` and will automatically initialize any imported modules.
|
||||
Module initializers are idempotent (when run with the same `builtin` flag), but not thread-safe.
|
||||
|
||||
**Important for process-related functionality**: If your application needs to use process-related functions from libuv, such as `Std.Internal.IO.Process.getProcessTitle` and `Std.Internal.IO.Process.setProcessTitle`, you must call `lean_setup_args(argc, argv)` (which returns a potentially modified `argv` that must be used in place of the original) **before** calling `lean_initialize()` or `lean_initialize_runtime_module()`. This sets up process handling capabilities correctly, which is essential for certain system-level operations that Lean's runtime may depend on.
|
||||
|
||||
@@ -140,8 +141,8 @@ void lean_initialize_runtime_module();
|
||||
void lean_initialize();
|
||||
char ** lean_setup_args(int argc, char ** argv);
|
||||
|
||||
lean_object * initialize_A_B(uint8_t builtin);
|
||||
lean_object * initialize_C(uint8_t builtin);
|
||||
lean_object * initialize_A_B(uint8_t builtin, lean_object *);
|
||||
lean_object * initialize_C(uint8_t builtin, lean_object *);
|
||||
...
|
||||
|
||||
argv = lean_setup_args(argc, argv); // if using process-related functionality
|
||||
@@ -151,7 +152,7 @@ lean_initialize_runtime_module();
|
||||
lean_object * res;
|
||||
// use same default as for Lean executables
|
||||
uint8_t builtin = 1;
|
||||
res = initialize_A_B(builtin);
|
||||
res = initialize_A_B(builtin, lean_io_mk_world());
|
||||
if (lean_io_result_is_ok(res)) {
|
||||
lean_dec_ref(res);
|
||||
} else {
|
||||
@@ -159,7 +160,7 @@ if (lean_io_result_is_ok(res)) {
|
||||
lean_dec(res);
|
||||
return ...; // do not access Lean declarations if initialization failed
|
||||
}
|
||||
res = initialize_C(builtin);
|
||||
res = initialize_C(builtin, lean_io_mk_world());
|
||||
if (lean_io_result_is_ok(res)) {
|
||||
...
|
||||
|
||||
|
||||
@@ -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.
|
||||
|
||||
@@ -15,8 +15,7 @@
|
||||
],
|
||||
"settings": {
|
||||
// Open terminal at root, not current workspace folder
|
||||
// (there is not way to directly refer to the root folder included as `.` above)
|
||||
"terminal.integrated.cwd": "${workspaceFolder:src}/..",
|
||||
"terminal.integrated.cwd": "${workspaceFolder:.}",
|
||||
"files.insertFinalNewline": true,
|
||||
"files.trimTrailingWhitespace": true,
|
||||
"cmake.buildDirectory": "${workspaceFolder}/build/release",
|
||||
|
||||
@@ -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).
|
||||
132
script/AnalyzeGrindAnnotations.lean
Normal file
132
script/AnalyzeGrindAnnotations.lean
Normal 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 {}
|
||||
@@ -57,19 +57,19 @@ def main (args : List String) : IO Unit := do
|
||||
sec := "\n\n" ++ sec
|
||||
if insertPos?.isNone then
|
||||
sec := sec ++ "\n\n"
|
||||
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.rawEndPos
|
||||
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.endPos
|
||||
|
||||
-- prepend each import with `public `
|
||||
for imp in imps.reverse do
|
||||
let insertPos := imp.raw.getPos?.get!
|
||||
let prfx := if doMeta then "public meta " else "public "
|
||||
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.rawEndPos
|
||||
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.endPos
|
||||
|
||||
-- insert `module` header
|
||||
let mut initText := text.extract 0 startPos
|
||||
if !initText.trim.isEmpty then
|
||||
-- If there is a header comment, preserve it and put `module` in the line after
|
||||
initText := initText.trimRight ++ "\n"
|
||||
text := initText ++ "module\n\n" ++ text.extract startPos text.rawEndPos
|
||||
text := initText ++ "module\n\n" ++ text.extract startPos text.endPos
|
||||
|
||||
IO.FS.writeFile path text
|
||||
|
||||
@@ -131,11 +131,10 @@ structure State where
|
||||
`transDeps[i]` is the (non-reflexive) transitive closure of `mods[i].imports`. More specifically,
|
||||
* `j ∈ transDeps[i].pub` if `i -(public import)->+ j`
|
||||
* `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
|
||||
* `j ∈ transDeps[i].priv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].pub/priv`
|
||||
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import)->* j`
|
||||
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import)->* j`
|
||||
* `j ∈ transDeps[i].metaPriv` if `i -(import ...)-> i'` and `j ∈ transDeps[i'].metaPub`
|
||||
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].metaPub/metaPriv`
|
||||
* `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
|
||||
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
|
||||
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
|
||||
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
|
||||
-/
|
||||
transDeps : Array Needs := #[]
|
||||
/--
|
||||
@@ -163,10 +162,10 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
|
||||
-- `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
|
||||
transImps := transImps.union .priv {j} |>.union .priv (impTransImps.get .pub)
|
||||
if imp.importAll then
|
||||
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].pub/priv`
|
||||
transImps := transImps.union .priv (impTransImps.get .pub ∪ impTransImps.get .priv)
|
||||
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
|
||||
transImps := transImps.union .priv (impTransImps.get .pub)
|
||||
|
||||
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import)->* j`
|
||||
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
|
||||
if imp.isExported then
|
||||
transImps := transImps.union .metaPub (impTransImps.get .metaPub)
|
||||
if imp.isMeta then
|
||||
@@ -174,13 +173,10 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
|
||||
|
||||
if !imp.isExported then
|
||||
if imp.isMeta then
|
||||
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import)->* j`
|
||||
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
|
||||
transImps := transImps.union .metaPriv {j} |>.union .metaPriv (impTransImps.get .pub ∪ impTransImps.get .metaPub)
|
||||
if imp.importAll then
|
||||
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].metaPub/metaPriv`
|
||||
transImps := transImps.union .metaPriv (impTransImps.get .metaPub ∪ impTransImps.get .metaPriv)
|
||||
else
|
||||
-- `j ∈ transDeps[i].metaPriv` if `i -(import ...)-> i'` and `j ∈ transDeps[i'].metaPub`
|
||||
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
|
||||
transImps := transImps.union .metaPriv (impTransImps.get .metaPub)
|
||||
|
||||
transImps
|
||||
@@ -189,8 +185,7 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
|
||||
def calcNeeds (env : Environment) (i : ModuleIdx) : Needs := Id.run do
|
||||
let mut needs := default
|
||||
for ci in env.header.moduleData[i]!.constants do
|
||||
-- Added guard for cases like `structure` that are still exported even if private
|
||||
let pubCI? := guard (!isPrivateName ci.name) *> (env.setExporting true).find? ci.name
|
||||
let pubCI? := env.setExporting true |>.find? ci.name
|
||||
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
|
||||
needs := visitExpr k ci.type needs
|
||||
if let some e := ci.value? (allowOpaque := true) then
|
||||
@@ -221,8 +216,7 @@ def getExplanations (env : Environment) (i : ModuleIdx) :
|
||||
Std.HashMap (ModuleIdx × NeedsKind) (Option (Name × Name)) := Id.run do
|
||||
let mut deps := default
|
||||
for ci in env.header.moduleData[i]!.constants do
|
||||
-- Added guard for cases like `structure` that are still exported even if private
|
||||
let pubCI? := guard (!isPrivateName ci.name) *> (env.setExporting true).find? ci.name
|
||||
let pubCI? := env.setExporting true |>.find? ci.name
|
||||
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
|
||||
deps := visitExpr k ci.name ci.type deps
|
||||
if let some e := ci.value? (allowOpaque := true) then
|
||||
@@ -292,7 +286,7 @@ and `endPos` is the position of the end of the header.
|
||||
-/
|
||||
def parseHeaderFromString (text path : String) :
|
||||
IO (System.FilePath × Parser.InputContext ×
|
||||
TSyntax ``Parser.Module.header × String.Pos.Raw) := do
|
||||
TSyntaxArray ``Parser.Module.import × String.Pos) := do
|
||||
let inputCtx := Parser.mkInputContext text path
|
||||
let (header, parserState, msgs) ← Parser.parseHeader inputCtx
|
||||
if !msgs.toList.isEmpty then -- skip this file if there are parse errors
|
||||
@@ -300,8 +294,8 @@ def parseHeaderFromString (text path : String) :
|
||||
throw <| .userError "parse errors in file"
|
||||
-- the insertion point for `add` is the first newline after the imports
|
||||
let insertion := header.raw.getTailPos?.getD parserState.pos
|
||||
let insertion := text.findAux (· == '\n') text.rawEndPos insertion + '\n'
|
||||
pure (path, inputCtx, header, insertion)
|
||||
let insertion := text.findAux (· == '\n') text.endPos insertion + ⟨1⟩
|
||||
pure (path, inputCtx, .mk header.raw[2].getArgs, insertion)
|
||||
|
||||
/-- Parse a source file to extract the location of the import lines, for edits and error messages.
|
||||
|
||||
@@ -310,18 +304,13 @@ and `endPos` is the position of the end of the header.
|
||||
-/
|
||||
def parseHeader (srcSearchPath : SearchPath) (mod : Name) :
|
||||
IO (System.FilePath × Parser.InputContext ×
|
||||
TSyntax ``Parser.Module.header × String.Pos.Raw) := do
|
||||
TSyntaxArray ``Parser.Module.import × String.Pos) := do
|
||||
-- Parse the input file
|
||||
let some path ← srcSearchPath.findModuleWithExt "lean" mod
|
||||
| throw <| .userError s!"error: failed to find source file for {mod}"
|
||||
let text ← IO.FS.readFile path
|
||||
parseHeaderFromString text path.toString
|
||||
|
||||
def decodeHeader : TSyntax ``Parser.Module.header → Option (TSyntax `module) × Option (TSyntax `prelude) × TSyntaxArray ``Parser.Module.import
|
||||
| `(Parser.Module.header| $[module%$moduleTk?]? $[prelude%$preludeTk?]? $imports*) =>
|
||||
(moduleTk?.map .mk, preludeTk?.map .mk, imports)
|
||||
| _ => unreachable!
|
||||
|
||||
def decodeImport : TSyntax ``Parser.Module.import → Import
|
||||
| `(Parser.Module.import| $[public%$pubTk?]? $[meta%$metaTk?]? import $[all%$allTk?]? $id) =>
|
||||
{ module := id.getId, isExported := pubTk?.isSome, isMeta := metaTk?.isSome, importAll := allTk?.isSome }
|
||||
@@ -337,20 +326,11 @@ def decodeImport : TSyntax ``Parser.Module.import → Import
|
||||
* `addOnly`: if true, only add missing imports, do not remove unused ones
|
||||
-/
|
||||
def visitModule (srcSearchPath : SearchPath)
|
||||
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits) (headerStx : TSyntax ``Parser.Module.header)
|
||||
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits)
|
||||
(addOnly := false) (githubStyle := false) (explain := false) : StateT State IO Edits := do
|
||||
let s ← get
|
||||
-- Do transitive reduction of `needs` in `deps`.
|
||||
let mut deps := needs
|
||||
let (_, prelude?, imports) := decodeHeader headerStx
|
||||
if prelude?.isNone then
|
||||
deps := deps.union .pub {s.env.getModuleIdx? `Init |>.get!}
|
||||
for imp in imports do
|
||||
if addOnly || imp.raw.getTrailing?.any (·.toString.toSlice.contains "shake: keep") then
|
||||
let imp := decodeImport imp
|
||||
let j := s.env.getModuleIdx? imp.module |>.get!
|
||||
let k := NeedsKind.ofImport imp
|
||||
deps := deps.union k {j}
|
||||
for j in [0:s.mods.size] do
|
||||
let transDeps := s.transDeps[j]!
|
||||
for k in NeedsKind.all do
|
||||
@@ -374,8 +354,7 @@ def visitModule (srcSearchPath : SearchPath)
|
||||
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
|
||||
else
|
||||
let k := NeedsKind.ofImport imp
|
||||
-- A private import should also be removed if the public version is needed
|
||||
if !deps.has k j || !k.isExported && deps.has { k with isExported := true } j then
|
||||
if !addOnly && !deps.has k j && !deps.has { k with isExported := false } j then
|
||||
toRemove := toRemove.push imp
|
||||
else
|
||||
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
|
||||
@@ -406,8 +385,7 @@ def visitModule (srcSearchPath : SearchPath)
|
||||
|
||||
if githubStyle then
|
||||
try
|
||||
let (path, inputCtx, stx, endHeader) ← parseHeader srcSearchPath s.modNames[i]!
|
||||
let (_, _, imports) := decodeHeader stx
|
||||
let (path, inputCtx, imports, endHeader) ← parseHeader srcSearchPath s.modNames[i]!
|
||||
for stx in imports do
|
||||
if toRemove.any fun imp => imp == decodeImport stx then
|
||||
let pos := inputCtx.fileMap.toPosition stx.raw.getPos?.get!
|
||||
@@ -551,61 +529,51 @@ def main (args : List String) : IO UInt32 := do
|
||||
let needs := s.mods.mapIdx fun i _ =>
|
||||
Task.spawn fun _ => calcNeeds s.env i
|
||||
|
||||
-- Parse headers in parallel
|
||||
let headers ← s.mods.mapIdxM fun i _ =>
|
||||
BaseIO.asTask (parseHeader srcSearchPath s.modNames[i]! |>.toBaseIO)
|
||||
|
||||
if args.fix then
|
||||
println! "The following changes will be made automatically:"
|
||||
|
||||
-- Check all selected modules
|
||||
let mut edits : Edits := ∅
|
||||
let mut revNeeds : Needs := default
|
||||
for i in [0:s.mods.size], t in needs, header in headers do
|
||||
match header.get with
|
||||
| .ok (_, _, stx, _) =>
|
||||
edits ← visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!)
|
||||
srcSearchPath i t.get revNeeds edits stx args.githubStyle args.explain
|
||||
if isExtraRevModUse s.env i then
|
||||
revNeeds := revNeeds.union .priv {i}
|
||||
| .error e =>
|
||||
println! e.toString
|
||||
for i in [0:s.mods.size], t in needs do
|
||||
edits ← visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!) srcSearchPath i t.get revNeeds edits args.githubStyle args.explain
|
||||
if isExtraRevModUse s.env i then
|
||||
revNeeds := revNeeds.union .priv {i}
|
||||
|
||||
if !args.fix then
|
||||
-- return error if any issues were found
|
||||
return if edits.isEmpty then 0 else 1
|
||||
|
||||
-- Apply the edits to existing files
|
||||
let mut count := 0
|
||||
for mod in s.modNames, header? in headers do
|
||||
let some (remove, add) := edits[mod]? | continue
|
||||
let count ← edits.foldM (init := 0) fun count mod (remove, add) => do
|
||||
let add : Array Import := add.qsortOrd
|
||||
|
||||
-- Parse the input file
|
||||
let .ok (path, inputCtx, stx, insertion) := header?.get | continue
|
||||
let (_, _, imports) := decodeHeader stx
|
||||
let (path, inputCtx, imports, insertion) ←
|
||||
try parseHeader srcSearchPath mod
|
||||
catch e => println! e.toString; return count
|
||||
let text := inputCtx.fileMap.source
|
||||
|
||||
-- Calculate the edit result
|
||||
let mut pos : String.Pos.Raw := 0
|
||||
let mut pos : String.Pos := 0
|
||||
let mut out : String := ""
|
||||
let mut seen : Std.HashSet Import := {}
|
||||
for stx in imports do
|
||||
let mod := decodeImport stx
|
||||
if remove.contains mod || seen.contains mod then
|
||||
out := out ++ String.Pos.Raw.extract text pos stx.raw.getPos?.get!
|
||||
out := out ++ text.extract pos stx.raw.getPos?.get!
|
||||
-- We use the end position of the syntax, but include whitespace up to the first newline
|
||||
pos := text.findAux (· == '\n') text.rawEndPos stx.raw.getTailPos?.get! + '\n'
|
||||
pos := text.findAux (· == '\n') text.endPos stx.raw.getTailPos?.get! + ⟨1⟩
|
||||
seen := seen.insert mod
|
||||
out := out ++ String.Pos.Raw.extract text pos insertion
|
||||
out := out ++ text.extract pos insertion
|
||||
for mod in add do
|
||||
if !seen.contains mod then
|
||||
seen := seen.insert mod
|
||||
out := out ++ s!"{mod}\n"
|
||||
out := out ++ String.Pos.Raw.extract text insertion text.rawEndPos
|
||||
out := out ++ text.extract insertion text.endPos
|
||||
|
||||
IO.FS.writeFile path out
|
||||
count := count + 1
|
||||
return count + 1
|
||||
|
||||
-- Since we throw an error upon encountering issues, we can be sure that everything worked
|
||||
-- if we reach this point of the script.
|
||||
|
||||
@@ -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
96
script/bench.sh
Executable 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
|
||||
@@ -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)
|
||||
|
||||
@@ -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
|
||||
@@ -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"
|
||||
|
||||
@@ -13,15 +13,8 @@ What this script does:
|
||||
- Checks that the release branch (releases/vX.Y.0) exists
|
||||
- Verifies CMake version settings are correct
|
||||
- Confirms the release tag exists
|
||||
- Validates the release page exists on GitHub (created automatically by CI after tag push)
|
||||
- Checks the release notes page on lean-lang.org (updated while bumping the `reference-manual` repository)
|
||||
|
||||
**IMPORTANT: If the release page doesn't exist, the script will skip checking
|
||||
downstream repositories and the master branch configuration. The preliminary
|
||||
infrastructure must be in place before the release process can proceed.**
|
||||
|
||||
**NOTE: The GitHub release page is created AUTOMATICALLY by CI after the tag is pushed.
|
||||
DO NOT create it manually. Wait for CI to complete after pushing the tag.**
|
||||
- Validates the release page exists on GitHub
|
||||
- Checks the release notes page on lean-lang.org
|
||||
|
||||
2. For each downstream repository (batteries, mathlib4, etc.):
|
||||
- Checks if dependencies are ready (e.g., mathlib4 depends on batteries)
|
||||
@@ -31,8 +24,6 @@ What this script does:
|
||||
- Ensures tags are merged into stable branches (for non-RC releases)
|
||||
- Verifies bump branches exist and are configured correctly
|
||||
- Special handling for ProofWidgets4 release tags
|
||||
- For mathlib4: runs verify_version_tags.py to validate the release tag
|
||||
(checks git/GitHub consistency, toolchain, elan, cache, and build)
|
||||
|
||||
3. Optionally automates missing steps (when not in --dry-run mode):
|
||||
- Creates missing release tags using push_repo_release_tag.py
|
||||
@@ -131,39 +122,6 @@ def release_page_exists(repo_url, tag_name, github_token):
|
||||
response = requests.get(api_url, headers=headers)
|
||||
return response.status_code == 200
|
||||
|
||||
def get_tag_workflow_status(repo_url, tag_name, github_token):
|
||||
"""Get the status of CI workflows running for a specific tag."""
|
||||
api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
|
||||
headers = {'Authorization': f'token {github_token}'} if github_token else {}
|
||||
|
||||
# Get workflow runs for the tag
|
||||
# GitHub's workflow runs API uses the branch/tag name in the 'head_branch' field
|
||||
api_url = f"{api_base}/actions/runs?event=push&head_branch={tag_name}"
|
||||
response = requests.get(api_url, headers=headers)
|
||||
|
||||
if response.status_code != 200:
|
||||
return None
|
||||
|
||||
data = response.json()
|
||||
workflow_runs = data.get('workflow_runs', [])
|
||||
|
||||
if not workflow_runs:
|
||||
return None
|
||||
|
||||
# Get the most recent workflow run for this tag
|
||||
run = workflow_runs[0]
|
||||
status = run.get('status')
|
||||
conclusion = run.get('conclusion')
|
||||
workflow_name = run.get('name', 'CI')
|
||||
run_id = run.get('id')
|
||||
|
||||
return {
|
||||
'status': status,
|
||||
'conclusion': conclusion,
|
||||
'workflow_name': workflow_name,
|
||||
'run_id': run_id
|
||||
}
|
||||
|
||||
def get_release_notes(tag_name):
|
||||
"""Fetch release notes page title from lean-lang.org."""
|
||||
# Strip -rcX suffix if present for the URL
|
||||
@@ -172,17 +130,20 @@ def get_release_notes(tag_name):
|
||||
try:
|
||||
response = requests.get(reference_url)
|
||||
response.raise_for_status() # Raise HTTPError for bad responses (4xx or 5xx)
|
||||
|
||||
|
||||
# Extract title using regex
|
||||
match = re.search(r"<title>(.*?)</title>", response.text, re.IGNORECASE | re.DOTALL)
|
||||
if match:
|
||||
return match.group(1).strip()
|
||||
else:
|
||||
print(f" ⚠️ Could not find <title> tag in {reference_url}")
|
||||
return None
|
||||
|
||||
except requests.exceptions.RequestException:
|
||||
|
||||
except requests.exceptions.RequestException as e:
|
||||
print(f" ❌ Error fetching release notes from {reference_url}: {e}")
|
||||
return None
|
||||
except Exception:
|
||||
except Exception as e:
|
||||
print(f" ❌ An unexpected error occurred while processing release notes: {e}")
|
||||
return None
|
||||
|
||||
def get_branch_content(repo_url, branch, file_path, github_token):
|
||||
@@ -501,57 +462,6 @@ def check_proofwidgets4_release(repo_url, target_toolchain, github_token):
|
||||
print(f" You will need to create and push a tag v0.0.{next_version}")
|
||||
return False
|
||||
|
||||
def run_mathlib_verify_version_tags(toolchain, verbose=False):
|
||||
"""Run mathlib4's verify_version_tags.py script to validate the release tag.
|
||||
|
||||
This clones mathlib4 to a temp directory and runs the verification script.
|
||||
Returns True if verification passes, False otherwise.
|
||||
"""
|
||||
import tempfile
|
||||
|
||||
print(f" ... Running mathlib4 verify_version_tags.py {toolchain}")
|
||||
|
||||
with tempfile.TemporaryDirectory() as tmpdir:
|
||||
# Clone mathlib4 (shallow clone is sufficient for running the script)
|
||||
clone_result = subprocess.run(
|
||||
['git', 'clone', '--depth', '1', 'https://github.com/leanprover-community/mathlib4.git', tmpdir],
|
||||
capture_output=True,
|
||||
text=True
|
||||
)
|
||||
if clone_result.returncode != 0:
|
||||
print(f" ❌ Failed to clone mathlib4: {clone_result.stderr.strip()[:200]}")
|
||||
return False
|
||||
|
||||
# Run the verification script
|
||||
script_path = os.path.join(tmpdir, 'scripts', 'verify_version_tags.py')
|
||||
if not os.path.exists(script_path):
|
||||
print(f" ❌ verify_version_tags.py not found in mathlib4 (expected at scripts/verify_version_tags.py)")
|
||||
return False
|
||||
|
||||
# Run from the mathlib4 directory so git operations work
|
||||
result = subprocess.run(
|
||||
['python3', script_path, toolchain],
|
||||
cwd=tmpdir,
|
||||
capture_output=True,
|
||||
text=True,
|
||||
timeout=900 # 15 minutes timeout for cache download etc.
|
||||
)
|
||||
|
||||
# Print output with indentation
|
||||
if result.stdout:
|
||||
for line in result.stdout.strip().split('\n'):
|
||||
print(f" {line}")
|
||||
if result.stderr:
|
||||
for line in result.stderr.strip().split('\n'):
|
||||
print(f" {line}")
|
||||
|
||||
if result.returncode != 0:
|
||||
print(f" ❌ mathlib4 verify_version_tags.py failed")
|
||||
return False
|
||||
|
||||
print(f" ✅ mathlib4 verify_version_tags.py passed")
|
||||
return True
|
||||
|
||||
def main():
|
||||
parser = argparse.ArgumentParser(description="Check release status of Lean4 repositories")
|
||||
parser.add_argument("toolchain", help="The toolchain version to check (e.g., v4.6.0)")
|
||||
@@ -602,57 +512,30 @@ def main():
|
||||
print(f" ❌ Short commit hash {commit_hash[:SHORT_HASH_LENGTH]} is numeric and starts with 0, causing issues for version parsing. Try regenerating the last commit to get a new hash.")
|
||||
lean4_success = False
|
||||
|
||||
release_page_ready = release_page_exists(lean_repo_url, toolchain, github_token)
|
||||
if not release_page_ready:
|
||||
print(f" ❌ Release page for {toolchain} does not exist (This will be created by CI.)")
|
||||
|
||||
# Check CI workflow status
|
||||
workflow_status = get_tag_workflow_status(lean_repo_url, toolchain, github_token)
|
||||
if workflow_status:
|
||||
status = workflow_status['status']
|
||||
conclusion = workflow_status['conclusion']
|
||||
workflow_name = workflow_status['workflow_name']
|
||||
run_id = workflow_status['run_id']
|
||||
workflow_url = f"{lean_repo_url}/actions/runs/{run_id}"
|
||||
|
||||
if status == 'in_progress' or status == 'queued':
|
||||
print(f" 🔄 {workflow_name} workflow is {status}: {workflow_url}")
|
||||
elif status == 'completed':
|
||||
if conclusion == 'success':
|
||||
print(f" ✅ {workflow_name} workflow completed successfully: {workflow_url}")
|
||||
elif conclusion == 'failure':
|
||||
print(f" ❌ {workflow_name} workflow failed: {workflow_url}")
|
||||
else:
|
||||
print(f" ⚠️ {workflow_name} workflow completed with status: {conclusion}: {workflow_url}")
|
||||
else:
|
||||
print(f" ℹ️ {workflow_name} workflow status: {status}: {workflow_url}")
|
||||
|
||||
if not release_page_exists(lean_repo_url, toolchain, github_token):
|
||||
print(f" ❌ Release page for {toolchain} does not exist")
|
||||
lean4_success = False
|
||||
else:
|
||||
print(f" ✅ Release page for {toolchain} exists")
|
||||
|
||||
# Check the actual release notes page title (informational only - does not block)
|
||||
|
||||
# Check the actual release notes page title
|
||||
actual_title = get_release_notes(toolchain)
|
||||
expected_title_prefix = f"Lean {toolchain.lstrip('v')}" # e.g., "Lean 4.19.0" or "Lean 4.19.0-rc1"
|
||||
base_tag = toolchain.split('-')[0]
|
||||
release_notes_url = f"https://lean-lang.org/doc/reference/latest/releases/{base_tag}/"
|
||||
|
||||
if actual_title is None:
|
||||
print(f" ⚠️ Release notes not found at {release_notes_url} (this will be fixed while updating the reference-manual repository)")
|
||||
# Error already printed by get_release_notes
|
||||
lean4_success = False
|
||||
elif not actual_title.startswith(expected_title_prefix):
|
||||
print(f" ⚠️ Release notes page title mismatch. Expected prefix '{expected_title_prefix}', got '{actual_title}'. Check {release_notes_url}")
|
||||
# Construct URL for the error message (using the base tag)
|
||||
base_tag = toolchain.split('-')[0]
|
||||
check_url = f"https://lean-lang.org/doc/reference/latest/releases/{base_tag}/"
|
||||
print(f" ❌ Release notes page title mismatch. Expected prefix '{expected_title_prefix}', got '{actual_title}'. Check {check_url}")
|
||||
lean4_success = False
|
||||
else:
|
||||
print(f" ✅ Release notes page title looks good ('{actual_title}').")
|
||||
|
||||
repo_status["lean4"] = lean4_success
|
||||
|
||||
# If the release page doesn't exist, skip repository checks and master branch checks
|
||||
# The preliminary infrastructure must be in place first
|
||||
if not release_page_exists(lean_repo_url, toolchain, github_token):
|
||||
print("\n⚠️ Release process blocked: preliminary Lean4 infrastructure incomplete.")
|
||||
print(" Complete the steps above, then rerun this script to proceed with downstream repositories.")
|
||||
return
|
||||
|
||||
# Load repositories and perform further checks
|
||||
print("\nChecking repositories...")
|
||||
|
||||
@@ -816,12 +699,6 @@ def main():
|
||||
repo_status[name] = False
|
||||
continue
|
||||
|
||||
# For mathlib4, run verify_version_tags.py to validate the release tag
|
||||
if name == "mathlib4":
|
||||
if not run_mathlib_verify_version_tags(toolchain, verbose):
|
||||
repo_status[name] = False
|
||||
continue
|
||||
|
||||
repo_status[name] = success
|
||||
|
||||
# Final check for lean4 master branch
|
||||
|
||||
@@ -589,19 +589,8 @@ def execute_release_steps(repo, version, config):
|
||||
|
||||
# Clean lake cache for a fresh build
|
||||
print(blue("Cleaning lake cache..."))
|
||||
run_command("lake clean", cwd=repo_path)
|
||||
|
||||
# Check if downstream of Mathlib and get cache if so
|
||||
mathlib_package_dir = repo_path / ".lake" / "packages" / "mathlib"
|
||||
if mathlib_package_dir.exists():
|
||||
print(blue("Project is downstream of Mathlib, fetching cache..."))
|
||||
try:
|
||||
run_command("lake exe cache get", cwd=repo_path, stream_output=True)
|
||||
print(green("Cache fetched successfully"))
|
||||
except subprocess.CalledProcessError as e:
|
||||
print(yellow("Failed to fetch cache, continuing anyway..."))
|
||||
print(yellow(f"Cache fetch error: {e}"))
|
||||
|
||||
run_command("rm -rf .lake", cwd=repo_path)
|
||||
|
||||
try:
|
||||
run_command("lake build", cwd=repo_path, stream_output=True)
|
||||
print(green("Build completed successfully"))
|
||||
|
||||
@@ -10,7 +10,7 @@ endif()
|
||||
include(ExternalProject)
|
||||
project(LEAN CXX C)
|
||||
set(LEAN_VERSION_MAJOR 4)
|
||||
set(LEAN_VERSION_MINOR 27)
|
||||
set(LEAN_VERSION_MINOR 25)
|
||||
set(LEAN_VERSION_PATCH 0)
|
||||
set(LEAN_VERSION_IS_RELEASE 0) # This number is 1 in the release revision, and 0 otherwise.
|
||||
set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")
|
||||
@@ -42,7 +42,7 @@ if(LLD_PATH)
|
||||
endif()
|
||||
|
||||
set(LEAN_EXTRA_LINKER_FLAGS ${LEAN_EXTRA_LINKER_FLAGS_DEFAULT} CACHE STRING "Additional flags used by the linker")
|
||||
set(LEAN_EXTRA_CXX_FLAGS "" CACHE STRING "Additional flags used by the C++ compiler. Unlike `CMAKE_CXX_FLAGS`, these will not be used to build e.g. cadical.")
|
||||
set(LEAN_EXTRA_CXX_FLAGS "" CACHE STRING "Additional flags used by the C++ compiler")
|
||||
set(LEAN_TEST_VARS "LEAN_CC=${CMAKE_C_COMPILER}" CACHE STRING "Additional environment variables used when running tests")
|
||||
|
||||
if (NOT CMAKE_BUILD_TYPE)
|
||||
@@ -191,7 +191,7 @@ endif()
|
||||
set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${CMAKE_SOURCE_DIR}/cmake/Modules")
|
||||
|
||||
# Initialize CXXFLAGS.
|
||||
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${LEAN_EXTRA_CXX_FLAGS} -DLEAN_BUILD_TYPE=\"${CMAKE_BUILD_TYPE}\" -DLEAN_EXPORTING")
|
||||
set(CMAKE_CXX_FLAGS "${LEAN_EXTRA_CXX_FLAGS} -DLEAN_BUILD_TYPE=\"${CMAKE_BUILD_TYPE}\" -DLEAN_EXPORTING")
|
||||
set(CMAKE_CXX_FLAGS_DEBUG "-DLEAN_DEBUG")
|
||||
set(CMAKE_CXX_FLAGS_MINSIZEREL "-DNDEBUG")
|
||||
set(CMAKE_CXX_FLAGS_RELEASE "-DNDEBUG")
|
||||
|
||||
@@ -14,6 +14,7 @@ public import Init.ByCases
|
||||
public import Init.RCases
|
||||
public import Init.Core
|
||||
public import Init.Control
|
||||
public import Init.Data.Basic
|
||||
public import Init.WF
|
||||
public import Init.WFTactics
|
||||
public import Init.Data
|
||||
|
||||
@@ -7,6 +7,7 @@ Authors: Joachim Breitner
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Prelude
|
||||
public import Init.Tactics
|
||||
|
||||
public section
|
||||
|
||||
@@ -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
|
||||
|
||||
@@ -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
|
||||
|
||||
@@ -25,7 +25,7 @@ instances are provided for the same type.
|
||||
instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α where
|
||||
forIn x b f := forIn' x b fun a _ => f a
|
||||
|
||||
@[simp] theorem forIn'_eq_forIn [d : Membership α ρ] [ForIn' m ρ α d] {β} (x : ρ) (b : β)
|
||||
@[simp] theorem forIn'_eq_forIn [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m] (x : ρ) (b : β)
|
||||
(f : (a : α) → a ∈ x → β → m (ForInStep β)) (g : (a : α) → β → m (ForInStep β))
|
||||
(h : ∀ a m b, f a m b = g a b) :
|
||||
forIn' x b f = forIn x b g := by
|
||||
@@ -40,11 +40,14 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
|
||||
simp [h]
|
||||
rfl
|
||||
|
||||
@[wf_preprocess] theorem forIn_eq_forIn' [d : Membership α ρ] [ForIn' m ρ α d] {β}
|
||||
@[wf_preprocess] theorem forIn_eq_forIn' [d : Membership α ρ] [ForIn' m ρ α d] {β} [Monad m]
|
||||
(x : ρ) (b : β) (f : (a : α) → β → m (ForInStep β)) :
|
||||
forIn x b f = forIn' x b (fun x h => binderNameHint x f <| binderNameHint h () <| f x) := by
|
||||
rfl
|
||||
|
||||
@[deprecated forIn_eq_forIn' (since := "2025-04-04")]
|
||||
abbrev forIn_eq_forin' := @forIn_eq_forIn'
|
||||
|
||||
/--
|
||||
Extracts the value from a `ForInStep`, ignoring whether it is `ForInStep.done` or `ForInStep.yield`.
|
||||
-/
|
||||
@@ -403,7 +406,7 @@ class ForM (m : Type u → Type v) (γ : Type w₁) (α : outParam (Type w₂))
|
||||
/--
|
||||
Runs the monadic action `f` on each element of the collection `coll`.
|
||||
-/
|
||||
forM (coll : γ) (f : α → m PUnit) : m PUnit
|
||||
forM [Monad m] (coll : γ) (f : α → m PUnit) : m PUnit
|
||||
|
||||
export ForM (forM)
|
||||
|
||||
|
||||
@@ -6,6 +6,8 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Control.State
|
||||
public import Init.Control.Except
|
||||
public import Init.Data.ToString.Basic
|
||||
|
||||
public section
|
||||
|
||||
@@ -10,6 +10,7 @@ module
|
||||
prelude
|
||||
public import Init.Control.Basic
|
||||
public import Init.Control.Id
|
||||
public import Init.Coe
|
||||
|
||||
@[expose] public section
|
||||
|
||||
@@ -148,23 +149,6 @@ This is the inverse of `ExceptT.mk`.
|
||||
@[always_inline, inline, expose]
|
||||
def ExceptT.run {ε : Type u} {m : Type u → Type v} {α : Type u} (x : ExceptT ε m α) : m (Except ε α) := x
|
||||
|
||||
/--
|
||||
Use a monadic action that may throw an exception by providing explicit success and failure
|
||||
continuations.
|
||||
-/
|
||||
@[always_inline, inline, expose]
|
||||
def ExceptT.runK [Monad m] (x : ExceptT ε m α) (ok : α → m β) (error : ε → m β) : m β :=
|
||||
x.run >>= (·.casesOn error ok)
|
||||
|
||||
/--
|
||||
Returns the value of a computation, forgetting whether it was an exception or a success.
|
||||
|
||||
This corresponds to early return.
|
||||
-/
|
||||
@[always_inline, inline, expose]
|
||||
def ExceptT.runCatch [Monad m] (x : ExceptT α m α) : m α :=
|
||||
x.runK pure pure
|
||||
|
||||
namespace ExceptT
|
||||
|
||||
variable {ε : Type u} {m : Type u → Type v} [Monad m]
|
||||
|
||||
@@ -7,6 +7,8 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Ext
|
||||
public import Init.SimpLemmas
|
||||
public import Init.Meta
|
||||
|
||||
public section
|
||||
|
||||
@@ -170,7 +172,6 @@ theorem bind_pure_unit [Monad m] [LawfulMonad m] {x : m PUnit} : (x >>= fun _ =>
|
||||
theorem map_congr [Functor m] {x : m α} {f g : α → β} (h : ∀ a, f a = g a) : (f <$> x : m β) = g <$> x := by
|
||||
simp [funext h]
|
||||
|
||||
@[deprecated seq_eq_bind_map (since := "2025-10-26")]
|
||||
theorem seq_eq_bind {α β : Type u} [Monad m] [LawfulMonad m] (mf : m (α → β)) (x : m α) : mf <*> x = mf >>= fun f => f <$> x := by
|
||||
rw [bind_map]
|
||||
|
||||
@@ -256,4 +257,20 @@ instance : LawfulMonad Id := by
|
||||
@[simp] theorem run_seqLeft (x y : Id α) : (x <* y).run = x.run := rfl
|
||||
@[simp] theorem run_seq (f : Id (α → β)) (x : Id α) : (f <*> x).run = f.run x.run := rfl
|
||||
|
||||
-- These lemmas are bad as they abuse the defeq of `Id α` and `α`
|
||||
@[deprecated run_map (since := "2025-03-05")] theorem map_eq (x : Id α) (f : α → β) : f <$> x = f x := rfl
|
||||
@[deprecated run_bind (since := "2025-03-05")] theorem bind_eq (x : Id α) (f : α → id β) : x >>= f = f x := rfl
|
||||
@[deprecated run_pure (since := "2025-03-05")] theorem pure_eq (a : α) : (pure a : Id α) = a := rfl
|
||||
|
||||
end Id
|
||||
|
||||
/-! # Option -/
|
||||
|
||||
instance : LawfulMonad Option := LawfulMonad.mk'
|
||||
(id_map := fun x => by cases x <;> rfl)
|
||||
(pure_bind := fun _ _ => rfl)
|
||||
(bind_assoc := fun x _ _ => by cases x <;> rfl)
|
||||
(bind_pure_comp := fun _ x => by cases x <;> rfl)
|
||||
|
||||
instance : LawfulApplicative Option := inferInstance
|
||||
instance : LawfulFunctor Option := inferInstance
|
||||
|
||||
@@ -7,11 +7,14 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Control.Lawful.Basic
|
||||
public import Init.Control.Except
|
||||
import all Init.Control.Except
|
||||
public import Init.Control.Option
|
||||
import all Init.Control.Option
|
||||
public import Init.Control.State
|
||||
import all Init.Control.State
|
||||
public import Init.Control.StateRef
|
||||
public import Init.Ext
|
||||
|
||||
public section
|
||||
|
||||
@@ -189,12 +192,12 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (OptionT m) where
|
||||
|
||||
@[simp] theorem run_seq [Monad m] [LawfulMonad m] (f : OptionT m (α → β)) (x : OptionT m α) :
|
||||
(f <*> x).run = Option.elimM f.run (pure none) (fun f => Option.map f <$> x.run) := by
|
||||
simp [seq_eq_bind_map, Option.elimM, Option.elim]
|
||||
simp [seq_eq_bind, Option.elimM, Option.elim]
|
||||
|
||||
@[simp] theorem run_seqLeft [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
|
||||
(x <* y).run = Option.elimM x.run (pure none)
|
||||
(fun x => Option.map (Function.const β x) <$> y.run) := by
|
||||
simp [seqLeft_eq, seq_eq_bind_map, Option.elimM, OptionT.run_bind]
|
||||
simp [seqLeft_eq, seq_eq_bind, Option.elimM, OptionT.run_bind]
|
||||
|
||||
@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
|
||||
(x *> y).run = Option.elimM x.run (pure none) (Function.const α y.run) := by
|
||||
@@ -219,7 +222,7 @@ instance : LawfulMonad Option := LawfulMonad.mk'
|
||||
(id_map := fun x => by cases x <;> rfl)
|
||||
(pure_bind := fun _ _ => by rfl)
|
||||
(bind_assoc := fun a _ _ => by cases a <;> rfl)
|
||||
(bind_pure_comp := fun _ x => by cases x <;> rfl)
|
||||
(bind_pure_comp := bind_pure_comp)
|
||||
|
||||
instance : LawfulApplicative Option := inferInstance
|
||||
instance : LawfulFunctor Option := inferInstance
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Control.Lawful.Basic
|
||||
public import Init.RCases
|
||||
public import Init.ByCases
|
||||
|
||||
public section
|
||||
|
||||
@@ -6,13 +6,17 @@ Authors: Quang Dao, Paul Reichert
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Control.Option
|
||||
import all Init.Control.Option
|
||||
public import Init.Control.Except
|
||||
import all Init.Control.Except
|
||||
public import Init.Control.ExceptCps
|
||||
import all Init.Control.ExceptCps
|
||||
public import Init.Control.StateRef
|
||||
import all Init.Control.StateRef
|
||||
public import Init.Control.StateCps
|
||||
import all Init.Control.StateCps
|
||||
public import Init.Control.Id
|
||||
import all Init.Control.Id
|
||||
public import Init.Control.Lawful.MonadLift.Lemmas
|
||||
public import Init.Control.Lawful.Instances
|
||||
|
||||
@@ -23,7 +23,7 @@ theorem monadLift_map [LawfulMonad m] [LawfulMonad n] (f : α → β) (ma : m α
|
||||
|
||||
theorem monadLift_seq [LawfulMonad m] [LawfulMonad n] (mf : m (α → β)) (ma : m α) :
|
||||
monadLift (mf <*> ma) = monadLift mf <*> (monadLift ma : n α) := by
|
||||
simp only [seq_eq_bind_map, monadLift_map, monadLift_bind]
|
||||
simp only [seq_eq_bind, monadLift_map, monadLift_bind]
|
||||
|
||||
theorem monadLift_seqLeft [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
|
||||
monadLift (x <* y) = (monadLift x : n α) <* (monadLift y : n β) := by
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Option.Basic
|
||||
public import Init.Control.Basic
|
||||
public import Init.Control.Except
|
||||
|
||||
public section
|
||||
@@ -27,7 +28,7 @@ failure occurred.
|
||||
/--
|
||||
Executes an action that might fail in the underlying monad `m`, returning `none` in case of failure.
|
||||
-/
|
||||
@[always_inline, inline, expose]
|
||||
@[always_inline, inline]
|
||||
def OptionT.run {m : Type u → Type v} {α : Type u} (x : OptionT m α) : m (Option α) :=
|
||||
x
|
||||
|
||||
@@ -69,7 +70,7 @@ instance {m : Type u → Type v} [Pure m] : Inhabited (OptionT m α) where
|
||||
/--
|
||||
Recovers from failures. Typically used via the `<|>` operator.
|
||||
-/
|
||||
@[always_inline, inline, expose] protected def orElse (x : OptionT m α) (y : Unit → OptionT m α) : OptionT m α := OptionT.mk do
|
||||
@[always_inline, inline] protected def orElse (x : OptionT m α) (y : Unit → OptionT m α) : OptionT m α := OptionT.mk do
|
||||
match (← x) with
|
||||
| some a => pure (some a)
|
||||
| _ => y ()
|
||||
@@ -77,7 +78,7 @@ Recovers from failures. Typically used via the `<|>` operator.
|
||||
/--
|
||||
A recoverable failure.
|
||||
-/
|
||||
@[always_inline, inline, expose] protected def fail : OptionT m α := OptionT.mk do
|
||||
@[always_inline, inline] protected def fail : OptionT m α := OptionT.mk do
|
||||
pure none
|
||||
|
||||
instance : Alternative (OptionT m) where
|
||||
@@ -90,7 +91,7 @@ Converts a computation from the underlying monad into one that could fail, even
|
||||
This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
|
||||
lifting](lean-manual://section/monad-lifting).
|
||||
-/
|
||||
@[always_inline, inline, expose] protected def lift (x : m α) : OptionT m α := OptionT.mk do
|
||||
@[always_inline, inline] protected def lift (x : m α) : OptionT m α := OptionT.mk do
|
||||
return some (← x)
|
||||
|
||||
instance : MonadLift m (OptionT m) := ⟨OptionT.lift⟩
|
||||
@@ -100,11 +101,11 @@ instance : MonadFunctor m (OptionT m) := ⟨fun f x => f x⟩
|
||||
/--
|
||||
Handles failures by treating them as exceptions of type `Unit`.
|
||||
-/
|
||||
@[always_inline, inline, expose] protected def tryCatch (x : OptionT m α) (handle : PUnit → OptionT m α) : OptionT m α := OptionT.mk do
|
||||
let some a ← x | handle ⟨⟩
|
||||
@[always_inline, inline] protected def tryCatch (x : OptionT m α) (handle : Unit → OptionT m α) : OptionT m α := OptionT.mk do
|
||||
let some a ← x | handle ()
|
||||
pure <| some a
|
||||
|
||||
instance : MonadExceptOf PUnit (OptionT m) where
|
||||
instance : MonadExceptOf Unit (OptionT m) where
|
||||
throw := fun _ => OptionT.fail
|
||||
tryCatch := OptionT.tryCatch
|
||||
|
||||
|
||||
@@ -8,6 +8,8 @@ The Reader monad transformer for passing immutable State.
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Control.Basic
|
||||
public import Init.Control.Id
|
||||
public import Init.Control.Except
|
||||
|
||||
public section
|
||||
|
||||
@@ -8,6 +8,8 @@ The State monad transformer.
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Control.Basic
|
||||
public import Init.Control.Id
|
||||
public import Init.Control.Except
|
||||
|
||||
public section
|
||||
|
||||
@@ -8,6 +8,7 @@ notation, basic datatypes and type classes
|
||||
module
|
||||
|
||||
prelude
|
||||
public meta import Init.Prelude
|
||||
public import Init.SizeOf
|
||||
|
||||
public section
|
||||
@@ -377,7 +378,7 @@ class ForIn (m : Type u₁ → Type u₂) (ρ : Type u) (α : outParam (Type v))
|
||||
More information about the translation of `for` loops into `ForIn.forIn` is available in [the Lean
|
||||
reference manual](lean-manual://section/monad-iteration-syntax).
|
||||
-/
|
||||
forIn {β} (xs : ρ) (b : β) (f : α → β → m (ForInStep β)) : m β
|
||||
forIn {β} [Monad m] (xs : ρ) (b : β) (f : α → β → m (ForInStep β)) : m β
|
||||
|
||||
export ForIn (forIn)
|
||||
|
||||
@@ -405,7 +406,7 @@ class ForIn' (m : Type u₁ → Type u₂) (ρ : Type u) (α : outParam (Type v)
|
||||
More information about the translation of `for` loops into `ForIn'.forIn'` is available in [the
|
||||
Lean reference manual](lean-manual://section/monad-iteration-syntax).
|
||||
-/
|
||||
forIn' {β} (x : ρ) (b : β) (f : (a : α) → a ∈ x → β → m (ForInStep β)) : m β
|
||||
forIn' {β} [Monad m] (x : ρ) (b : β) (f : (a : α) → a ∈ x → β → m (ForInStep β)) : m β
|
||||
|
||||
export ForIn' (forIn')
|
||||
|
||||
@@ -600,6 +601,17 @@ export LawfulSingleton (insert_empty_eq)
|
||||
|
||||
attribute [simp] insert_empty_eq
|
||||
|
||||
@[deprecated insert_empty_eq (since := "2025-03-12")]
|
||||
theorem insert_emptyc_eq [EmptyCollection β] [Insert α β] [Singleton α β]
|
||||
[LawfulSingleton α β] (x : α) : (insert x ∅ : β) = singleton x :=
|
||||
insert_empty_eq _
|
||||
|
||||
@[deprecated insert_empty_eq (since := "2025-03-12")]
|
||||
theorem LawfulSingleton.insert_emptyc_eq [EmptyCollection β] [Insert α β] [Singleton α β]
|
||||
[LawfulSingleton α β] (x : α) : (insert x ∅ : β) = singleton x :=
|
||||
insert_empty_eq _
|
||||
|
||||
|
||||
/-- Type class used to implement the notation `{ a ∈ c | p a }` -/
|
||||
class Sep (α : outParam <| Type u) (γ : Type v) where
|
||||
/-- Computes `{ a ∈ c | p a }`. -/
|
||||
@@ -1084,6 +1096,14 @@ theorem of_toBoolUsing_eq_true {p : Prop} {d : Decidable p} (h : toBoolUsing d =
|
||||
theorem of_toBoolUsing_eq_false {p : Prop} {d : Decidable p} (h : toBoolUsing d = false) : ¬p :=
|
||||
of_decide_eq_false h
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated of_toBoolUsing_eq_true (since := "2025-04-04")]
|
||||
abbrev ofBoolUsing_eq_true := @of_toBoolUsing_eq_true
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated of_toBoolUsing_eq_false (since := "2025-04-04")]
|
||||
abbrev ofBoolUsing_eq_false := @of_toBoolUsing_eq_false
|
||||
|
||||
instance : Decidable True :=
|
||||
isTrue trivial
|
||||
|
||||
@@ -1146,7 +1166,6 @@ end
|
||||
else isFalse (fun h => absurd (h hp) hq)
|
||||
else isTrue (fun h => absurd h hp)
|
||||
|
||||
@[inline]
|
||||
instance {p q} [Decidable p] [Decidable q] : Decidable (p ↔ q) :=
|
||||
if hp : p then
|
||||
if hq : q then
|
||||
@@ -1188,13 +1207,17 @@ theorem dif_neg {c : Prop} {h : Decidable c} (hnc : ¬c) {α : Sort u} {t : c
|
||||
| isTrue hc => absurd hc hnc
|
||||
| isFalse _ => rfl
|
||||
|
||||
@[macro_inline]
|
||||
-- Remark: dite and ite are "defally equal" when we ignore the proofs.
|
||||
theorem dif_eq_if (c : Prop) {h : Decidable c} {α : Sort u} (t : α) (e : α) : dite c (fun _ => t) (fun _ => e) = ite c t e :=
|
||||
match h with
|
||||
| isTrue _ => rfl
|
||||
| isFalse _ => rfl
|
||||
|
||||
instance {c t e : Prop} [dC : Decidable c] [dT : Decidable t] [dE : Decidable e] : Decidable (if c then t else e) :=
|
||||
match dC with
|
||||
| isTrue _ => dT
|
||||
| isFalse _ => dE
|
||||
|
||||
@[inline]
|
||||
instance {c : Prop} {t : c → Prop} {e : ¬c → Prop} [dC : Decidable c] [dT : ∀ h, Decidable (t h)] [dE : ∀ h, Decidable (e h)] : Decidable (if h : c then t h else e h) :=
|
||||
match dC with
|
||||
| isTrue hc => dT hc
|
||||
@@ -1345,12 +1368,12 @@ namespace Subtype
|
||||
theorem exists_of_subtype {α : Type u} {p : α → Prop} : { x // p x } → Exists (fun x => p x)
|
||||
| ⟨a, h⟩ => ⟨a, h⟩
|
||||
|
||||
variable {α : Sort u} {p : α → Prop}
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated exists_of_subtype (since := "2025-04-04")]
|
||||
abbrev existsOfSubtype := @exists_of_subtype
|
||||
|
||||
protected theorem ext : ∀ {a1 a2 : {x // p x}}, val a1 = val a2 → a1 = a2
|
||||
| ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
|
||||
variable {α : Type u} {p : α → Prop}
|
||||
|
||||
@[deprecated Subtype.ext (since := "2025-10-26")]
|
||||
protected theorem eq : ∀ {a1 a2 : {x // p x}}, val a1 = val a2 → a1 = a2
|
||||
| ⟨_, _⟩, ⟨_, _⟩, rfl => rfl
|
||||
|
||||
@@ -1365,9 +1388,9 @@ instance {α : Type u} {p : α → Prop} [BEq α] [ReflBEq α] : ReflBEq {x : α
|
||||
rfl {x} := BEq.refl x.1
|
||||
|
||||
instance {α : Type u} {p : α → Prop} [BEq α] [LawfulBEq α] : LawfulBEq {x : α // p x} where
|
||||
eq_of_beq h := Subtype.ext (eq_of_beq h)
|
||||
eq_of_beq h := Subtype.eq (eq_of_beq h)
|
||||
|
||||
instance {α : Sort u} {p : α → Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
|
||||
instance {α : Type u} {p : α → Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
|
||||
fun ⟨a, h₁⟩ ⟨b, h₂⟩ =>
|
||||
if h : a = b then isTrue (by subst h; exact rfl)
|
||||
else isFalse (fun h' => Subtype.noConfusion h' (fun h' => absurd h' h))
|
||||
@@ -1468,8 +1491,6 @@ def Prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂
|
||||
|
||||
@[simp] theorem Prod.map_apply (f : α → β) (g : γ → δ) (x) (y) :
|
||||
Prod.map f g (x, y) = (f x, g y) := rfl
|
||||
|
||||
-- We add `@[grind =]` to these in `Init.Data.Prod`.
|
||||
@[simp] theorem Prod.map_fst (f : α → β) (g : γ → δ) (x) : (Prod.map f g x).1 = f x.1 := rfl
|
||||
@[simp] theorem Prod.map_snd (f : α → β) (g : γ → δ) (x) : (Prod.map f g x).2 = g x.2 := rfl
|
||||
|
||||
@@ -1486,24 +1507,20 @@ protected theorem PSigma.eta {α : Sort u} {β : α → Sort v} {a₁ a₂ : α}
|
||||
|
||||
/-! # Universe polymorphic unit -/
|
||||
|
||||
theorem PUnit.ext (a b : PUnit) : a = b := by
|
||||
cases a; cases b; exact rfl
|
||||
|
||||
@[deprecated PUnit.ext (since := "2025-10-26")]
|
||||
theorem PUnit.subsingleton (a b : PUnit) : a = b := by
|
||||
cases a; cases b; exact rfl
|
||||
|
||||
theorem PUnit.eq_punit (a : PUnit) : a = ⟨⟩ :=
|
||||
PUnit.ext a ⟨⟩
|
||||
PUnit.subsingleton a ⟨⟩
|
||||
|
||||
instance : Subsingleton PUnit :=
|
||||
Subsingleton.intro PUnit.ext
|
||||
Subsingleton.intro PUnit.subsingleton
|
||||
|
||||
instance : Inhabited PUnit where
|
||||
default := ⟨⟩
|
||||
|
||||
instance : DecidableEq PUnit :=
|
||||
fun a b => isTrue (PUnit.ext a b)
|
||||
fun a b => isTrue (PUnit.subsingleton a b)
|
||||
|
||||
/-! # Setoid -/
|
||||
|
||||
@@ -1590,7 +1607,7 @@ gen_injective_theorems% PSum
|
||||
gen_injective_theorems% Sigma
|
||||
gen_injective_theorems% String
|
||||
gen_injective_theorems% String.Pos.Raw
|
||||
gen_injective_theorems% Substring.Raw
|
||||
gen_injective_theorems% Substring
|
||||
gen_injective_theorems% Subtype
|
||||
gen_injective_theorems% Sum
|
||||
gen_injective_theorems% Task
|
||||
@@ -2507,7 +2524,8 @@ class Antisymm (r : α → α → Prop) : Prop where
|
||||
/-- An antisymmetric relation `r` satisfies `r a b → r b a → a = b`. -/
|
||||
antisymm (a b : α) : r a b → r b a → a = b
|
||||
|
||||
/-- `Asymm r` means that the binary relation `r` is asymmetric, that is, `r a b → ¬ r b a`. -/
|
||||
/-- `Asymm r` means that the binary relation `r` is asymmetric, that is,
|
||||
`r a b → ¬ r b a`. -/
|
||||
class Asymm (r : α → α → Prop) : Prop where
|
||||
/-- An asymmetric relation satisfies `r a b → ¬ r b a`. -/
|
||||
asymm : ∀ a b, r a b → ¬r b a
|
||||
@@ -2517,19 +2535,16 @@ class Symm (r : α → α → 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
|
||||
|
||||
@@ -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
|
||||
|
||||
@@ -7,6 +7,7 @@ Authors: Dany Fabian
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Classical
|
||||
public import Init.ByCases
|
||||
|
||||
@[expose] public section
|
||||
|
||||
@@ -6,7 +6,10 @@ Authors: Joachim Breitner, Mario Carneiro
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Mem
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.Array.Count
|
||||
public import Init.Data.List.Attach
|
||||
import all Init.Data.List.Attach
|
||||
|
||||
public section
|
||||
@@ -749,6 +752,9 @@ and simplifies these to the function directly taking the value.
|
||||
(Array.replicate n x).unattach = Array.replicate n x.1 := by
|
||||
simp [unattach]
|
||||
|
||||
@[deprecated unattach_replicate (since := "2025-03-18")]
|
||||
abbrev unattach_mkArray := @unattach_replicate
|
||||
|
||||
/-! ### Well-founded recursion preprocessing setup -/
|
||||
|
||||
@[wf_preprocess] theorem map_wfParam {xs : Array α} {f : α → β} :
|
||||
|
||||
@@ -6,6 +6,10 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.WFTactics
|
||||
public import Init.Data.Nat.Basic
|
||||
public import Init.Data.Fin.Basic
|
||||
public import Init.Data.UInt.BasicAux
|
||||
public import Init.GetElem
|
||||
public import Init.Data.List.ToArrayImpl
|
||||
import all Init.Data.List.ToArrayImpl
|
||||
@@ -209,6 +213,20 @@ Examples:
|
||||
def replicate {α : Type u} (n : Nat) (v : α) : Array α where
|
||||
toList := List.replicate n v
|
||||
|
||||
/--
|
||||
Creates an array that contains `n` repetitions of `v`.
|
||||
|
||||
The corresponding `List` function is `List.replicate`.
|
||||
|
||||
Examples:
|
||||
* `Array.mkArray 2 true = #[true, true]`
|
||||
* `Array.mkArray 3 () = #[(), (), ()]`
|
||||
* `Array.mkArray 0 "anything" = #[]`
|
||||
-/
|
||||
@[extern "lean_mk_array", deprecated replicate (since := "2025-03-18")]
|
||||
def mkArray {α : Type u} (n : Nat) (v : α) : Array α where
|
||||
toList := List.replicate n v
|
||||
|
||||
/--
|
||||
Swaps two elements of an array. The modification is performed in-place when the reference to the
|
||||
array is unique.
|
||||
@@ -226,7 +244,7 @@ def swap (xs : Array α) (i j : @& Nat) (hi : i < xs.size := by get_elem_tactic)
|
||||
let xs' := xs.set i v₂
|
||||
xs'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set _).symm)
|
||||
|
||||
@[simp, grind =] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
|
||||
@[simp] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
|
||||
change ((xs.set i xs[j]).set j xs[i]
|
||||
(Nat.lt_of_lt_of_eq hj (size_set _).symm)).size = xs.size
|
||||
rw [size_set, size_set]
|
||||
@@ -242,7 +260,7 @@ Examples:
|
||||
* `#["red", "green", "blue", "brown"].swapIfInBounds 0 4 = #["red", "green", "blue", "brown"]`
|
||||
* `#["red", "green", "blue", "brown"].swapIfInBounds 9 2 = #["red", "green", "blue", "brown"]`
|
||||
-/
|
||||
@[extern "lean_array_swap", expose]
|
||||
@[extern "lean_array_swap", grind]
|
||||
def swapIfInBounds (xs : Array α) (i j : @& Nat) : Array α :=
|
||||
if h₁ : i < xs.size then
|
||||
if h₂ : j < xs.size then swap xs i j
|
||||
@@ -448,7 +466,7 @@ Examples:
|
||||
-/
|
||||
abbrev take (xs : Array α) (i : Nat) : Array α := extract xs 0 i
|
||||
|
||||
@[simp, grind =] theorem take_eq_extract {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i := rfl
|
||||
@[simp] theorem take_eq_extract {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i := rfl
|
||||
|
||||
/--
|
||||
Removes the first `i` elements of `xs`. If `xs` has fewer than `i` elements, the new array is empty.
|
||||
@@ -462,7 +480,7 @@ Examples:
|
||||
-/
|
||||
abbrev drop (xs : Array α) (i : Nat) : Array α := extract xs i xs.size
|
||||
|
||||
@[simp, grind =] theorem drop_eq_extract {xs : Array α} {i : Nat} : xs.drop i = xs.extract i xs.size := rfl
|
||||
@[simp] theorem drop_eq_extract {xs : Array α} {i : Nat} : xs.drop i = xs.extract i xs.size := rfl
|
||||
|
||||
@[inline]
|
||||
unsafe def modifyMUnsafe [Monad m] (xs : Array α) (i : Nat) (f : α → m α) : m (Array α) := do
|
||||
@@ -570,7 +588,7 @@ protected def forIn' {α : Type u} {β : Type v} {m : Type v → Type w} [Monad
|
||||
| ForInStep.yield b => loop i (Nat.le_of_lt h') b
|
||||
loop as.size (Nat.le_refl _) b
|
||||
|
||||
instance [Monad m] : ForIn' m (Array α) α inferInstance where
|
||||
instance : ForIn' m (Array α) α inferInstance where
|
||||
forIn' := Array.forIn'
|
||||
|
||||
-- No separate `ForIn` instance is required because it can be derived from `ForIn'`.
|
||||
@@ -1001,7 +1019,7 @@ unless `start < stop`. By default, the entire array is used.
|
||||
protected def forM {α : Type u} {m : Type v → Type w} [Monad m] (f : α → m PUnit) (as : Array α) (start := 0) (stop := as.size) : m PUnit :=
|
||||
as.foldlM (fun _ => f) ⟨⟩ start stop
|
||||
|
||||
instance [Monad m] : ForM m (Array α) α where
|
||||
instance : ForM m (Array α) α where
|
||||
forM xs f := Array.forM f xs
|
||||
|
||||
-- We simplify `Array.forM` to `forM`.
|
||||
@@ -1295,7 +1313,7 @@ decreasing_by simp_wf; decreasing_trivial_pre_omega
|
||||
|
||||
|
||||
/--
|
||||
Returns the index of the first element equal to `a`, or `none` if no element is equal
|
||||
Returns the index of the first element equal to `a`, or the size of the array if no element is equal
|
||||
to `a`. The index is returned as a `Fin`, which guarantees that it is in bounds.
|
||||
|
||||
Examples:
|
||||
@@ -1704,7 +1722,7 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
|
||||
as
|
||||
decreasing_by simp_wf; decreasing_trivial_pre_omega
|
||||
|
||||
@[simp, grind =] theorem popWhile_empty {p : α → Bool} :
|
||||
@[simp] theorem popWhile_empty {p : α → Bool} :
|
||||
popWhile p #[] = #[] := by
|
||||
simp [popWhile]
|
||||
|
||||
@@ -1751,8 +1769,7 @@ termination_by xs.size - i
|
||||
decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
|
||||
|
||||
-- This is required in `Lean.Data.PersistentHashMap`.
|
||||
@[simp, grind =]
|
||||
theorem size_eraseIdx {xs : Array α} (i : Nat) (h) : (xs.eraseIdx i h).size = xs.size - 1 := by
|
||||
@[simp] theorem size_eraseIdx {xs : Array α} (i : Nat) (h) : (xs.eraseIdx i h).size = xs.size - 1 := by
|
||||
induction xs, i, h using Array.eraseIdx.induct with
|
||||
| @case1 xs i h h' xs' ih =>
|
||||
unfold eraseIdx
|
||||
@@ -2134,3 +2151,5 @@ instance [ToString α] : ToString (Array α) where
|
||||
toString xs := String.Internal.append "#" (toString xs.toList)
|
||||
|
||||
end Array
|
||||
|
||||
export Array (mkArray)
|
||||
|
||||
@@ -6,8 +6,10 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Nat.Linear
|
||||
public import Init.NotationExtra
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -6,7 +6,9 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
public import Init.Data.Int.DivMod.Lemmas
|
||||
public import Init.Omega
|
||||
|
||||
public section
|
||||
universe u v
|
||||
|
||||
@@ -8,6 +8,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.List.TakeDrop
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
|
||||
public section
|
||||
@@ -31,7 +32,7 @@ theorem foldlM_toList.aux [Monad m]
|
||||
· cases Nat.not_le_of_gt ‹_› (Nat.zero_add _ ▸ H)
|
||||
· rename_i i; rw [Nat.succ_add] at H
|
||||
simp [foldlM_toList.aux (j := j+1) H]
|
||||
rw (occs := [2]) [← List.getElem_cons_drop ‹_›]
|
||||
rw (occs := [2]) [← List.getElem_cons_drop_succ_eq_drop ‹_›]
|
||||
simp
|
||||
· rw [List.drop_of_length_le (Nat.ge_of_not_lt ‹_›)]; simp
|
||||
|
||||
@@ -100,15 +101,9 @@ abbrev push_toList := @toList_push
|
||||
@[simp, grind =] theorem empty_append {xs : Array α} : #[] ++ xs = xs := by
|
||||
apply ext'; simp only [toList_append, List.nil_append]
|
||||
|
||||
@[simp] theorem append_assoc {xs ys zs : Array α} : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
|
||||
@[simp, grind _=_] theorem append_assoc {xs ys zs : Array α} : xs ++ ys ++ zs = xs ++ (ys ++ zs) := by
|
||||
apply ext'; simp only [toList_append, List.append_assoc]
|
||||
|
||||
grind_pattern append_assoc => (xs ++ ys) ++ zs where
|
||||
xs =/= #[]; ys =/= #[]; zs =/= #[]
|
||||
|
||||
grind_pattern append_assoc => xs ++ (ys ++ zs) where
|
||||
xs =/= #[]; ys =/= #[]; zs =/= #[]
|
||||
|
||||
@[simp] theorem appendList_eq_append {xs : Array α} {l : List α} : xs.appendList l = xs ++ l := rfl
|
||||
|
||||
@[simp, grind =] theorem toList_appendList {xs : Array α} {l : List α} :
|
||||
@@ -116,4 +111,6 @@ grind_pattern append_assoc => xs ++ (ys ++ zs) where
|
||||
rw [← appendList_eq_append]; unfold Array.appendList
|
||||
induction l generalizing xs <;> simp [*]
|
||||
|
||||
|
||||
|
||||
end Array
|
||||
|
||||
@@ -6,6 +6,7 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.List.Nat.Count
|
||||
@@ -99,6 +100,9 @@ theorem countP_le_size : countP p xs ≤ xs.size := by
|
||||
theorem countP_replicate {a : α} {n : Nat} : countP p (replicate n a) = if p a then n else 0 := by
|
||||
simp [← List.toArray_replicate, List.countP_replicate]
|
||||
|
||||
@[deprecated countP_replicate (since := "2025-03-18")]
|
||||
abbrev countP_mkArray := @countP_replicate
|
||||
|
||||
theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
|
||||
(if p xs[i] then 1 else 0) ≤ xs.countP p := by
|
||||
rcases xs with ⟨xs⟩
|
||||
@@ -259,9 +263,15 @@ theorem count_eq_size {xs : Array α} : count a xs = xs.size ↔ ∀ b ∈ xs, a
|
||||
@[simp] theorem count_replicate_self {a : α} {n : Nat} : count a (replicate n a) = n := by
|
||||
simp [← List.toArray_replicate]
|
||||
|
||||
@[deprecated count_replicate_self (since := "2025-03-18")]
|
||||
abbrev count_mkArray_self := @count_replicate_self
|
||||
|
||||
theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
|
||||
simp [← List.toArray_replicate, List.count_replicate]
|
||||
|
||||
@[deprecated count_replicate (since := "2025-03-18")]
|
||||
abbrev count_mkArray := @count_replicate
|
||||
|
||||
theorem filter_beq {xs : Array α} (a : α) : xs.filter (· == a) = replicate (count a xs) a := by
|
||||
rcases xs with ⟨xs⟩
|
||||
simp [List.filter_beq]
|
||||
@@ -275,6 +285,9 @@ theorem replicate_count_eq_of_count_eq_size {xs : Array α} (h : count a xs = xs
|
||||
rw [← toList_inj]
|
||||
simp [List.replicate_count_eq_of_count_eq_length (by simpa using h)]
|
||||
|
||||
@[deprecated replicate_count_eq_of_count_eq_size (since := "2025-03-18")]
|
||||
abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
|
||||
|
||||
@[simp] theorem count_filter {xs : Array α} (h : p a) : count a (filter p xs) = count a xs := by
|
||||
rcases xs with ⟨xs⟩
|
||||
simp [List.count_filter, h]
|
||||
|
||||
@@ -6,9 +6,11 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.BEq
|
||||
public import Init.Data.List.Nat.BEq
|
||||
public import Init.ByCases
|
||||
|
||||
public section
|
||||
|
||||
@@ -89,41 +91,11 @@ theorem isEqv_self_beq [BEq α] [ReflBEq α] (xs : Array α) : Array.isEqv xs xs
|
||||
theorem isEqv_self [DecidableEq α] (xs : Array α) : Array.isEqv xs xs (· = ·) = true := by
|
||||
simp [isEqv, isEqvAux_self]
|
||||
|
||||
def instDecidableEqImpl [DecidableEq α] : DecidableEq (Array α) := fun xs ys =>
|
||||
match h:isEqv xs ys (fun a b => a = b) with
|
||||
| true => isTrue (eq_of_isEqv xs ys h)
|
||||
| false => isFalse (by subst ·; rw [isEqv_self] at h; contradiction)
|
||||
|
||||
instance instDecidableEq [DecidableEq α] : DecidableEq (Array α) := fun xs ys =>
|
||||
match xs with
|
||||
| ⟨[]⟩ =>
|
||||
match ys with
|
||||
| ⟨[]⟩ => isTrue rfl
|
||||
| ⟨_ :: _⟩ => isFalse (Array.noConfusion · (List.noConfusion ·))
|
||||
| ⟨a :: as⟩ =>
|
||||
match ys with
|
||||
| ⟨[]⟩ => isFalse (Array.noConfusion · (List.noConfusion ·))
|
||||
| ⟨b :: bs⟩ => instDecidableEqImpl ⟨a :: as⟩ ⟨b :: bs⟩
|
||||
|
||||
@[csimp]
|
||||
theorem instDecidableEq_csimp : @instDecidableEq = @instDecidableEqImpl :=
|
||||
Subsingleton.allEq _ _
|
||||
|
||||
/--
|
||||
Equality with `#[]` is decidable even if the underlying type does not have decidable equality.
|
||||
-/
|
||||
instance instDecidableEqEmp (xs : Array α) : Decidable (xs = #[]) :=
|
||||
match xs with
|
||||
| ⟨[]⟩ => isTrue rfl
|
||||
| ⟨_ :: _⟩ => isFalse (Array.noConfusion · (List.noConfusion ·))
|
||||
|
||||
/--
|
||||
Equality with `#[]` is decidable even if the underlying type does not have decidable equality.
|
||||
-/
|
||||
instance instDecidableEmpEq (ys : Array α) : Decidable (#[] = ys) :=
|
||||
match ys with
|
||||
| ⟨[]⟩ => isTrue rfl
|
||||
| ⟨_ :: _⟩ => isFalse (Array.noConfusion · (List.noConfusion ·))
|
||||
instance [DecidableEq α] : DecidableEq (Array α) :=
|
||||
fun xs ys =>
|
||||
match h:isEqv xs ys (fun a b => a = b) with
|
||||
| true => isTrue (eq_of_isEqv xs ys h)
|
||||
| false => isFalse fun h' => by subst h'; rw [isEqv_self] at h; contradiction
|
||||
|
||||
theorem beq_eq_decide [BEq α] (xs ys : Array α) :
|
||||
(xs == ys) = if h : xs.size = ys.size then
|
||||
|
||||
@@ -6,8 +6,11 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.List.Nat.Erase
|
||||
public import Init.Data.List.Nat.Basic
|
||||
|
||||
public section
|
||||
|
||||
@@ -139,16 +142,25 @@ theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
|
||||
simp only [← List.toArray_replicate, List.eraseP_toArray, List.eraseP_replicate]
|
||||
split <;> simp
|
||||
|
||||
@[deprecated eraseP_replicate (since := "2025-03-18")]
|
||||
abbrev eraseP_mkArray := @eraseP_replicate
|
||||
|
||||
@[simp] theorem eraseP_replicate_of_pos {n : Nat} {a : α} (h : p a) :
|
||||
(replicate n a).eraseP p = replicate (n - 1) a := by
|
||||
simp only [← List.toArray_replicate, List.eraseP_toArray]
|
||||
simp [h]
|
||||
|
||||
@[deprecated eraseP_replicate_of_pos (since := "2025-03-18")]
|
||||
abbrev eraseP_mkArray_of_pos := @eraseP_replicate_of_pos
|
||||
|
||||
@[simp] theorem eraseP_replicate_of_neg {n : Nat} {a : α} (h : ¬p a) :
|
||||
(replicate n a).eraseP p = replicate n a := by
|
||||
simp only [← List.toArray_replicate, List.eraseP_toArray]
|
||||
simp [h]
|
||||
|
||||
@[deprecated eraseP_replicate_of_neg (since := "2025-03-18")]
|
||||
abbrev eraseP_mkArray_of_neg := @eraseP_replicate_of_neg
|
||||
|
||||
theorem eraseP_eq_iff {p} {xs : Array α} :
|
||||
xs.eraseP p = ys ↔
|
||||
((∀ a ∈ xs, ¬ p a) ∧ xs = ys) ∨
|
||||
@@ -269,6 +281,9 @@ theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
|
||||
simp only [List.erase_replicate, beq_iff_eq, List.toArray_replicate]
|
||||
split <;> simp
|
||||
|
||||
@[deprecated erase_replicate (since := "2025-03-18")]
|
||||
abbrev erase_mkArray := @erase_replicate
|
||||
|
||||
-- The arguments `a b` are explicit,
|
||||
-- so they can be specified to prevent `simp` repeatedly applying the lemma.
|
||||
@[grind =]
|
||||
@@ -296,11 +311,17 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
|
||||
simp only [← List.toArray_replicate, List.erase_toArray]
|
||||
simp
|
||||
|
||||
@[deprecated erase_replicate_self (since := "2025-03-18")]
|
||||
abbrev erase_mkArray_self := @erase_replicate_self
|
||||
|
||||
@[simp] theorem erase_replicate_ne [LawfulBEq α] {a b : α} (h : !b == a) :
|
||||
(replicate n a).erase b = replicate n a := by
|
||||
rw [erase_of_not_mem]
|
||||
simp_all
|
||||
|
||||
@[deprecated erase_replicate_ne (since := "2025-03-18")]
|
||||
abbrev erase_mkArray_ne := @erase_replicate_ne
|
||||
|
||||
end erase
|
||||
|
||||
/-! ### eraseIdxIfInBounds -/
|
||||
@@ -411,6 +432,9 @@ theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} {h} :
|
||||
simp only [← List.toArray_replicate, List.eraseIdx_toArray]
|
||||
simp [List.eraseIdx_replicate, h]
|
||||
|
||||
@[deprecated eraseIdx_replicate (since := "2025-03-18")]
|
||||
abbrev eraseIdx_mkArray := @eraseIdx_replicate
|
||||
|
||||
theorem mem_eraseIdx_iff_getElem {x : α} {xs : Array α} {k} {h} : x ∈ xs.eraseIdx k h ↔ ∃ i w, i ≠ k ∧ xs[i]'w = x := by
|
||||
rcases xs with ⟨xs⟩
|
||||
simp [List.mem_eraseIdx_iff_getElem, *]
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.List.Nat.TakeDrop
|
||||
|
||||
public section
|
||||
|
||||
@@ -200,7 +201,7 @@ theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
|
||||
simp [getElem?_extract]
|
||||
omega
|
||||
|
||||
@[simp] theorem extract_extract {as : Array α} {i j k l : Nat} :
|
||||
@[simp, grind =] theorem extract_extract {as : Array α} {i j k l : Nat} :
|
||||
(as.extract i j).extract k l = as.extract (i + k) (min (i + l) j) := by
|
||||
ext m h₁ h₂
|
||||
· simp
|
||||
@@ -208,9 +209,6 @@ theorem getElem?_extract_of_succ {as : Array α} {j : Nat} :
|
||||
· simp only [size_extract] at h₁ h₂
|
||||
simp [Nat.add_assoc]
|
||||
|
||||
grind_pattern extract_extract => (as.extract i j).extract k l where
|
||||
as =/= #[]
|
||||
|
||||
theorem extract_eq_empty_of_eq_empty {as : Array α} {i j : Nat} (h : as = #[]) :
|
||||
as.extract i j = #[] := by
|
||||
simp [h]
|
||||
@@ -292,6 +290,9 @@ theorem extract_append_right {as bs : Array α} :
|
||||
· simp only [size_extract, size_replicate] at h₁ h₂
|
||||
simp only [getElem_extract, getElem_replicate]
|
||||
|
||||
@[deprecated extract_replicate (since := "2025-03-18")]
|
||||
abbrev extract_mkArray := @extract_replicate
|
||||
|
||||
theorem extract_eq_extract_right {as : Array α} {i j j' : Nat} :
|
||||
as.extract i j = as.extract i j' ↔ min (j - i) (as.size - i) = min (j' - i) (as.size - i) := by
|
||||
rcases as with ⟨as⟩
|
||||
@@ -409,6 +410,8 @@ theorem popWhile_append {xs ys : Array α} :
|
||||
rcases ys with ⟨ys⟩
|
||||
simp only [List.append_toArray, List.popWhile_toArray, List.reverse_append, List.dropWhile_append,
|
||||
List.isEmpty_iff, List.isEmpty_toArray, List.isEmpty_reverse]
|
||||
-- Why do these not fire with `simp`?
|
||||
rw [List.popWhile_toArray, List.isEmpty_toArray, List.isEmpty_reverse]
|
||||
split
|
||||
· rfl
|
||||
· simp
|
||||
@@ -427,20 +430,32 @@ theorem popWhile_append {xs ys : Array α} :
|
||||
(replicate n a).takeWhile p = (replicate n a).filter p := by
|
||||
simp [← List.toArray_replicate]
|
||||
|
||||
@[deprecated takeWhile_replicate_eq_filter (since := "2025-03-18")]
|
||||
abbrev takeWhile_mkArray_eq_filter := @takeWhile_replicate_eq_filter
|
||||
|
||||
theorem takeWhile_replicate {p : α → Bool} :
|
||||
(replicate n a).takeWhile p = if p a then replicate n a else #[] := by
|
||||
simp [takeWhile_replicate_eq_filter, filter_replicate]
|
||||
|
||||
@[deprecated takeWhile_replicate (since := "2025-03-18")]
|
||||
abbrev takeWhile_mkArray := @takeWhile_replicate
|
||||
|
||||
@[simp] theorem popWhile_replicate_eq_filter_not {p : α → Bool} :
|
||||
(replicate n a).popWhile p = (replicate n a).filter (fun a => !p a) := by
|
||||
simp [← List.toArray_replicate, ← List.filter_reverse]
|
||||
|
||||
@[deprecated popWhile_replicate_eq_filter_not (since := "2025-03-18")]
|
||||
abbrev popWhile_mkArray_eq_filter_not := @popWhile_replicate_eq_filter_not
|
||||
|
||||
theorem popWhile_replicate {p : α → Bool} :
|
||||
(replicate n a).popWhile p = if p a then #[] else replicate n a := by
|
||||
simp only [popWhile_replicate_eq_filter_not, size_replicate, filter_replicate, Bool.not_eq_eq_eq_not,
|
||||
Bool.not_true]
|
||||
split <;> simp_all
|
||||
|
||||
@[deprecated popWhile_replicate (since := "2025-03-18")]
|
||||
abbrev popWhile_mkArray := @popWhile_replicate
|
||||
|
||||
theorem extract_takeWhile {as : Array α} {i : Nat} :
|
||||
(as.takeWhile p).extract 0 i = (as.extract 0 i).takeWhile p := by
|
||||
rcases as with ⟨as⟩
|
||||
|
||||
@@ -6,6 +6,7 @@ Authors: François G. Dorais
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.List.FinRange
|
||||
public import Init.Data.Array.OfFn
|
||||
|
||||
public section
|
||||
|
||||
@@ -7,7 +7,10 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.List.Nat.Find
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.Array.Attach
|
||||
public import Init.Data.Array.Range
|
||||
|
||||
public section
|
||||
@@ -129,19 +132,31 @@ theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
|
||||
theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
|
||||
simp [← List.toArray_replicate, List.findSome?_replicate]
|
||||
|
||||
@[deprecated findSome?_replicate (since := "2025-03-18")]
|
||||
abbrev findSome?_mkArray := @findSome?_replicate
|
||||
|
||||
@[simp] theorem findSome?_replicate_of_pos (h : 0 < n) : findSome? f (replicate n a) = f a := by
|
||||
simp [findSome?_replicate, Nat.ne_of_gt h]
|
||||
|
||||
@[deprecated findSome?_replicate_of_pos (since := "2025-03-18")]
|
||||
abbrev findSome?_mkArray_of_pos := @findSome?_replicate_of_pos
|
||||
|
||||
-- Argument is unused, but used to decide whether `simp` should unfold.
|
||||
@[simp] theorem findSome?_replicate_of_isSome (_ : (f a).isSome) :
|
||||
findSome? f (replicate n a) = if n = 0 then none else f a := by
|
||||
simp [findSome?_replicate]
|
||||
|
||||
@[deprecated findSome?_replicate_of_isSome (since := "2025-03-18")]
|
||||
abbrev findSome?_mkArray_of_isSome := @findSome?_replicate_of_isSome
|
||||
|
||||
@[simp] theorem findSome?_replicate_of_isNone (h : (f a).isNone) :
|
||||
findSome? f (replicate n a) = none := by
|
||||
rw [Option.isNone_iff_eq_none] at h
|
||||
simp [findSome?_replicate, h]
|
||||
|
||||
@[deprecated findSome?_replicate_of_isNone (since := "2025-03-18")]
|
||||
abbrev findSome?_mkArray_of_isNone := @findSome?_replicate_of_isNone
|
||||
|
||||
/-! ### find? -/
|
||||
|
||||
@[simp, grind =] theorem find?_empty : find? p #[] = none := rfl
|
||||
@@ -306,10 +321,16 @@ theorem find?_replicate :
|
||||
find? p (replicate n a) = if p a then some a else none := by
|
||||
simp [find?_replicate, Nat.ne_of_gt h]
|
||||
|
||||
@[deprecated find?_replicate_of_size_pos (since := "2025-03-18")]
|
||||
abbrev find?_mkArray_of_length_pos := @find?_replicate_of_size_pos
|
||||
|
||||
@[simp] theorem find?_replicate_of_pos (h : p a) :
|
||||
find? p (replicate n a) = if n = 0 then none else some a := by
|
||||
simp [find?_replicate, h]
|
||||
|
||||
@[deprecated find?_replicate_of_pos (since := "2025-03-18")]
|
||||
abbrev find?_mkArray_of_pos := @find?_replicate_of_pos
|
||||
|
||||
@[simp] theorem find?_replicate_of_neg (h : ¬ p a) : find? p (replicate n a) = none := by
|
||||
simp [find?_replicate, h]
|
||||
|
||||
@@ -565,6 +586,9 @@ theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
|
||||
simp only [List.findIdx?_toArray]
|
||||
simp
|
||||
|
||||
@[deprecated findIdx?_replicate (since := "2025-03-18")]
|
||||
abbrev findIdx?_mkArray := @findIdx?_replicate
|
||||
|
||||
theorem findIdx?_eq_findSome?_zipIdx {xs : Array α} {p : α → Bool} :
|
||||
xs.findIdx? p = xs.zipIdx.findSome? fun ⟨a, i⟩ => if p a then some i else none := by
|
||||
rcases xs with ⟨xs⟩
|
||||
|
||||
@@ -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
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.List.Nat.InsertIdx
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -6,10 +6,17 @@ Authors: Mario Carneiro, Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Nat.Lemmas
|
||||
public import Init.Data.List.Range
|
||||
public import Init.Data.List.Nat.TakeDrop
|
||||
public import Init.Data.List.Nat.Modify
|
||||
public import Init.Data.List.Nat.Basic
|
||||
public import Init.Data.List.Monadic
|
||||
public import Init.Data.List.OfFn
|
||||
public import Init.Data.Array.Mem
|
||||
public import Init.Data.Array.DecidableEq
|
||||
public import Init.Data.Range.Lemmas
|
||||
public import Init.TacticsExtra
|
||||
public import Init.Data.List.ToArray
|
||||
import all Init.Data.List.Control
|
||||
import all Init.Data.Array.Basic
|
||||
@@ -245,13 +252,12 @@ theorem back_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.pus
|
||||
replace h := List.append_inj_right' h (by simp)
|
||||
simpa using h
|
||||
|
||||
theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b ↔ a = b ∧ xs = ys := by
|
||||
theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys := by
|
||||
cases xs
|
||||
cases ys
|
||||
simp [And.comm]
|
||||
|
||||
theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys :=
|
||||
(push_eq_push.1 h).2
|
||||
simp at h
|
||||
replace h := List.append_inj_left' h (by simp)
|
||||
simp [h]
|
||||
|
||||
theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a ↔ xs = ys :=
|
||||
⟨pop_eq_of_push_eq, fun h => by simp [h]⟩
|
||||
@@ -259,6 +265,15 @@ theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a ↔ xs
|
||||
theorem push_inj_right {a b : α} {xs : Array α} : xs.push a = xs.push b ↔ a = b :=
|
||||
⟨back_eq_of_push_eq, fun h => by simp [h]⟩
|
||||
|
||||
theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b ↔ a = b ∧ xs = ys := by
|
||||
constructor
|
||||
· intro h
|
||||
exact ⟨back_eq_of_push_eq h, pop_eq_of_push_eq h⟩
|
||||
· rintro ⟨rfl, rfl⟩
|
||||
rfl
|
||||
|
||||
theorem push_eq_append_singleton {as : Array α} {x : α} : as.push x = as ++ #[x] := rfl
|
||||
|
||||
theorem exists_push_of_ne_empty {xs : Array α} (h : xs ≠ #[]) :
|
||||
∃ (ys : Array α) (a : α), xs = ys.push a := by
|
||||
rcases xs with ⟨xs⟩
|
||||
@@ -309,23 +324,41 @@ theorem singleton_inj : #[a] = #[b] ↔ a = b := by
|
||||
@[simp, grind =] theorem size_replicate {n : Nat} {v : α} : (replicate n v).size = n :=
|
||||
List.length_replicate ..
|
||||
|
||||
@[deprecated size_replicate (since := "2025-03-18")]
|
||||
abbrev size_mkArray := @size_replicate
|
||||
|
||||
@[simp] theorem toList_replicate : (replicate n a).toList = List.replicate n a := by
|
||||
simp only [replicate]
|
||||
|
||||
@[deprecated toList_replicate (since := "2025-03-18")]
|
||||
abbrev toList_mkArray := @toList_replicate
|
||||
|
||||
@[simp, grind =] theorem replicate_zero : replicate 0 a = #[] := rfl
|
||||
|
||||
@[deprecated replicate_zero (since := "2025-03-18")]
|
||||
abbrev mkArray_zero := @replicate_zero
|
||||
|
||||
@[grind =]
|
||||
theorem replicate_succ : replicate (n + 1) a = (replicate n a).push a := by
|
||||
apply toList_inj.1
|
||||
simp [List.replicate_succ']
|
||||
|
||||
@[deprecated replicate_succ (since := "2025-03-18")]
|
||||
abbrev mkArray_succ := @replicate_succ
|
||||
|
||||
@[simp, grind =] theorem getElem_replicate {n : Nat} {v : α} {i : Nat} (h : i < (replicate n v).size) :
|
||||
(replicate n v)[i] = v := by simp [← getElem_toList]
|
||||
|
||||
@[deprecated getElem_replicate (since := "2025-03-18")]
|
||||
abbrev getElem_mkArray := @getElem_replicate
|
||||
|
||||
@[grind =] theorem getElem?_replicate {n : Nat} {v : α} {i : Nat} :
|
||||
(replicate n v)[i]? = if i < n then some v else none := by
|
||||
simp [getElem?_def]
|
||||
|
||||
@[deprecated getElem?_replicate (since := "2025-03-18")]
|
||||
abbrev getElem?_mkArray := @getElem?_replicate
|
||||
|
||||
/-! ### mem -/
|
||||
|
||||
@[grind ←]
|
||||
@@ -809,11 +842,6 @@ theorem contains_eq_true_of_mem [BEq α] [ReflBEq α] {a : α} {as : Array α} (
|
||||
theorem elem_iff [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
|
||||
elem a xs = true ↔ a ∈ xs := ⟨mem_of_contains_eq_true, contains_eq_true_of_mem⟩
|
||||
|
||||
@[grind =]
|
||||
theorem contains_iff_mem [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
|
||||
xs.contains a = true ↔ a ∈ xs := ⟨mem_of_contains_eq_true, contains_eq_true_of_mem⟩
|
||||
|
||||
@[deprecated contains_iff_mem (since := "2025-10-26")]
|
||||
theorem contains_iff [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
|
||||
xs.contains a = true ↔ a ∈ xs := ⟨mem_of_contains_eq_true, contains_eq_true_of_mem⟩
|
||||
|
||||
@@ -1053,6 +1081,12 @@ theorem mem_or_eq_of_mem_setIfInBounds
|
||||
cases xs
|
||||
simp
|
||||
|
||||
@[deprecated beq_empty_eq (since := "2025-04-04")]
|
||||
abbrev beq_empty_iff := @beq_empty_eq
|
||||
|
||||
@[deprecated empty_beq_eq (since := "2025-04-04")]
|
||||
abbrev empty_beq_iff := @empty_beq_eq
|
||||
|
||||
@[simp, grind =] theorem push_beq_push [BEq α] {a b : α} {xs ys : Array α} :
|
||||
(xs.push a == ys.push b) = (xs == ys && a == b) := by
|
||||
cases xs
|
||||
@@ -1073,6 +1107,9 @@ theorem size_eq_of_beq [BEq α] {xs ys : Array α} (h : xs == ys) : xs.size = ys
|
||||
rw [Bool.eq_iff_iff]
|
||||
simp +contextual
|
||||
|
||||
@[deprecated replicate_beq_replicate (since := "2025-03-18")]
|
||||
abbrev mkArray_beq_mkArray := @replicate_beq_replicate
|
||||
|
||||
private theorem beq_of_beq_singleton [BEq α] {a b : α} : #[a] == #[b] → a == b := by
|
||||
intro h
|
||||
have : isEqv #[a] #[b] BEq.beq = true := h
|
||||
@@ -1136,7 +1173,7 @@ where
|
||||
aux (i bs) :
|
||||
mapM.map f xs i bs = (xs.toList.drop i).foldlM (fun bs a => bs.push <$> f a) bs := by
|
||||
unfold mapM.map; split
|
||||
· rw [← List.getElem_cons_drop ‹_›]
|
||||
· rw [← List.getElem_cons_drop_succ_eq_drop ‹_›]
|
||||
simp only [aux (i + 1), map_eq_pure_bind, List.foldlM_cons, bind_assoc,
|
||||
pure_bind]
|
||||
rfl
|
||||
@@ -1628,15 +1665,12 @@ theorem filterMap_eq_filter {p : α → Bool} (w : stop = as.size) :
|
||||
cases as
|
||||
simp
|
||||
|
||||
@[grind =]
|
||||
theorem filterMap_filterMap {f : α → Option β} {g : β → Option γ} {xs : Array α} :
|
||||
filterMap g (filterMap f xs) = filterMap (fun x => (f x).bind g) xs := by
|
||||
cases xs
|
||||
simp [List.filterMap_filterMap]
|
||||
|
||||
grind_pattern filterMap_filterMap => filterMap g (filterMap f xs) where
|
||||
f =/= some
|
||||
g =/= some
|
||||
|
||||
@[grind =]
|
||||
theorem map_filterMap {f : α → Option β} {g : β → γ} {xs : Array α} :
|
||||
map g (filterMap f xs) = filterMap (fun x => (f x).map g) xs := by
|
||||
@@ -1691,6 +1725,9 @@ theorem forall_none_of_filterMap_eq_empty (h : filterMap f xs = #[]) : ∀ x ∈
|
||||
cases xs
|
||||
simp
|
||||
|
||||
@[deprecated filterMap_eq_empty_iff (since := "2025-04-04")]
|
||||
abbrev filterMap_eq_nil_iff := @filterMap_eq_empty_iff
|
||||
|
||||
theorem filterMap_eq_push_iff {f : α → Option β} {xs : Array α} {ys : Array β} {b : β} :
|
||||
filterMap f xs = ys.push b ↔ ∃ as a bs,
|
||||
xs = as.push a ++ bs ∧ filterMap f as = ys ∧ f a = some b ∧ (∀ x, x ∈ bs → f x = none) := by
|
||||
@@ -1853,9 +1890,6 @@ theorem getElem_of_append {xs ys zs : Array α} (eq : xs = ys.push a ++ zs) (h :
|
||||
|
||||
theorem push_eq_append {a : α} {as : Array α} : as.push a = as ++ #[a] := rfl
|
||||
|
||||
@[deprecated push_eq_append (since := "2025-10-26")]
|
||||
theorem push_eq_append_singleton {as : Array α} {x : α} : as.push x = as ++ #[x] := rfl
|
||||
|
||||
theorem append_inj {xs₁ xs₂ ys₁ ys₂ : Array α} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) :
|
||||
xs₁ = xs₂ ∧ ys₁ = ys₂ := by
|
||||
rcases xs₁ with ⟨s₁⟩
|
||||
@@ -2056,22 +2090,11 @@ theorem append_eq_map_iff {f : α → β} :
|
||||
| nil => simp
|
||||
| cons as => induction as.toList <;> simp [*]
|
||||
|
||||
@[simp] theorem flatten_toArray_map_toArray {L : List (List α)} :
|
||||
@[simp] theorem flatten_toArray_map {L : List (List α)} :
|
||||
(L.map List.toArray).toArray.flatten = L.flatten.toArray := by
|
||||
apply ext'
|
||||
simp [Function.comp_def]
|
||||
|
||||
@[deprecated flatten_toArray_map_toArray (since := "2025-10-26")]
|
||||
theorem flatten_toArray_map {L : List (List α)} :
|
||||
(L.map List.toArray).toArray.flatten = L.flatten.toArray := by
|
||||
simp
|
||||
|
||||
@[grind =]
|
||||
theorem flatten_map_toArray_toArray {L : List (List α)} :
|
||||
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
|
||||
simp
|
||||
|
||||
@[deprecated flatten_map_toArray_toArray (since := "2025-10-26")]
|
||||
theorem flatten_map_toArray {L : List (List α)} :
|
||||
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
|
||||
simp
|
||||
@@ -2118,33 +2141,32 @@ theorem forall_mem_flatten {p : α → Prop} {xss : Array (Array α)} :
|
||||
|
||||
theorem flatten_eq_flatMap {xss : Array (Array α)} : flatten xss = xss.flatMap id := by
|
||||
induction xss using array₂_induction
|
||||
rw [flatten_toArray_map_toArray, List.flatten_eq_flatMap]
|
||||
rw [flatten_toArray_map, List.flatten_eq_flatMap]
|
||||
simp [List.flatMap_map]
|
||||
|
||||
@[simp, grind _=_] theorem map_flatten {f : α → β} {xss : Array (Array α)} :
|
||||
(flatten xss).map f = (map (map f) xss).flatten := by
|
||||
induction xss using array₂_induction with
|
||||
| of xss =>
|
||||
simp only [flatten_toArray_map_toArray, List.map_toArray, List.map_flatten, List.map_map,
|
||||
simp only [flatten_toArray_map, List.map_toArray, List.map_flatten, List.map_map,
|
||||
Function.comp_def]
|
||||
rw [← Function.comp_def, ← List.map_map, flatten_toArray_map_toArray]
|
||||
rw [← Function.comp_def, ← List.map_map, flatten_toArray_map]
|
||||
|
||||
@[simp, grind =] theorem filterMap_flatten {f : α → Option β} {xss : Array (Array α)} {stop : Nat} (w : stop = xss.flatten.size) :
|
||||
filterMap f (flatten xss) 0 stop = flatten (map (filterMap f) xss) := by
|
||||
subst w
|
||||
induction xss using array₂_induction
|
||||
simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
|
||||
List.filterMap_toArray', List.filterMap_flatten, List.map_toArray, List.map_map,
|
||||
Function.comp_def]
|
||||
rw [← Function.comp_def, ← List.map_map, flatten_toArray_map_toArray]
|
||||
simp only [flatten_toArray_map, List.size_toArray, List.length_flatten, List.filterMap_toArray',
|
||||
List.filterMap_flatten, List.map_toArray, List.map_map, Function.comp_def]
|
||||
rw [← Function.comp_def, ← List.map_map, flatten_toArray_map]
|
||||
|
||||
@[simp, grind =] theorem filter_flatten {p : α → Bool} {xss : Array (Array α)} {stop : Nat} (w : stop = xss.flatten.size) :
|
||||
filter p (flatten xss) 0 stop = flatten (map (filter p) xss) := by
|
||||
subst w
|
||||
induction xss using array₂_induction
|
||||
simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
|
||||
List.filter_toArray', List.filter_flatten, List.map_toArray, List.map_map, Function.comp_def]
|
||||
rw [← Function.comp_def, ← List.map_map, flatten_toArray_map_toArray]
|
||||
simp only [flatten_toArray_map, List.size_toArray, List.length_flatten, List.filter_toArray',
|
||||
List.filter_flatten, List.map_toArray, List.map_map, Function.comp_def]
|
||||
rw [← Function.comp_def, ← List.map_map, flatten_toArray_map]
|
||||
|
||||
theorem flatten_filter_not_isEmpty {xss : Array (Array α)} :
|
||||
flatten (xss.filter fun xs => !xs.isEmpty) = xss.flatten := by
|
||||
@@ -2167,23 +2189,23 @@ theorem flatten_filter_ne_empty [DecidablePred fun xs : Array α => xs ≠ #[]]
|
||||
induction xss using array₂_induction
|
||||
rcases xs with ⟨l⟩
|
||||
have this : [l.toArray] = [l].map List.toArray := by simp
|
||||
simp only [List.push_toArray, flatten_toArray_map_toArray, List.append_toArray]
|
||||
rw [this, ← List.map_append, flatten_toArray_map_toArray]
|
||||
simp only [List.push_toArray, flatten_toArray_map, List.append_toArray]
|
||||
rw [this, ← List.map_append, flatten_toArray_map]
|
||||
simp
|
||||
|
||||
theorem flatten_flatten {xss : Array (Array (Array α))} : flatten (flatten xss) = flatten (map flatten xss) := by
|
||||
induction xss using array₃_induction with
|
||||
| of xss =>
|
||||
rw [flatten_toArray_map_toArray]
|
||||
rw [flatten_toArray_map]
|
||||
have : (xss.map (fun xs => xs.map List.toArray)).flatten = xss.flatten.map List.toArray := by
|
||||
induction xss with
|
||||
| nil => simp
|
||||
| cons xs xss ih =>
|
||||
simp only [List.map_cons, List.flatten_cons, ih, List.map_append]
|
||||
rw [this, flatten_toArray_map_toArray, List.flatten_flatten, ← List.map_toArray, Array.map_map,
|
||||
rw [this, flatten_toArray_map, List.flatten_flatten, ← List.map_toArray, Array.map_map,
|
||||
← List.map_toArray, map_map, Function.comp_def]
|
||||
simp only [Function.comp_apply, flatten_toArray_map_toArray]
|
||||
rw [List.map_toArray, ← Function.comp_def, ← List.map_map, flatten_toArray_map_toArray]
|
||||
simp only [Function.comp_apply, flatten_toArray_map]
|
||||
rw [List.map_toArray, ← Function.comp_def, ← List.map_map, flatten_toArray_map]
|
||||
|
||||
theorem flatten_eq_push_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
|
||||
xss.flatten = ys.push y ↔
|
||||
@@ -2192,13 +2214,13 @@ theorem flatten_eq_push_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
|
||||
induction xss using array₂_induction with
|
||||
| of xs =>
|
||||
rcases ys with ⟨ys⟩
|
||||
rw [flatten_toArray_map_toArray, List.push_toArray, mk.injEq, List.flatten_eq_append_iff]
|
||||
rw [flatten_toArray_map, List.push_toArray, mk.injEq, List.flatten_eq_append_iff]
|
||||
constructor
|
||||
· rintro (⟨as, bs, rfl, rfl, h⟩ | ⟨as, bs, c, cs, ds, rfl, rfl, h⟩)
|
||||
· rw [List.singleton_eq_flatten_iff] at h
|
||||
obtain ⟨xs, ys, rfl, h₁, h₂⟩ := h
|
||||
exact ⟨((as ++ xs).map List.toArray).toArray, #[], (ys.map List.toArray).toArray, by simp,
|
||||
by simpa using h₂, by rw [flatten_toArray_map_toArray]; simpa⟩
|
||||
by simpa using h₂, by rw [flatten_toArray_map]; simpa⟩
|
||||
· rw [List.singleton_eq_append_iff] at h
|
||||
obtain (⟨h₁, h₂⟩ | ⟨h₁, h₂⟩) := h
|
||||
· simp at h₁
|
||||
@@ -2231,8 +2253,8 @@ theorem push_eq_flatten_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
|
||||
-- zs = cs ++ ds.flatten := by sorry
|
||||
|
||||
|
||||
/-- Two arrays of arrays are equal iff their flattens coincide, as well as the sizes of the
|
||||
arrays. -/
|
||||
/-- Two arrays of subarrays are equal iff their flattens coincide, as well as the sizes of the
|
||||
subarrays. -/
|
||||
theorem eq_iff_flatten_eq {xss₁ xss₂ : Array (Array α)} :
|
||||
xss₁ = xss₂ ↔ xss₁.flatten = xss₂.flatten ∧ map size xss₁ = map size xss₂ := by
|
||||
cases xss₁ using array₂_induction with
|
||||
@@ -2243,12 +2265,18 @@ theorem eq_iff_flatten_eq {xss₁ xss₂ : Array (Array α)} :
|
||||
rw [List.map_inj_right]
|
||||
simp +contextual
|
||||
|
||||
theorem flatten_toArray_map_toArray {xss : List (List α)} :
|
||||
(xss.map List.toArray).toArray.flatten = xss.flatten.toArray := by
|
||||
simp
|
||||
|
||||
/-! ### flatMap -/
|
||||
|
||||
theorem flatMap_def {xs : Array α} {f : α → Array β} : xs.flatMap f = flatten (map f xs) := by
|
||||
rcases xs with ⟨l⟩
|
||||
simp [flatten_toArray, Function.comp_def, List.flatMap_def]
|
||||
|
||||
@[simp, grind =] theorem flatMap_empty {β} {f : α → Array β} : (#[] : Array α).flatMap f = #[] := rfl
|
||||
|
||||
theorem flatMap_toList {xs : Array α} {f : α → List β} :
|
||||
xs.toList.flatMap f = (xs.flatMap (fun a => (f a).toArray)).toList := by
|
||||
rcases xs with ⟨l⟩
|
||||
@@ -2259,7 +2287,6 @@ theorem flatMap_toList {xs : Array α} {f : α → List β} :
|
||||
rcases xs with ⟨l⟩
|
||||
simp
|
||||
|
||||
@[deprecated List.flatMap_toArray_cons (since := "2025-10-29")]
|
||||
theorem flatMap_toArray_cons {β} {f : α → Array β} {a : α} {as : List α} :
|
||||
(a :: as).toArray.flatMap f = f a ++ as.toArray.flatMap f := by
|
||||
simp [flatMap]
|
||||
@@ -2270,7 +2297,6 @@ theorem flatMap_toArray_cons {β} {f : α → Array β} {a : α} {as : List α}
|
||||
intro cs
|
||||
induction as generalizing cs <;> simp_all
|
||||
|
||||
@[deprecated List.flatMap_toArray (since := "2025-10-29")]
|
||||
theorem flatMap_toArray {β} {f : α → Array β} {as : List α} :
|
||||
as.toArray.flatMap f = (as.flatMap (fun a => (f a).toList)).toArray := by
|
||||
simp
|
||||
@@ -2371,44 +2397,77 @@ theorem flatMap_eq_foldl {f : α → Array β} {xs : Array α} :
|
||||
|
||||
@[simp] theorem replicate_one : replicate 1 a = #[a] := rfl
|
||||
|
||||
@[deprecated replicate_one (since := "2025-03-18")]
|
||||
abbrev mkArray_one := @replicate_one
|
||||
|
||||
/-- Variant of `replicate_succ` that prepends `a` at the beginning of the array. -/
|
||||
theorem replicate_succ' : replicate (n + 1) a = #[a] ++ replicate n a := by
|
||||
apply Array.ext'
|
||||
simp [List.replicate_succ]
|
||||
|
||||
@[deprecated replicate_succ' (since := "2025-03-18")]
|
||||
abbrev mkArray_succ' := @replicate_succ'
|
||||
|
||||
@[simp, grind =] theorem mem_replicate {a b : α} {n} : b ∈ replicate n a ↔ n ≠ 0 ∧ b = a := by
|
||||
unfold replicate
|
||||
simp only [List.mem_toArray, List.mem_replicate]
|
||||
|
||||
@[deprecated mem_replicate (since := "2025-03-18")]
|
||||
abbrev mem_mkArray := @mem_replicate
|
||||
|
||||
@[grind →] theorem eq_of_mem_replicate {a b : α} {n} (h : b ∈ replicate n a) : b = a := (mem_replicate.1 h).2
|
||||
|
||||
@[deprecated eq_of_mem_mkArray (since := "2025-03-18")]
|
||||
abbrev eq_of_mem_mkArray := @eq_of_mem_replicate
|
||||
|
||||
theorem forall_mem_replicate {p : α → Prop} {a : α} {n} :
|
||||
(∀ b, b ∈ replicate n a → p b) ↔ n = 0 ∨ p a := by
|
||||
cases n <;> simp [mem_replicate]
|
||||
|
||||
@[deprecated forall_mem_replicate (since := "2025-03-18")]
|
||||
abbrev forall_mem_mkArray := @forall_mem_replicate
|
||||
|
||||
@[simp] theorem replicate_succ_ne_empty {n : Nat} {a : α} : replicate (n+1) a ≠ #[] := by
|
||||
simp [replicate_succ]
|
||||
|
||||
@[deprecated replicate_succ_ne_empty (since := "2025-03-18")]
|
||||
abbrev mkArray_succ_ne_empty := @replicate_succ_ne_empty
|
||||
|
||||
@[simp] theorem replicate_eq_empty_iff {n : Nat} {a : α} : replicate n a = #[] ↔ n = 0 := by
|
||||
cases n <;> simp
|
||||
|
||||
@[deprecated replicate_eq_empty_iff (since := "2025-03-18")]
|
||||
abbrev mkArray_eq_empty_iff := @replicate_eq_empty_iff
|
||||
|
||||
@[simp] theorem replicate_inj : replicate n a = replicate m b ↔ n = m ∧ (n = 0 ∨ a = b) := by
|
||||
rw [← toList_inj]
|
||||
simp
|
||||
|
||||
@[deprecated replicate_inj (since := "2025-03-18")]
|
||||
abbrev mkArray_inj := @replicate_inj
|
||||
|
||||
theorem eq_replicate_of_mem {a : α} {xs : Array α} (h : ∀ (b) (_ : b ∈ xs), b = a) : xs = replicate xs.size a := by
|
||||
rw [← toList_inj]
|
||||
simpa using List.eq_replicate_of_mem (by simpa using h)
|
||||
|
||||
@[deprecated eq_replicate_of_mem (since := "2025-03-18")]
|
||||
abbrev eq_mkArray_of_mem := @eq_replicate_of_mem
|
||||
|
||||
theorem eq_replicate_iff {a : α} {n} {xs : Array α} :
|
||||
xs = replicate n a ↔ xs.size = n ∧ ∀ (b) (_ : b ∈ xs), b = a := by
|
||||
rw [← toList_inj]
|
||||
simpa using List.eq_replicate_iff (l := xs.toList)
|
||||
|
||||
@[deprecated eq_replicate_iff (since := "2025-03-18")]
|
||||
abbrev eq_mkArray_iff := @eq_replicate_iff
|
||||
|
||||
theorem map_eq_replicate_iff {xs : Array α} {f : α → β} {b : β} :
|
||||
xs.map f = replicate xs.size b ↔ ∀ x ∈ xs, f x = b := by
|
||||
simp [eq_replicate_iff]
|
||||
|
||||
@[deprecated map_eq_replicate_iff (since := "2025-03-18")]
|
||||
abbrev map_eq_mkArray_iff := @map_eq_replicate_iff
|
||||
|
||||
@[simp] theorem map_const {xs : Array α} {b : β} : map (Function.const α b) xs = replicate xs.size b :=
|
||||
map_eq_replicate_iff.mpr fun _ _ => rfl
|
||||
|
||||
@@ -2425,86 +2484,143 @@ theorem map_const' {xs : Array α} {b : β} : map (fun _ => b) xs = replicate xs
|
||||
apply Array.ext'
|
||||
simp
|
||||
|
||||
@[deprecated set_replicate_self (since := "2025-03-18")]
|
||||
abbrev set_mkArray_self := @set_replicate_self
|
||||
|
||||
@[simp] theorem setIfInBounds_replicate_self : (replicate n a).setIfInBounds i a = replicate n a := by
|
||||
apply Array.ext'
|
||||
simp
|
||||
|
||||
@[deprecated setIfInBounds_replicate_self (since := "2025-03-18")]
|
||||
abbrev setIfInBounds_mkArray_self := @setIfInBounds_replicate_self
|
||||
|
||||
@[simp] theorem replicate_append_replicate : replicate n a ++ replicate m a = replicate (n + m) a := by
|
||||
apply Array.ext'
|
||||
simp
|
||||
|
||||
@[deprecated replicate_append_replicate (since := "2025-03-18")]
|
||||
abbrev mkArray_append_mkArray := @replicate_append_replicate
|
||||
|
||||
theorem append_eq_replicate_iff {xs ys : Array α} {a : α} :
|
||||
xs ++ ys = replicate n a ↔
|
||||
xs.size + ys.size = n ∧ xs = replicate xs.size a ∧ ys = replicate ys.size a := by
|
||||
simp [← toList_inj, List.append_eq_replicate_iff]
|
||||
|
||||
@[deprecated append_eq_replicate_iff (since := "2025-03-18")]
|
||||
abbrev append_eq_mkArray_iff := @append_eq_replicate_iff
|
||||
|
||||
theorem replicate_eq_append_iff {xs ys : Array α} {a : α} :
|
||||
replicate n a = xs ++ ys ↔
|
||||
xs.size + ys.size = n ∧ xs = replicate xs.size a ∧ ys = replicate ys.size a := by
|
||||
rw [eq_comm, append_eq_replicate_iff]
|
||||
|
||||
@[deprecated replicate_eq_append_iff (since := "2025-03-18")]
|
||||
abbrev replicate_eq_mkArray_iff := @replicate_eq_append_iff
|
||||
|
||||
@[simp] theorem map_replicate : (replicate n a).map f = replicate n (f a) := by
|
||||
apply Array.ext'
|
||||
simp
|
||||
|
||||
@[deprecated map_replicate (since := "2025-03-18")]
|
||||
abbrev map_mkArray := @map_replicate
|
||||
|
||||
@[grind =] theorem filter_replicate (w : stop = n) :
|
||||
(replicate n a).filter p 0 stop = if p a then replicate n a else #[] := by
|
||||
apply Array.ext'
|
||||
simp only [w]
|
||||
split <;> simp_all
|
||||
|
||||
@[deprecated filter_replicate (since := "2025-03-18")]
|
||||
abbrev filter_mkArray := @filter_replicate
|
||||
|
||||
@[simp] theorem filter_replicate_of_pos (w : stop = n) (h : p a) :
|
||||
(replicate n a).filter p 0 stop = replicate n a := by
|
||||
simp [filter_replicate, h, w]
|
||||
|
||||
@[deprecated filter_replicate_of_pos (since := "2025-03-18")]
|
||||
abbrev filter_mkArray_of_pos := @filter_replicate_of_pos
|
||||
|
||||
@[simp] theorem filter_replicate_of_neg (w : stop = n) (h : ¬ p a) :
|
||||
(replicate n a).filter p 0 stop = #[] := by
|
||||
simp [filter_replicate, h, w]
|
||||
|
||||
@[deprecated filter_replicate_of_neg (since := "2025-03-18")]
|
||||
abbrev filter_mkArray_of_neg := @filter_replicate_of_neg
|
||||
|
||||
theorem filterMap_replicate {f : α → Option β} (w : stop = n := by simp) :
|
||||
(replicate n a).filterMap f 0 stop = match f a with | none => #[] | .some b => replicate n b := by
|
||||
apply Array.ext'
|
||||
simp only [w, size_replicate, toList_filterMap', toList_replicate, List.filterMap_replicate]
|
||||
split <;> simp_all
|
||||
|
||||
@[deprecated filterMap_replicate (since := "2025-03-18")]
|
||||
abbrev filterMap_mkArray := @filterMap_replicate
|
||||
|
||||
-- This is not a useful `simp` lemma because `b` is unknown.
|
||||
theorem filterMap_replicate_of_some {f : α → Option β} (h : f a = some b) :
|
||||
(replicate n a).filterMap f = replicate n b := by
|
||||
simp [filterMap_replicate, h]
|
||||
|
||||
@[deprecated filterMap_replicate_of_some (since := "2025-03-18")]
|
||||
abbrev filterMap_mkArray_of_some := @filterMap_replicate_of_some
|
||||
|
||||
@[simp] theorem filterMap_replicate_of_isSome {f : α → Option β} (h : (f a).isSome) :
|
||||
(replicate n a).filterMap f = replicate n (Option.get _ h) := by
|
||||
match w : f a, h with
|
||||
| some b, _ => simp [filterMap_replicate, w]
|
||||
|
||||
@[deprecated filterMap_replicate_of_isSome (since := "2025-03-18")]
|
||||
abbrev filterMap_mkArray_of_isSome := @filterMap_replicate_of_isSome
|
||||
|
||||
@[simp] theorem filterMap_replicate_of_none {f : α → Option β} (h : f a = none) :
|
||||
(replicate n a).filterMap f = #[] := by
|
||||
simp [filterMap_replicate, h]
|
||||
|
||||
@[deprecated filterMap_replicate_of_none (since := "2025-03-18")]
|
||||
abbrev filterMap_mkArray_of_none := @filterMap_replicate_of_none
|
||||
|
||||
@[simp] theorem flatten_replicate_empty : (replicate n (#[] : Array α)).flatten = #[] := by
|
||||
rw [← toList_inj]
|
||||
simp
|
||||
|
||||
@[deprecated flatten_replicate_empty (since := "2025-03-18")]
|
||||
abbrev flatten_mkArray_empty := @flatten_replicate_empty
|
||||
|
||||
@[simp] theorem flatten_replicate_singleton : (replicate n #[a]).flatten = replicate n a := by
|
||||
rw [← toList_inj]
|
||||
simp
|
||||
|
||||
@[deprecated flatten_replicate_singleton (since := "2025-03-18")]
|
||||
abbrev flatten_mkArray_singleton := @flatten_replicate_singleton
|
||||
|
||||
@[simp] theorem flatten_replicate_replicate : (replicate n (replicate m a)).flatten = replicate (n * m) a := by
|
||||
rw [← toList_inj]
|
||||
simp
|
||||
|
||||
@[deprecated flatten_replicate_replicate (since := "2025-03-18")]
|
||||
abbrev flatten_mkArray_replicate := @flatten_replicate_replicate
|
||||
|
||||
theorem flatMap_replicate {f : α → Array β} : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
|
||||
rw [← toList_inj]
|
||||
simp [List.flatMap_replicate]
|
||||
|
||||
@[deprecated flatMap_replicate (since := "2025-03-18")]
|
||||
abbrev flatMap_mkArray := @flatMap_replicate
|
||||
|
||||
@[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
|
||||
rw [← List.toArray_replicate, List.isEmpty_toArray]
|
||||
simp
|
||||
|
||||
@[deprecated isEmpty_replicate (since := "2025-03-18")]
|
||||
abbrev isEmpty_mkArray := @isEmpty_replicate
|
||||
|
||||
@[simp] theorem sum_replicate_nat {n : Nat} {a : Nat} : (replicate n a).sum = n * a := by
|
||||
rw [← List.toArray_replicate, List.sum_toArray]
|
||||
simp
|
||||
|
||||
@[deprecated sum_replicate_nat (since := "2025-03-18")]
|
||||
abbrev sum_mkArray_nat := @sum_replicate_nat
|
||||
|
||||
/-! ### Preliminaries about `swap` needed for `reverse`. -/
|
||||
|
||||
@[grind =]
|
||||
@@ -2546,8 +2662,8 @@ theorem getElem?_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} : (xs.swap i
|
||||
split <;> rename_i h₃
|
||||
· simp only [← h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
|
||||
exact (List.getElem?_reverse' (Eq.trans (by simp +arith) h)).symm
|
||||
simp only [Nat.succ_le_iff, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
|
||||
Nat.lt_succ_iff.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
|
||||
simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
|
||||
Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
|
||||
· rw [H]; split <;> rename_i h₂
|
||||
· cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
|
||||
cases Nat.le_antisymm h₂.1 h₂.2
|
||||
@@ -2562,7 +2678,7 @@ theorem getElem?_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} : (xs.swap i
|
||||
split
|
||||
· rfl
|
||||
· rename_i h
|
||||
simp only [← show k < _ + 1 ↔ _ from Nat.lt_succ_iff (n := xs.size - 1), this, Nat.zero_le,
|
||||
simp only [← show k < _ + 1 ↔ _ from Nat.lt_succ (n := xs.size - 1), this, Nat.zero_le,
|
||||
true_and, Nat.not_lt] at h
|
||||
rw [List.getElem?_eq_none_iff.2 ‹_›, List.getElem?_eq_none_iff.2 (xs.toList.length_reverse ▸ ‹_›)]
|
||||
|
||||
@@ -2691,6 +2807,9 @@ theorem flatten_reverse {xss : Array (Array α)} :
|
||||
rw [← toList_inj]
|
||||
simp
|
||||
|
||||
@[deprecated reverse_replicate (since := "2025-03-18")]
|
||||
abbrev reverse_mkArray := @reverse_replicate
|
||||
|
||||
/-! ### extract -/
|
||||
|
||||
theorem extract_loop_zero {xs ys : Array α} {start : Nat} : extract.loop xs 0 start ys = ys := by
|
||||
@@ -2710,8 +2829,8 @@ theorem extract_loop_eq_aux {xs ys : Array α} {size start : Nat} :
|
||||
| zero => rw [extract_loop_zero, extract_loop_zero, append_empty]
|
||||
| succ size ih =>
|
||||
if h : start < xs.size then
|
||||
rw [extract_loop_succ (h := h), ih, push_eq_append]
|
||||
rw [extract_loop_succ (h := h), ih (ys := #[].push _), push_eq_append, empty_append]
|
||||
rw [extract_loop_succ (h := h), ih, push_eq_append_singleton]
|
||||
rw [extract_loop_succ (h := h), ih (ys := #[].push _), push_eq_append_singleton, empty_append]
|
||||
rw [append_assoc]
|
||||
else
|
||||
rw [extract_loop_of_ge (h := Nat.le_of_not_lt h)]
|
||||
@@ -3328,16 +3447,6 @@ theorem foldr_filterMap {f : α → Option β} {g : β → γ → γ} {xs : Arra
|
||||
(xs.filterMap f).foldr g init = xs.foldr (fun x y => match f x with | some b => g b y | none => y) init := by
|
||||
simp [foldr_filterMap']
|
||||
|
||||
theorem foldl_flatMap {f : α → Array β} {g : γ → β → γ} {xs : Array α} {init : γ} :
|
||||
(xs.flatMap f).foldl g init = xs.foldl (fun acc x => (f x).foldl g acc) init := by
|
||||
rcases xs with ⟨l⟩
|
||||
simp [List.foldl_flatMap]
|
||||
|
||||
theorem foldr_flatMap {f : α → Array β} {g : β → γ → γ} {xs : Array α} {init : γ} :
|
||||
(xs.flatMap f).foldr g init = xs.foldr (fun x acc => (f x).foldr g acc) init := by
|
||||
rcases xs with ⟨l⟩
|
||||
simp [List.foldr_flatMap]
|
||||
|
||||
theorem foldl_map_hom' {g : α → β} {f : α → α → α} {f' : β → β → β} {a : α} {xs : Array α}
|
||||
{stop : Nat} (h : ∀ x y, f' (g x) (g y) = g (f x y)) (w : stop = xs.size) :
|
||||
(xs.map g).foldl f' (g a) 0 stop = g (xs.foldl f a) := by
|
||||
@@ -3555,6 +3664,11 @@ theorem mem_of_back? {xs : Array α} {a : α} (h : xs.back? = some a) : a ∈ xs
|
||||
rcases ys with ⟨ys⟩
|
||||
simp only [List.append_toArray, List.back_toArray, List.getLast_append, List.isEmpty_iff,
|
||||
List.isEmpty_toArray]
|
||||
split
|
||||
· rw [dif_pos]
|
||||
simpa only [List.isEmpty_toArray]
|
||||
· rw [dif_neg]
|
||||
simpa only [List.isEmpty_toArray]
|
||||
|
||||
theorem back_append_right {xs ys : Array α} (h : 0 < ys.size) :
|
||||
(xs ++ ys).back (by simp; omega) = ys.back h := by
|
||||
@@ -3605,9 +3719,15 @@ theorem back?_replicate {a : α} {n : Nat} :
|
||||
rw [replicate_eq_toArray_replicate]
|
||||
simp only [List.back?_toArray, List.getLast?_replicate]
|
||||
|
||||
@[deprecated back?_replicate (since := "2025-03-18")]
|
||||
abbrev back?_mkArray := @back?_replicate
|
||||
|
||||
@[simp] theorem back_replicate {xs : Array α} (w : 0 < n) : (replicate n xs).back (by simpa using w) = xs := by
|
||||
simp [back_eq_getElem]
|
||||
|
||||
@[deprecated back_replicate (since := "2025-03-18")]
|
||||
abbrev back_mkArray := @back_replicate
|
||||
|
||||
/-! ## Additional operations -/
|
||||
|
||||
/-! ### leftpad -/
|
||||
@@ -3625,6 +3745,9 @@ theorem size_rightpad {n : Nat} {a : α} {xs : Array α} :
|
||||
|
||||
theorem elem_push_self [BEq α] [LawfulBEq α] {xs : Array α} {a : α} : (xs.push a).elem a = true := by simp
|
||||
|
||||
@[deprecated elem_push_self (since := "2025-04-04")]
|
||||
abbrev elem_cons_self := @elem_push_self
|
||||
|
||||
theorem contains_eq_any_beq [BEq α] {xs : Array α} {a : α} : xs.contains a = xs.any (a == ·) := by
|
||||
rcases xs with ⟨xs⟩
|
||||
simp [List.contains_eq_any_beq]
|
||||
@@ -3638,6 +3761,11 @@ theorem contains_iff_exists_mem_beq [BEq α] {xs : Array α} {a : α} :
|
||||
-- With `LawfulBEq α`, it would be better to use `contains_iff_mem` directly.
|
||||
grind_pattern contains_iff_exists_mem_beq => xs.contains a
|
||||
|
||||
@[grind _=_]
|
||||
theorem contains_iff_mem [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
|
||||
xs.contains a ↔ a ∈ xs := by
|
||||
simp
|
||||
|
||||
@[simp, grind =]
|
||||
theorem contains_toList [BEq α] {xs : Array α} {x : α} :
|
||||
xs.toList.contains x = xs.contains x := by
|
||||
@@ -3697,6 +3825,9 @@ theorem pop_append {xs ys : Array α} :
|
||||
@[simp, grind =] theorem pop_replicate {n : Nat} {a : α} : (replicate n a).pop = replicate (n - 1) a := by
|
||||
ext <;> simp
|
||||
|
||||
@[deprecated pop_replicate (since := "2025-03-18")]
|
||||
abbrev pop_mkArray := @pop_replicate
|
||||
|
||||
/-! ## Logic -/
|
||||
|
||||
/-! ### any / all -/
|
||||
@@ -3926,10 +4057,16 @@ theorem all_filterMap {xs : Array α} {f : α → Option β} {p : β → Bool} :
|
||||
(replicate n a).any f = if n = 0 then false else f a := by
|
||||
induction n <;> simp_all [replicate_succ']
|
||||
|
||||
@[deprecated any_replicate (since := "2025-03-18")]
|
||||
abbrev any_mkArray := @any_replicate
|
||||
|
||||
@[simp] theorem all_replicate {n : Nat} {a : α} :
|
||||
(replicate n a).all f = if n = 0 then true else f a := by
|
||||
induction n <;> simp_all +contextual [replicate_succ']
|
||||
|
||||
@[deprecated all_replicate (since := "2025-03-18")]
|
||||
abbrev all_mkArray := @all_replicate
|
||||
|
||||
/-! ### modify -/
|
||||
|
||||
@[simp, grind =] theorem size_modify {xs : Array α} {i : Nat} {f : α → α} : (xs.modify i f).size = xs.size := by
|
||||
@@ -3966,29 +4103,28 @@ theorem getElem_modify_of_ne {xs : Array α} {i : Nat} (h : i ≠ j)
|
||||
|
||||
/-! ### swap -/
|
||||
|
||||
@[grind =]
|
||||
theorem getElem_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} (hk : k < (xs.swap i j hi hj).size) :
|
||||
(xs.swap i j hi hj)[k] = if k = i then xs[j] else if k = j then xs[i] else xs[k]'(by simp_all) := by
|
||||
simp only [swap_def, getElem_set, eq_comm (a := k)]
|
||||
split <;> split <;> simp_all
|
||||
|
||||
@[simp] theorem getElem_swap_right {xs : Array α} {i j : Nat} {hi hj} :
|
||||
(xs.swap i j hi hj)[j]'(by simpa using hj) = xs[i] := by
|
||||
simp +contextual [getElem_swap]
|
||||
simp [swap_def]
|
||||
|
||||
@[simp] theorem getElem_swap_left {xs : Array α} {i j : Nat} {hi hj} :
|
||||
(xs.swap i j hi hj)[i]'(by simpa using hi) = xs[j] := by
|
||||
simp [getElem_swap]
|
||||
simp +contextual [swap_def, getElem_set]
|
||||
|
||||
@[simp] theorem getElem_swap_of_ne {xs : Array α} {i j : Nat} {hi hj}
|
||||
{h : k < (xs.swap i j hi hj).size} (hi' : k ≠ i) (hj' : k ≠ j) :
|
||||
(xs.swap i j hi hj)[k] = xs[k]'(by simp_all) := by
|
||||
simp [getElem_swap, hi', hj']
|
||||
@[simp] theorem getElem_swap_of_ne {xs : Array α} {i j : Nat} {hi hj} (hp : k < xs.size)
|
||||
(hi' : k ≠ i) (hj' : k ≠ j) : (xs.swap i j hi hj)[k]'(xs.size_swap .. |>.symm ▸ hp) = xs[k] := by
|
||||
simp [swap_def, getElem_set, hi'.symm, hj'.symm]
|
||||
|
||||
@[deprecated getElem_swap (since := "2025-10-10")]
|
||||
theorem getElem_swap' {xs : Array α} {i j : Nat} {hi hj} {k : Nat} (hk : k < xs.size) :
|
||||
(xs.swap i j hi hj)[k]'(by simp_all) = if k = i then xs[j] else if k = j then xs[i] else xs[k] :=
|
||||
getElem_swap _ _ _
|
||||
(xs.swap i j hi hj)[k]'(by simp_all) = if k = i then xs[j] else if k = j then xs[i] else xs[k] := by
|
||||
split
|
||||
· simp_all only [getElem_swap_left]
|
||||
· split <;> simp_all
|
||||
|
||||
@[grind =]
|
||||
theorem getElem_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} (hk : k < (xs.swap i j hi hj).size) :
|
||||
(xs.swap i j hi hj)[k] = if k = i then xs[j] else if k = j then xs[i] else xs[k]'(by simp_all) := by
|
||||
apply getElem_swap'
|
||||
|
||||
@[simp] theorem swap_swap {xs : Array α} {i j : Nat} (hi hj) :
|
||||
(xs.swap i j hi hj).swap i j ((xs.size_swap ..).symm ▸ hi) ((xs.size_swap ..).symm ▸ hj) = xs := by
|
||||
@@ -4009,66 +4145,8 @@ theorem swap_comm {xs : Array α} {i j : Nat} (hi hj) : xs.swap i j hi hj = xs.s
|
||||
· split <;> simp_all
|
||||
· split <;> simp_all
|
||||
|
||||
/-! ### swapIfInBounds -/
|
||||
|
||||
@[grind =] theorem swapIfInBounds_def {xs : Array α} {i j : Nat} :
|
||||
xs.swapIfInBounds i j = if h₁ : i < xs.size then
|
||||
if h₂ : j < xs.size then swap xs i j else xs else xs := rfl
|
||||
|
||||
@[simp, grind =] theorem size_swapIfInBounds {xs : Array α} {i j : Nat} :
|
||||
(xs.swapIfInBounds i j).size = xs.size := by
|
||||
unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
|
||||
|
||||
@[grind =] theorem getElem_swapIfInBounds {xs : Array α} {i j k : Nat}
|
||||
(hk : k < (xs.swapIfInBounds i j).size) :
|
||||
(xs.swapIfInBounds i j)[k] =
|
||||
if h₁ : k = i ∧ j < xs.size then xs[j]'h₁.2 else if h₂ : k = j ∧ i < xs.size then xs[i]'h₂.2
|
||||
else xs[k]'(by simp_all) := by
|
||||
rw [size_swapIfInBounds] at hk
|
||||
unfold swapIfInBounds
|
||||
split <;> rename_i hi
|
||||
· split <;> rename_i hj
|
||||
· simp only [hi, hj, and_true]
|
||||
exact getElem_swap _ _ _
|
||||
· simp only [hi, hj, and_true, and_false, dite_false]
|
||||
split <;> simp_all
|
||||
· simp only [hi, and_false, dite_false]
|
||||
split <;> simp_all
|
||||
|
||||
@[simp]
|
||||
theorem getElem_swapIfInBounds_of_size_le_left {xs : Array α} {i j k : Nat} (hi : xs.size ≤ i)
|
||||
(hk : k < (xs.swapIfInBounds i j).size) :
|
||||
(xs.swapIfInBounds i j)[k] = xs[k]'(Nat.lt_of_lt_of_eq hk size_swapIfInBounds) := by
|
||||
have h₁ : k ≠ i := Nat.ne_of_lt <| Nat.lt_of_lt_of_le hk <|
|
||||
Nat.le_trans (Nat.le_of_eq (size_swapIfInBounds)) hi
|
||||
have h₂ : ¬ (i < xs.size) := Nat.not_lt_of_le hi
|
||||
simp [getElem_swapIfInBounds, h₁, h₂]
|
||||
|
||||
@[simp]
|
||||
theorem getElem_swapIfInBounds_of_size_le_right {xs : Array α} {i j k : Nat} (hj : xs.size ≤ j)
|
||||
(hk : k < (xs.swapIfInBounds i j).size) :
|
||||
(xs.swapIfInBounds i j)[k] = xs[k]'(Nat.lt_of_lt_of_eq hk size_swapIfInBounds) := by
|
||||
have h₁ : ¬ (j < xs.size) := Nat.not_lt_of_le hj
|
||||
have h₂ : k ≠ j := Nat.ne_of_lt <| Nat.lt_of_lt_of_le hk <|
|
||||
Nat.le_trans (Nat.le_of_eq (size_swapIfInBounds)) hj
|
||||
simp [getElem_swapIfInBounds, h₁, h₂]
|
||||
|
||||
@[simp]
|
||||
theorem getElem_swapIfInBounds_left {xs : Array α} {i j : Nat} (hj : j < xs.size)
|
||||
(hi : i < (xs.swapIfInBounds i j).size) : (xs.swapIfInBounds i j)[i] = xs[j] := by
|
||||
simp [getElem_swapIfInBounds, hj]
|
||||
|
||||
@[simp]
|
||||
theorem getElem_swapIfInBounds_right {xs : Array α} {i j : Nat} (hi : i < xs.size)
|
||||
(hj : j < (xs.swapIfInBounds i j).size) :
|
||||
(xs.swapIfInBounds i j)[j] = xs[i] := by
|
||||
simp +contextual [getElem_swapIfInBounds, hi]
|
||||
|
||||
@[simp]
|
||||
theorem getElem_swapIfInBounds_of_ne_of_ne {xs : Array α} {i j k : Nat} (hi : k ≠ i) (hj : k ≠ j)
|
||||
(hk : k < (xs.swapIfInBounds i j).size) :
|
||||
(xs.swapIfInBounds i j)[k] = xs[k]'(Nat.lt_of_lt_of_eq hk size_swapIfInBounds) := by
|
||||
simp [getElem_swapIfInBounds, hi, hj]
|
||||
(xs.swapIfInBounds i j).size = xs.size := by unfold swapIfInBounds; split <;> (try split) <;> simp [size_swap]
|
||||
|
||||
/-! ### swapAt -/
|
||||
|
||||
@@ -4163,11 +4241,17 @@ theorem replace_extract {xs : Array α} {i : Nat} :
|
||||
(replicate n a).replace a b = #[b] ++ replicate (n - 1) a := by
|
||||
cases n <;> simp_all [replicate_succ', replace_append]
|
||||
|
||||
@[deprecated replace_replicate_self (since := "2025-03-18")]
|
||||
abbrev replace_mkArray_self := @replace_replicate_self
|
||||
|
||||
@[simp] theorem replace_replicate_ne {a b c : α} (h : !b == a) :
|
||||
(replicate n a).replace b c = replicate n a := by
|
||||
rw [replace_of_not_mem]
|
||||
simp_all
|
||||
|
||||
@[deprecated replace_replicate_ne (since := "2025-03-18")]
|
||||
abbrev replace_mkArray_ne := @replace_replicate_ne
|
||||
|
||||
end replace
|
||||
|
||||
/-! ### toListRev -/
|
||||
@@ -4330,15 +4414,14 @@ theorem size_uset {xs : Array α} {v : α} {i : USize} (h : i.toNat < xs.size) :
|
||||
theorem getElem!_eq_getD [Inhabited α] {xs : Array α} {i} : xs[i]! = xs.getD i default := by
|
||||
rfl
|
||||
|
||||
theorem getElem_eq_getD {xs : Array α} {i} {h : i < xs.size} (fallback : α) :
|
||||
xs[i]'h = xs.getD i fallback := by
|
||||
rw [getD_eq_getD_getElem?, getElem_eq_getElem?_get, Option.get_eq_getD]
|
||||
|
||||
/-! # mem -/
|
||||
|
||||
@[deprecated mem_toList_iff (since := "2025-05-26")]
|
||||
theorem mem_toList {a : α} {xs : Array α} : a ∈ xs.toList ↔ a ∈ xs := mem_def.symm
|
||||
|
||||
@[deprecated not_mem_empty (since := "2025-03-25")]
|
||||
theorem not_mem_nil (a : α) : ¬ a ∈ #[] := nofun
|
||||
|
||||
/-! # get lemmas -/
|
||||
|
||||
theorem lt_of_getElem {x : α} {xs : Array α} {i : Nat} {hidx : i < xs.size} (_ : xs[i] = x) :
|
||||
@@ -4350,7 +4433,6 @@ theorem getElem_fin_eq_getElem_toList {xs : Array α} {i : Fin xs.size} : xs[i]
|
||||
@[simp] theorem ugetElem_eq_getElem {xs : Array α} {i : USize} (h : i.toNat < xs.size) :
|
||||
xs[i] = xs[i.toNat] := rfl
|
||||
|
||||
@[deprecated getElem?_eq_none (since := "2025-10-26")]
|
||||
theorem getElem?_size_le {xs : Array α} {i : Nat} (h : xs.size ≤ i) : xs[i]? = none := by
|
||||
simp [getElem?_neg, h]
|
||||
|
||||
@@ -4370,7 +4452,6 @@ theorem getElem?_push_lt {xs : Array α} {x : α} {i : Nat} (h : i < xs.size) :
|
||||
(xs.push x)[i]? = some xs[i] := by
|
||||
rw [getElem?_pos (xs.push x) i (size_push _ ▸ Nat.lt_succ_of_lt h), getElem_push_lt]
|
||||
|
||||
@[deprecated getElem?_push_size (since := "2025-10-26")]
|
||||
theorem getElem?_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size]? = some x := by
|
||||
rw [getElem?_pos (xs.push x) xs.size (size_push _ ▸ Nat.lt_succ_self xs.size), getElem_push_eq]
|
||||
|
||||
@@ -4389,6 +4470,12 @@ theorem getElem?_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size]? = some
|
||||
cases xs
|
||||
simp
|
||||
|
||||
/-! ### contains -/
|
||||
|
||||
@[deprecated contains_iff (since := "2025-04-07")]
|
||||
abbrev contains_def [DecidableEq α] {a : α} {xs : Array α} : xs.contains a ↔ a ∈ xs :=
|
||||
contains_iff
|
||||
|
||||
/-! ### isPrefixOf -/
|
||||
|
||||
@[simp, grind =] theorem isPrefixOf_toList [BEq α] {xs ys : Array α} :
|
||||
@@ -4502,8 +4589,7 @@ theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray
|
||||
apply ext'
|
||||
simp
|
||||
|
||||
@[deprecated Array.flatten_map_toArray_toArray (since := "2025-10-26")]
|
||||
theorem flatten_toArray {L : List (List α)} :
|
||||
@[simp, grind =] theorem flatten_toArray {L : List (List α)} :
|
||||
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
|
||||
apply ext'
|
||||
simp
|
||||
|
||||
@@ -6,6 +6,9 @@ Author: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Core
|
||||
import Init.Data.Array.Basic
|
||||
import Init.Data.Nat.Lemmas
|
||||
public import Init.Data.Range.Polymorphic.Iterators
|
||||
public import Init.Data.Range.Polymorphic.Nat
|
||||
import Init.Data.Iterators.Consumers
|
||||
|
||||
@@ -10,7 +10,9 @@ import all Init.Data.Array.Lex.Basic
|
||||
public import Init.Data.Array.Lex.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.List.Lex
|
||||
import Init.Data.Range.Polymorphic.Lemmas
|
||||
import Init.Data.Range.Polymorphic.NatLemmas
|
||||
import Init.Data.Order.Lemmas
|
||||
|
||||
public section
|
||||
|
||||
@@ -34,18 +36,7 @@ grind_pattern _root_.List.le_toArray => l₁.toArray ≤ l₂.toArray
|
||||
grind_pattern lt_toList => xs.toList < ys.toList
|
||||
grind_pattern le_toList => xs.toList ≤ ys.toList
|
||||
|
||||
@[simp]
|
||||
protected theorem not_lt [LT α] {xs ys : Array α} : ¬ xs < ys ↔ ys ≤ xs := Iff.rfl
|
||||
|
||||
@[deprecated Array.not_lt (since := "2025-10-26")]
|
||||
protected theorem not_lt_iff_ge [LT α] {xs ys : Array α} : ¬ xs < ys ↔ ys ≤ xs := Iff.rfl
|
||||
|
||||
@[simp]
|
||||
protected theorem not_le [LT α] {xs ys : Array α} :
|
||||
¬ xs ≤ ys ↔ ys < xs :=
|
||||
Classical.not_not
|
||||
|
||||
@[deprecated Array.not_le (since := "2025-10-26")]
|
||||
protected theorem not_le_iff_gt [LT α] {xs ys : Array α} :
|
||||
¬ xs ≤ ys ↔ ys < xs :=
|
||||
Classical.not_not
|
||||
@@ -75,11 +66,11 @@ private theorem cons_lex_cons [BEq α] {lt : α → α → Bool} {a b : α} {xs
|
||||
Nat.add_min_add_left, Nat.add_lt_add_iff_left, Std.Rco.forIn'_eq_forIn'_toList]
|
||||
conv =>
|
||||
lhs; congr; congr
|
||||
rw [cons_lex_cons.forIn'_congr_aux Std.Rco.toList_eq_if_roo rfl (fun _ _ _ => rfl)]
|
||||
rw [cons_lex_cons.forIn'_congr_aux Std.Rco.toList_eq_if rfl (fun _ _ _ => rfl)]
|
||||
simp only [bind_pure_comp, map_pure]
|
||||
rw [cons_lex_cons.forIn'_congr_aux (if_pos (by omega)) rfl (fun _ _ _ => rfl)]
|
||||
simp only [Std.toList_roo_eq_toList_rco_of_isSome_succ? (lo := 0) (h := rfl),
|
||||
Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_rco_succ_succ,
|
||||
simp only [Std.toList_Roo_eq_toList_Rco_of_isSome_succ? (lo := 0) (h := rfl),
|
||||
Std.PRange.UpwardEnumerable.succ?, Nat.add_comm 1, Std.PRange.Nat.toList_Rco_succ_succ,
|
||||
Option.get_some, List.forIn'_cons, List.size_toArray, List.length_cons, List.length_nil,
|
||||
Nat.lt_add_one, getElem_append_left, List.getElem_toArray, List.getElem_cons_zero]
|
||||
cases lt a b
|
||||
@@ -151,7 +142,7 @@ protected theorem lt_of_le_of_lt [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrd
|
||||
@[deprecated Array.lt_of_le_of_lt (since := "2025-08-01")]
|
||||
protected theorem lt_of_le_of_lt' [LT α]
|
||||
[i₁ : Std.Asymm (· < · : α → α → Prop)]
|
||||
[i₂ : Std.Trichotomous (· < · : α → α → Prop)]
|
||||
[i₂ : Std.Antisymm (¬ · < · : α → α → Prop)]
|
||||
[i₃ : Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
|
||||
{xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys < zs) : xs < zs :=
|
||||
letI := LE.ofLT α
|
||||
@@ -165,7 +156,7 @@ protected theorem le_trans [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α]
|
||||
@[deprecated Array.le_trans (since := "2025-08-01")]
|
||||
protected theorem le_trans' [LT α]
|
||||
[i₁ : Std.Asymm (· < · : α → α → Prop)]
|
||||
[i₂ : Std.Trichotomous (· < · : α → α → Prop)]
|
||||
[i₂ : Std.Antisymm (¬ · < · : α → α → Prop)]
|
||||
[i₃ : Trans (¬ · < · : α → α → Prop) (¬ · < ·) (¬ · < ·)]
|
||||
{xs ys zs : Array α} (h₁ : xs ≤ ys) (h₂ : ys ≤ zs) : xs ≤ zs :=
|
||||
letI := LE.ofLT α
|
||||
@@ -189,6 +180,12 @@ protected theorem le_total [LT α]
|
||||
[i : Std.Asymm (· < · : α → α → Prop)] (xs ys : Array α) : xs ≤ ys ∨ ys ≤ xs :=
|
||||
List.le_total xs.toList ys.toList
|
||||
|
||||
@[simp] protected theorem not_lt [LT α]
|
||||
{xs ys : Array α} : ¬ xs < ys ↔ ys ≤ xs := Iff.rfl
|
||||
|
||||
@[simp] protected theorem not_le [LT α]
|
||||
{xs ys : Array α} : ¬ ys ≤ xs ↔ xs < ys := Classical.not_not
|
||||
|
||||
protected theorem le_of_lt [LT α]
|
||||
[i : Std.Asymm (· < · : α → α → Prop)]
|
||||
{xs ys : Array α} (h : xs < ys) : xs ≤ ys :=
|
||||
@@ -196,7 +193,7 @@ protected theorem le_of_lt [LT α]
|
||||
|
||||
protected theorem le_iff_lt_or_eq [LT α]
|
||||
[Std.Irrefl (· < · : α → α → Prop)]
|
||||
[Std.Trichotomous (· < · : α → α → Prop)]
|
||||
[Std.Antisymm (¬ · < · : α → α → Prop)]
|
||||
[Std.Asymm (· < · : α → α → Prop)]
|
||||
{xs ys : Array α} : xs ≤ ys ↔ xs < ys ∨ xs = ys := by
|
||||
simpa using List.le_iff_lt_or_eq (l₁ := xs.toList) (l₂ := ys.toList)
|
||||
@@ -285,7 +282,7 @@ protected theorem lt_iff_exists [LT α] {xs ys : Array α} :
|
||||
|
||||
protected theorem le_iff_exists [LT α]
|
||||
[Std.Asymm (· < · : α → α → Prop)]
|
||||
[Std.Trichotomous (· < · : α → α → Prop)] {xs ys : Array α} :
|
||||
[Std.Antisymm (¬ · < · : α → α → Prop)] {xs ys : Array α} :
|
||||
xs ≤ ys ↔
|
||||
(xs = ys.take xs.size) ∨
|
||||
(∃ (i : Nat) (h₁ : i < xs.size) (h₂ : i < ys.size),
|
||||
@@ -304,7 +301,7 @@ theorem append_left_lt [LT α] {xs ys zs : Array α} (h : ys < zs) :
|
||||
|
||||
theorem append_left_le [LT α]
|
||||
[Std.Asymm (· < · : α → α → Prop)]
|
||||
[Std.Trichotomous (· < · : α → α → Prop)]
|
||||
[Std.Antisymm (¬ · < · : α → α → Prop)]
|
||||
{xs ys zs : Array α} (h : ys ≤ zs) :
|
||||
xs ++ ys ≤ xs ++ zs := by
|
||||
cases xs
|
||||
@@ -327,9 +324,9 @@ protected theorem map_lt [LT α] [LT β]
|
||||
|
||||
protected theorem map_le [LT α] [LT β]
|
||||
[Std.Asymm (· < · : α → α → Prop)]
|
||||
[Std.Trichotomous (· < · : α → α → Prop)]
|
||||
[Std.Antisymm (¬ · < · : α → α → Prop)]
|
||||
[Std.Asymm (· < · : β → β → Prop)]
|
||||
[Std.Trichotomous (· < · : β → β → Prop)]
|
||||
[Std.Antisymm (¬ · < · : β → β → Prop)]
|
||||
{xs ys : Array α} {f : α → β} (w : ∀ x y, x < y → f x < f y) (h : xs ≤ ys) :
|
||||
map f xs ≤ map f ys := by
|
||||
cases xs
|
||||
|
||||
@@ -6,7 +6,10 @@ Authors: Mario Carneiro, Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.Array.Attach
|
||||
public import Init.Data.Array.OfFn
|
||||
public import Init.Data.List.MapIdx
|
||||
import all Init.Data.List.MapIdx
|
||||
@@ -296,6 +299,9 @@ theorem mapFinIdx_eq_replicate_iff {xs : Array α} {f : (i : Nat) → α → (h
|
||||
rw [← toList_inj]
|
||||
simp [List.mapFinIdx_eq_replicate_iff]
|
||||
|
||||
@[deprecated mapFinIdx_eq_replicate_iff (since := "2025-03-18")]
|
||||
abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
|
||||
|
||||
@[simp, grind =] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) → α → (h : i < xs.reverse.size) → β} :
|
||||
xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
|
||||
rcases xs with ⟨l⟩
|
||||
@@ -435,6 +441,9 @@ theorem mapIdx_eq_replicate_iff {xs : Array α} {f : Nat → α → β} {b : β}
|
||||
rw [← toList_inj]
|
||||
simp [List.mapIdx_eq_replicate_iff]
|
||||
|
||||
@[deprecated mapIdx_eq_replicate_iff (since := "2025-03-18")]
|
||||
abbrev mapIdx_eq_mkArray_iff := @mapIdx_eq_replicate_iff
|
||||
|
||||
@[simp, grind =] theorem mapIdx_reverse {xs : Array α} {f : Nat → α → β} :
|
||||
xs.reverse.mapIdx f = (mapIdx (fun i => f (xs.size - 1 - i)) xs).reverse := by
|
||||
rcases xs with ⟨xs⟩
|
||||
|
||||
@@ -6,6 +6,8 @@ Authors: Leonardo de Moura, Joachim Breitner
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
public import Init.Data.Nat.Linear
|
||||
public import Init.Data.List.BasicAux
|
||||
|
||||
public section
|
||||
|
||||
@@ -6,9 +6,13 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.List.Control
|
||||
import all Init.Data.List.Control
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.Array.Attach
|
||||
public import Init.Data.List.Monadic
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -6,8 +6,11 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.Array.Monadic
|
||||
public import Init.Data.List.OfFn
|
||||
public import Init.Data.List.FinRange
|
||||
|
||||
public section
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.List.Nat.Perm
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
|
||||
@@ -84,6 +85,9 @@ theorem Perm.size_eq {xs ys : Array α} (p : xs ~ ys) : xs.size = ys.size := by
|
||||
simp only [perm_iff_toList_perm] at p
|
||||
simpa using p.length_eq
|
||||
|
||||
@[deprecated Perm.size_eq (since := "2025-04-17")]
|
||||
abbrev Perm.length_eq := @Perm.size_eq
|
||||
|
||||
theorem Perm.mem_iff {a : α} {xs ys : Array α} (p : xs ~ ys) : a ∈ xs ↔ a ∈ ys := by
|
||||
rcases xs with ⟨xs⟩
|
||||
rcases ys with ⟨ys⟩
|
||||
@@ -104,7 +108,7 @@ grind_pattern Perm.append => xs ~ ys, as ~ bs, ys ++ bs
|
||||
|
||||
theorem Perm.push (x : α) {xs ys : Array α} (p : xs ~ ys) :
|
||||
xs.push x ~ ys.push x := by
|
||||
rw [push_eq_append]
|
||||
rw [push_eq_append_singleton]
|
||||
exact p.append .rfl
|
||||
|
||||
grind_pattern Perm.push => xs ~ ys, xs.push x
|
||||
|
||||
@@ -6,10 +6,14 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.OfFn
|
||||
import all Init.Data.Array.OfFn
|
||||
public import Init.Data.Array.MapIdx
|
||||
public import Init.Data.Array.Zip
|
||||
public import Init.Data.List.Nat.Range
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.GetElem
|
||||
public import Init.Data.Array.Basic
|
||||
import Init.Data.Array.GetLit
|
||||
public import Init.Data.Slice.Basic
|
||||
|
||||
@@ -7,6 +7,7 @@ Authors: David Thrane Christiansen
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Subarray
|
||||
import all Init.Data.Array.Subarray
|
||||
public import Init.Omega
|
||||
|
||||
@@ -6,8 +6,10 @@ Authors: Markus Himmel
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.Lemmas
|
||||
public import Init.Data.List.Nat.TakeDrop
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -6,8 +6,10 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
import all Init.Data.Array.Basic
|
||||
public import Init.Data.Array.TakeDrop
|
||||
public import Init.Data.List.Zip
|
||||
|
||||
public section
|
||||
|
||||
@@ -166,6 +168,9 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {as : Array α} {bs : Array
|
||||
zipWith f (replicate m a) (replicate n b) = replicate (min m n) (f a b) := by
|
||||
simp [← List.toArray_replicate]
|
||||
|
||||
@[deprecated zipWith_replicate (since := "2025-03-18")]
|
||||
abbrev zipWith_mkArray := @zipWith_replicate
|
||||
|
||||
theorem map_uncurry_zip_eq_zipWith {f : α → β → γ} {as : Array α} {bs : Array β} :
|
||||
map (Function.uncurry f) (as.zip bs) = zipWith f as bs := by
|
||||
cases as
|
||||
@@ -291,6 +296,9 @@ theorem zip_eq_append_iff {as : Array α} {bs : Array β} :
|
||||
zip (replicate m a) (replicate n b) = replicate (min m n) (a, b) := by
|
||||
simp [← List.toArray_replicate]
|
||||
|
||||
@[deprecated zip_replicate (since := "2025-03-18")]
|
||||
abbrev zip_mkArray := @zip_replicate
|
||||
|
||||
theorem zip_eq_zip_take_min {as : Array α} {bs : Array β} :
|
||||
zip as bs = zip (as.take (min as.size bs.size)) (bs.take (min as.size bs.size)) := by
|
||||
cases as
|
||||
@@ -342,6 +350,9 @@ theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option
|
||||
zipWithAll f (replicate n a) (replicate n b) = replicate n (f (some a) (some b)) := by
|
||||
simp [← List.toArray_replicate]
|
||||
|
||||
@[deprecated zipWithAll_replicate (since := "2025-03-18")]
|
||||
abbrev zipWithAll_mkArray := @zipWithAll_replicate
|
||||
|
||||
/-! ### zipWithM -/
|
||||
|
||||
@[simp, grind =]
|
||||
@@ -399,4 +410,7 @@ theorem zip_of_prod {as : Array α} {bs : Array β} {xs : Array (α × β)} (hl
|
||||
unzip (replicate n (a, b)) = (replicate n a, replicate n b) := by
|
||||
ext1 <;> simp
|
||||
|
||||
@[deprecated unzip_replicate (since := "2025-03-18")]
|
||||
abbrev unzip_mkArray := @unzip_replicate
|
||||
|
||||
end Array
|
||||
|
||||
18
src/Init/Data/Basic.lean
Normal file
18
src/Init/Data/Basic.lean
Normal file
@@ -0,0 +1,18 @@
|
||||
/-
|
||||
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
|
||||
Released under Apache 2.0 license as described in the file LICENSE.
|
||||
Authors: Leonardo de Moura
|
||||
-/
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Nat.Basic
|
||||
public import Init.Data.Fin.Basic
|
||||
public import Init.Data.List.Basic
|
||||
public import Init.Data.Char.Basic
|
||||
public import Init.Data.String.Basic
|
||||
public import Init.Data.Option.Basic
|
||||
public import Init.Data.UInt
|
||||
public import Init.Data.Repr
|
||||
public import Init.Data.ToString.Basic
|
||||
public import Init.Data.String.Extra
|
||||
@@ -6,8 +6,11 @@ Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Fin.Basic
|
||||
public import Init.Data.Nat.Bitwise.Lemmas
|
||||
public import Init.Data.Nat.Power2
|
||||
public import Init.Data.Int.Bitwise.Basic
|
||||
public import Init.Data.BitVec.BasicAux
|
||||
|
||||
@[expose] public section
|
||||
|
||||
@@ -203,8 +206,8 @@ If `n` is `0`, then one digit is returned. Otherwise, `⌊(n + 3) / 4⌋` digits
|
||||
-- `Internal` string functions by moving this definition out to a separate file that can live
|
||||
-- downstream of `Init.Data.String.Basic`.
|
||||
protected def toHex {n : Nat} (x : BitVec n) : String :=
|
||||
let s := String.ofList (Nat.toDigits 16 x.toNat)
|
||||
let t := String.ofList (List.replicate ((n+3) / 4 - String.Internal.length s) '0')
|
||||
let s := (Nat.toDigits 16 x.toNat).asString
|
||||
let t := (List.replicate ((n+3) / 4 - String.Internal.length s) '0').asString
|
||||
String.Internal.append t s
|
||||
|
||||
/-- `BitVec` representation. -/
|
||||
|
||||
@@ -6,11 +6,16 @@ Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Nat.Bitwise.Basic
|
||||
import all Init.Data.Nat.Bitwise.Basic
|
||||
public import Init.Data.Nat.Mod
|
||||
public import Init.Data.Int.DivMod
|
||||
import all Init.Data.Int.DivMod
|
||||
public import Init.Data.Int.LemmasAux
|
||||
public import Init.Data.BitVec.Basic
|
||||
import all Init.Data.BitVec.Basic
|
||||
public import Init.Data.BitVec.Decidable
|
||||
public import Init.Data.BitVec.Lemmas
|
||||
public import Init.Data.BitVec.Folds
|
||||
import Init.BinderPredicates
|
||||
|
||||
@@ -635,11 +640,12 @@ theorem mulRec_eq_mul_signExtend_setWidth (x y : BitVec w) (s : Nat) :
|
||||
simp only [mulRec_zero_eq, ofNat_eq_ofNat, Nat.reduceAdd]
|
||||
by_cases y.getLsbD 0
|
||||
case pos hy =>
|
||||
simp only [hy, ↓reduceIte, setWidth_one, ofBool_true, ofNat_eq_ofNat]
|
||||
simp only [hy, ↓reduceIte, setWidth_one_eq_ofBool_getLsb_zero,
|
||||
ofBool_true, ofNat_eq_ofNat]
|
||||
rw [setWidth_ofNat_one_eq_ofNat_one_of_lt (by omega)]
|
||||
simp
|
||||
case neg hy =>
|
||||
simp [hy, setWidth_one]
|
||||
simp [hy, setWidth_one_eq_ofBool_getLsb_zero]
|
||||
case succ s' hs =>
|
||||
rw [mulRec_succ_eq, hs]
|
||||
have heq :
|
||||
@@ -1024,7 +1030,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
|
||||
case neg.hrWidth =>
|
||||
simp only
|
||||
have hdr' : d ≤ (qr.r.shiftConcat (n.getLsbD (qr.wn - 1))) :=
|
||||
BitVec.not_lt.mp rltd
|
||||
BitVec.not_lt_iff_le.mp rltd
|
||||
have hr' : ((qr.r.shiftConcat (n.getLsbD (qr.wn - 1)))).toNat < 2 ^ (qr.wr + 1) := by
|
||||
apply toNat_shiftConcat_lt_of_lt <;> bv_omega
|
||||
rw [BitVec.toNat_sub_of_le hdr']
|
||||
@@ -1032,7 +1038,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
|
||||
case neg.hqWidth =>
|
||||
apply toNat_shiftConcat_lt_of_lt <;> omega
|
||||
case neg.hdiv =>
|
||||
have rltd' := (BitVec.not_lt.mp rltd)
|
||||
have rltd' := (BitVec.not_lt_iff_le.mp rltd)
|
||||
simp only [qr.toNat_shiftRight_sub_one_eq h,
|
||||
BitVec.toNat_sub_of_le rltd',
|
||||
toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hrWidth]
|
||||
@@ -1406,7 +1412,7 @@ theorem eq_iff_eq_of_inv (f : α → BitVec w) (g : BitVec w → α) (h : ∀ x,
|
||||
have := congrArg g h'
|
||||
simpa [h] using this
|
||||
|
||||
@[deprecated BitVec.ne_intMin_of_msb_eq_false (since := "2025-10-26")]
|
||||
@[simp]
|
||||
theorem ne_intMin_of_lt_of_msb_false {x : BitVec w} (hw : 0 < w) (hx : x.msb = false) :
|
||||
x ≠ intMin w := by
|
||||
have := toNat_lt_of_msb_false hx
|
||||
@@ -1511,7 +1517,7 @@ theorem sdiv_ne_intMin_of_ne_intMin {x y : BitVec w} (h : x ≠ intMin w) :
|
||||
by_cases hx : x.msb <;> by_cases hy : y.msb
|
||||
<;> simp only [hx, hy, neg_ne_intMin_inj]
|
||||
<;> simp only [Bool.not_eq_true] at hx hy
|
||||
<;> apply ne_intMin_of_msb_eq_false (by omega)
|
||||
<;> apply ne_intMin_of_lt_of_msb_false (by omega)
|
||||
<;> rw [msb_udiv]
|
||||
<;> try simp only [hx, Bool.false_and]
|
||||
· simp [h, ne_zero_of_msb_true, hx]
|
||||
@@ -1623,7 +1629,7 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w ∨ b ≠ -1
|
||||
· have ry := (intMin_udiv_eq_intMin_iff b).mp
|
||||
simp only [hb1, imp_false] at ry
|
||||
simp [msb_udiv, ha_intMin, hb1, ry, intMin_udiv_ne_zero_of_ne_zero, hb, hb0]
|
||||
· have := @BitVec.ne_intMin_of_msb_eq_false w wpos ((-a) / b) (by simp [ha, ha0, ha_intMin])
|
||||
· have := @BitVec.ne_intMin_of_lt_of_msb_false w ((-a) / b) wpos (by simp [ha, ha0, ha_intMin])
|
||||
simp [msb_neg, h', this, ha, ha_intMin]
|
||||
rw [toInt_eq_toNat_of_msb hb, toInt_eq_neg_toNat_neg_of_msb_true ha, Int.neg_tdiv,
|
||||
Int.tdiv_eq_ediv_of_nonneg (by omega), sdiv_toInt_of_msb_true_of_msb_false]
|
||||
@@ -1634,7 +1640,7 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w ∨ b ≠ -1
|
||||
rw [toInt_udiv_of_msb ha, toInt_eq_toNat_of_msb ha]
|
||||
rw [toInt_eq_neg_toNat_neg_of_msb_true hb, Int.tdiv_neg, Int.tdiv_eq_ediv_of_nonneg (by omega)]
|
||||
· apply sdiv_ne_intMin_of_ne_intMin
|
||||
apply ne_intMin_of_msb_eq_false (by omega) ha
|
||||
apply ne_intMin_of_lt_of_msb_false (by omega) ha
|
||||
· rw [sdiv, Int.tdiv_cases, udiv_eq, neg_eq, if_pos (toInt_nonneg_of_msb_false ha),
|
||||
if_pos (toInt_nonneg_of_msb_false hb), ha, hb, toInt_udiv_of_msb ha,
|
||||
toInt_eq_toNat_of_msb ha, toInt_eq_toNat_of_msb hb]
|
||||
@@ -1926,7 +1932,7 @@ theorem toInt_sub_neg_umod {x y : BitVec w} (hxmsb : x.msb = true) (hymsb : y.ms
|
||||
rw [Int.bmod_eq_of_le (by omega) (by omega)]
|
||||
simp only [toInt_eq_toNat_of_msb hymsb, BitVec.toInt_eq_neg_toNat_neg_of_msb_true hxmsb,
|
||||
Int.dvd_neg] at hdvd
|
||||
simp only [hdvd, ↓reduceIte, Int.natAbs_natCast]
|
||||
simp only [hdvd, ↓reduceIte, Int.natAbs_cast]
|
||||
|
||||
theorem srem_zero_of_dvd {x y : BitVec w} (h : y.toInt ∣ x.toInt) :
|
||||
x.srem y = 0#w := by
|
||||
|
||||
@@ -6,8 +6,10 @@ Authors: Joe Hendrix, Harun Khan
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.BitVec.Basic
|
||||
import all Init.Data.BitVec.Basic
|
||||
public import Init.Data.BitVec.Lemmas
|
||||
public import Init.Data.Nat.Lemmas
|
||||
public import Init.Data.Fin.Iterate
|
||||
|
||||
public section
|
||||
@@ -82,7 +84,7 @@ theorem iunfoldr_getLsbD' {f : Fin w → α → α × 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]
|
||||
|
||||
@@ -6,14 +6,25 @@ Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth B
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Bool
|
||||
public import Init.Data.BitVec.Basic
|
||||
import all Init.Data.BitVec.Basic
|
||||
public import Init.Data.BitVec.BasicAux
|
||||
import all Init.Data.BitVec.BasicAux
|
||||
public import Init.Data.Fin.Lemmas
|
||||
public import Init.Data.Nat.Lemmas
|
||||
public import Init.Data.Nat.Div.Lemmas
|
||||
public import Init.Data.Nat.Mod
|
||||
public import Init.Data.Nat.Div.Lemmas
|
||||
public import Init.Data.Int.Bitwise.Lemmas
|
||||
public import Init.Data.Int.LemmasAux
|
||||
public import Init.Data.Int.Pow
|
||||
public import Init.Data.Int.LemmasAux
|
||||
public import Init.Data.BitVec.Bootstrap
|
||||
public import Init.Data.Order.Factories
|
||||
public import Init.Data.List.BasicAux
|
||||
import Init.Data.List.Lemmas
|
||||
import Init.Data.BEq
|
||||
|
||||
public section
|
||||
|
||||
@@ -34,6 +45,14 @@ namespace BitVec
|
||||
simp only [Bool.and_eq_false_imp, decide_eq_true_eq]
|
||||
omega
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getLsbD_of_ge (since := "2025-04-04")]
|
||||
abbrev getLsbD_ge := @getLsbD_of_ge
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getMsbD_of_ge (since := "2025-04-04")]
|
||||
abbrev getMsbD_ge := @getMsbD_of_ge
|
||||
|
||||
theorem lt_of_getLsbD {x : BitVec w} {i : Nat} : getLsbD x i = true → i < w := by
|
||||
if h : i < w then
|
||||
simp [h]
|
||||
@@ -64,7 +83,6 @@ theorem getElem?_eq_none_iff {l : BitVec w} : l[n]? = none ↔ w ≤ n := by
|
||||
theorem none_eq_getElem?_iff {l : BitVec w} : none = l[n]? ↔ w ≤ n := by
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem getElem?_eq_none {l : BitVec w} (h : w ≤ n) : l[n]? = none := getElem?_eq_none_iff.mpr h
|
||||
|
||||
theorem getElem?_eq (l : BitVec w) (i : Nat) :
|
||||
@@ -133,6 +151,9 @@ theorem two_pow_le_toNat_of_getElem_eq_true {i : Nat} {x : BitVec w}
|
||||
rw [← getElem_eq_testBit_toNat x i hi]
|
||||
exact hx
|
||||
|
||||
@[grind =] theorem msb_eq_getMsbD (x : BitVec w) : x.msb = x.getMsbD 0 := by
|
||||
simp [BitVec.msb]
|
||||
|
||||
@[grind =] theorem getMsb_eq_getLsb (x : BitVec w) (i : Fin w) :
|
||||
x.getMsb i = x.getLsb ⟨w - 1 - i, by omega⟩ := by
|
||||
simp only [getMsb, getLsb]
|
||||
@@ -159,13 +180,18 @@ theorem getLsbD_eq_getMsbD (x : BitVec w) (i : Nat) : x.getLsbD i = (decide (i <
|
||||
apply getLsbD_of_ge
|
||||
omega
|
||||
|
||||
@[deprecated getElem?_eq_none (since := "2025-10-29")]
|
||||
theorem getElem?_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : x[i]? = none := by
|
||||
@[simp] theorem getElem?_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : x[i]? = none := by
|
||||
simp [ge]
|
||||
|
||||
@[simp] theorem getMsb?_of_ge (x : BitVec w) (i : Nat) (ge : w ≤ i) : getMsb? x i = none := by
|
||||
simp [getMsb?_eq_getLsb?]; omega
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getElem?_of_ge (since := "2025-04-04")] abbrev getLsb?_ge := @getElem?_of_ge
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getMsb?_of_ge (since := "2025-04-04")] abbrev getMsb?_ge := @getMsb?_of_ge
|
||||
|
||||
theorem lt_of_getElem?_eq_some (x : BitVec w) (i : Nat) : x[i]? = some b → i < w := by
|
||||
cases h : x[i]? with
|
||||
| none => simp
|
||||
@@ -188,6 +214,18 @@ theorem lt_of_isSome_getMsb? (x : BitVec w) (i : Nat) : (getMsb? x i).isSome →
|
||||
else
|
||||
simp [Nat.ge_of_not_lt h]
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated lt_of_getElem?_eq_some (since := "2025-04-04")]
|
||||
abbrev lt_of_getLsb?_eq_some := @lt_of_getElem?_eq_some
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated lt_of_isSome_getElem? (since := "2025-04-04")]
|
||||
abbrev lt_of_getLsb?_isSome := @lt_of_isSome_getElem?
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated lt_of_isSome_getMsb? (since := "2025-04-04")]
|
||||
abbrev lt_of_getMsb?_isSome := @lt_of_isSome_getMsb?
|
||||
|
||||
theorem getMsbD_eq_getMsb?_getD (x : BitVec w) (i : Nat) :
|
||||
x.getMsbD i = (x.getMsb? i).getD false := by
|
||||
rw [getMsbD_eq_getLsbD]
|
||||
@@ -417,18 +455,12 @@ theorem getElem?_zero_ofNat_one : (BitVec.ofNat (w+1) 1)[0]? = some true := by
|
||||
|
||||
-- This does not need to be a `@[simp]` theorem as it is already handled by `getElem?_eq_getElem`.
|
||||
theorem getElem?_zero_ofBool (b : Bool) : (ofBool b)[0]? = some b := by
|
||||
simp only [ofBool, ofNat_eq_ofNat, cond_eq_ite]
|
||||
simp only [ofBool, ofNat_eq_ofNat, cond_eq_if]
|
||||
split <;> simp_all
|
||||
|
||||
@[simp, grind =]
|
||||
theorem getElem_ofBool_zero {b : Bool} : (ofBool b)[0] = b := by
|
||||
@[simp, grind =] theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
|
||||
rw [getElem_eq_iff, getElem?_zero_ofBool]
|
||||
|
||||
|
||||
@[deprecated getElem_ofBool_zero (since := "2025-10-29")]
|
||||
theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
|
||||
simp
|
||||
|
||||
theorem getElem?_succ_ofBool (b : Bool) (i : Nat) : (ofBool b)[i + 1]? = none := by
|
||||
simp
|
||||
|
||||
@@ -439,6 +471,8 @@ theorem getLsbD_ofBool (b : Bool) (i : Nat) : (ofBool b).getLsbD i = ((i = 0) &&
|
||||
· simp only [ofBool, ofNat_eq_ofNat, cond_true, getLsbD_ofNat, Bool.and_true]
|
||||
by_cases hi : i = 0 <;> simp [hi] <;> omega
|
||||
|
||||
theorem getElem_ofBool_zero {b : Bool} : (ofBool b)[0] = b := by simp
|
||||
|
||||
@[simp]
|
||||
theorem getElem_ofBool {b : Bool} {h : i < 1}: (ofBool b)[i] = b := by
|
||||
simp [← getLsbD_eq_getElem]
|
||||
@@ -521,10 +555,6 @@ theorem toNat_ge_of_msb_true {x : BitVec n} (p : BitVec.msb x = true) : x.toNat
|
||||
@[grind _=_] theorem msb_eq_getMsbD_zero (x : BitVec w) : x.msb = x.getMsbD 0 := by
|
||||
cases w <;> simp [getMsbD_eq_getLsbD, msb_eq_getLsbD_last]
|
||||
|
||||
@[deprecated msb_eq_getMsbD_zero (since := "2025-10-26")]
|
||||
theorem msb_eq_getMsbD (x : BitVec w) : x.msb = x.getMsbD 0 := by
|
||||
simp [BitVec.msb]
|
||||
|
||||
/-! ### cast -/
|
||||
|
||||
@[simp, grind =] theorem toFin_cast (h : w = v) (x : BitVec w) :
|
||||
@@ -586,7 +616,7 @@ theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) :=
|
||||
simp only [toInt_eq_toNat_cond]
|
||||
split
|
||||
next g =>
|
||||
rw [Int.bmod_eq_emod_of_lt] <;> simp only [←Int.natCast_emod, toNat_mod_cancel]
|
||||
rw [Int.bmod_pos] <;> simp only [←Int.natCast_emod, toNat_mod_cancel]
|
||||
omega
|
||||
next g =>
|
||||
rw [Int.bmod_neg] <;> simp only [←Int.natCast_emod, toNat_mod_cancel]
|
||||
@@ -994,14 +1024,7 @@ theorem msb_setWidth' (x : BitVec w) (h : w ≤ v) : (x.setWidth' h).msb = (deci
|
||||
theorem msb_setWidth'' (x : BitVec w) : (x.setWidth (k + 1)).msb = x.getLsbD k := by
|
||||
simp [BitVec.msb, getMsbD]
|
||||
|
||||
/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
|
||||
theorem setWidth_one {x : BitVec w} :
|
||||
x.setWidth 1 = ofBool (x.getLsbD 0) := by
|
||||
ext i
|
||||
simp [show i = 0 by omega]
|
||||
|
||||
/-- zero extending a bitvector to width 1 equals the boolean of the lsb. -/
|
||||
@[deprecated setWidth_one (since := "2025-10-29")]
|
||||
theorem setWidth_one_eq_ofBool_getLsb_zero (x : BitVec w) :
|
||||
x.setWidth 1 = BitVec.ofBool (x.getLsbD 0) := by
|
||||
ext i h
|
||||
@@ -1017,6 +1040,12 @@ theorem setWidth_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
|
||||
have hv := (@Nat.testBit_one_eq_true_iff_self_eq_zero i)
|
||||
by_cases h : Nat.testBit 1 i = true <;> simp_all
|
||||
|
||||
/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
|
||||
theorem setWidth_one {x : BitVec w} :
|
||||
x.setWidth 1 = ofBool (x.getLsbD 0) := by
|
||||
ext i
|
||||
simp [show i = 0 by omega]
|
||||
|
||||
@[simp, grind =] theorem setWidth_ofNat_of_le (h : v ≤ w) (x : Nat) : setWidth v (BitVec.ofNat w x) = BitVec.ofNat v x := by
|
||||
apply BitVec.eq_of_toNat_eq
|
||||
simp only [toNat_setWidth, toNat_ofNat]
|
||||
@@ -1056,7 +1085,7 @@ theorem toInt_setWidth' {m n : Nat} (p : m ≤ n) {x : BitVec m} :
|
||||
@[simp, grind =] theorem toFin_setWidth' {m n : Nat} (p : m ≤ n) (x : BitVec m) :
|
||||
(setWidth' p x).toFin = x.toFin.castLE (Nat.pow_le_pow_right (by omega) (by omega)) := by
|
||||
ext
|
||||
rw [setWidth'_eq, toFin_setWidth, Fin.val_ofNat, Fin.val_castLE, val_toFin,
|
||||
rw [setWidth'_eq, toFin_setWidth, Fin.val_ofNat, Fin.coe_castLE, val_toFin,
|
||||
Nat.mod_eq_of_lt (by apply BitVec.toNat_lt_twoPow_of_le p)]
|
||||
|
||||
theorem toNat_setWidth_of_le {w w' : Nat} {b : BitVec w} (h : w ≤ w') : (b.setWidth w').toNat = b.toNat := by
|
||||
@@ -1190,7 +1219,7 @@ let x' = x.extractLsb' 7 5 = _ _ 9 8 7
|
||||
|
||||
@[simp] theorem getLsbD_extract (hi lo : Nat) (x : BitVec n) (i : Nat) :
|
||||
getLsbD (extractLsb hi lo x) i = (i ≤ (hi-lo) && getLsbD x (lo+i)) := by
|
||||
simp [getLsbD, Nat.lt_succ_iff]
|
||||
simp [getLsbD, Nat.lt_succ]
|
||||
|
||||
@[simp] theorem getLsbD_extractLsb {hi lo : Nat} {x : BitVec n} {i : Nat} :
|
||||
(extractLsb hi lo x).getLsbD i = (decide (i < hi - lo + 1) && x.getLsbD (lo + i)) := by
|
||||
@@ -1646,11 +1675,11 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
|
||||
|
||||
@[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
|
||||
BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
|
||||
simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_natCast, toNat_eq, toNat_ofNatLT, toNat_not,
|
||||
simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLT, toNat_not,
|
||||
toNat_ofNat]
|
||||
cases h : Int.negSucc n % ((2 ^ w : Nat) : Int)
|
||||
case ofNat =>
|
||||
rw [Int.ofNat_eq_natCast, Int.negSucc_emod] at h
|
||||
rw [Int.ofNat_eq_coe, Int.negSucc_emod] at h
|
||||
· dsimp only
|
||||
omega
|
||||
· omega
|
||||
@@ -1732,6 +1761,9 @@ theorem not_eq_comm {x y : BitVec w} : ~~~ x = y ↔ x = ~~~ y := by
|
||||
rw [h]
|
||||
simp
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getMsbD_not (since := "2025-04-04")] abbrev getMsb_not := @getMsbD_not
|
||||
|
||||
@[simp] theorem msb_not {x : BitVec w} : (~~~x).msb = (decide (0 < w) && !x.msb) := by
|
||||
simp [BitVec.msb]
|
||||
|
||||
@@ -2551,6 +2583,10 @@ theorem signExtend_eq_setWidth_of_le (x : BitVec w) {v : Nat} (hv : v ≤ w) :
|
||||
ext i h
|
||||
simp [getElem_signExtend, show i < w by omega]
|
||||
|
||||
@[deprecated signExtend_eq_setWidth_of_le (since := "2025-03-07")]
|
||||
theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v ≤ w) :
|
||||
x.signExtend v = x.setWidth v := signExtend_eq_setWidth_of_le x hv
|
||||
|
||||
/-- Sign extending to the same bitwidth is a no op. -/
|
||||
@[simp] theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
|
||||
rw [signExtend_eq_setWidth_of_le _ (Nat.le_refl _), setWidth_eq]
|
||||
@@ -3610,6 +3646,9 @@ theorem sub_eq_add_neg {n} (x y : BitVec n) : x - y = x + - y := by
|
||||
simp only [toNat_sub, toNat_add, toNat_neg, Nat.add_mod_mod]
|
||||
rw [Nat.add_comm]
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated sub_eq_add_neg (since := "2025-04-04")] abbrev sub_toAdd := @sub_eq_add_neg
|
||||
|
||||
theorem add_left_neg (x : BitVec w) : -x + x = 0#w := by
|
||||
apply toInt_inj.mp
|
||||
simp [toInt_neg, Int.add_left_neg]
|
||||
@@ -3649,6 +3688,10 @@ theorem neg_one_eq_allOnes : -1#w = allOnes w := by
|
||||
have r : (2^w - 1) < 2^w := by omega
|
||||
simp [Nat.mod_eq_of_lt q, Nat.mod_eq_of_lt r]
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated neg_one_eq_allOnes (since := "2025-04-04")]
|
||||
abbrev negOne_eq_allOnes := @neg_one_eq_allOnes
|
||||
|
||||
theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1#w := by
|
||||
apply eq_of_toNat_eq
|
||||
simp only [toNat_neg, toNat_add, toNat_not, toNat_ofNat, Nat.add_mod_mod]
|
||||
@@ -4065,7 +4108,6 @@ protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x % y < y :=
|
||||
simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod]
|
||||
apply Nat.mod_lt
|
||||
|
||||
@[deprecated BitVec.not_lt (since := "2025-10-26")]
|
||||
theorem not_lt_iff_le {x y : BitVec w} : (¬ x < y) ↔ y ≤ x := by
|
||||
constructor <;>
|
||||
(intro h; simp only [lt_def, Nat.not_lt, le_def] at h ⊢; omega)
|
||||
@@ -4082,7 +4124,7 @@ theorem not_lt_zero {x : BitVec w} : ¬x < 0#w := of_decide_eq_false rfl
|
||||
theorem le_zero_iff {x : BitVec w} : x ≤ 0#w ↔ x = 0#w := by
|
||||
constructor
|
||||
· intro h
|
||||
have : x ≥ 0 := BitVec.not_lt.mp not_lt_zero
|
||||
have : x ≥ 0 := not_lt_iff_le.mp not_lt_zero
|
||||
exact Eq.symm (BitVec.le_antisymm this h)
|
||||
· simp_all
|
||||
|
||||
@@ -4105,7 +4147,7 @@ theorem not_allOnes_lt {x : BitVec w} : ¬allOnes w < x := by
|
||||
theorem allOnes_le_iff {x : BitVec w} : allOnes w ≤ x ↔ x = allOnes w := by
|
||||
constructor
|
||||
· intro h
|
||||
have : x ≤ allOnes w := BitVec.not_lt.mp not_allOnes_lt
|
||||
have : x ≤ allOnes w := not_lt_iff_le.mp not_allOnes_lt
|
||||
exact Eq.symm (BitVec.le_antisymm h this)
|
||||
· simp_all
|
||||
|
||||
@@ -4651,6 +4693,9 @@ theorem zero_smod {x : BitVec w} : (0#w).smod x = 0#w := by
|
||||
@[simp, grind =] theorem getLsbD_ofBoolListLE : (ofBoolListLE bs).getLsbD i = bs.getD i false := by
|
||||
induction bs generalizing i <;> cases i <;> simp_all [ofBoolListLE]
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getLsbD_ofBoolListLE (since := "2025-04-04")] abbrev getLsb_ofBoolListLE := @getLsbD_ofBoolListLE
|
||||
|
||||
@[simp, grind =] theorem getMsbD_ofBoolListLE :
|
||||
(ofBoolListLE bs).getMsbD i = (decide (i < bs.length) && bs.getD (bs.length - 1 - i) false) := by
|
||||
simp [getMsbD_eq_getLsbD]
|
||||
@@ -4721,6 +4766,14 @@ theorem getLsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
|
||||
apply getLsbD_of_ge
|
||||
omega
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getLsbD_rotateLeftAux_of_lt (since := "2025-04-04")]
|
||||
abbrev getLsbD_rotateLeftAux_of_le := @getLsbD_rotateLeftAux_of_lt
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getLsbD_rotateLeftAux_of_ge (since := "2025-04-04")]
|
||||
abbrev getLsbD_rotateLeftAux_of_geq := @getLsbD_rotateLeftAux_of_ge
|
||||
|
||||
/-- When `r < w`, we give a formula for `(x.rotateLeft r).getLsbD i`. -/
|
||||
theorem getLsbD_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
|
||||
(x.rotateLeft r).getLsbD i =
|
||||
@@ -4877,6 +4930,14 @@ theorem getLsbD_rotateRightAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
|
||||
apply getLsbD_of_ge
|
||||
omega
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getLsbD_rotateRightAux_of_lt (since := "2025-04-04")]
|
||||
abbrev getLsbD_rotateRightAux_of_le := @getLsbD_rotateRightAux_of_lt
|
||||
|
||||
set_option linter.missingDocs false in
|
||||
@[deprecated getLsbD_rotateRightAux_of_ge (since := "2025-04-04")]
|
||||
abbrev getLsbD_rotateRightAux_of_geq := @getLsbD_rotateRightAux_of_ge
|
||||
|
||||
/-- `rotateRight` equals the bit fiddling definition of `rotateRightAux` when the rotation amount is
|
||||
smaller than the bitwidth. -/
|
||||
theorem rotateRight_eq_rotateRightAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :
|
||||
|
||||
@@ -111,11 +111,35 @@ Needed for confluence of term `(a && b) ↔ a` which reduces to `(a && b) = a` v
|
||||
@[simp] theorem eq_self_and : ∀ {a b : Bool}, (a = (a && b)) ↔ (a → b) := by decide
|
||||
@[simp] theorem eq_and_self : ∀ {a b : Bool}, (b = (a && b)) ↔ (b → a) := by decide
|
||||
|
||||
@[deprecated and_eq_left_iff_imp (since := "2025-04-04")]
|
||||
abbrev and_iff_left_iff_imp := @and_eq_left_iff_imp
|
||||
|
||||
@[deprecated and_eq_right_iff_imp (since := "2025-04-04")]
|
||||
abbrev and_iff_right_iff_imp := @and_eq_right_iff_imp
|
||||
|
||||
@[deprecated eq_self_and (since := "2025-04-04")]
|
||||
abbrev iff_self_and := @eq_self_and
|
||||
|
||||
@[deprecated eq_and_self (since := "2025-04-04")]
|
||||
abbrev iff_and_self := @eq_and_self
|
||||
|
||||
@[simp] theorem not_and_eq_left_iff_and : ∀ {a b : Bool}, ((!a && b) = a) ↔ !a ∧ !b := by decide
|
||||
@[simp] theorem and_not_eq_right_iff_and : ∀ {a b : Bool}, ((a && !b) = b) ↔ !a ∧ !b := by decide
|
||||
@[simp] theorem eq_not_self_and : ∀ {a b : Bool}, (a = (!a && b)) ↔ !a ∧ !b := by decide
|
||||
@[simp] theorem eq_and_not_self : ∀ {a b : Bool}, (b = (a && !b)) ↔ !a ∧ !b := by decide
|
||||
|
||||
@[deprecated not_and_eq_left_iff_and (since := "2025-04-04")]
|
||||
abbrev not_and_iff_left_iff_imp := @not_and_eq_left_iff_and
|
||||
|
||||
@[deprecated and_not_eq_right_iff_and (since := "2025-04-04")]
|
||||
abbrev and_not_iff_right_iff_imp := @and_not_eq_right_iff_and
|
||||
|
||||
@[deprecated eq_not_self_and (since := "2025-04-04")]
|
||||
abbrev iff_not_self_and := @eq_not_self_and
|
||||
|
||||
@[deprecated eq_and_not_self (since := "2025-04-04")]
|
||||
abbrev iff_and_not_self := @eq_and_not_self
|
||||
|
||||
/-! ### or -/
|
||||
|
||||
@[simp] theorem or_self_left : ∀ (a b : Bool), (a || (a || b)) = (a || b) := by decide
|
||||
@@ -145,11 +169,35 @@ Needed for confluence of term `(a || b) ↔ a` which reduces to `(a || b) = a` v
|
||||
@[simp] theorem eq_self_or : ∀ {a b : Bool}, (a = (a || b)) ↔ (b → a) := by decide
|
||||
@[simp] theorem eq_or_self : ∀ {a b : Bool}, (b = (a || b)) ↔ (a → b) := by decide
|
||||
|
||||
@[deprecated or_eq_left_iff_imp (since := "2025-04-04")]
|
||||
abbrev or_iff_left_iff_imp := @or_eq_left_iff_imp
|
||||
|
||||
@[deprecated or_eq_right_iff_imp (since := "2025-04-04")]
|
||||
abbrev or_iff_right_iff_imp := @or_eq_right_iff_imp
|
||||
|
||||
@[deprecated eq_self_or (since := "2025-04-04")]
|
||||
abbrev iff_self_or := @eq_self_or
|
||||
|
||||
@[deprecated eq_or_self (since := "2025-04-04")]
|
||||
abbrev iff_or_self := @eq_or_self
|
||||
|
||||
@[simp] theorem not_or_eq_left_iff_and : ∀ {a b : Bool}, ((!a || b) = a) ↔ a ∧ b := by decide
|
||||
@[simp] theorem or_not_eq_right_iff_and : ∀ {a b : Bool}, ((a || !b) = b) ↔ a ∧ b := by decide
|
||||
@[simp] theorem eq_not_self_or : ∀ {a b : Bool}, (a = (!a || b)) ↔ a ∧ b := by decide
|
||||
@[simp] theorem eq_or_not_self : ∀ {a b : Bool}, (b = (a || !b)) ↔ a ∧ b := by decide
|
||||
|
||||
@[deprecated not_or_eq_left_iff_and (since := "2025-04-04")]
|
||||
abbrev not_or_iff_left_iff_imp := @not_or_eq_left_iff_and
|
||||
|
||||
@[deprecated or_not_eq_right_iff_and (since := "2025-04-04")]
|
||||
abbrev or_not_iff_right_iff_imp := @or_not_eq_right_iff_and
|
||||
|
||||
@[deprecated eq_not_self_or (since := "2025-04-04")]
|
||||
abbrev iff_not_self_or := @eq_not_self_or
|
||||
|
||||
@[deprecated eq_or_not_self (since := "2025-04-04")]
|
||||
abbrev iff_or_not_self := @eq_or_not_self
|
||||
|
||||
theorem or_comm : ∀ (x y : Bool), (x || y) = (y || x) := by decide
|
||||
instance : Std.Commutative (· || ·) := ⟨or_comm⟩
|
||||
|
||||
@@ -514,7 +562,6 @@ theorem exists_bool {p : Bool → Prop} : (∃ b, p b) ↔ p false ∨ p true :=
|
||||
theorem cond_eq_ite {α} (b : Bool) (t e : α) : cond b t e = if b then t else e := by
|
||||
cases b <;> simp
|
||||
|
||||
@[deprecated cond_eq_ite (since := "2025-10-29")]
|
||||
theorem cond_eq_if : (bif b then x else y) = (if b then x else y) := cond_eq_ite b x y
|
||||
|
||||
@[simp] theorem cond_not (b : Bool) (t e : α) : cond (!b) t e = cond b e t := by
|
||||
@@ -574,6 +621,11 @@ protected theorem cond_false {α : Sort u} {a b : α} : cond false a b = b := co
|
||||
@[simp] theorem cond_then_self : ∀ (c b : Bool), cond c c b = (c || b) := by decide
|
||||
@[simp] theorem cond_else_self : ∀ (c b : Bool), cond c b c = (c && b) := by decide
|
||||
|
||||
@[deprecated cond_then_not_self (since := "2025-04-04")] abbrev cond_true_not_same := @cond_then_not_self
|
||||
@[deprecated cond_else_not_self (since := "2025-04-04")] abbrev cond_false_not_same := @cond_else_not_self
|
||||
@[deprecated cond_then_self (since := "2025-04-04")] abbrev cond_true_same := @cond_then_self
|
||||
@[deprecated cond_else_self (since := "2025-04-04")] abbrev cond_false_same := @cond_else_self
|
||||
|
||||
theorem cond_pos {b : Bool} {a a' : α} (h : b = true) : (bif b then a else a') = a := by
|
||||
rw [h, cond_true]
|
||||
|
||||
@@ -613,7 +665,7 @@ theorem decide_beq_decide (p q : Prop) [dpq : Decidable (p ↔ q)] [dp : Decidab
|
||||
|
||||
end Bool
|
||||
|
||||
export Bool (cond_eq_if cond_eq_ite xor and or not)
|
||||
export Bool (cond_eq_if xor and or not)
|
||||
|
||||
/-! ### decide -/
|
||||
|
||||
|
||||
@@ -6,8 +6,11 @@ Author: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.DecidableEq
|
||||
public import Init.Data.UInt.Basic
|
||||
public import Init.Data.UInt.BasicAux
|
||||
import all Init.Data.UInt.BasicAux
|
||||
public import Init.Data.Option.Basic
|
||||
public import Init.Data.Array.Extract
|
||||
|
||||
set_option doc.verso true
|
||||
@@ -24,6 +27,9 @@ attribute [ext] ByteArray
|
||||
instance : DecidableEq ByteArray :=
|
||||
fun _ _ => decidable_of_decidable_of_iff ByteArray.ext_iff.symm
|
||||
|
||||
@[deprecated emptyWithCapacity (since := "2025-03-12")]
|
||||
abbrev mkEmpty := emptyWithCapacity
|
||||
|
||||
instance : Inhabited ByteArray where
|
||||
default := empty
|
||||
|
||||
@@ -132,11 +138,6 @@ Copies the bytes with indices {name}`b` (inclusive) to {name}`e` (exclusive) to
|
||||
def extract (a : ByteArray) (b e : Nat) : ByteArray :=
|
||||
a.copySlice b empty 0 (e - b)
|
||||
|
||||
/--
|
||||
Appends two byte arrays using fast array primitives instead of converting them into lists and back.
|
||||
|
||||
In compiled code, this function replaces calls to {name}`ByteArray.append`.
|
||||
-/
|
||||
@[inline]
|
||||
protected def fastAppend (a : ByteArray) (b : ByteArray) : ByteArray :=
|
||||
-- we assume that `append`s may be repeated, so use asymptotic growing; use `copySlice` directly to customize
|
||||
@@ -248,7 +249,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : ByteAr
|
||||
| ForInStep.yield b => loop i (Nat.le_of_lt h') b
|
||||
loop as.size (Nat.le_refl _) b
|
||||
|
||||
instance [Monad m] : ForIn m ByteArray UInt8 where
|
||||
instance : ForIn m ByteArray UInt8 where
|
||||
forIn := ByteArray.forIn
|
||||
|
||||
/--
|
||||
|
||||
@@ -6,6 +6,7 @@ Author: Markus Himmel
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Prelude
|
||||
public import Init.Data.List.Basic
|
||||
|
||||
public section
|
||||
|
||||
@@ -7,11 +7,10 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.ByteArray.Basic
|
||||
public import Init.Data.Array.Extract
|
||||
|
||||
public section
|
||||
|
||||
namespace ByteArray
|
||||
|
||||
-- At present the preferred normal form for empty byte arrays is `ByteArray.empty`
|
||||
@[simp]
|
||||
theorem emptyc_eq_empty : (∅ : ByteArray) = ByteArray.empty := rfl
|
||||
@@ -20,10 +19,10 @@ theorem emptyc_eq_empty : (∅ : ByteArray) = ByteArray.empty := rfl
|
||||
theorem emptyWithCapacity_eq_empty : ByteArray.emptyWithCapacity 0 = ByteArray.empty := rfl
|
||||
|
||||
@[simp]
|
||||
theorem data_empty : ByteArray.empty.data = #[] := rfl
|
||||
theorem ByteArray.data_empty : ByteArray.empty.data = #[] := rfl
|
||||
|
||||
@[simp]
|
||||
theorem data_extract {a : ByteArray} {b e : Nat} :
|
||||
theorem ByteArray.data_extract {a : ByteArray} {b e : Nat} :
|
||||
(a.extract b e).data = a.data.extract b e := by
|
||||
simp [extract, copySlice]
|
||||
by_cases b ≤ e
|
||||
@@ -31,39 +30,39 @@ theorem data_extract {a : ByteArray} {b e : Nat} :
|
||||
· rw [Array.extract_eq_empty_of_le (by omega), Array.extract_eq_empty_of_le (by omega)]
|
||||
|
||||
@[simp]
|
||||
theorem extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
|
||||
theorem ByteArray.extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
|
||||
theorem ByteArray.extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
|
||||
ext1
|
||||
simp [Nat.min_le_left]
|
||||
|
||||
theorem fastAppend_eq_copySlice {a b : ByteArray} :
|
||||
theorem ByteArray.fastAppend_eq_copySlice {a b : ByteArray} :
|
||||
a.fastAppend b = b.copySlice 0 a a.size b.size false := rfl
|
||||
|
||||
@[simp]
|
||||
theorem _root_.List.toByteArray_append {l l' : List UInt8} :
|
||||
theorem List.toByteArray_append {l l' : List UInt8} :
|
||||
(l ++ l').toByteArray = l.toByteArray ++ l'.toByteArray := by
|
||||
simp [List.toByteArray_append']
|
||||
|
||||
@[simp]
|
||||
theorem toList_data_append {l l' : ByteArray} :
|
||||
theorem ByteArray.toList_data_append {l l' : ByteArray} :
|
||||
(l ++ l').data.toList = l.data.toList ++ l'.data.toList := by
|
||||
simp [← append_eq]
|
||||
|
||||
@[simp]
|
||||
theorem data_append {l l' : ByteArray} :
|
||||
theorem ByteArray.data_append {l l' : ByteArray} :
|
||||
(l ++ l').data = l.data ++ l'.data := by
|
||||
simp [← Array.toList_inj]
|
||||
|
||||
@[simp]
|
||||
theorem size_empty : ByteArray.empty.size = 0 := by
|
||||
theorem ByteArray.size_empty : ByteArray.empty.size = 0 := by
|
||||
simp [← ByteArray.size_data]
|
||||
|
||||
@[simp]
|
||||
theorem _root_.List.data_toByteArray {l : List UInt8} :
|
||||
theorem List.data_toByteArray {l : List UInt8} :
|
||||
l.toByteArray.data = l.toArray := by
|
||||
rw [List.toByteArray]
|
||||
suffices ∀ a b, (List.toByteArray.loop a b).data = b.data ++ a.toArray by
|
||||
@@ -72,159 +71,153 @@ theorem _root_.List.data_toByteArray {l : List UInt8} :
|
||||
fun_induction List.toByteArray.loop a b with simp_all
|
||||
|
||||
@[simp]
|
||||
theorem _root_.List.size_toByteArray {l : List UInt8} :
|
||||
theorem List.size_toByteArray {l : List UInt8} :
|
||||
l.toByteArray.size = l.length := by
|
||||
simp [← ByteArray.size_data]
|
||||
|
||||
@[simp]
|
||||
theorem _root_.List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
|
||||
theorem List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
|
||||
|
||||
@[simp]
|
||||
theorem empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
|
||||
theorem ByteArray.empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
|
||||
theorem ByteArray.append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
@[simp, grind =]
|
||||
theorem size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
|
||||
theorem ByteArray.size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
|
||||
simp [← size_data]
|
||||
|
||||
@[simp]
|
||||
theorem size_eq_zero_iff {a : ByteArray} : a.size = 0 ↔ a = ByteArray.empty := by
|
||||
theorem ByteArray.size_eq_zero_iff {a : ByteArray} : a.size = 0 ↔ a = ByteArray.empty := by
|
||||
refine ⟨fun h => ?_, fun h => h ▸ ByteArray.size_empty⟩
|
||||
ext1
|
||||
simp [← Array.size_eq_zero_iff, h]
|
||||
|
||||
theorem getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
|
||||
theorem ByteArray.getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
|
||||
a[i] = a.data[i]'(by simpa [← size_data]) := rfl
|
||||
|
||||
@[simp]
|
||||
theorem getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
|
||||
theorem ByteArray.getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
|
||||
(hlt : i < a.size) : (a ++ b)[i] = a[i] := by
|
||||
simp only [getElem_eq_getElem_data, data_append]
|
||||
rw [Array.getElem_append_left (by simpa)]
|
||||
|
||||
theorem getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
|
||||
theorem ByteArray.getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
|
||||
(hle : a.size ≤ i) : (a ++ b)[i] = b[i - a.size]'(by simp_all; omega) := by
|
||||
simp only [getElem_eq_getElem_data, data_append]
|
||||
rw [Array.getElem_append_right (by simpa)]
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem _root_.List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
|
||||
theorem List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
|
||||
l.toByteArray[i]'h = l[i]'(by simp_all) := by
|
||||
simp [ByteArray.getElem_eq_getElem_data]
|
||||
|
||||
theorem _root_.List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
|
||||
theorem List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
|
||||
l[i]'h = l.toByteArray[i]'(by simp_all) := by
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem size_extract {a : ByteArray} {b e : Nat} :
|
||||
theorem ByteArray.size_extract {a : ByteArray} {b e : Nat} :
|
||||
(a.extract b e).size = min e a.size - b := by
|
||||
simp [← size_data]
|
||||
|
||||
@[simp]
|
||||
theorem extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty ↔ min j b.size ≤ i := by
|
||||
theorem ByteArray.extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty ↔ min j b.size ≤ i := by
|
||||
rw [← size_eq_zero_iff, size_extract]
|
||||
omega
|
||||
|
||||
@[simp]
|
||||
theorem extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
|
||||
theorem ByteArray.extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
|
||||
simp only [extract_eq_empty_iff]
|
||||
exact Nat.le_trans (Nat.min_le_left _ _) (by simp)
|
||||
|
||||
@[simp]
|
||||
theorem append_eq_empty_iff {a b : ByteArray} :
|
||||
theorem ByteArray.append_eq_empty_iff {a b : ByteArray} :
|
||||
a ++ b = ByteArray.empty ↔ a = ByteArray.empty ∧ b = ByteArray.empty := by
|
||||
simp [← size_eq_zero_iff, size_append]
|
||||
|
||||
@[simp]
|
||||
theorem toByteArray_eq_empty {l : List UInt8} :
|
||||
theorem List.toByteArray_eq_empty {l : List UInt8} :
|
||||
l.toByteArray = ByteArray.empty ↔ l = [] := by
|
||||
simp [← ByteArray.size_eq_zero_iff]
|
||||
|
||||
@[simp]
|
||||
theorem append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
|
||||
theorem ByteArray.append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
|
||||
xs ++ ys₁ = xs ++ ys₂ ↔ ys₁ = ys₂ := by
|
||||
simp [ByteArray.ext_iff, Array.append_right_inj]
|
||||
|
||||
@[simp]
|
||||
theorem append_left_inj {xs₁ xs₂ : ByteArray} (ys : ByteArray) :
|
||||
xs₁ ++ ys = xs₂ ++ ys ↔ xs₁ = xs₂ := by
|
||||
simp [ByteArray.ext_iff, Array.append_left_inj]
|
||||
|
||||
@[simp]
|
||||
theorem extract_append_extract {a : ByteArray} {i j k : Nat} :
|
||||
theorem ByteArray.extract_append_extract {a : ByteArray} {i j k : Nat} :
|
||||
a.extract i j ++ a.extract j k = a.extract (min i j) (max j k) := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
theorem extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
|
||||
theorem ByteArray.extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
|
||||
(hi : i ≤ j) (hk : j ≤ k) :
|
||||
a.extract i k = a.extract i j ++ a.extract j k := by
|
||||
simp
|
||||
rw [Nat.min_eq_left hi, Nat.max_eq_right hk]
|
||||
|
||||
theorem append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
|
||||
theorem ByteArray.append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
|
||||
simp only [ByteArray.ext_iff, ← ByteArray.size_data, ByteArray.data_append] at *
|
||||
exact Array.append_inj_left h hl
|
||||
|
||||
theorem extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
|
||||
theorem ByteArray.extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
|
||||
(a ++ b).extract i j = b := by
|
||||
subst hi hj
|
||||
ext1
|
||||
simp [← size_data]
|
||||
|
||||
theorem extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
|
||||
theorem ByteArray.extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
|
||||
(a ++ b).extract 0 i = a := by
|
||||
subst hi
|
||||
ext1
|
||||
simp
|
||||
|
||||
theorem extract_append_size_left {a b : ByteArray} {i : Nat} :
|
||||
theorem ByteArray.extract_append_size_left {a b : ByteArray} {i : Nat} :
|
||||
(a ++ b).extract i a.size = a.extract i a.size := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
theorem extract_append_size_add {a b : ByteArray} {i j : Nat} :
|
||||
theorem ByteArray.extract_append_size_add {a b : ByteArray} {i j : Nat} :
|
||||
(a ++ b).extract (a.size + i) (a.size + j) = b.extract i j := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
theorem extract_append {as bs : ByteArray} {i j : Nat} :
|
||||
theorem ByteArray.extract_append {as bs : ByteArray} {i j : Nat} :
|
||||
(as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
theorem extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
|
||||
theorem ByteArray.extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
|
||||
(a ++ b).extract (k + i) (k + j) = b.extract i j := by
|
||||
cases h
|
||||
rw [extract_append_size_add]
|
||||
|
||||
theorem extract_extract {a : ByteArray} {i j k l : Nat} :
|
||||
theorem ByteArray.extract_extract {a : ByteArray} {i j k l : Nat} :
|
||||
(a.extract i j).extract k l = a.extract (i + k) (min (i + l) j) := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
theorem getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
|
||||
theorem ByteArray.getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
|
||||
start + i < xs.size := by
|
||||
rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
|
||||
apply Nat.sub_le_sub_right; apply Nat.min_le_right
|
||||
|
||||
theorem getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
|
||||
theorem ByteArray.getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
|
||||
(h) : (b.extract start stop)[i]'h = b[start + i]'(getElem_extract_aux h) := by
|
||||
simp [getElem_eq_getElem_data]
|
||||
|
||||
theorem extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
|
||||
theorem ByteArray.extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
|
||||
a.extract i j = a.extract i' j ↔ min j a.size - i = min j a.size - i' := by
|
||||
simp [ByteArray.ext_iff, Array.extract_eq_extract_left]
|
||||
|
||||
theorem extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 ≤ a.size) :
|
||||
theorem ByteArray.extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 ≤ a.size) :
|
||||
a.extract i (i + 1) = [a[i]].toByteArray := by
|
||||
ext
|
||||
· simp
|
||||
@@ -233,57 +226,34 @@ theorem extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 ≤ a.size) :
|
||||
obtain rfl : j = 0 := by simpa using hj'
|
||||
simp [ByteArray.getElem_eq_getElem_data]
|
||||
|
||||
theorem extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 ≤ a.size) :
|
||||
theorem ByteArray.extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 ≤ a.size) :
|
||||
a.extract i (i + 2) = [a[i], a[i + 1]].toByteArray := by
|
||||
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
|
||||
extract_add_one (by omega), extract_add_one (by omega)]
|
||||
simp [← List.toByteArray_append]
|
||||
|
||||
theorem extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 ≤ a.size) :
|
||||
theorem ByteArray.extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 ≤ a.size) :
|
||||
a.extract i (i + 3) = [a[i], a[i + 1], a[i + 2]].toByteArray := by
|
||||
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
|
||||
extract_add_one (by omega), extract_add_two (by omega)]
|
||||
simp [← List.toByteArray_append]
|
||||
|
||||
theorem extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 ≤ a.size) :
|
||||
theorem ByteArray.extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 ≤ a.size) :
|
||||
a.extract i (i + 4) = [a[i], a[i + 1], a[i + 2], a[i + 3]].toByteArray := by
|
||||
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
|
||||
extract_add_one (by omega), extract_add_three (by omega)]
|
||||
simp [← List.toByteArray_append]
|
||||
|
||||
theorem append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
|
||||
theorem ByteArray.append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem toList_empty : ByteArray.empty.toList = [] := by
|
||||
theorem ByteArray.toList_empty : ByteArray.empty.toList = [] := by
|
||||
simp [ByteArray.toList, ByteArray.toList.loop]
|
||||
|
||||
theorem copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
|
||||
theorem ByteArray.copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
|
||||
ByteArray.copySlice src srcOff dest destOff len exact =
|
||||
dest.extract 0 destOff ++ src.extract srcOff (srcOff +len) ++ dest.extract (destOff + min len (src.data.size - srcOff)) dest.data.size := by
|
||||
ext1
|
||||
simp [copySlice]
|
||||
|
||||
@[simp]
|
||||
theorem data_set {as : ByteArray} {i : Nat} {h : i < as.size} {a : UInt8} :
|
||||
(as.set i a h).data = as.data.set i a (by simpa) := by
|
||||
simp [set]
|
||||
|
||||
theorem set_eq_push_extract_append_extract {as : ByteArray} {i : Nat} (h : i < as.size) {a : UInt8} :
|
||||
as.set i a h = (as.extract 0 i).push a ++ as.extract (i + 1) as.size := by
|
||||
ext1
|
||||
simpa using Array.set_eq_push_extract_append_extract _
|
||||
|
||||
@[simp]
|
||||
theorem append_toByteArray_singleton {as : ByteArray} {a : UInt8} :
|
||||
as ++ [a].toByteArray = as.push a := by
|
||||
ext1
|
||||
simp
|
||||
|
||||
@[simp]
|
||||
theorem extract_zero_max_size {a : ByteArray} {i : Nat} : a.extract 0 (max i a.size) = a := by
|
||||
ext1
|
||||
simp [Nat.le_max_right]
|
||||
|
||||
end ByteArray
|
||||
|
||||
@@ -6,6 +6,7 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Char.Basic
|
||||
import all Init.Data.Char.Basic
|
||||
public import Init.Data.UInt.Lemmas
|
||||
|
||||
@@ -13,16 +14,12 @@ public section
|
||||
|
||||
namespace Char
|
||||
|
||||
@[deprecated Char.ext (since := "2025-10-26")]
|
||||
protected theorem eq_of_val_eq : {a b : Char} → a.val = b.val → a = b
|
||||
@[ext] protected theorem ext : {a b : Char} → a.val = b.val → a = b
|
||||
| ⟨_,_⟩, ⟨_,_⟩, rfl => rfl
|
||||
|
||||
theorem le_def {a b : Char} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
|
||||
theorem lt_def {a b : Char} : a < b ↔ a.1 < b.1 := .rfl
|
||||
|
||||
@[deprecated lt_def (since := "2025-10-26")]
|
||||
theorem lt_iff_val_lt_val {a b : Char} : a < b ↔ a.val < b.val := Iff.rfl
|
||||
|
||||
@[simp] protected theorem not_le {a b : Char} : ¬ a ≤ b ↔ b < a := UInt32.not_le
|
||||
@[simp] protected theorem not_lt {a b : Char} : ¬ a < b ↔ b ≤ a := UInt32.not_lt
|
||||
@[simp] protected theorem le_refl (a : Char) : a ≤ a := by simp [le_def]
|
||||
@@ -55,12 +52,8 @@ instance leAntisymm : Std.Antisymm (· ≤ · : Char → Char → Prop) where
|
||||
antisymm _ _ := Char.le_antisymm
|
||||
|
||||
-- This instance is useful while setting up instances for `String`.
|
||||
instance ltTrichotomous : Std.Trichotomous (· < · : Char → Char → Prop) where
|
||||
trichotomous _ _ h₁ h₂ := Char.le_antisymm (by simpa using h₂) (by simpa using h₁)
|
||||
|
||||
@[deprecated ltTrichotomous (since := "2025-10-27")]
|
||||
def notLTAntisymm : Std.Antisymm (¬ · < · : Char → Char → Prop) where
|
||||
antisymm := Char.ltTrichotomous.trichotomous
|
||||
antisymm _ _ h₁ h₂ := Char.le_antisymm (by simpa using h₂) (by simpa using h₁)
|
||||
|
||||
instance ltAsymm : Std.Asymm (· < · : Char → Char → Prop) where
|
||||
asymm _ _ := Char.lt_asymm
|
||||
@@ -77,9 +70,4 @@ def notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
|
||||
rw [Char.ofNat, dif_pos]
|
||||
rfl
|
||||
|
||||
@[simp]
|
||||
theorem toUInt8_val {c : Char} : c.val.toUInt8 = c.toUInt8 := rfl
|
||||
|
||||
theorem toString_eq_singleton {c : Char} : c.toString = String.singleton c := rfl
|
||||
|
||||
end Char
|
||||
|
||||
@@ -8,6 +8,7 @@ module
|
||||
prelude
|
||||
public import Init.Data.Rat.Lemmas
|
||||
import Init.Data.Int.Bitwise.Lemmas
|
||||
import Init.Data.Int.DivMod.Lemmas
|
||||
import Init.Hints
|
||||
|
||||
/-!
|
||||
@@ -287,7 +288,7 @@ theorem toRat_add (x y : Dyadic) : toRat (x + y) = toRat x + toRat y := by
|
||||
· rename_i h
|
||||
cases Int.sub_eq_iff_eq_add.mp h
|
||||
rw [toRat_ofOdd_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
|
||||
simp only [succ_eq_add_one, Int.ofNat_eq_natCast, Int.add_shiftLeft, ← Int.shiftLeft_add,
|
||||
simp only [succ_eq_add_one, Int.ofNat_eq_coe, Int.add_shiftLeft, ← Int.shiftLeft_add,
|
||||
Int.natCast_mul, Int.natCast_shiftLeft, Int.shiftLeft_mul_shiftLeft, Int.add_mul]
|
||||
congr 2 <;> omega
|
||||
· rename_i h
|
||||
@@ -438,13 +439,13 @@ theorem toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
|
||||
rcases h : mkRat a b with ⟨n, d, hnz, hr⟩
|
||||
obtain ⟨m, hm, rfl, rfl⟩ := Rat.mkRat_num_den hb h
|
||||
cases prec
|
||||
· simp only [Rat.toDyadic, Int.ofNat_eq_natCast, Int.toNat_natCast, Int.toNat_neg_natCast,
|
||||
· simp only [Rat.toDyadic, Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast,
|
||||
shiftLeft_zero, Int.natCast_mul]
|
||||
rw [Int.mul_comm d, ← Int.ediv_ediv_of_nonneg (by simp), ← Int.shiftLeft_mul,
|
||||
rw [Int.mul_comm d, ← Int.ediv_ediv (by simp), ← Int.shiftLeft_mul,
|
||||
Int.mul_ediv_cancel _ (by simpa using hm)]
|
||||
· simp only [Rat.toDyadic, Int.natCast_shiftLeft, Int.negSucc_eq, ← Int.natCast_add_one,
|
||||
Int.toNat_neg_natCast, Int.shiftLeft_zero, Int.neg_neg, Int.toNat_natCast, Int.natCast_mul]
|
||||
rw [Int.mul_comm d, ← Int.mul_shiftLeft, ← Int.ediv_ediv_of_nonneg (by simp),
|
||||
rw [Int.mul_comm d, ← Int.mul_shiftLeft, ← Int.ediv_ediv (by simp),
|
||||
Int.mul_ediv_cancel _ (by simpa using hm)]
|
||||
|
||||
theorem toDyadic_eq_ofIntWithPrec (x : Rat) (prec : Int) :
|
||||
@@ -463,7 +464,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
|
||||
rw [Rat.floor_def, Int.shiftLeft_eq, Nat.shiftLeft_eq]
|
||||
match prec with
|
||||
| .ofNat prec =>
|
||||
simp only [Int.ofNat_eq_natCast, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
|
||||
simp only [Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
|
||||
Nat.mul_one]
|
||||
have : (2 ^ prec : Rat) = ((2 ^ prec : Nat) : Rat) := by simp
|
||||
rw [Rat.zpow_natCast, this, Rat.mul_def']
|
||||
@@ -472,7 +473,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
|
||||
Rat.den_ofNat, Nat.one_pow, Nat.mul_one]
|
||||
split
|
||||
· simp_all
|
||||
· rw [Int.ediv_ediv_of_nonneg (Int.natCast_nonneg _)]
|
||||
· rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
|
||||
congr 1
|
||||
rw [Int.natCast_ediv, Int.mul_ediv_cancel']
|
||||
rw [Int.natCast_dvd_natCast]
|
||||
@@ -495,7 +496,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
|
||||
simp only [this, Int.mul_one]
|
||||
split
|
||||
· simp_all
|
||||
· rw [Int.ediv_ediv_of_nonneg (Int.natCast_nonneg _)]
|
||||
· rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
|
||||
congr 1
|
||||
rw [Int.natCast_ediv, Int.mul_ediv_cancel']
|
||||
· simp
|
||||
@@ -682,11 +683,9 @@ instance : LE Dyadic where
|
||||
instance : DecidableLT Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
|
||||
instance : DecidableLE Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
|
||||
|
||||
@[simp]
|
||||
theorem toRat_lt_toRat_iff {x y : Dyadic} : x.toRat < y.toRat ↔ x < y := blt_iff_toRat.symm
|
||||
theorem lt_iff_toRat {x y : Dyadic} : x < y ↔ x.toRat < y.toRat := blt_iff_toRat
|
||||
|
||||
@[simp]
|
||||
theorem toRat_le_toRat_iff {x y : Dyadic} : x.toRat ≤ y.toRat ↔ x ≤ y := ble_iff_toRat.symm
|
||||
theorem le_iff_toRat {x y : Dyadic} : x ≤ y ↔ x.toRat ≤ y.toRat := ble_iff_toRat
|
||||
|
||||
@[simp]
|
||||
protected theorem not_le {x y : Dyadic} : ¬x < y ↔ y ≤ x := by
|
||||
@@ -698,20 +697,20 @@ protected theorem not_lt {x y : Dyadic} : ¬x ≤ y ↔ y < x := by
|
||||
|
||||
@[simp]
|
||||
protected theorem le_refl (x : Dyadic) : x ≤ x := by
|
||||
rw [← toRat_le_toRat_iff]
|
||||
rw [le_iff_toRat]
|
||||
exact Rat.le_refl
|
||||
|
||||
protected theorem le_trans {x y z : Dyadic} (h : x ≤ y) (h' : y ≤ z) : x ≤ z := by
|
||||
rw [← toRat_le_toRat_iff] at h h' ⊢
|
||||
rw [le_iff_toRat] at h h' ⊢
|
||||
exact Rat.le_trans h h'
|
||||
|
||||
protected theorem le_antisymm {x y : Dyadic} (h : x ≤ y) (h' : y ≤ x) : x = y := by
|
||||
rw [← toRat_le_toRat_iff] at h h'
|
||||
rw [le_iff_toRat] at h h'
|
||||
rw [← toRat_inj]
|
||||
exact Rat.le_antisymm h h'
|
||||
|
||||
protected theorem le_total (x y : Dyadic) : x ≤ y ∨ y ≤ x := by
|
||||
rw [← toRat_le_toRat_iff, ← toRat_le_toRat_iff]
|
||||
rw [le_iff_toRat, le_iff_toRat]
|
||||
exact Rat.le_total
|
||||
|
||||
instance : Std.LawfulOrderLT Dyadic where
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Dyadic.Basic
|
||||
public import Init.Grind.Ring.Basic
|
||||
public import Init.Grind.Ordered.Ring
|
||||
|
||||
/-! # Internal `grind` algebra instances for `Dyadic`. -/
|
||||
@@ -52,8 +53,8 @@ instance : NoNatZeroDivisors Dyadic where
|
||||
|
||||
instance : OrderedRing Dyadic where
|
||||
zero_lt_one := by decide
|
||||
add_le_left_iff _ := by simp [← toRat_le_toRat_iff, Rat.add_le_add_right]
|
||||
mul_lt_mul_of_pos_left {_ _ _} := by simpa [← toRat_lt_toRat_iff] using Rat.mul_lt_mul_of_pos_left
|
||||
mul_lt_mul_of_pos_right {_ _ _} := by simpa [← toRat_lt_toRat_iff] using Rat.mul_lt_mul_of_pos_right
|
||||
add_le_left_iff _ := by simp [le_iff_toRat, Rat.add_le_add_right]
|
||||
mul_lt_mul_of_pos_left {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_left
|
||||
mul_lt_mul_of_pos_right {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_right
|
||||
|
||||
end Dyadic
|
||||
|
||||
@@ -5,6 +5,7 @@ Authors: Kim Morrison
|
||||
-/
|
||||
module
|
||||
prelude
|
||||
import Init.Data.Dyadic.Basic
|
||||
import Init.Data.Dyadic.Round
|
||||
import Init.Grind.Ordered.Ring
|
||||
|
||||
@@ -27,7 +28,7 @@ def invAtPrec (x : Dyadic) (prec : Int) : Dyadic :=
|
||||
/-- For a positive dyadic `x`, `invAtPrec x prec * x ≤ 1`. -/
|
||||
theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
|
||||
invAtPrec x prec * x ≤ 1 := by
|
||||
rw [← toRat_le_toRat_iff]
|
||||
rw [le_iff_toRat]
|
||||
rw [toRat_mul]
|
||||
rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
|
||||
unfold invAtPrec
|
||||
@@ -39,19 +40,19 @@ theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
|
||||
simp only
|
||||
have h_le : ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat ≤ (ofOdd n k hn).toRat.inv := Rat.toRat_toDyadic_le
|
||||
have h_pos : 0 ≤ (ofOdd n k hn).toRat := by
|
||||
rw [← toRat_lt_toRat_iff, toRat_zero] at hx
|
||||
rw [lt_iff_toRat, toRat_zero] at hx
|
||||
exact Rat.le_of_lt hx
|
||||
calc ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat * (ofOdd n k hn).toRat
|
||||
≤ (ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := Rat.mul_le_mul_of_nonneg_right h_le h_pos
|
||||
_ = 1 := by
|
||||
apply Rat.inv_mul_cancel
|
||||
rw [← toRat_lt_toRat_iff, toRat_zero] at hx
|
||||
rw [lt_iff_toRat, toRat_zero] at hx
|
||||
exact Rat.ne_of_gt hx
|
||||
|
||||
/-- For a positive dyadic `x`, `1 < (invAtPrec x prec + 2^(-prec)) * x`. -/
|
||||
theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
|
||||
1 < (invAtPrec x prec + ofIntWithPrec 1 prec) * x := by
|
||||
rw [← toRat_lt_toRat_iff]
|
||||
rw [lt_iff_toRat]
|
||||
rw [toRat_mul]
|
||||
rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
|
||||
unfold invAtPrec
|
||||
@@ -64,12 +65,12 @@ theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
|
||||
have h_le : (ofOdd n k hn).toRat.inv < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat :=
|
||||
Rat.lt_toRat_toDyadic_add
|
||||
have h_pos : 0 < (ofOdd n k hn).toRat := by
|
||||
rwa [← toRat_lt_toRat_iff, toRat_zero] at hx
|
||||
rwa [lt_iff_toRat, toRat_zero] at hx
|
||||
calc
|
||||
1 = (ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := by
|
||||
symm
|
||||
apply Rat.inv_mul_cancel
|
||||
rw [← toRat_lt_toRat_iff, toRat_zero] at hx
|
||||
rw [lt_iff_toRat, toRat_zero] at hx
|
||||
exact Rat.ne_of_gt hx
|
||||
_ < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat * (ofOdd n k hn).toRat :=
|
||||
Rat.mul_lt_mul_of_pos_right h_le h_pos
|
||||
|
||||
@@ -8,6 +8,7 @@ module
|
||||
prelude
|
||||
public import Init.Data.Dyadic.Basic
|
||||
import all Init.Data.Dyadic.Instances
|
||||
import Init.Data.Int.Bitwise.Lemmas
|
||||
import Init.Grind.Ordered.Rat
|
||||
import Init.Grind.Ordered.Field
|
||||
|
||||
@@ -28,7 +29,7 @@ theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
|
||||
match h : k - prec with
|
||||
| .ofNat l =>
|
||||
dsimp
|
||||
rw [ofOdd_eq_ofIntWithPrec, ← toRat_le_toRat_iff]
|
||||
rw [ofOdd_eq_ofIntWithPrec, le_iff_toRat]
|
||||
replace h : k = Int.ofNat l + prec := by omega
|
||||
subst h
|
||||
simp only [toRat_ofIntWithPrec_eq_mul_two_pow]
|
||||
@@ -36,7 +37,7 @@ theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
|
||||
refine Lean.Grind.OrderedRing.mul_le_mul_of_nonneg_right ?_ (Rat.zpow_nonneg (by decide))
|
||||
rw [Int.shiftRight_eq_div_pow]
|
||||
rw [← Lean.Grind.Field.IsOrdered.mul_le_mul_iff_of_pos_right (c := 2^(Int.ofNat l)) (Rat.zpow_pos (by decide))]
|
||||
simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_natCast]
|
||||
simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_coe]
|
||||
rw [Rat.mul_assoc, ← Rat.zpow_add (by decide), Int.add_left_neg, Rat.zpow_zero, Rat.mul_one]
|
||||
have : (2 : Rat) ^ (l : Int) = (2 ^ l : Int) := by
|
||||
rw [Rat.zpow_natCast, Rat.intCast_pow, Rat.intCast_ofNat]
|
||||
|
||||
@@ -246,11 +246,6 @@ instance neg (n : Nat) : Neg (Fin n) :=
|
||||
|
||||
theorem neg_def (a : Fin n) : -a = ⟨(n - a) % n, Nat.mod_lt _ a.pos⟩ := rfl
|
||||
|
||||
-- Later we give another version called `Fin.val_neg` that splits on `a = 0`.
|
||||
protected theorem val_neg' (a : Fin n) : ((-a : Fin n) : Nat) = (n - a) % n :=
|
||||
rfl
|
||||
|
||||
@[deprecated Fin.val_neg' (since := "2025-11-21")]
|
||||
protected theorem coe_neg (a : Fin n) : ((-a : Fin n) : Nat) = (n - a) % n :=
|
||||
rfl
|
||||
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Nat.Bitwise
|
||||
public import Init.Data.Fin.Basic
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -6,6 +6,7 @@ Authors: François G. Dorais
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Nat.Linear
|
||||
public import Init.Control.Lawful.Basic
|
||||
public import Init.Data.Fin.Lemmas
|
||||
|
||||
|
||||
@@ -7,6 +7,7 @@ module
|
||||
|
||||
prelude
|
||||
public import Init.PropLemmas
|
||||
public import Init.Data.Fin.Basic
|
||||
|
||||
public section
|
||||
|
||||
|
||||
@@ -8,6 +8,10 @@ module
|
||||
prelude
|
||||
public import Init.Data.Nat.Lemmas
|
||||
public import Init.Ext
|
||||
public import Init.ByCases
|
||||
public import Init.Conv
|
||||
public import Init.Omega
|
||||
public import Init.Data.Order.Factories
|
||||
import Init.Data.Order.Lemmas
|
||||
|
||||
@[expose] public section
|
||||
@@ -16,25 +20,17 @@ open Std
|
||||
|
||||
namespace Fin
|
||||
|
||||
@[simp, grind =] theorem ofNat_zero (n : Nat) [NeZero n] : Fin.ofNat n 0 = 0 := rfl
|
||||
@[simp] theorem ofNat_zero (n : Nat) [NeZero n] : Fin.ofNat n 0 = 0 := rfl
|
||||
|
||||
@[deprecated ofNat_zero (since := "2025-05-28")] abbrev ofNat'_zero := @ofNat_zero
|
||||
|
||||
theorem mod_def (a m : Fin n) : a % m = Fin.mk (a.val % m.val) (Nat.lt_of_le_of_lt (Nat.mod_le _ _) a.2) :=
|
||||
rfl
|
||||
|
||||
theorem val_mod (a m : Fin n) : (a % m).val = a.val % m.val := rfl
|
||||
|
||||
theorem mul_def (a b : Fin n) : a * b = Fin.mk ((a.val * b.val) % n) (Nat.mod_lt _ a.pos) := rfl
|
||||
|
||||
theorem val_mul (a b : Fin n) : (a * b).val = (a.val * b.val) % n := rfl
|
||||
|
||||
theorem sub_def (a b : Fin n) : a - b = Fin.mk (((n - b.val) + a.val) % n) (Nat.mod_lt _ a.pos) := rfl
|
||||
|
||||
@[grind =]
|
||||
theorem val_sub (a b : Fin n) : (a - b).val = ((n - b.val) + a.val) % n := rfl
|
||||
|
||||
@[grind →]
|
||||
theorem pos' : ∀ [Nonempty (Fin n)], 0 < n | ⟨i⟩ => i.pos
|
||||
|
||||
@[simp] theorem is_lt (a : Fin n) : (a : Nat) < n := a.2
|
||||
@@ -46,8 +42,7 @@ theorem pos_iff_nonempty {n : Nat} : 0 < n ↔ Nonempty (Fin n) :=
|
||||
|
||||
@[simp] protected theorem eta (a : Fin n) (h : a < n) : (⟨a, h⟩ : Fin n) = a := rfl
|
||||
|
||||
@[ext, grind ext]
|
||||
protected theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
|
||||
@[ext] protected theorem ext {a b : Fin n} (h : (a : Nat) = b) : a = b := eq_of_val_eq h
|
||||
|
||||
theorem val_ne_iff {a b : Fin n} : a.1 ≠ b.1 ↔ a ≠ b := not_congr val_inj
|
||||
|
||||
@@ -78,7 +73,7 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
|
||||
|
||||
@[deprecated val_ofNat (since := "2025-05-28")] abbrev val_ofNat' := @val_ofNat
|
||||
|
||||
@[simp, grind =] theorem ofNat_self {n : Nat} [NeZero n] : Fin.ofNat n n = 0 := by
|
||||
@[simp] theorem ofNat_self {n : Nat} [NeZero n] : Fin.ofNat n n = 0 := by
|
||||
ext
|
||||
simp
|
||||
congr
|
||||
@@ -98,7 +93,7 @@ theorem mk_val (i : Fin n) : (⟨i, i.isLt⟩ : Fin n) = i := Fin.eta ..
|
||||
@[simp] theorem div_val (a b : Fin n) : (a / b).val = a.val / b.val :=
|
||||
rfl
|
||||
|
||||
@[simp, grind =] theorem modn_val (a : Fin n) (b : Nat) : (a.modn b).val = a.val % b :=
|
||||
@[simp] theorem modn_val (a : Fin n) (b : Nat) : (a.modn b).val = a.val % b :=
|
||||
rfl
|
||||
|
||||
@[simp] theorem val_eq_zero (a : Fin 1) : a.val = 0 :=
|
||||
@@ -166,7 +161,6 @@ theorem le_def {a b : Fin n} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
|
||||
|
||||
theorem lt_def {a b : Fin n} : a < b ↔ a.1 < b.1 := .rfl
|
||||
|
||||
@[deprecated lt_def (since := "2025-10-26")]
|
||||
theorem lt_iff_val_lt_val {a b : Fin n} : a < b ↔ a.val < b.val := Iff.rfl
|
||||
|
||||
@[simp] protected theorem not_le {a b : Fin n} : ¬ a ≤ b ↔ b < a := Nat.not_le
|
||||
@@ -268,15 +262,13 @@ instance : LawfulOrderLT (Fin n) where
|
||||
lt_iff := by
|
||||
simp [← Fin.not_le, Decidable.imp_iff_not_or, Std.Total.total]
|
||||
|
||||
@[simp] theorem val_rev (i : Fin n) : (rev i).val = n - (i + 1) := rfl
|
||||
|
||||
grind_pattern val_rev => i.rev
|
||||
@[simp, grind =] theorem val_rev (i : Fin n) : (rev i).val = n - (i + 1) := rfl
|
||||
|
||||
@[simp] theorem rev_rev (i : Fin n) : rev (rev i) = i := Fin.ext <| by
|
||||
rw [val_rev, val_rev, ← Nat.sub_sub, Nat.sub_sub_self (by exact i.2), Nat.add_sub_cancel]
|
||||
|
||||
@[simp] theorem rev_le_rev {i j : Fin n} : rev i ≤ rev j ↔ j ≤ i := by
|
||||
simp only [le_def, val_rev, Nat.sub_le_sub_iff_left (Nat.succ_le_iff.2 j.is_lt)]
|
||||
simp only [le_def, val_rev, Nat.sub_le_sub_iff_left (Nat.succ_le.2 j.is_lt)]
|
||||
exact Nat.succ_le_succ_iff
|
||||
|
||||
@[simp] theorem rev_inj {i j : Fin n} : rev i = rev j ↔ i = j :=
|
||||
@@ -295,8 +287,6 @@ theorem rev_eq {n a : Nat} (i : Fin (n + 1)) (h : n = a + i) :
|
||||
|
||||
@[simp] theorem val_last (n : Nat) : (last n).1 = n := rfl
|
||||
|
||||
grind_pattern val_last => last n
|
||||
|
||||
@[simp] theorem last_zero : (Fin.last 0 : Fin 1) = 0 := by
|
||||
ext
|
||||
simp
|
||||
@@ -397,17 +387,14 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
|
||||
rw [Fin.lt_def, val_add, val_zero, val_one, Nat.mod_eq_of_lt h]
|
||||
exact Nat.zero_lt_succ _
|
||||
|
||||
@[deprecated zero_lt_one (since := "2025-10-26")]
|
||||
theorem one_pos : (0 : Fin (n + 2)) < 1 := Nat.succ_pos 0
|
||||
|
||||
theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 := Fin.ne_of_lt zero_lt_one
|
||||
theorem zero_ne_one : (0 : Fin (n + 2)) ≠ 1 := Fin.ne_of_lt one_pos
|
||||
|
||||
/-! ### succ and casts into larger Fin types -/
|
||||
|
||||
@[simp] theorem val_succ (j : Fin n) : (j.succ : Nat) = j + 1 := rfl
|
||||
|
||||
grind_pattern val_succ => j.succ
|
||||
|
||||
@[simp] theorem succ_pos (a : Fin n) : (0 : Fin (n + 1)) < a.succ := by
|
||||
simp [Fin.lt_def]
|
||||
|
||||
@@ -468,18 +455,12 @@ theorem one_lt_succ_succ (a : Fin n) : (1 : Fin (n + 2)) < a.succ.succ := by
|
||||
theorem succ_succ_ne_one (a : Fin n) : Fin.succ (Fin.succ a) ≠ 1 :=
|
||||
Fin.ne_of_gt (one_lt_succ_succ a)
|
||||
|
||||
@[simp, grind =] theorem val_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : Nat) = i := rfl
|
||||
|
||||
@[deprecated val_castLT (since := "2025-11-21")]
|
||||
theorem coe_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : Nat) = i := rfl
|
||||
@[simp] theorem coe_castLT (i : Fin m) (h : i.1 < n) : (castLT i h : Nat) = i := rfl
|
||||
|
||||
@[simp] theorem castLT_mk (i n m : Nat) (hn : i < n) (hm : i < m) : castLT ⟨i, hn⟩ hm = ⟨i, hm⟩ :=
|
||||
rfl
|
||||
|
||||
@[simp, grind =] theorem val_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : Nat) = i := rfl
|
||||
|
||||
@[deprecated val_castLE (since := "2025-11-21")]
|
||||
theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : Nat) = i := rfl
|
||||
@[simp, grind =] theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : Nat) = i := rfl
|
||||
|
||||
@[simp] theorem castLE_mk (i n m : Nat) (hn : i < n) (h : n ≤ m) :
|
||||
castLE h ⟨i, hn⟩ = ⟨i, Nat.lt_of_lt_of_le hn h⟩ := rfl
|
||||
@@ -491,16 +472,13 @@ theorem coe_castLE (h : n ≤ m) (i : Fin n) : (castLE h i : Nat) = i := rfl
|
||||
|
||||
@[simp] theorem castLE_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) (i : Fin k) :
|
||||
Fin.castLE mn (Fin.castLE km i) = Fin.castLE (Nat.le_trans km mn) i :=
|
||||
Fin.ext (by simp only [val_castLE])
|
||||
Fin.ext (by simp only [coe_castLE])
|
||||
|
||||
@[simp] theorem castLE_comp_castLE {k m n} (km : k ≤ m) (mn : m ≤ n) :
|
||||
Fin.castLE mn ∘ Fin.castLE km = Fin.castLE (Nat.le_trans km mn) :=
|
||||
funext (castLE_castLE km mn)
|
||||
|
||||
@[simp, grind =] theorem val_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
|
||||
|
||||
@[deprecated val_cast (since := "2025-11-21")]
|
||||
theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
|
||||
@[simp] theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
|
||||
|
||||
@[simp] theorem cast_castLE {k m n} (km : k ≤ m) (mn : m = n) (i : Fin k) :
|
||||
Fin.cast mn (i.castLE km) = i.castLE (mn ▸ km) :=
|
||||
@@ -513,7 +491,7 @@ theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
|
||||
@[simp] theorem cast_zero [NeZero n] [NeZero m] (h : n = m) : Fin.cast h 0 = 0 := rfl
|
||||
|
||||
@[simp] theorem cast_last {n' : Nat} {h : n + 1 = n' + 1} : (last n).cast h = last n' :=
|
||||
Fin.ext (by rw [val_cast, val_last, val_last, Nat.succ.inj h])
|
||||
Fin.ext (by rw [coe_cast, val_last, val_last, Nat.succ.inj h])
|
||||
|
||||
@[simp] theorem cast_mk (h : n = m) (i : Nat) (hn : i < n) : Fin.cast h ⟨i, hn⟩ = ⟨i, h ▸ hn⟩ := rfl
|
||||
|
||||
@@ -528,10 +506,7 @@ theorem coe_cast (h : n = m) (i : Fin n) : (i.cast h : Nat) = i := rfl
|
||||
|
||||
theorem castLE_of_eq {m n : Nat} (h : m = n) {h' : m ≤ n} : castLE h' = Fin.cast h := rfl
|
||||
|
||||
@[simp, grind =] theorem val_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
|
||||
|
||||
@[deprecated val_castAdd (since := "2025-11-21")]
|
||||
theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
|
||||
@[simp] theorem coe_castAdd (m : Nat) (i : Fin n) : (castAdd m i : Nat) = i := rfl
|
||||
|
||||
@[simp] theorem castAdd_zero : (castAdd 0 : Fin n → Fin (n + 0)) = Fin.cast rfl := rfl
|
||||
|
||||
@@ -567,18 +542,15 @@ the reverse direction. -/
|
||||
theorem succ_cast_eq {n' : Nat} (i : Fin n) (h : n = n') :
|
||||
(i.cast h).succ = i.succ.cast (by rw [h]) := rfl
|
||||
|
||||
@[simp, grind =] theorem val_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
|
||||
@[simp] theorem coe_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
|
||||
|
||||
@[deprecated val_castSucc (since := "2025-11-21")]
|
||||
theorem coe_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
|
||||
|
||||
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt_succ_of_lt h⟩ := rfl
|
||||
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc ⟨i, h⟩ = ⟨i, Nat.lt.step h⟩ := rfl
|
||||
|
||||
@[simp] theorem cast_castSucc {n' : Nat} {h : n + 1 = n' + 1} {i : Fin n} :
|
||||
i.castSucc.cast h = (i.cast (Nat.succ.inj h)).castSucc := rfl
|
||||
|
||||
theorem castSucc_lt_succ {i : Fin n} : i.castSucc < i.succ :=
|
||||
lt_def.2 <| by simp only [val_castSucc, val_succ, Nat.lt_succ_self]
|
||||
theorem castSucc_lt_succ (i : Fin n) : i.castSucc < i.succ :=
|
||||
lt_def.2 <| by simp only [coe_castSucc, val_succ, Nat.lt_succ_self]
|
||||
|
||||
theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i ≤ j.castSucc ↔ i < j.succ := by
|
||||
simpa only [lt_def, le_def] using Nat.add_one_le_add_one_iff.symm
|
||||
@@ -617,12 +589,8 @@ theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < i.castSucc := by
|
||||
theorem castSucc_ne_zero_iff [NeZero n] {a : Fin n} : a.castSucc ≠ 0 ↔ a ≠ 0 :=
|
||||
not_congr <| castSucc_eq_zero_iff
|
||||
|
||||
@[simp, grind _=_]
|
||||
theorem castSucc_succ (i : Fin n) : i.succ.castSucc = i.castSucc.succ := rfl
|
||||
|
||||
@[deprecated castSucc_succ (since := "2025-10-29")]
|
||||
theorem castSucc_fin_succ (n : Nat) (j : Fin n) :
|
||||
j.succ.castSucc = (j.castSucc).succ := by simp
|
||||
j.succ.castSucc = (j.castSucc).succ := by simp [Fin.ext_iff]
|
||||
|
||||
@[simp]
|
||||
theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
|
||||
@@ -630,9 +598,8 @@ theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
|
||||
· exact a.elim0
|
||||
· simp [Fin.ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
|
||||
|
||||
@[deprecated castSucc_lt_succ (since := "2025-10-29")]
|
||||
theorem lt_succ {a : Fin n} : a.castSucc < a.succ := by
|
||||
rw [castSucc, lt_def, val_castAdd, val_succ]; exact Nat.lt_succ_self a.val
|
||||
rw [castSucc, lt_def, coe_castAdd, val_succ]; exact Nat.lt_succ_self a.val
|
||||
|
||||
theorem exists_castSucc_eq {n : Nat} {i : Fin (n + 1)} : (∃ j, castSucc j = i) ↔ i ≠ last n :=
|
||||
⟨fun ⟨j, hj⟩ => hj ▸ Fin.ne_of_lt j.castSucc_lt_last,
|
||||
@@ -640,10 +607,7 @@ theorem exists_castSucc_eq {n : Nat} {i : Fin (n + 1)} : (∃ j, castSucc j = i)
|
||||
|
||||
theorem succ_castSucc {n : Nat} (i : Fin n) : i.castSucc.succ = i.succ.castSucc := rfl
|
||||
|
||||
@[simp, grind =] theorem val_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
|
||||
|
||||
@[deprecated val_addNat (since := "2025-11-21")]
|
||||
theorem coe_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
|
||||
@[simp] theorem coe_addNat (m : Nat) (i : Fin n) : (addNat i m : Nat) = i + m := rfl
|
||||
|
||||
@[simp] theorem addNat_zero (n : Nat) (i : Fin n) : addNat i 0 = i := by
|
||||
ext
|
||||
@@ -671,10 +635,7 @@ theorem cast_addNat_left {n n' m : Nat} (i : Fin n') (h : n' + m = n + m) :
|
||||
(addNat i m').cast h = addNat i m :=
|
||||
Fin.ext <| (congrArg ((· + ·) (i : Nat)) (Nat.add_left_cancel h) : _)
|
||||
|
||||
@[simp, grind =] theorem val_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
|
||||
|
||||
@[deprecated val_natAdd (since := "2025-11-21")]
|
||||
theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
|
||||
@[simp] theorem coe_natAdd (n : Nat) {m : Nat} (i : Fin m) : (natAdd n i : Nat) = n + i := rfl
|
||||
|
||||
@[simp] theorem natAdd_mk (n i : Nat) (hi : i < m) :
|
||||
natAdd n ⟨i, hi⟩ = ⟨n + i, Nat.add_lt_add_left hi n⟩ := rfl
|
||||
@@ -731,7 +692,7 @@ theorem natAdd_castSucc {m n : Nat} {i : Fin m} : natAdd n (castSucc i) = castSu
|
||||
omega
|
||||
|
||||
theorem rev_castAdd (k : Fin n) (m : Nat) : rev (castAdd m k) = addNat (rev k) m := Fin.ext <| by
|
||||
rw [val_rev, val_castAdd, val_addNat, val_rev, Nat.sub_add_comm (Nat.succ_le_of_lt k.is_lt)]
|
||||
rw [val_rev, coe_castAdd, coe_addNat, val_rev, Nat.sub_add_comm (Nat.succ_le_of_lt k.is_lt)]
|
||||
|
||||
theorem rev_addNat (k : Fin n) (m : Nat) : rev (addNat k m) = castAdd m (rev k) := by
|
||||
rw [← rev_rev (castAdd ..), rev_castAdd, rev_rev]
|
||||
@@ -740,6 +701,9 @@ theorem rev_castSucc (k : Fin n) : rev (castSucc k) = succ (rev k) := k.rev_cast
|
||||
|
||||
theorem rev_succ (k : Fin n) : rev (succ k) = castSucc (rev k) := k.rev_addNat 1
|
||||
|
||||
@[simp, grind _=_]
|
||||
theorem castSucc_succ (i : Fin n) : i.succ.castSucc = i.castSucc.succ := rfl
|
||||
|
||||
@[simp, grind =]
|
||||
theorem castLE_refl (h : n ≤ n) (i : Fin n) : i.castLE h = i := rfl
|
||||
|
||||
@@ -753,12 +717,7 @@ theorem castSucc_natAdd (n : Nat) (i : Fin k) :
|
||||
|
||||
/-! ### pred -/
|
||||
|
||||
@[simp] theorem val_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : Nat) = j - 1 := rfl
|
||||
|
||||
grind_pattern val_pred => j.pred h
|
||||
|
||||
@[deprecated val_pred (since := "2025-11-21")]
|
||||
theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : Nat) = j - 1 := rfl
|
||||
@[simp] theorem coe_pred (j : Fin (n + 1)) (h : j ≠ 0) : (j.pred h : Nat) = j - 1 := rfl
|
||||
|
||||
@[simp] theorem succ_pred : ∀ (i : Fin (n + 1)) (h : i ≠ 0), (i.pred h).succ = i
|
||||
| ⟨0, _⟩, hi => by simp only [mk_zero, ne_eq, not_true] at hi
|
||||
@@ -776,7 +735,7 @@ theorem pred_eq_iff_eq_succ {n : Nat} {i : Fin (n + 1)} (hi : i ≠ 0) {j : Fin
|
||||
theorem pred_mk_succ (i : Nat) (h : i < n + 1) :
|
||||
Fin.pred ⟨i + 1, Nat.add_lt_add_right h 1⟩ (ne_of_val_ne (Nat.ne_of_gt (mk_succ_pos i h))) =
|
||||
⟨i, h⟩ := by
|
||||
simp only [Fin.ext_iff, val_pred, Nat.add_sub_cancel]
|
||||
simp only [Fin.ext_iff, coe_pred, Nat.add_sub_cancel]
|
||||
|
||||
@[simp] theorem pred_mk_succ' (i : Nat) (h₁ : i + 1 < n + 1 + 1) (h₂) :
|
||||
Fin.pred ⟨i + 1, h₁⟩ h₂ = ⟨i, Nat.lt_of_succ_lt_succ h₁⟩ := pred_mk_succ i _
|
||||
@@ -799,17 +758,14 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
|
||||
| ⟨i + 1, hi⟩, ⟨j + 1, hj⟩, ha, hb => by simp [Fin.ext_iff]
|
||||
|
||||
@[simp] theorem pred_one {n : Nat} :
|
||||
Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt zero_lt_one)) = 0 := rfl
|
||||
Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
|
||||
|
||||
theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
|
||||
pred (i + 1) (Fin.ne_of_gt (add_one_pos _ (lt_def.2 h))) = castLT i h := by
|
||||
rw [Fin.ext_iff, val_pred, val_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
|
||||
rw [Fin.ext_iff, coe_pred, coe_castLT, val_add, val_one, Nat.mod_eq_of_lt, Nat.add_sub_cancel]
|
||||
exact Nat.add_lt_add_right h 1
|
||||
|
||||
@[simp, grind =] theorem val_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : Nat) = i - m := rfl
|
||||
|
||||
@[deprecated val_subNat (since := "2025-11-21")]
|
||||
theorem coe_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : Nat) = i - m := rfl
|
||||
@[simp] theorem coe_subNat (i : Fin (n + m)) (h : m ≤ i) : (i.subNat m h : Nat) = i - m := rfl
|
||||
|
||||
@[simp] theorem subNat_mk {i : Nat} (h₁ : i < n + m) (h₂ : m ≤ i) :
|
||||
subNat m ⟨i, h₁⟩ h₂ = ⟨i - m, Nat.sub_lt_right_of_lt_add h₂ h₁⟩ := rfl
|
||||
@@ -874,11 +830,11 @@ step. `Fin.succRec` is a version of this induction principle that takes the `Fin
|
||||
(zero : ∀ n, motive (n + 1) 0) (succ : ∀ n i, motive n i → motive (Nat.succ n) i.succ) :
|
||||
motive n i := i.succRec zero succ
|
||||
|
||||
@[simp, grind =] theorem succRecOn_zero {motive : ∀ n, Fin n → Sort _} {zero succ} (n) :
|
||||
@[simp] theorem succRecOn_zero {motive : ∀ n, Fin n → Sort _} {zero succ} (n) :
|
||||
@Fin.succRecOn (n + 1) 0 motive zero succ = zero n := by
|
||||
cases n <;> rfl
|
||||
|
||||
@[simp, grind =] theorem succRecOn_succ {motive : ∀ n, Fin n → Sort _} {zero succ} {n} (i : Fin n) :
|
||||
@[simp] theorem succRecOn_succ {motive : ∀ n, Fin n → Sort _} {zero succ} {n} (i : Fin n) :
|
||||
@Fin.succRecOn (n + 1) i.succ motive zero succ = succ n i (Fin.succRecOn i zero succ) := by
|
||||
cases i; rfl
|
||||
|
||||
@@ -906,11 +862,11 @@ where
|
||||
| 0, hi => by rwa [Fin.mk_zero]
|
||||
| i+1, hi => succ ⟨i, Nat.lt_of_succ_lt_succ hi⟩ (go i (Nat.lt_of_succ_lt hi))
|
||||
|
||||
@[simp, grind =] theorem induction_zero {motive : Fin (n + 1) → Sort _} (zero : motive 0)
|
||||
@[simp] theorem induction_zero {motive : Fin (n + 1) → Sort _} (zero : motive 0)
|
||||
(hs : ∀ i : Fin n, motive (castSucc i) → motive i.succ) :
|
||||
(induction zero hs : ∀ i : Fin (n + 1), motive i) 0 = zero := rfl
|
||||
|
||||
@[simp, grind =] theorem induction_succ {motive : Fin (n + 1) → Sort _} (zero : motive 0)
|
||||
@[simp] theorem induction_succ {motive : Fin (n + 1) → Sort _} (zero : motive 0)
|
||||
(succ : ∀ i : Fin n, motive (castSucc i) → motive i.succ) (i : Fin n) :
|
||||
induction (motive := motive) zero succ i.succ = succ i (induction zero succ (castSucc i)) := rfl
|
||||
|
||||
@@ -942,13 +898,13 @@ The corresponding induction principle is `Fin.induction`.
|
||||
(zero : motive 0) (succ : ∀ i : Fin n, motive i.succ) :
|
||||
∀ i : Fin (n + 1), motive i := induction zero fun i _ => succ i
|
||||
|
||||
@[simp, grind =] theorem cases_zero {n} {motive : Fin (n + 1) → Sort _} {zero succ} :
|
||||
@[simp] theorem cases_zero {n} {motive : Fin (n + 1) → Sort _} {zero succ} :
|
||||
@Fin.cases n motive zero succ 0 = zero := rfl
|
||||
|
||||
@[simp, grind =] theorem cases_succ {n} {motive : Fin (n + 1) → Sort _} {zero succ} (i : Fin n) :
|
||||
@[simp] theorem cases_succ {n} {motive : Fin (n + 1) → Sort _} {zero succ} (i : Fin n) :
|
||||
@Fin.cases n motive zero succ i.succ = succ i := rfl
|
||||
|
||||
@[simp, grind =] theorem cases_succ' {n} {motive : Fin (n + 1) → Sort _} {zero succ}
|
||||
@[simp] theorem cases_succ' {n} {motive : Fin (n + 1) → Sort _} {zero succ}
|
||||
{i : Nat} (h : i + 1 < n + 1) :
|
||||
@Fin.cases n motive zero succ ⟨i.succ, h⟩ = succ ⟨i, Nat.lt_of_succ_lt_succ h⟩ := rfl
|
||||
|
||||
@@ -998,7 +954,7 @@ For the induction:
|
||||
| j + 1 => go j (by omega) (by omega) (cast ⟨j, by omega⟩ x)
|
||||
go _ _ (by omega) last
|
||||
|
||||
@[simp, grind =] theorem reverseInduction_last {n : Nat} {motive : Fin (n + 1) → Sort _} {zero succ} :
|
||||
@[simp] theorem reverseInduction_last {n : Nat} {motive : Fin (n + 1) → Sort _} {zero succ} :
|
||||
(reverseInduction zero succ (Fin.last n) : motive (Fin.last n)) = zero := by
|
||||
rw [reverseInduction, reverseInduction.go]; simp
|
||||
|
||||
@@ -1015,7 +971,7 @@ private theorem reverseInduction_castSucc_aux {n : Nat} {motive : Fin (n + 1)
|
||||
dsimp only
|
||||
rw [ih _ _ (by omega), eq_comm, reverseInduction.go, dif_neg (by change i.1 + 1 ≠ _; omega)]
|
||||
|
||||
@[simp, grind =] theorem reverseInduction_castSucc {n : Nat} {motive : Fin (n + 1) → Sort _} {zero succ}
|
||||
@[simp] theorem reverseInduction_castSucc {n : Nat} {motive : Fin (n + 1) → Sort _} {zero succ}
|
||||
(i : Fin n) : reverseInduction (motive := motive) zero succ (castSucc i) =
|
||||
succ i (reverseInduction zero succ i.succ) := by
|
||||
rw [reverseInduction, reverseInduction_castSucc_aux _ _ _ i.isLt, reverseInduction]
|
||||
@@ -1034,11 +990,11 @@ The corresponding induction principle is `Fin.reverseInduction`.
|
||||
(cast : ∀ i : Fin n, motive (castSucc i)) (i : Fin (n + 1)) : motive i :=
|
||||
reverseInduction last (fun i _ => cast i) i
|
||||
|
||||
@[simp, grind =] theorem lastCases_last {n : Nat} {motive : Fin (n + 1) → Sort _} {last cast} :
|
||||
@[simp] theorem lastCases_last {n : Nat} {motive : Fin (n + 1) → Sort _} {last cast} :
|
||||
(Fin.lastCases last cast (Fin.last n) : motive (Fin.last n)) = last :=
|
||||
reverseInduction_last ..
|
||||
|
||||
@[simp, grind =] theorem lastCases_castSucc {n : Nat} {motive : Fin (n + 1) → Sort _} {last cast}
|
||||
@[simp] theorem lastCases_castSucc {n : Nat} {motive : Fin (n + 1) → Sort _} {last cast}
|
||||
(i : Fin n) : (Fin.lastCases last cast (Fin.castSucc i) : motive (Fin.castSucc i)) = cast i :=
|
||||
reverseInduction_castSucc ..
|
||||
|
||||
@@ -1058,11 +1014,11 @@ as `Fin.natAdd m (j : Fin n)`.
|
||||
if hi : (i : Nat) < m then (castAdd_castLT n i hi) ▸ (left (castLT i hi))
|
||||
else (natAdd_subNat_cast (Nat.le_of_not_lt hi)) ▸ (right _)
|
||||
|
||||
@[simp, grind =] theorem addCases_left {m n : Nat} {motive : Fin (m + n) → Sort _} {left right} (i : Fin m) :
|
||||
@[simp] theorem addCases_left {m n : Nat} {motive : Fin (m + n) → Sort _} {left right} (i : Fin m) :
|
||||
addCases (motive := motive) left right (Fin.castAdd n i) = left i := by
|
||||
rw [addCases, dif_pos (castAdd_lt _ _)]; rfl
|
||||
|
||||
@[simp, grind =]
|
||||
@[simp]
|
||||
theorem addCases_right {m n : Nat} {motive : Fin (m + n) → Sort _} {left right} (i : Fin n) :
|
||||
addCases (motive := motive) left right (natAdd m i) = right i := by
|
||||
have : ¬(natAdd m i : Nat) < m := Nat.not_lt.2 (le_coe_natAdd ..)
|
||||
@@ -1095,7 +1051,6 @@ theorem add_ofNat [NeZero n] (x : Fin n) (y : Nat) :
|
||||
|
||||
/-! ### sub -/
|
||||
|
||||
@[deprecated val_sub (since := "2025-11-21")]
|
||||
protected theorem coe_sub (a b : Fin n) : ((a - b : Fin n) : Nat) = ((n - b) + a) % n := by
|
||||
cases a; cases b; rfl
|
||||
|
||||
@@ -1147,7 +1102,6 @@ theorem coe_sub_iff_lt {a b : Fin n} : (↑(a - b) : Nat) = n + a - b ↔ a < b
|
||||
|
||||
/-! ### neg -/
|
||||
|
||||
@[grind =]
|
||||
theorem val_neg {n : Nat} [NeZero n] (x : Fin n) :
|
||||
(-x).val = if x = 0 then 0 else n - x.val := by
|
||||
change (n - ↑x) % n = _
|
||||
@@ -1163,7 +1117,7 @@ protected theorem sub_eq_add_neg {n : Nat} (x y : Fin n) : x - y = x + -y := by
|
||||
apply elim0 x
|
||||
· replace h : NeZero n := ⟨h⟩
|
||||
ext
|
||||
rw [Fin.val_sub, Fin.val_add, val_neg]
|
||||
rw [Fin.coe_sub, Fin.val_add, val_neg]
|
||||
split
|
||||
· simp_all
|
||||
· simp [Nat.add_comm]
|
||||
@@ -1184,7 +1138,9 @@ theorem mul_ofNat [NeZero n] (x : Fin n) (y : Nat) :
|
||||
|
||||
@[deprecated mul_ofNat (since := "2025-05-28")] abbrev mul_ofNat' := @mul_ofNat
|
||||
|
||||
@[deprecated val_mul (since := "2025-10-26")]
|
||||
theorem val_mul {n : Nat} : ∀ a b : Fin n, (a * b).val = a.val * b.val % n
|
||||
| ⟨_, _⟩, ⟨_, _⟩ => rfl
|
||||
|
||||
theorem coe_mul {n : Nat} : ∀ a b : Fin n, ((a * b : Fin n) : Nat) = a * b % n
|
||||
| ⟨_, _⟩, ⟨_, _⟩ => rfl
|
||||
|
||||
|
||||
@@ -6,6 +6,8 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Core
|
||||
public import Init.Data.Int.Basic
|
||||
public import Init.Data.ToString.Basic
|
||||
|
||||
public section
|
||||
|
||||
@@ -6,6 +6,9 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Core
|
||||
public import Init.Data.Int.Basic
|
||||
public import Init.Data.ToString.Basic
|
||||
public import Init.Data.Float
|
||||
|
||||
public section
|
||||
|
||||
@@ -6,7 +6,9 @@ Author: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Array.Basic
|
||||
public import Init.Data.Float
|
||||
public import Init.Data.Option.Basic
|
||||
import Init.Ext
|
||||
public import Init.Data.Array.DecidableEq
|
||||
|
||||
@@ -29,6 +31,9 @@ attribute [ext] FloatArray
|
||||
def emptyWithCapacity (c : @& Nat) : FloatArray :=
|
||||
{ data := #[] }
|
||||
|
||||
@[deprecated emptyWithCapacity (since := "2025-03-12")]
|
||||
abbrev mkEmpty := emptyWithCapacity
|
||||
|
||||
def empty : FloatArray :=
|
||||
emptyWithCapacity 0
|
||||
|
||||
@@ -129,7 +134,7 @@ protected def forIn {β : Type v} {m : Type v → Type w} [Monad m] (as : FloatA
|
||||
| ForInStep.yield b => loop i (Nat.le_of_lt h') b
|
||||
loop as.size (Nat.le_refl _) b
|
||||
|
||||
instance [Monad m] : ForIn m FloatArray Float where
|
||||
instance : ForIn m FloatArray Float where
|
||||
forIn := FloatArray.forIn
|
||||
|
||||
/-- See comment at `forInUnsafe` -/
|
||||
|
||||
@@ -170,7 +170,7 @@ private def spaceUptoLine : Format → Bool → Int → Nat → SpaceResult
|
||||
| text s, flatten, _, _ =>
|
||||
let p := String.Internal.posOf s '\n'
|
||||
let off := String.Internal.offsetOfPos s p
|
||||
{ foundLine := p != s.rawEndPos, foundFlattenedHardLine := flatten && p != s.rawEndPos, space := off }
|
||||
{ foundLine := p != s.endPos, foundFlattenedHardLine := flatten && p != s.endPos, space := off }
|
||||
| append f₁ f₂, flatten, m, w => merge w (spaceUptoLine f₁ flatten m w) (spaceUptoLine f₂ flatten m)
|
||||
| nest n f, flatten, m, w => spaceUptoLine f flatten (m - n) w
|
||||
| group f _, _, m, w => spaceUptoLine f true m w
|
||||
@@ -264,14 +264,14 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
|
||||
| nest n f => be w (gs' ({ i with f, indent := i.indent + n }::is))
|
||||
| text s =>
|
||||
let p := String.Internal.posOf s '\n'
|
||||
if p == s.rawEndPos then
|
||||
if p == s.endPos then
|
||||
pushOutput s
|
||||
endTags i.activeTags
|
||||
be w (gs' is)
|
||||
else
|
||||
pushOutput (String.Internal.extract s {} p)
|
||||
pushNewline i.indent.toNat
|
||||
let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.rawEndPos) }::is
|
||||
let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.endPos) }::is
|
||||
-- after a hard line break, re-evaluate whether to flatten the remaining group
|
||||
-- note that we shouldn't start flattening after a hard break outside a group
|
||||
if g.fla == .disallow then
|
||||
@@ -411,6 +411,7 @@ Renders a `Format` to a string.
|
||||
* `column`: begin the first line wrap `column` characters earlier than usual
|
||||
(this is useful when the output String will be printed starting at `column`)
|
||||
-/
|
||||
@[export lean_format_pretty]
|
||||
def pretty (f : Format) (width : Nat := defWidth) (indent : Nat := 0) (column := 0) : String :=
|
||||
let act : StateM State Unit := prettyM f width indent
|
||||
State.out <| act (State.mk "" column) |>.snd
|
||||
|
||||
@@ -6,8 +6,10 @@ Author: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Format.Basic
|
||||
public import Init.Data.Array.Basic
|
||||
import Init.Data.String.Search
|
||||
public import Init.Data.ToString.Basic
|
||||
import Init.Data.String.Basic
|
||||
|
||||
public section
|
||||
|
||||
@@ -47,7 +49,7 @@ Converts a string to a pretty-printer document, replacing newlines in the string
|
||||
`Std.Format.line`.
|
||||
-/
|
||||
def String.toFormat (s : String) : Std.Format :=
|
||||
Std.Format.joinSep (s.split '\n').toList Std.Format.line
|
||||
Std.Format.joinSep (s.splitOn "\n") Std.Format.line
|
||||
|
||||
instance : ToFormat String.Pos.Raw where
|
||||
format p := format p.byteIdx
|
||||
|
||||
@@ -9,6 +9,7 @@ prelude
|
||||
public import Init.Data.Format.Macro
|
||||
public import Init.Data.Format.Instances
|
||||
public import Init.Meta
|
||||
import Init.Data.String.Basic
|
||||
import Init.Data.ToString.Name
|
||||
|
||||
public section
|
||||
|
||||
@@ -5,6 +5,7 @@ Authors: Kim Morrison
|
||||
-/
|
||||
module
|
||||
prelude
|
||||
public import Init.Core
|
||||
public import Init.Grind.Tactics
|
||||
public section
|
||||
namespace Function
|
||||
|
||||
@@ -6,7 +6,9 @@ Authors: Leonardo de Moura
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.UInt.Basic
|
||||
public import Init.Data.String.Basic
|
||||
public import Init.Data.ByteArray.Basic
|
||||
|
||||
public section
|
||||
universe u
|
||||
|
||||
@@ -80,10 +80,7 @@ protected theorem zero_ne_one : (0 : Int) ≠ 1 := nofun
|
||||
|
||||
/-! ## Coercions -/
|
||||
|
||||
@[simp] theorem ofNat_eq_natCast (n : Nat) : Int.ofNat n = n := rfl
|
||||
|
||||
@[deprecated ofNat_eq_natCast (since := "2025-10-29")]
|
||||
theorem ofNat_eq_coe : Int.ofNat n = Nat.cast n := rfl
|
||||
@[simp] theorem ofNat_eq_coe : Int.ofNat n = Nat.cast n := rfl
|
||||
|
||||
@[simp] theorem ofNat_zero : ((0 : Nat) : Int) = 0 := rfl
|
||||
|
||||
@@ -316,7 +313,7 @@ the logical model.
|
||||
Examples:
|
||||
* `(7 : Int).natAbs = 7`
|
||||
* `(0 : Int).natAbs = 0`
|
||||
* `(-11 : Int).natAbs = 11`
|
||||
* `((-11 : Int).natAbs = 11`
|
||||
-/
|
||||
@[extern "lean_nat_abs", expose]
|
||||
def natAbs (m : @& Int) : Nat :=
|
||||
@@ -372,6 +369,9 @@ def toNat? : Int → Option Nat
|
||||
| (n : Nat) => some n
|
||||
| -[_+1] => none
|
||||
|
||||
@[deprecated toNat? (since := "2025-03-11"), inherit_doc toNat?]
|
||||
abbrev toNat' := toNat?
|
||||
|
||||
/-! ## divisibility -/
|
||||
|
||||
/--
|
||||
@@ -392,9 +392,9 @@ Examples:
|
||||
* `(0 : Int) ^ 10 = 0`
|
||||
* `(-7 : Int) ^ 3 = -343`
|
||||
-/
|
||||
protected def pow : Int → Nat → Int
|
||||
| (m : Nat), n => Int.ofNat (m ^ n)
|
||||
| m@-[_+1], n => if n % 2 = 0 then Int.ofNat (m.natAbs ^ n) else - Int.ofNat (m.natAbs ^ n)
|
||||
protected def pow (m : Int) : Nat → Int
|
||||
| 0 => 1
|
||||
| succ n => Int.pow m n * m
|
||||
|
||||
instance : NatPow Int where
|
||||
pow := Int.pow
|
||||
|
||||
@@ -24,17 +24,12 @@ theorem natCast_shiftRight (n s : Nat) : n >>> s = (n : Int) >>> s := rfl
|
||||
theorem negSucc_shiftRight (m n : Nat) :
|
||||
-[m+1] >>> n = -[m >>>n +1] := rfl
|
||||
|
||||
@[grind _=_]
|
||||
theorem shiftRight_add (i : Int) (m n : Nat) :
|
||||
i >>> (m + n) = i >>> m >>> n := by
|
||||
simp only [shiftRight_eq, Int.shiftRight]
|
||||
cases i <;> simp [Nat.shiftRight_add]
|
||||
|
||||
grind_pattern shiftRight_add => i >>> (m + n) where
|
||||
i =/= 0
|
||||
|
||||
grind_pattern shiftRight_add => i >>> m >>> n where
|
||||
i =/= 0
|
||||
|
||||
theorem shiftRight_eq_div_pow (m : Int) (n : Nat) :
|
||||
m >>> n = m / ((2 ^ n) : Nat) := by
|
||||
simp only [shiftRight_eq, Int.shiftRight, Nat.shiftRight_eq_div_pow]
|
||||
@@ -52,10 +47,10 @@ theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
|
||||
simp [Int.shiftRight_eq_div_pow]
|
||||
|
||||
theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : n ≤ n >>> s := by
|
||||
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_natCast]
|
||||
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
|
||||
split
|
||||
case _ _ _ m =>
|
||||
simp only [ofNat_eq_natCast] at h
|
||||
simp only [ofNat_eq_coe] at h
|
||||
by_cases hm : m = 0
|
||||
· simp [hm]
|
||||
· omega
|
||||
@@ -66,14 +61,14 @@ theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : n ≤ n >>>
|
||||
omega
|
||||
|
||||
theorem shiftRight_le_of_nonneg {n : Int} {s : Nat} (h : 0 ≤ n) : n >>> s ≤ n := by
|
||||
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_natCast]
|
||||
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
|
||||
split
|
||||
case _ _ _ m =>
|
||||
simp only [Int.ofNat_eq_natCast] at h
|
||||
simp only [Int.ofNat_eq_coe] at h
|
||||
by_cases hm : m = 0
|
||||
· simp [hm]
|
||||
· have := Nat.shiftRight_le m s
|
||||
rw [ofNat_eq_natCast]
|
||||
rw [ofNat_eq_coe]
|
||||
omega
|
||||
case _ _ _ m =>
|
||||
omega
|
||||
@@ -113,7 +108,7 @@ theorem shiftLeft_succ (m : Int) (n : Nat) : m <<< (n + 1) = (m <<< n) * 2 := by
|
||||
change Int.shiftLeft _ _ = Int.shiftLeft _ _ * 2
|
||||
match m with
|
||||
| (m : Nat) =>
|
||||
dsimp only [Int.shiftLeft, Int.ofNat_eq_natCast]
|
||||
dsimp only [Int.shiftLeft, Int.ofNat_eq_coe]
|
||||
rw [Nat.shiftLeft_succ, Nat.mul_comm, natCast_mul, ofNat_two]
|
||||
| Int.negSucc m =>
|
||||
dsimp only [Int.shiftLeft]
|
||||
|
||||
@@ -6,6 +6,7 @@ Authors: Kim Morrison
|
||||
module
|
||||
|
||||
prelude
|
||||
public import Init.Data.Int.DivMod.Lemmas
|
||||
public import Init.Data.Int.Gcd
|
||||
|
||||
public section
|
||||
|
||||
@@ -9,4 +9,3 @@ prelude
|
||||
public import Init.Data.Int.DivMod.Basic
|
||||
public import Init.Data.Int.DivMod.Bootstrap
|
||||
public import Init.Data.Int.DivMod.Lemmas
|
||||
public import Init.Data.Int.DivMod.Pow
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user