feat(Algorithms): add verified binary search with O(log n) time proof#443
Open
zacn04 wants to merge 1 commit intoleanprover:mainfrom
Open
feat(Algorithms): add verified binary search with O(log n) time proof#443zacn04 wants to merge 1 commit intoleanprover:mainfrom
zacn04 wants to merge 1 commit intoleanprover:mainfrom
Conversation
Add binary search on sorted arrays using the TimeM monad to count comparisons. Proves correctness (found implies arr[mid] = target, not found on sorted array implies target absent) and time complexity (at most ⌈log₂(n+1)⌉ comparisons), all without sorry. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Contributor
|
Duplicate of #237 |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Summary
binarySearchon sorted arrays using theTimeM ℕmonad to count comparisonsbinarySearch_found(result impliesarr[mid] = target) andbinarySearch_not_found(absence on sorted array)⌈log₂(n + 1)⌉comparisons (binarySearch_time)module,@[expose] public section,Cslib.Algorithms.Lean.TimeMnamespaceTest plan
lake build --wfail --iofailpasseslake exe mk_all --module(Cslib.lean updated)lake exe lint-stylepasseslake test(CI)lake lint(CI)🤖 Generated with Claude Code