Formally verified polygon intersection – Opus 4.8 oneshots, prev failed
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps. Trust in the correctness comes entirely from the Lean checker and human review of a small specification, not from the LLM. Also check out the web demo built around the verified core linked in…
In plain words
Formally verified polygon intersection is a Lean implementation of a polygon intersection algorithm with mathematical proof of correctness. Designed for developers who need reliable geometric computation, it stands out as apparently the first formally verified polygon intersection algorithm. The implementation handles complex cases including multipolygons with holes, self-intersections, and overlapping edges. Correctness is guaranteed by Lean's proof checker and human review rather than relying on AI output alone. A web demo is available for testing the verified core.
written from the facts on this page · September 2026
From the sources
In the maker’s words, at launch
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps. Trust in the correctness comes entirely from the Lean checker and human review of a small specification, not from the LLM. Also check out the web demo built around the verified core linked in the readme: https://schildep.github.io/verified-polygon-intersection/. It supports multipolygons including holes, self intersections, and overlapping edges.
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