A GitHub project presents what appears to be the first formally verified implementation of polygon intersection algorithms. The work uses Lean 4 to mathematically prove correctness for all possible polygon configurations, addressing a fundamental challenge in computational geometry where classical testing cannot cover infinite input variations.

The author leveraged Claude models throughout development, noting dramatic improvements in autonomous proof generation. Claude Opus 4.8 reportedly completed complex proofs in single attempts that previously required step-by-step guidance. The 87-line specification humans review remains separate from the AI-generated implementation files, allowing verification without trusting the language model output.

Formal verification matters because computational geometry code has subtle edge cases that break with rare input configurations. The algorithm handles multipolygons including holes, self-intersections, and overlapping edges through Eulerian cycle partitioning. This mathematical rigor ensures the intersection equality holds for infinite point sets, something impossible to validate through traditional testing alone.

The web demo demonstrates practical application, though the author observes that formal verification constraints produce slower code. Training data lacks formally verified software examples, limiting AI optimization capabilities. This represents a significant milestone in applying proof assistants to geometry libraries that power graphics and mapping applications.

The repository separates specification from implementation, minimizing human review burden while maintaining mathematical guarantees.