First Formally Verified 3D CSG Implementation in Lean 4

Researchers Achieve Breakthrough in Verified 3D Mesh Intersection

A significant milestone has been reached in the field of verified computer-aided design (CAD) with the implementation of a 3D constructive solid geometry (CSG) operation, specifically mesh intersection, in Lean 4. This achievement marks the first formally verified implementation of its kind, where the resulting mesh's surface is precisely pinned down by a concise specification. The project's developers have also successfully avoided relying on AI-generated code by utilizing a human reviewer to verify the correctness of the kernel through a formal specification and the Lean checker.

The verification process involved AI autonomously writing over 60,000 lines of Lean proofs, which were then certified by the Lean checker at compile time. This ensured conformance to the specification without requiring human inspection. The development team guided an AI agent through the necessary milestones to arrive at the verified mesh intersection kernel. The result is a robust and reliable implementation that can be treated as a black box, with zero trust placed in any large language model (LLM). The verified kernel has been compiled to WebAssembly and is now available for testing through a web demo at https://schildep.github.io/verified-3d-mesh-intersection/.

This achievement has significant implications for the field of CAD and computer-aided engineering, where reliable and trustworthy implementations are crucial. The team's innovative approach to verification and the use of formal specifications and Lean checker ensure that the implementation meets practical well-formedness conditions on the triangulation, providing a high degree of confidence in the accuracy and reliability of the results.