verified-3d-mesh-intersection - Formally verified 3D CSG mesh intersection
Show HN: Formally verified 3D CSG: Trust 93 lines spec, not 1000 lines AI code
verified-3d-mesh-intersection is the first formally verified implementation of 3D constructive solid geometry (CSG) mesh intersection, built in Lean 4. This project revolutionizes trust in AI-generated code by allowing human reviewers to verify only 93 lines of concise specification, while the Lean checker guarantees the correctness of over 1,000 lines of complex AI-written implementation. Users can test the verified kernel via a local web demo that processes STL files without sending data to a server. While prioritizing mathematical certainty over raw speed, it ensures watertight, well-formed output meshes, proving that rigorous formal verification can coexist with AI-driven development.
A human reviewer only needs to read 93 lines of formal specification and run the Lean checker to certify the correctness of the kernel, skipping the intricate 1000+ lines of AI-written implementation.
- permute
Note that the claims are about the kernel that computes the mesh intersection, not the web demo: While the kernel is formally verified, the UI and glue code (that call the kernel) are not. I once hit a bug that looked like there were holes in the resulting mesh: I found that it was an overflow in the glue code (now fixed) that converts the exact rationals coordinates of the output mesh, for which we prove the specification, to floats before sending them to the GPU. All geometry is happening inside the kernel, for which we know the specification holds.
- bob1029
This is really neat. I think CSG is one of the more intuitive ways to build 3d environments (especially 'indoor' ones). No geometry is ever destroyed in a proper CSG workflow. A hierarchy of brushes makes it possible to very rapidly iterate parameters like how long a hallway is or the time it takes to get from one objective to another. Often, you only have to apply a transform to a single brush to affect something that would take a non-CSG workflow an entire afternoon to recover from.
The current story with CSG around commercial game engines is pretty awful. Unity has some 3rd party options that can work well but they're also glitchy and don't integrate well with the other parts of the ecosystem. For a while I thinking about building my own CSG implementation but the exact things this project solved were what was stopping me. The EditorWindow integration stuff is not as scary to me (although it is painful). The advanced geometry and set operations is what kept me from trying. It appears that dragon has been (at least partially) slain.
- brandonpelfrey
This seems like very cool work. I'm sorry if I missed it: I'm still not sure how we go from verified proof (Great!) to an implementation (by LLM or by Human) which you're sure actually conforms to the proof? How do we know that the implementation maps precisely to the description within the proof?
- agentultra
> A human reviewer only needs to read 93 lines of formal specification and run the Lean checker to certify the correctness of the kernel, skipping the intricate 1000+ lines of AI-written implementation. To prove correctness, AI autonomously wrote over 60,000 lines of Lean proofs, which also never have to be inspected by a human.
I am curious about the approach as I find claims like this hard to believe. There is a theory behind proof kernels that they must be small because they have to be trusted and verifiable by a human. Otherwise the whole system breaks.
How does one trust an LLM generated kernel is proving the right things?
- swiftcoder
Ok, that's very cool. I don't yet grasp exactly how this deals with numerical stability - the one true enemy of mesh-based CSG operations