New project: a coding and formal verification agent for computational physics and applied mathematics. Auto-generate type-correct DSL code for equations and numerical schemes, autoformalize correctness properties in Lean/Isabelle/Rocq, then compile down to provably-correct C code

the part i wonder about is the gap between 'code is formally correct' and 'the physics model is right'. in computational physics the hard errors are often in modeling assumptions (turbulence closures, boundary conditions), not in numerics. fv guarantees the implementation but the model itself stays experimental

How do you plan to bridge the gap between the continuous math model and the discrete DSL without gettin stuck on floating point rounding and stanility issues

This work is based on our existing DSL + theorem-prover work which axiomatized the IEEE-754 for floating-point arithmetic as an algebraic structure: All correctness theorems are proved up to machine precision.

This might already be in one of your papers, but: I think the case for formal verification is clear wrt cryptography for example, or pure math. But I’m not sure I understand the case in physics. What does FV add in addition to the theory + experimentation loop?

This project is essentially an extremely powerful agentic extension of which perhaps gives some insight into what formal verification means in the context of a numerical code.

i think research on domain specific languages for llms would be quite interesting; sort of the next logical evolution of the racket program; like when do llms benefit from domain specific languages, can they create them usefully, etc...

Now you are talking -- hope you will open source this -- this has so many good uses

That is a big step toward this, Will you be adding deeper layers to deal with the behavioral differences between CISC and RISC CPU architectures so that determinism is nailed down completely? If you can the complete system can generate massive amounts of very high quality synthetic data for further LLM training.

what happens if you give it something like this: tomorrow or over the next few days i will make a video explaining the total proof on paper from start to finish it's lean formalized as far as i can get it on vibes

I am working on a similar harness! Strong typing and automatic projection to solvers is very valuable in operationalized proof frameworks. Do you mind sharing more of your plans for this project as software, broad release plans, etc.?

Hmm..

Incredible, I didn't know numerical simulations could even be provably correct

How are you implementing the agent? Custom loop or using some framework?

🤔

We might have to stop you, you're getting too close to our stuff LOL!