The usual way to check whether a definition is correct is to prove properties about it that you think should hold. TLA+ has good support for this, both with model checking as well as simple proofs.

maybe run it through few other LLMs depending on how much confidence you need - o3 pro, gemini 2.5 pro, claude 3.7, grok 3, etc..

Then you need to be able to formally prove the equivalence of various TLA+ programs (maybe that's a solved problem?)

No idea about SOTA but naively it doesn't seem like a very difficult problem:

- Ensure all TLA+ specs produced have the same inputs/outputs (domains, mostly a prompting problem and can solved with retries)

- That all TLA+ produce the same outputs for the same inputs (making them functionally equivalent in practice, might be computationally intensive)

Of course that assumes your input domains are countable but it's probably okay to sample from large ranges for a certain "level" of equivalence.

EDIT: Not sure how that will work with non-determinism though.

I didn't mean generate separate TLA programs. Rather, other LLMs review and comment on whether this TLA program satisfies the user's specification.