Among other general advice, my CLAUDE.md insists Claude prove to me each unit of change works as expected, and I'm usually just hoping for it to write tests and convince me they're actually running and passing. A proof assistant seems overkill here, and yet Claude often struggles to assemble these informal proofs. I can see the benefit of a more formal proof language, along with adding a source of programmatic feedback, compared to open-ended verbal proof.

"Overkill" of course is an editorial word, and if you know about https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon... then you know many statically typed programming languages are essentially proof assistants, where the proof goal is producing well-typed programs. LLMs are already quite good at interacting with these programming language proof assistants, as you can see any time a competent LLM interacts with the Rust borrow checker, for example.