I don't have experience with proof based tools, so I'm not sure what's feasible.
I can imagine prompting an LLM to build provably correct software. Aren't we already doing something similar already when we remind it to write unit tests and account for all edge cases?
Actually writing provably correct software from scratch sounds terribly tedious, which is why I've never explored it. But maybe an LLM could make that task more approachable.
It gave me something which looked pretty legit. Of course, the generated output very likely to be subtly wrong, but as starting input to a formal checked specification/proof process it seemed like a good start.
I wrote some UTF-8 based string handling software back in the day. It doesn't seem unreasonable to write up a set of requirements and edge cases and then have a formal mechanism prove correctness for common UTF-8 string manipulation operations.
[PEAK HN ON] Now if we could just write provably correct exception handling, we could solve one of the two PHP vulns from today. [PEAK HN OFF]
I should check it against my email address validator that would be a nice benchmark. It's interesting that there are people that are using email addresses that are not actually valid according to the standard.
We can have an LLM enumerate all those edge cases, and we can assemble them into a spec. Then we can integrate that spec into a proof.
And because the spec is functional rather than expressive, we can produce copyright-free, provably correct reference implementations whose correctness is as strong as our spec and our proof process.
This reference implementation would then be available for use by a language like PHP, or perhaps an LLM generating a vibe-coded dependency.
Over time, then, the accumulation of such proven reference works grows. We'll never prove all the application code out there correct, but incremental progress is possible.