Sorry for the slow reply here Jason! And thank you for the thoughtful comment.
If you carve reality at the right points, specification is easy.
I think I am just very skeptical this can, in general, be done. In your example of a sandbox, your spec would have excluded anything with any kind of web access whatsoever, since any web access necessarily opens the door to side-effects. Such a sandbox would never have been used by the big labs on account of excluding the specific web-browsing behaviors they want to train for. Therefore, it is a useless, academic specification.
In general, I maintain nearly all systems which are “easily” specified like that are actually not easily specifiable, once the specifier encounters the reality of the needs of capital.
Alas, nobody has released a full machine-readable model of any hardware used in production yet.
MIPS is used in production, e.g. in some internet routers, and is simple enough you could do this quite quickly with Claude. I’m sure there’s plenty of hardware that’s simple enough to reverse engineer and formalize. Maybe it’s worth doing so just to show it’s possible?
Verified compilers are just a cost-saving (proof sharing) technique for binary-level verification.
Totally disagree, they are also a way to bootstrap specification, since all the types in the language form a kind of latent spec. Moreover it is considerably easier to write a spec relative to an abstraction than it is relative to a concretization.
If we are verifying everything, why not just verify that we have caught all bugs that could ever be caught by fuzzing?
I assume an adversarial world in which, due to the needs of capital, many systems remain black boxes, and it is nevertheless a social good to report bugs/vulns to maintainers. This is a considerably more realistic assumption than the idea that you will get to formally verify Microsoft Word.
Relevant yes, but not to the outcome of the conjecture. Ramana found this bug and used it cheekily as part of the rollout for his company, which uses Candle, a verified verifier he co-authored. But in that case, anyone (including Claude) who reviewed his Collatz proof, was able to find the fact that the “proof” was cheating. My claim (which Thomas disputes) is that within one year, such a “proof” will survive AI-based and human scrutiny, despite being incorrect.