prover

We used the Boyer-Moore theorem prover and the Stanford Pascal Verifier, but the tools were not there yet.

Usually, it involves cajoling a theorem prover by adding lots of annotations to your code.

Main benefit those tools gave, per users, was making verification easier just because the prover's needs (and weaknesses) forced simplification of specs.

Hopefully it's now clear why having 'fix' in your prover language won't work!

You would actually need a full theorem prover to check the correctness of your code for you (which obviously Rust does not provide).

I know people talk about it as a theorem-prover, but how do I actually _use_ that?

Now you can at least change your prover while maintaining your axioms.

The F* type-checker aims to prove that programs meet their specifications using an automated theorem prover (usually Z3) behind the scenes to discharge proof obligations.

Everything in AI looked like a theorem prover back then.

I am hazy on the details, but I think TLA+ proofs are just checked by brute force, and not with an actual theorem prover?

I'm not familiar enough with Idris to know exactly how state is handled, but yes, Idris is a prover, since it has dependent types.

It was originally developed for a theorem prover.

If "prover" just means "has dependent types" then that's a much larger class than it sounds like.

I read the Shen language book on "logic, proof and computation" which got me into the idea of a theorem prover inside of your normal language.

Sometime in the not-too-distant future someone will make a natural language AI sophisticated enough to use this corpus as a scaffolding for "assisted" theorem proving, where the prover being assisted is a program generating completely formalized proofs and the assistance is coming from the natural-language AI parsing textbooks and journal articles.

The only industry language I'm aware of that meets these criteria and isn't a full-fledged theorem prover is ATS, and to call it a "mature alternative that is just as good" is kind of laughable.

Glad too see that I am not the only person to quite excited about the The Little Prover.