Most software verification is proved "for all possible inputs", e.g. the system maintains some invariant regardless of which sequence of actions is taken. Those inputs could be from a user interacting with the software, or they could be API calls made to our library, etc. There's no reason you couldn't model an AI agent's choices in a similar way: i.e. prove that the desired invariants hold, for all possible sequences of actions the AI component might choose.
That might be straightforward, if the AI agent is constrained to pick from a simple set of domain-specific actions. In contrast, we can't say much about a system involving an AI agent with a full Bash shell.
> What scenarios does it make sense to have a lean proof from the start?
It's usually much easier to verify software that was written and structured with that in mind; rather than trying to reason about some arbitrary blob of code after-the-fact. So, if you do want to prove stuff, it should very much be in there from the start.
Without suggesting that this has no value-- it must be noted that such verification only applies on theoretical hardware and to the specific behavior in scope of the verification. Actual hardware is nondeterministic, and an algorithm can be correct while suffering from a side-channel.
We need proof systems that are designed to work with our programming languages- working with the code so it more likely represents reality. I like verus with Rust and I have a skill for using it: https://github.com/gregwebs/skills-sdlc/blob/main/skills/rus...
At least in domains that are "important" (and perhaps everyone thinks their business/API is important?), I'd want this.
For example - Stripe. If I'm using the stripe API, I want it to be guaranteed to work exactly as documented in all scenarios, given that money is at stake?
Getting the Stripe API written in Lean is a different challenge, of course.