> Respectfully, no, it sounds like you write them yourself, instead

I write them myself and prove them, and then use them.

Or, more likely, I take code from elsewhere, reduce it to its core, prove that — if possible; it often isn't, because code from elsewhere is often fundamentally Turing-hard — and then, if I was able to prove it, use it.

Or, even more likely, I use a library of self-contained code that lives inside the prover's model, that someone else already did all the hard work of getting the prover to accept.

Think of it like this: would you call an arbitrary utility function from an HTTP library inside a reference implementation of a cryptographic cipher?

No, because that arbitrary utility function has no abstract-mathematical equivalent. You can't prove anything about code that contains a black-box like that. The code, with the call to the HTTP library inside it, isn't a discrete-mathematics-specified-in-procedural-language proof of anything any more.

If you want to prove anything about code, the code needs to 1. live inside your proof (along with all its transitive dependencies), and 2. be modified such that all its base types are types that have complete models in your chosen prover's algebra (e.g. no non-fixed-size bit-vectors.)

> I apologize, but you and I have strongly contrasting opinions here.

What are FSMs "for" in your mind, then?

I use them when I want to be able to prove the behavior of something formally, and then reuse the proof as a production-quality implementation of that thing as-is. This allows the design↔implementation equivalent of "documentation drift" to be avoided — you don't have to trust that the programmer that translated the math into code did it correctly this time; you just have to trust a single compiler/code generator (that itself can have been proof-verified.)

I use FSMs for the same reason I use PEGs, or cellular automata, or other such formalisms, in place of just trying to prove an abstract Turing machine: because there are known ways to prove certain properties of these low-power formalisms in bounded time, while there's no known (or sometimes, no possible) equivalent for Turing machines generally.

> My library, and finite state machines, which are the superfamily containing DFA and a great many other things. DFA is not a common interpretation of the phrase FSM; usually that phrase means a Mealy machine or a Moore machine, or maybe a Harel machine.

You're being a lot more pedantic here than I was attempting to be. I meant to refer to "deterministic finite-state transducers" — the class of thing to which Mealy machines are a subset. But people on HN don't know what those are, while they do generally know what a DFA is. And a DFA has the same computational power as a Mealy machine generally; it's just a special construction of one (like a Binary Search Tree is just a special construction of a Binary Tree.)

I was trying to contrast with NFAs, which aren't FSMs (deterministic finite-state transducers) at all, but rather are computationally-equivalent to pushdown automata.

Maybe, rather than a DFA, I should have made the analogy to LR parsing, which also has equivalent abstract-computational-power requirements.