[lmm]

> Sure, but again when you want to verify an algorithm, it may use lots of black boxes, but the algorithm you are actually verifying is a white box. That algorithm is not a function; if it were, then you're not verifying the how just stating the what. The how of whatever it is that you actually want to verify (not the black boxes you're using) is a state machine. Other ways of thinking about it include, say, process calculi, lambda calculus etc., but at the point of verifying that, considering it a function is the one thing you cannot do, because that would be assuming what you're trying to prove.

Well a function is necessarily a function (if we enforce purity and totality at the language level). Presumably what we want to verify is that its output has certain properties, or that certain relations between input and output hold. But that seems like very much the kind of thing we can approach in the same way we'd analyse a mathematical function.