> Obviously, we want to stick with useful data structures, so we use constructive logic for programming.

I don't know who "we" are, but most proofs of algorithm correctness use classical logic.

Also, there's nothing "obvious" about what you said unless you want proof objects, and why you'd want that is far from obvious in itself.

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amavect 15 minutes ago | parent | next [-]

Well, to translate my words to your liking: "In my opinion, everyone already uses a sort of constructive logic for programming."

I challenge you on "most proofs of algorithm correctness use classical logic". That means double negation elimination, or excluded middle. I bet most proofs don't use those. Give examples.

	▲	zozbot234 3 minutes ago \| parent [-]
		Proofs of safety are proving a negative: they're all about what an algorithm won't do. So constructivism is irrelevant to those, because the algorithm has provided all the constructive content already! Proofs of liveness/termination are the interesting case. You might also add formulating an algirithm to begin with, or porting it from a less restrictive to a more restrictive model of computation, as kinds of proofs in CS that are closely aligned to what we'd call constructive.

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zozbot234 3 hours ago | parent | prev [-]

The difference only becomes evident when proving liveness/termination (since if your algorithm terminates successfully it has to construct something, and it only has to be proven that it's not incorrect) and then it turns out that these proofs do use something quite aligned to constructive logic.

	▲	pron an hour ago \| parent [-]
		... and also to classical logic. Liveness proofs typically require finding a variant that converges to some terminal value, and that's just as easy to do in classical logic as in constructive logic. I've been using formal methods for years now and have yet to see where constructive logic makes things easier (I'm not saying it necessarily makes things harder, either).