The deep link equating math proofs and computer programs
Okay. Today I'll be the idiot.I don't get it. Or rather, I don't get the significance of the Curry-Howard Isomorphism. Questions:1) Is there an example of a proof and its corresponding program that makes you say "whoa, trippy, I didn't expect those to be related"? Like, yeah, an Int -> Boolean function "proves" you can construct a Boolean from an integer, but ... so what? What would a non-trivial proof (say, on the order of the Pons Asinorum) look like as a program?2) Are the "programs" referred to here to merely pure functions (i.e. side effect-free, global state-free ones)? It sounds like it is based on lines like this:>When a computer program runs, each line is “evaluated” to yield a single output.That ... seems to cram  "computer programs" into some kind of Procrustean bed unless we're taking about pure functions. But then it also talks about how CHI has applications in verifiable programs, which, I'm told, can reason about side effects.Feel free to call me an idiot, as long as you can also inspire an aha-moment.