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i've always wondered how web and functional programming interact. there's, for example TypeScript and Elm. These are not designed for mathematical proofs.

https://www.typescriptlang.org/ https://elm-lang.org/

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You'd probably do it in the theorem prover extracting it to a language with a web framework or use a language with a web framework that are both easier to prove. Here's a few places to explore:

http://www.impredicative.com/ur/

https://wiki.haskell.org/Web/Frameworks

Note: You'd pick the purest of them probably.

Most work I've seen on web applications with formal focus used model checkers, though.

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.397....

https://www.iro.umontreal.ca/~sahraouh/papers/Forte2004.pdf

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