Isomorphism and Embedding

To me as a programmer, to write mathematical proofs that are mechanically checked by a computer feels empowering. To have these proofs as executable programs feels even more empowering. Therefore, our proofs have a computational aspect and vice-versa: our programs have a logical aspect. To be able to get an instant feedback while proving a theorem is amazing. With Agda, a dependently typed functional programming language, one can interactively write a proof by getting guidance from Agda as to what is left to prove. Furthermore, Agda checks the correctness of proofs by following a set of rules. Unlike with pen and paper proofs, proofs in Agda are much more rigorous because there is no room for hand-waving nor unwarranted claims for something to be trivial. An uninformed mathematician will likely find this comparison to Agda hard to believe.

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