One Monad to Prove Them All (Functional Pearl)
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One Monad to Prove Them All is a modern fairy tale about curiosity and perseverance, two important properties of a successful PhD student. We follow the PhD student Mona on her adventurous journey of proving properties about Haskell programs in the proof assistant Coq. In quest for a solution Mona goes on an educating journey through the land of functional programming. We follow her on her journey when she learns about concepts like free monads and containers as well as basics and restrictions of proof assistants like Coq. These concepts are well-known individually, but their interplay gives rise to a solution for Mona's problem that has not been presented before. More precisely, Mona's final solution does not only work for a specific monad instance but even allows her to prove monad-generic properties. That is, instead of proving properties over and over again for specific monad instances she is able to prove properties that hold for all monads. In the end of her journey Mona comes to the land of functional logic and the land of probabilistic programming. She learns that, because her proofs are monad-generic, they even hold in languages with other effects like non-determinism or probabilism. If you are a citizen of the land of functional programming or are at least familiar with its customs, had a journey that involved reasoning about functional programs of your own, or are just a curious soul looking for the next story about monads and proofs, then this tale is for you.
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