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haskell-coq
Common Haskell type classes written up in the Coq (GALLINA) theorem prover language for proving properties about Haskell data types and functions [Coq]
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There are theorem proving languages which do what you describe, but this is well beyond the scope of what rust can do. For example, here is a typeclass (trait) for a monoid written in coq: https://github.com/domdere/haskell-coq/blob/master/src/classes/Monoid.v
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