Inheritance is great 1- the simplest, purest for thereof is prototype inheritance; but if your language only offers classes, this happens at the metalevel only. 2- classes are fine; but if your language only offers typeclasses, this happens at the metalevel only, with no state.
You incrementally refine the constraint-specifying classes, then you let the solver run wild (or with suitable hints) on the complete specification after you compute the fix-points types for the classes you instantiate.
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Equivalently, you use typeclasses to specify your problem in Coq, then use suitable magic tactics to find terms that inhabit the specified types.
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