Type classes are a very useful mechanism to write programs on abstract structures and support notational abuse by overloading. That's ample good reason to have them in a proof-assistant like Coq. I implemented with Nicolas Oury a port of type classes in Coq and some libraries using the system: a port of the Haskell prelude, a development of category theory and the beginning of order theory. If you would like to take any of these to the next step or have any kind of reaction after seeing them I will gladly answer your mail. I've also given some talks about classes and setoid rewriting , .