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One limitation of this approach seems to be (meaning I haven't found a paper/article stating otherwise yet) that it cannot express all of the possibilities of function overloading. For example, in GLSL it is valid to multiply a matrix by a vector. It is also valid to multiply a vector by a matrix. Both forms return a matrix, but the signatures are different. The first is 'a, b -> a' and the second is 'b, a -> a'. This would require two differently named functions in a qualified type system.