Polytypic Programming in Haskell

A polytypic (or generic) program captures a common pattern of computation over di erent datatypes by abstracting over the structure of the datatype. Examples of algorithms that can be de ned polytypically are equality tests, mapping functions and pretty printers. A commonly used technique to implement polytypic programming is specialization, where a specialized version of a polytypic function is generated for every datatype it is used at. In this paper we describe an alternative technique that allows polytypic functions to be de ned using Haskell's class system (extended with multi-parameter type classes and functional dependencies). This technique brings the power of polytypic programming inside Haskell allowing us to de ne a Haskell library of polytypic functions. It also increases our exibility, reducing the dependency on a polytypic language compiler.