Polyp | a Polytypic Programming Language Extension

Many functions have to be written over and over again for di erent datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on di erent datatypes. Examples of such functions are pretty printers, debuggers, equality functions, uni ers, pattern matchers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is de ned by induction on the structure of user-de ned datatypes. This paper extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks de nitions of polytypic functions, and infers the types of all other expressions using an extension of Jones' theories of quali ed types and higher-order polymorphism. The semantics of the programs in the extended language is obtained by adding type arguments to functions in a dictionary passing style. Programs in the extended language are translated to Haskell.