Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equality functions, unifiers, rewriting functions, etc. Such functions are called polytypic functions.
A polytypic function is a function that is defined by induction on the structure of user-defined datatypes. This talk introduces polytypic functions, shows how to construct and reason about polytypic functions and says a few words about the implementation of the polytypic programming system PolyP.
PolyP extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions. Programs in the extended language are translated to Haskell.