Haskell-style Overloading is NP Hard

Abstract

Extensions of the ML type system, based on constrained type schemes, have been proposed for languages with overloading. Type inference in these systems requires solving the following satisfiability problems. Given a set of type assumptions C over finite types, and a type basis A, is there is a substitution S that satisfies C in that A 1- CS is derivable? Under arbitrary overloading, the problem is undecidable. Haskell limits overloading to a form similar to that proposed by Keas called parametric overloading. We formally characterize parametric overloading in terms of a regular tree language and prove that although decidable, satisfiability is NP-hard when overloading is parametric.