Haskell - style Overloading is NP - hardDennis

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 satissability problem. Given a set of type assumptions C over nite types and a type basis A, is there is a substitution S that satisses C in that A ` CS is derivable? Under arbitrary overloading, the problem is undecidable. Haskell limits overloading to a form similar to that proposed by Kaes called parametric overloading. We formally characterize parametric overloading in terms of a regular tree language and prove that although de-cidable, satissability is NP-hard when overloading is parametric.