Haskell-style Overloading is NP Hard
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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.
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