Satisfying subtype inequalities in polynomial space

This paper studies the complexity of type inference in l-calculus with subtyping. Infering types is equivalent to solving systems of subtype inequalities. These inequalities are solved over simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a new PSPACE upper bound. Together with the previously known lower bound, this result settles completely the complexity of the problem, which is PSPACE-complete. We use a technique of independent theoretical interest that simplifies existing methods developed in the literature. Finally, we show how our polynomial space algorithm, although mainly theoretical, can lead to a slight practical improvement of existing implementations. Copyright 2002 Elsevier Science B.V.

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