Satisfying Subtype Inequalities in Polynomial Space

This paper studies the complexity of type inference in λ-calculus with subtyping. Type inference is equivalent to solving systems of subtype inequalities. We consider simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a PSPACE upper bound. Together with the known lower bound, this result settles completely the complexity of type inference over simple types, which is PSPACE-complete. We use a technique of independent theoretical interest that simplifies existing methods developed in the literature. Finally the algorithm, although mainly theoretical, can lead to a slight practical improvement of existing implementations.

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