Intersection Types for the Computational lambda-Calculus

07/12/2019

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by   Ugo de'Liguoro, et al.

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We study polymorphic type assignment systems for untyped lambda-calculi with effects. We introduce an intersection type assignment system for Moggi's computational lambda-calculus, where a generic monad T is considered, and provide models of the calculus via inverse limit and filter model constructions and relate them. We prove soundness and completeness of the type system, together with subject reduction and expansion properties. Finally we establish the computational adequacy of the filter model via a characterization theorem of convergent terms.