Logic and Computation in a Lambda Calculus with Intersection and Union Types

Abstract

AbstractWe present an explicitly typed lambda calculus “à la Church” based on the union and intersection types discipline; this system is the counterpart of the standard type assignment calculus “à la Curry.” Our typed calculus enjoys the Subject Reduction and Church-Rosser properties, and typed terms are strongly normalizing when the universal type is omitted. Moreover both type checking and type reconstruction are decidable. In contrast to other typed calculi, a system with union types will fail to be “coherent” in the sense of Tannen, Coquand, Gunter, and Scedrov: different proofs of the same typing judgment will not necessarily have the same meaning. In response, we introduce a decidable notion of equality on type-assignment derivations inspired by the equational theory of bicartesian-closed categories.KeywordsType TheoryUnion TypeType AssignmentType CheckLambda CalculusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.