Logic and computation in a lambda calculus with intersection and union types

Authors:
Daniel J. Dougherty;Luigi Liquori
Affiliations:
Worcester Polytechnic Institute;INRIA, France
Venue:
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Year:
2010

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Abstract

We 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.