Journal of Symbolic Logic

The Emptiness Problem for Intersection Types

Pawel Urzyczyn

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We study the intersection type assignment system as defined by Barendregt, Coppo and Dezani. For the four essential variants of the system (with and without a universal type and with and without subtyping) we show that the emptiness (inhabitation) problem is recursively unsolvable. That is, there is no effective algorithm to decide if there is a closed term of a given type. It follows that provability in the logic of "strong conjunction" of Mints and Lopez-Escobar is also undecidable.

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J. Symbolic Logic, Volume 64, Issue 3 (1999), 1195-1215.

First available in Project Euclid: 6 July 2007

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Urzyczyn, Pawel. The Emptiness Problem for Intersection Types. J. Symbolic Logic 64 (1999), no. 3, 1195--1215.

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