Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 64, Issue 3 (1999), 1195-1215.
The Emptiness Problem for Intersection Types
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.
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. https://projecteuclid.org/euclid.jsl/1183745876