Journal of Symbolic Logic

The Emptiness Problem for Intersection Types

Pawel Urzyczyn

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745876

Mathematical Reviews number (MathSciNet)
MR1779757

Zentralblatt MATH identifier
0937.03022

JSTOR
links.jstor.org

Citation

Urzyczyn, Pawel. The Emptiness Problem for Intersection Types. J. Symbolic Logic 64 (1999), no. 3, 1195--1215. https://projecteuclid.org/euclid.jsl/1183745876


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