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The emptiness problem for intersection types

Published online by Cambridge University Press:  12 March 2014

Paweł Urzyczyn
Paweł Urzyczyn*
Affiliation:
Institute of Informatics, University of Warsaw, Ul. Banacha 2, 02-097 Warszawa, Poland E-mail: urzy@mimuw.edu.pl
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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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1195 - 1215
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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