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Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory (2001)
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| Venue: | Pages 221–230 of: Symposium on Logic in Computer Science |
| Citations: | 5 - 3 self |
BibTeX
@INPROCEEDINGS{Pfenning01intensionality,extensionality,,
author = {Frank Pfenning},
title = {Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory},
booktitle = {Pages 221–230 of: Symposium on Logic in Computer Science},
year = {2001},
pages = {01}
}
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Abstract
We develop a uniform type theory that integrates intensionality, extensionality, and proof irrelevance as judgmental concepts. Any object may be treated intensionally (subject only to #-conversion), extensionally (subject also to ##-conversion), or as irrelevant (equal to any other object at the same type), depending on where it occurs. Modal restrictions developed in prior work for simple types are generalized and employed to guarantee consistency between these views of objects. Potential applications are in logical frameworks, functional programming, and the foundations of first-order modal logics.
