License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2019.11
URN: urn:nbn:de:0030-drops-105188
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10518/
Coquand, Thierry ;
Huber, Simon ;
Sattler, Christian
Homotopy Canonicity for Cubical Type Theory
Abstract
Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. In this paper we show by a sconing argument that if we remove these equations for the path lifting operation from the system, we still retain homotopy canonicity: every natural number is path equal to a numeral.
BibTeX - Entry
@InProceedings{coquand_et_al:LIPIcs:2019:10518,
author = {Thierry Coquand and Simon Huber and Christian Sattler},
title = {{Homotopy Canonicity for Cubical Type Theory}},
booktitle = {4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
pages = {11:1--11:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-107-8},
ISSN = {1868-8969},
year = {2019},
volume = {131},
editor = {Herman Geuvers},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10518},
URN = {urn:nbn:de:0030-drops-105188},
doi = {10.4230/LIPIcs.FSCD.2019.11},
annote = {Keywords: cubical type theory, univalence, canonicity, sconing, Artin glueing}
}
Keywords: |
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cubical type theory, univalence, canonicity, sconing, Artin glueing |
Collection: |
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4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019) |
Issue Date: |
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2019 |
Date of publication: |
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18.06.2019 |