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/
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Coquand, Thierry ; Huber, Simon ; Sattler, Christian

Homotopy Canonicity for Cubical Type Theory

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LIPIcs-FSCD-2019-11.pdf (0.6 MB)

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: cubical type theory, univalence, canonicity, sconing, Artin glueing
Collection: 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)
Issue Date: 2019
Date of publication: 18.06.2019

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