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.CSL.2020.13
URN: urn:nbn:de:0030-drops-116564
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11656/
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Cavallo, Evan ; Harper, Robert

Internal Parametricity for Cubical Type Theory

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LIPIcs-CSL-2020-13.pdf (0.7 MB)


Abstract

We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we call relativity. We demonstrate the use of the theory by analyzing polymorphic functions between higher inductive types, and we give an account of the identity extension lemma for internal parametricity.

BibTeX - Entry

@InProceedings{cavallo_et_al:LIPIcs:2020:11656,
  author =	{Evan Cavallo and Robert Harper},
  title =	{{Internal Parametricity for Cubical Type Theory}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11656},
  URN =		{urn:nbn:de:0030-drops-116564},
  doi =		{10.4230/LIPIcs.CSL.2020.13},
  annote =	{Keywords: parametricity, cubical type theory, higher inductive types}
}

Keywords: parametricity, cubical type theory, higher inductive types
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020


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