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DOI: 10.4230/LIPIcs.TLCA.2015.17
URN: urn:nbn:de:0030-drops-51522
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5152/
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Ahrens, Benedikt ; Capriotti, Paolo ; Spadotti, Régis

Non-Wellfounded Trees in Homotopy Type Theory

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Abstract

We prove a conjecture about the constructibility of conductive types - in the principled form of indexed M-types - in Homotopy Type Theory. The conjecture says that in the presence of inductive types, coinductive types are derivable. Indeed, in this work, we construct coinductive types in a subsystem of Homotopy Type Theory; this subsystem is given by Intensional Martin-Löf type theory with natural numbers and Voevodsky's Univalence Axiom. Our results are mechanized in the computer proof assistant Agda.

BibTeX - Entry

@InProceedings{ahrens_et_al:LIPIcs:2015:5152,
  author =	{Benedikt Ahrens and Paolo Capriotti and R{\'e}gis Spadotti},
  title =	{{Non-Wellfounded Trees in Homotopy Type Theory}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{17--30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Thorsten Altenkirch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5152},
  URN =		{urn:nbn:de:0030-drops-51522},
  doi =		{10.4230/LIPIcs.TLCA.2015.17},
  annote =	{Keywords: Homotopy Type Theory, coinductive types, computer theorem proving, Agda}
}

Keywords: Homotopy Type Theory, coinductive types, computer theorem proving, Agda
Seminar: 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)
Issue Date: 2015
Date of publication: 12.06.2015


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