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.TYPES.2014.1
URN: urn:nbn:de:0030-drops-54891
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5489/
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Ahrens, Benedikt ; Spadotti, Régis

Terminal Semantics for Codata Types in Intensional Martin-Löf Type Theory

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Abstract

We study the notions of relative comonad and comodule over a relative comonad. We use these notions to give categorical semantics for the coinductive type families of streams and of infinite triangular matrices and their respective cosubstitution operations in intensional Martin-Löf type theory. Our results are mechanized in the proof assistant Coq.

BibTeX - Entry

@InProceedings{ahrens_et_al:LIPIcs:2015:5489,
  author =	{Benedikt Ahrens and R{\'e}gis Spadotti},
  title =	{{Terminal Semantics for Codata Types in Intensional Martin-L{\"o}f Type Theory}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{1--26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Hugo Herbelin and Pierre Letouzey and Matthieu Sozeau},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5489},
  URN =		{urn:nbn:de:0030-drops-54891},
  doi =		{10.4230/LIPIcs.TYPES.2014.1},
  annote =	{Keywords: relative comonad, Martin-L{\"o}f type theory, coinductive type, computer theorem proving}
}

Keywords: relative comonad, Martin-Löf type theory, coinductive type, computer theorem proving
Collection: 20th International Conference on Types for Proofs and Programs (TYPES 2014)
Issue Date: 2015
Date of publication: 12.10.2015

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