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DOI: 10.4230/LIPIcs.TYPES.2014.1

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

Authors: Benedikt Ahrens and Régis Spadotti

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

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.

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Benedikt Ahrens and Régis Spadotti. Terminal Semantics for Codata Types in Intensional Martin-Löf Type Theory. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 1-26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{ahrens_et_al:LIPIcs.TYPES.2014.1,
  author =	{Ahrens, Benedikt and Spadotti, R\'{e}gis},
  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 =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.1},
  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}
}

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DOI: 10.4230/LIPIcs.TLCA.2015.17

Non-Wellfounded Trees in Homotopy Type Theory

Authors: Benedikt Ahrens, Paolo Capriotti, and Régis Spadotti

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

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.

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Benedikt Ahrens, Paolo Capriotti, and Régis Spadotti. Non-Wellfounded Trees in Homotopy Type Theory. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 17-30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{ahrens_et_al:LIPIcs.TLCA.2015.17,
  author =	{Ahrens, Benedikt and Capriotti, Paolo and Spadotti, R\'{e}gis},
  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 =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.17},
  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}
}

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Documents authored by Spadotti, Régis

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

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Non-Wellfounded Trees in Homotopy Type Theory

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