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Documents authored by Danielsson, Nils Anders

Document
DOI: 10.4230/LIPIcs.TYPES.2019.10
Higher Inductive Type Eliminators Without Paths

Authors: Nils Anders Danielsson

Published in: LIPIcs, Volume 175, 25th International Conference on Types for Proofs and Programs (TYPES 2019)

Abstract
Cubical Agda has support for higher inductive types. Paths are integral to the working of this feature. However, there are other notions of equality. For instance, Cubical Agda comes with an identity type family for which the J rule computes in the usual way when applied to the canonical proof of reflexivity, whereas typical implementations of the J rule for paths do not. This text shows how one can use some of the higher inductive types definable in Cubical Agda with arbitrary notions of equality satisfying certain axioms. The method works for several examples taken from the HoTT book, including the interval, the circle, suspensions, pushouts, the propositional truncation, a general truncation operator, and set quotients.
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Nils Anders Danielsson. Higher Inductive Type Eliminators Without Paths. In 25th International Conference on Types for Proofs and Programs (TYPES 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 175, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{danielsson:LIPIcs.TYPES.2019.10,
  author =	{Danielsson, Nils Anders},
  title =	{{Higher Inductive Type Eliminators Without Paths}},
  booktitle =	{25th International Conference on Types for Proofs and Programs (TYPES 2019)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-158-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{175},
  editor =	{Bezem, Marc and Mahboubi, Assia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2019.10},
  URN =		{urn:nbn:de:0030-drops-130749},
  doi =		{10.4230/LIPIcs.TYPES.2019.10},
  annote =	{Keywords: Cubical Agda, higher inductive types}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.TYPES.2011
LIPIcs, Volume 19, TYPES'11, Complete Volume

Authors: Nils Anders Danielsson and Bengt Nordström

Published in: LIPIcs, Volume 19, 18th International Workshop on Types for Proofs and Programs (TYPES 2011)

Abstract
LIPIcs, Volume 19, TYPES'11, Complete Volume
Cite as

18th International Workshop on Types for Proofs and Programs (TYPES 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Proceedings{danielsson_et_al:LIPIcs.TYPES.2011,
  title =	{{LIPIcs, Volume 19, TYPES'11, Complete Volume}},
  booktitle =	{18th International Workshop on Types for Proofs and Programs (TYPES 2011)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-49-1},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{19},
  editor =	{Danielsson, Nils Anders and Nordstr\"{o}m, Bengt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2011},
  URN =		{urn:nbn:de:0030-drops-41132},
  doi =		{10.4230/LIPIcs.TYPES.2011},
  annote =	{Keywords: Applicative (Functional) Programming, Software/Program Verification, Specifying and Verifying and Reasoning about Programs, Mathematical Logic}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TYPES.2011.i
Frontmatter, Table of Contents, Preface, Workshop Organization

Authors: Nils Anders Danielsson and Bengt Nordström

Published in: LIPIcs, Volume 19, 18th International Workshop on Types for Proofs and Programs (TYPES 2011)

Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization
Cite as

18th International Workshop on Types for Proofs and Programs (TYPES 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 19, pp. i-vii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{danielsson_et_al:LIPIcs.TYPES.2011.i,
  author =	{Danielsson, Nils Anders and Nordstr\"{o}m, Bengt},
  title =	{{Frontmatter, Table of Contents, Preface, Workshop Organization}},
  booktitle =	{18th International Workshop on Types for Proofs and Programs (TYPES 2011)},
  pages =	{i--vii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-49-1},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{19},
  editor =	{Danielsson, Nils Anders and Nordstr\"{o}m, Bengt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2011.i},
  URN =		{urn:nbn:de:0030-drops-38957},
  doi =		{10.4230/LIPIcs.TYPES.2011.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
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