Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Castellan, Simon; Clairambault, Pierre; Dybjer, Peter https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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Undecidability of Equality in the Free Locally Cartesian Closed Category

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Abstract

We show that a version of Martin-Löf type theory with extensional identity, a unit type N1, Sigma, Pi, and a base type is a free category with families (supporting these type formers) both in a 1- and a 2-categorical sense. It follows that the underlying category of contexts is a free locally cartesian closed category in a 2-categorical sense because of a previously proved biequivalence. We then show that equality in this category is undecidable by reducing it to the undecidability of convertibility in combinatory logic.

BibTeX - Entry

@InProceedings{castellan_et_al:LIPIcs:2015:5160,
  author =	{Simon Castellan and Pierre Clairambault and Peter Dybjer},
  title =	{{Undecidability of Equality in the Free Locally Cartesian Closed Category}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{138--152},
  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/2015/5160},
  URN =		{urn:nbn:de:0030-drops-51602},
  doi =		{10.4230/LIPIcs.TLCA.2015.138},
  annote =	{Keywords: Extensional type theory, locally cartesian closed categories, undecidab- ility}
}

Keywords: Extensional type theory, locally cartesian closed categories, undecidab- ility
Seminar: 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)
Issue date: 2015
Date of publication: 15.06.2015


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