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.2015.8
URN: urn:nbn:de:0030-drops-84787
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8478/
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Parmann, Erik

Functional Kan Simplicial Sets: Non-Constructivity of Exponentiation

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LIPIcs-TYPES-2015-8.pdf (0.5 MB)


Abstract

Functional Kan simplicial sets are simplicial sets in which the horn-fillers required by the Kan extension condition are given explicitly by functions. We show the non-constructivity of the following basic result: if B and A are functional Kan simplicial sets, then A^B is a Kan simplicial set. This strengthens a similar result for the case of non-functional Kan simplicial sets shown by Bezem, Coquand and Parmann [TLCA 2015, v. 38 of LIPIcs]. Our result shows that-from a constructive point of view-functional Kan simplicial sets are, as it stands, unsatisfactory as a model of even simply typed lambda calculus. Our proof is based on a rather involved Kripke countermodel which has been encoded and verified in the Coq proof assistant.

BibTeX - Entry

@InProceedings{parmann:LIPIcs:2018:8478,
  author =	{Erik Parmann},
  title =	{{Functional Kan Simplicial Sets: Non-Constructivity of Exponentiation}},
  booktitle =	{21st International Conference on Types for Proofs and Programs (TYPES 2015)},
  pages =	{8:1--8:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-030-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{69},
  editor =	{Tarmo Uustalu},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8478},
  URN =		{urn:nbn:de:0030-drops-84787},
  doi =		{10.4230/LIPIcs.TYPES.2015.8},
  annote =	{Keywords: constructive logic, simplicial sets, semantics of simple types}
}

Keywords: constructive logic, simplicial sets, semantics of simple types
Collection: 21st International Conference on Types for Proofs and Programs (TYPES 2015)
Issue Date: 2018
Date of publication: 15.03.2018


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