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DOI: 10.4230/LIPIcs.TYPES.2016.6
URN: urn:nbn:de:0030-drops-98541
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9854/
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Bezem, Marc ; Coquand, Thierry ; Nakata, Keiko ; Parmann, Erik

Realizability at Work: Separating Two Constructive Notions of Finiteness

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LIPIcs-TYPES-2016-6.pdf (0.5 MB)


Abstract

We elaborate in detail a realizability model for Martin-Löf dependent type theory with the purpose to analyze a subtle distinction between two constructive notions of finiteness of a set A. The two notions are: (1) A is Noetherian: the empty list can be constructed from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every enumeration of A contains a duplicate.

BibTeX - Entry

@InProceedings{bezem_et_al:LIPIcs:2018:9854,
  author =	{Marc Bezem and Thierry Coquand and Keiko Nakata and Erik Parmann},
  title =	{{Realizability at Work: Separating Two Constructive Notions of Finiteness}},
  booktitle =	{22nd International Conference on Types for Proofs and  Programs (TYPES 2016)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-065-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{97},
  editor =	{Silvia Ghilezan and Herman Geuvers and Jelena Ivetić},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9854},
  URN =		{urn:nbn:de:0030-drops-98541},
  doi =		{10.4230/LIPIcs.TYPES.2016.6},
  annote =	{Keywords: Type theory, realizability, constructive notions of finiteness}
}

Keywords: Type theory, realizability, constructive notions of finiteness
Seminar: 22nd International Conference on Types for Proofs and Programs (TYPES 2016)
Issue Date: 2018
Date of publication: 24.10.2018


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