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DOI: 10.4230/LIPIcs.TYPES.2016.7
URN: urn:nbn:de:0030-drops-98554
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9855/
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Booij, Auke B. ; Escardó, Martín H. ; Lumsdaine, Peter LeFanu ; Shulman, Michael

Parametricity, Automorphisms of the Universe, and Excluded Middle

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Abstract

It is known that one can construct non-parametric functions by assuming classical axioms. Our work is a converse to that: we prove classical axioms in dependent type theory assuming specific instances of non-parametricity. We also address the interaction between classical axioms and the existence of automorphisms of a type universe. We work over intensional Martin-Löf dependent type theory, and for some results assume further principles including function extensionality, propositional extensionality, propositional truncation, and the univalence axiom.

BibTeX - Entry

@InProceedings{booij_et_al:LIPIcs:2018:9855,
  author =	{Auke B. Booij and Mart{\'i}n H. Escard{\'o} and Peter LeFanu Lumsdaine and Michael Shulman},
  title =	{{Parametricity, Automorphisms of the Universe, and Excluded Middle}},
  booktitle =	{22nd International Conference on Types for Proofs and  Programs (TYPES 2016)},
  pages =	{7:1--7:14},
  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/2018/9855},
  URN =		{urn:nbn:de:0030-drops-98554},
  doi =		{10.4230/LIPIcs.TYPES.2016.7},
  annote =	{Keywords: relational parametricity, dependent type theory, univalent foundations, homotopy type theory, excluded middle, classical mathematics, constructive mat}
}

Keywords: relational parametricity, dependent type theory, univalent foundations, homotopy type theory, excluded middle, classical mathematics, constructive mat
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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