License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2021.6
URN: urn:nbn:de:0030-drops-167759
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16775/
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Donkó, István ; Kaposi, Ambrus

Internal Strict Propositions Using Point-Free Equations

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LIPIcs-TYPES-2021-6.pdf (0.8 MB)


Abstract

The setoid model of Martin-Löf’s type theory bootstraps extensional features of type theory from intensional type theory equipped with a universe of definitionally proof irrelevant (strict) propositions. Extensional features include a Prop-valued identity type with a strong transport rule and function extensionality. We show that a setoid model supporting these features can be defined in intensional type theory without any of these features. The key component is a point-free notion of propositions. Our construction suggests that strict algebraic structures can be defined along the same lines in intensional type theory.

BibTeX - Entry

@InProceedings{donko_et_al:LIPIcs.TYPES.2021.6,
  author =	{Donk\'{o}, Istv\'{a}n and Kaposi, Ambrus},
  title =	{{Internal Strict Propositions Using Point-Free Equations}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{6:1--6:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16775},
  URN =		{urn:nbn:de:0030-drops-167759},
  doi =		{10.4230/LIPIcs.TYPES.2021.6},
  annote =	{Keywords: Martin-L\"{o}f’s type theory, intensional type theory, function extensionality, setoid model, homotopy type theory}
}

Keywords: Martin-Löf’s type theory, intensional type theory, function extensionality, setoid model, homotopy type theory
Collection: 27th International Conference on Types for Proofs and Programs (TYPES 2021)
Issue Date: 2022
Date of publication: 04.08.2022
Supplementary Material: Software (Formalisation): https://bitbucket.org/akaposi/prop archived at: https://archive.softwareheritage.org/swh:1:dir:6648713cc70e9c6fa8a71cccaa31c1d91cfbc418


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