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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16775/
Donkó, István ;
Kaposi, Ambrus
Internal Strict Propositions Using Point-Free Equations
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}
}
