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.2016.7
URN: urn:nbn:de:0030-drops-98554
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9855/
Booij, Auke B. ; Escardó, Martín H. ; Lumsdaine, Peter LeFanu ; Shulman, Michael
Parametricity, Automorphisms of the Universe, and Excluded Middle
| pdf-format: |
|
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: | 05.11.2018 |
