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Last update: 9/11/2012 3:13 PM
| Authors |
M. Bezem Thierry Coquand Simon Huber |
|---|---|
| Published in | Journal of Automated Reasoning |
| Volume | 63 |
| Issue | 2 |
| Pages | 159-171 |
| ISSN | 0168-7433 |
| Publication year | 2019 |
| Published at |
Department of Computer Science and Engineering, Computing Science, Programming Logic Department of Computer Science and Engineering (GU) |
| Pages | 159-171 |
| Language | en |
| Links |
dx.doi.org/10.1007/s10817-018-9472-... |
| Keywords | Dependent type theory, Univalence axiom, Cubical sets, Computer Science |
| Subject categories | Computer and Information Science |
In this note we show that Voevodsky's univalence axiom holds in the model of type theory based on cubical sets as described inBezem et al. (in: Matthes and Schubert (eds.) 19th international conference on types for proofs and programs (TYPES 2013), Leibniz international proceedings in informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum fur Informatik, Dagstuhl, Germany, vol26, pp 107-128, 2014. 10.4230/LIPIcs.TYPES.2013.107. http://drops.dagstuhl.de/opus/volltexte/2014/4628) and Huber (A model of type theory in cubical sets. Licentiate thesis, University of Gothenburg, 2015). We will also discuss Swan's construction of the identity type in this variation of cubical sets. This proves that we have a model of type theory supporting dependent products, dependent sums, univalent universes, and identity types with the usual judgmental equality, and this model is formulated in a constructive metatheory.
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