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DOI: 10.4230/LIPIcs.CSL.2018.6
URN: urn:nbn:de:0030-drops-96734
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9673/
Angiuli, Carlo ; Hou (Favonia), Kuen-Bang ; Harper, Robert
Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities
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Abstract
We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both fibrant and non-fibrant types. The fibrant fragment validates Voevodsky's univalence axiom and includes a circle type, while the non-fibrant fragment includes exact (strict) equality types satisfying equality reflection. Our type theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the canonicity property: all closed terms of boolean type evaluate to either true or false.
BibTeX - Entry
@InProceedings{angiuli_et_al:LIPIcs:2018:9673,
author = {Carlo Angiuli and Kuen-Bang {Hou (Favonia)} and Robert Harper},
title = {{Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities}},
booktitle = {27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
pages = {6:1--6:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-088-0},
ISSN = {1868-8969},
year = {2018},
volume = {119},
editor = {Dan Ghica and Achim Jung},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9673},
URN = {urn:nbn:de:0030-drops-96734},
doi = {10.4230/LIPIcs.CSL.2018.6},
annote = {Keywords: Homotopy Type Theory, Two-Level Type Theory, Computational Type Theory, Cubical Sets}
}
| Keywords: | Homotopy Type Theory, Two-Level Type Theory, Computational Type Theory, Cubical Sets | |
| Seminar: | 27th EACSL Annual Conference on Computer Science Logic (CSL 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 29.08.2018 |
