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DOI: 10.4230/LIPIcs.FSCD.2019.31
URN: urn:nbn:de:0030-drops-105387
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10538/
Sterling, Jonathan ; Angiuli, Carlo ; Gratzer, Daniel
Cubical Syntax for Reflection-Free Extensional Equality
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Abstract
We contribute XTT, a cubical reconstruction of Observational Type Theory [Altenkirch et al., 2007] which extends Martin-Löf's intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of identity proofs principle (UIP): any two elements of the same equality type are judgmentally equal. Moreover, we conjecture that the typing relation can be decided in a practical way. In this paper, we establish an algebraic canonicity theorem using a novel extension of the logical families or categorical gluing argument inspired by Coquand and Shulman [Coquand, 2018; Shulman, 2015]: every closed element of boolean type is derivably equal to either true or false.
BibTeX - Entry
@InProceedings{sterling_et_al:LIPIcs:2019:10538,
author = {Jonathan Sterling and Carlo Angiuli and Daniel Gratzer},
title = {{Cubical Syntax for Reflection-Free Extensional Equality}},
booktitle = {4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
pages = {31:1--31:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-107-8},
ISSN = {1868-8969},
year = {2019},
volume = {131},
editor = {Herman Geuvers},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10538},
URN = {urn:nbn:de:0030-drops-105387},
doi = {10.4230/LIPIcs.FSCD.2019.31},
annote = {Keywords: Dependent type theory, extensional equality, cubical type theory, categorical gluing, canonicity}
}
| Keywords: | Dependent type theory, extensional equality, cubical type theory, categorical gluing, canonicity | |
| Seminar: | 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 18.06.2019 |
