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Conference papers
Cubical Type Theory: a constructive interpretation of the univalence axiom
Abstract : This paper presents a type theory in which it is possible to directly manipulate n-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function extensionality is directly provable in the system. Further, Voevodsky's univalence axiom is provable in this system. We also explain an extension with some higher inductive types like the circle and propositional truncation. Finally we provide semantics for this cubical type theory in a constructive meta-theory.
Cited literature [25 references]
https://hal.inria.fr/hal-01378906
Contributor : Cyril Cohen Connect in order to contact the contributor
Submitted on : Tuesday, April 17, 2018 - 1:45:31 PM
Last modification on : Saturday, June 25, 2022 - 11:29:55 PM
Contributor : Cyril Cohen Connect in order to contact the contributor
Submitted on : Tuesday, April 17, 2018 - 1:45:31 PM
Last modification on : Saturday, June 25, 2022 - 11:29:55 PM
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LIPIcs-TYPES-2015-5.pdf
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