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Naive cubical type theory

Published online by Cambridge University Press:  15 March 2022

Bruno Bentzen Open the ORCID record for Bruno Bentzen [Opens in a new window]
Bruno Bentzen*
Affiliation:
School of Philosophy, Zhejiang University, Hangzhou, China
*
Email: bbentzen@zju.edu.cn
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Abstract

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality.

Keywords

Cubical type theorynaive type theoryinformal type theoryhomotopy type theory
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Special Issue 10: Homotopy Type Theory 2019 , November 2021 , pp. 1205 - 1231
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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