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Naive cubical type theory
Published online by Cambridge University Press: 15 March 2022
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.
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- Information
- Mathematical Structures in Computer Science , Volume 31 , Special Issue 10: Homotopy Type Theory 2019 , November 2021 , pp. 1205 - 1231
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press