Bentzen, Bruno (2021) Naive cubical type theory. [Preprint]

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Abstract

This paper 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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Item Type:	Preprint
Creators:	Creators Email ORCID Bentzen, Bruno b.bentzen@hotmail.com 0000-0002-5987-7806
Keywords:	Naive type theory, Homotopy type theory, Cubical type theory
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof
Depositing User:	Dr. Bruno Bentzen
Date Deposited:	12 May 2021 16:38
Last Modified:	12 May 2021 16:38
Item ID:	19029
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof
Date:	May 2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19029

Available Versions of this Item

• Naive cubical type theory. (deposited 06 May 2020 18:05)
  • Naive cubical type theory. (deposited 12 May 2021 16:38) [Currently Displayed]
    • Naive cubical type theory. (deposited 27 May 2024 15:55)

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