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Naive cubical type theory

Bentzen, Bruno (2019) 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:
CreatorsEmailORCID
Bentzen, Brunob.bentzen@hotmail.com0000-0002-5987-7806
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: 06 May 2020 18:05
Last Modified: 06 May 2020 18:05
Item ID: 17148
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Date: 2019
URI: http://philsci-archive.pitt.edu/id/eprint/17148

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