Bentzen, Bruno (2021) Naive cubical type theory. Mathematical Structures in Computer Science, 31. pp. 1205-1231.
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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 Eckmann-Hilton duality.
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| Item Type: | Published Article or Volume | ||||||
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| Keywords: | Naive type theory, Homotopy type theory, Cubical type theory | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof |
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| Depositing User: | Dr. Bruno Bentzen | ||||||
| Date Deposited: | 27 May 2024 15:55 | ||||||
| Last Modified: | 27 May 2024 15:55 | ||||||
| Item ID: | 23487 | ||||||
| Journal or Publication Title: | Mathematical Structures in Computer Science | ||||||
| Official URL: | https://doi.org/10.1017/S096012952200007X | ||||||
| DOI or Unique Handle: | 10.1017/S096012952200007X | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Proof |
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| Date: | 2021 | ||||||
| Page Range: | pp. 1205-1231 | ||||||
| Volume: | 31 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23487 |
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Naive cubical type theory. (deposited 06 May 2020 18:05)
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Naive cubical type theory. (deposited 12 May 2021 16:38)
- Naive cubical type theory. (deposited 27 May 2024 15:55) [Currently Displayed]
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Naive cubical type theory. (deposited 12 May 2021 16:38)
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