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Naïve Type Theory

In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 101-136 (2019)

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  1. Naive cubical type theory.Bruno Bentzen - 2021 - Mathematical Structures in Computer Science 31:1205–1231.
    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 (...)
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  • Stefania Centrone, Deborah Kant, Deniz Serikaya, Reflections on the Foundations of Mathematics. Univalent Foundations, Set Theory and General Thoughts, vol. 407 of Synthese Library, Springer, 2019, pp. 494+xxviii; ISBN: 978-3-030-15654-1 (Hardcover) 149.79€, ISBN: 978-3-030-15655-8 (eBook). [REVIEW]Matteo de Ceglie - forthcoming - Studia Logica:1-7.
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