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• W2765255795 abstract "Martin-Löf’s intuitionistic type theory is a widely-used framework for constructive mathematics and computer programming. In its most popular form, type theory consists of a collection of inference rules inductively defining formal proofs. These rules are justified by Martin-Löf’s meaning explanations, which extend the Brouwer–Heyting–Kolmogorov interpretation of connectives to a rich collection of types, and therefore provide a constructive realizability interpretation of formal proofs. Around 2005, researchers noticed that the rules of type theory also admit homotopy-theoretic models, and subsequently extended type theory with constructs inspired by these models: higher inductive types and Voevodsky’s univalence axiom. Although the resulting homotopy type theory has proved useful for homotopy-theoretic reasoning, it lacks a constructive interpretation. In this overview, we discuss a cubical generalization of the meaning explanations of type theory that constitutes an inherently constructive account of higher-dimensional structure in types." @default.
• W2765255795 created "2017-11-10" @default.
• W2765255795 creator A5028720578 @default.
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• W2765255795 date "2018-02-01" @default.
• W2765255795 modified "2023-09-26" @default.
• W2765255795 title "Meaning explanations at higher dimension" @default.
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• W2765255795 doi "https://doi.org/10.1016/j.indag.2017.07.010" @default.
• W2765255795 hasPublicationYear "2018" @default.
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