Normalization for Cubical Type Theory

Jonathan Sterling; Carlo Angiuli

doi:10.1109/lics52264.2021.9470719

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arXiv · 2101.11479

Normalization for Cubical Type Theory

Jonathan Sterling·Carlo Angiuli

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Abstract

We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory of cubical type theory. Our normalization result is reduction-free, in the sense of yielding a bijection between equivalence classes of terms in context and a tractable language of $\beta/\eta$-normal forms. As corollaries we obtain both decidability of judgmental equality and the injectivity of type constructors.

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Jonathan Sterling, Carlo Angiuli. 2021-01-27. Normalization for Cubical Type Theory. https://doi.org/10.1109/lics52264.2021.9470719

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