三次型理论的规范化

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-01-27 DOI:10.1109/LICS52264.2021.9470719

Jonathan Sterling, C. Angiuli

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引用次数: 33

摘要

我们证明了(一元笛卡尔)三次型理论的归一化，结束了三次型理论句法元理论中最后一个主要的开放问题。我们的归一化结果是无约化的，在某种意义上，在上下文中的等价类和β/η-正规形式的可处理语言之间产生双射。作为推论，我们得到了判断相等的可判定性和类型构造函数的注入性。

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Normalization for Cubical Type Theory

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 β/η-normal forms. As corollaries we obtain both decidability of judgmental equality and the injectivity of type constructors.

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来源期刊

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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