Normalization for Cubical Type Theory

  title={Normalization for Cubical Type Theory},
  author={Jonathan Sterling and Carlo Angiuli},
  journal={2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  • Jonathan Sterling, C. Angiuli
  • Published 27 January 2021
  • Mathematics
  • 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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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