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A cubical language for bishop sets

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  • Jonathan Sterling
  • ,
  • Carlo Angiuli, Carnegie Mellon University
  • ,
  • Daniel Gratzer

We present XTT, a version of Cartesian cubical type theory specialized for Bishop sets à la Coquand, in which every type enjoys a definitional version of the uniqueness of identity proofs. Using cubical notions, XTT reconstructs many of the ideas underlying Observational Type Theory, a version of intensional type theory that supports function extensionality. We prove the canonicity property of XTT (that every closed boolean is definitionally equal to a constant) using Artin gluing.

Original languageEnglish
JournalLogical Methods in Computer Science
Pages (from-to)43:1-43:80
Number of pages80
Publication statusPublished - Mar 2022

    Research areas

  • Artin gluing, Bishop sets, cubical type theory, logical predicates, proof irrelevance

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