Jonathan Sterling ; Carlo Angiuli ; Daniel Gratzer - A Cubical Language for Bishop Sets

lmcs:9069 - Logical Methods in Computer Science, March 29, 2022, Volume 18, Issue 1 -
A Cubical Language for Bishop Sets

Authors: Jonathan Sterling ORCID-iD; Carlo Angiuli ORCID-iD; Daniel Gratzer ORCID-iD

    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.

    Volume: Volume 18, Issue 1
    Published on: March 29, 2022
    Accepted on: February 9, 2022
    Submitted on: February 9, 2022
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic

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