Abstract
We present XTT, a version of Cartesian cubical type theory specialized for
Bishop sets \`a 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.
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
General Computer Science,Theoretical Computer Science
Cited by
1 articles.
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