Internal Parametricity for Cubical Type Theory [article]

Evan Cavallo, Robert Harper
2021 arXiv   pre-print
We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we call relativity. We demonstrate the use of the theory by analyzing polymorphic functions between higher inductive types, observe how cubical equality regularizes parametric type theory, and examine the similarities and discrepancies between cubical and
more » ... ric type theory, which are closely related. We also abstract a formal interface to the computational interpretation and show that this also has a presheaf model.
arXiv:2005.11290v5 fatcat:rnbnor535jcbbeb74726r7mltm