  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 parametric 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.
