Internal parametricity, without an interval
summary
Presents a compact type theory extending Martin-Löf with a few new type and term formers that internalises parametricity without introducing an interval; syntax is extracted from presheaf semantics over the BCH cube category and uses span-based parametricity so no fibrancy or interval substitution is needed. Builds a gluing model that proves external parametricity and canonicity, implements Church-encoded naturals with induction, but computational univalence and full identity eliminators remain only up to isomorphism.
AI-written summary · about