Parametric quantifiers for dependent type theory

Dependent type theory allows us to write programs and to prove properties about those programs in the same language. However, some properties do not require much proof, as they are evident from a program's implementation, e.g. if a polymorphic program ...

Sized types have been developed to make termination checking more perspicuous, more powerful, and more modular by integrating termination into type checking. In dependently-typed proof assistants where proofs by induction are just recursive functional ...

Two approaches exist to incorporate parametricity into proof assistants based on dependent type theory. On the one hand, parametricity translations conveniently compute parametricity statements and their proofs solely based on individual well-typed ...