relational-parametricity-prover

To derive free theorems for polymorphic functions in Coq or Agda, you use type-indexed relations and abstraction theorems to prove that terms respect the relational interpretation of their types, automatically generating properties that hold across all instantiations.

Relational parametricity in type theory is the principle that polymorphic terms respect the relational interpretation of their types, ensuring uniform behavior across type instantiations and enabling the derivation of free theorems for abstract data types.

Yes, you can formally verify abstract data types and reason about generic programming by applying relational parametricity proofs to ensure polymorphic functions behave uniformly across all possible type instantiations within formal proof assistants.

You prove a term respects its relational interpretation by defining types as relations and applying abstraction theorems within formal proof assistants like Coq or Agda, demonstrating the term adheres to parametricity constraints.

Yes, you need a formal proof assistant like Coq or Agda to define type-indexed relations and prove parametricity properties, as the process requires formal metatheory environments to automate abstraction theorem application and free theorem generation.

The best way to prove parametricity for a function type like forall a b. a -> b is to apply a relational interpretation to the types, using abstraction theorems to automatically derive the free theorem governing the function's behavior.