Por Luca Tranchini (University of Tubingen).

In this talk I will present a family of type isomorphisms in System F (i.e. second-order propositional intuitionistic logic) whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under notions of identity of proofs (or programs) stronger than the one induced by βη-equivalence, like those induced by parametricity and dinaturality. We show that the Yoneda type isomorphisms yield a rewriting over types (i.e. formulas), that we call Yoneda reduction, which can be used to eliminate quantifiers from a polymorphic type, replacing them with a combination of monomorphic type constructors. We establish some sufficient conditions under which quantifiers can be fully eliminated from a polymorphic type, and we show some application of these conditions to count the inhabitants of a type and to study proof/program equivalence in some fragments of System F.

This is a joint session with SAL (CMA/FCT-UNL).

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