Representing Continuous Functions between Greatest Fixed Points of Indexed Containers

Pierre Hyvernat (1)

1 LAMA - Laboratoire de Mathématiques

We describe a way to represent computable functions between coinductive types as particular transducers in type theory. This generalizes earlier work on functions between streams by P. Hancock to a much richer class of coinductive types. Those transducers can be defined in dependent type theory without any notion of equality but require inductive-recursive definitions. Most of the properties of these constructions only rely on a mild notion of equality (intensional equality) and can thus be formalized in the dependently typed language Agda.

Mots clés: dependent type theory; coinductive types; continuous functions; indexed containers; inductive recursive definitions; Agda

Domaines: Logique en informatique [cs.LO]

Pierre Hyvernat. Representing Continuous Functions between Greatest Fixed Points of Indexed Containers. 2021. ⟨hal-02050711v3⟩