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Pré-Publication, Document De Travail Année : 2020

Representing Continuous Functions between Greatest Fixed Points of Indexed Containers

Pierre Hyvernat

Résumé

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.
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Dates et versions

hal-02050711 , version 1 (27-02-2019)
hal-02050711 , version 2 (15-10-2020)
hal-02050711 , version 3 (15-04-2021)

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Pierre Hyvernat. Representing Continuous Functions between Greatest Fixed Points of Indexed Containers. 2020. ⟨hal-02050711v2⟩
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