Companions, Codensity and Causality

Abstract : In the context of abstract coinduction in complete lattices, the notion of compatible function makes it possible to introduce enhancements of the coinduction proof principle. The largest compatible function, called the companion, subsumes most enhancements and has been proved to enjoy many good properties. Here we move to universal coalgebra, where the corresponding notion is that of a final distributive law. We show that when it exists the final distributive law is a monad, and that it coincides with the codensity monad of the final sequence of the given functor. On sets, we moreover characterise this codensity monad using a new abstract notion of causality. In particular, we recover the fact that on streams, the functions definable by a distributive law or GSOS specification are precisely the causal functions. Going back to enhancements of the coinductive proof principle, we finally obtain that any causal function gives rise to a valid up-to-context technique.
Type de document :
Communication dans un congrès
FoSSaCS, Apr 2017, Uppsala, Sweden
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01442222
Contributeur : Damien Pous <>
Soumis le : vendredi 20 janvier 2017 - 14:57:01
Dernière modification le : jeudi 15 juin 2017 - 09:09:03
Document(s) archivé(s) le : vendredi 21 avril 2017 - 15:02:04

Fichier

final-dl.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01442222, version 1

Collections

Citation

Damien Pous, Jurriaan Rot. Companions, Codensity and Causality. FoSSaCS, Apr 2017, Uppsala, Sweden. <hal-01442222>

Partager

Métriques

Consultations de
la notice

165

Téléchargements du document

149