Linear continuations and duality - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2007

Linear continuations and duality

Paul-André Melliès
Nicolas Tabareau

Résumé

One fundamental aspect of linear logic is that its conjunction behaves in the same way as a tensor product in linear algebra. Guided by this intuition, we investigate the algebraic status of disjunction -- the dual of conjunction -- in the presence of linear continuations. We start from the observation that every monoidal category equipped with a tensorial negation inherits a lax monoidal structure from its opposite category. This lax structure interprets disjunction, and induces a multicategory whose underlying category coincides with the kleisli category associated to the continuation monad. We study the structure of this multicategory, and establish a structure theorem adapting to linear continuations a result by Peter Selinger on control categories and cartesian continuations.
Fichier principal
Vignette du fichier
linear-control.pdf (189.48 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00339156 , version 1 (17-11-2008)

Identifiants

  • HAL Id : hal-00339156 , version 1

Citer

Paul-André Melliès, Nicolas Tabareau. Linear continuations and duality. 2007. ⟨hal-00339156⟩
256 Consultations
1092 Téléchargements

Partager

Gmail Facebook X LinkedIn More