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Linear continuations and duality

paul-andré melliès 1, Nicolas Tabareau 1

(2007)

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.

1 :	Preuves, Programmes et Systèmes (PPS)
	CNRS : UMR7126 – Université Paris VII - Paris Diderot

Équipe de recherche : PPS

Domaine

:

Mathématiques/Catégories et ensembles Informatique/Langage de programmation

Mots Clés : Linear logic – monoidal categories – tensorial negation – control categories – linear continuations

hal-00339156, version 1

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Contributeur : Nicolas Tabareau <>

Soumis le : Lundi 17 Novembre 2008, 11:05:02

Dernière modification le : Lundi 17 Novembre 2008, 11:09:16