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Linear continuations and duality

Abstract : 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.
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Contributor : Nicolas Tabareau Connect in order to contact the contributor
Submitted on : Monday, November 17, 2008 - 11:05:02 AM
Last modification on : Thursday, January 7, 2021 - 11:40:03 PM
Long-term archiving on: : Tuesday, October 9, 2012 - 3:30:16 PM


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  • HAL Id : hal-00339156, version 1



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



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