Weighted Relational Models of Typed Lambda-Calculi

Jim Laird 1 Manzonetto Giulio 2 Guy Mccusker 1 Michele Pagani 2
1 University of Bath [Bath]
2 LCR - Logic, Computation and Reasoning [Villetaneuse]
LIPN - Laboratoire d'Informatique de Paris-Nord
Abstract : The category Rel of sets and relations yields one of the simplest denotational semantics of Linear Logic (LL). It is known that Rel is the biproduct completion of the Boolean ring. We consider the generalization of this construction to an arbitrary continuous semiring R, producing a cpo-enriched category which is a semantics of LL, and its (co)Kleisli category is an adequate model of an extension of PCF, parametrized by R. Specific instances of R allow us to compare programs not only with respect to “what they can do”, but also “in how many steps” or “in how many different ways” (for non-deterministic PCF) or even “with what probability” (for probabilistic PCF).
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Communication dans un congrès
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https://hal-univ-paris13.archives-ouvertes.fr/hal-01144064
Contributeur : Giulio Manzonetto <>
Soumis le : lundi 20 avril 2015 - 17:54:44
Dernière modification le : mercredi 6 février 2019 - 01:25:43

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UNIV-PARIS13 | LIPN | USPC | GALILE

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Jim Laird, Manzonetto Giulio, Guy Mccusker, Michele Pagani. Weighted Relational Models of Typed Lambda-Calculi. 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013, New Orleans, LA, USA, June 25-28, 2013, Jun 2013, New Orleans, LA, United States. ⟨10.1109/LICS.2013.36⟩. ⟨hal-01144064⟩

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