Weighted Relational Models of Typed Lambda-Calculi

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 cat...

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Bibliographic Details
Published in:2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 301 - 310
Main Authors: Laird, Jim, Manzonetto, Giulio, McCusker, Guy, Pagani, Michele
Format: Conference Proceeding
Language:English
Published: IEEE 01.01.2013
Subjects:
Coherence
Computational modeling
denotational semantics
Equalizers
Games
lambda-calculus
linear logic
Probabilistic logic
quantitative semantics
Semantics
Tensile stress
ISBN:1479904139, 9781479904136
ISSN:1043-6871
Online Access:Get full text
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Summary: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).
ISBN:1479904139
9781479904136
ISSN:1043-6871
DOI:10.1109/LICS.2013.36