Title :
Weighted Relational Models of Typed Lambda-Calculi
Author :
Laird, Jeff ; Manzonetto, Giulio ; McCusker, Guy ; Pagani, Mattia
Author_Institution :
Dept. of Comput. Sci., Univ. of Bath, Bath, UK
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).
Keywords :
Boolean functions; category theory; lambda calculus; probabilistic logic; programming language semantics; set theory; type theory; Boolean ring; Kleisli category; LL; arbitrary continuous semiring; biproduct completion; category Rel; cpo-enriched category; denotational semantics; linear logic; nondeterministic PCF; probabilistic PCF; sets; typed lambda-calculi; weighted relational model; Coherence; Computational modeling; Equalizers; Games; Probabilistic logic; Semantics; Tensile stress; denotational semantics; lambda-calculus; linear logic; quantitative semantics;
Conference_Titel :
Logic in Computer Science (LICS), 2013 28th Annual IEEE/ACM Symposium on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4799-0413-6
DOI :
10.1109/LICS.2013.36