Weighted Relational Models of Typed Lambda-Calculi

Jim Laird, Giulio Manzonetto, Guy McCusker, Michele Pagani
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
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
more » ... t 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).
doi:10.1109/lics.2013.36 dblp:conf/lics/LairdMMP13 fatcat:5rlghyqarndr3a5lqesk2ygsru