Probabilistic non-determinism
Variations on the bagdomain theme
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics. Part II : lambda calculus and domain theory: lambda calculus and domain theory
Handbook of logic in computer science (vol. 3)
The Powerdomain of Indexed Valuations
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Closure Properties of a Probabilistic Domain Construction
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
Mathematical Structures in Computer Science
Discrete random variables over domains
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Fundamenta Informaticae
Hi-index | 5.23 |
In this paper we initiate the study of discrete random variables over domains. Our work is inspired by that of Daniele Varacca, who devised indexed valuations as models of probabilistic computation within domain theory. Our approach relies on new results about commutative monoids defined on domains that also allow actions of the non-negative reals. Using our approach, we define two such families of real domain monoids, one of which allows us to recapture Varacca's construction of the Plotkin indexed valuations over a domain. Each of these families leads to the construction of a family of discrete random variables over domains, the second of which forms the object level of a continuous endofunctor on the categories RB (domains that are retracts of bifinite domains), and on FS (domains where the identity map is the directed supremum of deflations finitely separated from the identity). The significance of this last result lies in the fact that there is no known category of continuous domains that is closed under the probabilistic power domain, which forms the standard approach to modelling probabilistic choice over domains. The fact that RB and FS are Cartesian closed and also are closed under a power domain of discrete random variables means we can now model, e.g. the untyped lambda calculus extended with a probabilistic choice operator, implemented via random variables.