Motivated by many practical applications that have to compute in the presence of uncertainty, we propose a monadic probabilistic language based upon the mathematical notion of sampling function. Our language provides a unified representation scheme for probability distributions, enjoys rich expressiveness, and o#ers high versatility in encoding probability distributions. We also develop a novel style of operational semantics called a horizontal operational semantics, under which an evaluation returns not a single outcome but multiple outcomes. We have preliminary evidence that the horizontal operational semantics improves the ordinary operational semantics with respect to both execution time and accuracy in representing probability distributions.

Several extensions of bayesian belief networks to the rst order logic or relational framework have been proposed. Many of these have in common that they are embedded in some kind of probabilistic or other extension of logic programming. In this paper we take yet another approach, which could be called a meta-interpreter approach. We discuss the representation of \ rst order" bayesian belief networks in standard Prolog. The representation formalism we propose is very simple, does not make use of any extensions to logic programming, allows inference using a simple interpreter written in Prolog, and the formalism has an expressiveness similar to other relational variants of bayesian belief networks.