A Banach Space Based Semantics for Probabilistic Concurrent Constraint Programming

The aim of this work is to provide a probabilistic foundation for nondeterministic computations in Concurrent Constraint Programming (CCP). Differently from common approaches in (imperative) high-level programming languages, which rely on some kind of random() function, we introduce randomness in the very definition of the language by means of a probabilistic choice construct. This allows a program to make stochastic moves during its execution. We call the resulting language Probabilistic Concurrent Constraint Programming (PCCP). We present an operational and denotational semantics for PCCP both capturing a notion of observables which combines results of computations and the probability of those results being computed. For the denotational semantics, we consider linear (Banach) structures and the mathematics behind them, as appropriate candidates for the definition of the domain of denotations. This approach differs from the ones typically adopted in the semantics of constraint progr..