We introduce a labelled transition semantics for the reversible π-calculus. It is the first account of a compositional definition of a reversible calculus, that has both concurrency primitives and name mobility.The notion of reversibility is strictly linked to the notion of causality. We discuss the notion of causality induced by our calculus, and we compare it with the existing notions in the literature, in particular for what concerns the syntactic feature of scope extrusion, typical of the π-calculus.

We study the combination of probability and non-determinism from a categorical point of view. In category theory, non-determinism and probability are represented by suitable monads. However, these two monads do not combine well as they are. To overcome this problem, we introduce the notion of indexed valuations. This notion is used to define a new monad that can be combined with the usual non-deterministic monad via a categorical distributive law. We give an equational characterisation of our construction. We discuss the computational meaning of indexed valuations, and we show how they can be used by giving a denotational semantics of a simple imperative language.

Abstract. We give a compositional event structure semantics of the π-calculus. The main issues to deal with are the communication of free names and the extrusion of bound names. These are the source of the expressiveness of the π-calculus, but they also allow subtle forms of causal dependencies. We show that free name communications can be modeled in terms of "incomplete/potential synchronization" events. On the other hand, we argue that it is not possible to satisfactorily model parallel extrusion within the framework of stable event structures. We propose to model a process as a pair (E, X) where E is a prime event structure and X is a set of (bound) names. Intuitively, E encodes the structural causality of the process, while the set X affects the computation on E so as to capture the causal dependencies introduced by scope extrusion. The correctness of our true concurrent semantics is shown by an operational adequacy theorem with respect to the standard late semantics of the π-calculus.