A Well-behaved LTS for the Pi-calculus: (Abstract)

The Pi-calculus [2,10] is one of the most well-known and widely-studied process calculi – roughly, it extends the binary synchronisations along a channel/name, familiar from ccs, with the ability to pass names as arguments. Thus, the input prefix becomes a binder and the synchronisation itself results in a substitution of the communicated name for the bound variable. The Pi-calculus inherits another binder from ccs – the restriction operator. The ability to pass names as part of a synchronous communication means that it behaves rather differently in this setting in particular, the scope of a restriction, static in ccs, becomes dynamic essentially because restricted names can be communicated along public channels. Additionally, it behaves somewhat like a global generator of new-names since α-conversion ensures that whichever concrete name is chosen for a restricted name, it is different from all other names in the term – in fact, the global nature of new names is also enforced in the definition of bisimulation as we shall recall below. See also [12]. The (reduction) semantics of the Pi-calculus is very similar to that of css, in fact, in the sum-free fragment we can express it essentially as the axiom