A behavioural theory for a π-calculus with preorders

We study the behavioural theory of πP, a π-calculus in the tradition of Fusions and Chi calculi. In contrast with such calculi, reduction in πP generates a preorder on names rather than an equivalence relation. We present two characterisations of barbed congruence in πP: the first is based on a compositional LTS, and the second is an axiomatisation. The results in this paper bring out basic properties of πP, mostly related to the interplay between the restriction operator and the preorder on names. Consequently, πP is a calculus in the tradition of Fusion calculi, in which both types and behavioural equivalences can be exploited in order to reason rigorously about concurrent and mobile systems.