Pi-nets: A graphical form of π-calculus

Abstract

An, action calculus which closely corresponds to the π-calculus is presented in graphical form, as so-called π -nets. First an elementary form of π-net, with no sequential control, is presented. Then, using a construction by Honda and Tokoro, it is shown informally that by adding a single control construction box to elementary π-nets, the sequential control present in the π-calculus can be recovered. (Another construction, rep, provides replication.) The graphical presentation suggests a few interesting variants of this control regime, which are studied briefly. The main purpose of the paper is to explore informally the power and utility of graphical forms of the π-calculus, in the context of action calculi. It also suggests that graphical forms of other action calculi should be explored.