Modeling Fresh Names in the ?-calculus Using Abstractions

In this paper, we model fresh names in the π-calculus using abstractions w.r.t. a new binding operator θ. Both the theory and the metatheory of the π-calculus benefit from this simple extension. The operational semantics of this new calculus is finitely branching. Bisimulation can be given without mentioning any constraint on names, thus allowing for a straightforward definition of a coalgebraic semantics. This is cast within a category of coalgebras over algebras with infinitely many unary operators, in order to capitalize on θ. Following previous work by Montanari and Pistore, we present also a finite representation for finitary processes and a finite state verification procedure for bisimilarity, based on the new notion of θ-automaton. Finally, we improve previous encodings of the π-calculus in the Calculus of Inductive Constructions.