Orderly communication in the Ambient Calculus

The Ambient Calculus (henceforth, AC) was developed by Cardelli and Gordon as a formal framework to study issues of mobility and migrant code [9]. We present a type system for AC that allows the type of exchanged data within the same ambient to vary over time. Our type system assigns what we call behaviors to processes; a denotational semantics of behaviors is proposed, here called trace semantics, underlying much of the remaining analysis. We state and prove a Subject Reduction property for our typed version of AC. Based on techniques borrowed from finite automata theory, type checking of fully type-annotated processes is shown to be decidable. We show that the typed version of AC originally proposed by Cardelli and Gordon [10] can be naturally embedded into our typed version of AC.