What are Polymorphic Ambients?

The Ambient Calculus was developed by Cardelli and Gordon as a formal framework to study issues of mobility and migrant code [CG98]. We consider an Ambient Calculus where ambients transport and exchange programs rather that just inert data. We propose different senses in which such a calculus can be said to be polymorphic, and design accordingly a polymorphic type system for it. Our type system assigns types to embedded programs and what we call behaviors to processes; a denotational semantics of behaviors is then proposed, here called trace semantics, underlying much of the remaining analysis. A Subject Reduction property for our polymorphically-typed calculus is stated. Based on techniques borrowed from finite automata theory, type-checking of fully type-annotated processes is shown to be decidable; the time complexity of our decision procedure is exponential (this is a worst-case in theory, arguably not encountered in practice). Our polymorphically-typed calculus is a conservative extension of the type system for the Ambient Calculus originally proposed by Cardelli and Gordon [CG99, CGG99].