PolyA: True Type Polymorphism for Mobile Ambients

Previous type systems for mobility calculi (the original Mobile Ambients, its variants and descendants, e.g., Boxed Ambients and Safe Ambients, and other related systems) offer little support for generic mobile agents. Previous systems either do not handle communication at all or globally assign fixed communication types to ambient names that do not change as an ambient moves around or interacts with other ambients. This makes it hard to type examples such as a “messenger” ambient that uses communication primitives to collect a message of nonpredetermined type and deliver it to a non-predetermined destination. In contrast, we present our new type system PolyA. Instead of assigning communication types to ambient names, PolyA assigns a type to each process P that gives upper bounds on (1) the possible ambient nesting shapes of any process P ′ to which P can evolve, (2) the values that may be communicated at each location, and (3) the capabilities that can be used at each location. Because PolyA can type generic mobile agents, we believe PolyA is the first type system for a mobility calculus that provides type polymorphism comparable in power to polymorphic type systems for the λ-calculus. PolyA is easily extended to ambient calculus variants. A restriction of PolyA has principal typings.