The Expressiveness of Poly✶, a Generic Process Calculus Type System

Meta✶ is a generic process calculus that can be instantiated by supplying rewriting rules defining an operational semantics to make numerous process calculi such as the π-calculus, the system of Mobile Ambients, and many of their variants. Poly✶ is a generic type system that makes a sound type system with principal types and a type inference algorithm for any instantiation of Meta✶. This paper evaluates the expressiveness of Poly✶ by comparing it with two quite dissimilar static analysis systems in the literature. One comparison is with a typed version of Mobile Ambients defined by Cardelli and Gordon; we name this system TMA. The other comparison is with a flow analysis for BioAmbients by Nielson, Nielson, Priami, and Rosa; we name this flow analysis SABA. We instantiate Meta✶ and Poly✶ to the two process calculi (TMA and BioAmbients) and compare the types provided by Poly✶ with the predicates provided by the previous static analysis systems (the typing judgments of TMA and the flow analysis results of SABA). We show that Poly✶ types can express essentially the same information as the previous static analysis systems and can also express more precise information. To do the comparisons, we needed to alter how Meta✶ handles αconversion in order to develop a new method for handling name restriction in Poly✶.