The Expressiveness of Generic Process Shape Types

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✶. POLY✶ provides a generic notion of shape types which describe behavior of processes by a direct description of allowed syntactic configurations. This paper evaluates the expressiveness of generic process shape types by comparing POLY✶ with three quite dissimilar type/static analysis systems in the literature. The first comparison is with Turner’s type system for the π-calculus without type annotations (which is essentially Milner’s system of sorts). The second comparison is with an explicitly typed version of Mobile Ambients by Cardelli and Gordon. Finally, the third comparison is with a static analysis for BioAmbients developed by Nielson, Nielson, Priami, and Rosa. We instantiate META✶ to the process calculi in question and compare expressiveness of POLY✶ shape types with the predicates provided by the three systems. We show that POLY✶ shape types can express much more precise information than the previous type/static analysis systems and can also express essentially the same information as the previous systems. 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✶.