Semantic Subtyping for the p-Calculus

Subtyping relations for the π-calculus are usually defined in a syntactic way, by means of structural rules. We propose a semantic characterisation of channel types and use it to derive a subtyping relation. The type system we consider includes read-only and write-only channel types, as well as boolean combinations of types. A set-theoretic interpretation of types is provided, in which boolean combinations of types are interpreted as the corresponding set-theoretic operations. Subtyping is defined as inclusion of the interpretations. We prove decidability of the subtyping relation and sketch the subtyping algorithm. In order to fully exploit the type system, we define a variant of the π-calculus where communication is subjected to pattern matching that performs dynamic typecase. Dedicated to the 60th birthday of Mario Coppo, Mariangiola Dezani-Ciancaglini, and Simona Ronchi della Rocca