Composing processes

We present a theory of types for concurrency based on a simple notion of typed algebras, and discuss its applications. The basic idea is to determine a partial algebra of processes by a partial algebra of types, thus controlling process composability, just as types in a typed applicative structure [25] determine composability of elements of the underlying applicative structure. A class of typed algebras with a simple operator for process composition are introduced, which are shown to encompass a wide range of type disciplines for processes, placing extant theories such as Milner's sorting [22] and Lafont's typed nets [20] on a uniform technical footing, suggesting generalisations, and offering a secure basis for integration. We also prove that the class of typable operations in the underlying partial algebras is completely characterised by a certain modularity principle in process composition, which gives us the basic understanding on the nature of the type disciplines representable in the proposed construction.