Typing and subtyping for mobile processes

Abstract

The pi -calculus is a process algebra that supports process mobility by focusing on the communication of channels. R. Milner's (1991) presentation of the pi -calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. The authors extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed lambda -calculi. The greater precision of their type discipline yields stronger versions of some standard theorems about the pi -calculus. These can be used, for example, to obtain the validity of beta -reduction for the more efficient of Milner's encodings of the call-by-value lambda -calculus, for which beta -reduction does not hold in the ordinary pi -calculus. The authors define the syntax, typing, subtyping, and operational semantics of their calculus, prove that the typing rules are sound, apply the system to Milner's lambda -calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.<>