Typing and subtyping for mobile processes

The π-calculus is a process algebra that supports process mobility by focusing on the communication of channels. R. Milner´s (1991) presentation of the π-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 λ-calculi. The greater precision of their type discipline yields stronger versions of some standard theorems about the π-calculus. These can be used, for example, to obtain the validity of β-reduction for the more efficient of Milner´s encodings of the call-by-value λ-calculus, for which β-reduction does not hold in the ordinary π-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 λ-calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing