Typing and subtyping for mobile processes 论文

摘要

The π -calculus is a process algebra that supports mobility by focusing on the communication of channels. Milner's presentation of the π -calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. We 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 our type discipline yields stronger versions of standard theorems on 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, which fails in the ordinary π -calculus. We define the syntax, typing, subtyping, and operational semantics of our 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.