Global Principal Typing in Partially Commutative Asynchronous Sessions

We generalise a theory of multiparty session types for the π-calculus through asynchronous communication subtyping, which allows partial commutativity of actions with maximal flexibility and safe optimisation in message choreography. A sound and complete algorithm for the subtyping relation, which can calculate conformance of optimised end-point processes to an agreed global specification, is presented. As a complementing result, we show a type inference algorithm for deriving the principal global specification from end-point processes which is minimal with respect to subtyping. The resulting theory allows a programmer to choose between a top-down and a bottom-up style of communication programming, ensuring the same desirable properties of typable processes.