Abstract
A type system with asynchronous binary sessions is generalised by asynchronous communication subtyping, which actually permutes and optimises the actions on each participant. With the types of messages being distinguished between dependent and independent types, a series of action asynchronous subtyping rules for the two kinds of message types are proposed, respectively. To make such action permutations automatic, an algorithmic asynchronous subtyping is introduced, associating the subtyping for session types with asynchronous communication subtyping. However, action permutation and optimisation will change the sequence and structure of messages sent and received. To ensure runtime safety, the cases of communication errors that may occur in asynchronous sessions are revealed by examples. In addition, the type compliance we defined assures the progress property, i.e., once a communication has been established, well-formed programmes will never starve at communication points. Finally, the soundness and communication safety of the type system are proved, and some possible future work in this field is discussed.
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