On Action Permutation and Progress for Partially Commutative Asynchronous Binary Sessions

A theory of asynchronous binary sessions is generalized by asynchronous communication subtyping, which actually permutates and optimizes the actions on each participant. With the types of messages 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 presented, associating the subtyping for session types with asynchronous communication subtyping. In addition, action permutation and optimization 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. What's more, the type compliance we defined assures the progress property, i.e., once a communication has been established, well-formed programs will never starve at communication points. Finally, we conclude and discuss some possible future work in this area.

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