Synthetic Behavioural Typing: Sound, Regular Multiparty Sessions via Implicit Local Types

Programming distributed systems is difficult. Multiparty session typing (MPST) is a method to automatically prove safety and liveness of protocol implementations relative to protocol specifications. In this paper, we introduce two new techniques to significantly improve the expressiveness of the MPST method: projection is based on implicit local types instead of explicit; type checking is based on the operational semantics of implicit local types instead of on the syntax. That is, the reduction relation on implicit local types is used not only "a posteriori" to prove type soundness (as usual), but also "a priori" to define the typing rules - synthetically. Classes of protocols that can now be specified/implemented/verified for the first time using the MPST method include: recursive protocols in which different roles participate in different branches; protocols in which a receiver chooses the sender of the first communication; protocols in which multiple roles synchronously choose both the sender and the receiver of a next communication, implemented as mixed input/output processes. We present the theory of the new techniques, as well as their future potential, and we demonstrate their present capabilities to effectively support regular expressions as global types (not possible before).