We propose a refinement and a simplification of the behavioural semantics of session types, based on the concepts of compliance and subbehaviour from the theory of web contracts. We introduce three relations on a suitable class of behaviours with higher-order input/output, called "session behaviors". Such relations, depending on each other, represent the idea of sub-behaviour from the point of view of a client, a server or a peer, respectively. A restriction of the intersection of the first two characterizes the usual sub-behaviour relation (from the literature). We then device a formal system for three subtyping relations (dubbed CSPsubtyping) for session types that takes into account the role played by a user of a channel during an interaction, so extending Gay and Hole subtyping theory. We show that our session behaviors and sub-behaviour relations provide a sound and complete semantics for CSP-subtyping (and for Gay and Hole subtyping as a by-product).
Automata models are well-established in many areas of computer science and are supported by a wealth of theoretical results including a wide range of algorithms and techniques to specify and analyse systems. We introduce choreography automata for the choreographic modelling of communicating systems. The projection of a choreography automaton yields a system of communicating finite-state machines. We consider both the standard asynchronous semantics of communicating systems and a synchronous variant of it. For both, the projections of well-formed automata are proved to be live as well as lock-and deadlockfree.
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