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Abstract. We propose a new typing system for the π-calculus with sessions, which ensures the progress property, i.e. once a session has been initiated, typable processes will never starve at session channels. In the current literature progress for session types has been guaranteed only in the case of nested sessions, disallowing more than two session channels interfered in a single thread. This was a severe restriction since many structured communications need combinations of sessions. We overcome this restriction by inferring the order of channel usage, but avoiding any tagging of channels and names, neither explicit nor inferred. The simplicity of the typing system essentially relies on the session typing discipline, where sequencing and branching of communications are already structured by types. The resulting typing enjoys a stronger progress property than that one in the literature: it assures that for each well-typed process P which contains an open session there is an irreducible process Q such that the parallel composition P|Q is well-typed too and it always reduces, also in presence of interfered sessions.

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).

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Abstract. We illustrate the concepts of sessions and session types as they have been developed in the setting of the π-calculus. Motivated by the goal of obtaining a formalisation closer to existing standards and aiming at their enhancement and strengthening, several extensions of the original core system have been proposed, which we survey together with the embodying of sessions into functional and object-oriented languages, as well as some implementations.

Global-type formalisms enable to describe the overall behaviour of distributed systems and at the same time to enforce safety properties for communications between system components. Our goal is that of amending a weakness of such formalisms: the difficulty in describing open systems, i.e. systems which can be connected and interact with other open systems. We parametrically extend, with the notion of interface role and interface connection, the syntax of global-type formalisms. Semantically, global types with interface roles denote open systems of communicating finite state machines connected by means of gateways obtained from compatible interfaces. We show that safety properties are preserved when open systems are connected that way. We prefer to use the word role rather then participant since interface role sounds more suitable for the present setting than interface participant.

In calculi for modelling communication protocols, internal and external choices play dual roles. Two external choices can be viewed naturally as dual too, as they represent an agreement between the communicating parties. If the interaction fails, the past agreements are good candidates as points where to roll back, in order to take a different agreement. We propose a variant of contracts with synchronous rollbacks to agreement points in case of deadlock. The new calculus is equipped with a compliance relation which is shown to be decidable.