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Behavioural type systems, usually associated to concurrent or distributed computations, encompass concepts such as interfaces, communication protocols, and contracts, in addition to the traditional input/output operations. The behavioural type of a software component specifies its expected patterns of interaction using expressive type languages, so types can be used to determine automatically whether the component interacts correctly with other components. Two related important notions of behavioural types are those of session types and behavioural contracts. This article surveys the main accomplishments of the last 20 years within these two approaches.

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We propose two abstract semantics of the global view of choreographies given in terms of partial orders. The first semantics is formalised as pomsets of communication events while the second one is based on hypergraphs of events. These semantics can accommodate different levels of abstractions. We discuss the adequacy of our models by considering their relation with communicating machines, that we use to formalise the local view. Our approach increases expressiveness and allows us to overcome some limitations that affect alternative semantics of global views. This will be illustrated by discussing some interesting examples. Finally, we show that the two semantics are equivalent and have different merits. More precisely, the semantics based on pomsets yields a more elegant presentation, but it is less suitable for implementation. The semantics based on hypergraphs instead is amenable to a straightforward implementation. 2 to social interaction, to providing e-health and e-government services. For such (and other) reasons, developers are required to carefully design their applications so that unintended behaviours do not happen at runtime.The problem. It is widely accepted that distributed systems and applications are not easy to design, implement, verify, deploy, and maintain. A key issue to tackle is the coordination of distributed components. For this, two primary (and in our view, complementary) approaches have been identified: orchestration and choreography. We focus here on the latter. More precisely, we propose a new semantics of a model of choreographies for message-passing software. We argue that our semantics offer a framework that (i) generalises existing linguistic constructs of choreographies by removing some unnecessary constraints adopted elsewhere, (ii) allows architects to design the coordination of distributed applications without forcing them to consider low level details, and (iii) enables the possibility of tool support at earlier stages of the development.Choreographies have been advocated as a suitable methodology for the design and analysis of distributed applications since, unlike models based on orchestration, they do not require an explicit coordinator. Roughly, a choreography describes how two or more distributed components coordinate with each other by exchanging messages. Among the possible interpretations of what choreographies are (see [2] for a discussion and references), we embrace the one suggested by W3C's [23]:Using the Web Services Choreography specification, a contract containing a global definition of the common ordering conditions and constraints under which messages are exchanged, is produced that describes, from a global viewpoint [...] observable behaviour [...]. Each party can then use the global definition to build and test solutions that conform to it. The global specification is in turn realised by combination of the resulting local systems [...] This description conceptualises two views, a global and a local one, which enable the relations represented by the follo...

Abstract. Decentralised smart contracts represent the next step in the development of protocols that support the interaction of independent players without the presence of a coercing authority. Based on protocols a la BitCoin for digital currencies, smart contracts are believed to be a potentially enabling technology for a wealth of future applications. The validation of such an early developing technology is as necessary as it is complex. In this paper we combine game theory and formal models to tackle the new challenges posed by the validation of such systems.

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.

Designing and analysing multiparty distributed interactions can be achieved either by means of a global view (e.g. in choreography-based approaches) or by composing available computational entities (e.g. in service orchestration). This paper proposes a typing systems which allows, under some conditions, to synthesise a choreography (i.e. a multiparty global type) from a set of local session types which describe end-point behaviours (i.e. local types).is the behaviour of b 1 P 2 = t 2 !order.p 2 ?price.r!price.(c 2 ?.t 2 !addr + c 1 ?.no 2 !) is the behaviour of b 2 S i = t i ?order.p i !price.(t i ?addr + no i ?), i ∈ {1, 2} is the behaviour of s i with a!e (resp. a?e) representing the action of sending (resp. receiving) a message of type e on a channel a (we omit e when the message is immaterial), ⊕ representing an internal choice, and + a choice made by the environment.

We introduce an abstract semantics of the global view of choreographies. Our semantics is given in terms of pre-orders and can accommodate different lower level semantics. We discuss the adequacy of our model by considering its relation with communicating machines, that we use to formalise the local view. Interestingly, our framework seems to be more expressive than others where semantics of global views have been considered. This will be illustrated by discussing some interesting examples.