This document presents two different paradigms of description of communication behaviour, one focussing on global message flows and another on end-point behaviours, as formal calculi based on session types. The global calculus originates from Choreography Description Language, a web service description language developed by W3C WS-CDL working group. The end-point calculus is a typed π-calculus. The global calculus describes an interaction scenario from a vantage viewpoint; the endpoint calculus precisely identifies a local behaviour of each participant. After introducing the static and dynamic semantics of these two calculi, we explore a theory of endpoint projection which defines three principles for well-structured global description. The theory then defines a translation under the three principles which is sound and complete in the sense that all and only behaviours specified in the global description are realised as communications among end-point processes. Throughout the theory, underlying type structures play a fundamental role. The document is divided in two parts: part I introduces the two descriptive frameworks using simple but non-trivial examples; the second part establishes a theory of the global and end-point formalisms.

We study reduction congruence, a popular notion of process equality, for the asynchronous π-calculus with timers, and derive several alternative characterisations, one of them being a labelled asynchronous bisimilarity. These results are adapted to an asynchronous π-calculus with timers, locations and message failure. In addition we investigate the problem of how to distribute value-passing processes in a semantics-preserving way.

For historical, sociological and technical reasons, -calculi have been the dominant theoretical paradigm in the study of functional computation. Similarly, but to a lesser degree, -calculi dominate advanced mathematical accounts of concurrency. Alas, and despite its ever increasing ubiquity, an equally convincing formal foundation for distributed computing has not been forthcoming. This thesis seeks to contribute towards ameliorating that omission. To this end, guided by the assumption that distributed computing is concurrent computing with partial failures of various kinds, we extend the asynchronous -calculus with a notion of sites, the possibility of site failure, a persistence mechanism to deal with site failures, the distinction between inter-site and intra-site communication, the possibility of message loss in inter-site communication and a timer construct, as is often used in distributed algorithms to deal with various failure scenarios.

Bigraphs have been introduced with the aim to provide a topographical meta-model for mobile, distributed agents that can manipulate their own linkages and nested locations, generalising both characteristics of the π-calculus and the Mobile Ambients calculus. We give the first bigraphical presentation of a non-linear, higher-order process calculus with nested locations, non-linear active process mobility, and local names, the calculus of Higher-Order Mobile Embedded Resources (Homer). The presentation is based on Milner’s recent presentation of the λ-calculus in local bigraphs. The combination of non-linear active process mobility and local names requires a new definition of parametric reaction rules and a representation of the location of names. We suggest localised bigraphs as a generalisation of local bigraphs in which links can be further localised. Key words: bigraphs, local names, non-linear process mobility

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 a well typed and irreducible process Q such that the parallel composition P|Q always reduces, also in presence of interfered sessions. 1

We study behavioural equivalences for dynamic web data in Xd#, a model for reasoning about behaviour found in (for example) dynamic web page programming, applet interaction, and web-service orchestration. Xd# is based on an idealised model of semistructured data, and an extension of the #-calculus with locations and operations for interacting with data. The equivalences are non-standard due to the integration of data and processes, and the presence of locations. Contents 1

Powerful proof techniques, such as logical relation arguments, have been developed for establishing the strong normalisation property of term-rewriting systems. The first author used such a logical relation argument to establish strong normalising for a cut-elimination procedure in classical logic. He presented a rather complicated, but informal, proof establishing this property. The difficulties in this proof arise from a quite subtle substitution operation. We have formalised this proof in the theorem prover Isabelle/HOL using the Nominal Datatype Package, closely following the first authors PhD. In the process, we identified and resolved a gap in one central lemma and a number of smaller problems in others. We also needed to make one informal definition rigorous. We thus show that the original proof is indeed a proof and that present automated proving technology is adequate for formalising such difficult proofs.

Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of confluence to systems that allow nondeterminism. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the π-calculi with internal mobility. The semantics we provide is the first event structure semantics of the π-calculus and generalises Winskel’s original event structure semantics of CCS. 1

Peer to peer systems, exchanging dynamic documents through Web services, are a simple and effective platform for data integration on the internet. Dynamic documents can contain both data and references to external sources in the form of links, calls to web services, or coordination scripts. XML standards, and industrial platforms for web services, provide the technological basis for building such systems. We argue that process algebras are a promising tool for studying and understanding their formal properties. In this thesis, we define the Xdπ-calculus with the aim of reasoning about dynamic Web data. Xdπ terms represent networks of peers, each consisting of an XML data repository and a working space where processes are allowed to run. Processes, inspired by the π-calculus, can communicate with each other, query and update the local repository, or migrate to other peers to continue execution. Data can contain scripted processes, which can be executed by other processes. For example, Xdπ processes can be used to embed service calls in documents and to model Web services. We investigate behavioural equivalences for Xdπ, comparing several observable

Abstract. We study an extension of Hennessy-Milner logic for the π-calculus which gives a sound and complete characterisation of representative behavioural preorders and equivalences over typed processes. New connectives are introduced representing actual and hypothetical typed parallel composition and hiding. We study three compositional proof systems, characterising the May/Must testing preorders and bisimilarity. The proof systems are uniformly applicable to different type disciplines. Logical axioms distill proof rules for parallel composition studied by Amadio and Dam. We demonstrate the expressiveness of our logic embeddings of program logics for higher-order functions. 1