Session primitives and types provide a flexible programming style for structured interaction, and are used to statically check the safe and consistent composition of protocols in communication-centric distributed software. Unfortunately authors working on session types have recently realised that some of the previously published systems fail to satisfy the basic theorems of Subject Reduction and Type Safety. This report discusses the issues involved in higher-order session communication, presents a formulation of the recursive types as well as proofs of the Subject Reduction and Type Safety Theorems of the original session typing system by Honda-Vasconcelos-Kubo in ESOP’98. It also proposes a variant which allows a more liberal higher-order session communication, based on an idea of Gay and Hole.

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Polyphonic C# is an extension of the C# language with new asynchronous concurrency constructs, based on the join calculus. We describe the design and implementation of the language and give examples of its use in addressing a range of concurrent programming problems.

We study the distributed infrastructures required for location-independent communication between migrating agents. These infrastructures are problematic: different applications may have very different patterns of migration and communication, and require different performance and robustness properties; algorithms must be designed with these in mind. To study this problem we introduce an agent programming language - Nomadic Pict. It is designed to allow infrastructure algorithms to be expressed as clearly as possible, as translations from a high-level language to a low level. The levels are based on rigorously-defined process calculi, they provide sharp levels of abstraction. In this paper we describe the language and use it to develop an infrastructure for an example application. The language and examples have been implemented; we conclude with a description of the compiler and runtime.

We investigate whether the π-calculus is able to serve as a good foundation for the design and implementation of a strongly-typed concurrent programming language. The first half of the dissertation examines whether the π-calculus supports a simple type system which is flexible enough to provide a suitable foundation for the type system of a concurrent programming language. The second half of the dissertation considers how to implement the π-calculus efficiently, starting with an abstract machine for π-calculus and finally presenting a compilation of π-calculus to C. We start the dissertation by presenting a simple, structural type system for π-calculus, and then, after proving the soundness of our type system, show how to infer principal types for π-terms. This simple type system can be extended to include useful type-theoretic constructions such as recursive types and higherorder polymorphism. Higher-order polymorphism is important, since it gives us the ability to implement abstract datatypes in a type-safe manner, thereby providing a greater degree of modularity for π-calculus programs. The functional computational paradigm plays an important part in many programming languages. It is well-known that the π-calculus can encode functional computation. We go further and show that the type structure of λ-terms is preserved by such encodings, in the sense that we can relate the type of a λ-term to the type of its encoding in the π-calculus. This means that a π-calculus programming language can genuinely support typed functional programming as a special case. An efficient implementation of π-calculus is necessary if we wish to consider π-calculus as an operational foundation for concurrent programming. We first give a simple abstract machine for π-calculus and prove it correct. We then show how this abstract machine inspires a simple, but efficient, compilation of π-calculus to C (which now forms the basis of the Pict programming language implementation).

We study two encodings of the asynchronous #-calculus with input-guarded choice into its choice-free fragment. One encoding is divergence-free, but refines the atomic commitment of choice into gradual commitment. The other preserves atomicity, but introduces divergence. The divergent encoding is fully abstract with respect to weak bisimulation, but the more natural divergence-free encoding is not. Instead, we show that it is fully abstract with respect to coupled simulation, a slightly coarser---but still coinductively defined---equivalence that does not enforce bisimilarity of internal branching decisions. The correctness proofs for the two choice encodings introduce a novel proof technique exploiting the properties of explicit decodings from translations to source terms.

By adding reflexion to the chemical machine of Berry and Boudol, we obtain a formal model of concurrency that is consistent with mobility and distribution. Our model provides the foundations of a programming language with functional and object-oriented features. It can also be seen as a process calculus, the join-calculus, which we prove equivalent to the pi-calculus of Milner, Parrow and Walker.

The asynchronous pi-calculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and Blue calculus. However, at a closer inspection, these languages are based on an even simpler calculus, called Local (L), where: (a) only the output capability of names may be transmitted; (b) there is no matching or similar constructs for testing equality between names. We study the basic operational and algebraic theory of Lpi. We focus on bisimulation-based behavioural equivalences, precisely on barbed congruence. We prove two coinductive characterisations of barbed congruence in Lpi, and some basic algebraic laws. We then show applications of this theory, including: the derivability of delayed input; the correctness of an optimisation of the encoding of call-by-name lambda-calculus; the validity of some laws for Join.

We obtain a new formalism for concurrent object-oriented languages by extending Abadi and Cardelli's imperative object calculus with operators for concurrency from the-calculus and with operators for synchronisation based on mutexes. Our syntax of terms is extremely expressive; in a precise sense it unifies notions of expression, process, store, thread, and configuration. We present a chemical-style reduction semantics, and prove it equivalent to a structural operational semantics. We identify a deterministic fragment that is closed under reduction and show that it includes the imperative object calculus. A collection of type systems for object-oriented constructs is at the heart of Abadi and Cardelli's work. We recast one of Abadi and Cardelli's first-order type systems with object types and subtyping in the setting of our calculus and prove subject reduction. Since our syntax of terms includes both stores and running expressions, we avoid the need to separate store typing from typing of expressions. We translate asynchronous communication channels and the choice-free asynchronous-calculus into our calculus to illustrate its expressiveness; the types of read-only and write-only channels are supertypes of read-write channels.

Abstract. This paper relates two different paradigms of descriptions of communication behaviour, one focussing on global message flows and another on end-point behaviours, using formal calculi based on session types. The global calculus, which originates from a web service description language (W3C WS-CDL), describes an interaction scenario from a vantage viewpoint; the end-point calculus, an applied typed π-calculus, precisely identifies a local behaviour of each participant. We explore a theory of end-point projection, by which we can map a global description to its end-point counterpart preserving types and dynamics. Three principles of well-structured description and the type structures play a fundamental role in the theory. 1