Introduction 2 The semantic universe: transducers Similar ideas appeared independently in the work of Hans Bekic [Bek71]. Samson Abramsky Laboratory for the Foundations of Computer Science University of Edinburgh The very existence of the conference bears witness to the fact that "concurrency theory" has developed into a subject unto itself, with substantially di#erent emphases and techniques to those prominent elsewhere in the semantics of computation. Whatever the past merits of this separate development, it seems timely to look for some convergence and unification. In addressing these issues, I have found it instructive to trace some of the received ideas in concurrency back to their origins in the early 1970's. In particular, I want to focus on a seminal paper by Robin Milner [Mil75] , which led in a fairly direct line to his enormously influential work on [Mil80, Mil89]. I will take (to the extreme) the liberty of of applying hindsight, and show how some di

The “classical ” paradigm for denotational semantics models data types as domains, ��� � structured sets of some kind, and programs as (suitable) functions between domains. The semantic universe in which the denotational modelling is carried out is thus a category with domains as objects, functions as morphisms, and composition of morphisms given by function composition. A sharp distinction is then drawn between denotational and operational semantics. Denotational semantics is often referred to as “mathematical semantics ” because it exhibits a high degree of mathematical structure; this is in part achieved by the fact that denotational semantics abstracts away from the dynamics of computation—from time. By contrast, operational semantics is formulated in terms of the syntax of the language being modelled; it is highly intensional in character; and it is capable of expressing the dynamical aspects of computation. The classical denotational paradigm has been very successful, but has some definite limitations. Firstly, fine-structural features of computation, such as sequentiality,

We develop a notion of Kripke-like parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their category-theoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal cocompletion. As applications, we obtain full completeness results of translations between linear type theories.

We present a type-based technique for the verification of deadlock-freedom in asynchronous concurrent systems. Our approach is to start with an interaction category such as ASProc, where objects are types containing safety specifications and morphisms are processes. We then use a specification structure to add information to the types so that they specify stronger properties. The extra information in this case concerns deadlock-freedom, and in the resulting category ASProc D , combining well-typed processes preserves deadlock-freedom. It is also possible to accommodate non-compositional methods within the same framework. The systems we consider are asynchronous, hence issues of divergence become significant; our approach incorporates an elegant treatment of both divergence and successful termination. As an example, we use our methods to verify the deadlock-freedom of an implementation of the alternating-bit protocol. Address for Correspondence Dr S. J. Gay Department of ...

Synchronous languages have been designed to ease the development of reactive systems, by providing a methodological framework for assisting system designers from the early stages of requirement specifications to the final stages of code generation or circuit production. Synchronous languages enable a very high-level specification and an extremely modular design of complex reactive systems by structural decomposition of them into elementary processes. We define an order-theoretical model that gives a unified mathematical formalisation of all the above aspects of the synchronous methodology and characterises the essentials of the synchronous paradigm.

This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of di#erent and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency.

We give a series of glueing constructions for categorical models of fragments of linear logic. Specifically, we consider the glueing of (i) symmetric monoidal closed categories (models of Multiplicative Intuitionistic Linear Logic), (ii) symmetric monoidal adjunctions (for interpreting the modality !) and (iii) -autonomous categories (models of Multiplicative Linear Logic); the glueing construction for -autonomous categories is a mild generalization of the double glueing construction due to Hyland and Tan. Each of the glueing techniques can be used for creating interesting models of linear logic. In particular, we use them, together with the free symmetric monoidal cocompletion, for deriving Kripke-like parameterized logical predicates (logical relations) for the fragments of linear logic. As an application, we show full completeness results for translations between linear type theories. Contents 1 Introduction 3 2 Preliminaries 4 2.1 Symmetric Monoidal Structures . . . . . . . ....

1 Introduction It has been known for some years that formal systems of various kinds correspond to certain flavours of categorical structure. The first person to observe this phenomenon seems to have been Lawvere, who formulated a connection between certain kinds of algebraic theories and categories with finite products. Since Lawvere's original insight, there has been much progress in understanding

Many different notions of "program property", and many different methods of verifying such properties, arise naturally in programming. We present a general framework of Specification Structures for combining different notions and methods in a coherent fashion. We then apply the idea of specification structures to concurrency in the setting of Interaction Categories. As a specific example, a certain specification

This report focuses on research into models and logics for concurrency and their application in specifying, verifying, and implementing concurrent systems. This general area has become known as concurrency theory , and its roots may be traced back to the 1960s [Dij68, Pet62]. Our aim is to survey the rich collection of mature theories and models for concurrency that exist; to review the powerful specification, design, and verification methods and tools that have been developed; and to highlight ongoing active areas of research and suggest fruitful directions for future investigation. By focusing on concurrency theory and its use in verification, we necessarily omit consideration of other concurrency-related topics such as concurrency control in database systems, concurrent program debugging, operating systems, distributed system architecture, and real-time systems. The interested reader is referred to other working group reports, which address many of these topics.