ion for the Lazy -calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy -calculus, a type-free functional language based on evaluation to weak head normal form, is given in G, yielding an extensional model in E . This model is shown to be fully abstract with respect to applicative simulation. This is, so far as we know, the first purely semantic construction of a fully abstract model for a reflexively-typed sequential language. 1 Introduction Full Abstraction is a key concept in programming language semantics [9, 12, 23, 26]. The ingredients are as follows. We are given a language L, with an `observational preorder' - on terms in L such that P - Q means that every observable property of P is also satisfied by Q; and a denotational model MJ\DeltaK. The model M is then said to be f...

The manipulation of objects with state which changes over time is allpervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focusses on "Idealized Algol", an elegant synthesis of imperative and functional features. We present a novel semantics for Idealized Algol using games, which is quite unlike traditional denotational models of state. The model takes into account the irreversibility of changes in state, and makes explicit the difference between copying and sharing of entities. As a formal measure of the accuracy of our model, we obtain a full abstraction theorem for Idealized Algol with active expressions.

The \pi-calculus is a formalism of computing in which we can compositionally represent dynamics of major programming constructs by decomposing them into a single communication primitive, the name passing. This work reports our experience in using a linear/affine typed \pi-calculus for the analysis and development of type systems of programming languages, focussing on secure information flow analysis. After presenting a basic typed calculus for secrecy, we demonstrate its usage by a sound embedding of the dependency core calculus (DCC) and by the development of a novel type discipline for imperative programs which extends both a secure multi-threaded imperative language by Smith and Volpano and (a call-by-value version of) DCC. In each case, the embedding gives a simple proof of noninterference.

This paper considers the consequences of relaxing the bracketing condition on `dialogue games', showing that this leads to a category of games which can be `factorized' into a well-bracketed substructure, and a set of classically typed morphisms. These are shown to be sound denotations for control operators, allowing the factorization to be used to extend the definability result for PCF to one for PCF with control operators at atomic types. Thus we define a fully abstract and effectively presentable model of a functional language with non-local control as part of a modular approach to modelling non-functional features using games. 1.

. We present a general semantic universe of call-by-value computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for call-by-value PCF, a generic typed programming language with call-by-value evaluation. The key idea is to consider the distinction between call-by-name and call-by-value as that of the structure of information flow, which determines the basic form of games. In this way the call-by-name computation and call-by-value computation arise as two independent instances of sequential functional computation with distinct algebraic structures. We elucidate the type structures of the universe following the standard categorical framework developed in the context of domain theory. Mutual relationship between the presented category of games and the corresponding call-by-name universe is also clarified. 1. Introduction The call-by-value is a mode of calling procedures widely used in imperative and function...

We propose a new type discipline for the -calculus in which secure information ow is guaranteed by static type checking. Secrecy levels are assigned to channels and are controlled by subtyping. A behavioural notion of types capturing causality of actions plays an essential role for ensuring safe information ow in diverse interactive behaviours, making the calculus powerful enough to embed known calculi for type-based security. The paper introduces the core part of the calculus, presents its basic syntactic properties, and illustrates its use as a tool for programming language analysis by a sound embedding of a secure multi-threaded imperative calculus of Volpano and Smith. The embedding leads to a practically meaningful extension of their original type discipline.

Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntax-independent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with non-functional features such as control operators and locally-scoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6]. Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in computer-assisted verification and program analysis. Some promising steps have already been taken in this

this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by Stefanescu (Stefanescu 2000).) However, the first author realized, following a stimulating discussion with Gordon Plotkin, that traced monoidal categories provided a common denominator for the axiomatics of both the Girard-style and Abramsky-Jagadeesan-style versions of the Geometry of Interaction, at the basic level of the multiplicatives. This insight was presented in (Abramsky 1996), in which Girard-style GoI was dubbed "particle-style", since it concerns information particles or tokens flowing around a network, while the Abramsky-Jagadeesan style GoI was dubbed "wave-style", since it concerns the evolution of a global information state or "wave". Formally, this distinction is based on whether the tensor product (i.e. the symmetric monoidal structure) in the underlying category is interpreted as a coproduct (particle style) or as a product (wave style). This computational distinction between coproduct and product interpretations of the same underlying network geometry turned out to have been partially anticipated, in a rather di#erent context, in a pioneering paper by E. S. Bainbridge (Bainbridge 1976), as observed by Dusko Pavlovic. These two forms of interpretation, and ways of combining them, have also been studied recently in (Stefanescu 2000). He uses the terminology "additive" for coproduct-based (i.e. our "particle-style") and "multiplicative" for product-based (i.e. our "wave-style"); this is not suitable for our purposes, because of the clash with Linear Logic term...

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This paper provides a fully abstract semantics for a variant of the concurrent object calculus. We define may testing for concurrent object components and then characterise it using a trace semantics inspired by UML interaction diagrams. The main result of this paper is to show that the trace semantics is fully abstract for may testing. This is the first such result for a concurrent object language. 1.