Semantic subtyping for objects and classes

In this paper we propose an integration of structural subtyping with boolean connectives and semantic subtyping to define a Java-like programming language that exploits the benefits of both techniques. Semantic subtyping is an approach for defining subtyping relation based on set-theoretic models, rather than syntactic rules. On the one hand, this approach involves some non trivial mathematical machinery in the background. On the other hand, final users of the language need not know this machinery and the resulting subtyping relation is very powerful and intuitive. While semantic subtyping is naturally linked to the structural one, we show how our framework can also accommodate the nominal subtyping. Several examples show the expressivity and the practical advantages of our proposal

Conflict vs causality in event structures

Event structures are one of the best known models for concurrency. Many variants of the basic model and many possible notions of equivalence for them have been devised in the literature. In this paper, we study how the spectrum of equivalences for Labelled Prime Event Structures built by Van Glabbeek and Goltz changes if we consider two simplified notions of event structures: the first is obtained by removing the causality relation (Coherence Spaces) and the second by removing the conflict relation (Elementary Event Structures). As expected, in both cases the spectrum turns out to be simplified, since some notions of equivalence coincide in the simplified settings; actually, we prove that removing causality simplifies the spectrum considerably more than removing conflict. Furthermore, while the labeling of events and their cardinality play no role when removing causality, both the labeling function and the cardinality of the event set dramatically influence the spectrum of equivalences in the conflict-free setting

Modal Logic and the Approximation Induction Principle

We prove a compactness theorem in the context of Hennessy-Milner logic. It is used to derive a sufficient condition on modal characterizations for the Approximation Induction Principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators

Full abstraction for expressiveness: history, myths and facts

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.What does it mean that an encoding is fully abstract? What does it not mean? In this position paper, we want to help the reader to evaluate the real benefits of using such a notion when studying the expressiveness of programming languages. Several examples and counterexamples are given. In some cases, we work at a very abstract level; in other cases, we give concrete samples taken from the field of process calculi, where the theory of expressiveness has been mostly developed in the last years

A doctrinal approach to modal/temporal Heyting logic and non-determinism in processes

The study of algebraic modelling of labelled non-deterministic concurrent processes leads us to consider a category LB , obtained from a complete meet-semilattice B and from B-valued equivalence relations. We prove that, if B has enough properties, then LB presents a two-fold internal logical structure, induced by two doctrines definable on it: one related to its families of subobjects and one to its families of regular subobjects. The first doctrine is Heyting and makes LB a Heyting category, the second one is Boolean. We will see that the difference between these two logical structures, namely the different behaviour of the negation operator, can be interpreted in terms of a distinction between non-deterministic and deterministic behaviours of agents able to perform computations in the context of the same process. Moreover, the sorted first-order logic naturally associated with LB can be extended to a modal/temporal logic, again using the doctrinal setting. Relations are also drawn to other computational model

Algebra and Coalgebra of Stream Products

We study connections among polynomials, differential equations and streams over a field ?, in terms of algebra and coalgebra. We first introduce the class of (F,G)-products on streams, those where the stream derivative of a product can be expressed as a polynomial of the streams themselves and their derivatives. Our first result is that, for every (F,G)-product, there is a canonical way to construct a transition function on polynomials such that the induced unique final coalgebra morphism from polynomials into streams is the (unique) ?-algebra homomorphism - and vice-versa. This implies one can reason algebraically on streams, via their polynomial representation. We apply this result to obtain an algebraic-geometric decision algorithm for polynomial stream equivalence, for an underlying generic (F,G)-product. As an example of reasoning on streams, we focus on specific products (convolution, shuffle, Hadamard) and show how to obtain closed forms of algebraic generating functions of combinatorial sequences, as well as solutions of nonlinear ordinary differential equations

Security Policies as Membranes in Systems for Global Computing

We propose a simple global computing framework, whose main concern is code migration. Systems are structured in sites, and each site is divided into two parts: a computing body, and a membrane which regulates the interactions between the computing body and the external environment. More precisely, membranes are filters which control access to the associated site, and they also rely on the well-established notion of trust between sites. We develop a basic theory to express and enforce security policies via membranes. Initially, these only control the actions incoming agents intend to perform locally. We then adapt the basic theory to encompass more sophisticated policies, where the number of actions an agent wants to perform, and also their order, are considered

A Concurrent Pattern Calculus

International audienceConcurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes symmetrical, with information flowing in both directions. CPC provides a natural language to express trade where information exchange is pivotal to interaction. The unification allows some patterns to be more discriminating than others; hence, the behavioural theory must take this aspect into account, so that bisimulation becomes subject to compatibility of patterns. Many popular process calculi can be encoded in CPC; this allows for a gain in expressiveness, formalised through encodings

Process calculi and the verification of security protocols, Journal of Telecommunications and Information Technology, 2002, nr 4

Recently there has been much interest towards using formal methods in the analysis of security protocols. Some recent approaches take advantage of concepts and techniques from the field of process calculi. Process calculi can be given a formal yet simple semantics, which permits rigorous definitions of such concepts as “attacker”, “secrecy” and “authentication”. This feature has led to the development of solid reasoning methods and verification techniques, a few of which we outline in this paper