In this paper we show how a resource-oriented logic, separation logic, can be used to reason about the usage of resources in concurrent programs.

We present a foundational language for distributed programming, called Lambda 5, that addresses both mobilityof code and locality of resources. In order to construct our system, we appeal to the powerful propositions-as-types interpretation of logic. Specifically, we take the possible worlds of the intuitionistic modal logic IS5 to be nodes ona network, and the connectives 2 and 3 to reflect mobility and locality, respectively. We formulate a novel systemof natural deduction for IS5, decomposing the introduction and elimination rules for 2 and 3, thereby allowing thecorresponding programs to be more direct. We then give an operational semantics to our calculus that is type-safe, logically faithful, and computationally realistic.

Spatial logics have been used to describe properties of tree-like structures (Ambient Logic) and in a Hoare style to reason about dynamic updates of heap-like structures (Separation Logic). We integrate this work by analyzing dynamic updates to tree structures with pointers (such as XML with identifiers and idrefs). Na ve adaptations of the previous logics are not expressive enough to capture such local updates. Instead we must explicitly reason about arbitrary tree contexts --- not just horizontal composition and vertical branching --- in order to capture updates throughout the tree. To illustrate the point, we introduce a small imperative programming language for updating our trees, small Hoare-style axioms for the commands in the style of O'Hearn, Reynolds and Yang, and show how weakest preconditions are derivable from the small axioms with a generalized frame rule. We demonstrate the generality of our approach by showing that it collapses to Separation Logic for a heap model. 1.

We study a typing scheme derived from a semantic situation where a single category possesses several closed structures, corresponding to dierent varieties of function type. In this scheme typing contexts are trees built from two (or more) binary combining operations, or in short, bunches. Bunched typing and its logical counterpart, bunched implications, have arisen in joint work of the author and David Pym. The present paper gives a basic account of the type system, and then focusses on concrete models that illustrate how it may be understood in terms of resource access and sharing. The most

Abstract. We define a variant of Lamport’s Temporal Logic of Actions, extended by spatial modalities, that is intended for the specification of mobile systems with distributed state. We discuss notions of refinement appropriate for mobile systems, specifically concerning the topological structure of the system, and show how these can be represented in the logic via quantification and implication, ensuring transitivity and compositionality of refinements. 1

In this dissertation I argue that modal type systems provide an elegant and practical means for controlling local resources in spatially distributed computer programs. A distributed program is one that executes in multiple physical or logical places. It usually does so because those places have local resources that can only be used in those locations. Such resources can include processing power, proximity to data, hardware, or the physical presence of a user. Programmers that write distributed applications therefore need to be able to reason about the places in which their programs will execute. This work provides an elegant and practical way to think about such programs in the form of a type system derived from modal logic. Modal logic allows for reasoning about truth from multiple simultaneous perspectives. These perspectives, called "worlds," are identified with the locations in the distributed program. This enables the programming language to be simultaneously aware of the various hosts involved in a program, their

The global usage and continuing exponential growth of the World-Wide-Web poses a host of challenges to the research community. In particular, thereis an urgent need to understand and manage the dynamics of the Web, in order to develop new techniques which will make the Web tractable. We provide an overview of recent statistics relating to the size of the Web graph and its growth. We then briefly review some of the key areas relating to Webdynamics with reference to the recent literature. Finally, we summarise the talks given in a recent workshop devoted to Webdynamics which was held in the beginning of January 2001 at the University of London. Keywords. Web dynamics, Web graph, information retrieval, collaborative filtering, Web navigation,Website design, data-intensive Web applications, workflow management, e-commerce,mobile computation.

First of all, I would like to thank my supervisor Dr. Iain C. C. Phillips, for his support and collaboration during this period of research. I thank Iain for having taught me to be more precise and sharp, and for long, detailed and inspiring discussions on the topic of this dissertation. Finally I thank him for his enormous patience towards my stubbornness. I would like to thank Dr. Nobuko Yoshida for many useful discussions and for being very supportive and positive about my work. To Sergio Maffeis go thanks for many discussions on various subjects of research and philosophy during the last two years at Imperial College. He suggested an improvement to the solution for the leader election problem for the Ambient Calculus. I would like to thank also Andrew Phillips, and the concurrency group at Imperial for the Monday lunch meetings. This has been a wonderful forum for discussing various aspects of my work. I like to thank Prof. Chris Hankin and Dr. Sophia Drossopoulou for helping me on various occasions with administrative problems and (especially Chris) for supporting most of my travelling. I do not know how I could have ever achieved this without my husband, Steffen van Bakel. He

We present a bottom-up algorithm which, given an untyped process P , calculates the minimal set of constraints on security levels such that all the actions during a run of P can be performed without violating the security level priorities. Our algorithm appears as a preliminary step in order to use type systems to ensure security properties in the web scenario.

An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced in [17, 18]. The modalities of the logic allow validation of properties in a particular place, in some place and in all places. We give a sound and complete Kripke semantics for the logic extended with disjunctive connectives. The extended logic can be seen as an instance of Hybrid IS5. We also give a sound and complete birelational semantics, and show that it enjoys the finite model property: if a judgement is not valid in the logic, then there is a finite birelational counter-model. Hence, we prove that the logic is decidable.