Least fixpoints as meanings of recursive definitions.

We develop a new schema for unstructured data. Traditional schemas resemble the type systems of programming languages. For unstructured data, however, the underlying type may be much less constrained and hence an alternative way of expressing constraints on the data is needed. Here, we propose that both data and schema be represented as edge-labeled graphs. We develop notions of conformance between a graph database and a graph schema and show that there is a natural and e ciently computable ordering on graph schemas. We then examine certain subclasses of schemas and show that schemas are closed under query applications. Finally, we discuss how they may be used in query decomposition and optimization. 1

This paper presents an overview of the programming language Modula-3, and a more detailed description of its type system. 1

Abstract. The permutation model of set theory with atoms (FM-sets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘name-abstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variable-binding operations. Inductively defined FM-sets involving the name-abstraction set former (together with Cartesian product and disjoint union) can correctly encode syntax modulo renaming of bound variables. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated notion of structural recursion for defining syntax-manipulating functions (such as capture avoiding substitution, set of free variables, etc.) and a notion of proof by structural induction, both of which remain pleasingly close to informal practice in computer science. 1.

This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal Logic, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping and for freshness of names, from which a notion of binding can be derived. Its axioms express...

PolyTOIL is a new statically-typed polymorphic object-oriented programming language that is provably type-safe. By separating the de nitions of subtyping and inheritance, providing a name for the type of self, and carefully de ning the type-checking rules, we have obtained a language that is very expressive while supporting modular type-checking of classes. The matching relation on types, which is related to F-bounded quanti cation, is used both in stating type-checking rules and expressing the bounds on type parameters for polymorphism. The design of PolyTOIL is based on a careful formal de nition of type-checking rules and semantics.

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...

Active networks must balance the flexibility of a programmable network infrastructure against the safety and security requirements inherent in sharing that infrastructure. Furthermore, this balance must be achieved while maintaining the usability of the network. The SwitchWare active network architecture is a novel approach to achieving this balance using three layers: active packets, which contain mobile programs that replace traditional packets; active extensions, which provide services on the network elements, and which can be dynamically loaded, and; a secure active router infrastructure, which forms a high integrity base upon which the security of the other layers depends. In addition to integrity-checking and cryptography-based authentication, security in our architecture depends heavily on verification techniques from programming languages, such as strong type checking.

Syntax Involving Binders Murdoch Gabbay Cambridge University DPMMS Cambridge CB2 1SB, UK M.J.Gabbay@cantab.com Andrew Pitts Cambridge University Computer Laboratory Cambridge CB2 3QG, UK ap@cl.cam.ac.uk Abstract The Fraenkel-Mostowski permutation model of set theory with atoms (FM-sets) can serve as the semantic basis of meta-logics for specifying and reasoning about formal systems involving name binding, ff-conversion, capture avoiding substitution, and so on. We show that in FM-set theory one can express statements quantifying over `fresh' names and we use this to give a novel set-theoretic interpretation of name abstraction. Inductively defined FM-sets involving this name-abstraction set former (together with cartesian product and disjoint union) can correctly encode object-level syntax modulo ff-conversion. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated n...

In order to illuminate the fundamental concepts involved in object-oriented programming languages, we describe the design of TOOPL, a paradigmatic, statically-typed, functional, object-oriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and inheritance. It has proven to be quite difficult to design such a language which has a secure type system. A particular problem with statically type checking object-oriented languages is designing type-checking rules which ensure that methods provided in a superclass will continue to be type correct when inherited in a subclass. The type-checking rules for TOOPL have this feature, enabling library suppliers to provide only the interfaces of classes with actual executable code, while still allowing users to safely create subclasses. In order to achieve greater expressibility while retaining type-safety, we choose to separate the inheritance and subtyping hierarchy in the language. The design of...