This paper introduces $\lambda^\widehat$, a simply typed lambda calculus supporting inductive types and recursive function definitions with termination ensured by types. The system is shown to enjoy subject reduction, strong normalisation of typable terms and to be stronger than a related system $\lambda_{\mathcal{G}}$ in which termination is ensured by a syntactic guard condition. The system can, at will, be extended to support coinductive types and corecursive function definitions also.

This paper describes the design and semantics of METAKLAIM, which is a higher order distributed process calculus equipped with staging mechanisms. METAKLAIM integrates METAML (an extension of SML for multi-stage programming) and KLAIM (a Kernel Language for Agents Interaction and Mobility), to permit interleaving of meta-programming activities (such as assembly and linking of code fragments), dynamic checking of security policies at administrative boundaries and ‘traditional’ computational activities on a wide area network (such as remote communication and code mobility). METAKLAIM exploits a powerful type system (including polymorphic types á la system F) to deal with highly parameterised mobile components and to enforce security policies dynamically: types are metadata that are extracted from code at run-time and are used to express trustiness guarantees. The dynamic type checking ensures that the trustiness guarantees of wide area network applications are maintained whenever computations interoperate with potentially untrusted components.

We show that a measurement $\mu$ on a continuous dcpo $D$ extends to a measurement $\skew3\bar{\mu}$ on the convex powerdomain ${\mathbf C} D$ iff it is a Lebesgue measurement. In particular, $\ker\mu$ must be metrisable in its relative Scott topology. Moreover, the space $\ker\skew3\bar{\mu}$ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of $\ker\mu$, that is, the space of non-empty compact subsets of $\ker\mu$ in its Vietoris topology – the topology induced by any Hausdorff metric. This enables one to show that Hutchinson's theorem holds for any finite set of contractions on a domain with a Lebesgue measurement. Finally, after resolving the existence question for Lebesgue measurements on countably based domains, we uncover the following relationship between classical analysis and domain theory: for an $\omega$-continuous dcpo $D$ with $\max(D)$ regular, the Vietoris hyperspace of $\max(D)$ embeds in $\max({\mathbf C} D)$ as the kernel of a measurement on ${\mathbf C} D$.

We show how to extend any commutative ring (or semiring) so that division by any element, including 0, is, in a sense, possible. The resulting structure is called a wheel. Wheels are similar to rings, but $0x=0$ does not hold in general; the subset $\{x|0x=0\}$ of any wheel is a commutative ring (or semiring), and any commutative ring (or semiring) with identity can be described as such a subset of a wheel. The main goal of this paper is to show that the given axioms for wheels are natural, and to clarify how valid identities for wheels relate to valid identities for commutative rings and semirings.

The choice of suitable high-level communication primitives for wide area network programming languages remains an open problem. This paper is driven by the practical consideration of providing an efficient and secure communication infrastructure for mobile agent systems. This has led us to formalise the Lime coordination middleware and propose a simplified model, which we call CoreLime, that addresses some of the main shortcomings of Lime while retaining its distinguishing feature, namely transient sharing of tuple spaces. We further discuss a prototype implementation along with security extensions. Our contribution is thus an exploration of the language design space rather than a theoretical investigation of properties of these models.

Since the publication of the paper Carboni and Johnstone (1995), we have become aware of two independent errors in it. Although neither of them has any effect on the main results of the paper, concerning when a category obtained by Artin glueing is a topos, we feel it is appropriate to publish this correction in the hope that it may prevent future readers of Carboni and Johnstone (1995) from being misled. We are grateful to Tom Leinster and to Marek Zawadowski for drawing our attention to the two errors.

Nowadays concepts, languages and models for coordination cannot leave aside the needs of the increasing number of commercial applications based on global computing over the (inter)net. For example, platforms like Microsoft .NET and Sun Microsystems Java come equipped with packages for supporting ad hoc transactional features, which are essential for most business applications. We show how to extend the coordination language par excellence (viz. Linda) with basic primitives for transactions, while retaining a formal model for its concurrent computations. This is achieved by exploiting a variation of Petri nets, called zero-safe nets, where transactions can be suitably modelled by distinguishing between stable places (ordinary ones) and zero places (where tokens can only be temporarily allocated, defining hidden states). The relevance of the transaction mechanism is illustrated in terms of expressive power. Finally, it is shown that stable places and transactions viewed as atomic steps define an abstract semantics that is apt for a fully algebraic treatment, as demonstrated via categorical adjunctions between suitable categories of nets.

Every compact metric space $X$ is homeomorphically embedded in an $\omega$-algebraic domain $D$ as the set of minimal limit (that is, non-finite) elements. Moreover, $X$ is a retract of the set $L(D)$ of all limit elements of $D$. Such a domain $D$ can be chosen so that it has property M and finite-branching, and the height of $L(D)$ is equal to the small inductive dimension of $X$. We also show that the small inductive dimension of $L(D)$ as a topological space is equal to the height of $L(D)$ for domains with property M. These results give a characterisation of the dimension of a space $X$ as the minimal height of $L(D)$ in which $X$ is embedded as the set of minimal elements. The domain in which we embed an $n$-dimensional compact metric space $X$ ($n \leq \infinity$) has a concrete structure in that it consists of finite/infinite sequences in $\{0,1,\bot\}$ with at most $n$ copies of $\bot$.