Least fixpoints as meanings of recursive definitions.

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Abstract not found

Increasingly, the style of computation is changing. Instead of one machine running a program sequentially, we have systems with many individual agents running in parallel. The need for mathematical models of such computations is therefore ever greater. There are many models of concurrent computations. Such models can, for example, provide a semantics to process calculi and thereby suggest behavioural equivalences between processes. They are also key to the development of automated tools for reasoning about concurrent systems. In this thesis we explore some applications and generalisations of one particular model – event structures. We describe a variety of kinds of morphism between event structures. Each kind expresses a different sort of behavioural relationship. We demonstrate the way in which event structures can model both processes and types of processes by recalling a semantics for Affine HOPLA, a higher order process language. This is given in terms of asymmetric spans of event structures. We show that such spans support a trace construction. This allows the modelling of feedback and suggests a semantics for non-deterministic dataflow processes in terms of spans. The semantics given is shown to be consistent with Kahn’s fixed point construction when we consider spans modelling deterministic processes. A generalisation of event structures to include persistent events is proposed. Based on previously described morphisms between classical event structures, we define several categories of event structures with persistence. We show that, unlike for the corresponding categories of classical event structures, all are isomorphic to Kleisli categories of monads

The problem of decomposing domains into sensible factors is addressed and solved for the case of dI-domains. A decomposition theorem is proved which allows the represention of a large subclass of dI-domains in a product of flat domains. Direct product decompositions of Scott-domains are studied separately. 1 Introduction This work was initiated by Peter Buneman's interest in generalizing relational databases, see [6]. He --- quite radically --- dismissed the idea that a database should be forced into the format of an n-ary relation. Instead he allowed it to be an arbitrary anti-chain in a Scott-domain. The reason for this was that advanced concepts in database theory, such as `null values', `nested relations', and `complex objects' force one to augment relations and values with a notion of information order. Following Buneman's general approach, the question arises how to define basic database theoretic concepts such as `functional dependency' for anti-chains in Scott-domains. For...