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A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 28 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
Domain theory for concurrency
, 2003
"... Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. ..."
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Cited by 23 (6 self)
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Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey.
Events, Causality and Symmetry
, 2008
"... The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences ..."
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Cited by 4 (2 self)
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The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.
Event structures with persistence
, 2008
"... 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 computation ..."
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Cited by 1 (0 self)
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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 nondeterministic 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
Twenty years on: Reflections on the CEDISYS project. Combining true concurrency with
"... process algebra. ..."
CATEGORICAL LOGIC AND PROOF THEORY EPSRC INDIVIDUAL GRANT REPORT – GR/R95975/01
"... Abstract. I describe the main results obtained during the EPSRC postdoctoral fellowship that I held at the University of Cambridge. The fellowship focused on the interplay between category theory and mathematical logic. 1. Wellfounded trees Wtypes in categories. Types of wellfounded trees, or Wtyp ..."
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Abstract. I describe the main results obtained during the EPSRC postdoctoral fellowship that I held at the University of Cambridge. The fellowship focused on the interplay between category theory and mathematical logic. 1. Wellfounded trees Wtypes in categories. Types of wellfounded trees, or Wtypes, are one of the most important components of MartinLöf’s dependent type theories. They allow us to define a wide class of inductive types, play an essential role in the ‘setsastrees’ interpretation of constructive set theories, and contribute considerably to the prooftheoretic strength of dependent type theories. A categorical counterpart of Wtypes was introduced in [18] by defining Wtypes in a locally cartesian closed category to be initial algebras for endofunctors of a special kind, generally referred to as polynomial functors. In collaboration with Martin Hyland, I set out to investigate the consequences of the assumption that a locally cartesian closed category has Wtypes. To explore these consequences we introduced the notion of a dependent polynomial functor, a
ON THE COHERENCE CONDITIONS FOR
, 907
"... Abstract. We survey the development of the formal theory of pseudomonads, the analogue for pseudomonads of the formal theory of monads. One of the main achievements of the theory is a satisfactory axiomatisation of the notion of a pseudodistributive law between pseudomonads. ..."
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Abstract. We survey the development of the formal theory of pseudomonads, the analogue for pseudomonads of the formal theory of monads. One of the main achievements of the theory is a satisfactory axiomatisation of the notion of a pseudodistributive law between pseudomonads.