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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 27 (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.
ON THE COHERENCE CONDITIONS FOR Pseudodistributive Laws
, 2009
"... 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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Cited by 3 (0 self)
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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.
Twenty years on: Reflections on the CEDISYS project. Combining true concurrency with process algebra
"... ..."
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
1 Physics, Topology, Logic and Computation:
"... Category theory is a very general formalism, but there is a certain special way that physicists use categories which turns out to have close analogues in topology, logic and computation. A category has objects and morphisms, which represent things and ways to go between things. In physics, the objec ..."
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Category theory is a very general formalism, but there is a certain special way that physicists use categories which turns out to have close analogues in topology, logic and computation. A category has objects and morphisms, which represent things and ways to go between things. In physics, the objects are often physical systems, and the morphisms are processes turning
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"... 1 Introduction Denotational semantics and domain theory of Scott and Strachey provide a global mathematical setting for sequential computation, and thereby place programming languages in connection with each other; connect with the mathematical worlds of algebra, topology and logic; and inspire prog ..."
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1 Introduction Denotational semantics and domain theory of Scott and Strachey provide a global mathematical setting for sequential computation, and thereby place programming languages in connection with each other; connect with the mathematical worlds of algebra, topology and logic; and inspire programming languages, type disciplines and methods of reasoning.