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Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
A Theory of Recursive Domains with Applications to Concurrency
 In Proc. of LICS ’98
, 1997
"... Marcelo Fiore , Glynn Winskel (1) BRICS , University of Aarhus, Denmark (2) LFCS, University of Edinburgh, Scotland December 1997 Abstract We develop a 2categorical theory for recursively defined domains. ..."
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Cited by 23 (14 self)
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Marcelo Fiore , Glynn Winskel (1) BRICS , University of Aarhus, Denmark (2) LFCS, University of Edinburgh, Scotland December 1997 Abstract We develop a 2categorical theory for recursively defined domains.
Solving Recursive Domain Equations with Enriched Categories
, 1994
"... Both preorders and metric spaces have been used at various times as a foundation for the solution of recursive domain equations in the area of denotational semantics. In both cases the central theorem states that a `converging' sequence of `complete' domains/spaces with `continuous' retraction pair ..."
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Cited by 21 (0 self)
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Both preorders and metric spaces have been used at various times as a foundation for the solution of recursive domain equations in the area of denotational semantics. In both cases the central theorem states that a `converging' sequence of `complete' domains/spaces with `continuous' retraction pairs between them has a limit in the category of complete domains/spaces with retraction pairs as morphisms. The preorder version was discovered first by Scott in 1969, and is referred to as Scott's inverse limit theorem. The metric version was mainly developed by de Bakker and Zucker and refined and generalized by America and Rutten. The theorem in both its versions provides the main tool for solving recursive domain equations. The proofs of the two versions of the theorem look astonishingly similar, but until now the preconditions for the preorder and the metric versions have seemed to be fundamentally different. In this thesis we establish a more general theory of domains based on the noti...
Profunctors, open maps and bisimulation
 Mathematical Structures in Computer Science, To appear. Available from the Glynn Winskel’s web
, 2000
"... ..."
On a Question of Friedman
 Information and Computation
, 1995
"... In this paper we answer a question of Friedman, providing an !separable model M of the fijcalculus. There therefore exists an ffseparable model for any ff 0. The model M permits no nontrivial enrichment as a partial order; neither does it permit an enrichment as a category with an initial ob ..."
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Cited by 4 (0 self)
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In this paper we answer a question of Friedman, providing an !separable model M of the fijcalculus. There therefore exists an ffseparable model for any ff 0. The model M permits no nontrivial enrichment as a partial order; neither does it permit an enrichment as a category with an initial object. The open term model embeds in M: by way of contrast we provide a model which cannot embed in any nontrivial model separating all pairs of distinct elements. 1 Introduction Separability is a recurring topic in the calculus. It is usually defined syntactically; there is also an interesting modeltheoretic definition. Say that a subset A of an applicative structure (X; \Delta) is separable if any function f : A ! X is realised by some f in X , by which is meant, that for all a in A, f(a) = f \Delta a. This idea first appears in work of Flagg and Myhill [FM]. They termed the concept "discreteness," employing a topological analogy; we prefer to extend the usual calculus terminology....