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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 49 (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
Profunctors, open maps and bisimulation
 Mathematical Structures in Computer Science, To appear. Available from the Glynn Winskelâ€™s web
, 2000
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, 2002
"... 1 Introduction Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higherorder and functional features as kno ..."
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1 Introduction Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higherorder and functional features as known from sequential programming are most often treated in an ad hoc fashion, if at all. The study of presheaf models of processes [1, 10] can be seen as an attempt to bring concurrency back within the realm of traditional denotational semantics by providing a domain theory for concurrent computation. In particular, presheaf models come with a builtin notion of bisimulation, derived from open maps [11].
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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.
unknown title
"... 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 ..."
Abstract
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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.