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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 Coinduction Principle for Recursive Data Types Based on Bisimulation
, 1996
"... This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programmin ..."
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Cited by 37 (3 self)
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This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programming languages [SS71], but also arise explicitly as recursive data types in functional programming languages like Standard ML [MTH90] or Haskell [HPJW92]. In the latter context, the coinduction principle provides a powerful technique for establishing the equality of programs with values in recursive data types (see examples herein and in [Pit94]).
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
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Mongruences and Cofree Coalgebras
 Algebraic Methods and Software Technology, number 936 in Lect. Notes Comp. Sci
, 1995
"... . A coalgebra is introduced here as a model of a certain signature consisting of a type X with various "destructor" function symbols, satisfying certain equations. These destructor function symbols are like methods and attributes in objectoriented programming: they provide access to the t ..."
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Cited by 30 (10 self)
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. A coalgebra is introduced here as a model of a certain signature consisting of a type X with various "destructor" function symbols, satisfying certain equations. These destructor function symbols are like methods and attributes in objectoriented programming: they provide access to the type (or state) X. We show that the category of such coalgebras and structure preserving functions is comonadic over sets. Therefore we introduce the notion of a `mongruence' (predicate) on a coalgebra. It plays the dual role of a congrence (relation) on an algebra. An algebra is a set together with a number of operations on this set which tell how to form (derived) elements in this set, possibly satisfying some equations. A typical example is a monoid, given by a set M with operations 1 ! M , M \Theta M ! M . Here 1 = f;g is a singleton set. In mathematics one usually considers only singletyped algebras, but in computer science one more naturally uses manytyped algebras like 1 ! list(A), A \Theta l...
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 24 (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.
This document in subdirectoryRS/97/35/ A Theory of Recursive Domains with Applications to Concurrency (Extended Abstract)
, 1997
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
Bisimulation and Apartness in Coalgebraic Specification
, 1995
"... . A first basic fact in algebra (or, in algebraic specification) is the existence of free algebras, as suitable sets of terms. In coalgebraic specification, terminal coalgebras are known to exist in Sets (and in other categories) via the standard limit construction. Here we characterize these termin ..."
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. A first basic fact in algebra (or, in algebraic specification) is the existence of free algebras, as suitable sets of terms. In coalgebraic specification, terminal coalgebras are known to exist in Sets (and in other categories) via the standard limit construction. Here we characterize these terminal coalgebras as sets of "trees of observations". It is a standard result that elements of (the carrier of) a coalgebra are bisimilar (i.e. indistinguishable via the coalgebra operations) if and only if they have the same interpretation in the terminal coalgebra. This now becomes: if and only if they have the same tree of observations. Instead of putting emphasis on bisimulationwhich is a rather evasive notionwe consider its negation, which we write as #, and call "apartness ". It behaves like apartness in constructive mathematics. Indeed, the big advantage of apartness over bisimulation is that it can be established in a finite number of steps. It is a positive notion. Finally we show...