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On the Duality between Observability and Reachability
 PROC. 4TH INT. CONF. FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS'01
, 2001
"... Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper ..."
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Cited by 12 (5 self)
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Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper, we show that there is a duality between observability and reachability, both from a methodological and from a formal point of view. In particular, we establish a correspondence between observer operations and datatype constructors, observational algebras and constructorbased algebras, and observational and inductive properties of specifications. Our study is based on the observational logic institution [11] and on a novel treatment of reachability which introduces the constructorbased logic institution. Both institutions are tailored to capture the semantically correct realizations of a specification from the observational and reachability points of view. The duality between the observability and reachability concepts is then formalized in a categorytheoretic setting.
From Algebras and Coalgebras to Dialgebras
, 2001
"... This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras. ..."
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Cited by 10 (0 self)
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This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras.
Coalgebras For Binary Methods: Properties Of Bisimulations And Invariants
, 2001
"... Coalgebras for endofunctors C > C can be used to model classes of objectoriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension ..."
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Cited by 9 (3 self)
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Coalgebras for endofunctors C > C can be used to model classes of objectoriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results. 1991 Mathematics Subject Classification. 03E20, 03G30, 68Q55, 68Q65.
Coalgebras for Binary Methods
, 2000
"... Coalgebras for endofunctors C > C can be used to model classes of object oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension ..."
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Cited by 8 (2 self)
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Coalgebras for endofunctors C > C can be used to model classes of object oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation for coalgebras of extended polynomial functors and proves some standard results.
Greatest Bisimulations for Binary Methods
 In Proceedings of CMCS’02, volume 65(1) of ENTCS
, 2002
"... In previous work I introduced a generalised notion of coalgebra that is capable of modelling binary methods as they occur in objectoriented programming. An important problem with this generalisation is that bisimulations are not closed under union and that a greatest bisimulation does not exists in ..."
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Cited by 2 (0 self)
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In previous work I introduced a generalised notion of coalgebra that is capable of modelling binary methods as they occur in objectoriented programming. An important problem with this generalisation is that bisimulations are not closed under union and that a greatest bisimulation does not exists in general. There are two possible approaches to improve this situation: First, to strengthen the definition of bisimulation, and second, to place constraints on the coalgebras (i.e., on the behaviour of the binary methods). In this paper I combine both approaches to show that (under reasonable assumptions) the greatest bisimulation does exist for all coalgebras of extended polynomial functors.