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Invariants, Bisimulations and the Correctness of Coalgebraic Refinements
 Techn. Rep. CSIR9704, Comput. Sci. Inst., Univ. of Nijmegen
, 1997
"... . Coalgebraic specifications are used to formally describe the behaviour of classes in objectoriented languages. In this paper, a general notion of refinement between two such coalgebraic specifications is defined, capturing the idea that one "concrete" class specification realises the behaviour of ..."
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Cited by 12 (4 self)
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. Coalgebraic specifications are used to formally describe the behaviour of classes in objectoriented languages. In this paper, a general notion of refinement between two such coalgebraic specifications is defined, capturing the idea that one "concrete" class specification realises the behaviour of the other, "abstract" class specification. Two (complete) prooftechniques are given to establish such refinements: one involving an invariant (a predicate that is closed under transitions) on the concrete class, and one involving a bisimulation (a relation that is closed under transitions) between the concrete and the abstract class. The latter can only be used if the abstract class is what we call totally specified. Parts of the underlying theory of invariants and bisimulations in a coalgebraic setting are included, involving least and greatest invariants and connections between invariants and bisimulations. Also, the proofprinciples are illustrated in examples (which are fully formalise...
A Hidden Herbrand Theorem: Combining the Object and Logic Paradigms
 Principles of Declarative Programming
, 1998
"... : The benefits of the object, logic (or relational), functional, and constraint paradigms ..."
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Cited by 11 (3 self)
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: The benefits of the object, logic (or relational), functional, and constraint paradigms
ObjectOriented Specification of Distributed Systems in the µCalculus and Maude
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 1997
"... We refine an abstract propertyoriented specification in the µcalculus to a specification in Maude. As an intermediate step, we use a structured specification in the µcalculus blended with propositions on states appropriate for objectoriented specification. We use the loose approach in refinement ..."
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Cited by 6 (1 self)
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We refine an abstract propertyoriented specification in the µcalculus to a specification in Maude. As an intermediate step, we use a structured specification in the µcalculus blended with propositions on states appropriate for objectoriented specification. We use the loose approach in refinement and refine data types as well as behavior. Throughout, our example is the bounded buffer.
ObjectOriented Hybrid Systems of Coalgebras plus Monoid Actions
 Algebraic Methodology and Software Technology (AMAST
, 1996
"... . Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (nontempora ..."
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Cited by 5 (1 self)
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. Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (nontemporal) objectoriented systems). The monoid action captures the influence of time on the state space, where the monoids that we consider are the natural numbers monoid (N; 0; +) of discrete time, and the positive reals monoid (R0 ; 0; +) of real time. Based on this semantics we develop a hybrid specification formalism with timed method applications: it involves expressions like s:meth@ff, with the following meaning: in state s let the state evolve for ff units of time (according to the monoid action), and then apply the (coalgebraic) method meth. In this formalism we specify various (elementary) hybrid systems, investigate their correctness, and display their behaviour in simulations. We furthe...
A Hidden Herbrand Theorem
"... . The benefits of the object, logic (or relational), functional, and constraint paradigms can be combined, by providing existential queries over objects and their attributes, subject to constraints. This paper provides a precise mathematical foundation for this novel programming paradigm, and sh ..."
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Cited by 4 (2 self)
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. The benefits of the object, logic (or relational), functional, and constraint paradigms can be combined, by providing existential queries over objects and their attributes, subject to constraints. This paper provides a precise mathematical foundation for this novel programming paradigm, and shows that it is computationally feasible by reducing it to familiar problems over term algebras (i.e., Herbrand universes) . We use the formalism of hidden logic, and our main result is a version of Herbrand's Theorem for that setting. By extending a result of Diaconescu, we lift our results from equational logic to Horn clause logic with equality. ? The research reported in this paper has been supported in part by the Science and Engineering Research Council, the EC under ESPRIT2 BRA Working Groups 6071, ISCORE and 6112, COMPASS, Fujitsu Laboratories Limited, and a contract under the management of the Information Technology Promotion Agency (IPA), Japan, as part of the Industrial Sc...
Coalgebras in Specification and Verification for ObjectOriented Languages
, 1999
"... The aim of this short note is to give an impression of the use of coalgebras in specification and verification for objectoriented languages. Particular emphasis will be given to the rôle of coalgebraic operations in describing statebased systems. At the end some active research topics in coalgebra ..."
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The aim of this short note is to give an impression of the use of coalgebras in specification and verification for objectoriented languages. Particular emphasis will be given to the rôle of coalgebraic operations in describing statebased systems. At the end some active research topics in coalgebra will be sketched, together with pointers to the literature.
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.