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An approach to objectorientation in action systems
 MATHEMATICS OF PROGRAM CONSTRUCTION, LNCS 1422
, 1998
"... We extend the action system formalism with a notion of objects that can be active and distributed. With this extension we can model classbased systems as action systems. Moreover, as the introduced constructs can be translated into ordinary action systems, we can use the theory developed for action ..."
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Cited by 16 (4 self)
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We extend the action system formalism with a notion of objects that can be active and distributed. With this extension we can model classbased systems as action systems. Moreover, as the introduced constructs can be translated into ordinary action systems, we can use the theory developed for action systems, especially the refinement calculus, even for classbased systems. We show how inheritance can be modelled in different ways via class refinement. Re ning a class with an other class within the refinement calculus ensures that the original behavior of the class is maintained throughout the refinements. Finally, weshowhow to reuse proofs and entire class modules in a refinement step.
A fixpoint theory for nonmonotonic parallelism
, 2002
"... This paper studies parallel recursion. The trace specification language used in this paper incorporates sequential,j nondeterminism, reactiveness(inclvenessg,F'k traces), three forms of paral'VgJj (inclVgJjqMkEglglgl fairinterlkEglgl synchronous paralonousg and general recursion. In order to use Ta ..."
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Cited by 8 (5 self)
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This paper studies parallel recursion. The trace specification language used in this paper incorporates sequential,j nondeterminism, reactiveness(inclvenessg,F'k traces), three forms of paral'VgJj (inclVgJjqMkEglglgl fairinterlkEglgl synchronous paralonousg and general recursion. In order to use Tarski's theorem to determine the fixpoints of recursions, we need to identify awelVjgJ,FIq partial order.Several orders are considered,incldered new order calrg the lexical order, which tends tosimulM, the execution of a recursion in asimilk manner as the EglVqgJ,E, order. A theorem of this paper shows that no appropriate order exists for the lhegIIIE Tarski's theoremalor is not enough to determine the fixpoints ofparalVI recursions. Instead of usingTarski's theoremdirectl, we reason about the fixpoints of terminatingand nonterminatingbehavioursseparateli Such reasoningis supported by the leg of a new compositioncalio partition. We propose a fixpoint techniquecalni the partitioned fixpoint, which is thelgqk fixpoint of the nonterminatingbehaviours after the terminatingbehaviours reach their greatest fixpoint. The surprisingresul is thataltg,M, a recursion may not beljV"EgJqVE' monotonic, it must have the partitioned fixpoint, which isequal to thelegj lgjIjI,gJqF' fixpoint. Since the partitioned #xpoint iswel defined in anycompl,q lmpl,q theresulq areappljFMgJ to various semanticmodeli Existing fixpoint techniques simpl becomespecial cases of the partitioned fixpoint. Forexamplj an EglIIqgJq',EFglEFg recursion has itslsgj EglMMFIgJq fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is moregeneral than thelegq EglEEkIgJq fixpoint in that the partitioned fixpoint can be determined even when a recursion is notEglVjjVgJq monotonic.Exampln of nonmonotonic recur...
On the Semantics of Refinement Calculi
, 2000
"... Refinement calculi for imperative programs provide an integrated framework for programs and specifications and allow one to develop programs from specifications in a systematic fashion. The semantics of these calculi has traditionally been de ned in terms of predicate transformers and poses several ..."
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Cited by 2 (1 self)
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Refinement calculi for imperative programs provide an integrated framework for programs and specifications and allow one to develop programs from specifications in a systematic fashion. The semantics of these calculi has traditionally been de ned in terms of predicate transformers and poses several challenges in defining a state transformer semantics in the denotational style. We de ne a novel semantics in terms of sets of state transformers and prove it to be isomorphic to positively multiplicative predicate transformers. This semantics disagrees with the traditional semantics in some places and the consequences of the disagreement are analyzed.
Distributed service composition
, 1999
"... In this paper we explore the use of action systems for distributed service composition. Distributed systems can be composed out of a basic computation and a set of services. Even though this way of designing a system out of components helps in managing the derivation task, formal description techniq ..."
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Cited by 2 (0 self)
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In this paper we explore the use of action systems for distributed service composition. Distributed systems can be composed out of a basic computation and a set of services. Even though this way of designing a system out of components helps in managing the derivation task, formal description techniques are needed due to the complexity of distributed systems. We propose a method where services, or features as they are often called, are speci ed in isolation by the service provider. The services when available are used by clients in a distributed manner. Reasoning about the services and their interactions with each other and with the basic computation of the clients is carried out within the re nement calculus. To exemplify the proposed methodology we study feature composition and feature interaction in telecommunications software.
Metric Predicate Transformers: Towards a Notion of Refinement for Concurrency
, 1994
"... For two parallel languages with recursion a compositional weakest precondition semantics is given using two new metric resumption domains. The underlying domains are characterized by domain equations involving functors that deliver `observable' and `safety' predicate transformers. Further a refineme ..."
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For two parallel languages with recursion a compositional weakest precondition semantics is given using two new metric resumption domains. The underlying domains are characterized by domain equations involving functors that deliver `observable' and `safety' predicate transformers. Further a refinement relation is defined for this domains and illustrated by rules dealing with concurrent composition. It turns out, by extending the classical duality of predicate vs. state transformers, that the weakest precondition semantics for the parallel languages is isomorphic to the standard metric state transformers semantics. Moreover, the proposed refinement relation on the predicate transformer domain will correspond to the familiar notion of simulation in the state transformer domain. Contents 1 Introduction 1 2 Mathematical Preliminaries 3 3 Four Languages with Recursion 5 4 Domains for Predicate Transformers 8 5 Predicate Transformer Semantics 14 6 Refinement, Simulation and State Transforme...