Compactness in semantics for merge and fair merge

Bakker, J. W. de; Zucker, Jeffery I.

doi:10.1007/3-540-12896-4_352

Cited by 13 publications

(5 citation statements)

References 16 publications

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“…KF AR is the algebraic formulation of this idea, whereas the semantical implementation of fairness is already implicit in the notion of bisimulation on graphs, so is already implicit in the work of Milner [23]. Some other recent papers on fairness are [4,5,13,14,16,17,18,22,25].…”

Section: Introductionmentioning

confidence: 99%

On the consistency of Koomen's Fair Abstraction Rule

Baeten

Bergstra

Klop³

1987

Theoretical Computer Science

114

111

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We construct a graph model for ACP"' the algebra of communicating processes with silent steps, in which Koomen's Fair Abstraction Rule (KFAR) holds, and also versions of the Approximation Induction Principle (AIP) and the Recursive Definition & Specification Principles (RDP&RSP). We use this model to prove that in ACP" (but not in ACP!) each computably recursively definable process is finitely recursively definable.

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Section: Introductionmentioning

confidence: 99%

On the consistency of Koomen's Fair Abstraction Rule

Baeten

Bergstra

Klop³

1987

Theoretical Computer Science

114

111

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“…Examples of functions f would be "U" (non deterministic choice) and "II" (merge), as defined in [4]. Fair merge, however, does not preserve closedness and does not fit naturally into our framework.…”

Section: Remarksmentioning

confidence: 99%

Towards a uniform topological treatment of streams and functions on streams

Bakker¹,

Kok²

1985

Automata, Languages and Programming

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We study the semantics of functional languages on streams such as Turner's SASL or KRC. The basis of these languages is recursive equations for (functions on) finite or infinite sequences. The paper presents a start towards a mathematical (denotational) description of such languages using tools from metric topology. The description is based on the Banach fixed point theorem and a restricted version of a typed lambda calculus. To a system of recursive stream (function) declarations a system of functions is associated in an appropriate topological domain. These functions have to be contracting in certain arguments and non distance increasing in others; a syntax is designed which ensures the right interplay between these conditions. Nondeterminism is handled by considering compact sets of streams, and preservation of compactness is another important technical issue. Not all concepts in a language such as KRC are covered, and some indications on possible extensions of the framework are provided. IntroductionWe present a semantic study of languages with streams and functions on streams as exemplified by Turner's languages SASL and KRC. The tools we use are from metric topology; ultimately, our model relies on Banach's fixed point theorem for contracting functions on a complete metric space.

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“…( [3,4,5,6]) for a denotational one, and the Oxford School ( [8,18,19,21]) serving -for the purposes of our paper -an intermediate role.…”

Section: Introductionmentioning

confidence: 99%

Transition systems, infinitary languages and the semantics of uniform concurrency

Bakker¹,

Meyer²,

Olderog³

et al. 1985

Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing - STOC '85

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Transition systems as proposed by Hennessy & Plotkin are defined for a series of three languages featuring concurrency. The first has shuffle and local nondeterminancy, the second synchronization merge and local nondeterminacy, and the third synchronization merge and global nondeterminacy. The languages are all uniform in the sense that the elementary actions are uninterpreted. Throughout, infinite behaviour is taken into account and modelled with infinitary languages in the sense of Nivat. A comparison with denotational semantics is provided. For the first two languages, a linear time model suffices; for the third language a braching time model with processes in the sense of De Bakker & Zucker is described. In the comparison an important role is played by an intermediate semantics in the style of Hoare & Olderog's specification oriented semantics. A variant on the notion of ready set is employed here. Precise statements are given relating the various semantics in terms of a number of abstraction operators.

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Compactness in semantics for merge and fair merge

Cited by 13 publications

References 16 publications

On the consistency of Koomen's Fair Abstraction Rule

On the consistency of Koomen's Fair Abstraction Rule

Towards a uniform topological treatment of streams and functions on streams

Transition systems, infinitary languages and the semantics of uniform concurrency

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