# Correctness and full abstraction of metric semantics for concurrency

## Abstract

Four different semantic models are given for a simple uniform programming language, containing constructs for parallel composition, global nondeterminism and communication: linear semantics, failure semantics, readiness semantics, and branching semantics. The mathematical framework used consists of complete metric spaces. All models and operators are given as fixed points of suitably defined contractions. This allows for a uniform presentation and an easy comparison of these models. It is shown that the latter three semantics all are correct and that the failure semantics is fully abstract with respect to the linear semantics. Although these results are not new, we believe the uniformity of the way they are presented here to be of some interest.

## Key words and phrases

concurrency complete metric spaces contractions operational semantics denotational semantics compositionality correctness full abstraction## Preview

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## 8. References

- [AP86]K. Apt, G. Plotkin,
*Countable nondeterminism and random assignment*, Journal of the Association for Computing Machinery, Vol. 33, No. 4, 1986, pp. 724–767.Google Scholar - [AR88]P. America, J.J.M.M. Rutten,
*Solving reflexive domain equations in a category of complete metric spaces*, in: Proceedings of the Third Workshop on Mathematical Foundations of Programming Language Semantics (M. Main, A. Melton, M. Mislove, D. Schmidt, Eds.), Lecture Notes in Computer Science 298, Springer-Verlag, 1988, pp. 254–288. (To appear in the Journal of Computer and System Sciences.)Google Scholar - [BHR84]S. Brookes, C. Hoare, W. Roscoe,
*A theory of communicating sequential processes*, J. Assoc. Comput. Mach. 31, No. 3, 1984, pp. 560–599.MathSciNetGoogle Scholar - [BK87]J.A. Bergstra, J.W. Klop,
*A convergence theorem in process algebra*, Report CS-R8733, Centre for Mathematics and Computer Science, Amsterdam, 1987.Google Scholar - [BKO87]J.A. Bergstra, J.W. Klop, E.-R. Olderog,
*Readies and failures in the algebra of communicating processes (revised version)*, Report CS-R8748, Centre for Mathematics and Computer Science, Amsterdam, 1987. (To appear in: SIAM Journal of Computing, 1988.)Google Scholar - [BM88]J.W. de Bakker, J.-J. Ch. Meyer,
*Metric semantics for concurrency*, Report CS-R8803, Centre for Mathematics and Computer Science, Amsterdam, 1988.Google Scholar - [BKMOZ86]J.W. de Bakker, J.N. Kok, J.-J. Ch. Meyer, E.-R. Olderog, J.I. Zucker,
*Contrasting themes in the semantics of imperative concurrency*, in: Current Trends in Concurrency (J.W. de Bakker, W.P. de Roever, G. Rozenberg, Eds.), Lecture Notes in Computer Science 224, Springer-Verlag, 1986, pp. 51–121.Google Scholar - [BMOZ88]J.W. de Bakker, J.-J. Ch. Meyer, E.-R. Olderog, J.I. Zucker,
*Transition systems, metric spaces and ready sets in the semantics of uniform concurrency*, Journal of Computer and System Sciences Vol 36 (number 2), 1988, pp. 158–224.CrossRefGoogle Scholar - [BZ82]J.W. de Bakker, J.I. Zucker,
*Processes and the denotational semantics of concurrency*, Information and Control 54 (1982), pp. 70–120.CrossRefGoogle Scholar - [De85]R. De Nicola,
*Testing equivalences and fully abstract models for communicating processes*, Ph.D. Thesis, report CST-36-85, Department of Computer Science, University of Edinburgh, 1985.Google Scholar - [Du66]
- [En77]
- [HP79]M. Hennessy, G.D. Plotkin,
*Full abstraction for a simple parallel programming language*, in: Proceedings 8th MFCS (J. Bečvář ed.), Lecture Notes in Computer Science 74, Springer-Verlag, 1979, pp. 108–120.Google Scholar - [Ho85]
- [KR88]J.N. Kok, J.J.M.M. Rutten,
*Contractions in comparing concurrency semantics*, in: Proceedings 15th ICALP, Tampere, 1988, Lecture Notes in Computer Science 317, Springer-Verlag, 1988, pp. 317–332.Google Scholar - [Mic51]
- [Mil80]R. Milner,
*A Calculus of communicating systems*, Lecture Notes in Computer Science 92, Springer-Verlag, 1980.Google Scholar - [Mu85]K. Mulmuley,
*Full abstraction and semantic equivalence*, Ph.D. Thesis, report CMU-CS-85-148, Computer Science Department, Carnegie-Mellon, 1985.Google Scholar - [OH86]E.-R. Olderog, C.A.R. Hoare,
*Specification-oriented semantics for communicating processes*, Acta Informaticae 23, 1986, pp. 9–66.Google Scholar - [Pl76]G.D. Plotkin,
*A powerdomain construction*, SIAM J. Comp. 5 (1976), pp. 452–487.CrossRefGoogle Scholar - [Pl81]G.D. Plotkin,
*A structural approach to operational semantics*, Report DAIMI FN-19, Comp. Sci. Dept., Aarhus Univ. 1981.Google Scholar - [Pl83]G.D. Plotkin,
*An operational semantics for CSP*, in:*Formal Description of Programming Concepts II*(D. Bjørner ed.) North-Holland, Amsterdam (1983), pp. 199–223.Google Scholar - [St86]A. Stoughton,
*Fully abstract models of programming languages*, Ph.D. Thesis, report CST-40-86, Department of Computer Science, University of Edinburgh, 1986.Google Scholar