Skip to main content

Compositional Refinement of Interactive Systems Modelled by Relations

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1536))

Abstract

We introduce a mathematical model of components that can be used for the description of both hardware and software units forming distributed interactive systems. As part of a distributed system a component interacts with its environment by exchanging messages in a time frame. The interaction is performed by accepting input and by producing output messages on named channels. We describe forms of composition and three forms of refinement, namely property refinement, glass box refinement, and interaction refinement. Finally, we prove the compositionality of the mathematical model with respect to the introduced refinement relations.

This work was partially sponsored by the Sonderforschungsbereich 342 “Werkzeuge und Methoden für die Nutzung paralleler Rechnerarchitekturen”e, the BMBF-project KORSYS and the industrial research project SysLab sponsored by Siemens Nixdorf and by the DFG under the Leibniz program.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Abadi, L. Lamport: The Existence of Refinement Mappings. Digital Systems Research Center, SRC Report 29, August 1988

    Google Scholar 

  2. M. Abadi, L. Lamport: Composing Specifications. Digital Systems Research Center, SRC Report 66, October 1990

    Google Scholar 

  3. L. Aceto, M. Hennessy: Adding Action Refinement to a Finite Process Algebra. Proc. ICALP 91, Lecture Notes in Computer Science 510, (1991), 506–519

    Google Scholar 

  4. F. Huber, B. Schätz, G. Einert: Consistent Graphical Specification of Distributed Systems. In: J. Fitzgerald, C. B. Jones, P. Lucas (ed.): FME’ 97: 4th International Symposium of Formal Methods Europe, Lecture Notes in Computer Science 1313, 1997, 122–141

    Google Scholar 

  5. R.J.R. Back: Refinement Calculus, Part I: Sequential Nondeterministic Programs. REX Workshop. In: J. W. de Bakker, W.-P. de Roever, G. Rozenberg (eds): Stepwise Refinement of Distributed Systems. Lecture Notes in Computer Science 430, 42–66

    Google Scholar 

  6. R.J.R. Back: Refinement Calculus, Part II: Parallel and Reactive Programs. REX Workshop. In: J. W. de Bakker, W.-P. de Roever, G. Rozenberg (eds): Stepwise Refinement of Distributed Systems. Lecture Notes in Computer Science 430, 67–93

    Google Scholar 

  7. R. Breu, R. Grosu, Franz Huber, B. Rumpe, W. Schwerin: Towards a Precise Semantics for Object-Oriented Modeling Techniques. In: H. Kilov, B. Rumpe (eds.): Proceedings ECOOP’97 Workshop on Precise Semantics for Object-Oriented Modeling Techniques, 1997, Also: Technische Universität München, Institut für Informatik, TUM-I9725, 1997

    Google Scholar 

  8. M. Broy, B. Möller, P. Pepper, M. Wirsing: Algebraic Implementations Preserve Program Correctness. Science of Computer Programming 8 (1986), 1–19

    Google Scholar 

  9. M. Broy: Functional Specification of Time Sensitive Communicating Systems. REX Workshop. In: J. W. de Bakker, W.-P. de Roever, G. Rozenberg (eds): Stepwise Refinement of Distributed Systems. Lecture Notes in Computer Science 430, 153–179

    Google Scholar 

  10. M. Broy: Compositional Refinement of Interactive Systems. Digital Systems Research Center, SRC Report 89, July 1992, To appear in JACM

    Google Scholar 

  11. M. Broy, F. Dederichs, C. Dendorfer, M. Fuchs, T. F. Gritzner, R. Weber: The Design of Distributed Systems-An Introduction to Focus. Technische Universität München, Institut für Informatik, Sonderforschungsbereich 342: Methoden und Werkzeuge für die Nutzung paralleler Architekturen TUM-I9202, January 1992

    Google Scholar 

  12. M. Broy, F. Dederichs, C. Dendorfer, M. Fuchs, T. F. Gritzner, R. Weber: Summary of Case Studies in FOCUS-a Design Method for Distributed Systems. Technische Universität München, Institut für Informatik, Sonderforschungsbereich 342: Methoden und Werkzeuge für die Nutzung paralleler Architekturen TUM-I9203, January 1992

    Google Scholar 

  13. M. Broy: Interaction Refinement-The Easy Way. In: M. Broy (ed.): Program Design Calculi. Springer NATO ASI Series, Series F: Computer and System Sciences, Vol. 118, 1993

    Google Scholar 

  14. M. Broy: Algebraic Specification of Reactive Systems. M. Nivat, M. Wirsing (eds): Algebraic Methodology and Software Technology. 5th International Conference, AMAST’ 96, Lecture Notes of Computer Science 1101, Hidelberg: Springer 1996, 487–503

    Chapter  Google Scholar 

  15. M. Broy: Towards a Mathematical Concept of a Component and its Use. First Components’ User Conference, Munich 1996. Revised version in: Software-Concepts and Tools 18, 1997, 137–148

    Google Scholar 

  16. M. Broy: Refinement of Time. M. Bertran, Th. Rus (eds.): Transformation-Based Reactive System Development. ARTS’97, Mallorca 1997. Lecture Notes in Computer Science 1231, 1997, 44–63, To appear in TCS

    Google Scholar 

  17. J. Coenen, W.P. deRoever, J. Zwiers: Assertional Data Reification Proofs: Survey and Perspective. Christian-Albrechts-Universität Kiel, Institut für Informatik und praktische Mathematik, Bericht Nr. 9106, Februar 1991.

    Google Scholar 

  18. C.A.R. Hoare: Proofs of Correctness of Data Representations. Acta Informatica 1, 1972, 271–281

    Google Scholar 

  19. N. Lynch, E. Stark: A Proof of the Kahn Principle for Input/Output Automata. Information and Computation 82, 1989, 81–92

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Broy, M. (1998). Compositional Refinement of Interactive Systems Modelled by Relations. In: de Roever, WP., Langmaack, H., Pnueli, A. (eds) Compositionality: The Significant Difference. COMPOS 1997. Lecture Notes in Computer Science, vol 1536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49213-5_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-49213-5_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65493-3

  • Online ISBN: 978-3-540-49213-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics