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Proving the correctness of algebraic implementations by the ISAR system

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Design and Implementation of Symbolic Computation Systems (DISCO 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 722))

Abstract

We present an interactive system, called ISAR, which provides an environment for correctness proofs of algebraic implementation steps. The correctness notion of implementation is based on behavioural semantics and the underlying proof procedure of the system is based on the principle of context induction (which is a particular instance of structural induction). The input of the ISAR system is an implementation step consisting of an abstract specification to be implemented, a concrete specification used as a basis for the implementation and an implementation construction. If all steps of the (interactive) proof procedure are performed the system has proved the correctness of the implementation step.

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References

  1. An interactive system for algebraic implementation proofs: The ISAR system from the user's point of view. Universität München, Technical Report (to appear), 1993.

    Google Scholar 

  2. C. Beierle, A. Vo\: Algebraic specification and implementation in an integrated software development and verification system. MEMO SEKI-12, FB Informatik, Universität Kaiserslautern, 1985.

    Google Scholar 

  3. How to prove observational theorems with LP. Proc. of the First International Workshop on Larch, July 1992, Boston, USA, Springer Verlag Workshop in Computing Series, 1993. Also in: Laboratoire d'Informatique de l' Ecole Normale Supérieure, Paris, LIENS-92-23, 1992.

    Google Scholar 

  4. R. S. Boyer, J. S. Moore: A computational logic handbook. Academic Press, New York, 1988.

    Google Scholar 

  5. R. M. Burstall: Proving properties of programs by structural induction. Comp. Journal 12, 41–48, 1969.

    Google Scholar 

  6. P. S. Chen, R. Hennicker, M. Jarke: On the retrieval of reusable software components. In: R. Prieto-Diaz, W. B. Frakes (eds.): Advances in Software Reuse. Selected Papers from the Second International Workshop on Software Reusability. Lucca, Italy, 1993. IEEE Computer Society Press, Los Alamitos, California, Order Number 3130, 99–108, 1993.

    Google Scholar 

  7. H. Ehrig, H.-J. Kreowski, B. Mahr, P. Padawitz: Algebraic Imple-mentation of Abstract Data Types. Theoretical Computer Science 20, 209–263, 1982.

    Google Scholar 

  8. H. Ehrig, B. Mahr: Fundamentals of algebraic specification 1, EATCS Monographs on Theoretical Computer Science 6, Springer, Berlin, 1985.

    Google Scholar 

  9. U. Fraus, H. Hu\mann: A narrowing-based theorem prover. Extended Abstract. In: Proc. RTA '91, Rewriting Techniques and its Applications, Lecture Notes in Computer Science 488, 435–436, 1991.

    Google Scholar 

  10. S. J. Garland, J. V. Guttag: An overview of LP, the Larch Prover. In: Proc. RTA '89, Rewriting Techniques and its Applications, Lecture Notes in Computer Science 355, 137–151, 1989.

    Google Scholar 

  11. R. Hennicker: Context Induction: a proof principle for behavioural abstractions. In: A. Miola (ed.): Proc. DISCO '90, International Symposium on Design and Implementation of Symbolic Computation Systems, Capri, April 1990. Lecture Notes in Computer Science 429, 101–110, 1990.

    Google Scholar 

  12. A semi-algorithm for algebraic implementation proofs. Theoretical Computer Science 104, Special Issue, 53–87, 1992.

    Google Scholar 

  13. M\(M^{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a} }\)P. Nivela, F. Orejas: Initial behaviour semantics for algebraic specifications. In: D. T. Sannella, A. Tarlecki (eds.): Proc. 5th Workshop on Algebraic Specifications of Abstract Data Types, Lecture Notes in Computer Science 332, 184–207, 1988.

    Google Scholar 

  14. P. Padawitz: Computing in Horn clause theories. EATCS Monographs on Theoretical Computer Science 16, Springer, Berlin, 1988.

    Google Scholar 

  15. H. Reichel: Initial restrictions of behaviour. IFIP Working Conference, The Role of Abstract Models in Information Processing, 1985.

    Google Scholar 

  16. D. T. Sannella, A. Tarlecki: Toward formal development of programs from algebraic specifications: implementation revisited. Acta Informatica 25, 233–281, 1988.

    Article  Google Scholar 

  17. M. Wirsing: Structured algebraic specifications: a kernel language. Theoretical Computer Science 42, 123–249, 1986.

    Article  Google Scholar 

  18. Algebraic description of reusable software components. In: Proc. COMPEURO '88, Comp. Society Order Number 834, 300–312, 1988.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstr. 16, D-8000, München 2

    Bernhard Bauer

  2. Institut für Informatik, Ludwig-Maximilians-Universität München, Leopoldstr. 11b, D-8000, München 40

    Rolf Hennicker

Authors
  1. Bernhard Bauer
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  2. Rolf Hennicker
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Alfonso Miola

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© 1993 Springer-Verlag Berlin Heidelberg

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Bauer, B., Hennicker, R. (1993). Proving the correctness of algebraic implementations by the ISAR system. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1993. Lecture Notes in Computer Science, vol 722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013164

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  • DOI: https://doi.org/10.1007/BFb0013164

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57235-0

  • Online ISBN: 978-3-540-47985-7

  • eBook Packages: Springer Book Archive

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