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Algebraic Imperative Specifications

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1755))

Abstract

Algebraic imperative specifications (AIS) are specifications with implicit state represented by an algebra and with a number of transition rules indicating state transformations. They are designed for the formal definition of complex dynamic systems.

Two approaches to algebraic imperative specifications have been developed in parallel during the last decade: Abstract State Machines (ASMs), initially known as evolving algebras, and Algebraic Specifications with Implicit State (AS-IS). Moreover typed versions of ASM have been developed which have incorporated some aspects of AS-IS.

This survey paper provides a guided tour of these imperative approaches of specification based on the state-as-algebra paradigm, and sketches a synthesis of two of them, under the name of dynamic systems with implicit state.

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References

  1. J. R. Abrial. The B book-Assigning programs to meanings. Cambridge University Press, 1996.

    Google Scholar 

  2. E. Astesiano and E. Zucca. D-oids: a Model for Dynamic Data Types. Mathematical Structures in Computer Science, 5(2), June 1995, 257–282.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Baumeister. Relations as Abstract Data Types: An Institution to Specify Relations between Algebras. TAPSOFT’95, LNCS, vol. 915, Springer Verlag, pp. 756–771.

    Google Scholar 

  4. E. Boerger and D. Rosenzweig. The WAM-Definition and Compiler Correctness. Logic Programming: Formal Methods and Practical Applications, North-Holland Series in Computer Science and Artificial Intelligence, 1994.

    Google Scholar 

  5. E. Boerger, J. Huggins. Commented ASM Bibliography. Formal Specification Column (H. Erhig, ed.), EATCS Bulletin, vol. 64, February 1998, pp. 105–127.

    MATH  Google Scholar 

  6. K.M. Chandy and J. Misra. Parallel Program Design: a foundation. Addison-Wesley, 1988.

    Google Scholar 

  7. Dauchy P., Développement et exploitation d’une spécification algébrique du logiciel embarqué d’un métro. Thèese de Docteur en Sciences de l’Université de Paris-Sud, Orsay, July 1992.

    Google Scholar 

  8. P. Dauchy and M.C. Gaudel. Algebraic Specifications with Implicit State. Tech. report No 887, Laboratoire de Recherche en Informatique, Univ. Paris-Sud, 1994.

    Google Scholar 

  9. Dauchy P., Marre B., Test data selection from algebraic specifications: application to an automatic subway module. 3rd European Software Engineering Conference, ESEC’91, LNCS, vol. 550, 1991, pp. 80–100.

    Google Scholar 

  10. Dauchy P., Gaudel M.-C., Marre B., Using Algebraic Specifications in Software Testing: a case study on the software of an automatic subway. Journal of Systems and Software, vol. 21, no 3, June 1993, pp. 229–244.

    Article  Google Scholar 

  11. G. Del Castillo, Y. Gurevich, and K. Stroetmann. Typed Abstract State Machines. Submitted to Journal of Universal Computer Science, available from http://www.eecs.umich.edu/gasm/), 1998.

  12. H. Ehrig, B. Mahr. Fundamentals of Algebraic Specifications 1, Equations and Initial Semantics. EATCS Monographs on Theoretical Computer Science, vol. 6, Springer, Berlin, 1985.

    Google Scholar 

  13. H. Ehrig, B. Mahr. Fundamentals of Algebraic Specifications 2. EATCS Monographs on Theoretical Computer Science, vol. 21, Springer, Berlin, 1990.

    MATH  Google Scholar 

  14. Gaudel M.-C., Génération et Preuve de Compilateurs basées sur une Sémantique Formelle des Langages de Programmation, Thèse d’état, INPL (Nancy, France), 1980.

    Google Scholar 

  15. Gaudel M.-C., Correctness Proof of Programming Language Translations. Formal Description of Programming Concepts-II, D. Bjorner ed., North-Holland, 1983, pp.25–43.

    Google Scholar 

  16. Gaudel M-C., Structuring and Modularizing Algebraic Specifications: the PLUSS specification language, evolutions and perspectives 9th Annual Symposium on Theoretical Aspects of Computer Science (STACS’92), Cachan, feb. 1992, LNCS, vol. 577, pp. 3–18.

    Google Scholar 

  17. Marie-Claude Gaudel, Pierre Dauchy, Carole Khoury, A Formal Specification of the Steam-Boiler Control Problem by Algebraic Specifications with Implicit State. Formal Methods for Industrial Applications: specifying and programming the Steam Boiler Control, LNCS, vol. 1165, Springer Verlag, 1996, pp. 233–264.

    Google Scholar 

  18. H.B.M. Jonkers. An Introduction to COLD-K. Algebraic Methods: Theory, Tools and Applications, LNCS, vol. 394, 1989, pp. 139–205.

    Google Scholar 

  19. Gaudel, M.-C., Khoury, C. and Zamulin, A., Dynamic systems with implicit state, Rapport interne no 1172, Laboratoire de Recherche en Informatique, May 1998.

    Google Scholar 

  20. M.-C. Gaudel, C. Khoury, A. Zamulin. Dynamic systems with implicit state. Fundamental Approaches to Software Engineering, LNCS, vol. 1577, 1999, pp.114–128.

    Google Scholar 

  21. M. Gogolla & R. Herzig. An Algebraic Semantics for the Object Specification Language TROLL light. Recent Trends in Data Type Specifications, LNCS, vol. 906, pp. 290–306, 1994.

    Chapter  Google Scholar 

  22. R. Groenboom and R. Renardel de Lavalette. Reasoning about Dynamic Features in Specification Languages. Workshop in Semantics of Specification Languages, Springer Verlag, 1994, pp. 340–355.

    Google Scholar 

  23. M. Grosse-Rhode. Concurrent State Transformation On Abstract data Types. Recent Trends in Data Type Specifications, LNCS, vol. 1130, pp. 222–236, 1995.

    Google Scholar 

  24. M. Grosse-Rhode. Algebra Transformation Systems And Their Composition. Fundamental Approaches to Software Engineering, LNCS, vol. 1382, pp. 107–122, 1998.

    Chapter  Google Scholar 

  25. Y. Gurevich. Logic and the Challenge of Computer Science. Trends in Theoretical Computer Sciience, Computer Science Pres, ed. E. Boerger, 1988, pp. 1–57.

    Google Scholar 

  26. Y. Gurevich. Evolving Algebras: An Attempt to Discover Semantics. Current Trends in Theoretical Computer Science, World Scientific, 1993, pp. 266–292.

    Google Scholar 

  27. Y. Gurevich and J. Huggins. The semantics of the C programming language. Computer Science Logic, LNCS, vol. 702, 1993, pp. 274–309.

    Google Scholar 

  28. Y. Gurevich. Evolving Algebras 1993: Lipary Guide. Specification and Validation Methods, Oxford University Press, 1995, pp. 9–36.

    Google Scholar 

  29. Y. Gurevich. May 1997 Draft of the ASM Guide. Available electronically from http://www.eecs.umich.edu/gasm/.

  30. T. Hartmann, G. Saake, R. Jungclaus, P. Hartel, and J. Kush. Revised Version of the Modeling Language TROLL. Technishe Universitaet Braunschweig, Informatik-Berichte 94-03, 1994.

    Google Scholar 

  31. C. B. Jones. Systematic Software Development using VDM. Prentice Hall, 1990.

    Google Scholar 

  32. Carole Khoury, Définition d’une approche orientée-objet de la spécification algébrique des systèmes informatiques. Thèse de Docteur en Sciences de l’Université de Paris-Sud, Orsay, March 1999.

    Google Scholar 

  33. C. Khoury, M.C. Gaudel and P. Dauchy. AS-IS. Tech. report No 1119, Laboratoire de Recherche en Informatique, Univ. Paris-Sud, 1997.

    Google Scholar 

  34. R. Milner. A Theory of Type Polymorphism in Programming. Journal of Computer and System Sciences, 1978.

    Google Scholar 

  35. B. Monahan and R. Shaw. Model-Based Specifications. Software Engineer’s Reference Book, chapter 21, Butterworth-Heineman, 1991.

    Google Scholar 

  36. J. M. Spivey. Understanding Z. A specification language and its formal semantics. Cambridge University Press, 1988.

    Google Scholar 

  37. J. M. Spivey. The Z Notation. A Reference Manual. Prentice Hall, 1989.

    Google Scholar 

  38. M. Wirsing. Algebraic Specifications. Handbook of Theoretical Computer Science, Elsevier Science Publishers B.V., 1990, pp. 665–788.

    Google Scholar 

  39. A.V. Zamulin. Typed Gurevich Machines. Institute of Informatics Systems, Preprint No 36, Novosibirsk, 1996 (ftp://ftp.xsite.iis.nsk.su/pub/articles/tgm.ps.gz).

  40. A.V. Zamulin. Typed Gurevich Machines Revisited. Joint NCC&ISS Bull., Comp. Science, 7 (1997), pp. 95–121 (available electronically from http://www.eecs.umich.edu/gasm/).

    Google Scholar 

  41. A.V. Zamulin. Specification of an Oberon Compiler by means of a Typed Gurevich Machine. Institute of Informatics Systems of the Siberian Division of the Russian Academy of Sciences, Report No. 589. 3945009.00007-01, Novosibirsk, 1997 (available electronically from http://www.eecs.umich.edu/gasm/).

  42. A.V. Zamulin. Object-Oriented Abstract State Machines. Proc. Int. Workshop on Abstract State Machines, Magderburg, Germany, September 21–22, 1998, pp 1–21.

    Google Scholar 

  43. A.V. Zamulin. Dynamic System Specification by Typed Gurevich Machines. Proc. Int. Conf. on Systems Science, Wroclaw, Poland, September 15–18, 1998.

    Google Scholar 

  44. A.V. Zamulin. Object-Oriented Specification by Typed Gurevich Machines. Joint NCC&ISS Bull., Comp. Science, 8 (1998), pp. 77–103.

    Google Scholar 

  45. E. Zucca. From Static to Dynamic Data Types. Mathematical Foundations of Computer Science, LNCS, vol. 1113, 1996, pp. 579–590.

    Google Scholar 

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Gaudel, MC., Zamulin, A. (2000). Algebraic Imperative Specifications. In: Bjøner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 1999. Lecture Notes in Computer Science, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46562-6_3

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  • DOI: https://doi.org/10.1007/3-540-46562-6_3

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