An Institution for Object-Z with Inheritance and Polymorphism

  • Hubert Baumeister
  • Mohamed Bettaz
  • Mourad Maouche
  • M’hamed Mosteghanemi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8950)

Abstract

Large software systems are best specified using a multi-paradigm approach. Depending on which aspects of a system one wants to model, some logic formalisms are better suited than others. The theory of institutions and (co)morphisms between institutions provides a general framework for describing logical systems and their connections. This is the foundation of multi-modelling languages allowing one to deal with heterogeneous specifications in a consistent way. To make Object-Z accessible as part of such a multi-modelling language, we define the institution OZS for Object-Z. We have chosen Object-Z in part because it is a prominent software modelling language and in part because it allows us to study the formalisation of object-oriented concepts, like object identity, object state, dynamic behaviour, polymorphic sorts and inheritance.

Keywords

software engineering models Object-Z category theory institution inheritance polymorphic types 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language. Reference Manual, 2nd edn. Addison-Wesley Professional (2004)Google Scholar
  2. 2.
    Mossakowski, T., Maeder, C., Codescu, M.: Hets user guide - verion 0.99. DKFI GmbH, Bremen, Germany (2013)Google Scholar
  3. 3.
    Mossakowski, T.: Heterogeneous specification and the heterogeneous tool set. Habilitation thesis, University of Bremen (2005)Google Scholar
  4. 4.
    Goguen, J.A., Burstall, R.M.: Introducing institutions. In: Clarke, E., Kozen, D. (eds.) Logic of Programs 1983. LNCS, vol. 164, pp. 221–256. Springer, Heidelberg (1984)CrossRefGoogle Scholar
  5. 5.
    Burstall, R.M., Goguen, J.A.: The semantics of Clear, a specification language. In: Bjorner, D. (ed.) Abstract Software Specifications. LNCS, vol. 86, pp. 292–332. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  6. 6.
    Sannella, D., Tarlecki, A.: Specifications in an arbitrary institution. Information and Computation (1988)Google Scholar
  7. 7.
    Mosses, P.D. (ed.): CASL Reference Manual. LNCS, vol. 2960. Springer, Heidelberg (2004)MATHGoogle Scholar
  8. 8.
    Ehrig, H., Mahr, B.: Fundamentals of algebraic specification 1: Equations and initial semantics. Springer (1985)Google Scholar
  9. 9.
    Smith, D.R.: Composition by colimit and formal software development. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.) Algebra, Meaning, and Computation. LNCS, vol. 4060, pp. 317–332. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Smith, G.: The Object-Z specification language. Kluwer Academic Publisher (2000)Google Scholar
  11. 11.
    Spivey, J.M.: The Z Notation - A Reference manual. Prentice-Hall (1989)Google Scholar
  12. 12.
    Kim, S.-K., Carrington, D.: A formal mapping between UML models and object-Z specifications. In: Bowen, J.P., Dunne, S., Galloway, A., King, S. (eds.) B 2000, ZUM 2000, and ZB 2000. LNCS, vol. 1878, pp. 2–21. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Baumeister, H.: Relating abstract datatypes and Z-schemata. In: Bert, D., Choppy, C., Mosses, P.D. (eds.) WADT 1999. LNCS, vol. 1827, pp. 366–382. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Cengarle, M.V., Knapp, A.: An institution for UML 2.0 static structures. Technical Report TUM-10807, Technische Universität München (2008)Google Scholar
  15. 15.
    Cengarle, M.V., Knapp, A., Tarlecki, A., Wirsing, M.: A heterogeneous approach to UML semantics. In: Degano, P., De Nicola, R., Meseguer, J. (eds.) Concurrency, Graphs and Models. LNCS, vol. 5065, pp. 383–402. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Boronat, A., Knapp, A., Meseguer, J., Wirsing, M.: What is a multi-modeling language? In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 71–87. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Baumeister, H.: Relations between Abstract Datatypes modeled as Abstract Datatypes. PhD thesis, University of Saarbrücken (1999)Google Scholar
  18. 18.
    Goguen, J.A., Meseguer, J.: Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science 105(2), 217–273 (1992)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  20. 20.
    Goguen, J.A., Burstall, R.M.: Institutions: Abstract model theory for specification and programming. Journal of the ACM (JACM) 39(1), 95–146 (1992)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
  22. 22.
    Baumeister, H., Bettaz, M., Maouche, M., Mosteghanemi, M.: Institutions for Object-Z — technical report (2014), http://people.compute.dtu.dk/huba/publications/OZReport.pdf
  23. 23.
    Mac Lane, S.: Categories for the working mathematician, 2nd edn., vol. 5. Springer (1998)Google Scholar
  24. 24.
    Wen, Z., Miao, H., Zeng, H.: Generating proof obligation to verify Object-Z specification. In: IEEE International Conference on Software Engineering Advances, pp. 38–38 (2006)Google Scholar
  25. 25.
    Stevens, B.: Implementing Object-Z with Perfect Developer. Journal of Object Technology 5(2), 189–202 (2006)CrossRefGoogle Scholar
  26. 26.
    Paige, R.F., Brooke, P.J.: Integrating BON and Object-Z. Journal of Object Technology 3(3), 121–141 (2004)CrossRefGoogle Scholar
  27. 27.
    Codescu, M., Horozal, F., Jakubauskas, A., Mossakowski, T., Rabe, F.: Compiling logics. In: Martí-Oliet, N., Palomino, M. (eds.) WADT 2012. LNCS, vol. 7841, pp. 111–126. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hubert Baumeister
    • 1
  • Mohamed Bettaz
    • 2
    • 3
  • Mourad Maouche
    • 3
  • M’hamed Mosteghanemi
    • 2
  1. 1.DTU ComputeTechnical University of DenmarkDenmark
  2. 2.Laboratoire Méthodes de Conception de SystèmesESIAlgeria
  3. 3.Philadelphia UniversityJordan

Personalised recommendations