Software & Systems Modeling

, Volume 2, Issue 3, pp 187–210

VPM: A visual, precise and multilevel metamodeling framework for describing mathematical domains and UML (The Mathematics of Metamodeling is Metamodeling Mathematics)

Special Issue on UML 2002

Abstract

As UML 2.0 is evolving into a family of languages with individually specified semantics, there is an increasing need for automated and provenly correct model transformations that (i) assure the integration of local views (different diagrams) of the system into a consistent global view, and, (ii) provide a well-founded mapping from UML models to different semantic domains (Petri nets, Kripke automaton, process algebras, etc.) for formal analysis purposes as foreseen, for instance, in submissions for the OMG RFP for Schedulability, Performance and Time. However, such transformations into different semantic domains typically require the deep understanding of the underlying mathematics, which hinders the use of formal specification techniques in industrial applications. In the paper, we propose a multilevel metamodeling technique with precise static and dynamic semantics (based on a refinement calculus and graph transformation) where the structure and operational semantics of mathematical models can be defined in a UML notation without cumbersome mathematical formulae.

Keywords

Metamodeling Formal semantics Refinement Model transformation Graph transformation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Petri Net Markup Language. http://www.informatik.hu-berlin.de/top/pnml Google Scholar
  2. 2.
    Akehurst, D.: Model Translation: A UML-based specification technique and active implementation approach. Ph.D. thesis, University of Kent, Canterbury, 2000 Google Scholar
  3. 3.
    Akehurst, D., Kent, S.: A relational approach to defining transformations in a metamodel. In: Jézéquel, J.-M., Hussmann, H., Cook, S. (eds.) Proc. Fifth International Conference on the Unified Modeling Language – The Language and its Applications, LNCS, vol. 2460. Springer-Verlag, Dresden, Germany, 2002, pp. 243–258 Google Scholar
  4. 4.
    Alvarez, J., Evans, A., Sammut, P.: Mapping between levels in the metamodel architecture. In: Gogolla, M., Kobryn, C. (eds.) Proc. UML 2001 – The Unified Modeling Language. Modeling Languages, Concepts and Tools, LNCS, vol. 2185. Springer, 2001, pp. 34–46 Google Scholar
  5. 5.
    Atkinson, C., Kühne, T.: The essence of multilevel metamodelling. In: Gogolla, M., Kobryn, C. (eds.) Proc. UML 2001 – The Unified Modeling Language. Modeling Languages, Concepts and Tools, LNCS, vol. 2185. Springer, 2001, pp. 19–33 Google Scholar
  6. 6.
    Atkinson, C., Kühne, T., Henderson-Sellers, B.: Stereotypical encounters of the third kind. In: Jézéquel, J.-M., Hussmann, H., Cook, S. (eds.) Proc. Fifth International Conference on the Unified Modeling Language – The Language and its Applications, LNCS, vol. 2460. Springer, Dresden, Germany, 2002, pp. 100–114 Google Scholar
  7. 7.
    Bondavalli, A., Dal Cin, M., Latella, D., Majzik, I., Pataricza, A., Savoia, G.: Dependability analysis in the early phases of UML based system design. International Journal of Computer Systems - Science & Engineering, 16(5): 265–275, 2001 Google Scholar
  8. 8.
    Bondavalli, A., Majzik, I., Mura, I.: Automatic dependability analyses for supporting design decisions in UML. In: Proc. HASE’99: The 4th IEEE International Symposium on High Assurance Systems Engineering. 1999, pp. 64–71 Google Scholar
  9. 9.
    Clark, T., Evans, A., Kent, S.: The Metamodelling Language Calculus: Foundation semantics for UML. In: Hussmann, H. (ed.) Proc. Fundamental Approaches to Software Engineering, FASE 2001 Genova, Italy, LNCS, vol. 2029. Springer, 2001, pp. 17–31 Google Scholar
  10. 10.
    Cousot, P., Cousot, R.: Systematic design of program transformation frameworks by abstract interpretation. In: Conference Record of the Twentyninth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM Press, New York, NY, Portland, Oregon, 2002, pp. 178–190 Google Scholar
  11. 11.
    Csertán, G., Huszerl, G., Majzik, I., Pap, Z., Pataricza, A., Varró, D.: VIATRA: Visual automated transformations for formal verification and validation of UML models. In: Proc. ASE 2002: 17th IEEE International Conference on Automated Software Engineering. IEEE Press, Edinburgh, UK, 2002, pp. 267–270 Google Scholar
  12. 12.
    Csertán, G., Pataricza, A., Harang, P., Dobán, O., Biros, G., Dancsecz, A., Friedler, F.: BPM based robust E-Business application development. In: Proc EDCC-4 Fourth European Dependable Computing Conference, LNCS, vol. 2485. Springer, Toulouse, France, 2002, pp. 32–43 Google Scholar
  13. 13.
    Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) Handbook on Graph Grammars and Computing by Graph Transformation, vol. 2: Applications, Languages and Tools. World Scientific, 1999 Google Scholar
  14. 14.
    Engels, G., Hausmann, J.H., Heckel, R., Sauer, S.: Dynamic meta modeling: A graphical approach to the operational semantics of behavioral diagrams in UML. In: Evans, A., Kent, S., Selic, B. (eds.) UML 2000 – The Unified Modeling Language. Advancing the Standard, LNCS, vol. 1939. Springer, 2000, pp. 323–337 Google Scholar
  15. 15.
    Engels, G., Heckel, R., Küster, J.M.: Rule-based specification of behavioral consistency based on the UML meta-model. In: Gogolla, M., Kobryn, C. (eds.) UML 2001: The Unified Modeling Language. Modeling Languages, Concepts and Tools, LNCS, vol. 2185. Springer, 2001, pp. 272–286 Google Scholar
  16. 16.
    Heckel, R., Küster, J., Taentzer, G.: Towards automatic translation of UML models into semantic domains. In: Proc. AGT 2002: Workshop on Applied Graph Transformation. Grenoble, France, 2002, pp. 11–21 Google Scholar
  17. 17.
    Huszerl, G., Majzik, I.: Quantitative analysis of dependability critical systems based on UML statechart models. In: HASE 2000, Fifth IEEE International Symposium on High Assurance Systems Engineering. 2000, pp. 83–92 Google Scholar
  18. 18.
    Kobryn, C.: UML 2001: A standardization Odyssey. Communications of the ACM, 42(10), 1999 Google Scholar
  19. 19.
    Latella, D., Majzik, I., Massink, M.: Automatic verification of UML statechart diagrams using the SPIN model-checker. Formal Aspects of Computing, 11(6): 637–664, 1999 Google Scholar
  20. 20.
    Ledeczi, A.:, Maroti, M., Bakay, A., Karsai, G., Garrett, J., Thomason, C., Nordstrom, G., Sprinkle, J., Volgyesi, P.: The Generic Modeling Environment. In: Proc. Workshop on Intelligent Signal Processing. 2001 Google Scholar
  21. 21.
    Naumenko, A., Wegmann, A.: A metamodel for the unified modeling language. In: Jézéquel, J.-M., Hussmann, H., Cook, S. (eds.) Proc. Fifth International Conference on the Unified Modeling Language – The Language and its Applications, LNCS, vol. 2460. Springer, Dresden, Germany, 2002, pp. 2–17 Google Scholar
  22. 22.
    Object Management Group. Software Process Engineering Metamodel (SPEM). http://www.omg.org Google Scholar
  23. 23.
    Object Management Group. UML Profile for Enterprise Distributed Object Computing (EDOC). http://www.omg.org Google Scholar
  24. 24.
    Object Management Group. UML Profile for Schedulability, Performance and Time. http://www.omg.org Google Scholar
  25. 25.
    Object Management Group. Meta Object Facility Version 1.3, 1999. http://www.omg.org Google Scholar
  26. 26.
    Object Management Group. Model Driven Architecture – A Technical Perspective, 2001. http://www.omg.org Google Scholar
  27. 27.
    Object Management Group. Object Constraint Language Specification (in UML 1.4), 2001. http://www.omg.org Google Scholar
  28. 28.
    Övergaard, G.: Formal specification of object-oriented meta-modelling. In: Maibaum, T. (ed.) Proc. Fundamental Approaches to Software Engineering (FASE 2000), Berlin, Germany, LNCS, vol. 1783. Springer, 2000 Google Scholar
  29. 29.
    Pap, Z., Majzik, I., Pataricza, A.: Checking general safety criteria on UML statecharts. In: Voges, U. (ed.) Computer Safety, Reliability and Security (Proc. 20th Int. Conf., SAFECOMP-2001), LNCS, vol. 2187. Springer, 2001, pp. 46–55 Google Scholar
  30. 30.
    Pataricza, A.: Semi-decisions in the validation of dependable systems. In: Suppl. Proc. DSN 2001: The International IEEE Conference on Dependable Systems and Networks. Göteborg, Sweden, 2001, pp. 114–115 Google Scholar
  31. 31.
    Pataricza, A.: From the general resource model to a general fault modeling paradigm? In: Workshop on Critical Systems Development with UML at UML 2002. Dresden, Germany, 2002 Google Scholar
  32. 32.
    Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformations: Foundations. World Scientific, 1997 Google Scholar
  33. 33.
    Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language Reference Manual. Addison-Wesley, 1999 Google Scholar
  34. 34.
    Schürr, A., Sim, S.E., Holt, R., Winter, A.: The GXL Graph eXchange Language. http://www.gupro.de/GXL/ Google Scholar
  35. 35.
    Schürr, A., Winter, A.J., Zündorf, A.: In: [13], chap. The PROGRES Approach: Language and Environment. World Scientific, 1999, pp. 487–550 Google Scholar
  36. 36.
    Singh, A., Billington, J.: A formal service specification for IIOP based on ISO/IEC 14752. In: Jacobs, B., Rensink, A. (eds.) Proc. Fifth International Conference on Formal Methods for Open Object-Based Distributed Systems (FMOODS 2002). Kluwer, Enschede, The Netherlands, 2002, pp. 111–126 Google Scholar
  37. 37.
    Taentzer, G.: Towards common exchange formats for graphs and graph transformation systems. In: Padberg, J. (ed.) UNIGRA 2001: Uniform Approaches to Graphical Process Specification Techniques, ENTCS, vol. 44(4). 2001 Google Scholar
  38. 38.
    U2-Partners. UML: Infrastructure v. 2.0 (Third revised proposal), 2003. http://www.u2-partners.org/artifacts.htm Google Scholar
  39. 39.
    Varró, D.: Automatic program generation for and by model transformation systems. In: Kreowski, H.-J., Knirsch, P. (eds.) Proc. AGT 2002: Workshop on Applied Graph Transformation. Grenoble, France, 2002, pp. 161–173 Google Scholar
  40. 40.
    Varró, D.: A formal semantics of UML Statecharts by model transition systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) Proc. ICGT 2002: 1st International Conference on Graph Transformation, LNCS, vol. 2505. Springer-Verlag, Barcelona, Spain, 2002, pp. 378–392 Google Scholar
  41. 41.
    Varró, D., Gyapay, S., Pataricza, A.: Automatic transformation of UML models for system verification. In: Aranjo, J., Whittle, J., Toval, A., France, R., Moreira, A. (eds.) WTUML’01: Workshop on Transformations in UML. Genova, Italy, 2001, pp. 123–127 Google Scholar
  42. 42.
    Varró, D., Pataricza, A.: Metamodeling mathematics: A precise and visual framework for describing semantics domains of UML models. In: Jézéquel, J.-M., Hussmann, H., Cook, S. (eds.) Proc. Fifth International Conference on the Unified Modeling Language – The Language and its Applications, LNCS, vol. 2460. Springer-Verlag, Dresden, Germany, 2002, pp. 18–33 Google Scholar
  43. 43.
    Varró, D., G. Varró, Pataricza, A.: Designing the automatic transformation of visual languages. Science of Computer Programming, 44(2): 205–227, 2002 Google Scholar
  44. 44.
    Whittle, J.: Transformations and software modeling languages: Automating transformations in UML. In: Jézéquel, J.-M., Hussmann, H., Cook, S. (eds.) Proc. Fifth International Conference on the Unified Modeling Language – The Language and its Applications, LNCS, vol. 2460. Springer-Verlag, Dresden, Germany, 2002, pp. 227–242 Google Scholar
  45. 45.
    World Wide Web Consortium. MathML 2.0. http://www.w3c.org/MathGoogle Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Measurement and Information SystemsBudapest University of Technology and EconomicsBudapestHungary

Personalised recommendations