Inductive UML

  • Franck Barbier
  • Eric Cariou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7602)


The increasing importance of metamodeling calls for metamodels that are free of ambiguities, contradictions and redundancies. This is specifically the case for the core of UML (Infrastructure). This paper proposes to rewrite a part of this core, the Class and Property metaclasses especially. To avoid infinite regression, the notion of meta-circularity is used. This rewriting is done by means of inductive types in constructive logic. The proposed specification is proven correct using the Coq automated prover. Proven lemmas and theorems about a “metaness” relationship are proposed.


Unified Modeling Language Metamodeling Constructive logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    OMG Unified Modeling LanguageTM, Superstructure, Version 2.3 (May 2010)Google Scholar
  2. 2.
    Atkinson, C., Kühne, T.: Model-Driven Development: A Metamodeling Foundation. IEEE Software 20(5), 5–22 (2002)Google Scholar
  3. 3.
    Kühne, T.: Matters of (Meta-) modeling. Software and Systems Modeling 5(4), 369–385 (2006)CrossRefGoogle Scholar
  4. 4.
    France, R., Rumpe, B.: Model-driven Development of Complex Software: A Research Roadmap. In: The ICSE 2007 Future of Software Engineering Workshop, Minneapolis, USA (2007)Google Scholar
  5. 5.
    Steinberg, D., Budinsky, F., Paternostro, M., Merks, E.: EMF - Eclipse Modeling Framework, 2nd edn. Addison-Wesley (2008)Google Scholar
  6. 6.
    OMG Unified Modeling LanguageTM, Infrastructure, Version 2.3 (May 2010)Google Scholar
  7. 7.
    Meta Object Facility (MOF) Core Specification, Version 2.0 (January 2006)Google Scholar
  8. 8.
    Clark, T., Evans, A., Kent, S.: The Meta-Modeling Language Calculus: Foundation Semantics for UML. In: The 4th International Conference on Fundamental Approaches to Software Engineering, Genova, Italy, pp. 17–31 (2001)Google Scholar
  9. 9.
    Bézivin, J., Gerbé, O.: Towards a Precise Definition of the OMG/MDA Framework. In: Automated Software Engineering, San Diego, USA, pp. 273–280 (2001)Google Scholar
  10. 10.
    Kuske, S., Gogolla, M., Kreowski, H.-J., Ziemann, P.: Towards an integrated graph-based semantics for UML. Software and Systems Modeling 8(3), 403–422 (2009)CrossRefGoogle Scholar
  11. 11.
    Jackson, E., Sztipanovits, J.: Formalizing the structural semantics of domain-specific modeling languages. Software and Systems Modeling 8(4), 451–478 (2009)CrossRefGoogle Scholar
  12. 12.
    Paige, R., Brooke, P., Ostroff, J.: Metamodel-based model conformance and multiview consistency checking. ACM Transactions on Software Engineering and Methodology 16(3) (2007)Google Scholar
  13. 13.
    Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development Coq’Art: The Calculus of Inductive Constructions. Springer (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Franck Barbier
    • 1
  • Eric Cariou
    • 1
  1. 1.University of PauPau cedexFrance

Personalised recommendations