On submodels and submetamodels with their relation

A uniform formalization through inclusion properties
  • Bernard Carré
  • Gilles Vanwormhoudt
  • Olivier Caron
Regular Paper


Model-driven engineering (MDE) recognized software models as first-class objects with their own relationships and operations, up to constitute full structured model spaces. We focus on inclusion capacities through the concepts of submodel and submetamodel which contribute a lot to the structuring effort. Submodels and submetamodels underlie many MDE practices which require their precise characterization for plain control. A typical application is model management as offered by model repositories. On the basis of results on submodel inclusion we stated in a preceding paper, we concentrate on the special form of submodels which are submetamodels and their specific role in model space structuring. Pointing out that relating submodels and submetamodels is two ways, their respective inclusion hierarchies will be systematically characterized and symmetrically compared under the logical relationships of metamodel membership and model well-formedness. As a major result, it will be shown that submodel well-formedness w.r.t submetamodels closely relates to submodel invariance (a property which guarantees transitive structure preservation) applied at both levels. The uniform formalization offers algebraic grounding to better comprehension and control of model spaces which underlie MDE activities. At a much more practical level, reusable technology which takes advantage of established results will be offered.


Submodel Submetamodel Model space Set-theoretic formalization Model repository 



The authors would like to thank Prof. J. Gray and the anonymous reviewers for their work and comments in order to improve the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Bernard Carré
    • 1
  • Gilles Vanwormhoudt
    • 1
    • 2
  • Olivier Caron
    • 1
  1. 1.CRIStAL, UMR CNRS 9189University of LilleVilleneuve d’Ascq CedexFrance
  2. 2.Institut Mines-TélécomParis Cedex 13France

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