Correctness, Completeness and Termination of Pattern-Based Model-to-Model Transformation

  • Fernando Orejas
  • Esther Guerra
  • Juan de Lara
  • Hartmut Ehrig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5728)


Model-to-model (M2M) transformation consists in trans- forming models from a source to a target language. Many transformation languages exist, but few of them combine a declarative and relational style with a formal underpinning able to show properties of the transformation. Pattern-based transformation is an algebraic, bidirectional, and relational approach to M2M transformation. Specifications are made of patterns stating the allowed or forbidden relations between source and target models, and then compiled into low level operational mechanisms to perform source-to-target or target-to-source transformations. In this paper, we study the compilation into operational triple graph grammar rules and show: (i) correctness of the compilation of a specification without negative patterns; (ii) termination of the rules, and (iii) completeness, in the sense that every model considered relevant can be built by the rules.


Model Transformation Target Model Graph Transformation Graph Grammar Negative Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akehurst, D.H., Kent, S.: A relational approach to defining transformations in a metamodel. In: Jézéquel, J.-M., Hussmann, H., Cook, S. (eds.) UML 2002. LNCS, vol. 2460, pp. 243–258. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Braun, P., Marschall, F.: Transforming object oriented models with BOTL. ENTCS 72(3) (2003)Google Scholar
  3. 3.
    de Lara, J., Guerra, E.: Pattern-based model-to-model transformation. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 426–441. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Ehrig, H., Ehrig, K., de Lara, J., Taentzer, G., Varró, D., Varró-Gyapay, S.: Termination criteria for model transformation. In: Cerioli, M. (ed.) FASE 2005. LNCS, vol. 3442, pp. 49–63. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Ehrig, H., Ehrig, K., Ermel, C., Hermann, F., Taentzer, G.: Information preserving bidirectional model transformations. In: Dwyer, M.B., Lopes, A. (eds.) FASE 2007. LNCS, vol. 4422, pp. 72–86. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of algebraic graph transformation. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  7. 7.
    Ehrig, H., Ermel, C., Hermann, F.: On the relationship of model transformations based on triple and plain graph grammars. In: Proc. GRAMOT 2008 (2008)Google Scholar
  8. 8.
    Ehrig, H., Hermann, F., Sartorius, C.: Completeness and correctness of model transformations based on triple graph grammars with negative application conditions. In: GT-VMT 2009. Electronic Communications of the EASST (to appear, 2009)Google Scholar
  9. 9.
    Heckel, R., Wagner, A.: Ensuring consistency of conditional graph rewriting - a constructive approach. ENTCS 2 (1995)Google Scholar
  10. 10.
    Königs, A.: Model transformation with triple graph grammars. In: Proc. MTiP 2005 (2005)Google Scholar
  11. 11.
    Königs, A., Schürr, A.: Tool integration with triple graph grammars - a survey. ENTCS 148(1), 113–150 (2006)Google Scholar
  12. 12.
    Lack, S., Sobocinski, P.: Adhesive categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Lawley, M., Steel, J.: Practical declarative model transformation with Tefkat. In: Bruel, J.-M. (ed.) MoDELS 2005. LNCS, vol. 3844, pp. 139–150. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    MOLA. MOdel transformation LAnguage,
  15. 15.
    MTF. Model Transformation Framework ,
  16. 16.
    Orejas, F., Guerra, E., de Lara, J., Ehrig, H.: Correctness, completeness and termination of pattern-based model-to-model transformation (long version). Technical Report 2009/09, TU Berlin, Fak. IV (2009)Google Scholar
  17. 17.
  18. 18.
    Schürr, A.: Specification of graph translators with triple graph grammars. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds.) WG 1994. LNCS, vol. 903, pp. 151–163. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  19. 19.
    Stevens, P.: Bidirectional model transformations in QVT: Semantic issues and open questions. In: Engels, G., Opdyke, B., Schmidt, D.C., Weil, F. (eds.) MODELS 2007. LNCS, vol. 4735, pp. 1–15. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Tratt, L.: A change propagating model transformation language. JOT 7(3), 107–126 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Fernando Orejas
    • 1
  • Esther Guerra
    • 2
  • Juan de Lara
    • 3
  • Hartmut Ehrig
    • 4
  1. 1.Universitat Politècnica de CatalunyaSpain
  2. 2.Universidad Carlos III de MadridSpain
  3. 3.Universidad Autónoma de MadridSpain
  4. 4.Technische Universität BerlinGermany

Personalised recommendations