Correctness of Incremental Model Synchronization with Triple Graph Grammars

  • Fernando Orejas
  • Elvira Pino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8568)


In model-driven software development, we may have several models describing the same system or artifact, by providing different views on it. In this case, we say that these models are consistently integrated.

Triple Graph Grammars (TGGs), defined by Schürr, are a general and powerful tool to describe (bidirectional) model transformations. In this context, model synchronization is the operation that, given two consistent models and an update or modification of one of them, finds the corresponding update on the other model, so that consistency is restored. There are different approaches to describe this operation in terms of TGGs, but most of them have a computational cost that depends on the size of the given models. In general this may be very costly since these models may be quite large. To avoid this problem, Giese and Wagner have advocated for the need of incremental synchronization procedures, meaning that their cost should depend only on the size of the given update. In particular they proposed one such procedure. Unfortunately, the correctness of their approach is not studied and, anyhow, it could only be ensured under severe restrictions on the kind of TGGs considered.

In the work presented, we study the problem from a different point of view. First, we discuss what it means for a procedure to be incremental, defining a correctness notion that we call incremental consistency. Moreover, we present a general incremental synchronization procedure and we show its correctness, completeness and incrementality.


Model Transformation Model Synchronization Triple Graph Grammars Incremental Model Synchronization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dayal, U., Bernstein, P.A.: On the Correct Translation of Update Operations on Relational Views. ACM Trans. Database Syst. 7(3), 381–416 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. EATCS Monographs of Theoretical Comp. Sc., Springer (2006)Google Scholar
  3. 3.
    Ehrig, H., Ehrig, K., Hermann, F.: From model transformation to model integration based on the algebraic approach to triple graph grammars. ECEASST 10 (2008)Google Scholar
  4. 4.
    Giese, H., Wagner, R.: From model transformation to incremental bidirectional model synchronization. Software and System Modeling 8(1), 21–43 (2009)CrossRefGoogle Scholar
  5. 5.
    Greenyer, J., Pook, S., Rieke, J.: Preventing information loss in incremental model synchronization by reusing elements. In: France, R.B., Kuester, J.M., Bordbar, B., Paige, R.F. (eds.) ECMFA 2011. LNCS, vol. 6698, pp. 144–159. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Hermann, F., Ehrig, H., Golas, U., Orejas, F.: Formal analysis of model transformations based on triple graph grammars. Software and System Modeling (2012) (to appear)Google Scholar
  7. 7.
    Hermann, F., Ehrig, H., Orejas, F., Czarnecki, K., Diskin, Z., Xiong, Y.: Correctness of Model Synchronization Based on Triple Graph Grammars. In: Whittle, J., Clark, T., Kühne, T. (eds.) MODELS 2011. LNCS, vol. 6981, pp. 668–682. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Hermann, F., Ehrig, H., Orejas, F., Golas, U.: Formal analysis of functional behaviour for model transformations based on triple graph grammars. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 155–170. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Hofmann, M., Pierce, B.C., Wagner, D.: Symmetric lenses. In: POPL 2011, pp. 371–384. ACM (2011)Google Scholar
  10. 10.
    Lauder, M., Anjorin, A., Varró, G., Schürr, A.: Efficient model synchronization with precedence triple graph grammars. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 401–415. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Schürr, A.: Specification of graph translators with triple graph grammars. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds.) Graph-Theoretic Concepts in Computer Science. LNCS, vol. 903, pp. 151–163. Springer, Heidelberg (1995)Google Scholar
  12. 12.
    Schürr, A., Klar, F.: 15 years of triple graph grammars. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 411–425. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Stevens, P.: Towards an Algebraic Theory of Bidirectional Transformations. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 1–17. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Terwilliger, J.F., Cleve, A., Curino, C.A.: How Clean Is Your Sandbox? - Towards a Unified Theoretical Framework for Incremental Bidirectional Transformations. In: Hu, Z., de Lara, J. (eds.) ICMT 2012. LNCS, vol. 7307, pp. 1–23. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Fernando Orejas
    • 1
  • Elvira Pino
    • 1
  1. 1.Universitat Politècnica de CatalunyaSpain

Personalised recommendations