A Unified Categorical Approach for Attributed Graph Rewriting

  • Maxime Rebout
  • Louis Féraud
  • Sergei Soloviev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


Attributed graphs are often used in software engineering. Mainly algorithms concerning programs and models transformations are based on rewriting techniques. We suggest a unified categorical approach for the description and the verification of such algorithms and programs. This contribution which is a generalization of the double pushout approach can be seen as a mix between pushout and pullback. This will facilitate the computations on attributes within a unified framework. It should be particularly helpful for model to model transformation in the domain of “Model Driven Architecture”.


Model Transformation Categorical Approach Computation Function Graph Transformation Attribute Graph 
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.
    Aho, A.V., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques and Tools. Addison-Wesley, Reading (1988)Google Scholar
  2. 2.
    Aizawa, K., Nakamura, A.: Path-controlled graph grammars for multi-resolution image processing and analysis. In: Ehrig, H., Schneider, H.-J. (eds.) Dagstuhl Seminar 1993. LNCS, vol. 776, pp. 1–18. Springer, Heidelberg (1994)Google Scholar
  3. 3.
    Assmann, U.: How to uniformly specify program analysis and transformation with graph rewrite systems. In: Gyimóthy, T. (ed.) CC 1996. LNCS, vol. 1060. Springer, Heidelberg (1996)Google Scholar
  4. 4.
    Baresi, L., Heckel, R.: Tutorial introduction to graph transformation: A software engineering perspective. In: Corradini et al. [6], pp. 402–429Google Scholar
  5. 5.
    Chemouil, D.: Types inductifs, isomorphismes et récriture extensionnelle. PhD thesis, Université Paul Sabatier (2004)Google Scholar
  6. 6.
    Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.): ICGT 2002. LNCS, vol. 2505. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  7. 7.
    The Coq development team. The Coq proof assistant reference manual: Version 8.1. Technical report, LogiCal Project (2006)Google Scholar
  8. 8.
    Ehrig, H.: Introduction to the algebraic theory of graph grammars (A survey). In: Ng, E.W., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1–69. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  9. 9.
    Ehrig, H., Ehrig, K.: Overview of formal concepts for model transformations based on typed attributed graph transformation. Electr. Notes Theor. Comput. Sci. 152, 3–22 (2006)CrossRefGoogle Scholar
  10. 10.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  11. 11.
    Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: An algebraic approach. In: FOCS, pp. 167–180. IEEE, Los Alamitos (1973)Google Scholar
  12. 12.
    Ehrig, H., Prange, U., Taentzer, G.: Fundamental theory for typed attributed graph transformation. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 161–177. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Grunske, L., Geiger, L., Zündorf, A., Van Eetvelde, N., Van Gorp, P., Varró, D.: Using Graph Transformation for Practical Model Driven Software Engineering. In: Model Driven Software Engineering, pp. 91–118. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Habel, A., Plump, D.: Relabelling in graph transformation. In: Corradini et al. [6], pp. 135–147Google Scholar
  15. 15.
    Kahl, W.: A relational-algebraic approach to graph structure transformation. PhD thesis, Universität der Bundeswehr München (2001)Google Scholar
  16. 16.
    Kastenberg, H.: Towards attributed graphs in Groove: Work in progress. Electr. Notes Theor. Comput. Sci. 154(2), 47–54 (2006)CrossRefGoogle Scholar
  17. 17.
    Lack, S., Sobocinski, P.: Adhesive categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004)Google Scholar
  18. 18.
    Lladós, J., Sánchez, G.: Symbol recognition using graphs. In: ICIP (2), pp. 49–52 (2003)Google Scholar
  19. 19.
    Rebout, M.: Algebraic transformations for attributed graphs. Technical report, IRIT, Toulouse (2007)Google Scholar
  20. 20.
    Rozenberg, G.: Handbook of Graph Grammars and Computing by Graph Transformations. Foundations, vol. 1. World Scientific, Singapore (1997)zbMATHGoogle Scholar
  21. 21.
    Taentzer, G.: AGG: A tool environment for algebraic graph transformation. In: Münch, M., Nagl, M. (eds.) AGTIVE 1999. LNCS, vol. 1779, pp. 481–488. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maxime Rebout
    • 1
  • Louis Féraud
    • 1
  • Sergei Soloviev
    • 1
  1. 1.IRITUniversité Paul SabatierTOULOUSE CEDEX 9

Personalised recommendations