Delaying Constraint Solving in Symbolic Graph Transformation

  • Fernando Orejas
  • Leen Lambers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6372)


Applying an attributed graph transformation rule to a given object graph always implies some kind of constraint solving. In many cases, the given constraints are almost trivial to solve. For instance, this is the case when a rule describes a transformation \(G \Rightarrow H\), where the attributes of H are obtained by some simple computation from the attributes of G. However there are many other cases where the constraints to solve may be not so trivial and, moreover, may have several answers. This is the case, for instance, when the transformation process includes some kind of searching. In the current approaches to attributed graph transformation these constraints must be completely solved when defining the matching of the given transformation rule. This kind of early binding is well-known from other areas of Computer Science to be inadequate. For instance, the solution chosen for the constraints associated to a given transformation step may be not fully adequate, meaning that later, in the search for a better solution, we may need to backtrack this transformation step.

In this paper, based on our previous work on the use of symbolic graphs to deal with different aspects related with attributed graphs, including attributed graph transformation, we present a new approach that allows us to delay constraint solving when doing attributed graph transformation. In particular we show that the approach is sound and complete with respect to standard attributed graph transformation. A running example, where a graph transformation system describes some basic operations of a travel agency, shows the practical interest of the approach.


Attributed graph transformation symbolic graph transformation lazy transformation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berthold, M., Fischer, I., Koch, M.: Attributed graph transformation with partial attribution. In: GRATRA 2000. Joint APPLIGRAPH and GETGRATS Workshop on Graph Transformation Systems, pp. 171–178 (2000)Google Scholar
  2. 2.
    Ehrig, H.: Attributed graphs and typing: Relationship between different representations. Bulletin of the EATCS 82, 175–190 (2004)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamental theory of typed attributed graph transformation based on adhesive HLR-categories. Fundamenta Informaticae 74(1), 31–61 (2006)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. In: EATCS Monographs of Theoretical Computer Science. Springer, Heidelberg (2006)Google Scholar
  5. 5.
    Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics. In: EATCS Monographs of Theoretical Computer Science. Springer, Heidelberg (1985)Google Scholar
  6. 6.
    Ehrig, H., Padberg, J., Prange, U., Habel, A.: Adhesive high-level replacement systems: A new categorical framework for graph transformation. Fundamenta Informaticae 74(1), 1–29 (2006)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Heckel, R., Küster, J., Taentzer, G.: Towards automatic translation of uml models into semantic domains. In: APPLIGRAPH Workshop on Applied Graph Transformation, pp. 11–22 (2002)Google Scholar
  8. 8.
    Jaffar, J., Maher, M., Marriot, K., Stuckey, P.: The semantics of constraint logic programs. The Journal of Logic Programming 37, 1–46 (1998)zbMATHCrossRefGoogle Scholar
  9. 9.
    Knuth, D.: Semantics of context-free languages. Mathematical Systems Theory 2, 127–145 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lack, S., Sobocinski, P.: Adhesive and quasiadhesive categories. Theoretical Informatics and Applications 39, 511–545 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Löwe, M., Korff, M., Wagner, A.: An algebraic framework for the transformation of attributed graphs. In: Term Graph Rewriting: Theory and Practice, pp. 185–199. John Wiley, New York (1993)Google Scholar
  12. 12.
    Orejas, F.: Attributed graph constraints. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Orejas, F., Lambers, L.: Symbolic attributed graphs for attributed graph transformation. In: Int. Coll. on Graph and Model Transformation on the Occasion of the 65th Birthday of Hartmut Ehrig (2010)Google Scholar
  14. 14.
    Plump, D., Steinert, S.: Towards graph programs for graph algorithms. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 128–143. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Fernando Orejas
    • 1
  • Leen Lambers
    • 2
  1. 1.Universitat Politècnica de CatalunyaSpain
  2. 2.Hasso Plattner InstitutUniversität PotsdamGermany

Personalised recommendations