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International Conference on Graph Transformation

ICGT 2014: Graph Transformation pp 222–236Cite as

Van Kampen Squares for Graph Transformation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8571))

Abstract

This paper demonstrates the benefits of a recent result by the authors, proving a necessary and sufficient condition for a pushout of two morphisms to be a Van Kampen Square, even if both morphisms are not monomorphisms. The theorem can be applied in categories that are based on graph structure signatures. We discuss its value in the context of general views on co-transformations and illustrate an application in a software co-evolution scenario.

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References

  1. Ambler, S.: Refactoring Databases: Evolutionary Database Design. Addison-Wesley (2006)

    Google Scholar 

  2. Brown, R., Janelidze, G.: Van Kampen Theorems for Categories of Covering Morphisms in Lextensive Categories. Journal of Pure and Applied Algebra 119, 255–263 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cicchetti, A., Ruscio, D.D., Eramo, R., Pierantonio, A.: Automating Co-Evolution in Model-Driven Engineering. In: Proceedings of the 2008 12th International IEEE Enterprise Distributed Object Computing Conference, EDOC 2008, pp. 222–231. IEEE Computer Society, Washington, DC (2008), http://dx.doi.org/10.1109/EDOC.2008.44

    Chapter  Google Scholar 

  4. Corradini, A., Heindel, T., Hermann, F., König, B.: Sesqui-Pushout Rewriting. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 30–45. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Duval, D., Echahed, R., Prost, F., Ribeiro, L.: Transformation of Attributed Structures with Cloning (long version). CoRR abs/1401.2751 (2014)

    Google Scholar 

  6. Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformations. Springer (2006)

    Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Fiadeiro, J.L.: Categories for Software Engineering. Springer (2005)

    Google Scholar 

  9. Goldblatt, R.: Topoi: The Categorial Analysis of Logic. Dover Publications (1984)

    Google Scholar 

  10. Heindel, T., Sobociński, P.: Van Kampen Colimits as Bicolimits in Span. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 335–349. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-03741-2_23

    Chapter  Google Scholar 

  11. Heumüller, M., Joshi, S., König, B., Stückrath, J.: Construction of Pushout Complements in the Category of Hypergraphs. ECEASST 39 (2011)

    Google Scholar 

  12. Hu, Z., Schürr, A., Stevens, P., Terwilliger, J.: Bidirectional Transformation “bx” (Dagstuhl Seminar 11031). Dagstuhl Reports 1(1), 42–67 (2011), http://drops.dagstuhl.de/opus/volltexte/2011/3144

    Google Scholar 

  13. König, H., Löwe, M., Schulz, C.: Model Transformation and Induced Instance Migration: A Universal Framework. In: Simao, A., Morgan, C. (eds.) SBMF 2011. LNCS, vol. 7021, pp. 1–15. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  14. Lack, S., Sobociński, P.: Toposes are Adhesive. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 184–198. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Löwe, M.: Van-Kampen Pushouts for Sets and Graphs. Technical Report. FHDW Hannover 4 (2010)

    Google Scholar 

  16. Löwe, M.: Refined Graph Rewriting in Span-Categories - A Framework for Algebraic Graph Transformation. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 111–125. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  17. Löwe, M., König, H., Schulz, C., Schultchen, M.: Algebraic Graph Transformations with Inheritance. In: Iyoda, J., de Moura, L. (eds.) SBMF 2013. LNCS, vol. 8195, pp. 211–226. Springer, Heidelberg (2013)

    Google Scholar 

  18. Mantz, F., Taentzer, G., Lamo, Y.: Co-Transformation of Type and Instance Graphs Supporting Merging of Types and Retyping. ECEASST 61 (2013)

    Google Scholar 

  19. Müller, J.: Shifting Derivations of non-injective Rules in the Algebraic Graph Rewriting Approaches. Techn. Report. TU, Berlin 16 (1997)

    Google Scholar 

  20. Schuerr, 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)

    Chapter  Google Scholar 

  21. Taentzer, G., Mantz, F., Lamo, Y.: Co-Transformation of Graphs and Type Graphs with Application to Model Co-Evolution. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 326–340. Springer, Heidelberg (2012), http://dx.doi.org/10.1007/978-3-642-33654-6_22

    Chapter  Google Scholar 

  22. Wolter, U., Diskin, Z.: From Indexed to Fibred Semantics – The Generalized Sketch File –. Reports in Informatics 361. Dep. of Informatics, University of Bergen (2007)

    Google Scholar 

  23. Wolter, U., König, H.: Fibred Amalgamation, Descent Data, and Van Kampen Squares in Topoi. Applied Categorical Structures, 1–40 (2013), http://dx.doi.org/10.1007/s10485-013-9339-2

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Author information

Authors and Affiliations

  1. FHDW Hannover, University of Applied Sciences, Freundallee 15, 30173, Hannover, Germany

    Harald König, Michael Löwe & Christoph Schulz

  2. Department of Informatics, University of Bergen, P.O.Box 7803, 5020, Bergen, Norway

    Uwe Wolter

Authors
  1. Harald König
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  2. Michael Löwe
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  3. Christoph Schulz
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  4. Uwe Wolter
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Editor information

Editors and Affiliations

  1. Hasso Plattner Institut an der Universität Potsdam, Prof.-Dr.-Helmert-Strasse 2-3, 14482, Potsdam, Germany

    Holger Giese

  2. Fakultät für Ingenieurwissenschaften, Abteilung für Informatik und Angewandte Kognitionswissenscaft, Universität Duisburg-Essen, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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König, H., Löwe, M., Schulz, C., Wolter, U. (2014). Van Kampen Squares for Graph Transformation. In: Giese, H., König, B. (eds) Graph Transformation. ICGT 2014. Lecture Notes in Computer Science, vol 8571. Springer, Cham. https://doi.org/10.1007/978-3-319-09108-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-09108-2_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09107-5

  • Online ISBN: 978-3-319-09108-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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