Abstract
Some recent algebraic approaches to graph transformation include a pullback construction involving the match, that allows one to specify the cloning of items of the host graph. We pursue further this trend by proposing the Pullback-Pushout (pb-po) Approach, where we combine smoothly the classical modifications to a host graph specified by a rule (a span of graph morphisms) with the cloning of structures specified by another rule. The approach is shown to be a conservative extension of agree (and thus of the sqpo approach), and we show that it can be extended with standard techniques to attributed graphs. We discuss conditions to ensure a form of locality of transformations, and conditions to ensure that the attribution of transformed graphs is total.
This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) funded by the French program Investissement d’avenir and by the Brazilian agency CNPq.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bauderon, M., Jacquet, H.: Node rewriting in graphs and hypergraphs: a categorical framework. Theor. Comput. Sci. 266(1–2), 463–487 (2001)
Cockett, J., Lack, S.: Restriction categories II: partial map classification. Theor. Comput. Sci. 294(1–2), 61–102 (2003)
Corradini, A., Duval, D., Echahed, R., Prost, F., Ribeiro, L.: AGREE – algebraic graph rewriting with controlled embedding. In: Parisi-Presicce, F., Westfechtel, B. (eds.) ICGT 2015. LNCS, vol. 9151, pp. 35–51. Springer, Cham (2015). doi:10.1007/978-3-319-21145-9_3
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). doi:10.1007/11841883_4
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation - part I: basic concepts and double pushout approach. In: Rozenberg [18], pp. 163–246
Drewes, F., Hoffmann, B., Janssens, D., Minas, M.: Adaptive star grammars and their languages. Theor. Comput. Sci. 411(34–36), 3090–3109 (2010)
Duval, D., Echahed, R., Prost, F., Ribeiro, L.: Transformation of attributed structures with cloning. In: Gnesi, S., Rensink, A. (eds.) FASE 2014. LNCS, vol. 8411, pp. 310–324. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54804-8_22
Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic approaches to graph transformation - part II: single pushout approach and comparison with double pushout approach. In: Rozenberg [18], pp. 247–312
Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: an algebraic approach. In: 14th Annual Symposium on Switching and Automata Theory, Iowa City, Iowa, USA, 15–17 October, pp. 167–180. IEEE Computer Society (1973)
Engelfriet, J., Rozenberg, G.: Node replacement graph grammars. In: Rozenberg [18], pp. 1–94
Heckel, R., Ehrig, H., Wolter, U., Corradini, A.: Double-pullback transitions and coalgebraic loose semantics for graph transformation systems. Appl. Categorical Struct. 9(1), 83–110 (2001)
Kahl, W.: Amalgamating pushout and pullback graph transformation in collagories. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 362–378. Springer, Heidelberg (2010). doi:10.1007/978-3-642-15928-2_24
Lack, S., Sobociński, P.: Adhesive categories. In: Walukiewicz, I. (ed.) FoSSaCS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004). doi:10.1007/978-3-540-24727-2_20
Löwe, M.: Algebraic approach to single-pushout graph transformation. Theor. Comput. Sci. 109(1&2), 181–224 (1993)
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). doi:10.1007/978-3-642-33654-6_8
Mantz, F.: Coupled Transformations of Graph Structures applied to Model Migration. Ph.D. thesis, University of Marburg (2014)
Mantz, F., Taentzer, G., Lamo, Y., Wolter, U.: Co-evolving meta-models and their instance models: a formal approach based on graph transformation. Sci. Comput. Program. 104, 2–43 (2015)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformations, vol. 1: Foundations. World Scientific (1997)
Schulz, C., Löwe, M., König, H.: A categorical framework for the transformation of object-oriented systems: models and data. J. Symb. Comput. 46(3), 316–337 (2011)
Wouters, L., Gervais, M.P.: Ontology transformations. In: IEEE International Enterprise Distributed Object Computing Conference, pp. 71–80 (2012)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Corradini, A., Duval, D., Echahed, R., Prost, F., Ribeiro, L. (2017). The Pullback-Pushout Approach to Algebraic Graph Transformation. In: de Lara, J., Plump, D. (eds) Graph Transformation. ICGT 2017. Lecture Notes in Computer Science(), vol 10373. Springer, Cham. https://doi.org/10.1007/978-3-319-61470-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-61470-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-61469-4
Online ISBN: 978-3-319-61470-0
eBook Packages: Computer ScienceComputer Science (R0)