Abstract
In this paper, we propose a new approach to inheritance in the context of algebraic graph transformation by providing a suitable categorial framework which reflects the semantics of class-based inheritance in software engineering. Inheritance is modelled by a type graph T that comes equipped with a partial order. Typed graphs are arrows with codomain T which preserve graph structures up to inheritance. Morphisms between typed graphs are “down typing” graph morphisms: An object of class t can be mapped to an object of a subclass of t. We prove that this structure is an adhesive HLR category, i.e. pushouts along extremal monomorphisms are “well-behaved”. This infers validity of classical results such as the Local Church-Rosser Theorem, the Parallelism Theorem, and the Concurrency Theorem.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Adámek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories: The Joy of Cats. Free Software Foundation (2004)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer (2006)
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)
Ehrig, H., Habel, A., Kreowski, H.J., Parisi-Presicce, F.: Parallelism and concurrency in high-level replacement systems. Mathematical Structures in Computer Science 1, 361–404 (1991)
Ehrig, H., Padberg, J., Prange, U., Habel, A.: Adhesive high-level replacement systems: A new categorical framework for graph transformation. Fundam. Inf. 74(1), 1–29 (2006)
Lüdtke Ferreira, A.P., Ribeiro, L.: Derivations in object-oriented graph grammars. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 416–430. Springer, Heidelberg (2004)
Golas, U., Lambers, L., Ehrig, H., Orejas, F.: Attributed graph transformation with inheritance: Efficient conflict detection and local confluence analysis using abstract critical pairs. Theoretical Computer Science 424, 46–68 (2012)
Guerra, E., de Lara, J.: Attributed typed triple graph transformation with inheritance in the Double Pushout approach. Tech. Rep. UC3M-TR-CS-06- 01, Universidad Carlos III de Madrid (2006)
Hermann, F., Ehrig, H., Ermel, C.: Transformation of type graphs with inheritance for ensuring security in e-government networks. In: Chechik, M., Wirsing, M. (eds.) FASE 2009. LNCS, vol. 5503, pp. 325–339. Springer, Heidelberg (2009)
Lack, S., Sobociński, P.: Adhesive categories. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 273–288. Springer, Heidelberg (2004)
Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoret. Comput. Sci. 109, 181–224 (1993)
Löwe, M., König, H., Schulz, C., Schultchen, M.: Algebraic graph transformations with inheritance. Tech. Rep. 02013/03, University of Applied Sciences, FHDW Hannover (2013)
Pilone, D.: UML 2.0 in a Nutshell. O’Reilly (2006)
Rutle, A., Wolter, U., Lamo, Y.: A diagrammatic approach to model transformations. In: Proceedings of the 2008 Euro American Conference on Telematics and Information Systems (EATIS 2008), pp. 1–8. ACM (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Löwe, M., König, H., Schulz, C., Schultchen, M. (2013). Algebraic Graph Transformations with Inheritance. In: Iyoda, J., de Moura, L. (eds) Formal Methods: Foundations and Applications. SBMF 2013. Lecture Notes in Computer Science, vol 8195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41071-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-41071-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41070-3
Online ISBN: 978-3-642-41071-0
eBook Packages: Computer ScienceComputer Science (R0)