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An Algebra of Graph Derivations Using Finite (co—) Limit Double Theories

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Recent Trends in Algebraic Development Techniques

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1589))

Abstract

Graph transformation systems have been introduced for the formal specification of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specification. Operations on graph derivations provide means to reason about the distribution and composition of computations. In this paper we discuss the development of an algebra of graph derivations as a descriptive model of graph transformation systems. For that purpose we use a categorical three level approach for the construction of models of computations based on structured transition systems. Categorically the algebra of graph derivations can then be characterized as a free double category with finite horizontal colimits.

One of the main objectives of this paper is to show how we used algebraic techniques for the development of this formal model, in particular to obtain a clear and well structured theory. Thus it may be seen as a case study in theory design and its support by algebraic development techniques.

★

This work has been carried out during a stay of the second and third author at the University of Pisa, supported by the EEC TMR network GETGRATS (General Theory of Graph Transformation Systems) ERB-FMRX-CT960061.

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Author information

Authors and Affiliations

  1. Dip. Informatica, Università di Pisa, Germany

    Andrea Corradini

  2. TU Berlin, FB Informatik, Germany

    Martin Groβe-Rhode

  3. Universität-GH Paderborn, FB Mathematik-Informatik, Germany

    Reiko Heckel

Authors
  1. Andrea Corradini
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  2. Martin Groβe-Rhode
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  3. Reiko Heckel
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Lisbon, Campo Grande 1700, Lisbon, Portugal

    José Luiz Fiadeiro

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© 1999 Springer-Verlag Berlin Heidelberg

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Corradini, A., Groβe-Rhode, M., Heckel, R. (1999). An Algebra of Graph Derivations Using Finite (co—) Limit Double Theories. In: Fiadeiro, J.L. (eds) Recent Trends in Algebraic Development Techniques. Lecture Notes in Computer Science, vol 1589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48483-3_7

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  • DOI: https://doi.org/10.1007/3-540-48483-3_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66246-4

  • Online ISBN: 978-3-540-48483-7

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