Algebraic approach to single-pushout graph transformation
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Elementary categories, elementary toposes
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There are three variations of algebraic graph rewriting, the double-pushout, the single-pushout, and the sesqui-pushout approach. In this paper, we show that all three approaches can be considered special cases of a general rewriting framework in suitable categories of spans over a graph-like base category. From this new view point, it is possible to provide a general and unifying theory for all approaches. We demonstrate this fact by the investigation of general parallel independence. Besides this, the new and more general framework offers completely new ways of rewriting: Using spans as matches, for example, provides a simple mechanism for universal quantification. The general theory, however, applies to these new types of rewriting as well.