Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation

Issue title: SPECIAL ISSUE ON ICGT 2004

Article type: Research Article

Authors: Ehrig, Hartmut | Padberg, Julia | Prange, Ulrike | Habel, Annegret

Affiliations: Technical University of Berlin, Germany. E-mail: {ehrig,padberg,uprange}@cs.tu-berlin.de | Carl v. Ossietzky University of Oldenburg, Germany. E-mail: annegret.habel@informatik.uni-oldenburg.de

Abstract: Adhesive high-level replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the well-known concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobocinacute;ski. In this paper we show that most of the HLR properties, which had been introduced to generalize some basic results from the category of graphs to high-level structures, are valid already in adhesive HLR categories. This leads to a smooth categorical theory of HLR systems which can be applied to a large variety of graphs and other visual models. As a main new result in a categorical framework we show the Critical Pair Lemma for the local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.

Keywords: high-level replacement systems, adhesive categories, adhesive HLR categories, graph transformation, local confluence of transformations, Critical Pair Lemma

Journal: Fundamenta Informaticae, vol. 74, no. 1, pp. 1-29, 2006