Local confluence analysis of hypergraph transformation systems with application conditions based on [formula omitted]-functors and Agg

Abstract

For typed attributed graph transformation systems, the tool environment Agg supports modelling, simulation and analysis of graph transformations. A corresponding tool for analysis of hypergraph transformation systems does not exist up to now. In this paper we establish a formal relationship between the corresponding M-adhesive transformation systems, which allows us the translation of hypergraph transformations into typed attributed graph transformations with equivalent behaviour, and, vice versa, the creation of hypergraph transformations from typed attributed graph transformations. This relationship is based on the general theory of M-functors between different M-adhesive transformation systems which is extended in this paper to rules with application conditions. Our main result shows the creation of local confluence based on F-reachable critical pairs for rules with application conditions, where F is a suitable M-functor. We construct a functor between the M-adhesive categories of hypergraphs and of typed attributed graphs, and show that our construction yields an M-functor with properties required by the general theory. Hence, analysis results for hypergraph transformation systems can be obtained using Agg for analysing the translated typed attributed graph transformation systems.