Categorical Approach to Horizontal Structuring andRe nement of High - Level Replacement

Based on the well-known theory of high-level replacement systems { a categorical formulation of graph grammars { we present new results concerning reenement of high-level replacement systems. Motivated by Petri nets, where reenement is often given by morphisms, we give a categorical notion of reenement. This concept is called Q-transformations and is established within the framework of high-level replacement systems. The main idea is to supply rules with an additional morphism, which belongs to a speciic class Q of morphisms. This leads to the new notions of Q-rules and Q-transformations. Moreover, several concepts and results of high-level replacement systems are extended to Q-transformations. These are sequential and parallel transformations , union, and fusion, based on diierent colimit constructions. The main results concern the compatibility of these constructions with Q-transformations that is the corresponding theorems for usual transformations are extended to Q-transformations. Finally, we demonstrate the application of these techniques for the special case of Petri nets to a case study concerning the requirements engineering of a medical information system.