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Categorical Approach to Horizontal Structuring and Refinement of High-Level Replacement Systems

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Abstract

Based on the well-known theory of high-level replacement systems – a categorical formulation of graph grammars – we present new results concerning refinement of high-level replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of refinement. 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 specific 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 different 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.

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  1. Institute for Communication and Software Technology, Technical University of Berlin, Berlin, Germany

    Julia Padberg

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  1. Julia Padberg
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Padberg, J. Categorical Approach to Horizontal Structuring and Refinement of High-Level Replacement Systems. Applied Categorical Structures 7, 371–403 (1999). https://doi.org/10.1023/A:1008695316594

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