Object-Oriented Structure Refinement – A Graph Transformational Approach

Abstract

In UML, the general structure of objects, their attributes and relations are modeled as a class graph, and an instance of a class graph is defined as an object graph. The class graph of a system determines the general properties of objects and how objects collaborate in realizing a use case. In this paper, we define class graphs and their object graphs as directed labelled graphs, and investigate in a graph theoretical approach what changes in the object structure maintain the capability of providing services. We define the general notion of structure refinements. A structure refinement is a transformation from one graph to another that preserves the capability of providing services, that is the resulting class graph should be able to provide at least as well as the original graph. We give a small set of structure refinement rules that is proved to be sound and complete for a kind of structure refinement.