Ensuring Structural Constraints in Graph-Based Models with Type Inheritance

Graphs are a common means to represent structures in models and meta-models of software systems. In this context, the description of model domains by classifying the domain entities and their relations using class diagrams or type graphs has emerged as a very valuable principle. The constraints that can be imposed by pure typing are, however, relatively weak; it is therefore common practice to enrich type information with structural properties (such as local invariants or multiplicity conditions) or inheritance. In this paper, we show how to formulate structural properties using graph constraints in type graphs with inheritance, and we show how to translate constrained type graphs with inheritance to equivalent constrained simple type graphs. From existing theory it then follows that graph constraints can be translated into pre-conditions for productions of a typed graph transformation system which ensures those graph constraints. This result can be regarded as a further important step of integrating graph transformation with object-orientation concepts.