De nition of an Encapsulated Hierarchical Graph Data

Graph grammars have been successfully used as a formalism for the speciication of realistic problems but, as far as speciication-in-the-large activities are concerned, they still have some deeciencies. In particular, most of them only support the use of at graphs, whereas for certain applications hierarchical graphs would be a more suitable modelling tool. Furthermore, there is still the need for a graph grammar module concept that allows to split large speciications into smaller sub-speciications. We want to address this problem by applying object-oriented concepts to develop a hierarchical graph data model that supports a suitable module concept for graph grammars. In this paper, we present the rst step in the deenition of our encapsulated hierarchical graph (EHG) data model. We introduce the notion of EHG that supports complex nodes (i.e. nodes with an encapsulated graph as their content), edges, encapsulated graphs (i.e. graphs that support importing and exporting of nodes and edges), hierarchical structuring of complex nodes (through a node-subnode relationship), and appropriate conditions for exporting elements of a node along a hierarchy of nodes. We illustrate the introduced notions by modelling the underlying data structure of a WWW application. An advantage of graph grammar approaches over existing object-oriented approaches is that the rst allow a better coupling between the deenition of data constraints and operations. Therefore our data model should also give some insight on how to achieve such integration between constraints and operations in object-oriented data models.