A seven-tuple representation for hierarchical data structures

摘要

Different kinds of data structure diagrams, especially Bachman's, and tabular representations are very often used to visualize hierarchical data structures. The popularity of these visual modes of representation is due to the possibility they afford of describing data structures clearly and regardless of any implementation. However, it has been observed in diverse contexts that instead of the visualization we need a general and exact representation containing the same structural components as these visual representations. In this paper we introduce a seven-tuple representation which can be used for exact description of any hierarchical data structure. We give both the explicit construction operations and the implicit rules which can be utilized in forming any hierarchical data structure. We show that the formal representation introduced contains the descriptive power of the visualization methods mentioned above. Furthermore we examine how, in the context of this representation, it is possible to define flexibly general analyzing functions for hierarchical data structures.