Re-grouping information in a domain-theoretic data model

Abstract

In recent years, the problem of incorporating a set-building type-constructor into a domain theoretic data model has been addressed by different authors. In Jung and Puhlmann (1995) and Puhlmann (1995) we have shown why the so-called snack powerdomain is particularly suitable for modelling a set constructor. We obtain a generalized database model that covers the nested relational model.While, with the snack powerconstruction, the data structure of domain theoretic databases seems clear, suitable operations for the data model are still to be defined.In this paper we start this task by defining the operations nest and unnest for the passage between different nesting-levels of the snack powerconstruction. These functions are shown to form an embedding-projection pair, a property that the corresponding functions of nested relational databases do not have. This demonstrates the usefulness of the domain-theoretic approach for modelling databases: for the first time we have operators for re-grouping nested data that respect the idea of an information ordering.The use of the snack powerdomain leads to fairly complex formulas. To help the reader, illustrations and pictorial interpretations of formulas are given throughout the paper.