Description of a set-theoretic data structure

The overall goal, of which this paper is a part, is the development of a machine-independent data structure allowing rapid processing of data related by arbitrary assignment such as: the contents of a telephone book, library files, census reports, family lineage, graphic displays, information retrieval systems, networks, etc. Data which are non-intrinsically related have to be expressed (stored) in such a way as to define the way in which they are related before any data structure is applicable. Since any relation can be expressed in set theory as a set of ordered pairs and since set theory provides a wealth of operations for dealing with relations, a set-theoretic data structure appears worth investigation.