**Set and Type Denote Complementary Abstractions**

J.H. ter Bekke

**Abstract**

Abstraction can be conceived as a description of the reality in which some
details are emphasized while other details are suppressed. Abstractions can
be given in two separate ways. First by considering only object
identifications and second by considering only object properties. In data
structuring much attention has been given to the use of the set concept from
mathematics, and the definition of the concept of type is often based on it.
However, this results in descriptions in which only one kind of abstraction
appears to full advantage, and the fundamental problems arising from such an
approach justify an alternative. Independent set and type definitions result
in operations which are easily formalized and which have repercussions in the
use of these concepts in data structuring practice. The concepts denote two
complementary abstractions and form an adequate means for describing the
reality.

**Keywords:**
data abstraction, relational database, relational algebra, invariants,
set theory, set algebra, theory of types, algebra of types, data semantics.

**Publication Data**

Reports of the Department of Mathematics and Informatics, Report no. 82-11,

Delft University of Technology, Delft, The Netherlands

Year: 1982

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Reprint of the report in pdf-format [138 KB]