Set and Type Denote Complementary Abstractions
J.H. ter Bekke
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.
Reports of the Department of Mathematics and Informatics, Report no. 82-11,
Delft University of Technology, Delft, The Netherlands
From the personal digital library:
Reprint of the report in pdf-format [138 KB]