Mathematical foundations of relational databases. Part 2: The properties of generalized table operations

Abstract

The article is devoted to creation of a fragment of the theory for table algebras, which constitute a generalization of classical Codd's relational algebras. A distinctive feature of this technique is that the set-theoretic properties of some specific constructions are used and transferred to the table case. Such transfer is possible because there exist simple representations of signature operations in terms of these set-theoretic constructions. The fact of these representations existence allows to get rid of some requirements to generalized table algebra: firstly, tables have not to be the finite set of rows, and secondly, rows in a table can have different schemas.