Mathematical foundations of relational databases. Part 1: presentation of the main table operations

Abstract

Article is devoted to the creation of a fragment of the theory of table algebras, which are a generalization of the classical Codd's relational algebras. A distinctive feature of the technique is the use of set-theoretic properties of the some constructions (whole image of the set with respect to the function, restriction the function over the set, the generalized Cartesian product, a binary relation of functions consistency) and their transfer to the table case. The transfer is possible because simple representations of signature operations in terms of these set-theoretic constructions are hold.