Partial Algebras and Their Theories (Hardcover)

The concept of dht-symmetric categories was introduced as a language that permits calculation (algebraic manipulation) with partial functions. Programs able to carry out performations in a suitable termal language (especially within term-rewriting systems) will be based on their rules. The object-oriented programming in use today has its algebraic counterpart in an algebraic system originally introduced by A.I. Malbcev, but in practice mainly partial functions occur. Any calculus based on dht-symmetric categories may be as successful as relational database systems with the SQL language, supported by the category of relations and the calculus of relations. The recognition of this connection was the decisive reason behind Oraclebs worldwide business success. This rather new theoretical feature is proof of the categorical equivalence of partial theories, partial Dale monoids, and Malbcev clones. Each one of them may serve, for instance, as a defining invariant for a constructive classification of varieties of partial algebras.