DEALING WITH SIDE EFFECTS OF TRANSACTIONS IN DATA BASE SYSTEMS USING A MULTI-SET ALGEBRA

Apparatus and methods for reducing the amount of computation required to determine the consequences of a side effect resulting from a transaction on a relation in a data base system. The apparatus and methods use equational reasoning based on a bag algebra representation of a class of transaction and the relation to produce a pre-expression which describes the side effect. The pre-expression is included in the data base system's data dictionary, and when a transaction of the class is received in the data base system, the pre-expression is used to determine the side effect. The pre-expression is formed with a strongly-minimal pair of delete and insert bags. The apparatus and methods may be used to maintain materialized views, to check for violation of constraints on the data base, and to activate triggers, monitors, and active queries.