1. A method employed in a data base system of determining a side effect on the data base system of a transaction on a relation in the data base system, the method comprising the steps of: receiving a description of the transaction in terms of the relation; transforming the description in accordance with a set of change propagation equations which correctly deal with duplicates to produce a pre-expression which specifies the side effect; and responding to the transaction by producing the side effect specified in the pre-expression.