DIFFERENTIAL RECURSIVE EVALUATION OF RECURSIVE AGGREGATES

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing differential recursive evaluation of recursive aggregates. One of the methods includes receiving an original recursive expression that defines tuples belonging to an output relation, wherein the original recursive expression has a recursive aggregation construct, the recursive aggregation construct having a range and a recursive term. An aggregates delta rule is applied to the initial delta expression to generate a final delta expression having an existential term and a gamma term. The existential term is evaluated to generate tuples related by the range and tuples in the delta relation, and the aggregation construct is evaluated using tuples generated by the existential term as the range of the aggregation construct. The output relation is updated including adding to the output relation any tuples newly generated by evaluating the final delta expression.