Efficient Bottom-Up Execution of Logic Programs Using Abstract Interpretation

B o t t o m u p evaluation of logic programs has recently at tracted much attention in the logic programming and the deductive database field. It is complete [7], and if the number of all possible facts is finite, it is guaranteed to terminate, while t op -down evaluation may not. B o t t o m u p evaluation, however, may be inefficient since it may generate many facts irrelevant to the query. To overcome this drawback, a number of optimization strategies have been proposed on seminaive b o t t o m u p evaluation [1,6,7,9]. Filtering is a query optimization strategy based on the seminaive evaluation on system graphs, which evaluates a query in terms of the b o t t o m u p data flow on system graphs. Filtering methods try to restrict data flow on system graphs as much as possible by means of filters, which are selections attached on arcs of system graphs [3,6,7]. Static filtering restricts data flow using static filters which are computed at compile-time by propagating dataindependent bindings. Dynamic filtering uses dynamic filters which are computed by propagating "actual data" generated during evaluation [6]. In this paper, we propose a new filter called abstract fil ter which is computed at compile time using the result of a two-phase abstract interpretation. The two-phase abstract interpretation consists of a b o t t o m u p phase followed by a t op -down one, and it provides an approximation of (possibly nonground) success pat terns relevant to a given query. The b o t t o m u p phase extends the b o t t o m u p abstract interpretation in [2] following the f ramework in [8]. A two-phase abstract interpretation is not a new idea in this area even though it has not been published in our form. The abstract filter prevents facts not in that approximation from being passed in the evaluation of system graphs. From a theoretical point of view, the abstract filter is shown to be at least as powerful as the static filter under some assumption. The next section gives preliminaries. Section 3 describe filtering on system graphs. Section 4 describes abstract interpretation. In Section 5, the abstract filter is computed. Section 6 concludes the paper.