An Almost Perfect Abstraction Operator for Partial Deduction

A partial deduction strategy for logic programs usually uses an abstraction operator to guarantee the niteness of the set of goals for which partial deductions are produced. Finding an abstraction operator which guarantees niteness and still does not loose relevant information (with respect to the partial deduction) is a diicult problem. In 4] and 7] Gallagher and Bruynooghe proposed to base the abstraction operator on characteristic paths and trees. A characteristic tree captures the structure of the generated partial SLDNF-tree for a given goal, i.e. it captures the relevant information for partial deduction. The generation of more general atoms having the same characteristic tree would lead to an almost perfect abstraction operator. Unfortunately the abstraction operators proposed in 4] and 7] do not always produce more general atoms and do not always preserve the characteristic trees. In this paper we propose to solve this problem through the use of constraints in the partial deduction process. We show that satissability of these constraints is decidable and that they do not introduce a termination problem of their own. We will thus present a partial deduction strategy which has an almost perfect abstraction operator. almost perfect control of polyvariance. always terminates while ensuring the closedness and independence conditions (slightly adapted to allow constraints) of 12].