Abstract
This paper gives a theoretical foundation for partial evaluation in logic programming. Let P be a normal program, G a normal goal, A a finite set of atoms, and P ′ a partial evaluation of P wrt A. We study, for both the declarative and procedural semantics, conditions under which P ′ is sound and complete wrt P for the goal G. We identify two relevant conditions, those of closedness and independence. For the procedural semantics, we show that, if P ′ ∪ { G} is A-closed and A is independent, then P ′ is sound and complete wrt P for the goal G. For the declarative semantics, we show that, if P ′ ∪ { G} is A-closed, then P ′ is sound wrt P for the goal G. However, we show that, unless strong conditions are imposed, we do not have completeness for the declarative semantics. A practical consequence of our results is that partial evaluators should enforce the closedness and independence conditions.
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