Optimal Groundness Analysis Using Propositional Logic

It is well known that propositional formulas form a useful and computationally efficient abstract interpretation for different data-flow analyses of logic programs and, in particular, for groundness analysis. This article gives a complete and precise description of an abstract interpretation, called Prop, composed of a domain of positive, propositional formulas and three operations: abstract unification, least upper bound, and abstract projection. All three abstract operations are known to be correct. They are shown to be optimal in the classical sense. Two alternative stronger notions of optimality of abstract operations are introduced, which characterize very precise analyses. We determine whether the operations of Prop also satisfy these stronger forms of optimality.

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