Correctness of Logic Program Transformations Based on Existential Termination

We study the relationships between the correctness of logic program transformation and program termination. We consider deenite programs and we identify somèinvariants' of the program transformation process. The validity of these invariants ensures the preservation of the success set semantics, provided that the existential termination of the initial program implies the existential termination of the nal program. We also identify invariants for the preservation of the nite failure set semantics. We consider four very general transformation rules: deenition introduction, definition elimination, ii-replacement, and nite failure. Many versions of the transformation rules proposed in the literature, including unfolding, folding, and goal replacement, are instances of the ii-replacement rule. By using our proposed invariants which are based on Clark completion, we prove, for our transformation rules, various results concerning the preservation of both the success set and nite failure set semantics. By exploiting some powerful properties of the Clark completion, we are able to derive simple proofs of these preservation results. These proofs are much simpler than those done by induction on the construction of the SLD-trees, like the ones proposed in the literature for related results.