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 definite programs and we identify some 'invariants' 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 final program. We also identify invariants for the preservation of the finite failure set semantics

We consider four very general transformation rules: definition introduction, definition elimination, iff-replacement, and finite failure. Many versions of the transformation rules proposed in the literature, including unfolding, folding, and goal replacement, are instances of the iff-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 finite 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