On Inductive and Coinductive Proofs via Unfold/Fold Transformations

We consider a new application condition of negative unfolding, which guarantees its safe use in unfold/fold transformation of stratified logic programs. The new condition of negative unfolding is a natural one, since it is considered as a special case of replacement rule. The correctness of our unfold/fold transformation system in the sense of the perfect model semantics is proved. We then consider the coinductive proof rules proposed by Jaffar et al. We show that our unfold/fold transformation system, when used together with Lloyd-Topor transformation, can prove a proof problem which is provable by the coinductive proof rules by Jaffar et al. To this end, we propose a new replacement rule, called sowed replacement, which is not necessarily equivalence-preserving, but is essential to perform a reasoning step corresponding to coinduction.