On Safe Folding

In [3] a general fold operation has been introduced for definite programs wrt computed answer substitution semantics. It differs from the fold operation defined by Tamaki and Sato in [26,25] because its application does not depend on the transformation history. This paper extends the results in [3] by giving a more powerful sufficient condition for the preservation of computed answer substitutions. Such a condition is meant to deal with the critical case when the atom introduced by folding depends on the clause to which the fold applies. The condition compares the dependency degree between the fonding atom and the folded clause, with the semantic delay between the folding atom and the ones to be folded. The result is also extended to a more general replacement operation, by showing that it can be decomposed into a sequence of definition, general folding and unfolding operations.