Generalizing completeness results for loop checks in logic programming

AbstractLoop checking is a mechanism for pruning infinite SLD-derivations. In (Bol, Apt and Klop, 1991) simple loop checks were introduced and their soundness, completeness and relative strength was studied. Since no sound and complete simple loop check exists even in the absence of function symbols, subclasses of programs were determined for which the (sound) loop checks introduced by Bol are complete.In this paper, the Generalization Theorem is proved. This theorem presents a method to extend (under certain conditions) a class of programs for which a given loop check is complete to a larger class, for which the loop check is still complete. Then this theorem is applied to the results of Bol, giving rise to stronger completeness theorems.It appears that unnecessary complications in the proof of the theorem can be avoided by introducing a normal form for SLD-derivations, allowing only certain most general unifiers. This normal form might have other applications than those in the area of loop checking