Non-Termination Inference for Optimal Ter- mination Conditions of Logic Programs

ABSTRACT. In this paper, we present an approach to non-termination inference of logic programs. Our framework relies on an extension of the Lifting Theorem, where some specific argument po-sitions can be instantiated while others are generalized. Atomic left looping queries are then generated bottom-up from selected subsets of the binary unfoldings of the program of interest. Then non-termination inference is tailored to attempt proofs of optimality of left termination conditions computed by a termination inference tool. For each class of atomic queries not cov-ered by a termination condition, the aim is to ensure the existence of one query from this class which leads to an infinite search tree. When termination and non-termination analysis produce complementary results for a logic pro-cedure, they induce a characterization of the operational behavior of the logic procedure with respect to the left most selection rule and the language used to describe sets of atomic queries. RÉSUMÉ. Dans cet article, nous présentons une technique d’inférence de conditions de non-termination de programmes logiques. Notre travail repose sur une extension du “Lifting Theo-rem”, où des positions d’argument spécifiques peuvent être instanciées alors que les autres sont généralisées. Des requêtes atomiques qui bouclent à gauche sont alors générées de façon as