Francis Alexandre

Spes: A System for Logic Program Transformation

Spes is an interactive system for transforming logic programs. It is intended as a formal tool for transforming Horn clauses specifications into correct and more efficient programs. The main transformations used in the Spes system are Unfolding and Folding.

On Using Mode Input-output for Transforming Logic Programs

This paper discusses the transformation of logic programs by using mode input-output. We consider a system based on the Unfold/Fold transformations. First we introduce a notion of well-moded clause and well-moded definite program. We prove that under certain conditions the application of the Unfold/Fold transformations preserves the notion of well-modedness. We also define a transformation of a definite program into term rewriting system and we establish the correctness of this transformation.

A technique for Transforming Logic Programs by Fold-Unfold Transformations

This paper deals with the logic program transformation using the fold-unfold technique. The major problem in the strategies using fold-unfold transformation is to find a sequence of unfolding that permits the folding. In this paper we propose a technique that solves this problem for a particular class of logic programs. This technique consists in studying the possibility of folding for some simple or basic programs and then to apply these results for some more general logic programs. This technique permits to compute the sequence of unfolding to achieve a folding or to detect the impossibility of a folding, in the latter case the technique permits the invention of new predicates.

Predicate Synthesis from Inductive Proof Attempt of Faulty Conjectures

We present a method for patching faulty conjectures in automatic theorem proving. The method is based on well-known folding /unfolding deduction rules. The conjectures we are interested in here are implicative formulas that are of the following form: \(\forall \overline{x} \phi( \overline{ x})=\forall \overline{x} \exists \overline{Y} \Gamma(\overline{x},\overline{Y}) \leftarrow \Delta(\overline{x})\). A faulty conjecture is a statement \(\forall \overline{x} \phi( \overline{x})\), which is not provable in some given program \({\cal T}\), defining all the predicates occurring in φ, i.e, \({\cal M(T)}\not \models \forall \overline{x} \phi( \overline{ x})\), where \({\cal M(T)}\) means the least Herbrand model of \({\cal T}\), but it would be if enough conditions, say P, were assumed to hold, i.e., \({\cal M(T\cup P)}\models \forall \overline{x} \phi( \overline{x})\leftarrow P\), where \({\cal P}\) is the definition of P. The missing hypothesis P is called a corrective predicate for φ. To construct P, we use the abduction mechanism that is the process of hypothesis formation. In this paper, we use the logic based approach because it is suitable for the application of deductive rules.