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A Folding Rule for Eliminating Existential Variables from Constraint Logic Programs

Senni V., Pettorossi A., Proietti M.

Fundamenta Informaticae

2009

Vol. 96, nr 3

373-393

The existential variables of a clause in a constraint logic program are the variables which occur in the body of the clause and not in its head. The elimination of these variables is a transformation technique which is often used for improving program efficiency and verifying program properties. We consider a folding transformation rule which ensures the elimination of existential variables and we propose an algorithm for applying this rule in the case where the constraints are linear inequations over rational or real numbers. The algorithm combines techniques for matching terms modulo equational theories and techniques for solving systems of linear inequations. Through some examples we show that an implementation of our folding algorithm has a good performance in practice.

A Multiple-Clause Folding Rule Using Instantiation and Generalization

Rosenblueth D.A.

Fundamenta Informaticae

2006

Vol. 69, nr 1,2

219-249

A program-transformation system is determined by a repertoire of correctness-preserving rules, such as folding and unfolding. Normally, we would like the folding rule to be in some sense the inverse of the unfolding rule. Typically, however, the folding rule of logic program transformation systems is an inverse of a limited kind of unfolding. In many cases this limited kind of folding suffices. We argue, nevertheless, that it is both important and possible to extend such a folding so as to be able to fold the clauses resulting from any unfolding of a positive literal. This extended folding rule allows us to derive some programs underivable by the existing version of this rule alone. In addition, our folding rule has applications to decompilation and reengineering, where we are interested in obtaining high-level program constructs from low-level program constructs. Moreover, we establish a connection between logic program transformation and inductive logic programming. This connection stems from viewing our folding rule as a common extension of the existing multiple-clause folding rule, on the one hand, and an operator devised in inductive logic programming, called ``intra-construction,'' on the other hand. Hence, our folding rule can be regarded as a step towards incorporating inductive inference into logic program transformation. We prove correctness with respect to Dung and Kanchanasut's semantic kernel.