Transformations of CLP modules

Abstract

We propose a transformation system for Constraint Logic Programming (CLP) programs and modules. The framework is inspired by the one of Tamaki and Sato (1984) for pure logic programs. However, the use of CLP allows us to introduce some new operations such as splitting and constraint replacement. We provide two sets of applicability conditions. The first one guarantees that the original and the transformed programs have the same computational behaviour, in terms of answer constraints. The second set contains more restrictive conditions that ensure compositional#y: we prove that under these conditions the original and the transformed modules have the same answer constraints also when they are composed with other modules. This result is proved by first introducing a new formulation, in terms of trees, of a resultants semantics for CLP. As corollaries we obtain the correctness of both the modular and the nonmodular system w.r.t, the least model semantics.

A Folding Algorithm for Eliminating Existential Variables from Constraint Logic Programs

“…In this section we introduce our folding transformation rule which is a variant of the rules considered in the literature [7,8,9,10]. In particular, by using our variant of the folding rule we may replace a constrained goal occurring in the body of a clause where some existential variables occur, by an atom which has no existential variables in the folded clause.…”

“…This technique makes use of the definition, unfolding, and folding rules [5,6,7,8,9,10]. In this paper we have considered constraint logic programs, where the constraints are linear inequations over the rational (or real) numbers, and we have focused on the problem of automating the application of the folding rule.…”

“…The transformation techniques for the elimination of the existential variables make use of the unfolding and folding rules which have been first proposed in the context of functional programming by Burstall and Darlington [4], and then extended to logic programming [5,6] and to constraint logic programming [7,8,9,10]. In the techniques for eliminating existential variables a particularly relevant role is played by the folding rule, which can be defined as follows.…”

Using Real Relaxations during Program Specialization

“…In order to do so, we need: (i) a suitable reformulation of the familiar unfold/fold transformation rules for CLP programs [14,18] so that: (i.1) the applicability conditions of the rules are based on the satisfiability or entailment of constraints over the reals R, and (i.2) every application of the rules transforms a given program into a new program with the same perfect model constructed over the integers Z, called perfect Z-model, and then (ii) the introduction of a transformation strategy which applies the reformulated transformation rules for specializing a given CLP(Z) program with respect to a given query.…”

Safe folding/unfolding with conditional narrowing

“…A lot of literature has been devoted to proving the correctness of unfold/fold systems w.r.t. the various semantics proposed for functional programs [7,20], logic programs [18,25,27,28], and constraint logic programs [12]. However, to the best of our knowledge, these techniques have not been studied for functional logic programs so far.…”