Controlling generalization and polyvariance in partial deduction of normal logic programs

Abstract

Given a program and some input data, partial deduction computes a specialized program handling any remaining input more efficiently. However, controlling the process well is a rather difficult problem. In this article, we elaborate global control for partial deduction: for which atoms, among possibly infinitely many, should specialized relations be produced, meanwhile guaranteeing correctness as well as termination? Our work is based on two ingredients. First, we use the concept of a characteristic tree, encapsulating specialization behavior rather than syntactic structure, to guide generalization and polyvariance, and we show how this can be done in a correct and elegant way. Second, we structure combinations of atoms and associated characteristic trees in global trees registering "causal" relationships among such pairs. This allows us to spot looming nontermination and perform proper generalization in order to avert the danger, without having to impose a depth bound on characteristic trees. The practical relevance and benefits of the work are illustrated through extensive experiments. Finally, a similar approach may improve upon current (on-line) control strategies for program transformation in general such as (positive) supercompilation of functional programs. It also seems valuable in the context of abstract interpretation to handle infinite domains of infinite height with more precision.

Program Specialization for Verifying Infinite State Systems: An Experimental Evaluation

“…An uncontrolled application of the Generalize&Fold procedure may lead to the introduction of infinitely many new definitions and, therefore, it may make the Specialize procedure not to terminate. In order to guarantee termination, we will extend to constraint logic programs some techniques which have been proposed for controlling generalization in positive supercompilation [38] and partial deduction [24,27]. More details on the Generalize&Fold procedure will be given in the next section.…”

“…These strategies combine various by now standard techniques used in the fields of program transformation and static analysis, such as well-quasi orderings, widening, and convex hull operators, and variants thereof [4,10,24,25,27,31,38]. All these strategies guarantee the termination of the Specialize procedure.…”

“…The root of the Definition Tree is labelled by clause γ 2 (recall that {γ 2 } is the initial value of InDefs) and the children of a clause γ in Defs ∪{γ 2 } are the clauses NewDefs derived after applying the procedures Unfold (γ, Γ ) and Generalize&Fold(Defs, Γ, NewDefs, Φ). Similarly to [24,25,27,38], our Generalize&Fold procedure is based on the combined use of well-quasi orderings and clause generalization operators. The wellquasi orderings determine when to generalize and guarantee that generalization is eventually applied, while generalization operators determine how to generalize and guarantee that each definition can be generalized a finite number of times only.…”

“…Now we present three wqo's between constraints in Lin k , which are based on the integer coefficients of the polynomials. The first wqo is an adaptation to Lin k of the homeomorphic embedding operator [24,25,27,38] and the other two are wqo's based on the maximum and on the sum, respectively, of the absolute values of the coefficients occurring in a constraint. (W1) The wqo HomeoCoeff, denoted by HC , compares sequences of absolute values of integer coefficients occurring in the polynomials.…”

LIX: an Effective Self-applicable Partial Evaluator for Prolog

“…Other specialisers like mixtus [27], paddy [26] and ecce [22] use the non-ground representation, but none of them are able to effectively specialise themselves.…”