Narrowing vs. SLD-resolution

Proceedings of 1994 IEEE International Conference on Computer Languages (ICCL'94)

Ramis³

et al.

This paper considers compositions of conditional term rewriting systems as a basis for a modular approach to the design and analysis of equational logic programs. In this context, an equational logic program is viewed as consisting of a set of modules, each module defining a part of the program's functions. We define a compositional semantics for conditional term rewriting systems which we show to be rich enough to capture computational properties related to the use of logical variables. We also study how such a semantics may be safely approximated, and how the results of such approximations may be composed to yield a bottom-up abstract semantics adequate for modular data-flow analysis. A compositional analysis for equational unsatisfiability illustrates our approach.General topics: Theory/semantics, functional/logic languages, abstract interpretation.

“…Note that this definition essentially coincides with the one reported in [7,23], with unimportant modifications aimed at facilitating the subsequent definitions and proofs.…”

Section: Operational Semanticssupporting

confidence: 64%

“…, n. A flat equation set is a set of flat equations. Any set of equations S can be transformed into an equivalent one, f lat(S), which is flat [7,23]. For a given program E, C < < E denotes that C is a new variant of a clause in E such that C contains no variable previously met (standardised apart).…”

Section: Preliminariesmentioning

confidence: 99%

A compositional semantics for conditional term rewriting systems

Proceedings of 1994 IEEE International Conference on Computer Languages (ICCL'94)

Ramis³

et al.

“…, x n ) = x n+1 or x n = x n+1 , where x i = x j for all i = j. Any goal g can be transformed into an equivalent one, flat(g), which is flat [5].…”

Section: Operational Semanticsmentioning

confidence: 99%

Safe folding/unfolding with conditional narrowing

Algebraic and Logic Programming

Moreno

et al. 1997

Abstract. Functional logic languages with a complete operational semantics are based on narrowing, a generalization of term rewriting where unification replaces matching. In this paper, we study the semantic properties of a general transformation technique called unfolding in the context of functional logic languages. Unfolding a program is defined as the application of narrowing steps to the calls in the program rules in some appropriate form. We show that, unlike the case of pure logic or pure functional programs, where unfolding is correct w.r.t. practically all available semantics, unrestricted unfolding using narrowing does not preserve program meaning, even when we consider the weakest notion of semantics the program can be given. We single out the conditions which guarantee that an equivalent program w.r.t. the semantics of computed answers is produced. Then, we study the combination of this technique with a folding transformation rule in the case of innermost conditional narrowing, and prove that the resulting transformation still preserves the computed answer semantics of the initial program, under the usual conditions for the completeness of innermost conditional narrowing. We also discuss a relationship between unfold/fold transformations and partial evaluation of functional logic programs.

“…In this context, completeness means that for every solution to a given set of equations, a more general solution can be found by narrowing. Since unrestricted narrowing has quite a large search space, several strategies to control the selection of redexes have been devised to improve the efficiency of narrowing by getting rid of some useless derivations [7,15,16,21]. Narrowing at only basic positions has been proven to be a complete method for solving equations in the theory defined by a level-canonical conditional term rewriting system [14,15,16,21,22].…”

Section: Introductionmentioning

confidence: 99%

“…Narrowing at only basic positions has been proven to be a complete method for solving equations in the theory defined by a level-canonical conditional term rewriting system [14,15,16,21,22]. In [7,14], a further refinement is considered which derives from simulating SLD-resolution on flattened equations and in which the search reduces to an innermost selection strategy.…”

Section: Introductionmentioning

confidence: 99%

Narrowing approximations as an optimization for equational logic programs

Lecture Notes in Computer Science

Ramis

et al. 1993

Solving equations in equational theories is a relevant programming paradigm which integrates logic and equational programming into one unified framework. Efficient methods based on narrowing strategies to solve systems of equations have been devised. In this paper, we formulate a narrowing-based equation solving calculus which makes use of a top-down abstract interpretation strategy to control the branching of the search tree. We define a refined, but still complete, equation solving procedure which allows us to reduce the branching factor. Our main idea consists of building an abstract narrower for equational theories and executing the set of equations to be solved in the approximated narrower. We prove that the set of answers computed by the abstract narrower has the property that each concrete solution of the set of equations is an instance of one of the substitutions in the answer set. Thus we define a strategy which computes such a set and uses the substitutions in it for cutting down the search space of the program without losing completeness. We also report on experimental results which demonstrate that our optimization can result in significant speed-ups in program execution.