Transformation of Logic Programs

Abstract

Program transformation is a methodology for deriving correct and efficient programs from specifications. In this chapter, we will look at the so called ’rules + strategies’ approach, and we will report on the main techniques which have been introduced in the literature for that approach, in the case of logic programs. We will also present some examples of program transformation, and we hope that through those examples the reader may acquire some familiarity with the techniques we will describe. The program transformation approach to the development of programs has been first advocated in the case of functional languages by Burstall and Darlington [1977]. In that seminal paper the authors give a comprehensive account of some basic transformation techniques which they had already presented in [Darlington, 1972; Burstall and Darlington, 1975]. Similar techniques were also developed in the case of logic languages by Clark and Sickel [1977], and Hogger [1981], who investigated the use of predicate logic as a language for both program specification and program derivation. In the transformation approach the task of writing a correct and efficient program is realized in two phases. The first phase consists in writing an initial, maybe inefficient, program whose correctness can easily be shown, and the second phase, possibly divided into various subphases, consists in transforming the initial program with the objective of deriving a new program which is more efficient. The separation of the correctness concern from the efficiency concern is one of the major advantages of the transformation methodology. Indeed, using this methodology one may avoid some difficulties often encountered in other approaches. One such difficulty, which may occur when following the stepwise refinement approach, is the design of the invariant assertions, which may be quite intricate, especially when developing very efficient programs. The experience gained during the past two decades or so shows that the methodology of program transformation is very valuable and attractive, in particular for the task of programming ‘in the small’, that is, for writing single modules of large software systems.