A Transformation System for Developing Recursive Programs

Abstract

A system of rules for transforming programs is described, with the programs in the form of recurslon equations An imtlally very simple, lucid, and hopefully correct program is transformed into a more efficient one by altering the recurslon structure Illustrative examples of program transformations are given, and a tentative implementation is described Alternative structures for programs are shown, and a possible initial phase for an automatic or semiautomatic program mampulatlon system is indicated KEY WORDS AND PHRASES program transformation, program manipulation, optimization, recursion CR CATEGORIES" 3 69, 4 12, 4 22, 5 24, 5 25

Generic Accumulations

“…This is a natural consequence of having defined downwards accumulation as an afold . For example, law dace-fold fusion follows immediately from afold-fold fusion after observing that ina 8 …”

“…In functional programming, the notion of accumulation is usually associated with the so-called accumulation technique [8,4,17,3], which transforms recursive definitions by the introduction of additional arguments over which intermediate results are computed. The accumulation technique is strongly connected with the familiar procedure of generalization for induction that arises in the field of theorem proving [7,1,26]: A proof by induction often fails because the property to be proved is too particular.…”

Transformational System Design Based on Formal Computational Model and Skeletons

“…Such kind of design methodology can reduce the overall design time and ensure the correctness of the implemented system. A great deal of the pioneering work in transformation systems was undertaken by Burstall and Darlington [6]. Their system transformed applicative recursive programs to imperative ones and their ideas have heavily influenced today's transformation systems.…”

“…• Transformation rules are primitive transformations as developed over the last three decades [6,17] Orthogonal to this we classify transformations in the following way:…”

Denotational semantics of a para-functional programming language

“…which returns the list (2,6,24). In this example it is assumed that if , =, * , −, pair, head, tail, nil and the integers are elements of Con.…”