A system of rules for transforming programs is described, with the programs in the form of recursion equations An initially very simple, lucid. and hopefully correct program IS transformed into a more efficient one by altering the recursion structure Illustrative examples of program transformations are given, and a tentative implementation !s described Alternative structures for programs are shown, and a possible initial phase for an automatic or semiautomatic program manipulation system is lndmated KEY WORDS AND PHRASES program transformation, program mampulatlon, optimization, recursion CR CATEGORIES' 3 69, 4 12, 4 22, 5 24, 5 25 1.

Abstract. We present the theoretical aspects and a prototype implementation in the Theorema system of a method for the verification of recursive imperative programs. The method is based on forward symbolic execution and functional semantics and generates first order verification conditions for the total correctness which use only the underlying theory of the program. All verification conditions are generated automatically by our prototype implementation in the frame of the Theorema system based on Mathematica. The termination property is expressed as an induction principle depending on the structure of the program with respect to recursion. It turns out that part of the verification conditions (notably the termination condition) are crucial for the existence of the function defined by the program, without which the total correctness formula is trivial due to inconsistency of the assumptions. The formal description of the method is the basis for the implementation and also for the proof of its correctness. 1

Program transformation has been advocated as a potentially appropriate methodology for program development. The ability to transform large programs is crucial to the practicality of such an approach. This paper describes research directed toward applying one particular transformation method to problems of increasing scale. The method adopted is that developed by Burstall and Darlington, and familiarity with their work is assumed. The problems which arise when attempting transformation of larger scale programs are discussed, and an approach to overcoming them is presented. Parts of the approach have been embodied in a machine-based system which assists a user in transforming his programs. The approach, and the use of this system, are illustrated by presenting portions of the transformation of a compiler for a "toy" language.

Abstract not found