Towards programming as a mathematical activity

Of the various approaches to program correctness, that of "Transformational Programming " appears to be the most helpful i n constructing correct pro-grams. T he essence of the method is to start with an obviously correct—but possibly hopelessly inefficient—algorithm, and to improve i t by successively applying correctness-preserving transformations. T he manipulations involved are akin to those used in mathematics. T w o important impediments to this method are the verbosity of algorithmic notations, making the process cumber-some, and the semantic baroqueness of many primitives, making it hard to ver-ify the validity of transformations. Computer Science can profit here from the lessons taught by the history of Mathematics. Another major step, comparable to one made long ago in Mathematics, is not to insist on the "executability " of algorithmic descriptions. This makes it possible to treat initial high-level specifi-cations in the same framework as the final programs. J us t as Mathematics evolved fr om "Transformational Arithmetic", Transformational Programming may come of age as "Algorithmics". Mathematical reasoning does play an essential role in all areas of computer science which have developed or are developing from an art to a science. Where such reason-ing plays litt le or no role in an area of computer science, that portion of our discipline is st ill in its infancy and needs the support of mathematical thinking i f i t is t o mature. RALsToN and SHAW [25] O