Combining Top-Down and Bottom-Up Techniques in Program Derivation

The traditional stepwise refinement based program derivation methodologies are primarily top-down. Strictly following the top-down program derivation approach may require backtracking resulting in rework. Moreover, the top down approach does not directly help in suggesting the next course of action in case of a failed derivation attempt. In this work we seamlessly incorporate a bottom up assumption propagation technique into a primarily top down derivation methodology. We present new tactics for back-propagating the assumptions made during the top-down phase. These tactics help in reducing the guesswork during the derivations. We have implemented these tactics in a program derivation system. With the help of simple examples, we show how this approach is useful for avoiding backtracking thereby simplifying the derivations.