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 topdown 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.