Program Correctness: Strategies

Abstract

As in other applications of mathematical induction (see Example 4.1), the main challenge in applying the inductive assertion method is discovering extra information to make the inductive argument succeed. Consider a typical partial correctness property that asserts that a function’s output satisfies some relation with its input. Assuming this property as the inductive hypothesis does not provide any information about how the function behaves between entry and exit. It is a weak hypothesis. Therefore, one must provide more information about the function in the form of additional program annotations. Section 6.1 discusses strategies for discovering this additional information. Section 6.2 applies the strategies to prove that QuickSort always returns a sorted array.