Program derivation with verified transformations — a case study

Abstract

AbstractA program development methodology based on verified program transformations is described and illustrated through derivations of a high level bisimulation algorithm and an improved minimum‐state DFA algorithm. Certain doubts that were raised about the correctness of an initial paper‐and‐pencil derivation of the DFA minimization algorithm were laid to rest by machine‐checked formal proofs of the most difficult derivational steps. Although the protracted labor involved in designing and checking these proofs was almost overwhelming, the expense was somewhat offset by a successful reuse of major portions of these proofs. In particular, the DFA minimization algorithm is obtained by specializing and then extending the last step in the derivation of the high level bisimulation algorithm.Our experience suggests that a major focus of future research should be aimed towards improving the technology of machine checkable proofs — their construction, presentation, and reuse. This paper demonstrates the importance of such a technology to the verification of programs and program transformations. We believe that the utility of transformational systems to program development will ultimately rest on a practical program correctness technology. © 1996 John Wiley & Sons, Inc.