Is “sometime” sometimes better than “always”?: Intermittent assertions in proving program correctness

This paper explores a technique for proving the correctness and termination of programs simultaneously. This approach, which we call the intermittent-assertion method, involves documenting the program with assertions that must be true at some time when control is passing through the corresponding point, but that need not be true every time. The method, introduced by Knuth and further developed by Burstall, promises to provide a valuable complement to the more conventional methods. We first introduce and illustrate the technique with a number of examples. We then show that a correctness proof using the invariant assertion method can always be expressed using intermittent assertions instead, but argue that the reverse is not always the case. The method can also be used just to prove termination, and any proof of termination using the conventional well-founded sets approach can be rephrased as a proof using intermittent assertions. Finally, we show how the method can be applied to prove the validity of program transformations and the correctness of continuously operating programs. This research was supported in part by the Advanced Research Projects Agency of the Department of Defense under Contract DAHC15-73-C-0435, by the National Science Foundation under Grant GJ-36146, by the Office of Naval Research under Contract N00014-75-C-0816, and by a grant from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.