Structured Programming with go to Statements
ACM Computing Surveys (CSUR)
An axiomatic basis for computer programming
Communications of the ACM
Some transformations for developing recursive programs
Proceedings of the international conference on Reliable software
Mathematical Theory of Computation
Mathematical Theory of Computation
A critique of the foundations of Hoare style programming logics
Communications of the ACM
Nondeterminism in logics of programs
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Recursion in logics of programs
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Computability and completeness in logics of programs (Preliminary Report)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
A proof-checker for dynamic logic
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
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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.