Mathematical theory of partial correctness*

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In this work we show that it is possible to express most properties regularly observed in algorithms in terms of ‘partial correctness’ (i.e., the property that the final results of the algorithm, if any, satisfy some given input-output relation). This result is of special interest since ‘partial correctness’ has already been formulated in predicate calculus and in partial function logic for many classes of algorithms.

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This research was supported in part by the Advanced Research Projects Agency of the Office of the Secretary of Defense (SD-183). A preliminary version of this work was presented under the title “Second-Order Mathematical Theory of Computation” at the ACM Symposium on Theory of Computing (May 1970).