On the Mechanical Derivation of Loop Invariants

We describe an iterative algorithm for mechanically deriving loop invariants \u000Afor the purpose of proving the partial correctness of programs. The algorithm \u000Ais based on resolution and a novel unskolemization technique for deriving \u000Alogical consequences of first‐order formulas. Our method is complete in the \u000Asense that if a loop invariant exists for a loop in a given first‐order \u000Alanguage relative to a given finite set of first‐order axioms, then the \u000Aalgorithm produces a loop invariant for that loop which can be used for proving \u000Athe partial correctness of the program. Existing techniques in the literature \u000Aare not complete