On the mechanical derivation of loop invariants

Authors:
Ritu Chadha;David A. Plaisted
Affiliations:
Bell Communications Research, Morristown NJ, U.S.A.;Department of Computer Science, University of North Carolina at Chapel Hill, U.S.A.
Venue:
Journal of Symbolic Computation - Special issue on automatic programming
Year:
1993

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Abstract

We describe an iterative algorithm for mechanically deriving loop invariants for the purpose of proving the partial correctness of programs. The algorithm is based on resolution and a novel unskolemization technique for deriving logical consequences of first-order formulas. Our method is complete in the sense that if a loop invariant exists for a loop in a given first-order language relative to a given finite set of first-order axioms, then the algorithm produces a loop invariant for that loop which can be used for proving the partial correctness of the program. Existing techniques in the literature are not complete.