Extracting the Resolution Algorithm from a Completeness Proof for the Propositional Calculus.

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by Wojciech Moczydlowski and Robert L. Constable

Cornell University Technical Report 2006-2061. Proceedings of Symposium on Logical Foundations of Computer Science (LFCS 2007), LNCS 4514, 147-161, Springer. Invited to the special issue of Annals of Pure and Applied Logic.

Abstract

We prove constructively that for any propositional formula in Conjunctive Normal Form, we can either find a satisfying assignment of true and false to its variables, or a refutation of showing that it is unsatisfiable. T his refutation is a resolution proof of From the formalization of our proof in Coq, we extract Robinson's famous resolution algorithm as a Haskell program correct by construction.  The account is an example of the genre of highly readable formalized mathematics.