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

Authors:
Robert Constable;Wojciech Moczydłowski
Affiliations:
Department of Computer Science, Cornell University, Ithaca, NY 14853, USA;Department of Computer Science, Cornell University, Ithaca, NY 14853, USA
Venue:
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Year:
2007

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Abstract

We prove constructively that for any propositional formula 驴in Conjunctive Normal Form, we can either find a satisfying assignment of true and false to its variables, or a refutation of 驴showing that it is unsatisfiable. This refutation is a resolution proof of ¬驴. 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.