Extracting the Resolution Algorithm from a Completeness
Proof for the Propositional Calculus.
Previous Versions: Cornell Digital Repository: http://dspace.library.cornell.edu/handle/1813/5754
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.
We prove constructively that for any propositional formula Ø in Conjunctive Normal Form, we can either find a satisfying assignment of true and false to its variables, or a refutation of Ø showing that it is unsatisfiable. T his refutation is a resolution proof of ¬Ø. 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.