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

  • Robert Constable
  • Wojciech Moczydłowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4514)

Abstract

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

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Robert Constable
    • 1
  • Wojciech Moczydłowski
    • 1
  1. 1.Department of Computer Science, Cornell University, Ithaca, NY 14853USA

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