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Classical Propositional Decidability via Nuprl Proof Extraction
 THEOREM PROVING IN HIGER ORDER LOGICS, VOLUME 1479 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... This paper highlights a methodology of Nuprl proof that results in efficient programs that are more readable than those produced by other established methods for extracting programs from proofs. We describe a formal constructive proof of the decidability of a sequent calculus for classical pro ..."
Abstract

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This paper highlights a methodology of Nuprl proof that results in efficient programs that are more readable than those produced by other established methods for extracting programs from proofs. We describe a formal constructive proof of the decidability of a sequent calculus for classical propositional logic. The proof is implemented in the Nuprl system and the resulting proof object yields a "correctbyconstruction" program for deciding propositional sequents. If the sequent is valid, the program reports that fact; otherwise, the program returns a counterexample in the form of a falsifying assignment. We employ Kleene's strong threevalued logic to give more informativecounterexamples, it is also shown how this semantics agrees with the standard twovalued presentation.