Classical propositional decidability via Nuprl proof extraction

Abstract

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 “correct-by-construction≓ program for deciding propositional sequents. If the sequent is valid, the program reports that fact; otherwise, the program returns a counter-example in the form of a falsifying assignment. We employ Kleene's strong three-valued logic to give more informative counter-examples, it is also shown how this semantics agrees with the standard two-valued presentation.

Part of this work was performed while the author was a member of the Formal Methods Group at NASA Langley Research Center in Hampton VA.