From 3735b033da730f532de39af4c069f3a0d00e6484 Mon Sep 17 00:00:00 2001 From: Lachnitt Date: Tue, 26 Oct 2021 04:46:26 -0700 Subject: [PATCH] [proofs] Alethe: Translate NOT_NOT_ELIM rule (#7402) Implementation of the translation of NOT_NOT_ELIM rules into the Alethe calculus. Co-authored-by: Haniel Barbosa --- src/proof/alethe/alethe_post_processor.cpp | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/src/proof/alethe/alethe_post_processor.cpp b/src/proof/alethe/alethe_post_processor.cpp index 167b885f4..dd2927ead 100644 --- a/src/proof/alethe/alethe_post_processor.cpp +++ b/src/proof/alethe/alethe_post_processor.cpp @@ -909,6 +909,28 @@ bool AletheProofPostprocessCallback::update(Node res, {}, *cdp); } + // ======== Double negation elimination + // See proof_rule.h for documentation on the NOT_NOT_ELIM rule. This comment + // uses variable names as introduced there. + // + // ---------------------------------- NOT_NOT + // (VP1:(cl (not (not (not F))) F)) (P:(not (not F))) + // ------------------------------------------------------------- RESOLUTION + // (cl F)* + // + // * the corresponding proof node is F + case PfRule::NOT_NOT_ELIM: + { + Node vp1 = nm->mkNode(kind::SEXPR, d_cl, children[0].notNode(), res); + + return addAletheStep(AletheRule::NOT_NOT, vp1, vp1, {}, {}, *cdp) + && addAletheStep(AletheRule::RESOLUTION, + res, + nm->mkNode(kind::SEXPR, d_cl, res), + {vp1, children[0]}, + {}, + *cdp); + } default: { return addAletheStep(AletheRule::UNDEFINED, -- 2.30.2