gapt.proofs.lk.transformations.cleanCuts.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.proofs.lk.transformations

import gapt.proofs.Ant
import gapt.proofs.SequentConnector
import gapt.proofs.Suc
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.LKVisitor
import gapt.proofs.lk.rules.CutRule
import gapt.proofs.lk.rules.LogicalAxiom

/**
 * Algorithm that removes some unnecessary cuts.
 * At the moment it only removes cuts where one of the premises is a logical axiom.
 */
object cleanCuts {

  def apply(p: LKProof): LKProof = cleanCutsVisitor(p, ())

  private object cleanCutsVisitor extends LKVisitor[Unit] {

    override def visitCut(p: CutRule, otherArg: Unit): (LKProof, SequentConnector) = {
      val CutRule(leftSubProof, aux1, rightSubProof, aux2) = p

      (leftSubProof, rightSubProof) match {
        case (LogicalAxiom(_), _) =>
          val (subProofNew, subConnector) = recurse(rightSubProof, ())
          (
            subProofNew,
            subConnector * p.getRightSequentConnector.inv.+(
              subConnector.child(aux2),
              p.getLeftSequentConnector.child(Ant(0))
            )
          )

        case (_, LogicalAxiom(_)) =>
          val (subProofNew, subConnector) = recurse(leftSubProof, ())
          (
            subProofNew,
            subConnector * p.getLeftSequentConnector.inv.+(
              subConnector.child(aux1),
              p.getRightSequentConnector.child(Suc(0))
            )
          )

        case _ => super.visitCut(p, ())
      }
    }

  }

}