gapt.provers.ResolutionProver.scala Maven / Gradle / Ivy

Go to download
Show more of this group Show more artifacts with this name
Show all versions of gapt_3 Show documentation
General Architecture for Proof Theory
The newest version!
package gapt.provers

import gapt.expr._
import gapt.expr.formula.Atom
import gapt.expr.formula.Formula
import gapt.proofs.expansion.ExpansionProof
import gapt.proofs.expansion.ExpansionProofToLK
import gapt.proofs.expansion.deskolemizeET
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.lkProofReplaceable
import gapt.proofs.resolution.Input
import gapt.proofs.resolution.ResolutionProof
import gapt.proofs.resolution.ResolutionToExpansionProof
import gapt.proofs.resolution.ResolutionToLKProof
import gapt.proofs.resolution.eliminateSplitting
import gapt.proofs.resolution.mapInputClauses
import gapt.proofs.resolution.structuralCNF
import gapt.proofs.ContextSection
import gapt.proofs.HOLClause
import gapt.proofs.HOLSequent
import gapt.proofs.Sequent
import gapt.proofs.context.Context
import gapt.proofs.context.mutable.MutableContext
import gapt.proofs.lk.rules.macros.WeakeningContractionMacroRule
import gapt.proofs.withSection
import gapt.utils.Maybe

trait ResolutionProver extends OneShotProver { self =>

  override def getLKProof(seq: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[LKProof] = getLKProof(seq, addWeakenings = true)

  def getLKProof(seq0: HOLSequent, addWeakenings: Boolean)(implicit ctx0: Maybe[MutableContext]): Option[LKProof] = {
    implicit val ctx: MutableContext = ctx0.getOrElse(MutableContext.guess(seq0))
    withSection { section =>
      val seq = section.groundSequent(seq0)
      getResolutionProof(seq)(ctx) map { resolution =>
        val lk = ResolutionToLKProof(resolution)
        if (addWeakenings) WeakeningContractionMacroRule(lk, seq)
        else lk
      }
    }
  }

  override def isValid(seq: HOLSequent)(implicit ctx: Maybe[Context]): Boolean =
    getResolutionProof(seq)(ctx.map(_.newMutable)).isDefined

  def getResolutionProof(cnf: Iterable[ResolutionProof])(implicit ctx: Maybe[MutableContext], dummyImplicit: DummyImplicit): Option[ResolutionProof] = {
    val cnfMap = cnf.view.map(p => p.conclusion -> p).toMap
    getResolutionProof(cnfMap.keySet.map(_.map(_.asInstanceOf[Atom]))) map { resolution =>
      mapInputClauses(resolution)(cnfMap)
    }
  }

  def getResolutionProof(sequentSet: Iterable[HOLSequent])(implicit ctx0: Maybe[MutableContext], dummyImplicit1: DummyImplicit, dummyImplicit2: DummyImplicit): Option[ResolutionProof] = {
    implicit val ctx = ctx0.getOrElse(MutableContext.guess(sequentSet)(dummyImplicit1))
    val cnf = structuralCNF.onProofs(
      sequentSet.map(Input.apply).toSet,
      propositional = false,
      structural = true,
      bidirectionalDefs = false,
      cse = false
    )
    getResolutionProof(cnf)(ctx, dummyImplicit1)
  }

  def getResolutionProof(formula: Formula)(implicit ctx: Maybe[MutableContext]): Option[ResolutionProof] = getResolutionProof(Sequent() :+ formula)
  def getResolutionProof(seq: HOLSequent)(implicit ctx0: Maybe[MutableContext]): Option[ResolutionProof] = {
    val ctx = ctx0.getOrElse(MutableContext.guess(seq))

    val section = new ContextSection(ctx)
    val ground = section.groundSequent(seq)

    val cnf = structuralCNF(ground, propositional = false)(ctx)
    getResolutionProof(cnf)(ctx, implicitly)
  }

  def getResolutionProof(seq: Iterable[HOLClause])(implicit ctx: Maybe[MutableContext]): Option[ResolutionProof]

  override def getExpansionProof(seq: HOLSequent)(implicit ctx0: Maybe[MutableContext]): Option[ExpansionProof] = {
    implicit val ctx: MutableContext = ctx0.getOrElse(MutableContext.guess(seq))
    withSection { section =>
      getResolutionProof(section.groundSequent(seq))(ctx).map(ResolutionToExpansionProof(_)(ctx))
    }
  }

  def extendToManySortedViaPredicates = new ResolutionProver {
    import gapt.proofs.reduction._
    override def isValid(sequent: HOLSequent)(implicit ctx: Maybe[Context]): Boolean = {
      val reduction = CNFReductionLKRes |> PredicateReductionCNF |> ErasureReductionCNF
      val (folProblem, _) = reduction forward sequent
      self.getResolutionProof(folProblem)(ctx.map(_.newMutable)).isDefined
    }

    override def getExpansionProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[ExpansionProof] = {
      val reduction = PredicateReductionET |> ErasureReductionET
      val (folProblem, back) = reduction forward sequent
      self.getExpansionProof(folProblem).map(back)
    }

    override def getLKProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[LKProof] = {
      val reduction = CNFReductionLKRes |> PredicateReductionCNF |> ErasureReductionCNF
      val (folProblem, back) = reduction forward sequent
      self.getResolutionProof(folProblem).map(proof => back(eliminateSplitting(proof)))
    }

    override def getResolutionProof(seq: Iterable[HOLClause])(implicit ctx: Maybe[MutableContext]): Option[ResolutionProof] = {
      val reduction = PredicateReductionCNF |> ErasureReductionCNF
      val (folProblem, back) = reduction forward seq.toSet
      self.getResolutionProof(folProblem).map(eliminateSplitting(_)).map(back)
    }

    override def toString = s"$self.extendToManySortedViaPredicates"
  }

  def extendToManySortedViaErasure = new ResolutionProver {
    import gapt.proofs.reduction._
    override def isValid(sequent: HOLSequent)(implicit ctx: Maybe[Context]): Boolean = {
      val reduction = CNFReductionLKRes |> ErasureReductionCNF
      val (folProblem, _) = reduction forward sequent
      self.getResolutionProof(folProblem)(ctx.map(_.newMutable)).isDefined
    }

    override def getExpansionProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[ExpansionProof] = {
      val reduction = ErasureReductionET
      val (folProblem, back) = reduction forward sequent
      self.getExpansionProof(folProblem).map(back)
    }

    override def getLKProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[LKProof] = {
      val reduction = CNFReductionLKRes |> ErasureReductionCNF
      val (folProblem, back) = reduction forward sequent
      self.getResolutionProof(folProblem).map(proof => back(eliminateSplitting(proof)))
    }

    override def getResolutionProof(seq: Iterable[HOLClause])(implicit ctx: Maybe[MutableContext]): Option[ResolutionProof] = {
      val reduction = ErasureReductionCNF
      val (folProblem, back) = reduction forward seq.toSet
      self.getResolutionProof(folProblem).map(eliminateSplitting(_)).map(back)
    }

    override def toString = s"$self.extendToManySortedViaErasure"
  }

  def extendToManySortedViaTagging = new ResolutionProver {
    import gapt.proofs.reduction._
    override def isValid(sequent: HOLSequent)(implicit ctx: Maybe[Context]): Boolean = {
      val reduction = CNFReductionLKRes |> TagReductionCNF
      val (folProblem, _) = reduction forward sequent
      self.getResolutionProof(folProblem)(ctx.map(_.newMutable)).isDefined
    }

    override def getExpansionProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[ExpansionProof] = {
      val reduction = TagReductionET
      val (folProblem, back) = reduction forward sequent
      self.getExpansionProof(folProblem).map(back)
    }

    override def getLKProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[LKProof] = {
      val reduction = CNFReductionLKRes |> TagReductionCNF
      val (folProblem, back) = reduction forward sequent
      self.getResolutionProof(folProblem).map(proof => back(eliminateSplitting(proof)))
    }

    override def getResolutionProof(seq: Iterable[HOLClause])(implicit ctx: Maybe[MutableContext]): Option[ResolutionProof] = {
      val reduction = TagReductionCNF
      val (folProblem, back) = reduction forward seq.toSet
      self.getResolutionProof(folProblem).map(eliminateSplitting(_)).map(back)
    }

    override def toString = s"$self.extendToManySortedViaTagging"
  }

  def withDeskolemization = new ResolutionProver {
    override def isValid(sequent: HOLSequent)(implicit ctx: Maybe[Context]): Boolean =
      self.isValid(sequent)

    override def getExpansionProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[ExpansionProof] =
      self.getExpansionProof(sequent).map(deskolemizeET(_))

    override def getLKProof(sequent: HOLSequent)(implicit ctx: Maybe[MutableContext]): Option[LKProof] =
      getExpansionProof(sequent).flatMap(ep =>
        ExpansionProofToLK(ep) match {
          case Right(lk) => Some(lk)
          case Left(_)   => None
        }
      )

    override def getResolutionProof(seq: Iterable[HOLClause])(implicit ctx: Maybe[MutableContext]): Option[ResolutionProof] =
      self.getResolutionProof(seq)

    override def toString = s"$self.withDeskolemization"
  }

}