gapt.logic.clauseSubsumption.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory
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package gapt.logic

import gapt.expr.Expr
import gapt.expr.formula.Eq
import gapt.expr.subst.PreSubstitution
import gapt.expr.subst.Substitution
import gapt.expr.util.syntacticMatching
import gapt.proofs.Sequent

object clauseSubsumption {
  def apply(
      from: Sequent[Expr],
      to: Sequent[Expr],
      alreadyFixed: PreSubstitution = PreSubstitution(),
      multisetSubsumption: Boolean = false
  ): Option[Substitution] = scala.util.boundary {
    if (multisetSubsumption)
      if (from.antecedent.size > to.antecedent.size || from.succedent.size > to.succedent.size)
        return None
    if (from isEmpty) return Some(alreadyFixed.toSubstitution)
    val chosenFrom = from.indices.head
    for {
      chosenTo <- to.indices if chosenTo sameSideAs chosenFrom
      newSubst <- syntacticMatching(from(chosenFrom), to(chosenTo), alreadyFixed)
      subsumption <- apply(
        from delete chosenFrom,
        if (multisetSubsumption) to delete chosenTo else to,
        newSubst,
        multisetSubsumption
      )
    } scala.util.boundary.break(Some(subsumption))
    None
  }

  private def eqVariants(e: Expr): Seq[Expr] =
    e match {
      case Eq(l, r) => Seq(e, Eq(r, l))
      case _        => Seq(e)
    }
  def modEqSymm(
      from: Sequent[Expr],
      to: Sequent[Expr],
      alreadyFixed: PreSubstitution = PreSubstitution(),
      multisetSubsumption: Boolean = false
  ): Option[Substitution] = scala.util.boundary {
    if (multisetSubsumption)
      if (from.antecedent.size > to.antecedent.size || from.succedent.size > to.succedent.size)
        return None
    if (from isEmpty) return Some(alreadyFixed.toSubstitution)
    val chosenFrom = from.indices.head
    for {
      chosenTo <- to.indices if chosenTo sameSideAs chosenFrom
      toE <- eqVariants(to(chosenTo))
      newSubst <- syntacticMatching(from(chosenFrom), toE, alreadyFixed)
      subsumption <- modEqSymm(
        from delete chosenFrom,
        if (multisetSubsumption) to delete chosenTo else to,
        newSubst,
        multisetSubsumption
      )
    } scala.util.boundary.break(Some(subsumption))
    None
  }
}