gapt.proofs.expansion.unifyInstancesET.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.proofs.expansion

import gapt.expr._
import gapt.expr.subst.Substitution
import gapt.expr.util.freeVariables
import gapt.expr.util.rename
import gapt.expr.util.syntacticMGU

/** Decreases the number of instances in an expansion proof by unifying the instance terms. */
object unifyInstancesET {
  def apply(ep: ExpansionProof): ExpansionProof = {
    val instances = for (case ETWeakQuantifier(_, insts) <- ep.subProofs.toSeq) yield insts.keySet

    // TODO: this is not enough to ensure acyclicity
    val subst = unifyInstances(instances, ep.eigenVariables ++ freeVariables(ep.shallow))

    if (subst.isIdentity) ep
    else apply(eliminateMerges(subst(ep)))
  }

  private def unifyInstances(instances: Seq[Set[Expr]], forbiddenVariables: Set[Var]): Substitution = {
    val nameGen = rename.awayFrom(containedNames(instances))
    val grounding = forbiddenVariables.map(ev => ev -> Const(nameGen.fresh(ev.name), ev.ty))
    TermReplacement(unifyInstances(TermReplacement(instances, grounding.toMap)), grounding.map(_.swap).toMap)
  }

  private def unifyInstances(instances: Seq[Set[Expr]]): Substitution = scala.util.boundary {
    for {
      group <- instances
      (a, i) <- group.zipWithIndex
      (b, j) <- group.zipWithIndex
      if i < j
      mgu <- syntacticMGU(a, b)
    } scala.util.boundary.break(unifyInstances(mgu(instances)) compose mgu)

    Substitution()
  }

}