gapt.proofs.lk.rules.macros.EqualityLeftMacroRule.scala Maven / Gradle / Ivy

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package gapt.proofs.lk.rules.macros

import gapt.expr.Abs
import gapt.proofs.Ant
import gapt.proofs.IndexOrFormula
import gapt.proofs.IndexOrFormula.IsFormula
import gapt.proofs.SequentConnector
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.rules.ConvenienceConstructor
import gapt.proofs.lk.rules.EqualityLeftRule
import gapt.proofs.lk.rules.WeakeningLeftRule

object EqualityLeftMacroRule extends ConvenienceConstructor("EqualityLeftMacroRule") {

  /**
   * Like EqualityLeftRule, but the equation need not exist in the premise.
   * If it doesn't, it will automatically be added via weakening.
   * Note that the auxiliary formula does have to occur in the premise.
   *
   * @param subProof The subproof.
   * @param equation Index of the equation or the equation itself.
   * @param auxFormula Index of the aux formula or the formula itself.
   * @return
   */
  def apply(subProof: LKProof, equation: IndexOrFormula, auxFormula: IndexOrFormula, con: Abs): EqualityLeftRule =
    withSequentConnector(subProof, equation, auxFormula, con)._1

  /**
   * Like EqualityLeftRule, but the equation need not exist in the premise. If it doesn't, it will automatically be added via weakening.
   * Note that the auxiliary formula does have to occur in the premise.
   *
   * @param subProof The subproof.
   * @param equation Index of the equation or the equation itself.
   * @param auxFormula Index of the aux formula or the formula itself.
   * @return An LKProof and an SequentConnector connecting its end sequent with the end sequent of subProof.
   */
  def withSequentConnector(subProof: LKProof, equation: IndexOrFormula, auxFormula: IndexOrFormula, con: Abs): (EqualityLeftRule, SequentConnector) = {
    val (_, indices, _, _) =
      findIndicesOrFormulasInPremise(subProof.endSequent)(Seq(equation, auxFormula), Seq())

    (indices(0), indices(1)) match {
      case (_, -1) => // The aux formula has not been found.  We don't allow this case.
        throw LKRuleCreationException(s"Aux formula has not been found in succedent of ${subProof.endSequent}.")

      case (-1, i) => // Aux formula has been found at index Ant(i).
        val IsFormula(e) = equation: @unchecked
        // This match cannot fail: if the index of the equation is -1, it cannot have been passed as an index.
        val subProof_ = WeakeningLeftRule(subProof, e)
        val oc = subProof_.getSequentConnector
        val proof = EqualityLeftRule(subProof_, subProof_.mainIndices(0), oc.child(Ant(i)), con)
        (proof, proof.getSequentConnector * oc)

      case (_, _) => // Both equation and aux formula have been found. Simply construct the inference.
        val proof = EqualityLeftRule(subProof, equation, auxFormula, con)
        (proof, proof.getSequentConnector)
    }
  }
}