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

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General Architecture for Proof Theory
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package gapt.proofs.lk.rules.macros

import gapt.proofs.Ant
import gapt.proofs.IndexOrFormula
import gapt.proofs.IndexOrFormula.IsFormula
import gapt.proofs.SequentConnector
import gapt.proofs.Suc
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.rules.ConvenienceConstructor
import gapt.proofs.lk.rules.ImpRightRule
import gapt.proofs.lk.rules.WeakeningLeftRule
import gapt.proofs.lk.rules.WeakeningRightRule

object ImpRightMacroRule extends ConvenienceConstructor("ImpRightMacroRule") {

  /**
   * This simulates an additive →:r-rule: if either aux formula (but not both) is missing, it will be added to the
   * premise by weakening before creating the →:r inference.
   *
   * Each of the aux formulas can be given as an index or a formula. If it is given as a formula, the constructor
   * will attempt to find an appropriate index on its own.
   *
   * @param subProof The subproof.
   * @param impPremise Index of the premise or the premise itself.
   * @param impConclusion Index of the conclusion or the conclusion itself.
   * @return
   */
  def apply(subProof: LKProof, impPremise: IndexOrFormula, impConclusion: IndexOrFormula): ImpRightRule =
    withSequentConnector(subProof, impPremise, impConclusion)._1

  /**
   * This simulates an additive →:r-rule: if either aux formula (but not both) is missing, it will be added to the
   * premise by weakening before creating the →:r inference.
   *
   * Each of the aux formulas can be given as an index or a formula. If it is given as a formula, the constructor
   * will attempt to find an appropriate index on its own.
   *
   * @param subProof The subproof.
   * @param impPremise Index of the premise or the premise itself.
   * @param impConclusion Index of the conclusion or the conclusion itself.
   * @return An LKProof and an SequentConnector connecting its end sequent with the end sequent of subProof.
   */
  def withSequentConnector(
      subProof: LKProof,
      impPremise: IndexOrFormula,
      impConclusion: IndexOrFormula
  ): (ImpRightRule, SequentConnector) = {
    val (_, indicesAnt, _, indicesSuc) = findIndicesOrFormulasInPremise(subProof.endSequent)(
      Seq(impPremise),
      Seq(impConclusion)
    )

    (indicesAnt.head, indicesSuc.head) match {
      case (-1, -1) => // Neither aux formula has been found. We don't allow this case.
        throw LKRuleCreationException(
          s"Neither $impPremise nor $impConclusion has been found in succedent of ${subProof.endSequent}."
        )

      case (-1, i) => // The conclusion has been found at index Suc(i).
        // This match cannot fail: if the index of the premise is -1, it cannot have been passed as an index.
        val IsFormula(ip) = impPremise: @unchecked
        val subProof_ = WeakeningLeftRule(subProof, ip)
        val oc = subProof_.getSequentConnector
        val proof = ImpRightRule(subProof_, subProof_.mainIndices(0), oc.child(Suc(i)))
        (proof, proof.getSequentConnector * oc)

      case (i, -1) => // The premise has been found at indext Ant(i).
        // This match cannot fail: if the index of the conclusion is -1, it cannot have been passed as an index.
        val IsFormula(ic) = impConclusion: @unchecked
        val subProof_ = WeakeningRightRule(subProof, ic)
        val oc = subProof_.getSequentConnector
        val proof = ImpRightRule(subProof_, oc.child(Ant(i)), subProof_.mainIndices(0))
        (proof, proof.getSequentConnector * oc)

      case _ => // Both aux formulas have been found. Simply construct the inference.
        val proof = ImpRightRule(subProof, impPremise, impConclusion)
        (proof, proof.getSequentConnector)
    }
  }
}