gapt.proofs.lk.rules.ContractionRightRule.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.proofs.lk.rules

import gapt.expr.formula.Formula
import gapt.proofs.HOLSequent
import gapt.proofs.Sequent
import gapt.proofs.SequentIndex
import gapt.proofs.Suc
import gapt.proofs.lk.LKProof

/**
 * An LKProof ending with a right contraction:
 *  *         (π)
 *     Γ :- Δ, A, A
 *    --------------
 *      Γ :- Δ, A
 * 
 *
 * @param subProof The subproof π.
 * @param aux1 The index of one occurrence of A.
 * @param aux2 The index of the other occurrence of A.
 */
case class ContractionRightRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends ContractionRule {

  validateIndices(premise, Seq(), Seq(aux1, aux2))

  if (premise(aux1) != premise(aux2))
    throw LKRuleCreationException(s"Auxiliary formulas ${premise(aux1)} and ${premise(aux2)} are not equal.")

  override def name: String = "c:r"

  override def mainFormulaSequent: HOLSequent = Sequent() :+ mainFormula

}

object ContractionRightRule extends ConvenienceConstructor("ContractionRightRule") {

  /**
   * Convenience constructor for c:r that, given a formula to contract on the right,
   * will automatically pick the first two occurrences of that formula.
   *
   * @param subProof The subproof π.
   * @param f The formula to contract.
   * @return
   */
  def apply(subProof: LKProof, f: Formula): ContractionRightRule = {
    val premise = subProof.endSequent

    val (_, indices) = findAndValidate(premise)(Seq(), Seq(f, f))
    val p = ContractionRightRule(subProof, Suc(indices(0)), Suc(indices(1)))
    assert(p.mainFormula == f)
    p
  }

}