gapt.proofs.lk.rules.NegLeftRule.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.expr.formula.Neg
import gapt.proofs.HOLSequent
import gapt.proofs.Sequent
import gapt.proofs.SequentIndex
import gapt.proofs.Suc
import gapt.proofs.lk.LKProof

/**
 * Index of the left cut formula or the formula itself.
 * An LKProof ending with a negation on the left:
 *  *       (π)
 *    Γ :- Δ, A
 *   -----------¬:l
 *   ¬A, Γ :- Δ
 * 
 *
 * @param subProof The proof π.
 * @param aux The index of A in the succedent.
 */
case class NegLeftRule(subProof: LKProof, aux: SequentIndex)
    extends UnaryLKProof with CommonRule {

  validateIndices(premise, Seq(), Seq(aux))

  def auxFormula: Formula = premise(aux)
  val mainFormula: Formula = Neg(auxFormula)

  override def auxIndices: Seq[Seq[SequentIndex]] = Seq(Seq(aux))
  override def name: String = "¬:l"

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

object NegLeftRule extends ConvenienceConstructor("NegLeftRule") {

  /**
   * Convenience constructor that automatically uses the first occurrence of supplied aux formula.
   *
   * @param subProof The subproof.
   * @param auxFormula The formula to be negated.
   * @return
   */
  def apply(subProof: LKProof, auxFormula: Formula): NegLeftRule = {
    val premise = subProof.endSequent

    val (_, indices) = findAndValidate(premise)(Seq(), Seq(auxFormula))

    new NegLeftRule(subProof, Suc(indices(0)))
  }
}