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

Go to download

Show more of this group Show more artifacts with this name
Show all versions of gapt_3 Show documentation

General Architecture for Proof Theory

The newest version!

package gapt.proofs.lk.rules

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

/**
 * An LKProof ending with a left contraction:
 *  *         (π)
 *     A, A, Γ :- Δ
 *    --------------
 *      A, Γ :- Δ
 * 
 *
 * @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 ContractionLeftRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends ContractionRule {

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

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

  override def name: String = "c:l"

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

object ContractionLeftRule extends ConvenienceConstructor("ContractionLeftRule") {

  /**
   * Convenience constructor for c:l that, given a formula to contract on the left,
   * 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): ContractionLeftRule = {
    val premise = subProof.endSequent

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

    val p = ContractionLeftRule(subProof, Ant(indices(0)), Ant(indices(1)))
    assert(p.mainFormula == f)
    p
  }

}