gapt.proofs.lk.rules.macros.WeakeningRightMacroRule.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.expr.formula.Formula
import gapt.proofs.SequentConnector
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.rules.WeakeningRightRule

/**
 * This macro rule simulates a series of weakenings in the succedent.
 *
 */
object WeakeningRightMacroRule {

  /**
   *
   * @param p A proof.
   * @param formulas A list of formulas.
   * @return A new proof whose succedent contains new occurrences of the formulas in formulas.
   */
  def apply(p: LKProof, formulas: Seq[Formula]): LKProof = withSequentConnector(p, formulas)._1

  /**
   *
   * @param p A proof.
   * @param formulas A list of formulas.
   * @return A new proof whose succedent contains new occurrences of the formulas in formulas and an SequentConnector.
   */
  def withSequentConnector(p: LKProof, formulas: Seq[Formula]): (LKProof, SequentConnector) = {
    formulas.foldLeft((p, SequentConnector(p.endSequent))) { (acc, f) =>
      val subProof = WeakeningRightRule(acc._1, f)
      (subProof, subProof.getSequentConnector * acc._2)
    }
  }

  /**
   *
   * @param p An LKProof.
   * @param formula A Formula.
   * @param n A natural number.
   * @return p extended with weakenings such that formula occurs at least n times in the succedent of the end sequent.
   */
  def apply(p: LKProof, formula: Formula, n: Int): LKProof = withSequentConnector(p, formula, n)._1

  /**
   *
   * @param p An LKProof.
   * @param formula A Formula.
   * @param n A natural number.
   * @return p extended with weakenings such that formula occurs at least n times
   *         in the succedent of the end sequent and an SequentConnector.
   */
  def withSequentConnector(p: LKProof, formula: Formula, n: Int): (LKProof, SequentConnector) = {
    val nCurrent = p.endSequent.succedent.count(_ == formula)

    WeakeningRightMacroRule.withSequentConnector(p, Seq.fill(n - nCurrent)(formula))
  }
}