gapt.proofs.lk.rules.macros.WeakeningMacroRule.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.HOLSequent
import gapt.proofs.SequentConnector
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.rules.ConvenienceConstructor

/**
 * This macro rule simulates a series of weakenings in both cedents.
 *
 */
object WeakeningMacroRule extends ConvenienceConstructor("WeakeningMacroRule") {

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

  /**
   *
   * @param p A proof.
   * @param antList A list of formulas.
   * @param sucList A list of formulas.
   * @return A new proof whose antecedent and succedent contain new occurrences of the formulas
   *         in antList and sucList, respectively, and an SequentConnector.
   */
  def withSequentConnector(
      p: LKProof,
      antList: Seq[Formula],
      sucList: Seq[Formula]
  ): (LKProof, SequentConnector) = {
    val (subProof, upperConnector) = WeakeningLeftMacroRule.withSequentConnector(p, antList)
    val (proof, lowerConnector) = WeakeningRightMacroRule.withSequentConnector(subProof, sucList)
    (proof, lowerConnector * upperConnector)
  }

  /**
   *
   * @param p A proof.
   * @param targetSequent A sequent of formulas.
   * @param strict If true, will require that targetSequent contains the end sequent of p.
   * @return A proof whose end sequent is targetSequent.
   */
  def apply(p: LKProof, targetSequent: HOLSequent, strict: Boolean = true): LKProof =
    withSequentConnector(p, targetSequent, strict)._1

  /**
   *
   * @param p A proof.
   * @param targetSequent A sequent of formulas.
   * @param strict If true, will require that targetSequent contains the end sequent of p.
   * @return A proof whose end sequent is targetSequent and an SequentConnector.
   */
  def withSequentConnector(p: LKProof, targetSequent: HOLSequent, strict: Boolean = true): (LKProof, SequentConnector) = {
    val currentSequent = p.endSequent

    if (strict & !(currentSequent isSubMultisetOf targetSequent))
      throw LKRuleCreationException("Sequent " + targetSequent + " cannot be reached from " +
        currentSequent + " by weakenings.")

    val (antDiff, sucDiff) = (targetSequent diff currentSequent).toTuple

    WeakeningMacroRule.withSequentConnector(p, antDiff, sucDiff)
  }
}