gapt.logic.toImplications.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.logic

import gapt.expr.formula.All
import gapt.expr.formula.And
import gapt.expr.formula.Ex
import gapt.expr.formula.Formula
import gapt.expr.formula.Imp
import gapt.expr.formula.Neg
import gapt.expr.formula.Or
import gapt.expr.formula.fol.FOLFormula

object toImplications {

  /**
   * Transforms subformulas of the form ¬A ∨ B or A ∨ ¬B to A → B or B → A, respectively.
   *
   * @param formula
   * @return
   */
  def apply(formula: Formula): Formula = formula match {
    case Or(Neg(f), g) =>
      Imp(apply(f), apply(g))
    case Or(f, Neg(g)) =>
      Imp(apply(g), apply(f))
    case Or(f, g) =>
      Or(apply(f), apply(g))
    case And(f, g) =>
      And(apply(f), apply(g))
    case Neg(f)    => Neg(apply(f))
    case Ex(v, f)  => Ex(v, apply(f))
    case All(v, f) => All(v, apply(f))
    case _         => formula
  }

  def apply(formula: FOLFormula): FOLFormula = apply(formula.asInstanceOf[Formula]).asInstanceOf[FOLFormula]
}