gapt.proofs.lk.rules.ReflexivityAxiom.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.Expr
import gapt.expr.formula.Eq
import gapt.expr.formula.Formula
import gapt.proofs.HOLSequent

/**
 * An LKProof consisting of a reflexivity axiom:
 *  *    ------------ax
 *      :- s = s
 * 
 * with s a term.
 *
 * @param s The term s.
 */
case class ReflexivityAxiom(s: Expr) extends InitialSequent {
  override def name: String = "refl"
  override def conclusion: HOLSequent = HOLSequent(Seq(), Seq(Eq(s, s)))
  def mainFormula: Formula = Eq(s, s)
}