gapt.proofs.lk.util.IsKSimple.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.proofs.lk.util

import gapt.expr.Const
import gapt.expr.Expr
import gapt.expr.ty.TArr
import gapt.expr.ty.TBase
import gapt.expr.ty.Ty
import gapt.proofs.context.update.InductiveType
import gapt.proofs.lk.LKProof
import gapt.proofs.lk.rules.InductionRule

object IsKSimple {
  def apply(proof: LKProof): Boolean = {
    val base: Ty = TBase("nat", List())
    val successor: Const = Const("s", TArr(base, base))
    val zero: Const = Const("0", base)
    val nat = InductiveType(base, zero, successor)
    val inducProofs = proof.subProofs.collect { case p: InductionRule if p.indTy == nat.ty => p }
    (for (p <- inducProofs; c <- p.cases if c.constructor.name == "s")
      yield (c.eigenVars, p.term)).foldRight((true, Const("", TBase("nat")).asInstanceOf[Expr]))((a, z) =>
      if (a._1.contains(a._2) && z._2.equals(Const("", TBase("nat")))) (z._1, a._2)
      else (a._1.contains(a._2) && a._2 == z._2 && z._1, z._2)
    )._1
  }

}