package object recs {

//Recursive Functions

abstract class Rec {

  def eval(ns: List[Int]) : Int

}

case object Z extends Rec {

  override def eval(ns: List[Int]) = ns match {

    case n::Nil => 0

  }

} 

case object S extends Rec {

  override def eval(ns: List[Int]) = ns match {

    case n::Nil => n + 1

  }

} 

case class Id(n: Int, m: Int) extends Rec {

  override def eval(ns: List[Int]) = 

    if (ns.length == n && m < n) ns(m)

}

case class Cn(n: Int, f: Rec, gs: List[Rec]) extends Rec {

  override def eval(ns: List[Int]) = 

    if (ns.length == n) f.eval(gs.map(_.eval(ns)))

    else throw new IllegalArgumentException("Cn: args")

}

case class Pr(n: Int, f: Rec, g: Rec) extends Rec {

  override def eval(ns: List[Int]) = 

    if (ns.length == n + 1) {

      if (ns.last == 0) f.eval(ns.init)

      else {

        val r = Pr(n, f, g).eval(ns.init ::: List(ns.last - 1))

        g.eval(ns.init ::: List(ns.last - 1, r))

      }

    }

    else throw new IllegalArgumentException("Pr: args")

}

case class Mn(n: Int, f: Rec) extends Rec {

  def evaln(ns: List[Int], n: Int) : Int = 

    if (f.eval(ns ::: List(n)) == 0) n else evaln(ns, n + 1)

  override def eval(ns: List[Int]) = 

    if (ns.length == n) evaln(ns, 0) 

    else throw new IllegalArgumentException("Mn: args")

}

}