193 

   194 

   195 

   196 //Recursive Functions

   197 abstract class Rec {

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

   199 }

   200 case object Z extends Rec {

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

   202     case n::Nil => 0

   203     case _ => throw new IllegalArgumentException("Z: args")

   204   }

   205 } 

   206 case object S extends Rec {

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

   208     case n::Nil => n + 1

   209     case _ => throw new IllegalArgumentException("S: args")

   210   }

   211 } 

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

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

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

   215     else throw new IllegalArgumentException("Id: args")

   216 }

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

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

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

   220     else throw new IllegalArgumentException("Cn: args")

   221 }

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

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

   224     if (ns.length == n - 1) {

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

   226       else {

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

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

   229       }

   230     }

   231     else throw new IllegalArgumentException("Cn: args")

   232 }

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

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

   235     

   236 }

   237