# HG changeset patch
# User Christian Urban <christian dot urban at kcl dot ac dot uk>
# Date 1361146736 0
# Node ID 650e7a7a389b171e5bfad585d61b679c28eaf0a1
# Parent  8248f8adf17d91d2aef046a0a6477f56283723ce
tuned

diff -r 8248f8adf17d -r 650e7a7a389b turing.scala
--- a/turing.scala	Sat Feb 16 11:02:08 2013 +0000
+++ b/turing.scala	Mon Feb 18 00:18:56 2013 +0000
@@ -190,3 +190,48 @@
 
 
 println("Ab: " + (new Plus(0, 1, 2)).run(Map(0 -> 3, 1 -> 4)))
+
+
+
+//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 _ => throw new IllegalArgumentException("Z: args")
+  }
+} 
+case object S extends Rec {
+  override def eval(ns: List[Int]) = ns match {
+    case n::Nil => n + 1
+    case _ => throw new IllegalArgumentException("S: args")
+  }
+} 
+case class Id(n: Int, m: Int) extends Rec {
+  override def eval(ns: List[Int]) = 
+    if (ns.length == n && m < n) ns(m)
+    else throw new IllegalArgumentException("Id: args")
+}
+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("Cn: args")
+}
+case class Mn(n: Int, f: Rec) extends Rec {
+  override def eval(ns: List[Int]) =
+    
+}
+