--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scala/turing.scala	Thu Feb 21 16:07:40 2013 +0000
@@ -0,0 +1,100 @@
+package object turing {
+
+import scala.annotation.tailrec
+import lib._
+
+sealed abstract class Cell {
+  def * (n: Int) : List[Cell] = n match {
+    case 0 => Nil
+    case n => this :: this * (n - 1)
+  }
+}
+case object Bk extends Cell { override def toString = "0" }
+case object Oc extends Cell { override def toString = "1" }
+
+sealed abstract class Action
+case object WBk extends Action
+case object WOc extends Action
+case object R extends Action
+case object L extends Action
+case object Nop extends Action
+
+type State = Int
+type Inst = (Action, State)
+type Prog = List[Inst]
+
+//tapes
+case class Tape(l: List[Cell], r: List[Cell]) {
+  
+  def update(a: Action) = a match {
+    case WBk => Tape(l, Bk::tl(r))
+    case WOc => Tape(l, Oc::tl(r))
+    case L => if (l == Nil) Tape(Nil, Bk::r) else Tape (tl(l), hd(l)::r)
+    case R => if (r == Nil) Tape(Bk::l, Nil) else Tape(hd(r)::l, tl(r))
+    case Nop => Tape(l, r)
+  }
+
+  def read = r match {
+    case Nil => Bk
+    case x::_ => x
+  }
+
+  override def toString = join(l.reverse) + ">" + join(r)
+}
+
+//standard tapes
+object Tape {
+  def apply(ns: Int*) : Tape = 
+    Tape(Nil, ns.map(n => Oc * (n + 1)).reduceLeft(_ ::: List(Bk) ::: _))
+}
+
+
+// configurations
+case class Config(s: State, tp: Tape) {
+  def is_final = s == 0
+
+  override def toString = tp.toString
+}
+
+
+// Turing machines
+case class TM(p: Prog) {
+
+  def ++ (that: TM) = TM(this.p ::: that.p)
+
+  def shift(n: Int) =
+    TM(p.map{case (a, s) => (a, if (s == 0) 0 else s + n)})
+  def adjust(n: Int) : TM =
+    TM(p.map{case (a, s) => (a, if (s == 0) n else s)})
+  def adjust : TM = adjust(p.length / 2 + 1)
+  
+  def fetch(s: State, a: Cell) = (s, a) match {
+    case (0, _) => (Nop, 0)
+    case (s, Bk) => nth_of(p, 2 * (s - 1)) match {
+      case None => (Nop, 0)
+      case Some(i) => i
+    }
+    case (s, Oc) => nth_of(p, 2 * (s - 1) + 1) match {
+      case None => (Nop, 0)
+      case Some(i) => i
+    }
+  } 
+
+  def step(cf: Config) : Config = fetch (cf.s, cf.tp.read) match {
+    case (a, s_next) => Config(s_next, cf.tp.update(a))
+  }
+
+  def steps(cf: Config, n: Int) : Config = n match {
+    case 0 => cf
+    case n => steps(step(cf), n - 1)
+  } 
+
+  @tailrec
+  final def run(cf: Config) : Config = {
+    if (cf.is_final) cf else run(step(cf))
+  }
+ 
+  def run(tp: Tape) : Tape = run(Config(1, tp)).tp
+}
+
+}