--- a/scala/turing.scala	Thu Feb 21 16:07:40 2013 +0000
+++ b/scala/turing.scala	Fri Feb 22 14:31:34 2013 +0000
@@ -3,6 +3,7 @@
 import scala.annotation.tailrec
 import lib._
 
+// tape cells
 sealed abstract class Cell {
   def * (n: Int) : List[Cell] = n match {
     case 0 => Nil
@@ -12,6 +13,7 @@
 case object Bk extends Cell { override def toString = "0" }
 case object Oc extends Cell { override def toString = "1" }
 
+// actions
 sealed abstract class Action
 case object WBk extends Action
 case object WOc extends Action
@@ -23,7 +25,7 @@
 type Inst = (Action, State)
 type Prog = List[Inst]
 
-//tapes
+// tapes
 case class Tape(l: List[Cell], r: List[Cell]) {
   
   def update(a: Action) = a match {
@@ -42,13 +44,12 @@
   override def toString = join(l.reverse) + ">" + join(r)
 }
 
-//standard tapes
+// 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
@@ -56,10 +57,10 @@
   override def toString = tp.toString
 }
 
-
 // Turing machines
 case class TM(p: Prog) {
 
+  // simple composition
   def ++ (that: TM) = TM(this.p ::: that.p)
 
   def shift(n: Int) =
@@ -97,4 +98,9 @@
   def run(tp: Tape) : Tape = run(Config(1, tp)).tp
 }
 
+// some syntactical convenience
+object TM {
+  def apply(is: Inst*) : TM = TM(is.toList)
 }
+
+}