--- a/progs/re3.scala	Mon Sep 22 13:42:14 2014 +0100
+++ b/progs/re3.scala	Fri Sep 26 14:06:55 2014 +0100
@@ -1,57 +1,37 @@
-import scala.language.implicitConversions    
-    
-abstract class Rexp {
-  def simp : Rexp = this
-}
-
+abstract class Rexp 
 case object NULL extends Rexp
 case object EMPTY extends Rexp
 case class CHAR(c: Char) extends Rexp
-case class ALT(r1: Rexp, r2: Rexp) extends Rexp {
-  override def simp = (r1.simp, r2.simp) match {
-    case (NULL, r) => r
-    case (r, NULL) => r
-    case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)
-    case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)
-    case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
+case class STAR(r: Rexp) extends Rexp 
+case class NTIMES(r: Rexp, n: Int) extends Rexp 
+
+def simp(r: Rexp): Rexp = r match {
+  case ALT(r1, r2) => {
+    val r1s = simp(r1)
+    val r2s = simp(r2)
+    (r1s, r2s) match {
+      case (NULL, _) => r2s
+      case (_, NULL) => r1s
+      case _ => if (r1s == r2s) r1s else ALT(r1s, r2s)
+    }
   }
-}
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
-  override def simp = (r1.simp, r2.simp) match {
-    case (NULL, _) => NULL
-    case (_, NULL) => NULL
-    case (EMPTY, r) => r
-    case (r, EMPTY) => r
-    case (r1, r2) => SEQ(r1, r2)
+  case SEQ(r1, r2) => {
+    val r1s = simp(r1)
+    val r2s = simp(r2)
+    (r1s, r2s) match {
+      case (NULL, _) => NULL
+      case (_, NULL) => NULL
+      case (EMPTY, _) => r2s
+      case (_, EMPTY) => r1s
+      case _ => SEQ(r1s, r2s)
+    }
   }
-}
-case class STAR(r: Rexp) extends Rexp {
-  override def simp = r.simp match {
-    case NULL => EMPTY
-    case EMPTY => EMPTY
-    case r => STAR(r)
-  }
-}
-case class NTIMES(r: Rexp, n: Int) extends Rexp {
-  override def simp = if (n == 0) EMPTY else 
-    r.simp match {
-      case NULL => NULL
-      case EMPTY => EMPTY
-      case r => NTIMES(r, n)
-    }
+  case NTIMES(r, n) => NTIMES(simp(r), n)    
+  case r => r
 }
 
-// some convenience for typing in regular expressions
-def charlist2rexp(s : List[Char]) : Rexp = s match {
-  case Nil => EMPTY
-  case c::Nil => CHAR(c)
-  case c::s => SEQ(CHAR(c), charlist2rexp(s))
-}
-implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
-
-
-// nullable function: tests whether the regular 
-// expression can recognise the empty string
 def nullable (r: Rexp) : Boolean = r match {
   case NULL => false
   case EMPTY => true
@@ -62,7 +42,6 @@
   case NTIMES(r, i) => if (i == 0) true else nullable(r)
 }
 
-// derivative of a regular expression w.r.t. a character
 def der (c: Char, r: Rexp) : Rexp = r match {
   case NULL => NULL
   case EMPTY => NULL
@@ -76,20 +55,18 @@
     if (i == 0) NULL else SEQ(der(c, r), NTIMES(r, i - 1))
 }
 
-// derivative w.r.t. a string (iterates der)
 def ders (s: List[Char], r: Rexp) : Rexp = s match {
   case Nil => r
-  case c::s => ders(s, der(c, r).simp)
+  case c::s => ders(s, simp(der(c, r)))
 }
 
-// main matcher function
 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
 
 
 //one or zero
 def OPT(r: Rexp) = ALT(r, EMPTY)
 
-def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
+def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()