--- a/progs/app6.scala	Sun Sep 28 18:07:58 2014 +0100
+++ b/progs/app6.scala	Sun Sep 28 22:30:25 2014 +0100
@@ -1,16 +1,30 @@
-def der (r: Rexp, c: Char) : Rexp = r match {
-  case NULL => NULL
-  case EMPTY => NULL
-  case CHAR(d) => if (c == d) EMPTY else NULL
-  case ALT(r1, r2) => ALT(der(r1, c), der(r2, c))
-  case SEQ(r1, r2) => 
-    if (nullable(r1)) ALT(SEQ(der(r1, c), r2), der(r2, c))
-    else SEQ(der(r1, c), r2)
-  case STAR(r) => SEQ(der(r, c), STAR(r))
+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 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 NTIMES(r, n) => NTIMES(simp(r), n)    
+  case r => r
 }
 
 def ders (s: List[Char], r: Rexp) : Rexp = s match {
   case Nil => r
-  case c::s => ders(s, der(c, r))
+  case c::s => ders(s, simp(der(c, r)))
 }