--- a/progs/re3.scala	Sat May 05 10:31:00 2018 +0100
+++ b/progs/re3.scala	Fri Jun 01 15:28:37 2018 +0100
@@ -13,6 +13,32 @@
 case class NTIMES(r: Rexp, n: Int) extends Rexp 
 
 
+// string of a regular expressions - for testing purposes 
+def string(r: Rexp) : String = r match {
+  case ZERO => "0"
+  case ONE => "1"
+  case CHAR(c) => c.toString 
+  case ALT(r1, r2) => s"(${string(r1)} + ${string(r2)})"
+  case SEQ(CHAR(c), CHAR(d)) => s"${c}${d}"
+  case SEQ(ONE, CHAR(c)) => s"1${c}"
+  case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})"
+  case STAR(r) => s"(${string(r)})*"
+  case NTIMES(r, n) =>  s"(${string(r)}){${n}}"
+}
+
+// size of a regular expressions - for testing purposes 
+def size(r: Rexp) : Int = r match {
+  case ZERO => 1
+  case ONE => 1
+  case CHAR(_) => 1
+  case ALT(r1, r2) => 1 + size(r1) + size(r2)
+  case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+  case STAR(r) => 1 + size(r)
+  case NTIMES(r, _) => 1 + size(r)
+}
+
+
+
 // nullable function: tests whether the regular 
 // expression can recognise the empty string
 def nullable (r: Rexp) : Boolean = r match {
@@ -39,27 +65,38 @@
     if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
 }
 
-def simp(r: Rexp) : Rexp = r match {
-  case ALT(r1, r2) => (simp(r1), simp(r2)) match {
-    case (ZERO, r2s) => r2s
-    case (r1s, ZERO) => r1s
-    case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
+
+
+def simp(r: Rexp, seen: Set[Rexp]) : (Rexp, Set[Rexp]) = r match {
+  case ALT(r1, r2) => {
+    val (r1s, seen1) = simp(r1, seen)
+    val (r2s, seen2) = simp(r2, seen1)
+    (r1s, r2s) match {
+      case (ZERO, r2s) => (r2s, seen2)
+      case (r1s, ZERO) => (r1s, seen2)
+      case (r1s, r2s) => (ALT(r1s, r2s), seen2)
+    }
   }
-  case SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {
-    case (ZERO, _) => ZERO
-    case (_, ZERO) => ZERO
-    case (ONE, r2s) => r2s
-    case (r1s, ONE) => r1s
-    case (r1s, r2s) => SEQ(r1s, r2s)
+  case SEQ(r1, r2) =>  {
+    val (r1s, _) = simp(r1, Set())
+    val (r2s, _) = simp(r2, Set())
+    if (seen.contains(SEQ(r1s, r2s))) (ZERO, seen)
+    else (r1s, r2s) match {
+      case (ZERO, _) => (ZERO, seen)
+      case (_, ZERO) => (ZERO, seen)
+      case (ONE, r2s) => (r2s, seen + r2s)
+      case (r1s, ONE) => (r1s, seen + r1s)
+      case (r1s, r2s) => (SEQ(r1s, r2s), seen + SEQ(r1s, r2s))
+    }
   }
-  case r => r
+  case r => if (seen.contains(r)) (ZERO, seen) else (r, seen + r)
 }
 
 
 // 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, simp(der(c, r)))
+  case c::s => ders(s, simp(der(c, r), Set())._1)
 }
 
 
@@ -71,6 +108,75 @@
 def OPT(r: Rexp) = ALT(r, ONE)
 
 
+
+
+
+
+
+
+
+def time_needed[T](i: Int, code: => T) = {
+  val start = System.nanoTime()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  (end - start)/(i * 1.0e9)
+}
+
+
+// star example
+val Tstar = STAR(STAR(STAR(CHAR('a'))))
+
+string(ders("".toList, Tstar))
+size(ders("".toList, Tstar))      // 4
+string(ders("a".toList, Tstar))
+size(ders("a".toList, Tstar))     // 11
+string(ders("aa".toList, Tstar))
+size(ders("aa".toList, Tstar))    // 11
+string(ders("aaa".toList, Tstar))
+size(ders("aaa".toList, Tstar))   // 11
+string(ders("aaaa".toList, Tstar))
+size(ders("aaaa".toList, Tstar))  // 11
+string(ders("aaaa".toList, Tstar))
+size(ders("aaaaa".toList, Tstar)) // 11
+string(ders("aaaab".toList, Tstar))
+size(ders("aaaaab".toList, Tstar)) // 1
+
+// test: ("a" | "aa")*
+val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))
+
+for (i <- 1 to 100 by 1) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL3, "a" * i))) + 
+	  " size: " + size(ders(("a" * i).toList, EVIL3)))
+}
+
+
+println("start " + string(EVIL3) + "    " + size(EVIL3))
+val t1  = der('a', EVIL3)
+println(string(t1) + "    " + size(t1))
+val t1s = simp(t1, Set())._1 
+println("simplified " + string(t1s) + "    " + size(t1s))
+val t2  = der('a', t1s)
+println(string(t2) + "    " + size(t2))
+val t2s = simp(t2, Set())._1 
+println("simplified " + string(t2s) + "    " + size(t2s))
+val t3  = der('a', t2s)
+println(string(t3) + "    " + size(t3))
+val t3s = simp(t3, Set())._1 
+println("simplified " + string(t3s) + "    " + size(t3s))
+val t4  = der('a', t3s)
+val t4s = simp(t4, Set())._1 
+
+
+
+
+
+
+
+
+println(string(t4) + "    " + size(t4))
+println("simplified " + string(t4s) + "    " + size(t4s))
+
+
 // Test Cases
 
 //evil regular expressions: (a?){n} a{n}  and (a*)* b
@@ -143,3 +249,8 @@
 for (i <- 1 to 4501 by 500) {
   println(i + ": " + "%.5f".format(time_needed(1, matcher(sulzmann, "ab" * i))))
 }
+
+
+
+
+(((1 + 1a) ~ ((a + aa))*) + (((0 + 1) ~ ((a + aa))*) + ((1 + 1a) ~ ((a + aa))*)))