--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/re5.scala	Mon Aug 22 23:05:43 2016 +0200
@@ -0,0 +1,118 @@
+import scala.annotation.tailrec    
+import scala.language.implicitConversions
+    
+abstract class Rexp {
+  def simp : Rexp = this
+}
+
+case object ZERO extends Rexp
+case object ONE 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 (ZERO, r) => r
+    case (r, ZERO) => r
+    case (r, ONE) => if (nullable(r)) r else ALT(r, ONE)
+    case (ONE, r) => if (nullable(r)) r else ALT(r, ONE)
+    case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
+  }
+}
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
+  override def simp = (r1.simp, r2.simp) match {
+    case (ZERO, _) => ZERO
+    case (_, ZERO) => ZERO
+    case (ONE, r) => r
+    case (r, ONE) => r
+    case (r1, r2) => SEQ(r1, r2)
+  }
+}
+case class STAR(r: Rexp) extends Rexp {
+  override def simp = r.simp match {
+    case ZERO => ONE
+    case ONE => ONE
+    case r => STAR(r)
+  }
+}
+case class NTIMES(r: Rexp, n: Int) extends Rexp {
+  override def simp = if (n == 0) ONE else 
+    r.simp match {
+      case ZERO => ZERO
+      case ONE => ONE
+      case r => NTIMES(r, n)
+    }
+}
+
+// some convenience for typing in regular expressions
+def charlist2rexp(s : List[Char]) : Rexp = s match {
+  case Nil => ONE
+  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 ZERO => false
+  case ONE => true
+  case CHAR(_) => false
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  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 ZERO => ZERO
+  case ONE => ZERO
+  case CHAR(d) => if (c == d) ONE else ZERO
+  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
+  case SEQ(r1, r2) => 
+    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
+    else SEQ(der(c, r1), r2)
+  case STAR(r) => SEQ(der(c, r), STAR(r))
+  case NTIMES(r, i) => 
+    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
+}
+
+// derivative w.r.t. a string (iterates der)
+def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match {
+  case (Nil, r) => r
+  case (s, ZERO) => ZERO
+  case (s, ONE) => if (s == Nil) ONE else ZERO
+  case (s, CHAR(c)) => if (s == List(c)) ONE else 
+                       if (s == Nil) CHAR(c) else ZERO
+  case (s, ALT(r1, r2)) => ALT(ders2(s, r2), ders2(s, r2))
+  case (c::s, r) => ders2(s, der(c, r).simp)
+}
+
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r))
+
+
+//one or zero
+def OPT(r: Rexp) = ALT(r, ONE)
+
+def EVIL1(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
+val EVIL2 = SEQ(STAR("a"), "b")
+
+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)
+}
+
+val i = 5000
+println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL1(i), "a" * i))))
+
+for (i <- 1 to 80000 by 10000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
+}
+
+for (i <- 1 to 10000001 by 1000000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
+}
+