--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/re3a.scala	Thu Jul 30 13:50:54 2020 +0100
@@ -0,0 +1,112 @@
+
+abstract class Rexp
+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 
+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 
+case class UPNTIMES(r: Rexp, n: Int) extends Rexp 
+
+// the 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)
+  case UPNTIMES(r: Rexp, n: Int) => true
+}
+
+// the 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(r1) => SEQ(der(c, r1), STAR(r1))
+  case NTIMES(r1, i) => 
+    if (i == 0) ZERO else
+    if (nullable(r1)) SEQ(der(c, r1), UPNTIMES(r1, i - 1))
+    else SEQ(der(c, r1), NTIMES(r1, i - 1))
+  case UPNTIMES(r1, i) => 
+    if (i == 0) ZERO
+    else SEQ(der(c, r1), UPNTIMES(r1, 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)
+  }
+  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 r => r
+}
+
+
+// the 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)))
+}
+
+
+// the main matcher function
+def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
+
+// one or zero
+def OPT(r: Rexp) = ALT(r, ONE)
+
+// evil regular expressions
+def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
+val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+val EVIL3 = SEQ(STAR(ALT(CHAR('a'), SEQ(CHAR('a'),CHAR('a')))), CHAR('b'))
+
+def time_needed[T](i: Int, code: => T) = {
+  val start = System.nanoTime()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  "%.5f".format((end - start) / (i * 1.0e9))
+}
+
+
+// test: (a?{n}) (a{n})
+for (i <- 0 to 8000 by 1000) {
+  println(s"$i: ${time_needed(2, matches(EVIL1(i), "a" * i))}")
+}
+
+// test: (a*)* b
+for (i <- 0 to 6000000 by 500000) {
+  println(s"$i: ${time_needed(2, matches(EVIL2, "a" * i))}")
+}
+
+
+val r0 = simp(der('a', EVIL3))
+val r1 = simp(der('a', r0))
+val r2 = simp(der('a', r1))
+val r3 = simp(der('a', r2))
+val r4 = simp(der('a', r3))
+val r5 = simp(der('a', r4))
+val r6 = simp(der('a', r5))
+
+//test: (a|aa)* b
+/*
+for (i <- 0 to 100 by 10) {
+  println(s"$i: ${time_needed(2, matches(EVIL3, "a" * i ++ "c"))}")
+}
+ */
+