--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/re2.scala	Thu Jul 30 13:50:54 2020 +0100
@@ -0,0 +1,118 @@
+// A Version with an explicit n-times regular expression;
+// this keeps the size of the regular expression in the
+// EVIL1 test-case quite small
+
+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   //explicit constructor for n-times
+
+
+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)
+}
+
+
+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 SEQ(der(c, r1), NTIMES(r1, i - 1))
+}
+
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
+
+
+// the optional regular expression: one or zero times
+// this regular expression is still defined in terms of ALT
+def OPT(r: Rexp) = ALT(r, ONE)
+
+
+// Test Cases
+
+// 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'))
+
+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)
+}
+
+
+
+// test: (a?{n}) (a{n})
+for (i <- 0 to 1000 by 100) {
+  println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f")
+}
+
+// test: (a*)* b
+for (i <- 0 to 20) {
+  println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f")
+}
+
+
+// the 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)
+}
+
+// EVIL1(n) has now a constant size, no matter
+// what n is; also the derivative only grows 
+// moderately 
+
+size(EVIL1(1))  // 7
+size(EVIL1(3))  // 7
+size(EVIL1(5))  // 7
+size(EVIL1(7))  // 7
+size(EVIL1(20)) // 7
+
+size(ders("".toList, EVIL1(5)))       // 7
+size(ders("a".toList, EVIL1(5)))      // 16
+size(ders("aa".toList, EVIL1(5)))     // 35
+size(ders("aaa".toList, EVIL1(5)))    // 59
+size(ders("aaaa".toList, EVIL1(5)))   // 88
+size(ders("aaaaa".toList, EVIL1(5)))  // 122
+size(ders("aaaaaa".toList, EVIL1(5))) // 151
+
+// but the size of the derivatives can still grow 
+// quite dramatically in case of EVIL2
+
+size(ders("".toList, EVIL2))       // 5
+size(ders("a".toList, EVIL2))      // 12
+size(ders("aa".toList, EVIL2))     // 28
+size(ders("aaa".toList, EVIL2))    // 58
+size(ders("aaaa".toList, EVIL2))   // 116
+size(ders("aaaaa".toList, EVIL2))  // 230
+size(ders("aaaaaa".toList, EVIL2)) // 456
+
+size(ders(("a" * 20).toList, EVIL2)) // 7340068
\ No newline at end of file