--- a/progs/re4.scala	Mon Jul 27 11:02:48 2020 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,156 +0,0 @@
-// A version which attempts to move whole strings, not
-// just characters, under derivatives whenever possible
-   
-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 
-
-// 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)
-}
-
-// 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 SEQ(der(c, r1), NTIMES(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
-}
-
-// an example
-val r = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z'))
-der('x', r)
-der('y', der('x', r))
-der('z', der('y', der('x', r)))
-simp(der('z', der('y', der('x', r))))
-
-// *new*
-// the 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, r1), ders2(s, r2))
-  case (c::s, r) => ders2(s, simp(der(c, r)))
-}
-
-// the 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)
-
-
-// Test Cases
-
-def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
-val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-
-// for measuring time
-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 11000 by 1000) {
-  println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f")
-}
-
-
-// test: (a*)* b
-for (i <- 0 to 7000000 by 500000) {
-  println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f")
-}
-
-
-
-// the size of a regular expressions - for testing purposes 
-def size(r: Rexp) : Int = r match {
-  case ZERO => 1
-  case ONE => 1
-  case CHAR(_) => 1
-  case ALT(r1, r2) => 1 + size(r1) + size(r2)
-  case SEQ(r1, r2) => 1 + size(r1) + size(r2)
-  case STAR(r) => 1 + size(r)
-  case NTIMES(r, _) => 1 + size(r)
-}
-
-
-// string of a regular expressions - for testing purposes 
-def string(r: Rexp) : String = r match {
-  case ZERO => "0"
-  case ONE => "1"
-  case CHAR(c) => c.toString 
-  case ALT(r1, r2) => s"(${string(r1)} + ${string(r2)})"
-  case SEQ(CHAR(c), CHAR(d)) => s"${c}${d}"
-  case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})"
-  case STAR(r) => s"(${string(r)})*"
-  case NTIMES(r, n) =>  s"(${string(r)}){${n}}"
-}
-
-
-// test: ("a" | "aa")*
-val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))
-
-// test: ("" | "a" | "aa")*
-val EVIL4 = STAR(ALT(ONE, ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))))
-
-val t1  = ders2("a".toList, EVIL3)
-val t1s = simp(t1) 
-val t2  = ders2("aa".toList, t1s)
-val t2s = simp(t2)
-val t3  = ders2("aaa".toList, t2s)
-val t3s = simp(t3)
-val t4  = ders2("aaaa".toList, t3s)
-val t4s = simp(t4)
-println(string(t1) + "    " + size(t1))
-println("s " + string(t1s) + "    " + size(t1s))
-println(string(t2) + "    " + size(t2))
-println("s " + string(t2s) + "    " + size(t2s))
-println(string(t3) + "    " + size(t3))
-println("s " + string(t3s) + "    " + size(t3s))
-println(string(t4) + "    " + size(t4))
-println("s " + string(t4s) + "    " + size(t4s))