--- a/progs/re3.scala	Tue Aug 23 23:12:55 2016 +0200
+++ b/progs/re3.scala	Tue Sep 20 12:24:29 2016 +0100
@@ -1,36 +1,18 @@
-abstract class Rexp 
-case object NULL extends Rexp
-case object EMPTY extends Rexp
+
+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 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 
 
-def simp(r: Rexp): Rexp = r match {
-  case ALT(r1, r2) => {
-    (simp(r1), simp(r2)) match {
-      case (NULL, r2s) => r2s
-      case (r1s, NULL) => r1s
-      case (r1s, r2s) => if (r1s == r2s) r1s else ALT(r1s, r2s)
-    }
-  }
-  case SEQ(r1, r2) => {
-    (simp(r1), simp(r2)) match {
-      case (NULL, _) => NULL
-      case (_, NULL) => NULL
-      case (EMPTY, r2s) => r2s
-      case (r1s, EMPTY) => r1s
-      case (r1s, r2s) => SEQ(r1s, r2s)
-    }
-  }
-  case NTIMES(r, n) => NTIMES(simp(r), n)    
-  case r => r
-}
-
+// nullable function: tests whether the regular 
+// expression can recognise the empty string
 def nullable (r: Rexp) : Boolean = r match {
-  case NULL => false
-  case EMPTY => true
+  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)
@@ -38,31 +20,56 @@
   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 NULL => NULL
-  case EMPTY => NULL
-  case CHAR(d) => if (c == d) EMPTY else NULL
+  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) NULL else SEQ(der(c, r), NTIMES(r, i - 1))
+    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)
+  }
+  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 NTIMES(r1, n) => NTIMES(simp(r), n)
+  case r => 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)))
 }
 
-def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
+
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
 
 
 //one or zero
-def OPT(r: Rexp) = ALT(r, EMPTY)
+def OPT(r: Rexp) = ALT(r, ONE)
 
-def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
+//evil regular expressions
+def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
+val EVIL2 = SEQ(STAR(CHAR('a')), CHAR('b'))
+
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -71,70 +78,16 @@
   (end - start)/(i * 1.0e9)
 }
 
+val i = 5000
+println(i + " " + "%.5f".format(time_needed(10, matcher(EVIL1(i), "a" * i))))
 
-for (i <- 1 to 12001 by 500) {
-  println(i + " " + "%.5f".format(time_needed(1, matches(EVIL(i), "a" * i))))
+for (i <- 1 to 9001 by 1000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
 }
 
-
-// some convenience for typing in regular expressions
-import scala.language.implicitConversions    
-import scala.language.reflectiveCalls 
-def charlist2rexp(s : List[Char]) : Rexp = s match {
-  case Nil => EMPTY
-  case c::Nil => CHAR(c)
-  case c::s => SEQ(CHAR(c), charlist2rexp(s))
-}
-implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
-
-implicit def RexpOps (r: Rexp) = new {
-  def | (s: Rexp) = ALT(r, s)
-  def % = STAR(r)
-  def ~ (s: Rexp) = SEQ(r, s)
-}
-
-implicit def stringOps (s: String) = new {
-  def | (r: Rexp) = ALT(s, r)
-  def | (r: String) = ALT(s, r)
-  def % = STAR(s)
-  def ~ (r: Rexp) = SEQ(s, r)
-  def ~ (r: String) = SEQ(s, r)
+for (i <- 1 to 7500001 by 500000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
 }
 
 
 
-def PLUS(r: Rexp) = SEQ(r, STAR(r))
-def RANGE(s: List[Char]) : Rexp = s match {
-  case Nil => NULL
-  case c::s => ALT(CHAR(c), RANGE(s))
-} 
-
-println("EVILS:")
-val EVIL1 = PLUS(PLUS("a" ~ "a" ~ "a"))
-val EVIL2 = PLUS(PLUS("aaaaaaaaaaaaaaaaaaa" ~ OPT("a")))  // 19 as ~ a?
-
-
-//40 * aaa matches
-//43 * aaa + aa does not
-//45 * aaa + a
-
-println("EVIL1:")
-println(matches(EVIL1, "aaa" * 40))
-println(matches(EVIL1, "aaa" * 43 + "aa"))
-println(matches(EVIL1, "aaa" * 45 + "a"))
-println("EVIL2:")
-println(matches(EVIL2, "aaa" * 40))
-println(matches(EVIL2, "aaa" * 43 + "aa"))
-println(matches(EVIL2, "aaa" * 45 + "a"))
-
-
-
-
-println("EMAIL:")
-val LOWERCASE = "abcdefghijklmnopqrstuvwxyz"
-val DIGITS = "0123456789"
-val EMAIL = PLUS(RANGE((LOWERCASE + DIGITS + "_" + "." + "-").toList)) ~ "@" ~ 
-            PLUS(RANGE((LOWERCASE + DIGITS + "." + "-").toList)) ~ "." ~
-            NMTIMES(RANGE((LOWERCASE + ".").toList), 2, 6)
-
-val my_email = "christian.urban@kcl.ac.uk"