diff -r e74c696821a2 -r 5deefcc8cffa progs/re3ext.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/re3ext.scala	Tue Sep 20 12:24:29 2016 +0100
@@ -0,0 +1,151 @@
+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 
+
+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(r, n) => NTIMES(simp(r), n)    
+  case r => r
+}
+
+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(r) => SEQ(der(c, r), STAR(r))
+  case NTIMES(r, i) => 
+    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
+}
+
+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))
+
+
+//one or zero
+def OPT(r: Rexp) = ALT(r, ONE)
+
+def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
+
+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)
+}
+
+/*
+for (i <- 1 to 9001 by 1000) {
+  println(i + " " + "%.5f".format(time_needed(1, matches(EVIL(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 => ONE
+  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)
+}
+
+
+def PLUS(r: Rexp) = SEQ(r, STAR(r))
+def RANGE(s: List[Char]) : Rexp = s match {
+  case Nil => ZERO
+  case c::s => ALT(CHAR(c), RANGE(s))
+} 
+def NMTIMES(r: Rexp, n: Int, m: Int) : Rexp =
+  if (n >= m) NTIMES(r, n) else ALT(NTIMES(r, m), NMTIMES(r, n, m - 1))
+
+
+println("Coursework:")
+val REG1 = PLUS(PLUS("a" ~ "a" ~ "a"))
+val REG2 = PLUS(PLUS("aaaaaaaaaaaaaaaaaaa" ~ OPT("a")))  // 19 as ~ a?
+
+
+//40 * aaa matches
+//43 * aaa + aa does not
+//45 * aaa + a
+
+println("EVIL1:")
+println(matches(REG1, "aaa" * 40))
+println(matches(REG1, "aaa" * 43 + "aa"))
+println(matches(REG1, "aaa" * 45 + "a"))
+println("EVIL2:")
+println(matches(REG2, "aaa" * 40))
+println(matches(REG2, "aaa" * 43 + "aa"))
+println(matches(REG2, "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"
+
+println(matches(EMAIL, my_email))
+
+println(matches(NTIMES("a", 2), "a"))
+println(matches(NTIMES("a", 2), "aa"))
+println(matches(NTIMES("a", 2), "aaa"))
+
+println(matches(NMTIMES("a", 2, 3), "a"))
+println(matches(NMTIMES("a", 2, 3), "aa"))
+println(matches(NMTIMES("a", 2, 3), "aaa"))
+println(matches(NMTIMES("a", 2, 3), "aaaa"))