abstract class Rexp 

case object NULL extends Rexp

case object EMPTY 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 (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

}

def nullable (r: Rexp) : Boolean = r match {

  case NULL => false

  case EMPTY => 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 NULL => NULL

  case EMPTY => NULL

  case CHAR(d) => if (c == d) EMPTY else NULL

  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))

}

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, EMPTY)

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 12001 by 500) {

  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 => 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)

}

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"