import scala.language.implicitConversions    

import scala.language.reflectiveCalls 

abstract class Rexp {

  def simp : Rexp = this

}

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 {

  override def toString = r1.toString + " | " + r2.toString

  override def simp = (r1.simp, r2.simp) match {

    case (NULL, r) => r

    case (r, NULL) => r

    case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)

    case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)

    case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)

  }

}

case class RANGE(cs: List[Char]) extends Rexp {

  //override def toString = cs.mkString("[",",","]")

  override def toString = "[" + cs.head + " .. " + cs.last + "]"

}

object RANGE {

  def apply(s: String) : RANGE = RANGE(s.toList)

}

case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {

  override def toString = r1.toString + " ~ " + r2.toString

  override def simp = (r1.simp, r2.simp) match {

    case (NULL, _) => NULL

    case (_, NULL) => NULL

    case (EMPTY, r) => r

    case (r, EMPTY) => r

    case (r1, r2) => SEQ(r1, r2)

  }

}

case class PLUS(r: Rexp) extends Rexp {

  override def simp = r.simp match {

    case NULL => EMPTY

    case EMPTY => EMPTY

    case r => PLUS(r)

  }

}

case class STAR(r: Rexp) extends Rexp {

  override def simp = r.simp match {

    case NULL => EMPTY

    case EMPTY => EMPTY

    case r => STAR(r)

  }

}

case class NTIMES(r: Rexp, n: Int) extends Rexp {

  override def simp = if (n == 0) EMPTY else 

    r.simp match {

      case NULL => NULL

      case EMPTY => EMPTY

      case r => NTIMES(r, n)

    }

}

case class NMTIMES(r: Rexp, n: Int, m: Int) extends Rexp {

  if(m < n) throw new IllegalArgumentException("the number m cannot be smaller than n.")

  override def simp = if (m == 0) EMPTY else 

    r.simp match {

      case NULL => NULL

      case EMPTY => EMPTY

      case r => NMTIMES(r, n, m)

    }

}

case class NOT(r: Rexp) extends Rexp {

  override def simp = NOT(r.simp)

}

case class OPT(r: Rexp) extends Rexp {

  override def simp = OPT(r.simp)

}

// 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 CHAR(_) => false

  case ALT(r1, r2) => nullable(r1) || nullable(r2)

  case SEQ(r1, r2) => nullable(r1) && nullable(r2)

  case STAR(_) => true

  case PLUS(r) => nullable(r)

  case NTIMES(r, i) => if (i == 0) true else nullable(r)

  case NMTIMES(r, i, j) => if (i == 0) true else nullable(r)

  case RANGE(_) => false

  case NOT(r) => !(nullable(r))

  case OPT(_) => true

}

// 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 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 PLUS(r) => der(c, SEQ(r, STAR(r)))

  case NTIMES(r, i) => 

    if (i == 0) NULL else der(c, SEQ(r, NTIMES(r, i - 1)))

  case NMTIMES(r, i, j) => 

    if (j == 0) NULL 

    if (i == 0) der(c, NTIMES(r, j))

    else der(c, SEQ(r, NMTIMES(r, i - 1, j - 1)))

  case RANGE(cs) => if (cs contains c) EMPTY else NULL

  case NOT(r) => NOT(der (c, r))

  case OPT(r) => der(c, 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, der(c, r))

}

def ders_simp (s: List[Char], r: Rexp) : Rexp = s match {

  case Nil => r

  case c::s => ders_simp(s, der(c, r).simp)

}

// main matcher function

def matcher(r: Rexp, s: String) : Boolean = nullable(ders_simp(s.toList, r))

// some convenience for typing in regular expressions

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)

}

println("EMAIL:")

val LOWERCASE = "abcdefghijklmnopqrstuvwxyz"

val DIGITS = "0123456789"

val EMAIL = PLUS(RANGE(LOWERCASE + DIGITS + "_" + "." + "-")) ~ "@" ~ 

            PLUS(RANGE(LOWERCASE + DIGITS + "." + "-")) ~ "." ~

            NMTIMES(RANGE(LOWERCASE + "."), 2, 6)

val my_email = "christian.urban@kcl.ac.uk"

println(EMAIL);

println(matcher(EMAIL, my_email))

println(ders_simp(my_email.toList, EMAIL))

println("COMMENTS:")

val ALL = RANGE(LOWERCASE + " ")

val COMMENT = "/*" ~ (NOT(ALL.% ~ "*/" ~ ALL.%)) ~ "*/"

println(matcher(COMMENT, "/**/"))

println(matcher(COMMENT, "/*foobar_comment*/"))

println(matcher(COMMENT, "/*test*/test*/"))

println(matcher(COMMENT, "/*test/*test*/"))

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(matcher(EVIL1, "aaa" * 40))

println(matcher(EVIL1, "aaa" * 43 + "aa"))

println(matcher(EVIL1, "aaa" * 45 + "a"))

println("EVIL2:")

println(matcher(EVIL2, "aaa" * 40))

println(matcher(EVIL2, "aaa" * 43 + "aa"))

println(matcher(EVIL2, "aaa" * 45 + "a"))