// regular expressions including NOT

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 NOT(r: Rexp) extends Rexp

// 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)

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

}

// tests whether a regular expression 

// cannot recognise more

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

  case NULL => true

  case EMPTY => false

  case CHAR(_) => false

  case ALT(r1, r2) => no_more(r1) && no_more(r2)

  case SEQ(r1, r2) => if (nullable(r1)) (no_more(r1) && no_more(r2)) else no_more(r1)

  case STAR(_) => false

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

}

// regular expression for specifying 

// ranges of characters

def RANGE(s : List[Char]) : Rexp = s match {

  case Nil => NULL

  case c::Nil => CHAR(c)

  case c::s => ALT(CHAR(c), RANGE(s))

}

// one or more

def PLUS(r: Rexp) = SEQ(r, STAR(r))

type Rule[T] = (Rexp, List[Char] => T)

def error (s: String) = throw new IllegalArgumentException ("Cannot tokenize: " + s)

def munch[T](r: Rexp, action: List[Char] => T, s: List[Char], t: List[Char]) : Option[(List[Char], T)] = 

  s match {

    case Nil if (nullable(r)) => Some(Nil, action(t))

    case Nil => None

    case c::s if (no_more(der (c, r)) && nullable(r)) => Some(c::s, action(t))

    case c::s if (no_more(der (c, r))) => None

    case c::s => munch(der (c, r), action, s, t ::: List(c))

  }

def one_token[T](rs: List[Rule[T]], s: List[Char]) : (List[Char], T) = {

 val somes = rs.map { (r) => munch(r._1, r._2, s, Nil) } .flatten

 if (somes == Nil) error(s.mkString) else (somes sortBy (_._1.length) head)

}

def tokenize[T](rs: List[Rule[T]], s: List[Char]) : List[T] = s match {

  case Nil => Nil

  case _ => one_token(rs, s) match {

    case (rest, token) => token :: tokenize(rs, rest) 

  }

}