// regular expressions

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 

// recognises nothing

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

  case NULL => true

  case EMPTY => false

  case CHAR(_) => false

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

  case STAR(_) => false

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

}

// 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))

}

// main matcher function

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

//some regular expressions

val LOWERCASE = RANGE("abcdefghijklmnopqrstuvwxyz".toList)

val UPPERCASE = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZ".toList)

val LETTER = ALT(LOWERCASE, UPPERCASE)

val DIGITS = RANGE("0123456789".toList)

val NONZERODIGITS = RANGE("123456789".toList)

val IDENT = SEQ(LETTER, STAR(ALT(LETTER,DIGITS)))

val NUMBER = ALT(SEQ(NONZERODIGITS, STAR(DIGITS)), "0")

val WHITESPACE = RANGE(" \n".toList)

val ALL = ALT(ALT(LETTER, DIGITS), WHITESPACE)

val COMMENT = SEQ(SEQ("/*", NOT(SEQ(SEQ(STAR(ALL), "*/"), STAR(ALL)))), "*/")

println(matcher(NUMBER, "0"))

println(matcher(NUMBER, "01"))

println(matcher(NUMBER, "123450"))

println(matcher(SEQ(STAR("a"), STAR("b")), "bbaaa"))

println(matcher(ALT(STAR("a"), STAR("b")), ""))

println(matcher("abc", ""))

println(matcher(STAR(ALT(EMPTY, "a")), ""))

println(matcher(STAR(EMPTY), "a"))

println(matcher("cab","cab"))

println(matcher(STAR("a"),"aaa"))

println(matcher("cab" ,"cab"))

println(matcher(STAR("a"),"aaa"))

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

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

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

// an example list of regular expressions

def error (s: String) = throw new IllegalArgumentException ("Could not lex " + s)

def munch(r: Rexp, s: List[Char], t: List[Char]) : Option[(List[Char], List[Char])] = s match {

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

  case Nil => None

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

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

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

}

def lex_one (regs: List[Rexp], s: List[Char]) : (List[Char], List[Char]) = {

 val somes = regs.map { munch(_, s, Nil) } .flatten

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

}

def lex_all (regs: List[Rexp], s: List[Char]) : List[String] = s match {

  case Nil => Nil

  case _ => lex_one(regs, s) match {

    case (rest, s) => s.mkString :: lex_all(regs, rest) 

  }

}