val DIGIT = RANGE("0123456789")

val NONZERODIGIT = RANGE("123456789")

val NUMBER = ALT(SEQ(NONZERODIGIT, STAR(DIGIT)), "0")

val LPAREN = CHAR('(')

val RPAREN = CHAR(')')

val WHITESPACE = PLUS(RANGE(" \n"))

val OPS = RANGE("+-*")

// for classifying the strings that have been recognised

abstract class Token

case object T_WHITESPACE extends Token

case class T_NUM(s: String) extends Token

case class T_OP(s: String) extends Token

case object T_LPAREN extends Token

case object T_RPAREN extends Token

val lexing_rules: List[Rule[Token]]= 

  List((NUMBER, (s) => T_NUM(s.mkString)),

       (WHITESPACE, (s) => T_WHITESPACE),

       (LPAREN, (s) => T_LPAREN),

       (RPAREN, (s) => T_RPAREN),

       (OPS, (s) => T_OP(s.mkString)))

val Tk = Tokenizer(lexing_rules, List(T_WHITESPACE))

// parser combinators with input type I and return type T

// and memoisation

case class SubList[T](s: List[T], l: Int, h: Int) {

  def low = l

  def high = h

  def length = h - l

  def sublist(l: Int = l, h: Int = h) = s.slice(l, h)

  def set(low: Int = l, high: Int = h) = SubList(s, low, high)

}

type Ctxt[T] = List[(String, SubList[T])]

abstract class Parser[I, T] {

  def parse(ts: SubList[I], ctxt: Ctxt[I]): Set[(T, SubList[I])]

  def parse_all(s: List[I]) : Set[T] =

    for ((head, tail) <- parse(SubList(s, 0, s.length), Nil); if (tail.sublist() == Nil)) yield head

  def || (right : => Parser[I, T]) : Parser[I, T] = new AltParser(this, right)

  def ==>[S] (f: => T => S) : Parser [I, S] = new FunParser(this, f)

  def ~[S] (right : => Parser[I, S]) : Parser[I, (T, S)] = new SeqParser(this, right)

  def ~>[S] (right : => Parser[I, S]) : Parser[I, S] = this ~ right ==> (_._2)

  def <~[S] (right : => Parser[I, S]) : Parser[I, T] = this ~ right ==> (_._1)

}

class SeqParser[I, T, S](p: => Parser[I, T], q: => Parser[I, S]) extends Parser[I, (T, S)] {

  def parse(sb: SubList[I], ctxt: Ctxt[I]) = 

    for ((head1, tail1) <- p.parse(sb, ctxt); 

         (head2, tail2) <- q.parse(tail1, ctxt)) yield ((head1, head2), tail2)

}

class AltParser[I, T](p: => Parser[I, T], q: => Parser[I, T]) extends Parser[I, T] {

  def parse(sb: SubList[I], ctxt: Ctxt[I]) = p.parse(sb, ctxt) ++ q.parse(sb, ctxt)   

}

class FunParser[I, T, S](p: => Parser[I, T], f: T => S) extends Parser[I, S] {

  def parse(sb: SubList[I], ctxt: Ctxt[I]) = 

    for ((head, tail) <- p.parse(sb, ctxt)) yield (f(head), tail)

}

case object NumParser extends Parser[Token, Int] {

  def parse(sb: SubList[Token], ctxt: Ctxt[Token]) = {

    if (0 < sb.length) sb.sublist(sb.low, sb.low + 1) match { 

      case T_NUM(i)::Nil => Set((i.toInt, sb.set(low = sb.low + 1))) 

      case _ => Set()

    }

    else Set()

  }

}

case class TokParser(t: Token) extends Parser[Token, Token] {

  def parse(sb: SubList[Token], ctxt: Ctxt[Token]) = {

    if (0 < sb.length && sb.sublist(sb.low, sb.low + 1) == List(t)) Set((t, sb.set(low = sb.low + 1))) 

    else Set()

  }

}

implicit def token2tparser(t: Token) = TokParser(t)

class IgnLst[I, T](p: => Parser[I, T]) extends Parser[I, T] {

  def parse(sb: SubList[I], ctxt: Ctxt[I]) = {

    if (sb.length == 0) Set()

    else for ((head, tail) <- p.parse(sb.set(high = sb.high - 1), ctxt)) 

         yield (head, tail.set(high = tail.high + 1))

  }

}

class CHECK[I, T](nt: String, p: => Parser[I, T]) extends Parser[I, T] {

  def parse(sb: SubList[I], ctxt: Ctxt[I]) = {

    val should_trim = ctxt.contains (nt, sb)

    if (should_trim && sb.length == 0) Set()

    else if (should_trim) new IgnLst(p).parse(sb, (nt, sb)::ctxt)

    else p.parse(sb, (nt, sb)::ctxt)

  }

}

lazy val E: Parser[Token, Int] = 

  new CHECK("E", (E ~ T_OP("+") ~ E) ==> { case ((x, y), z) => x + z} || 

                 (E ~ T_OP("*") ~ E) ==> { case ((x, y), z) => x * z} ||

                 (T_LPAREN ~ E ~ T_RPAREN) ==> { case ((x, y), z) => y} ||

                 NumParser)

println(E.parse_all(Tk.fromString("1 + 2 * 3")))

println(E.parse_all(Tk.fromString("(1 + 2) * 3")))