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

case class SubString(s: String, l: Int, h: Int) {

  def low = l

  def high = h

  def length = h - l

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

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

}

type Ctxt = List[(String, SubString)]

abstract class Parser[T] {

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

  def parse_all(s: String) : Set[T] =

    for ((head, tail) <- parse(SubString(s, 0, s.length), Nil); if (tail.substring() == "")) yield head

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

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

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

}

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

  def parse(sb: SubString, ctxt: Ctxt) = 

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

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

}

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

  def parse(sb: SubString, ctxt: Ctxt) = p.parse(sb, ctxt) ++ q.parse(sb, ctxt)   

}

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

  def parse(sb: SubString, ctxt: Ctxt) = 

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

}

case class SubStringParser(s: String) extends Parser[SubString] {

  val n = s.length

  def parse(sb: SubString, ctxt: Ctxt) = {

    if (n <= sb.length && sb.substring(sb.low, sb.low + n) == s) 

      Set((sb.set(high = sb.low + n), sb.set(low = sb.low + n))) 

    else Set()

  }

}

implicit def string2parser(s: String) = SubStringParser(s) ==> (_.substring())

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

  def parse(sb: SubString, ctxt: Ctxt) = {

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

  def parse(sb: SubString, ctxt: Ctxt) = {

    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)

  }

}

// ambigous grammar

lazy val E: Parser[Int] = 

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

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

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

                 "0" ==> { (s) => 0 } ||

                 "1" ==> { (s) => 1 } ||

                 "2" ==> { (s) => 2 } ||

                 "3" ==> { (s) => 3 })

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