// 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"))