import scala.language.implicitConversions
import scala.language.reflectiveCalls

abstract class Parser[I <% Seq[_], T] {
  def parse(ts: I): Set[(T, I)]

  def parse_all(ts: I) : Set[T] =
    for ((head, tail) <- parse(ts); if (tail.isEmpty)) yield head
}

class SeqParser[I <% Seq[_], T, S](p: => Parser[I, T], q: => Parser[I, S]) extends Parser[I, (T, S)] {
  def parse(sb: I) = 
    for ((head1, tail1) <- p.parse(sb); 
         (head2, tail2) <- q.parse(tail1)) yield ((head1, head2), tail2)
}

class AltParser[I <% Seq[_], T](p: => Parser[I, T], q: => Parser[I, T]) extends Parser[I, T] {
  def parse(sb: I) = p.parse(sb) ++ q.parse(sb)   
}

class FunParser[I <% Seq[_], T, S](p: => Parser[I, T], f: T => S) extends Parser[I, S] {
  def parse(sb: I) = 
    for ((head, tail) <- p.parse(sb)) yield (f(head), tail)
}

// atomic parsers
case class CharParser(c: Char) extends Parser[String, Char] {
  def parse(sb: String) = 
    if (sb.head == c) Set((c, sb.tail)) else Set()
}

case class StringParser(s: String) extends Parser[String, String] {
  def parse(sb: String) = {
    val (prefix, suffix) = sb.splitAt(s.length)
    if (prefix == s) Set((prefix, suffix)) else Set()
  }
}

case object NumParser extends Parser[String, String] {
  val reg = "[0-9]+".r
  def parse(sb: String) = reg.findPrefixOf(sb) match {
    case None => Set()
    case Some(s) => Set(sb.splitAt(s.length)) 
  }
}


implicit def string2parser(s : String) = StringParser(s)

implicit def ParserOps[I<% Seq[_], T](p: Parser[I, T]) = new {
  def || (q : => Parser[I, T]) = new AltParser[I, T](p, q)
  def ==>[S] (f: => T => S) = new FunParser[I, T, S](p, f)
  def ~[S] (q : => Parser[I, S]) = new SeqParser[I, T, S](p, q)
}

implicit def StringOps(s: String) = new {
  def || (q : => Parser[String, String]) = new AltParser[String, String](s, q)
  def || (r: String) = new AltParser[String, String](s, r)
  def ==>[S] (f: => String => S) = new FunParser[String, String, S](s, f)
  def ~[S] (q : => Parser[String, S]) = 
    new SeqParser[String, String, S](s, q)
  def ~ (r: String) = 
    new SeqParser[String, String, String](s, r)
}




lazy val Pal : Parser[String, String] = 
  (("a" ~ Pal ~ "a") ==> { case ((x, y), z) => x + y + z } ||
   ("b" ~ Pal ~ "b") ==> { case ((x, y), z) => x + y + z } || "")

Pal.parse_all("ababbaba")


lazy val P : Parser[String, String] = 
  "(" ~ P ~ ")" ~ P ==> { case (((u, x), y), z) => "{" + x + "}" + z } || ""

P.parse_all("(((()()))())")
P.parse_all("(((()()))()))")
P.parse_all(")(")

lazy val E: Parser[String, String] = 
  (F ~ "*" ~ F) ==> { case ((x, y), z) => x + y + z } || F  
lazy val F: Parser[String, String] = 
  ((T ~ "+" ~ T) ==> { case ((x, y), z) => x + y + z } ||
   (T ~ "-" ~ T) ==> { case ((x, y), z) => x + y + z } || T)
lazy val T: Parser[String, String] = 
  ("(" ~ E ~ ")") ==> { case ((x, y), z) => x + y + z } || NumParser


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



// non-ambiguous vs ambiguous
lazy val U : Parser[String, String] =
  ("1" ~ U) ==> { case (x, y) => x + y } || ""

U.parse_all("1" * 100 + "0")

lazy val S : Parser[String, String] =
  ("1" ~ S ~ S) ==> { case ((x, y), z) => x + y + z } || ""

S.parse_all("1" * 15)