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 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)