// A naive bottom-up parser with backtracking
//
// Needs:
//   :load matcher.scala

// some regular expressions
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 object T_NUM extends Token
case class T_OP(s: String) extends Token
case object T_LPAREN extends Token
case object T_RPAREN extends Token
case class NT(s: String) extends Token

// lexing rules for arithmetic expressions
val lexing_rules: List[Rule[Token]]= 
  List((NUMBER, (s) => T_NUM),
       (WHITESPACE, (s) => T_WHITESPACE),
       (LPAREN, (s) => T_LPAREN),
       (RPAREN, (s) => T_RPAREN),
       (OPS, (s) => T_OP(s.mkString)))

// the tokenizer
val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE))

type Grammar = List[(String, List[Token])]

// grammar for arithmetic expressions
val grammar = 
  List ("F" -> List(T_NUM),
        "E" -> List(T_NUM),
        "E" -> List(NT("E"), T_OP("+"), NT("E")),
        "E" -> List(NT("E"), T_OP("-"), NT("E")),
        "E" -> List(NT("E"), T_OP("*"), NT("E")),    
        "E" -> List(T_LPAREN, NT("E"), T_RPAREN))


def chop[A](ts1: List[A], prefix: List[A], ts2: List[A]) : Option[(List[A], List[A])] = 
  ts1 match {
    case Nil => None
    case t::ts => 
      if (ts1.startsWith(prefix)) Some(ts2.reverse, ts1.drop(prefix.length))
      else chop(ts, prefix, t::ts2)
  }

// examples for chop 
chop(List(1,2,3,4,5,6,7,8,9), List(4,5), Nil)  
chop(List(1,2,3,4,5,6,7,8,9), List(3,5), Nil)  

def replace[A](ts: List[A], out: List[A], in: List [A]) = 
  chop(ts, out, Nil) match {
    case None => None
    case Some((before, after)) => Some(before ::: in ::: after)
  }  

def parse(g: Grammar, ts: List[Token]) : Boolean = {
  println(ts)
  if (ts == List(NT("E"))) true
  else {
    val tss = for ((lhs, rhs) <- g) yield replace(ts, rhs, List(NT(lhs)))
    tss.flatten.exists(parse(g, _))
  }
}
 
def parser(g: Grammar, s: String) = {
  println("\n")
  parse(g, Tok.fromString(s))
}
  


parser(grammar, "2 + 3 *    4 +       1")
parser(grammar, "(2 + 3) * (4 + 1)")
parser(grammar, "(2 + 3) * 4 (4 + 1)")