:load matcher.scala

// some regular expressions

val DIGIT = RANGE("0123456789".toList)

val NONZERODIGIT = RANGE("123456789".toList)

val NUMBER = ALT(SEQ(NONZERODIGIT, STAR(DIGIT)), "0")

val LPAREN = CHAR('(')

val RPAREN = CHAR(')')

val WHITESPACE = PLUS(RANGE(" \n".toList))

val OPS = RANGE("+-*".toList)

// 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

def tokenizer(rs: List[Rule[Token]], s: String) : List[Token] = 

  tokenize(rs, s.toList).filterNot(_ match {

    case T_WHITESPACE => true

    case _ => false

  })

// 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)))

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

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, rs: List[Rule[Token]], s: String) = {

  println("\n")

  parse(g, tokenizer(rs, s))

}

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

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

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