:load matcher.scala

// some regular expressions

val LETTER = RANGE("abcdefghijklmnopqrstuvwxyz".toList)

val ID = PLUS(LETTER)

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 class T_NUM(s: String) extends Token

case class T_ID(s: String) extends Token

case class T_OP(s: String) extends Token

case object T_LPAREN extends Token

case object T_RPAREN extends Token

case object T_IF extends Token

case object T_THEN extends Token

case object T_ELSE 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(("if", (s) => T_IF),

       ("then", (s) => T_THEN),

       ("else", (s) => T_ELSE),

       (NUMBER, (s) => T_NUM(s.mkString)),

       (ID, (s) => T_ID(s.mkString)),

       (WHITESPACE, (s) => T_WHITESPACE),

       (LPAREN, (s) => T_LPAREN),

       (RPAREN, (s) => T_RPAREN),

       (OPS, (s) => T_OP(s.mkString)))

// parse trees

abstract class ParseTree

case class Leaf(t: Token) extends ParseTree

case class Branch(pts: List[ParseTree]) extends ParseTree

def combine(pt1: ParseTree, pt2: ParseTree) = pt1 match {

  case Leaf(t) => Branch(List(Leaf(t), pt2))

  case Branch(pts) => Branch(pts ++ List(pt2))

}

// parser combinators

abstract class Parser {

  def parse(ts: List[Token]): Set[(ParseTree, List[Token])]

  def parse_all(ts: List[Token]) : Set[ParseTree] =

    for ((head, tail) <- parse(ts); if (tail == Nil)) yield head

  def || (right : => Parser) : Parser = new AltParser(this, right)

  def ~ (right : => Parser) : Parser = new SeqParser(this, right)

}

class AltParser(p: => Parser, q: => Parser) extends Parser {

  def parse (ts: List[Token]) = p.parse(ts) ++ q.parse(ts)   

}

class SeqParser(p: => Parser, q: => Parser) extends Parser {

  def parse(ts: List[Token]) = 

    for ((head1, tail1) <- p.parse(ts); 

         (head2, tail2) <- q.parse(tail1)) yield (combine(head1, head2), tail2)

}

class ListParser(ps: => List[Parser]) extends Parser {

  def parse(ts: List[Token]) = ps match {

    case Nil => Set()

    case p::Nil => p.parse(ts)

    case p::ps =>

      for ((head1, tail1) <- p.parse(ts); 

           (head2, tail2) <- new ListParser(ps).parse(tail1)) yield (Branch(List(head1, head2)), tail2)

  }

}

case class TokParser(tok: Token) extends Parser {

  def parse(ts: List[Token]) = ts match {

    case t::ts if (t == tok) => Set((Leaf(t), ts)) 

    case _ => Set ()

  }

}

implicit def token2tparser(t: Token) = TokParser(t)

case object IdParser extends Parser {

  def parse(ts: List[Token]) = ts match {

    case T_ID(s)::ts => Set((Leaf(T_ID(s)), ts)) 

    case _ => Set ()

  }

}

case object NumParser extends Parser {

  def parse(ts: List[Token]) = ts match {

    case T_NUM(s)::ts => Set((Leaf(T_NUM(s)), ts)) 

    case _ => Set ()

  }

}

lazy val E: Parser = (T ~ T_OP("+") ~ E) || T  // start symbol

lazy val T: Parser = (F ~ T_OP("*") ~ T) || F

lazy val F: Parser = (T_LPAREN ~ E ~ T_RPAREN) || NumParser

println(E.parse_all(tokenizer(lexing_rules, "1 + 2 + 3")))

def eval(t: ParseTree) : Int = t match {

  case Leaf(T_NUM(n)) => n.toInt

  case Branch(List(t1, Leaf(T_OP("+")), t2)) => eval(t1) + eval(t2)

  case Branch(List(t1, Leaf(T_OP("*")), t2)) => eval(t1) * eval(t2)

  case Branch(List(Leaf(T_LPAREN), t, Leaf(T_RPAREN))) => eval(t) 

}

(E.parse_all(tokenizer(lexing_rules, "1 + 2 + 3"))).map(eval(_))

(E.parse_all(tokenizer(lexing_rules, "1 + 2 * 3"))).map(eval(_))

(E.parse_all(tokenizer(lexing_rules, "(1 + 2) * 3"))).map(eval(_))

lazy val EXPR: Parser = 

  new ListParser(List(T_IF, EXPR, T_THEN, EXPR)) || 

  new ListParser(List(T_IF, EXPR, T_THEN, EXPR, T_ELSE, EXPR)) || 

  IdParser

println(EXPR.parse_all(tokenizer(lexing_rules, "if a then b else c")))

println(EXPR.parse_all(tokenizer(lexing_rules, "if a then if x then y else c")))