diff -r d2c6852ca8da -r 7a777d9cc343 parser.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/parser.scala	Wed Oct 31 02:05:12 2012 +0000
@@ -0,0 +1,182 @@
+
+// regular expressions including NOT
+abstract class Rexp
+
+case object NULL extends Rexp
+case object EMPTY extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
+case class STAR(r: Rexp) extends Rexp
+case class NOT(r: Rexp) extends Rexp
+
+
+// some convenience for typing in regular expressions
+def charlist2rexp(s : List[Char]) : Rexp = s match {
+  case Nil => EMPTY
+  case c::Nil => CHAR(c)
+  case c::s => SEQ(CHAR(c), charlist2rexp(s))
+}
+implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
+
+
+// nullable function: tests whether the regular 
+// expression can recognise the empty string
+def nullable (r: Rexp) : Boolean = r match {
+  case NULL => false
+  case EMPTY => true
+  case CHAR(_) => false
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  case NOT(r) => !(nullable(r))
+}
+
+// tests whether a regular expression 
+// cannot recognise more
+def no_more (r: Rexp) : Boolean = r match {
+  case NULL => true
+  case EMPTY => false
+  case CHAR(_) => false
+  case ALT(r1, r2) => no_more(r1) && no_more(r2)
+  case SEQ(r1, r2) => if (nullable(r1)) (no_more(r1) && no_more(r2)) else no_more(r1)
+  case STAR(_) => false
+  case NOT(r) => !(no_more(r))
+}
+
+
+// derivative of a regular expression w.r.t. a character
+def der (c: Char, r: Rexp) : Rexp = r match {
+  case NULL => NULL
+  case EMPTY => NULL  case CHAR(d) => if (c == d) EMPTY else NULL
+  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
+  case SEQ(r1, r2) => 
+    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
+    else SEQ(der(c, r1), r2)
+  case STAR(r) => SEQ(der(c, r), STAR(r))
+  case NOT(r) => NOT(der (c, r))
+}
+
+// regular expression for specifying 
+// ranges of characters
+def RANGE(s : List[Char]) : Rexp = s match {
+  case Nil => NULL
+  case c::Nil => CHAR(c)
+  case c::s => ALT(CHAR(c), RANGE(s))
+}
+
+// one or more
+def PLUS(r: Rexp) = SEQ(r, STAR(r))
+
+// 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 T_NT(s: String) extends Token
+
+type Rule = (Rexp, List[Char] => Token)
+
+def error (s: String) = throw new IllegalArgumentException ("Cannot tokenize: " + s)
+
+def munch(r: Rexp, action: List[Char] => Token, s: List[Char], t: List[Char]) : Option[(List[Char], Token)] = 
+  s match {
+    case Nil if (nullable(r)) => Some(Nil, action(t))
+    case Nil => None
+    case c::s if (no_more(der (c, r)) && nullable(r)) => Some(c::s, action(t))
+    case c::s if (no_more(der (c, r))) => None
+    case c::s => munch(der (c, r), action, s, t ::: List(c))
+  }
+
+def one_token (rs: List[Rule], s: List[Char]) : (List[Char], Token) = {
+ val somes = rs.map { (r) => munch(r._1, r._2, s, Nil) } .flatten
+ if (somes == Nil) error(s.mkString) else (somes sortBy (_._1.length) head)
+}
+
+def tokenize (rs: List[Rule], s: List[Char]) : List[Token] = s match {
+  case Nil => Nil
+  case _ => one_token(rs, s) match {
+    case (rest, token) => token :: tokenize(rs, rest) 
+  }
+}
+
+def tokenizer(rs: List[Rule], 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]= 
+  List((NUMBER, (s) => T_NUM),
+       (WHITESPACE, (s) => T_WHITESPACE),
+       (LPAREN, (s) => T_LPAREN),
+       (RPAREN, (s) => T_RPAREN),
+       (OPS, (s) => T_OP(s.mkString)))
+
+
+// examples
+println(tokenizer(lexing_rules, "2 + 3 * 4 + 1"))
+println(tokenizer(lexing_rules, "(2 + 3) * (4 + 1)"))
+
+
+type Grammar = List[(String, List[Token])]
+
+// grammar for arithmetic expressions
+val grammar = 
+  List ("E" -> List(T_NUM),
+        "E" -> List(T_NT("E"), T_OP("+"), T_NT("E")),
+        "E" -> List(T_NT("E"), T_OP("-"), T_NT("E")),
+        "E" -> List(T_NT("E"), T_OP("*"), T_NT("E")),    
+        "E" -> List(T_LPAREN, T_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 parse1(g: Grammar, ts: List[Token]) : Boolean = {
+  //println(ts)
+  if (ts == List(T_NT("E"))) true
+  else {
+    val tss = for ((lhs, rhs) <- g) yield replace(ts, rhs, List(T_NT(lhs)))
+    tss.flatten.exists(parse1(g, _))
+  }
+}
+ 
+
+println() ; parse1(grammar, tokenizer(lexing_rules, "2 + 3 * 4 + 1"))
+println() ; parse1(grammar, tokenizer(lexing_rules, "(2 + 3) * (4 + 1)"))
+println() ; parse1(grammar, tokenizer(lexing_rules, "(2 + 3) * 4 (4 + 1)"))
+
+
+