--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/regexp2.scala	Wed Oct 10 08:39:24 2012 +0100
@@ -0,0 +1,143 @@
+// regular expressions
+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 
+// recognises nothing
+def zeroable (r: Rexp) : Boolean = r match {
+  case NULL => true
+  case EMPTY => false
+  case CHAR(_) => false
+  case ALT(r1, r2) => zeroable(r1) && zeroable(r2)
+  case SEQ(r1, r2) => zeroable(r1) || zeroable(r2)
+  case STAR(_) => false
+  case NOT(r) => !(zeroable(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))
+}
+
+// derivative w.r.t. a string (iterates der)
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, 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 LOWERCASE = RANGE("abcdefghijklmnopqrstuvwxyz".toList)
+val UPPERCASE = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZ".toList)
+val LETTER = ALT(LOWERCASE, UPPERCASE)
+val DIGITS = RANGE("0123456789".toList)
+val NONZERODIGITS = RANGE("123456789".toList)
+
+val IDENT = SEQ(LETTER, STAR(ALT(LETTER,DIGITS)))
+val NUMBER = ALT(SEQ(NONZERODIGITS, STAR(DIGITS)), "0")
+val WHITESPACE = RANGE(" \n".toList)
+
+val ALL = ALT(ALT(LETTER, DIGITS), WHITESPACE)
+
+val COMMENT = SEQ(SEQ("/*", NOT(SEQ(SEQ(STAR(ALL), "*/"), STAR(ALL)))), "*/")
+
+println(matcher(NUMBER, "0"))
+println(matcher(NUMBER, "01"))
+println(matcher(NUMBER, "123450"))
+
+println(matcher(SEQ(STAR("a"), STAR("b")), "bbaaa"))
+println(matcher(ALT(STAR("a"), STAR("b")), ""))
+println(matcher("abc", ""))
+println(matcher(STAR(ALT(EMPTY, "a")), ""))
+println(matcher(STAR(EMPTY), "a"))
+println(matcher("cab","cab"))
+println(matcher(STAR("a"),"aaa"))
+println(matcher("cab" ,"cab"))
+println(matcher(STAR("a"),"aaa"))
+
+println(matcher(COMMENT, "/* */"))
+println(matcher(COMMENT, "/* foobar comment */"))
+println(matcher(COMMENT, "/* test */ test */"))
+
+// an example list of regular expressions
+val regs: List[Rexp]=  List("if", "then", "else", "+", IDENT, NUMBER, WHITESPACE) 
+
+def error (s: String) = throw new IllegalArgumentException ("Could not lex " + s)
+
+def munch(r: Rexp, s: List[Char], t: List[Char]) : Option[(List[Char], List[Char])] = s match {
+  case Nil if (nullable(r)) => Some(Nil, t)
+  case Nil => None
+  case c::s if (zeroable(der (c, r)) && nullable(r)) => Some(c::s, t)
+  case c::s if (zeroable(der (c, r))) => None
+  case c::s => munch(der (c, r), s, t ::: List(c))
+}
+
+def lex_one (regs: List[Rexp], s: List[Char]) : (List[Char], List[Char]) = {
+ val somes = regs.map { munch(_, s, Nil) } .flatten
+ if (somes == Nil) error(s.mkString) else (somes sortBy (_._1.length) head)
+}
+
+def lex_all (regs: List[Rexp], s: List[Char]) : List[String] = s match {
+  case Nil => Nil
+  case _ => lex_one(regs, s) match {
+    case (rest, s) => s.mkString :: lex_all(regs, rest) 
+  }
+}
+
+println(lex_all(rules, "if true then 42 else +".toList))
+println(lex_all(rules, "ifff if     34 34".toList))
+println(lex_all(rules, "ifff $ if 34".toList))
+