--- a/regexp.scala	Wed Oct 03 02:14:55 2012 +0100
+++ b/regexp.scala	Thu Oct 04 09:07:33 2012 +0100
@@ -1,3 +1,4 @@
+// regular expressions
 abstract class Rexp
 
 case object NULL extends Rexp
@@ -7,7 +8,54 @@
 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
 case class STAR(r: Rexp) extends Rexp
 
-// whether it can match the empty string
+// some convenience for typing in regular expressions
+implicit def string2rexp(s : String) : Rexp = {
+  s.foldRight (EMPTY: Rexp) ( (c, r) => SEQ(CHAR(c), r) )
+}
+
+// for example
+println(STAR("abc"))
+
+// produces STAR(SEQ(CHAR(a),SEQ(CHAR(b),SEQ(CHAR(c),EMPTY))))
+
+
+
+// a simple-minded regular expression matcher:
+// it loops for examples like STAR(EMPTY) with
+// strings this regular expression does not match
+
+def smatchers(rs: List[Rexp], s: List[Char]) : Boolean = (rs, s) match {
+  case (NULL::rs, s) => false
+  case (EMPTY::rs, s) => smatchers(rs, s)
+  case (CHAR(c)::rs, Nil) => false
+  case (CHAR(c)::rs, d::s) => (c ==d) && smatchers(rs, s) 
+  case (ALT(r1, r2)::rs, s) => smatchers(r1::rs, s) || smatchers(r2::rs, s)
+  case (SEQ(r1, r2)::rs, s) => smatchers(r1::r2::rs, s) 
+  case (STAR(r)::rs, s) => smatchers(rs, s) || smatchers(r::STAR(r)::rs, s) 
+  case (Nil, s) => s == Nil
+}
+
+def smatcher(r: Rexp, s: String) = smatchers(List(r), s.toList)
+
+// regular expression: a
+println(smatcher(CHAR('a'), "ab")) 
+
+// regular expression: a + (b o c)
+println(smatcher(ALT(CHAR('a'), SEQ(CHAR('b'), CHAR('c'))), "ab")) 
+
+// regular expression: a + (b o c)
+println(smatcher(ALT(CHAR('a'), SEQ(CHAR('b'), CHAR('c'))), "bc")) 
+
+// loops for regular expression epsilon* 
+//println(smatcher(STAR(EMPTY), "a"))
+
+
+
+// Regular expression matcher that works properly
+//================================================
+
+// 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
@@ -17,36 +65,37 @@
   case STAR(_) => true
 }
 
-// derivative of a regular expression
-def deriv (r: Rexp, c: Char) : Rexp = r match {
+// 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(deriv(r1, c), deriv(r2, c))
+  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
   case SEQ(r1, r2) => 
-    if (nullable(r1)) ALT(SEQ(deriv(r1, c), r2), deriv(r2, c))
-    else SEQ(deriv(r1, c), r2)
-  case STAR(r) => SEQ(deriv(r, c), STAR(r))
+    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))
 }
 
-def derivs (r: Rexp, s: List[Char]) : Rexp = s match {
+// derivative w.r.t. a string (iterates der)
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
   case Nil => r
-  case c::cs => derivs(deriv(r, c), cs)
+  case c::s => ders(s, der(c, r))
 }
 
-// regular expression matching
-def matches(r: Rexp, s: String) : Boolean = nullable(derivs(r, s.toList))
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
 
-/* Examples */
 
-println(matches(SEQ(SEQ(CHAR('c'), CHAR('a')), CHAR('b')),"cab"))
-println(matches(STAR(CHAR('a')),"aaa"))
+//examples
 
-/* Convenience using implicits */
-implicit def string2rexp(s : String) : Rexp = {
-  s.foldRight (EMPTY: Rexp) ( (c, r) => SEQ(CHAR(c), r) )
-}
+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(matches("cab" ,"cab"))
-println(matches(STAR("a"),"aaa"))
-println(matches(STAR("a"),"aaab"))