--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/cw1.scala	Wed Nov 13 20:07:26 2013 +0000
@@ -0,0 +1,190 @@
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls 
+
+abstract class Rexp {
+  def simp : Rexp = this
+}
+
+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 {
+  override def toString = r1.toString + " | " + r2.toString
+  override def simp = (r1.simp, r2.simp) match {
+    case (NULL, r) => r
+    case (r, NULL) => r
+    case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)
+    case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)
+    case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
+  }
+}
+case class RANGE(cs: List[Char]) extends Rexp {
+  //override def toString = cs.mkString("[",",","]")
+  override def toString = "[" + cs.head + " .. " + cs.last + "]"
+}
+object RANGE {
+  def apply(s: String) : RANGE = RANGE(s.toList)
+}
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
+  override def toString = r1.toString + " ~ " + r2.toString
+  override def simp = (r1.simp, r2.simp) match {
+    case (NULL, _) => NULL
+    case (_, NULL) => NULL
+    case (EMPTY, r) => r
+    case (r, EMPTY) => r
+    case (r1, r2) => SEQ(r1, r2)
+  }
+}
+case class PLUS(r: Rexp) extends Rexp {
+  override def simp = r.simp match {
+    case NULL => EMPTY
+    case EMPTY => EMPTY
+    case r => PLUS(r)
+  }
+}
+case class STAR(r: Rexp) extends Rexp {
+  override def simp = r.simp match {
+    case NULL => EMPTY
+    case EMPTY => EMPTY
+    case r => STAR(r)
+  }
+}
+case class NTIMES(r: Rexp, n: Int) extends Rexp {
+  override def simp = if (n == 0) EMPTY else 
+    r.simp match {
+      case NULL => NULL
+      case EMPTY => EMPTY
+      case r => NTIMES(r, n)
+    }
+}
+case class NMTIMES(r: Rexp, n: Int, m: Int) extends Rexp {
+  if(m < n) throw new IllegalArgumentException("the number m cannot be smaller than n.")
+
+  override def simp = if (m == 0) EMPTY else 
+    r.simp match {
+      case NULL => NULL
+      case EMPTY => EMPTY
+      case r => NMTIMES(r, n, m)
+    }
+}
+case class NOT(r: Rexp) extends Rexp {
+  override def simp = NOT(r.simp)
+}
+case class OPT(r: Rexp) extends Rexp {
+  override def simp = OPT(r.simp)
+}
+
+// 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 PLUS(r) => nullable(r)
+  case NTIMES(r, i) => if (i == 0) true else nullable(r)
+  case NMTIMES(r, i, j) => if (i == 0) true else nullable(r)
+  case RANGE(_) => false
+  case NOT(r) => !(nullable(r))
+  case OPT(_) => true
+}
+
+// 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 PLUS(r) => der(c, SEQ(r, STAR(r)))
+  case NTIMES(r, i) => 
+    if (i == 0) NULL else der(c, SEQ(r, NTIMES(r, i - 1)))
+  case NMTIMES(r, i, j) => 
+    if (j == 0) NULL 
+    if (i == 0) der(c, NTIMES(r, j))
+    else der(c, SEQ(r, NMTIMES(r, i - 1, j - 1)))
+  case RANGE(cs) => if (cs contains c) EMPTY else NULL
+  case NOT(r) => NOT(der (c, r))
+  case OPT(r) => 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))
+}
+
+def ders_simp (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders_simp(s, der(c, r).simp)
+}
+
+// main matcher function
+def matcher(r: Rexp, s: String) : Boolean = nullable(ders_simp(s.toList, r))
+
+// 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)
+
+implicit def RexpOps (r: Rexp) = new {
+  def | (s: Rexp) = ALT(r, s)
+  def % = STAR(r)
+  def ~ (s: Rexp) = SEQ(r, s)
+}
+
+implicit def stringOps (s: String) = new {
+  def | (r: Rexp) = ALT(s, r)
+  def | (r: String) = ALT(s, r)
+  def % = STAR(s)
+  def ~ (r: Rexp) = SEQ(s, r)
+  def ~ (r: String) = SEQ(s, r)
+}
+
+println("EMAIL:")
+val LOWERCASE = "abcdefghijklmnopqrstuvwxyz"
+val DIGITS = "0123456789"
+val EMAIL = PLUS(RANGE(LOWERCASE + DIGITS + "_" + "." + "-")) ~ "@" ~ 
+            PLUS(RANGE(LOWERCASE + DIGITS + "." + "-")) ~ "." ~
+            NMTIMES(RANGE(LOWERCASE + "."), 2, 6)
+
+val my_email = "christian.urban@kcl.ac.uk"
+
+println(EMAIL);
+println(matcher(EMAIL, my_email))
+println(ders_simp(my_email.toList, EMAIL))
+
+println("COMMENTS:")
+val ALL = RANGE(LOWERCASE + " ")
+val COMMENT = "/*" ~ (NOT(ALL.% ~ "*/" ~ ALL.%)) ~ "*/"
+
+println(matcher(COMMENT, "/**/"))
+println(matcher(COMMENT, "/*foobar_comment*/"))
+println(matcher(COMMENT, "/*test*/test*/"))
+println(matcher(COMMENT, "/*test/*test*/"))
+
+println("EVILS:")
+val EVIL1 = PLUS(PLUS("a" ~ "a" ~ "a"))
+val EVIL2 = PLUS(PLUS("aaaaaaaaaaaaaaaaaaa" ~ OPT("a")))  // 19 as ~ a?
+
+
+//40 * aaa matches
+//43 * aaa + aa does not
+//45 * aaa + a
+
+println("EVIL1:")
+println(matcher(EVIL1, "aaa" * 40))
+println(matcher(EVIL1, "aaa" * 43 + "aa"))
+println(matcher(EVIL1, "aaa" * 45 + "a"))
+println("EVIL2:")
+println(matcher(EVIL2, "aaa" * 40))
+println(matcher(EVIL2, "aaa" * 43 + "aa"))
+println(matcher(EVIL2, "aaa" * 45 + "a"))