diff -r ca5884c2e3bd -r 8da9e0c16194 progs/re.scala
--- a/progs/re.scala	Thu Nov 24 01:44:38 2016 +0000
+++ b/progs/re.scala	Thu Nov 24 09:42:49 2016 +0000
@@ -1,68 +1,92 @@
+// Part 1 about Regular Expression Matching
+//==========================================
 
 abstract class Rexp
 case object ZERO extends Rexp
 case object ONE 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 ALT(r1: Rexp, r2: Rexp) extends Rexp   // alternative 
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp   // sequence
+case class STAR(r: Rexp) extends Rexp             // star
+
+
+// some convenience for typing in regular expressions
+
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls 
 
-// nullable function: tests whether the regular 
-// expression can recognise the empty string
-def nullable (r: Rexp) : Boolean = r match {
-  case ZERO => false
-  case ONE => true
-  case CHAR(_) => false
-  case ALT(r1, r2) => nullable(r1) || nullable(r2)
-  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
-  case STAR(_) => true
+def charlist2rexp(s: List[Char]): Rexp = s match {
+  case Nil => ONE
+  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)
 }
 
-// derivative of a regular expression w.r.t. a character
-def der (c: Char, r: Rexp) : Rexp = r match {
-  case ZERO => ZERO
-  case ONE => ZERO
-  case CHAR(d) => if (c == d) ONE else ZERO
-  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(r1) => SEQ(der(c, r1), STAR(r1))
+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)
 }
 
-def simp(r: Rexp) : Rexp = r match {
-  case ALT(r1, r2) => (simp(r1), simp(r2)) match {
-    case (ZERO, r2s) => r2s
-    case (r1s, ZERO) => r1s
-    case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
-  }
-  case SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {
-    case (ZERO, _) => ZERO
-    case (_, ZERO) => ZERO
-    case (ONE, r2s) => r2s
-    case (r1s, ONE) => r1s
-    case (r1s, r2s) => SEQ(r1s, r2s)
-  }
-  case r => r
-}
+// (1a) Complete the function nullable according to
+// the definition given in the coursework; this 
+// function checks whether a regular expression
+// can match the empty string
+
+def nullable (r: Rexp) : Boolean = ...
 
 
-// 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, simp(der(c, r)))
-}
+// (1b) Complete the function der according to
+// the definition given in the coursework; this
+// function calculates the derivative of a 
+// regular expression w.r.t. a character
+
+def der (c: Char, r: Rexp) : Rexp = ...
+
+// (1c) Complete the function der according to
+// the specification given in the coursework; this
+// function simplifies a regular expression;
+// however it does not simplify inside STAR-regular
+// expressions
+
+def simp(r: Rexp) : Rexp = ... 
+
+// (1d) Complete the two functions below; the first 
+// calculates the derivative w.r.t. a string; the second
+// is the regular expression matcher taking a regular
+// expression and a string and checks whether the
+// string matches the regular expression
+
+def ders (s: List[Char], r: Rexp) : Rexp = ... 
+
+def matcher(r: Rexp, s: String): Boolean = ...
 
 
-// main matcher function
-def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
+// (1e) Complete the function below: it searches (from the left to 
+// right) in string s1 all the non-empty substrings that match the 
+// regular expression -- these substrings are assumed to be
+// the longest substrings matched by the regular expression and
+// assumed to be non-overlapping. All these substrings in s1 are replaced
+// by s2.
+
+def replace(r: Rexp, s1: String, s2: String): String = ...
 
-//one or zero
-def OPT(r: Rexp) = ALT(r, ONE)
+
 
-//evil regular expressions
-def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
-val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+// some testing data
+// the supposedly 'evil' regular expression (a*)* b
+/*
+val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+println(matcher(EVIL, "a" * 1000 ++ "b"))
+println(matcher(EVIL, "a" * 1000))
 
 
 def time_needed[T](i: Int, code: => T) = {
@@ -72,22 +96,9 @@
   (end - start)/(i * 1.0e9)
 }
 
-
-//test: (a?{n}) (a{n})
-for (i <- 1 to 8001 by 1000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
+for (i <- 1 to 5000001 by 500000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))
 }
-
-for (i <- 1 to 8001 by 1000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
-}
+*/
 
-//test: (a*)* b
-for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
-}
 
-for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
-}
-