# HG changeset patch
# User Christian Urban <christian dot urban at kcl dot ac dot uk>
# Date 1380669052 -3600
# Node ID 3e71efb25ce9f661d74879c76111f68cc187cc03
# Parent  a6684e8961d0c4f8f823132cf29532466b8df24c
added

diff -r a6684e8961d0 -r 3e71efb25ce9 progs/re2.scala
--- a/progs/re2.scala	Tue Oct 01 23:59:36 2013 +0100
+++ b/progs/re2.scala	Wed Oct 02 00:10:52 2013 +0100
@@ -1,36 +1,13 @@
     
-abstract class Rexp {
-  def simp : Rexp = this
-}
+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 {
-  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 SEQ(r1: Rexp, r2: Rexp) extends Rexp {
-  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 STAR(r: Rexp) extends Rexp {
-  override def simp = r.simp match {
-    case NULL => EMPTY
-    case EMPTY => EMPTY
-    case r => STAR(r)
-  }
-}
+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 NTIMES(r: Rexp, n: Int) extends Rexp 
 
 // some convenience for typing in regular expressions
 def charlist2rexp(s : List[Char]) : Rexp = s match {
@@ -50,6 +27,7 @@
   case ALT(r1, r2) => nullable(r1) || nullable(r2)
   case SEQ(r1, r2) => nullable(r1) && nullable(r2)
   case STAR(_) => true
+  case NTIMES(r, i) => if (i == 0) true else nullable(r)
 }
 
 // derivative of a regular expression w.r.t. a character
@@ -62,12 +40,14 @@
     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 NTIMES(r, i) => 
+    if (i == 0) NULL else SEQ(der(c, r), NTIMES(r, i - 1))
 }
 
 // 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).simp)
+  case c::s => ders(s, der(c, r))
 }
 
 // main matcher function
@@ -77,14 +57,7 @@
 //one or zero
 def OPT(r: Rexp) = ALT(r, EMPTY)
 
-//n-times
-def NTIMES(r: Rexp, n: Int) : Rexp = n match {
-  case 0 => EMPTY
-  case 1 => r
-  case n => SEQ(r, NTIMES(r, n - 1))
-}
-
-def RTEST(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
+def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -94,7 +67,12 @@
 }
 
 for (i <- 1 to 100) {
-  println(i + ": " + "%.5f".format(time_needed(1, matcher(RTEST(i), "a" * i))))
+  println(i + ": " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i))))
 }
 
 
+for (i <- 1 to 1000 by 50) {
+  println(i + " " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i))))
+}
+
+
diff -r a6684e8961d0 -r 3e71efb25ce9 slides/slides02.pdf
Binary file slides/slides02.pdf has changed
diff -r a6684e8961d0 -r 3e71efb25ce9 slides/slides02.tex
--- a/slides/slides02.tex	Tue Oct 01 23:59:36 2013 +0100
+++ b/slides/slides02.tex	Wed Oct 02 00:10:52 2013 +0100
@@ -765,21 +765,48 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}Problem\end{tabular}}
+\frametitle{\begin{tabular}{c}A Problem\end{tabular}}
 
-We represented ``n-times'' as a sequence regular expression:
+We represented the ``n-times'' \bl{$a\{n\}$} as a sequence regular expression:
 
 \begin{center}
-\begin{tabular}{ll}
-1:
+\begin{tabular}{rl}
+1: & \bl{$a$}\\
+2: & \bl{$a\cdot a$}\\
+3: & \bl{$a\cdot a\cdot a$}\\
+& \ldots\\
+13: & \bl{$a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a$}\\
+& \ldots\\
+20:
 \end{tabular}
 \end{center}
 
+This problem is aggravated with \bl{$a?$} being represented as \bl{$\epsilon + a$}.
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Solving the Problem\end{tabular}}
+
+What happens if we extend our regular expressions
+
+\begin{center}
+\begin{tabular}{rcl}
+\bl{$r$} & \bl{$::=$} & \bl{\ldots}\\
+             & \bl{$\mid$} & \bl{$r\{n\}$}\\
+             & \bl{$\mid$} & \bl{$r?$} 
+\end{tabular}
+\end{center}
+
+What is their meaning? What are the cases for \bl{$nullable$} and \bl{$der$}?
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[t]
 \frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}