# HG changeset patch
# User Christian Urban <christian dot urban at kcl dot ac dot uk>
# Date 1353464416 0
# Node ID 9215b9fb88520b2b9e6586304d42219459829e63
# Parent  ade6af51402cc241b7e696ade5e06b6d95cf2e16
tuned

diff -r ade6af51402c -r 9215b9fb8852 app7.scala
--- a/app7.scala	Tue Nov 20 22:06:05 2012 +0000
+++ b/app7.scala	Wed Nov 21 02:20:16 2012 +0000
@@ -1,17 +1,14 @@
-def matches(r: Rexp, s: String) : Boolean = 
-  nullable(derivs(r, s.toList))
+abstract class Parser[I, T] {
+  def parse(ts: I): Set[(T, I)]
+
+  def parse_all(ts: I) : Set[T] =
+    for ((head, tail) <- parse(ts); if (tail.isEmpty)) 
+      yield head
+
+  def || (right : => Parser[I, T]) : Parser[I, T] = 
+      new AltParser(this, right)
+  def ==>[S] (f: => T => S) : Parser [I, S] = 
+      new FunParser(this, f)
+}
 
 
-/* Examples */
-
-println(matches(SEQ(SEQ(CHAR('c'), CHAR('a')), CHAR('b')),"cab"))
-println(matches(STAR(CHAR('a')),"aaa"))
-
-/* Convenience using implicits */
-implicit def string2rexp(s : String) : Rexp = {
-  s.foldRight (EMPTY: Rexp) ( (c, r) => SEQ(CHAR(c), r) )
-}
-
-println(matches("cab" ,"cab"))
-println(matches(STAR("a"),"aaa"))
-println(matches(STAR("a"),"aaab"))
diff -r ade6af51402c -r 9215b9fb8852 app8.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/app8.scala	Wed Nov 21 02:20:16 2012 +0000
@@ -0,0 +1,23 @@
+class SeqParser[I, T, S](p: => Parser[I, T], 
+                         q: => Parser[I, S]) 
+                             extends Parser[I, (T, S)] {
+  def parse(sb: I) = 
+    for ((head1, tail1) <- p.parse(sb); 
+         (head2, tail2) <- q.parse(tail1)) 
+            yield ((head1, head2), tail2)
+}
+
+class AltParser[I, T](p: => Parser[I, T], 
+                      q: => Parser[I, T]) 
+                          extends Parser[I, T] {
+  def parse(sb: I) = p.parse(sb) ++ q.parse(sb)   
+}
+
+class FunParser[I, T, S](p: => Parser[I, T], f: T => S) 
+  extends Parser[I, S] {
+  def parse(sb: I) = 
+    for ((head, tail) <- p.parse(sb)) 
+      yield (f(head), tail)
+}
+
+
diff -r ade6af51402c -r 9215b9fb8852 html-tokens.scala
--- a/html-tokens.scala	Tue Nov 20 22:06:05 2012 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,112 +0,0 @@
-import Console._
-
-// regular expressions including NOT
-abstract class Rexp {
-  def ~ (right : Rexp) = SEQ(this, right)
-  def || (right : Rexp) = ALT(this, right)
-}
-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 
-// cannot recognise more
-def no_more (r: Rexp) : Boolean = r match {
-  case NULL => true
-  case EMPTY => false
-  case CHAR(_) => false
-  case ALT(r1, r2) => no_more(r1) && no_more(r2)
-  case SEQ(r1, r2) => if (nullable(r1)) (no_more(r1) && no_more(r2)) else no_more(r1)
-  case STAR(_) => false
-  case NOT(r) => !(no_more(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))
-}
-
-def error (s: String) = "Could not lex " + s
-
-def munch(r: Rexp, s: List[Char], t: List[Char]) : Option[(List[Char], List[Char])] = {
-  //println("Look at" + s);
-  s match {
-    case Nil if (nullable(r)) => Some(Nil, t)
-    case Nil => None
-    case c::s if (no_more(der (c, r)) && nullable(r)) => Some(c::s, t)
-    case c::s if (no_more(der (c, r))) => None
-    case c::s => munch(der (c, r), s, t ::: List(c))
-  }
-}
-
-def one_string (regs: List[Rexp], s: List[Char]) : Either[(List[Char], List[Char]), String] = {
- val somes = regs.map { munch(_, s, Nil) } .flatten
- if (somes == Nil) Right(error(s.mkString)) else Left(somes sortBy (_._1.length) head)
-}
-
-def tokenize (regs: List[Rexp], s: List[Char]) : List[String] = s match {
-  case Nil => Nil
-  case _ => one_string(regs, s) match {
-    case Left((rest, s)) => { println("tokenized: " + s.mkString) ; s.mkString :: tokenize(regs, rest) }
-    case Right(msg) => { println(msg); sys.exit() }
-  }
-}
-
-
-// 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 => CHAR(c) || RANGE(s)
-}
-
-//one or more
-def PLUS(r: Rexp) = r ~ STAR(r)
-
-<font color="red">
-//some regular expressions
-val COLOUR = "BLACK" || "BLUE" || "CYAN" || "GREEN" || "MAGENTA" || "RED" || "WHITE" || "YELLOW"
-
-//BOLD || BLINK
-//INVISIBLE
-//RESET
-//REVERSED
-//UNDERLINED
-
-println(RED + BOLD + "test")
-println(RESET)
diff -r ade6af51402c -r 9215b9fb8852 html.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/html.scala	Wed Nov 21 02:20:16 2012 +0000
@@ -0,0 +1,59 @@
+
+//:load matcher.scala
+
+// some regular expressions
+val SYM = RANGE("""ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz.,!?-{[()]}':;%0123456789""")
+val WORD = PLUS(SYM)
+
+val BTAG = SEQS("<", WORD, ">") 
+val ETAG = SEQS("</", WORD, ">")
+
+val WHITESPACE = PLUS(RANGE(" \n"))
+
+// for classifying the strings that have been recognised
+abstract class Token
+case object T_WHITESPACE extends Token
+case class T_WORD(s: String) extends Token
+case class T_ETAG(s: String) extends Token
+case class T_BTAG(s: String) extends Token
+case class T_NT(s: String, rhs: List[Token]) extends Token
+
+val lexing_rules: List[Rule[Token]] = 
+  List((BTAG, (s) => T_BTAG(s.mkString)),
+       (ETAG, (s) => T_ETAG(s.mkString)),
+       (WORD, (s) => T_WORD(s.mkString)),
+       (WHITESPACE, (s) => T_WHITESPACE))
+
+// the tokenizer
+val T = Tokenizer(lexing_rules)
+
+// width for printing
+val WIDTH = 60
+
+
+def interpret(ts: List[Token], c: Int, ctr: List[String]) : Unit= ts match {
+  case Nil => println(Console.RESET)
+  case T_WHITESPACE::rest => print(Console.RESET + " "); interpret(rest, c + 1, ctr)
+  case T_WORD(s)::rest => {
+    val newstr = Console.RESET + ctr.reverse.mkString + s
+    if (c + s.length < WIDTH) {
+      print(newstr);
+      interpret(rest, c + s.length, ctr)
+    }
+    else {
+      print("\n" + newstr)
+      interpret(rest, s.length, ctr)
+    } 
+  }
+  case T_BTAG("<p>")::rest => print("\n"); interpret(rest, 0, ctr)
+  case T_ETAG("</p>")::rest => print("\n"); interpret(rest, 0, ctr)
+  case T_BTAG("<b>")::rest => interpret(rest, c, Console.BOLD :: ctr)
+  case T_BTAG("<a>")::rest => interpret(rest, c, Console.UNDERLINED :: ctr)
+  case T_BTAG("<cyan>")::rest => interpret(rest, c, Console.CYAN :: ctr)
+  case T_BTAG("<red>")::rest => interpret(rest, c, Console.RED :: ctr)
+  case T_BTAG("<blink>")::rest => interpret(rest, c, Console.BLINK :: ctr)
+  case T_ETAG(_)::rest => interpret(rest, c, ctr.tail)
+  case _::rest => interpret(rest, c, ctr)
+}
+ 
+interpret(T.fromFile("test.html"), 0, Nil)
diff -r ade6af51402c -r 9215b9fb8852 slides08.pdf
Binary file slides08.pdf has changed
diff -r ade6af51402c -r 9215b9fb8852 slides08.tex
--- a/slides08.tex	Tue Nov 20 22:06:05 2012 +0000
+++ b/slides08.tex	Wed Nov 21 02:20:16 2012 +0000
@@ -151,6 +151,360 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
+\frametitle{\begin{tabular}{c}Building a Web Browser\end{tabular}}
+
+Using a lexer: assume the following regular expressions
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$SY\!M$ & $\dn$ & $(\text{a}..\text{zA}..\text{Z0}..\text{9}..)$\\
+$W\!O\!RD$ & $\dn$ & $SY\!M^+$\\
+$BT\!AG$ & $\dn$ & $<\!W\!O\!RD\!>$\\
+$ET\!AG$ & $\dn$ & $<\!/W\!O\!RD\!>$\\
+$W\!HIT\!E$ & $\dn$ & $\texttt{" "} + \texttt{"}\slash{}n\texttt{"}$\\
+\end{tabular}}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Interpreting a List of Token\end{tabular}}
+
+\begin{itemize}
+\item text should be formatted consistently up to a specified width, say 60 characters 
+\item potential linebreaks are inserted by the formatter
+\item repeated whitespaces are ``condensed'' to a single whitepace
+\item \bl{$<\!p\!>$} \bl{$<\!\slash{}p\!>$}  start/end paragraph
+\item \bl{$<\!b\!>$} \bl{$<\!\slash{}b\!>$}  start/end bold
+\item \bl{$<\!red\!>$} \bl{$<\!\slash{}red\!>$}  start/end red (cyan, etc)
+
+
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Interpreting a List of Token\end{tabular}}
+
+The lexer cannot prevent errors like
+
+\begin{center}
+\bl{$<\!b\!>$} \ldots \bl{$<\!p\!>$} \ldots \bl{$<\!\slash{}b\!>$} \ldots \bl{$<\!\slash{}p\!>$} 
+\end{center}
+
+or
+
+\begin{center}
+\bl{$<\!\slash{}b\!>$} \ldots \bl{$<\!b\!>$}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Parser Combinators\end{tabular}}
+
+Parser combinators: \bigskip
+
+\begin{minipage}{1.1\textwidth}
+\begin{center}
+\mbox{}\hspace{-12mm}\mbox{}$\underbrace{\text{list of tokens}}_{\text{input}}$ \bl{$\Rightarrow$} 
+$\underbrace{\text{set of (parsed input, unparsed input)}}_{\text{output}}$
+\end{center}
+\end{minipage}\bigskip
+
+\begin{itemize}
+\item sequencing
+\item alternative
+\item semantic action
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+Alternative parser (code \bl{$p\;||\;q$})\bigskip
+
+\begin{itemize}
+\item apply \bl{$p$} and also \bl{$q$}; then combine the outputs
+\end{itemize}
+
+\begin{center}
+\large \bl{$p(\text{input}) \cup q(\text{input})$}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+Sequence parser (code \bl{$p\sim q$})\bigskip
+
+\begin{itemize}
+\item apply \bl{$p$} first producing a set of pairs
+\item then apply \bl{$q$} to the unparsed parts
+\item the combine the results:\\ \mbox{}\;\;((input$_1$, input$_2$), unparsed part)
+\end{itemize}
+
+\begin{center}
+\begin{tabular}{l}
+\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm] 
+\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
+\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
+\end{tabular}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+Function parser (code \bl{$p \Longrightarrow f$})\bigskip
+
+\begin{itemize}
+\item apply \bl{$p$} producing a set of pairs
+\item then apply the function \bl{$f$} to each fist component
+\end{itemize}
+
+\begin{center}
+\begin{tabular}{l}
+\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
+\end{tabular}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+Token parser:\bigskip
+
+\begin{itemize}
+\item if the input is
+
+\begin{center}
+\large \bl{$tok_1:: tok_2 :: \ldots :: tok_n$}
+\end{center}
+
+then return
+
+\begin{center}
+\large \bl{$\{(tok_1,\; tok_2 :: \ldots :: tok_n)\}$}
+\end{center}
+
+or
+
+\begin{center}
+\large \bl{$\{\}$}
+\end{center}
+
+if \bl{$tok_1$} is not the right token we are looking for
+\end{itemize}
+
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+Number-Token parser:\bigskip
+
+\begin{itemize}
+\item if the input is
+
+\begin{center}
+\large \bl{$num\_tok(42):: tok_2 :: \ldots :: tok_n$}
+\end{center}
+
+then return
+
+\begin{center}
+\large \bl{$\{(42,\; tok_2 :: \ldots :: tok_n)\}$}
+\end{center}
+
+or
+
+\begin{center}
+\large \bl{$\{\}$}
+\end{center}
+
+if \bl{$tok_1$} is not the right token we are looking for
+\end{itemize}\pause
+
+\begin{center}
+list of tokens \bl{$\Rightarrow$} set of (\alert{int}, list of tokens)
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{itemize}
+\item if the input is
+
+\begin{center}
+\begin{tabular}{l}
+\large \bl{$num\_tok(42)::$}\\
+\hspace{7mm}\large \bl{$num\_tok(3) ::$}\\
+\hspace{14mm}\large \bl{$tok_3 :: \ldots :: tok_n$}
+\end{tabular}
+\end{center}
+
+and the parser is 
+
+\begin{center}
+\bl{$ntp \sim ntp$}
+\end{center}
+
+the successful output will be
+
+\begin{center}
+\large \bl{$\{((42, 3),\; tok_2 :: \ldots :: tok_n)\}$}
+\end{center}\pause
+
+Now we can form
+\begin{center}
+\bl{$(ntp \sim ntp) \Longrightarrow f$}
+\end{center}
+
+where \bl{$f$} is the semantic action (what to do with the pair)
+
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Semantic Actions\end{tabular}}
+
+Addition
+
+\begin{center}
+\bl{$T \sim + \sim E \Longrightarrow \underbrace{f((x,y), z) \Rightarrow x + z}_{\text{semantic action}}$}
+\end{center}\pause
+
+Multiplication
+
+\begin{center}
+\bl{$F \sim * \sim T \Longrightarrow f((x,y), z) \Rightarrow x * z$}
+\end{center}\pause
+
+Parenthesis
+
+\begin{center}
+\bl{$\text{(} \sim E \sim \text{)} \Longrightarrow f((x,y), z) \Rightarrow y$}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Types of Parsers\end{tabular}}
+
+\begin{itemize}
+\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
+then \bl{$p \sim q$} returns results of type
+
+\begin{center}
+\bl{$T \times S$}
+\end{center}\pause
+
+\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then  \bl{$q$} \alert{must} also have results of type \bl{$T$},
+and \bl{$p \;||\; q$} returns results of type
+
+\begin{center}
+\bl{$T$}
+\end{center}\pause
+
+\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
+\bl{$T$} to \bl{$S$}, then
+\bl{$p \Longrightarrow f$} returns results of type
+
+\begin{center}
+\bl{$S$}
+\end{center}
+
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Input Types of Parsers\end{tabular}}
+
+\begin{itemize}
+\item input: \alert{list of tokens}
+\item output: set of (output\_type, \alert{list of tokens})
+\end{itemize}\bigskip\pause
+
+actually it can be any input type as long as it is a kind of sequence
+(for example a string)
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+{\lstset{language=Scala}\fontsize{10}{12}\selectfont
+\texttt{\lstinputlisting{app7.scala}}}
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+{\lstset{language=Scala}\fontsize{10}{12}\selectfont
+\texttt{\lstinputlisting{app7.scala}}}
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+{\lstset{language=Scala}\fontsize{10}{12}\selectfont
+\texttt{\lstinputlisting{app8.scala}}}
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
 \frametitle{\begin{tabular}{c}Two Grammars\end{tabular}}
 
 Which languages are recognised by the following two grammars?