
diff -r 31295bb945c6 -r 8aa406adfde0 slides/slides07.tex
--- a/slides/slides07.tex	Thu Nov 26 00:11:10 2015 +0000
+++ b/slides/slides07.tex	Thu Nov 26 12:55:59 2015 +0000
@@ -1,12 +1,14 @@
 \documentclass[dvipsnames,14pt,t]{beamer}
 \usepackage{../slides}
+\usepackage{../graphics}
 \usepackage{../langs}
 \usepackage{../data}
-\usepackage{../graphics}
+
 
 % beamer stuff 
 \renewcommand{\slidecaption}{AFL 07, King's College London}
 \newcommand{\bl}[1]{\textcolor{blue}{#1}}       
+%\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
 
 \begin{document}
 
@@ -16,7 +18,7 @@
   \begin{tabular}{@ {}c@ {}}
   \\[-3mm]
   \LARGE Automata and \\[-2mm] 
-  \LARGE Formal Languages (8)\\[3mm] 
+  \LARGE Formal Languages (7)\\[3mm] 
   \end{tabular}}
 
   \normalsize
@@ -31,52 +33,322 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
+
+\newcommand{\qq}{\mbox{\texttt{"}}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{Bird's Eye View}
+\frametitle{CFGs}
+
+A \alert{context-free} grammar (CFG) \bl{$G$} consists of:
 
+\begin{itemize}
+\item a finite set of nonterminal symbols (upper case)
+\item a finite terminal symbols or tokens (lower case)
+\item a start symbol (which must be a nonterminal)
+\item a set of rules
 \begin{center}
-\begin{tikzpicture}
-\node (rexp)  {\bl{\bf Lexer}};
-\node (nfa) [right=of rexp] {\bl{\bf Parser}};
-\node (dfa) [right=of nfa] 
- {\bl{\begin{tabular}{c}\bf Machine Code/\\\bf Java Byte Code\end{tabular}}};
-\path[->, red, line width=2mm] (rexp) edge node [above=4mm, black] {\begin{tabular}{c@{\hspace{9mm}}}token\\[-1mm]
-sequence\end{tabular}} (nfa);
-\path[->, red, line width=2mm] (nfa) edge node [above=4mm, black] {\begin{tabular}{c}parse\\[-1mm] tree\end{tabular}}(dfa);
-\end{tikzpicture}\\
+\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
 \end{center}
 
+where \bl{rhs} are sequences involving terminals and nonterminals (can also be empty).\medskip\pause
+
+\end{itemize}
+
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
- 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}}
+
+Recall that languages are sets of strings.
+
+\begin{center}
+\begin{tikzpicture}
+[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
+
+\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
+\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
+\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
+\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
+\draw (0,-1.4) node [rect] {regular languages};
+\end{tikzpicture}
+
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\begin{textblock}{10}(0.5,0.5)
-  \LARGE
-  \fontspec{Hoefler Text Black}
-  \textcolor{ProcessBlue}{JVM\\ Code}
-\end{textblock}
-\fontsize{8}{10}\selectfont
-%\footnotesize
-\mbox{}\\[-8mm]\mbox{}
+\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
+
+A grammar for arithmetic expressions and numbers:
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  $E \cdot + \cdot E \;|\;E \cdot * \cdot E \;|\;( \cdot E \cdot ) \;|\;N$ \\
+$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1 \;|\: \ldots \;|\; 9$ 
+\end{tabular}}
+\end{center}
+
+Unfortunately it is left-recursive (and ambiguous).\medskip\\
+A problem for \alert{recursive descent parsers} (e.g.~parser combinators).
+\bigskip\pause
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}Numbers\end{tabular}}
+
+
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ &  $N \cdot N \;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\
+\end{tabular}}
+\end{center}
+
+A non-left-recursive, non-ambiguous grammar for numbers:
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ &  $0 \cdot N \;|\;1 \cdot N \;|\;\ldots\;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\
+\end{tabular}}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Operator Precedences\end{tabular}}
+
+
+To disambiguate
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  $E \cdot + \cdot E \;|\;E \cdot * \cdot E \;|\;( \cdot E \cdot ) \;|\;N$ \\
+\end{tabular}}
+\end{center}
+
+Decide on how many precedence levels, say\medskip\\
+\hspace{5mm}highest for \bl{$()$}, medium for \bl{*}, lowest for \bl{+}
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E_{low}$ & $\rightarrow$ & $E_{med} \cdot + \cdot E_{low} \;|\; E_{med}$ \\
+$E_{med}$ & $\rightarrow$ & $E_{hi} \cdot * \cdot E_{med} \;|\; E_{hi}$\\
+$E_{hi}$ & $\rightarrow$ &  $( \cdot E_{low} \cdot ) \;|\;N$ \\
+\end{tabular}}
+\end{center}\pause
+
+\small What happens with \bl{$1 + 3  + 4$}?
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Removing Left-Recursion\end{tabular}}
+
+The rule for numbers is directly left-recursive:
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ & $N \cdot N \;|\; 0 \;|\; 1\;\;\;\;(\ldots)$ 
+\end{tabular}}
+\end{center}
+
+Translate
+
+\begin{center}
+\begin{tabular}{ccc}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ & $N \cdot \alpha$\\
+ &  $\;|\;$ & $\beta$\\
+ \\ 
+\end{tabular}} 
+& {\Large$\Rightarrow$} &
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ & $\beta \cdot N'$\\
+$N'$ & $\rightarrow$ & $\alpha \cdot N'$\\
+ &  $\;|\;$ & $\epsilon$ 
+\end{tabular}}
+\end{tabular}
+\end{center}\pause
+
+Which means
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1 \cdot N'$\\
+$N'$ & $\rightarrow$ & $N \cdot N' \;|\; \epsilon$\\
+\end{tabular}}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-\begin{columns}
-\begin{column}{2cm} 
-\lstinputlisting[numbers=none]{../progs/appHa.j}
-\end{column}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Chomsky Normal Form\end{tabular}}
+
+All rules must be of the form
+
+\begin{center}
+\bl{$A \rightarrow a$}
+\end{center}
+
+or
+
+\begin{center}
+\bl{$A \rightarrow B\cdot C$}
+\end{center}
+
+No rule can contain \bl{$\epsilon$}.
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}$\epsilon$-Removal\end{tabular}}
+
+\begin{enumerate}
+\item If \bl{$A\rightarrow \alpha \cdot B \cdot \beta$} and \bl{$B \rightarrow \epsilon$} are in the grammar,
+then add \bl{$A\rightarrow \alpha \cdot \beta$} (iterate if necessary).
+\item Throw out all \bl{$B \rightarrow \epsilon$}.
+\end{enumerate}
+
+\small
+\begin{center}
+\begin{tabular}{ccc}
+\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
+$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'$\\
+$N'$ & $\rightarrow$ & $N \cdot N'\;|\;\epsilon$\\
+\\ 
+\\
+\\
+\\
+\\
+\end{tabular}} &
+\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
+\\
+$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\
+$N'$ & $\rightarrow$ & $N \cdot N'\;|\;N\;|\;\epsilon$\\
+\\
+$N$ & $\rightarrow$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\
+$N'$ & $\rightarrow$ & $N \cdot N'\;|\;N$\\
+\end{tabular}}
+\end{tabular}
+\end{center}
+
+\pause\normalsize
+\begin{center}
+\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
+$N$ & $\rightarrow$ & $0 \cdot N\;|\; 1\cdot N\;|\;0\;|\;1$\\
+\end{tabular}}
+
+\end{center}
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
+
+If grammar is in Chomsky normalform \ldots
 
-\begin{column}{2cm} 
-\lstinputlisting[numbers=none]{../progs/appHb.j}
-\end{column}
+\begin{center}
+\bl{\begin{tabular}{@ {}lcl@ {}}
+$S$ & $\rightarrow$ &  $N\cdot P$ \\
+$P$ & $\rightarrow$ &  $V\cdot N$ \\
+$N$ & $\rightarrow$ &  $N\cdot N$ \\
+$N$ & $\rightarrow$ &  $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
+$V$ & $\rightarrow$ &  $\texttt{trains}$ 
+\end{tabular}}
+\end{center}
+
+\bl{\texttt{Jeff trains geometry students}}
 
-\end{columns}
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
+
+
+\begin{itemize}
+\item fastest possible algorithm for recognition problem
+\item runtime is \bl{$O(n^3)$}\bigskip
+\item grammars need to be transferred into CNF
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}}
+
+Recall that languages are sets of strings.
 
-\end{frame}
+\begin{center}
+\begin{tikzpicture}
+[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
+
+\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
+\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
+\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
+\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
+\draw (0,-1.4) node [rect] {regular languages};
+\end{tikzpicture}
+
+\end{center}
+
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
- 
- 
- 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Context Sensitive Grms\end{tabular}}
+
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$S$ & $\Rightarrow$ &  $bSAA\;|\; \epsilon$\\
+$A$ & $\Rightarrow$ & $a$\\
+$bA$ & $\Rightarrow$ & $Ab$\\
+\end{tabular}}
+\end{center}\pause
+
+\begin{center}
+\bl{$S \Rightarrow\ldots\Rightarrow^? "ababaa"$}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
@@ -98,26 +370,48 @@
 \textit{BExp} & $\rightarrow$ & \ldots\\
 \end{tabular}}
 \end{center}
-
-
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}Fibonacci Numbers\end{tabular}}
-
-\mbox{}\\[-18mm]\mbox{}
 
-{\lstset{language=While}\fontsize{10}{12}\selectfont
-\texttt{\lstinputlisting{../progs/fib.while}}}
+\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
 
-\end{frame}
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\frametitle{Interpreter}
+\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}}
+
+\begin{center}
+\bl{\begin{tabular}{l}
+$\{$\\
+\;\;$x := 5 \text{;}$\\
+\;\;$y := x * 3\text{;}$\\
+\;\;$y := x * 4\text{;}$\\
+\;\;$x := u * 3$\\
+$\}$
+\end{tabular}}
+\end{center}
+
+\begin{itemize}
+\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
+\item \bl{\text{eval}(stmt, env)}
+\end{itemize}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Interpreter\end{tabular}}
 
 \begin{center}
 \bl{\begin{tabular}{@{}lcl@{}}
@@ -132,12 +426,12 @@
 \end{tabular}}
 \end{center}
 
-\end{frame}
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\frametitle{Interpreter (2)}
+\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}}
 
 \begin{center}
 \bl{\begin{tabular}{@{}lcl@{}}
@@ -156,42 +450,27 @@
 \end{tabular}}
 \end{center}
 
-\end{frame}
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\frametitle{Test Program}
+\frametitle{\begin{tabular}{c}Test Program\end{tabular}}
 
 \mbox{}\\[-18mm]\mbox{}
 
-{\lstset{language=While}\fontsize{10}{12}\selectfont
+{\lstset{language=While}%%\fontsize{10}{12}\selectfont
 \texttt{\lstinputlisting{../progs/loops.while}}}
 
-\end{frame}
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\fontsize{7}{9}\selectfont
-
-
-\begin{columns}
-\begin{column}{7cm} 
-\lstinputlisting[numbers=none]{../progs/appHa.j}
-\end{column}
-
-\begin{column}{7cm} 
-\lstinputlisting[numbers=none]{../progs/appHb.j}
-\end{column}
-\end{columns}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
- 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[t]
-\frametitle{Interpreted Code}
+\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -201,12 +480,13 @@
 \end{tikzpicture}
 \end{center}
 
-\end{frame}
+\end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\frametitle{Java Virtual Machine}
+\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}}
 
 \begin{itemize}
 \item introduced in 1995
@@ -214,583 +494,12 @@
 \item contains a JIT compiler
 \item many languages take advantage of JVM's infrastructure (JRE)
 \item is garbage collected $\Rightarrow$ no buffer overflows
-\item some languages compiled to the JVM: Scala, Clojure\ldots
+\item some languages compile to the JVM: Scala, Clojure\ldots
 \end{itemize}
 
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling AExps}
-
-{\Large\bl{1 + 2}}
-
-\begin{center}
-\bl{\begin{tabular}{l}
-ldc 1\\
-ldc 2\\
-iadd\\
-\end{tabular}}
-\end{center}
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}
-
-{\Large\bl{1 + 2 + 3}}
-
-\begin{center}
-\bl{\begin{tabular}{l}
-ldc 1\\
-ldc 2\\
-iadd\\
-ldc 3\\
-iadd\\
-\end{tabular}}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}
-
-{\Large\bl{1 + (2 + 3)}}
-
-\begin{center}
-\bl{\begin{tabular}{l}
-ldc 1\\
-ldc 2\\
-ldc 3\\
-iadd\\
-iadd\\
-\end{tabular}}
-\end{center}\bigskip\pause
-\vfill
-
-\bl{dadd, fadd, ladd, \ldots}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling AExps}
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$\text{compile}(n)$ & $\dn$ & $\text{ldc}\;n$\\
-$\text{compile}(a_1 + a_2)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\;\text{compile}(a_2)\;@\; \text{iadd}$}\smallskip\\
-$\text{compile}(a_1 - a_2)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\; \text{compile}(a_2)\;@\; \text{isub}$}\smallskip\\
-$\text{compile}(a_1 * a_2)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1) \;@\; \text{compile}(a_2)\;@\; \text{imul}$}\smallskip\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}
-
-{\Large\bl{1 + 2 * 3 + (4 - 3)}}
-
-\begin{center}
-\bl{\begin{tabular}{l}
-ldc 1\\
-ldc 2\\
-ldc 3\\
-imul\\
-ldc 4\\
-ldc 3\\
-isub\\
-iadd\\
-iadd\\
-\end{tabular}}
-\end{center}
-
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Variables}
-
-{\Large\bl{$x := 5 + y * 2$}}\bigskip\pause   
-
-\begin{itemize}
-\item lookup: \bl{$\text{iload}\; index$}
-\item store: \bl{$\text{istore}\; index$}
-\end{itemize}\bigskip\pause
-
-while compilating we have to maintain a map between our identifiers and the
-Java bytecode indices
-
-\begin{center}
-\bl{$\text{compile}(a, E)$}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling AExps}
-
-\begin{center}
-\bl{\begin{tabular}{@{}lcl@{}}
-$\text{compile}(n, E)$ & $\dn$ & $\text{ldc}\;n$\\
-$\text{compile}(a_1 + a_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1, E) \;@\;\text{compile}(a_2, E)\;@\; \text{iadd}$}\smallskip\\
-$\text{compile}(a_1 - a_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1, E) \;@\; \text{compile}(a_2, E)\;@\; \text{isub}$}\smallskip\\
-$\text{compile}(a_1 * a_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\qquad\text{compile}(a_1, E) \;@\; \text{compile}(a_2, E)\;@\; \text{imul}$}\bigskip\\
-$\text{compile}(x, E)$ & $\dn$ & $\text{iload}\;E(x)$\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c, fragile]
-\frametitle{Mathematical Functions}
-
-Compilation of some mathematical functions:
-
-\begin{center}
-\begin{tabular}{lcl}
-\texttt{Aop("+", a1, a2)} & $\Rightarrow$ & \texttt{...iadd}\\
-\texttt{Aop("-", a1, a2)} & $\Rightarrow$ & \texttt{...isub}\\
-\texttt{Aop("*", a1, a2)} & $\Rightarrow$ & \texttt{...imul}\\
-\texttt{Aop("/", a1, a2)} & $\Rightarrow$ & \texttt{...idiv}\\
-\texttt{Aop("\%", a1, a2)} & $\Rightarrow$ & \texttt{...irem}\\
-\end{tabular}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Statements}
-
-We return a list of instructions and an environment for the
-variables
-
-\begin{center}
-\bl{\begin{tabular}{@{}l@{\hspace{1mm}}c@{\hspace{1mm}}l@{}}
-$\text{compile}(\text{skip}, E)$ & $\dn$ & $(\textit{Nil}, E)$\bigskip\\
-$\text{compile}(x := a, E)$ & $\dn$\\
-\multicolumn{3}{l}{$(\text{compile}(a, E) \;@\;\text{istore}\;index, E(x\mapsto index))$}\\
-\end{tabular}}
-\end{center}\medskip
-
-where \bl{$index$} is \bl{$E(x)$} if it is already defined, 
-or if it is not, then the largest index not yet seen
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Compiling Assignments}
-
-{\Large\bl{$x := x + 1$}}
-
-\begin{center}
-\bl{\begin{tabular}{l}
-iload $n_x$\\
-ldc 1\\
-iadd\\
-istore $n_x$\\
-\end{tabular}}
-\end{center}
-
-where \bl{$n_x$} is the index corresponding to the variable~\bl{$x$}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Ifs}
-
-{\Large\bl{$\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2$}}\bigskip\bigskip
-
-\onslide<2->{Case }\only<2>{{\bf True}:}\only<3>{{\bf False}:}
-
-\begin{center}
-\begin{tikzpicture}[node distance=2mm and 4mm,
- block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
- point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
- skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
-\node (A1) [point] {};
-\node (b) [block, right=of A1] {code of \bl{$b$}};
-\node (A2) [point, right=of b] {};
-\node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};
-\node (A3) [point, right=of cs1] {};
-\node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};
-\node (A4) [point, right=of cs2] {};
-
-\only<2>{
-\draw (A1) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (cs1);
-\draw (cs1) edge [->, red, line width=1mm] (A3);
-\draw (A3) edge [->,skip loop] (A4);
-\node [below=of cs2] {\raisebox{-5mm}{\small{}jump}};}
-\only<3>{
-\draw (A1) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (A2);
-\draw (A2) edge [skip loop] (A3);
-\draw (A3) edge [->, red, line width=1mm] (cs2);
-\draw (cs2) edge [->,red, line width=1mm] (A4);
-\node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Conditional Jumps}
-
-\begin{minipage}{1.1\textwidth}
-\begin{itemize}
-\item \bl{if\_icmpeq $label$} if two ints are equal, then jump\medskip
-\item \bl{if\_icmpne $label$} if two ints aren't equal, then jump\medskip
-\item \bl{if\_icmpge $label$} if one int is greater or equal then another, then jump
-\item[]\ldots
-\end{itemize}
-\end{minipage}\pause
-
-
-\begin{center}
-\bl{\begin{tabular}{l}
-$L_1$:\\
-\hspace{5mm}if\_icmpeq\;$L_2$\\
-\hspace{5mm}iload 1\\
-\hspace{5mm}ldc 1\\
-\hspace{5mm}iadd\\
-\hspace{5mm}if\_icmpeq\;$L_1$\\
-$L_2$:
-\end{tabular}}
-\end{center}
-
-\begin{textblock}{3.5}(11,12)
-\only<3>{labels must be unique}
-\end{textblock}
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling BExps}
-
-{\Large\bl{$a_1 = a_2$}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$\text{compile}(a_1 = a_2, E, lab)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\quad\text{compile}(a_1, E) \;@\;\text{compile}(a_2, E)\;@\; \text{if\_icmpne}\;lab$}
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c, fragile]
-\frametitle{Boolean Expressions}
-
-Compilation of boolean expressions:
-
-\begin{center}
-\begin{tikzpicture}[node distance=2mm and 4mm,
- block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
- point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
- skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
-\node (A1) [point] {};
-\node (b) [block, right=of A1] {code of \bl{$b$}};
-\node (A2) [point, right=of b] {};
-\node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};
-\node (A3) [point, right=of cs1] {};
-\node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};
-\node (A4) [point, right=of cs2] {};
-
-\only<1>{
-\draw (A1) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (A2);
-\draw (A2) edge [skip loop] (A3);
-\draw (A3) edge [->, red, line width=1mm] (cs2);
-\draw (cs2) edge [->,red, line width=1mm] (A4);
-\node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}
-\end{tikzpicture}
-\end{center}
-
-\begin{center}
-\begin{tabular}{lcl}
-\texttt{Bop("==", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpne...}\\
-\texttt{Bop("!=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpeq...}\\
-\texttt{Bop("<", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpge...}\\
-\texttt{Bop("<=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpgt...}\\
-\end{tabular}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Ifs}
-
-{\Large\bl{if $b$ then $cs_1$ else $cs_2$}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$\text{compile}(\text{if}\;b\;\text{then}\; cs_1\;\text{else}\; cs_2, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\quad l_{ifelse}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad l_{ifend}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad (is_1, E') = \text{compile}(cs_1, E)$}\\
-\multicolumn{3}{l}{$\quad (is_2, E'') = \text{compile}(cs_2, E')$}\\
-\multicolumn{3}{l}{$\quad(\text{compile}(b, E, l_{ifelse})$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;is_1$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\; \text{goto}\;l_{ifend}$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;l_{ifelse}:$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;is_2$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;l_{ifend}:, E'')$}\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Whiles}
-
-{\Large\bl{$\text{while}\;b\;\text{do}\;cs$}}\bigskip\bigskip
-
-\onslide<2->{Case }\only<2>{{\bf True}:}\only<3>{{\bf False}:}
-
-\begin{center}
-\begin{tikzpicture}[node distance=2mm and 4mm,
- block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
- point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
- skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
-\node (A0) [point, left=of A1] {};
-\node (A1) [point] {};
-\node (b) [block, right=of A1] {code of \bl{$b$}};
-\node (A2) [point, right=of b] {};
-\node (cs1) [block, right=of A2] {code of \bl{$cs$}};
-\node (A3) [point, right=of cs1] {};
-\node (A4) [point, right=of A3] {};
-
-\only<2>{
-\draw (A0) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (cs1);
-\draw (cs1) edge [->, red, line width=1mm] (A3);
-\draw (A3) edge [->,skip loop] (A1);}
-\only<3>{
-\draw (A0) edge [->, red, line width=1mm] (b);
-\draw (b) edge [->, red, line width=1mm] (A2);
-\draw (A2) edge [skip loop] (A3);
-\draw (A3) edge [->, red, line width=1mm] (A4);}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Whiles}
-
-{\Large\bl{while $b$ do $cs$}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$\text{compile}(\text{while}\; b\; \text{do} \;cs, E)$ & $\dn$\\ 
-\multicolumn{3}{l}{$\quad l_{wbegin}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad l_{wend}\;$ \textcolor{black}{(fresh label)}}\\
-\multicolumn{3}{l}{$\quad (is, E') = \text{compile}(cs_1, E)$}\\
-\multicolumn{3}{l}{$\quad(l_{wbegin}:$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;\text{compile}(b, E, l_{wend})$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;is$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\; \text{goto}\;l_{wbegin}$}\\
-\multicolumn{3}{l}{$\quad\phantom{(}@\;l_{wend}:, E')$}\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Compiling Writes}
-
-{\Large\bl{write $x$}}
-
-\begin{center}
-\small\bl{\begin{tabular}{l}
-.method public static write(I)V\hspace{1cm}\textcolor{black}{(library function)}\\ 
-\;\;    .limit locals 5 \\
-\;\;    .limit stack 5 \\
-\;\;    iload 0 \\
-\;\;    getstatic java/lang/System/out Ljava/io/PrintStream;\\ 
-\;\;    swap \\
-\;\;    invokevirtual java/io/PrintStream/println(I)V \\
-\;\;    return \\
-.end method\bigskip\bigskip\\
-%
-\normalsize
-iload $E(x)$\\
-invokestatic write(I)V\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-
-\begin{center}
-\small\bl{\begin{tabular}{l}
-.class public XXX.XXX\\
-.super java/lang/Object\\
-\\
-.method public <init>()V\\
-\;\;     aload\_0\\
-\;\;     invokenonvirtual java/lang/Object/<init>()V\\
- \;\;    return\\
-.end method\\
-\\
-.method public static main([Ljava/lang/String;)V\\
-\;\;   .limit locals 200\\
-\;\;     .limit stack 200\\
-\\
-   \textcolor{black}{(here comes the compiled code)}\\
-\\
-\;\;     return\\
-.end method\\
-\end{tabular}}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Next Compiler Phases\end{tabular}}
-
-\begin{itemize}
-\item assembly $\Rightarrow$ byte code (class file)
-\item labels $\Rightarrow$ absolute or relative jumps\bigskip\bigskip
-\item \texttt{javap} is a disassembler for class files
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiled Code\end{tabular}}
-
-\begin{center}
-\begin{tikzpicture}
-\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
-\addplot+[smooth] file {compiled.data};
-\end{axis}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}Compiler vs.~Interpreter\end{tabular}}
-
-\begin{center}
-\begin{tikzpicture}
-\begin{axis}[axis x line=bottom, axis y line=left, ylabel=secs,
-    xlabel=n,
-    enlargelimits=0.05,
-    ybar interval=0.7, legend style=small]
-\addplot file {interpreted2.data};
-\addplot file {compiled2.data};
-%\legend{interpreted, compiled}
-\end{axis}
-\end{tikzpicture}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{Backend}
-
-\begin{center}
-\begin{tikzpicture}
-\node (rexp)  {\bl{\bf Lexer}};
-\node (nfa) [right=of rexp] {\bl{\bf Parser}};
-\node (dfa) [right=of nfa] {\bl{\begin{tabular}{c}\bf Optimizations\end{tabular}}};
-\path[->, red, line width=2mm] (rexp) edge node [above=4mm, black] {\begin{tabular}{c@{\hspace{9mm}}}token\\[-1mm]
-sequence\end{tabular}} (nfa);
-\node (final) [below=of dfa] {\bl{\begin{tabular}{c}\bf Machine Code/\\\bf Byte Code\end{tabular}}};
-\path[->, red, line width=2mm] (nfa) edge node [above=4mm, black] {\begin{tabular}{c}parse\\[-1mm] tree
-\end{tabular}}(dfa);
-\path[->, red, line width=2mm] (dfa) edge (final);
-\end{tikzpicture}\\
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[t]
-\frametitle{\begin{tabular}{c}What Next\end{tabular}}
-
-\begin{itemize}
-\item register spilling
-\item dead code removal
-\item loop optimisations
-\item instruction selection
-\item type checking
-\item concurrency
-\item fuzzy testing
-\item verification\bigskip\\
-
-\item GCC, LLVM, tracing JITs
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
-
 
 \end{document}
 




