\documentclass[dvipsnames,14pt,t]{beamer}
\usepackage{../slides}
\usepackage{../langs}
\usepackage{../data}
\usepackage{../graphics}

% beamer stuff 
\renewcommand{\slidecaption}{AFL 09, King's College London}
\newcommand{\bl}[1]{\textcolor{blue}{#1}}       

\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{%
  \begin{tabular}{@ {}c@ {}}
  \\[-3mm]
  \LARGE Automata and \\[-2mm] 
  \LARGE Formal Languages (8)\\[3mm] 
  \end{tabular}}

  \normalsize
  \begin{center}
  \begin{tabular}{ll}
  Email:  & christian.urban at kcl.ac.uk\\
  Office: & S1.27 (1st floor Strand Building)\\
  Slides: & KEATS (also home work is there)\\
  \end{tabular}
  \end{center}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Bird's Eye View}

\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 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}\\
\end{center}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{JVM Code}
\footnotesize
\mbox{}\\[-20mm]\mbox{}

\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}[c]

\begin{center}
\bl{\begin{tabular}{@{}lcl@{}}
\textit{Stmt} & $\rightarrow$ &  $\texttt{skip}$\\
              & $|$ & \textit{Id}\;\texttt{:=}\;\textit{AExp}\\
              & $|$ & \texttt{if}\; \textit{BExp} \;\texttt{then}\; \textit{Block} \;\texttt{else}\; \textit{Block}\\
              & $|$ & \texttt{while}\; \textit{BExp} \;\texttt{do}\; \textit{Block}\\
              & $|$ & \texttt{read}\;\textit{Id}\\
              & $|$ & \texttt{write}\;\textit{Id}\\
              & $|$ & \texttt{write}\;\textit{String}\medskip\\
\textit{Stmts} & $\rightarrow$ &  \textit{Stmt} \;\texttt{;}\; \textit{Stmts}\\
              & $|$ & \textit{Stmt}\medskip\\
\textit{Block} & $\rightarrow$ &  \texttt{\{}\,\textit{Stmts}\,\texttt{\}}\\
                & $|$ & \textit{Stmt}\medskip\\
\textit{AExp} & $\rightarrow$ & \ldots\\
\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}}}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Interpreter\end{tabular}}

\begin{center}
\bl{\begin{tabular}{@{}lcl@{}}
$\text{eval}(n, E)$ & $\dn$ & $n$\\
$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
\end{tabular}}
\end{center}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}}

\begin{center}
\bl{\begin{tabular}{@{}lcl@{}}
$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
\text{eval}(cs_1,E)$}\\
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
\end{tabular}}
\end{center}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Test Program\end{tabular}}

\mbox{}\\[-18mm]\mbox{}

{\lstset{language=While}\fontsize{10}{12}\selectfont
\texttt{\lstinputlisting{../progs/loops.while}}}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\tiny

\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{\begin{tabular}{c}Interpreted 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 {interpreted.data};
\end{axis}
\end{tikzpicture}
\end{center}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}}

\begin{itemize}
\item introduced in 1995
\item is a stack-based VM (like Postscript, CLR of .Net)
\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
\end{itemize}

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}

\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}\pause

\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Variables\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}

\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}\pause

\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling Statements\end{tabular}}

We return a list of instructions and an environment for the variables

\begin{center}
\bl{\begin{tabular}{@{}l@{\hspace{1mm}}c@{\hspace{1mm}}l@{}}
$\text{compile}(\text{skip}, E)$ & $\dn$ & $(N\!il, E)$\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling Ifs\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Conditional Jumps\end{tabular}}

\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling BExps\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling Ifs\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling Whiles\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling Whiles\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
\frametitle{\begin{tabular}{c}Compiling Writes\end{tabular}}

{\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}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\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}

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