% !TEX program = xelatex
\documentclass[dvipsnames,14pt,t]{beamer}
\usepackage{../slides}
\usepackage{../langs}
\usepackage{../data}
\usepackage{../graphics}
\usepackage{../grammar}

% beamer stuff 
\renewcommand{\slidecaption}{CFL 07, King's College London}
\newcommand{\bl}[1]{\textcolor{blue}{#1}}       

\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{%
  \begin{tabular}{@ {}c@ {}}
  \\[-3mm]
  \LARGE Compilers and \\[-2mm] 
  \LARGE Formal Languages (7)\\[3mm] 
  \end{tabular}}

  \normalsize
  \begin{center}
  \begin{tabular}{ll}
    Email:  & christian.urban at kcl.ac.uk\\
    Office Hours: & Thursdays 12 -- 14\\
    Location: & N7.07 (North Wing, Bush House)\\
    Slides \& Progs: & KEATS (also homework 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 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}\\
\end{center}

\end{frame}
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\begin{frame}[c]
\frametitle{CW3}

Atomic parsers for tokens

\begin{center}
\bl{$\texttt{T\_Num(123)}::rest \;\Rightarrow\; \{(\texttt{T\_Num(123)}, rest)\}$} 
\end{center}\bigskip

\begin{itemize}
\item you consume one or more token from the\\ 
  input (stream)
\item \bl{\texttt{T\_NUM(1), T\_OP(+), T\_NUM(2)}}\bigskip
\item a good starting point would be \texttt{comb2.scala} 
\item in case CW2 did not work, use \texttt{toks.scala} as 
  input to the parser
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\begin{textblock}{10}(0.5,0.5)
  \LARGE
  \fontspec{Hoefler Text Black}
  \textcolor{ProcessBlue}{JVM\\ Code}
  \\[12mm]

  \normalsize
  Jasmin\\
  Krakatau\\
  ASM lib
\end{textblock}


\fontsize{8}{10}\selectfont
%\footnotesize
\mbox{}\\[-8mm]\mbox{}

\begin{columns}
\begin{column}{2cm} 
\lstinputlisting[numbers=none]{../progs/appHa.j}
\end{column}

\begin{column}{2cm} 
\lstinputlisting[numbers=none]{../progs/appHb.j}
\end{column}

\end{columns}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]

\begin{center}
\bl{\begin{tabular}{@{}lcl@{}}
\\[-12mm]        
\meta{Stmt} & $::=$ &  $\texttt{skip}$\\
              & $|$ & \textit{Id}\;\texttt{:=}\;\meta{AExp}\\
              & $|$ & \texttt{if}\; \meta{BExp} \;\texttt{then}\; \meta{Block} \;\texttt{else}\; \meta{Block}\\
              & $|$ & \texttt{while}\; \meta{BExp} \;\texttt{do}\; \meta{Block}\\
              & $|$ & \texttt{read}\;\textit{Id}\\
              & $|$ & \texttt{write}\;\textit{Id}\\
              & $|$ & \texttt{write}\;\textit{String}\medskip\\
\meta{Stmts} & $::=$ &  \meta{Stmt} \;\texttt{;}\; \meta{Stmts}\\
              & $|$ & \meta{Stmt}\medskip\\
\meta{Block} & $::=$ &  \texttt{\{}\,\meta{Stmts}\,\texttt{\}}\\
                & $|$ & \meta{Stmt}\medskip\\
\meta{AExp} & $::=$ & \ldots\\
\meta{BExp} & $::=$ & \ldots\\
\end{tabular}}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Interpreter}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Interpreter (2)}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Test Program}

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

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

\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{frame}[t]
%\frametitle{Interpreted Code}
%
%\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{frame}[c]
%\frametitle{Java Virtual Machine}
%
%\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t,fragile]
\frametitle{Compiling AExps}

For example \textbf{\bl{1 + ((2 * 3) + (4 - 3))}}:\medskip
  
\begin{columns}[T]
\begin{column}{.3\textwidth}
\begin{center}
\bl{\begin{tikzpicture}
\tikzset{level distance=12mm,sibling distance=4mm}
\tikzset{edge from parent/.style={draw,very thick}}
\Tree [.$+$ [.$1$ ] [.$+$ [.$*$ $2$ $3$ ] [.$-$ $4$ $3$ ]]]
\end{tikzpicture}}
\end{center}
\end{column}
\begin{column}{.3\textwidth}  
\begin{lstlisting}[language=JVMIS,numbers=none]
ldc 1 
ldc 2 
ldc 3 
imul 
ldc 4 
ldc 3 
isub 
iadd 
iadd
\end{lstlisting}
\end{column}
\end{columns}\bigskip

\small
Traverse tree in post-order \bl{$\Rightarrow$} code for 
stack-machine

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t,fragile]
\frametitle{Compiling AExps}

\liningnums{\textbf{\Large\bl{(1 + 2) + 3}}}

\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]  
ldc 1
ldc 2
iadd
ldc 3
iadd
\end{lstlisting}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t,fragile]
\frametitle{Compiling AExps}

\liningnums{\textbf{\Large\bl{1 + (2 + 3)}}}

\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]  
ldc 1
ldc 2
ldc 3
iadd
iadd
\end{lstlisting}
\bigskip\pause
\vfill

\textcolor{codepurple}{\textbf{\texttt{dadd}}},
\textcolor{codepurple}{\textbf{\texttt{fadd}}},
\textcolor{codepurple}{\textbf{\texttt{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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t,fragile]
\frametitle{\begin{tabular}{c}Compiling AExps\end{tabular}}

\liningnums{\textbf{\Large\bl{1 $+$ 2 $*$ 3 $+$ (4 $-$ 3)}}}

\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]         
ldc 1
ldc 2
ldc 3
imul
ldc 4
ldc 3
isub
iadd
iadd
\end{lstlisting}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Variables}
\liningnums{\textbf{\Large\bl{x $:=$ 5 $+$ y $*$ 2}}}\bigskip\pause   

\begin{itemize}
\item lookup: \bl{$\textcolor{codepurple}{\textbf{\texttt{iload}}}\; index$}
\item store: \bl{$\textcolor{codepurple}{\textbf{\texttt{istore}}}\; index$}
\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}[c]
\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,fragile]
\frametitle{Compiling Assignments}

\liningnums{\textbf{\Large\bl{x $:=$ x $+$ 1}}}

\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=6cm]        
iload /*@\bl{$n_x$}@*/
ldc 1
iadd
istore /*@\bl{$n_x$}@*/
\end{lstlisting}\medskip

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,fragile]
\frametitle{Conditional Jumps}

\begin{minipage}{1.1\textwidth}
\begin{itemize}
\item \textcolor{codepurple}{\textbf{\texttt{if\_icmpeq}}} \bl{$label$}
  if two ints are equal, then jump\medskip
\item \textcolor{codepurple}{\textbf{\texttt{if\_icmpne}}} \bl{$label$}
  if two ints aren't equal, then jump\medskip
\item \textcolor{codepurple}{\textbf{\texttt{if\_icmpge}}} \bl{$label$}
  if one int is greater or equal then another, then jump
\item[]\ldots
\end{itemize}
\end{minipage}\pause

\begin{lstlisting}[language=JVMIS,numbers=none,xleftmargin=2cm]
/*@\bl{$L_1$:}@*/
  if_icmpeq /*@\bl{$L_2$}@*/
  iload 1
  ldc 1
  iadd
  if_icmpeq /*@\bl{$L_1$}@*/
/*@\bl{$L_2$:}@*/
\end{lstlisting}


\begin{textblock}{3.5}(11,12)
\only<3>{labels must be unique}
\end{textblock}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{Compiling Ifs}

For example

\begin{lstlisting}[mathescape,numbers=none,language=While]
if 1 = 1 then x := 2 else y := 3
\end{lstlisting}


\begin{center}
\begin{lstlisting}[mathescape,language=JVMIS,numbers=none]
   ldc 1
   ldc 1
   if_icmpne L_ifelse $\quad\tikz[remember picture] \node (C) {\mbox{}};$
   ldc 2
   istore 0
   goto L_ifend $\quad\tikz[remember picture] \node (A) {\mbox{}};$
L_ifelse: $\quad\tikz[remember picture] \node[] (D) {\mbox{}};$
   ldc 3
   istore 1
L_ifend: $\quad\tikz[remember picture] \node[] (B) {\mbox{}};$
\end{lstlisting}
\end{center}

\begin{tikzpicture}[remember picture,overlay]
  \draw[->,very thick] (A) edge [->,to path={-- ++(10mm,0mm) 
           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (B.east);
  \draw[->,very thick] (C) edge [->,to path={-- ++(10mm,0mm) 
           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (D.east);
\end{tikzpicture}

\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}[c,fragile]
\frametitle{Compiling Whiles}

For example

\begin{lstlisting}[mathescape,numbers=none,language=While]
while x <= 10 do x := x + 1
\end{lstlisting}


\begin{center}
\begin{lstlisting}[mathescape,language=JVMIS,numbers=none]
L_wbegin: $\quad\tikz[remember picture] \node[] (LB) {\mbox{}};$
   iload 0
   ldc 10
   if_icmpgt L_wend $\quad\tikz[remember picture] \node (LC) {\mbox{}};$
   iload 0
   ldc 1
   iadd
   istore 0
   goto L_wbegin $\quad\tikz[remember picture] \node (LA) {\mbox{}};$
L_wend: $\quad\tikz[remember picture] \node[] (LD) {\mbox{}};$
\end{lstlisting}
\end{center}

\begin{tikzpicture}[remember picture,overlay]
  \draw[->,very thick] (LA) edge [->,to path={-- ++(12mm,0mm) 
           -- ++(0mm,17.3mm) |- (\tikztotarget)},line width=1mm] (LB.east);
  \draw[->,very thick] (LC) edge [->,to path={-- ++(12mm,0mm) 
           -- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (LD.east);
\end{tikzpicture}

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{Compiling Writes}

\small
\begin{lstlisting}[language=JVMIS,mathescape,
                   numbers=none,xleftmargin=-6mm]
.method public static write(I)V 
  .limit locals 1 
  .limit stack 2 
  getstatic java/lang/System/out 
                            Ljava/io/PrintStream; 
  iload 0
  invokevirtual java/io/PrintStream/println(I)V 
  return 
.end method



iload $E(x)$ 
invokestatic XXX/XXX/write(I)V
\end{lstlisting}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\begin{frame}[c,fragile]
\frametitle{Compiling Main}

\footnotesize
\begin{lstlisting}[language=JVMIS,mathescape,
                   numbers=none,xleftmargin=-6mm]
.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

      $\textit{\ldots{}here comes the compiled code\ldots}$

    return
.end method
\end{lstlisting}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
\frametitle{Next Compiler Phases}

\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
\item jasmin and krakatau are assemblers for jvm code
\end{itemize}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Recall: Interpreted Code}

\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}

Loop program
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Compiled Code}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Compiler vs.~Interpreter}

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c]
  \frametitle{A ``Compiler'' for BF*** to C}
  
  \begin{center}
  \begin{tabular}{lcl}
  \bl{\texttt{>}} & $\Rightarrow$ & \texttt{ptr++}\\
  \bl{\texttt{<}} & $\Rightarrow$ & \texttt{ptr--}\\
  \bl{\texttt{+}} & $\Rightarrow$ & \texttt{(*ptr)++}\\
  \bl{\texttt{-}} & $\Rightarrow$ & \texttt{(*ptr)--}\\
  \bl{\texttt{.}} & $\Rightarrow$ & \texttt{putchar(*ptr)}\\
  \bl{\texttt{,}} & $\Rightarrow$ & \texttt{*ptr = getchar()}\\
  \bl{\texttt{[}} & $\Rightarrow$ & \texttt{while(*ptr)\{}\\
  \bl{\texttt{]}} & $\Rightarrow$ & \texttt{\}}\medskip\\
                  & $\Rightarrow$ & ignore everything else\\
  \end{tabular}  
  \end{center}\bigskip  
  
  \texttt{char field[30000]\\ char *ptr = \&field[15000]}
  
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{BF***}

we need some big array, say \texttt{arr} and 7 (8) instructions:\medskip

\begin{itemize}
\item \texttt{>} move \texttt{ptr++}
\item \texttt{<} move \texttt{ptr-{}-}
\item \texttt{+} add \texttt{arr[ptr]++}
\item \texttt{-} subtract \texttt{arr[ptr]-{}-}
\item \texttt{.} print out \texttt{arr[ptr]} as ASCII
\item \texttt{[} if \texttt{arr[ptr] == 0} jump just after the corresponding \texttt{]}; otherwise \texttt{ptr++}
\item \texttt{]} if \texttt{arr[ptr] != 0} jump just after the corresponding \texttt{[}; otherwise \texttt{ptr++}

\end{itemize}  

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{Arrays in While}

\begin{itemize}
\item \texttt{new arr[15000]}\medskip 
\item \texttt{x := 3 + arr[3 + y]}\medskip 
\item \texttt{arr[42 * n] := ...}
\end{itemize}  

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{New Arrays}

\begin{lstlisting}[mathescape,numbers=none,language=While]
  new arr[number]
\end{lstlisting}\bigskip\bigskip

\begin{lstlisting}[mathescape,numbers=none,language=JVMIS]
  ldc number
  newarray int
  astore loc_var
\end{lstlisting}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{Array Update}

\begin{lstlisting}[mathescape,numbers=none,language=While]
  arr[...] := 
\end{lstlisting}\bigskip\bigskip

\begin{lstlisting}[mathescape,numbers=none,language=JVMIS]
  aload loc_var
  index_aexp
  value_aexp
  iastore
\end{lstlisting}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[c,fragile]
\frametitle{Array Lookup in AExp}

\begin{lstlisting}[mathescape,numbers=none,language=While]
  ...arr[...]... 
\end{lstlisting}\bigskip\bigskip

\begin{lstlisting}[mathescape,numbers=none,language=JVMIS]
  aload loc_var
  index_aexp
  iaload
\end{lstlisting}


\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 is 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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