\usepackage{../graphics}

  \LARGE Formal Languages (8)\\[3mm] 

\frametitle{Bird's Eye View}

\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{frame}

\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{}

\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}[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}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

\frametitle{Interpreter}

\end{frame}

\frametitle{Interpreter (2)}

\end{frame}

\frametitle{Test Program}

{\lstset{language=While}\fontsize{10}{12}\selectfont

\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}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\frametitle{Interpreted Code}

\end{frame}

\frametitle{Java Virtual Machine}

\item some languages compiled 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}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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\\