\documentclass[dvipsnames,14pt,t]{beamer}

\usepackage{../langs}

\usepackage{../data}

% beamer stuff 

\newcommand{\bl}[1]{\textcolor{blue}{#1}}       

\begin{document}

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\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}

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\mode<presentation>{

\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\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}}

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\mode<presentation>{

\begin{frame}[t]

\frametitle{\begin{tabular}{c}Compiling Whiles\end{tabular}}

{\Large\bl{$\text{while}\;b\;\text{do}\;cs$}}\bigskip\bigskip