\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}

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\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: & N\liningnums{7.07} (North Wing, Bush House)\\

  \end{tabular}

  \end{center}

\end{frame}

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\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]

\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}

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\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}

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\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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\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}

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\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}

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\begin{frame}[c]

\frametitle{Test Program}

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

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

\texttt{\lstinputlisting{../progs/loops.while}}}

\end{frame}

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\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}

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\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}

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\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}

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\begin{frame}[t,fragile]

\frametitle{Compiling AExps}

For example \liningnums{\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}

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\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}

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\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}

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\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}

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\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}

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\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}

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\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}

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\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}

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\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}

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\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}

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\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}