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\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{../slides}
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\usepackage{../langs}
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\usepackage{../data}
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\usepackage{../graphics}
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\usepackage{../grammar}
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\usepackage{soul}
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\tikzset{onslide/.code args={<#1>#2}{%
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\only<#1>{\pgfkeysalso{#2}} % \pgfkeysalso doesn't change the path
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}}
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\makeatletter
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\newenvironment<>{btHighlight}[1][]
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{\begin{onlyenv}#2\begingroup\tikzset{bt@Highlight@par/.style={#1}}\begin{lrbox}{\@tempboxa}}
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{\end{lrbox}\bt@HL@box[bt@Highlight@par]{\@tempboxa}\endgroup\end{onlyenv}}
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\newcommand<>\btHL[1][]{%
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\only#2{\begin{btHighlight}[#1]\bgroup\aftergroup\bt@HL@endenv}%
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}
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\def\bt@HL@endenv{%b jm
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\end{btHighlight}%
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\egroup
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}
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\newcommand{\bt@HL@box}[2][]{%
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\tikz[#1]{%
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\pgfpathrectangle{\pgfpoint{1pt}{0pt}}{\pgfpoint{\wd #2}{\ht #2}}%
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\pgfusepath{use as bounding box}%
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\node[anchor=base west, fill=orange!30,outer sep=0pt,inner xsep=1pt, inner ysep=0pt, rounded corners=3pt, minimum height=\ht\strutbox+1pt,#1]{\raisebox{1pt}{\strut}\strut\usebox{#2}};
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}%
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}
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\makeatother
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\lstset{morekeywords={def,if,then,else,write,read},keywordstyle=\color{codepurple}\bfseries}
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% beamer stuff
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\renewcommand{\slidecaption}{CFL 09, King's College London}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm]
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\LARGE Compilers and \\[-2mm]
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\LARGE Formal Languages (8)\\[3mm]
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\end{tabular}}
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\normalsize
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\
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Office: & N7.07 (North Wing, Bush House)\\
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Slides: & KEATS (also home work is there)\\
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\end{tabular}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t,fragile]
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\frametitle{Compiling AExps}
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For example \bl{$1 + ((2 * 3) + (4 - 3))$}:\medskip
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\begin{columns}[T]
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\begin{column}{.3\textwidth}
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\begin{center}
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\bl{\begin{tikzpicture}
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\tikzset{level distance=12mm,sibling distance=4mm}
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\tikzset{edge from parent/.style={draw,very thick}}
\Tree [.$+$ [.$1$ ] [.$+$ [.$*$ $2$ $3$ ] [.$-$ $4$ $3$ ]]]
\end{tikzpicture}}
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\end{center}
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\end{column}
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\begin{column}{.3\textwidth}
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\begin{lstlisting}[language=JVMIS,numbers=none]
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ldc 1
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ldc 2
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ldc 3
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imul
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ldc 4
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ldc 3
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isub
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iadd
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iadd
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\end{lstlisting}
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\end{column}
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\end{columns}\bigskip
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\small
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Traverse tree in post-order \bl{$\Rightarrow$} code for
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stack-machine
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Compiling AExps}
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\bl{
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\begin{center}
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\begin{tabular}{lcl}
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$\textit{compile}(n, E)$ & $\dn$ & $\pcode{ldc}\;n$\smallskip\\
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$\textit{compile}(a_1 + a_2, E)$ & $\dn$ \\
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\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\;\textit{compile}(a_2, E)\;@\; \pcode{iadd}$}\smallskip\\
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$\textit{compile}(a_1 - a_2, E)$ & $\dn$ \\
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\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\; \textit{compile}(a_2, E)\;@\; \pcode{isub}$}\smallskip\\
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$\textit{compile}(a_1 * a_2, E)$ & $\dn$ \\
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\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\; \textit{compile}(a_2, E)\;@\; \pcode{imul}$}\smallskip\\
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$\textit{compile}(a_1 \backslash a_2, E)$ & $\dn$\\
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\multicolumn{3}{c}{$\qquad\textit{compile}(a_1, E) \;@\; \textit{compile}(a_2, E)\;@\; \pcode{idiv}$}\smallskip\\
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$\textit{compile}(x, E)$ & $\dn$ & $\pcode{iload}\;E(x)$\\
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\end{tabular}
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\end{center}}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Compiling Ifs}
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For example
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\begin{lstlisting}[mathescape,numbers=none,language=While]
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if 1 = 1 then x := 2 else y := 3
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\end{lstlisting}
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\begin{center}
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\begin{lstlisting}[mathescape,language=JVMIS,numbers=none]
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ldc 1
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ldc 1
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if_icmpne L_ifelse $\quad\tikz[remember picture] \node (C) {\mbox{}};$
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ldc 2
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istore 0
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goto L_ifend $\quad\tikz[remember picture] \node (A) {\mbox{}};$
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L_ifelse: $\quad\tikz[remember picture] \node[] (D) {\mbox{}};$
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ldc 3
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istore 1
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L_ifend: $\quad\tikz[remember picture] \node[] (B) {\mbox{}};$
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\end{lstlisting}
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\end{center}
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\begin{tikzpicture}[remember picture,overlay]
\draw[->,very thick] (A) edge [->,to path={-- ++(10mm,0mm)
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-- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (B.east);
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\draw[->,very thick] (C) edge [->,to path={-- ++(10mm,0mm)
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-- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (D.east);
\end{tikzpicture}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Compiling Whiles}
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For example
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\begin{lstlisting}[mathescape,numbers=none,language=While]
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while x <= 10 do x := x + 1
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\end{lstlisting}
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\begin{center}
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\begin{lstlisting}[mathescape,language=JVMIS,numbers=none]
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L_wbegin: $\quad\tikz[remember picture] \node[] (LB) {\mbox{}};$
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iload 0
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ldc 10
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if_icmpgt L_wend $\quad\tikz[remember picture] \node (LC) {\mbox{}};$
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iload 0
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ldc 1
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iadd
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istore 0
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goto L_wbegin $\quad\tikz[remember picture] \node (LA) {\mbox{}};$
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L_wend: $\quad\tikz[remember picture] \node[] (LD) {\mbox{}};$
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\end{lstlisting}
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\end{center}
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\begin{tikzpicture}[remember picture,overlay]
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\draw[->,very thick] (LA) edge [->,to path={-- ++(12mm,0mm)
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-- ++(0mm,17.3mm) |- (\tikztotarget)},line width=1mm] (LB.east);
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\draw[->,very thick] (LC) edge [->,to path={-- ++(12mm,0mm)
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-- ++(0mm,-17.3mm) |- (\tikztotarget)},line width=1mm] (LD.east);
\end{tikzpicture}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Compiling Writes}
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\small
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\begin{lstlisting}[language=JVMIS,mathescape,
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numbers=none,xleftmargin=-6mm]
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.method public static write(I)V
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.limit locals 1
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.limit stack 2
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getstatic java/lang/System/out
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Ljava/io/PrintStream;
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iload 0
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invokevirtual java/io/PrintStream/println(I)V
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return
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.end method
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iload $E(x)$
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invokestatic XXX/XXX/write(I)V
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Compiling Main}
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\footnotesize
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\begin{lstlisting}[language=JVMIS,mathescape,
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numbers=none,xleftmargin=-6mm]
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.class public XXX.XXX
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.super java/lang/Object
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.method public <init>()V
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aload_0
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invokenonvirtual java/lang/Object/<init>()V
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return
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.end method
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.method public static main([Ljava/lang/String;)V
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.limit locals 200
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.limit stack 200
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$\textit{\ldots{}here comes the compiled code\ldots}$
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return
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.end method
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c,fragile]
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\frametitle{Functional Programming}
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\footnotesize
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\begin{textblock}{13}(0.9,3)
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\begin{lstlisting}[]numbers=none]
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def fib(n) = if n == 0 then 0
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else if n == 1 then 1
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else fib(n - 1) + fib(n - 2);
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def fact(n) = if n == 0 then 1 else n * fact(n - 1);
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def ack(m, n) = if m == 0 then n + 1
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else if n == 0 then ack(m - 1, 1)
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else ack(m - 1, ack(m, n - 1));
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def gcd(a, b) = if b == 0 then a else gcd(b, a % b);
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\end{lstlisting}
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\end{textblock}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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\frametitle{Fun Grammar}
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\bl{
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\begin{plstx}[rhs style=]
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: \meta{Exp} ::= \meta{Var} | \meta{Num}{\hspace{3cm}}
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| \meta{Exp} + \meta{Exp} | ... | (\meta{Exp})
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| \code{if} \meta{BExp} \code{then} \meta{Exp} \code{else} \meta{Exp}
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| \code{write} \meta{Exp} {\hspace{3cm}}
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| \meta{Exp} ; \meta{Exp}
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| \textit{FunName} (\meta{Exp}, ... , \meta{Exp})\\
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: \meta{BExp} ::= ...\\
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: \meta{Decl} ::= \meta{Def} ; \meta{Decl}
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| \meta{Exp}\\
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: \meta{Def} ::= \code{def} \textit{FunName} ($\hspace{0.4mm}x_1$, ... , $x_n$) = \meta{Exp}\\
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\end{plstx}}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c, fragile]
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\frametitle{Abstract Syntax Trees}
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\footnotesize
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\begin{lstlisting}[language=Scala, numbers=none, xleftmargin=-1mm]
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abstract class Exp
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abstract class BExp
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abstract class Decl
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case class Var(s: String) extends Exp
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case class Num(i: Int) extends Exp
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case class Aop(o: String, a1: Exp, a2: Exp) extends Exp
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case class If(a: BExp, e1: Exp, e2: Exp) extends Exp
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case class Write(e: Exp) extends Exp
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case class Sequ(e1: Exp, e2: Exp) extends Exp
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case class Call(name: String, args: List[Exp]) extends Exp
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case class Bop(o: String, a1: Exp, a2: Exp) extends BExp
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case class Def(name: String,
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args: List[String],
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body: Exp) extends Decl
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case class Main(e: Exp) extends Decl
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c, fragile]
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\frametitle{Sequences}
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Compiling \texttt{exp1 ; exp2}:\bigskip
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\begin{lstlisting}[mathescape,language=JVMIS, numbers=none]
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$\textit{compile}$(exp1)
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pop
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$\textit{compile}$(exp2)
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c, fragile]
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\frametitle{Write}
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Compiling call to \texttt{write(1+2)}:\bigskip
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346 |
\begin{lstlisting}[mathescape,language=JVMIS, numbers=none]
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|
|
347 |
$\textit{compile}$(1+2)
|
|
|
348 |
dup
|
|
|
349 |
invokestatic XXX/XXX/write(I)V
|
|
|
350 |
\end{lstlisting}\bigskip
|
|
|
351 |
|
|
|
352 |
\small
|
|
|
353 |
needs the helper method
|
|
|
354 |
|
|
|
355 |
\footnotesize
|
|
|
356 |
\begin{lstlisting}[language=JVMIS,
|
|
|
357 |
xleftmargin=2mm,
|
|
|
358 |
numbers=none]
|
|
|
359 |
.method public static write(I)V
|
|
|
360 |
.limit locals 1
|
|
|
361 |
.limit stack 2
|
|
|
362 |
getstatic java/lang/System/out Ljava/io/PrintStream;
|
|
|
363 |
iload 0
|
|
|
364 |
invokevirtual java/io/PrintStream/println(I)V
|
|
|
365 |
return
|
|
|
366 |
.end method
|
|
|
367 |
\end{lstlisting}
|
|
|
368 |
\end{frame}
|
|
|
369 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
370 |
|
|
|
371 |
|
|
|
372 |
|
|
|
373 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
374 |
\begin{frame}[t, fragile]
|
|
|
375 |
\frametitle{Function Definitions}
|
|
|
376 |
|
|
|
377 |
\footnotesize
|
|
|
378 |
\begin{lstlisting}[language=JVMIS,
|
|
|
379 |
xleftmargin=2mm,
|
|
|
380 |
numbers=none]
|
|
|
381 |
.method public static write(I)V
|
|
|
382 |
.limit locals 1
|
|
|
383 |
.limit stack 2
|
|
|
384 |
getstatic java/lang/System/out Ljava/io/PrintStream;
|
|
|
385 |
iload 0
|
|
|
386 |
invokevirtual java/io/PrintStream/println(I)V
|
|
|
387 |
return
|
|
|
388 |
.end method
|
|
|
389 |
\end{lstlisting}\bigskip
|
|
|
390 |
|
|
|
391 |
\small We will need for definitions, like\footnotesize\medskip
|
|
|
392 |
|
|
|
393 |
\begin{lstlisting}[language=JVMIS,
|
|
|
394 |
xleftmargin=2mm,
|
|
|
395 |
numbers=none]
|
|
|
396 |
def fname (x1, ... , xn) = ...
|
|
|
397 |
|
|
|
398 |
.method public static fname (I...I)I
|
|
|
399 |
.limit locals ??
|
|
|
400 |
.limit stack ??
|
|
|
401 |
??
|
|
|
402 |
.end method
|
|
|
403 |
\end{lstlisting}
|
|
|
404 |
|
|
|
405 |
\end{frame}
|
|
|
406 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
407 |
|
|
|
408 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
409 |
\begin{frame}[c, fragile]
|
|
|
410 |
\frametitle{Stack Estimation}
|
|
|
411 |
\small
|
|
|
412 |
\mbox{}\\[-15mm]
|
|
|
413 |
|
|
|
414 |
\bl{\begin{center}
|
|
|
415 |
\begin{tabular}{@{\hspace{-4mm}}l@{\hspace{2mm}}c@{\hspace{2mm}}l@{}}
|
|
|
416 |
$\textit{estimate}(n)$ & $\dn$ & $1$\\
|
|
|
417 |
$\textit{estimate}(x)$ & $\dn$ & $1$\\
|
|
|
418 |
$\textit{estimate}(a_1\;aop\;a_2)$ & $\dn$ &
|
|
|
419 |
$\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\
|
|
|
420 |
$\textit{estimate}(\pcode{if}\;b\;\pcode{then}\;e_1\;\pcode{else}\;e_2)$ & $\dn$ &
|
|
|
421 |
$\textit{estimate}(b) +$\\
|
|
|
422 |
& & $\quad max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\
|
|
|
423 |
$\textit{estimate}(\pcode{write}(e))$ & $\dn$ &
|
|
|
424 |
$\textit{estimate}(e) + 1$\\
|
|
|
425 |
$\textit{estimate}(e_1 ; e_2)$ & $\dn$ &
|
|
|
426 |
$max(\textit{estimate}(e_1), \textit{estimate}(e_2))$\\
|
|
|
427 |
$\textit{estimate}(f(e_1, ..., e_n))$ & $\dn$ &
|
|
|
428 |
$\sum_{i = 1..n}\;estimate(e_i)$\medskip\\
|
|
|
429 |
$\textit{estimate}(a_1\;bop\;a_2)$ & $\dn$ &
|
|
|
430 |
$\textit{estimate}(a_1) + \textit{estimate}(a_2)$\\
|
|
|
431 |
\end{tabular}
|
|
|
432 |
\end{center}}
|
|
|
433 |
|
|
|
434 |
\end{frame}
|
|
|
435 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
436 |
|
|
|
437 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
438 |
\begin{frame}[fragile]
|
|
|
439 |
\frametitle{Successor Function}
|
|
|
440 |
|
|
|
441 |
\begin{textblock}{7}(1,2.5)\footnotesize
|
|
|
442 |
\begin{minipage}{6cm}
|
|
|
443 |
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
|
|
|
444 |
.method public static suc(I)I
|
|
|
445 |
.limit locals 1
|
|
|
446 |
.limit stack 2
|
|
|
447 |
iload 0
|
|
|
448 |
ldc 1
|
|
|
449 |
iadd
|
|
|
450 |
ireturn
|
|
|
451 |
.end method
|
|
|
452 |
\end{lstlisting}
|
|
|
453 |
\end{minipage}
|
|
|
454 |
\end{textblock}
|
|
|
455 |
|
|
|
456 |
\begin{textblock}{7}(6,8)
|
|
|
457 |
\begin{bubble}[5cm]\small
|
|
|
458 |
\begin{lstlisting}[language=Lisp,
|
|
|
459 |
basicstyle=\ttfamily,
|
|
|
460 |
numbers=none,
|
|
|
461 |
xleftmargin=1mm]
|
|
|
462 |
def suc(x) = x + 1;
|
|
|
463 |
\end{lstlisting}
|
|
|
464 |
\end{bubble}
|
|
|
465 |
\end{textblock}
|
|
|
466 |
|
|
|
467 |
\end{frame}
|
|
|
468 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
469 |
|
|
|
470 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
471 |
\begin{frame}[fragile]
|
|
|
472 |
\frametitle{Addition Function}
|
|
|
473 |
|
|
|
474 |
\begin{textblock}{7}(1,1.9)\footnotesize
|
|
|
475 |
\begin{minipage}{6cm}
|
|
|
476 |
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
|
|
|
477 |
.method public static add(II)I
|
|
|
478 |
.limit locals 2
|
|
|
479 |
.limit stack 5
|
|
|
480 |
iload 0
|
|
|
481 |
ldc 0
|
|
|
482 |
if_icmpne If_else
|
|
|
483 |
iload 1
|
|
|
484 |
goto If_end
|
|
|
485 |
If_else:
|
|
|
486 |
iload 0
|
|
|
487 |
ldc 1
|
|
|
488 |
isub
|
|
|
489 |
iload 1
|
|
|
490 |
invokestatic XXX/XXX/add(II)I
|
|
|
491 |
invokestatic XXX/XXX/suc(I)I
|
|
|
492 |
If_end:
|
|
|
493 |
ireturn
|
|
|
494 |
.end method
|
|
|
495 |
\end{lstlisting}
|
|
|
496 |
\end{minipage}
|
|
|
497 |
\end{textblock}
|
|
|
498 |
|
|
|
499 |
\begin{textblock}{7}(6,6.6)
|
|
|
500 |
\begin{bubble}[7cm]\small
|
|
|
501 |
\begin{lstlisting}[language=Lisp,
|
|
|
502 |
basicstyle=\ttfamily,
|
|
|
503 |
numbers=none,
|
|
|
504 |
xleftmargin=1mm]
|
|
|
505 |
def add(x, y) =
|
|
|
506 |
if x == 0 then y
|
|
|
507 |
else suc(add(x - 1, y));
|
|
|
508 |
\end{lstlisting}
|
|
|
509 |
\end{bubble}
|
|
|
510 |
\end{textblock}
|
|
|
511 |
|
|
|
512 |
\end{frame}
|
|
|
513 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
514 |
|
|
|
515 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
516 |
\begin{frame}[fragile]
|
|
|
517 |
\frametitle{Factorial}
|
|
|
518 |
|
|
|
519 |
\begin{textblock}{7}(1,1.5)\footnotesize
|
|
|
520 |
\begin{minipage}{6cm}
|
|
|
521 |
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
|
|
|
522 |
.method public static facT(II)I
|
|
|
523 |
.limit locals 2
|
|
|
524 |
.limit stack 6
|
|
|
525 |
iload 0
|
|
|
526 |
ldc 0
|
|
|
527 |
if_icmpne If_else_2
|
|
|
528 |
iload 1
|
|
|
529 |
goto If_end_3
|
|
|
530 |
If_else_2:
|
|
|
531 |
iload 0
|
|
|
532 |
ldc 1
|
|
|
533 |
isub
|
|
|
534 |
iload 0
|
|
|
535 |
iload 1
|
|
|
536 |
imul
|
|
|
537 |
invokestatic fact/fact/facT(II)I
|
|
|
538 |
If_end_3:
|
|
|
539 |
ireturn
|
|
|
540 |
.end method
|
|
|
541 |
\end{lstlisting}
|
|
|
542 |
\end{minipage}
|
|
|
543 |
\end{textblock}
|
|
|
544 |
|
|
|
545 |
\begin{textblock}{7}(6,7)
|
|
|
546 |
\begin{bubble}[7cm]\small
|
|
|
547 |
\begin{lstlisting}[language=Lisp,
|
|
|
548 |
basicstyle=\ttfamily,
|
|
|
549 |
numbers=none,
|
|
|
550 |
xleftmargin=1mm]
|
|
|
551 |
def facT(n, acc) =
|
|
|
552 |
if n == 0 then acc
|
|
|
553 |
else facT(n - 1, n * acc);
|
|
|
554 |
\end{lstlisting}
|
|
|
555 |
\end{bubble}
|
|
|
556 |
\end{textblock}
|
|
|
557 |
|
|
|
558 |
\end{frame}
|
|
|
559 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
560 |
|
|
|
561 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
562 |
\begin{frame}[fragile]
|
|
|
563 |
|
|
|
564 |
\begin{textblock}{7}(1,-0.2)\footnotesize
|
|
|
565 |
\begin{minipage}{6cm}
|
|
|
566 |
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none, escapeinside={(*@}{@*)}]
|
|
|
567 |
.method public static facT(II)I
|
|
|
568 |
.limit locals 2
|
|
|
569 |
.limit stack 6
|
|
|
570 |
(*@\hl{facT\_Start:} @*)
|
|
|
571 |
iload 0
|
|
|
572 |
ldc 0
|
|
|
573 |
if_icmpne If_else_2
|
|
|
574 |
iload 1
|
|
|
575 |
goto If_end_3
|
|
|
576 |
If_else_2:
|
|
|
577 |
iload 0
|
|
|
578 |
ldc 1
|
|
|
579 |
isub
|
|
|
580 |
iload 0
|
|
|
581 |
iload 1
|
|
|
582 |
imul
|
|
|
583 |
(*@\hl{istore 1} @*)
|
|
|
584 |
(*@\hl{istore 0} @*)
|
|
|
585 |
(*@\hl{goto facT\_Start} @*)
|
|
|
586 |
If_end_3:
|
|
|
587 |
ireturn
|
|
|
588 |
.end method
|
|
|
589 |
\end{lstlisting}
|
|
|
590 |
\end{minipage}
|
|
|
591 |
\end{textblock}
|
|
|
592 |
|
|
|
593 |
\begin{textblock}{7}(6,7)
|
|
|
594 |
\begin{bubble}[7cm]\small
|
|
|
595 |
\begin{lstlisting}[language=Lisp,
|
|
|
596 |
basicstyle=\ttfamily,
|
|
|
597 |
numbers=none,
|
|
|
598 |
xleftmargin=1mm]
|
|
|
599 |
def facT(n, acc) =
|
|
|
600 |
if n == 0 then acc
|
|
|
601 |
else facT(n - 1, n * acc);
|
|
|
602 |
\end{lstlisting}
|
|
|
603 |
\end{bubble}
|
|
|
604 |
\end{textblock}
|
|
|
605 |
|
|
|
606 |
\end{frame}
|
|
|
607 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
608 |
|
|
|
609 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
610 |
\begin{frame}[c, fragile]
|
|
|
611 |
\frametitle{Tail Recursion}
|
|
|
612 |
|
|
|
613 |
A call to \texttt{f(args)} is usually compiled as\medskip
|
|
|
614 |
|
|
|
615 |
{\small\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
|
|
|
616 |
args onto stack
|
|
|
617 |
invokestatic .../f
|
|
|
618 |
\end{lstlisting}}\pause
|
|
|
619 |
|
|
|
620 |
|
|
|
621 |
A call is in tail position provided:\medskip
|
|
|
622 |
|
|
|
623 |
{\small\begin{itemize}
|
|
|
624 |
\item \texttt{if Bexp then \hl{Exp} else \hl{Exp}}
|
|
|
625 |
\item \texttt{Exp ; \hl{Exp}}
|
|
|
626 |
\item \texttt{Exp op Exp}
|
|
|
627 |
\end{itemize}}\medskip
|
|
|
628 |
|
|
|
629 |
then a call \texttt{f(args)} can be compiled as\medskip\small
|
|
|
630 |
|
|
|
631 |
\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
|
|
|
632 |
prepare environment
|
|
|
633 |
jump to start of function
|
|
|
634 |
\end{lstlisting}
|
|
|
635 |
|
|
|
636 |
\end{frame}
|
|
|
637 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
638 |
|
|
|
639 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
640 |
\begin{frame}[c, fragile]
|
|
|
641 |
\frametitle{Tail Recursive Call}
|
|
|
642 |
\footnotesize
|
|
|
643 |
|
|
|
644 |
\begin{textblock}{13}(-0.3,2)
|
|
|
645 |
\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
|
|
|
646 |
def compile_expT(a: Exp, env: Mem, name: String): Instrs =
|
|
|
647 |
...
|
|
|
648 |
case Call(n, args) => if (name == n)
|
|
|
649 |
{
|
|
|
650 |
val stores = args.zipWithIndex.map
|
|
|
651 |
{ case (x, y) => "istore " + y.toString + "\n" }
|
|
|
652 |
args.flatMap(a => compile_expT(a, env, "")) ++
|
|
|
653 |
stores.reverse ++
|
|
|
654 |
List ("goto " + n + "_Start\n")
|
|
|
655 |
}
|
|
|
656 |
else
|
|
|
657 |
{
|
|
|
658 |
val is = "I" * args.length
|
|
|
659 |
args.flatMap(a => compile_expT(a, env, "")) ++
|
|
|
660 |
List ("invokestatic XXX/XXX/" + n + "(" + is + ")I\n")
|
|
|
661 |
}
|
|
|
662 |
\end{lstlisting}
|
|
|
663 |
\end{textblock}
|
|
|
664 |
|
|
|
665 |
\end{frame}
|
|
|
666 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
667 |
|
|
|
668 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
669 |
\begin{frame}[c]
|
|
|
670 |
\frametitle{Dijkstra on Testing}
|
|
|
671 |
|
|
|
672 |
\begin{bubble}[10cm]
|
|
|
673 |
``Program testing can be a very effective way to show the
|
|
|
674 |
presence of bugs, but it is hopelessly inadequate for showing
|
|
|
675 |
their absence.''
|
|
|
676 |
\end{bubble}\bigskip
|
|
|
677 |
|
|
|
678 |
\small
|
|
|
679 |
What is good about compilers: the either seem to work,
|
|
|
680 |
or go horribly wrong (most of the time).
|
|
|
681 |
|
|
|
682 |
\end{frame}
|
|
|
683 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
684 |
|
|
|
685 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
686 |
\begin{frame}[c]
|
|
|
687 |
\frametitle{\Large Proving Programs to be Correct}
|
|
|
688 |
|
|
|
689 |
\begin{bubble}[10cm]
|
|
|
690 |
\small
|
|
|
691 |
{\bf Theorem:} There are infinitely many prime
|
|
|
692 |
numbers.\medskip\\
|
|
|
693 |
|
|
|
694 |
{\bf Proof} \ldots\\
|
|
|
695 |
\end{bubble}\bigskip
|
|
|
696 |
|
|
|
697 |
|
|
|
698 |
similarly\bigskip
|
|
|
699 |
|
|
|
700 |
\begin{bubble}[10cm]
|
|
|
701 |
\small
|
|
|
702 |
{\bf Theorem:} The program is doing what
|
|
|
703 |
it is supposed to be doing.\medskip
|
|
|
704 |
|
|
|
705 |
{\bf Long, long proof} \ldots\\
|
|
|
706 |
\end{bubble}\bigskip\medskip
|
|
|
707 |
|
|
|
708 |
\small This can be a gigantic proof. The only hope is to have
|
|
|
709 |
help from the computer. `Program' is here to be understood to be
|
|
|
710 |
quite general (compiler, OS, \ldots).
|
|
|
711 |
|
|
|
712 |
\end{frame}
|
|
|
713 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
714 |
|
|
|
715 |
|
|
|
716 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
717 |
|
|
|
718 |
\begin{frame}[c]
|
|
|
719 |
\frametitle{Can This Be Done?}
|
|
|
720 |
|
|
|
721 |
\begin{itemize}
|
|
|
722 |
\item in 2008, verification of a small C-compiler
|
|
|
723 |
\begin{itemize}
|
|
|
724 |
\item ``if my input program has a certain behaviour, then the compiled machine code has the same behaviour''
|
|
|
725 |
\item is as good as \texttt{gcc -O1}, but much, much less buggy
|
|
|
726 |
\end{itemize}
|
|
|
727 |
\end{itemize}
|
|
|
728 |
|
|
|
729 |
\begin{center}
|
|
|
730 |
\includegraphics[scale=0.12]{../pics/compcert.png}
|
|
|
731 |
\end{center}
|
|
|
732 |
|
|
|
733 |
\end{frame}
|
|
|
734 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
735 |
|
|
|
736 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
737 |
\begin{frame}[c]
|
|
|
738 |
\frametitle{Fuzzy Testing C-Compilers}
|
|
|
739 |
|
|
|
740 |
\begin{itemize}
|
|
|
741 |
\item tested GCC, LLVM and others by randomly generating
|
|
|
742 |
C-programs
|
|
|
743 |
\item found more than 300 bugs in GCC and also
|
|
|
744 |
many in LLVM (some of them highest-level critical)\bigskip
|
|
|
745 |
\item about CompCert:
|
|
|
746 |
|
|
|
747 |
\begin{bubble}[10cm]\small ``The striking thing about our CompCert
|
|
|
748 |
results is that the middle-end bugs we found in all other
|
|
|
749 |
compilers are absent. As of early 2011, the under-development
|
|
|
750 |
version of CompCert is the only compiler we have tested for
|
|
|
751 |
which Csmith cannot find wrong-code errors. This is not for
|
|
|
752 |
lack of trying: we have devoted about six CPU-years to the
|
|
|
753 |
task.''
|
|
|
754 |
\end{bubble}
|
|
|
755 |
\end{itemize}
|
|
|
756 |
|
|
|
757 |
\end{frame}
|
|
|
758 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
759 |
|
|
|
760 |
\end{document}
|
|
|
761 |
|
|
|
762 |
%%% Local Variables:
|
|
|
763 |
%%% mode: latex
|
|
|
764 |
%%% TeX-master: t
|
|
|
765 |
%%% End:
|
|
|
766 |
|