| author | Christian Urban <urbanc@in.tum.de> |
| Thu, 28 Nov 2019 08:18:57 +0000 | |
| changeset 701 | 681c36b2af27 |
| parent 612 | 7a12053567d4 |
| child 702 | 39e21a33ffb0 |
| permissions | -rw-r--r-- |
| 701 | 1 |
% !TEX program = xelatex |
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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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\usepackage{mathpartir}
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\usetikzlibrary{shapes,arrows,shadows}
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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 (9)\\[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 Hours: & Thursdays 12 -- 14\\ |
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Location: & N7.07 (North Wing, Bush House)\\ |
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Slides \& Progs: & KEATS (also homework 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}[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,fragile]
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\frametitle{Factorial on the JVM}
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\begin{textblock}{7}(1,1.8)\footnotesize
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\begin{minipage}{6cm}
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\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
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.method public static facT(II)I |
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.limit locals 2 |
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.limit stack 6 |
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iload 0 |
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ldc 0 |
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if_icmpne If_else_2 |
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iload 1 |
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goto If_end_3 |
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If_else_2: |
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iload 0 |
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ldc 1 |
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isub |
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iload 0 |
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iload 1 |
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imul |
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invokestatic fact/fact/facT(II)I |
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If_end_3: |
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ireturn |
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.end method |
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\end{lstlisting}
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\end{minipage}
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\end{textblock}
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\begin{textblock}{7}(6,7)
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\begin{bubble}[7cm]\small
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\begin{lstlisting}[language=Lisp,
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basicstyle=\ttfamily, |
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numbers=none, |
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xleftmargin=1mm,linebackgroundcolor=\color{cream}]
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def facT(n, acc) = |
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if n == 0 then acc |
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else facT(n - 1, n * acc); |
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\end{lstlisting}
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\end{bubble}
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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}[fragile,c]
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\frametitle{LLVM}
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\begin{itemize}
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\item Chris Lattner, Vikram Adve (started in 2000) |
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\item Apple hired Lattner in 2006 |
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\item modular architecture, LLVM-IR |
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\item \texttt{lli} and \texttt{llc}
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\tikzstyle{sensor}=[draw, fill=blue!20, text width=3.8em, line width=1mm,
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text centered, minimum height=2em,drop shadow] |
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\tikzstyle{ann} = [above, text width=4em, text centered]
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\tikzstyle{sc} = [sensor, text width=7em, fill=red!20,
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minimum height=6em, rounded corners, drop shadow,line width=1mm] |
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\begin{frame}[fragile,c]
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\frametitle{LLVM: Overview}
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\begin{tikzpicture}
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% Validation Layer is the same except that there are a set of nodes and links which are added |
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\path (0,0) node (IR) [sc] {\textbf{LLVM-IR}\\ Optimisations};
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\path (IR.west)+(-2.2,1.7) node (sou1) [sensor] {C++};
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\path (IR.west)+(-2.2,0.5) node (sou2)[sensor] {C};
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\path (IR.west)+(-2.2,-1.0) node (dots)[ann] {$\vdots$};
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\path (IR.west)+(-2.2,-1.8) node (sou3)[sensor] {Haskell};
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\path [draw,->,line width=1mm] (sou1.east) -- node [above] {} (IR.160);
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\path [draw,->,line width=1mm] (sou2.east) -- node [above] {} (IR.180);
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\path [draw,->,line width=1mm] (sou3.east) -- node [above] {} (IR.200);
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\path (IR.east)+(2.2,2.0) node (tar1)[sensor] {x86};
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\path (IR.east)+(2.2,0.8) node (tar2)[sensor] {ARM};
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\path (IR.east)+(2.2,-0.4) node (tar3)[sensor] {MIPS};
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\path (IR.east)+(2.2,-1.6) node (tar4)[sensor] {RISC};
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\path (IR.east)+(2.2,-2.8) node (tar5)[sensor] {Power PC};
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\path (IR.east)+(2.2,-4.2) node (dots2)[ann] {$\vdots$};
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\path [draw,<-,line width=1mm] (tar1.west) -- node [above] {} (IR.10);
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\path [draw,<-,line width=1mm] (tar2.west) -- node [above] {} (IR.5);
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\path [draw,<-,line width=1mm] (tar3.west) -- node [above] {} (IR.0);
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\path [draw,<-,line width=1mm] (tar4.west) -- node [above] {} (IR.-5);
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\path [draw,<-,line width=1mm] (tar5.west) -- node [above] {} (IR.-10);
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\end{tikzpicture}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[fragile,t]
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\frametitle{LLVM-IR}
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\small |
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\begin{textblock}{7.7}(8,11.4)
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\begin{bubble}[5cm]\small
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\begin{lstlisting}[language=Lisp,
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numbers=none, |
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xleftmargin=1mm,linebackgroundcolor=\color{cream}]
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def fact(n) = |
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if n == 0 then 1 |
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else n * fact(n - 1) |
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\end{lstlisting}
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\end{bubble}
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\end{textblock}
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\begin{lstlisting}[language=LLVM,xleftmargin=-7mm]
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define i32 @fact (i32 %n) {
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%tmp_19 = icmp eq i32 %n, 0 |
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br i1 %tmp_19, label %if_br_23, label %else_br_24 |
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if_br_23: |
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ret i32 1 |
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else_br_24: |
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%tmp_21 = sub i32 %n, 1 |
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%tmp_22 = call i32 @fact (i32 %tmp_21) |
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%tmp_20 = mul i32 %n, %tmp_22 |
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ret i32 %tmp_20 |
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} |
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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}[fragile,c]
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\frametitle{LLVM Types}
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\tt |
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\begin{center}
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\begin{tabular}{ll}
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boolean & i1 \\ |
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byte & i8 \\ |
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short & i16\\ |
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char & i16\\ |
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integer & i32\\ |
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long & i64\\ |
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float & float\\ |
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double & double\\ |
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*\_ & pointer to \\ |
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**\_ & pointer to a pointer to\\ |
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\mbox{}[\_] & arrays of\\
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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}[fragile,c]
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\frametitle{LLVM Instructions}
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\small |
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233 |
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\begin{lstlisting}[language=LLVM]
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br i1 %var, label %if_br, label %else_br |
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icmp eq i32 %x, %y ; for equal |
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icmp sle i32 %x, %y ; signed less or equal |
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icmp slt i32 %x, %y ; signed less than |
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icmp ult i32 %x, %y ; unsigned less than |
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%var = call i32 @foo(...args...) |
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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||
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[fragile,c]
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\frametitle{SSA Format}
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\bl{$(1 + a) + (3 + (b * 5))$}\bigskip\bigskip
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\begin{lstlisting}[language=LLVM]
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let tmp0 = add 1 a in |
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let tmp1 = mul b 5 in |
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let tmp2 = add 3 tmp1 in |
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let tmp3 = add tmp0 tmp2 in |
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tmp3 |
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\end{lstlisting}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[fragile,c]
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267 |
\frametitle{Abstract Syntax Trees}
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\footnotesize |
|
269 |
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\begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-3mm]
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// Fun language (expressions) |
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abstract class Exp |
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abstract class BExp |
|
274 |
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case class Call(name: String, args: List[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 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 Sequence(e1: Exp, e2: Exp) extends Exp |
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case class Bop(o: String, a1: Exp, a2: Exp) extends BExp |
|
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\end{lstlisting}
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\end{frame}
|
286 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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287 |
||
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[fragile,c]
|
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\frametitle{K-(Intermediate)Language}
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\footnotesize |
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| 609 | 292 |
|
| 701 | 293 |
\begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-3mm]
|
294 |
abstract class KExp |
|
295 |
abstract class KVal |
|
296 |
||
297 |
case class KVar(s: String) extends KVal |
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case class KNum(i: Int) extends KVal |
|
299 |
case class Kop(o: String, v1: KVal, v2: KVal) extends KVal |
|
300 |
case class KCall(o: String, vrs: List[KVal]) extends KVal |
|
301 |
case class KWrite(v: KVal) extends KVal |
|
302 |
||
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case class KIf(x1: String, e1: KExp, e2: KExp) extends KExp |
|
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case class KLet(x: String, v: KVal, e: KExp) extends KExp |
|
305 |
case class KReturn(v: KVal) extends KExp |
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| 609 | 306 |
\end{lstlisting}
|
307 |
||
| 701 | 308 |
\end{frame}
|
309 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
310 |
||
311 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
312 |
\begin{frame}[fragile,c]
|
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313 |
\frametitle{CPS-Translation}
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314 |
\small |
|
315 |
||
316 |
\begin{lstlisting}[language=Scala,numbers=none]
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|
317 |
def CPS(e: Exp)(k: KVal => KExp) : KExp = |
|
318 |
e match { ... }
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319 |
\end{lstlisting}
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|
320 |
\bigskip\bigskip |
|
321 |
||
322 |
\small |
|
323 |
\begin{lstlisting}[language=LLVMIR,numbers=none,xleftmargin=30mm,escapeinside={(*@}{@*)}]
|
|
324 |
let tmp0 = add 1 a in |
|
325 |
let tmp1 = mul (*@$\Box$@*) 5 in |
|
326 |
let tmp2 = add 3 tmp1 in |
|
327 |
let tmp3 = add tmp0 tmp2 in |
|
328 |
KReturn tmp3 |
|
329 |
\end{lstlisting}
|
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| 609 | 330 |
|
331 |
\end{frame}
|
|
| 701 | 332 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
333 |
||
334 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
335 |
\begin{frame}[fragile,c]
|
|
336 |
\frametitle{CPS-Translation}
|
|
337 |
\small |
|
338 |
||
339 |
\begin{lstlisting}[language=Scala,numbers=none]
|
|
340 |
def CPS(e: Exp)(k: KVal => KExp) : KExp = |
|
341 |
e match {
|
|
342 |
case Var(s) => k(KVar(s)) |
|
343 |
case Num(i) => k(KNum(i)) |
|
344 |
... |
|
345 |
} |
|
346 |
\end{lstlisting}
|
|
347 |
\bigskip\bigskip |
|
348 |
||
349 |
\small |
|
350 |
\begin{lstlisting}[language=LLVMIR,numbers=none,xleftmargin=30mm,escapeinside={(*@}{@*)}]
|
|
351 |
let tmp0 = add 1 a in |
|
352 |
let tmp1 = mul (*@$\Box$@*) 5 in |
|
353 |
let tmp2 = add 3 tmp1 in |
|
354 |
let tmp3 = add tmp0 tmp2 in |
|
355 |
KReturn tmp3 |
|
356 |
\end{lstlisting}
|
|
357 |
||
358 |
\end{frame}
|
|
359 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 609 | 360 |
|
361 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 701 | 362 |
\begin{frame}[fragile,c]
|
363 |
\frametitle{CPS-Translation}
|
|
364 |
\small |
|
| 609 | 365 |
|
| 701 | 366 |
\begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-5mm]
|
367 |
def CPS(e: Exp)(k: KVal => KExp) : KExp = e match {
|
|
368 |
case Aop(o, e1, e2) => {
|
|
369 |
val z = Fresh("tmp")
|
|
370 |
CPS(e1)(y1 => |
|
371 |
CPS(e2)(y2 => |
|
372 |
KLet(z, Kop(o, y1, y2), k(KVar(z))))) |
|
373 |
} ... |
|
374 |
} |
|
| 609 | 375 |
\end{lstlisting}
|
376 |
||
| 701 | 377 |
\small |
378 |
\begin{lstlisting}[language=LLVMIR,numbers=none,xleftmargin=30mm,escapeinside={(*@}{@*)}]
|
|
379 |
... |
|
380 |
let z = op (*@$\Box_{y_1}$@*) (*@$\Box_{y_2}$@*)
|
|
381 |
let tmp0 = add 1 a in |
|
382 |
let tmp1 = mul (*@$\Box\!\!\!\!\raisebox{0.6mm}{\texttt{z}}$@*) 5 in
|
|
383 |
let tmp2 = add 3 tmp1 in |
|
384 |
let tmp3 = add tmp0 tmp2 in |
|
385 |
KReturn tmp3 |
|
386 |
\end{lstlisting}
|
|
| 609 | 387 |
|
388 |
\end{frame}
|
|
| 701 | 389 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 609 | 390 |
|
391 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 701 | 392 |
\begin{frame}[fragile,c]
|
393 |
\frametitle{CPS-Translation}
|
|
394 |
\small |
|
| 609 | 395 |
|
| 701 | 396 |
\begin{lstlisting}[language=Scala,numbers=none]
|
397 |
def CPS(e: Exp)(k: KVal => KExp) : KExp = |
|
398 |
e match {
|
|
399 |
case Sequence(e1, e2) => |
|
400 |
CPS(e1)(_ => CPS(e2)(y2 => k(y2))) |
|
401 |
... |
|
402 |
} |
|
403 |
\end{lstlisting}
|
|
404 |
\bigskip\bigskip |
|
| 609 | 405 |
|
| 701 | 406 |
\small |
407 |
\begin{lstlisting}[language=LLVMIR,numbers=none,xleftmargin=30mm,escapeinside={(*@}{@*)}]
|
|
408 |
let tmp0 = add 1 a in |
|
409 |
let tmp1 = mul (*@$\Box$@*) 5 in |
|
410 |
let tmp2 = add 3 tmp1 in |
|
411 |
let tmp3 = add tmp0 tmp2 in |
|
412 |
KReturn tmp3 |
|
| 609 | 413 |
\end{lstlisting}
|
414 |
||
| 701 | 415 |
\end{frame}
|
416 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
417 |
||
418 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
419 |
\begin{frame}[fragile,c]
|
|
420 |
\frametitle{CPS-Translation}
|
|
421 |
\small |
|
422 |
||
423 |
\begin{lstlisting}[language=Scala,numbers=none]
|
|
424 |
def CPS(e: Exp)(k: KVal => KExp) : KExp = |
|
425 |
e match {
|
|
426 |
... |
|
427 |
case Sequence(e1, e2) => |
|
428 |
CPS(e1)(_ => CPS(e2)(y2 => k(y2))) |
|
429 |
... |
|
430 |
} |
|
431 |
\end{lstlisting}
|
|
432 |
\bigskip\bigskip |
|
433 |
||
434 |
\small |
|
435 |
\begin{lstlisting}[language=LLVMIR,numbers=none,xleftmargin=30mm,escapeinside={(*@}{@*)}]
|
|
436 |
let tmp0 = add 1 a in |
|
437 |
let tmp1 = mul (*@$\Box$@*) 5 in |
|
438 |
let tmp2 = add 3 tmp1 in |
|
439 |
let tmp3 = add tmp0 tmp2 in |
|
440 |
KReturn tmp3 |
|
441 |
\end{lstlisting}
|
|
| 609 | 442 |
|
443 |
\end{frame}
|
|
| 701 | 444 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
310
d384fe01d0e8
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
309
diff
changeset
|
445 |
|
| 610 | 446 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 701 | 447 |
\begin{frame}[fragile,c]
|
448 |
\frametitle{CPS-Translation}
|
|
449 |
\small |
|
450 |
||
451 |
\begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-3mm]
|
|
452 |
def CPS(e: Exp)(k: KVal => KExp) : KExp = |
|
453 |
e match {
|
|
454 |
... |
|
455 |
case If(Bop(o, b1, b2), e1, e2) => {
|
|
456 |
val z = Fresh("tmp")
|
|
457 |
CPS(b1)(y1 => |
|
458 |
CPS(b2)(y2 => |
|
459 |
KLet(z, Kop(o, y1, y2), |
|
460 |
KIf(z, CPS(e1)(k), CPS(e2)(k))))) |
|
461 |
} |
|
462 |
... |
|
463 |
} |
|
464 |
\end{lstlisting}
|
|
465 |
||
466 |
\end{frame}
|
|
467 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
468 |
||
469 |
||
470 |
||
471 |
||
472 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 610 | 473 |
\begin{frame}[c]
|
474 |
||
475 |
\large\bf |
|
| 701 | 476 |
Using a compiler, \\ |
477 |
how can you mount the\\ |
|
478 |
perfect attack against a system? |
|
| 610 | 479 |
|
| 701 | 480 |
\end{frame}
|
| 610 | 481 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
482 |
||
483 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
484 |
\mode<presentation>{
|
|
485 |
\begin{frame}[c]
|
|
486 |
||
487 |
{\large\bf
|
|
488 |
What is a \alert{perfect} attack?}\bigskip
|
|
489 |
||
490 |
\begin{enumerate}
|
|
491 |
\item you can potentially completely take over a target system |
|
492 |
\item your attack is (nearly) undetectable |
|
493 |
\item the victim has (almost) no chance to recover |
|
494 |
\end{enumerate}
|
|
495 |
||
496 |
\end{frame}}
|
|
497 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
498 |
||
499 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
500 |
\mode<presentation>{
|
|
501 |
\begin{frame}[c]
|
|
502 |
||
503 |
||
504 |
\begin{center}
|
|
505 |
\begin{tikzpicture}[scale=1]
|
|
506 |
||
507 |
\onslide<1->{
|
|
508 |
\node (A) at (0,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=17mm] {};
|
|
509 |
\node [below right] at (A.north west) {\footnotesize\begin{tabular}{@{}l@{}}
|
|
510 |
\only<1,2>{clean}\only<3->{\alert{hacked}}\\compiler\end{tabular}};}
|
|
511 |
||
512 |
||
513 |
\onslide<2->{
|
|
514 |
\node (B) at (-2,2) [draw=black, rectangle, very thick, minimum height=10mm, minimum width=12mm] {};
|
|
515 |
\node [below right] at (B.north west) {\footnotesize\begin{tabular}{@{}l@{}}login\\(src)\end{tabular}};
|
|
516 |
||
517 |
\node (C) at (2,2) [draw=black, rectangle, very thick, minimum height=10mm, minimum width=12mm] {};
|
|
518 |
\node [below right] at (C.north west) {\footnotesize\begin{tabular}{@{}l@{}}login\\(bin)\end{tabular}};
|
|
519 |
||
520 |
\draw[->, line width=2mm] (B) -- (C); |
|
521 |
} |
|
522 |
||
523 |
\onslide<3->{\node [above left=-1.5mm] at (C.south east) {\footnotesize \alert{$\blacksquare$}};}
|
|
524 |
||
525 |
\end{tikzpicture}
|
|
526 |
\end{center}
|
|
527 |
||
528 |
\end{frame}}
|
|
529 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
530 |
||
531 |
||
532 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
533 |
\mode<presentation>{
|
|
534 |
\begin{frame}[c]
|
|
535 |
||
536 |
\begin{center}
|
|
537 |
\begin{tikzpicture}[scale=1]
|
|
538 |
||
539 |
\onslide<1->{
|
|
540 |
\node (A) at (0,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
541 |
\node [below right] at (A.north west) {\small V0.01};
|
|
542 |
\node [below right] (A1) at (A.south west) {\small Scala};
|
|
543 |
\node [below right] (A1) at (A1.south west) {\small\textcolor{gray}{host language}};
|
|
544 |
\node [above right] at (A.north west) {my compiler (src)};}
|
|
545 |
||
546 |
\onslide<2->{
|
|
547 |
\node (B) at (1.8,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
548 |
\node [below right] at (B.north west) {\small V0.02};
|
|
549 |
\node [below right] at (B.south west) {\small Scala};
|
|
550 |
\node at (3,0) {\ldots};
|
|
551 |
||
552 |
\node (C) at (5,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
553 |
\node [below right] at (C.north west) {\small V1.00};
|
|
554 |
\node [below right] at (C.south west) {\small Scala};}
|
|
555 |
||
556 |
\onslide<3->{
|
|
557 |
\node (D) at (6.8,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
558 |
\node [below right] at (D.north west) {\small V1.00};
|
|
559 |
||
560 |
\node (E) at (6.8,2) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
561 |
\node [below right] at (E.north west) {\small V1.01};}
|
|
562 |
||
563 |
\onslide<4->{
|
|
564 |
\node (F) at (8.6,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
565 |
\node [below right] at (F.north west) {\small V1.01};
|
|
566 |
||
567 |
\node (G) at (8.6,2) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
|
|
568 |
\node [below right] at (G.north west) {\small V1.02};
|
|
569 |
\node at (9.8,0) {\ldots};
|
|
570 |
\node at (9.8,2) {\ldots};
|
|
571 |
\node at (8,-2) {\textcolor{gray}{\begin{tabular}{@{}l@{}}no host language\\needed\end{tabular}}};
|
|
572 |
} |
|
573 |
||
574 |
\end{tikzpicture}
|
|
575 |
\end{center}
|
|
576 |
||
577 |
\end{frame}}
|
|
578 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
579 |
||
580 |
||
581 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
582 |
\mode<presentation>{
|
|
583 |
\begin{frame}<1-3>
|
|
584 |
\frametitle{\LARGE\begin{tabular}{c}Hacking Compilers
|
|
585 |
\end{tabular}}
|
|
586 |
||
587 |
%Why is it so paramount to have a small trusted code base (TCB)? |
|
588 |
\bigskip\bigskip |
|
589 |
||
590 |
\begin{columns}
|
|
591 |
\begin{column}{2.7cm}
|
|
592 |
\begin{minipage}{2.5cm}%
|
|
593 |
\begin{tabular}{c@ {}}
|
|
594 |
\includegraphics[scale=0.2]{../pics/ken-thompson.jpg}\\[-1.8mm]
|
|
595 |
\footnotesize Ken Thompson\\[-1.8mm] |
|
596 |
\footnotesize Turing Award, 1983\\ |
|
597 |
\end{tabular}
|
|
598 |
\end{minipage}
|
|
599 |
\end{column}
|
|
600 |
\begin{column}{9cm}
|
|
601 |
\begin{tabular}{l@ {\hspace{1mm}}p{8cm}}
|
|
602 |
||
603 |
& Ken Thompson showed how to hide a Trojan Horse in a |
|
604 |
compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm]
|
|
605 |
||
606 |
& No amount of source level verification will protect |
|
607 |
you from such Thompson-hacks.\\[2mm] |
|
608 |
||
609 |
\end{tabular}
|
|
610 |
\end{column}
|
|
611 |
\end{columns}
|
|
612 |
||
613 |
\only<2>{
|
|
614 |
\begin{textblock}{6}(4,2)
|
|
615 |
\begin{tikzpicture}
|
|
616 |
\draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
|
617 |
{\normalsize
|
|
618 |
\begin{minipage}{8cm}
|
|
619 |
\begin{quote}
|
|
620 |
\includegraphics[scale=0.05]{../pics/evil.png}
|
|
621 |
\begin{enumerate}
|
|
622 |
\item[1)] Assume you ship the compiler as binary and also with sources. |
|
623 |
\item[2)] Make the compiler aware when it compiles itself. |
|
624 |
\item[3)] Add the Trojan horse. |
|
625 |
\item[4)] Compile. |
|
626 |
\item[5)] Delete Trojan horse from the sources of the compiler. |
|
627 |
\item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{}
|
|
628 |
\end{enumerate}
|
|
629 |
\end{quote}
|
|
630 |
\end{minipage}};
|
|
631 |
\end{tikzpicture}
|
|
632 |
\end{textblock}}
|
|
633 |
||
634 |
\end{frame}}
|
|
635 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
636 |
||
| 701 | 637 |
|
638 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
639 |
\begin{frame}[c]
|
|
640 |
\frametitle{Dijkstra on Testing}
|
|
641 |
||
642 |
\begin{bubble}[10cm]
|
|
643 |
``Program testing can be a very effective way to show the |
|
644 |
presence of bugs, but it is hopelessly inadequate for showing |
|
645 |
their absence.'' |
|
646 |
\end{bubble}\bigskip
|
|
647 |
||
648 |
\small |
|
649 |
What is good about compilers: the either seem to work, |
|
650 |
or go horribly wrong (most of the time). |
|
651 |
||
652 |
\end{frame}
|
|
653 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
654 |
||
655 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
656 |
\begin{frame}[c]
|
|
657 |
\frametitle{\Large Proving Programs to be Correct}
|
|
658 |
||
659 |
\begin{bubble}[10cm]
|
|
660 |
\small |
|
661 |
{\bf Theorem:} There are infinitely many prime
|
|
662 |
numbers.\medskip\\ |
|
663 |
||
664 |
{\bf Proof} \ldots\\
|
|
665 |
\end{bubble}\bigskip
|
|
666 |
||
667 |
||
668 |
similarly\bigskip |
|
669 |
||
670 |
\begin{bubble}[10cm]
|
|
671 |
\small |
|
672 |
{\bf Theorem:} The program is doing what
|
|
673 |
it is supposed to be doing.\medskip |
|
674 |
||
675 |
{\bf Long, long proof} \ldots\\
|
|
676 |
\end{bubble}\bigskip\medskip
|
|
677 |
||
678 |
\small This can be a gigantic proof. The only hope is to have |
|
679 |
help from the computer. `Program' is here to be understood to be |
|
680 |
quite general (compiler, OS, \ldots). |
|
681 |
||
682 |
\end{frame}
|
|
683 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
684 |
||
685 |
||
686 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
687 |
||
688 |
\begin{frame}[c]
|
|
689 |
\frametitle{Can This Be Done?}
|
|
690 |
||
691 |
\begin{itemize}
|
|
692 |
\item in 2008, verification of a small C-compiler |
|
693 |
\begin{itemize}
|
|
694 |
\item ``if my input program has a certain behaviour, then the compiled machine code has the same behaviour'' |
|
695 |
\item is as good as \texttt{gcc -O1}, but much, much less buggy
|
|
696 |
\end{itemize}
|
|
697 |
\end{itemize}
|
|
698 |
||
699 |
\begin{center}
|
|
700 |
\includegraphics[scale=0.12]{../pics/compcert.png}
|
|
701 |
\end{center}
|
|
702 |
||
703 |
\end{frame}
|
|
704 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
705 |
||
706 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
707 |
\begin{frame}[t]
|
|
708 |
\frametitle{Fuzzy Testing C-Compilers}
|
|
709 |
||
710 |
\begin{itemize}
|
|
711 |
\item tested GCC, LLVM and others by randomly generating |
|
712 |
C-programs |
|
713 |
\item found more than 300 bugs in GCC and also |
|
714 |
many in LLVM (some of them highest-level critical)\bigskip |
|
715 |
\item about CompCert: |
|
716 |
||
717 |
\begin{bubble}[10.7cm]\small ``The striking thing about our CompCert
|
|
718 |
results is that the middle-end bugs we found in all other |
|
719 |
compilers are absent. As of early 2011, the under-development |
|
720 |
version of CompCert is the only compiler we have tested for |
|
721 |
which Csmith cannot find wrong-code errors. This is not for |
|
722 |
lack of trying: we have devoted about six CPU-years to the |
|
723 |
task.'' |
|
724 |
\end{bubble}
|
|
725 |
\end{itemize}
|
|
726 |
||
727 |
\end{frame}
|
|
728 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
729 |
||
730 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
731 |
||
732 |
\begin{frame}[c]
|
|
733 |
\frametitle{Next Week}
|
|
734 |
||
735 |
\begin{itemize}
|
|
736 |
\item Revision Lecture\medskip |
|
737 |
\item How many strings are in $\bl{L(a^*)}$?\pause\medskip
|
|
738 |
\item How many strings are in $\bl{L((a + b)^*)}$?\\ Are there more than
|
|
739 |
in $\bl{L(a^*)}$?
|
|
740 |
\end{itemize}
|
|
741 |
||
742 |
||
743 |
||
744 |
\end{frame}
|
|
745 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
746 |
||
747 |
||
748 |
||
749 |
\end{document}
|
|
750 |
||
751 |
%%% Local Variables: |
|
752 |
%%% mode: latex |
|
753 |
%%% TeX-master: t |
|
754 |
%%% End: |
|
755 |
||
756 |
||
757 |
||
758 |
||
759 |
||
| 610 | 760 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
761 |
\begin{frame}[c]
|
|
762 |
||
763 |
\begin{center}
|
|
764 |
\includegraphics[scale=0.6]{../pics/bridge-limits.png}
|
|
765 |
\end{center}
|
|
766 |
||
767 |
\end{frame}
|
|
768 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
769 |
||
770 |
||
771 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
772 |
\begin{frame}[c]
|
|
773 |
\frametitle{Compilers \& Boeings 777}
|
|
774 |
||
775 |
First flight in 1994. They want to achieve triple redundancy in hardware |
|
776 |
faults.\bigskip |
|
777 |
||
778 |
They compile 1 Ada program to\medskip |
|
779 |
||
780 |
\begin{itemize}
|
|
781 |
\item Intel 80486 |
|
782 |
\item Motorola 68040 (old Macintosh's) |
|
783 |
\item AMD 29050 (RISC chips used often in laser printers) |
|
784 |
\end{itemize}\medskip
|
|
785 |
||
786 |
using 3 independent compilers.\bigskip\pause |
|
787 |
||
788 |
\small Airbus uses C and static analysers. Recently started using CompCert. |
|
789 |
||
790 |
\end{frame}
|
|
791 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
792 |
||
793 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
794 |
\begin{frame}[c]
|
|
795 |
\frametitle{Goal}
|
|
796 |
||
797 |
Remember the Bridges example? |
|
798 |
||
799 |
\begin{itemize}
|
|
800 |
\item Can we look at our programs and somehow ensure |
|
801 |
they are bug free/correct?\pause\bigskip |
|
802 |
||
803 |
\item Very hard: Anything interesting about programs is equivalent |
|
804 |
to the Halting Problem, which is undecidable.\pause\bigskip |
|
805 |
||
806 |
\item \alert{Solution:} We avoid this ``minor'' obstacle by
|
|
807 |
being as close as possible of deciding the halting |
|
808 |
problem, without actually deciding the halting problem. |
|
809 |
\small$\quad\Rightarrow$ yes, no, don't know (static analysis) |
|
810 |
\end{itemize}
|
|
811 |
||
812 |
\end{frame}
|
|
813 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
814 |
||
815 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
816 |
\begin{frame}[c]
|
|
817 |
\frametitle{What is Static Analysis?}
|
|
818 |
||
819 |
\begin{center}
|
|
820 |
\includegraphics[scale=0.4]{../pics/state.png}
|
|
821 |
\end{center}
|
|
822 |
||
823 |
\begin{itemize}
|
|
824 |
\item depending on some initial input, a program |
|
825 |
(behaviour) will ``develop'' over time. |
|
826 |
\end{itemize}
|
|
827 |
||
828 |
\end{frame}
|
|
829 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
830 |
||
831 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
832 |
\begin{frame}[c]
|
|
833 |
\frametitle{What is Static Analysis?}
|
|
834 |
||
835 |
\begin{center}
|
|
836 |
\includegraphics[scale=0.4]{../pics/state2.png}
|
|
837 |
\end{center}
|
|
838 |
||
839 |
\end{frame}
|
|
840 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
841 |
||
842 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
843 |
\begin{frame}[c]
|
|
844 |
\frametitle{What is Static Analysis?}
|
|
845 |
||
846 |
\begin{center}
|
|
847 |
\includegraphics[scale=0.4]{../pics/state3.jpg}
|
|
848 |
\end{center}
|
|
849 |
||
850 |
\end{frame}
|
|
851 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
852 |
||
853 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
854 |
\begin{frame}[c]
|
|
855 |
\frametitle{What is Static Analysis?}
|
|
856 |
||
857 |
\begin{center}
|
|
858 |
\includegraphics[scale=0.4]{../pics/state4.jpg}
|
|
859 |
\end{center}
|
|
860 |
||
861 |
\begin{itemize}
|
|
862 |
\item to be avoided |
|
863 |
\end{itemize}
|
|
864 |
||
865 |
\end{frame}
|
|
866 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
867 |
||
868 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
869 |
\begin{frame}[c]
|
|
870 |
\frametitle{What is Static Analysis?}
|
|
871 |
||
872 |
\begin{center}
|
|
873 |
\includegraphics[scale=0.4]{../pics/state5.png}
|
|
874 |
\end{center}
|
|
875 |
||
876 |
\begin{itemize}
|
|
877 |
\item this needs more work |
|
878 |
\end{itemize}
|
|
879 |
||
880 |
\end{frame}
|
|
881 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
882 |
||
883 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
884 |
\begin{frame}[c]
|
|
885 |
\frametitle{What is Static Analysis?}
|
|
886 |
||
887 |
\begin{center}
|
|
888 |
\includegraphics[scale=0.4]{../pics/state6.png}
|
|
889 |
\end{center}
|
|
890 |
||
891 |
\end{frame}
|
|
892 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
893 |
||
894 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
895 |
\begin{frame}[c,fragile]
|
|
896 |
\frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm]
|
|
897 |
Are Vars Definitely Initialised?\end{tabular}}
|
|
898 |
||
899 |
Assuming \texttt{x} is initialised, what about \texttt{y}?\bigskip
|
|
900 |
||
901 |
Prog.~1:\\ |
|
902 |
\begin{lstlisting}[numbers=none,
|
|
903 |
basicstyle=\ttfamily, |
|
904 |
language=While,xleftmargin=3mm] |
|
905 |
if x < 1 then y := x else y := x + 1; |
|
906 |
y := y + 1 |
|
907 |
\end{lstlisting}\medskip
|
|
908 |
||
909 |
Prog.~2:\\ |
|
910 |
\begin{lstlisting}[numbers=none,
|
|
911 |
basicstyle=\ttfamily, |
|
912 |
language=While,xleftmargin=3mm] |
|
913 |
if x < x then y := y + 1 else y := x; |
|
914 |
y := y + 1 |
|
915 |
\end{lstlisting}
|
|
916 |
||
917 |
\end{frame}
|
|
918 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
919 |
||
920 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
921 |
\begin{frame}[c,fragile]
|
|
922 |
\frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm]
|
|
923 |
Are Vars Definitely Initialised?\end{tabular}}
|
|
924 |
||
925 |
What should the rules be for deciding when a |
|
926 |
variable is initialised?\bigskip\pause |
|
927 |
||
928 |
\begin{itemize}
|
|
929 |
\item variable \texttt{x} is definitely initialized after
|
|
930 |
\texttt{skip}\\
|
|
931 |
iff \texttt{x} is definitely initialized before \texttt{skip}.
|
|
932 |
\end{itemize}
|
|
933 |
||
934 |
\end{frame}
|
|
935 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
936 |
||
937 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
938 |
\begin{frame}[c,fragile]
|
|
939 |
% \frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm]
|
|
940 |
% Are Vars Definitely Initialised?\end{tabular}}
|
|
941 |
||
942 |
$\bl{A}$ is the set of definitely defined variables:
|
|
943 |
||
944 |
\begin{center}
|
|
945 |
\begin{tabular}{c}
|
|
| 612 | 946 |
\bl{\infer{\mbox{}}{A\triangleright\texttt{skip}\triangleright{}A}}\qquad
|
947 |
\bl{\infer{vars(a) \subseteq A}{A\triangleright
|
|
948 |
(\texttt{x\,:=\,a})\triangleright\{x\}\cup A}}
|
|
| 610 | 949 |
\medskip\\\pause |
950 |
||
| 612 | 951 |
\bl{\infer{A_1\triangleright{}s_1\triangleright{}A_2
|
952 |
\quad A_2\triangleright{}s_2\triangleright{}A_3}
|
|
953 |
{A_1\triangleright{}(s_1 ; s_2)\triangleright{}A_3}}
|
|
| 610 | 954 |
\medskip\\\pause |
955 |
||
| 612 | 956 |
\bl{\infer{vars(b)\subseteq A\quad A\triangleright{}s_1\triangleright{}A_1
|
957 |
\quad A\triangleright{}s_2\triangleright{}A_2}
|
|
958 |
{A\triangleright(\texttt{if}\;b\;\texttt{then}\;s_1\;\texttt{else}\;s_2)\triangleright{}A_1\cap A_2}}
|
|
| 610 | 959 |
\medskip\\\pause |
960 |
||
| 612 | 961 |
\bl{\infer{vars(b)\subseteq A\quad A\triangleright{}s\triangleright{}A'}
|
962 |
{A\triangleright(\texttt{while}\;b\;\texttt{do}\;s)\triangleright{}A}}\pause
|
|
| 610 | 963 |
\end{tabular}
|
964 |
\end{center}
|
|
965 |
||
966 |
\hfill we start with $\bl{A = \{\}}$
|
|
967 |
\end{frame}
|
|
968 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
969 |