24 \end{tabular}} |
26 \end{tabular}} |
25 |
27 |
26 \normalsize |
28 \normalsize |
27 \begin{center} |
29 \begin{center} |
28 \begin{tabular}{ll} |
30 \begin{tabular}{ll} |
29 Email: & christian.urban at kcl.ac.uk\\ |
31 Email: & christian.urban at kcl.ac.uk\\ |
30 Office: & N\liningnums{7.07} (North Wing, Bush House)\\ |
32 Office Hours: & Thursdays 12 -- 14\\ |
31 Slides: & KEATS (also homework is there)\\ |
33 Location: & N7.07 (North Wing, Bush House)\\ |
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34 Slides \& Progs: & KEATS (also homework is there)\\ |
32 \end{tabular} |
35 \end{tabular} |
33 \end{center} |
36 \end{center} |
34 |
37 |
35 \end{frame} |
38 \end{frame} |
36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
37 |
40 |
38 |
41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
42 \begin{frame}[c,fragile] |
40 \begin{frame}[t] |
43 \frametitle{Functional Programming} |
41 \frametitle{While Language} |
44 |
42 |
45 \footnotesize |
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46 \begin{textblock}{13}(0.9,3) |
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47 \begin{lstlisting}[]numbers=none] |
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48 def fib(n) = if n == 0 then 0 |
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49 else if n == 1 then 1 |
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50 else fib(n - 1) + fib(n - 2); |
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51 |
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52 def fact(n) = if n == 0 then 1 else n * fact(n - 1); |
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53 |
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54 def ack(m, n) = if m == 0 then n + 1 |
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55 else if n == 0 then ack(m - 1, 1) |
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56 else ack(m - 1, ack(m, n - 1)); |
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57 |
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58 def gcd(a, b) = if b == 0 then a else gcd(b, a % b); |
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59 \end{lstlisting} |
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60 \end{textblock} |
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61 |
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62 \end{frame} |
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63 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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64 |
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65 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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66 \begin{frame}[c,fragile] |
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67 \frametitle{Factorial on the JVM} |
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68 |
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69 \begin{textblock}{7}(1,1.8)\footnotesize |
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70 \begin{minipage}{6cm} |
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71 \begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none] |
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72 .method public static facT(II)I |
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73 .limit locals 2 |
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74 .limit stack 6 |
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75 iload 0 |
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76 ldc 0 |
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77 if_icmpne If_else_2 |
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78 iload 1 |
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79 goto If_end_3 |
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80 If_else_2: |
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81 iload 0 |
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82 ldc 1 |
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83 isub |
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84 iload 0 |
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85 iload 1 |
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86 imul |
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87 invokestatic fact/fact/facT(II)I |
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88 If_end_3: |
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89 ireturn |
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90 .end method |
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91 \end{lstlisting} |
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92 \end{minipage} |
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93 \end{textblock} |
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94 |
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95 \begin{textblock}{7}(6,7) |
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96 \begin{bubble}[7cm]\small |
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97 \begin{lstlisting}[language=Lisp, |
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98 basicstyle=\ttfamily, |
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99 numbers=none, |
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100 xleftmargin=1mm,linebackgroundcolor=\color{cream}] |
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101 def facT(n, acc) = |
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102 if n == 0 then acc |
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103 else facT(n - 1, n * acc); |
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104 \end{lstlisting} |
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105 \end{bubble} |
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106 \end{textblock} |
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107 |
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108 \end{frame} |
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109 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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110 |
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111 |
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112 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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113 \begin{frame}[fragile,c] |
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114 \frametitle{LLVM} |
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115 |
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116 \begin{itemize} |
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117 \item Chris Lattner, Vikram Adve (started in 2000) |
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118 \item Apple hired Lattner in 2006 |
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119 \item modular architecture, LLVM-IR |
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120 \item \texttt{lli} and \texttt{llc} |
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121 \end{itemize} |
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122 |
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123 \end{frame} |
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124 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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125 |
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126 |
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127 |
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128 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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129 \tikzstyle{sensor}=[draw, fill=blue!20, text width=3.8em, line width=1mm, |
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130 text centered, minimum height=2em,drop shadow] |
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131 \tikzstyle{ann} = [above, text width=4em, text centered] |
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132 \tikzstyle{sc} = [sensor, text width=7em, fill=red!20, |
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133 minimum height=6em, rounded corners, drop shadow,line width=1mm] |
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134 |
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135 \begin{frame}[fragile,c] |
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136 \frametitle{LLVM: Overview} |
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137 |
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138 \begin{tikzpicture} |
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139 % Validation Layer is the same except that there are a set of nodes and links which are added |
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140 |
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141 \path (0,0) node (IR) [sc] {\textbf{LLVM-IR}\\ Optimisations}; |
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142 \path (IR.west)+(-2.2,1.7) node (sou1) [sensor] {C++}; |
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143 \path (IR.west)+(-2.2,0.5) node (sou2)[sensor] {C}; |
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144 \path (IR.west)+(-2.2,-1.0) node (dots)[ann] {$\vdots$}; |
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145 \path (IR.west)+(-2.2,-1.8) node (sou3)[sensor] {Haskell}; |
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146 |
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147 \path [draw,->,line width=1mm] (sou1.east) -- node [above] {} (IR.160); |
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148 \path [draw,->,line width=1mm] (sou2.east) -- node [above] {} (IR.180); |
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149 \path [draw,->,line width=1mm] (sou3.east) -- node [above] {} (IR.200); |
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150 |
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151 \path (IR.east)+(2.2,2.0) node (tar1)[sensor] {x86}; |
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152 \path (IR.east)+(2.2,0.8) node (tar2)[sensor] {ARM}; |
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153 \path (IR.east)+(2.2,-0.4) node (tar3)[sensor] {MIPS}; |
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154 \path (IR.east)+(2.2,-1.6) node (tar4)[sensor] {RISC}; |
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155 \path (IR.east)+(2.2,-2.8) node (tar5)[sensor] {Power PC}; |
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156 \path (IR.east)+(2.2,-4.2) node (dots2)[ann] {$\vdots$}; |
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157 |
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158 \path [draw,<-,line width=1mm] (tar1.west) -- node [above] {} (IR.10); |
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159 \path [draw,<-,line width=1mm] (tar2.west) -- node [above] {} (IR.5); |
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160 \path [draw,<-,line width=1mm] (tar3.west) -- node [above] {} (IR.0); |
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161 \path [draw,<-,line width=1mm] (tar4.west) -- node [above] {} (IR.-5); |
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162 \path [draw,<-,line width=1mm] (tar5.west) -- node [above] {} (IR.-10); |
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163 |
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164 \end{tikzpicture} |
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165 \end{frame} |
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166 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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167 |
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168 |
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169 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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170 \begin{frame}[fragile,t] |
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171 \frametitle{LLVM-IR} |
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172 \small |
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173 |
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174 \begin{textblock}{7.7}(8,11.4) |
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175 \begin{bubble}[5cm]\small |
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176 \begin{lstlisting}[language=Lisp, |
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177 numbers=none, |
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178 xleftmargin=1mm,linebackgroundcolor=\color{cream}] |
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179 def fact(n) = |
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180 if n == 0 then 1 |
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181 else n * fact(n - 1) |
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182 \end{lstlisting} |
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183 \end{bubble} |
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184 \end{textblock} |
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185 |
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186 \begin{lstlisting}[language=LLVM,xleftmargin=-7mm] |
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187 define i32 @fact (i32 %n) { |
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188 %tmp_19 = icmp eq i32 %n, 0 |
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189 br i1 %tmp_19, label %if_br_23, label %else_br_24 |
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190 |
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191 if_br_23: |
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192 ret i32 1 |
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193 |
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194 else_br_24: |
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195 %tmp_21 = sub i32 %n, 1 |
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196 %tmp_22 = call i32 @fact (i32 %tmp_21) |
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197 %tmp_20 = mul i32 %n, %tmp_22 |
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198 ret i32 %tmp_20 |
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199 } |
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200 \end{lstlisting} |
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201 |
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202 \end{frame} |
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203 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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204 |
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205 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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206 \begin{frame}[fragile,c] |
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207 \frametitle{LLVM Types} |
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208 |
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209 \tt |
43 \begin{center} |
210 \begin{center} |
44 \bl{\begin{tabular}{@{}lcl@{}} |
211 \begin{tabular}{ll} |
45 \\[-12mm] |
212 boolean & i1 \\ |
46 \meta{Stmt} & $::=$ & $\texttt{skip}$\\ |
213 byte & i8 \\ |
47 & $|$ & \textit{Id}\;\texttt{:=}\;\meta{AExp}\\ |
214 short & i16\\ |
48 & $|$ & \texttt{if}\; \meta{BExp} \;\texttt{then}\; \meta{Block} \;\texttt{else}\; \meta{Block}\\ |
215 char & i16\\ |
49 & $|$ & \texttt{while}\; \meta{BExp} \;\texttt{do}\; \meta{Block}\\ |
216 integer & i32\\ |
50 & $|$ & \texttt{read}\;\textit{Id}\\ |
217 long & i64\\ |
51 & $|$ & \texttt{write}\;\textit{Id}\\ |
218 float & float\\ |
52 & $|$ & \texttt{write}\;\textit{String}\medskip\\ |
219 double & double\\ |
53 \meta{Stmts} & $::=$ & \meta{Stmt} \;\texttt{;}\; \meta{Stmts} $|$ \meta{Stmt}\medskip\\ |
220 *\_ & pointer to \\ |
54 \meta{Block} & $::=$ & \texttt{\{}\,\meta{Stmts}\,\texttt{\}} $|$ \meta{Stmt}\medskip\\ |
221 **\_ & pointer to a pointer to\\ |
55 \meta{AExp} & $::=$ & \ldots\\ |
222 \mbox{}[\_] & arrays of\\ |
56 \meta{BExp} & $::=$ & \ldots\\ |
223 \end{tabular} |
57 \end{tabular}} |
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58 \end{center} |
224 \end{center} |
59 \end{frame} |
225 |
60 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
226 \end{frame} |
|
227 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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228 |
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229 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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230 \begin{frame}[fragile,c] |
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231 \frametitle{LLVM Instructions} |
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232 \small |
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233 |
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234 \begin{lstlisting}[language=LLVM] |
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235 br i1 %var, label %if_br, label %else_br |
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236 |
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237 icmp eq i32 %x, %y ; for equal |
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238 icmp sle i32 %x, %y ; signed less or equal |
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239 icmp slt i32 %x, %y ; signed less than |
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240 icmp ult i32 %x, %y ; unsigned less than |
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241 |
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242 %var = call i32 @foo(...args...) |
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243 \end{lstlisting} |
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244 |
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245 \end{frame} |
|
246 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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247 |
|
248 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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249 \begin{frame}[fragile,c] |
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250 \frametitle{SSA Format} |
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251 |
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252 \bl{$(1 + a) + (3 + (b * 5))$}\bigskip\bigskip |
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253 |
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254 \begin{lstlisting}[language=LLVM] |
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255 let tmp0 = add 1 a in |
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256 let tmp1 = mul b 5 in |
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257 let tmp2 = add 3 tmp1 in |
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258 let tmp3 = add tmp0 tmp2 in |
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259 tmp3 |
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260 \end{lstlisting} |
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261 |
|
262 \end{frame} |
|
263 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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264 |
|
265 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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266 \begin{frame}[fragile,c] |
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267 \frametitle{Abstract Syntax Trees} |
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268 \footnotesize |
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269 |
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270 \begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-3mm] |
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271 // Fun language (expressions) |
|
272 abstract class Exp |
|
273 abstract class BExp |
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274 |
|
275 case class Call(name: String, args: List[Exp]) extends Exp |
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276 case class If(a: BExp, e1: Exp, e2: Exp) extends Exp |
|
277 case class Write(e: Exp) extends Exp |
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278 case class Var(s: String) extends Exp |
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279 case class Num(i: Int) extends Exp |
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280 case class Aop(o: String, a1: Exp, a2: Exp) extends Exp |
|
281 case class Sequence(e1: Exp, e2: Exp) extends Exp |
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282 case class Bop(o: String, a1: Exp, a2: Exp) extends BExp |
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283 \end{lstlisting} |
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284 |
|
285 \end{frame} |
|
286 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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287 |
|
288 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
289 \begin{frame}[fragile,c] |
|
290 \frametitle{K-(Intermediate)Language} |
|
291 \footnotesize |
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292 |
|
293 \begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-3mm] |
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294 abstract class KExp |
|
295 abstract class KVal |
|
296 |
|
297 case class KVar(s: String) extends KVal |
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298 case class KNum(i: Int) extends KVal |
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299 case class Kop(o: String, v1: KVal, v2: KVal) extends KVal |
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300 case class KCall(o: String, vrs: List[KVal]) extends KVal |
|
301 case class KWrite(v: KVal) extends KVal |
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302 |
|
303 case class KIf(x1: String, e1: KExp, e2: KExp) extends KExp |
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304 case class KLet(x: String, v: KVal, e: KExp) extends KExp |
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305 case class KReturn(v: KVal) extends KExp |
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306 \end{lstlisting} |
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307 |
|
308 \end{frame} |
|
309 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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310 |
|
311 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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312 \begin{frame}[fragile,c] |
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313 \frametitle{CPS-Translation} |
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314 \small |
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315 |
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316 \begin{lstlisting}[language=Scala,numbers=none] |
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317 def CPS(e: Exp)(k: KVal => KExp) : KExp = |
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318 e match { ... } |
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319 \end{lstlisting} |
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320 \bigskip\bigskip |
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321 |
|
322 \small |
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323 \begin{lstlisting}[language=LLVMIR,numbers=none,xleftmargin=30mm,escapeinside={(*@}{@*)}] |
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324 let tmp0 = add 1 a in |
|
325 let tmp1 = mul (*@$\Box$@*) 5 in |
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326 let tmp2 = add 3 tmp1 in |
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327 let tmp3 = add tmp0 tmp2 in |
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328 KReturn tmp3 |
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329 \end{lstlisting} |
|
330 |
|
331 \end{frame} |
|
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={(*@}{@*)}] |
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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 |
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355 KReturn tmp3 |
|
356 \end{lstlisting} |
|
357 |
|
358 \end{frame} |
|
359 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
360 |
|
361 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
362 \begin{frame}[fragile,c] |
|
363 \frametitle{CPS-Translation} |
|
364 \small |
|
365 |
|
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 } |
|
375 \end{lstlisting} |
|
376 |
|
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} |
|
387 |
|
388 \end{frame} |
|
389 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
390 |
|
391 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
392 \begin{frame}[fragile,c] |
|
393 \frametitle{CPS-Translation} |
|
394 \small |
|
395 |
|
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 |
|
405 |
|
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 |
|
413 \end{lstlisting} |
|
414 |
|
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} |
|
442 |
|
443 \end{frame} |
|
444 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
445 |
|
446 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
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 |
61 |
471 |
62 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
472 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
63 \begin{frame}[c] |
473 \begin{frame}[c] |
64 \frametitle{\begin{tabular}{c}Fibonacci Numbers\end{tabular}} |
|
65 |
|
66 \mbox{}\\[-18mm]\mbox{} |
|
67 |
|
68 {\lstset{language=While}\fontsize{10}{12}\selectfont |
|
69 \texttt{\lstinputlisting{../progs/fib.while}}} |
|
70 |
|
71 \end{frame} |
|
72 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
73 |
|
74 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
75 \begin{frame}[c,fragile] |
|
76 \frametitle{BF***} |
|
77 |
|
78 some big array, say \texttt{a}; 7 (8) instructions: |
|
79 |
|
80 \begin{itemize} |
|
81 \item \texttt{>} move \texttt{ptr++} |
|
82 \item \texttt{<} move \texttt{ptr-{}-} |
|
83 \item \texttt{+} add \texttt{a[ptr]++} |
|
84 \item \texttt{-} subtract \texttt{a[ptr]-{}-} |
|
85 \item \texttt{.} print out \texttt{a[ptr]} as ASCII |
|
86 \item \texttt{[} if \texttt{a[ptr] == 0} jump just after the corresponding \texttt{]}; otherwise \texttt{ptr++} |
|
87 \item \texttt{]} if \texttt{a[ptr] != 0} jump just after the corresponding \texttt{[}; otherwise \texttt{ptr++} |
|
88 |
|
89 \end{itemize} |
|
90 |
|
91 \end{frame} |
|
92 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
93 |
|
94 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
95 \begin{frame}[c,fragile] |
|
96 \frametitle{Arrays in While} |
|
97 |
|
98 \begin{itemize} |
|
99 \item \texttt{new arr[15000]}\medskip |
|
100 \item \texttt{x := 3 + arr[3 + y]}\medskip |
|
101 \item \texttt{arr[42 * n] := ...} |
|
102 \end{itemize} |
|
103 |
|
104 \end{frame} |
|
105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
106 |
|
107 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
108 \begin{frame}[c,fragile] |
|
109 \frametitle{New Arrays} |
|
110 |
|
111 \begin{lstlisting}[mathescape,numbers=none,language=While] |
|
112 new arr[number] |
|
113 \end{lstlisting}\bigskip\bigskip |
|
114 |
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115 \begin{lstlisting}[mathescape,numbers=none,language=While] |
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116 ldc number |
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117 newarray int |
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118 astore loc_var |
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119 \end{lstlisting} |
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120 |
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121 |
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122 \end{frame} |
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123 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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124 |
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125 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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126 \begin{frame}[c,fragile] |
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127 \frametitle{Array Update} |
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128 |
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129 \begin{lstlisting}[mathescape,numbers=none,language=While] |
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130 arr[...] := |
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131 \end{lstlisting}\bigskip\bigskip |
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132 |
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133 \begin{lstlisting}[mathescape,numbers=none,language=While] |
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134 aload loc_var |
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135 index_aexp |
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136 value_aexp |
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137 iastore |
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138 \end{lstlisting} |
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139 |
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140 |
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141 \end{frame} |
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142 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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143 |
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144 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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145 \begin{frame}[c,fragile] |
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146 \frametitle{Array Lookup in AExp} |
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147 |
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148 \begin{lstlisting}[mathescape,numbers=none,language=While] |
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149 ...arr[...]... |
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150 \end{lstlisting}\bigskip\bigskip |
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151 |
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152 \begin{lstlisting}[mathescape,numbers=none,language=While] |
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153 aload loc_var |
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154 index_aexp |
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155 iaload |
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156 \end{lstlisting} |
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157 |
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158 |
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159 \end{frame} |
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160 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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161 |
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162 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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163 \mode<presentation>{ |
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164 \begin{frame}[c] |
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165 |
474 |
166 \large\bf |
475 \large\bf |
167 Using a compiler, \\how can you mount the\\ perfect attack against a system? |
476 Using a compiler, \\ |
168 |
477 how can you mount the\\ |
169 \end{frame}} |
478 perfect attack against a system? |
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479 |
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480 \end{frame} |
170 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
481 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
171 |
482 |
172 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
483 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
173 \mode<presentation>{ |
484 \mode<presentation>{ |
174 \begin{frame}[c] |
485 \begin{frame}[c] |
321 \end{textblock}} |
632 \end{textblock}} |
322 |
633 |
323 \end{frame}} |
634 \end{frame}} |
324 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
635 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
325 |
636 |
326 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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327 \begin{frame}[c] |
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328 |
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329 \begin{center} |
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330 \includegraphics[scale=0.6]{../pics/bridge-limits.png} |
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331 \end{center} |
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332 |
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333 \end{frame} |
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334 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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335 |
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336 |
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337 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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338 \begin{frame}[c] |
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339 \frametitle{Compilers \& Boeings 777} |
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340 |
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341 First flight in 1994. They want to achieve triple redundancy in hardware |
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342 faults.\bigskip |
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343 |
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344 They compile 1 Ada program to\medskip |
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345 |
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346 \begin{itemize} |
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347 \item Intel 80486 |
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348 \item Motorola 68040 (old Macintosh's) |
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349 \item AMD 29050 (RISC chips used often in laser printers) |
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350 \end{itemize}\medskip |
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351 |
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352 using 3 independent compilers.\bigskip\pause |
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353 |
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354 \small Airbus uses C and static analysers. Recently started using CompCert. |
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355 |
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356 \end{frame} |
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357 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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358 |
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359 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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360 \begin{frame}[c] |
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361 \frametitle{Goal} |
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362 |
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363 Remember the Bridges example? |
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364 |
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365 \begin{itemize} |
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366 \item Can we look at our programs and somehow ensure |
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367 they are bug free/correct?\pause\bigskip |
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368 |
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369 \item Very hard: Anything interesting about programs is equivalent |
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370 to the Halting Problem, which is undecidable.\pause\bigskip |
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371 |
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372 \item \alert{Solution:} We avoid this ``minor'' obstacle by |
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373 being as close as possible of deciding the halting |
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374 problem, without actually deciding the halting problem. |
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375 \small$\quad\Rightarrow$ yes, no, don't know (static analysis) |
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376 \end{itemize} |
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377 |
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378 \end{frame} |
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379 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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380 |
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381 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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382 \begin{frame}[c] |
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383 \frametitle{What is Static Analysis?} |
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384 |
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385 \begin{center} |
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386 \includegraphics[scale=0.4]{../pics/state.png} |
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387 \end{center} |
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388 |
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389 \begin{itemize} |
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390 \item depending on some initial input, a program |
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391 (behaviour) will ``develop'' over time. |
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392 \end{itemize} |
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393 |
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394 \end{frame} |
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395 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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396 |
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397 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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398 \begin{frame}[c] |
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399 \frametitle{What is Static Analysis?} |
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400 |
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401 \begin{center} |
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402 \includegraphics[scale=0.4]{../pics/state2.png} |
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403 \end{center} |
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404 |
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405 \end{frame} |
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406 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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407 |
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408 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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409 \begin{frame}[c] |
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410 \frametitle{What is Static Analysis?} |
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411 |
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412 \begin{center} |
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413 \includegraphics[scale=0.4]{../pics/state3.jpg} |
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414 \end{center} |
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415 |
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416 \end{frame} |
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417 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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418 |
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419 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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420 \begin{frame}[c] |
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421 \frametitle{What is Static Analysis?} |
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422 |
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423 \begin{center} |
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424 \includegraphics[scale=0.4]{../pics/state4.jpg} |
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425 \end{center} |
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426 |
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427 \begin{itemize} |
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428 \item to be avoided |
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429 \end{itemize} |
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430 |
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431 \end{frame} |
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432 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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433 |
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434 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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435 \begin{frame}[c] |
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436 \frametitle{What is Static Analysis?} |
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437 |
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438 \begin{center} |
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439 \includegraphics[scale=0.4]{../pics/state5.png} |
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440 \end{center} |
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441 |
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442 \begin{itemize} |
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443 \item this needs more work |
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444 \end{itemize} |
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445 |
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446 \end{frame} |
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447 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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448 |
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449 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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450 \begin{frame}[c] |
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451 \frametitle{What is Static Analysis?} |
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452 |
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453 \begin{center} |
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454 \includegraphics[scale=0.4]{../pics/state6.png} |
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455 \end{center} |
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456 |
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457 \end{frame} |
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458 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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459 |
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460 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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461 \begin{frame}[c,fragile] |
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462 \frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm] |
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463 Are Vars Definitely Initialised?\end{tabular}} |
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464 |
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465 Assuming \texttt{x} is initialised, what about \texttt{y}?\bigskip |
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466 |
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467 Prog.~1:\\ |
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468 \begin{lstlisting}[numbers=none, |
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469 basicstyle=\ttfamily, |
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470 language=While,xleftmargin=3mm] |
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471 if x < 1 then y := x else y := x + 1; |
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472 y := y + 1 |
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473 \end{lstlisting}\medskip |
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474 |
|
475 Prog.~2:\\ |
|
476 \begin{lstlisting}[numbers=none, |
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477 basicstyle=\ttfamily, |
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478 language=While,xleftmargin=3mm] |
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479 if x < x then y := y + 1 else y := x; |
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480 y := y + 1 |
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481 \end{lstlisting} |
|
482 |
|
483 \end{frame} |
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484 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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485 |
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486 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
487 \begin{frame}[c,fragile] |
|
488 \frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm] |
|
489 Are Vars Definitely Initialised?\end{tabular}} |
|
490 |
|
491 What should the rules be for deciding when a |
|
492 variable is initialised?\bigskip\pause |
|
493 |
|
494 \begin{itemize} |
|
495 \item variable \texttt{x} is definitely initialized after |
|
496 \texttt{skip}\\ |
|
497 iff \texttt{x} is definitely initialized before \texttt{skip}. |
|
498 \end{itemize} |
|
499 |
|
500 \end{frame} |
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501 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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502 |
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503 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
504 \begin{frame}[c,fragile] |
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505 % \frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm] |
|
506 % Are Vars Definitely Initialised?\end{tabular}} |
|
507 |
|
508 $\bl{A}$ is the set of definitely defined variables: |
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509 |
|
510 \begin{center} |
|
511 \begin{tabular}{c} |
|
512 \bl{\infer{\mbox{}}{A\triangleright\texttt{skip}\triangleright{}A}}\qquad |
|
513 \bl{\infer{vars(a) \subseteq A}{A\triangleright |
|
514 (\texttt{x\,:=\,a})\triangleright\{x\}\cup A}} |
|
515 \medskip\\\pause |
|
516 |
|
517 \bl{\infer{A_1\triangleright{}s_1\triangleright{}A_2 |
|
518 \quad A_2\triangleright{}s_2\triangleright{}A_3} |
|
519 {A_1\triangleright{}(s_1 ; s_2)\triangleright{}A_3}} |
|
520 \medskip\\\pause |
|
521 |
|
522 \bl{\infer{vars(b)\subseteq A\quad A\triangleright{}s_1\triangleright{}A_1 |
|
523 \quad A\triangleright{}s_2\triangleright{}A_2} |
|
524 {A\triangleright(\texttt{if}\;b\;\texttt{then}\;s_1\;\texttt{else}\;s_2)\triangleright{}A_1\cap A_2}} |
|
525 \medskip\\\pause |
|
526 |
|
527 \bl{\infer{vars(b)\subseteq A\quad A\triangleright{}s\triangleright{}A'} |
|
528 {A\triangleright(\texttt{while}\;b\;\texttt{do}\;s)\triangleright{}A}}\pause |
|
529 \end{tabular} |
|
530 \end{center} |
|
531 |
|
532 \hfill we start with $\bl{A = \{\}}$ |
|
533 \end{frame} |
|
534 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
535 |
|
536 |
637 |
537 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
638 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
538 \begin{frame}[c] |
639 \begin{frame}[c] |
539 \frametitle{Dijkstra on Testing} |
640 \frametitle{Dijkstra on Testing} |
540 |
641 |
650 %%% Local Variables: |
751 %%% Local Variables: |
651 %%% mode: latex |
752 %%% mode: latex |
652 %%% TeX-master: t |
753 %%% TeX-master: t |
653 %%% End: |
754 %%% End: |
654 |
755 |
|
756 |
|
757 |
|
758 |
|
759 |
|
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} |
|
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}} |
|
949 \medskip\\\pause |
|
950 |
|
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}} |
|
954 \medskip\\\pause |
|
955 |
|
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}} |
|
959 \medskip\\\pause |
|
960 |
|
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 |
|
963 \end{tabular} |
|
964 \end{center} |
|
965 |
|
966 \hfill we start with $\bl{A = \{\}}$ |
|
967 \end{frame} |
|
968 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
969 |