1 (*<*) |
|
2 theory Slides4 |
|
3 imports "~~/src/HOL/Library/LaTeXsugar" "Nominal" |
|
4 begin |
|
5 |
|
6 declare [[show_question_marks = false]] |
|
7 |
|
8 notation (latex output) |
|
9 set ("_") and |
|
10 Cons ("_::/_" [66,65] 65) |
|
11 |
|
12 (*>*) |
|
13 |
|
14 text_raw {* |
|
15 \renewcommand{\slidecaption}{Nanjing, 31.~August 2010} |
|
16 |
|
17 \newcommand{\abst}[2]{#1.#2}% atom-abstraction |
|
18 \newcommand{\pair}[2]{\langle #1,#2\rangle} % pairing |
|
19 \newcommand{\susp}{{\boldsymbol{\cdot}}}% for suspensions |
|
20 \newcommand{\unit}{\langle\rangle}% unit |
|
21 \newcommand{\app}[2]{#1\,#2}% application |
|
22 \newcommand{\eqprob}{\mathrel{{\approx}?}} |
|
23 \newcommand{\freshprob}{\mathrel{\#?}} |
|
24 \newcommand{\redu}[1]{\stackrel{#1}{\Longrightarrow}}% reduction |
|
25 \newcommand{\id}{\varepsilon}% identity substitution |
|
26 |
|
27 \newcommand{\bl}[1]{\textcolor{blue}{#1}} |
|
28 \newcommand{\gr}[1]{\textcolor{gray}{#1}} |
|
29 \newcommand{\rd}[1]{\textcolor{red}{#1}} |
|
30 |
|
31 \newcommand{\ok}{\includegraphics[scale=0.07]{ok.png}} |
|
32 \newcommand{\notok}{\includegraphics[scale=0.07]{notok.png}} |
|
33 \newcommand{\largenotok}{\includegraphics[scale=1]{notok.png}} |
|
34 |
|
35 \renewcommand{\Huge}{\fontsize{61.92}{77}\selectfont} |
|
36 \newcommand{\veryHuge}{\fontsize{74.3}{93}\selectfont} |
|
37 \newcommand{\VeryHuge}{\fontsize{89.16}{112}\selectfont} |
|
38 \newcommand{\VERYHuge}{\fontsize{107}{134}\selectfont} |
|
39 |
|
40 \newcommand{\LL}{$\mathbb{L}\,$} |
|
41 |
|
42 |
|
43 \pgfdeclareradialshading{smallbluesphere}{\pgfpoint{0.5mm}{0.5mm}}% |
|
44 {rgb(0mm)=(0,0,0.9); |
|
45 rgb(0.9mm)=(0,0,0.7); |
|
46 rgb(1.3mm)=(0,0,0.5); |
|
47 rgb(1.4mm)=(1,1,1)} |
|
48 |
|
49 \def\myitemi{\begin{pgfpicture}{-1ex}{-0.55ex}{1ex}{1ex} |
|
50 \usebeamercolor[fg]{subitem projected} |
|
51 {\pgftransformscale{0.8}\pgftext{\normalsize\pgfuseshading{bigsphere}}} |
|
52 \pgftext{% |
|
53 \usebeamerfont*{subitem projected}} |
|
54 \end{pgfpicture}} |
|
55 |
|
56 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57 \mode<presentation>{ |
|
58 \begin{frame}<1>[t] |
|
59 \frametitle{% |
|
60 \begin{tabular}{@ {\hspace{-3mm}}c@ {}} |
|
61 \\ |
|
62 \huge Error-Free Programming\\[-1mm] |
|
63 \huge with Theorem Provers\\[5mm] |
|
64 \end{tabular}} |
|
65 \begin{center} |
|
66 Christian Urban |
|
67 \end{center} |
|
68 \begin{center} |
|
69 \small Technical University of Munich, Germany\\[7mm] |
|
70 |
|
71 \small in Nanjing on the kind invitation of\\ Professor Xingyuan Zhang |
|
72 and his group |
|
73 \end{center} |
|
74 \end{frame}} |
|
75 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
76 |
|
77 *} |
|
78 text_raw {* |
|
79 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
80 \mode<presentation>{ |
|
81 \begin{frame}<1->[c] |
|
82 \frametitle{My Background} |
|
83 |
|
84 \begin{itemize} |
|
85 \item researcher in Theoretical Computer Science\medskip |
|
86 |
|
87 \item programmer on a \alert<2->{software system} with 800 kloc (though I am |
|
88 responsible only for 35 kloc) |
|
89 \end{itemize} |
|
90 |
|
91 \only<2->{ |
|
92 \begin{textblock}{6}(2,11) |
|
93 \begin{tikzpicture} |
|
94 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
|
95 {\color{darkgray} |
|
96 \begin{minipage}{4cm}\raggedright |
|
97 A theorem prover called {\bf Isabelle}. |
|
98 \end{minipage}}; |
|
99 \end{tikzpicture} |
|
100 \end{textblock}} |
|
101 |
|
102 |
|
103 \only<3>{ |
|
104 \begin{textblock}{6}(9,11) |
|
105 \begin{tikzpicture} |
|
106 \draw (0,0) node[inner sep=2mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
|
107 {\color{darkgray} |
|
108 \begin{minipage}{4cm}\raggedright |
|
109 Like every other code, this code is very hard to |
|
110 get correct. |
|
111 \end{minipage}}; |
|
112 \end{tikzpicture} |
|
113 \end{textblock}} |
|
114 |
|
115 \end{frame}} |
|
116 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
117 *} |
|
118 |
|
119 text_raw {* |
|
120 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
121 \mode<presentation>{ |
|
122 \begin{frame}<1->[t] |
|
123 \frametitle{Regular Expressions} |
|
124 |
|
125 An example many (should) know about:\\ |
|
126 \rd{\bf Regular Expressions:} |
|
127 |
|
128 \only<2>{ |
|
129 \begin{center} |
|
130 \bl{[] $\;\;\;|\;\;\;$ c $\;\;\;|\;\;\;$ r$_1$$|$r$_2$ $\;\;\;|\;\;\;$ |
|
131 r$_1$$\cdot$r$_2$ $\;\;\;|\;\;\;$ r$^*$} |
|
132 \end{center}} |
|
133 \only<3->{ |
|
134 \begin{center} |
|
135 \begin{tabular}{@ {}rrll@ {}} |
|
136 \bl{r} & \bl{$::=$} & \bl{NULL} & \gr{(matches no string)}\\ |
|
137 & \bl{$\mid$} & \bl{EMPTY} & \gr{(matches the empty string, [])}\\ |
|
138 & \bl{$\mid$} & \bl{CHR c} & \gr{(matches the character c)}\\ |
|
139 & \bl{$\mid$} & \bl{ALT r$_1$ r$_2$} & \gr{(alternative, r$_1 |\,$r$_2$)}\\ |
|
140 & \bl{$\mid$} & \bl{SEQ r$_1$ r$_2$} & \gr{(sequential, r$_1\cdot\,$r$_2$)}\\ |
|
141 & \bl{$\mid$} & \bl{STAR r} & \gr{(repeat, r$^*$)}\\ |
|
142 \end{tabular} |
|
143 \end{center}\medskip} |
|
144 |
|
145 \small |
|
146 \begin{textblock}{14.5}(1,12.5) |
|
147 \only<2->{\gr{(a$\cdot$b)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} \{[], ab, abab, ababab, \ldots\}}\\} |
|
148 \only<2->{\gr{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9)$^*$ \hspace{3mm}$\mapsto$\hspace{3mm} |
|
149 \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}} |
|
150 \end{textblock} |
|
151 \end{frame}} |
|
152 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
153 *} |
|
154 |
|
155 text_raw {* |
|
156 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
157 \mode<presentation>{ |
|
158 \begin{frame}<1>[c] |
|
159 \frametitle{RegExp Matcher} |
|
160 |
|
161 Let's implement a regular expression matcher:\bigskip |
|
162 |
|
163 \begin{center} |
|
164 \begin{tikzpicture} |
|
165 %%\draw[help lines, black] (-3,0) grid (6,3); |
|
166 |
|
167 \draw[line width=1mm, red] (0.0,0.0) rectangle (4,2.3); |
|
168 \node[anchor=base] at (2,1) |
|
169 {\small\begin{tabular}{@ {}c@ {}}\Large\bf Regular\\ |
|
170 \Large\bf Expression \\ |
|
171 \Large\bf Matcher\end{tabular}}; |
|
172 |
|
173 \coordinate (m1) at (0,1.5); |
|
174 \draw (-2,2) node (m2) {\small\begin{tabular}{c}\bl{regular}\\[-1mm] \bl{expression}\end{tabular}}; |
|
175 \path[overlay, ->, line width = 1mm, shorten <=-3mm] (m2) edge (m1); |
|
176 |
|
177 \coordinate (s1) at (0,0.5); |
|
178 \draw (-1.8,-0) node (s2) {\small\begin{tabular}{c}\bl{string}\end{tabular}}; |
|
179 \path[overlay, ->, line width = 1mm, shorten <=-3mm] (s2) edge (s1); |
|
180 |
|
181 \coordinate (r1) at (4,1.2); |
|
182 \draw (6,1.2) node (r2) {\small\begin{tabular}{c}\bl{true}, \bl{false}\end{tabular}}; |
|
183 \path[overlay, ->, line width = 1mm, shorten >=-3mm] (r1) edge (r2); |
|
184 |
|
185 \end{tikzpicture} |
|
186 \end{center} |
|
187 |
|
188 |
|
189 \end{frame}} |
|
190 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
191 *} |
|
192 |
|
193 text_raw {* |
|
194 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
195 \mode<presentation>{ |
|
196 \begin{frame}<1->[t] |
|
197 \frametitle{RegExp Matcher} |
|
198 \small |
|
199 |
|
200 {\bf input:} a \underline{list} of RegExps and a string \hspace{6mm}{\bf output:} true or false |
|
201 |
|
202 \only<2->{ |
|
203 \begin{center} |
|
204 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}} |
|
205 \bl{match [] []} & \bl{$=$} & \bl{true}\\ |
|
206 \bl{match [] \_} & \bl{$=$} & \bl{false}\\ |
|
207 \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\ |
|
208 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
|
209 \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\ |
|
210 \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\ |
|
211 \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\ |
|
212 & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ |
|
213 \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\ |
|
214 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
|
215 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
|
216 \end{tabular} |
|
217 \end{center}} |
|
218 |
|
219 \onslide<3->{we start the program with\\ |
|
220 \hspace{6mm}\bl{matches r s $=$ match [r] s}} |
|
221 |
|
222 \end{frame}} |
|
223 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
224 *} |
|
225 |
|
226 |
|
227 text_raw {* |
|
228 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
229 \mode<presentation>{ |
|
230 \begin{frame}<1>[c] |
|
231 \frametitle{Program in Scala} |
|
232 |
|
233 \bl{\footnotesize |
|
234 \begin{tabular}{l} |
|
235 sealed abstract class Rexp\\ |
|
236 sealed case class Null extends Rexp\\ |
|
237 sealed case class Empty extends Rexp\\ |
|
238 sealed case class Chr(c: Char) extends Rexp\\ |
|
239 sealed case class Alt(r1 : Rexp, r2 : Rexp) extends Rexp\\ |
|
240 sealed case class Seq(r1 : Rexp, r2 : Rexp) extends Rexp\\ |
|
241 sealed case class Star(r : Rexp) extends Rexp\medskip\\ |
|
242 def match1 (rs : List[Rexp], s : List[Char]) : Boolean = rs match \{\\ |
|
243 \hspace{3mm}case Nil @{text "\<Rightarrow>"} if (s == Nil) true else false\\ |
|
244 \hspace{3mm}case (Null()::rs) @{text "\<Rightarrow>"} false\\ |
|
245 \hspace{3mm}case (Empty()::rs) @{text "\<Rightarrow>"} match1 (rs, s)\\ |
|
246 \hspace{3mm}case (Chr(c)::rs) @{text "\<Rightarrow>"} s match \\ |
|
247 \hspace{6mm}\{ case Nil @{text "\<Rightarrow>"} false\\ |
|
248 \hspace{8mm}case (d::s) @{text "\<Rightarrow>"} if (c==d) match1 (rs,s) else false \}\\ |
|
249 \hspace{3mm}case (Alt (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::rs, s) || match1 (r2::rs, s)\\ |
|
250 \hspace{3mm}case (Seq (r1, r2)::rs) @{text "\<Rightarrow>"} match1 (r1::r2::rs, s) \\ |
|
251 \hspace{3mm}case (Star (r)::rs) @{text "\<Rightarrow>"} match1 (r::rs, s) || match1 (r::Star (r)::rs, s)\\ |
|
252 \} |
|
253 \end{tabular}} |
|
254 |
|
255 \end{frame}} |
|
256 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
257 *} |
|
258 |
|
259 |
|
260 text_raw {* |
|
261 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
262 \mode<presentation>{ |
|
263 \begin{frame}<1->[c] |
|
264 \frametitle{Testing} |
|
265 |
|
266 \small |
|
267 Every good programmer should do thourough tests: |
|
268 |
|
269 |
|
270 \begin{center} |
|
271 \begin{tabular}{@ {\hspace{-20mm}}lcl} |
|
272 \bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\ |
|
273 \bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\ |
|
274 \bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\ |
|
275 \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ |
|
276 \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\ |
|
277 \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}}\\ |
|
278 \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}}\\ |
|
279 \onslide<2->{\bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false}} |
|
280 \end{tabular} |
|
281 \end{center} |
|
282 |
|
283 \onslide<3-> |
|
284 {looks OK \ldots let's ship it to customers\hspace{5mm} |
|
285 \raisebox{-5mm}{\includegraphics[scale=0.05]{sun.png}}} |
|
286 |
|
287 \end{frame}} |
|
288 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
289 *} |
|
290 |
|
291 text_raw {* |
|
292 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
293 \mode<presentation>{ |
|
294 \begin{frame}<1->[t] |
|
295 \frametitle{Testing} |
|
296 |
|
297 \begin{itemize} |
|
298 \item While testing is an important part in the process of programming development\pause |
|
299 |
|
300 \item we can only test a {\bf finite} amount of examples\bigskip\pause |
|
301 |
|
302 \begin{center} |
|
303 \colorbox{cream} |
|
304 {\gr{\begin{minipage}{10cm} |
|
305 ``Testing can only show the presence of errors, never their |
|
306 absence'' (Edsger W.~Dijkstra) |
|
307 \end{minipage}}} |
|
308 \end{center}\bigskip\pause |
|
309 |
|
310 \item In a theorem prover we can establish properties that apply to |
|
311 {\bf all} input and {\bf all} output.\pause |
|
312 |
|
313 \item For example we can establish that the matcher terminates |
|
314 on all input. |
|
315 \end{itemize} |
|
316 |
|
317 \end{frame}} |
|
318 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
319 *} |
|
320 |
|
321 text_raw {* |
|
322 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
323 \mode<presentation>{ |
|
324 \begin{frame}<1->[t] |
|
325 \frametitle{RegExp Matcher} |
|
326 |
|
327 \small |
|
328 We need to find a measure that gets smaller in each recursive call.\bigskip |
|
329 |
|
330 \onslide<1->{ |
|
331 \begin{center} |
|
332 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-9mm}}l@ {}} |
|
333 \bl{match [] []} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\ |
|
334 \bl{match [] \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
|
335 \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
|
336 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<3->{\ok}\\ |
|
337 \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s} & \onslide<4->{\ok}\\ |
|
338 \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
|
339 \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s} & \onslide<5->{\ok}\\ |
|
340 & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ |
|
341 \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s} & \onslide<6->{\ok}\\ |
|
342 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s} & \onslide<7->{\notok}\\ |
|
343 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
|
344 \end{tabular} |
|
345 \end{center}} |
|
346 |
|
347 |
|
348 \begin{textblock}{5}(4,4) |
|
349 \begin{tikzpicture} |
|
350 %%\draw[help lines, black] (-3,0) grid (6,3); |
|
351 |
|
352 \coordinate (m1) at (-2,0); |
|
353 \coordinate (m2) at ( 2,0); |
|
354 \path[overlay, ->, line width = 0.6mm, color = red] (m1) edge (m2); |
|
355 \draw (0,0) node[above=-1mm] {\footnotesize\rd{needs to get smaller}}; |
|
356 \end{tikzpicture} |
|
357 \end{textblock} |
|
358 |
|
359 |
|
360 \end{frame}} |
|
361 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
362 *} |
|
363 |
|
364 text_raw {* |
|
365 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
366 \mode<presentation>{ |
|
367 \begin{frame}<1->[c] |
|
368 \frametitle{Bug Hunting} |
|
369 |
|
370 \only<1>{Several hours later\ldots}\pause |
|
371 |
|
372 |
|
373 \begin{center} |
|
374 \begin{tabular}{@ {\hspace{-20mm}}lcl} |
|
375 \bl{matches (STAR (EMPTY)) s} & \bl{$\mapsto$} & loops\\ |
|
376 \onslide<4->{\bl{matches (STAR (EMPTY $|$ \ldots)) s} & \bl{$\mapsto$} & loops\\} |
|
377 \end{tabular} |
|
378 \end{center} |
|
379 |
|
380 \small |
|
381 \onslide<3->{ |
|
382 \begin{center} |
|
383 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}} |
|
384 \ldots\\ |
|
385 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
|
386 \ldots\\ |
|
387 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
|
388 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
|
389 \end{tabular} |
|
390 \end{center}} |
|
391 |
|
392 |
|
393 \end{frame}} |
|
394 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
395 *} |
|
396 |
|
397 text_raw {* |
|
398 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
399 \mode<presentation>{ |
|
400 \begin{frame}<1->[c] |
|
401 \frametitle{RegExp Matcher} |
|
402 \small |
|
403 |
|
404 \begin{center} |
|
405 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}} |
|
406 \bl{match [] []} & \bl{$=$} & \bl{true}\\ |
|
407 \bl{match [] \_} & \bl{$=$} & \bl{false}\\ |
|
408 \bl{match (NULL::rs) s} & \bl{$=$} & \bl{false}\\ |
|
409 \bl{match (EMPTY::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
|
410 \bl{match (CHR c::rs) (c::s)} & \bl{$=$} & \bl{match rs s}\\ |
|
411 \bl{match (CHR c::rs) \_} & \bl{$=$} & \bl{false}\\ |
|
412 \bl{match (ALT r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::rs) s}\\ |
|
413 & & \bl{\;\;\;\;orelse match (r$_2$::rs) s}\\ |
|
414 \bl{match (SEQ r$_1$ r$_2$::rs) s} & \bl{$=$} & \bl{match (r$_1$::r$_2$::rs) s}\\ |
|
415 \bl{match (STAR r::rs) s} & \bl{$=$} & \bl{match rs s}\\ |
|
416 & & \bl{\;\;\;\;orelse match (r::STAR r::rs) s}\\ |
|
417 \end{tabular} |
|
418 \end{center} |
|
419 |
|
420 \only<1>{ |
|
421 \begin{textblock}{5}(4,4) |
|
422 \largenotok |
|
423 \end{textblock}} |
|
424 |
|
425 \end{frame}} |
|
426 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
427 *} |
|
428 |
|
429 |
|
430 |
|
431 text_raw {* |
|
432 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
433 \mode<presentation>{ |
|
434 \begin{frame}<1->[t] |
|
435 \frametitle{Second Attempt} |
|
436 |
|
437 Can a regular expression match the empty string? |
|
438 |
|
439 \small |
|
440 \begin{center} |
|
441 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}} |
|
442 \bl{nullable (NULL)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
|
443 \bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\ |
|
444 \bl{nullable (CHR c)} & \bl{$=$} & \bl{false} & \onslide<2->{\ok}\\ |
|
445 \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} |
|
446 & \onslide<2->{\ok}\\ |
|
447 \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} |
|
448 & \onslide<2->{\ok}\\ |
|
449 \bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \onslide<2->{\ok}\\ |
|
450 \end{tabular} |
|
451 \end{center} |
|
452 |
|
453 \end{frame}} |
|
454 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
455 *} |
|
456 |
|
457 |
|
458 text_raw {* |
|
459 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
460 \mode<presentation>{ |
|
461 \begin{frame}<1->[t] |
|
462 \frametitle{RegExp Matcher 2} |
|
463 |
|
464 If \bl{r} matches \bl{c::s}, which regular expression can match the string \bl{s}? |
|
465 |
|
466 \small |
|
467 \begin{center} |
|
468 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}} |
|
469 \bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\ |
|
470 \bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \onslide<3->{\ok}\\ |
|
471 \bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \onslide<3->{\ok}\\ |
|
472 \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \onslide<3->{\ok}\\ |
|
473 \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \onslide<3->{\ok}\\ |
|
474 & & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\ |
|
475 \bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} & \onslide<3->{\ok}\medskip\\ |
|
476 \pause |
|
477 |
|
478 \bl{derivative r []} & \bl{$=$} & \bl{r} & \onslide<3->{\ok}\\ |
|
479 \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \onslide<3->{\ok}\\ |
|
480 \end{tabular} |
|
481 \end{center} |
|
482 |
|
483 we call the program with\\ |
|
484 \bl{matches r s $=$ nullable (derivative r s)} |
|
485 |
|
486 |
|
487 \end{frame}} |
|
488 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
489 *} |
|
490 |
|
491 text_raw {* |
|
492 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
493 \mode<presentation>{ |
|
494 \begin{frame}<1->[c] |
|
495 \frametitle{But Now What?} |
|
496 |
|
497 \begin{center} |
|
498 {\usefont{T1}{ptm}{b}{N}\VERYHuge{\rd{?}}} |
|
499 \end{center} |
|
500 |
|
501 \end{frame}} |
|
502 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
503 *} |
|
504 |
|
505 text_raw {* |
|
506 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
507 \mode<presentation>{ |
|
508 \begin{frame}<1->[c] |
|
509 \frametitle{Testing} |
|
510 |
|
511 \small |
|
512 |
|
513 \begin{center} |
|
514 \begin{tabular}{@ {\hspace{-20mm}}lcl} |
|
515 \bl{matches []$^*$ []} & \bl{$\mapsto$} & \bl{true}\\ |
|
516 \bl{matches ([]$|$a)$^*$ a} & \bl{$\mapsto$} & \bl{true}\medskip\\ |
|
517 |
|
518 \bl{matches (a$\cdot$b)$^*\;$ []} & \bl{$\mapsto$} & \bl{true}\\ |
|
519 \bl{matches (a$\cdot$b)$^*\;$ ab} & \bl{$\mapsto$} & \bl{true}\\ |
|
520 \bl{matches (a$\cdot$b)$^*\;$ aba} & \bl{$\mapsto$} & \bl{false}\\ |
|
521 \bl{matches (a$\cdot$b)$^*\;$ abab} & \bl{$\mapsto$} & \bl{true}\\ |
|
522 \bl{matches (a$\cdot$b)$^*\;$ abaa} & \bl{$\mapsto$} & \bl{false}\medskip\\ |
|
523 |
|
524 \bl{matches x$\cdot$(0$|$1)$^*\;$ x} & \bl{$\mapsto$} & \bl{true}\\ |
|
525 \bl{matches x$\cdot$(0$|$1)$^*\;$ x0} & \bl{$\mapsto$} & \bl{true}\\ |
|
526 \bl{matches x$\cdot$(0$|$1)$^*\;$ x3} & \bl{$\mapsto$} & \bl{false} |
|
527 \end{tabular} |
|
528 \end{center} |
|
529 |
|
530 |
|
531 \end{frame}} |
|
532 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
533 *} |
|
534 |
|
535 text_raw {* |
|
536 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
537 \mode<presentation>{ |
|
538 \begin{frame}<1->[t] |
|
539 \frametitle{Specification} |
|
540 |
|
541 We have to specify what it means for a regular expression to match |
|
542 a string. |
|
543 % |
|
544 \only<2>{ |
|
545 \mbox{}\\[8mm] |
|
546 \bl{(a$\cdot$b)$^*$}\\ |
|
547 \hspace{7mm}\bl{$\mapsto$\hspace{3mm}\{[], ab, abab, ababab, \ldots\}}\bigskip\\ |
|
548 \bl{x$\cdot$(0 $|$ 1 $|$ 2 \ldots 8 $|$ 9 )$^*$}\\ |
|
549 \hspace{7mm}\bl{$\mapsto$\hspace{3mm} |
|
550 \{x, x0, x1, \ldots, x00, \ldots, x123, \ldots\}}} |
|
551 % |
|
552 \only<3->{ |
|
553 \begin{center} |
|
554 \begin{tabular}{rcl} |
|
555 \bl{\LL (NULL)} & \bl{$\dn$} & \bl{\{\}}\\ |
|
556 \bl{\LL (EMPTY)} & \bl{$\dn$} & \bl{\{[]\}}\\ |
|
557 \bl{\LL (CHR c)} & \bl{$\dn$} & \bl{\{c\}}\\ |
|
558 \bl{\LL (ALT r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<4->{\bl{\LL (r$_1$) $\cup$ \LL (r$_2$)}}\\ |
|
559 \bl{\LL (SEQ r$_1$ r$_2$)} & \bl{$\dn$} & \onslide<6->{\bl{\LL (r$_1$) ; \LL (r$_2$)}}\\ |
|
560 \bl{\LL (STAR r)} & \bl{$\dn$} & \onslide<8->{\bl{(\LL (r))$^\star$}}\\ |
|
561 \end{tabular} |
|
562 \end{center}} |
|
563 |
|
564 \only<5-6>{ |
|
565 \begin{textblock}{6}(2.9,13.3) |
|
566 \colorbox{cream}{\bl{S$_1$ ; S$_2$ $\;\dn\;$ \{ s$_1$@s$_2$ $|$ s$_1$$\in$S$_1$ $\wedge$ |
|
567 s$_2$$\in$S$_2$ \}}} |
|
568 \end{textblock}} |
|
569 |
|
570 \only<7->{ |
|
571 \begin{textblock}{9}(4,13) |
|
572 \colorbox{cream}{\bl{$\infer{\mbox{[]} \in \mbox{S}^\star}{}$}}\hspace{3mm} |
|
573 \colorbox{cream}{\bl{$\infer{\mbox{s}_1\mbox{@}\mbox{s}_2 \in \mbox{S}^\star} |
|
574 {\mbox{s}_1 \in \mbox{S} & \mbox{s}_2 \in \mbox{S}^\star}$}} |
|
575 \end{textblock}} |
|
576 |
|
577 \end{frame}} |
|
578 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
579 *} |
|
580 |
|
581 text_raw {* |
|
582 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
583 \mode<presentation>{ |
|
584 \begin{frame}<1->[t] |
|
585 \frametitle{Is the Matcher Error-Free?} |
|
586 |
|
587 We expect that |
|
588 |
|
589 \begin{center} |
|
590 \begin{tabular}{lcl} |
|
591 \bl{matches r s = true} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}% |
|
592 \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\in$ \LL(r)}\\ |
|
593 \bl{matches r s = false} & \only<1>{\rd{$\Longrightarrow\,\,$}}\only<2>{\rd{$\Longleftarrow\,\,$}}% |
|
594 \only<3->{\rd{$\Longleftrightarrow$}} & \bl{s $\notin$ \LL(r)}\\ |
|
595 \end{tabular} |
|
596 \end{center} |
|
597 \pause\pause\bigskip |
|
598 By \alert<4->{induction}, we can {\bf prove} these properties.\bigskip |
|
599 |
|
600 \begin{tabular}{lrcl} |
|
601 Lemmas: & \bl{nullable (r)} & \bl{$\Longleftrightarrow$} & \bl{[] $\in$ \LL (r)}\\ |
|
602 & \bl{s $\in$ \LL (der c r)} & \bl{$\Longleftrightarrow$} & \bl{(c::s) $\in$ \LL (r)}\\ |
|
603 \end{tabular} |
|
604 |
|
605 \only<4->{ |
|
606 \begin{textblock}{3}(0.9,4.5) |
|
607 \rd{\huge$\forall$\large{}r s.} |
|
608 \end{textblock}} |
|
609 \end{frame}} |
|
610 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
611 *} |
|
612 |
|
613 text_raw {* |
|
614 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
615 \mode<presentation>{ |
|
616 \begin{frame}<1->[t] |
|
617 |
|
618 \mbox{}\\[-2mm] |
|
619 |
|
620 \small |
|
621 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}ll@ {}} |
|
622 \bl{nullable (NULL)} & \bl{$=$} & \bl{false} &\\ |
|
623 \bl{nullable (EMPTY)} & \bl{$=$} & \bl{true} &\\ |
|
624 \bl{nullable (CHR c)} & \bl{$=$} & \bl{false} &\\ |
|
625 \bl{nullable (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) orelse (nullable r$_2$)} & \\ |
|
626 \bl{nullable (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{(nullable r$_1$) andalso (nullable r$_2$)} & \\ |
|
627 \bl{nullable (STAR r)} & \bl{$=$} & \bl{true} & \\ |
|
628 \end{tabular}\medskip |
|
629 |
|
630 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}} |
|
631 \bl{der c (NULL)} & \bl{$=$} & \bl{NULL} & \\ |
|
632 \bl{der c (EMPTY)} & \bl{$=$} & \bl{NULL} & \\ |
|
633 \bl{der c (CHR d)} & \bl{$=$} & \bl{if c=d then EMPTY else NULL} & \\ |
|
634 \bl{der c (ALT r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (der c r$_1$) (der c r$_2$)} & \\ |
|
635 \bl{der c (SEQ r$_1$ r$_2$)} & \bl{$=$} & \bl{ALT (SEQ (der c r$_1$) r$_2$)} & \\ |
|
636 & & \bl{\phantom{ALT} (if nullable r$_1$ then der c r$_2$ else NULL)}\\ |
|
637 \bl{der c (STAR r)} & \bl{$=$} & \bl{SEQ (der c r) (STAR r)} &\smallskip\\ |
|
638 |
|
639 \bl{derivative r []} & \bl{$=$} & \bl{r} & \\ |
|
640 \bl{derivative r (c::s)} & \bl{$=$} & \bl{derivative (der c r) s} & \\ |
|
641 \end{tabular}\medskip |
|
642 |
|
643 \bl{matches r s $=$ nullable (derivative r s)} |
|
644 |
|
645 \only<2>{ |
|
646 \begin{textblock}{8}(1.5,4) |
|
647 \includegraphics[scale=0.3]{approved.png} |
|
648 \end{textblock}} |
|
649 |
|
650 |
|
651 \end{frame}} |
|
652 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
653 *} |
|
654 |
|
655 |
|
656 text_raw {* |
|
657 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
658 \mode<presentation>{ |
|
659 \begin{frame}<1->[c] |
|
660 \frametitle{Interlude: TCB} |
|
661 |
|
662 \begin{itemize} |
|
663 \item The \alert{\bf Trusted Code Base} (TCB) is the code that can make your |
|
664 program behave in unintended ways (i.e.~cause bugs).\medskip |
|
665 |
|
666 \item Typically the TCB includes: CPUs, operating systems, C-libraries, |
|
667 device drivers, (J)VMs\ldots\bigskip |
|
668 \pause |
|
669 |
|
670 \item It also includes the compiler. |
|
671 \end{itemize} |
|
672 |
|
673 \end{frame}} |
|
674 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
675 *} |
|
676 |
|
677 text_raw {* |
|
678 |
|
679 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
680 \mode<presentation>{ |
|
681 \begin{frame}<1-3> |
|
682 \frametitle{\LARGE\begin{tabular}{c}Hacking Compilers |
|
683 \end{tabular}} |
|
684 |
|
685 %Why is it so paramount to have a small trusted code base (TCB)? |
|
686 \bigskip\bigskip |
|
687 |
|
688 \begin{columns} |
|
689 \begin{column}{2.7cm} |
|
690 \begin{minipage}{2.5cm}% |
|
691 \begin{tabular}{c@ {}} |
|
692 \includegraphics[scale=0.2]{ken-thompson.jpg}\\[-1.8mm] |
|
693 \footnotesize Ken Thompson\\[-1.8mm] |
|
694 \footnotesize Turing Award, 1983\\ |
|
695 \end{tabular} |
|
696 \end{minipage} |
|
697 \end{column} |
|
698 \begin{column}{9cm} |
|
699 \begin{tabular}{l@ {\hspace{1mm}}p{8cm}} |
|
700 \myitemi |
|
701 & Ken Thompson showed how to hide a Trojan Horse in a |
|
702 compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm] |
|
703 \myitemi |
|
704 & No amount of source level verification will protect |
|
705 you from such Thompson-hacks.\\[2mm] |
|
706 |
|
707 \myitemi |
|
708 & Therefore in safety-critical systems it is important to rely |
|
709 on only a very small TCB. |
|
710 \end{tabular} |
|
711 \end{column} |
|
712 \end{columns} |
|
713 |
|
714 \only<2>{ |
|
715 \begin{textblock}{6}(4,2) |
|
716 \begin{tikzpicture} |
|
717 \draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm] |
|
718 {\normalsize |
|
719 \begin{minipage}{8cm} |
|
720 \begin{quote} |
|
721 \includegraphics[scale=0.05]{evil.png} |
|
722 \begin{enumerate} |
|
723 \item[1)] Assume you ship the compiler as binary and also with sources. |
|
724 \item[2)] Make the compiler aware when it compiles itself. |
|
725 \item[3)] Add the Trojan horse. |
|
726 \item[4)] Compile. |
|
727 \item[5)] Delete Trojan horse from the sources of the compiler. |
|
728 \item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{} |
|
729 \end{enumerate} |
|
730 \end{quote} |
|
731 \end{minipage}}; |
|
732 \end{tikzpicture} |
|
733 \end{textblock}} |
|
734 |
|
735 \end{frame}} |
|
736 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
737 |
|
738 *} |
|
739 |
|
740 text_raw {* |
|
741 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
742 \mode<presentation>{ |
|
743 \begin{frame} |
|
744 \frametitle{\LARGE\begin{tabular}{c}An Example: Small TCB for\\[-2mm] |
|
745 A Critical Infrastructure\end{tabular}} |
|
746 \mbox{}\\[-14mm]\mbox{} |
|
747 |
|
748 \begin{columns} |
|
749 \begin{column}{0.2\textwidth} |
|
750 \begin{tabular}{@ {} c@ {}} |
|
751 \includegraphics[scale=0.3]{appel.jpg}\\[-2mm] |
|
752 {\footnotesize Andrew Appel}\\[-2.5mm] |
|
753 {\footnotesize (Princeton)} |
|
754 \end{tabular} |
|
755 \end{column} |
|
756 |
|
757 \begin{column}{0.8\textwidth} |
|
758 \begin{textblock}{10}(4.5,3.95) |
|
759 \begin{block}{Proof-Carrying Code} |
|
760 \begin{center} |
|
761 \begin{tikzpicture} |
|
762 \draw[help lines,cream] (0,0.2) grid (8,4); |
|
763 |
|
764 \draw[line width=1mm, red] (5.5,0.6) rectangle (7.5,4); |
|
765 \node[anchor=base] at (6.5,2.8) |
|
766 {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering user needs to run untrusted code\end{tabular}}; |
|
767 |
|
768 \draw[line width=1mm, red] (0.5,0.6) rectangle (2.5,4); |
|
769 \node[anchor=base] at (1.5,2.3) |
|
770 {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\centering code developer/ web server/ Apple |
|
771 Store\end{tabular}}; |
|
772 |
|
773 \onslide<4->{ |
|
774 \draw[line width=1mm, red, fill=red] (5.5,0.6) rectangle (7.5,1.8); |
|
775 \node[anchor=base,white] at (6.5,1.1) |
|
776 {\small\begin{tabular}{@ {}p{1.9cm}@ {}}\bf\centering proof- checker\end{tabular}};} |
|
777 |
|
778 \node at (3.8,3.0) [single arrow, fill=red,text=white, minimum height=3cm]{\bf code}; |
|
779 \onslide<3->{ |
|
780 \node at (3.8,1.3) [single arrow, fill=red,text=white, minimum height=3cm]{\bf LF proof}; |
|
781 \node at (3.8,1.9) {\small certificate}; |
|
782 } |
|
783 |
|
784 \onslide<2>{\node at (4.0,1.3) [text=red]{\begin{tabular}{c}\bf Highly\\\bf Dangerous!\end{tabular}};} |
|
785 % Code Developer |
|
786 % User (runs untrusted code) |
|
787 % transmits a proof that the code is safe |
|
788 % |
|
789 \end{tikzpicture} |
|
790 \end{center} |
|
791 \end{block} |
|
792 \end{textblock} |
|
793 \end{column} |
|
794 \end{columns} |
|
795 |
|
796 \small\mbox{}\\[2.5cm] |
|
797 \begin{itemize} |
|
798 \item<4-> TCB of the checker is $\sim$2700 lines of code (1865 loc of\\ LF definitions; |
|
799 803 loc in C including 2 library functions)\\[-3mm] |
|
800 \item<5-> 167 loc in C implement a type-checker |
|
801 \end{itemize} |
|
802 |
|
803 \end{frame}} |
|
804 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
805 |
|
806 *} |
|
807 |
|
808 |
|
809 |
|
810 text {* |
|
811 \tikzstyle{every node}=[node distance=25mm,text height=1.5ex, text depth=.25ex] |
|
812 \tikzstyle{node1}=[rectangle, minimum size=10mm, rounded corners=3mm, very thick, |
|
813 draw=black!50, top color=white, bottom color=black!20] |
|
814 \tikzstyle{node2}=[rectangle, minimum size=12mm, rounded corners=3mm, very thick, |
|
815 draw=red!70, top color=white, bottom color=red!50!black!20] |
|
816 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
817 \mode<presentation>{ |
|
818 \begin{frame}[squeeze] |
|
819 \frametitle{Type-Checking in LF} |
|
820 |
|
821 \begin{columns} |
|
822 \begin{column}{0.2\textwidth} |
|
823 \begin{tabular}{@ {\hspace{-4mm}}c@ {}} |
|
824 \\[-4mm] |
|
825 \includegraphics[scale=0.1]{harper.jpg}\\[-2mm] |
|
826 {\footnotesize Bob Harper}\\[-2.5mm] |
|
827 {\footnotesize (CMU)}\\[2mm] |
|
828 |
|
829 \includegraphics[scale=0.3]{pfenning.jpg}\\[-2mm] |
|
830 {\footnotesize Frank Pfenning}\\[-2.5mm] |
|
831 {\footnotesize (CMU)}\\[2mm] |
|
832 |
|
833 \onslide<-6>{ |
|
834 {\footnotesize 31 pages in }\\[-2.5mm] |
|
835 {\footnotesize ACM Transact.~on}\\[-2.5mm] |
|
836 {\footnotesize Comp.~Logic.,~2005}\\} |
|
837 \end{tabular} |
|
838 \end{column} |
|
839 |
|
840 \begin{column}{0.8\textwidth} |
|
841 \begin{textblock}{0}(3.1,2) |
|
842 |
|
843 \begin{tikzpicture} |
|
844 \matrix[ampersand replacement=\&,column sep=7mm, row sep=5mm] |
|
845 { \&[-10mm] |
|
846 \node (def1) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}}; \& |
|
847 \node (proof1) [node1] {\large Proof}; \& |
|
848 \node (alg1) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}}; \\ |
|
849 |
|
850 \onslide<4->{\node {\begin{tabular}{c}\small 1st\\[-2.5mm] \footnotesize solution\end{tabular}};} \& |
|
851 \onslide<4->{\node (def2) [node2] {\large Spec$^\text{+ex}$};} \& |
|
852 \onslide<4->{\node (proof2) [node1] {\large Proof};} \& |
|
853 \onslide<4->{\node (alg2) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\ |
|
854 |
|
855 \onslide<5->{\node {\begin{tabular}{c}\small 2nd\\[-2.5mm] \footnotesize solution\end{tabular}};} \& |
|
856 \onslide<5->{\node (def3) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \& |
|
857 \onslide<5->{\node (proof3) [node1] {\large Proof};} \& |
|
858 \onslide<5->{\node (alg3) [node2] {\large Alg$^\text{-ex}$};} \\ |
|
859 |
|
860 \onslide<6->{\node {\begin{tabular}{c}\small 3rd\\[-2.5mm] \footnotesize solution\end{tabular}};} \& |
|
861 \onslide<6->{\node (def4) [node1] {\large\hspace{1mm}Spec\hspace{1mm}\mbox{}};} \& |
|
862 \onslide<6->{\node (proof4) [node2] {\large\hspace{1mm}Proof\hspace{1mm}};} \& |
|
863 \onslide<6->{\node (alg4) [node1] {\large\hspace{1mm}Alg\hspace{1mm}\mbox{}};} \\ |
|
864 }; |
|
865 |
|
866 \draw[->,black!50,line width=2mm] (proof1) -- (def1); |
|
867 \draw[->,black!50,line width=2mm] (proof1) -- (alg1); |
|
868 |
|
869 \onslide<4->{\draw[->,black!50,line width=2mm] (proof2) -- (def2);} |
|
870 \onslide<4->{\draw[->,black!50,line width=2mm] (proof2) -- (alg2);} |
|
871 |
|
872 \onslide<5->{\draw[->,black!50,line width=2mm] (proof3) -- (def3);} |
|
873 \onslide<5->{\draw[->,black!50,line width=2mm] (proof3) -- (alg3);} |
|
874 |
|
875 \onslide<6->{\draw[->,black!50,line width=2mm] (proof4) -- (def4);} |
|
876 \onslide<6->{\draw[->,black!50,line width=2mm] (proof4) -- (alg4);} |
|
877 |
|
878 \onslide<3->{\draw[white,line width=1mm] (1.1,3.2) -- (0.9,2.85) -- (1.1,2.35) -- (0.9,2.0);} |
|
879 \end{tikzpicture} |
|
880 |
|
881 \end{textblock} |
|
882 \end{column} |
|
883 \end{columns} |
|
884 |
|
885 \only<2>{% |
|
886 \begin{textblock}{2}(.1,12.85) |
|
887 \begin{tikzpicture} |
|
888 \draw[line width=1mm, red] (0,0) ellipse (1.5cm and 0.88cm); |
|
889 \end{tikzpicture} |
|
890 \end{textblock} |
|
891 } |
|
892 |
|
893 \begin{textblock}{3}(14,3.6) |
|
894 \onslide<4->{ |
|
895 \begin{tikzpicture} |
|
896 \node at (0,0) [single arrow, shape border rotate=270, fill=red,text=white]{2h}; |
|
897 \end{tikzpicture}} |
|
898 \end{textblock} |
|
899 |
|
900 \only<7->{ |
|
901 \begin{textblock}{14}(0.6,12.8) |
|
902 \begin{block}{} |
|
903 \small Each time one needs to check $\sim$31pp~of informal paper proofs. |
|
904 You have to be able to keep definitions and proofs consistent. |
|
905 \end{block} |
|
906 \end{textblock}} |
|
907 |
|
908 \end{frame}} |
|
909 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
910 |
|
911 *} |
|
912 |
|
913 text_raw {* |
|
914 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
915 \mode<presentation>{ |
|
916 \begin{frame}<1>[c] |
|
917 \frametitle{Theorem Provers} |
|
918 |
|
919 \begin{itemize} |
|
920 \item Theorem provers help with keeping large proofs consistent; |
|
921 make them modifiable.\medskip |
|
922 |
|
923 \item They can ensure that all cases are covered.\medskip |
|
924 |
|
925 \item Sometimes, tedious reasoning can be automated. |
|
926 \end{itemize} |
|
927 |
|
928 \end{frame}} |
|
929 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
930 *} |
|
931 |
|
932 text_raw {* |
|
933 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
934 \mode<presentation>{ |
|
935 \begin{frame}<1>[c] |
|
936 \frametitle{Theorem Provers} |
|
937 |
|
938 \begin{itemize} |
|
939 \item You also pay a (sometimes heavy) price: reasoning can be much, much harder.\medskip |
|
940 |
|
941 \item Depending on your domain, suitable reasoning infrastructure |
|
942 might not yet be available. |
|
943 \end{itemize} |
|
944 |
|
945 \end{frame}} |
|
946 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
947 *} |
|
948 |
|
949 text_raw {* |
|
950 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
951 \mode<presentation>{ |
|
952 \begin{frame}<1>[c] |
|
953 \frametitle{Theorem Provers} |
|
954 |
|
955 Recently impressive work has been accomplished proving the correctness |
|
956 |
|
957 \begin{itemize} |
|
958 \item of a compiler for C-light (compiled code has the same observable |
|
959 behaviour as the original source code),\medskip |
|
960 |
|
961 \item a mirco-kernel operating system (absence of certain |
|
962 bugs\ldots no nil pointers, no buffer overflows). |
|
963 \end{itemize} |
|
964 |
|
965 \end{frame}} |
|
966 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
967 *} |
|
968 |
|
969 |
|
970 text_raw {* |
|
971 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
972 \mode<presentation>{ |
|
973 \begin{frame}<1>[c] |
|
974 \frametitle{Trust in Theorem Provers} |
|
975 |
|
976 \begin{center} |
|
977 Why should we trust theorem provers? |
|
978 \end{center} |
|
979 |
|
980 \end{frame}} |
|
981 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
982 *} |
|
983 |
|
984 text_raw {* |
|
985 |
|
986 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
987 \mode<presentation>{ |
|
988 \begin{frame} |
|
989 \frametitle{Theorem Provers} |
|
990 |
|
991 \begin{itemize} |
|
992 \item Theorem provers are a \textcolor{red}{special kind} of software. |
|
993 |
|
994 \item We do \textcolor{red}{\bf not} need to trust them; we only need to trust: |
|
995 \end{itemize} |
|
996 |
|
997 \begin{quote} |
|
998 \begin{itemize} |
|
999 \item The logic they are based on \textcolor{gray}{(e.g.~HOL)}, and\smallskip |
|
1000 \item a proof checker that checks the proofs |
|
1001 \textcolor{gray}{(this can be a very small program)}.\smallskip\pause |
|
1002 \item To a little extend, we also need to trust our definitions |
|
1003 \textcolor{gray}{(this can be mitigated)}. |
|
1004 \end{itemize} |
|
1005 \end{quote} |
|
1006 |
|
1007 \end{frame}} |
|
1008 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1009 |
|
1010 *} |
|
1011 |
|
1012 text_raw {* |
|
1013 |
|
1014 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1015 \mode<presentation>{ |
|
1016 \begin{frame} |
|
1017 \frametitle{Isabelle} |
|
1018 |
|
1019 \begin{itemize} |
|
1020 \item I am using the Isabelle theorem prover (development since 1990).\bigskip\bigskip\bigskip |
|
1021 |
|
1022 \item It follows the LCF-approach: |
|
1023 |
|
1024 \begin{itemize} |
|
1025 \item Have a special abstract type \alert{\bf thm}. |
|
1026 \item Make the constructors of this abstract type the inference rules |
|
1027 of your logic. |
|
1028 \item Implement the theorem prover in a strongly-typed language (e.g.~ML). |
|
1029 \end{itemize} |
|
1030 |
|
1031 $\Rightarrow$ everything of type {\bf thm} has been proved (even if we do not |
|
1032 have to explicitly generate proofs). |
|
1033 \end{itemize} |
|
1034 |
|
1035 \only<1>{ |
|
1036 \begin{textblock}{5}(11,2.3) |
|
1037 \begin{center} |
|
1038 \includegraphics[scale=0.18]{robin-milner.jpg}\\[-0.8mm] |
|
1039 \footnotesize Robin Milner\\[-0.8mm] |
|
1040 \footnotesize Turing Award, 1991\\ |
|
1041 \end{center} |
|
1042 \end{textblock}} |
|
1043 |
|
1044 |
|
1045 \end{frame}} |
|
1046 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1047 *} |
|
1048 |
|
1049 text_raw {* |
|
1050 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1051 \mode<presentation>{ |
|
1052 \begin{frame}<1>[c] |
|
1053 \frametitle{ |
|
1054 \begin{tabular}{c} |
|
1055 \mbox{}\\[23mm] |
|
1056 \LARGE Demo |
|
1057 \end{tabular}} |
|
1058 |
|
1059 \end{frame}} |
|
1060 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1061 *} |
|
1062 |
|
1063 |
|
1064 text_raw {* |
|
1065 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1066 \mode<presentation>{ |
|
1067 \begin{frame}<1->[c] |
|
1068 \frametitle{Future Research} |
|
1069 |
|
1070 \begin{itemize} |
|
1071 \item Make theorem provers more like a programming environment.\medskip\pause |
|
1072 |
|
1073 \item Use all the computational power we get from the hardware to |
|
1074 automate reasoning (GPUs).\medskip\pause |
|
1075 |
|
1076 \item Provide a comprehensive reasoning infrastructure for many domains and |
|
1077 design automated decision procedures. |
|
1078 \end{itemize}\pause |
|
1079 |
|
1080 |
|
1081 \begin{center} |
|
1082 \colorbox{cream}{ |
|
1083 \begin{minipage}{10cm} |
|
1084 \color{gray} |
|
1085 \small |
|
1086 ``Formal methods will never have a significant impact until |
|
1087 they can be used by people that don't understand them.''\smallskip\\ |
|
1088 \mbox{}\footnotesize\hfill attributed to Tom Melham |
|
1089 \end{minipage}} |
|
1090 \end{center} |
|
1091 |
|
1092 \end{frame}} |
|
1093 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1094 *} |
|
1095 |
|
1096 text_raw {* |
|
1097 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1098 \mode<presentation>{ |
|
1099 \begin{frame}<1->[c] |
|
1100 \frametitle{Conclusion} |
|
1101 |
|
1102 \begin{itemize} |
|
1103 \item The plan is to make this kind of programming the ``future''.\medskip\pause |
|
1104 |
|
1105 \item Though the technology is already there\\ (compiler + micro-kernel os).\medskip\pause |
|
1106 |
|
1107 \item Logic and reasoning (especially induction) are important skills for |
|
1108 Computer Scientists. |
|
1109 \end{itemize} |
|
1110 |
|
1111 \end{frame}} |
|
1112 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1113 *} |
|
1114 |
|
1115 |
|
1116 text_raw {* |
|
1117 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1118 \mode<presentation>{ |
|
1119 \begin{frame}<1>[c] |
|
1120 \frametitle{ |
|
1121 \begin{tabular}{c} |
|
1122 \mbox{}\\[23mm] |
|
1123 \alert{\LARGE Thank you very much!}\\ |
|
1124 \alert{\Large Questions?} |
|
1125 \end{tabular}} |
|
1126 |
|
1127 \end{frame}} |
|
1128 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1129 *} |
|
1130 |
|
1131 |
|
1132 |
|
1133 (*<*) |
|
1134 end |
|
1135 (*>*) |
|