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34e49164 C |
1 | \documentclass{article} |
2 | \usepackage{fullpage} | |
3 | ||
4 | \newcommand{\U}{\,\mbox{\sf{U}}\,} | |
5 | \newcommand{\A}{\mbox{\sf{A}}} | |
6 | \newcommand{\E}{\mbox{\sf{E}}} | |
7 | \newcommand{\AX}{\mbox{\sf{AX}}} | |
8 | \newcommand{\EX}{\mbox{\sf{EX}}} | |
9 | \newcommand{\AF}{\mbox{\sf{AF}}} | |
10 | \newcommand{\EF}{\mbox{\sf{EF}}} | |
11 | \newcommand{\AG}{\mbox{\sf{AG}}} | |
12 | \newcommand{\EG}{\mbox{\sf{EG}}} | |
13 | ||
14 | \newcommand{\mita}[1]{\mbox{\it{{#1}}}} | |
15 | \newcommand{\mtt}[1]{\mbox{\tt{{#1}}}} | |
16 | \newcommand{\msf}[1]{\mbox{\sf{{#1}}}} | |
17 | \newcommand{\mrm}[1]{\mbox{\rm{{#1}}}} | |
18 | \newcommand{\mth}[1]{\({#1}\)} | |
19 | ||
20 | \newcommand{\ttlb}{\mbox{\tt \char'173}} | |
21 | \newcommand{\ttrb}{\mbox{\tt \char'175}} | |
22 | ||
23 | \begin{document} | |
24 | ||
25 | \begin{quote}\begin{verbatim} | |
26 | ||
27 | @@ | |
28 | @@ | |
29 | ||
30 | f(); | |
31 | ... | |
32 | ?g(); | |
33 | ... | |
34 | h(); | |
35 | \end{verbatim}\end{quote} | |
36 | ||
37 | \[\begin{array}{l} | |
38 | \mita{\sf{let}} \, \mita{l9} = \mita{f();} \, \mita{\sf{in}} \, \mita{l9} \wedge (\AX(\mita{\sf{let}} \, \mita{l0} = \mita{g();} \, \mita{\sf{in}} \, \A[\neg (\mita{l0} \vee \mita{l9}) \U (\mita{\sf{let}} \, \mita{l7} = \msf{After}\\\mbox{} \vee \msf{ErrorExit} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l10} = (\mita{\sf{let}} \, \mita{l5} = \mita{h();} \, \mita{\sf{in}} \, \A[\neg (\mita{l5} \vee \mita{l0}) \U (\mita{l5} \vee \mita{l7})] | |
39 | ||
40 | ) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l3} = \mita{l0}\\\mbox{} \wedge (\AX\mita{l10}) \, \mita{\sf{in}} \, \mita{l3} \vee ((\neg \mita{l3}) \wedge \mita{l10}) | |
41 | ) | |
42 | ) \vee \mita{l7} | |
43 | )] | |
44 | ||
45 | )) | |
46 | ||
47 | \end{array}\] | |
48 | ||
49 | \begin{quote}\begin{verbatim} | |
50 | ||
51 | @@ | |
52 | @@ | |
53 | ||
54 | foo(...) { | |
55 | ||
56 | ( | |
57 | -f-(-3-, -E-)-; | |
58 | >>> f(3, 3, E); | |
59 | ||
60 | | | |
61 | -f-(-E-, -4-)-; | |
62 | >>> f(E, 4, 4); | |
63 | ||
64 | | | |
65 | -E-; | |
66 | >>> g(E); | |
67 | ||
68 | ) | |
69 | ||
70 | ( | |
71 | -f-(-3-, -X-)-; | |
72 | >>> f(3, 3, X); | |
73 | ||
74 | | | |
75 | -f-(-Y-, -4-)-; | |
76 | >>> f(Y, 4, 4); | |
77 | ||
78 | | | |
79 | -Z-; | |
80 | >>> g(Z); | |
81 | ||
82 | ) | |
83 | ||
84 | ( | |
85 | -f-(-3-)-; | |
86 | >>> f(3, 3); | |
87 | ||
88 | | | |
89 | -f-(-4-)-; | |
90 | >>> f(4, 4); | |
91 | ||
92 | ) | |
93 | } | |
94 | \end{verbatim}\end{quote} | |
95 | ||
96 | \[\begin{array}{l} | |
97 | (\exists \mita{foo} . \mita{foo(...) }) \wedge (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l17} = \msf{Paren}(p0) \, \mita{\sf{in}} \, \mita{{\ttlb} | |
98 | } \wedge \mita{l17} \wedge (\AX(\mita{\sf{let}} \, \mita{l32} = \AX(\mita{\sf{let}} \, \mita{l2} = \AX(\mita{\sf{let}} \, \mita{l12} = \AX(\mita{ | |
99 | {\ttrb}}\\\mbox{} \wedge \mita{l17}) \, \mita{\sf{in}} \, ((\exists \mita{v0} . \mita{-f-(-3-)-; | |
100 | \mth{>}\mth{>}\mth{>} f(3, 3);}_{\mita{v0}}) \wedge \mita{l12}) \vee ((\exists \mita{v0} . \mita{-f-(-4-)-; | |
101 | \mth{>}\mth{>}\mth{>} f(4, 4);}_{\mita{v0}})\\\mbox{} \wedge \mita{l12}) | |
102 | ) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l7} = \exists \mita{X} . \exists \mita{v0} . \mita{-f-(-3-, -X-)-; | |
103 | \mth{>}\mth{>}\mth{>} f(3, 3, X);}_{\mita{v0}} \, \mita{\sf{in}} \, (\mita{l7}\\\mbox{} \wedge \mita{l2}) \vee (\mita{\sf{let}} \, \mita{l21} = \neg \mita{l7} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l6} = \exists \mita{Y} . \exists \mita{v0} . \mita{-f-(-Y-, -4-)-; | |
104 | \mth{>}\mth{>}\mth{>} f(Y, 4, 4);}_{\mita{v0}}\\\mbox{} \, \mita{\sf{in}} \, (\mita{l21} \wedge \mita{l6} \wedge \mita{l2}) \vee ((\neg \mita{l6}) \wedge \mita{l21} \wedge (\exists \mita{Z} . \exists \mita{v0} . \mita{-Z-; | |
105 | \mth{>}\mth{>}\mth{>} g(Z);}_{\mita{v0}}) \wedge \mita{l2}) | |
106 | ) | |
107 | ) | |
108 | ) | |
109 | ) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l8} = \exists \mita{E}\\\mbox{} . \exists \mita{v0} . \mita{-f-(-3-, -E-)-; | |
110 | \mth{>}\mth{>}\mth{>} f(3, 3, E);}_{\mita{v0}} \, \mita{\sf{in}} \, (\mita{l8} \wedge \mita{l32}) \vee (\mita{\sf{let}} \, \mita{l19} = \neg \mita{l8}\\\mbox{} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l4} = \exists \mita{E} . \exists \mita{v0} . \mita{-f-(-E-, -4-)-; | |
111 | \mth{>}\mth{>}\mth{>} f(E, 4, 4);}_{\mita{v0}} \, \mita{\sf{in}} \, (\mita{l19} \wedge \mita{l4}\\\mbox{} \wedge \mita{l32}) \vee ((\neg \mita{l4}) \wedge \mita{l19} \wedge (\exists \mita{E} . \exists \mita{v0} . \mita{-E-; | |
112 | \mth{>}\mth{>}\mth{>} g(E);}_{\mita{v0}}) \wedge \mita{l32}) | |
113 | ) | |
114 | ) | |
115 | ) | |
116 | )) | |
117 | ))) | |
118 | \end{array}\] | |
119 | ||
120 | \begin{quote}\begin{verbatim} | |
121 | ||
122 | @@ | |
123 | @@ | |
124 | ||
125 | p( | |
126 | <<< int hostptr, | |
127 | char buffer) { | |
128 | -int -hostptr-; | |
129 | } | |
130 | \end{verbatim}\end{quote} | |
131 | ||
132 | \[\begin{array}{l} | |
133 | \exists \mita{hostptr} . ((\exists \mita{buffer} . \exists \mita{v0} . \mita{p( | |
134 | <<< int hostptr, | |
135 | char buffer) }_{\mita{v0}})\\\mbox{} \wedge (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l0} = \msf{Paren}(p0) \, \mita{\sf{in}} \, \mita{{\ttlb} | |
136 | } \wedge \mita{l0} \wedge (\AX((\exists \mita{v0} . \mita{-int -hostptr-;}_{\mita{v0}})\\\mbox{} \wedge (\AX(\mita{ | |
137 | {\ttrb}} \wedge \mita{l0})))) | |
138 | )))) | |
139 | \end{array}\] | |
140 | ||
141 | \begin{quote}\begin{verbatim} | |
142 | ||
143 | @@ | |
144 | @@ | |
145 | ||
146 | f(X); | |
147 | -... WHEN != -h-(-X-) | |
148 | g(Y); | |
149 | \end{verbatim}\end{quote} | |
150 | ||
151 | \[\begin{array}{l} | |
152 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l1} = \mita{f(X);} \, \mita{\sf{in}} \, \mita{l1} \wedge (\AX(\mita{\sf{let}} \, \mita{l0} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[((\exists \mita{v0} . \mita{-\_S0}_{\mita{v0}}) \wedge (\neg (\exists \mita{v0}\\\mbox{} . \mita{-h-(-X-)}_{\mita{v0}})) \wedge (\neg (\mita{l0} \vee \mita{l1}))) \U (\mita{l0} \vee \msf{After} \vee \msf{ErrorExit})] | |
153 | ||
154 | )) | |
155 | ) | |
156 | \end{array}\] | |
157 | ||
158 | \begin{quote}\begin{verbatim} | |
159 | ||
160 | @@ | |
161 | @@ | |
162 | ||
163 | f(X); | |
164 | -... | |
165 | g(Y); | |
166 | \end{verbatim}\end{quote} | |
167 | ||
168 | \[\begin{array}{l} | |
169 | \mita{\sf{let}} \, \mita{l1} = \exists \mita{X} . \mita{f(X);} \, \mita{\sf{in}} \, \mita{l1} \wedge (\AX(\mita{\sf{let}} \, \mita{l2} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[((\exists \mita{v0} . \mita{-\_S0}_{\mita{v0}}) \wedge (\neg (\mita{l2}\\\mbox{} \vee \mita{l1}))) \U (\mita{l2} \vee \msf{After} \vee \msf{ErrorExit})] | |
170 | ||
171 | )) | |
172 | ||
173 | \end{array}\] | |
174 | ||
175 | \begin{quote}\begin{verbatim} | |
176 | ||
177 | @@ | |
178 | @@ | |
179 | ||
180 | f(X); | |
181 | g(Y); | |
182 | h(X); | |
183 | f(Y); | |
184 | g(X); | |
185 | h(Y); | |
186 | \end{verbatim}\end{quote} | |
187 | ||
188 | \[\begin{array}{l} | |
189 | \exists \mita{X} . (\mita{f(X);} \wedge (\AX(\exists \mita{Y} . (\mita{g(Y);} \wedge (\AX(\mita{h(X);} \wedge (\AX(\mita{f(Y);} \wedge (\AX(\mita{g(X);} \wedge (\AX(\mita{h(Y);})))))))))))) | |
190 | \end{array}\] | |
191 | ||
192 | \begin{quote}\begin{verbatim} | |
193 | ||
194 | @@ | |
195 | @@ | |
196 | ||
197 | f(X); | |
198 | ... | |
199 | g(X); | |
200 | h(X); | |
201 | \end{verbatim}\end{quote} | |
202 | ||
203 | \[\begin{array}{l} | |
204 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l0} = \mita{f(X);} \, \mita{\sf{in}} \, \mita{l0} \wedge (\AX(\mita{\sf{let}} \, \mita{l1} = \mita{g(X);} \, \mita{\sf{in}} \, \A[\neg (\mita{l1} \vee \mita{l0}) \U ((\mita{l1} \wedge (\AX(\mita{h(X);})))\\\mbox{} \vee \msf{After} \vee \msf{ErrorExit})] | |
205 | ||
206 | )) | |
207 | ) | |
208 | \end{array}\] | |
209 | ||
210 | \begin{quote}\begin{verbatim} | |
211 | ||
212 | @@ | |
213 | @@ | |
214 | ||
215 | if (X) { | |
216 | ... | |
217 | } else { | |
218 | ... | |
219 | } | |
220 | f(X); | |
221 | \end{verbatim}\end{quote} | |
222 | ||
223 | \[\begin{array}{l} | |
224 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l0} = \msf{FalseBranch} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l1} = \msf{After} \, \mita{\sf{in}} \, \mita{if (X) } \wedge (\AX(\mita{\sf{let}} \, \mita{l15} = \AX(\exists \mita{p0}\\\mbox{} . (\mita{\sf{let}} \, \mita{l7} = \msf{Paren}(p0) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l14} = \mita{{\ttlb} | |
225 | } \wedge \mita{l7} \, \mita{\sf{in}} \, \mita{l14} \wedge (\AX(\mita{\sf{let}} \, \mita{l13} = \mita{ | |
226 | {\ttrb}} \wedge \mita{l7}\\\mbox{} \, \mita{\sf{in}} \, \A[\neg (\mita{l13} \vee \mita{l14}) \U (\mita{l13} \vee \mita{l1} \vee \msf{ErrorExit})] | |
227 | ||
228 | )) | |
229 | ) | |
230 | )) \, \mita{\sf{in}} \, (\msf{TrueBranch} \wedge \mita{l15}) \vee (\mita{l0}\\\mbox{} \wedge \mita{l15}) \vee (\mita{l1} \wedge (\AX(\mita{f(X);}))) | |
231 | )) \wedge (\EX\mita{l0}) \wedge (\EX\mita{l1}) | |
232 | ) | |
233 | ) | |
234 | \end{array}\] | |
235 | ||
236 | \begin{quote}\begin{verbatim} | |
237 | ||
238 | @@ | |
239 | @@ | |
240 | ||
241 | if (X) { | |
242 | ... | |
243 | } | |
244 | f(X); | |
245 | \end{verbatim}\end{quote} | |
246 | ||
247 | \[\begin{array}{l} | |
248 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l0} = \msf{After} \, \mita{\sf{in}} \, \mita{if (X) } \wedge (\AX((\msf{TrueBranch} \wedge (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l2} = \msf{Paren}(p0)\\\mbox{} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l4} = \mita{{\ttlb} | |
249 | } \wedge \mita{l2} \, \mita{\sf{in}} \, \mita{l4} \wedge (\AX(\mita{\sf{let}} \, \mita{l3} = \mita{ | |
250 | {\ttrb}} \wedge \mita{l2} \, \mita{\sf{in}} \, \A[\neg (\mita{l3} \vee \mita{l4}) \U (\mita{l3} \vee \mita{l0}\\\mbox{} \vee \msf{ErrorExit})] | |
251 | ||
252 | )) | |
253 | ) | |
254 | )))) \vee \msf{FallThrough} \vee (\mita{l0} \wedge (\AX(\mita{f(X);}))))) \wedge (\EX\mita{l0}) | |
255 | ) | |
256 | \end{array}\] | |
257 | ||
258 | \begin{quote}\begin{verbatim} | |
259 | ||
260 | @@ | |
261 | @@ | |
262 | ||
263 | while (X) { | |
264 | ... | |
265 | } | |
266 | f(X); | |
267 | \end{verbatim}\end{quote} | |
268 | ||
269 | \[\begin{array}{l} | |
270 | \exists \mita{X} . (\mita{while (X) } \wedge (\mita{\sf{let}} \, \mita{l0} = \msf{After} \, \mita{\sf{in}} \, (\AX((\msf{TrueBranch} \rightarrow (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l3} = \msf{Paren}(p0)\\\mbox{} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l5} = \mita{{\ttlb} | |
271 | } \wedge \mita{l3} \, \mita{\sf{in}} \, \mita{l5} \wedge (\AX(\mita{\sf{let}} \, \mita{l4} = \mita{ | |
272 | {\ttrb}} \wedge \mita{l3} \, \mita{\sf{in}} \, \A[\neg (\mita{l4} \vee \mita{l5}) \U (\mita{l4} \vee \mita{l0}\\\mbox{} \vee \msf{ErrorExit})] | |
273 | ||
274 | )) | |
275 | ) | |
276 | )))) \wedge (\mita{l0} \rightarrow (\AX(\mita{f(X);}))))) \wedge (\EX\mita{l0}) | |
277 | )) | |
278 | \end{array}\] | |
279 | ||
280 | \begin{quote}\begin{verbatim} | |
281 | ||
282 | @@ | |
283 | @@ | |
284 | ||
285 | while (X) { | |
286 | ... | |
287 | } | |
288 | \end{verbatim}\end{quote} | |
289 | ||
290 | \[\begin{array}{l} | |
291 | (\exists \mita{X} . \mita{while (X) }) \wedge (\AX(\msf{TrueBranch} \rightarrow (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l1} = \msf{Paren}(p0) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l4} = \mita{{\ttlb} | |
292 | }\\\mbox{} \wedge \mita{l1} \, \mita{\sf{in}} \, \mita{l4} \wedge (\AX(\mita{\sf{let}} \, \mita{l3} = \mita{ | |
293 | {\ttrb}} \wedge \mita{l1} \, \mita{\sf{in}} \, \A[\neg (\mita{l3} \vee \mita{l4}) \U (\mita{l3} \vee \msf{After} \vee \msf{ErrorExit})] | |
294 | \\\mbox{} | |
295 | )) | |
296 | ) | |
297 | ))))) | |
298 | \end{array}\] | |
299 | ||
300 | \begin{quote}\begin{verbatim} | |
301 | ||
302 | @@ | |
303 | @@ | |
304 | ||
305 | { | |
306 | ... WHEN != g(Y) | |
307 | f(X); | |
308 | ... WHEN != h(Y) | |
309 | } | |
310 | \end{verbatim}\end{quote} | |
311 | ||
312 | \[\begin{array}{l} | |
313 | \exists \mita{p0} . (\mita{\sf{let}} \, \mita{l6} = \msf{Paren}(p0) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l9} = \mita{{\ttlb} | |
314 | } \wedge \mita{l6} \, \mita{\sf{in}} \, \mita{l9} \wedge (\AX(\exists \mita{Y} . (\mita{\sf{let}} \, \mita{l3} = \exists \mita{X} . \mita{f(X);}\\\mbox{} \, \mita{\sf{in}} \, \A[((\neg \mita{g(Y)}) \wedge (\neg (\mita{l3} \vee \mita{l9}))) \U (\mita{\sf{let}} \, \mita{l5} = \msf{After} \vee \msf{ErrorExit} \, \mita{\sf{in}} \, (\mita{l3} \wedge (\AX(\mita{\sf{let}} \, \mita{l8} = \mita{ | |
315 | {\ttrb}}\\\mbox{} \wedge \mita{l6} \, \mita{\sf{in}} \, \A[((\neg \mita{h(Y)}) \wedge (\neg (\mita{l8} \vee \mita{l3}))) \U (\mita{l8} \vee \mita{l5})] | |
316 | ||
317 | ))) \vee \mita{l5} | |
318 | )] | |
319 | ||
320 | ))) | |
321 | ) | |
322 | ) | |
323 | \end{array}\] | |
324 | ||
325 | \begin{quote}\begin{verbatim} | |
326 | ||
327 | @@ | |
328 | @@ | |
329 | ||
330 | f(X); | |
331 | ... | |
332 | -g-(-Y-)-; | |
333 | >>> h(X, Y); | |
334 | ||
335 | \end{verbatim}\end{quote} | |
336 | ||
337 | \[\begin{array}{l} | |
338 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l0} = \mita{f(X);} \, \mita{\sf{in}} \, \mita{l0} \wedge (\AX\A[\neg ((\exists \mita{Y} . \mita{-g-(-Y-)-; | |
339 | \mth{>}\mth{>}\mth{>} h(X, Y);}) \vee \mita{l0})\\\mbox{} \U ((\exists \mita{Y} . \exists \mita{v0} . \mita{-g-(-Y-)-; | |
340 | \mth{>}\mth{>}\mth{>} h(X, Y);}_{\mita{v0}}) \vee \msf{After} \vee \msf{ErrorExit})] | |
341 | ) | |
342 | ) | |
343 | \end{array}\] | |
344 | ||
345 | \begin{quote}\begin{verbatim} | |
346 | ||
347 | @@ | |
348 | @@ | |
349 | ||
350 | -f-(-X-)-; | |
351 | >>> f(Z); | |
352 | ||
353 | -... | |
354 | g(Y); | |
355 | h(Z); | |
356 | \end{verbatim}\end{quote} | |
357 | ||
358 | \[\begin{array}{l} | |
359 | \exists \mita{Z} . ((\exists \mita{X} . \exists \mita{v0} . \mita{-f-(-X-)-; | |
360 | \mth{>}\mth{>}\mth{>} f(Z);}_{\mita{v0}}) \wedge (\AX(\mita{\sf{let}} \, \mita{l0} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[((\exists \mita{v0}\\\mbox{} . \mita{-\_S0}_{\mita{v0}}) \wedge (\neg (\mita{l0} \vee (\exists \mita{X} . \mita{-f-(-X-)-; | |
361 | \mth{>}\mth{>}\mth{>} f(Z);})))) \U ((\mita{l0} \wedge (\AX(\mita{h(Z);})))\\\mbox{} \vee \msf{After} \vee \msf{ErrorExit})] | |
362 | ||
363 | ))) | |
364 | \end{array}\] | |
365 | ||
366 | \begin{quote}\begin{verbatim} | |
367 | ||
368 | @@ | |
369 | @@ | |
370 | ||
371 | -f-(-X-)-; | |
372 | >>> f(Z); | |
373 | ||
374 | ... | |
375 | g(Y); | |
376 | h(Z); | |
377 | \end{verbatim}\end{quote} | |
378 | ||
379 | \[\begin{array}{l} | |
380 | \exists \mita{Z} . ((\exists \mita{X} . \exists \mita{v0} . \mita{-f-(-X-)-; | |
381 | \mth{>}\mth{>}\mth{>} f(Z);}_{\mita{v0}}) \wedge (\AX(\mita{\sf{let}} \, \mita{l0} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[\neg (\mita{l0}\\\mbox{} \vee (\exists \mita{X} . \mita{-f-(-X-)-; | |
382 | \mth{>}\mth{>}\mth{>} f(Z);})) \U ((\mita{l0} \wedge (\AX(\mita{h(Z);}))) \vee \msf{After} \vee \msf{ErrorExit})] | |
383 | \\\mbox{} | |
384 | ))) | |
385 | \end{array}\] | |
386 | ||
387 | \begin{quote}\begin{verbatim} | |
388 | ||
389 | @@ | |
390 | @@ | |
391 | ||
392 | f(X); | |
393 | ... | |
394 | g(Y); | |
395 | h(Z); | |
396 | \end{verbatim}\end{quote} | |
397 | ||
398 | \[\begin{array}{l} | |
399 | \mita{\sf{let}} \, \mita{l1} = \exists \mita{X} . \mita{f(X);} \, \mita{\sf{in}} \, \mita{l1} \wedge (\AX(\mita{\sf{let}} \, \mita{l2} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[\neg (\mita{l2} \vee \mita{l1}) \U ((\mita{l2} \wedge (\AX(\exists \mita{Z}\\\mbox{} . \mita{h(Z);}))) \vee \msf{After} \vee \msf{ErrorExit})] | |
400 | ||
401 | )) | |
402 | ||
403 | \end{array}\] | |
404 | ||
405 | \begin{quote}\begin{verbatim} | |
406 | ||
407 | @@ | |
408 | @@ | |
409 | ||
410 | f(X); | |
411 | ... WHEN != h(Z) | |
412 | g(Y); | |
413 | h(Z); | |
414 | \end{verbatim}\end{quote} | |
415 | ||
416 | \[\begin{array}{l} | |
417 | \mita{\sf{let}} \, \mita{l1} = \exists \mita{X} . \mita{f(X);} \, \mita{\sf{in}} \, \mita{l1} \wedge (\AX(\exists \mita{Z} . (\mita{\sf{let}} \, \mita{l2} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[((\neg \mita{h(Z)}) \wedge (\neg (\mita{l2} \vee \mita{l1})))\\\mbox{} \U ((\mita{l2} \wedge (\AX(\mita{h(Z);}))) \vee \msf{After} \vee \msf{ErrorExit})] | |
418 | ||
419 | ))) | |
420 | ||
421 | \end{array}\] | |
422 | ||
423 | \begin{quote}\begin{verbatim} | |
424 | ||
425 | @@ | |
426 | @@ | |
427 | ||
428 | f(X); | |
429 | ... WHEN != h(Q) | |
430 | g(Y); | |
431 | h(Z); | |
432 | \end{verbatim}\end{quote} | |
433 | ||
434 | \[\begin{array}{l} | |
435 | \mita{\sf{let}} \, \mita{l1} = \exists \mita{X} . \mita{f(X);} \, \mita{\sf{in}} \, \mita{l1} \wedge (\AX(\mita{\sf{let}} \, \mita{l2} = \exists \mita{Y} . \mita{g(Y);} \, \mita{\sf{in}} \, \A[((\neg (\exists \mita{Q} . \mita{h(Q)})) \wedge (\neg (\mita{l2}\\\mbox{} \vee \mita{l1}))) \U ((\mita{l2} \wedge (\AX(\exists \mita{Z} . \mita{h(Z);}))) \vee \msf{After} \vee \msf{ErrorExit})] | |
436 | ||
437 | )) | |
438 | ||
439 | \end{array}\] | |
440 | ||
441 | \begin{quote}\begin{verbatim} | |
442 | ||
443 | @@ | |
444 | @@ | |
445 | ||
446 | if (X) { | |
447 | ... | |
448 | } else { | |
449 | g(X); | |
450 | } | |
451 | h(Z); | |
452 | \end{verbatim}\end{quote} | |
453 | ||
454 | \[\begin{array}{l} | |
455 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l0} = \msf{FalseBranch} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l1} = \msf{After} \, \mita{\sf{in}} \, \mita{if (X) } \wedge (\AX(\mita{\sf{let}} \, \mita{l2} = \msf{Paren}(p0)\\\mbox{} \, \mita{\sf{in}} \, (\msf{TrueBranch} \wedge (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l6} = \mita{{\ttlb} | |
456 | } \wedge \mita{l2} \, \mita{\sf{in}} \, \mita{l6} \wedge (\AX(\mita{\sf{let}} \, \mita{l5} = \mita{ | |
457 | {\ttrb}} \wedge \mita{l2} \, \mita{\sf{in}} \, \A[\neg (\mita{l5}\\\mbox{} \vee \mita{l6}) \U (\mita{l5} \vee \mita{l1} \vee \msf{ErrorExit})] | |
458 | ||
459 | )) | |
460 | )))) \vee (\mita{l0} \wedge (\AX(\exists \mita{p0} . (\mita{{\ttlb} | |
461 | } \wedge \mita{l2} \wedge (\AX(\mita{g(X);} \wedge (\AX(\mita{ | |
462 | {\ttrb}}\\\mbox{} \wedge \mita{l2})))))))) \vee (\mita{l1} \wedge (\AX(\exists \mita{Z} . \mita{h(Z);}))) | |
463 | )) \wedge (\EX\mita{l0}) \wedge (\EX\mita{l1}) | |
464 | ) | |
465 | ) | |
466 | \end{array}\] | |
467 | ||
468 | \begin{quote}\begin{verbatim} | |
469 | ||
470 | @@ | |
471 | @@ | |
472 | ||
473 | <... | |
474 | ||
475 | ( | |
476 | h(X) | |
477 | | | |
478 | g(Y) | |
479 | ) | |
480 | ...> | |
481 | \end{verbatim}\end{quote} | |
482 | ||
483 | \[\begin{array}{l} | |
484 | \AG(\mita{\sf{let}} \, \mita{l2} = \exists \mita{Y} . \exists \mita{X} . \mita{ | |
485 | ( | |
486 | h(X) | |
487 | | | |
488 | g(Y) | |
489 | )} \, \mita{\sf{in}} \, \mita{l2} \vee (\neg \mita{l2}) | |
490 | ) | |
491 | \end{array}\] | |
492 | ||
493 | \begin{quote}\begin{verbatim} | |
494 | ||
495 | @@ | |
496 | @@ | |
497 | ||
498 | <... | |
499 | ||
500 | ( | |
501 | h(X) | |
502 | | | |
503 | g(Y) | |
504 | ) | |
505 | ...> | |
506 | r(X); | |
507 | \end{verbatim}\end{quote} | |
508 | ||
509 | \[\begin{array}{l} | |
510 | \exists \mita{X} . (\mita{\sf{let}} \, \mita{l1} = \mita{r(X);} \, \mita{\sf{in}} \, \A[((\neg \mita{l1}) \wedge (\mita{\sf{let}} \, \mita{l0} = \exists \mita{Y} . \mita{ | |
511 | ( | |
512 | h(X) | |
513 | | | |
514 | g(Y) | |
515 | )} \, \mita{\sf{in}} \, \mita{l0} \vee (\neg \mita{l0})\\\mbox{} | |
516 | )) \U (\mita{l1} \vee \msf{After} \vee \msf{ErrorExit})] | |
517 | ||
518 | ) | |
519 | \end{array}\] | |
520 | ||
521 | \begin{quote}\begin{verbatim} | |
522 | ||
523 | @@ | |
524 | @@ | |
525 | ||
526 | ||
527 | ( | |
528 | h(X) | |
529 | | | |
530 | g(Y) | |
531 | ) | |
532 | \end{verbatim}\end{quote} | |
533 | ||
534 | \[\begin{array}{l} | |
535 | \exists \mita{Y} . \exists \mita{X} . \mita{ | |
536 | ( | |
537 | h(X) | |
538 | | | |
539 | g(Y) | |
540 | )} | |
541 | \end{array}\] | |
542 | ||
543 | \begin{quote}\begin{verbatim} | |
544 | ||
545 | @@ | |
546 | @@ | |
547 | ||
548 | m(Y); | |
549 | ?h(X); | |
550 | g(Y); | |
551 | \end{verbatim}\end{quote} | |
552 | ||
553 | \[\begin{array}{l} | |
554 | \exists \mita{Y} . (\mita{m(Y);} \wedge (\AX(\mita{\sf{let}} \, \mita{l0} = \mita{g(Y);} \, \mita{\sf{in}} \, ((\exists \mita{X} . \mita{h(X);}) \wedge (\AX\mita{l0})) \vee \mita{l0} | |
555 | ))) | |
556 | \end{array}\] | |
557 | ||
558 | \begin{quote}\begin{verbatim} | |
559 | ||
560 | @@ | |
561 | @@ | |
562 | ||
563 | sht/*struct Scsi_Host_Template */.proc_info = proc_info_func; | |
564 | \end{verbatim}\end{quote} | |
565 | ||
566 | \[\begin{array}{l} | |
567 | \exists \mita{proc\_info\_func} . \exists \mita{sht} . \mita{sht/*struct Scsi\_Host\_Template */.proc\_info = proc\_info\_func;} | |
568 | \end{array}\] | |
569 | ||
570 | \begin{quote}\begin{verbatim} | |
571 | ||
572 | @@ | |
573 | @@ | |
574 | ||
575 | proc_info_func(char *buffer, char **start, off_t offset, int length, | |
576 | int hostno, int inout) { | |
577 | ... | |
578 | struct Scsi_Host *hostptr; | |
579 | ... | |
580 | hostptr = scsi_host_hn_get(hostno); | |
581 | ... | |
582 | ?if (hostptr == NULL) ?{ | |
583 | ?... | |
584 | ?} | |
585 | ... | |
586 | ?scsi_host_put(hostptr); | |
587 | ... | |
588 | } | |
589 | \end{verbatim}\end{quote} | |
590 | ||
591 | \[\begin{array}{l} | |
592 | \exists \mita{hostno} . ((\exists \mita{buffer} . \exists \mita{start} . \exists \mita{offset} . \exists \mita{length} . \exists \mita{inout} . \mita{proc\_info\_func(char *buffer, char **start, off\_t offset, int length, | |
593 | int hostno, int inout) })\\\mbox{} \wedge (\AX(\exists \mita{p1} . (\mita{\sf{let}} \, \mita{l33} = \msf{Paren}(p1) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l5} = \mita{{\ttlb} | |
594 | } \wedge \mita{l33} \, \mita{\sf{in}} \, \mita{l5} \wedge (\AX(\mita{\sf{let}} \, \mita{l53} = \mita{struct Scsi\_Host *hostptr;}\\\mbox{} \, \mita{\sf{in}} \, \A[\neg ((\exists \mita{hostptr} . \mita{l53}) \vee \mita{l5}) \U (\mita{\sf{let}} \, \mita{l1} = \msf{After} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l6} = \mita{l1} \vee \msf{ErrorExit}\\\mbox{} \, \mita{\sf{in}} \, (\exists \mita{hostptr} . (\mita{l53} \wedge (\AX(\mita{\sf{let}} \, \mita{l30} = \mita{hostptr = scsi\_host\_hn\_get(hostno);}\\\mbox{} \, \mita{\sf{in}} \, \A[\neg (\mita{l30} \vee \mita{l53}) \U ((\mita{l30} \wedge (\AX(\mita{\sf{let}} \, \mita{l32} = \msf{Paren}(p0) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l50} = \mita{ | |
595 | {\ttrb}} \wedge \mita{l32}\\\mbox{} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l14} = \mita{l50} \vee \mita{l6} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l2} = \msf{FallThrough} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l29} = \mita{l2} \vee \mita{l1} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l51} = \mita{{\ttlb} | |
596 | }\\\mbox{} \wedge \mita{l32} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l0} = \msf{TrueBranch} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l52} = \mita{if (hostptr == NULL) } \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l20} = \mita{l52}\\\mbox{} \wedge (\AX((\mita{l0} \wedge (\AX(\exists \mita{p0} . (\mita{l51} \wedge (\AX\AF\mita{l14}))))) \vee \mita{l29})) \, \mita{\sf{in}} \, \A[\neg (\mita{l20} \vee \mita{l30}) \U ((\mita{\sf{let}} \, \mita{l8} = \mita{scsi\_host\_put(hostptr);}\\\mbox{} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l11} = \A[\neg \mita{l8} \U \mita{l6}] | |
597 | \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l25} = \mita{l8} \wedge (\AX\mita{l11}) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l39} = \neg \mita{l25} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l13} = (\mita{\sf{let}} \, \mita{l48} = (\mita{\sf{let}} \, \mita{l4} = \mita{ | |
598 | {\ttrb}}\\\mbox{} \wedge \mita{l33} \, \mita{\sf{in}} \, \A[\neg (\mita{l4} \vee \mita{l8}) \U (\mita{l4} \vee \mita{l6})] | |
599 | ||
600 | ) \, \mita{\sf{in}} \, (\mita{l8} \wedge (\AX\mita{l48})) \vee (\mita{l39} \wedge \mita{l48}) | |
601 | ) \vee \mita{l6} \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l36} = \neg (\mita{l8}\\\mbox{} \vee \mita{l20}) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l34} = \mita{l0} \wedge (\AX(\exists \mita{p0} . (\mita{l51} \wedge (\AX\A[\neg (\mita{l50} \vee \mita{l51}) \U \mita{l14}] | |
602 | )))) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l16} = \EX\mita{l1}\\\mbox{} \, \mita{\sf{in}} \, (\mita{l52} \wedge (\AX(\mita{l34} \vee \mita{l2} \vee (\mita{l1} \wedge (\AX\A[\mita{l36} \U \mita{l13}] | |
603 | )))) \wedge \mita{l16}) \vee ((\neg (\mita{l52} \wedge (\AX(\mita{l34}\\\mbox{} \vee \mita{l2} \vee (\mita{l1} \wedge (\AX\A[\mita{l36} \U (\mita{l25} \vee (\mita{l39} \wedge \mita{l11}) \vee \mita{l6})] | |
604 | )))) \wedge \mita{l16})) \wedge (\A[\neg (\mita{l8} \vee (\mita{l52} \wedge (\AX(\mita{l34}\\\mbox{} \vee \mita{l29})))) \U \mita{l13}] | |
605 | )) | |
606 | ) | |
607 | ) | |
608 | ) | |
609 | ) | |
610 | ) | |
611 | ) | |
612 | ) | |
613 | ) \vee \mita{l6})] | |
614 | ||
615 | ) | |
616 | ) | |
617 | ) | |
618 | ) | |
619 | ) | |
620 | ) | |
621 | ) | |
622 | ) | |
623 | ))) \vee \mita{l6})] | |
624 | ||
625 | )))) \vee \mita{l6} | |
626 | ) | |
627 | )] | |
628 | ||
629 | )) | |
630 | ) | |
631 | )))) | |
632 | \end{array}\] | |
633 | ||
634 | \begin{quote}\begin{verbatim} | |
635 | ||
636 | @@ | |
637 | @@ | |
638 | ||
639 | proc_info_func(...) { | |
640 | <... | |
641 | ||
642 | ( | |
643 | E->host_no == hostno | |
644 | | | |
645 | hostno | |
646 | ) | |
647 | ...> | |
648 | } | |
649 | \end{verbatim}\end{quote} | |
650 | ||
651 | \[\begin{array}{l} | |
652 | \mita{proc\_info\_func(...) } \wedge (\AX(\exists \mita{p0} . (\mita{\sf{let}} \, \mita{l3} = \msf{Paren}(p0) \, \mita{\sf{in}} \, (\mita{\sf{let}} \, \mita{l6} = \mita{{\ttlb} | |
653 | } \wedge \mita{l3}\\\mbox{} \, \mita{\sf{in}} \, \mita{l6} \wedge (\AX(\mita{\sf{let}} \, \mita{l5} = \mita{ | |
654 | {\ttrb}} \wedge \mita{l3} \, \mita{\sf{in}} \, \A[((\neg (\mita{l5} \vee \mita{l6})) \wedge (\mita{\sf{let}} \, \mita{l2} = \exists \mita{E} . \mita{ | |
655 | ( | |
656 | E-\mth{>}host\_no == hostno | |
657 | | | |
658 | hostno | |
659 | )}\\\mbox{} \, \mita{\sf{in}} \, \mita{l2} \vee (\neg \mita{l2}) | |
660 | )) \U (\mita{l5} \vee \msf{After} \vee \msf{ErrorExit})] | |
661 | ||
662 | )) | |
663 | ) | |
664 | ))) | |
665 | \end{array}\] | |
666 | ||
667 | \end{document} |