1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
|
; X86ISA Library
; Note: The license below is based on the template at:
; http://opensource.org/licenses/BSD-3-Clause
; Copyright (C) 2015, Regents of the University of Texas
; All rights reserved.
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions are
; met:
; o Redistributions of source code must retain the above copyright
; notice, this list of conditions and the following disclaimer.
; o Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
; o Neither the name of the copyright holders nor the names of its
; contributors may be used to endorse or promote products derived
; from this software without specific prior written permission.
; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
; HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
; Original Author(s):
; Shilpi Goel <shigoel@cs.utexas.edu>
(in-package "X86ISA")
(include-book "basics" :ttags (:include-raw :undef-flg :syscall-exec :other-non-det))
(local (include-book "centaur/bitops/ihs-extensions" :dir :system))
;; ===================================================================
(defsection x86-RoW-WoW-thms
:parents (proof-utilities)
:short "Miscellaneous RoW and WoW theorems"
)
(local (xdoc::set-default-parents x86-RoW-WoW-thms))
;; ======================================================================
(defthm assoc-equal-put-assoc-equal-diff
(equal (assoc-equal x (put-assoc-equal y z ss))
(if (equal x y)
(cons x z)
(assoc-equal x ss))))
(defthm assoc-equal-consp
(implies (consp (assoc-equal x ss))
(consp (assoc-equal x (put-assoc-equal x z ss)))))
(local
(defthm read-x86-file-des-write-x86-file-des-different-indices-helper
(implies (or (env-alistp env) (not env))
(env-alistp
(list
(cons :file-descriptors
(put-assoc-equal
fd2 fd2-field
(cdr (assoc-equal :file-descriptors env))))
(cons :file-contents (cdr (assoc-equal :file-contents env)))
(cons :oracle (cdr (assoc-equal :oracle env))))))
:hints (("Goal" :in-theory (e/d (env-alistp) ())))))
(defthm read-x86-file-des-write-x86-file-des-different-indices
(implies (not (equal fd1 fd2))
(equal (read-x86-file-des fd1 (write-x86-file-des fd2 fd2-field x86))
(read-x86-file-des fd1 x86)))
:hints (("Goal"
:cases ((x86p x86))
:in-theory (e/d (read-x86-file-des
read-x86-file-des-logic
write-x86-file-des
write-x86-file-des-logic)
()))))
(defthm read-x86-file-des-write-x86-file-des-same-indices
(implies (x86p x86)
(equal (read-x86-file-des fd (write-x86-file-des fd fd-field x86))
(cdr
(assoc-equal
fd
(put-assoc-equal fd fd-field
(cdr (assoc-equal :file-descriptors (env-read x86))))))))
:hints (("Goal" :in-theory (e/d (read-x86-file-des
write-x86-file-des
read-x86-file-des-logic
write-x86-file-des-logic)
()))))
(local
(defthm read-x86-file-des-write-x86-file-des-same-indices-helper
(implies (or (env-alistp env) (not env))
(env-alistp
(list
(cons :file-descriptors
(cdr (assoc-equal :file-descriptors env)))
(cons
:file-contents
(put-assoc-equal name name-field
(cdr (assoc-equal :file-contents env))))
(cons :oracle (cdr (assoc-equal :oracle env))))))
:hints (("Goal"
:in-theory (e/d (env-alistp rip-ret-alistp) ())))))
(defthm read-x86-file-contents-write-x86-file-contents-same-indices
(equal
(read-x86-file-contents name (write-x86-file-contents name name-field x86))
(cdr
(assoc-equal
name
(put-assoc-equal name name-field
(cdr (assoc-equal :file-contents (env-read x86)))))))
:hints (("Goal" :cases ((x86p x86))
:in-theory (e/d (read-x86-file-contents
write-x86-file-contents
read-x86-file-contents-logic
write-x86-file-contents-logic)
()))))
(defthm read-x86-file-contents-write-x86-file-contents-different-indices
(implies (and (not (equal name1 name2))
(x86p x86))
(equal (read-x86-file-contents
name1 (write-x86-file-contents name2 name-field x86))
(read-x86-file-contents name1 x86)))
:hints (("Goal" :in-theory (e/d (read-x86-file-contents
write-x86-file-contents
read-x86-file-contents-logic
write-x86-file-contents-logic)
()))))
(defthm read-x86-file-des-write-x86-file-contents
(equal (read-x86-file-des id (write-x86-file-contents i v x86))
(read-x86-file-des id x86))
:hints (("Goal" :in-theory (e/d (read-x86-file-des
read-x86-file-des-logic
write-x86-file-contents
write-x86-file-contents-logic)
()))))
(defthm read-x86-file-contents-write-x86-file-des
(equal (read-x86-file-contents name (write-x86-file-des i v x86))
(read-x86-file-contents name x86))
:hints (("Goal" :in-theory (e/d (read-x86-file-contents
read-x86-file-contents-logic
write-x86-file-des
write-x86-file-des-logic)
()))))
(defthm read-x86-file-des-wb-1
(implies (app-view x86)
(equal (read-x86-file-des id (mv-nth 1 (wb-1 n addr w value x86)))
(read-x86-file-des id x86)))
:hints (("Goal"
:in-theory (e/d* (read-x86-file-des read-x86-file-des-logic)
()))))
(defthm read-x86-file-des-wb
(implies (app-view x86)
(equal (read-x86-file-des id (mv-nth 1 (wb n addr w value x86)))
(read-x86-file-des id x86)))
:hints (("Goal"
:use ((:instance read-x86-file-des-wb-1))
:in-theory (e/d* (read-x86-file-des read-x86-file-des-logic)
(wb wb-1 read-x86-file-des-wb-1)))))
(defthm write-x86-file-des-wb
(implies (app-view x86)
(equal (write-x86-file-des i v (mv-nth 1 (wb n addr w value x86)))
(mv-nth 1 (wb n addr w value (write-x86-file-des i v x86)))))
:hints (("Goal"
:in-theory (e/d* (write-x86-file-des write-x86-file-des-logic)
()))))
(defthm read-x86-file-contents-wb-1
(implies (app-view x86)
(equal (read-x86-file-contents id (mv-nth 1 (wb-1 n addr w value x86)))
(read-x86-file-contents id x86)))
:hints (("Goal"
:in-theory (e/d* (read-x86-file-contents read-x86-file-contents-logic)
()))))
(defthm read-x86-file-contents-wb
(implies (app-view x86)
(equal (read-x86-file-contents id (mv-nth 1 (wb n addr w value x86)))
(read-x86-file-contents id x86)))
:hints (("Goal"
:use ((:instance read-x86-file-contents-wb-1))
:in-theory (e/d* (read-x86-file-contents read-x86-file-contents-logic)
(wb wb-1 read-x86-file-contents-wb-1)))))
;; ======================================================================
;; Some rules about alignment-checking-enabled-p:
(defthm alignment-checking-enabled-p-write-x86-file-des
(equal (alignment-checking-enabled-p (write-x86-file-des i v x86))
(alignment-checking-enabled-p x86))
:hints (("Goal" :in-theory (e/d* (write-x86-file-des write-x86-file-des-logic)
()))))
(defthm alignment-checking-enabled-p-write-x86-file-contents
(equal (alignment-checking-enabled-p (write-x86-file-contents i v x86))
(alignment-checking-enabled-p x86))
:hints (("Goal" :in-theory (e/d* (write-x86-file-contents write-x86-file-contents-logic)
()))))
;; ======================================================================
;; Some rules about flags:
(defthm read-x86-file-des-write-user-rflags
(equal (read-x86-file-des i (write-user-rflags flags mask x86))
(read-x86-file-des i x86))
:hints (("Goal" :in-theory (e/d* (write-user-rflags)
(force (force))))))
(defthm read-x86-file-contents-write-user-rflags
(equal (read-x86-file-contents i (write-user-rflags flags mask x86))
(read-x86-file-contents i x86))
:hints (("Goal" :in-theory (e/d* (write-user-rflags)
(force (force))))))
(defthm logbitp-0-and-loghead-1
(iff (logbitp 0 n) (equal (loghead 1 n) 1))
:hints (("Goal" :in-theory (e/d* (bitops::ihsext-inductions
bitops::ihsext-recursive-redefs)
()))))
(defthm write-user-rflags-and-xw
(implies (and (not (equal fld :rflags))
(not (equal fld :undef)))
(equal (write-user-rflags flags mask (xw fld index value x86))
(xw fld index value (write-user-rflags flags mask x86))))
:hints (("Goal" :in-theory (e/d* (write-user-rflags)
((tau-system) force (force))))))
(defthm write-user-rflags-write-user-rflags-when-no-mask
(implies (x86p x86)
(equal (write-user-rflags flags1 0 (write-user-rflags flags2 0 x86))
(write-user-rflags flags1 0 x86)))
:hints (("Goal" :in-theory (e/d* (rflag-RoWs-enables) ()))))
(defthm alignment-checking-enabled-p-and-write-user-rflags
(implies (x86p x86)
(equal (alignment-checking-enabled-p (write-user-rflags flgs mask x86))
(alignment-checking-enabled-p x86)))
:hints (("Goal" :in-theory (e/d* (rflag-RoWs-enables
write-user-rflags)
()))))
;; ======================================================================
;; Making some functions untouchable after proving RoW/WoW thms about
;; them:
(push-untouchable (
;; Accessors
env$inline
env$a
env$c
env-read-logic
env-write-logic
read-x86-file-des-logic
read-x86-file-contents-logic
;; Updaters
!env$inline
!env$a
!env$c
write-x86-file-des-logic
delete-x86-file-des-logic
write-x86-file-contents-logic
delete-x86-file-contents-logic
pop-x86-oracle-logic
!undef$inline
)
t)
;; ======================================================================
|
