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
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
|
(in-package "BCV")
(include-book "typechecker")
(include-book "typechecker-ext")
(include-book "typechecker-simple")
(include-book "bcv-base")
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-instructionIsTypeSafe-if-verified"))
(defthm mergedcodeIsTypesafe-implies-instructionIsTypeSafe
(implies (and (mergedcodeIsTypesafe env mergedcode stackframe)
(pc-wff-mergedcode1 0 (allinstructions env))
(is-suffix mergedcode (allinstructions env))
(member inst (extract-code mergedcode)))
(instructionIsTypeSafe
inst
env
(searchStackFrame (instrOffset inst)
(stack-map-wrap
(collect-sig-frame-vector env
mergedcode
stackframe)))))))
;----------------------------------------------------------------------
(defun mergedcodeIsTypeSafe-induct (env init-frame mergedcode stackmap)
(if (endp mergedcode)
(list env init-frame mergedcode stackmap)
(if (endp (cdr mergedcode))
(list (list env init-frame mergedcode stackmap))
(cond ((isinstruction (car mergedcode))
(cond ((isStackMap (cadr mergedcode))
(mergedcodeIsTypeSafe-induct env init-frame
(forward-to-next-inst (cdr mergedcode))
(next-stackframe (cdr mergedcode))))
((isInstruction (cadr mergedcode))
(mv-let (next-stack-frame exception-frame)
(sig-do-inst (car mergedcode) env stackmap)
(declare (ignore exception-frame))
(mergedcodeIsTypeSafe-induct env init-frame
(cdr mergedcode)
next-stack-frame)))))
((isStackMap (car mergedcode))
(mergedcodeIsTypeSafe-induct env init-frame
(forward-to-next-inst mergedcode)
(next-stackframe mergedcode)))))))
;----------------------------------------------------------------------
(defthm is-suffix-forward-to-next-is-suffix
(implies (is-suffix mergedcode1 mergedcode)
(IS-SUFFIX (FORWARD-TO-NEXT-INST mergedcode1) mergedcode))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction)
:induct (forward-to-next-inst mergedcode1))))
;----------------------------------------------------------------------
(defthm pc-wff-mergedcode1-never-end-on-a-stackmap
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(isStackMap stackmap)
(isEnd end))
(not (is-suffix (list* stackmap end any)
mergedcode)))
:hints (("Goal" :in-theory (disable isStackMap isEnd
jvm::inst-size
isInstruction))))
;----------------------------------------------------------------------
;;;
;;; it is critical for sun's bcv, we could not have aftergoto as part of the
;;; marking. Wed Dec 28 14:26:13 2005
;;;
(defthm pc-wff-mergedcode1-never-aftergoto
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(isStackMap stackmap)
(member stackmap mergedcode))
(not (equal (mapFrame (getMap stackmap))
'aftergoto)))
:hints (("Goal" :in-theory (disable isStackMap isEnd
jvm::inst-size
isInstruction))))
(encapsulate ()
(local (include-book "bcv-wff-code"))
(defthm is-suffix-member-f
(implies (IS-SUFFIX (cons instr mergedcode1)
MERGEDCODE)
(member instr mergedcode))
:rule-classes :forward-chaining))
;----------------------------------------------------------------------
(defthm pc-wff-mergedcode1-f
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(not (isEnd (car mergedcode))))
(pc-wff-mergedcode1 (next-pc mergedcode) mergedcode))
:hints (("Goal" :in-theory (disable jvm::inst-size
isInstruction
isStackMap
isEnd)
:do-not '(generalize)))
:rule-classes :forward-chaining)
(defthm mergedcodeIsTypesafe-forward-to-next-inst
(implies (and (mergedcodeIsTypesafe env mergedcode stackframe)
(not (isInstruction (car mergedcode)))
(pc-wff-mergedcode1 (next-pc mergedcode) mergedcode))
(mergedcodeIsTypesafe env
(forward-to-next-inst mergedcode)
(next-stackframe mergedcode)))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:do-not '(generalize)))
:rule-classes :forward-chaining)
(defthm mergedcodeIsTypesafe-forward-to-next-inst-b
(implies (and (mergedcodeIsTypesafe env mergedcode (mapFrame (getMap mergedcode1)))
(isStackMap mergedcode1)
(pc-wff-mergedcode1 (next-pc mergedcode) mergedcode))
(mergedcodeIsTypesafe env
(forward-to-next-inst (cons mergedcode1 mergedcode))
(next-stackframe (cons mergedcode1 mergedcode))))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:do-not '(generalize))))
(defthm forward-to-next-inst-get-inst-if-pc-wff-merged-code
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(consp mergedcode)
(isStackMap (car mergedcode)))
(isinstruction (car (forward-to-next-inst mergedcode))))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
mapFrame
jvm::inst-size
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)))
:rule-classes :forward-chaining)
(local (in-theory (disable next-stackframe forward-to-next-inst)))
(encapsulate ()
(local (include-book "bcv-pc-wff-mergedcode1"))
(defthm is-suffix-pc-wff-mergecode1
(implies (and (is-suffix mergedcode1 mergedcode)
(consp mergedcode1)
(not (isEnd (car mergedcode1)))
(pc-wff-mergedcode1 pc mergedcode))
(pc-wff-mergedcode1 (next-pc mergedcode1)
mergedcode1))
:rule-classes :forward-chaining)
(defthm pc-wff-mergedcode1-isStackMap-consp-remaining
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(isStackMap (car mergedcode)))
(consp (cdr mergedcode)))
:rule-classes :forward-chaining))
;----------------------------------------------------------------------
;;;
;;(i-am-here) ;; Sat Dec 31 02:22:06 2005
(encapsulate ()
(local (include-book "bcv-is-suffix-facts"))
(defthm is-suffix-facts
(implies (IS-SUFFIX (LIST* MERGEDCODE1 any) mergedcode)
(is-suffix any mergedcode))
:rule-classes :forward-chaining)
(defthm is-suffix-facts-member
(implies (IS-SUFFIX (LIST* MERGEDCODE1 any) mergedcode)
(member mergedcode1 mergedcode))
:rule-classes :forward-chaining))
(defthm forward-to-next-inst-get-inst-if-pc-wff-merged-code-specific
(implies (and (is-suffix (list* mergedcode1 mergedcode) (allinstructions env))
(pc-wff-mergedcode1 0 (allinstructions env))
(isStackMap mergedcode1))
(isinstruction (car (forward-to-next-inst (cons mergedcode1 mergedcode)))))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
;;next-pc
mapFrame
jvm::inst-size
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:use ((:instance forward-to-next-inst-get-inst-if-pc-wff-merged-code
(mergedcode (list* mergedcode1 mergedcode))
(pc (next-pc mergedcode)))
(:instance is-suffix-pc-wff-mergecode1
(mergedcode1 (list* mergedcode1 mergedcode))
(mergedcode (allinstructions env))
(pc 0)))))
:rule-classes :forward-chaining)
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-collect-sig-frame-vector-never-aftergoto"))
(defthm collect-sig-frame-vector-never-aftergoto
(not (equal (searchstackframe
any
(stack-map-wrap (collect-sig-frame-vector any-env any-code
any-init-frame)))
'aftergoto))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-searchStackFrame-reduce"))
(defthm searchStackFrame-is-if-stack-map
(implies (and (isStackMap (car mergedcode))
(equal (forward-to-next-inst mergedcode)
(forward-to-next-inst x))
(is-suffix mergedcode all-merged-code)
(PC-WFF-MERGEDCODE1 PC ALL-MERGED-CODE)
(mergedcodeistypesafe env all-merged-code init-frame))
(EQUAL
(SEARCHSTACKFRAME
(INSTROFFSET (CAR (FORWARD-TO-NEXT-INST x)))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV all-merged-code
INIT-FRAME)))
(NEXT-STACKFRAME mergedcode)))))
;;; Sat Dec 31 02:19:30 2005
;----------------------------------------------------------------------
;; Subgoal *1/5'
;; (IMPLIES
;; (AND
;; (CONSP MERGEDCODE)
;; (CONSP (CDR MERGEDCODE))
;; (ISINSTRUCTION (CAR MERGEDCODE))
;; (NOT (ISSTACKMAP (CADR MERGEDCODE)))
;; (NOT (ISINSTRUCTION (CADR MERGEDCODE)))
;; (MERGEDCODEISTYPESAFE ENV (ALLINSTRUCTIONS ENV)
;; INIT-FRAME)
;; (EQUAL
;; STACKFRAME
;; (SEARCHSTACKFRAME
;; (NEXT-PC MERGEDCODE)
;; (STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
;; INIT-FRAME))))
;; (MERGEDCODEISTYPESAFE ENV MERGEDCODE STACKFRAME)
;; (PC-WFF-MERGEDCODE1 0 (ALLINSTRUCTIONS ENV))
;; (IS-SUFFIX MERGEDCODE (ALLINSTRUCTIONS ENV)))
;; (BCV-SIMPLE-METHOD1 (EXTRACT-CODE MERGEDCODE)
;; (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
;; INIT-FRAME)
;; ENV)).
(defthm extract-code-forward-next-inst-reduce
(implies (wff-merged-code-weak mergedcode)
(equal (EXTRACT-CODE (FORWARD-TO-NEXT-INST MERGEDCODE))
(extract-code mergedcode)))
:hints (("Goal" :in-theory (enable forward-to-next-inst))))
;; (i-am-here) ;; Sun Jan 1 15:50:54 2006
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-searchStackFrame-reduce"))
(defthm mergecodeIsTypeSafe-implies-collect-sig-vector-compatible-1
(implies (and (mergedcodeIsTypeSafe env mergecode stackframe)
(member inst mergecode)
(isInstruction inst)
(isInstruction (next-inst inst mergecode))
(pc-wff-mergedcode1 (next-pc mergecode) mergecode))
(equal (car (sig-do-inst inst
env
(searchStackFrame (instroffset inst)
(stack-map-wrap
(collect-sig-frame-vector
env mergecode
stackframe)))))
(searchStackFrame (instroffset (next-inst inst mergecode))
(stack-map-wrap (collect-sig-frame-vector
env mergecode
stackframe)))))))
;----------------------------------------------------------------------
;;(i-am-here) ;; Sun Jan 1 23:22:11 2006
;;(i-am-here)
(defthm typelist-assignable-reflexive
(TYPELISTASSIGNABLE x x ENV))
(defthm frameisassignable-reflexive
(FRAMEISASSIGNABLE frame frame env))
;;(i-am-here) ;; Sun Jan 1 18:22:32 2006
(encapsulate ()
(local (include-book "bcv-sig-do-produce-compatible-next-state"))
(defthm frameIsAssignable-transitive-specific
(implies (and (FRAMEISASSIGNABLE
(CAR
(SIG-DO-INST
MERGEDCODE1 ENV
(SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))))
(MAPFRAME (GETMAP MERGEDCODE3))
ENV)
(isStackMap mergedcode3)
(equal (mapOffset (getMap mergedcode3)) npc)
(member mergedcode3 (allinstructions env))
(pc-wff-mergedcode1 0 (allinstructions env))
(mergedcodeIsTypesafe env (allinstructions env) init-frame)
(GOOD-FRAME
(SEARCHSTACKFRAME
(MAPOFFSET (GETMAP MERGEDCODE3))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))
ENV)
(good-frame (SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))
env)
(all-good-frames (extract-frames (allinstructions env)) env)
(good-env env))
(FRAMEISASSIGNABLE
(CAR
(SIG-DO-INST
MERGEDCODE1 ENV
(SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))))
(SEARCHSTACKFRAME
npc
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))
env))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-is-suffix-facts"))
(defthm is-suffix-pc-equal
(implies (and (IS-SUFFIX (LIST* MERGEDCODE1 mergedcode4) mergedcode)
(isStackMap mergedcode1)
(pc-wff-mergedcode1 pc mergedcode))
(equal (instrOffset (car (extract-code mergedcode4)))
(mapOffset (getMap mergedcode1)))))
(defthm is-suffix-extract-code-is-code
(implies (and (IS-SUFFIX (LIST* MERGEDCODE1 mergedcode4) mergedcode)
(isStackMap mergedcode1)
(pc-wff-mergedcode1 pc mergedcode))
(isInstruction (car (extract-code mergedcode4))))
:rule-classes :forward-chaining))
;----------------------------------------------------------------------
;; (i-am-here) ;; Mon Jan 2 19:49:18 2006
(encapsulate ()
(local (include-book "bcv-collected-frames-are-good-frames"))
(defthm good-frame-searchStackMap
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(member inst mergedcode)
(isInstruction inst)
(all-good-frames (extract-frames mergedcode) env)
(good-frame init-frame env)
(good-env env))
(good-frame (searchstackframe (instrOffset inst)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV mergedcode
INIT-FRAME)))
env)))
(defthm good-frame-searchStackMap-2
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(all-good-frames (extract-frames mergedcode) env)
(member frame mergedcode)
(isStackMap frame)
(wff-mergedcode-instr mergedcode)
(wff-stack-map-offset mergedcode)
(good-frame init-frame env)
(good-env env))
(good-frame (searchstackframe (mapOffset (getMap frame))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV mergedcode
INIT-FRAME)))
env))))
;----------------------------------------------------------------------
(defthm is-suffix-implies-member-code
(implies (and (is-suffix mergedcode1 mergedcode)
(member x mergedcode1))
(member x mergedcode))
:hints (("Goal" :in-theory (disable isInstruction
isStackMap
isEnd))))
(defthm member-extract-code-member
(implies (member x (extract-code mergedcode))
(member x mergedcode))
:rule-classes :forward-chaining)
(defthm forward-to-next-inst-reduce
(implies (isStackMap mergedcode1)
(equal (FORWARD-TO-NEXT-INST (CONS MERGEDCODE1 MERGEDCODE2))
(forward-to-next-inst mergedcode2)))
:hints (("Goal" :in-theory (disable isInstruction
isStackMap)
:expand (FORWARD-TO-NEXT-INST (CONS MERGEDCODE1 MERGEDCODE2)))))
(defthm extract-code-forward-to-next
(implies (wff-merged-code-weak mergedcode)
(equal (EXTRACT-CODE (FORWARD-TO-NEXT-INST MERGEDCODE))
(extract-code mergedcode)))
:hints (("Goal" :in-theory (e/d (forward-to-next-inst)
(isInstruction
isStackMap
isEnd)))))
(encapsulate ()
(local (include-book "bcv-next-inst-is"))
(defthm is-suffix-implies-next-inst-specific
(implies (and (IS-SUFFIX mergedcode (allinstructions env))
(pc-wff-mergedcode1 0 (allinstructions env))
(consp mergedcode)
(consp (cdr mergedcode))
(isInstruction (car mergedcode)))
(equal (next-inst (car mergedcode) (allinstructions env))
(cadr mergedcode)))
:hints (("Goal" :do-not '(generalize)))))
;----------------------------------------------------------------------
(defthm pc-wff-mergedcode1-pc-wff-mergedcode-pc-specific
(implies (and (pc-wff-mergedcode1 0 (allinstructions env))
(consp (allinstructions env))
(not (isEnd (car (allinstructions env)))))
(pc-wff-mergedcode1 (next-pc (allinstructions env))
(allinstructions env)))
:hints (("Goal" :in-theory (disable isInstruction
isStackMap
isEnd))))
(defthm is-suffix-consp-consp
(implies (and (is-suffix mergedcode1 mergedcode)
(consp mergedcode1))
(consp mergedcode))
:rule-classes :forward-chaining)
(defthm is-suffix-not-end-not-end
(implies (and (is-suffix mergedcode1 mergedcode)
(wff-merged-code-weak mergedcode)
(consp mergedcode1)
(not (isEnd (car mergedcode1))))
(not (isEnd (car mergedcode))))
:rule-classes :forward-chaining)
;;(in-theory (disable forward-to-next-inst-reduce ))
(defthm is-suffix-wff-mergecode-weak
(implies (and (is-suffix mergedcode1 mergedcode)
(consp mergedcode1)
(wff-merged-code-weak mergedcode))
(wff-merged-code-weak mergedcode1))
:rule-classes :forward-chaining)
;; (defthm pc-wff-mergedcode1-implies-wff-merged-code-instr
;; (implies (pc-wff-mergedcode1 pc mergedcode)
;; (wff-mergedcode-instr mergedcode))
;; :hints (("Goal" :in-theory (disable isInstruction isStackMap
;; isEnd
;; jvm::inst-size)))
;; :rule-classes :forward-chaining)
(defthm is-suffix-wff-merged-code-instr
(implies (and (is-suffix (list* map mergedcode) all-mergedcode)
(isStackMap map)
(wff-mergedcode-instr all-mergedcode)
(wff-merged-code-weak all-mergedcode))
(consp (extract-code mergedcode)))
:rule-classes :forward-chaining)
(in-theory (enable forward-to-next-inst))
(defthm is-suffix-wff-merged-code-instr-wff-merged-code-instr
(implies (and (is-suffix mergedcode1 mergedcode2)
(wff-mergedcode-instr mergedcode2))
(wff-mergedcode-instr mergedcode1))
:rule-classes :forward-chaining)
(defthm is-suffix-wff-merged-code-instr-2
(implies (and (wff-mergedcode-instr mergedcode)
(isStackMap (car mergedcode)))
(isInstruction (car (forward-to-next-inst mergedcode)))))
(include-book "bcv-mergedcodeIsTypesafe")
;;(i-am-here) ;; Mon Jan 2 20:41:32 2006
(defthm mergedcodeIsTypeSafe-implies-bcv-simple-method1-lemma
(implies (and (mergedcodeIsTypesafe env (allinstructions env) init-frame)
(good-frame init-frame env)
(equal (searchStackFrame (next-pc mergedcode)
(stack-map-wrap (collect-sig-frame-vector env
(allinstructions env)
init-frame)))
stackframe)
(mergedcodeIsTypesafe env mergedcode stackframe)
(pc-wff-mergedcode1 0 (allinstructions env))
(is-suffix mergedcode (allinstructions env))
(all-good-frames (extract-frames (allinstructions env)) env)
(good-env env))
(bcv-simple-method1 (extract-code mergedcode)
(collect-sig-frame-vector env
(allinstructions env)
init-frame)
env))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
good-frame
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:induct (mergedcodeistypesafe-induct env init-frame
mergedcode stackframe)
:do-not '(generalize))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
;----------------------------------------------------------------------
;; (local
;; (defthm extract-code-no-change
;; (implies (wff-merged-code-weak mergedcode)
;; (equal (EXTRACT-CODE (FORWARD-TO-NEXT-INST mergedcode))
;; (extract-code mergedcode)))))
;; (local
;; (defthm is-suffix-forward-to-next-inst
;; (IS-SUFFIX (FORWARD-TO-NEXT-INST mergedcode)
;; mergedcode)))
(defthm mergedcodeIsTypeSafe-implies-bcv-simple-method1
(implies (and (mergedcodeIsTypesafe env (allinstructions env) init-frame)
(good-frame init-frame env)
(pc-wff-mergedcode1 0 (allinstructions env))
(all-good-frames (extract-frames (allinstructions env)) env)
(good-env env))
(bcv-simple-method1 (extract-code (allinstructions env))
(collect-sig-frame-vector env
(allinstructions env)
init-frame)
env))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
next-pc
good-frame
mapFrame
mergedcodeIsTypesafe
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:do-not-induct t
:use ((:instance
mergedcodeIsTypeSafe-implies-bcv-simple-method1-lemma
(mergedcode (forward-to-next-inst (allinstructions env)))
(stackframe (searchstackframe
(next-pc (forward-to-next-inst (allinstructions env)))
(stack-map-wrap
(collect-sig-frame-vector
env
(allinstructions env)
init-frame))))))
:do-not '(generalize))))
|
