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
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
|
(in-package "ACL2")
(include-book "bcv-model")
(include-book "bcv-simple-model")
(include-book "generic")
(encapsulate ()
(local (include-book "bcv-find-correct-witness-bcv-check-pre"))
(defthm merge-code-safe-implies-bcv-check-step-pre-lemma
(implies (and (merged-code-safe merged-code sig-frame)
(member inst merged-code)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code)))
(inst? inst)
(equal pc (g 'pc inst)))
(bcv-check-step-pre inst
(cdr (assoc-equal pc
(collect-witness-merged-code-safe
merged-code sig-frame)))))))
(defthm all-next-state-safe-reduction-when-PUSH-POP-INVOKE
(implies (case-split (member (bcv-op-code inst) '(PUSH POP INVOKE)))
(equal (all-next-state-safe
(bcv-simple-execute-step (g 'inst inst) pre)
sig-vector)
(sig-frame-compatible
(car (bcv-simple-execute-step (g 'inst inst) pre))
(cdr (assoc-equal (+ 1 (g 'pc pre))
sig-vector)))))
:hints (("Goal" :in-theory (disable sig-frame-compatible))))
(defthm all-next-state-safe-reduction-when-RETURN-HALT
(implies (case-split (member (bcv-op-code inst) '(RETURN HALT)))
(all-next-state-safe
(bcv-simple-execute-step (g 'inst inst) pre)
sig-vector)))
;----------------------------------------------------------------------
;;
;; This following is useless we want to express the theorem in terms of
;; merged-code instead of ...
;;
;; (encapsulate ()
;; (local (include-book "bcv-find-correct-witness-sig-vector"))
;; (defthm verified-implies-partial-sig-vector-compatible-with-full-vector
;; (implies (and (merged-code-safe (mergeStackMapAndCode maps code
;; method-table)
;; init-frame)
;; (wff-code code)
;; (wff-maps maps)
;; (stack-map? init-frame)
;; (equal (g 'pc init-frame) 0)
;; (equal (g 'method-table init-frame) method-table)
;; (bound? pc (extract-partial-sig-vector maps)))
;; (sig-frame-compatible
;; (cdr (assoc-equal pc (extract-partial-sig-vector
;; (update-maps-with-method-table maps method-table))))
;; (cdr (assoc-equal pc (collect-witness-merged-code-safe
;; (mergeStackMapAndCode maps code method-table)
;; init-frame)))))))
;; (defthm targeIsSafe-on-partial-sig-vector
;; (implies (targetIsSafe pc frame partial-sig-vector)
;; (sig-frame-compatible
;; frame
;; (cdr (assoc-equal pc partial-sig-vector)))))
;; (defthm targeIsSafe-implies-bounded?
;; (implies (targetIsSafe pc frame partial-sig-vector)
;; (assoc-equal pc partial-sig-vector)))
;; (defthm targetIsSafe-implies-bound-f
;; (implies (targetIsSafe pc frame vector)
;; (assoc-equal pc vector))
;; :rule-classes :forward-chaining)
;; (defthm targetIsSafe-implies-bound-specific-f
;; (implies (targetIsSafe pc frame (extract-partial-sig-vector
;; (update-maps-with-method-table maps method-table)))
;; (assoc-equal pc (extract-partial-sig-vector maps)))
;; :rule-classes :forward-chaining)
;; (defthm verified-and-target-is-safe-implies-sig-frame-compatible
;; (implies (and (merged-code-safe (mergeStackMapAndCode maps code method-table)
;; init-frame)
;; (wff-code code)
;; (wff-maps maps)
;; (stack-map? init-frame)
;; (equal (g 'pc init-frame) 0)
;; (equal (g 'method-table init-frame) method-table)
;; (targetIsSafe pc frame (extract-partial-sig-vector
;; (update-maps-with-method-table maps
;; method-table))))
;; (sig-frame-compatible
;; frame
;; (cdr (assoc-equal pc (collect-witness-merged-code-safe
;; (mergeStackMapAndCode maps code method-table)
;; init-frame)))))
;; :hints (("Goal" :in-theory (disable sig-frame-compatible targetIsSafe)
;; :use ((:instance sig-frame-compatible-transitive
;; (frame1 frame)
;; (frame2 (cdr (assoc-equal pc
;; (extract-partial-sig-vector
;; (update-maps-with-method-table maps
;; method-table)))))
;; (frame3 (cdr (assoc-equal pc
;; (collect-witness-merged-code-safe
;; (mergeStackMapAndCode
;; maps code method-table)
;; init-frame))))))
;; :do-not-induct t)))
;; ;; note this is not good enough. We want something expressed in terms of
;; ;; merged-code
(defthm sig-frame-compatible-transitive
(implies (and (sig-frame-compatible frame1 frame2)
(sig-frame-compatible frame2 frame3))
(sig-frame-compatible frame1 frame3)))
(local (in-theory (disable sig-frame-compatible-transitive)))
;
; All this above is for reasoning about targetIsSafe!
; where we demand that a signature state exists at the branch target!!
; we assert this signature state is more specific than the one we see
; at the
;
;----------------------------------------------------------------------
;; the following should be easier!!
;; (i-am-here) ;; Mon Nov 7 17:35:35 2005
;; (i-am-here) ;; Mon Nov 7 19:37:09 2005
;; (i-am-here) ;; Mon Nov 7 21:00:25 2005
;; (i-am-here) ;; Mon Nov 7 21:08:31 2005
(encapsulate ()
(local (include-book "bcv-simple-execute-produce-compatible-next-states"))
(defthm merge-code-safe-implies-sig-frame-compatible
(implies (and (case-split (member (bcv-op-code inst) '(PUSH POP IFEQ INVOKE)))
(merged-code-safe merged-code sig-frame)
(equal (g 'pc sig-frame) 0)
(wff-code (extract-code merged-code))
(member inst (extract-code merged-code))
(equal pc (g 'pc inst)))
(sig-frame-compatible
(car (bcv-simple-execute-step (g 'inst inst)
(cdr (assoc-equal pc
(collect-witness-merged-code-safe merged-code sig-frame)))))
(cdr (assoc-equal (+ 1 pc)
(collect-witness-merged-code-safe
merged-code sig-frame)))))))
;;; Mon Nov 7 19:13:56 2005
;;; note this is not true if inst is HALT or RETURN!!!
;;; Mon Nov 7 19:13:59 2005
(defthm g-pc-collect-witness-pc
(implies (bound? pc (collect-witness-merged-code-safe merged-code
sig-frame))
(equal (g 'pc (cdr (assoc-equal pc
(collect-witness-merged-code-safe
merged-code sig-frame))))
pc)))
;;;
;;; basic facts about collect-witness-merged-code-safe!!
;;; Mon Nov 7 19:58:17 2005
;;;
(defthm all-next-state-safe-bcv-simple-execute-step-if-car-cadr
(implies (and (equal pc (g 'pc pre))
(equal (op-code inst) 'IFEQ)
(equal pre (cdr (assoc-equal pc sig-vector))))
(equal (all-next-state-safe (bcv-simple-execute-step inst pre) sig-vector)
(and (sig-frame-compatible
(car (bcv-simple-execute-step inst
(cdr (assoc-equal pc sig-vector))))
(cdr (assoc-equal (+ 1 pc) sig-vector)))
(sig-frame-compatible
(cadr (bcv-simple-execute-step inst (cdr (assoc-equal
pc sig-vector))))
(cdr (assoc-equal (cadr inst) sig-vector))))))
:hints (("Goal" :in-theory (disable sig-frame-compatible))))
;----------------------------------------------------------------------
;; (encapsulate ()
;; (local (include-book "bcv-partial-signature-vector-full-signature-vector"))
;; (defthm verified-extract-partial-sig-compatible-with-full-sig
;; (implies (merged-code-safe merged-code init-frame)
;; (partial-sig-vector-compatible
;; (extract-partial-sig-vector
;; (extract-maps merged-code))
;; (collect-witness-merged-code-safe merged-code init-frame)))
;; :hints (("Goal" :in-theory (disable sig-frame-compatible)))))
;;; original form!
;; (i-am-here) ;; Thu Nov 10 22:23:17 2005
(encapsulate ()
(local (include-book "bcv-partial-signature-vector-full-signature-vector"))
(defthm verified-extract-partial-sig-compatible-with-full-sig
(implies (and (merged-code-safe merged-code init-frame)
(stack-map? init-frame)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code))))
(partial-sig-vector-compatible
(extract-partial-sig-vector (extract-maps merged-code))
(collect-witness-merged-code-safe merged-code init-frame)))))
(defthm bound-partial-sig-vector-implies-sig-frame-compatible-lemma
(implies (and (bound? pc l)
(partial-sig-vector-compatible1 l partial-sig-vector full))
(sig-frame-compatible
(cdr (assoc-equal pc partial-sig-vector))
(cdr (assoc-equal pc full))))
:hints (("Goal" :in-theory (disable sig-frame-compatible))))
(defthm bound-partial-sig-vector-implies-sig-frame-compatible
(implies (and (bound? pc partial-sig-vector)
(partial-sig-vector-compatible partial-sig-vector full))
(sig-frame-compatible
(cdr (assoc-equal pc partial-sig-vector))
(cdr (assoc-equal pc full))))
:hints (("Goal" :in-theory (disable sig-frame-compatible
partial-sig-vector-compatible1)
:restrict
((bound-partial-sig-vector-implies-sig-frame-compatible-lemma
((l partial-sig-vector)))))))
;; (defthm verified-and-target-is-safe-implies-sig-frame-compatible-general
;; (implies (and (merged-code-safe merged-code init-frame)
;; (targetIsSafe pc frame (extract-partial-sig-vector
;; (extract-maps merged-code))))
;; (sig-frame-compatible
;; frame
;; (cdr (assoc-equal pc (collect-witness-merged-code-safe merged-code
;; init-frame)))))
;; :hints (("Goal" :in-theory (disable sig-frame-compatible targetIsSafe)
;; :use ((:instance sig-frame-compatible-transitive
;; (frame1 frame)
;; (frame2 (cdr (assoc-equal pc
;; (extract-partial-sig-vector
;; (extract-maps merged-code)))))
;; (frame3 (cdr (assoc-equal pc
;; (collect-witness-merged-code-safe
;; merged-code
;; init-frame))))))
;; :do-not-induct t)))
;; >L (DEFUN SIG-FRAME-COMPATIBLE (SFRAME GFRAME)
;; (AND (EQUAL (G 'PC SFRAME) (G 'PC GFRAME))
;; (EQUAL (G 'MAX-STACK SFRAME)
;; (G 'MAX-STACK GFRAME))
;; (EQUAL (G 'METHOD-NAME SFRAME)
;; (G 'METHOD-NAME GFRAME))
;; (EQUAL (G 'METHOD-TABLE SFRAME)
;; (G 'METHOD-TABLE GFRAME))
;; (SIG-OPSTACK-COMPATIBLE SFRAME GFRAME)
;; (SIG-LOCAL-COMPATIBLE (G 'LOCALS SFRAME)
;; (G 'LOCALS GFRAME))))
;; 1 ACL2 >:pe bcv-check-ifeq
;; d 1 (INCLUDE-BOOK "bcv-model")
;; \
;; [Included books, outermost to innermost:
;; "/home/hbl/currentwork/src/small/bcv-model.lisp"
;; ]
;; \
;; >L (DEFUN
;; BCV-CHECK-IFEQ (INST SIG-FRAME)
;; (AND (<= 1 (G 'OP-STACK SIG-FRAME))
;; (TARGETISSAFE
;; (ARG INST)
;; (SIG-FRAME-POP-VALUE SIG-FRAME)
;; (EXTRACT-PARTIAL-SIG-VECTOR
;; (G 'STACKMAPS
;; (BINDING (G 'METHOD-NAME SIG-FRAME)
;; (G 'METHOD-TABLE SIG-FRAME)))))))
;;;;
;;;; identified one error with bcv-check-ifeq.
;;;; we need to advance the pc!!!
;;;;
;; ;; (defun bcv-check-IFEQ (inst sig-frame)
;; ;; (and (<= 1 (g 'op-stack sig-frame))
;; ;; (targetIsSafe
;; ;; (arg inst)
;; ;; (s 'pc (arg inst)
;; ;; (sig-frame-pop-value sig-frame))
;; ;; (extract-partial-sig-vector
;; ;; (g 'stackmaps
;; ;; (binding (g 'method-name sig-frame)
;; ;; (g 'method-table sig-frame)))))))
;; ;; ;; (extract-sig-vector (g 'stackmaps sig-frame)))
;;;;
;;;; This adds a lot ofcomplexity because targetIsSafe is stated with respect to
;;;;
;;;; partial sig vector!!
;;;;
(defthm bcv-check-step-pre-IFEQ-implies-target-is-safe-bcv-extract-sig-vector
(implies (and (bcv-check-step-pre inst sig-frame)
(equal (bcv-op-code inst) 'IFEQ))
(targetIsSafe
(cadr (g 'inst inst))
(cadr (bcv-simple-execute-step (g 'inst inst) sig-frame))
(extract-partial-sig-vector
(update-maps-with-method-table
(g 'stackmaps
(cdr (assoc-equal (g 'method-name sig-frame)
(g 'method-table sig-frame))))
(g 'method-name sig-frame)
(g 'method-table sig-frame))))))
(defthm bcv-check-step-pre-IFEQ-implies-target-is-safe-bcv-extract-sig-vector-specific
(implies (and (bcv-check-step-pre inst sig-frame)
(equal (bcv-op-code inst) 'IFEQ)
(equal (extract-maps merged-code)
(update-maps-with-method-table
(g 'stackmaps
(cdr (assoc-equal (g 'method-name sig-frame)
(g 'method-table sig-frame))))
(g 'method-name sig-frame)
(g 'method-table sig-frame))))
(targetIsSafe
(cadr (g 'inst inst))
(cadr (bcv-simple-execute-step (g 'inst inst) sig-frame))
(extract-partial-sig-vector
(extract-maps merged-code)))))
;; (i-am-here) ;; Thu Nov 10 22:35:54 2005
(encapsulate ()
(local (include-book "bcv-verified-implies-method-name-method-table-fixed"))
(defthm verified-implies-method-table-no-change
(implies (and (merged-code-safe merged-code init-frame)
(wff-maps-consistent (extract-maps merged-code) init-frame)
(stack-map? init-frame)
(bound? pc (collect-witness-merged-code-safe merged-code init-frame)))
(equal (G 'method-table
(CDR (ASSOC-EQUAL pc
(COLLECT-WITNESS-MERGED-CODE-SAFE
MERGED-CODE INIT-FRAME))))
(g 'method-table init-frame))))
(DEFTHM verified-implies-method-name-no-change
(implies (and (merged-code-safe merged-code init-frame)
(wff-maps-consistent (extract-maps merged-code) init-frame)
(stack-map? init-frame)
(bound? pc (collect-witness-merged-code-safe merged-code init-frame)))
(equal (G 'METHOD-NAME
(CDR (ASSOC-EQUAL pc
(COLLECT-WITNESS-MERGED-CODE-SAFE
MERGED-CODE init-FRAME))))
(g 'method-name init-frame)))))
;;;
;;; Fri Nov 11 10:24:23 2005, after adding wff-maps-consistent the above is
;;; provable!!
;;;
(encapsulate ()
(local (include-book "bcv-find-correct-witness-bcv-check-pre"))
(defthm merge-code-safe-implies-bcv-check-step-pre
(implies (and (merged-code-safe merged-code sig-frame)
(equal (g 'pc sig-frame) 0)
(wff-code (extract-code merged-code))
(member inst (extract-code merged-code))
(equal pc (g 'pc inst)))
(bcv-check-step-pre inst
(cdr (assoc-equal pc
(collect-witness-merged-code-safe
merged-code sig-frame)))))))
(defthm not-member-implies-not-merge-code-safe
(implies (and (member inst (extract-code merged-code))
(not (member (bcv-op-code inst) '(RETURN HALT PUSH POP INVOKE IFEQ))))
(not (MERGED-CODE-SAFE MERGED-CODE SIG-FRAME))))
(defthm member-inst-extract-code-implies-bound-pc
(implies (and (merged-code-safe merged-code sig-frame)
(member inst (extract-code merged-code)))
(ASSOC-EQUAL (G 'PC INST)
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME))))
;; (ASSOC-EQUAL (CAR (CDR (G 'INST INST)))
;; (EXTRACT-PARTIAL-SIG-VECTOR (EXTRACT-MAPS MERGED-CODE))).
;; (defthm targeIsSafe-implies-bound
;; (implies (targetIsSafe pc frame sig-vector)
;; (assoc-equal pc sig-vector)))
;; (defthm targeIsSafe-implies-bound-specific
;; (implies (targetIsSafe pc frame (EXTRACT-PARTIAL-SIG-VECTOR
;; (update-maps-with-method-table maps method-table)))
;; (assoc-equal pc (extract-partial-sig-vector maps))))
(defthm assoc-equal-extract-partial-sig-vector
(implies (assoc-equal pc (extract-partial-sig-vector
(update-maps-with-method-table maps method-name method-table)))
(assoc-equal pc (extract-partial-sig-vector maps)))
:rule-classes :forward-chaining)
(defthm bcv-check-step-pre-IFEQ-implies-lemma
(implies (and (equal (op-code (g 'inst inst)) 'IFEQ)
(bcv-check-step-pre inst sig-frame)
(equal (extract-maps merged-code)
(update-maps-with-method-table
(g 'stackmaps
(cdr (assoc-equal (g 'method-name sig-frame)
(g 'method-table sig-frame))))
(g 'method-name sig-frame)
(g 'method-table sig-frame))))
(assoc-equal (cadr (g 'inst inst))
(extract-partial-sig-vector
(extract-maps merged-code))))
:hints (("Goal" :in-theory (e/d (bcv-check-step-pre)
(stack-map? inst?))
:do-not-induct t)))
;; (defthm bcv-check-step-pre-IFEQ-implies-lemma
;; (implies (and (equal (op-code (g 'inst inst)) 'IFEQ)
;; (bcv-check-step-pre inst sig-frame)
;; (equal (extract-maps merged-code)
;; (update-maps-with-method-table
;; (g 'stackmaps
;; (cdr (assoc-equal (g 'method-name sig-frame)
;; (g 'method-table sig-frame))))
;; (g 'method-table sig-frame))))
;; (assoc-equal (cadr (g 'inst inst))
;; (extract-partial-sig-vector
;; (extract-maps merged-code))))
;; :hints (("Goal" :in-theory (e/d (bcv-check-step-pre)
;; (stack-map? inst?))
;; :do-not-induct t)))
(defthm update-maps-with-method-table-produces-consistent-maps
(wff-maps-consistent
(update-maps-with-method-table maps
(g 'method-name sig-frame)
(g 'method-table sig-frame))
sig-frame))
(defthm merge-code-safe-implies-bcv-check-step-pre-specific-lemma
(implies (and (merged-code-safe merged-code sig-frame)
(equal (g 'pc sig-frame) 0)
(stack-map? sig-frame)
(wff-code (extract-code merged-code))
(wff-maps-consistent (extract-maps merged-code) sig-frame)
(equal (extract-maps merged-code)
(update-maps-with-method-table
(g 'stackmaps
(cdr (assoc-equal (g 'method-name sig-frame)
(g 'method-table sig-frame))))
(g 'method-name sig-frame)
(g 'method-table sig-frame)))
(member inst (extract-code merged-code))
(equal pc (g 'pc inst))
(equal (op-code (g 'inst inst)) 'IFEQ))
(SIG-FRAME-COMPATIBLE
(S
'PC
(CADR (G 'INST INST))
(SIG-FRAME-POP-VALUE
(CDR (ASSOC-EQUAL
(G 'PC INST)
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)))))
(CDR (ASSOC-EQUAL (CADR (G 'INST INST))
(extract-partial-sig-vector (extract-maps merged-code))))))
:hints (("Goal" :in-theory (disable merged-code-safe wff-code
MERGE-CODE-SAFE-IMPLIES-BCV-CHECK-STEP-PRE
sig-frame-compatible
inst? stack-map?
sig-frame-pop-value
wff-code extract-partial-sig-vector)
:use ((:instance merge-code-safe-implies-bcv-check-step-pre))
:do-not-induct t)))
(defthm merge-code-safe-implies-bcv-check-step-pre-specific
(implies (and (merged-code-safe merged-code sig-frame)
(equal (g 'pc sig-frame) 0)
(stack-map? sig-frame)
(wff-code (extract-code merged-code))
(equal (extract-maps merged-code)
(update-maps-with-method-table
(g 'stackmaps
(cdr (assoc-equal (g 'method-name sig-frame)
(g 'method-table sig-frame))))
(g 'method-name sig-frame)
(g 'method-table sig-frame)))
(member inst (extract-code merged-code))
(equal pc (g 'pc inst))
(equal (op-code (g 'inst inst)) 'IFEQ))
(SIG-FRAME-COMPATIBLE
(S
'PC
(CADR (G 'INST INST))
(SIG-FRAME-POP-VALUE
(CDR (ASSOC-EQUAL
(G 'PC INST)
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)))))
(CDR (ASSOC-EQUAL (CADR (G 'INST INST))
(extract-partial-sig-vector (extract-maps
merged-code))))))
:hints (("Goal" :in-theory (disable merged-code-safe wff-code
MERGE-CODE-SAFE-IMPLIES-BCV-CHECK-STEP-PRE
sig-frame-compatible
inst? stack-map?
sig-frame-pop-value
wff-code extract-partial-sig-vector)
:cases ((wff-maps-consistent (extract-maps merged-code) sig-frame)))))
(encapsulate ()
(local (include-book "bcv-find-correct-witness-sig-vector-1"))
(defthm merged-code-safe-implies-merged-code-pc-is-pc
(implies (and (merged-code-safe merged-code init-frame)
(stack-map? init-frame))
(equal (g 'pc (car merged-code))
(g 'pc init-frame)))))
(defthm |IFEQ-other-branch-ok-lemma|
(IMPLIES
(AND (EQUAL (CAR (g 'inst INST)) 'IFEQ)
(MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)
(wff-maps-consistent (extract-maps merged-code) sig-frame)
(EQUAL (EXTRACT-MAPS MERGED-CODE)
(UPDATE-MAPS-WITH-METHOD-TABLE
(G 'STACKMAPS
(CDR (ASSOC-EQUAL (G 'METHOD-NAME SIG-FRAME)
(G 'METHOD-TABLE SIG-FRAME))))
(g 'method-name sig-frame)
(G 'METHOD-TABLE SIG-FRAME)))
(EQUAL (G 'PC SIG-FRAME) 0)
(stack-map? sig-frame)
(wff-maps (extract-maps merged-code))
(CONSP (EXTRACT-CODE MERGED-CODE))
(WFF-CODE1 (EXTRACT-CODE MERGED-CODE) 0)
(WFF-MAPS (EXTRACT-MAPS MERGED-CODE))
(MEMBER INST (EXTRACT-CODE MERGED-CODE))
(INST? INST))
(SIG-FRAME-COMPATIBLE
(CADR
(BCV-SIMPLE-EXECUTE-STEP
(g 'inst INST)
(CDR (ASSOC-EQUAL
(G 'PC INST)
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)))))
(CDR
(ASSOC-EQUAL (CADR (g 'inst INST))
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)))))
:hints (("Goal" :in-theory (e/d (bcv-simple-execute-step)
(inst? extract-code
targetIsSafe
partial-sig-vector-compatible
bcv-check-step-pre-IFEQ-implies-lemma
sig-frame-compatible-transitive
sig-frame-pop-value
sig-frame-compatible))
:use ((:instance sig-frame-compatible-transitive
(frame1
(S
'PC
(CADR (G 'INST INST))
(SIG-FRAME-POP-VALUE
(CDR (ASSOC-EQUAL
(G 'PC INST)
(COLLECT-WITNESS-MERGED-CODE-SAFE
MERGED-CODE SIG-FRAME))))))
(frame2
(CDR (ASSOC-EQUAL (CADR (G 'INST INST))
(extract-partial-sig-vector
(extract-maps merged-code)))))
(frame3
(CDR
(ASSOC-EQUAL (CADR (g 'inst INST))
(COLLECT-WITNESS-MERGED-CODE-SAFE
MERGED-CODE SIG-FRAME)))))
(:instance bcv-check-step-pre-IFEQ-implies-lemma
(sig-frame
(cdr (assoc-equal (g 'pc inst)
(collect-witness-merged-code-safe
merged-code sig-frame))))))
:do-not '(generalize fertilize)
:do-not-induct t)))
(defthm |IFEQ-other-branch-ok|
(IMPLIES
(AND (EQUAL (CAR (g 'inst INST)) 'IFEQ)
(MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)
(EQUAL (EXTRACT-MAPS MERGED-CODE)
(UPDATE-MAPS-WITH-METHOD-TABLE
(G 'STACKMAPS
(CDR (ASSOC-EQUAL (G 'METHOD-NAME SIG-FRAME)
(G 'METHOD-TABLE SIG-FRAME))))
(g 'method-name sig-frame)
(G 'METHOD-TABLE SIG-FRAME)))
(EQUAL (G 'PC SIG-FRAME) 0)
(stack-map? sig-frame)
(wff-maps (extract-maps merged-code))
(CONSP (EXTRACT-CODE MERGED-CODE))
(WFF-CODE1 (EXTRACT-CODE MERGED-CODE) 0)
(WFF-MAPS (EXTRACT-MAPS MERGED-CODE))
(MEMBER INST (EXTRACT-CODE MERGED-CODE))
(INST? INST))
(SIG-FRAME-COMPATIBLE
(CADR
(BCV-SIMPLE-EXECUTE-STEP
(g 'inst INST)
(CDR (ASSOC-EQUAL
(G 'PC INST)
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)))))
(CDR
(ASSOC-EQUAL (CADR (g 'inst INST))
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE SIG-FRAME)))))
:hints (("Goal" :cases ((wff-maps-consistent (extract-maps merged-code)
sig-frame))
:in-theory (e/d ()
(inst? extract-code
bcv-simple-execute-step
targetIsSafe
partial-sig-vector-compatible
bcv-check-step-pre-IFEQ-implies-lemma
sig-frame-compatible-transitive
sig-frame-pop-value
sig-frame-compatible)))))
(defthm merged-code-safe-implies-all-next-state-safe
(implies (and (merged-code-safe merged-code sig-frame)
(equal (extract-maps merged-code)
(update-maps-with-method-table
(g 'stackmaps
(cdr (assoc-equal (g 'method-name sig-frame)
(g 'method-table sig-frame))))
(g 'method-name sig-frame)
(g 'method-table sig-frame)))
(equal (g 'pc sig-frame) 0)
(stack-map? sig-frame)
(wff-code (extract-code merged-code))
(wff-maps (extract-maps merged-code))
(member inst (extract-code merged-code))
(inst? inst)
(equal pre (binding (g 'pc inst) (collect-witness-merged-code-safe
merged-code sig-frame))))
(all-next-state-safe
(bcv-simple-execute-step (g 'inst inst) pre)
(collect-witness-merged-code-safe merged-code sig-frame)))
:hints (("Goal" :cases (
(member (bcv-op-code inst) '(RETURN HALT))
(member (bcv-op-code inst) '(PUSH POP INVOKE))
(equal (bcv-op-code inst) 'IFEQ))
:in-theory (disable sig-frame-compatible
bcv-check-step-pre
inst? stack-map?
bcv-execute-step
bcv-simple-execute-step)
:do-not '(generalize fertilize)
:do-not-induct t)))
|
