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
|
; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "skeletonp")
(%interactive)
(encapsulate
()
(%autoadmit build.stepwise-modus-ponens-2)
(%autoprove true-listp-of-build.stepwise-modus-ponens-2
(%autoinduct build.stepwise-modus-ponens-2)
(%restrict default build.stepwise-modus-ponens-2 (equal x 'x)))
(%autoprove forcing-logic.appeal-list-of-build.stepwise-modus-ponens-2
(%autoinduct build.stepwise-modus-ponens-2)
(%restrict default build.stepwise-modus-ponens-2 (equal x 'x)))
(%autoprove forcing-logic.strip-conclusions-of-build.stepwise-modus-ponens-2
(%autoinduct build.stepwise-modus-ponens-2)
(%restrict default build.stepwise-modus-ponens-2 (equal x 'x)))
(%autoprove forcing-logic.proof-list-of-build.stepwise-modus-ponens-2
(%autoinduct build.stepwise-modus-ponens-2)
(%restrict default build.stepwise-modus-ponens-2 (equal x 'x))))
(encapsulate
()
(%autoadmit tactic.induct-basis-clause)
(%autoprove forcing-logic.term-listp-of-tactic.induct-basis-clause
(%enable default tactic.induct-basis-clause))
(%autoprove consp-of-tactic.induct-basis-clause
(%enable default tactic.induct-basis-clause)))
(encapsulate
()
(%autoadmit tactic.compile-induct-basis-clause)
(local (%enable default
logic.term-formula
tactic.induct-basis-clause
tactic.compile-induct-basis-clause))
(%autoprove forcing-logic.appealp-of-tactic.compile-induct-basis-clause)
(%autoprove forcing-logic.conclusion-of-tactic.compile-induct-basis-clause)
(%autoprove forcing-logic.proofp-of-tactic.compile-induct-basis-clause))
(defthmd lemma-for-tactic.compile-induct-inductive-clauses
;; BOZO unlocalize/rename in tactics/induct
(implies (equal (logic.strip-conclusions proofs)
(logic.negate-formulas x))
(equal (len proofs)
(len x)))
:hints(("Goal"
:in-theory (disable len-of-logic.negate-formulas
len-of-logic.strip-conclusions)
:use ((:instance len-of-logic.negate-formulas)
(:instance len-of-logic.strip-conclusions (x proofs))))))
(encapsulate
()
(%autoadmit tactic.induct-inductive-clauses)
(%autoadmit tactic.compile-induct-inductive-clauses)
(local (%enable default
tactic.induct-inductive-clauses
tactic.compile-induct-inductive-clauses))
(%autoprove forcing-logic.term-list-listp-of-tactic.induct-inductive-clauses)
(%autoprove cons-listp-of-tactic.induct-inductive-clauses)
(%autoprove true-listp-of-tactic.induct-inductive-clauses)
(%autoprove lemma-for-tactic.compile-induct-inductive-clauses
(%disable default
len-of-logic.negate-formulas
[outside]len-of-logic.negate-formulas
len-of-logic.strip-conclusions
[outside]len-of-logic.strip-conclusions)
(%use (%instance (%thm len-of-logic.negate-formulas)))
(%use (%instance (%thm len-of-logic.strip-conclusions) (x proofs))))
(local (%enable default lemma-for-tactic.compile-induct-inductive-clauses))
(%autoprove forcing-logic.appeal-listp-of-tactic.compile-induct-inductive-clauses)
(%autoprove forcing-logic.strip-conclusions-of-tactic.compile-induct-inductive-clauses)
(%autoprove forcing-logic.proof-listp-of-tactic.compile-induct-inductive-clauses))
(encapsulate
()
(%autoadmit tactic.induct-ordinal-clause)
(%autoadmit tactic.compile-induct-ordinal-clause)
(local (%enable default
logic.term-formula
tactic.induct-ordinal-clause
tactic.compile-induct-ordinal-clause))
(%autoprove forcing-logic.term-listp-of-tactic.induct-ordinal-clause)
(%autoprove consp-of-tactic.induct-ordinal-clause)
(%autoprove forcing-logic.appealp-of-tactic.compile-induct-ordinal-clause)
(%autoprove forcing-logic.conclusion-of-tactic.compile-induct-ordinal-clause)
(%autoprove forcing-logic.proofp-of-tactic.compile-induct-ordinal-clause))
(encapsulate
()
(%autoadmit tactic.induct-measure-clauses)
(%autoadmit tactic.compile-induct-measure-clauses)
(local (%enable default
tactic.induct-measure-clauses
tactic.compile-induct-measure-clauses))
(%autoprove forcing-logic.term-list-listp-of-tactic.induct-measure-clauses)
(%autoprove cons-listp-of-tactic.induct-measure-clauses)
(%autoprove true-listp-of-tactic.induct-measure-clauses)
(local (%enable default lemma-for-tactic.compile-induct-inductive-clauses)) ;; ugly, but it's the same lemma.
(%autoprove true-listp-of-tactic.compile-induct-measure-clauses)
(%autoprove forcing-logic.appeal-list-of-tactic.compile-induct-measure-clauses)
(%autoprove forcing-logic.strip-conclusions-of-tactic.compile-induct-measure-clauses)
(%autoprove forcing-logic.proof-listp-of-tactic.compile-induct-measure-clauses))
(%autoadmit tactic.induct-okp)
(%autoprove booleanp-of-tactic.induct-okp
(%enable default tactic.induct-okp))
(%autoadmit tactic.induct-env-okp)
(%autoprove booleanp-of-tactic.induct-env-okp
(%enable default tactic.induct-env-okp))
(%autoadmit tactic.induct-tac)
(%autoprove forcing-tactic.skeletonp-of-tactic.induct-tac
(%enable default tactic.induct-tac))
(%autoprove forcing-tactic.induct-okp-of-tactic.induct-tac
(%enable default tactic.induct-tac tactic.induct-okp))
;; BOZO shouldn't we have an env-okp lemma too??
(encapsulate
()
(%autoadmit tactic.induct-compile-aux)
(local (%enable default tactic.induct-compile-aux))
(%autoprove forcing-logic.appealp-of-tactic.induct-compile-aux)
(%autoprove forcing-logic.conclusion-of-tactic.induct-compile-aux)
(%autoprove forcing-logic.proofp-of-tactic.induct-compile-aux))
;; BOZO all of this stuff has to get unlocalized/renamed.
(defthm crock1-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions proofs)
(LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))
(defthm crock2-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (firstn n proofs))
(LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (firstn n goals)))))
:hints(("Goal"
:in-theory (disable FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
:use ((:instance FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))))
(defthm crock3-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (firstn n (cdr (cdr proofs))))
(LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (firstn n (cdr (cdr goals)))))))
:hints(("Goal"
:in-theory (disable FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
:use ((:instance FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (cdr (cdr goals)))))))))
(defthm crock4-for-tactic.induct-compile
(implies (equal (app a b) x)
(equal (firstn (len a) x)
(list-fix a))))
(defthm crock5-for-tactic.induct-compile
(implies (equal (app a b) x)
(equal (restn (len a) x)
(list-fix b))))
(defthm crock6-for-tactic.induct-compile
(implies (equal (app a (app b c)) x)
(equal (firstn (len b) (restn (len a) x))
(list-fix b))))
(defthm crock7-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.conclusion (car proofs))
(logic.disjoin-formulas (logic.term-list-formulas (car goals))))))
(defthm crock8-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.conclusion (second proofs))
(logic.disjoin-formulas (logic.term-list-formulas (second goals))))))
(defthm crock9-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (consp proofs)
(consp goals))))
(defthm crock10-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (consp (cdr proofs))
(consp (cdr goals)))))
(defthm crock11-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (restn n (cdr (cdr proofs))))
(LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (restn n (cdr (cdr goals)))))))
:hints(("Goal"
:in-theory (disable RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
:use ((:instance RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (cdr (cdr goals)))))))))
(defthm crock12-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (firstn n (restn m proofs)))
(LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (firstn n (restn m goals))))))
:hints(("Goal"
:in-theory (disable FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
:use ((:instance FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (restn m goals))))
(:instance RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y m)
(X (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))))
(defthm crock13-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (firstn n (restn m (cdr (cdr proofs)))))
(LOGIC.DISJOIN-EACH-FORMULA-LIST
(LOGIC.TERM-LIST-LIST-FORMULAS (firstn n (restn m (cdr (cdr goals)))))))))
(defthm crock14-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (restn n (restn m proofs)))
(LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS (restn n (restn m goals))))))
:hints(("Goal"
:in-theory (disable RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
:use ((:instance RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (restn m goals))))
(:instance RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
(Y m)
(X (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))))
(defthm crock15-for-tactic.induct-compile
(implies (EQUAL (LOGIC.DISJOIN-EACH-FORMULA-LIST (LOGIC.TERM-LIST-LIST-FORMULAS goals))
(LOGIC.STRIP-CONCLUSIONS PROOFS))
(equal (logic.strip-conclusions (restn n (restn m (cdr (cdr proofs)))))
(LOGIC.DISJOIN-EACH-FORMULA-LIST
(LOGIC.TERM-LIST-LIST-FORMULAS (restn n (restn m (cdr (cdr goals)))))))))
(%autoprove crock1-for-tactic.induct-compile)
(%autoprove crock2-for-tactic.induct-compile
(%disable default
FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
[outside]FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(%use (%instance (%thm FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))
(%autoprove crock3-for-tactic.induct-compile
(%disable default
FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
[outside]FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(%use (%instance (%thm FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (cdr (cdr goals)))))))
(%autoprove crock4-for-tactic.induct-compile)
(%autoprove crock5-for-tactic.induct-compile)
(%autoprove crock6-for-tactic.induct-compile)
(%autoprove crock7-for-tactic.induct-compile)
(%autoprove crock8-for-tactic.induct-compile
(%restrict default logic.strip-conclusions (or (equal x 'proofs)
(equal x '(cdr proofs)))))
(%autoprove crock9-for-tactic.induct-compile)
(%autoprove crock10-for-tactic.induct-compile)
(%autoprove crock11-for-tactic.induct-compile
(%disable default
RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
[outside]RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(%use (%instance (%thm RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (cdr (cdr goals)))))))
(%autoprove crock12-for-tactic.induct-compile
(%disable default
FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
[outside]FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
[outside]RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
;; causing rewrite loop??
crock1-for-tactic.induct-compile
)
(%use (%instance (%thm FIRSTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (restn m goals)))))
(%use (%instance (%thm RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y m)
(X (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))
(%autoprove crock13-for-tactic.induct-compile)
(%autoprove crock14-for-tactic.induct-compile
(%disable default
RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
[outside]RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST
;; loop again??
crock1-for-tactic.induct-compile)
(%use (%instance (%thm RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y n)
(X (LOGIC.TERM-LIST-LIST-FORMULAS (restn m goals)))))
(%use (%instance (%thm RESTN-OF-LOGIC.DISJOIN-EACH-FORMULA-LIST)
(Y m)
(X (LOGIC.TERM-LIST-LIST-FORMULAS goals)))))
(%autoprove crock15-for-tactic.induct-compile
(%disable default
expensive-arithmetic-rules
expensive-term/formula-inference))
(in-theory (disable
CROCK1-FOR-TACTIC.INDUCT-COMPILE
CROCK2-FOR-TACTIC.INDUCT-COMPILE
CROCK3-FOR-TACTIC.INDUCT-COMPILE
CROCK4-FOR-TACTIC.INDUCT-COMPILE
CROCK5-FOR-TACTIC.INDUCT-COMPILE
CROCK6-FOR-TACTIC.INDUCT-COMPILE
CROCK7-FOR-TACTIC.INDUCT-COMPILE
CROCK8-FOR-TACTIC.INDUCT-COMPILE
CROCK9-FOR-TACTIC.INDUCT-COMPILE
CROCK10-FOR-TACTIC.INDUCT-COMPILE
CROCK11-FOR-TACTIC.INDUCT-COMPILE
CROCK12-FOR-TACTIC.INDUCT-COMPILE
CROCK13-FOR-TACTIC.INDUCT-COMPILE
CROCK14-FOR-TACTIC.INDUCT-COMPILE
CROCK15-FOR-TACTIC.INDUCT-COMPILE))
(encapsulate
()
(%autoadmit tactic.induct-compile)
(local (%enable default
tactic.induct-okp
tactic.induct-env-okp
tactic.induct-compile))
(%autoprove forcing-logic.appeal-listp-of-tactic.induct-compile)
(%autoprove forcing-logic.strip-conclusions-of-tactic.induct-compile)
(%autoprove forcing-logic.proof-listp-of-tactic.induct-compile))
(%disable default
CROCK1-FOR-TACTIC.INDUCT-COMPILE
CROCK2-FOR-TACTIC.INDUCT-COMPILE
CROCK3-FOR-TACTIC.INDUCT-COMPILE
CROCK4-FOR-TACTIC.INDUCT-COMPILE
CROCK5-FOR-TACTIC.INDUCT-COMPILE
CROCK6-FOR-TACTIC.INDUCT-COMPILE
CROCK7-FOR-TACTIC.INDUCT-COMPILE
CROCK8-FOR-TACTIC.INDUCT-COMPILE
CROCK9-FOR-TACTIC.INDUCT-COMPILE
CROCK10-FOR-TACTIC.INDUCT-COMPILE
CROCK11-FOR-TACTIC.INDUCT-COMPILE
CROCK12-FOR-TACTIC.INDUCT-COMPILE
CROCK13-FOR-TACTIC.INDUCT-COMPILE
CROCK14-FOR-TACTIC.INDUCT-COMPILE
CROCK15-FOR-TACTIC.INDUCT-COMPILE)
(%ensure-exactly-these-rules-are-missing "../../tactics/induct")
|
