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
|
; 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 "update-clause-bldr") ;; BOZO needed for rev-disjunction for now, stupid.
(%interactive)
(local (%enable default build.rev-disjunction))
(%autoadmit clause.aux-update-clause-iff-bldr)
(defmacro %clause.aux-update-clause-iff-bldr-induction (todo done t-proofs proof)
`(%induct (rank ,todo)
((not (consp ,todo))
nil)
((and (consp ,todo)
(not (consp (cdr ,todo)))
(not (consp ,done)))
nil)
((and (consp ,todo)
(not (consp (cdr ,todo)))
(consp ,done))
(((,todo (cdr ,todo))
(,done (cons (first (logic.function-args (logic.=lhs (logic.conclusion (car ,t-proofs)))))
,done))
(,t-proofs (cdr ,t-proofs))
(,proof (clause.aux-update-clause-iff-lemma1-bldr ,proof (car ,t-proofs))))))
((and (consp ,todo)
(consp (cdr ,todo))
(not (consp ,done)))
(((,todo (cdr ,todo))
(,done (cons (first (logic.function-args (logic.=lhs (logic.conclusion (car ,t-proofs)))))
,done))
(,t-proofs (cdr ,t-proofs))
(,proof (clause.aux-update-clause-iff-lemma1-bldr (build.commute-or ,proof) (car ,t-proofs))))))
((and (consp ,todo)
(consp (cdr ,todo))
(consp ,done))
(((,todo (cdr ,todo))
(,done (cons (first (logic.function-args (logic.=lhs (logic.conclusion (car ,t-proofs)))))
,done))
(,t-proofs (cdr ,t-proofs))
(,proof (clause.aux-update-clause-iff-lemma2-bldr ,proof (car ,t-proofs))))))))
(%autoprove clause.aux-update-clause-iff-bldr-under-iff
(%clause.aux-update-clause-iff-bldr-induction todo done t-proofs proof)
(%restrict default clause.aux-update-clause-iff-bldr (equal todo 'todo))
(%enable default logic.term-formula))
(defthm lemma-1-for-forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr
;; BOZO unlocalize this
(implies (and (all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions x)))))
(force (and (logic.appeal-listp x)
(logic.all-atomicp (logic.strip-conclusions x))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions x))))))
(equal (consp (cdr (logic.function-args (logic.=lhs (logic.conclusion (car x))))))
(consp x))))
(%autoprove lemma-1-for-forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr
(%forcingp nil))
(defthm lemma-for-forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr
;; BOZO unlocalize this
(implies (and (logic.term-listp todo)
(logic.term-listp done)
(or (consp todo) (consp done))
(logic.appealp proof)
(equal (logic.conclusion proof)
(cond ((and (consp done) (consp todo))
(logic.por (clause.clause-formula done) (clause.clause-formula todo)))
((consp done)
(clause.clause-formula done))
(t
(clause.clause-formula todo))))
(logic.appeal-listp t-proofs)
(logic.all-atomicp (logic.strip-conclusions t-proofs))
(all-equalp ''t (logic.=rhses (logic.strip-conclusions t-proofs)))
(logic.all-functionsp (logic.=lhses (logic.strip-conclusions t-proofs)))
(all-equalp 'iff (logic.strip-function-names (logic.=lhses (logic.strip-conclusions t-proofs))))
(all-equalp 2 (strip-lens (logic.strip-function-args (logic.=lhses (logic.strip-conclusions t-proofs)))))
(equal (strip-seconds (logic.strip-function-args (logic.=lhses (logic.strip-conclusions t-proofs)))) todo))
(and (logic.appealp (clause.aux-update-clause-iff-bldr todo done t-proofs proof))
(equal (logic.conclusion (clause.aux-update-clause-iff-bldr todo done t-proofs proof))
(clause.clause-formula
(app (rev (strip-firsts (logic.strip-function-args (logic.=lhses (logic.strip-conclusions t-proofs)))))
done)))))
;; Gonna need a different theory hint.
:rule-classes nil)
(%autoprove lemma-for-forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr
(%clause.aux-update-clause-iff-bldr-induction todo done t-proofs proof)
(%auto :strategy (cleanup urewrite split))
(%restrict default clause.aux-update-clause-iff-bldr (equal todo 'todo))
(%enable default logic.term-formula)
(%auto :strategy (cleanup urewrite split))
(%forcingp nil)
(%auto) ;; out of steps
(%forcingp t)
(%auto))
(%autoprove forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr))))
(%autoprove forcing-logic.conclusion-of-clause.aux-update-clause-iff-bldr
(%use (%instance (%thm lemma-for-forcing-logic.appealp-of-clause.aux-update-clause-iff-bldr))))
(%autoprove forcing-logic.proofp-of-clause.aux-update-clause-iff-bldr
(%clause.aux-update-clause-iff-bldr-induction todo done t-proofs proof)
(%auto :strategy (cleanup urewrite split))
(%restrict default clause.aux-update-clause-iff-bldr (equal todo 'todo))
(%enable default logic.term-formula)
(%auto :strategy (cleanup urewrite split))
(%forcingp nil)
(%auto)
(%forcingp t)
(%auto))
(defsection clause.update-clause-iff-bldr
(%autoadmit clause.update-clause-iff-bldr)
(local (%enable default
strip-lens-of-rev
clause.update-clause-iff-bldr))
(local (%disable default
rev-of-logic.strip-conclusions
rev-of-logic.=lhses
rev-of-logic.strip-function-args
rev-of-strip-lens))
(%autoprove clause.update-clause-iff-bldr-under-iff)
(%autoprove forcing-logic.appealp-of-clause.update-clause-iff-bldr)
(%autoprove forcing-logic.conclusion-of-clause.update-clause-iff-bldr)
(%autoprove forcing-logic.proofp-of-clause.update-clause-iff-bldr))
(defsection clause.update-clause-iff-bldr-okp
(%autoadmit clause.update-clause-iff-bldr-okp)
(%autoprove booleanp-of-clause.update-clause-iff-bldr-okp
(%enable default clause.update-clause-iff-bldr-okp))
(%autoprove clause.update-clause-iff-bldr-okp-of-logic.appeal-identity
(%enable default clause.update-clause-iff-bldr-okp))
(local (%enable default backtracking-logic.formula-atblp-rules))
(local (%disable default
forcing-logic.formula-atblp-rules
forcing-lookup-of-logic.function-name-free))
(%autoprove lemma-1-for-soundness-of-clause.update-clause-iff-bldr-okp
(%enable default clause.update-clause-iff-bldr-okp))
(%autoprove lemma-2-for-soundness-of-clause.update-clause-iff-bldr-okp
(%enable default clause.update-clause-iff-bldr-okp))
(%autoprove forcing-soundness-of-clause.update-clause-iff-bldr-okp
(%enable default
lemma-1-for-soundness-of-clause.update-clause-iff-bldr-okp
lemma-2-for-soundness-of-clause.update-clause-iff-bldr-okp
clause.update-clause-iff-bldr-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (clause.update-clause-iff-bldr
(strip-seconds
(logic.strip-function-args
(logic.=lhses
(logic.strip-conclusions
(logic.provable-list-witness (logic.strip-conclusions (cdr (logic.subproofs x)))
axioms thms atbl)))))
(logic.provable-witness (logic.conclusion (car (logic.subproofs x))) axioms thms atbl)
(logic.provable-list-witness (logic.strip-conclusions (cdr (logic.subproofs x)))
axioms thms atbl)))))))
|
