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
|
; $Id: lnf.scm,v 1.9 2008/01/25 13:30:10 logik Exp $
; (proceed thm1 ...) searches for a proof of the goal from the present
; hypotheses plus the optionally provided theorems, as long as this can
; be done uniquely, i.e. only one of all the given facts is applicable
; (tested with match). If there is a choice, proceed stops.
; Notice that proceed may well lead into dead ends: the allegedly
; unique way to preceed may have a better alternative by using a
; not explicitely listed theorem or global assumption.
; Notice also that proceed may create infinite loops, e.g. for
; (A -> A) -> A.
(define (proceed . names)
(if
(null? (pproof-state-to-num-goals))
(begin (display-comment " Proof finished.")
(if COMMENT-FLAG (newline)))
(let* ((num-goals (pproof-state-to-num-goals))
(proof (pproof-state-to-proof))
(num-goal (car num-goals))
(number (num-goal-to-number num-goal))
(goal (num-goal-to-goal num-goal))
(context (goal-to-context goal))
(sig-vars (context-to-vars context))
(avars (context-to-avars context))
(goal-formula (goal-to-formula goal))
(hypname-info (num-goal-to-hypname-info num-goal))
(indices (hypname-info-to-indices hypname-info))
(labeled-avar-hyps
(do ((l avars (cdr l))
(i 1 (+ 1 i))
(res '() (let* ((avar (car l))
(avar-proof (make-proof-in-avar-form avar))
(info (member i indices))
(string (if info
(index-and-hypname-info-to-name
i hypname-info)
(number-to-string i))))
(cons (list string avar-proof) res))))
((null? l) (reverse res))))
(labeled-hyps
(append
labeled-avar-hyps
(map (lambda (name)
(cond
((not (string? name))
(myerror "proceed: string expected" name))
((string=? "Truth-Axiom" name)
(list name (make-proof-in-aconst-form truth-aconst)))
((assoc name THEOREMS)
(list name (theorem-name-to-proof name)))
((assoc name GLOBAL-ASSUMPTIONS)
(list name (make-proof-in-aconst-form
(global-assumption-name-to-aconst name))))
(else (myerror "proceed: name of theorem or"
"global assumption expected" name))))
names)))
(labels (map car labeled-hyps))
(hyps (map cadr labeled-hyps))
(hyp-formulas (map proof-to-formula hyps))
(sig-tvars-and-sig-vars-list
(map (lambda (labeled-hyp)
(if (assoc (car labeled-hyp)
(append THEOREMS GLOBAL-ASSUMPTIONS))
sig-vars
(append (formula-to-tvars
(proof-to-formula (cadr labeled-hyp)))
sig-vars)))
labeled-hyps))
(match-results
(map (lambda (x y)
(let ((result
(fla-and-sig-tvars-and-vars-and-goal-fla-to-use-data
x y goal-formula)))
(if result
(let ((x-list (car result))
(vars (cadr result)) ;we omit the alist (cddr)
(toinst (cadddr result)))
(list x-list vars toinst))
#f)))
hyp-formulas sig-tvars-and-sig-vars-list))
(labeled-match-results
(map (lambda (x y) (list x y)) labels match-results))
(labeled-hits
(list-transform-positive labeled-match-results
(lambda (x) (pair? (cadr x))))))
(cond
((= 1 (length labeled-hits))
(let* ((labeled-hit (car labeled-hits))
(label (car labeled-hit))
(x-list-and-vars-and-alist-and-toinst (cadr labeled-hit))
(x-list (car x-list-and-vars-and-alist-and-toinst))
(vars (cadr x-list-and-vars-and-alist-and-toinst))
(toinst (caddr x-list-and-vars-and-alist-and-toinst))
(x (cadr (assoc label labeled-hyps)))
(types
(let ((info1 (assoc label THEOREMS))
(info2 (assoc label GLOBAL-ASSUMPTIONS))
(tsubst (list-transform-positive toinst
(lambda (x) (tvar-form? (car x))))))
(if (and (or info1 info2) (pair? tsubst)) ;else '()
(let* ((aconst (if
info1
(theorem-name-to-aconst label)
(global-assumption-name-to-aconst label)))
(fla (aconst-to-formula aconst))
(tvars (formula-to-tvars fla)))
(map (lambda (tvar) (type-substitute tvar tsubst))
tvars))
'()))))
(if ;no terms required
(null? vars)
(begin
(if COMMENT-FLAG (newline))
(display-comment "proceed: (use-with " label " ...)")
(if COMMENT-FLAG (newline))
(apply use-with (cons x (append types x-list)))
(if
(null? (pproof-state-to-num-goals))
*the-non-printing-object*
(let* ((num-goals (pproof-state-to-num-goals))
(num-goal (car num-goals))
(goal (num-goal-to-goal num-goal))
(goal-formula (goal-to-formula goal)))
(if (or (prime-form? goal-formula)
(and-form? goal-formula)
(ex-form? goal-formula))
(apply proceed names)
(begin (if COMMENT-FLAG (newline))
(display-comment "proceed: (strip)")
(if COMMENT-FLAG (newline))
(strip)
(apply proceed names))))))
(begin (if COMMENT-FLAG (newline))
(display-comment
"proceed: terms required for hypothesis " label)
(if COMMENT-FLAG (newline))))))
((= 0 (length labeled-hits))
(if
(and-form? goal-formula)
(begin (if COMMENT-FLAG (newline))
(display-comment "proceed: (split)")
(if COMMENT-FLAG (newline))
(split)
(apply proceed names))
(if (or (prime-form? goal-formula) (ex-form? goal-formula))
(begin (display-comment "no (more) usable hypotheses")
(if COMMENT-FLAG (newline)))
(begin (if COMMENT-FLAG (newline))
(display-comment "proceed: (strip)")
(if COMMENT-FLAG (newline))
(strip) (apply proceed names)))))
(else
(let ((labeled-hits-not-requiring-terms-and-not-creating-goals
(list-transform-positive labeled-hits
(lambda (labeled-hit)
(and (pair? (cadr labeled-hit))
(let* ((x-list-and-vars-and-alist-and-toinst (cadr labeled-hit))
(x-list (car x-list-and-vars-and-alist-and-toinst))
(vars (cadr x-list-and-vars-and-alist-and-toinst)))
(and (null? vars)
(not (member DEFAULT-GOAL-NAME x-list)))))))))
(if
(pair? labeled-hits-not-requiring-terms-and-not-creating-goals)
(let* ((labeled-hit
(car
labeled-hits-not-requiring-terms-and-not-creating-goals))
(label (car labeled-hit))
(x-list-and-vars-and-alist-and-toinst (cadr labeled-hit))
(x-list (car x-list-and-vars-and-alist-and-toinst))
(toinst (caddr x-list-and-vars-and-alist-and-toinst))
(x (cadr (assoc label labeled-hyps)))
(types
(let ((info1 (assoc label THEOREMS))
(info2 (assoc label GLOBAL-ASSUMPTIONS))
(tsubst (list-transform-positive toinst
(lambda (x) (tvar-form? (car x))))))
(if (and (or info1 info2) (pair? tsubst)) ;else '()
(let* ((aconst (if
info1
(theorem-name-to-aconst label)
(global-assumption-name-to-aconst
label)))
(fla (aconst-to-formula aconst))
(tvars (formula-to-tvars fla)))
(map (lambda (tvar) (type-substitute tvar tsubst))
tvars))
'()))))
(if COMMENT-FLAG (newline))
(display-comment "proceed: (use-with " label ")")
(if COMMENT-FLAG (newline))
(apply use-with (cons x (append types x-list)))
(if (null? (pproof-state-to-num-goals))
*the-non-printing-object*
(let* ((num-goals (pproof-state-to-num-goals))
(num-goal (car num-goals))
(goal (num-goal-to-goal num-goal))
(goal-formula (goal-to-formula goal)))
(if (or (prime-form? goal-formula)
(and-form? goal-formula)
(ex-form? goal-formula))
(apply proceed names)
(begin (if COMMENT-FLAG (newline))
(display-comment "proceed: (strip)")
(if COMMENT-FLAG (newline))
(strip)
(apply proceed names))))))
(begin (if COMMENT-FLAG (newline))
(apply display-comment
(cons "proceed: more than one usable hypothesis: "
(map (lambda (x) (string-append (car x) " "))
labeled-hits)))
(if COMMENT-FLAG (newline))))))))))
|
