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
|
(in-package "PROOF-CHECKER-ARRAY")
;; ===================================================================
;; ========================== TERNARY LOGIC ==========================
(defun truep (x)
(declare (xargs :guard t))
(equal x t))
(defun falsep (x)
(declare (xargs :guard t))
(equal x nil))
(defun undefp (x)
(declare (xargs :guard t))
(equal x 0))
(defun true ()
(declare (xargs :guard t))
t)
(defun false ()
(declare (xargs :guard t))
nil)
(defun undef ()
(declare (xargs :guard t))
0)
(defthm truep-true
(truep (true)))
(defthm falsep-false
(falsep (false)))
(defthm undefp-undef
(undefp (undef)))
(defthm truep-implies-not-falsep
(implies (truep x)
(not (falsep x))))
(defthm truep-implies-not-undefp
(implies (truep x)
(not (undefp x))))
(defthm falsep-implies-not-truep
(implies (falsep x)
(not (truep x))))
(defthm falsep-implies-not-undefp
(implies (falsep x)
(not (undefp x))))
(defthm undefp-implies-not-falsep
(implies (undefp x)
(not (falsep x))))
(defthm undefp-implies-not-truep
(implies (undefp x)
(not (truep x))))
(in-theory (disable truep
falsep
undefp
true
false
undef
(:executable-counterpart truep)
(:executable-counterpart falsep)
(:executable-counterpart undefp)
(:executable-counterpart true)
(:executable-counterpart false)
(:executable-counterpart undef)
(:type-prescription truep)
(:type-prescription falsep)
(:type-prescription undefp)
(:type-prescription true)
(:type-prescription false)
(:type-prescription undef)))
;; ===================================================================
;; ============================= TERNARY =============================
(defun ternaryp (x)
(declare (xargs :guard t))
(or (truep x)
(falsep x)
(undefp x)))
(defthm ternaryp-true
(ternaryp (true)))
(defthm ternaryp-false
(ternaryp (false)))
(defthm ternaryp-undef
(ternaryp (undef)))
; These rules may cause problems. Comment them out if there are problems.
(defthm ternaryp-not-true-not-undef
(implies (and (ternaryp x)
(not (truep x))
(not (undefp x)))
(falsep x)))
(defthm ternaryp-not-true-not-false
(implies (and (ternaryp x)
(not (truep x))
(not (falsep x)))
(undefp x)))
(defthm ternaryp-not-false-not-undef
(implies (and (ternaryp x)
(not (falsep x))
(not (undefp x)))
(truep x)))
(in-theory (disable ternaryp))
|
