/usr/share/acl2-6.5/books/regex/defset-encapsulates.lisp is in acl2-books-source 6.5-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | (in-package "ACL2")
(include-book "defset-macros")
(defun true-fun0 (x)
(declare (xargs :guard t)
(ignore x))
t)
(defun true-fun1 (x p)
(declare (xargs :guard t)
(ignore x p))
t)
(encapsulate
(((defset-element-equiv * *) => *))
(local (defun defset-element-equiv (a b)
(declare (xargs :guard t))
(equal a b)))
(defequiv defset-element-equiv))
;; (encapsulate
;; (((equiv * *) => *)
;; ((elemp *) => *)
;; ((elempp * *) => *)
;; ;; ((binary-op * *) => *)
;; )
;; (local (defun elemp (x)
;; (declare (xargs :guard t))
;; (integerp x)))
;; (local (defun elempp (x p)
;; (declare (xargs :guard t))
;; (and (integerp x)
;; (integerp p)
;; (< 0 x)
;; (< p x))))
;; (local (defun equiv (x y)
;; (declare (xargs :guard (and (elemp x) (elemp y))))
;; (= x y)))
;; (local (defun binary-op (x y)
;; (declare (xargs :guard (and (elemp x) (elemp y))))
;; (+ x y)))
;; (defequiv equiv)
;; (defun ensure-guards-ok (x)
;; (declare (xargs :guard (elemp x)))
;; (equiv x x))
;; ;; (defthm binary-op-elemp
;; ;; (implies (and (elemp a) (elemp b))
;; ;; (elemp (binary-op a b))))
;; ;; (defthm binary-op-elempp
;; ;; (implies (and (elempp a p) (elempp b p))
;; ;; (elempp (binary-op a b) p)))
;; (defcong equiv iff (elemp x) 1)
;; (defcong equiv iff (elempp x p) 1))
(defun empty-guard (x)
(declare (xargs :guard t)
(ignore x))
t)
(def-set-equiv defset-element-equiv :use-f-i nil
:equiv-guard empty-guard)
;;(in-theory (disable defset-element-equiv-based-set-theory))
;; (def-set-equiv equal :prove-elem-congruences nil)
;; (defequiv =)
;; (def-set-equiv = :equiv-guard integerp)
(encapsulate
(((deftypedset-element-p0 *) => *)
((deftypedset-element-equiv0 * *) => *))
(local (defun deftypedset-element-p0 (x)
(declare (xargs :guard t)
(ignore x))
t))
(local (defun deftypedset-element-equiv0 (a b)
(declare (xargs :guard t))
(equal a b)))
(defequiv deftypedset-element-equiv0)
(defcong deftypedset-element-equiv0 iff (deftypedset-element-p0 x) 1))
(def-set-equiv deftypedset-element-equiv0)
(def-typed-set deftypedset-element-p0 deftypedset-set-type-0
:equiv deftypedset-element-equiv0 :use-f-i nil)
(encapsulate
(((deftypedset-element-p1 * *) => *)
((deftypedset-element-equiv1 * *) => *))
(local (defun deftypedset-element-p1 (x p)
(declare (xargs :guard t)
(ignore x p))
t))
(local (defun deftypedset-element-equiv1 (a b)
(declare (xargs :guard t))
(equal a b)))
(defequiv deftypedset-element-equiv1)
(defcong deftypedset-element-equiv1 iff (deftypedset-element-p1 x p) 1))
(def-set-equiv deftypedset-element-equiv1)
(def-typed-set deftypedset-element-p1 deftypedset-set-type-1
:equiv deftypedset-element-equiv1 :additional-param t :use-f-i nil)
;; (in-theory (disable deftypedset-element-equiv-based-set-theory ||#
;; deftypedset-set-type-0-typed-set-theory ||#
;; deftypedset-set-type-1-typed-set-theory)) ||#
;; (def-typed-set integerp intset :equiv =)
;; (defun lessp (x p)
;; (declare (xargs :guard t))
;; (and (rationalp x)
;; (rationalp p)
;; (< x p)))
;; (def-typed-set lessp less-than-r-set :additional-param t)
(encapsulate
(((set-union-op-equiv0 * *) => *))
(local (defun set-union-op-equiv0 (x y)
(declare (xargs :guard t))
(equal x y)))
(defequiv set-union-op-equiv0))
(encapsulate
(((set-union-op-f0 *) => *)
((elt-guard0 *) => *)
((bad-input-fn0) => *))
(local (defun set-union-op-f0 (x) (declare (ignore x)) nil))
(local (defun elt-guard0 (x) (declare (ignore x)) t))
(local (defun bad-input-fn0 () nil))
(def-set-equiv set-union-op-equiv0)
(defcong set-union-op-equiv0 set-equiv-set-union-op-equiv0
(set-union-op-f0 x) 1)
(defcong set-union-op-equiv0 iff (elt-guard0 x) 1))
(def-typed-set elt-guard0 guard0-ok :equiv set-union-op-equiv0)
(prove-set-congruence-of-f set-union-op-f0 :use-f-i nil
:equiv set-union-op-equiv0
:elem-guard elt-guard0
:set-guard guard0-okp
:bad-input-fn bad-input-fn0
)
(encapsulate
(((set-union-op-equiv1 * *) => *))
(local (defun set-union-op-equiv1 (x y)
(declare (xargs :guard t))
(equal x y)))
(defequiv set-union-op-equiv1))
(encapsulate
(((set-union-op-f1 * *) => *)
((elt-guard1 * *) => *)
((bad-input-fn1) => *))
(local (defun set-union-op-f1 (x p)
(declare (ignore x p))
nil))
(local (defun elt-guard1 (x p) (declare (ignore x p)) t))
(local (defun bad-input-fn1 () nil))
(def-set-equiv set-union-op-equiv1)
(defcong set-union-op-equiv1 set-equiv-set-union-op-equiv1
(set-union-op-f1 x p) 1)
(defcong set-union-op-equiv1 iff (elt-guard1 x p) 1))
(def-typed-set elt-guard1 guard1-ok :equiv set-union-op-equiv1
:additional-param t)
(prove-set-congruence-of-f set-union-op-f1
:use-f-i nil
:additional-param t
:equiv set-union-op-equiv1
:elem-guard elt-guard1
:set-guard guard1-okp
:bad-input-fn bad-input-fn1)
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