/usr/share/acl2-4.3/books/str/eqv.lisp is in acl2-books-source 4.3-3.
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 | ; ACL2 String Library
; Copyright (C) 2009-2010 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version. This program is distributed in the hope that it will be useful but
; WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
; FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
; more details. You should have received a copy of the GNU General Public
; License along with this program; if not, write to the Free Software
; Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "STR")
(include-book "doc")
(local (include-book "arithmetic"))
(local (include-book "char-support"))
(in-theory (disable char<))
(defund char-fix (x)
(declare (type character x))
(mbe :logic (if (characterp x)
x
(code-char 0))
:exec x))
(defthm char-fix-when-characterp
(implies (characterp x)
(equal (char-fix x)
x))
:hints(("Goal" :in-theory (enable char-fix))))
(defthm equal-of-char-codes
(equal (equal (char-code x) (char-code y))
(equal (char-fix x)
(char-fix y)))
:hints(("Goal" :in-theory (enable char-fix))))
(defund chareqv (x y)
":Doc-Section Str
Case-sensitive character equivalence test~/
~c[(chareqv x y)] determines if x and y are equivalent when interpreted as characters.
That is, non-characters are first coerced to be the zero-character, then we ask whether
the results are equal.~/
~l[str::ichareqv] and ~pl[str::charlisteqv]"
(declare (type character x)
(type character y))
(mbe :logic (equal (char-fix x) (char-fix y))
:exec (eql x y)))
(defequiv chareqv
:hints(("Goal" :in-theory (enable chareqv))))
(defthm chareqv-of-char-fix
(chareqv (char-fix x)
x)
:hints(("Goal" :in-theory (enable chareqv))))
(defcong chareqv equal (char-fix x) 1
:hints(("Goal" :in-theory (enable chareqv))))
(defcong chareqv equal (char-code x) 1
:hints(("Goal" :in-theory (enable chareqv char-fix))))
(defcong chareqv equal (char< x y) 1
:hints(("Goal" :in-theory (enable chareqv char-fix char<))))
(defcong chareqv equal (char< x y) 2
:hints(("Goal" :in-theory (enable chareqv char-fix char<))))
(defthm char<-irreflexive
(equal (char< x x)
nil)
:hints(("Goal" :in-theory (enable char<))))
(defthm char<-antisymmetric
(implies (char< x y)
(not (char< y x)))
:hints(("Goal" :in-theory (enable char<))))
(defthm char<-transitive
(implies (and (char< x y)
(char< y x))
(char< x z))
:hints(("Goal" :in-theory (enable char<))))
(defthm char<-trichotomy-weak
(implies (and (not (char< x y))
(not (char< y x)))
(equal (chareqv x y)
t))
:hints(("Goal" :in-theory (enable char< chareqv char-fix))))
(defthm char<-trichotomy-strong
(equal (char< x y)
(and (not (chareqv x y))
(not (char< y x))))
:rule-classes ((:rewrite :loop-stopper ((x y)))))
(defund charlisteqv (x y)
":Doc-Section Str
Case-sensitive character-list equivalence test~/
~c[(charlisteqv x y)] determines if x and y are equivalent when interpreted as character
lists. That is, ~c[x] and ~c[y] must have the same length, and their elements must be
~il[str::chareqv] to one another.~/
~l[str::icharlisteqv]"
(declare (xargs :guard (and (character-listp x)
(character-listp y))))
(if (consp x)
(and (consp y)
(chareqv (car x) (car y))
(charlisteqv (cdr x) (cdr y)))
(atom y)))
(defequiv charlisteqv
:hints(("Goal" :in-theory (enable charlisteqv))))
(defcong charlisteqv chareqv (car x) 1
:hints(("Goal" :in-theory (enable charlisteqv))))
(defcong charlisteqv charlisteqv (cdr x) 1
:hints(("Goal" :in-theory (enable charlisteqv))))
(defcong charlisteqv equal (len x) 1
:hints(("Goal" :in-theory (enable charlisteqv))))
(defcong charlisteqv chareqv (nth n x) 2
:hints(("Goal" :in-theory (enable charlisteqv))))
(defcong charlisteqv charlisteqv (nthcdr n x) 2
:hints(("Goal" :in-theory (enable charlisteqv))))
(defthm charlisteqv-when-not-consp-left
(implies (not (consp x))
(equal (charlisteqv x y)
(atom y)))
:hints(("Goal" :in-theory (enable charlisteqv))))
(defthm charlisteqv-when-not-consp-right
(implies (not (consp y))
(equal (charlisteqv x y)
(atom x)))
:hints(("Goal" :in-theory (enable charlisteqv))))
(defthm charlisteqv-of-cons-right
(equal (charlisteqv x (cons a y))
(and (consp x)
(chareqv (car x) (double-rewrite a))
(charlisteqv (cdr x) (double-rewrite y))))
:hints(("Goal" :in-theory (enable charlisteqv))))
(defthm charlisteqv-of-cons-left
(equal (charlisteqv (cons a x) y)
(and (consp y)
(chareqv (double-rewrite a) (car y))
(charlisteqv (double-rewrite x) (cdr y))))
:hints(("Goal" :in-theory (enable charlisteqv))))
(defthm charlisteqv-when-not-same-lens
(implies (not (equal (len x) (len y)))
(not (charlisteqv x y)))
:hints(("Goal" :in-theory (enable charlisteqv))))
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