/usr/share/acl2-4.3/books/unicode/app.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 | ;; Processing Unicode Files with ACL2
;; Copyright (C) 2005-2006 by Jared Davis <jared@cs.utexas.edu>
;;
;; 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., 59 Temple
;; Place - Suite 330, Boston, MA 02111-1307, USA.
(in-package "ACL2")
(include-book "list-fix")
(local (include-book "take"))
(local (include-book "nthcdr"))
(defund binary-app (x y)
(declare (xargs :guard t))
(if (consp x)
(cons (car x)
(binary-app (cdr x) y))
(list-fix y)))
(defmacro app (x y &rest rst)
(xxxjoin 'binary-app (list* x y rst)))
(add-macro-alias app binary-app)
(defthm app-when-not-consp
(implies (not (consp x))
(equal (app x y)
(list-fix y)))
:hints(("Goal" :in-theory (enable app))))
(defthm app-of-cons
(equal (app (cons a x) y)
(cons a (app x y)))
:hints(("Goal" :in-theory (enable app))))
(defthm app-of-list-fix-one
(equal (app (list-fix x) y)
(app x y))
:hints(("Goal" :in-theory (enable app))))
(defthm app-of-list-fix-two
(equal (app x (list-fix y))
(app x y))
:hints(("Goal" :in-theory (enable app))))
(defthm app-of-app
(equal (app (app x y) z)
(app x (app y z)))
:hints(("Goal" :induct (len x))))
(defthm true-listp-of-app
(equal (true-listp (app x y))
t)
:hints(("Goal" :induct (len x))))
(defthm consp-of-app
(equal (consp (app x y))
(or (consp x)
(consp y)))
:hints(("Goal" :induct (len x))))
(defthm app-under-iff
(iff (app x y)
(or (consp x)
(consp y)))
:hints(("Goal" :induct (len x))))
(defthm len-of-app
(equal (len (app x y))
(+ (len x)
(len y)))
:hints(("Goal" :induct (len x))))
(local (include-book "arithmetic/top" :dir :system))
(defthm nth-of-app
(implies (and (integerp n)
(<= 0 n))
(equal (nth n (app x y))
(if (< n (len x))
(nth n x)
(nth (- n (len x)) y))))
:hints(("Goal"
:in-theory (enable nth)
:induct (nth n x))))
(encapsulate
()
(local (defthm lemma
(implies (< n (len x))
(equal (app (simpler-take n x)
(nthcdr n x))
(list-fix x)))
:hints(("Goal" :in-theory (enable simpler-take nthcdr)))))
(local (defthm lemma2
(implies (and (natp n)
(<= (len x) n))
(equal (app (simpler-take n x) (nthcdr n x))
(simpler-take n x)))
:hints(("Goal" :in-theory (enable simpler-take nthcdr)))))
(defthm app-of-take-and-nthcdr
(equal (app (simpler-take n x) (nthcdr n x))
(if (< (nfix n) (len x))
(list-fix x)
(simpler-take n x)))
:hints(("Goal" :in-theory (enable simpler-take nthcdr)))))
(defthm append-to-app
(implies (true-listp y)
(equal (append x y)
(app x y))))
(defthm car-of-app
(equal (car (app a x))
(if (consp a)
(car a)
(car x))))
(defthm simpler-take-of-len-from-app
(equal (simpler-take (len x) (app x y))
(list-fix x))
:hints(("Goal"
:in-theory (enable simpler-take)
:induct (len x))))
(defthm take-of-len-from-app
(equal (take (len x) (app x y))
(list-fix x)))
(defthm nthcdr-of-len-from-app
(equal (nthcdr (len x) (app x y))
(list-fix y))
:hints(("Goal"
:induct (len x))))
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