/usr/share/acl2-4.3/books/unicode/revappend.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 | ;; 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")
(set-verify-guards-eagerness 2)
(local (include-book "arithmetic/top" :dir :system))
(local (defthm len-when-consp
(implies (consp x)
(< 0 (len x)))
:rule-classes ((:linear) (:rewrite))))
(defthm true-listp-of-revappend
(equal (true-listp (revappend x y))
(true-listp y)))
(defthm consp-of-revappend
(equal (consp (revappend x y))
(or (consp x)
(consp y))))
(defthm len-of-revappend
(equal (len (revappend x y))
(+ (len x)
(len y))))
(defthm nth-of-revappend
(equal (nth n (revappend x y))
(if (<= (len x) (nfix n))
(nth (- (nfix n) (len x))
y)
(nth (+ (1- (len x)) (- (nfix n)))
x))))
(defthm equal-when-revappend-same
(equal (equal (revappend x y1)
(revappend x y2))
(equal y1 y2)))
(local (defthm revappend-last-is-car
(implies (consp x)
(equal (nth (1- (len x))
(revappend x y))
(car x)))))
(local (defthm revappend-lengths-x
(implies (not (equal (len x1) (len x2)))
(not (equal (revappend x1 y)
(revappend x2 y))))
:hints(("Goal" :use ((:instance len (x (revappend x1 y)))
(:instance len (x (revappend x2 y))))))))
(local (defthm revappend-equal-x-cdrs-lemma
(implies (and (true-listp x1) (consp x1)
(true-listp x2) (consp x2)
(not (equal x1 x2))
(equal (cdr x1) (cdr x2)))
(not (equal (revappend x1 y)
(revappend x2 y))))))
(local (defthm revappend-equal-x-cars-lemma
(implies (and (true-listp x1) (consp x1)
(true-listp x2) (consp x2)
(not (equal (car x1) (car x2))))
(not (equal (revappend x1 y)
(revappend x2 y))))
:hints(("Goal"
:in-theory (disable revappend-lengths-x
revappend-last-is-car)
:use ((:instance revappend-lengths-x)
(:instance revappend-last-is-car (x x1))
(:instance revappend-last-is-car (x x2)))))))
(local (defthm revappend-nonempty-list
(implies (consp x)
(not (equal (revappend x y) y)))
:hints(("Goal" :use ((:instance len (x (revappend x y)))
(:instance len (x y)))))))
(local (defun revappend-induction-2 (x y acc)
(if (and (consp x)
(consp y))
(revappend-induction-2 (cdr x) (cdr y) (cons (car x) acc))
(list x y acc))))
(defthm equal-of-revappends-when-true-listps
(implies (and (true-listp x1)
(true-listp x2))
(equal (equal (revappend x1 y)
(revappend x2 y))
(equal x1 x2)))
:hints(("Goal"
:induct (revappend-induction-2 x1 x2 y))
("Subgoal *1/1"
:in-theory (disable revappend-equal-x-cdrs-lemma
revappend-equal-x-cars-lemma)
:use ((:instance revappend-equal-x-cdrs-lemma)
(:instance revappend-equal-x-cars-lemma)))))
|