/usr/share/acl2-4.3/books/unicode/take.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 | ;; 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")
(local (include-book "arithmetic/top" :dir :system))
(defund simpler-take (n xs)
(declare (xargs :guard (and (natp n)
(true-listp xs))))
(if (zp n)
nil
(cons (car xs)
(simpler-take (1- n) (cdr xs)))))
(local (in-theory (enable simpler-take)))
(encapsulate
()
(local (defthm equivalence-lemma
(implies (true-listp acc)
(equal (first-n-ac n xs acc)
(revappend acc (simpler-take n xs))))))
(defthm take-redefinition
(equal (take n xs)
(simpler-take n xs))
:rule-classes :definition)
(in-theory (disable (:definition take))))
(defthm consp-of-simpler-take
(equal (consp (simpler-take n xs))
(not (zp n))))
(defthm len-of-simpler-take
(equal (len (simpler-take n xs))
(nfix n)))
(defthm simpler-take-of-cons
(equal (simpler-take n (cons a x))
(if (zp n)
nil
(cons a (simpler-take (1- n) x)))))
(local (defun simpler-take-induction (n x)
(declare (xargs :guard (natp n)))
(if (zp n)
(list n x)
(if (consp x)
(simpler-take-induction (1- n) (cdr x))
(list n x)))))
(defthm simpler-take-of-append
(equal (simpler-take n (append x y))
(if (< (nfix n) (len x))
(simpler-take n x)
(append x (simpler-take (- n (len x)) y))))
:hints(("Goal" :induct (simpler-take-induction n x))))
(defthm simpler-take-of-1
(equal (simpler-take 1 x)
(list (car x))))
(defthm car-of-simple-take
(implies (<= 1 (nfix n))
(equal (car (simpler-take n x))
(car x))))
(defthm second-of-simple-take
(implies (<= 2 (nfix n))
(equal (second (simpler-take n x))
(second x))))
(defthm third-of-simple-take
(implies (<= 3 (nfix n))
(equal (third (simpler-take n x))
(third x))))
(defthm fourth-of-simple-take
(implies (<= 4 (nfix n))
(equal (fourth (simpler-take n x))
(fourth x))))
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