/usr/share/acl2-4.3/books/unicode/sign-byte.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 | ;; 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)
(defund sign-byte (x)
(declare (type (unsigned-byte 8) x))
(if (< x 128)
x
(- x 256)))
(local (in-theory (enable sign-byte)))
(defthm sign-byte-type
(implies (integerp x)
(integerp (sign-byte x)))
:rule-classes ((:type-prescription) (:rewrite)))
(local (defun logbitp-equiv (i x y)
(declare (xargs :guard (and (natp i)
(integerp x)
(integerp y))))
(and (equal (logbitp i x) (logbitp i y))
(or (zp i)
(logbitp-equiv (1- i) x y)))))
(local (defthm logbitp-equiv-lemma
(implies (and (logbitp-equiv n x y)
(syntaxp (not (equal x y)))
(integerp n)
(<= 0 n)
(integerp i)
(<= 0 i)
(<= i n))
(equal (logbitp i y)
(logbitp i x)))
:hints(("Goal" :in-theory (disable logbitp)))))
(local (defun test-sign-byte (i)
(declare (type (unsigned-byte 8) i))
(and (logbitp-equiv 7 i (sign-byte i))
(or (zp i)
(test-sign-byte (1- i))))))
(local (defthm test-sign-byte-lemma
(implies (and (test-sign-byte n)
(integerp n) (<= 0 n)
(integerp i) (<= 0 i) (<= i n)
(integerp k) (<= 0 k) (< k 8))
(equal (logbitp k (sign-byte i))
(logbitp k i)))
:hints(("Goal" :in-theory (disable logbitp)))))
(defthm sign-byte-bit-correct
(implies (and (unsigned-byte-p 8 i)
(integerp k)
(<= 0 k)
(< k 8))
(equal (logbitp k (sign-byte i))
(logbitp k i)))
:hints(("Goal" :use (:instance test-sign-byte-lemma (n 255)))))
(defthm sign-byte-range-correct
(implies (unsigned-byte-p 8 i)
(signed-byte-p 8 (sign-byte i))))
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