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;; 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")
(defund base10-digit-charp (x)
(if (member x '(#\0 #\1 #\2 #\3 #\4 #\5 #\6 #\7 #\8 #\9))
t
nil))
(defthm characterp-when-base10-digit-charp
(implies (base10-digit-charp x)
(characterp x))
:hints(("Goal" :in-theory (enable base10-digit-charp))))
(defund base10-digit-char-listp (x)
(if (consp x)
(and (base10-digit-charp (car x))
(base10-digit-char-listp (cdr x)))
(eq x nil)))
(defthm base10-digit-char-listp-when-not-consp
(implies (not (consp x))
(equal (base10-digit-char-listp x)
(not x)))
:hints(("Goal" :in-theory (enable base10-digit-char-listp))))
(defthm base10-digit-char-listp-of-cons
(equal (base10-digit-char-listp (cons a x))
(and (base10-digit-charp a)
(base10-digit-char-listp x)))
:hints(("Goal" :in-theory (enable base10-digit-char-listp))))
(defthm character-listp-when-base10-digit-char-listp
(implies (base10-digit-char-listp x)
(character-listp x))
:hints(("Goal" :induct (len x))))
(defthm base10-digit-char-listp-of-revappend
(implies (and (base10-digit-char-listp x)
(base10-digit-char-listp acc))
(base10-digit-char-listp (revappend x acc))))
(in-theory (disable digit-to-char))
(defthm base10-digit-charp-of-digit-to-char
(implies (and (natp n)
(< n 10))
(base10-digit-charp (digit-to-char n)))
:hints(("Goal" :in-theory (enable digit-to-char
base10-digit-charp))))
(defthm equal-of-digit-to-chars
(implies (and (natp i) (< i 10)
(natp j) (< j 10))
(equal (equal (digit-to-char i)
(digit-to-char j))
(equal i j)))
:hints(("Goal" :in-theory (enable digit-to-char))))
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