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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")
(include-book "nat-listp")
(defund sum-list (x)
(declare (xargs :guard (nat-listp x)))
(if (consp x)
(+ (car x)
(sum-list (cdr x)))
0))
(defthm sum-list-when-not-consp
(implies (not (consp x))
(equal (sum-list x)
0))
:hints(("Goal" :in-theory (enable sum-list))))
(defthm sum-list-of-cons
(equal (sum-list (cons a x))
(+ a (sum-list x)))
:hints(("Goal" :in-theory (enable sum-list))))
(defthm sum-list-of-list-fix
(equal (sum-list (list-fix x))
(sum-list x))
:hints(("Goal" :induct (len x))))
(defthm sum-list-of-app
(equal (sum-list (app x y))
(+ (sum-list x)
(sum-list y)))
:hints(("Goal" :induct (len x))))
(defthm natp-of-sum-list-when-nat-listp
(implies (nat-listp x)
(and (integerp (sum-list x))
(<= 0 (sum-list x))))
:hints(("Goal" :induct (len x))))
(defthm natp-of-sum-list-when-nat-listp-linear
(implies (nat-listp x)
(<= 0 (sum-list x)))
:rule-classes :linear)
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