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; Processing Unicode Files with ACL2
; Copyright (C) 2005-2006 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "ACL2")
(include-book "arithmetic/nat-listp" :dir :system)
(include-book "std/lists/list-fix" :dir :system)
(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-append
(equal (sum-list (append 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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