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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 "flatten")
(include-book "sum-list")
(local (include-book "z-listp"))
(local (include-book "arithmetic/top-with-meta" :dir :system))
(local (include-book "nthcdr"))
(defund partition (sizes x)
(declare (xargs :guard (and (nat-listp sizes)
(true-listp x))))
(if (consp sizes)
(cons (take (car sizes) x)
(partition (cdr sizes)
(nthcdr (car sizes) x)))
nil))
(defthm partition-when-not-consp
(implies (not (consp sizes))
(equal (partition sizes x)
nil))
:hints(("Goal" :in-theory (enable partition))))
(defthm partition-of-cons
(equal (partition (cons size sizes) x)
(cons (take size x)
(partition sizes (nthcdr size x))))
:hints(("Goal" :in-theory (enable partition))))
(defthm consp-of-partition-under-iff
(equal (consp (partition sizes x))
(if (partition sizes x)
t
nil))
:hints(("Goal" :in-theory (enable partition))))
(local (defthm consless-listp-of-partition
(equal (consless-listp (partition sizes x))
(z-listp sizes))
:hints(("Goal" :in-theory (enable partition)))))
(local (defthm sum-list-when-nat-listp-and-z-listp
(implies (and (nat-listp x)
(z-listp x))
(equal (sum-list x)
0))
:hints(("Goal" :induct (len x)))))
(local (defthm equal-of-simpler-take-and-list-fix
(equal (equal (simpler-take n x) (list-fix x))
(equal (nfix n) (len x)))))
(defthm flatten-of-partition
(implies (and (nat-listp sizes)
(equal (sum-list sizes) (len x)))
(equal (flatten (partition sizes x))
(list-fix x)))
:hints(("Goal" :in-theory (enable partition))))
(defthm len-of-car-of-partition
(equal (len (car (partition sizes x)))
(nfix (car sizes))))
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