;; 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")

(local (include-book "update-state"))
(local (include-book "open-input-channels"))
(local (include-book "unsigned-byte-listp"))
(local (include-book "signed-byte-listp"))

(local (defthm assoc-eq-is-assoc-equal
         (equal (assoc-eq a x)
                (assoc-equal a x))))

(local (defthm car-of-assoc-equal-when-assoc-equal
         (implies (assoc-equal a x)
                  (equal (car (assoc-equal a x))
                         a))))

(defthm state-p1-of-read-byte$
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel :byte state))
                (force (symbolp channel)))
           (state-p1 (mv-nth 1 (read-byte$ channel state))))
  :hints(("Goal" :in-theory (disable statep-functions)
          :use ((:instance state-p1 
                           (x state))
                (:instance state-p1 
                           (x (mv-nth 1 (read-byte$ channel state))))))))

(defthm open-input-channel-p1-of-read-byte$
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel :byte state))
                (force (symbolp channel)))
           (open-input-channel-p1 channel 
                                  :byte
                                  (mv-nth 1 (read-byte$ channel state))))
  :hints(("Goal" :in-theory (disable statep-functions)
          :use ((:instance state-p1 
                           (x state))
                (:instance state-p1 
                           (x (mv-nth 1 (read-byte$ channel state))))))))

(local (defthmd car-typed-io-list-byte
  (implies (and (typed-io-listp x :byte)
                (consp x))
           (and (integerp (car x))
                (<= 0 (car x))
                (< (car x) 256)))))

(defthm integerp-of-read-byte$
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel :byte state))
                (car (read-byte$ channel state)))
           (integerp (car (read-byte$ channel state))))
  :hints(("Goal" :in-theory (disable open-input-channel-p1
                                     open-input-channels)
          :use (:instance car-typed-io-list-byte
                          (x (cddr (assoc-equal 
                                    channel 
                                    (open-input-channels state))))))))
  
(defthm range-of-read-byte$
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel :byte state))
                (car (read-byte$ channel state)))
           (and (<= 0 (car (read-byte$ channel state)))
                (< (car (read-byte$ channel state)) 256)
                (< (car (read-byte$ channel state)) (expt 2 8))))
  :rule-classes :linear
  :hints(("Goal" :in-theory (disable open-input-channel-p1
                                     open-input-channels)
          :use (:instance car-typed-io-list-byte
                          (x (cddr (assoc-equal 
                                    channel 
                                    (open-input-channels state))))))))          

(defthm unsigned-byte-p-of-read-byte$
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel :byte state))
                (car (read-byte$ channel state))
                (<= 8 size)
                (integerp size))
           (unsigned-byte-p size (car (read-byte$ channel state))))
  :hints(("Goal" 
          :in-theory (e/d (unsigned-byte-p) (read-byte$))
          :use (:instance unsigned-byte-promote
                          (size1 8)
                          (size2 size)
                          (x (car (read-byte$ channel state)))))))

(defthm signed-byte-p-of-read-byte$
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel :byte state))
                (car (read-byte$ channel state))
                (<= 9 size)
                (integerp size))
           (signed-byte-p size (car (read-byte$ channel state))))
  :hints(("Goal" 
          :in-theory (disable read-byte$)
          :use (:instance unsigned-to-signed-promote
                          (size1 8)
                          (size2 size)
                          (x (car (read-byte$ channel state)))))))


(encapsulate
 ()

 (local (defthm lemma
          (implies (and (typed-io-listp x :byte)
                        (not (car x)))
                   (not (cadr x)))))

 (defthm car-of-read-byte$-after-eof
   (implies (and (force (state-p state))
                 (force (symbolp channel))
                 (force (open-input-channel-p channel :byte state))
                 (not (car (read-byte$ channel state))))
            (not (car (read-byte$ channel (mv-nth 1 (read-byte$ channel state))))))
   :hints(("Goal" :in-theory (e/d (read-byte$)
                                  (statep-functions))))))


(encapsulate
 ()

 (local (defthm lemma
          (equal (equal a (cons x y))
                 (and (consp a)
                      (equal (car a) x)
                      (equal (cdr a) y)))))

 (local (defthm lemma2
          (implies (and (open-channel1 foo)
                        (equal (cadar foo) :byte)
                        (not (cadr foo)))
                   (equal (equal (cdr foo) (cddr foo))
                          t))))

 (defthm mv-nth-of-read-byte$-when-eof
   (implies (and (state-p state)
                 (symbolp channel)
                 (open-input-channel-p channel :byte state)
                 (not (car (read-byte$ channel state))))
            (equal (mv-nth 1 (read-byte$ channel state))
                   state))
   :hints(("Goal" :in-theory (e/d (read-byte$) 
                                  (statep-functions
                                   open-channel1
                                   open-channels-assoc))
           :use ((:instance open-channels-assoc
                            (x (open-input-channels state))))))))
         

(in-theory (disable state-p1 open-input-channel-p1 read-byte$))