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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 "utf8-table35")
(include-book "utf8-table36")
(local (include-book "append"))
(local (include-book "signed-byte-listp")) ;; for the-fixnum
;; Conversion From Unicode to UTF-8 ===========================================
;;
;; Recall that as uchar?s and within ustring?s, we store code points atomically
;; as single integers. It is relatively straightforward to convert these
;; codepoints into UTF8 byte sequences.
;;
;; We now introduce the function uchar=>utf8, which, as its name suggests will
;; take any uchar and return to us the corresponding byte sequence in UTF-8.
;; This function is based on Table 3-5, and is in essence a straightforward
;; translation of this table, based on shifting the bits of the codepoints into
;; the correct locations for our output bytes.
(defund uchar=>utf8 (x)
"Encode a Unicode character as a UTF8 byte sequence."
(declare (xargs :guard (uchar? x)))
(cond ((<= (the-fixnum x) #x007F)
(list x))
((in-range? (the-fixnum x) #x0080 #x07FF)
(let ((110yyyyy (logior #xC0 (the-fixnum (ash (the-fixnum x) -6))))
(10xxxxxx (logior #X80 (the-fixnum
(logand (the-fixnum x) #x3F)))))
(list 110yyyyy 10xxxxxx)))
((in-range? (the-fixnum x) #x0800 #xFFFF)
(let ((1110zzzz (logior #xE0 (the-fixnum (ash (the-fixnum x) -12))))
(10yyyyyy (logior #x80 (the-fixnum
(logand (the-fixnum
(ash (the-fixnum x) -6))
#x3F))))
(10xxxxxx (logior #x80 (the-fixnum
(logand (the-fixnum x) #x3F)))))
(list 1110zzzz 10yyyyyy 10xxxxxx)))
(t (let ((11110uuu (logior #xF0 (the-fixnum (ash (the-fixnum x) -18))))
(10uuzzzz (logior #x80 (the-fixnum
(logand (the-fixnum
(ash (the-fixnum x) -12))
#x3F))))
(10yyyyyy (logior #x80 (the-fixnum
(logand (the-fixnum
(ash (the-fixnum x) -6))
#x3F))))
(10xxxxxx (logior #x80 (the-fixnum
(logand (the-fixnum x) #x3F)))))
(list 11110uuu 10uuzzzz 10yyyyyy 10xxxxxx)))))
(defthm unsigned-byte-list-of-uchar=>utf8-when-uchar?
(implies (uchar? x)
(unsigned-byte-listp 8 (uchar=>utf8 x)))
:hints(("Goal" :in-theory (enable uchar=>utf8))))
(defthm len-of-uchar=>utf8
(implies (uchar? x)
(and (<= 1 (len (uchar=>utf8 x)))
(<= (len (uchar=>utf8 x)) 4)))
:rule-classes :linear
:hints(("Goal" :in-theory (enable uchar=>utf8))))
;; Now we would like to show that our encoding function actually respects the
;; constraints of Tables 3-5 and 3-6 which we formalized above.
;;
;; How can we prove something like this? I have no deep insight about why the
;; table is written as it is, it all seems rather random/arbitrary. Rather
;; than try to actually understand any sort of deeper meaning here, I will just
;; have ACL2 run an exhaustive test to prove that every uchar has a
;; satisfactory encoding under our function.
;;
;; This is so easy it feels like cheating. It is a really easy way to get this
;; complicated theorem through, and it is useful later in the file as well.
;; Our method is to first write a testing function, to test all the integers
;; between 0 and i.
(encapsulate
()
(local (defun test-uchar=>utf8 (i)
(declare (xargs :guard (natp i)))
(and (if (uchar? i)
(and (utf8-table36-ok? i (uchar=>utf8 i))
(utf8-table35-ok? i (uchar=>utf8 i)))
t)
(or (zp i)
(test-uchar=>utf8 (1- i))))))
;; We now show that if we have successfully tested all the integers between 0
;; and i, then each of these integers satisfies our desired property.
(local (defthmd lemma
(implies (and (test-uchar=>utf8 i)
(natp i)
(natp j)
(<= j i)
(uchar? j))
(and (utf8-table35-ok? j (uchar=>utf8 j))
(utf8-table36-ok? j (uchar=>utf8 j))))))
;; Finally, by instantiation of the above theorem, we can show that all of the
;; integers in the range [0, #x10ffff] satisfy our property, and then trivially
;; all uchar's satisfy our property, since all uchar's are in this range. This
;; means we run our testing function for about 1.1 million iterations, so we
;; need to compile things first. The entire process takes only about 2 seconds
;; on a P4-2800.
(comp t)
(local (defthm lemma2
(implies (uchar? x)
(and (utf8-table35-ok? x (uchar=>utf8 x))
(utf8-table36-ok? x (uchar=>utf8 x))))
:hints(("Goal"
:use (:instance lemma
(i #x10FFFF)
(j x))))))
(defthm utf8-table35-ok?-of-uchar=>utf8-when-uchar?
(implies (uchar? x)
(utf8-table35-ok? x (uchar=>utf8 x))))
(defthm utf8-table36-ok?-of-uchar=>utf8-when-uchar?
(implies (uchar? x)
(utf8-table36-ok? x (uchar=>utf8 x)))))
;; We also introduce ustring=>utf8, which simply repeatedly applies uchar=>utf8
;; in order to create a UTF-8 encoding of a string.
(defund ustring=>utf8 (x)
"Encode a Unicode string as a UTF-8 byte sequence."
(declare (xargs :guard (ustring? x)))
(if (atom x)
nil
(append (uchar=>utf8 (car x))
(ustring=>utf8 (cdr x)))))
(defthm ustring=>utf8-when-not-consp
(implies (not (consp x))
(equal (ustring=>utf8 x)
nil))
:hints(("Goal" :in-theory (enable ustring=>utf8))))
(defthm ustring=>utf8-of-cons
(equal (ustring=>utf8 (cons a x))
(append (uchar=>utf8 a)
(ustring=>utf8 x)))
:hints(("Goal" :in-theory (enable ustring=>utf8))))
(defthm true-listp-of-ustring=>utf8
(true-listp (ustring=>utf8 x))
:rule-classes (:rewrite :type-prescription)
:hints(("Goal" :induct (len x))))
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