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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.
;; utf8.lisp
;;
;; We introduce functions to process UTF-8 encoding.
;;
;; There is a fair amount of description in the Unicode Specification about the
;; UTF-8 encoding form. Here are the parts of the 4.0.1 specification which
;; deal with UTF-8 directly. This is all really quite straightforward.
;;
;; D36: UTF-8 Encoding Form: The Unicode encoding form which assigns each
;; Unicode scalar value to an unsigned byte sequence of one to four bytes in
;; length, as specified in Table 3-5.
;;
;; 1. In UTF-8, the code point sequence <004D 0430 4E8C 10302> is
;; represented as <4D D0 B0 D4 BA 8C F0 90 8C 82>, where <4D> corresponds to
;; U+004D, <D0 B0> corresponds to U+0430, <E4 BA 8C> corresponds to U+4E8C,
;; and <F0 90 8C 82> corresponds to U+10302.
;;
;; 2. Any UTF-8 byte sequence that does not match the patterns listed in
;; Table 3-6 is ill formed.
;;
;; 3. Before the Unicode Standard, Version 3.1, the problematic "non-
;; shortest form" byte sequences in UTF-8 were those where BMP characters
;; could be represented in more than one way. These sequences are ill
;; formed, because they are not allowed by Table 3-6.
;;
;; 4. Because surrogate code points are not Unicode scalar values, any
;; UTF-8 byte sequence that would otherwise map to code points D800..DFFF is
;; ill formed.
;;
;; Table 3-5 Specifies the bit distribution for the UTF-8 encoding form,
;; showing the ranges of Unicode scalar values corresponding to one-, two-,
;; three-, and four-byte sequences.
;;
;; Table 3-5. UTF-8 Bit Distribution
;;
;; Scalar Value 1st Byte 2nd Byte 3rd Byte 4th Byte
;; 00000000 0xxxxxxx 0xxxxxxx
;; 00000yyy yyxxxxxx 110yyyyy 10xxxxxx
;; zzzzyyyy yyxxxxxx 1110zzzz 10yyyyyy 10xxxxxx
;; 000uuuuu zzzzyyyy yyxxxxx 11110uuu 10uuzzzz 10yyyyyy 10xxxxxx
;;
;;
;; Table 3-6 lists all of the byte sequences that are well formed in UTF-8.
;; A range of byte values such as A0..BF indicates that any byte from A0 to
;; BF, inclusive, is well formed in that position. Any byte value outside
;; the ranges listed is ill formed. For example:
;;
;; 1. The byte sequence <C0 AF> is ill fomred because C0 is not well formed
;; in the "1st Byte" column.
;;
;; 2. The byte sequence <E0 9F 80> is ill formed, because in the row where
;; E0 is well formed as a first byte, 9F is not well formed as a second
;; byte.
;;
;; 3. The byte sequence <F4 80 83 92> is well formed, because every byte in
;; that sequence matches a byte range in the row of the table (the last
;; row).
;;
;; Table 3-6: Well-Formed UTF-8 Byte Sequences
;;
;; Code Points 1st Byte 2nd Byte 3rd Byte 4th Byte
;; U+0000..U+007F 00..7F
;; U+0080..U+07FF C2..DF 80..BF
;; U+0800..U+0FFF E0 A0..BF 80..BF
;; U+1000..U+CFFF E1..EC 80..BF 80..BF
;; U+D000..U+D7FF ED 80..9F 80..BF
;; U+E000..U+FFFF EE..EF 80..BF 80..BF
;; U+10000..U+3FFFF F0 90..BF 80..BF 80..BF
;; U+40000..U+FFFFF F1..F3 80..BF 80..BF 80..BF
;; U+100000..U+10FFFF F4 80..8F 80..BF 80..BF
;;
;; As a consequence of the well formedness conditions specified in Table
;; 3-6, the following byte values are disallowed in UTF-8: C0-C1, F5-FF.
;;
;; D39: UTF-8 Encoding Scheme: The Unicode encoding scheme that serializes
;; a UTF-8 code unit sequence in exactly the same order as the code unit
;; sequence itself.
;;
;; 1. In the UTF-8 encoding scheme, the UTF-8 code unit sequence <4D D0 B0
;; E4 BA 8C F0 90 8C 82> is serialized as <4D D0 B0 E4 BA 8C F0 90 8C 82>
;;
;; 2. Because the UTF-8 encoding form already deals in ordered byte
;; sequences, the UTF-8 encoding scheme is trivial. The byre ordering is
;; already obvious and completely defined by the UTF-8 code unit sequence
;; itself. The UTF-8 encoding scheme is defined merely for completeness of
;; the Unicode character encoding model.
;;
;; 3. While there is no need for a byte order signature when using UTF-8,
;; there are occasions when processes convert UTF-16 or UTF-32 data
;; containing a byte order mark into UTF-8. When represented in UTF-8, the
;; byte order mark turns into the byte sequence <EF BB BF>. Its usage at
;; the beginning of a UTF-8 data stream is neither required nor recommended
;; by the Unicode Standard, but its presence does not affect conformance to
;; the UTF-8 encoding scheme. Identification of the <EF BB BF> byte
;; sequence at the beginning of a data stream can, however, be taken as a
;; near certain indication that the data stream is using the UTF-8 encoding
;; scheme.
(in-package "ACL2")
(include-book "uchar")
(include-book "utf8-table35")
(include-book "utf8-table36")
(set-verify-guards-eagerness 2)
(set-state-ok t)
(in-theory (disable nthcdr take))
(include-book "acl2-basics")
(local (include-book "arithmetic/top-with-meta" :dir :system))
(defthm nat-listp-of-cdr-when-nat-listp
(implies (nat-listp x)
(nat-listp (cdr x))))
;; (defthm nthcdr-of-cons
;; (equal (nthcdr n (cons a x))
;; (if (and (integerp n)
;; (< 0 n))
;; (nthcdr (+ -1 n) x)
;; (cons a x)))
;; :hints(("Goal" :in-theory (enable nthcdr))))
(defthm len-of-nthcdr
(equal (len (nthcdr n l))
(if (natp n)
(max 0 (- (len l) n))
(len l)))
:hints (("Goal"
:in-theory (enable nthcdr)
:induct (nthcdr n l))))
(defthm list-fix-of-nthcdr
(equal (list-fix (nthcdr n l))
(nthcdr n (list-fix l)))
:hints(("Goal" :in-theory (enable nthcdr))))
(defthm partition-list-identity
(implies (and (nat-listp sizes)
(equal (sum-list sizes) (len x)))
(equal (flatten-cons-list
(partition-list sizes x))
(list-fix x)))
:hints(("Goal"
:induct (partition-list sizes x)
:in-theory (enable partition-list))))
;; I first claim (and prove) that the Table 3-5 1st Byte entries are distinct.
;; That is, given any x as input, x either matches none of the acceptable 1st
;; Byte patterns, or it matches exactly one of them. Because of this, we can
;; use the 1st Byte to determine how many bytes we need to read total.
(defthm utf8-table35-byte-1/x-distinct
(and (implies (utf8-table35-byte-1/1? x)
(and (not (utf8-table35-byte-1/2? x))
(not (utf8-table35-byte-1/3? x))
(not (utf8-table35-byte-1/4? x))
(not (utf8-table35-trailing-byte? x))))
(implies (utf8-table35-byte-1/2? x)
(and (not (utf8-table35-byte-1/1? x))
(not (utf8-table35-byte-1/3? x))
(not (utf8-table35-byte-1/4? x))
(not (utf8-table35-trailing-byte? x))))
(implies (utf8-table35-byte-1/3? x)
(and (not (utf8-table35-byte-1/1? x))
(not (utf8-table35-byte-1/2? x))
(not (utf8-table35-byte-1/4? x))
(not (utf8-table35-trailing-byte? x))))
(implies (utf8-table35-byte-1/4? x)
(and (not (utf8-table35-byte-1/1? x))
(not (utf8-table35-byte-1/2? x))
(not (utf8-table35-byte-1/3? x))
(not (utf8-table35-trailing-byte? x))))
(implies (utf8-table35-trailing-byte? x)
(and (not (utf8-table35-byte-1/1? x))
(not (utf8-table35-byte-1/2? x))
(not (utf8-table35-byte-1/3? x))
(not (utf8-table35-byte-1/4? x)))))
:rule-classes nil
:hints(("Goal" :in-theory (enable utf8-table35-byte-1/1?
utf8-table35-byte-1/2?
utf8-table35-byte-1/3?
utf8-table35-byte-1/4?
utf8-table35-trailing-byte?))))
;; Since the first bytes are all distinct, we can simply examine the first
;; byte of a purported UTF-8 sequence in order to determine how long the
;; sequence will have to be in order to be acceptable.
(defun utf8-table35-expected-length (x)
"Given that x is allegedly the first byte of a UTF-8 sequence, use Table 3-5
to determine how long this sequence is expected to be."
(declare (type (unsigned-byte 8) x))
(cond ((utf8-table35-byte-1/1? x) 1)
((utf8-table35-byte-1/2? x) 2)
((utf8-table35-byte-1/3? x) 3)
((utf8-table35-byte-1/4? x) 4)
(t nil)))
;; As a result, we can wee that UTF-8 byte sequences can only be acceptable
;; under Tables 3-5 and 3-6 if they have the length which is predicted by
;; utf8-table35-expected-length.
(defthm utf8-table35-ok?-when-not-expected-length
(implies (not (equal (utf8-table35-expected-length (first x))
(len x)))
(not (utf8-table35-ok? cp x)))
:hints(("Goal" :in-theory (enable utf8-table35-ok?
utf8-table35-row-1?
utf8-table35-row-2?
utf8-table35-row-3?
utf8-table35-row-4?
utf8-table35-byte-1/1?
utf8-table35-byte-1/2?
utf8-table35-byte-1/3?
utf8-table35-byte-1/4?
utf8-table35-trailing-byte?
utf8-table35-expected-length))))
(defthm utf8-table35-expected-length-when-utf8-table35-ok?
(implies (utf8-table35-ok? cp x)
(equal (utf8-table35-expected-length (first x))
(len x))))
(defthm utf8-table36-okp-when-not-expected-length
(implies (not (equal (utf8-table35-expected-length (first x))
(len x)))
(not (utf8-table36-ok? cp x)))
:hints(("Goal" :in-theory (enable utf8-table36-ok?
utf8-table35-byte-1/1?
utf8-table35-byte-1/2?
utf8-table35-byte-1/3?
utf8-table35-byte-1/4?
utf8-table35-trailing-byte?
utf8-table36-rows
utf8-table36-codepoint-1?
utf8-table36-codepoint-2?
utf8-table36-codepoint-3?
utf8-table36-codepoint-4?
utf8-table36-codepoint-5?
utf8-table36-codepoint-6?
utf8-table36-codepoint-7?
utf8-table36-codepoint-8?
utf8-table36-codepoint-9?
utf8-table36-bytes-1?
utf8-table36-bytes-2?
utf8-table36-bytes-3?
utf8-table36-bytes-4?
utf8-table36-bytes-5?
utf8-table36-bytes-6?
utf8-table36-bytes-7?
utf8-table36-bytes-8?
utf8-table36-bytes-9?
utf8-table35-expected-length))))
(defthm utf8-table35-expected-length-when-utf8-table36-ok?
(implies (utf8-table36-ok? cp x)
(equal (utf8-table35-expected-length (first x))
(len x))))
;; Suppose we have a list of bytes which are a UTF8 encoded string or file. We
;; want to convert these bytes into a list of atomic code points. The most
;; straightforward thing to do would be the following:
;;
;; 1. Consider the bytes which make up the first codepoint. Extract
;; the codepoint they represent.
;;
;; 2. Repeat
(defun read-utf8-codepoint (channel state)
"Read the next codepoint from a UTF-8 encoded file."
(declare (xargs :guard (and (state-p state)
(symbolp channel)
(open-input-channel-p channel :byte state))))
(mv-let (x1 state) (read-byte$ channel state)
(if (eq x1 nil)
(mv nil state)
(case (utf8-table35-expected-length x1)
(1 (mv x1 state))
(2 (mv-let (x2 state) (read-byte$ channel state)
(mv (if (and x2 (utf8-combine2-guard x1 x2))
(utf8-combine2 x1 x2)
'fail)
state)))
(3 (mv-let (x2 state) (read-byte$ channel state)
(mv-let (x3 state) (read-byte$ channel state)
(mv (if (and x2 x3 (utf8-combine3-guard x1 x2 x3))
(utf8-combine3 x1 x2 x3)
'fail)
state))))
(4 (mv-let (x2 state) (read-byte$ channel state)
(mv-let (x3 state) (read-byte$ channel state)
(mv-let (x4 state) (read-byte$ channel state)
(mv (if (and x2 x3 x4 (utf8-combine4-guard x1 x2 x3 x4))
(utf8-combine4 x1 x2 x3 x4)
'fail)
state)))))
(otherwise (mv 'fail state))))))
(defun read-utf8-codepoints (n channel state acc)
"Read the next n codepoints from a UTF-8 encoded file."
(declare (xargs :guard (and (natp n)
(state-p state)
(symbolp channel)
(open-input-channel-p channel :byte state)
(true-listp acc))))
(if (zp n)
(mv (reverse acc) state)
(mv-let (codepoint state)
(read-utf8-codepoint channel state)
(if (or (eq codepoint nil)
(eq codepoint 'fail))
(mv (reverse acc) state)
(read-utf8-codepoints (1- n) channel state
(cons codepoint acc))))))
(defun read-utf8-file (n filename state)
(declare (xargs :mode :program))
(mv-let (channel state)
(open-input-channel filename :byte state)
(mv-let (data state)
(read-utf8-codepoints n channel state nil)
(let ((state (close-input-channel channel state)))
(mv data state)))))
#|
(defun read-utf8-char (channel state)
"Read the next codepoint from a UTF-8 encoded file."
(declare (xargs :guard (and (state-p state)
(symbolp channel)
(open-input-channel-p channel :byte state))))
(mv-let (x1 state)
(read-byte$ channel state)
(cond ((eq x1 nil)
(mv nil state))
((utf8-table35-expected-length
(cond ((eq x1 nil)
(mv nil state))
((< (the-fixnum x1) #b01111111)
(mv x1 state))
((= (logand (the-fixnum x1) #b11100000) #b11000000)
(mv-let (x2 state)
(read-byte$ channel state)
(if (eq x2 nil)
(mv 'fail state)
(mv (mbe :logic (read-utf8-combine2 x1 x2)
:exec (let ((000yyyyy (logand (the-fixnum x1) #b00011111))
(00xxxxxx (logand (the-fixnum x2) #b00111111)))
(logior (the-fixnum (ash (the-fixnum 000yyyyy) 6))
(the-fixnum 00xxxxxx))))
state))))
((= (logand (the-fixnum x1) #b11110000) #b11100000)
(mv-let (x2 state) (read-byte$ channel state)
(mv-let (x3 state) (read-byte$ channel state)
(if (or (eq x2 nil) (eq x3 nil))
(mv 'fail state)
(mv (mbe :logic (read-utf8-combine3 x1 x2 x3)
:exec (let ((0000zzzz (logand (the-fixnum x1) #b00001111))
(00yyyyyy (logand (the-fixnum x2) #b00111111))
(00xxxxxx (logand (the-fixnum x3) #b00111111)))
(logior (the-fixnum (ash (the-fixnum 0000zzzz) 12))
(the-fixnum (ash (the-fixnum 00yyyyyy) 6))
(the-fixnum 00xxxxxx))))
state)))))
((= (logand (the-fixnum x1) #b11111000) #b11110000)
(mv-let (x2 state) (read-byte$ channel state)
(mv-let (x3 state) (read-byte$ channel state)
(mv-let (x4 state) (read-byte$ channel state)
(if (or (eq x2 nil) (eq x3 nil) (eq x4 nil))
(mv 'fail state)
(mv (mbe :logic (read-utf8-combine4 x1 x2 x3 x4)
:exec (let ((00000uuu (logand (the-fixnum x1) #b00000111))
(00uuzzzz (logand (the-fixnum x2) #b00111111))
(00yyyyyy (logand (the-fixnum x3) #b00111111))
(00xxxxxx (logand (the-fixnum x4) #b00111111)))
(logior (the-fixnum (ash (the-fixnum 00000uuu) 18))
(the-fixnum (ash (the-fixnum 00uuzzzz) 12))
(the-fixnum (ash (the-fixnum 00yyyyyy) 6))
(the-fixnum 00xxxxxx))))
state))))))
(t (mv 'fail state)))))
(defthm read-utf8-state
(implies (and (force (state-p1 state))
(force (symbolp channel))
(force (open-input-channel-p1 channel :byte state)))
(state-p1 (mv-nth 1 (read-utf8-char channel state)))))
(defthm read-utf8-open-input-channel
(implies (and (force (state-p1 state))
(force (symbolp channel))
(force (open-input-channel-p1 channel :byte state)))
(open-input-channel-p1 channel
:byte
(mv-nth 1 (read-utf8-char channel state)))))
(i-am-here)
;; first we would like to show that reading from a utf8 stream gives us a
;; unicode scalar value
(defthm read-utf8-uchar
(implies (and (force (state-p1 state))
(force (symbolp channel))
(force (open-input-channel-p1 channel :byte state))
(car (read-utf8-char channel state))
(not (equal (car (read-utf8-char channel state)) 'fail)))
(uchar? (car (read-utf8-char channel state)))))
;; we would also like to show that this value is not in any of the forbidden
;; ranges, as indicated by the table. actually, a good way to do this might
;; be to simply do exhaustive testing. that is, write something like
;; combine16u and use mbe to put its definition into the logical definition
;; for read-utf8-char. then, we can exhaustively show that as long as you
;; feed it good values, it never produces a bad output.
;;
;; right now, i think this conjecture is false, and we will have to add some
;; extra cases to discard the bad ranges and so forth.
(encapsulate nil
(local (in-theory (disable read-utf8-combine2)))
(local (defun test-x2 (x1 i)
(declare (type (unsigned-byte 8) x1)
(type (unsigned-byte 8) i))
(and (uchar? (read-utf8-combine2 x1 i))
(or (zp i)
(test-x2 x1 (1- i))))))
(local (defun test-x1 (i)
(declare (type (unsigned-byte 8) i))
(and (test-x2 i 255)
(or (zp i)
(test-x1 (1- i))))))
(local (defthm test-x2-lemma
(implies (and (test-x2 x1 x2)
(integerp x2)
(integerp j)
(<= 0 j)
(<= j x2))
(uchar? (read-utf8-combine2 x1 j)))))
(local (defthm test-x1-lemma
(implies (and (test-x1 x1)
(integerp x1)
(integerp i)
(<= 0 i)
(<= i x1)
(integerp j)
(<= 0 j)
(<= j 255))
(uchar? (read-utf8-combine2 i j)))
:hints(("Subgoal *1/1"
:use (:instance test-x2-lemma
(x1 i)
(x2 255)
(j j))))))
(defthm read-utf8-combine2-uchar
(implies (and (force (unsigned-byte-p 8 x1))
(force (unsigned-byte-p 8 x2)))
(uchar? (read-utf8-combine2 x1 x2)))
:hints(("Goal" :in-theory (enable unsigned-byte-p)
:use (:instance test-x1-lemma
(x1 255)
(i x1)
(j x2)))))
)
(= (logand (the-fixnum x1) #b11110000) #b11100000)
(local (defun test-x3 (x1 x2 i)
(declare (type (unsigned-byte 8) x1)
(type (unsigned-byte 8) x2)
(type (unsigned-byte 8) i))
(and (or (implies (and (= (logand x1 #b11110000) #b11100000)
(= (logand x2 #b11000000) #b10000000)
(= (logand i #b11000000) #b10000000))
(uchar? (read-utf8-combine3 x1 x2 i)))
(cw "test-x3 fails for ~x0 ~x1 ~x2.~%" x1 x2 i))
(or (zp i)
(test-x3 x1 x2 (1- i))))))
(local (defun test-x2 (x1 i)
(declare (type (unsigned-byte 8) x1)
(type (unsigned-byte 8) i))
(and (test-x3 x1 i 255)
(or (zp i)
(test-x2 x1 (1- i))))))
(local (defun test-x1 (i)
(declare (type (unsigned-byte 8) i))
(and (test-x2 i 255)
(or (zp i)
(test-x1 (1- i))))))
(i-am-here)
(set-state-ok t)
; =============================================================================
;
; D43: UTF-32BE Encoding Scheme: The Unicode encoding scheme that serializes
; a UTF-32 code sequence as a byte sequence in big-endian format.
;
; - In UTF-32BE, the UTF-32 code sequence <0000004D, 00000430, 00004E8C,
; 00010302> is serialized as <00 00 00 4D 00 00 04 30 00 00 4E 8C 00 01
; 03 02>
;
; - In UTF-32BE, an initial byte sequence <00 00 FE FF> is interpreted as
; U+FEFF, ZERO WIDTH NO-BREAK SPACE.
;
; =============================================================================
; Well, this is all very simple. All we have to do is read four-byte big
; endian quantities from the stream.
(defun read-utf32be-char (channel state)
(declare (xargs :guard (and (state-p state)
(symbolp channel)
(open-input-channel-p channel :byte state))))
(mv-let (uchar state)
(read-bytes$ channel :bytes 4 :signed nil :end big)
(mv (cond ((eq uchar nil) nil)
((eq uchar 'fail) 'fail)
((uchar? uchar) uchar)
(t 'fail))
state)))
(defun utf-channel? (x)
(and (listn x 2)
(or (eq (first x) 'UTF-32BE)
(eq (first x) 'UTF-32LE)
(eq (first x) 'UTF-16BE)
(eq (first x) 'UTF-16LE)
(eq (first x) 'UTF-8))
(symbolp (second x))))
(defun read-utf-channel (utfc state)
(declare (xargs :guard (and (utf-channel? utfc)
(state-p state)
(open-input-channel-p (cadr utfc) :byte state))))
(let ((type (car utfc))
(channel (cadr utfc)))
(case type
('UTF-8 (read-utf-8-char channel state))
('UTF-16BE (read-utf-16be-char channel state))
('UTF-16LE (read-utf-16le-char channel state))
('UTF-32BE (read-utf-32be-char channel state))
(t (read-utf-32le-char channel state)))))
; =============================================================================
; From Section 3.9
;
; D31: UTF-32 Encoding FORM: The Unicode encoding form which assigns each
; Unicode scalar value to a single unsigned 32-bit code unit with the same
; numeric value as the Unicode scalar value.
;
; - In UTF-32, the code sequence <004D, 0430, 4E8C, 10302> is represented
; as <0000004D, 00000430, 00004E8C, 00010302>.
;
; - Because surrogate code points are not included in the set of Unicode
; scalar values, UTF-32 code units in the range 0000D800..0000DFFF(16) are
; ill formed.
;
; - Any UTF-32 code unit greater than 0010FFFF(16) is ill formed.
;
;
; D38: Unicode Encoding SCHEME: A specified byte serialization for a Unicode
; encoding form, including the specification of the handling of a byte order
; mark (BOM), if allowed.
;
; - For historical reasons, the Unicode encoding schemes are also referred
; to as Unicode (or UCS) transformation formats (UTF). That term is,
; however, ambiguous between its usage for encoding forms and encoding
; schemes.
;
; =============================================================================
|#
;; Formalization of Valid UTF-8 Sequences =====================================
;;
;; We say that the valid utf8-sequence are those objects, x, for which there
;; exists some unicode scalar value, cp, which can be used so that <cp, x>
;; matches with tables 3-5 and 3-6. We use quantifiers to capture this idea.
(set-verify-guards-eagerness 0)
(defun-sk utf8-sequence? (x)
(exists cp
(and (utf8-table35-ok? cp x)
(utf8-table36-ok? cp x))))
(set-verify-guards-eagerness 2)
;; The following theorems show that when x is a valid utf8 sequence, we can
;; choose (using utf8-sequence?-witness) an object which is a Unicode scalar
;; value, and meets our table requirements.
(defthm uchar?-of-utf8-sequence?-witness
(implies (utf8-sequence? x)
(uchar? (utf8-sequence?-witness x))))
(defthm utf8-table35-ok?-of-utf8-sequence?-witness
(implies (utf8-sequence? x)
(utf8-table35-ok? (utf8-sequence?-witness x) x))
:hints(("Goal" :in-theory (disable utf8-table35-ok?))))
(defthm utf8-table36-ok?-of-utf8-sequence?-witness
(implies (utf8-sequence? x)
(utf8-table36-ok? (utf8-sequence?-witness x) x))
:hints(("Goal" :in-theory (disable utf8-table36-ok?))))
|