This file is indexed.

/usr/share/acl2-8.0dfsg/books/unicode/utf8-table36.lisp is in acl2-books-source 8.0dfsg-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
; 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 "uchar")
(include-book "std/typed-lists/unsigned-byte-listp" :dir :system)
(local (include-book "centaur/bitops/ihsext-basics" :dir :system))
(local (include-book "centaur/bitops/signed-byte-p" :dir :system))
(local (include-book "std/typed-lists/signed-byte-listp" :dir :system))
(local (in-theory (disable signed-byte-p)))
(local (defthm signed-byte-p-resolver
         (implies (and (integerp n)
                       (<= 1 n)
                       (integerp x)
                       (<= (- (expt 2 (1- n))) x)
                       (< x (expt 2 (1- n))))
                  (signed-byte-p n x))
         :hints(("Goal" :in-theory (enable signed-byte-p)))))



;; UTF-8 sequences are required to satisfy the informal constraints imposed by
;; Table 3-6, which we recreate below:
;;
;;  Row   Scalar Value                1st Byte  2nd Byte  3rd Byte  4th Byte
;;  1     00000000 0xxxxxxx           0xxxxxxx
;;  2     00000yyy yyxxxxxx           110yyyyy  10xxxxxx
;;  3     zzzzyyyy yyxxxxxx           1110zzzz  10yyyyyy  10xxxxxx
;;  4     000uuuuu zzzzyyyy yyxxxxx   11110uuu  10uuzzzz  10yyyyyy  10xxxxxx
;;
;; To ensure that these constraints are respected by our UTF-8 functions, we
;; formalize the constraints of this table rigorously below.
;;
;; Because we are formalizing the Unicode specification here, the thorough
;; reader should check to ensure that our formalization is in agreement with
;; the Unicode standard.  In particular, one should check that our copy of
;; Table 3-6 above is an accurate copy of Table 3-6 from the Standard, and
;; should also convince themselves that the functions below accurately capture
;; the meaning of matching these bit patterns.



;; We begin by explaining which code points are acceptable entries for each row
;; (i.e., in the "scalar value" column).  Note that the code points accepted by
;; each row are subsumed by the later rows, i.e., any codepoint which is
;; acceptable under row 1 is also acceptable under row 2 by simply letting
;; yyyyy = 00000.  We do nothing to try to require least row constraints, since
;; these are handled by Table 3-7.

(defund utf8-table36-codepoint-1? (x)
  "Return true iff x matches 0xxxxxxx, i.e., if it could be a codepoint for
   Row 1 in Table 3-6."
  (declare (xargs :guard (uchar? x)))
  (and (mbt (uchar? x))
       (in-range? (the-fixnum x) 0 #x7F))) ; match 0xxxxxxx

(defund utf8-table36-codepoint-2? (x)
  "Return true iff x matches 00000yyy yyxxxxxx, i.e., if it could be a
   codepoint for Row 2 in Table 3-6."
  (declare (xargs :guard (uchar? x)))
  (and (mbt (uchar? x))
       (in-range? (the-fixnum x) 0 #x7FF))) ; match 00000yyy yyxxxxxx

(defund utf8-table36-codepoint-3? (x)
  "Return true iff x matches zzzzyyyy yyxxxxxx, i.e., if it could be a
   codepoint for Row 3 in Table 3-6."
  (declare (xargs :guard (uchar? x)))
  (and (mbt (uchar? x))
       (in-range? (the-fixnum x) 0 #xFFFF))) ; match zzzzyyyy yyxxxxxx

(defund utf8-table36-codepoint-4? (x)
  "Return true iff x matches 000uuuuu zzzzyyyy yyxxxxxx, i.e., if it could
   be a codepoint for Row 4 in Table 3-6."
  (declare (xargs :guard (uchar? x)))
  (and (mbt (uchar? x))
       (in-range? (the-fixnum x) 0 #x1FFFFF))) ; match 000uuuuu zzzzyyyy yyxxxxxx

(deftheory utf8-table36-codepoints
  '(utf8-table36-codepoint-1?
    utf8-table36-codepoint-2?
    utf8-table36-codepoint-3?
    utf8-table36-codepoint-4?))



;; We now rigorously explain what the valid entries are for the "Byte" columns
;; in the table.  Note that we really only have five bit patterns to consider:
;; one for each row in the 1st Byte column, and the pattern 10xxxxxx which is
;; used universally for all trailing bytes.

(defund utf8-table36-byte-1/1? (x)
  "Return true iff x matches 0xxxxxxx, i.e., it is the first byte of a one-
   byte UTF-8 sequence, as specified by Table 3-6."
  (declare (type (unsigned-byte 8) x))
  (and (mbt (unsigned-byte-p 8 x))
       (in-range? (the-fixnum x) 0 #x7F))) ; match 0xxxxxxx

(defund utf8-table36-byte-1/2? (x)
  "Return true iff x matches 110yyyyy, i.e., if it is the first byte of a
   two-byte UTF-8 sequence, as specified by Table 3-6."
  (declare (type (unsigned-byte 8) x))
  (and (mbt (unsigned-byte-p 8 x))
       (in-range? (the-fixnum x) #xC0 #xDF))) ; match 110yyyyy

(defund utf8-table36-byte-1/3? (x)
  "Return true iff x matches 1110zzzz, i.e., if it is the first byte of a
   three-byte UTF-8 sequence, as specified by Table 3-6."
  (declare (type (unsigned-byte 8) x))
  (and (mbt (unsigned-byte-p 8 x))
       (in-range? (the-fixnum x) #xE0 #xEF))) ; match 1110zzzz

(defund utf8-table36-byte-1/4? (x)
  "Return true iff x matches 11110uuu, i.e., if it is the first byte of a
   four-byte UTF-8 sequence, as specified by Table 3-6."
  (declare (type (unsigned-byte 8) x))
  (and (mbt (unsigned-byte-p 8 x))
       (in-range? (the-fixnum x) #xF0 #xF7))) ; match 11110uuu

(defund utf8-table36-trailing-byte? (x)
  "Return true iff x matches 10xxxxxx, i.e., if it is a trailing byte in
   any of the rows in Table 3-6."
  (declare (type (unsigned-byte 8) x))
  (and (mbt (unsigned-byte-p 8 x))
       (in-range? (the-fixnum x) #x80 #xBF))) ; match 10xxxxxx

(deftheory utf8-table36-bytes
  '(utf8-table36-byte-1/1?
    utf8-table36-byte-1/2?
    utf8-table36-byte-1/3?
    utf8-table36-byte-1/4?
    utf8-table36-trailing-byte?))




;; We now combine our individual cell checking functions (codepoint and byte
;; matching) into checks of full rows.  In particular, we write functions which
;; answer the question, given some codepoint and byte sequence, do these match
;; a particular row of Table 3-6?

(defund utf8-table36-row-1? (cp x)
  "True iff cp is a codepoint and x is a byte sequence which match the
   first row in Table 3-6."
  (declare (xargs :guard (and (uchar? cp)
                              (unsigned-byte-listp 8 x)
                              (equal (len x) 1))))
  (and
   ;; input checking (these can be inferred from guards)
   (mbt (uchar? cp))
   (mbt (unsigned-byte-listp 8 x))
   (mbt (equal (len x) 1))

   ;; check that the codepoint/bytes are acceptable
   (utf8-table36-codepoint-1? cp)
   (utf8-table36-byte-1/1? (first x))

   ;; check that the codepoint/bytes correspond as expected
   (= (the-fixnum cp)
      (the-fixnum (first x)))))

(defund utf8-table36-row-2? (cp x)
  "True iff cp is a codepoint and x is a byte sequence which match the
   second row in Table 3-6."
  (declare (xargs :guard (and (uchar? cp)
                              (unsigned-byte-listp 8 x)
                              (equal (len x) 2))))
  (and
   ;; input checking (these can be inferred from guards)
   (mbt (uchar? cp))
   (mbt (unsigned-byte-listp 8 x))
   (mbt (equal (len x) 2))

   ;; check that the codepoint/bytes are acceptable
   (utf8-table36-codepoint-2? cp)
   (utf8-table36-byte-1/2? (first x))
   (utf8-table36-trailing-byte? (second x))

   ;; check that the codepoint/bytes correspond as expected
   (mbe :logic (let ((000yyyyy (logand (first x) #x1F))
                     (00xxxxxx (logand (second x) #x3F)))
                 (equal (logior (ash 000yyyyy 6)
                                00xxxxxx)
                        cp))
        :exec  (let ((000yyyyy (the-fixnum
                                (logand (the-fixnum (first x)) #x1F)))
                     (00xxxxxx (the-fixnum
                                (logand (the-fixnum (second x)) #x3F))))
                 (= (the-fixnum
                     (logior (the-fixnum (ash (the-fixnum 000yyyyy) 6))
                             (the-fixnum 00xxxxxx)))
                    (the-fixnum cp))))))

(defund utf8-table36-row-3? (cp x)
  "True iff cp is a codepoint and x is a byte sequence which match the
   third row in Table 3-6."
  (declare (xargs :guard (and (uchar? cp)
                              (unsigned-byte-listp 8 x)
                              (equal (len x) 3))))
  (and
   ;; input checking (these can be inferred from guards)
   (mbt (uchar? cp))
   (mbt (unsigned-byte-listp 8 x))
   (mbt (equal (len x) 3))

   ;; check that the codepoint/bytes are acceptable
   (utf8-table36-codepoint-3? cp)
   (utf8-table36-byte-1/3? (first x))
   (utf8-table36-trailing-byte? (second x))
   (utf8-table36-trailing-byte? (third x))

   ;; check that the codepoint/bytes correspond as expected
   (mbe :logic (let ((0000zzzz (logand (first x) #x0F))
                     (00yyyyyy (logand (second x) #x3F))
                     (00xxxxxx (logand (third x) #x3F)))
                 (equal (logior (ash 0000zzzz 12)
                                (ash 00yyyyyy 6)
                                00xxxxxx)
                        cp))
        :exec (let ((0000zzzz (the-fixnum (logand (the-fixnum (first x)) #x0F)))
                    (00yyyyyy (the-fixnum (logand (the-fixnum (second x)) #x3F)))
                    (00xxxxxx (the-fixnum (logand (the-fixnum (third x)) #x3F))))
                (= (the-fixnum
                    (logior (the-fixnum (ash (the-fixnum 0000zzzz) 12))
                            (the-fixnum (ash (the-fixnum 00yyyyyy) 6))
                            (the-fixnum 00xxxxxx)))
                   (the-fixnum cp))))))

(defund utf8-table36-row-4? (cp x)
  "True iff cp is a codepoint and x is a byte sequence which match the
   third row in Table 3-6."
  (declare (xargs :guard (and (uchar? cp)
                              (unsigned-byte-listp 8 x)
                              (equal (len x) 4))))
  (and
   ;; input checking (these can be inferred from guards)
   (mbt (uchar? cp))
   (mbt (unsigned-byte-listp 8 x))
   (mbt (equal (len x) 4))

   ;; check that the codepoint/bytes are acceptable
   (utf8-table36-codepoint-4? cp)
   (utf8-table36-byte-1/4? (first x))
   (utf8-table36-trailing-byte? (second x))
   (utf8-table36-trailing-byte? (third x))
   (utf8-table36-trailing-byte? (fourth x))

   ;; check that the codepoint/bytes correspond as expected
   (mbe :logic (let ((00000uuu (logand (first x)  #x07))
                     (00uuzzzz (logand (second x) #x3F))
                     (00yyyyyy (logand (third x)  #x3F))
                     (00xxxxxx (logand (fourth x) #x3F)))
                 (equal (logior (ash 00000uuu 18)
                                (ash 00uuzzzz 12)
                                (ash 00yyyyyy 6)
                                00xxxxxx)
                        cp))
        :exec (let ((00000uuu (the-fixnum (logand (the-fixnum (first x)) #x07)))
                    (00uuzzzz (the-fixnum (logand (the-fixnum (second x)) #x3F)))
                    (00yyyyyy (the-fixnum (logand (the-fixnum (third x)) #x3F)))
                    (00xxxxxx (the-fixnum (logand (the-fixnum (fourth x)) #x3F))))
                (= (the-fixnum
                    (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)))
                   (the-fixnum cp))))))

(deftheory utf8-table36-rows
  '(utf8-table36-row-1?
    utf8-table36-row-2?
    utf8-table36-row-3?
    utf8-table36-row-4?))


;; Finally, we combine our row checking functions into a single, universal
;; check to ensure that a codepoint and a sequence of bytes are acceptable
;; under table 3-6.

(defthm utf8-table36-length-lemmas
  (and (implies (utf8-table36-row-1? cp x) (equal (len x) 1))
       (implies (utf8-table36-row-2? cp x) (equal (len x) 2))
       (implies (utf8-table36-row-3? cp x) (equal (len x) 3))
       (implies (utf8-table36-row-4? cp x) (equal (len x) 4)))
  :hints(("Goal" :in-theory (enable utf8-table36-rows))))

(defund utf8-table36-ok? (cp x)
  "True iff cp is a codepoint and x is a byte sequence which match some
   row in Table 3-6."
  (declare (xargs :guard (and (uchar? cp)
                              (unsigned-byte-listp 8 x)
                              (<= 1 (len x))
                              (<= (len x) 4))))
  (mbe :logic (or (utf8-table36-row-1? cp x)
                  (utf8-table36-row-2? cp x)
                  (utf8-table36-row-3? cp x)
                  (utf8-table36-row-4? cp x))
       :exec (case (len x)
               (1 (utf8-table36-row-1? cp x))
               (2 (utf8-table36-row-2? cp x))
               (3 (utf8-table36-row-3? cp x))
               (4 (utf8-table36-row-4? cp x))
               (t nil))))