aboutsummaryrefslogtreecommitdiffhomepage
path: root/vernac/metasyntax.ml
blob: 6c3dfec7d1f7952bd7d21ac8aa5986eed1e6dc70 (plain)
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
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Pp
open CErrors
open Util
open Names
open Constrexpr
open Constrexpr_ops
open Notation_term
open Notation_ops
open Ppextend
open Extend
open Libobject
open Constrintern
open Vernacexpr
open Libnames
open Tok
open Notation
open Nameops

(**********************************************************************)
(* Tokens                                                             *)

let cache_token (_,s) = CLexer.add_keyword s

let inToken : string -> obj =
  declare_object {(default_object "TOKEN") with
       open_function = (fun i o -> if Int.equal i 1 then cache_token o);
       cache_function = cache_token;
       subst_function = Libobject.ident_subst_function;
       classify_function = (fun o -> Substitute o)}

let add_token_obj s = Lib.add_anonymous_leaf (inToken s)

(**********************************************************************)
(* Printing grammar entries                                           *)

let entry_buf = Buffer.create 64

type any_entry = AnyEntry : 'a Pcoq.Gram.entry -> any_entry

let grammars : any_entry list String.Map.t ref = ref String.Map.empty

let register_grammar name grams =
  grammars := String.Map.add name grams !grammars

let pr_entry e =
  let () = Buffer.clear entry_buf in
  let ft = Format.formatter_of_buffer entry_buf in
  let () = Pcoq.Gram.entry_print ft e in
  str (Buffer.contents entry_buf)

let pr_registered_grammar name =
  let gram = try Some (String.Map.find name !grammars) with Not_found -> None in
  match gram with
  | None -> user_err Pp.(str "Unknown or unprintable grammar entry.")
  | Some entries ->
    let pr_one (AnyEntry e) =
      str "Entry " ++ str (Pcoq.Gram.Entry.name e) ++ str " is" ++ fnl () ++
      pr_entry e
    in
    prlist pr_one entries

let pr_grammar = function
  | "constr" | "operconstr" | "binder_constr" ->
      str "Entry constr is" ++ fnl () ++
      pr_entry Pcoq.Constr.constr ++
      str "and lconstr is" ++ fnl () ++
      pr_entry Pcoq.Constr.lconstr ++
      str "where binder_constr is" ++ fnl () ++
      pr_entry Pcoq.Constr.binder_constr ++
      str "and operconstr is" ++ fnl () ++
      pr_entry Pcoq.Constr.operconstr
  | "pattern" ->
      pr_entry Pcoq.Constr.pattern
  | "vernac" ->
      str "Entry vernac is" ++ fnl () ++
      pr_entry Pcoq.Vernac_.vernac ++
      str "Entry command is" ++ fnl () ++
      pr_entry Pcoq.Vernac_.command ++
      str "Entry syntax is" ++ fnl () ++
      pr_entry Pcoq.Vernac_.syntax ++
      str "Entry gallina is" ++ fnl () ++
      pr_entry Pcoq.Vernac_.gallina ++
      str "Entry gallina_ext is" ++ fnl () ++
      pr_entry Pcoq.Vernac_.gallina_ext
  | name -> pr_registered_grammar name

(**********************************************************************)
(* Parse a format (every terminal starting with a letter or a single
   quote (except a single quote alone) must be quoted) *)

let parse_format ((loc, str) : lstring) =
  let len = String.length str in
  (* TODO: update the line of the location when the string contains newlines *)
  let make_loc i j = Option.map (Loc.shift_loc (i+1) (j-len)) loc in
  let push_token loc a = function
    | (i,cur)::l -> (i,(loc,a)::cur)::l
    | [] -> assert false in
  let push_white i n l =
    if Int.equal n 0 then l else push_token (make_loc i (i+n)) (UnpTerminal (String.make n ' ')) l in
  let close_box start stop b = function
    | (_,a)::(_::_ as l) -> push_token (make_loc start stop) (UnpBox (b,a)) l
    | [a] -> user_err ?loc:(make_loc start stop) Pp.(str "Non terminated box in format.")
    | [] -> assert false in
  let close_quotation start i =
    if i < len && str.[i] == '\'' then
      if (Int.equal (i+1) len || str.[i+1] == ' ')
      then i+1
      else user_err ?loc:(make_loc (i+1) (i+1)) Pp.(str "Space expected after quoted expression.")
    else
      user_err ?loc:(make_loc start (i-1)) Pp.(str "Beginning of quoted expression expected to be ended by a quote.") in
  let rec spaces n i =
    if i < len && str.[i] == ' ' then spaces (n+1) (i+1)
    else n in
  let rec nonspaces quoted n i =
    if i < len && str.[i] != ' ' then
      if str.[i] == '\'' && quoted &&
        (i+1 >= len || str.[i+1] == ' ')
      then if Int.equal n 0 then user_err ?loc:(make_loc (i-1) i) Pp.(str "Empty quoted token.") else n
      else nonspaces quoted (n+1) (i+1)
    else
      if quoted then user_err ?loc:(make_loc i i) Pp.(str "Spaces are not allowed in (quoted) symbols.")
      else n in
  let rec parse_non_format i =
    let n = nonspaces false 0 i in
    push_token (make_loc i (i+n-1)) (UnpTerminal (String.sub str i n)) (parse_token 1 (i+n))
  and parse_quoted n i =
    if i < len then match str.[i] with
      (* Parse " // " *)
      | '/' when i+1 < len && str.[i+1] == '/' ->
          (* We discard the useless n spaces... *)
	  push_token (make_loc (i-n) (i+1)) (UnpCut PpFnl)
            (parse_token 1 (close_quotation i (i+2)))
      (* Parse " .. / .. " *)
      | '/' when i+1 < len ->
	  let p = spaces 0 (i+1) in
	  push_token (make_loc (i-n) (i+p)) (UnpCut (PpBrk (n,p)))
            (parse_token 1 (close_quotation i (i+p+1)))
      | c ->
      (* The spaces are real spaces *)
      push_white i n (match c with
      | '[' ->
	  if i+1 < len then match str.[i+1] with
	    (* Parse " [h .. ",  *)
	    | 'h' when i+1 <= len && str.[i+2] == 'v' ->
		  (parse_box i (fun n -> PpHVB n) (i+3))
		(* Parse " [v .. ",  *)
	    | 'v' ->
		    parse_box i (fun n -> PpVB n) (i+2)
		(* Parse " [ .. ",  *)
	    | ' ' | '\'' ->
		parse_box i (fun n -> PpHOVB n) (i+1)
	    | _ -> user_err ?loc:(make_loc i i) Pp.(str "\"v\", \"hv\", \" \" expected after \"[\" in format.")
	  else user_err ?loc:(make_loc i i) Pp.(str "\"v\", \"hv\" or \" \" expected after \"[\" in format.")
      (* Parse "]"  *)
      | ']' ->
	  ((i,[]) :: parse_token 1 (close_quotation i (i+1)))
      (* Parse a non formatting token *)
      | c ->
	  let n = nonspaces true 0 i in
	  push_token (make_loc i (i+n-1)) (UnpTerminal (String.sub str (i-1) (n+2)))
	    (parse_token 1 (close_quotation i (i+n))))
    else
      if Int.equal n 0 then []
      else user_err ?loc:(make_loc (len-n) len) Pp.(str "Ending spaces non part of a format annotation.")
  and parse_box start box i =
    let n = spaces 0 i in
    close_box start (i+n-1) (box n) (parse_token 1 (close_quotation i (i+n)))
  and parse_token k i =
    let n = spaces 0 i in
    let i = i+n in
    if i < len then match str.[i] with
      (* Parse a ' *)
      |	'\'' when i+1 >= len || str.[i+1] == ' ' ->
	  push_white (i-n) (n-k) (push_token (make_loc i (i+1)) (UnpTerminal "'") (parse_token 1 (i+1)))
      (* Parse the beginning of a quoted expression *)
      |	'\'' ->
          parse_quoted (n-k) (i+1)
      (* Otherwise *)
      | _ ->
          push_white (i-n) (n-k) (parse_non_format i)
    else push_white (i-n) n [(len,[])]
  in
  if not (String.is_empty str) then
    match parse_token 0 0 with
    | [_,l] -> l
    | (i,_)::_ -> user_err ?loc:(make_loc i i) Pp.(str "Box closed without being opened.")
    | [] -> assert false
  else
    []

(***********************)
(* Analyzing notations *)

type symbol_token = WhiteSpace of int | String of string

let split_notation_string str =
  let push_token beg i l =
    if Int.equal beg i then l else
      let s = String.sub str beg (i - beg) in
      String s :: l
  in
  let push_whitespace beg i l =
    if Int.equal beg i then l else WhiteSpace (i-beg) :: l
  in
  let rec loop beg i =
    if i < String.length str then
      if str.[i] == ' ' then
	push_token beg i (loop_on_whitespace (i+1) (i+1))
      else
	loop beg (i+1)
    else
      push_token beg i []
  and loop_on_whitespace beg i =
    if i < String.length str then
      if str.[i] != ' ' then
	push_whitespace beg i (loop i (i+1))
      else
	loop_on_whitespace beg (i+1)
    else
      push_whitespace beg i []
  in
  loop 0 0

(* Interpret notations with a recursive component *)

let out_nt = function NonTerminal x -> x | _ -> assert false

let msg_expected_form_of_recursive_notation =
  "In the notation, the special symbol \"..\" must occur in\na configuration of the form \"x symbs .. symbs y\"."

let rec find_pattern nt xl = function
  | Break n as x :: l, Break n' :: l' when Int.equal n n' ->
      find_pattern nt (x::xl) (l,l')
  | Terminal s as x :: l, Terminal s' :: l' when String.equal s s' ->
      find_pattern nt (x::xl) (l,l')
  | [], NonTerminal x' :: l' ->
      (out_nt nt,x',List.rev xl),l'
  | _, Break s :: _ | Break s :: _, _ ->
      user_err Pp.(str ("A break occurs on one side of \"..\" but not on the other side."))
  | _, Terminal s :: _ | Terminal s :: _, _ ->
      user_err ~hdr:"Metasyntax.find_pattern"
        (str "The token \"" ++ str s ++ str "\" occurs on one side of \"..\" but not on the other side.")
  | _, [] ->
      user_err Pp.(str msg_expected_form_of_recursive_notation)
  | ((SProdList _ | NonTerminal _) :: _), _ | _, (SProdList _ :: _) ->
      anomaly (Pp.str "Only Terminal or Break expected on left, non-SProdList on right.")

let rec interp_list_parser hd = function
  | [] -> [], List.rev hd
  | NonTerminal id :: tl when Id.equal id ldots_var ->
      if List.is_empty hd then user_err Pp.(str msg_expected_form_of_recursive_notation);
      let hd = List.rev hd in
      let ((x,y,sl),tl') = find_pattern (List.hd hd) [] (List.tl hd,tl) in
      let xyl,tl'' = interp_list_parser [] tl' in
      (* We remember each pair of variable denoting a recursive part to *)
      (* remove the second copy of it afterwards *)
      (x,y)::xyl, SProdList (x,sl) :: tl''
  | (Terminal _ | Break _) as s :: tl ->
      if List.is_empty hd then
        let yl,tl' = interp_list_parser [] tl in
        yl, s :: tl'
      else
        interp_list_parser (s::hd) tl
  | NonTerminal _ as x :: tl ->
      let xyl,tl' = interp_list_parser [x] tl in
      xyl, List.rev_append hd tl'
  | SProdList _ :: _ -> anomaly (Pp.str "Unexpected SProdList in interp_list_parser.")


(* Find non-terminal tokens of notation *)

(* To protect alphabetic tokens and quotes from being seen as variables *)
let quote_notation_token x =
  let n = String.length x in
  let norm = CLexer.is_ident x in
  if (n > 0 && norm) || (n > 2 && x.[0] == '\'') then "'"^x^"'"
  else x

let rec raw_analyze_notation_tokens = function
  | []    -> []
  | String ".." :: sl -> NonTerminal ldots_var :: raw_analyze_notation_tokens sl
  | String "_" :: _ -> user_err Pp.(str "_ must be quoted.")
  | String x :: sl when CLexer.is_ident x ->
      NonTerminal (Names.Id.of_string x) :: raw_analyze_notation_tokens sl
  | String s :: sl ->
      Terminal (String.drop_simple_quotes s) :: raw_analyze_notation_tokens sl
  | WhiteSpace n :: sl ->
      Break n :: raw_analyze_notation_tokens sl

let is_numeral symbs =
  match List.filter (function Break _ -> false | _ -> true) symbs with
  | ([Terminal "-"; Terminal x] | [Terminal x]) ->
      (try let _ = Bigint.of_string x in true with Failure _ -> false)
  | _ ->
      false

let rec get_notation_vars onlyprint = function
  | [] -> []
  | NonTerminal id :: sl ->
      let vars = get_notation_vars onlyprint sl in
      if Id.equal id ldots_var then vars else
	(* don't check for nonlinearity if printing only, see Bug 5526 *)
	if not onlyprint && Id.List.mem id vars then 
	  user_err ~hdr:"Metasyntax.get_notation_vars"
            (str "Variable " ++ Id.print id ++ str " occurs more than once.")
	else id::vars
  | (Terminal _ | Break _) :: sl -> get_notation_vars onlyprint sl
  | SProdList _ :: _ -> assert false

let analyze_notation_tokens ~onlyprint l =
  let l = raw_analyze_notation_tokens l in
  let vars = get_notation_vars onlyprint l in
  let recvars,l = interp_list_parser [] l in
  recvars, List.subtract Id.equal vars (List.map snd recvars), l

let error_not_same_scope x y =
  user_err ~hdr:"Metasyntax.error_not_name_scope"
    (str "Variables " ++ Id.print x ++ str " and " ++ Id.print y ++ str " must be in the same scope.")

(**********************************************************************)
(* Build pretty-printing rules                                        *)

let prec_assoc = function
  | RightA -> (L,E)
  | LeftA -> (E,L)
  | NonA -> (L,L)

let precedence_of_entry_type from = function
  | ETConstr (NumLevel n,BorderProd (_,None)) -> n, Prec n
  | ETConstr (NumLevel n,BorderProd (b,Some a)) ->
      n, let (lp,rp) = prec_assoc a in if b == Left then lp else rp
  | ETConstr (NumLevel n,InternalProd) -> n, Prec n
  | ETConstr (NextLevel,_) -> from, L
  | _ -> 0, E (* ?? *)

(* Some breaking examples *)
(* "x = y" : "x /1 = y" (breaks before any symbol) *)
(* "x =S y" : "x /1 =S /1 y" (protect from confusion; each side for symmetry)*)
(* "+ {" : "+ {" may breaks reversibility without space but oth. not elegant *)
(* "x y" : "x spc y" *)
(* "{ x } + { y }" : "{ x } / + { y }" *)
(* "< x , y > { z , t }" : "< x , / y > / { z , / t }" *)

let starts_with_left_bracket s =
  let l = String.length s in not (Int.equal l 0) &&
  (s.[0] == '{' || s.[0] == '[' || s.[0] == '(')

let ends_with_right_bracket s =
  let l = String.length s in not (Int.equal l 0) &&
  (s.[l-1] == '}' || s.[l-1] == ']' || s.[l-1] == ')')

let is_left_bracket s =
  starts_with_left_bracket s && not (ends_with_right_bracket s)

let is_right_bracket s =
  not (starts_with_left_bracket s) && ends_with_right_bracket s

let is_comma s =
  let l = String.length s in not (Int.equal l 0) &&
  (s.[0] == ',' || s.[0] == ';')

let is_operator s =
  let l = String.length s in not (Int.equal l 0) &&
  (s.[0] == '+' || s.[0] == '*' || s.[0] == '=' ||
   s.[0] == '-' || s.[0] == '/' || s.[0] == '<' || s.[0] == '>' ||
   s.[0] == '@' || s.[0] == '\\' || s.[0] == '&' || s.[0] == '~' || s.[0] == '$')

let is_non_terminal = function
  | NonTerminal _ | SProdList _ -> true
  | _ -> false

let is_next_non_terminal = function
| [] -> false
| pr :: _ -> is_non_terminal pr

let is_next_terminal = function Terminal _ :: _ -> true | _ -> false

let is_next_break = function Break _ :: _ -> true | _ -> false

let add_break n l = (None,UnpCut (PpBrk(n,0))) :: l

let add_break_if_none n = function
  | (((_,UnpCut (PpBrk _)) :: _) | []) as l -> l
  | l -> (None,UnpCut (PpBrk(n,0))) :: l

let check_open_binder isopen sl m =
  let pr_token = function
  | Terminal s -> str s
  | Break n -> str "␣"
  | _ -> assert false
  in
  if isopen && not (List.is_empty sl) then
    user_err  (str "as " ++ Id.print m ++
      str " is a non-closed binder, no such \"" ++
      prlist_with_sep spc pr_token sl
      ++ strbrk "\" is allowed to occur.")

(* Heuristics for building default printing rules *)

let index_id id l = List.index Id.equal id l

let make_hunks etyps symbols from =
  let vars,typs = List.split etyps in
  let rec make = function
    | NonTerminal m :: prods ->
	let i = index_id m vars in
	let _,prec = precedence_of_entry_type from (List.nth typs (i-1)) in
	let u = UnpMetaVar (i,prec) in
	if is_next_non_terminal prods then
	  (None,u) :: add_break_if_none 1 (make prods)
	else
	  (None,u) :: make_with_space prods
    | Terminal s :: prods when List.exists is_non_terminal prods ->
        if (is_comma s || is_operator s) then
          (* Always a breakable space after comma or separator *)
	  (None,UnpTerminal s) :: add_break_if_none 1 (make prods)
	else if is_right_bracket s && is_next_terminal prods then
          (* Always no space after right bracked, but possibly a break *)
	  (None,UnpTerminal s) :: add_break_if_none 0 (make prods)
        else if is_left_bracket s  && is_next_non_terminal prods then
	  (None,UnpTerminal s) :: make prods
	else if not (is_next_break prods) then
          (* Add rigid space, no break, unless user asked for something *)
          (None,UnpTerminal (s^" ")) :: make prods
        else
          (* Rely on user spaces *)
          (None,UnpTerminal s) :: make prods

    | Terminal s :: prods ->
        (* Separate but do not cut a trailing sequence of terminal *)
        (match prods with
        | Terminal _ :: _ -> (None,UnpTerminal (s^" ")) :: make prods
        | _ -> (None,UnpTerminal s) :: make prods)

    | Break n :: prods ->
	add_break n (make prods)

    | SProdList (m,sl) :: prods ->
	let i = index_id m vars in
	let typ = List.nth typs (i-1) in
	let _,prec = precedence_of_entry_type from typ in
        let sl' =
          (* If no separator: add a break *)
	  if List.is_empty sl then add_break 1 []
          (* We add NonTerminal for simulation but remove it afterwards *)
	  else snd (List.sep_last (make (sl@[NonTerminal m]))) in
	let hunk = match typ with
	  | ETConstr _ -> UnpListMetaVar (i,prec,List.map snd sl')
	  | ETBinder isopen ->
	      check_open_binder isopen sl m;
	      UnpBinderListMetaVar (i,isopen,List.map snd sl')
	  | _ -> assert false in
	(None,hunk) :: make_with_space prods

    | [] -> []

  and make_with_space prods =
    match prods with
    | Terminal s' :: prods'->
        if is_operator s' then
          (* A rigid space before operator and a breakable after *)
          (None,UnpTerminal (" "^s')) :: add_break_if_none 1 (make prods')
        else if is_comma s' then
          (* No space whatsoever before comma *)
          make prods
        else if is_right_bracket s' then
          make prods
        else
          (* A breakable space between any other two terminals *)
          add_break_if_none 1 (make prods)
    | (NonTerminal _ | SProdList _) :: _ ->
        (* A breakable space before a non-terminal *)
        add_break_if_none 1 (make prods)
    | Break _ :: _ ->
        (* Rely on user wish *)
        make prods
    | [] -> []

  in make symbols

(* Build default printing rules from explicit format *)

let error_format ?loc () = user_err ?loc Pp.(str "The format does not match the notation.")

let rec split_format_at_ldots hd = function
  | (loc,UnpTerminal s) :: fmt when String.equal s (Id.to_string ldots_var) -> loc, List.rev hd, fmt
  | u :: fmt ->
      check_no_ldots_in_box u;
      split_format_at_ldots (u::hd) fmt
  | [] -> raise Exit

and check_no_ldots_in_box = function
  | (_,UnpBox (_,fmt)) ->
      (try
        let loc,_,_ = split_format_at_ldots [] fmt in
        user_err ?loc Pp.(str ("The special symbol \"..\" must occur at the same formatting depth than the variables of which it is the ellipse."))
      with Exit -> ())
  | _ -> ()

let error_not_same ?loc () =
  user_err ?loc Pp.(str "The format is not the same on the right- and left-hand sides of the special token \"..\".")

let skip_var_in_recursive_format = function
  | (_,UnpTerminal s) :: sl (* skip first var *) when not (List.for_all (fun c -> c = " ") (String.explode s)) ->
      (* To do, though not so important: check that the names match
         the names in the notation *)
      sl
  | (loc,_) :: _ -> error_not_same ?loc ()
  | [] -> assert false

let read_recursive_format sl fmt =
  let get_head fmt =
    let sl = skip_var_in_recursive_format fmt in
    try split_format_at_ldots [] sl with Exit -> error_not_same ?loc:(fst (List.last (if sl = [] then fmt else sl))) () in
  let rec get_tail = function
    | (loc,a) :: sepfmt, (_,b) :: fmt when Pervasives.(=) a b -> get_tail (sepfmt, fmt) (* FIXME *)
    | [], tail -> skip_var_in_recursive_format tail
    | (loc,_) :: _, ([] | (_,UnpTerminal _) :: _)-> error_not_same ?loc ()
    | _, (loc,_)::_ -> error_not_same ?loc () in
  let loc, slfmt, fmt = get_head fmt in
  slfmt, get_tail (slfmt, fmt)

let hunks_of_format (from,(vars,typs)) symfmt =
  let rec aux = function
  | symbs, (_,(UnpTerminal s' as u)) :: fmt
      when String.equal s' (String.make (String.length s') ' ') ->
      let symbs, l = aux (symbs,fmt) in symbs, u :: l
  | Terminal s :: symbs, (_,UnpTerminal s') :: fmt
      when String.equal s (String.drop_simple_quotes s') ->
      let symbs, l = aux (symbs,fmt) in symbs, UnpTerminal s :: l
  | NonTerminal s :: symbs, (_,UnpTerminal s') :: fmt when Id.equal s (Id.of_string s') ->
      let i = index_id s vars in
      let _,prec = precedence_of_entry_type from (List.nth typs (i-1)) in
      let symbs, l = aux (symbs,fmt) in symbs, UnpMetaVar (i,prec) :: l
  | symbs, (_,UnpBox (a,b)) :: fmt ->
      let symbs', b' = aux (symbs,b) in
      let symbs', l = aux (symbs',fmt) in
      symbs', UnpBox (a,List.map (fun x -> (None,x)) b') :: l
  | symbs, (_,(UnpCut _ as u)) :: fmt ->
      let symbs, l = aux (symbs,fmt) in symbs, u :: l
  | SProdList (m,sl) :: symbs, fmt ->
      let i = index_id m vars in
      let typ = List.nth typs (i-1) in
      let _,prec = precedence_of_entry_type from typ in
      let slfmt,fmt = read_recursive_format sl fmt in
      let sl, slfmt = aux (sl,slfmt) in
      if not (List.is_empty sl) then error_format ?loc:(fst (List.last fmt)) ();
      let symbs, l = aux (symbs,fmt) in
      let hunk = match typ with
	| ETConstr _ -> UnpListMetaVar (i,prec,slfmt)
	| ETBinder isopen ->
	    check_open_binder isopen sl m;
	    UnpBinderListMetaVar (i,isopen,slfmt)
	| _ -> assert false in
      symbs, hunk :: l
  | symbs, [] -> symbs, []
  | _, fmt -> error_format ?loc:(fst (List.hd fmt)) ()
  in
  match aux symfmt with
  | [], l -> l
  | _ -> error_format ()

(**********************************************************************)
(* Build parsing rules                                                *)

let assoc_of_type n (_,typ) = precedence_of_entry_type n typ

let is_not_small_constr = function
    ETConstr _ -> true
  | ETOther("constr","binder_constr") -> true
  | _ -> false

let rec define_keywords_aux = function
  | GramConstrNonTerminal(e,Some _) as n1 :: GramConstrTerminal(IDENT k) :: l
      when is_not_small_constr e ->
      Flags.if_verbose Feedback.msg_info (str "Identifier '" ++ str k ++ str "' now a keyword");
      CLexer.add_keyword k;
      n1 :: GramConstrTerminal(KEYWORD k) :: define_keywords_aux l
  | n :: l -> n :: define_keywords_aux l
  | [] -> []

  (* Ensure that IDENT articulation terminal symbols are keywords *)
let define_keywords = function
  | GramConstrTerminal(IDENT k)::l ->
      Flags.if_verbose Feedback.msg_info (str "Identifier '" ++ str k ++ str "' now a keyword");
      CLexer.add_keyword k;
      GramConstrTerminal(KEYWORD k) :: define_keywords_aux l
  | l -> define_keywords_aux l

let distribute a ll = List.map (fun l -> a @ l) ll

  (* Expand LIST1(t,sep);sep;t;...;t (with the trailing pattern
     occurring p times, possibly p=0) into the combination of
     t;sep;t;...;t;sep;t (p+1 times)
     t;sep;t;...;t;sep;t;sep;t (p+2 times)
     ...
     t;sep;t;...;t;sep;t;...;t;sep;t (p+n times)
     t;sep;t;...;t;sep;t;...;t;sep;t;LIST1(t,sep) *)

let expand_list_rule typ tkl x n p ll =
  let camlp4_message_name = Some (add_suffix x ("_"^string_of_int n)) in
  let main = GramConstrNonTerminal (ETConstr typ, camlp4_message_name) in
  let tks = List.map (fun x -> GramConstrTerminal x) tkl in
  let rec aux i hds ll =
  if i < p then aux (i+1) (main :: tks @ hds) ll
  else if Int.equal i (p+n) then
    let hds =
      GramConstrListMark (p+n,true,p) :: hds
      @	[GramConstrNonTerminal (ETConstrList (typ,tkl), Some x)] in
    distribute hds ll
  else
    distribute (GramConstrListMark (i+1,false,p) :: hds @ [main]) ll @
       aux (i+1) (main :: tks @ hds) ll in
  aux 0 [] ll

let is_constr_typ typ x etyps =
  match List.assoc x etyps with
  | ETConstr typ' -> typ = typ'
  | _ -> false

let include_possible_similar_trailing_pattern typ etyps sl l =
  let rec aux n = function
  | Terminal s :: sl, Terminal s'::l' when s = s' -> aux n (sl,l')
  | [], NonTerminal x ::l' when is_constr_typ typ x etyps -> try_aux n l'
  | _ -> raise Exit
  and try_aux n l =
    try aux (n+1) (sl,l)
    with Exit -> n,l in
  try_aux 0 l

let make_production etyps symbols =
  let rec aux = function
    | [] -> [[]]
    | NonTerminal m :: l ->
        let typ = List.assoc m etyps in
        distribute [GramConstrNonTerminal (typ, Some m)] (aux l)
    | Terminal s :: l ->
        distribute [GramConstrTerminal (CLexer.terminal s)] (aux l)
    | Break _ :: l ->
        aux l
    | SProdList (x,sl) :: l ->
        let tkl = List.flatten
          (List.map (function Terminal s -> [CLexer.terminal s]
            | Break _ -> []
            | _ -> anomaly (Pp.str "Found a non terminal token in recursive notation separator.")) sl) in
	match List.assoc x etyps with
        | ETConstr typ ->
            let p,l' = include_possible_similar_trailing_pattern typ etyps sl l in
            expand_list_rule typ tkl x 1 p (aux l')
        | ETBinder o ->
	    distribute
              [GramConstrNonTerminal (ETBinderList (o,tkl), Some x)] (aux l)
        | _ ->
           user_err Pp.(str "Components of recursive patterns in notation must be terms or binders.") in
  let prods = aux symbols in
  List.map define_keywords prods

let rec find_symbols c_current c_next c_last = function
  | [] -> []
  | NonTerminal id :: sl ->
      let prec = if not (List.is_empty sl) then c_current else c_last in
      (id, prec) :: (find_symbols c_next c_next c_last sl)
  | Terminal s :: sl -> find_symbols c_next c_next c_last sl
  | Break n :: sl -> find_symbols c_current c_next c_last sl
  | SProdList (x,_) :: sl' ->
      (x,c_next)::(find_symbols c_next c_next c_last sl')

let border = function
  | (_,ETConstr(_,BorderProd (_,a))) :: _ -> a
  | _ -> None

let recompute_assoc typs =
  match border typs, border (List.rev typs) with
    | Some LeftA, Some RightA -> assert false
    | Some LeftA, _ -> Some LeftA
    | _, Some RightA -> Some RightA
    | _ -> None

(**************************************************************************)
(* Registration of syntax extensions (parsing/printing, no interpretation)*)

let pr_arg_level from (lev,typ) =
  let pplev = match lev with
  | (n,L) when Int.equal n from -> str "at next level"
  | (n,E) -> str "at level " ++ int n
  | (n,L) -> str "at level below " ++ int n
  | (n,Prec m) when Int.equal m n -> str "at level " ++ int n
  | (n,_) -> str "Unknown level" in
  let pptyp = match typ with
  | NtnInternTypeConstr -> mt ()
  | NtnInternTypeBinder -> str " " ++ surround (str "binder")
  | NtnInternTypeIdent -> str " " ++ surround (str "ident") in
  pplev ++ pptyp

let pr_level ntn (from,args,typs) =
  str "at level " ++ int from ++ spc () ++ str "with arguments" ++ spc() ++
  prlist_with_sep pr_comma (pr_arg_level from) (List.combine args typs)

let error_incompatible_level ntn oldprec prec =
  user_err 
    (str "Notation " ++ qstring ntn ++ str " is already defined" ++ spc() ++
    pr_level ntn oldprec ++
    spc() ++ str "while it is now required to be" ++ spc() ++
    pr_level ntn prec ++ str ".")

let error_parsing_incompatible_level ntn ntn' oldprec prec =
  user_err
    (str "Notation " ++ qstring ntn ++ str " relies on a parsing rule for " ++ qstring ntn' ++ spc() ++
    str " which is already defined" ++ spc() ++
    pr_level ntn oldprec ++
    spc() ++ str "while it is now required to be" ++ spc() ++
    pr_level ntn prec ++ str ".")

type syntax_extension = {
  synext_level : Notation_term.level;
  synext_notation : notation;
  synext_notgram : notation_grammar;
  synext_unparsing : unparsing list;
  synext_extra : (string * string) list;
  synext_compat : Flags.compat_version option;
}

let is_active_compat = function
| None -> true
| Some v -> 0 <= Flags.version_compare v !Flags.compat_version

type syntax_extension_obj = locality_flag * syntax_extension

let check_and_extend_constr_grammar ntn rule =
  try
    let ntn_for_grammar = rule.notgram_notation in
    if String.equal ntn ntn_for_grammar then raise Not_found;
    let prec = rule.notgram_level in
    let oldprec = Notation.level_of_notation ntn_for_grammar in
    if not (Notation.level_eq prec oldprec) then error_parsing_incompatible_level ntn ntn_for_grammar oldprec prec;
  with Not_found ->
    Egramcoq.extend_constr_grammar rule

let cache_one_syntax_extension se =
  let ntn = se.synext_notation in
  let prec = se.synext_level in
  let onlyprint = se.synext_notgram.notgram_onlyprinting in
  try
    let oldprec = Notation.level_of_notation ntn in
    if not (Notation.level_eq prec oldprec) then error_incompatible_level ntn oldprec prec;
  with Not_found ->
    if is_active_compat se.synext_compat then begin
      (* Reserve the notation level *)
      Notation.declare_notation_level ntn prec;
      (* Declare the parsing rule *)
      if not onlyprint then List.iter (check_and_extend_constr_grammar ntn) se.synext_notgram.notgram_rules;
      (* Declare the notation rule *)
      Notation.declare_notation_rule ntn
        ~extra:se.synext_extra (se.synext_unparsing, pi1 prec) se.synext_notgram
    end

let cache_syntax_extension (_, (_, sy)) =
  cache_one_syntax_extension sy

let subst_parsing_rule subst x = x

let subst_printing_rule subst x = x

let subst_syntax_extension (subst, (local, sy)) =
  (local, { sy with
    synext_notgram = { sy.synext_notgram with notgram_rules = List.map (subst_parsing_rule subst) sy.synext_notgram.notgram_rules };
    synext_unparsing = subst_printing_rule subst sy.synext_unparsing;
  })

let classify_syntax_definition (local, _ as o) =
  if local then Dispose else Substitute o

let inSyntaxExtension : syntax_extension_obj -> obj =
  declare_object {(default_object "SYNTAX-EXTENSION") with
       open_function = (fun i o -> if Int.equal i 1 then cache_syntax_extension o);
       cache_function = cache_syntax_extension;
       subst_function = subst_syntax_extension;
       classify_function = classify_syntax_definition}

(**************************************************************************)
(* Precedences                                                            *)

(* Interpreting user-provided modifiers *)

(* XXX: We could move this to the parser itself *)
module NotationMods = struct

type notation_modifier = {
  assoc         : gram_assoc option;
  level         : int option;
  etyps         : (Id.t * simple_constr_prod_entry_key) list;

  (* common to syn_data below *)
  only_parsing  : bool;
  only_printing : bool;
  compat        : Flags.compat_version option;
  format        : string Loc.located option;
  extra         : (string * string) list;
}

let default = {
  assoc         = None;
  level         = None;
  etyps         = [];
  only_parsing  = false;
  only_printing = false;
  compat        = None;
  format        = None;
  extra         = [];
}

end

let interp_modifiers modl = let open NotationMods in
  let rec interp acc = function
    | [] -> acc
    | SetEntryType (s,typ) :: l ->
	let id = Id.of_string s in
	if Id.List.mem_assoc id acc.etyps then
	  user_err ~hdr:"Metasyntax.interp_modifiers"
            (str s ++ str " is already assigned to an entry or constr level.");
        interp { acc with etyps = (id,typ) :: acc.etyps; } l
    | SetItemLevel ([],n) :: l ->
        interp acc l
    | SetItemLevel (s::idl,n) :: l ->
	let id = Id.of_string s in
	if Id.List.mem_assoc id acc.etyps then
	  user_err ~hdr:"Metasyntax.interp_modifiers"
            (str s ++ str " is already assigned to an entry or constr level.");
	let typ = ETConstr (n,()) in
        interp { acc with etyps = (id,typ)::acc.etyps; } (SetItemLevel (idl,n)::l)
    | SetLevel n :: l ->

        interp { acc with level = Some n; } l
    | SetAssoc a :: l ->
	if not (Option.is_empty acc.assoc) then user_err Pp.(str "An associativity is given more than once.");
        interp { acc with assoc = Some a; } l
     | SetOnlyParsing :: l ->
        interp { acc with only_parsing = true; } l
    | SetOnlyPrinting :: l ->
        interp { acc with only_printing = true; } l
    | SetCompatVersion v :: l ->
        interp { acc with compat = Some v; } l
    | SetFormat ("text",s) :: l ->
	if not (Option.is_empty acc.format) then user_err Pp.(str "A format is given more than once.");
        interp { acc with format = Some s; } l
    | SetFormat (k,(_,s)) :: l ->
        interp { acc with extra = (k,s)::acc.extra; } l
  in interp default modl

let check_infix_modifiers modifiers =
  let t = (interp_modifiers modifiers).NotationMods.etyps in
  if not (List.is_empty t) then
    user_err Pp.(str "Explicit entry level or type unexpected in infix notation.")

let check_useless_entry_types recvars mainvars etyps =
  let vars = let (l1,l2) = List.split recvars in l1@l2@mainvars in
  match List.filter (fun (x,etyp) -> not (List.mem x vars)) etyps with
  | (x,_)::_ -> user_err ~hdr:"Metasyntax.check_useless_entry_types"
                  (Id.print x ++ str " is unbound in the notation.")
  | _ -> ()

let check_binder_type recvars etyps =
  let l1,l2 = List.split recvars in
  let l = l1@l2 in
  List.iter (function
    | (x,ETBinder b) when not (List.mem x l) ->
       CErrors.user_err (str (if b then "binder" else "closed binder") ++
                 strbrk " is only for use in recursive notations for binders.")
    | _ -> ()) etyps

let not_a_syntax_modifier = function
| SetOnlyParsing -> true
| SetOnlyPrinting -> true
| SetCompatVersion _ -> true
| _ -> false

let no_syntax_modifiers mods = List.for_all not_a_syntax_modifier mods

let is_only_parsing mods =
  let test = function SetOnlyParsing -> true | _ -> false in
  List.exists test mods

let is_only_printing mods =
  let test = function SetOnlyPrinting -> true | _ -> false in
  List.exists test mods

let get_compat_version mods =
  let test = function SetCompatVersion v -> Some v | _ -> None in
  try Some (List.find_map test mods) with Not_found -> None

(* Compute precedences from modifiers (or find default ones) *)

let set_entry_type etyps (x,typ) =
  let typ = try
    match List.assoc x etyps, typ with
      | ETConstr (n,()), (_,BorderProd (left,_)) ->
          ETConstr (n,BorderProd (left,None))
      | ETConstr (n,()), (_,InternalProd) -> ETConstr (n,InternalProd)
      | (ETPattern | ETName | ETBigint | ETOther _ |
	 ETReference | ETBinder _ as t), _ -> t
      | (ETBinderList _ |ETConstrList _), _ -> assert false
    with Not_found -> ETConstr typ
  in (x,typ)

let join_auxiliary_recursive_types recvars etyps =
  List.fold_right (fun (x,y) typs ->
    let xtyp = try Some (List.assoc x etyps) with Not_found -> None in
    let ytyp = try Some (List.assoc y etyps) with Not_found -> None in
    match xtyp,ytyp with
    | None, None -> typs
    | Some _, None -> typs
    | None, Some ytyp -> (x,ytyp)::typs
    | Some xtyp, Some ytyp when Pervasives.(=) xtyp ytyp -> typs (* FIXME *)
    | Some xtyp, Some ytyp ->
	user_err 
	  (strbrk "In " ++ Id.print x ++ str " .. " ++ Id.print y ++
	   strbrk ", both ends have incompatible types."))
    recvars etyps

let internalization_type_of_entry_type = function
  | ETConstr _ -> NtnInternTypeConstr
  | ETBigint | ETReference -> NtnInternTypeConstr
  | ETBinder _ -> NtnInternTypeBinder
  | ETName -> NtnInternTypeIdent
  | ETPattern | ETOther _ -> user_err Pp.(str "Not supported.")
  | ETBinderList _ | ETConstrList _ -> assert false

let set_internalization_type typs =
  List.map (fun (_, e) -> internalization_type_of_entry_type e) typs

let make_internalization_vars recvars mainvars typs =
  let maintyps = List.combine mainvars typs in
  let extratyps = List.map (fun (x,y) -> (y,List.assoc x maintyps)) recvars in
  maintyps @ extratyps

let make_interpretation_type isrec isonlybinding = function
  | NtnInternTypeConstr when isrec -> NtnTypeConstrList
  | NtnInternTypeConstr | NtnInternTypeIdent ->
     if isonlybinding then NtnTypeOnlyBinder else NtnTypeConstr
  | NtnInternTypeBinder when isrec -> NtnTypeBinderList
   | NtnInternTypeBinder -> user_err Pp.(str "Type binder is only for use in recursive notations for binders.")

let make_interpretation_vars recvars allvars =
  let eq_subscope (sc1, l1) (sc2, l2) =
    Option.equal String.equal sc1 sc2 &&
    List.equal String.equal l1 l2
  in
  let check (x, y) =
    let (_,scope1, _) = Id.Map.find x allvars in
    let (_,scope2, _) = Id.Map.find y allvars in
    if not (eq_subscope scope1 scope2) then error_not_same_scope x y
  in
  let () = List.iter check recvars in
  let useless_recvars = List.map snd recvars in
  let mainvars =
    Id.Map.filter (fun x _ -> not (Id.List.mem x useless_recvars)) allvars in
  Id.Map.mapi (fun x (isonlybinding, sc, typ) ->
    (sc, make_interpretation_type (Id.List.mem_assoc x recvars) isonlybinding typ)) mainvars

let check_rule_productivity l =
  if List.for_all (function NonTerminal _ | Break _ -> true | _ -> false) l then
    user_err Pp.(str "A notation must include at least one symbol.");
  if (match l with SProdList _ :: _ -> true | _ -> false) then
    user_err Pp.(str "A recursive notation must start with at least one symbol.")

let warn_notation_bound_to_variable =
  CWarnings.create ~name:"notation-bound-to-variable" ~category:"parsing"
         (fun () ->
          strbrk "This notation will not be used for printing as it is bound to a single variable.")

let warn_non_reversible_notation =
  CWarnings.create ~name:"non-reversible-notation" ~category:"parsing"
         (fun () ->
          strbrk "This notation will not be used for printing as it is not reversible.")

let is_not_printable onlyparse nonreversible = function
| NVar _ ->
  if not onlyparse then warn_notation_bound_to_variable ();
  true
| _ ->
   if not onlyparse && nonreversible then
     (warn_non_reversible_notation (); true)
  else onlyparse

let find_precedence lev etyps symbols onlyprint =
  let first_symbol =
    let rec aux = function
      | Break _ :: t -> aux t
      | h :: t -> Some h
      | [] -> None in
    aux symbols in
  let last_is_terminal () =
    let rec aux b = function
      | Break _ :: t -> aux b t
      | Terminal _ :: t -> aux true t
      | _ :: t -> aux false t
      | [] -> b in
    aux false symbols in
  match first_symbol with
  | None -> [],0
  | Some (NonTerminal x) ->
      (try match List.assoc x etyps with
        | ETConstr _ ->
	   if onlyprint then
	     if Option.is_empty lev then
	       user_err Pp.(str "Explicit level needed in only-printing mode when the level of the leftmost non-terminal is given.")
	     else [],Option.get lev
	   else
	     user_err Pp.(str "The level of the leftmost non-terminal cannot be changed.")
	| ETName | ETBigint | ETReference ->
            begin match lev with
            | None ->
	      ([Feedback.msg_info ?loc:None ,strbrk "Setting notation at level 0."],0)
            | Some 0 ->
              ([],0)
            | _ ->
	      user_err Pp.(str "A notation starting with an atomic expression must be at level 0.")
            end
	| ETPattern | ETBinder _ | ETOther _ -> (* Give a default ? *)
	    if Option.is_empty lev then
	      user_err Pp.(str "Need an explicit level.")
	    else [],Option.get lev
        | ETConstrList _ | ETBinderList _ ->
	    assert false (* internally used in grammar only *)
      with Not_found ->
	if Option.is_empty lev then
	  user_err Pp.(str "A left-recursive notation must have an explicit level.")
	else [],Option.get lev)
  | Some (Terminal _) when last_is_terminal () ->
      if Option.is_empty lev then
	([Feedback.msg_info ?loc:None ,strbrk "Setting notation at level 0."], 0)
      else [],Option.get lev
  | Some _ ->
      if Option.is_empty lev then user_err Pp.(str "Cannot determine the level.");
      [],Option.get lev

let check_curly_brackets_notation_exists () =
  try let _ = Notation.level_of_notation "{ _ }" in ()
  with Not_found ->
    user_err Pp.(str "Notations involving patterns of the form \"{ _ }\" are treated \n\
specially and require that the notation \"{ _ }\" is already reserved.")

(* Remove patterns of the form "{ _ }", unless it is the "{ _ }" notation *)
let remove_curly_brackets l =
  let rec skip_break acc = function
    | Break _ as br :: l -> skip_break (br::acc) l
    | l -> List.rev acc, l in
  let rec aux deb = function
  | [] -> []
  | Terminal "{" as t1 :: l ->
      let br,next = skip_break [] l in
      (match next with
        | NonTerminal _ as x :: l' ->
            let br',next' = skip_break [] l' in
            (match next' with
              | Terminal "}" as t2 :: l'' ->
		  if deb && List.is_empty l'' then [t1;x;t2] else begin
                    check_curly_brackets_notation_exists ();
                    x :: aux false l''
                  end
              | l1 -> t1 :: br @ x :: br' @ aux false l1)
        | l0 -> t1 :: aux false l0)
  | x :: l -> x :: aux false l
  in aux true l

module SynData = struct

  type subentry_types = (Id.t * (production_level, production_position) constr_entry_key_gen) list

  (* XXX: Document *)
  type syn_data = {

    (* Notation name and location *)
    info          : notation * notation_location;

    (* Fields coming from the vernac-level modifiers *)
    only_parsing  : bool;
    only_printing : bool;
    compat        : Flags.compat_version option;
    format        : string Loc.located option;
    extra         : (string * string) list;

    (* XXX: Callback to printing, must remove *)
    msgs          : ((Pp.t -> unit) * Pp.t) list;

    (* Fields for internalization *)
    recvars       : (Id.t * Id.t) list;
    mainvars      : Id.List.elt list;
    intern_typs   : notation_var_internalization_type list;

    (* Notation data for parsing *)
    level         : level;
    pa_syntax_data : subentry_types * symbol list;
    pp_syntax_data : subentry_types * symbol list;
    not_data      : notation *                   (* notation *)
                    level *                      (* level, precedence, types *)
                    bool;                        (* needs_squash *)
  }

end

let find_subentry_types n assoc etyps symbols =
  let innerlevel = NumLevel 200 in
  let typs =
    find_symbols
      (NumLevel n,BorderProd(Left,assoc))
      (innerlevel,InternalProd)
      (NumLevel n,BorderProd(Right,assoc))
      symbols in
  let sy_typs = List.map (set_entry_type etyps) typs in
  let prec = List.map (assoc_of_type n) sy_typs in
  sy_typs, prec

let compute_syntax_data df modifiers =
  let open SynData in
  let open NotationMods in
  let mods = interp_modifiers modifiers in
  let onlyprint = mods.only_printing in
  let onlyparse = mods.only_parsing in
  if onlyprint && onlyparse then user_err (str "A notation cannot be both 'only printing' and 'only parsing'.");
  let assoc = Option.append mods.assoc (Some NonA) in
  let toks = split_notation_string df in
  let (recvars,mainvars,symbols) = analyze_notation_tokens ~onlyprint toks in
  let _ = check_useless_entry_types recvars mainvars mods.etyps in
  let _ = check_binder_type recvars mods.etyps in

  (* Notations for interp and grammar  *)
  let ntn_for_interp = make_notation_key symbols in
  let symbols_for_grammar = remove_curly_brackets symbols in
  let need_squash = not (List.equal Notation.symbol_eq symbols symbols_for_grammar) in
  let ntn_for_grammar = if need_squash then make_notation_key symbols_for_grammar else ntn_for_interp in
  if not onlyprint then check_rule_productivity symbols_for_grammar;
  let msgs,n = find_precedence mods.level mods.etyps symbols onlyprint in
  (* To globalize... *)
  let etyps = join_auxiliary_recursive_types recvars mods.etyps in
  let sy_typs, prec =
    find_subentry_types n assoc etyps symbols in
  let sy_typs_for_grammar, prec_for_grammar =
    if need_squash then
      find_subentry_types n assoc etyps symbols_for_grammar
    else
      sy_typs, prec in
  let i_typs = set_internalization_type sy_typs in
  let pa_sy_data = (sy_typs_for_grammar,symbols_for_grammar) in
  let pp_sy_data = (sy_typs,symbols) in
  let sy_fulldata = (ntn_for_grammar,(n,prec_for_grammar,i_typs),need_squash) in
  let df' = ((Lib.library_dp(),Lib.current_dirpath true),df) in
  let i_data = ntn_for_interp, df' in

  (* Return relevant data for interpretation and for parsing/printing *)
  { info = i_data;

    only_parsing  = mods.only_parsing;
    only_printing = mods.only_printing;
    compat        = mods.compat;
    format        = mods.format;
    extra         = mods.extra;

    msgs;

    recvars;
    mainvars;
    intern_typs = i_typs;

    level  = (n,prec,i_typs);
    pa_syntax_data = pa_sy_data;
    pp_syntax_data = pp_sy_data;
    not_data    = sy_fulldata;
  }

let compute_pure_syntax_data df mods =
  let open SynData in
  let sd = compute_syntax_data df mods in
  let msgs =
    if sd.only_parsing then
      (Feedback.msg_warning ?loc:None,
      strbrk "The only parsing modifier has no effect in Reserved Notation.")::sd.msgs
    else sd.msgs in
  { sd with msgs }

(**********************************************************************)
(* Registration of notations interpretation                            *)

type notation_obj = {
  notobj_local : bool;
  notobj_scope : scope_name option;
  notobj_interp : interpretation;
  notobj_onlyparse : bool;
  notobj_onlyprint : bool;
  notobj_compat : Flags.compat_version option;
  notobj_notation : notation * notation_location;
}

let load_notation _ (_, nobj) =
  Option.iter Notation.declare_scope nobj.notobj_scope

let open_notation i (_, nobj) =
  let scope = nobj.notobj_scope in
  let (ntn, df) = nobj.notobj_notation in
  let pat = nobj.notobj_interp in
  let onlyprint = nobj.notobj_onlyprint  in
  let fresh = not (Notation.exists_notation_in_scope scope ntn onlyprint pat) in
  let active = is_active_compat nobj.notobj_compat in
  if Int.equal i 1 && fresh && active then begin
    (* Declare the interpretation *)
    let () = Notation.declare_notation_interpretation ntn scope pat df ~onlyprint in
    (* Declare the uninterpretation *)
    if not nobj.notobj_onlyparse then
      Notation.declare_uninterpretation (NotationRule (scope, ntn)) pat
  end

let cache_notation o =
  load_notation 1 o;
  open_notation 1 o

let subst_notation (subst, nobj) =
  { nobj with notobj_interp = subst_interpretation subst nobj.notobj_interp; }

let classify_notation nobj =
  if nobj.notobj_local then Dispose else Substitute nobj

let inNotation : notation_obj -> obj =
  declare_object {(default_object "NOTATION") with
       open_function = open_notation;
       cache_function = cache_notation;
       subst_function = subst_notation;
       load_function = load_notation;
       classify_function = classify_notation}

(**********************************************************************)

let with_lib_stk_protection f x =
  let fs = Lib.freeze ~marshallable:`No in
  try let a = f x in Lib.unfreeze fs; a
  with reraise ->
    let reraise = CErrors.push reraise in
    let () = Lib.unfreeze fs in
    iraise reraise

let with_syntax_protection f x =
  with_lib_stk_protection
    (Pcoq.with_grammar_rule_protection
       (with_notation_protection f)) x

(**********************************************************************)
(* Recovering existing syntax                                         *)

exception NoSyntaxRule

let recover_notation_syntax ntn =
  try
    let prec = Notation.level_of_notation ntn in
    let pp_rule,_ = Notation.find_notation_printing_rule ntn in
    let pp_extra_rules = Notation.find_notation_extra_printing_rules ntn in
    let pa_rule = Notation.find_notation_parsing_rules ntn in
    { synext_level = prec;
      synext_notation = ntn;
      synext_notgram = pa_rule;
      synext_unparsing = pp_rule;
      synext_extra = pp_extra_rules;
      synext_compat = None;
    }
  with Not_found ->
    raise NoSyntaxRule

let recover_squash_syntax sy =
  let sq = recover_notation_syntax "{ _ }" in
  sy :: sq.synext_notgram.notgram_rules

(**********************************************************************)
(* Main entry point for building parsing and printing rules           *)

let make_pa_rule level (typs,symbols) ntn need_squash =
  let assoc = recompute_assoc typs in
  let prod = make_production typs symbols in
  let sy = {
    notgram_level = level;
    notgram_assoc = assoc;
    notgram_notation = ntn;
    notgram_prods = prod;
  } in
  (* By construction, the rule for "{ _ }" is declared, but we need to
     redeclare it because the file where it is declared needs not be open
     when the current file opens (especially in presence of -nois) *)
  if need_squash then recover_squash_syntax sy else [sy]

let make_pp_rule level (typs,symbols) fmt =
  match fmt with
  | None -> [UnpBox (PpHOVB 0, make_hunks typs symbols level)]
  | Some fmt -> hunks_of_format (level, List.split typs) (symbols, parse_format fmt)

(* let make_syntax_rules i_typs (ntn,prec,need_squash) sy_data fmt extra onlyprint compat = *)
let make_syntax_rules (sd : SynData.syn_data) = let open SynData in
  let ntn_for_grammar, prec_for_grammar, need_squash = sd.not_data in
  let pa_rule = make_pa_rule prec_for_grammar sd.pa_syntax_data ntn_for_grammar need_squash in
  let pp_rule = make_pp_rule (pi1 sd.level) sd.pp_syntax_data sd.format in {
    synext_level    = sd.level;
    synext_notation = fst sd.info;
    synext_notgram  = { notgram_onlyprinting = sd.only_printing; notgram_rules = pa_rule };
    synext_unparsing = pp_rule;
    synext_extra  = sd.extra;
    synext_compat = sd.compat;
  }

(**********************************************************************)
(* Main functions about notations                                     *)

let to_map l =
  let fold accu (x, v) = Id.Map.add x v accu in
  List.fold_left fold Id.Map.empty l

let add_notation_in_scope local df env c mods scope =
  let open SynData in
  let sd = compute_syntax_data df mods in
  (* Prepare the interpretation *)
  (* Prepare the parsing and printing rules *)
  let sy_rules = make_syntax_rules sd in
  let i_vars = make_internalization_vars sd.recvars sd.mainvars sd.intern_typs in
  let nenv = {
    ninterp_var_type = to_map i_vars;
    ninterp_rec_vars = to_map sd.recvars;
  } in
  let (acvars, ac, reversible) = interp_notation_constr env nenv c in
  let interp = make_interpretation_vars sd.recvars acvars in
  let map (x, _) = try Some (x, Id.Map.find x interp) with Not_found -> None in
  let onlyparse = is_not_printable sd.only_parsing (not reversible) ac in
  let notation = {
    notobj_local = local;
    notobj_scope = scope;
    notobj_interp = (List.map_filter map i_vars, ac);
    (** Order is important here! *)
    notobj_onlyparse = onlyparse;
    notobj_onlyprint = sd.only_printing;
    notobj_compat = sd.compat;
    notobj_notation = sd.info;
  } in
  (* Ready to change the global state *)
  Flags.if_verbose (List.iter (fun (f,x) -> f x)) sd.msgs;
  Lib.add_anonymous_leaf (inSyntaxExtension (local, sy_rules));
  Lib.add_anonymous_leaf (inNotation notation);
  sd.info

let add_notation_interpretation_core local df env ?(impls=empty_internalization_env) c scope onlyparse onlyprint compat =
  let dfs = split_notation_string df in
  let (recvars,mainvars,symbs) = analyze_notation_tokens ~onlyprint dfs in
  (* Recover types of variables and pa/pp rules; redeclare them if needed *)
  let i_typs, onlyprint = if not (is_numeral symbs) then begin
    let sy = recover_notation_syntax (make_notation_key symbs) in
    let () = Lib.add_anonymous_leaf (inSyntaxExtension (local,sy)) in
    (** If the only printing flag has been explicitly requested, put it back *)
    let onlyprint = onlyprint || sy.synext_notgram.notgram_onlyprinting in
    pi3 sy.synext_level, onlyprint
  end else [], false in
  (* Declare interpretation *)
  let path = (Lib.library_dp(), Lib.current_dirpath true) in
  let df'  = (make_notation_key symbs, (path,df)) in
  let i_vars = make_internalization_vars recvars mainvars i_typs in
  let nenv = {
    ninterp_var_type = to_map i_vars;
    ninterp_rec_vars = to_map recvars;
  } in
  let (acvars, ac, reversible) = interp_notation_constr env ~impls nenv c in
  let interp = make_interpretation_vars recvars acvars in
  let map (x, _) = try Some (x, Id.Map.find x interp) with Not_found -> None in
  let onlyparse = is_not_printable onlyparse (not reversible) ac in
  let notation = {
    notobj_local = local;
    notobj_scope = scope;
    notobj_interp = (List.map_filter map i_vars, ac);
    (** Order is important here! *)
    notobj_onlyparse = onlyparse;
    notobj_onlyprint = onlyprint;
    notobj_compat = compat;
    notobj_notation = df';
  } in
  Lib.add_anonymous_leaf (inNotation notation);
  df'

(* Notations without interpretation (Reserved Notation) *)

let add_syntax_extension local ((loc,df),mods) = let open SynData in
  let psd = compute_pure_syntax_data df mods in
  let sy_rules = make_syntax_rules {psd with compat = None} in
  Flags.if_verbose (List.iter (fun (f,x) -> f x)) psd.msgs;
  Lib.add_anonymous_leaf (inSyntaxExtension(local,sy_rules))

(* Notations with only interpretation *)

let add_notation_interpretation env ((loc,df),c,sc) =
  let df' = add_notation_interpretation_core false df env c sc false false None in
  Dumpglob.dump_notation (loc,df') sc true

let set_notation_for_interpretation env impls ((_,df),c,sc) =
  (try ignore
    (Flags.silently (fun () -> add_notation_interpretation_core false df env ~impls c sc false false None) ());
  with NoSyntaxRule ->
    user_err Pp.(str "Parsing rule for this notation has to be previously declared."));
  Option.iter (fun sc -> Notation.open_close_scope (false,true,sc)) sc

(* Main entry point *)

let add_notation local env c ((loc,df),modifiers) sc =
  let df' =
   if no_syntax_modifiers modifiers then
    (* No syntax data: try to rely on a previously declared rule *)
    let onlyparse = is_only_parsing modifiers in
    let onlyprint = is_only_printing modifiers in
    let compat = get_compat_version modifiers in
    try add_notation_interpretation_core local df env c sc onlyparse onlyprint compat
    with NoSyntaxRule ->
      (* Try to determine a default syntax rule *)
      add_notation_in_scope local df env c modifiers sc
   else
    (* Declare both syntax and interpretation *)
    add_notation_in_scope local df env c modifiers sc
  in
  Dumpglob.dump_notation (loc,df') sc true

let add_notation_extra_printing_rule df k v =
  let notk = 
    let dfs = split_notation_string df in
    let _,_, symbs = analyze_notation_tokens ~onlyprint:true dfs in
    make_notation_key symbs in
  Notation.add_notation_extra_printing_rule notk k v

(* Infix notations *)

let inject_var x = CAst.make @@ CRef (Ident (Loc.tag @@ Id.of_string x),None)

let add_infix local env ((loc,inf),modifiers) pr sc =
  check_infix_modifiers modifiers;
  (* check the precedence *)
  let metas = [inject_var "x"; inject_var "y"] in
  let c = mkAppC (pr,metas) in
  let df = "x "^(quote_notation_token inf)^" y" in
  add_notation local env c ((loc,df),modifiers) sc

(**********************************************************************)
(* Delimiters and classes bound to scopes                             *)

type scope_command =
  | ScopeDelim of string
  | ScopeClasses of scope_class list
  | ScopeRemove

let load_scope_command _ (_,(scope,dlm)) =
  Notation.declare_scope scope

let open_scope_command i (_,(scope,o)) =
  if Int.equal i 1 then
    match o with
    | ScopeDelim dlm -> Notation.declare_delimiters scope dlm
    | ScopeClasses cl -> List.iter (Notation.declare_scope_class scope) cl
    | ScopeRemove -> Notation.remove_delimiters scope

let cache_scope_command o =
  load_scope_command 1 o;
  open_scope_command 1 o

let subst_scope_command (subst,(scope,o as x)) = match o with
  | ScopeClasses cl ->
      let cl' = List.map_filter (subst_scope_class subst) cl in
      let cl' =
        if List.for_all2eq (==) cl cl' then cl
        else cl' in
      scope, ScopeClasses cl'
  | _ -> x

let inScopeCommand : scope_name * scope_command -> obj =
  declare_object {(default_object "DELIMITERS") with
      cache_function = cache_scope_command;
      open_function = open_scope_command;
      load_function = load_scope_command;
      subst_function = subst_scope_command;
      classify_function = (fun obj -> Substitute obj)}

let add_delimiters scope key =
  Lib.add_anonymous_leaf (inScopeCommand(scope,ScopeDelim key))

let remove_delimiters scope =
  Lib.add_anonymous_leaf (inScopeCommand(scope,ScopeRemove))

let add_class_scope scope cl =
  Lib.add_anonymous_leaf (inScopeCommand(scope,ScopeClasses cl))

(* Check if abbreviation to a name and avoid early insertion of
   maximal implicit arguments *)
let try_interp_name_alias = function
  | [], { CAst.v = CRef (ref,_) } -> intern_reference ref
  | _ -> raise Not_found

let add_syntactic_definition env ident (vars,c) local onlyparse =
  let nonprintable = ref false in
  let vars,pat =
    try [], NRef (try_interp_name_alias (vars,c))
    with Not_found ->
      let fold accu id = Id.Map.add id NtnInternTypeConstr accu in
      let i_vars = List.fold_left fold Id.Map.empty vars in
      let nenv = {
        ninterp_var_type = i_vars;
        ninterp_rec_vars = Id.Map.empty;
      } in
      let nvars, pat, reversible = interp_notation_constr env nenv c in
      let () = nonprintable := not reversible in
      let map id = let (_,sc,_) = Id.Map.find id nvars in (id, sc) in
      List.map map vars, pat
  in
  let onlyparse = match onlyparse with
    | None when (is_not_printable false !nonprintable pat) -> Some Flags.Current
    | p -> p
  in
  Syntax_def.declare_syntactic_definition local ident onlyparse (vars,pat)