summaryrefslogtreecommitdiff
path: root/src/elab_env.sml
blob: 16596622ac05a236484448f982b09eb9a2f90647 (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
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
(* Copyright (c) 2008-2009, Adam Chlipala
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * - Redistributions of source code must retain the above copyright notice,
 *   this list of conditions and the following disclaimer.
 * - Redistributions in binary form must reproduce the above copyright notice,
 *   this list of conditions and the following disclaimer in the documentation
 *   and/or other materials provided with the distribution.
 * - The names of contributors may not be used to endorse or promote products
 *   derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *)

structure ElabEnv :> ELAB_ENV = struct

open Elab

structure U = ElabUtil

structure IM = IntBinaryMap
structure SM = BinaryMapFn(struct
                           type ord_key = string
                           val compare = String.compare
                           end)

exception UnboundRel of int
exception UnboundNamed of int


(* AST utility functions *)

exception SynUnif

val liftKindInKind =
    U.Kind.mapB {kind = fn bound => fn k =>
                                       case k of
                                         KRel xn =>
                                         if xn < bound then
                                             k
                                         else
                                             KRel (xn + 1)
                                       | _ => k,
                 bind = fn (bound, _) => bound + 1}

val liftKindInCon =
    U.Con.mapB {kind = fn bound => fn k =>
                                      case k of
                                          KRel xn =>
                                          if xn < bound then
                                              k
                                          else
                                              KRel (xn + 1)
                                        | _ => k,
                con = fn _ => fn c => c,
                bind = fn (bound, U.Con.RelK _) => bound + 1
                        | (bound, _) => bound}

val liftConInCon =
    U.Con.mapB {kind = fn _ => fn k => k,
                con = fn bound => fn c =>
                                     case c of
                                         CRel xn =>
                                         if xn < bound then
                                             c
                                         else
                                             CRel (xn + 1)
                                       (*| CUnif _ => raise SynUnif*)
                                       | _ => c,
                bind = fn (bound, U.Con.RelC _) => bound + 1
                        | (bound, _) => bound}

val lift = liftConInCon 0

val liftKindInExp =
    U.Exp.mapB {kind = fn bound => fn k =>
                                      case k of
                                          KRel xn =>
                                          if xn < bound then
                                              k
                                          else
                                              KRel (xn + 1)
                                        | _ => k,
                con = fn _ => fn c => c,
                exp = fn _ => fn e => e,
                bind = fn (bound, U.Exp.RelK _) => bound + 1
                        | (bound, _) => bound}

val liftConInExp =
    U.Exp.mapB {kind = fn _ => fn k => k,
                con = fn bound => fn c =>
                                     case c of
                                         CRel xn =>
                                         if xn < bound then
                                             c
                                         else
                                             CRel (xn + 1)
                                       | _ => c,
                exp = fn _ => fn e => e,
                bind = fn (bound, U.Exp.RelC _) => bound + 1
                        | (bound, _) => bound}

val liftExpInExp =
    U.Exp.mapB {kind = fn _ => fn k => k,
                con = fn _ => fn c => c,
                exp = fn bound => fn e =>
                                     case e of
                                         ERel xn =>
                                         if xn < bound then
                                             e
                                         else
                                             ERel (xn + 1)
                                       | _ => e,
                bind = fn (bound, U.Exp.RelE _) => bound + 1
                        | (bound, _) => bound}


val liftExp = liftExpInExp 0

val subExpInExp =
    U.Exp.mapB {kind = fn _ => fn k => k,
                con = fn _ => fn c => c,
                exp = fn (xn, rep) => fn e =>
                                  case e of
                                      ERel xn' =>
                                      (case Int.compare (xn', xn) of
                                           EQUAL => #1 rep
                                         | GREATER=> ERel (xn' - 1)
                                         | LESS => e)
                                    | _ => e,
                bind = fn ((xn, rep), U.Exp.RelE _) => (xn+1, liftExpInExp 0 rep)
                        | ((xn, rep), U.Exp.RelC _) => (xn, liftConInExp 0 rep)
                        | (ctx, _) => ctx}

(* Back to environments *)

datatype 'a var' =
         Rel' of int * 'a
       | Named' of int * 'a

datatype 'a var =
         NotBound
       | Rel of int * 'a
       | Named of int * 'a

type datatyp = string list * (string * con option) IM.map

datatype class_name =
         ClNamed of int
       | ClProj of int * string list * string

fun class_name_out cn =
    case cn of
        ClNamed n => (CNamed n, ErrorMsg.dummySpan)
      | ClProj x => (CModProj x, ErrorMsg.dummySpan)

fun cn2s cn =
    case cn of
        ClNamed n => "Named(" ^ Int.toString n ^ ")"
      | ClProj (m, ms, x) => "Proj(" ^ Int.toString m ^ "," ^ String.concatWith "," ms ^ "," ^ x ^ ")"

structure CK = struct
type ord_key = class_name
open Order
fun compare x =
    case x of
        (ClNamed n1, ClNamed n2) => Int.compare (n1, n2)
      | (ClNamed _, _) => LESS
      | (_, ClNamed _) => GREATER

      | (ClProj (m1, ms1, x1), ClProj (m2, ms2, x2)) =>
        join (Int.compare (m1, m2),
              fn () => join (joinL String.compare (ms1, ms2),
                             fn () => String.compare (x1, x2)))
end

structure CS = BinarySetFn(CK)
structure CM = BinaryMapFn(CK)

type class = {ground : (con * exp) list,
              rules : (int * con list * con * exp) list}
val empty_class = {ground = [],
                   rules = []}

type env = {
     renameK : int SM.map,
     relK : string list,

     renameC : kind var' SM.map,
     relC : (string * kind) list,
     namedC : (string * kind * con option) IM.map,

     datatypes : datatyp IM.map,
     constructors : (datatype_kind * int * string list * con option * int) SM.map,

     classes : class CM.map,

     renameE : con var' SM.map,
     relE : (string * con) list,
     namedE : (string * con) IM.map,

     renameSgn : (int * sgn) SM.map,
     sgn : (string * sgn) IM.map,

     renameStr : (int * sgn) SM.map,
     str : (string * sgn) IM.map
}

val namedCounter = ref 0

fun newNamed () =
    let
        val r = !namedCounter
    in
        namedCounter := r + 1;
        r
    end

val empty = {
    renameK = SM.empty,
    relK = [],

    renameC = SM.empty,
    relC = [],
    namedC = IM.empty,

    datatypes = IM.empty,
    constructors = SM.empty,

    classes = CM.empty,

    renameE = SM.empty,
    relE = [],
    namedE = IM.empty,

    renameSgn = SM.empty,
    sgn = IM.empty,

    renameStr = SM.empty,
    str = IM.empty
}

fun pushKRel (env : env) x =
    let
        val renameK = SM.map (fn n => n+1) (#renameK env)
    in
        {renameK = SM.insert (renameK, x, 0),
         relK = x :: #relK env,

         renameC = SM.map (fn Rel' (n, k) => Rel' (n, liftKindInKind 0 k)
                            | x => x) (#renameC env),
         relC = map (fn (x, k) => (x, liftKindInKind 0 k)) (#relC env),
         namedC = #namedC env,

         datatypes = #datatypes env,
         constructors = #constructors env,

         classes = CM.map (fn cl => {ground = map (fn (c, e) =>
                                                      (liftKindInCon 0 c,
                                                       e))
                                                  (#ground cl),
                                     rules = #rules cl})
                          (#classes env),

         renameE = SM.map (fn Rel' (n, c) => Rel' (n, liftKindInCon 0 c)
                            | Named' (n, c) => Named' (n, c)) (#renameE env),
         relE = map (fn (x, c) => (x, liftKindInCon 0 c)) (#relE env),
         namedE = #namedE env,

         renameSgn = #renameSgn env,
         sgn = #sgn env,

         renameStr = #renameStr env,
         str = #str env
        }
    end

fun lookupKRel (env : env) n =
    (List.nth (#relK env, n))
    handle Subscript => raise UnboundRel n

fun lookupK (env : env) x = SM.find (#renameK env, x)

fun pushCRel (env : env) x k =
    let
        val renameC = SM.map (fn Rel' (n, k) => Rel' (n+1, k)
                               | x => x) (#renameC env)
    in
        {renameK = #renameK env,
         relK = #relK env,

         renameC = SM.insert (renameC, x, Rel' (0, k)),
         relC = (x, k) :: #relC env,
         namedC = #namedC env,

         datatypes = #datatypes env,
         constructors = #constructors env,

         classes = CM.map (fn class =>
                              {ground = map (fn (c, e) =>
                                                (liftConInCon 0 c,
                                                 e))
                                            (#ground class),
                               rules = #rules class})
                          (#classes env),

         renameE = SM.map (fn Rel' (n, c) => Rel' (n, lift c)
                            | Named' (n, c) => Named' (n, c)) (#renameE env),
         relE = map (fn (x, c) => (x, lift c)) (#relE env),
         namedE = #namedE env,

         renameSgn = #renameSgn env,
         sgn = #sgn env,

         renameStr = #renameStr env,
         str = #str env
        }
    end

fun lookupCRel (env : env) n =
    (List.nth (#relC env, n))
    handle Subscript => raise UnboundRel n

fun pushCNamedAs (env : env) x n k co =
    {renameK = #renameK env,
     relK = #relK env,

     renameC = SM.insert (#renameC env, x, Named' (n, k)),
     relC = #relC env,
     namedC = IM.insert (#namedC env, n, (x, k, co)),

     datatypes = #datatypes env,
     constructors = #constructors env,

     classes = #classes env,

     renameE = #renameE env,
     relE = #relE env,
     namedE = #namedE env,

     renameSgn = #renameSgn env,
     sgn = #sgn env,
     
     renameStr = #renameStr env,
     str = #str env}

fun pushCNamed env x k co =
    let
        val n = !namedCounter
    in
        namedCounter := n + 1;
        (pushCNamedAs env x n k co, n)
    end

fun lookupCNamed (env : env) n =
    case IM.find (#namedC env, n) of
        NONE => raise UnboundNamed n
      | SOME x => x

fun lookupC (env : env) x =
    case SM.find (#renameC env, x) of
        NONE => NotBound
      | SOME (Rel' x) => Rel x
      | SOME (Named' x) => Named x

fun pushDatatype (env : env) n xs xncs =
    let
        val dk = U.classifyDatatype xncs
    in
        {renameK = #renameK env,
         relK = #relK env,

         renameC = #renameC env,
         relC = #relC env,
         namedC = #namedC env,

         datatypes = IM.insert (#datatypes env, n,
                                (xs, foldl (fn ((x, n, to), cons) =>
                                               IM.insert (cons, n, (x, to))) IM.empty xncs)),
         constructors = foldl (fn ((x, n', to), cmap) =>
                                  SM.insert (cmap, x, (dk, n', xs, to, n)))
                              (#constructors env) xncs,

         classes = #classes env,

         renameE = #renameE env,
         relE = #relE env,
         namedE = #namedE env,

         renameSgn = #renameSgn env,
         sgn = #sgn env,

         renameStr = #renameStr env,
         str = #str env}
    end

fun lookupDatatype (env : env) n =
    case IM.find (#datatypes env, n) of
        NONE => raise UnboundNamed n
      | SOME x => x

fun lookupDatatypeConstructor (_, dt) n =
    case IM.find (dt, n) of
        NONE => raise UnboundNamed n
      | SOME x => x

fun lookupConstructor (env : env) s = SM.find (#constructors env, s)

fun datatypeArgs (xs, _) = xs
fun constructors (_, dt) = IM.foldri (fn (n, (x, to), ls) => (x, n, to) :: ls) [] dt

fun listClasses (env : env) =
    map (fn (cn, {ground, rules}) =>
            (class_name_out cn,
             ground
             @ map (fn (nvs, cs, c, e) =>
                       let
                           val loc = #2 c
                           val c = foldr (fn (c', c) => (TFun (c', c), loc)) c cs
                           val c = ListUtil.foldli (fn (n, (), c) => (TCFun (Explicit,
                                                                             "x" ^ Int.toString n,
                                                                             (KError, loc),
                                                                             c), loc))
                                                   c (List.tabulate (nvs, fn _ => ()))
                       in
                           (c, e)
                       end) rules)) (CM.listItemsi (#classes env))

fun pushClass (env : env) n =
    {renameK = #renameK env,
     relK = #relK env,

     renameC = #renameC env,
     relC = #relC env,
     namedC = #namedC env,

     datatypes = #datatypes env,
     constructors = #constructors env,

     classes = CM.insert (#classes env, ClNamed n, empty_class),

     renameE = #renameE env,
     relE = #relE env,
     namedE = #namedE env,

     renameSgn = #renameSgn env,
     sgn = #sgn env,

     renameStr = #renameStr env,
     str = #str env}

fun class_name_in (c, _) =
    case c of
        CNamed n => SOME (ClNamed n)
      | CModProj x => SOME (ClProj x)
      | CUnif (_, _, _, ref (SOME c)) => class_name_in c
      | _ => NONE

fun isClass (env : env) c =
    let
        fun find NONE = false
          | find (SOME c) = Option.isSome (CM.find (#classes env, c))
    in
        find (class_name_in c)
    end

fun class_head_in c =
    case #1 c of
        CApp (f, _) => class_head_in f
      | CUnif (_, _, _, ref (SOME c)) => class_head_in c
      | _ => class_name_in c

exception Unify

fun unifyKinds (k1, k2) =
    case (#1 k1, #1 k2) of
        (KType, KType) => ()
      | (KArrow (d1, r1), KArrow (d2, r2)) => (unifyKinds (d1, d2); unifyKinds (r1, r2))
      | (KName, KName) => ()
      | (KRecord k1, KRecord k2) => unifyKinds (k1, k2)
      | (KUnit, KUnit) => ()
      | (KTuple ks1, KTuple ks2) => (ListPair.appEq unifyKinds (ks1, ks2)
                                     handle ListPair.UnequalLengths => raise Unify)
      | (KUnif (_, _, ref (SOME k1)), _) => unifyKinds (k1, k2)
      | (_, KUnif (_, _, ref (SOME k2))) => unifyKinds (k1, k2)
      | (KRel n1, KRel n2) => if n1 = n2 then () else raise Unify
      | (KFun (_, k1), KFun (_, k2)) => unifyKinds (k1, k2)
      | _ => raise Unify

fun eqCons (c1, c2) =
    case (#1 c1, #1 c2) of
        (CUnif (_, _, _, ref (SOME c1)), _) => eqCons (c1, c2)
      | (_, CUnif (_, _, _, ref (SOME c2))) => eqCons (c1, c2)

      | (CRel n1, CRel n2) => if n1 = n2 then () else raise Unify

      | (TFun (d1, r1), TFun (d2, r2)) => (eqCons (d1, d2); eqCons (r1, r2))
      | (TCFun (_, _, k1, r1), TCFun (_, _, k2, r2)) => (unifyKinds (k1, k2); eqCons (r1, r2))
      | (TRecord c1, TRecord c2) => eqCons (c1, c2)
      | (TDisjoint (a1, b1, c1), TDisjoint (a2, b2, c2)) =>
        (eqCons (a1, a2); eqCons (b1, b2); eqCons (c1, c2))

      | (CNamed n1, CNamed n2) => if n1 = n2 then () else raise Unify
      | (CModProj (n1, ms1, x1), CModProj (n2, ms2, x2)) =>
        if n1 = n2 andalso ms1 = ms2 andalso x1 = x2 then () else raise Unify
      | (CApp (f1, x1), CApp (f2, x2)) => (eqCons (f1, f2); eqCons (x1, x2))
      | (CAbs (_, k1, b1), CAbs (_, k2, b2)) => (unifyKinds (k1, k2); eqCons (b1, b2))

      | (CKAbs (_, b1), CKAbs (_, b2)) => eqCons (b1, b2)
      | (CKApp (c1, k1), CKApp (c2, k2)) => (eqCons (c1, c2); unifyKinds (k1, k2))
      | (TKFun (_, c1), TKFun (_, c2)) => eqCons (c1, c2)

      | (CName s1, CName s2) => if s1 = s2 then () else raise Unify

      | (CRecord (k1, xcs1), CRecord (k2, xcs2)) =>
        (unifyKinds (k1, k2);
         ListPair.appEq (fn ((x1, c1), (x2, c2)) => (eqCons (x1, x2); eqCons (c1, c2))) (xcs1, xcs2)
         handle ListPair.UnequalLengths => raise Unify)
      | (CConcat (f1, x1), CConcat (f2, x2)) => (eqCons (f1, f2); eqCons (x1, x2))
      | (CMap (d1, r1), CMap (d2, r2)) => (unifyKinds (d1, d2); unifyKinds (r1, r2))

      | (CUnit, CUnit) => ()

      | (CTuple cs1, CTuple cs2) => (ListPair.appEq (eqCons) (cs1, cs2)
                                     handle ListPair.UnequalLengths => raise Unify)
      | (CProj (c1, n1), CProj (c2, n2)) => (eqCons (c1, c2);
                                             if n1 = n2 then () else raise Unify)

      | _ => raise Unify

fun unifyCons rs =
    let
        fun unify d (c1, c2) =
            case (#1 c1, #1 c2) of
                (CUnif (_, _, _, ref (SOME c1)), _) => unify d (c1, c2)
              | (_, CUnif (_, _, _, ref (SOME c2))) => unify d (c1, c2)

              | (CUnif _, _) => ()

              | (c1', CRel n2) =>
                if n2 < d then
                    case c1' of
                        CRel n1 => if n1 = n2 then () else raise Unify
                      | _ => raise Unify
                else if n2 - d >= length rs then
                    case c1' of
                        CRel n1 => if n1 = n2 - length rs then () else raise Unify
                      | _ => raise Unify
                else
                    let
                        val r = List.nth (rs, n2 - d)
                    in
                        case !r of
                            NONE => r := SOME c1
                          | SOME c2 => eqCons (c1, c2)
                    end

              | (TFun (d1, r1), TFun (d2, r2)) => (unify d (d1, d2); unify d (r1, r2))
              | (TCFun (_, _, k1, r1), TCFun (_, _, k2, r2)) => (unifyKinds (k1, k2); unify (d + 1) (r1, r2))
              | (TRecord c1, TRecord c2) => unify d (c1, c2)
              | (TDisjoint (a1, b1, c1), TDisjoint (a2, b2, c2)) =>
                (unify d (a1, a2); unify d (b1, b2); unify d (c1, c2))

              | (CNamed n1, CNamed n2) => if n1 = n2 then () else raise Unify
              | (CModProj (n1, ms1, x1), CModProj (n2, ms2, x2)) =>
                if n1 = n2 andalso ms1 = ms2 andalso x1 = x2 then () else raise Unify
              | (CApp (f1, x1), CApp (f2, x2)) => (unify d (f1, f2); unify d (x1, x2))
              | (CAbs (_, k1, b1), CAbs (_, k2, b2)) => (unifyKinds (k1, k2); unify (d + 1) (b1, b2))

              | (CKAbs (_, b1), CKAbs (_, b2)) => unify d (b1, b2)
              | (CKApp (c1, k1), CKApp (c2, k2)) => (unify d (c1, c2); unifyKinds (k1, k2))
              | (TKFun (_, c1), TKFun (_, c2)) => unify d (c1, c2)

              | (CName s1, CName s2) => if s1 = s2 then () else raise Unify

              | (CRecord (k1, xcs1), CRecord (k2, xcs2)) =>
                (unifyKinds (k1, k2);
                 ListPair.appEq (fn ((x1, c1), (x2, c2)) => (unify d (x1, x2); unify d (c1, c2))) (xcs1, xcs2)
                 handle ListPair.UnequalLengths => raise Unify)
              | (CConcat (f1, x1), CConcat (f2, x2)) => (unify d (f1, f2); unify d (x1, x2))
              | (CMap (d1, r1), CMap (d2, r2)) => (unifyKinds (d1, d2); unifyKinds (r1, r2))

              | (CUnit, CUnit) => ()

              | (CTuple cs1, CTuple cs2) => (ListPair.appEq (unify d) (cs1, cs2)
                                             handle ListPair.UnequalLengths => raise Unify)
              | (CProj (c1, n1), CProj (c2, n2)) => (unify d (c1, c2);
                                                     if n1 = n2 then () else raise Unify)

              | _ => raise Unify
    in
        unify
    end

fun tryUnify nRs (c1, c2) =
    let
        val rs = List.tabulate (nRs, fn _ => ref NONE)
    in
        (unifyCons rs 0 (c1, c2);
         SOME (map (fn r => case !r of
                                NONE => raise Unify
                              | SOME c => c) rs))
        handle Unify => NONE
    end

fun unifySubst (rs : con list) =
    U.Con.mapB {kind = fn _ => fn k => k,
                con = fn d => fn c =>
                                 case c of
                                     CRel n =>
                                     if n < d then
                                         c
                                     else
                                         #1 (List.nth (rs, n - d))
                                   | _ => c,
                bind = fn (d, U.Con.RelC _) => d + 1
                        | (d, _) => d}
               0

exception Bad of con * con

val hasUnif = U.Con.exists {kind = fn _ => false,
                            con = fn CUnif (_, _, _, ref NONE) => true
                                   | _ => false}

fun startsWithUnif c =
    let
        fun firstArg (c, acc) =
            case #1 c of
                CApp (f, x) => firstArg (f, SOME x)
              | _ => acc
    in
        case firstArg (c, NONE) of
            NONE => false
          | SOME x => hasUnif x
    end

fun resolveClass (hnorm : con -> con) (consEq : con * con -> bool) (env : env) =
    let
        fun resolve c =
            let
                fun doHead f =
                    case CM.find (#classes env, f) of
                        NONE => NONE
                      | SOME class =>
                        let
                            val loc = #2 c

                            fun generalize (c as (_, loc)) =
                                case #1 c of
                                    CApp (f, x) =>
                                    let
                                        val (f, equate) = generalize f

                                        fun isRecord () =
                                            let
                                                val rk = ref NONE
                                                val k = (KUnif (loc, "k", rk), loc)
                                                val r = ref NONE
                                                val rc = (CUnif (loc, k, "x", r), loc)
                                            in
                                                ((CApp (f, rc), loc),
                                              fn () => (if consEq (rc, x) then
                                                            true
                                                        else
                                                            (raise Bad (rc, x);
                                                             false))
                                                       andalso equate ())
                                            end
                                    in
                                        case #1 x of
                                            CConcat _ => isRecord ()
                                          | CRecord _ => isRecord ()
                                          | _ => ((CApp (f, x), loc), equate)
                                    end
                                  | _ => (c, fn () => true)

                            val (c, equate) = generalize c

                            fun tryRules rules =
                                case rules of
                                    [] => NONE
                                  | (nRs, cs, c', e) :: rules' =>
                                    case tryUnify nRs (c, c') of
                                        NONE => tryRules rules'
                                      | SOME rs =>
                                        let
                                            val eos = map (resolve o unifySubst rs) cs
                                        in
                                            if List.exists (not o Option.isSome) eos
                                               orelse not (equate ())
                                               orelse not (consEq (c, unifySubst rs c')) then
                                                tryRules rules'
                                            else
                                                let
                                                    val es = List.mapPartial (fn x => x) eos

                                                    val e = foldr (fn (c, e) => (ECApp (e, c), loc)) e rs
                                                    val e = foldl (fn (e', e) => (EApp (e, e'), loc)) e es
                                                in
                                                    SOME e
                                                end
                                        end

                            fun rules () = tryRules (#rules class)
  
                            fun tryGrounds ces =
                                case ces of
                                    [] => rules ()
                                  | (c', e) :: ces' =>
                                    case tryUnify 0 (c, c') of
                                        NONE => tryGrounds ces'
                                      | SOME _ => SOME e
                        in
                            tryGrounds (#ground class)
                        end
            in
                if startsWithUnif c then
                    NONE
                else
                    case #1 c of
                        TRecord c =>
                        (case #1 (hnorm c) of
                             CRecord (_, xts) =>
                             let
                                 fun resolver (xts, acc) =
                                     case xts of
                                         [] => SOME (ERecord acc, #2 c)
                                       | (x, t) :: xts =>
                                         let
                                             val t = hnorm t

                                             val t = case t of
                                                         (CApp (f, x), loc) => (CApp (hnorm f, hnorm x), loc)
                                                       | _ => t
                                         in
                                             case resolve t of
                                                 NONE => NONE
                                               | SOME e => resolver (xts, (x, e, t) :: acc)
                                         end
                             in
                                 resolver (xts, [])
                             end
                           | _ => NONE)
                      | _ =>
                        case class_head_in c of
                            SOME f => doHead f
                          | _ => NONE
            end
    in
        resolve
    end

fun pushERel (env : env) x t =
    let
        val renameE = SM.map (fn Rel' (n, t) => Rel' (n+1, t)
                               | x => x) (#renameE env)

        val classes = CM.map (fn class =>
                                 {ground = map (fn (c, e) => (c, liftExp e)) (#ground class),
                                  rules = #rules class}) (#classes env)
        val classes = case class_head_in t of
                          NONE => classes
                        | SOME f =>
                          case CM.find (classes, f) of
                              NONE => classes
                            | SOME class =>
                              let
                                  val class = {ground = (t, (ERel 0, #2 t)) :: #ground class,
                                               rules = #rules class}
                              in
                                  CM.insert (classes, f, class)
                              end
    in
        {renameK = #renameK env,
         relK = #relK env,

         renameC = #renameC env,
         relC = #relC env,
         namedC = #namedC env,

         datatypes = #datatypes env,
         constructors = #constructors env,

         classes = classes,

         renameE = SM.insert (renameE, x, Rel' (0, t)),
         relE = (x, t) :: #relE env,
         namedE = #namedE env,

         renameSgn = #renameSgn env,
         sgn = #sgn env,

         renameStr = #renameStr env,
         str = #str env}
    end

fun lookupERel (env : env) n =
    (List.nth (#relE env, n))
    handle Subscript => raise UnboundRel n

fun rule_in c =
    let
        fun quantifiers (c, nvars) =
            case #1 c of
                TCFun (_, _, _, c) => quantifiers (c, nvars + 1)
              | _ =>
                let
                    fun clauses (c, hyps) =
                        case #1 c of
                            TFun (hyp, c) =>
                            (case class_head_in hyp of
                                 SOME _ => clauses (c, hyp :: hyps)
                               | NONE => NONE)
                          | _ =>
                            case class_head_in c of
                                NONE => NONE
                              | SOME f => SOME (f, nvars, rev hyps, c)
                in
                    clauses (c, [])
                end
    in
        quantifiers (c, 0)
    end

fun pushENamedAs (env : env) x n t =
    let
        val classes = #classes env
        val classes = case rule_in t of
                          NONE => classes
                        | SOME (f, nvs, cs, c) =>
                          case CM.find (classes, f) of
                              NONE => classes
                            | SOME class =>
                              let
                                  val e = (ENamed n, #2 t)

                                  val class =
                                      {ground = #ground class,
                                       rules = (nvs, cs, c, e) :: #rules class}
                              in
                                  CM.insert (classes, f, class)
                              end
    in
        {renameK = #renameK env,
         relK = #relK env,

         renameC = #renameC env,
         relC = #relC env,
         namedC = #namedC env,

         datatypes = #datatypes env,
         constructors = #constructors env,

         classes = classes,

         renameE = SM.insert (#renameE env, x, Named' (n, t)),
         relE = #relE env,
         namedE = IM.insert (#namedE env, n, (x, t)),

         renameSgn = #renameSgn env,
         sgn = #sgn env,
         
         renameStr = #renameStr env,
         str = #str env}
    end

fun pushENamed env x t =
    let
        val n = !namedCounter
    in
        namedCounter := n + 1;
        (pushENamedAs env x n t, n)
    end

fun lookupENamed (env : env) n =
    case IM.find (#namedE env, n) of
        NONE => raise UnboundNamed n
      | SOME x => x

fun checkENamed (env : env) n =
    Option.isSome (IM.find (#namedE env, n))

fun lookupE (env : env) x =
    case SM.find (#renameE env, x) of
        NONE => NotBound
      | SOME (Rel' x) => Rel x
      | SOME (Named' x) => Named x

fun pushSgnNamedAs (env : env) x n sgis =
    {renameK = #renameK env,
     relK = #relK env,

     renameC = #renameC env,
     relC = #relC env,
     namedC = #namedC env,

     datatypes = #datatypes env,
     constructors = #constructors env,

     classes = #classes env,

     renameE = #renameE env,
     relE = #relE env,
     namedE = #namedE env,

     renameSgn = SM.insert (#renameSgn env, x, (n, sgis)),
     sgn = IM.insert (#sgn env, n, (x, sgis)),
     
     renameStr = #renameStr env,
     str = #str env}

fun pushSgnNamed env x sgis =
    let
        val n = !namedCounter
    in
        namedCounter := n + 1;
        (pushSgnNamedAs env x n sgis, n)
    end

fun lookupSgnNamed (env : env) n =
    case IM.find (#sgn env, n) of
        NONE => raise UnboundNamed n
      | SOME x => x

fun lookupSgn (env : env) x = SM.find (#renameSgn env, x)

fun lookupStrNamed (env : env) n =
    case IM.find (#str env, n) of
        NONE => raise UnboundNamed n
      | SOME x => x

fun lookupStr (env : env) x = SM.find (#renameStr env, x)


fun sgiSeek (sgi, (sgns, strs, cons)) =
    case sgi of
        SgiConAbs (x, n, _) => (sgns, strs, IM.insert (cons, n, x))
      | SgiCon (x, n, _, _) => (sgns, strs, IM.insert (cons, n, x))
      | SgiDatatype dts => (sgns, strs, foldl (fn ((x, n, _, _), cons) => IM.insert (cons, n, x)) cons dts)
      | SgiDatatypeImp (x, n, _, _, _, _, _) => (sgns, strs, IM.insert (cons, n, x))
      | SgiVal _ => (sgns, strs, cons)
      | SgiSgn (x, n, _) => (IM.insert (sgns, n, x), strs, cons)
      | SgiStr (x, n, _) => (sgns, IM.insert (strs, n, x), cons)
      | SgiConstraint _ => (sgns, strs, cons)
      | SgiClassAbs (x, n, _) => (sgns, strs, IM.insert (cons, n, x))
      | SgiClass (x, n, _, _) => (sgns, strs, IM.insert (cons, n, x))

fun sgnSeek f sgis =
    let
        fun seek (sgis, sgns, strs, cons) =
            case sgis of
                [] => NONE
              | (sgi, _) :: sgis =>
                case f sgi of
                    SOME v =>
                    let
                        val cons =
                            case sgi of
                                SgiDatatype dts => foldl (fn ((x, n, _, _), cons) => IM.insert (cons, n, x)) cons dts
                              | SgiDatatypeImp (x, n, _, _, _, _, _) => IM.insert (cons, n, x)
                              | _ => cons
                    in
                        SOME (v, (sgns, strs, cons))
                    end
                  | NONE =>
                    let
                        val (sgns, strs, cons) = sgiSeek (sgi, (sgns, strs, cons))
                    in
                        seek (sgis, sgns, strs, cons)
                    end
    in
        seek (sgis, IM.empty, IM.empty, IM.empty)
    end

fun id x = x

fun unravelStr (str, _) =
    case str of
        StrVar x => (x, [])
      | StrProj (str, m) =>
        let
            val (x, ms) = unravelStr str
        in
            (x, ms @ [m])
        end
      | _ => raise Fail "unravelStr"

fun sgnS_con (str, (sgns, strs, cons)) c =
    case c of
        CModProj (m1, ms, x) =>
        (case IM.find (strs, m1) of
             NONE => c
           | SOME m1x =>
             let
                 val (m1, ms') = unravelStr str
             in
                 CModProj (m1, ms' @ m1x :: ms, x)
             end)
      | CNamed n =>
        (case IM.find (cons, n) of
             NONE => c
           | SOME nx =>
             let
                 val (m1, ms) = unravelStr str
             in
                 CModProj (m1, ms, nx)
             end)
      | _ => c

fun sgnS_con' (m1, ms', (sgns, strs, cons)) =
    U.Con.map {kind = fn x => x,
               con = fn c =>
                        case c of
                            CModProj (m1, ms, x) =>
                            (case IM.find (strs, m1) of
                                 NONE => c
                               | SOME m1x => CModProj (m1, ms' @ m1x :: ms, x))
                          | CNamed n =>
                            (case IM.find (cons, n) of
                                 NONE => c
                               | SOME nx => CModProj (m1, ms', nx))
                          | _ => c}

fun sgnS_sgn (str, (sgns, strs, cons)) sgn =
    case sgn of
        SgnProj (m1, ms, x) =>
        (case IM.find (strs, m1) of
             NONE => sgn
           | SOME m1x =>
             let
                 val (m1, ms') = unravelStr str
             in
                 SgnProj (m1, ms' @ m1x :: ms, x)
             end)
      | SgnVar n =>
        (case IM.find (sgns, n) of
             NONE => sgn
           | SOME nx =>
             let
                 val (m1, ms) = unravelStr str
             in
                 SgnProj (m1, ms, nx)
             end)
      | _ => sgn

fun sgnSubSgn x =
    ElabUtil.Sgn.map {kind = id,
                      con = sgnS_con x,
                      sgn_item = id,
                      sgn = sgnS_sgn x}



and projectSgn env {sgn, str, field} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        (case sgnSeek (fn SgiSgn (x, _, sgn) => if x = field then SOME sgn else NONE | _ => NONE) sgis of
             NONE => NONE
           | SOME (sgn, subs) => SOME (sgnSubSgn (str, subs) sgn))
      | SgnError => SOME (SgnError, ErrorMsg.dummySpan)
      | _ => NONE

and hnormSgn env (all as (sgn, loc)) =
    case sgn of
        SgnError => all
      | SgnVar n => hnormSgn env (#2 (lookupSgnNamed env n))
      | SgnConst _ => all
      | SgnFun _ => all
      | SgnProj (m, ms, x) =>
        let
            val (_, sgn) = lookupStrNamed env m
        in
            case projectSgn env {str = foldl (fn (m, str) => (StrProj (str, m), loc)) (StrVar m, loc) ms,
                                 sgn = sgn,
                                 field = x} of
                NONE => raise Fail "ElabEnv.hnormSgn: projectSgn failed"
              | SOME sgn => hnormSgn env sgn
        end
      | SgnWhere (sgn, x, c) =>
        case #1 (hnormSgn env sgn) of
            SgnError => (SgnError, loc)
          | SgnConst sgis =>
            let
                fun traverse (pre, post) =
                    case post of
                        [] => raise Fail "ElabEnv.hnormSgn: Can't reduce 'where' [1]"
                      | (sgi as (SgiConAbs (x', n, k), loc)) :: rest =>
                        if x = x' then
                            List.revAppend (pre, (SgiCon (x', n, k, c), loc) :: rest)
                        else
                            traverse (sgi :: pre, rest)
                      | sgi :: rest => traverse (sgi :: pre, rest)

                val sgis = traverse ([], sgis)
            in
                (SgnConst sgis, loc)
            end
          | _ => raise Fail "ElabEnv.hnormSgn: Can't reduce 'where' [2]"

fun manifest (m, ms, loc) =
    foldl (fn (m, str) => (StrProj (str, m), loc)) (StrVar m, loc) ms

fun enrichClasses env classes (m1, ms) sgn =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        let
            val (classes, _, _, _) =
                foldl (fn (sgi, (classes, newClasses, fmap, env)) =>
                          let
                              fun found (x, n) =
                                  (CM.insert (classes,
                                              ClProj (m1, ms, x),
                                              empty_class),
                                   IM.insert (newClasses, n, x),
                                   sgiSeek (#1 sgi, fmap),
                                   env)

                              fun default () = (classes, newClasses, sgiSeek (#1 sgi, fmap), env)
                          in
                              case #1 sgi of
                                  SgiStr (x, _, sgn) =>
                                  let
                                      val str = manifest (m1, ms, #2 sgi)
                                      val sgn' = sgnSubSgn (str, fmap) sgn
                                  in
                                      (enrichClasses env classes (m1, ms @ [x]) sgn',
                                       newClasses,
                                       sgiSeek (#1 sgi, fmap),
                                       env)
                                  end
                                | SgiSgn (x, n, sgn) =>
                                  (classes,
                                   newClasses,
                                   fmap,
                                   pushSgnNamedAs env x n sgn)

                                | SgiClassAbs (x, n, _) => found (x, n)
                                | SgiClass (x, n, _, _) => found (x, n)
                                | SgiVal (x, n, c) =>
                                  (case rule_in c of
                                       NONE => default ()
                                     | SOME (cn, nvs, cs, c) =>
                                       let
                                           val loc = #2 c
                                           val globalize = sgnS_con' (m1, ms, fmap)

                                           val nc =
                                               case cn of
                                                   ClNamed f => IM.find (newClasses, f)
                                                 | _ => NONE
                                       in
                                           case nc of
                                               NONE =>
                                               let
                                                   val classes =
                                                       case CM.find (classes, cn) of
                                                           NONE => classes
                                                         | SOME class =>
                                                           let
                                                               val e = (EModProj (m1, ms, x), #2 sgn)

                                                               val class =
                                                                   {ground = #ground class,
                                                                    rules = (nvs,
                                                                             map globalize cs,
                                                                             globalize c,
                                                                             e) :: #rules class}
                                                           in
                                                               CM.insert (classes, cn, class)
                                                           end
                                               in
                                                   (classes,
                                                    newClasses,
                                                    fmap,
                                                    env)
                                               end
                                             | SOME fx =>
                                               let
                                                   val cn = ClProj (m1, ms, fx)

                                                   val classes =
                                                       case CM.find (classes, cn) of
                                                           NONE => classes
                                                         | SOME class =>
                                                           let
                                                               val e = (EModProj (m1, ms, x), #2 sgn)

                                                               val class = 
                                                                   {ground = #ground class,
                                                                    rules = (nvs,
                                                                             map globalize cs,
                                                                             globalize c,
                                                                             e) :: #rules class}
                                                           in
                                                               CM.insert (classes, cn, class)
                                                           end
                                               in
                                                   (classes,
                                                    newClasses,
                                                    fmap,
                                                    env)
                                               end
                                       end)
                                | _ => default ()
                          end)
                      (classes, IM.empty, (IM.empty, IM.empty, IM.empty), env) sgis
        in
            classes
        end
      | _ => classes

fun pushStrNamedAs (env : env) x n sgn =
    {renameK = #renameK env,
     relK = #relK env,

     renameC = #renameC env,
     relC = #relC env,
     namedC = #namedC env,

     datatypes = #datatypes env,
     constructors = #constructors env,

     classes = enrichClasses env (#classes env) (n, []) sgn,

     renameE = #renameE env,
     relE = #relE env,
     namedE = #namedE env,

     renameSgn = #renameSgn env,
     sgn = #sgn env,

     renameStr = SM.insert (#renameStr env, x, (n, sgn)),
     str = IM.insert (#str env, n, (x, sgn))}

fun pushStrNamed env x sgn =
    let
        val n = !namedCounter
    in
        namedCounter := n + 1;
        (pushStrNamedAs env x n sgn, n)
    end

fun sgiBinds env (sgi, loc) =
    case sgi of
        SgiConAbs (x, n, k) => pushCNamedAs env x n k NONE
      | SgiCon (x, n, k, c) => pushCNamedAs env x n k (SOME c)
      | SgiDatatype dts =>
        let
            fun doOne ((x, n, xs, xncs), env) =
                let
                    val k = (KType, loc)
                    val k' = foldr (fn (_, k') => (KArrow (k, k'), loc)) k xs

                    val env = pushCNamedAs env x n k' NONE
                in
                    foldl (fn ((x', n', to), env) =>
                              let
                                  val t =
                                      case to of
                                          NONE => (CNamed n, loc)
                                        | SOME t => (TFun (t, (CNamed n, loc)), loc)

                                  val k = (KType, loc)
                                  val t = foldr (fn (x, t) => (TCFun (Explicit, x, k, t), loc)) t xs
                              in
                                  pushENamedAs env x' n' t
                              end)
                          env xncs
                end
        in
            foldl doOne env dts
        end
      | SgiDatatypeImp (x, n, m1, ms, x', xs, xncs) =>
        let
            val k = (KType, loc)
            val k' = foldr (fn (_, k') => (KArrow (k, k'), loc)) k xs

            val env = pushCNamedAs env x n k' (SOME (CModProj (m1, ms, x'), loc))
        in
            foldl (fn ((x', n', to), env) =>
                      let
                          val t =
                              case to of
                                  NONE => (CNamed n, loc)
                                | SOME t => (TFun (t, (CNamed n, loc)), loc)

                          val k = (KType, loc)
                          val t = foldr (fn (x, t) => (TCFun (Explicit, x, k, t), loc)) t xs
                      in
                          pushENamedAs env x' n' t
                      end)
            env xncs
        end
      | SgiVal (x, n, t) => pushENamedAs env x n t
      | SgiStr (x, n, sgn) => pushStrNamedAs env x n sgn
      | SgiSgn (x, n, sgn) => pushSgnNamedAs env x n sgn
      | SgiConstraint _ => env

      | SgiClassAbs (x, n, k) => pushCNamedAs env x n k NONE
      | SgiClass (x, n, k, c) => pushCNamedAs env x n k (SOME c)

fun sgnSubCon x =
    ElabUtil.Con.map {kind = id,
                      con = sgnS_con x}

fun projectStr env {sgn, str, field} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        (case sgnSeek (fn SgiStr (x, _, sgn) => if x = field then SOME sgn else NONE | _ => NONE) sgis of
             NONE => NONE
           | SOME (sgn, subs) => SOME (sgnSubSgn (str, subs) sgn))
      | SgnError => SOME (SgnError, ErrorMsg.dummySpan)
      | _ => NONE

fun chaseMpath env (n, ms) =
    let
        val (_, sgn) = lookupStrNamed env n
    in
        foldl (fn (m, (str, sgn)) =>
                                   case projectStr env {sgn = sgn, str = str, field = m} of
                                       NONE => raise Fail "kindof: Unknown substructure"
                                     | SOME sgn => ((StrProj (str, m), #2 sgn), sgn))
                               ((StrVar n, #2 sgn), sgn) ms
    end

fun projectCon env {sgn, str, field} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        (case sgnSeek (fn SgiConAbs (x, _, k) => if x = field then SOME (k, NONE) else NONE
                        | SgiCon (x, _, k, c) => if x = field then SOME (k, SOME c) else NONE
                        | SgiDatatype dts =>
                          (case List.find (fn (x, _, xs, _) => x = field) dts of
                               SOME (_, _, xs, _) =>
                               let
                                   val k = (KType, #2 sgn)
                                   val k' = foldl (fn (_, k') => (KArrow (k, k'), #2 sgn)) k xs
                               in
                                   SOME (k', NONE)
                                   end
                             | NONE => NONE)
                        | SgiDatatypeImp (x, _, m1, ms, x', xs, _) =>
                          if x = field then
                              let
                                  val k = (KType, #2 sgn)
                                  val k' = foldl (fn (_, k') => (KArrow (k, k'), #2 sgn)) k xs
                              in
                                  SOME (k', SOME (CModProj (m1, ms, x'), #2 sgn))
                              end
                          else
                              NONE
                        | SgiClassAbs (x, _, k) => if x = field then
                                                       SOME ((KArrow (k, (KType, #2 sgn)), #2 sgn), NONE)
                                                   else
                                                       NONE
                        | SgiClass (x, _, k, c) => if x = field then
                                                       SOME ((KArrow (k, (KType, #2 sgn)), #2 sgn), SOME c)
                                                   else
                                                       NONE
                        | _ => NONE) sgis of
             NONE => NONE
           | SOME ((k, co), subs) => SOME (k, Option.map (sgnSubCon (str, subs)) co))
      | SgnError => SOME ((KError, ErrorMsg.dummySpan), SOME (CError, ErrorMsg.dummySpan))
      | _ => NONE

fun projectDatatype env {sgn, str, field} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        (case sgnSeek (fn SgiDatatype dts =>
                          (case List.find (fn (x, _, _, _) => x = field) dts of
                               SOME (_, _, xs, xncs) => SOME (xs, xncs)
                             | NONE => NONE)
                        | SgiDatatypeImp (x, _, _, _, _, xs, xncs) => if x = field then SOME (xs, xncs) else NONE
                        | _ => NONE) sgis of
             NONE => NONE
           | SOME ((xs, xncs), subs) => SOME (xs,
                                              map (fn (x, n, to) => (x, n, Option.map (sgnSubCon (str, subs)) to)) xncs))
      | _ => NONE

fun projectConstructor env {sgn, str, field} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        let
            fun consider (n, xs, xncs) =
                ListUtil.search (fn (x, n', to) =>
                                    if x <> field then
                                        NONE
                                    else
                                        SOME (U.classifyDatatype xncs, n', xs, to, (CNamed n, #2 str))) xncs
        in
            case sgnSeek (fn SgiDatatype dts =>
                             let
                                 fun search dts =
                                     case dts of
                                         [] => NONE
                                       | (_, n, xs, xncs) :: dts =>
                                         case consider (n, xs, xncs) of
                                             NONE => search dts
                                           | v => v
                             in
                                 search dts
                             end
                           | SgiDatatypeImp (_, n, _, _, _, xs, xncs) => consider (n, xs, xncs)
                           | _ => NONE) sgis of
                NONE => NONE
              | SOME ((dk, n, xs, to, t), subs) => SOME (dk, n, xs, Option.map (sgnSubCon (str, subs)) to,
                                                         sgnSubCon (str, subs) t)
        end
      | _ => NONE

fun projectVal env {sgn, str, field} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis =>
        let
            fun seek (n, xs, xncs) =
                ListUtil.search (fn (x, _, to) =>
                                    if x = field then
                                        SOME (let
                                                  val base = (CNamed n, #2 sgn)
                                                  val nxs = length xs
                                                  val base = ListUtil.foldli (fn (i, _, base) =>
                                                                                 (CApp (base,
                                                                                       (CRel (nxs - i - 1), #2 sgn)),
                                                                                  #2 sgn))
                                                                             base xs

                                                  val t =
                                                      case to of
                                                          NONE => base
                                                        | SOME t => (TFun (t, base), #2 sgn)
                                                  val k = (KType, #2 sgn)
                                              in
                                                  foldr (fn (x, t) => (TCFun (Implicit, x, k, t), #2 sgn))
                                                  t xs
                                              end)
                                    else
                                        NONE) xncs
        in
            case sgnSeek (fn SgiVal (x, _, c) => if x = field then SOME c else NONE
                           | SgiDatatype dts =>
                             let
                                 fun search dts =
                                     case dts of
                                         [] => NONE
                                       | (_, n, xs, xncs) :: dts =>
                                         case seek (n, xs, xncs) of
                                             NONE => search dts
                                           | v => v
                             in
                                 search dts
                             end
                           | SgiDatatypeImp (_, n, _, _, _, xs, xncs) => seek (n, xs, xncs)
                           | _ => NONE) sgis of
                NONE => NONE
              | SOME (c, subs) => SOME (sgnSubCon (str, subs) c)
        end
      | SgnError => SOME (CError, ErrorMsg.dummySpan)
      | _ => NONE

fun sgnSeekConstraints (str, sgis) =
    let
        fun seek (sgis, sgns, strs, cons, acc) =
            case sgis of
                [] => acc
              | (sgi, _) :: sgis =>
                case sgi of
                    SgiConstraint (c1, c2) =>
                    let
                        val sub = sgnSubCon (str, (sgns, strs, cons))
                    in
                        seek (sgis, sgns, strs, cons, (sub c1, sub c2) :: acc)
                    end
                  | SgiConAbs (x, n, _) => seek (sgis, sgns, strs, IM.insert (cons, n, x), acc)
                  | SgiCon (x, n, _, _) => seek (sgis, sgns, strs, IM.insert (cons, n, x), acc)
                  | SgiDatatype dts => seek (sgis, sgns, strs,
                                             foldl (fn ((x, n, _, _), cons) => IM.insert (cons, n, x)) cons dts, acc)
                  | SgiDatatypeImp (x, n, _, _, _, _, _) => seek (sgis, sgns, strs, IM.insert (cons, n, x), acc)
                  | SgiVal _ => seek (sgis, sgns, strs, cons, acc)
                  | SgiSgn (x, n, _) => seek (sgis, IM.insert (sgns, n, x), strs, cons, acc)
                  | SgiStr (x, n, _) => seek (sgis, sgns, IM.insert (strs, n, x), cons, acc)
                  | SgiClassAbs (x, n, _) => seek (sgis, sgns, strs, IM.insert (cons, n, x), acc)
                  | SgiClass (x, n, _, _) => seek (sgis, sgns, strs, IM.insert (cons, n, x), acc)
    in
        seek (sgis, IM.empty, IM.empty, IM.empty, [])
    end

fun projectConstraints env {sgn, str} =
    case #1 (hnormSgn env sgn) of
        SgnConst sgis => SOME (sgnSeekConstraints (str, sgis))
      | SgnError => SOME []
      | _ => NONE

fun patBinds env (p, loc) =
    case p of
        PWild => env
      | PVar (x, t) => pushERel env x t
      | PPrim _ => env
      | PCon (_, _, _, NONE) => env
      | PCon (_, _, _, SOME p) => patBinds env p
      | PRecord xps => foldl (fn ((_, p, _), env) => patBinds env p) env xps

fun patBindsN (p, _) =
    case p of
        PWild => 0
      | PVar _ => 1
      | PPrim _ => 0
      | PCon (_, _, _, NONE) => 0
      | PCon (_, _, _, SOME p) => patBindsN p
      | PRecord xps => foldl (fn ((_, p, _), n) => patBindsN p + n) 0 xps

fun edeclBinds env (d, loc) =
    case d of
        EDVal (p, _, _) => patBinds env p
      | EDValRec vis => foldl (fn ((x, t, _), env) => pushERel env x t) env vis

fun declBinds env (d, loc) =
    case d of
        DCon (x, n, k, c) => pushCNamedAs env x n k (SOME c)
      | DDatatype dts =>
        let
            fun doOne ((x, n, xs, xncs), env) =
                let
                    val k = (KType, loc) 
                    val nxs = length xs
                    val (tb, kb) = ListUtil.foldli (fn (i, x', (tb, kb)) =>
                                                       ((CApp (tb, (CRel (nxs - i - 1), loc)), loc),
                                                        (KArrow (k, kb), loc)))
                                                   ((CNamed n, loc), k) xs
                                   
                    val env = pushCNamedAs env x n kb NONE
                    val env = pushDatatype env n xs xncs
                in
                    foldl (fn ((x', n', to), env) =>
                              let
                                  val t =
                                      case to of
                                          NONE => tb
                                        | SOME t => (TFun (t, tb), loc)
                                  val t = foldr (fn (x, t) => (TCFun (Implicit, x, k, t), loc)) t xs
                              in
                                  pushENamedAs env x' n' t
                              end)
                          env xncs
                end
        in
            foldl doOne env dts
        end
      | DDatatypeImp (x, n, m, ms, x', xs, xncs) =>
        let
            val t = (CModProj (m, ms, x'), loc)
            val k = (KType, loc) 
            val nxs = length xs
            val (tb, kb) = ListUtil.foldli (fn (i, x', (tb, kb)) =>
                                               ((CApp (tb, (CRel (nxs - i - 1), loc)), loc),
                                                (KArrow (k, kb), loc)))
                                           ((CNamed n, loc), k) xs

            val env = pushCNamedAs env x n kb (SOME t)
            val env = pushDatatype env n xs xncs
        in
            foldl (fn ((x', n', to), env) =>
                      let
                          val t =
                              case to of
                                  NONE => tb
                                | SOME t => (TFun (t, tb), loc)
                          val t = foldr (fn (x, t) => (TCFun (Implicit, x, k, t), loc)) t xs
                      in
                          pushENamedAs env x' n' t
                      end)
                  env xncs
        end
      | DVal (x, n, t, _) => pushENamedAs env x n t
      | DValRec vis => foldl (fn ((x, n, t, _), env) => pushENamedAs env x n t) env vis
      | DSgn (x, n, sgn) => pushSgnNamedAs env x n sgn
      | DStr (x, n, sgn, _) => pushStrNamedAs env x n sgn
      | DFfiStr (x, n, sgn) => pushStrNamedAs env x n sgn
      | DConstraint _ => env
      | DExport _ => env
      | DTable (tn, x, n, c, _, pc, _, cc) =>
        let
            val ct = (CModProj (tn, [], "sql_table"), loc)
            val ct = (CApp (ct, c), loc)
            val ct = (CApp (ct, (CConcat (pc, cc), loc)), loc)
        in
            pushENamedAs env x n ct
        end
      | DSequence (tn, x, n) =>
        let
            val t = (CModProj (tn, [], "sql_sequence"), loc)
        in
            pushENamedAs env x n t
        end
      | DView (tn, x, n, _, c) =>
        let
            val ct = (CModProj (tn, [], "sql_view"), loc)
            val ct = (CApp (ct, c), loc)
        in
            pushENamedAs env x n ct
        end
      | DClass (x, n, k, c) =>
        let
            val k = (KArrow (k, (KType, loc)), loc)
            val env = pushCNamedAs env x n k (SOME c)
        in
            pushClass env n
        end
      | DDatabase _ => env
      | DCookie (tn, x, n, c) =>
        let
            val t = (CApp ((CModProj (tn, [], "cookie"), loc), c), loc)
        in
            pushENamedAs env x n t
        end
      | DStyle (tn, x, n) =>
        let
            val t = (CModProj (tn, [], "css_class"), loc)
        in
            pushENamedAs env x n t
        end
      | DTask _ => env
      | DPolicy _ => env
      | DOnError _ => env

end