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
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Compat
open Util
open Names
open Nameops
open Term
open Termops
open Namegen
open Declarations
open Inductiveops
open Environ
open Sign
open Reductionops
open Typeops
open Type_errors
open Glob_term
open Retyping
open Pretype_errors
open Evarutil
open Evarconv
open Evd
(* Pattern-matching errors *)
type pattern_matching_error =
| BadPattern of constructor * constr
| BadConstructor of constructor * inductive
| WrongNumargConstructor of constructor * int
| WrongNumargInductive of inductive * int
| WrongPredicateArity of constr * constr * constr
| NeedsInversion of constr * constr
| UnusedClause of cases_pattern list
| NonExhaustive of cases_pattern list
| CannotInferPredicate of (constr * types) array
exception PatternMatchingError of env * pattern_matching_error
let raise_pattern_matching_error (loc,ctx,te) =
Loc.raise loc (PatternMatchingError(ctx,te))
let error_bad_pattern_loc loc cstr ind =
raise_pattern_matching_error (loc, Global.env(), BadPattern (cstr,ind))
let error_bad_constructor_loc loc cstr ind =
raise_pattern_matching_error (loc, Global.env(), BadConstructor (cstr,ind))
let error_wrong_numarg_constructor_loc loc env c n =
raise_pattern_matching_error (loc, env, WrongNumargConstructor(c,n))
let error_wrong_numarg_inductive_loc loc env c n =
raise_pattern_matching_error (loc, env, WrongNumargInductive(c,n))
let error_wrong_predicate_arity_loc loc env c n1 n2 =
raise_pattern_matching_error (loc, env, WrongPredicateArity (c,n1,n2))
let error_needs_inversion env x t =
raise (PatternMatchingError (env, NeedsInversion (x,t)))
module type S = sig
val compile_cases :
loc -> case_style ->
(type_constraint -> env -> evar_map ref -> glob_constr -> unsafe_judgment) * evar_map ref ->
type_constraint ->
env -> glob_constr option * tomatch_tuples * cases_clauses ->
unsafe_judgment
end
let rec list_try_compile f = function
| [a] -> f a
| [] -> anomaly "try_find_f"
| h::t ->
try f h
with UserError _ | TypeError _ | PretypeError _
| Loc.Exc_located (_,(UserError _ | TypeError _ | PretypeError _)) ->
list_try_compile f t
let force_name =
let nx = Name (id_of_string "x") in function Anonymous -> nx | na -> na
(************************************************************************)
(* Pattern-matching compilation (Cases) *)
(************************************************************************)
(************************************************************************)
(* Configuration, errors and warnings *)
open Pp
let msg_may_need_inversion () =
strbrk "Found a matching with no clauses on a term unknown to have an empty inductive type."
(* Utils *)
let make_anonymous_patvars n =
list_make n (PatVar (dummy_loc,Anonymous))
(* Environment management *)
let push_rels vars env = List.fold_right push_rel vars env
(* We have x1:t1...xn:tn,xi':ti,y1..yk |- c and re-generalize
over xi:ti to get x1:t1...xn:tn,xi':ti,y1..yk |- c[xi:=xi'] *)
let relocate_rel n1 n2 k j = if j = n1+k then n2+k else j
let rec relocate_index n1 n2 k t = match kind_of_term t with
| Rel j when j = n1+k -> mkRel (n2+k)
| Rel j when j < n1+k -> t
| Rel j when j > n1+k -> t
| _ -> map_constr_with_binders succ (relocate_index n1 n2) k t
(**********************************************************************)
(* Structures used in compiling pattern-matching *)
type 'a rhs =
{ rhs_env : env;
rhs_vars : identifier list;
avoid_ids : identifier list;
it : 'a option}
type 'a equation =
{ patterns : cases_pattern list;
rhs : 'a rhs;
alias_stack : name list;
eqn_loc : loc;
used : bool ref }
type 'a matrix = 'a equation list
(* 1st argument of IsInd is the original ind before extracting the summary *)
type tomatch_type =
| IsInd of types * inductive_type * name list
| NotInd of constr option * types
type tomatch_status =
| Pushed of ((constr * tomatch_type) * int list * name)
| Alias of (constr * rel_declaration * bool Lazy.t)
| NonDepAlias
| Abstract of int * rel_declaration
type tomatch_stack = tomatch_status list
(* We keep a constr for aliases and a cases_pattern for error message *)
type pattern_history =
| Top
| MakeConstructor of constructor * pattern_continuation
and pattern_continuation =
| Continuation of int * cases_pattern list * pattern_history
| Result of cases_pattern list
let start_history n = Continuation (n, [], Top)
let feed_history arg = function
| Continuation (n, l, h) when n>=1 ->
Continuation (n-1, arg :: l, h)
| Continuation (n, _, _) ->
anomaly ("Bad number of expected remaining patterns: "^(string_of_int n))
| Result _ ->
anomaly "Exhausted pattern history"
(* This is for non exhaustive error message *)
let rec glob_pattern_of_partial_history args2 = function
| Continuation (n, args1, h) ->
let args3 = make_anonymous_patvars (n - (List.length args2)) in
build_glob_pattern (List.rev_append args1 (args2@args3)) h
| Result pl -> pl
and build_glob_pattern args = function
| Top -> args
| MakeConstructor (pci, rh) ->
glob_pattern_of_partial_history
[PatCstr (dummy_loc, pci, args, Anonymous)] rh
let complete_history = glob_pattern_of_partial_history []
(* This is to build glued pattern-matching history and alias bodies *)
let rec pop_history_pattern = function
| Continuation (0, l, Top) ->
Result (List.rev l)
| Continuation (0, l, MakeConstructor (pci, rh)) ->
feed_history (PatCstr (dummy_loc,pci,List.rev l,Anonymous)) rh
| _ ->
anomaly "Constructor not yet filled with its arguments"
let pop_history h =
feed_history (PatVar (dummy_loc, Anonymous)) h
(* Builds a continuation expecting [n] arguments and building [ci] applied
to this [n] arguments *)
let push_history_pattern n pci cont =
Continuation (n, [], MakeConstructor (pci, cont))
(* A pattern-matching problem has the following form:
env, evd |- match terms_to_tomatch return pred with mat end
where terms_to_match is some sequence of "instructions" (t1 ... tp)
and mat is some matrix
(p11 ... p1n -> rhs1)
( ... )
(pm1 ... pmn -> rhsm)
Terms to match: there are 3 kinds of instructions
- "Pushed" terms to match are typed in [env]; these are usually just
Rel(n) except for the initial terms given by user; in Pushed ((c,tm),deps,na),
[c] is the reference to the term (which is a Rel or an initial term), [tm] is
its type (telling whether we know if it is an inductive type or not),
[deps] is the list of terms to abstract before matching on [c] (these are
rels too)
- "Abstract" instructions mean that an abstraction has to be inserted in the
current branch to build (this means a pattern has been detected dependent
in another one and a generalization is necessary to ensure well-typing)
Abstract instructions extend the [env] in which the other instructions
are typed
- "Alias" instructions mean an alias has to be inserted (this alias
is usually removed at the end, except when its type is not the
same as the type of the matched term from which it comes -
typically because the inductive types are "real" parameters)
- "NonDepAlias" instructions mean the completion of a matching over
a term to match as for Alias but without inserting this alias
because there is no dependency in it
Right-hand sides:
They consist of a raw term to type in an environment specific to the
clause they belong to: the names of declarations are those of the
variables present in the patterns. Therefore, they come with their
own [rhs_env] (actually it is the same as [env] except for the names
of variables).
*)
type 'a pattern_matching_problem =
{ env : env;
evdref : evar_map ref;
pred : constr;
tomatch : tomatch_stack;
history : pattern_continuation;
mat : 'a matrix;
caseloc : loc;
casestyle : case_style;
typing_function: type_constraint -> env -> evar_map ref -> 'a option -> unsafe_judgment }
(*--------------------------------------------------------------------------*
* A few functions to infer the inductive type from the patterns instead of *
* checking that the patterns correspond to the ind. type of the *
* destructurated object. Allows type inference of examples like *
* match n with O => true | _ => false end *
* match x in I with C => true | _ => false end *
*--------------------------------------------------------------------------*)
(* Computing the inductive type from the matrix of patterns *)
(* We use the "in I" clause to coerce the terms to match and otherwise
use the constructor to know in which type is the matching problem
Note that insertion of coercions inside nested patterns is done
each time the matrix is expanded *)
let rec find_row_ind = function
[] -> None
| PatVar _ :: l -> find_row_ind l
| PatCstr(loc,c,_,_) :: _ -> Some (loc,c)
let inductive_template evdref env tmloc ind =
let arsign = get_full_arity_sign env ind in
let hole_source = match tmloc with
| Some loc -> fun i -> (loc, TomatchTypeParameter (ind,i))
| None -> fun _ -> (dummy_loc, InternalHole) in
let (_,evarl,_) =
List.fold_right
(fun (na,b,ty) (subst,evarl,n) ->
match b with
| None ->
let ty' = substl subst ty in
let e = e_new_evar evdref env ~src:(hole_source n) ty' in
(e::subst,e::evarl,n+1)
| Some b ->
(substl subst b::subst,evarl,n+1))
arsign ([],[],1) in
applist (mkInd ind,List.rev evarl)
let try_find_ind env sigma typ realnames =
let (IndType(_,realargs) as ind) = find_rectype env sigma typ in
let names =
match realnames with
| Some names -> names
| None -> list_make (List.length realargs) Anonymous in
IsInd (typ,ind,names)
let inh_coerce_to_ind evdref env ty tyi =
let expected_typ = inductive_template evdref env None tyi in
(* devrait être indifférent d'exiger leq ou pas puisque pour
un inductif cela doit être égal *)
let _ = e_cumul env evdref expected_typ ty in ()
let binding_vars_of_inductive = function
| NotInd _ -> []
| IsInd (_,IndType(_,realargs),_) -> List.filter isRel realargs
let extract_inductive_data env sigma (_,b,t) =
if b<>None then (NotInd (None,t),[]) else
let tmtyp =
try try_find_ind env sigma t None
with Not_found -> NotInd (None,t) in
let tmtypvars = binding_vars_of_inductive tmtyp in
(tmtyp,tmtypvars)
let unify_tomatch_with_patterns evdref env loc typ pats realnames =
match find_row_ind pats with
| None -> NotInd (None,typ)
| Some (_,(ind,_)) ->
inh_coerce_to_ind evdref env typ ind;
try try_find_ind env !evdref typ realnames
with Not_found -> NotInd (None,typ)
let find_tomatch_tycon evdref env loc = function
(* Try if some 'in I ...' is present and can be used as a constraint *)
| Some (_,ind,_,realnal) ->
mk_tycon (inductive_template evdref env loc ind),Some (List.rev realnal)
| None ->
empty_tycon,None
let coerce_row typing_fun evdref env pats (tomatch,(_,indopt)) =
let loc = Some (loc_of_glob_constr tomatch) in
let tycon,realnames = find_tomatch_tycon evdref env loc indopt in
let j = typing_fun tycon env evdref tomatch in
let typ = nf_evar !evdref j.uj_type in
let t =
try try_find_ind env !evdref typ realnames
with Not_found ->
unify_tomatch_with_patterns evdref env loc typ pats realnames in
(j.uj_val,t)
let coerce_to_indtype typing_fun evdref env matx tomatchl =
let pats = List.map (fun r -> r.patterns) matx in
let matx' = match matrix_transpose pats with
| [] -> List.map (fun _ -> []) tomatchl (* no patterns at all *)
| m -> m in
List.map2 (coerce_row typing_fun evdref env) matx' tomatchl
(************************************************************************)
(* Utils *)
let mkExistential env ?(src=(dummy_loc,InternalHole)) evdref =
e_new_evar evdref env ~src:src (new_Type ())
let evd_comb2 f evdref x y =
let (evd',y) = f !evdref x y in
evdref := evd';
y
module Cases_F(Coercion : Coercion.S) : S = struct
let adjust_tomatch_to_pattern pb ((current,typ),deps,dep) =
(* Ideally, we could find a common inductive type to which both the
term to match and the patterns coerce *)
(* In practice, we coerce the term to match if it is not already an
inductive type and it is not dependent; moreover, we use only
the first pattern type and forget about the others *)
let typ,names =
match typ with IsInd(t,_,names) -> t,Some names | NotInd(_,t) -> t,None in
let tmtyp =
try try_find_ind pb.env !(pb.evdref) typ names
with Not_found -> NotInd (None,typ) in
match tmtyp with
| NotInd (None,typ) ->
let tm1 = List.map (fun eqn -> List.hd eqn.patterns) pb.mat in
(match find_row_ind tm1 with
| None -> (current,tmtyp)
| Some (_,(ind,_)) ->
let indt = inductive_template pb.evdref pb.env None ind in
let current =
if deps = [] & isEvar typ then
(* Don't insert coercions if dependent; only solve evars *)
let _ = e_cumul pb.env pb.evdref indt typ in
current
else
(evd_comb2 (Coercion.inh_conv_coerce_to dummy_loc pb.env)
pb.evdref (make_judge current typ) (mk_tycon_type indt)).uj_val in
let sigma = !(pb.evdref) in
(current,try_find_ind pb.env sigma indt names))
| _ -> (current,tmtyp)
let type_of_tomatch = function
| IsInd (t,_,_) -> t
| NotInd (_,t) -> t
let mkDeclTomatch na = function
| IsInd (t,_,_) -> (na,None,t)
| NotInd (c,t) -> (na,c,t)
let map_tomatch_type f = function
| IsInd (t,ind,names) -> IsInd (f t,map_inductive_type f ind,names)
| NotInd (c,t) -> NotInd (Option.map f c, f t)
let liftn_tomatch_type n depth = map_tomatch_type (liftn n depth)
let lift_tomatch_type n = liftn_tomatch_type n 1
(**********************************************************************)
(* Utilities on patterns *)
let current_pattern eqn =
match eqn.patterns with
| pat::_ -> pat
| [] -> anomaly "Empty list of patterns"
let alias_of_pat = function
| PatVar (_,name) -> name
| PatCstr(_,_,_,name) -> name
let remove_current_pattern eqn =
match eqn.patterns with
| pat::pats ->
{ eqn with
patterns = pats;
alias_stack = alias_of_pat pat :: eqn.alias_stack }
| [] -> anomaly "Empty list of patterns"
let push_current_pattern (cur,ty) eqn =
match eqn.patterns with
| pat::pats ->
let rhs_env = push_rel (alias_of_pat pat,Some cur,ty) eqn.rhs.rhs_env in
{ eqn with
rhs = { eqn.rhs with rhs_env = rhs_env };
patterns = pats }
| [] -> anomaly "Empty list of patterns"
let prepend_pattern tms eqn = {eqn with patterns = tms@eqn.patterns }
(**********************************************************************)
(* Well-formedness tests *)
(* Partial check on patterns *)
exception NotAdjustable
let rec adjust_local_defs loc = function
| (pat :: pats, (_,None,_) :: decls) ->
pat :: adjust_local_defs loc (pats,decls)
| (pats, (_,Some _,_) :: decls) ->
PatVar (loc, Anonymous) :: adjust_local_defs loc (pats,decls)
| [], [] -> []
| _ -> raise NotAdjustable
let check_and_adjust_constructor env ind cstrs = function
| PatVar _ as pat -> pat
| PatCstr (loc,((_,i) as cstr),args,alias) as pat ->
(* Check it is constructor of the right type *)
let ind' = inductive_of_constructor cstr in
if eq_ind ind' ind then
(* Check the constructor has the right number of args *)
let ci = cstrs.(i-1) in
let nb_args_constr = ci.cs_nargs in
if List.length args = nb_args_constr then pat
else
try
let args' = adjust_local_defs loc (args, List.rev ci.cs_args)
in PatCstr (loc, cstr, args', alias)
with NotAdjustable ->
error_wrong_numarg_constructor_loc loc (Global.env())
cstr nb_args_constr
else
(* Try to insert a coercion *)
try
Coercion.inh_pattern_coerce_to loc pat ind' ind
with Not_found ->
error_bad_constructor_loc loc cstr ind
let check_all_variables typ mat =
List.iter
(fun eqn -> match current_pattern eqn with
| PatVar (_,id) -> ()
| PatCstr (loc,cstr_sp,_,_) ->
error_bad_pattern_loc loc cstr_sp typ)
mat
let check_unused_pattern env eqn =
if not !(eqn.used) then
raise_pattern_matching_error
(eqn.eqn_loc, env, UnusedClause eqn.patterns)
let set_used_pattern eqn = eqn.used := true
let extract_rhs pb =
match pb.mat with
| [] -> errorlabstrm "build_leaf" (msg_may_need_inversion())
| eqn::_ ->
set_used_pattern eqn;
eqn.rhs
(**********************************************************************)
(* Functions to deal with matrix factorization *)
let occur_in_rhs na rhs =
match na with
| Anonymous -> false
| Name id -> List.mem id rhs.rhs_vars
let is_dep_patt_in eqn = function
| PatVar (_,name) -> occur_in_rhs name eqn.rhs
| PatCstr _ -> true
let mk_dep_patt_row (pats,_,eqn) =
List.map (is_dep_patt_in eqn) pats
let dependencies_in_pure_rhs nargs eqns =
if eqns = [] then list_make nargs false (* Only "_" patts *) else
let deps_rows = List.map mk_dep_patt_row eqns in
let deps_columns = matrix_transpose deps_rows in
List.map (List.exists ((=) true)) deps_columns
let dependent_decl a = function
| (na,None,t) -> dependent a t
| (na,Some c,t) -> dependent a t || dependent a c
let rec dep_in_tomatch n = function
| (Pushed _ | Alias _ | NonDepAlias) :: l -> dep_in_tomatch n l
| Abstract (_,d) :: l -> dependent_decl (mkRel n) d or dep_in_tomatch (n+1) l
| [] -> false
let dependencies_in_rhs nargs current tms eqns =
match kind_of_term current with
| Rel n when dep_in_tomatch n tms -> list_make nargs true
| _ -> dependencies_in_pure_rhs nargs eqns
(* Computing the matrix of dependencies *)
(* [find_dependency_list tmi [d(i+1);...;dn]] computes in which
declarations [d(i+1);...;dn] the term [tmi] is dependent in.
[find_dependencies_signature (used1,...,usedn) ((tm1,d1),...,(tmn,dn))]
returns [(deps1,...,depsn)] where [depsi] is a subset of n,..,i+1
denoting in which of the d(i+1)...dn, the term tmi is dependent.
Dependencies are expressed by index, e.g. in dependency list
[n-2;1], [1] points to [dn] and [n-2] to [d3]
*)
let rec find_dependency_list tmblock = function
| [] -> []
| (used,tdeps,d)::rest ->
let deps = find_dependency_list tmblock rest in
if used && List.exists (fun x -> dependent_decl x d) tmblock
then list_add_set (List.length rest + 1) (list_union deps tdeps)
else deps
let find_dependencies is_dep_or_cstr_in_rhs (tm,(_,tmtypleaves),d) nextlist =
let deps = find_dependency_list (tm::tmtypleaves) nextlist in
if is_dep_or_cstr_in_rhs || deps <> []
then ((true ,deps,d)::nextlist)
else ((false,[] ,d)::nextlist)
let find_dependencies_signature deps_in_rhs typs =
let l = List.fold_right2 find_dependencies deps_in_rhs typs [] in
List.map (fun (_,deps,_) -> deps) l
(* Assume we had terms t1..tq to match in a context xp:Tp,...,x1:T1 |-
and xn:Tn has just been regeneralized into x:Tn so that the terms
to match are now to be considered in the context xp:Tp,...,x1:T1,x:Tn |-.
[relocate_index_tomatch n 1 tomatch] updates t1..tq so that
former references to xn1 are now references to x. Note that t1..tq
are already adjusted to the context xp:Tp,...,x1:T1,x:Tn |-.
[relocate_index_tomatch 1 n tomatch] will go the way back.
*)
let relocate_index_tomatch n1 n2 =
let rec genrec depth = function
| [] ->
[]
| Pushed ((c,tm),l,na) :: rest ->
let c = relocate_index n1 n2 depth c in
let tm = map_tomatch_type (relocate_index n1 n2 depth) tm in
let l = List.map (relocate_rel n1 n2 depth) l in
Pushed ((c,tm),l,na) :: genrec depth rest
| Alias (c,d,p) :: rest ->
let d = map_rel_declaration (relocate_index n1 n2 depth) d in
(* [c] is out of relocation scope *)
Alias (c,d,p) :: genrec depth rest
| NonDepAlias :: rest ->
NonDepAlias :: genrec depth rest
| Abstract (i,d) :: rest ->
let i = relocate_rel n1 n2 depth i in
Abstract (i,map_rel_declaration (relocate_index n1 n2 depth) d)
:: genrec (depth+1) rest in
genrec 0
(* [replace_tomatch n c tomatch] replaces [Rel n] by [c] in [tomatch] *)
let rec replace_term n c k t =
if isRel t && destRel t = n+k then lift k c
else map_constr_with_binders succ (replace_term n c) k t
let length_of_tomatch_type_sign na = function
| NotInd _ -> if na<>Anonymous then 1 else 0
| IsInd (_,_,names) -> List.length names + if na<>Anonymous then 1 else 0
let replace_tomatch n c =
let rec replrec depth = function
| [] -> []
| Pushed ((b,tm),l,na) :: rest ->
let b = replace_term n c depth b in
let tm = map_tomatch_type (replace_term n c depth) tm in
List.iter (fun i -> if i=n+depth then anomaly "replace_tomatch") l;
Pushed ((b,tm),l,na) :: replrec depth rest
| Alias (b,d,p) :: rest ->
let d = map_rel_declaration (replace_term n c depth) d in
(* [c] is out of replacement scope *)
Alias (b,d,p) :: replrec depth rest
| NonDepAlias :: rest ->
NonDepAlias :: replrec depth rest
| Abstract (i,d) :: rest ->
Abstract (i,map_rel_declaration (replace_term n c depth) d)
:: replrec (depth+1) rest in
replrec 0
(* [liftn_tomatch_stack]: a term to match has just been substituted by
some constructor t = (ci x1...xn) and the terms x1 ... xn have been
added to match; all pushed terms to match must be lifted by n
(knowing that [Abstract] introduces a binder in the list of pushed
terms to match).
*)
let rec liftn_tomatch_stack n depth = function
| [] -> []
| Pushed ((c,tm),l,na)::rest ->
let c = liftn n depth c in
let tm = liftn_tomatch_type n depth tm in
let l = List.map (fun i -> if i<depth then i else i+n) l in
Pushed ((c,tm),l,na)::(liftn_tomatch_stack n depth rest)
| Alias (c,d,p)::rest ->
Alias (liftn n depth c,map_rel_declaration (liftn n depth) d,p)
::(liftn_tomatch_stack n depth rest)
| NonDepAlias :: rest ->
NonDepAlias :: liftn_tomatch_stack n depth rest
| Abstract (i,d)::rest ->
let i = if i<depth then i else i+n in
Abstract (i,map_rel_declaration (liftn n depth) d)
::(liftn_tomatch_stack n (depth+1) rest)
let lift_tomatch_stack n = liftn_tomatch_stack n 1
(* if [current] has type [I(p1...pn u1...um)] and we consider the case
of constructor [ci] of type [I(p1...pn u'1...u'm)], then the
default variable [name] is expected to have which type?
Rem: [current] is [(Rel i)] except perhaps for initial terms to match *)
(************************************************************************)
(* Some heuristics to get names for variables pushed in pb environment *)
(* Typical requirement:
[match y with (S (S x)) => x | x => x end] should be compiled into
[match y with O => y | (S n) => match n with O => y | (S x) => x end end]
and [match y with (S (S n)) => n | n => n end] into
[match y with O => y | (S n0) => match n0 with O => y | (S n) => n end end]
i.e. user names should be preserved and created names should not
interfere with user names
The exact names here are not important for typing (because they are
put in pb.env and not in the rhs.rhs_env of branches. However,
whether a name is Anonymous or not may have an effect on whether a
generalization is done or not.
*)
let merge_name get_name obj = function
| Anonymous -> get_name obj
| na -> na
let merge_names get_name = List.map2 (merge_name get_name)
let get_names env sign eqns =
let names1 = list_make (List.length sign) Anonymous in
(* If any, we prefer names used in pats, from top to bottom *)
let names2,aliasname =
List.fold_right
(fun (pats,pat_alias,eqn) (names,aliasname) ->
(merge_names alias_of_pat pats names,
merge_name (fun x -> x) pat_alias aliasname))
eqns (names1,Anonymous) in
(* Otherwise, we take names from the parameters of the constructor but
avoiding conflicts with user ids *)
let allvars =
List.fold_left (fun l (_,_,eqn) -> list_union l eqn.rhs.avoid_ids)
[] eqns in
let names3,_ =
List.fold_left2
(fun (l,avoid) d na ->
let na =
merge_name
(fun (na,_,t) -> Name (next_name_away (named_hd env t na) avoid))
d na
in
(na::l,(out_name na)::avoid))
([],allvars) (List.rev sign) names2 in
names3,aliasname
(*****************************************************************)
(* Recovering names for variables pushed to the rhs' environment *)
(* We just factorized a match over a matrix of equations *)
(* "C xi1 .. xin as xi" as a single match over "C y1 .. yn as y" *)
(* We now replace the names y1 .. yn y by the actual names *)
(* xi1 .. xin xi to be found in the i-th clause of the matrix *)
let set_declaration_name x (_,c,t) = (x,c,t)
let recover_initial_subpattern_names = List.map2 set_declaration_name
let recover_alias_names get_name = List.map2 (fun x (_,c,t) ->(get_name x,c,t))
let push_rels_eqn sign eqn =
{eqn with rhs = {eqn.rhs with rhs_env = push_rels sign eqn.rhs.rhs_env} }
let push_rels_eqn_with_names sign eqn =
let subpats = List.rev (list_firstn (List.length sign) eqn.patterns) in
let subpatnames = List.map alias_of_pat subpats in
let sign = recover_initial_subpattern_names subpatnames sign in
push_rels_eqn sign eqn
let push_generalized_decl_eqn env n (na,c,t) eqn =
let na = match na with
| Anonymous -> Anonymous
| Name id -> pi1 (Environ.lookup_rel n eqn.rhs.rhs_env) in
push_rels_eqn [(na,c,t)] eqn
let drop_alias_eqn eqn =
{ eqn with alias_stack = List.tl eqn.alias_stack }
let push_alias_eqn alias eqn =
let aliasname = List.hd eqn.alias_stack in
let eqn = drop_alias_eqn eqn in
let alias = set_declaration_name aliasname alias in
push_rels_eqn [alias] eqn
(**********************************************************************)
(* Functions to deal with elimination predicate *)
(* Infering the predicate *)
(*
The problem to solve is the following:
We match Gamma |- t : I(u01..u0q) against the following constructors:
Gamma, x11...x1p1 |- C1(x11..x1p1) : I(u11..u1q)
...
Gamma, xn1...xnpn |- Cn(xn1..xnp1) : I(un1..unq)
Assume the types in the branches are the following
Gamma, x11...x1p1 |- branch1 : T1
...
Gamma, xn1...xnpn |- branchn : Tn
Assume the type of the global case expression is Gamma |- T
The predicate has the form phi = [y1..yq][z:I(y1..yq)]psi and it has to
satisfy the following n+1 equations:
Gamma, x11...x1p1 |- (phi u11..u1q (C1 x11..x1p1)) = T1
...
Gamma, xn1...xnpn |- (phi un1..unq (Cn xn1..xnpn)) = Tn
Gamma |- (phi u01..u0q t) = T
Some hints:
- Clearly, if xij occurs in Ti, then, a "match z with (Ci xi1..xipi)
=> ... end" or a "psi(yk)", with psi extracting xij from uik, should be
inserted somewhere in Ti.
- If T is undefined, an easy solution is to insert a "match z with
(Ci xi1..xipi) => ... end" in front of each Ti
- Otherwise, T1..Tn and T must be step by step unified, if some of them
diverge, then try to replace the diverging subterm by one of y1..yq or z.
- The main problem is what to do when an existential variables is encountered
*)
(* Propagation of user-provided predicate through compilation steps *)
let rec map_predicate f k ccl = function
| [] -> f k ccl
| Pushed ((_,tm),_,na) :: rest ->
let k' = length_of_tomatch_type_sign na tm in
map_predicate f (k+k') ccl rest
| (Alias _ | NonDepAlias) :: rest ->
map_predicate f k ccl rest
| Abstract _ :: rest ->
map_predicate f (k+1) ccl rest
let noccur_predicate_between n = map_predicate (noccur_between n)
let liftn_predicate n = map_predicate (liftn n)
let lift_predicate n = liftn_predicate n 1
let regeneralize_index_predicate n = map_predicate (relocate_index n 1) 0
let substnl_predicate sigma = map_predicate (substnl sigma)
(* This is parallel bindings *)
let subst_predicate (args,copt) ccl tms =
let sigma = match copt with
| None -> List.rev args
| Some c -> c::(List.rev args) in
substnl_predicate sigma 0 ccl tms
let specialize_predicate_var (cur,typ,dep) tms ccl =
let c = if dep<>Anonymous then Some cur else None in
let l =
match typ with
| IsInd (_,IndType(_,realargs),names) -> if names<>[] then realargs else []
| NotInd _ -> [] in
subst_predicate (l,c) ccl tms
(*****************************************************************************)
(* We have pred = [X:=realargs;x:=c]P typed in Gamma1, x:I(realargs), Gamma2 *)
(* and we want to abstract P over y:t(x) typed in the same context to get *)
(* *)
(* pred' = [X:=realargs;x':=c](y':t(x'))P[y:=y'] *)
(* *)
(* We first need to lift t(x) s.t. it is typed in Gamma, X:=rargs, x' *)
(* then we have to replace x by x' in t(x) and y by y' in P *)
(*****************************************************************************)
let generalize_predicate (names,na) ny d tms ccl =
if na=Anonymous then anomaly "Undetected dependency";
let p = List.length names + 1 in
let ccl = lift_predicate 1 ccl tms in
regeneralize_index_predicate (ny+p+1) ccl tms
(*****************************************************************************)
(* We just matched over cur:ind(realargs) in the following matching problem *)
(* *)
(* env |- match cur tms return ccl with ... end *)
(* *)
(* and we want to build the predicate corresponding to the individual *)
(* matching over cur *)
(* *)
(* pred = fun X:realargstyps x:ind(X)] PI tms.ccl *)
(* *)
(* where pred is computed by abstract_predicate and PI tms.ccl by *)
(* extract_predicate *)
(*****************************************************************************)
let rec extract_predicate ccl = function
| (Alias _ | NonDepAlias)::tms ->
(* substitution already done in build_branch *)
extract_predicate ccl tms
| Abstract (i,d)::tms ->
mkProd_wo_LetIn d (extract_predicate ccl tms)
| Pushed ((cur,NotInd _),_,na)::tms ->
let tms = if na<>Anonymous then lift_tomatch_stack 1 tms else tms in
let pred = extract_predicate ccl tms in
if na<>Anonymous then subst1 cur pred else pred
| Pushed ((cur,IsInd (_,IndType(_,realargs),_)),_,na)::tms ->
let realargs = List.rev realargs in
let k = if na<>Anonymous then 1 else 0 in
let tms = lift_tomatch_stack (List.length realargs + k) tms in
let pred = extract_predicate ccl tms in
substl (if na<>Anonymous then cur::realargs else realargs) pred
| [] ->
ccl
let abstract_predicate env sigma indf cur realargs (names,na) tms ccl =
let sign = make_arity_signature env true indf in
(* n is the number of real args + 1 (+ possible let-ins in sign) *)
let n = List.length sign in
(* Before abstracting we generalize over cur and on those realargs *)
(* that are rels, consistently with the specialization made in *)
(* build_branch *)
let tms = List.fold_right2 (fun par arg tomatch ->
match kind_of_term par with
| Rel i -> relocate_index_tomatch (i+n) (destRel arg) tomatch
| _ -> tomatch) (realargs@[cur]) (extended_rel_list 0 sign)
(lift_tomatch_stack n tms) in
(* Pred is already dependent in the current term to match (if *)
(* (na<>Anonymous) and its realargs; we just need to adjust it to *)
(* full sign if dep in cur is not taken into account *)
let ccl = if na <> Anonymous then ccl else lift_predicate 1 ccl tms in
let pred = extract_predicate ccl tms in
(* Build the predicate properly speaking *)
let sign = List.map2 set_declaration_name (na::names) sign in
it_mkLambda_or_LetIn_name env pred sign
(* [expand_arg] is used by [specialize_predicate]
if Yk denotes [Xk;xk] or [Xk],
it replaces gamma, x1...xn, x1...xk Yk+1...Yn |- pred
by gamma, x1...xn, x1...xk-1 [Xk;xk] Yk+1...Yn |- pred (if dep) or
by gamma, x1...xn, x1...xk-1 [Xk] Yk+1...Yn |- pred (if not dep) *)
let expand_arg tms (p,ccl) ((_,t),_,na) =
let k = length_of_tomatch_type_sign na t in
(p+k,liftn_predicate (k-1) (p+1) ccl tms)
let adjust_impossible_cases pb pred tomatch submat =
if submat = [] then
match kind_of_term (whd_evar !(pb.evdref) pred) with
| Evar (evk,_) when snd (evar_source evk !(pb.evdref)) = ImpossibleCase ->
let default = (coq_unit_judge ()).uj_type in
pb.evdref := Evd.define evk default !(pb.evdref);
(* we add an "assert false" case *)
let pats = List.map (fun _ -> PatVar (dummy_loc,Anonymous)) tomatch in
let aliasnames =
map_succeed (function Alias _ | NonDepAlias -> Anonymous | _ -> failwith"") tomatch
in
[ { patterns = pats;
rhs = { rhs_env = pb.env;
rhs_vars = [];
avoid_ids = [];
it = None };
alias_stack = Anonymous::aliasnames;
eqn_loc = dummy_loc;
used = ref false } ]
| _ ->
submat
else
submat
(*****************************************************************************)
(* Let pred = PI [X;x:I(X)]. PI tms. P be a typing predicate for the *)
(* following pattern-matching problem: *)
(* *)
(* Gamma |- match Pushed(c:I(V)) as x in I(X), tms return pred with...end *)
(* *)
(* where the branch with constructor Ci:(x1:T1)...(xn:Tn)->I(realargsi) *)
(* is considered. Assume each Ti is some Ii(argsi) with Ti:PI Ui. sort_i *)
(* We let subst = X:=realargsi;x:=Ci(x1,...,xn) and replace pred by *)
(* *)
(* pred' = PI [X1:Ui;x1:I1(X1)]...[Xn:Un;xn:In(Xn)]. (PI tms. P)[subst] *)
(* *)
(* s.t. the following well-typed sub-pattern-matching problem is obtained *)
(* *)
(* Gamma,x'1..x'n |- *)
(* match *)
(* Pushed(x'1) as x1 in I(X1), *)
(* .., *)
(* Pushed(x'n) as xn in I(Xn), *)
(* tms *)
(* return pred' *)
(* with .. end *)
(* *)
(*****************************************************************************)
let specialize_predicate newtomatchs (names,depna) arsign cs tms ccl =
(* Assume some gamma st: gamma |- PI [X,x:I(X)]. PI tms. ccl *)
let nrealargs = List.length names in
let k = nrealargs + (if depna<>Anonymous then 1 else 0) in
(* We adjust pred st: gamma, x1..xn |- PI [X,x:I(X)]. PI tms. ccl' *)
(* so that x can later be instantiated by Ci(x1..xn) *)
(* and X by the realargs for Ci *)
let n = cs.cs_nargs in
let ccl' = liftn_predicate n (k+1) ccl tms in
(* We prepare the substitution of X and x:I(X) *)
let realargsi =
if nrealargs <> 0 then
adjust_subst_to_rel_context arsign (Array.to_list cs.cs_concl_realargs)
else
[] in
let copti =
if depna<>Anonymous then Some (build_dependent_constructor cs) else None in
(* The substituends realargsi, copti are all defined in gamma, x1...xn *)
(* We need _parallel_ bindings to get gamma, x1...xn |- PI tms. ccl'' *)
(* Note: applying the substitution in tms is not important (is it sure?) *)
let ccl'' =
whd_betaiota Evd.empty (subst_predicate (realargsi, copti) ccl' tms) in
(* We adjust ccl st: gamma, x'1..x'n, x1..xn, tms |- ccl'' *)
let ccl''' = liftn_predicate n (n+1) ccl'' tms in
(* We finally get gamma,x'1..x'n,x |- [X1;x1:I(X1)]..[Xn;xn:I(Xn)]pred'''*)
snd (List.fold_left (expand_arg tms) (1,ccl''') newtomatchs)
let find_predicate loc env evdref p current (IndType (indf,realargs)) dep tms =
let pred = abstract_predicate env !evdref indf current realargs dep tms p in
(pred, whd_betaiota !evdref
(applist (pred, realargs@[current])))
(* Take into account that a type has been discovered to be inductive, leading
to more dependencies in the predicate if the type has indices *)
let adjust_predicate_from_tomatch tomatch (current,typ as ct) pb =
let ((_,oldtyp),deps,na) = tomatch in
match typ, oldtyp with
| IsInd (_,_,names), NotInd _ ->
let k = if na <> Anonymous then 2 else 1 in
let n = List.length names in
{ pb with pred = liftn_predicate n k pb.pred pb.tomatch },
(ct,List.map (fun i -> if i >= k then i+n else i) deps,na)
| _ ->
pb, (ct,deps,na)
(* Decide what to do with an alias *)
let is_dep_pred n pb =
(* Keep call to is_dep_pred lazy so that pb.evdref is fetched when really
needed, and hopefully with a maximum of information on evar resolution *)
let pred = nf_evar !(pb.evdref) pb.pred in
not (noccur_predicate_between 1 (n+1) pred pb.tomatch)
let mkSpecialLetIn orig (na,b,t) isdeppred c =
if na = Anonymous || not (dependent (mkRel 1) c) then
lift (-1) c
else if Lazy.force isdeppred then
mkLetIn (na,Option.get b,t,c)
else
(* Brutal replacement by the non-dependent alias if atomic *)
(* Caution: is might violate typing if the alias is internally used *)
(* to type the right-hand side even though it does not occur in the *)
(* external type (e.g. with "f x refl" with "f:forall x,x=0 -> Prop" *)
(* and x aliased to 0 *)
if isRel orig then subst1 orig c else subst1 (Option.get b) c
(* Remove commutative cuts that turn out to be non-dependent after
some evars have been instantiated *)
let rec ungeneralize n ng body =
match kind_of_term body with
| Lambda (_,_,c) when ng = 0 ->
subst1 (mkRel n) c
| Lambda (na,t,c) ->
(* We traverse an inner generalization *)
mkLambda (na,t,ungeneralize (n+1) (ng-1) c)
| LetIn (na,b,t,c) ->
(* We traverse an alias *)
mkLetIn (na,b,t,ungeneralize (n+1) ng c)
| Case (ci,p,c,brs) ->
(* We traverse a split *)
let p =
let sign,p = decompose_lam_assum p in
let sign2,p = decompose_prod_n_assum ng p in
let p = prod_applist p [mkRel (n+List.length sign+ng)] in
it_mkLambda_or_LetIn (it_mkProd_or_LetIn p sign2) sign in
mkCase (ci,p,c,array_map2 (fun q c ->
let sign,b = decompose_lam_n_assum q c in
it_mkLambda_or_LetIn (ungeneralize (n+q) ng b) sign)
ci.ci_cstr_ndecls brs)
| App (f,args) ->
(* We traverse an inner generalization *)
assert (isCase f);
mkApp (ungeneralize n (ng+Array.length args) f,args)
| _ -> assert false
let ungeneralize_branch n k (sign,body) cs =
(sign,ungeneralize (n+cs.cs_nargs) k body)
let postprocess_dependencies evd tocheck brs tomatch pred deps cs =
let rec aux k brs tomatch pred tocheck deps = match deps, tomatch with
| [], _ -> brs,tomatch,pred,[]
| n::deps, Abstract (i,d) :: tomatch ->
let d = map_rel_declaration (nf_evar evd) d in
if List.exists (fun c -> dependent_decl (lift k c) d) tocheck || pi2 d <> None then
(* Dependency in the current term to match and its dependencies is real *)
let brs,tomatch,pred,inst = aux (k+1) brs tomatch pred (mkRel n::tocheck) deps in
let inst = if pi2 d = None then mkRel n::inst else inst in
brs, Abstract (i,d) :: tomatch, pred, inst
else
(* Finally, no dependency remains, so, we can replace the generalized *)
(* terms by its actual value in both the remaining terms to match and *)
(* the bodies of the Case *)
let pred = lift_predicate (-1) pred tomatch in
let tomatch = relocate_index_tomatch 1 (n+1) tomatch in
let tomatch = lift_tomatch_stack (-1) tomatch in
let brs = array_map2 (ungeneralize_branch n k) brs cs in
aux k brs tomatch pred tocheck deps
| _ -> assert false
in aux 0 brs tomatch pred tocheck deps
(************************************************************************)
(* Sorting equations by constructor *)
let rec irrefutable env = function
| PatVar (_,name) -> true
| PatCstr (_,cstr,args,_) ->
let ind = inductive_of_constructor cstr in
let (_,mip) = Inductive.lookup_mind_specif env ind in
let one_constr = Array.length mip.mind_user_lc = 1 in
one_constr & List.for_all (irrefutable env) args
let first_clause_irrefutable env = function
| eqn::mat -> List.for_all (irrefutable env) eqn.patterns
| _ -> false
let group_equations pb ind current cstrs mat =
let mat =
if first_clause_irrefutable pb.env mat then [List.hd mat] else mat in
let brs = Array.create (Array.length cstrs) [] in
let only_default = ref true in
let _ =
List.fold_right (* To be sure it's from bottom to top *)
(fun eqn () ->
let rest = remove_current_pattern eqn in
let pat = current_pattern eqn in
match check_and_adjust_constructor pb.env ind cstrs pat with
| PatVar (_,name) ->
(* This is a default clause that we expand *)
for i=1 to Array.length cstrs do
let args = make_anonymous_patvars cstrs.(i-1).cs_nargs in
brs.(i-1) <- (args, name, rest) :: brs.(i-1)
done
| PatCstr (loc,((_,i)),args,name) ->
(* This is a regular clause *)
only_default := false;
brs.(i-1) <- (args, name, rest) :: brs.(i-1)) mat () in
(brs,!only_default)
(************************************************************************)
(* Here starts the pattern-matching compilation algorithm *)
(* Abstracting over dependent subterms to match *)
let rec generalize_problem names pb = function
| [] -> pb, []
| i::l ->
let (na,b,t as d) = map_rel_declaration (lift i) (Environ.lookup_rel i pb.env) in
let pb',deps = generalize_problem names pb l in
if na = Anonymous & b <> None then pb',deps else
let d = on_pi3 (whd_betaiota !(pb.evdref)) d in (* for better rendering *)
let tomatch = lift_tomatch_stack 1 pb'.tomatch in
let tomatch = relocate_index_tomatch (i+1) 1 tomatch in
{ pb' with
tomatch = Abstract (i,d) :: tomatch;
pred = generalize_predicate names i d pb'.tomatch pb'.pred },
i::deps
(* No more patterns: typing the right-hand side of equations *)
let build_leaf pb =
let rhs = extract_rhs pb in
let j = pb.typing_function (mk_tycon pb.pred) rhs.rhs_env pb.evdref rhs.it in
j_nf_evar !(pb.evdref) j
(* Build the sub-pattern-matching problem for a given branch "C x1..xn as x" *)
let build_branch current realargs deps (realnames,curname) pb arsign eqns const_info =
(* We remember that we descend through constructor C *)
let history =
push_history_pattern const_info.cs_nargs const_info.cs_cstr pb.history in
(* We prepare the matching on x1:T1 .. xn:Tn using some heuristic to *)
(* build the name x1..xn from the names present in the equations *)
(* that had matched constructor C *)
let cs_args = const_info.cs_args in
let names,aliasname = get_names pb.env cs_args eqns in
let typs = List.map2 (fun (_,c,t) na -> (na,c,t)) cs_args names in
(* We build the matrix obtained by expanding the matching on *)
(* "C x1..xn as x" followed by a residual matching on eqn into *)
(* a matching on "x1 .. xn eqn" *)
let submat = List.map (fun (tms,_,eqn) -> prepend_pattern tms eqn) eqns in
(* We adjust the terms to match in the context they will be once the *)
(* context [x1:T1,..,xn:Tn] will have been pushed on the current env *)
let typs' =
list_map_i (fun i d -> (mkRel i,map_rel_declaration (lift i) d)) 1 typs in
let extenv = push_rels typs pb.env in
let typs' =
List.map (fun (c,d) ->
(c,extract_inductive_data extenv !(pb.evdref) d,d)) typs' in
(* We compute over which of x(i+1)..xn and x matching on xi will need a *)
(* generalization *)
let dep_sign =
find_dependencies_signature
(dependencies_in_rhs const_info.cs_nargs current pb.tomatch eqns)
(List.rev typs') in
(* The dependent term to subst in the types of the remaining UnPushed
terms is relative to the current context enriched by topushs *)
let ci = build_dependent_constructor const_info in
(* Current context Gamma has the form Gamma1;cur:I(realargs);Gamma2 *)
(* We go from Gamma |- PI tms. pred to *)
(* Gamma;x1..xn;curalias:I(x1..xn) |- PI tms'. pred' *)
(* where, in tms and pred, those realargs that are vars are *)
(* replaced by the corresponding xi and cur replaced by curalias *)
let cirealargs = Array.to_list const_info.cs_concl_realargs in
(* Do the specialization for terms to match *)
let tomatch = List.fold_right2 (fun par arg tomatch ->
match kind_of_term par with
| Rel i -> replace_tomatch (i+const_info.cs_nargs) arg tomatch
| _ -> tomatch) (current::realargs) (ci::cirealargs)
(lift_tomatch_stack const_info.cs_nargs pb.tomatch) in
let pred_is_not_dep =
noccur_predicate_between 1 (List.length realnames + 1) pb.pred tomatch in
let typs' =
List.map2
(fun (tm,(tmtyp,_),(na,_,_)) deps ->
let na = match curname with
| Name _ -> (if na <> Anonymous then na else curname)
| Anonymous ->
if deps = [] && pred_is_not_dep then Anonymous else force_name na in
((tm,tmtyp),deps,na))
typs' (List.rev dep_sign) in
(* Do the specialization for the predicate *)
let pred =
specialize_predicate typs' (realnames,curname) arsign const_info tomatch pb.pred in
let currents = List.map (fun x -> Pushed x) typs' in
let ind =
appvect (
applist (mkInd (inductive_of_constructor const_info.cs_cstr),
List.map (lift const_info.cs_nargs) const_info.cs_params),
const_info.cs_concl_realargs) in
let alias =
if aliasname = Anonymous then
NonDepAlias
else
let cur_alias = lift const_info.cs_nargs current in
let lazy_dep_pred = lazy (is_dep_pred (List.length realnames) pb) in
Alias (cur_alias,(aliasname,Some ci,ind),lazy_dep_pred) in
let tomatch = List.rev_append (alias :: currents) tomatch in
let submat = adjust_impossible_cases pb pred tomatch submat in
if submat = [] then
raise_pattern_matching_error
(dummy_loc, pb.env, NonExhaustive (complete_history history));
typs,
{ pb with
env = extenv;
tomatch = tomatch;
pred = pred;
history = history;
mat = List.map (push_rels_eqn_with_names typs) submat }
(**********************************************************************
INVARIANT:
pb = { env, pred, tomatch, mat, ...}
tomatch = list of Pushed (c:T), Abstract (na:T), Alias (c:T) or NonDepAlias
all terms and types in Pushed, Abstract and Alias are relative to env
enriched by the Abstract coming before
*)
(**********************************************************************)
(* Main compiling descent *)
let rec compile pb =
match pb.tomatch with
| Pushed cur :: rest -> match_current { pb with tomatch = rest } cur
| Alias x :: rest -> compile_alias pb x rest
| NonDepAlias :: rest -> compile_non_dep_alias pb rest
| Abstract (i,d) :: rest -> compile_generalization pb i d rest
| [] -> build_leaf pb
(* Case splitting *)
and match_current pb tomatch =
let tm = adjust_tomatch_to_pattern pb tomatch in
let pb,tomatch = adjust_predicate_from_tomatch tomatch tm pb in
let ((current,typ),deps,dep) = tomatch in
match typ with
| NotInd (_,typ) ->
check_all_variables typ pb.mat;
shift_problem tomatch pb
| IsInd (_,(IndType(indf,realargs) as indt),names) ->
let mind,_ = dest_ind_family indf in
let cstrs = get_constructors pb.env indf in
let arsign, _ = get_arity pb.env indf in
let eqns,onlydflt = group_equations pb mind current cstrs pb.mat in
if (Array.length cstrs <> 0 or pb.mat <> []) & onlydflt then
shift_problem tomatch pb
else
(* We generalize over terms depending on current term to match *)
let pb,deps = generalize_problem (names,dep) pb deps in
(* We compile branches *)
let brvals = array_map2 (compile_branch current realargs (names,dep) deps pb arsign) eqns cstrs in
(* We build the (elementary) case analysis *)
let depstocheck = current::binding_vars_of_inductive typ in
let brvals,tomatch,pred,inst =
postprocess_dependencies !(pb.evdref) depstocheck
brvals pb.tomatch pb.pred deps cstrs in
let brvals = Array.map (fun (sign,body) ->
it_mkLambda_or_LetIn body sign) brvals in
let (pred,typ) =
find_predicate pb.caseloc pb.env pb.evdref
pred current indt (names,dep) tomatch in
let ci = make_case_info pb.env mind pb.casestyle in
let pred = nf_betaiota !(pb.evdref) pred in
let case = mkCase (ci,pred,current,brvals) in
Typing.check_allowed_sort pb.env !(pb.evdref) mind current pred;
{ uj_val = applist (case, inst);
uj_type = prod_applist typ inst }
(* Building the sub-problem when all patterns are variables *)
and shift_problem ((current,t),_,na) pb =
let ty = type_of_tomatch t in
let tomatch = lift_tomatch_stack 1 pb.tomatch in
let pred = specialize_predicate_var (current,t,na) pb.tomatch pb.pred in
let pb =
{ pb with
env = push_rel (na,Some current,ty) pb.env;
tomatch = tomatch;
pred = lift_predicate 1 pred tomatch;
history = pop_history pb.history;
mat = List.map (push_current_pattern (current,ty)) pb.mat } in
let j = compile pb in
{ uj_val = subst1 current j.uj_val;
uj_type = subst1 current j.uj_type }
(* Building the sub-problem when all patterns are variables *)
and compile_branch current realargs names deps pb arsign eqns cstr =
let sign, pb = build_branch current realargs deps names pb arsign eqns cstr in
sign, (compile pb).uj_val
(* Abstract over a declaration before continuing splitting *)
and compile_generalization pb i d rest =
let pb =
{ pb with
env = push_rel d pb.env;
tomatch = rest;
mat = List.map (push_generalized_decl_eqn pb.env i d) pb.mat } in
let j = compile pb in
{ uj_val = mkLambda_or_LetIn d j.uj_val;
uj_type = mkProd_wo_LetIn d j.uj_type }
and compile_alias pb (orig,(_,ci,_ as alias),isdeppred) rest =
let pb =
{ pb with
env = push_rel alias pb.env;
tomatch = lift_tomatch_stack 1 rest;
pred = lift_predicate 1 pb.pred pb.tomatch;
history = pop_history_pattern pb.history;
mat = List.map (push_alias_eqn alias) pb.mat } in
let j = compile pb in
{ uj_val = mkSpecialLetIn orig alias isdeppred j.uj_val;
uj_type = subst1 (Option.get ci) j.uj_type }
and compile_non_dep_alias pb rest =
let pb =
{ pb with
tomatch = rest;
history = pop_history_pattern pb.history;
mat = List.map drop_alias_eqn pb.mat } in
compile pb
(* pour les alias des initiaux, enrichir les env de ce qu'il faut et
substituer après par les initiaux *)
(**************************************************************************)
(* Preparation of the pattern-matching problem *)
(* builds the matrix of equations testing that each eqn has n patterns
* and linearizing the _ patterns.
* Syntactic correctness has already been done in astterm *)
let matx_of_eqns env tomatchl eqns =
let build_eqn (loc,ids,lpat,rhs) =
let initial_lpat,initial_rhs = lpat,rhs in
let initial_rhs = rhs in
let rhs =
{ rhs_env = env;
rhs_vars = free_glob_vars initial_rhs;
avoid_ids = ids@(ids_of_named_context (named_context env));
it = Some initial_rhs } in
{ patterns = initial_lpat;
alias_stack = [];
eqn_loc = loc;
used = ref false;
rhs = rhs }
in List.map build_eqn eqns
(***************** Building an inversion predicate ************************)
(* Let "match t1 in I1 u11..u1n_1 ... tm in Im um1..umn_m with ... end : T"
be a pattern-matching problem. We assume that each uij can be
decomposed under the form pij(vij1..vijq_ij) where pij(aij1..aijq_ij)
is a pattern depending on some variables aijk and the vijk are
instances of these variables. We also assume that each ti has the
form of a pattern qi(wi1..wiq_i) where qi(bi1..biq_i) is a pattern
depending on some variables bik and the wik are instances of these
variables (in practice, there is no reason that ti is already
constructed and the qi will be degenerated).
We then look for a type U(..a1jk..b1 .. ..amjk..bm) so that
T = U(..v1jk..t1 .. ..vmjk..tm). This a higher-order matching
problem with a priori different solutions (one of them if T itself!).
We finally invert the uij and the ti and build the return clause
phi(x11..x1n_1y1..xm1..xmn_mym) =
match x11..x1n_1 y1 .. xm1..xmn_m ym with
| p11..p1n_1 q1 .. pm1..pmn_m qm => U(..a1jk..b1 .. ..amjk..bm)
| _ .. _ _ .. _ .. _ _ => True
end
so that "phi(u11..u1n_1t1..um1..umn_mtm) = T" (note that the clause
returning True never happens and any inhabited type can be put instead).
*)
let adjust_to_extended_env_and_remove_deps env extenv subst t =
let n = rel_context_length (rel_context env) in
let n' = rel_context_length (rel_context extenv) in
(* We first remove the bindings that are dependently typed (they are
difficult to manage and it is not sure these are so useful in practice);
Notes:
- [subst] is made of pairs [(id,u)] where id is a name in [extenv] and
[u] a term typed in [env];
- [subst0] is made of items [(p,u,(u,ty))] where [ty] is the type of [u]
and both are adjusted to [extenv] while [p] is the index of [id] in
[extenv] (after expansion of the aliases) *)
let subst0 = map_succeed (fun (x,u) ->
(* d1 ... dn dn+1 ... dn'-p+1 ... dn' *)
(* \--env-/ (= x:ty) *)
(* \--------------extenv------------/ *)
let (p,_,_) = lookup_rel_id x (rel_context extenv) in
let rec traverse_local_defs p =
match pi2 (lookup_rel p extenv) with
| Some c -> assert (isRel c); traverse_local_defs (p + destRel c)
| None -> p in
let p = traverse_local_defs p in
let u = lift (n'-n) u in
(p,u,expand_vars_in_term extenv u)) subst in
let t0 = lift (n'-n) t in
(subst0,t0)
let push_binder d (k,env,subst) =
(k+1,push_rel d env,List.map (fun (na,u,d) -> (na,lift 1 u,d)) subst)
let rec list_assoc_in_triple x = function
[] -> raise Not_found
| (a,b,_)::l -> if compare a x = 0 then b else list_assoc_in_triple x l
(* Let vijk and ti be a set of dependent terms and T a type, all
* defined in some environment env. The vijk and ti are supposed to be
* instances for variables aijk and bi.
*
* [abstract_tycon Gamma0 Sigma subst T Gamma] looks for U(..v1jk..t1 .. ..vmjk..tm)
* defined in some extended context
* "Gamma0, ..a1jk:V1jk.. b1:W1 .. ..amjk:Vmjk.. bm:Wm"
* such that env |- T = U(..v1jk..t1 .. ..vmjk..tm). To not commit to
* a particular solution, we replace each subterm t in T that unifies with
* a subset u1..ul of the vijk and ti by a special evar
* ?id(x=t;c1:=c1,..,cl=cl) defined in context Gamma0,x,c1,...,cl |- ?id
* (where the c1..cl are the aijk and bi matching the u1..ul), and
* similarly for each ti.
*)
let abstract_tycon loc env evdref subst _tycon extenv t =
let sigma = !evdref in
let t = nf_betaiota sigma t in (* it helps in some cases to remove K-redex *)
let subst0,t0 = adjust_to_extended_env_and_remove_deps env extenv subst t in
(* We traverse the type T of the original problem Xi looking for subterms
that match the non-constructor part of the constraints (this part
is in subst); these subterms are the "good" subterms and we replace them
by an evar that may depend (and only depend) on the corresponding
convertible subterms of the substitution *)
let rec aux (k,env,subst as x) t =
let t = whd_evar !evdref t in match kind_of_term t with
| Rel n when pi2 (lookup_rel n env) <> None ->
map_constr_with_full_binders push_binder aux x t
| Evar ev ->
let ty = get_type_of env sigma t in
let inst =
list_map_i
(fun i _ ->
try list_assoc_in_triple i subst0 with Not_found -> mkRel i)
1 (rel_context env) in
let ev = e_new_evar evdref env ~src:(loc, CasesType) ty in
evdref := add_conv_pb (Reduction.CONV,env,substl inst ev,t) !evdref;
ev
| _ ->
let good = List.filter (fun (_,u,_) -> is_conv_leq env sigma t u) subst in
if good <> [] then
let u = pi3 (List.hd good) in (* u is in extenv *)
let vl = List.map pi1 good in
let ty = lift (-k) (aux x (get_type_of env !evdref t)) in
let depvl = free_rels ty in
let inst =
list_map_i
(fun i _ -> if List.mem i vl then u else mkRel i) 1
(rel_context extenv) in
let rel_filter =
List.map (fun a -> not (isRel a) || dependent a u
|| Intset.mem (destRel a) depvl) inst in
let named_filter =
List.map (fun (id,_,_) -> dependent (mkVar id) u)
(named_context extenv) in
let filter = rel_filter@named_filter in
let ev =
e_new_evar evdref extenv ~src:(loc, CasesType) ~filter:filter ty in
evdref := add_conv_pb (Reduction.CONV,extenv,substl inst ev,u) !evdref;
lift k ev
else
map_constr_with_full_binders push_binder aux x t in
aux (0,extenv,subst0) t0
let build_tycon loc env tycon_env subst tycon extenv evdref t =
let t,tt = match t with
| None ->
(* This is the situation we are building a return predicate and
we are in an impossible branch *)
let n = rel_context_length (rel_context env) in
let n' = rel_context_length (rel_context tycon_env) in
let tt = new_Type () in
let impossible_case_type =
e_new_evar evdref env ~src:(loc,ImpossibleCase) tt in
(lift (n'-n) impossible_case_type, tt)
| Some t ->
let t = abstract_tycon loc tycon_env evdref subst tycon extenv t in
let evd,tt = Typing.e_type_of extenv !evdref t in
evdref := evd;
(t,tt) in
{ uj_val = t; uj_type = tt }
(* For a multiple pattern-matching problem Xi on t1..tn with return
* type T, [build_inversion_problem Gamma Sigma (t1..tn) T] builds a return
* predicate for Xi that is itself made by an auxiliary
* pattern-matching problem of which the first clause reveals the
* pattern structure of the constraints on the inductive types of the t1..tn,
* and the second clause is a wildcard clause for catching the
* impossible cases. See above "Building an inversion predicate" for
* further explanations
*)
let build_inversion_problem loc env sigma tms t =
let make_patvar t (subst,avoid) =
let id = next_name_away (named_hd env t Anonymous) avoid in
PatVar (dummy_loc,Name id), ((id,t)::subst, id::avoid) in
let rec reveal_pattern t (subst,avoid as acc) =
match kind_of_term (whd_betadeltaiota env sigma t) with
| Construct cstr -> PatCstr (dummy_loc,cstr,[],Anonymous), acc
| App (f,v) when isConstruct f ->
let cstr = destConstruct f in
let n = constructor_nrealargs env cstr in
let l = list_lastn n (Array.to_list v) in
let l,acc = list_fold_map' reveal_pattern l acc in
PatCstr (dummy_loc,cstr,l,Anonymous), acc
| _ -> make_patvar t acc in
let rec aux n env acc_sign tms acc =
match tms with
| [] -> [], acc_sign, acc
| (t, IsInd (_,IndType(indf,realargs),_)) :: tms ->
let patl,acc = list_fold_map' reveal_pattern realargs acc in
let pat,acc = make_patvar t acc in
let indf' = lift_inductive_family n indf in
let sign = make_arity_signature env true indf' in
let sign = recover_alias_names alias_of_pat (pat :: List.rev patl) sign in
let p = List.length realargs in
let env' = push_rels sign env in
let patl',acc_sign,acc = aux (n+p+1) env' (sign@acc_sign) tms acc in
patl@pat::patl',acc_sign,acc
| (t, NotInd (bo,typ)) :: tms ->
let pat,acc = make_patvar t acc in
let d = (alias_of_pat pat,None,t) in
let patl,acc_sign,acc = aux (n+1) (push_rel d env) (d::acc_sign) tms acc in
pat::patl,acc_sign,acc in
let avoid0 = ids_of_context env in
(* [patl] is a list of patterns revealing the substructure of
constructors present in the constraints on the type of the
multiple terms t1..tn that are matched in the original problem;
[subst] is the substitution of the free pattern variables in
[patl] that returns the non-constructor parts of the constraints.
Especially, if the ti has type I ui1..uin_i, and the patterns associated
to ti are pi1..pin_i, then subst(pij) is uij; the substitution is
useful to recognize which subterms of the whole type T of the original
problem have to be abstracted *)
let patl,sign,(subst,avoid) = aux 0 env [] tms ([],avoid0) in
let n = List.length sign in
let decls =
list_map_i (fun i d -> (mkRel i,map_rel_declaration (lift i) d)) 1 sign in
let pb_env = push_rels sign env in
let decls =
List.map (fun (c,d) -> (c,extract_inductive_data pb_env sigma d,d)) decls in
let decls = List.rev decls in
let dep_sign = find_dependencies_signature (list_make n true) decls in
let sub_tms =
List.map2 (fun deps (tm,(tmtyp,_),(na,b,t)) ->
let na = if deps = [] then Anonymous else force_name na in
Pushed ((tm,tmtyp),deps,na))
dep_sign decls in
let subst = List.map (fun (na,t) -> (na,lift n t)) subst in
(* [eqn1] is the first clause of the auxiliary pattern-matching that
serves as skeleton for the return type: [patl] is the
substructure of constructors extracted from the list of
constraints on the inductive types of the multiple terms matched
in the original pattern-matching problem Xi *)
let eqn1 =
{ patterns = patl;
alias_stack = [];
eqn_loc = dummy_loc;
used = ref false;
rhs = { rhs_env = pb_env;
(* we assume all vars are used; in practice we discard dependent
vars so that the field rhs_vars is normally not used *)
rhs_vars = List.map fst subst;
avoid_ids = avoid;
it = Some (lift n t) } } in
(* [eqn2] is the default clause of the auxiliary pattern-matching: it will
catch the clauses of the original pattern-matching problem Xi whose
type constraints are incompatible with the constraints on the
inductive types of the multiple terms matched in Xi *)
let eqn2 =
{ patterns = List.map (fun _ -> PatVar (dummy_loc,Anonymous)) patl;
alias_stack = [];
eqn_loc = dummy_loc;
used = ref false;
rhs = { rhs_env = pb_env;
rhs_vars = [];
avoid_ids = avoid0;
it = None } } in
(* [pb] is the auxiliary pattern-matching serving as skeleton for the
return type of the original problem Xi *)
let evdref = ref sigma in
let pb =
{ env = pb_env;
evdref = evdref;
pred = new_Type();
tomatch = sub_tms;
history = start_history n;
mat = [eqn1;eqn2];
caseloc = loc;
casestyle = RegularStyle;
typing_function = build_tycon loc env pb_env subst} in
let pred = (compile pb).uj_val in
(!evdref,pred)
(* Here, [pred] is assumed to be in the context built from all *)
(* realargs and terms to match *)
let build_initial_predicate arsign pred =
let rec buildrec n pred tmnames = function
| [] -> List.rev tmnames,pred
| ((na,c,t)::realdecls)::lnames ->
let n' = n + List.length realdecls in
buildrec (n'+1) pred (force_name na::tmnames) lnames
| _ -> assert false
in buildrec 0 pred [] (List.rev arsign)
let extract_arity_signature env0 tomatchl tmsign =
let get_one_sign n tm (na,t) =
match tm with
| NotInd (bo,typ) ->
(match t with
| None -> [na,Option.map (lift n) bo,lift n typ]
| Some (loc,_,_,_) ->
user_err_loc (loc,"",
str"Unexpected type annotation for a term of non inductive type."))
| IsInd (term,IndType(indf,realargs),_) ->
let indf' = lift_inductive_family n indf in
let (ind,_) = dest_ind_family indf' in
let nparams_ctxt,nrealargs_ctxt = inductive_nargs env0 ind in
let arsign = fst (get_arity env0 indf') in
let realnal =
match t with
| Some (loc,ind',nparams,realnal) ->
if ind <> ind' then
user_err_loc (loc,"",str "Wrong inductive type.");
if nparams_ctxt <> nparams
or nrealargs_ctxt <> List.length realnal then
anomaly "Ill-formed 'in' clause in cases";
List.rev realnal
| None -> list_make nrealargs_ctxt Anonymous in
(na,None,build_dependent_inductive env0 indf')
::(List.map2 (fun x (_,c,t) ->(x,c,t)) realnal arsign) in
let rec buildrec n = function
| [],[] -> []
| (_,tm)::ltm, (_,x)::tmsign ->
let l = get_one_sign n tm x in
l :: buildrec (n + List.length l) (ltm,tmsign)
| _ -> assert false
in List.rev (buildrec 0 (tomatchl,tmsign))
let inh_conv_coerce_to_tycon loc env evdref j tycon =
match tycon with
| Some p ->
let (evd',j) = Coercion.inh_conv_coerce_to loc env !evdref j p in
evdref := evd';
j
| None -> j
(* We put the tycon inside the arity signature, possibly discovering dependencies. *)
let prepare_predicate_from_arsign_tycon loc tomatchs arsign c =
let nar = List.fold_left (fun n sign -> List.length sign + n) 0 arsign in
let subst, len =
List.fold_left2 (fun (subst, len) (tm, tmtype) sign ->
let signlen = List.length sign in
match kind_of_term tm with
| Rel n when dependent tm c
&& signlen = 1 (* The term to match is not of a dependent type itself *) ->
((n, len) :: subst, len - signlen)
| Rel n when signlen > 1 (* The term is of a dependent type,
maybe some variable in its type appears in the tycon. *) ->
(match tmtype with
NotInd _ -> (subst, len - signlen)
| IsInd (_, IndType(indf,realargs),_) ->
let subst =
if dependent tm c && List.for_all isRel realargs
then (n, 1) :: subst else subst
in
List.fold_left
(fun (subst, len) arg ->
match kind_of_term arg with
| Rel n when dependent arg c ->
((n, len) :: subst, pred len)
| _ -> (subst, pred len))
(subst, len) realargs)
| _ -> (subst, len - signlen))
([], nar) tomatchs arsign
in
let rec predicate lift c =
match kind_of_term c with
| Rel n when n > lift ->
(try
(* Make the predicate dependent on the matched variable *)
let idx = List.assoc (n - lift) subst in
mkRel (idx + lift)
with Not_found ->
(* A variable that is not matched, lift over the arsign. *)
mkRel (n + nar))
| _ ->
map_constr_with_binders succ predicate lift c
in predicate 0 c
(* Builds the predicate. If the predicate is dependent, its context is
* made of 1+nrealargs assumptions for each matched term in an inductive
* type and 1 assumption for each term not _syntactically_ in an
* inductive type.
* Each matched terms are independently considered dependent or not.
* A type constraint but no annotation case: we try to specialize the
* tycon to make the predicate if it is not closed.
*)
let prepare_predicate loc typing_fun sigma env tomatchs arsign tycon pred =
let preds =
match pred, tycon with
(* No type annotation *)
| None, Some (None, t) when not (noccur_with_meta 0 max_int t) ->
(* If the tycon is not closed w.r.t real variables, we try *)
(* two different strategies *)
(* First strategy: we abstract the tycon wrt to the dependencies *)
let pred1 =
prepare_predicate_from_arsign_tycon loc tomatchs arsign t in
(* Second strategy: we build an "inversion" predicate *)
let sigma2,pred2 = build_inversion_problem loc env sigma tomatchs t in
[sigma, pred1; sigma2, pred2]
| None, _ ->
(* No dependent type constraint, or no constraints at all: *)
(* we use two strategies *)
let sigma,t = match tycon with
| Some (None, t) -> sigma,t
| _ -> new_type_evar sigma env ~src:(loc, CasesType) in
(* First strategy: we build an "inversion" predicate *)
let sigma1,pred1 = build_inversion_problem loc env sigma tomatchs t in
(* Second strategy: we directly use the evar as a non dependent pred *)
let pred2 = lift (List.length arsign) t in
[sigma1, pred1; sigma, pred2]
(* Some type annotation *)
| Some rtntyp, _ ->
(* We extract the signature of the arity *)
let envar = List.fold_right push_rels arsign env in
let sigma, newt = new_sort_variable sigma in
let evdref = ref sigma in
let predcclj = typing_fun (mk_tycon (mkSort newt)) envar evdref rtntyp in
let sigma = Option.cata (fun tycon ->
let na = Name (id_of_string "x") in
let tms = List.map (fun tm -> Pushed(tm,[],na)) tomatchs in
let predinst = extract_predicate predcclj.uj_val tms in
Coercion.inh_conv_coerces_to loc env !evdref predinst tycon)
!evdref tycon in
let predccl = (j_nf_evar sigma predcclj).uj_val in
[sigma, predccl]
in
List.map
(fun (sigma,pred) ->
let (nal,pred) = build_initial_predicate arsign pred in
sigma,nal,pred)
preds
(**************************************************************************)
(* Main entry of the matching compilation *)
let compile_cases loc style (typing_fun, evdref) tycon env (predopt, tomatchl, eqns) =
(* We build the matrix of patterns and right-hand side *)
let matx = matx_of_eqns env tomatchl eqns in
(* We build the vector of terms to match consistently with the *)
(* constructors found in patterns *)
let tomatchs = coerce_to_indtype typing_fun evdref env matx tomatchl in
(* If an elimination predicate is provided, we check it is compatible
with the type of arguments to match; if none is provided, we
build alternative possible predicates *)
let arsign = extract_arity_signature env tomatchs tomatchl in
let preds = prepare_predicate loc typing_fun !evdref env tomatchs arsign tycon predopt in
let compile_for_one_predicate (sigma,nal,pred) =
(* We push the initial terms to match and push their alias to rhs' envs *)
(* names of aliases will be recovered from patterns (hence Anonymous *)
(* here) *)
let out_tmt na = function NotInd (c,t) -> (na,c,t) | IsInd (typ,_,_) -> (na,None,typ) in
let typs = List.map2 (fun na (tm,tmt) -> (tm,out_tmt na tmt)) nal tomatchs in
let typs =
List.map (fun (c,d) -> (c,extract_inductive_data env sigma d,d)) typs in
let dep_sign =
find_dependencies_signature
(list_make (List.length typs) true)
typs in
let typs' =
list_map3
(fun (tm,tmt) deps na ->
let deps = if not (isRel tm) then [] else deps in
((tm,tmt),deps,na))
tomatchs dep_sign nal in
let initial_pushed = List.map (fun x -> Pushed x) typs' in
(* A typing function that provides with a canonical term for absurd cases*)
let typing_fun tycon env evdref = function
| Some t -> typing_fun tycon env evdref t
| None -> coq_unit_judge () in
let myevdref = ref sigma in
let pb =
{ env = env;
evdref = myevdref;
pred = pred;
tomatch = initial_pushed;
history = start_history (List.length initial_pushed);
mat = matx;
caseloc = loc;
casestyle = style;
typing_function = typing_fun } in
let j = compile pb in
evdref := !myevdref;
j in
(* Return the term compiled with the first possible elimination *)
(* predicate for which the compilation succeeds *)
let j = list_try_compile compile_for_one_predicate preds in
(* We check for unused patterns *)
List.iter (check_unused_pattern env) matx;
(* We coerce to the tycon (if an elim predicate was provided) *)
inh_conv_coerce_to_tycon loc env evdref j tycon
end
|