Source file zify.ml
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
open Constr
open Names
open Pp
open Lazy
module NamedDecl = Context.Named.Declaration
let debug_zify = CDebug.create ~name:"zify" ()
let zify str =
EConstr.of_constr
(UnivGen.constr_of_monomorphic_global (Global.env ())
(Coqlib.lib_ref ("ZifyClasses." ^ str)))
(** classes *)
let coq_InjTyp = lazy (Coqlib.lib_ref "ZifyClasses.InjTyp")
let coq_BinOp = lazy (Coqlib.lib_ref "ZifyClasses.BinOp")
let coq_UnOp = lazy (Coqlib.lib_ref "ZifyClasses.UnOp")
let coq_CstOp = lazy (Coqlib.lib_ref "ZifyClasses.CstOp")
let coq_BinRel = lazy (Coqlib.lib_ref "ZifyClasses.BinRel")
let coq_PropBinOp = lazy (Coqlib.lib_ref "ZifyClasses.PropBinOp")
let coq_PropUOp = lazy (Coqlib.lib_ref "ZifyClasses.PropUOp")
let coq_BinOpSpec = lazy (Coqlib.lib_ref "ZifyClasses.BinOpSpec")
let coq_UnOpSpec = lazy (Coqlib.lib_ref "ZifyClasses.UnOpSpec")
let coq_Saturate = lazy (Coqlib.lib_ref "ZifyClasses.Saturate")
let mkapp2 = lazy (zify "mkapp2")
let mkapp = lazy (zify "mkapp")
let eq_refl = lazy (zify "eq_refl")
let eq = lazy (zify "eq")
let mkrel = lazy (zify "mkrel")
let iff_refl = lazy (zify "iff_refl")
let eq_iff = lazy (zify "eq_iff")
let rew_iff = lazy (zify "rew_iff")
let rew_iff_rev = lazy (zify "rew_iff_rev")
let op_and = lazy (zify "and")
let op_and_morph = lazy (zify "and_morph")
let op_or = lazy (zify "or")
let op_or_morph = lazy (zify "or_morph")
let op_impl_morph = lazy (zify "impl_morph")
let op_iff = lazy (zify "iff")
let op_iff_morph = lazy (zify "iff_morph")
let op_not = lazy (zify "not")
let op_not_morph = lazy (zify "not_morph")
let op_True = lazy (zify "True")
let op_I = lazy (zify "I")
(** [unsafe_to_constr c] returns a [Constr.t] without considering an evar_map.
This is useful for calling Constr.hash *)
let unsafe_to_constr = EConstr.Unsafe.to_constr
let pr_constr env evd e = Printer.pr_econstr_env env evd e
let gl_pr_constr e =
let genv = Global.env () in
let evd = Evd.from_env genv in
pr_constr genv evd e
let whd = Reductionops.clos_whd_flags CClosure.all
let is_convertible env evd t1 t2 = Reductionops.(is_conv env evd t1 t2)
(** [get_type_of] performs beta reduction ;
Is it ok for Retyping.get_type_of (Zpower_nat n q) to return (fun _ : nat => Z) q ? *)
let get_type_of env evd e =
Tacred.cbv_beta env evd (Retyping.get_type_of env evd e)
let rec find_option pred l =
match l with
| [] -> raise Not_found
| e :: l -> ( match pred e with Some r -> r | None -> find_option pred l )
module ConstrMap = struct
open Names.GlobRef
type 'a t = 'a list Map.t
let add gr e m =
Map.update gr (function None -> Some [e] | Some l -> Some (e :: l)) m
let empty = Map.empty
let find evd h m =
match Map.find (fst (EConstr.destRef evd h)) m with
| e :: _ -> e
| [] -> assert false
let find_all evd h m = Map.find (fst (EConstr.destRef evd h)) m
let fold f m acc =
Map.fold
(fun k l acc -> List.fold_left (fun acc e -> f k e acc) acc l)
m acc
end
module HConstr = struct
module M = Map.Make (struct
type t = EConstr.t
let compare c c' = Constr.compare (unsafe_to_constr c) (unsafe_to_constr c')
end)
type 'a t = 'a M.t
let add h e m = M.add h e m
let empty = M.empty
let find = M.find
end
(** [get_projections_from_constant (evd,c) ]
returns an array of constr [| a1,.. an|] such that [c] is defined as
Definition c := mk a1 .. an with mk a constructor.
ai is therefore either a type parameter or a projection.
*)
let get_projections_from_constant (evd, i) =
match EConstr.kind evd (whd (Global.env ()) evd i) with
| App (c, a) -> Some a
| _ ->
raise
(CErrors.user_err
Pp.(
str "The hnf of term "
++ pr_constr (Global.env ()) evd i
++ str " should be an application i.e. (c a1 ... an)"))
(** An instance of type, say T, is registered into a hashtable, say TableT. *)
type 'a decl =
{ decl : EConstr.t
;
deriv : 'a }
module EInjT = struct
type t =
{ isid : bool
;
source : EConstr.t
;
target : EConstr.t
;
inj : EConstr.t
;
pred : EConstr.t
;
cstr : EConstr.t option }
end
(** [classify_op] classify injected operators and detect special cases. *)
type classify_op =
| OpInj
| OpSame
| OpConv
| OpOther
let name x =
Context.make_annot (Name.mk_name (Names.Id.of_string x)) Sorts.Relevant
let mkconvert_unop i1 i2 op top =
let op =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkApp (i2.EInjT.inj, [|EConstr.mkApp (op, [|EConstr.mkRel 1|])|])
)
in
let top =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkApp
(top, [|EConstr.mkApp (i1.EInjT.inj, [|EConstr.mkRel 1|])|]) )
in
(op, top)
let mkconvert_binop i1 i2 i3 op top =
let op =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkLambda
( name "y"
, i1.EInjT.source
, EConstr.mkApp
( i3.EInjT.inj
, [|EConstr.mkApp (op, [|EConstr.mkRel 2; EConstr.mkRel 1|])|] )
) )
in
let top =
EConstr.mkLambda
( name "x"
, i1.EInjT.source
, EConstr.mkLambda
( name "y"
, i2.EInjT.source
, EConstr.mkApp
( top
, [| EConstr.mkApp (i1.EInjT.inj, [|EConstr.mkRel 2|])
; EConstr.mkApp (i2.EInjT.inj, [|EConstr.mkRel 1|]) |] ) ) )
in
(op, top)
let mkconvert_rel i r tr =
let tr =
EConstr.mkLambda
( name "x"
, i.EInjT.source
, EConstr.mkLambda
( name "y"
, i.EInjT.source
, EConstr.mkApp
( tr
, [| EConstr.mkApp (i.EInjT.inj, [|EConstr.mkRel 2|])
; EConstr.mkApp (i.EInjT.inj, [|EConstr.mkRel 1|]) |] ) ) )
in
(r, tr)
(** [classify_op mkconvert op top] takes the injection [inj] for the origin operator [op]
and the destination operator [top] -- both [op] and [top] are closed terms *)
let classify_op mkconvert inj op top =
let env = Global.env () in
let evd = Evd.from_env env in
if is_convertible env evd inj op then OpInj
else if EConstr.eq_constr evd op top then OpSame
else
let op, top = mkconvert op top in
if is_convertible env evd op top then OpConv else OpOther
module EBinOpT = struct
type t =
{
source1 : EConstr.t
; source2 : EConstr.t
; source3 : EConstr.t
; target1 : EConstr.t
; target2 : EConstr.t
; target3 : EConstr.t
; inj1 : EInjT.t
; inj2 : EInjT.t
; inj3 : EInjT.t
; bop : EConstr.t
; tbop : EConstr.t
; tbopinj : EConstr.t
; classify_binop : classify_op }
end
module ECstOpT = struct
type t =
{ source : EConstr.t
; target : EConstr.t
; inj : EInjT.t
; cst : EConstr.t
; cstinj : EConstr.t
; is_construct : bool }
end
module EUnOpT = struct
type t =
{ source1 : EConstr.t
; source2 : EConstr.t
; target1 : EConstr.t
; target2 : EConstr.t
; uop : EConstr.t
; inj1_t : EInjT.t
; inj2_t : EInjT.t
; tuop : EConstr.t
; tuopinj : EConstr.t
; classify_unop : classify_op
; is_construct : bool }
end
module EBinRelT = struct
type t =
{ source : EConstr.t
; target : EConstr.t
; inj : EInjT.t
; brel : EConstr.t
; tbrel : EConstr.t
; brelinj : EConstr.t
; classify_rel : classify_op }
end
module EPropBinOpT = struct
type t = {op : EConstr.t; op_iff : EConstr.t}
end
module EPropUnOpT = struct
type t = {op : EConstr.t; op_iff : EConstr.t}
end
module ESatT = struct
type t = {parg1 : EConstr.t; parg2 : EConstr.t; satOK : EConstr.t}
end
module ESpecT = struct
type t = {spec : EConstr.t}
end
type decl_kind =
| PropOp of EPropBinOpT.t decl
| PropUnOp of EPropUnOpT.t decl
| InjTyp of EInjT.t decl
| BinRel of EBinRelT.t decl
| BinOp of EBinOpT.t decl
| UnOp of EUnOpT.t decl
| CstOp of ECstOpT.t decl
| Saturate of ESatT.t decl
| UnOpSpec of ESpecT.t decl
| BinOpSpec of ESpecT.t decl
type term_kind = Application of EConstr.constr | OtherTerm of EConstr.constr
module type Elt = sig
type elt
(** name *)
val name : string
val gref : GlobRef.t Lazy.t
val table : (term_kind * decl_kind) ConstrMap.t ref
val cast : elt decl -> decl_kind
val dest : decl_kind -> elt decl option
(** [get_key] is the type-index used as key for the instance *)
val get_key : int
(** [mk_elt evd i [a0,..,an] returns the element of the table
built from the type-instance i and the arguments (type indexes and projections)
of the type-class constructor. *)
val mk_elt : Evd.evar_map -> EConstr.t -> EConstr.t array -> elt
end
let table = Summary.ref ~name:"zify_table" ConstrMap.empty
let saturate = Summary.ref ~name:"zify_saturate" ConstrMap.empty
let specs = Summary.ref ~name:"zify_specs" ConstrMap.empty
let table_cache = ref ConstrMap.empty
let saturate_cache = ref ConstrMap.empty
let specs_cache = ref ConstrMap.empty
(** Each type-class gives rise to a different table.
They only differ on how projections are extracted. *)
module EInj = struct
open EInjT
type elt = EInjT.t
let name = "EInj"
let gref = coq_InjTyp
let table = table
let cast x = InjTyp x
let dest = function InjTyp x -> Some x | _ -> None
let is_cstr_true evd c =
match EConstr.kind evd c with
| Lambda (_, _, c) -> EConstr.eq_constr_nounivs evd c (Lazy.force op_True)
| _ -> false
let mk_elt evd i (a : EConstr.t array) =
let isid = EConstr.eq_constr_nounivs evd a.(0) a.(1) in
{ isid
; source = a.(0)
; target = a.(1)
; inj = a.(2)
; pred = a.(3)
; cstr = (if is_cstr_true evd a.(3) then None else Some a.(4)) }
let get_key = 0
end
let get_inj evd c =
match get_projections_from_constant (evd, c) with
| None ->
let env = Global.env () in
let t = string_of_ppcmds (pr_constr env evd c) in
failwith ("Cannot register term " ^ t)
| Some a -> EInj.mk_elt evd c a
let rec decomp_type evd ty =
match EConstr.kind_of_type evd ty with
| EConstr.ProdType (_, t1, rst) -> t1 :: decomp_type evd rst
| _ -> [ty]
let pp_type env evd l =
Pp.prlist_with_sep (fun _ -> Pp.str " -> ") (pr_constr env evd) l
let check_typ evd expty op =
let env = Global.env () in
let ty = Retyping.get_type_of env evd op in
let ty = decomp_type evd ty in
if List.for_all2 (EConstr.eq_constr_nounivs evd) ty expty then ()
else
raise
(CErrors.user_err
Pp.(
str ": Cannot register operator "
++ pr_constr env evd op ++ str ". It has type " ++ pp_type env evd ty
++ str " instead of expected type "
++ pp_type env evd expty))
module EBinOp = struct
type elt = EBinOpT.t
open EBinOpT
let name = "BinOp"
let gref = coq_BinOp
let table = table
let mk_elt evd i a =
let i1 = get_inj evd a.(7) in
let i2 = get_inj evd a.(8) in
let i3 = get_inj evd a.(9) in
let bop = a.(6) in
let tbop = a.(10) in
check_typ evd EInjT.[i1.source; i2.source; i3.source] bop;
{ source1 = a.(0)
; source2 = a.(1)
; source3 = a.(2)
; target1 = a.(3)
; target2 = a.(4)
; target3 = a.(5)
; inj1 = i1
; inj2 = i2
; inj3 = i3
; bop
; tbop
; tbopinj = a.(11)
; classify_binop =
classify_op (mkconvert_binop i1 i2 i3) i3.EInjT.inj a.(6) tbop }
let get_key = 6
let cast x = BinOp x
let dest = function BinOp x -> Some x | _ -> None
end
module ECstOp = struct
type elt = ECstOpT.t
open ECstOpT
let name = "CstOp"
let gref = coq_CstOp
let table = table
let cast x = CstOp x
let dest = function CstOp x -> Some x | _ -> None
let isConstruct evd c =
match EConstr.kind evd c with
| Construct _ | Int _ | Float _ -> true
| _ -> false
let mk_elt evd i a =
{ source = a.(0)
; target = a.(1)
; inj = get_inj evd a.(3)
; cst = a.(4)
; cstinj = a.(5)
; is_construct = isConstruct evd a.(2) }
let get_key = 2
end
module EUnOp = struct
type elt = EUnOpT.t
open EUnOpT
let name = "UnOp"
let gref = coq_UnOp
let table = table
let cast x = UnOp x
let dest = function UnOp x -> Some x | _ -> None
let mk_elt evd i a =
let i1 = get_inj evd a.(5) in
let i2 = get_inj evd a.(6) in
let uop = a.(4) in
check_typ evd EInjT.[i1.source; i2.source] uop;
let tuop = a.(7) in
{ source1 = a.(0)
; source2 = a.(1)
; target1 = a.(2)
; target2 = a.(3)
; uop
; inj1_t = i1
; inj2_t = i2
; tuop
; tuopinj = a.(8)
; is_construct = EConstr.isConstruct evd uop
; classify_unop = classify_op (mkconvert_unop i1 i2) i2.EInjT.inj uop tuop
}
let get_key = 4
end
module EBinRel = struct
type elt = EBinRelT.t
open EBinRelT
let name = "BinRel"
let gref = coq_BinRel
let table = table
let cast x = BinRel x
let dest = function BinRel x -> Some x | _ -> None
let mk_elt evd i a =
let i = get_inj evd a.(3) in
let brel = a.(2) in
let tbrel = a.(4) in
check_typ evd EInjT.[i.source; i.source; EConstr.mkProp] brel;
{ source = a.(0)
; target = a.(1)
; inj = get_inj evd a.(3)
; brel
; tbrel
; brelinj = a.(5)
; classify_rel = classify_op (mkconvert_rel i) i.EInjT.inj brel tbrel }
let get_key = 2
end
module EPropBinOp = struct
type elt = EPropBinOpT.t
open EPropBinOpT
let name = "PropBinOp"
let gref = coq_PropBinOp
let table = table
let cast x = PropOp x
let dest = function PropOp x -> Some x | _ -> None
let mk_elt evd i a = {op = a.(0); op_iff = a.(1)}
let get_key = 0
end
module EPropUnOp = struct
type elt = EPropUnOpT.t
open EPropUnOpT
let name = "PropUOp"
let gref = coq_PropUOp
let table = table
let cast x = PropUnOp x
let dest = function PropUnOp x -> Some x | _ -> None
let mk_elt evd i a = {op = a.(0); op_iff = a.(1)}
let get_key = 0
end
let constr_of_term_kind = function Application c -> c | OtherTerm c -> c
module type S = sig
val register : Libnames.qualid -> unit
val print : unit -> unit
end
module MakeTable (E : Elt) = struct
(** Given a term [c] and its arguments ai,
we construct a HConstr.t table that is
indexed by ai for i = E.get_key.
The elements of the table are built using E.mk_elt c [|a0,..,an|]
*)
let make_elt (evd, i) =
match get_projections_from_constant (evd, i) with
| None ->
let env = Global.env () in
let t = string_of_ppcmds (pr_constr env evd i) in
failwith ("Cannot register term " ^ t)
| Some a -> E.mk_elt evd i a
let safe_ref evd c =
try
fst (EConstr.destRef evd c)
with DestKO -> CErrors.user_err Pp.(str "Add Zify "++str E.name ++ str ": the term "++
gl_pr_constr c ++ str " should be a global reference")
let register_hint evd t elt =
match EConstr.kind evd t with
| App (c, _) ->
let gr = safe_ref evd c in
E.table := ConstrMap.add gr (Application t, E.cast elt) !E.table
| _ ->
let gr = safe_ref evd t in
E.table := ConstrMap.add gr (OtherTerm t, E.cast elt) !E.table
let register_constr env evd c =
let c = EConstr.of_constr c in
let t = get_type_of env evd c in
match EConstr.kind evd t with
| App (intyp, args) when EConstr.isRefX evd (Lazy.force E.gref) intyp ->
let styp = args.(E.get_key) in
let elt = {decl = c; deriv = make_elt (evd, c)} in
register_hint evd styp elt
| _ ->
let env = Global.env () in
raise
(CErrors.user_err
Pp.(
str "Cannot register " ++ pr_constr env evd c
++ str ". It has type " ++ pr_constr env evd t
++ str " instead of type "
++ Printer.pr_global (Lazy.force E.gref)
++ str " X1 ... Xn"))
let register_obj : Constr.constr -> Libobject.obj =
let cache_constr c =
let env = Global.env () in
let evd = Evd.from_env env in
register_constr env evd c
in
let subst_constr (subst, c) = Mod_subst.subst_mps subst c in
Libobject.declare_object
@@ Libobject.superglobal_object_nodischarge
("register-zify-" ^ E.name)
~cache:cache_constr ~subst:(Some subst_constr)
(** [register c] is called from the VERNACULAR ADD [name] reference(t).
The term [c] is interpreted and
registered as a [superglobal_object_nodischarge].
TODO: pre-compute [get_type_of] - [cache_constr] is using another environment.
*)
let register c =
try
let c = UnivGen.constr_of_monomorphic_global (Global.env ()) (Nametab.locate c) in
let _ = Lib.add_leaf (register_obj c) in
()
with Not_found ->
raise
(CErrors.user_err Pp.(Libnames.pr_qualid c ++ str " does not exist."))
let pp_keys () =
let env = Global.env () in
let evd = Evd.from_env env in
ConstrMap.fold
(fun _ (k, d) acc ->
match E.dest d with
| None -> acc
| Some _ ->
Pp.(pr_constr env evd (constr_of_term_kind k) ++ str " " ++ acc))
!E.table (Pp.str "")
let print () = Feedback.msg_info (pp_keys ())
end
module InjTable = MakeTable (EInj)
module ESat = struct
type elt = ESatT.t
open ESatT
let name = "Saturate"
let gref = coq_Saturate
let table = saturate
let cast x = Saturate x
let dest = function Saturate x -> Some x | _ -> None
let mk_elt evd i a = {parg1 = a.(2); parg2 = a.(3); satOK = a.(5)}
let get_key = 1
end
module EUnopSpec = struct
open ESpecT
type elt = ESpecT.t
let name = "UnopSpec"
let gref = coq_UnOpSpec
let table = specs
let cast x = UnOpSpec x
let dest = function UnOpSpec x -> Some x | _ -> None
let mk_elt evd i a = {spec = a.(4)}
let get_key = 2
end
module EBinOpSpec = struct
open ESpecT
type elt = ESpecT.t
let name = "BinOpSpec"
let gref = coq_BinOpSpec
let table = specs
let cast x = BinOpSpec x
let dest = function BinOpSpec x -> Some x | _ -> None
let mk_elt evd i a = {spec = a.(5)}
let get_key = 3
end
module BinOp = MakeTable (EBinOp)
module UnOp = MakeTable (EUnOp)
module CstOp = MakeTable (ECstOp)
module BinRel = MakeTable (EBinRel)
module PropBinOp = MakeTable (EPropBinOp)
module PropUnOp = MakeTable (EPropUnOp)
module Saturate = MakeTable (ESat)
module UnOpSpec = MakeTable (EUnopSpec)
module BinOpSpec = MakeTable (EBinOpSpec)
let init_cache () =
table_cache := !table;
saturate_cache := !saturate;
specs_cache := !specs
open EInjT
(** Get constr of lemma and projections in ZifyClasses. *)
(** Module [CstrTable] records terms [x] injected into [inj x]
together with the corresponding type constraint.
The terms are stored by side-effect during the traversal
of the goal. It must therefore be cleared before calling
the main tactic.
*)
module CstrTable = struct
module HConstr = Hashtbl.Make (struct
type t = EConstr.t
let hash c = Constr.hash (unsafe_to_constr c)
let equal c c' = Constr.equal (unsafe_to_constr c) (unsafe_to_constr c')
end)
let table : EConstr.t HConstr.t = HConstr.create 10
let register evd t (i : EConstr.t) = HConstr.add table t i
let get () =
let l = HConstr.fold (fun k i acc -> (k, i) :: acc) table [] in
HConstr.clear table; l
(** [gen_cstr table] asserts (cstr k) for each element of the table (k,cstr).
NB: the constraint is only asserted if it does not already exist in the context.
*)
let gen_cstr table =
Proofview.Goal.enter (fun gl ->
let evd = Tacmach.project gl in
let has_hyp =
let hyps_table = HConstr.create 20 in
List.iter
(fun (_, (t : EConstr.types)) -> HConstr.add hyps_table t ())
(Tacmach.pf_hyps_types gl);
fun c ->
let m = HConstr.mem hyps_table c in
if not m then HConstr.add hyps_table c ();
m
in
let gen k cstr =
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let term = EConstr.mkApp (cstr, [|k|]) in
let types = get_type_of env evd term in
if has_hyp types then Tacticals.tclIDTAC
else
let n =
Tactics.fresh_id_in_env Id.Set.empty
(Names.Id.of_string "cstr")
env
in
Tactics.pose_proof (Names.Name n) term)
in
List.fold_left
(fun acc (k, i) -> Tacticals.tclTHEN (gen k i) acc)
Tacticals.tclIDTAC table)
end
type prf =
| Term
| Same
| Conv of EConstr.t
| Prf of EConstr.t * EConstr.t
(** [eq_proof typ source target] returns (target = target : source = target) *)
let eq_proof typ source target =
EConstr.mkCast
( EConstr.mkApp (force eq_refl, [|typ; target|])
, DEFAULTcast
, EConstr.mkApp (force eq, [|typ; source; target|]) )
let interp_prf evd inj source prf =
let inj_source =
if inj.EInjT.isid then source else EConstr.mkApp (inj.EInjT.inj, [|source|])
in
match prf with
| Term ->
let target = Tacred.compute (Global.env ()) evd inj_source in
(target, EConstr.mkApp (force eq_refl, [|inj.target; target|]))
| Same ->
(inj_source, EConstr.mkApp (force eq_refl, [|inj.target; inj_source|]))
| Conv trm -> (trm, eq_proof inj.target inj_source trm)
| Prf (target, prf) -> (target, prf)
let pp_prf prf =
match prf with
| Term -> Pp.str "Term"
| Same -> Pp.str "Same"
| Conv t -> Pp.(str "Conv " ++ gl_pr_constr t)
| Prf (_, _) -> Pp.str "Prf "
let interp_prf evd inj source prf =
let t, prf' = interp_prf evd inj source prf in
debug_zify (fun () ->
Pp.(
str "interp_prf " ++ gl_pr_constr inj.EInjT.inj ++ str " "
++ gl_pr_constr source ++ str " = " ++ gl_pr_constr t ++ str " by "
++ gl_pr_constr prf' ++ str " from " ++ pp_prf prf ++ fnl ()));
(t, prf')
let mkvar evd inj e =
(match inj.cstr with None -> () | Some ctr -> CstrTable.register evd e ctr);
Same
let pp_prf evd inj src prf =
let t, prf' = interp_prf evd inj src prf in
Pp.(
gl_pr_constr inj.EInjT.inj ++ str " " ++ gl_pr_constr src ++ str " = "
++ gl_pr_constr t ++ str " by "
++
match prf with
| Term -> Pp.str "Term"
| Same -> Pp.str "Same"
| Conv t -> Pp.str "Conv"
| Prf (_, p) -> Pp.str "Prf " ++ gl_pr_constr p)
let conv_of_term evd op isid arg =
Tacred.compute (Global.env ()) evd
(if isid then arg else EConstr.mkApp (op, [|arg|]))
let app_unop evd src unop arg prf =
let cunop = unop.EUnOpT.classify_unop in
let default a' prf' =
let target = EConstr.mkApp (unop.EUnOpT.tuop, [|a'|]) in
EUnOpT.(
Prf
( target
, EConstr.mkApp
( force mkapp
, [| unop.source1
; unop.source2
; unop.target1
; unop.target2
; unop.uop
; unop.inj1_t.EInjT.inj
; unop.inj2_t.EInjT.inj
; unop.tuop
; unop.tuopinj
; arg
; a'
; prf' |] ) ))
in
match prf with
| Term -> (
if unop.EUnOpT.is_construct then Term
else
match cunop with
| OpInj -> Conv (conv_of_term evd unop.EUnOpT.uop false arg)
| OpSame -> Same
| _ ->
let a', prf = interp_prf evd unop.EUnOpT.inj1_t arg prf in
default a' prf )
| Same -> (
match cunop with
| OpSame -> Same
| OpInj -> Same
| OpConv ->
Conv
(EConstr.mkApp
( unop.EUnOpT.tuop
, [|EConstr.mkApp (unop.EUnOpT.inj1_t.EInjT.inj, [|arg|])|] ))
| OpOther ->
let a', prf' = interp_prf evd unop.EUnOpT.inj1_t arg prf in
default a' prf' )
| Conv a' -> (
match cunop with
| OpSame | OpConv -> Conv (EConstr.mkApp (unop.EUnOpT.tuop, [|a'|]))
| OpInj -> Conv a'
| _ ->
let a', prf = interp_prf evd unop.EUnOpT.inj1_t arg prf in
default a' prf )
| Prf (a', prf') -> default a' prf'
let app_unop evd src unop arg prf =
let res = app_unop evd src unop arg prf in
debug_zify (fun () ->
Pp.(
str "\napp_unop "
++ pp_prf evd unop.EUnOpT.inj1_t arg prf
++ str " => "
++ pp_prf evd unop.EUnOpT.inj2_t src res));
res
let app_binop evd src binop arg1 prf1 arg2 prf2 =
EBinOpT.(
let mkApp a1 a2 = EConstr.mkApp (binop.tbop, [|a1; a2|]) in
let to_conv inj arg = function
| Term -> conv_of_term evd inj.EInjT.inj inj.EInjT.isid arg
| Same ->
if inj.EInjT.isid then arg else EConstr.mkApp (inj.EInjT.inj, [|arg|])
| Conv t -> t
| Prf _ -> failwith "Prf is not convertible"
in
let default a1 prf1 a2 prf2 =
let res = mkApp a1 a2 in
let prf =
EBinOpT.(
EConstr.mkApp
( force mkapp2
, [| binop.source1
; binop.source2
; binop.source3
; binop.target1
; binop.target2
; binop.target3
; binop.bop
; binop.inj1.EInjT.inj
; binop.inj2.EInjT.inj
; binop.inj3.EInjT.inj
; binop.tbop
; binop.tbopinj
; arg1
; a1
; prf1
; arg2
; a2
; prf2 |] ))
in
Prf (res, prf)
in
match (binop.EBinOpT.classify_binop, prf1, prf2) with
| OpSame, Same, Same -> Same
| OpSame, Term, Same | OpSame, Same, Term -> Same
| OpSame, (Term | Same | Conv _), (Term | Same | Conv _) ->
let t1 = to_conv binop.EBinOpT.inj1 arg1 prf1 in
let t2 = to_conv binop.EBinOpT.inj1 arg2 prf2 in
Conv (mkApp t1 t2)
| _, _, _ ->
let a1, prf1 = interp_prf evd binop.inj1 arg1 prf1 in
let a2, prf2 = interp_prf evd binop.inj2 arg2 prf2 in
default a1 prf1 a2 prf2)
type typed_constr = {constr : EConstr.t; typ : EConstr.t; inj : EInjT.t}
let get_injection env evd t =
try
match snd (ConstrMap.find evd t !table_cache) with
| InjTyp i -> i
| _ -> raise Not_found
with DestKO -> raise Not_found
let arrow =
let name x =
Context.make_annot (Name.mk_name (Names.Id.of_string x)) Sorts.Relevant
in
EConstr.mkLambda
( name "x"
, EConstr.mkProp
, EConstr.mkLambda
( name "y"
, EConstr.mkProp
, EConstr.mkProd
( Context.make_annot Names.Anonymous Sorts.Relevant
, EConstr.mkRel 2
, EConstr.mkRel 2 ) ) )
let is_prop env sigma term =
let sort = Retyping.get_sort_of env sigma term in
Sorts.is_prop sort
let is_arrow env evd a p1 p2 =
is_prop env evd p1
&& is_prop
(EConstr.push_rel (Context.Rel.Declaration.LocalAssum (a, p1)) env)
evd p2
&& (a.Context.binder_name = Names.Anonymous || EConstr.Vars.noccurn evd 1 p2)
(** [get_operator env evd e] expresses [e] as an application (c a)
where c is the head symbol and [a] is the array of arguments.
The function also transforms (x -> y) as (arrow x y) *)
let get_operator barrow env evd e =
let e' = EConstr.whd_evar evd e in
match EConstr.kind evd e' with
| Prod (a, p1, p2) ->
if barrow && is_arrow env evd a p1 p2 then (arrow, [|p1; p2|], false)
else raise Not_found
| App (c, a) -> (
let c' = EConstr.whd_evar evd c in
match EConstr.kind evd c' with
| Construct _ | Const _ | Proj _
|Lambda _ | Ind _ ->
(c', a, false)
| _ -> raise Not_found )
| Const _ -> (e', [||], false)
| Construct _ -> (e', [||], true)
| Int _ | Float _ -> (e', [||], true)
| _ -> raise Not_found
let decompose_app env evd e =
match EConstr.kind evd e with
| Prod (a, p1, p2) when is_arrow env evd a p1 p2 -> (arrow, [|p1; p2|])
| App (c, a) -> (c, a)
| _ -> (EConstr.whd_evar evd e, [||])
type 'op propop = {op : 'op; op_constr : EConstr.t; op_iff : EConstr.t}
let mk_propop op c1 c2 = {op; op_constr = c1; op_iff = c2}
type prop_binop = AND | OR | IFF | IMPL
type prop_unop = NOT
type prop_op =
| BINOP of prop_binop propop * EConstr.t * EConstr.t
| UNOP of prop_unop propop * EConstr.t
| OTHEROP of EConstr.t * EConstr.t array
let classify_prop env evd e =
match EConstr.kind evd e with
| Prod (a, p1, p2) when is_arrow env evd a p1 p2 ->
BINOP (mk_propop IMPL arrow (force op_impl_morph), p1, p2)
| App (c, a) -> (
match Array.length a with
| 1 ->
if EConstr.eq_constr_nounivs evd (force op_not) c then
UNOP (mk_propop NOT c (force op_not_morph), a.(0))
else OTHEROP (c, a)
| 2 ->
if EConstr.eq_constr_nounivs evd (force op_and) c then
BINOP (mk_propop AND c (force op_and_morph), a.(0), a.(1))
else if EConstr.eq_constr_nounivs evd (force op_or) c then
BINOP (mk_propop OR c (force op_or_morph), a.(0), a.(1))
else if EConstr.eq_constr_nounivs evd (force op_iff) c then
BINOP (mk_propop IFF c (force op_iff_morph), a.(0), a.(1))
else OTHEROP (c, a)
| _ -> OTHEROP (c, a) )
| _ -> OTHEROP (e, [||])
(** [match_operator env evd hd arg (t,d)]
- hd is head operator of t
- If t = OtherTerm _, then t = hd
- If t = Application _, then
we extract the relevant number of arguments from arg
and check for convertibility *)
let match_operator env evd hd args (t, d) =
let decomp t i =
let n = Array.length args in
let t' = EConstr.mkApp (hd, Array.sub args 0 (n - i)) in
if is_convertible env evd t' t then Some (d, t) else None
in
match t with
| OtherTerm t -> Some (d, t)
| Application t -> (
match d with
| CstOp _ -> decomp t 0
| UnOp _ -> decomp t 1
| BinOp _ -> decomp t 2
| BinRel _ -> decomp t 2
| PropOp _ -> decomp t 2
| PropUnOp _ -> decomp t 1
| _ -> None )
let pp_trans_expr env evd e res =
let {deriv = inj} = get_injection env evd e.typ in
debug_zify (fun () -> Pp.(str "\ntrans_expr " ++ pp_prf evd inj e.constr res));
res
let declared_term env evd hd args =
let match_operator (t, d) =
let decomp t i =
let n = Array.length args in
let t' = EConstr.mkApp (hd, Array.sub args 0 (n - i)) in
if is_convertible env evd t' t then Some (t, Array.sub args (n - i) i)
else None
in
match t with
| OtherTerm t -> ( match d with InjTyp _ -> None | _ -> Some (t, args) )
| Application t -> (
match d with
| CstOp _ -> decomp t 0
| UnOp _ -> decomp t 1
| BinOp _ -> decomp t 2
| BinRel _ -> decomp t 2
| PropOp _ -> decomp t 2
| PropUnOp _ -> decomp t 1
| _ -> None )
in
find_option match_operator (ConstrMap.find_all evd hd !table)
let rec trans_expr env evd e =
let inj = e.inj in
let e = e.constr in
try
let c, a, is_constant = get_operator false env evd e in
if is_constant then Term
else
let k, t =
find_option
(match_operator env evd c a)
(ConstrMap.find_all evd c !table_cache)
in
let n = Array.length a in
match k with
| CstOp {deriv = c'} ->
ECstOpT.(if c'.is_construct then Term else Prf (c'.cst, c'.cstinj))
| UnOp {deriv = unop} ->
let prf =
trans_expr env evd
{ constr = a.(n - 1)
; typ = unop.EUnOpT.source1
; inj = unop.EUnOpT.inj1_t }
in
app_unop evd e unop a.(n - 1) prf
| BinOp {deriv = binop} ->
let prf1 =
trans_expr env evd
{ constr = a.(n - 2)
; typ = binop.EBinOpT.source1
; inj = binop.EBinOpT.inj1 }
in
let prf2 =
trans_expr env evd
{ constr = a.(n - 1)
; typ = binop.EBinOpT.source2
; inj = binop.EBinOpT.inj2 }
in
app_binop evd e binop a.(n - 2) prf1 a.(n - 1) prf2
| d -> mkvar evd inj e
with Not_found | DestKO -> mkvar evd inj e
let trans_expr env evd e =
try pp_trans_expr env evd e (trans_expr env evd e)
with Not_found ->
raise
(CErrors.user_err
( Pp.str "Missing injection for type "
++ Printer.pr_leconstr_env env evd e.typ ))
type prfp =
| TProof of EConstr.t * EConstr.t (** Proof of tranformed proposition *)
| CProof of EConstr.t (** Transformed proposition is convertible *)
| IProof (** Transformed proposition is identical *)
let pp_prfp = function
| TProof (t, prf) ->
Pp.str "TProof " ++ gl_pr_constr t ++ Pp.str " by " ++ gl_pr_constr prf
| CProof t -> Pp.str "CProof " ++ gl_pr_constr t
| IProof -> Pp.str "IProof"
let trans_binrel evd src rop a1 prf1 a2 prf2 =
EBinRelT.(
match (rop.classify_rel, prf1, prf2) with
| OpSame, Same, Same -> IProof
| (OpSame | OpConv), Conv t1, Conv t2 ->
CProof (EConstr.mkApp (rop.tbrel, [|t1; t2|]))
| (OpSame | OpConv), (Same | Term | Conv _), (Same | Term | Conv _) ->
let a1', _ = interp_prf evd rop.inj a1 prf1 in
let a2', _ = interp_prf evd rop.inj a2 prf2 in
CProof (EConstr.mkApp (rop.tbrel, [|a1'; a2'|]))
| _, _, _ ->
let a1', prf1 = interp_prf evd rop.inj a1 prf1 in
let a2', prf2 = interp_prf evd rop.inj a2 prf2 in
TProof
( EConstr.mkApp (rop.EBinRelT.tbrel, [|a1'; a2'|])
, EConstr.mkApp
( force mkrel
, [| rop.source
; rop.target
; rop.brel
; rop.EBinRelT.inj.EInjT.inj
; rop.EBinRelT.tbrel
; rop.EBinRelT.brelinj
; a1
; a1'
; prf1
; a2
; a2'
; prf2 |] ) ))
let trans_binrel evd src rop a1 prf1 a2 prf2 =
let res = trans_binrel evd src rop a1 prf1 a2 prf2 in
debug_zify (fun () -> Pp.(str "\ntrans_binrel " ++ pp_prfp res));
res
let mkprf t p =
EConstr.(
match p with
| IProof -> (t, mkApp (force iff_refl, [|t|]))
| CProof t' -> (t', mkApp (force eq_iff, [|t; t'; eq_proof mkProp t t'|]))
| TProof (t', p) -> (t', p))
let mkprf t p =
let t', p = mkprf t p in
debug_zify (fun () ->
Pp.(
str "mkprf " ++ gl_pr_constr t ++ str " <-> " ++ gl_pr_constr t'
++ str " by " ++ gl_pr_constr p));
(t', p)
let trans_bin_prop op_constr op_iff t1 p1 t2 p2 =
match (p1, p2) with
| IProof, IProof -> IProof
| CProof t1', IProof -> CProof (EConstr.mkApp (op_constr, [|t1'; t2|]))
| IProof, CProof t2' -> CProof (EConstr.mkApp (op_constr, [|t1; t2'|]))
| CProof t1', CProof t2' -> CProof (EConstr.mkApp (op_constr, [|t1'; t2'|]))
| _, _ ->
let t1', p1 = mkprf t1 p1 in
let t2', p2 = mkprf t2 p2 in
TProof
( EConstr.mkApp (op_constr, [|t1'; t2'|])
, EConstr.mkApp (op_iff, [|t1; t2; t1'; t2'; p1; p2|]) )
let trans_bin_prop op_constr op_iff t1 p1 t2 p2 =
let prf = trans_bin_prop op_constr op_iff t1 p1 t2 p2 in
debug_zify (fun () -> pp_prfp prf);
prf
let trans_un_prop op_constr op_iff p1 prf1 =
match prf1 with
| IProof -> IProof
| CProof p1' -> CProof (EConstr.mkApp (op_constr, [|p1'|]))
| TProof (p1', prf) ->
TProof
( EConstr.mkApp (op_constr, [|p1'|])
, EConstr.mkApp (op_iff, [|p1; p1'; prf|]) )
let rec trans_prop env evd e =
match classify_prop env evd e with
| BINOP ({op_constr; op_iff}, p1, p2) ->
let prf1 = trans_prop env evd p1 in
let prf2 = trans_prop env evd p2 in
trans_bin_prop op_constr op_iff p1 prf1 p2 prf2
| UNOP ({op_constr; op_iff}, p1) ->
let prf1 = trans_prop env evd p1 in
trans_un_prop op_constr op_iff p1 prf1
| OTHEROP (c, a) -> (
try
let k, t =
find_option
(match_operator env evd c a)
(ConstrMap.find_all evd c !table_cache)
in
let n = Array.length a in
match k with
| BinRel {decl = br; deriv = rop} ->
let a1 =
trans_expr env evd
{ constr = a.(n - 2)
; typ = rop.EBinRelT.source
; inj = rop.EBinRelT.inj }
in
let a2 =
trans_expr env evd
{ constr = a.(n - 1)
; typ = rop.EBinRelT.source
; inj = rop.EBinRelT.inj }
in
trans_binrel evd e rop a.(n - 2) a1 a.(n - 1) a2
| _ -> IProof
with Not_found | DestKO -> IProof )
let trans_check_prop env evd t =
if is_prop env evd t then Some (trans_prop env evd t) else None
let get_hyp_typ = function
| NamedDecl.LocalDef (h, _, ty) | NamedDecl.LocalAssum (h, ty) ->
(h.Context.binder_name, EConstr.of_constr ty)
let trans_hyps env evd l =
List.fold_left
(fun acc decl ->
let h, ty = get_hyp_typ decl in
match trans_check_prop env evd ty with
| None -> acc
| Some p' -> (h, ty, p') :: acc)
[] l
let trans_hyp h t0 prfp =
debug_zify (fun () -> Pp.(str "trans_hyp: " ++ pp_prfp prfp ++ fnl ()));
match prfp with
| IProof -> Tacticals.tclIDTAC
| CProof t' ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let t' = Reductionops.nf_betaiota env evd t' in
Tactics.change_in_hyp ~check:true None
(Tactics.make_change_arg t')
(h, Locus.InHypTypeOnly))
| TProof (t', prf) ->
Tacticals.(
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let target = Reductionops.nf_betaiota env evd t' in
let h' = Tactics.fresh_id_in_env Id.Set.empty h env in
let prf =
EConstr.mkApp (force rew_iff, [|t0; target; prf; EConstr.mkVar h|])
in
tclTHEN
(Tactics.pose_proof (Name.Name h') prf)
(tclTRY
(tclTHEN (Tactics.clear [h]) (Tactics.rename_hyp [(h', h)])))))
let trans_concl prfp =
debug_zify (fun () -> Pp.(str "trans_concl: " ++ pp_prfp prfp ++ fnl ()));
match prfp with
| IProof -> Tacticals.tclIDTAC
| CProof t ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let t' = Reductionops.nf_betaiota env evd t in
Tactics.change_concl t')
| TProof (t, prf) ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let typ = get_type_of env evd prf in
match EConstr.kind evd typ with
| App (c, a) when Array.length a = 2 ->
Tactics.apply
(EConstr.mkApp (Lazy.force rew_iff_rev, [|a.(0); a.(1); prf|]))
| _ ->
raise (CErrors.anomaly Pp.(str "zify cannot transform conclusion")))
let tclTHENOpt e tac tac' =
match e with None -> tac' | Some e' -> Tacticals.tclTHEN (tac e') tac'
let assert_inj t =
init_cache ();
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
try
ignore (get_injection env evd t);
Tacticals.tclIDTAC
with Not_found ->
Tacticals.tclFAIL (Pp.str " InjTyp does not exist"))
let elim_binding x t ty =
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let h =
Tactics.fresh_id_in_env Id.Set.empty (Nameops.add_prefix "heq_" x) env
in
Tacticals.tclTHEN
(Tactics.pose_proof (Name h) (eq_proof ty (EConstr.mkVar x) t))
(Tacticals.tclTRY (Tactics.clear_body [x])))
let do_let tac (h : Constr.named_declaration) =
match h with
| Context.Named.Declaration.LocalAssum _ -> Tacticals.tclIDTAC
| Context.Named.Declaration.LocalDef (id, t, ty) ->
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
try
let x = id.Context.binder_name in
ignore
(let eq = Lazy.force eq in
find_option
(match_operator env evd eq
[|EConstr.of_constr ty; EConstr.mkVar x; EConstr.of_constr t|])
(ConstrMap.find_all evd eq !table_cache));
tac x (EConstr.of_constr t) (EConstr.of_constr ty)
with Not_found -> Tacticals.tclIDTAC)
let iter_let_aux tac =
Proofview.Goal.enter (fun gl ->
let env = Tacmach.pf_env gl in
let sign = Environ.named_context env in
init_cache ();
Tacticals.tclMAP (do_let tac) sign)
let iter_let (tac : Ltac_plugin.Tacinterp.Value.t) =
iter_let_aux (fun (id : Names.Id.t) t ty ->
Ltac_plugin.Tacinterp.Value.apply tac
[ Ltac_plugin.Tacinterp.Value.of_constr (EConstr.mkVar id)
; Ltac_plugin.Tacinterp.Value.of_constr t
; Ltac_plugin.Tacinterp.Value.of_constr ty ])
let elim_let = iter_let_aux elim_binding
let zify_tac =
Proofview.Goal.enter (fun gl ->
Coqlib.check_required_library ["Coq"; "micromega"; "ZifyClasses"];
Coqlib.check_required_library ["Coq"; "micromega"; "ZifyInst"];
init_cache ();
let evd = Tacmach.project gl in
let env = Tacmach.pf_env gl in
let sign = Environ.named_context env in
let concl = trans_check_prop env evd (Tacmach.pf_concl gl) in
let hyps = trans_hyps env evd sign in
let l = CstrTable.get () in
tclTHENOpt concl trans_concl
(Tacticals.tclTHEN
(Tacticals.tclTHENLIST
(List.rev_map (fun (h, p, t) -> trans_hyp h p t) hyps))
(CstrTable.gen_cstr l)))
type pscript = Set of Names.Id.t * EConstr.t | Pose of Names.Id.t * EConstr.t
type spec_env =
{ map : Names.Id.t HConstr.t
; spec_name : Names.Id.t
; term_name : Names.Id.t
; fresh : Nameops.Subscript.t
; proofs : pscript list }
let register_constr {map; spec_name; term_name; fresh; proofs} c thm =
let tname = Nameops.add_subscript term_name fresh in
let sname = Nameops.add_subscript spec_name fresh in
( EConstr.mkVar tname
, { map = HConstr.add c tname map
; spec_name
; term_name
; fresh = Nameops.Subscript.succ fresh
; proofs = Set (tname, c) :: Pose (sname, thm) :: proofs } )
let fresh_subscript env =
let ctx = (Environ.named_context_val env).Environ.env_named_map in
Nameops.Subscript.succ
(Names.Id.Map.fold
(fun id _ s ->
let _, s' = Nameops.get_subscript id in
let cmp = Nameops.Subscript.compare s s' in
if cmp = 0 then s else if cmp < 0 then s' else s)
ctx Nameops.Subscript.zero)
let init_env sname tname s =
{ map = HConstr.empty
; spec_name = sname
; term_name = tname
; fresh = s
; proofs = [] }
let rec spec_of_term env evd (senv : spec_env) t =
let get_name t env =
try EConstr.mkVar (HConstr.find t senv.map) with Not_found -> t
in
let c, a = decompose_app env evd t in
if a = [||] then
(get_name t senv, senv)
else
let a', senv' =
Array.fold_right
(fun e (l, senv) ->
let r, senv = spec_of_term env evd senv e in
(r :: l, senv))
a ([], senv)
in
let a' = Array.of_list a' in
let t' = EConstr.mkApp (c, a') in
try (EConstr.mkVar (HConstr.find t' senv'.map), senv')
with Not_found -> (
try
match snd (ConstrMap.find evd c !specs_cache) with
| UnOpSpec s | BinOpSpec s ->
let thm = EConstr.mkApp (s.deriv.ESpecT.spec, a') in
register_constr senv' t' thm
| _ -> (get_name t' senv', senv')
with Not_found | DestKO -> (t', senv') )
let interp_pscript s =
match s with
| Set (id, c) ->
Tacticals.tclTHEN
(Tactics.letin_tac None (Names.Name id) c None
{Locus.onhyps = None; Locus.concl_occs = Locus.AllOccurrences})
(Tactics.clear_body [id])
| Pose (id, c) -> Tactics.pose_proof (Names.Name id) c
let rec interp_pscripts l =
match l with
| [] -> Tacticals.tclIDTAC
| s :: l -> Tacticals.tclTHEN (interp_pscript s) (interp_pscripts l)
let spec_of_hyps =
Proofview.Goal.enter (fun gl ->
let terms =
Tacmach.pf_concl gl :: List.map snd (Tacmach.pf_hyps_types gl)
in
let env = Tacmach.pf_env gl in
let evd = Tacmach.project gl in
let s = fresh_subscript env in
let env =
List.fold_left
(fun acc t -> snd (spec_of_term env evd acc t))
(init_env (Names.Id.of_string "H") (Names.Id.of_string "z") s)
terms
in
interp_pscripts (List.rev env.proofs))
let iter_specs = spec_of_hyps
let find_hyp evd t l =
try
Some
(EConstr.mkVar
(fst (List.find (fun (h, t') -> EConstr.eq_constr evd t t') l)))
with Not_found -> None
let find_proof evd t l =
if EConstr.eq_constr evd t (Lazy.force op_True) then Some (Lazy.force op_I)
else find_hyp evd t l
(** [sat_constr env evd sub taclist hyps c d]= (sub',taclist',hyps') where
- sub' is a fresh subscript obtained from sub
- taclist' is obtained from taclist by posing the lemma 'd' applied to 'c'
- hyps' is obtained from hyps'
taclist and hyps are threaded to avoid adding duplicates
*)
let sat_constr env evd (sub,taclist, hyps) c d =
match EConstr.kind evd c with
| App (c, args) ->
if Array.length args = 2 then
let h1 =
Tacred.cbv_beta env evd
(EConstr.mkApp (d.ESatT.parg1, [|args.(0)|]))
in
let h2 =
Tacred.cbv_beta env evd
(EConstr.mkApp (d.ESatT.parg2, [|args.(1)|]))
in
let n = Nameops.add_subscript (Names.Id.of_string "__sat") sub in
let trm =
match (find_proof evd h1 hyps, find_proof evd h2 hyps) with
| Some h1, Some h2 ->
(EConstr.mkApp (d.ESatT.satOK, [|args.(0); args.(1); h1; h2|]))
| Some h1, _ ->
EConstr.mkApp (d.ESatT.satOK, [|args.(0); args.(1); h1|])
| _, _ -> EConstr.mkApp (d.ESatT.satOK, [|args.(0); args.(1)|])
in
let rtrm = Tacred.cbv_beta env evd trm in
let typ = Retyping.get_type_of env evd rtrm in
match find_hyp evd typ hyps with
| None -> (Nameops.Subscript.succ sub, (Tactics.pose_proof (Names.Name n) rtrm :: taclist) , (n,typ)::hyps)
| Some _ -> (sub, taclist, hyps)
else (sub,taclist,hyps)
| _ -> (sub,taclist,hyps)
let get_all_sat env evd c =
List.fold_left
(fun acc e -> match e with _, Saturate s -> s :: acc | _ -> acc)
[]
( try ConstrMap.find_all evd c !saturate_cache
with DestKO | Not_found -> [] )
let saturate =
Proofview.Goal.enter (fun gl ->
init_cache ();
let table = CstrTable.HConstr.create 20 in
let concl = Tacmach.pf_concl gl in
let hyps = Tacmach.pf_hyps_types gl in
let evd = Tacmach.project gl in
let env = Tacmach.pf_env gl in
let rec sat t =
match EConstr.kind evd t with
| App (c, args) ->
sat c;
Array.iter sat args;
if Array.length args = 2 then
let ds = get_all_sat env evd c in
if ds = [] || CstrTable.HConstr.mem table t
then ()
else List.iter (fun x ->
CstrTable.HConstr.add table t x.deriv) ds
else ()
| Prod (a, t1, t2) when a.Context.binder_name = Names.Anonymous ->
sat t1; sat t2
| _ -> ()
in
sat concl;
List.iter (fun (_, t) -> sat t) hyps;
let s0 = fresh_subscript env in
let (_,tacs,_) = CstrTable.HConstr.fold (fun c d acc -> sat_constr env evd acc c d) table (s0,[],hyps) in
Tacticals.tclTHENLIST tacs)