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
|
(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
(** [betree_main]: function definitions *)
module BetreeMain.Funs
open Primitives
include BetreeMain.Types
include BetreeMain.Opaque
include BetreeMain.Clauses
#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
(** [betree_main::betree::load_internal_node] *)
let betree_load_internal_node_fwd
(id : u64) (st : state) :
result (state & (betree_list_t (u64 & betree_message_t)))
=
begin match betree_utils_load_internal_node_fwd id st with
| Fail -> Fail
| Return (st0, l) -> Return (st0, l)
end
(** [betree_main::betree::store_internal_node] *)
let betree_store_internal_node_fwd
(id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
result (state & unit)
=
begin match betree_utils_store_internal_node_fwd id content st with
| Fail -> Fail
| Return (st0, _) -> Return (st0, ())
end
(** [betree_main::betree::load_leaf_node] *)
let betree_load_leaf_node_fwd
(id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
begin match betree_utils_load_leaf_node_fwd id st with
| Fail -> Fail
| Return (st0, l) -> Return (st0, l)
end
(** [betree_main::betree::store_leaf_node] *)
let betree_store_leaf_node_fwd
(id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
result (state & unit)
=
begin match betree_utils_store_leaf_node_fwd id content st with
| Fail -> Fail
| Return (st0, _) -> Return (st0, ())
end
(** [betree_main::betree::fresh_node_id] *)
let betree_fresh_node_id_fwd (counter : u64) : result u64 =
begin match u64_add counter 1 with
| Fail -> Fail
| Return _ -> Return counter
end
(** [betree_main::betree::fresh_node_id] *)
let betree_fresh_node_id_back (counter : u64) : result u64 =
begin match u64_add counter 1 with
| Fail -> Fail
| Return counter0 -> Return counter0
end
(** [betree_main::betree::NodeIdCounter::{0}::new] *)
let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
Return (Mkbetree_node_id_counter_t 0)
(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
let betree_node_id_counter_fresh_id_fwd
(self : betree_node_id_counter_t) : result u64 =
begin match u64_add self.betree_node_id_counter_next_node_id 1 with
| Fail -> Fail
| Return _ -> Return self.betree_node_id_counter_next_node_id
end
(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
let betree_node_id_counter_fresh_id_back
(self : betree_node_id_counter_t) : result betree_node_id_counter_t =
begin match u64_add self.betree_node_id_counter_next_node_id 1 with
| Fail -> Fail
| Return i -> Return (Mkbetree_node_id_counter_t i)
end
(** [core::num::u64::{9}::MAX] *)
let core_num_u64_max_body : result u64 = Return 18446744073709551615
let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
(** [betree_main::betree::upsert_update] *)
let betree_upsert_update_fwd
(prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
begin match prev with
| None ->
begin match st with
| BetreeUpsertFunStateAdd v -> Return v
| BetreeUpsertFunStateSub i -> Return 0
end
| Some prev0 ->
begin match st with
| BetreeUpsertFunStateAdd v ->
begin match u64_sub core_num_u64_max_c prev0 with
| Fail -> Fail
| Return margin ->
if margin >= v
then
begin match u64_add prev0 v with
| Fail -> Fail
| Return i -> Return i
end
else Return core_num_u64_max_c
end
| BetreeUpsertFunStateSub v ->
if prev0 >= v
then
begin match u64_sub prev0 v with
| Fail -> Fail
| Return i -> Return i
end
else Return 0
end
end
(** [betree_main::betree::List::{1}::len] *)
let rec betree_list_len_fwd
(t : Type0) (self : betree_list_t t) :
Tot (result u64) (decreases (betree_list_len_decreases t self))
=
begin match self with
| BetreeListCons x tl ->
begin match betree_list_len_fwd t tl with
| Fail -> Fail
| Return i ->
begin match u64_add 1 i with | Fail -> Fail | Return i0 -> Return i0 end
end
| BetreeListNil -> Return 0
end
(** [betree_main::betree::List::{1}::split_at] *)
let rec betree_list_split_at_fwd
(t : Type0) (self : betree_list_t t) (n : u64) :
Tot (result ((betree_list_t t) & (betree_list_t t)))
(decreases (betree_list_split_at_decreases t self n))
=
if n = 0
then Return (BetreeListNil, self)
else
begin match self with
| BetreeListCons hd tl ->
begin match u64_sub n 1 with
| Fail -> Fail
| Return i ->
begin match betree_list_split_at_fwd t tl i with
| Fail -> Fail
| Return p ->
let (ls0, ls1) = p in
let l = ls0 in Return (BetreeListCons hd l, ls1)
end
end
| BetreeListNil -> Fail
end
(** [betree_main::betree::List::{1}::push_front] *)
let betree_list_push_front_fwd_back
(t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
let l = tl in Return (BetreeListCons x l)
(** [betree_main::betree::List::{1}::pop_front] *)
let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
begin match ls with
| BetreeListCons x tl -> Return x
| BetreeListNil -> Fail
end
(** [betree_main::betree::List::{1}::pop_front] *)
let betree_list_pop_front_back
(t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
begin match ls with
| BetreeListCons x tl -> Return tl
| BetreeListNil -> Fail
end
(** [betree_main::betree::List::{1}::hd] *)
let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
begin match self with
| BetreeListCons hd l -> Return hd
| BetreeListNil -> Fail
end
(** [betree_main::betree::List::{2}::head_has_key] *)
let betree_list_head_has_key_fwd
(t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
begin match self with
| BetreeListCons hd l -> let (i, _) = hd in Return (i = key)
| BetreeListNil -> Return false
end
(** [betree_main::betree::List::{2}::partition_at_pivot] *)
let rec betree_list_partition_at_pivot_fwd
(t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
(decreases (betree_list_partition_at_pivot_decreases t self pivot))
=
begin match self with
| BetreeListCons hd tl ->
let (i, x) = hd in
if i >= pivot
then Return (BetreeListNil, BetreeListCons (i, x) tl)
else
begin match betree_list_partition_at_pivot_fwd t tl pivot with
| Fail -> Fail
| Return p ->
let (ls0, ls1) = p in
let l = ls0 in Return (BetreeListCons (i, x) l, ls1)
end
| BetreeListNil -> Return (BetreeListNil, BetreeListNil)
end
(** [betree_main::betree::Leaf::{3}::split] *)
let betree_leaf_split_fwd
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
(st : state) :
result (state & betree_internal_t)
=
begin match
betree_list_split_at_fwd (u64 & u64) content
params.betree_params_split_size with
| Fail -> Fail
| Return p ->
let (content0, content1) = p in
begin match betree_list_hd_fwd (u64 & u64) content1 with
| Fail -> Fail
| Return p0 ->
let (pivot, _) = p0 in
begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
| Fail -> Fail
| Return id0 ->
begin match betree_node_id_counter_fresh_id_back node_id_cnt with
| Fail -> Fail
| Return node_id_cnt0 ->
begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with
| Fail -> Fail
| Return id1 ->
begin match betree_store_leaf_node_fwd id0 content0 st with
| Fail -> Fail
| Return (st0, _) ->
begin match betree_store_leaf_node_fwd id1 content1 st0 with
| Fail -> Fail
| Return (st1, _) ->
let n = BetreeNodeLeaf (Mkbetree_leaf_t id0
params.betree_params_split_size) in
let n0 = BetreeNodeLeaf (Mkbetree_leaf_t id1
params.betree_params_split_size) in
Return
(st1,
Mkbetree_internal_t
self.betree_leaf_id
pivot
n
n0)
end
end
end
end
end
end
end
(** [betree_main::betree::Leaf::{3}::split] *)
let betree_leaf_split_back
(self : betree_leaf_t) (content : betree_list_t (u64 & u64))
(params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
(st : state) :
result betree_node_id_counter_t
=
begin match
betree_list_split_at_fwd (u64 & u64) content
params.betree_params_split_size with
| Fail -> Fail
| Return p ->
let (content0, content1) = p in
begin match betree_list_hd_fwd (u64 & u64) content1 with
| Fail -> Fail
| Return _ ->
begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
| Fail -> Fail
| Return id0 ->
begin match betree_node_id_counter_fresh_id_back node_id_cnt with
| Fail -> Fail
| Return node_id_cnt0 ->
begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with
| Fail -> Fail
| Return id1 ->
begin match betree_store_leaf_node_fwd id0 content0 st with
| Fail -> Fail
| Return (st0, _) ->
begin match betree_store_leaf_node_fwd id1 content1 st0 with
| Fail -> Fail
| Return (_, _) ->
begin match betree_node_id_counter_fresh_id_back node_id_cnt0
with
| Fail -> Fail
| Return node_id_cnt1 -> Return node_id_cnt1
end
end
end
end
end
end
end
end
(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
let rec betree_node_lookup_in_bindings_fwd
(key : u64) (bindings : betree_list_t (u64 & u64)) :
Tot (result (option u64))
(decreases (betree_node_lookup_in_bindings_decreases key bindings))
=
begin match bindings with
| BetreeListCons hd tl ->
let (i, i0) = hd in
if i = key
then Return (Some i0)
else
if i > key
then Return None
else
begin match betree_node_lookup_in_bindings_fwd key tl with
| Fail -> Fail
| Return opt -> Return opt
end
| BetreeListNil -> Return None
end
(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
let rec betree_node_lookup_first_message_for_key_fwd
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_lookup_first_message_for_key_decreases key msgs))
=
begin match msgs with
| BetreeListCons x next_msgs ->
let (i, m) = x in
if i >= key
then Return (BetreeListCons (i, m) next_msgs)
else
begin match betree_node_lookup_first_message_for_key_fwd key next_msgs
with
| Fail -> Fail
| Return l -> Return l
end
| BetreeListNil -> Return BetreeListNil
end
(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
let rec betree_node_lookup_first_message_for_key_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t))
(ret : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_lookup_first_message_for_key_decreases key msgs))
=
begin match msgs with
| BetreeListCons x next_msgs ->
let (i, m) = x in
if i >= key
then Return ret
else
begin match
betree_node_lookup_first_message_for_key_back key next_msgs ret with
| Fail -> Fail
| Return next_msgs0 -> Return (BetreeListCons (i, m) next_msgs0)
end
| BetreeListNil -> Return ret
end
(** [betree_main::betree::Node::{5}::apply_upserts] *)
let rec betree_node_apply_upserts_fwd
(msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
Tot (result (state & u64))
(decreases (betree_node_apply_upserts_decreases msgs prev key st))
=
begin match betree_list_head_has_key_fwd betree_message_t msgs key with
| Fail -> Fail
| Return b ->
if b
then
begin match betree_list_pop_front_fwd (u64 & betree_message_t) msgs with
| Fail -> Fail
| Return msg ->
let (_, m) = msg in
begin match m with
| BetreeMessageInsert i -> Fail
| BetreeMessageDelete -> Fail
| BetreeMessageUpsert s ->
begin match betree_upsert_update_fwd prev s with
| Fail -> Fail
| Return v ->
begin match
betree_list_pop_front_back (u64 & betree_message_t) msgs with
| Fail -> Fail
| Return msgs0 ->
begin match betree_node_apply_upserts_fwd msgs0 (Some v) key st
with
| Fail -> Fail
| Return (st0, i) -> Return (st0, i)
end
end
end
end
end
else
begin match core_option_option_unwrap_fwd u64 prev st with
| Fail -> Fail
| Return (st0, v) ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
BetreeMessageInsert v) with
| Fail -> Fail
| Return _ -> Return (st0, v)
end
end
end
(** [betree_main::betree::Node::{5}::apply_upserts] *)
let rec betree_node_apply_upserts_back
(msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
(key : u64) (st : state) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_apply_upserts_decreases msgs prev key st))
=
begin match betree_list_head_has_key_fwd betree_message_t msgs key with
| Fail -> Fail
| Return b ->
if b
then
begin match betree_list_pop_front_fwd (u64 & betree_message_t) msgs with
| Fail -> Fail
| Return msg ->
let (_, m) = msg in
begin match m with
| BetreeMessageInsert i -> Fail
| BetreeMessageDelete -> Fail
| BetreeMessageUpsert s ->
begin match betree_upsert_update_fwd prev s with
| Fail -> Fail
| Return v ->
begin match
betree_list_pop_front_back (u64 & betree_message_t) msgs with
| Fail -> Fail
| Return msgs0 ->
begin match betree_node_apply_upserts_back msgs0 (Some v) key st
with
| Fail -> Fail
| Return msgs1 -> Return msgs1
end
end
end
end
end
else
begin match core_option_option_unwrap_fwd u64 prev st with
| Fail -> Fail
| Return (_, v) ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
BetreeMessageInsert v) with
| Fail -> Fail
| Return msgs0 -> Return msgs0
end
end
end
(** [betree_main::betree::Node::{5}::lookup] *)
let rec betree_node_lookup_fwd
(self : betree_node_t) (key : u64) (st : state) :
Tot (result (state & (option u64)))
(decreases (betree_node_lookup_decreases self key st))
=
begin match self with
| BetreeNodeInternal node ->
begin match betree_load_internal_node_fwd node.betree_internal_id st with
| Fail -> Fail
| Return (st0, msgs) ->
begin match betree_node_lookup_first_message_for_key_fwd key msgs with
| Fail -> Fail
| Return pending ->
begin match pending with
| BetreeListCons p l ->
let (k, msg) = p in
if k <> key
then
begin match betree_internal_lookup_in_children_fwd node key st0
with
| Fail -> Fail
| Return (st1, opt) ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
(BetreeListCons (k, msg) l) with
| Fail -> Fail
| Return _ -> Return (st1, opt)
end
end
else
begin match msg with
| BetreeMessageInsert v ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
(BetreeListCons (k, BetreeMessageInsert v) l) with
| Fail -> Fail
| Return _ -> Return (st0, Some v)
end
| BetreeMessageDelete ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
(BetreeListCons (k, BetreeMessageDelete) l) with
| Fail -> Fail
| Return _ -> Return (st0, None)
end
| BetreeMessageUpsert ufs ->
begin match betree_internal_lookup_in_children_fwd node key st0
with
| Fail -> Fail
| Return (st1, v) ->
begin match
betree_node_apply_upserts_fwd (BetreeListCons (k,
BetreeMessageUpsert ufs) l) v key st1 with
| Fail -> Fail
| Return (st2, v0) ->
begin match
betree_internal_lookup_in_children_back node key st0 with
| Fail -> Fail
| Return node0 ->
begin match
betree_node_apply_upserts_back (BetreeListCons (k,
BetreeMessageUpsert ufs) l) v key st1 with
| Fail -> Fail
| Return pending0 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
pending0 with
| Fail -> Fail
| Return msgs0 ->
begin match
betree_store_internal_node_fwd
node0.betree_internal_id msgs0 st2 with
| Fail -> Fail
| Return (st3, _) -> Return (st3, Some v0)
end
end
end
end
end
end
end
| BetreeListNil ->
begin match betree_internal_lookup_in_children_fwd node key st0 with
| Fail -> Fail
| Return (st1, opt) ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
BetreeListNil with
| Fail -> Fail
| Return _ -> Return (st1, opt)
end
end
end
end
end
| BetreeNodeLeaf node ->
begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
| Fail -> Fail
| Return (st0, bindings) ->
begin match betree_node_lookup_in_bindings_fwd key bindings with
| Fail -> Fail
| Return opt -> Return (st0, opt)
end
end
end
(** [betree_main::betree::Node::{5}::lookup] *)
and betree_node_lookup_back
(self : betree_node_t) (key : u64) (st : state) :
Tot (result betree_node_t)
(decreases (betree_node_lookup_decreases self key st))
=
begin match self with
| BetreeNodeInternal node ->
begin match betree_load_internal_node_fwd node.betree_internal_id st with
| Fail -> Fail
| Return (st0, msgs) ->
begin match betree_node_lookup_first_message_for_key_fwd key msgs with
| Fail -> Fail
| Return pending ->
begin match pending with
| BetreeListCons p l ->
let (k, msg) = p in
if k <> key
then
begin match
betree_node_lookup_first_message_for_key_back key msgs
(BetreeListCons (k, msg) l) with
| Fail -> Fail
| Return _ ->
begin match betree_internal_lookup_in_children_back node key st0
with
| Fail -> Fail
| Return node0 -> Return (BetreeNodeInternal node0)
end
end
else
begin match msg with
| BetreeMessageInsert v ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
(BetreeListCons (k, BetreeMessageInsert v) l) with
| Fail -> Fail
| Return _ -> Return (BetreeNodeInternal node)
end
| BetreeMessageDelete ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
(BetreeListCons (k, BetreeMessageDelete) l) with
| Fail -> Fail
| Return _ -> Return (BetreeNodeInternal node)
end
| BetreeMessageUpsert ufs ->
begin match betree_internal_lookup_in_children_fwd node key st0
with
| Fail -> Fail
| Return (st1, v) ->
begin match
betree_node_apply_upserts_fwd (BetreeListCons (k,
BetreeMessageUpsert ufs) l) v key st1 with
| Fail -> Fail
| Return (st2, _) ->
begin match
betree_internal_lookup_in_children_back node key st0 with
| Fail -> Fail
| Return node0 ->
begin match
betree_node_apply_upserts_back (BetreeListCons (k,
BetreeMessageUpsert ufs) l) v key st1 with
| Fail -> Fail
| Return pending0 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
pending0 with
| Fail -> Fail
| Return msgs0 ->
begin match
betree_store_internal_node_fwd
node0.betree_internal_id msgs0 st2 with
| Fail -> Fail
| Return (_, _) -> Return (BetreeNodeInternal node0)
end
end
end
end
end
end
end
| BetreeListNil ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
BetreeListNil with
| Fail -> Fail
| Return _ ->
begin match betree_internal_lookup_in_children_back node key st0
with
| Fail -> Fail
| Return node0 -> Return (BetreeNodeInternal node0)
end
end
end
end
end
| BetreeNodeLeaf node ->
begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
| Fail -> Fail
| Return (_, bindings) ->
begin match betree_node_lookup_in_bindings_fwd key bindings with
| Fail -> Fail
| Return _ -> Return (BetreeNodeLeaf node)
end
end
end
(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
and betree_internal_lookup_in_children_fwd
(self : betree_internal_t) (key : u64) (st : state) :
Tot (result (state & (option u64)))
(decreases (betree_internal_lookup_in_children_decreases self key st))
=
if key < self.betree_internal_pivot
then
begin match betree_node_lookup_fwd self.betree_internal_left key st with
| Fail -> Fail
| Return (st0, opt) -> Return (st0, opt)
end
else
begin match betree_node_lookup_fwd self.betree_internal_right key st with
| Fail -> Fail
| Return (st0, opt) -> Return (st0, opt)
end
(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
and betree_internal_lookup_in_children_back
(self : betree_internal_t) (key : u64) (st : state) :
Tot (result betree_internal_t)
(decreases (betree_internal_lookup_in_children_decreases self key st))
=
if key < self.betree_internal_pivot
then
begin match betree_node_lookup_back self.betree_internal_left key st with
| Fail -> Fail
| Return n ->
Return (Mkbetree_internal_t self.betree_internal_id
self.betree_internal_pivot n self.betree_internal_right)
end
else
begin match betree_node_lookup_back self.betree_internal_right key st with
| Fail -> Fail
| Return n ->
Return (Mkbetree_internal_t self.betree_internal_id
self.betree_internal_pivot self.betree_internal_left n)
end
(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
let rec betree_node_lookup_mut_in_bindings_fwd
(key : u64) (bindings : betree_list_t (u64 & u64)) :
Tot (result (betree_list_t (u64 & u64)))
(decreases (betree_node_lookup_mut_in_bindings_decreases key bindings))
=
begin match bindings with
| BetreeListCons hd tl ->
let (i, i0) = hd in
if i >= key
then Return (BetreeListCons (i, i0) tl)
else
begin match betree_node_lookup_mut_in_bindings_fwd key tl with
| Fail -> Fail
| Return l -> Return l
end
| BetreeListNil -> Return BetreeListNil
end
(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
let rec betree_node_lookup_mut_in_bindings_back
(key : u64) (bindings : betree_list_t (u64 & u64))
(ret : betree_list_t (u64 & u64)) :
Tot (result (betree_list_t (u64 & u64)))
(decreases (betree_node_lookup_mut_in_bindings_decreases key bindings))
=
begin match bindings with
| BetreeListCons hd tl ->
let (i, i0) = hd in
if i >= key
then Return ret
else
begin match betree_node_lookup_mut_in_bindings_back key tl ret with
| Fail -> Fail
| Return tl0 -> Return (BetreeListCons (i, i0) tl0)
end
| BetreeListNil -> Return ret
end
(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
let betree_node_apply_to_leaf_fwd_back
(bindings : betree_list_t (u64 & u64)) (key : u64)
(new_msg : betree_message_t) :
result (betree_list_t (u64 & u64))
=
begin match betree_node_lookup_mut_in_bindings_fwd key bindings with
| Fail -> Fail
| Return bindings0 ->
begin match betree_list_head_has_key_fwd u64 bindings0 key with
| Fail -> Fail
| Return b ->
if b
then
begin match betree_list_pop_front_fwd (u64 & u64) bindings0 with
| Fail -> Fail
| Return hd ->
begin match new_msg with
| BetreeMessageInsert v ->
begin match betree_list_pop_front_back (u64 & u64) bindings0 with
| Fail -> Fail
| Return bindings1 ->
begin match
betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v)
with
| Fail -> Fail
| Return bindings2 ->
begin match
betree_node_lookup_mut_in_bindings_back key bindings
bindings2 with
| Fail -> Fail
| Return bindings3 -> Return bindings3
end
end
end
| BetreeMessageDelete ->
begin match betree_list_pop_front_back (u64 & u64) bindings0 with
| Fail -> Fail
| Return bindings1 ->
begin match
betree_node_lookup_mut_in_bindings_back key bindings bindings1
with
| Fail -> Fail
| Return bindings2 -> Return bindings2
end
end
| BetreeMessageUpsert s ->
let (_, i) = hd in
begin match betree_upsert_update_fwd (Some i) s with
| Fail -> Fail
| Return v ->
begin match betree_list_pop_front_back (u64 & u64) bindings0 with
| Fail -> Fail
| Return bindings1 ->
begin match
betree_list_push_front_fwd_back (u64 & u64) bindings1 (key,
v) with
| Fail -> Fail
| Return bindings2 ->
begin match
betree_node_lookup_mut_in_bindings_back key bindings
bindings2 with
| Fail -> Fail
| Return bindings3 -> Return bindings3
end
end
end
end
end
end
else
begin match new_msg with
| BetreeMessageInsert v ->
begin match
betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) with
| Fail -> Fail
| Return bindings1 ->
begin match
betree_node_lookup_mut_in_bindings_back key bindings bindings1
with
| Fail -> Fail
| Return bindings2 -> Return bindings2
end
end
| BetreeMessageDelete ->
begin match
betree_node_lookup_mut_in_bindings_back key bindings bindings0 with
| Fail -> Fail
| Return bindings1 -> Return bindings1
end
| BetreeMessageUpsert s ->
begin match betree_upsert_update_fwd None s with
| Fail -> Fail
| Return v ->
begin match
betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v)
with
| Fail -> Fail
| Return bindings1 ->
begin match
betree_node_lookup_mut_in_bindings_back key bindings bindings1
with
| Fail -> Fail
| Return bindings2 -> Return bindings2
end
end
end
end
end
end
(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
let rec betree_node_apply_messages_to_leaf_fwd_back
(bindings : betree_list_t (u64 & u64))
(new_msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & u64)))
(decreases (betree_node_apply_messages_to_leaf_decreases bindings new_msgs))
=
begin match new_msgs with
| BetreeListCons new_msg new_msgs_tl ->
let (i, m) = new_msg in
begin match betree_node_apply_to_leaf_fwd_back bindings i m with
| Fail -> Fail
| Return bindings0 ->
begin match
betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl with
| Fail -> Fail
| Return bindings1 -> Return bindings1
end
end
| BetreeListNil -> Return bindings
end
(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
let rec betree_node_filter_messages_for_key_fwd_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_filter_messages_for_key_decreases key msgs))
=
begin match msgs with
| BetreeListCons p l ->
let (k, m) = p in
if k = key
then
begin match
betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k,
m) l) with
| Fail -> Fail
| Return msgs0 ->
begin match betree_node_filter_messages_for_key_fwd_back key msgs0 with
| Fail -> Fail
| Return msgs1 -> Return msgs1
end
end
else Return (BetreeListCons (k, m) l)
| BetreeListNil -> Return BetreeListNil
end
(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
let rec betree_node_lookup_first_message_after_key_fwd
(key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_lookup_first_message_after_key_decreases key msgs))
=
begin match msgs with
| BetreeListCons p next_msgs ->
let (k, m) = p in
if k = key
then
begin match betree_node_lookup_first_message_after_key_fwd key next_msgs
with
| Fail -> Fail
| Return l -> Return l
end
else Return (BetreeListCons (k, m) next_msgs)
| BetreeListNil -> Return BetreeListNil
end
(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
let rec betree_node_lookup_first_message_after_key_back
(key : u64) (msgs : betree_list_t (u64 & betree_message_t))
(ret : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_lookup_first_message_after_key_decreases key msgs))
=
begin match msgs with
| BetreeListCons p next_msgs ->
let (k, m) = p in
if k = key
then
begin match
betree_node_lookup_first_message_after_key_back key next_msgs ret with
| Fail -> Fail
| Return next_msgs0 -> Return (BetreeListCons (k, m) next_msgs0)
end
else Return ret
| BetreeListNil -> Return ret
end
(** [betree_main::betree::Node::{5}::apply_to_internal] *)
let betree_node_apply_to_internal_fwd_back
(msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
(new_msg : betree_message_t) :
result (betree_list_t (u64 & betree_message_t))
=
begin match betree_node_lookup_first_message_for_key_fwd key msgs with
| Fail -> Fail
| Return msgs0 ->
begin match betree_list_head_has_key_fwd betree_message_t msgs0 key with
| Fail -> Fail
| Return b ->
if b
then
begin match new_msg with
| BetreeMessageInsert i ->
begin match betree_node_filter_messages_for_key_fwd_back key msgs0
with
| Fail -> Fail
| Return msgs1 ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1
(key, BetreeMessageInsert i) with
| Fail -> Fail
| Return msgs2 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs msgs2
with
| Fail -> Fail
| Return msgs3 -> Return msgs3
end
end
end
| BetreeMessageDelete ->
begin match betree_node_filter_messages_for_key_fwd_back key msgs0
with
| Fail -> Fail
| Return msgs1 ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1
(key, BetreeMessageDelete) with
| Fail -> Fail
| Return msgs2 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs msgs2
with
| Fail -> Fail
| Return msgs3 -> Return msgs3
end
end
end
| BetreeMessageUpsert s ->
begin match betree_list_hd_fwd (u64 & betree_message_t) msgs0 with
| Fail -> Fail
| Return p ->
let (_, m) = p in
begin match m with
| BetreeMessageInsert prev ->
begin match betree_upsert_update_fwd (Some prev) s with
| Fail -> Fail
| Return v ->
begin match
betree_list_pop_front_back (u64 & betree_message_t) msgs0
with
| Fail -> Fail
| Return msgs1 ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t)
msgs1 (key, BetreeMessageInsert v) with
| Fail -> Fail
| Return msgs2 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
msgs2 with
| Fail -> Fail
| Return msgs3 -> Return msgs3
end
end
end
end
| BetreeMessageDelete ->
begin match betree_upsert_update_fwd None s with
| Fail -> Fail
| Return v ->
begin match
betree_list_pop_front_back (u64 & betree_message_t) msgs0
with
| Fail -> Fail
| Return msgs1 ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t)
msgs1 (key, BetreeMessageInsert v) with
| Fail -> Fail
| Return msgs2 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
msgs2 with
| Fail -> Fail
| Return msgs3 -> Return msgs3
end
end
end
end
| BetreeMessageUpsert ufs ->
begin match
betree_node_lookup_first_message_after_key_fwd key msgs0 with
| Fail -> Fail
| Return msgs1 ->
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t)
msgs1 (key, BetreeMessageUpsert s) with
| Fail -> Fail
| Return msgs2 ->
begin match
betree_node_lookup_first_message_after_key_back key msgs0
msgs2 with
| Fail -> Fail
| Return msgs3 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs
msgs3 with
| Fail -> Fail
| Return msgs4 -> Return msgs4
end
end
end
end
end
end
end
else
begin match
betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key,
new_msg) with
| Fail -> Fail
| Return msgs1 ->
begin match
betree_node_lookup_first_message_for_key_back key msgs msgs1 with
| Fail -> Fail
| Return msgs2 -> Return msgs2
end
end
end
end
(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
let rec betree_node_apply_messages_to_internal_fwd_back
(msgs : betree_list_t (u64 & betree_message_t))
(new_msgs : betree_list_t (u64 & betree_message_t)) :
Tot (result (betree_list_t (u64 & betree_message_t)))
(decreases (betree_node_apply_messages_to_internal_decreases msgs new_msgs))
=
begin match new_msgs with
| BetreeListCons new_msg new_msgs_tl ->
let (i, m) = new_msg in
begin match betree_node_apply_to_internal_fwd_back msgs i m with
| Fail -> Fail
| Return msgs0 ->
begin match
betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl with
| Fail -> Fail
| Return msgs1 -> Return msgs1
end
end
| BetreeListNil -> Return msgs
end
(** [betree_main::betree::Node::{5}::apply_messages] *)
let rec betree_node_apply_messages_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
(msgs : betree_list_t (u64 & betree_message_t)) (st : state) :
Tot (result (state & unit))
(decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs
st))
=
begin match self with
| BetreeNodeInternal node ->
begin match betree_load_internal_node_fwd node.betree_internal_id st with
| Fail -> Fail
| Return (st0, content) ->
begin match betree_node_apply_messages_to_internal_fwd_back content msgs
with
| Fail -> Fail
| Return content0 ->
begin match betree_list_len_fwd (u64 & betree_message_t) content0 with
| Fail -> Fail
| Return num_msgs ->
if num_msgs >= params.betree_params_min_flush_size
then
begin match
betree_internal_flush_fwd node params node_id_cnt content0 st0
with
| Fail -> Fail
| Return (st1, content1) ->
begin match
betree_internal_flush_back node params node_id_cnt content0 st0
with
| Fail -> Fail
| Return (node0, _) ->
begin match
betree_store_internal_node_fwd node0.betree_internal_id
content1 st1 with
| Fail -> Fail
| Return (st2, _) -> Return (st2, ())
end
end
end
else
begin match
betree_store_internal_node_fwd node.betree_internal_id content0
st0 with
| Fail -> Fail
| Return (st1, _) -> Return (st1, ())
end
end
end
end
| BetreeNodeLeaf node ->
begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
| Fail -> Fail
| Return (st0, content) ->
begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with
| Fail -> Fail
| Return content0 ->
begin match betree_list_len_fwd (u64 & u64) content0 with
| Fail -> Fail
| Return len ->
begin match u64_mul 2 params.betree_params_split_size with
| Fail -> Fail
| Return i ->
if len >= i
then
begin match
betree_leaf_split_fwd node content0 params node_id_cnt st0 with
| Fail -> Fail
| Return (st1, _) ->
begin match
betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil
st1 with
| Fail -> Fail
| Return (st2, _) -> Return (st2, ())
end
end
else
begin match
betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
with
| Fail -> Fail
| Return (st1, _) -> Return (st1, ())
end
end
end
end
end
end
(** [betree_main::betree::Node::{5}::apply_messages] *)
and betree_node_apply_messages_back
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
(msgs : betree_list_t (u64 & betree_message_t)) (st : state) :
Tot (result (betree_node_t & betree_node_id_counter_t))
(decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs
st))
=
begin match self with
| BetreeNodeInternal node ->
begin match betree_load_internal_node_fwd node.betree_internal_id st with
| Fail -> Fail
| Return (st0, content) ->
begin match betree_node_apply_messages_to_internal_fwd_back content msgs
with
| Fail -> Fail
| Return content0 ->
begin match betree_list_len_fwd (u64 & betree_message_t) content0 with
| Fail -> Fail
| Return num_msgs ->
if num_msgs >= params.betree_params_min_flush_size
then
begin match
betree_internal_flush_fwd node params node_id_cnt content0 st0
with
| Fail -> Fail
| Return (st1, content1) ->
begin match
betree_internal_flush_back node params node_id_cnt content0 st0
with
| Fail -> Fail
| Return (node0, node_id_cnt0) ->
begin match
betree_store_internal_node_fwd node0.betree_internal_id
content1 st1 with
| Fail -> Fail
| Return (_, _) ->
Return (BetreeNodeInternal node0, node_id_cnt0)
end
end
end
else
begin match
betree_store_internal_node_fwd node.betree_internal_id content0
st0 with
| Fail -> Fail
| Return (_, _) -> Return (BetreeNodeInternal node, node_id_cnt)
end
end
end
end
| BetreeNodeLeaf node ->
begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
| Fail -> Fail
| Return (st0, content) ->
begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with
| Fail -> Fail
| Return content0 ->
begin match betree_list_len_fwd (u64 & u64) content0 with
| Fail -> Fail
| Return len ->
begin match u64_mul 2 params.betree_params_split_size with
| Fail -> Fail
| Return i ->
if len >= i
then
begin match
betree_leaf_split_fwd node content0 params node_id_cnt st0 with
| Fail -> Fail
| Return (st1, new_node) ->
begin match
betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil
st1 with
| Fail -> Fail
| Return (_, _) ->
begin match
betree_leaf_split_back node content0 params node_id_cnt st0
with
| Fail -> Fail
| Return node_id_cnt0 ->
Return (BetreeNodeInternal new_node, node_id_cnt0)
end
end
end
else
begin match
betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
with
| Fail -> Fail
| Return (_, _) ->
Return (BetreeNodeLeaf (Mkbetree_leaf_t node.betree_leaf_id
len), node_id_cnt)
end
end
end
end
end
end
(** [betree_main::betree::Internal::{4}::flush] *)
and betree_internal_flush_fwd
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
(content : betree_list_t (u64 & betree_message_t)) (st : state) :
Tot (result (state & (betree_list_t (u64 & betree_message_t))))
(decreases (betree_internal_flush_decreases self params node_id_cnt content
st))
=
begin match
betree_list_partition_at_pivot_fwd betree_message_t content
self.betree_internal_pivot with
| Fail -> Fail
| Return p ->
let (msgs_left, msgs_right) = p in
begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with
| Fail -> Fail
| Return len_left ->
if len_left >= params.betree_params_min_flush_size
then
begin match
betree_node_apply_messages_fwd self.betree_internal_left params
node_id_cnt msgs_left st with
| Fail -> Fail
| Return (st0, _) ->
begin match
betree_node_apply_messages_back self.betree_internal_left params
node_id_cnt msgs_left st with
| Fail -> Fail
| Return (_, node_id_cnt0) ->
begin match betree_list_len_fwd (u64 & betree_message_t) msgs_right
with
| Fail -> Fail
| Return len_right ->
if len_right >= params.betree_params_min_flush_size
then
begin match
betree_node_apply_messages_fwd self.betree_internal_right
params node_id_cnt0 msgs_right st0 with
| Fail -> Fail
| Return (st1, _) ->
begin match
betree_node_apply_messages_back self.betree_internal_right
params node_id_cnt0 msgs_right st0 with
| Fail -> Fail
| Return (_, _) -> Return (st1, BetreeListNil)
end
end
else Return (st0, msgs_right)
end
end
end
else
begin match
betree_node_apply_messages_fwd self.betree_internal_right params
node_id_cnt msgs_right st with
| Fail -> Fail
| Return (st0, _) ->
begin match
betree_node_apply_messages_back self.betree_internal_right params
node_id_cnt msgs_right st with
| Fail -> Fail
| Return (_, _) -> Return (st0, msgs_left)
end
end
end
end
(** [betree_main::betree::Internal::{4}::flush] *)
and betree_internal_flush_back
(self : betree_internal_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t)
(content : betree_list_t (u64 & betree_message_t)) (st : state) :
Tot (result (betree_internal_t & betree_node_id_counter_t))
(decreases (betree_internal_flush_decreases self params node_id_cnt content
st))
=
begin match
betree_list_partition_at_pivot_fwd betree_message_t content
self.betree_internal_pivot with
| Fail -> Fail
| Return p ->
let (msgs_left, msgs_right) = p in
begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with
| Fail -> Fail
| Return len_left ->
if len_left >= params.betree_params_min_flush_size
then
begin match
betree_node_apply_messages_fwd self.betree_internal_left params
node_id_cnt msgs_left st with
| Fail -> Fail
| Return (st0, _) ->
begin match
betree_node_apply_messages_back self.betree_internal_left params
node_id_cnt msgs_left st with
| Fail -> Fail
| Return (n, node_id_cnt0) ->
begin match betree_list_len_fwd (u64 & betree_message_t) msgs_right
with
| Fail -> Fail
| Return len_right ->
if len_right >= params.betree_params_min_flush_size
then
begin match
betree_node_apply_messages_back self.betree_internal_right
params node_id_cnt0 msgs_right st0 with
| Fail -> Fail
| Return (n0, node_id_cnt1) ->
Return (Mkbetree_internal_t self.betree_internal_id
self.betree_internal_pivot n n0, node_id_cnt1)
end
else
Return (Mkbetree_internal_t self.betree_internal_id
self.betree_internal_pivot n self.betree_internal_right,
node_id_cnt0)
end
end
end
else
begin match
betree_node_apply_messages_back self.betree_internal_right params
node_id_cnt msgs_right st with
| Fail -> Fail
| Return (n, node_id_cnt0) ->
Return (Mkbetree_internal_t self.betree_internal_id
self.betree_internal_pivot self.betree_internal_left n,
node_id_cnt0)
end
end
end
(** [betree_main::betree::Node::{5}::apply] *)
let betree_node_apply_fwd
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
(new_msg : betree_message_t) (st : state) :
result (state & unit)
=
let l = BetreeListNil in
begin match
betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
(key, new_msg) l) st with
| Fail -> Fail
| Return (st0, _) ->
begin match
betree_node_apply_messages_back self params node_id_cnt (BetreeListCons
(key, new_msg) l) st with
| Fail -> Fail
| Return (_, _) -> Return (st0, ())
end
end
(** [betree_main::betree::Node::{5}::apply] *)
let betree_node_apply_back
(self : betree_node_t) (params : betree_params_t)
(node_id_cnt : betree_node_id_counter_t) (key : u64)
(new_msg : betree_message_t) (st : state) :
result (betree_node_t & betree_node_id_counter_t)
=
let l = BetreeListNil in
begin match
betree_node_apply_messages_back self params node_id_cnt (BetreeListCons
(key, new_msg) l) st with
| Fail -> Fail
| Return (self0, node_id_cnt0) -> Return (self0, node_id_cnt0)
end
(** [betree_main::betree::BeTree::{6}::new] *)
let betree_be_tree_new_fwd
(min_flush_size : u64) (split_size : u64) (st : state) :
result (state & betree_be_tree_t)
=
begin match betree_node_id_counter_new_fwd with
| Fail -> Fail
| Return node_id_cnt ->
begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
| Fail -> Fail
| Return id ->
begin match betree_store_leaf_node_fwd id BetreeListNil st with
| Fail -> Fail
| Return (st0, _) ->
begin match betree_node_id_counter_fresh_id_back node_id_cnt with
| Fail -> Fail
| Return node_id_cnt0 ->
Return (st0, Mkbetree_be_tree_t (Mkbetree_params_t min_flush_size
split_size) node_id_cnt0 (BetreeNodeLeaf (Mkbetree_leaf_t id 0)))
end
end
end
end
(** [betree_main::betree::BeTree::{6}::apply] *)
let betree_be_tree_apply_fwd
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
result (state & unit)
=
begin match
betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
self.betree_be_tree_node_id_cnt key msg st with
| Fail -> Fail
| Return (st0, _) ->
begin match
betree_node_apply_back self.betree_be_tree_root
self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
with
| Fail -> Fail
| Return (_, _) -> Return (st0, ())
end
end
(** [betree_main::betree::BeTree::{6}::apply] *)
let betree_be_tree_apply_back
(self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
result betree_be_tree_t
=
begin match
betree_node_apply_back self.betree_be_tree_root self.betree_be_tree_params
self.betree_be_tree_node_id_cnt key msg st with
| Fail -> Fail
| Return (n, nic) ->
Return (Mkbetree_be_tree_t self.betree_be_tree_params nic n)
end
(** [betree_main::betree::BeTree::{6}::insert] *)
let betree_be_tree_insert_fwd
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result (state & unit)
=
begin match betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st
with
| Fail -> Fail
| Return (st0, _) ->
begin match
betree_be_tree_apply_back self key (BetreeMessageInsert value) st with
| Fail -> Fail
| Return _ -> Return (st0, ())
end
end
(** [betree_main::betree::BeTree::{6}::insert] *)
let betree_be_tree_insert_back
(self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
result betree_be_tree_t
=
begin match betree_be_tree_apply_back self key (BetreeMessageInsert value) st
with
| Fail -> Fail
| Return self0 -> Return self0
end
(** [betree_main::betree::BeTree::{6}::delete] *)
let betree_be_tree_delete_fwd
(self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
begin match betree_be_tree_apply_fwd self key BetreeMessageDelete st with
| Fail -> Fail
| Return (st0, _) ->
begin match betree_be_tree_apply_back self key BetreeMessageDelete st with
| Fail -> Fail
| Return _ -> Return (st0, ())
end
end
(** [betree_main::betree::BeTree::{6}::delete] *)
let betree_be_tree_delete_back
(self : betree_be_tree_t) (key : u64) (st : state) :
result betree_be_tree_t
=
begin match betree_be_tree_apply_back self key BetreeMessageDelete st with
| Fail -> Fail
| Return self0 -> Return self0
end
(** [betree_main::betree::BeTree::{6}::upsert] *)
let betree_be_tree_upsert_fwd
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
result (state & unit)
=
begin match betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st
with
| Fail -> Fail
| Return (st0, _) ->
begin match betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st
with
| Fail -> Fail
| Return _ -> Return (st0, ())
end
end
(** [betree_main::betree::BeTree::{6}::upsert] *)
let betree_be_tree_upsert_back
(self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
(st : state) :
result betree_be_tree_t
=
begin match betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st
with
| Fail -> Fail
| Return self0 -> Return self0
end
(** [betree_main::betree::BeTree::{6}::lookup] *)
let betree_be_tree_lookup_fwd
(self : betree_be_tree_t) (key : u64) (st : state) :
result (state & (option u64))
=
begin match betree_node_lookup_fwd self.betree_be_tree_root key st with
| Fail -> Fail
| Return (st0, opt) -> Return (st0, opt)
end
(** [betree_main::betree::BeTree::{6}::lookup] *)
let betree_be_tree_lookup_back
(self : betree_be_tree_t) (key : u64) (st : state) :
result betree_be_tree_t
=
begin match betree_node_lookup_back self.betree_be_tree_root key st with
| Fail -> Fail
| Return n ->
Return (Mkbetree_be_tree_t self.betree_be_tree_params
self.betree_be_tree_node_id_cnt n)
end
(** [betree_main::main] *)
let main_fwd : result unit = Return ()
(** Unit test for [betree_main::main] *)
let _ = assert_norm (main_fwd = Return ())
|