1
   2
   3
   4
   5
   6
   7
   8
   9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
//! Code for projecting associated types out of trait references.

use super::elaborate_predicates;
use super::specialization_graph;
use super::translate_substs;
use super::util;
use super::Obligation;
use super::ObligationCause;
use super::PredicateObligation;
use super::Selection;
use super::SelectionContext;
use super::SelectionError;
use super::{VtableClosureData, VtableFnPointerData, VtableGeneratorData, VtableImplData};

use crate::infer::type_variable::{TypeVariableOrigin, TypeVariableOriginKind};
use crate::infer::{InferCtxt, InferOk, LateBoundRegionConversionTime};
use crate::ty::fold::{TypeFoldable, TypeFolder};
use crate::ty::subst::{InternalSubsts, Subst};
use crate::ty::{self, ToPolyTraitRef, ToPredicate, Ty, TyCtxt, WithConstness};
use rustc_data_structures::snapshot_map::{Snapshot, SnapshotMap};
use rustc_hir::def_id::DefId;
use rustc_macros::HashStable;
use rustc_span::symbol::sym;
use rustc_span::DUMMY_SP;
use syntax::ast::Ident;

/// Depending on the stage of compilation, we want projection to be
/// more or less conservative.
#[derive(Debug, Copy, Clone, PartialEq, Eq, Hash, HashStable)]
pub enum Reveal {
    /// At type-checking time, we refuse to project any associated
    /// type that is marked `default`. Non-`default` ("final") types
    /// are always projected. This is necessary in general for
    /// soundness of specialization. However, we *could* allow
    /// projections in fully-monomorphic cases. We choose not to,
    /// because we prefer for `default type` to force the type
    /// definition to be treated abstractly by any consumers of the
    /// impl. Concretely, that means that the following example will
    /// fail to compile:
    ///
    /// ```
    /// trait Assoc {
    ///     type Output;
    /// }
    ///
    /// impl<T> Assoc for T {
    ///     default type Output = bool;
    /// }
    ///
    /// fn main() {
    ///     let <() as Assoc>::Output = true;
    /// }
    UserFacing,

    /// At codegen time, all monomorphic projections will succeed.
    /// Also, `impl Trait` is normalized to the concrete type,
    /// which has to be already collected by type-checking.
    ///
    /// NOTE: as `impl Trait`'s concrete type should *never*
    /// be observable directly by the user, `Reveal::All`
    /// should not be used by checks which may expose
    /// type equality or type contents to the user.
    /// There are some exceptions, e.g., around OIBITS and
    /// transmute-checking, which expose some details, but
    /// not the whole concrete type of the `impl Trait`.
    All,
}

pub type PolyProjectionObligation<'tcx> = Obligation<'tcx, ty::PolyProjectionPredicate<'tcx>>;

pub type ProjectionObligation<'tcx> = Obligation<'tcx, ty::ProjectionPredicate<'tcx>>;

pub type ProjectionTyObligation<'tcx> = Obligation<'tcx, ty::ProjectionTy<'tcx>>;

/// When attempting to resolve `<T as TraitRef>::Name` ...
#[derive(Debug)]
pub enum ProjectionTyError<'tcx> {
    /// ...we found multiple sources of information and couldn't resolve the ambiguity.
    TooManyCandidates,

    /// ...an error occurred matching `T : TraitRef`
    TraitSelectionError(SelectionError<'tcx>),
}

#[derive(Clone)]
pub struct MismatchedProjectionTypes<'tcx> {
    pub err: ty::error::TypeError<'tcx>,
}

#[derive(PartialEq, Eq, Debug)]
enum ProjectionTyCandidate<'tcx> {
    // from a where-clause in the env or object type
    ParamEnv(ty::PolyProjectionPredicate<'tcx>),

    // from the definition of `Trait` when you have something like <<A as Trait>::B as Trait2>::C
    TraitDef(ty::PolyProjectionPredicate<'tcx>),

    // from a "impl" (or a "pseudo-impl" returned by select)
    Select(Selection<'tcx>),
}

enum ProjectionTyCandidateSet<'tcx> {
    None,
    Single(ProjectionTyCandidate<'tcx>),
    Ambiguous,
    Error(SelectionError<'tcx>),
}

impl<'tcx> ProjectionTyCandidateSet<'tcx> {
    fn mark_ambiguous(&mut self) {
        *self = ProjectionTyCandidateSet::Ambiguous;
    }

    fn mark_error(&mut self, err: SelectionError<'tcx>) {
        *self = ProjectionTyCandidateSet::Error(err);
    }

    // Returns true if the push was successful, or false if the candidate
    // was discarded -- this could be because of ambiguity, or because
    // a higher-priority candidate is already there.
    fn push_candidate(&mut self, candidate: ProjectionTyCandidate<'tcx>) -> bool {
        use self::ProjectionTyCandidate::*;
        use self::ProjectionTyCandidateSet::*;

        // This wacky variable is just used to try and
        // make code readable and avoid confusing paths.
        // It is assigned a "value" of `()` only on those
        // paths in which we wish to convert `*self` to
        // ambiguous (and return false, because the candidate
        // was not used). On other paths, it is not assigned,
        // and hence if those paths *could* reach the code that
        // comes after the match, this fn would not compile.
        let convert_to_ambiguous;

        match self {
            None => {
                *self = Single(candidate);
                return true;
            }

            Single(current) => {
                // Duplicates can happen inside ParamEnv. In the case, we
                // perform a lazy deduplication.
                if current == &candidate {
                    return false;
                }

                // Prefer where-clauses. As in select, if there are multiple
                // candidates, we prefer where-clause candidates over impls.  This
                // may seem a bit surprising, since impls are the source of
                // "truth" in some sense, but in fact some of the impls that SEEM
                // applicable are not, because of nested obligations. Where
                // clauses are the safer choice. See the comment on
                // `select::SelectionCandidate` and #21974 for more details.
                match (current, candidate) {
                    (ParamEnv(..), ParamEnv(..)) => convert_to_ambiguous = (),
                    (ParamEnv(..), _) => return false,
                    (_, ParamEnv(..)) => unreachable!(),
                    (_, _) => convert_to_ambiguous = (),
                }
            }

            Ambiguous | Error(..) => {
                return false;
            }
        }

        // We only ever get here when we moved from a single candidate
        // to ambiguous.
        let () = convert_to_ambiguous;
        *self = Ambiguous;
        false
    }
}

/// Evaluates constraints of the form:
///
///     for<...> <T as Trait>::U == V
///
/// If successful, this may result in additional obligations. Also returns
/// the projection cache key used to track these additional obligations.
pub fn poly_project_and_unify_type<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &PolyProjectionObligation<'tcx>,
) -> Result<Option<Vec<PredicateObligation<'tcx>>>, MismatchedProjectionTypes<'tcx>> {
    debug!("poly_project_and_unify_type(obligation={:?})", obligation);

    let infcx = selcx.infcx();
    infcx.commit_if_ok(|snapshot| {
        let (placeholder_predicate, placeholder_map) =
            infcx.replace_bound_vars_with_placeholders(&obligation.predicate);

        let placeholder_obligation = obligation.with(placeholder_predicate);
        let result = project_and_unify_type(selcx, &placeholder_obligation)?;
        infcx
            .leak_check(false, &placeholder_map, snapshot)
            .map_err(|err| MismatchedProjectionTypes { err })?;
        Ok(result)
    })
}

/// Evaluates constraints of the form:
///
///     <T as Trait>::U == V
///
/// If successful, this may result in additional obligations.
fn project_and_unify_type<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionObligation<'tcx>,
) -> Result<Option<Vec<PredicateObligation<'tcx>>>, MismatchedProjectionTypes<'tcx>> {
    debug!("project_and_unify_type(obligation={:?})", obligation);

    let mut obligations = vec![];
    let normalized_ty = match opt_normalize_projection_type(
        selcx,
        obligation.param_env,
        obligation.predicate.projection_ty,
        obligation.cause.clone(),
        obligation.recursion_depth,
        &mut obligations,
    ) {
        Some(n) => n,
        None => return Ok(None),
    };

    debug!(
        "project_and_unify_type: normalized_ty={:?} obligations={:?}",
        normalized_ty, obligations
    );

    let infcx = selcx.infcx();
    match infcx
        .at(&obligation.cause, obligation.param_env)
        .eq(normalized_ty, obligation.predicate.ty)
    {
        Ok(InferOk { obligations: inferred_obligations, value: () }) => {
            obligations.extend(inferred_obligations);
            Ok(Some(obligations))
        }
        Err(err) => {
            debug!("project_and_unify_type: equating types encountered error {:?}", err);
            Err(MismatchedProjectionTypes { err })
        }
    }
}

/// Normalizes any associated type projections in `value`, replacing
/// them with a fully resolved type where possible. The return value
/// combines the normalized result and any additional obligations that
/// were incurred as result.
pub fn normalize<'a, 'b, 'tcx, T>(
    selcx: &'a mut SelectionContext<'b, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    cause: ObligationCause<'tcx>,
    value: &T,
) -> Normalized<'tcx, T>
where
    T: TypeFoldable<'tcx>,
{
    normalize_with_depth(selcx, param_env, cause, 0, value)
}

/// As `normalize`, but with a custom depth.
pub fn normalize_with_depth<'a, 'b, 'tcx, T>(
    selcx: &'a mut SelectionContext<'b, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    cause: ObligationCause<'tcx>,
    depth: usize,
    value: &T,
) -> Normalized<'tcx, T>
where
    T: TypeFoldable<'tcx>,
{
    debug!("normalize_with_depth(depth={}, value={:?})", depth, value);
    let mut normalizer = AssocTypeNormalizer::new(selcx, param_env, cause, depth);
    let result = normalizer.fold(value);
    debug!(
        "normalize_with_depth: depth={} result={:?} with {} obligations",
        depth,
        result,
        normalizer.obligations.len()
    );
    debug!("normalize_with_depth: depth={} obligations={:?}", depth, normalizer.obligations);
    Normalized { value: result, obligations: normalizer.obligations }
}

struct AssocTypeNormalizer<'a, 'b, 'tcx> {
    selcx: &'a mut SelectionContext<'b, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    cause: ObligationCause<'tcx>,
    obligations: Vec<PredicateObligation<'tcx>>,
    depth: usize,
}

impl<'a, 'b, 'tcx> AssocTypeNormalizer<'a, 'b, 'tcx> {
    fn new(
        selcx: &'a mut SelectionContext<'b, 'tcx>,
        param_env: ty::ParamEnv<'tcx>,
        cause: ObligationCause<'tcx>,
        depth: usize,
    ) -> AssocTypeNormalizer<'a, 'b, 'tcx> {
        AssocTypeNormalizer { selcx, param_env, cause, obligations: vec![], depth }
    }

    fn fold<T: TypeFoldable<'tcx>>(&mut self, value: &T) -> T {
        let value = self.selcx.infcx().resolve_vars_if_possible(value);

        if !value.has_projections() { value } else { value.fold_with(self) }
    }
}

impl<'a, 'b, 'tcx> TypeFolder<'tcx> for AssocTypeNormalizer<'a, 'b, 'tcx> {
    fn tcx<'c>(&'c self) -> TyCtxt<'tcx> {
        self.selcx.tcx()
    }

    fn fold_ty(&mut self, ty: Ty<'tcx>) -> Ty<'tcx> {
        if !ty.has_projections() {
            return ty;
        }
        // We don't want to normalize associated types that occur inside of region
        // binders, because they may contain bound regions, and we can't cope with that.
        //
        // Example:
        //
        //     for<'a> fn(<T as Foo<&'a>>::A)
        //
        // Instead of normalizing `<T as Foo<&'a>>::A` here, we'll
        // normalize it when we instantiate those bound regions (which
        // should occur eventually).

        let ty = ty.super_fold_with(self);
        match ty.kind {
            ty::Opaque(def_id, substs) if !substs.has_escaping_bound_vars() => {
                // (*)
                // Only normalize `impl Trait` after type-checking, usually in codegen.
                match self.param_env.reveal {
                    Reveal::UserFacing => ty,

                    Reveal::All => {
                        let recursion_limit = *self.tcx().sess.recursion_limit.get();
                        if self.depth >= recursion_limit {
                            let obligation = Obligation::with_depth(
                                self.cause.clone(),
                                recursion_limit,
                                self.param_env,
                                ty,
                            );
                            self.selcx.infcx().report_overflow_error(&obligation, true);
                        }

                        let generic_ty = self.tcx().type_of(def_id);
                        let concrete_ty = generic_ty.subst(self.tcx(), substs);
                        self.depth += 1;
                        let folded_ty = self.fold_ty(concrete_ty);
                        self.depth -= 1;
                        folded_ty
                    }
                }
            }

            ty::Projection(ref data) if !data.has_escaping_bound_vars() => {
                // (*)

                // (*) This is kind of hacky -- we need to be able to
                // handle normalization within binders because
                // otherwise we wind up a need to normalize when doing
                // trait matching (since you can have a trait
                // obligation like `for<'a> T::B : Fn(&'a int)`), but
                // we can't normalize with bound regions in scope. So
                // far now we just ignore binders but only normalize
                // if all bound regions are gone (and then we still
                // have to renormalize whenever we instantiate a
                // binder). It would be better to normalize in a
                // binding-aware fashion.

                let normalized_ty = normalize_projection_type(
                    self.selcx,
                    self.param_env,
                    data.clone(),
                    self.cause.clone(),
                    self.depth,
                    &mut self.obligations,
                );
                debug!(
                    "AssocTypeNormalizer: depth={} normalized {:?} to {:?}, \
                        now with {} obligations",
                    self.depth,
                    ty,
                    normalized_ty,
                    self.obligations.len()
                );
                normalized_ty
            }

            _ => ty,
        }
    }

    fn fold_const(&mut self, constant: &'tcx ty::Const<'tcx>) -> &'tcx ty::Const<'tcx> {
        constant.eval(self.selcx.tcx(), self.param_env)
    }
}

#[derive(Clone, TypeFoldable)]
pub struct Normalized<'tcx, T> {
    pub value: T,
    pub obligations: Vec<PredicateObligation<'tcx>>,
}

pub type NormalizedTy<'tcx> = Normalized<'tcx, Ty<'tcx>>;

impl<'tcx, T> Normalized<'tcx, T> {
    pub fn with<U>(self, value: U) -> Normalized<'tcx, U> {
        Normalized { value: value, obligations: self.obligations }
    }
}

/// The guts of `normalize`: normalize a specific projection like `<T
/// as Trait>::Item`. The result is always a type (and possibly
/// additional obligations). If ambiguity arises, which implies that
/// there are unresolved type variables in the projection, we will
/// substitute a fresh type variable `$X` and generate a new
/// obligation `<T as Trait>::Item == $X` for later.
pub fn normalize_projection_type<'a, 'b, 'tcx>(
    selcx: &'a mut SelectionContext<'b, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    projection_ty: ty::ProjectionTy<'tcx>,
    cause: ObligationCause<'tcx>,
    depth: usize,
    obligations: &mut Vec<PredicateObligation<'tcx>>,
) -> Ty<'tcx> {
    opt_normalize_projection_type(
        selcx,
        param_env,
        projection_ty.clone(),
        cause.clone(),
        depth,
        obligations,
    )
    .unwrap_or_else(move || {
        // if we bottom out in ambiguity, create a type variable
        // and a deferred predicate to resolve this when more type
        // information is available.

        let tcx = selcx.infcx().tcx;
        let def_id = projection_ty.item_def_id;
        let ty_var = selcx.infcx().next_ty_var(TypeVariableOrigin {
            kind: TypeVariableOriginKind::NormalizeProjectionType,
            span: tcx.def_span(def_id),
        });
        let projection = ty::Binder::dummy(ty::ProjectionPredicate { projection_ty, ty: ty_var });
        let obligation =
            Obligation::with_depth(cause, depth + 1, param_env, projection.to_predicate());
        obligations.push(obligation);
        ty_var
    })
}

/// The guts of `normalize`: normalize a specific projection like `<T
/// as Trait>::Item`. The result is always a type (and possibly
/// additional obligations). Returns `None` in the case of ambiguity,
/// which indicates that there are unbound type variables.
///
/// This function used to return `Option<NormalizedTy<'tcx>>`, which contains a
/// `Ty<'tcx>` and an obligations vector. But that obligation vector was very
/// often immediately appended to another obligations vector. So now this
/// function takes an obligations vector and appends to it directly, which is
/// slightly uglier but avoids the need for an extra short-lived allocation.
fn opt_normalize_projection_type<'a, 'b, 'tcx>(
    selcx: &'a mut SelectionContext<'b, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    projection_ty: ty::ProjectionTy<'tcx>,
    cause: ObligationCause<'tcx>,
    depth: usize,
    obligations: &mut Vec<PredicateObligation<'tcx>>,
) -> Option<Ty<'tcx>> {
    let infcx = selcx.infcx();

    let projection_ty = infcx.resolve_vars_if_possible(&projection_ty);
    let cache_key = ProjectionCacheKey { ty: projection_ty };

    debug!(
        "opt_normalize_projection_type(\
           projection_ty={:?}, \
           depth={})",
        projection_ty, depth
    );

    // FIXME(#20304) For now, I am caching here, which is good, but it
    // means we don't capture the type variables that are created in
    // the case of ambiguity. Which means we may create a large stream
    // of such variables. OTOH, if we move the caching up a level, we
    // would not benefit from caching when proving `T: Trait<U=Foo>`
    // bounds. It might be the case that we want two distinct caches,
    // or else another kind of cache entry.

    let cache_result = infcx.projection_cache.borrow_mut().try_start(cache_key);
    match cache_result {
        Ok(()) => {}
        Err(ProjectionCacheEntry::Ambiguous) => {
            // If we found ambiguity the last time, that generally
            // means we will continue to do so until some type in the
            // key changes (and we know it hasn't, because we just
            // fully resolved it). One exception though is closure
            // types, which can transition from having a fixed kind to
            // no kind with no visible change in the key.
            //
            // FIXME(#32286) refactor this so that closure type
            // changes
            debug!(
                "opt_normalize_projection_type: \
                    found cache entry: ambiguous"
            );
            if !projection_ty.has_closure_types() {
                return None;
            }
        }
        Err(ProjectionCacheEntry::InProgress) => {
            // If while normalized A::B, we are asked to normalize
            // A::B, just return A::B itself. This is a conservative
            // answer, in the sense that A::B *is* clearly equivalent
            // to A::B, though there may be a better value we can
            // find.

            // Under lazy normalization, this can arise when
            // bootstrapping.  That is, imagine an environment with a
            // where-clause like `A::B == u32`. Now, if we are asked
            // to normalize `A::B`, we will want to check the
            // where-clauses in scope. So we will try to unify `A::B`
            // with `A::B`, which can trigger a recursive
            // normalization. In that case, I think we will want this code:
            //
            // ```
            // let ty = selcx.tcx().mk_projection(projection_ty.item_def_id,
            //                                    projection_ty.substs;
            // return Some(NormalizedTy { value: v, obligations: vec![] });
            // ```

            debug!(
                "opt_normalize_projection_type: \
                    found cache entry: in-progress"
            );

            // But for now, let's classify this as an overflow:
            let recursion_limit = *selcx.tcx().sess.recursion_limit.get();
            let obligation =
                Obligation::with_depth(cause, recursion_limit, param_env, projection_ty);
            selcx.infcx().report_overflow_error(&obligation, false);
        }
        Err(ProjectionCacheEntry::NormalizedTy(ty)) => {
            // This is the hottest path in this function.
            //
            // If we find the value in the cache, then return it along
            // with the obligations that went along with it. Note
            // that, when using a fulfillment context, these
            // obligations could in principle be ignored: they have
            // already been registered when the cache entry was
            // created (and hence the new ones will quickly be
            // discarded as duplicated). But when doing trait
            // evaluation this is not the case, and dropping the trait
            // evaluations can causes ICEs (e.g., #43132).
            debug!(
                "opt_normalize_projection_type: \
                    found normalized ty `{:?}`",
                ty
            );

            // Once we have inferred everything we need to know, we
            // can ignore the `obligations` from that point on.
            if infcx.unresolved_type_vars(&ty.value).is_none() {
                infcx.projection_cache.borrow_mut().complete_normalized(cache_key, &ty);
            // No need to extend `obligations`.
            } else {
                obligations.extend(ty.obligations);
            }

            obligations.push(get_paranoid_cache_value_obligation(
                infcx,
                param_env,
                projection_ty,
                cause,
                depth,
            ));
            return Some(ty.value);
        }
        Err(ProjectionCacheEntry::Error) => {
            debug!(
                "opt_normalize_projection_type: \
                    found error"
            );
            let result = normalize_to_error(selcx, param_env, projection_ty, cause, depth);
            obligations.extend(result.obligations);
            return Some(result.value);
        }
    }

    let obligation = Obligation::with_depth(cause.clone(), depth, param_env, projection_ty);
    match project_type(selcx, &obligation) {
        Ok(ProjectedTy::Progress(Progress {
            ty: projected_ty,
            obligations: mut projected_obligations,
        })) => {
            // if projection succeeded, then what we get out of this
            // is also non-normalized (consider: it was derived from
            // an impl, where-clause etc) and hence we must
            // re-normalize it

            debug!(
                "opt_normalize_projection_type: \
                    projected_ty={:?} \
                    depth={} \
                    projected_obligations={:?}",
                projected_ty, depth, projected_obligations
            );

            let result = if projected_ty.has_projections() {
                let mut normalizer = AssocTypeNormalizer::new(selcx, param_env, cause, depth + 1);
                let normalized_ty = normalizer.fold(&projected_ty);

                debug!(
                    "opt_normalize_projection_type: \
                        normalized_ty={:?} depth={}",
                    normalized_ty, depth
                );

                projected_obligations.extend(normalizer.obligations);
                Normalized { value: normalized_ty, obligations: projected_obligations }
            } else {
                Normalized { value: projected_ty, obligations: projected_obligations }
            };

            let cache_value = prune_cache_value_obligations(infcx, &result);
            infcx.projection_cache.borrow_mut().insert_ty(cache_key, cache_value);
            obligations.extend(result.obligations);
            Some(result.value)
        }
        Ok(ProjectedTy::NoProgress(projected_ty)) => {
            debug!(
                "opt_normalize_projection_type: \
                    projected_ty={:?} no progress",
                projected_ty
            );
            let result = Normalized { value: projected_ty, obligations: vec![] };
            infcx.projection_cache.borrow_mut().insert_ty(cache_key, result.clone());
            // No need to extend `obligations`.
            Some(result.value)
        }
        Err(ProjectionTyError::TooManyCandidates) => {
            debug!(
                "opt_normalize_projection_type: \
                    too many candidates"
            );
            infcx.projection_cache.borrow_mut().ambiguous(cache_key);
            None
        }
        Err(ProjectionTyError::TraitSelectionError(_)) => {
            debug!("opt_normalize_projection_type: ERROR");
            // if we got an error processing the `T as Trait` part,
            // just return `ty::err` but add the obligation `T :
            // Trait`, which when processed will cause the error to be
            // reported later

            infcx.projection_cache.borrow_mut().error(cache_key);
            let result = normalize_to_error(selcx, param_env, projection_ty, cause, depth);
            obligations.extend(result.obligations);
            Some(result.value)
        }
    }
}

/// If there are unresolved type variables, then we need to include
/// any subobligations that bind them, at least until those type
/// variables are fully resolved.
fn prune_cache_value_obligations<'a, 'tcx>(
    infcx: &'a InferCtxt<'a, 'tcx>,
    result: &NormalizedTy<'tcx>,
) -> NormalizedTy<'tcx> {
    if infcx.unresolved_type_vars(&result.value).is_none() {
        return NormalizedTy { value: result.value, obligations: vec![] };
    }

    let mut obligations: Vec<_> = result
        .obligations
        .iter()
        .filter(|obligation| match obligation.predicate {
            // We found a `T: Foo<X = U>` predicate, let's check
            // if `U` references any unresolved type
            // variables. In principle, we only care if this
            // projection can help resolve any of the type
            // variables found in `result.value` -- but we just
            // check for any type variables here, for fear of
            // indirect obligations (e.g., we project to `?0`,
            // but we have `T: Foo<X = ?1>` and `?1: Bar<X =
            // ?0>`).
            ty::Predicate::Projection(ref data) => infcx.unresolved_type_vars(&data.ty()).is_some(),

            // We are only interested in `T: Foo<X = U>` predicates, whre
            // `U` references one of `unresolved_type_vars`. =)
            _ => false,
        })
        .cloned()
        .collect();

    obligations.shrink_to_fit();

    NormalizedTy { value: result.value, obligations }
}

/// Whenever we give back a cache result for a projection like `<T as
/// Trait>::Item ==> X`, we *always* include the obligation to prove
/// that `T: Trait` (we may also include some other obligations). This
/// may or may not be necessary -- in principle, all the obligations
/// that must be proven to show that `T: Trait` were also returned
/// when the cache was first populated. But there are some vague concerns,
/// and so we take the precautionary measure of including `T: Trait` in
/// the result:
///
/// Concern #1. The current setup is fragile. Perhaps someone could
/// have failed to prove the concerns from when the cache was
/// populated, but also not have used a snapshot, in which case the
/// cache could remain populated even though `T: Trait` has not been
/// shown. In this case, the "other code" is at fault -- when you
/// project something, you are supposed to either have a snapshot or
/// else prove all the resulting obligations -- but it's still easy to
/// get wrong.
///
/// Concern #2. Even within the snapshot, if those original
/// obligations are not yet proven, then we are able to do projections
/// that may yet turn out to be wrong. This *may* lead to some sort
/// of trouble, though we don't have a concrete example of how that
/// can occur yet. But it seems risky at best.
fn get_paranoid_cache_value_obligation<'a, 'tcx>(
    infcx: &'a InferCtxt<'a, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    projection_ty: ty::ProjectionTy<'tcx>,
    cause: ObligationCause<'tcx>,
    depth: usize,
) -> PredicateObligation<'tcx> {
    let trait_ref = projection_ty.trait_ref(infcx.tcx).to_poly_trait_ref();
    Obligation {
        cause,
        recursion_depth: depth,
        param_env,
        predicate: trait_ref.without_const().to_predicate(),
    }
}

/// If we are projecting `<T as Trait>::Item`, but `T: Trait` does not
/// hold. In various error cases, we cannot generate a valid
/// normalized projection. Therefore, we create an inference variable
/// return an associated obligation that, when fulfilled, will lead to
/// an error.
///
/// Note that we used to return `Error` here, but that was quite
/// dubious -- the premise was that an error would *eventually* be
/// reported, when the obligation was processed. But in general once
/// you see a `Error` you are supposed to be able to assume that an
/// error *has been* reported, so that you can take whatever heuristic
/// paths you want to take. To make things worse, it was possible for
/// cycles to arise, where you basically had a setup like `<MyType<$0>
/// as Trait>::Foo == $0`. Here, normalizing `<MyType<$0> as
/// Trait>::Foo> to `[type error]` would lead to an obligation of
/// `<MyType<[type error]> as Trait>::Foo`. We are supposed to report
/// an error for this obligation, but we legitimately should not,
/// because it contains `[type error]`. Yuck! (See issue #29857 for
/// one case where this arose.)
fn normalize_to_error<'a, 'tcx>(
    selcx: &mut SelectionContext<'a, 'tcx>,
    param_env: ty::ParamEnv<'tcx>,
    projection_ty: ty::ProjectionTy<'tcx>,
    cause: ObligationCause<'tcx>,
    depth: usize,
) -> NormalizedTy<'tcx> {
    let trait_ref = projection_ty.trait_ref(selcx.tcx()).to_poly_trait_ref();
    let trait_obligation = Obligation {
        cause,
        recursion_depth: depth,
        param_env,
        predicate: trait_ref.without_const().to_predicate(),
    };
    let tcx = selcx.infcx().tcx;
    let def_id = projection_ty.item_def_id;
    let new_value = selcx.infcx().next_ty_var(TypeVariableOrigin {
        kind: TypeVariableOriginKind::NormalizeProjectionType,
        span: tcx.def_span(def_id),
    });
    Normalized { value: new_value, obligations: vec![trait_obligation] }
}

enum ProjectedTy<'tcx> {
    Progress(Progress<'tcx>),
    NoProgress(Ty<'tcx>),
}

struct Progress<'tcx> {
    ty: Ty<'tcx>,
    obligations: Vec<PredicateObligation<'tcx>>,
}

impl<'tcx> Progress<'tcx> {
    fn error(tcx: TyCtxt<'tcx>) -> Self {
        Progress { ty: tcx.types.err, obligations: vec![] }
    }

    fn with_addl_obligations(mut self, mut obligations: Vec<PredicateObligation<'tcx>>) -> Self {
        debug!(
            "with_addl_obligations: self.obligations.len={} obligations.len={}",
            self.obligations.len(),
            obligations.len()
        );

        debug!(
            "with_addl_obligations: self.obligations={:?} obligations={:?}",
            self.obligations, obligations
        );

        self.obligations.append(&mut obligations);
        self
    }
}

/// Computes the result of a projection type (if we can).
///
/// IMPORTANT:
/// - `obligation` must be fully normalized
fn project_type<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
) -> Result<ProjectedTy<'tcx>, ProjectionTyError<'tcx>> {
    debug!("project(obligation={:?})", obligation);

    let recursion_limit = *selcx.tcx().sess.recursion_limit.get();
    if obligation.recursion_depth >= recursion_limit {
        debug!("project: overflow!");
        return Err(ProjectionTyError::TraitSelectionError(SelectionError::Overflow));
    }

    let obligation_trait_ref = &obligation.predicate.trait_ref(selcx.tcx());

    debug!("project: obligation_trait_ref={:?}", obligation_trait_ref);

    if obligation_trait_ref.references_error() {
        return Ok(ProjectedTy::Progress(Progress::error(selcx.tcx())));
    }

    let mut candidates = ProjectionTyCandidateSet::None;

    // Make sure that the following procedures are kept in order. ParamEnv
    // needs to be first because it has highest priority, and Select checks
    // the return value of push_candidate which assumes it's ran at last.
    assemble_candidates_from_param_env(selcx, obligation, &obligation_trait_ref, &mut candidates);

    assemble_candidates_from_trait_def(selcx, obligation, &obligation_trait_ref, &mut candidates);

    assemble_candidates_from_impls(selcx, obligation, &obligation_trait_ref, &mut candidates);

    match candidates {
        ProjectionTyCandidateSet::Single(candidate) => Ok(ProjectedTy::Progress(
            confirm_candidate(selcx, obligation, &obligation_trait_ref, candidate),
        )),
        ProjectionTyCandidateSet::None => Ok(ProjectedTy::NoProgress(
            selcx
                .tcx()
                .mk_projection(obligation.predicate.item_def_id, obligation.predicate.substs),
        )),
        // Error occurred while trying to processing impls.
        ProjectionTyCandidateSet::Error(e) => Err(ProjectionTyError::TraitSelectionError(e)),
        // Inherent ambiguity that prevents us from even enumerating the
        // candidates.
        ProjectionTyCandidateSet::Ambiguous => Err(ProjectionTyError::TooManyCandidates),
    }
}

/// The first thing we have to do is scan through the parameter
/// environment to see whether there are any projection predicates
/// there that can answer this question.
fn assemble_candidates_from_param_env<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
    candidate_set: &mut ProjectionTyCandidateSet<'tcx>,
) {
    debug!("assemble_candidates_from_param_env(..)");
    assemble_candidates_from_predicates(
        selcx,
        obligation,
        obligation_trait_ref,
        candidate_set,
        ProjectionTyCandidate::ParamEnv,
        obligation.param_env.caller_bounds.iter().cloned(),
    );
}

/// In the case of a nested projection like <<A as Foo>::FooT as Bar>::BarT, we may find
/// that the definition of `Foo` has some clues:
///
/// ```
/// trait Foo {
///     type FooT : Bar<BarT=i32>
/// }
/// ```
///
/// Here, for example, we could conclude that the result is `i32`.
fn assemble_candidates_from_trait_def<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
    candidate_set: &mut ProjectionTyCandidateSet<'tcx>,
) {
    debug!("assemble_candidates_from_trait_def(..)");

    let tcx = selcx.tcx();
    // Check whether the self-type is itself a projection.
    let (def_id, substs) = match obligation_trait_ref.self_ty().kind {
        ty::Projection(ref data) => (data.trait_ref(tcx).def_id, data.substs),
        ty::Opaque(def_id, substs) => (def_id, substs),
        ty::Infer(ty::TyVar(_)) => {
            // If the self-type is an inference variable, then it MAY wind up
            // being a projected type, so induce an ambiguity.
            candidate_set.mark_ambiguous();
            return;
        }
        _ => return,
    };

    // If so, extract what we know from the trait and try to come up with a good answer.
    let trait_predicates = tcx.predicates_of(def_id);
    let bounds = trait_predicates.instantiate(tcx, substs);
    let bounds = elaborate_predicates(tcx, bounds.predicates);
    assemble_candidates_from_predicates(
        selcx,
        obligation,
        obligation_trait_ref,
        candidate_set,
        ProjectionTyCandidate::TraitDef,
        bounds,
    )
}

fn assemble_candidates_from_predicates<'cx, 'tcx, I>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
    candidate_set: &mut ProjectionTyCandidateSet<'tcx>,
    ctor: fn(ty::PolyProjectionPredicate<'tcx>) -> ProjectionTyCandidate<'tcx>,
    env_predicates: I,
) where
    I: IntoIterator<Item = ty::Predicate<'tcx>>,
{
    debug!("assemble_candidates_from_predicates(obligation={:?})", obligation);
    let infcx = selcx.infcx();
    for predicate in env_predicates {
        debug!("assemble_candidates_from_predicates: predicate={:?}", predicate);
        if let ty::Predicate::Projection(data) = predicate {
            let same_def_id = data.projection_def_id() == obligation.predicate.item_def_id;

            let is_match = same_def_id
                && infcx.probe(|_| {
                    let data_poly_trait_ref = data.to_poly_trait_ref(infcx.tcx);
                    let obligation_poly_trait_ref = obligation_trait_ref.to_poly_trait_ref();
                    infcx
                        .at(&obligation.cause, obligation.param_env)
                        .sup(obligation_poly_trait_ref, data_poly_trait_ref)
                        .map(|InferOk { obligations: _, value: () }| {
                            // FIXME(#32730) -- do we need to take obligations
                            // into account in any way? At the moment, no.
                        })
                        .is_ok()
                });

            debug!(
                "assemble_candidates_from_predicates: candidate={:?} \
                    is_match={} same_def_id={}",
                data, is_match, same_def_id
            );

            if is_match {
                candidate_set.push_candidate(ctor(data));
            }
        }
    }
}

fn assemble_candidates_from_impls<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
    candidate_set: &mut ProjectionTyCandidateSet<'tcx>,
) {
    // If we are resolving `<T as TraitRef<...>>::Item == Type`,
    // start out by selecting the predicate `T as TraitRef<...>`:
    let poly_trait_ref = obligation_trait_ref.to_poly_trait_ref();
    let trait_obligation = obligation.with(poly_trait_ref.to_poly_trait_predicate());
    let _ = selcx.infcx().commit_if_ok(|_| {
        let vtable = match selcx.select(&trait_obligation) {
            Ok(Some(vtable)) => vtable,
            Ok(None) => {
                candidate_set.mark_ambiguous();
                return Err(());
            }
            Err(e) => {
                debug!("assemble_candidates_from_impls: selection error {:?}", e);
                candidate_set.mark_error(e);
                return Err(());
            }
        };

        let eligible = match &vtable {
            super::VtableClosure(_)
            | super::VtableGenerator(_)
            | super::VtableFnPointer(_)
            | super::VtableObject(_)
            | super::VtableTraitAlias(_) => {
                debug!("assemble_candidates_from_impls: vtable={:?}", vtable);
                true
            }
            super::VtableImpl(impl_data) => {
                // We have to be careful when projecting out of an
                // impl because of specialization. If we are not in
                // codegen (i.e., projection mode is not "any"), and the
                // impl's type is declared as default, then we disable
                // projection (even if the trait ref is fully
                // monomorphic). In the case where trait ref is not
                // fully monomorphic (i.e., includes type parameters),
                // this is because those type parameters may
                // ultimately be bound to types from other crates that
                // may have specialized impls we can't see. In the
                // case where the trait ref IS fully monomorphic, this
                // is a policy decision that we made in the RFC in
                // order to preserve flexibility for the crate that
                // defined the specializable impl to specialize later
                // for existing types.
                //
                // In either case, we handle this by not adding a
                // candidate for an impl if it contains a `default`
                // type.
                //
                // NOTE: This should be kept in sync with the similar code in
                // `rustc::ty::instance::resolve_associated_item()`.
                let node_item =
                    assoc_ty_def(selcx, impl_data.impl_def_id, obligation.predicate.item_def_id);

                let is_default = if node_item.node.is_from_trait() {
                    // If true, the impl inherited a `type Foo = Bar`
                    // given in the trait, which is implicitly default.
                    // Otherwise, the impl did not specify `type` and
                    // neither did the trait:
                    //
                    // ```rust
                    // trait Foo { type T; }
                    // impl Foo for Bar { }
                    // ```
                    //
                    // This is an error, but it will be
                    // reported in `check_impl_items_against_trait`.
                    // We accept it here but will flag it as
                    // an error when we confirm the candidate
                    // (which will ultimately lead to `normalize_to_error`
                    // being invoked).
                    node_item.item.defaultness.has_value()
                } else {
                    node_item.item.defaultness.is_default()
                        || super::util::impl_is_default(selcx.tcx(), node_item.node.def_id())
                };

                // Only reveal a specializable default if we're past type-checking
                // and the obligations is monomorphic, otherwise passes such as
                // transmute checking and polymorphic MIR optimizations could
                // get a result which isn't correct for all monomorphizations.
                if !is_default {
                    true
                } else if obligation.param_env.reveal == Reveal::All {
                    // NOTE(eddyb) inference variables can resolve to parameters, so
                    // assume `poly_trait_ref` isn't monomorphic, if it contains any.
                    let poly_trait_ref = selcx.infcx().resolve_vars_if_possible(&poly_trait_ref);
                    !poly_trait_ref.needs_infer() && !poly_trait_ref.needs_subst()
                } else {
                    false
                }
            }
            super::VtableParam(..) => {
                // This case tell us nothing about the value of an
                // associated type. Consider:
                //
                // ```
                // trait SomeTrait { type Foo; }
                // fn foo<T:SomeTrait>(...) { }
                // ```
                //
                // If the user writes `<T as SomeTrait>::Foo`, then the `T
                // : SomeTrait` binding does not help us decide what the
                // type `Foo` is (at least, not more specifically than
                // what we already knew).
                //
                // But wait, you say! What about an example like this:
                //
                // ```
                // fn bar<T:SomeTrait<Foo=usize>>(...) { ... }
                // ```
                //
                // Doesn't the `T : Sometrait<Foo=usize>` predicate help
                // resolve `T::Foo`? And of course it does, but in fact
                // that single predicate is desugared into two predicates
                // in the compiler: a trait predicate (`T : SomeTrait`) and a
                // projection. And the projection where clause is handled
                // in `assemble_candidates_from_param_env`.
                false
            }
            super::VtableAutoImpl(..) | super::VtableBuiltin(..) => {
                // These traits have no associated types.
                span_bug!(
                    obligation.cause.span,
                    "Cannot project an associated type from `{:?}`",
                    vtable
                );
            }
        };

        if eligible {
            if candidate_set.push_candidate(ProjectionTyCandidate::Select(vtable)) {
                Ok(())
            } else {
                Err(())
            }
        } else {
            Err(())
        }
    });
}

fn confirm_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
    candidate: ProjectionTyCandidate<'tcx>,
) -> Progress<'tcx> {
    debug!("confirm_candidate(candidate={:?}, obligation={:?})", candidate, obligation);

    match candidate {
        ProjectionTyCandidate::ParamEnv(poly_projection)
        | ProjectionTyCandidate::TraitDef(poly_projection) => {
            confirm_param_env_candidate(selcx, obligation, poly_projection)
        }

        ProjectionTyCandidate::Select(vtable) => {
            confirm_select_candidate(selcx, obligation, obligation_trait_ref, vtable)
        }
    }
}

fn confirm_select_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
    vtable: Selection<'tcx>,
) -> Progress<'tcx> {
    match vtable {
        super::VtableImpl(data) => confirm_impl_candidate(selcx, obligation, data),
        super::VtableGenerator(data) => confirm_generator_candidate(selcx, obligation, data),
        super::VtableClosure(data) => confirm_closure_candidate(selcx, obligation, data),
        super::VtableFnPointer(data) => confirm_fn_pointer_candidate(selcx, obligation, data),
        super::VtableObject(_) => confirm_object_candidate(selcx, obligation, obligation_trait_ref),
        super::VtableAutoImpl(..)
        | super::VtableParam(..)
        | super::VtableBuiltin(..)
        | super::VtableTraitAlias(..) =>
        // we don't create Select candidates with this kind of resolution
        {
            span_bug!(
                obligation.cause.span,
                "Cannot project an associated type from `{:?}`",
                vtable
            )
        }
    }
}

fn confirm_object_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    obligation_trait_ref: &ty::TraitRef<'tcx>,
) -> Progress<'tcx> {
    let self_ty = obligation_trait_ref.self_ty();
    let object_ty = selcx.infcx().shallow_resolve(self_ty);
    debug!("confirm_object_candidate(object_ty={:?})", object_ty);
    let data = match object_ty.kind {
        ty::Dynamic(ref data, ..) => data,
        _ => span_bug!(
            obligation.cause.span,
            "confirm_object_candidate called with non-object: {:?}",
            object_ty
        ),
    };
    let env_predicates = data
        .projection_bounds()
        .map(|p| p.with_self_ty(selcx.tcx(), object_ty).to_predicate())
        .collect();
    let env_predicate = {
        let env_predicates = elaborate_predicates(selcx.tcx(), env_predicates);

        // select only those projections that are actually projecting an
        // item with the correct name
        let env_predicates = env_predicates.filter_map(|p| match p {
            ty::Predicate::Projection(data) => {
                if data.projection_def_id() == obligation.predicate.item_def_id {
                    Some(data)
                } else {
                    None
                }
            }
            _ => None,
        });

        // select those with a relevant trait-ref
        let mut env_predicates = env_predicates.filter(|data| {
            let data_poly_trait_ref = data.to_poly_trait_ref(selcx.tcx());
            let obligation_poly_trait_ref = obligation_trait_ref.to_poly_trait_ref();
            selcx.infcx().probe(|_| {
                selcx
                    .infcx()
                    .at(&obligation.cause, obligation.param_env)
                    .sup(obligation_poly_trait_ref, data_poly_trait_ref)
                    .is_ok()
            })
        });

        // select the first matching one; there really ought to be one or
        // else the object type is not WF, since an object type should
        // include all of its projections explicitly
        match env_predicates.next() {
            Some(env_predicate) => env_predicate,
            None => {
                debug!(
                    "confirm_object_candidate: no env-predicate \
                        found in object type `{:?}`; ill-formed",
                    object_ty
                );
                return Progress::error(selcx.tcx());
            }
        }
    };

    confirm_param_env_candidate(selcx, obligation, env_predicate)
}

fn confirm_generator_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    vtable: VtableGeneratorData<'tcx, PredicateObligation<'tcx>>,
) -> Progress<'tcx> {
    let gen_sig = vtable.substs.as_generator().poly_sig(vtable.generator_def_id, selcx.tcx());
    let Normalized { value: gen_sig, obligations } = normalize_with_depth(
        selcx,
        obligation.param_env,
        obligation.cause.clone(),
        obligation.recursion_depth + 1,
        &gen_sig,
    );

    debug!(
        "confirm_generator_candidate: obligation={:?},gen_sig={:?},obligations={:?}",
        obligation, gen_sig, obligations
    );

    let tcx = selcx.tcx();

    let gen_def_id = tcx.lang_items().gen_trait().unwrap();

    let predicate = super::util::generator_trait_ref_and_outputs(
        tcx,
        gen_def_id,
        obligation.predicate.self_ty(),
        gen_sig,
    )
    .map_bound(|(trait_ref, yield_ty, return_ty)| {
        let name = tcx.associated_item(obligation.predicate.item_def_id).ident.name;
        let ty = if name == sym::Return {
            return_ty
        } else if name == sym::Yield {
            yield_ty
        } else {
            bug!()
        };

        ty::ProjectionPredicate {
            projection_ty: ty::ProjectionTy {
                substs: trait_ref.substs,
                item_def_id: obligation.predicate.item_def_id,
            },
            ty: ty,
        }
    });

    confirm_param_env_candidate(selcx, obligation, predicate)
        .with_addl_obligations(vtable.nested)
        .with_addl_obligations(obligations)
}

fn confirm_fn_pointer_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    fn_pointer_vtable: VtableFnPointerData<'tcx, PredicateObligation<'tcx>>,
) -> Progress<'tcx> {
    let fn_type = selcx.infcx().shallow_resolve(fn_pointer_vtable.fn_ty);
    let sig = fn_type.fn_sig(selcx.tcx());
    let Normalized { value: sig, obligations } = normalize_with_depth(
        selcx,
        obligation.param_env,
        obligation.cause.clone(),
        obligation.recursion_depth + 1,
        &sig,
    );

    confirm_callable_candidate(selcx, obligation, sig, util::TupleArgumentsFlag::Yes)
        .with_addl_obligations(fn_pointer_vtable.nested)
        .with_addl_obligations(obligations)
}

fn confirm_closure_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    vtable: VtableClosureData<'tcx, PredicateObligation<'tcx>>,
) -> Progress<'tcx> {
    let tcx = selcx.tcx();
    let infcx = selcx.infcx();
    let closure_sig_ty = vtable.substs.as_closure().sig_ty(vtable.closure_def_id, tcx);
    let closure_sig = infcx.shallow_resolve(closure_sig_ty).fn_sig(tcx);
    let Normalized { value: closure_sig, obligations } = normalize_with_depth(
        selcx,
        obligation.param_env,
        obligation.cause.clone(),
        obligation.recursion_depth + 1,
        &closure_sig,
    );

    debug!(
        "confirm_closure_candidate: obligation={:?},closure_sig={:?},obligations={:?}",
        obligation, closure_sig, obligations
    );

    confirm_callable_candidate(selcx, obligation, closure_sig, util::TupleArgumentsFlag::No)
        .with_addl_obligations(vtable.nested)
        .with_addl_obligations(obligations)
}

fn confirm_callable_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    fn_sig: ty::PolyFnSig<'tcx>,
    flag: util::TupleArgumentsFlag,
) -> Progress<'tcx> {
    let tcx = selcx.tcx();

    debug!("confirm_callable_candidate({:?},{:?})", obligation, fn_sig);

    // the `Output` associated type is declared on `FnOnce`
    let fn_once_def_id = tcx.lang_items().fn_once_trait().unwrap();

    let predicate = super::util::closure_trait_ref_and_return_type(
        tcx,
        fn_once_def_id,
        obligation.predicate.self_ty(),
        fn_sig,
        flag,
    )
    .map_bound(|(trait_ref, ret_type)| ty::ProjectionPredicate {
        projection_ty: ty::ProjectionTy::from_ref_and_name(
            tcx,
            trait_ref,
            Ident::with_dummy_span(rustc_hir::FN_OUTPUT_NAME),
        ),
        ty: ret_type,
    });

    confirm_param_env_candidate(selcx, obligation, predicate)
}

fn confirm_param_env_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    poly_cache_entry: ty::PolyProjectionPredicate<'tcx>,
) -> Progress<'tcx> {
    let infcx = selcx.infcx();
    let cause = &obligation.cause;
    let param_env = obligation.param_env;

    let (cache_entry, _) = infcx.replace_bound_vars_with_fresh_vars(
        cause.span,
        LateBoundRegionConversionTime::HigherRankedType,
        &poly_cache_entry,
    );

    let cache_trait_ref = cache_entry.projection_ty.trait_ref(infcx.tcx);
    let obligation_trait_ref = obligation.predicate.trait_ref(infcx.tcx);
    match infcx.at(cause, param_env).eq(cache_trait_ref, obligation_trait_ref) {
        Ok(InferOk { value: _, obligations }) => Progress { ty: cache_entry.ty, obligations },
        Err(e) => {
            let msg = format!(
                "Failed to unify obligation `{:?}` with poly_projection `{:?}`: {:?}",
                obligation, poly_cache_entry, e,
            );
            debug!("confirm_param_env_candidate: {}", msg);
            infcx.tcx.sess.delay_span_bug(obligation.cause.span, &msg);
            Progress { ty: infcx.tcx.types.err, obligations: vec![] }
        }
    }
}

fn confirm_impl_candidate<'cx, 'tcx>(
    selcx: &mut SelectionContext<'cx, 'tcx>,
    obligation: &ProjectionTyObligation<'tcx>,
    impl_vtable: VtableImplData<'tcx, PredicateObligation<'tcx>>,
) -> Progress<'tcx> {
    let tcx = selcx.tcx();

    let VtableImplData { impl_def_id, substs, nested } = impl_vtable;
    let assoc_item_id = obligation.predicate.item_def_id;
    let trait_def_id = tcx.trait_id_of_impl(impl_def_id).unwrap();

    let param_env = obligation.param_env;
    let assoc_ty = assoc_ty_def(selcx, impl_def_id, assoc_item_id);

    if !assoc_ty.item.defaultness.has_value() {
        // This means that the impl is missing a definition for the
        // associated type. This error will be reported by the type
        // checker method `check_impl_items_against_trait`, so here we
        // just return Error.
        debug!(
            "confirm_impl_candidate: no associated type {:?} for {:?}",
            assoc_ty.item.ident, obligation.predicate
        );
        return Progress { ty: tcx.types.err, obligations: nested };
    }
    let substs = obligation.predicate.substs.rebase_onto(tcx, trait_def_id, substs);
    let substs = translate_substs(selcx.infcx(), param_env, impl_def_id, substs, assoc_ty.node);
    let ty = if let ty::AssocKind::OpaqueTy = assoc_ty.item.kind {
        let item_substs = InternalSubsts::identity_for_item(tcx, assoc_ty.item.def_id);
        tcx.mk_opaque(assoc_ty.item.def_id, item_substs)
    } else {
        tcx.type_of(assoc_ty.item.def_id)
    };
    if substs.len() != tcx.generics_of(assoc_ty.item.def_id).count() {
        tcx.sess
            .delay_span_bug(DUMMY_SP, "impl item and trait item have different parameter counts");
        Progress { ty: tcx.types.err, obligations: nested }
    } else {
        Progress { ty: ty.subst(tcx, substs), obligations: nested }
    }
}

/// Locate the definition of an associated type in the specialization hierarchy,
/// starting from the given impl.
///
/// Based on the "projection mode", this lookup may in fact only examine the
/// topmost impl. See the comments for `Reveal` for more details.
fn assoc_ty_def(
    selcx: &SelectionContext<'_, '_>,
    impl_def_id: DefId,
    assoc_ty_def_id: DefId,
) -> specialization_graph::NodeItem<ty::AssocItem> {
    let tcx = selcx.tcx();
    let assoc_ty_name = tcx.associated_item(assoc_ty_def_id).ident;
    let trait_def_id = tcx.impl_trait_ref(impl_def_id).unwrap().def_id;
    let trait_def = tcx.trait_def(trait_def_id);

    // This function may be called while we are still building the
    // specialization graph that is queried below (via TraidDef::ancestors()),
    // so, in order to avoid unnecessary infinite recursion, we manually look
    // for the associated item at the given impl.
    // If there is no such item in that impl, this function will fail with a
    // cycle error if the specialization graph is currently being built.
    let impl_node = specialization_graph::Node::Impl(impl_def_id);
    for item in impl_node.items(tcx) {
        if matches!(item.kind, ty::AssocKind::Type | ty::AssocKind::OpaqueTy)
            && tcx.hygienic_eq(item.ident, assoc_ty_name, trait_def_id)
        {
            return specialization_graph::NodeItem {
                node: specialization_graph::Node::Impl(impl_def_id),
                item,
            };
        }
    }

    if let Some(assoc_item) =
        trait_def.ancestors(tcx, impl_def_id).leaf_def(tcx, assoc_ty_name, ty::AssocKind::Type)
    {
        assoc_item
    } else {
        // This is saying that neither the trait nor
        // the impl contain a definition for this
        // associated type.  Normally this situation
        // could only arise through a compiler bug --
        // if the user wrote a bad item name, it
        // should have failed in astconv.
        bug!("No associated type `{}` for {}", assoc_ty_name, tcx.def_path_str(impl_def_id))
    }
}

// # Cache

/// The projection cache. Unlike the standard caches, this can include
/// infcx-dependent type variables, therefore we have to roll the
/// cache back each time we roll a snapshot back, to avoid assumptions
/// on yet-unresolved inference variables. Types with placeholder
/// regions also have to be removed when the respective snapshot ends.
///
/// Because of that, projection cache entries can be "stranded" and left
/// inaccessible when type variables inside the key are resolved. We make no
/// attempt to recover or remove "stranded" entries, but rather let them be
/// (for the lifetime of the infcx).
///
/// Entries in the projection cache might contain inference variables
/// that will be resolved by obligations on the projection cache entry (e.g.,
/// when a type parameter in the associated type is constrained through
/// an "RFC 447" projection on the impl).
///
/// When working with a fulfillment context, the derived obligations of each
/// projection cache entry will be registered on the fulfillcx, so any users
/// that can wait for a fulfillcx fixed point need not care about this. However,
/// users that don't wait for a fixed point (e.g., trait evaluation) have to
/// resolve the obligations themselves to make sure the projected result is
/// ok and avoid issues like #43132.
///
/// If that is done, after evaluation the obligations, it is a good idea to
/// call `ProjectionCache::complete` to make sure the obligations won't be
/// re-evaluated and avoid an exponential worst-case.
//
// FIXME: we probably also want some sort of cross-infcx cache here to
// reduce the amount of duplication. Let's see what we get with the Chalk reforms.
#[derive(Default)]
pub struct ProjectionCache<'tcx> {
    map: SnapshotMap<ProjectionCacheKey<'tcx>, ProjectionCacheEntry<'tcx>>,
}

#[derive(Copy, Clone, Debug, Hash, PartialEq, Eq)]
pub struct ProjectionCacheKey<'tcx> {
    ty: ty::ProjectionTy<'tcx>,
}

impl<'cx, 'tcx> ProjectionCacheKey<'tcx> {
    pub fn from_poly_projection_predicate(
        selcx: &mut SelectionContext<'cx, 'tcx>,
        predicate: &ty::PolyProjectionPredicate<'tcx>,
    ) -> Option<Self> {
        let infcx = selcx.infcx();
        // We don't do cross-snapshot caching of obligations with escaping regions,
        // so there's no cache key to use
        predicate.no_bound_vars().map(|predicate| ProjectionCacheKey {
            // We don't attempt to match up with a specific type-variable state
            // from a specific call to `opt_normalize_projection_type` - if
            // there's no precise match, the original cache entry is "stranded"
            // anyway.
            ty: infcx.resolve_vars_if_possible(&predicate.projection_ty),
        })
    }
}

#[derive(Clone, Debug)]
enum ProjectionCacheEntry<'tcx> {
    InProgress,
    Ambiguous,
    Error,
    NormalizedTy(NormalizedTy<'tcx>),
}

// N.B., intentionally not Clone
pub struct ProjectionCacheSnapshot {
    snapshot: Snapshot,
}

impl<'tcx> ProjectionCache<'tcx> {
    pub fn clear(&mut self) {
        self.map.clear();
    }

    pub fn snapshot(&mut self) -> ProjectionCacheSnapshot {
        ProjectionCacheSnapshot { snapshot: self.map.snapshot() }
    }

    pub fn rollback_to(&mut self, snapshot: ProjectionCacheSnapshot) {
        self.map.rollback_to(snapshot.snapshot);
    }

    pub fn rollback_placeholder(&mut self, snapshot: &ProjectionCacheSnapshot) {
        self.map.partial_rollback(&snapshot.snapshot, &|k| k.ty.has_re_placeholders());
    }

    pub fn commit(&mut self, snapshot: ProjectionCacheSnapshot) {
        self.map.commit(snapshot.snapshot);
    }

    /// Try to start normalize `key`; returns an error if
    /// normalization already occurred (this error corresponds to a
    /// cache hit, so it's actually a good thing).
    fn try_start(
        &mut self,
        key: ProjectionCacheKey<'tcx>,
    ) -> Result<(), ProjectionCacheEntry<'tcx>> {
        if let Some(entry) = self.map.get(&key) {
            return Err(entry.clone());
        }

        self.map.insert(key, ProjectionCacheEntry::InProgress);
        Ok(())
    }

    /// Indicates that `key` was normalized to `value`.
    fn insert_ty(&mut self, key: ProjectionCacheKey<'tcx>, value: NormalizedTy<'tcx>) {
        debug!(
            "ProjectionCacheEntry::insert_ty: adding cache entry: key={:?}, value={:?}",
            key, value
        );
        let fresh_key = self.map.insert(key, ProjectionCacheEntry::NormalizedTy(value));
        assert!(!fresh_key, "never started projecting `{:?}`", key);
    }

    /// Mark the relevant projection cache key as having its derived obligations
    /// complete, so they won't have to be re-computed (this is OK to do in a
    /// snapshot - if the snapshot is rolled back, the obligations will be
    /// marked as incomplete again).
    pub fn complete(&mut self, key: ProjectionCacheKey<'tcx>) {
        let ty = match self.map.get(&key) {
            Some(&ProjectionCacheEntry::NormalizedTy(ref ty)) => {
                debug!("ProjectionCacheEntry::complete({:?}) - completing {:?}", key, ty);
                ty.value
            }
            ref value => {
                // Type inference could "strand behind" old cache entries. Leave
                // them alone for now.
                debug!("ProjectionCacheEntry::complete({:?}) - ignoring {:?}", key, value);
                return;
            }
        };

        self.map.insert(
            key,
            ProjectionCacheEntry::NormalizedTy(Normalized { value: ty, obligations: vec![] }),
        );
    }

    /// A specialized version of `complete` for when the key's value is known
    /// to be a NormalizedTy.
    pub fn complete_normalized(&mut self, key: ProjectionCacheKey<'tcx>, ty: &NormalizedTy<'tcx>) {
        // We want to insert `ty` with no obligations. If the existing value
        // already has no obligations (as is common) we don't insert anything.
        if !ty.obligations.is_empty() {
            self.map.insert(
                key,
                ProjectionCacheEntry::NormalizedTy(Normalized {
                    value: ty.value,
                    obligations: vec![],
                }),
            );
        }
    }

    /// Indicates that trying to normalize `key` resulted in
    /// ambiguity. No point in trying it again then until we gain more
    /// type information (in which case, the "fully resolved" key will
    /// be different).
    fn ambiguous(&mut self, key: ProjectionCacheKey<'tcx>) {
        let fresh = self.map.insert(key, ProjectionCacheEntry::Ambiguous);
        assert!(!fresh, "never started projecting `{:?}`", key);
    }

    /// Indicates that trying to normalize `key` resulted in
    /// error.
    fn error(&mut self, key: ProjectionCacheKey<'tcx>) {
        let fresh = self.map.insert(key, ProjectionCacheEntry::Error);
        assert!(!fresh, "never started projecting `{:?}`", key);
    }
}