aboutsummaryrefslogtreecommitdiff
path: root/crates/ra_hir/src/ty.rs
blob: 7a54856981490cc4913d15443b0d6328d207020b (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
//! The type system. We currently use this to infer types for completion.
//!
//! For type inference, compare the implementations in rustc (the various
//! check_* methods in librustc_typeck/check/mod.rs are a good entry point) and
//! IntelliJ-Rust (org.rust.lang.core.types.infer). Our entry point for
//! inference here is the `infer` function, which infers the types of all
//! expressions in a given function.
//!
//! The central struct here is `Ty`, which represents a type. During inference,
//! it can contain type 'variables' which represent currently unknown types; as
//! we walk through the expressions, we might determine that certain variables
//! need to be equal to each other, or to certain types. To record this, we use
//! the union-find implementation from the `ena` crate, which is extracted from
//! rustc.

mod autoderef;
pub(crate) mod primitive;
#[cfg(test)]
mod tests;
pub(crate) mod method_resolution;

use std::borrow::Cow;
use std::iter::repeat;
use std::ops::Index;
use std::sync::Arc;
use std::{fmt, mem};

use ena::unify::{InPlaceUnificationTable, UnifyKey, UnifyValue, NoError};
use ra_arena::map::ArenaMap;
use join_to_string::join;
use rustc_hash::FxHashMap;

use test_utils::tested_by;

use crate::{
    Module, Function, Struct, StructField, Enum, EnumVariant, Path, Name, ImplBlock,
    FnSignature, FnScopes, ModuleDef, AdtDef,
    db::HirDatabase,
    type_ref::{TypeRef, Mutability},
    name::KnownName,
    expr::{Body, Expr, BindingAnnotation, Literal, ExprId, Pat, PatId, UnaryOp, BinaryOp, Statement, FieldPat},
    generics::GenericParams,
    path::GenericArg,
    adt::VariantDef,
};

/// The ID of a type variable.
#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
pub struct TypeVarId(u32);

impl UnifyKey for TypeVarId {
    type Value = TypeVarValue;

    fn index(&self) -> u32 {
        self.0
    }

    fn from_index(i: u32) -> Self {
        TypeVarId(i)
    }

    fn tag() -> &'static str {
        "TypeVarId"
    }
}

/// The value of a type variable: either we already know the type, or we don't
/// know it yet.
#[derive(Clone, PartialEq, Eq, Debug)]
pub enum TypeVarValue {
    Known(Ty),
    Unknown,
}

impl TypeVarValue {
    fn known(&self) -> Option<&Ty> {
        match self {
            TypeVarValue::Known(ty) => Some(ty),
            TypeVarValue::Unknown => None,
        }
    }
}

impl UnifyValue for TypeVarValue {
    type Error = NoError;

    fn unify_values(value1: &Self, value2: &Self) -> Result<Self, NoError> {
        match (value1, value2) {
            // We should never equate two type variables, both of which have
            // known types. Instead, we recursively equate those types.
            (TypeVarValue::Known(t1), TypeVarValue::Known(t2)) => panic!(
                "equating two type variables, both of which have known types: {:?} and {:?}",
                t1, t2
            ),

            // If one side is known, prefer that one.
            (TypeVarValue::Known(..), TypeVarValue::Unknown) => Ok(value1.clone()),
            (TypeVarValue::Unknown, TypeVarValue::Known(..)) => Ok(value2.clone()),

            (TypeVarValue::Unknown, TypeVarValue::Unknown) => Ok(TypeVarValue::Unknown),
        }
    }
}

/// The kinds of placeholders we need during type inference. There's separate
/// values for general types, and for integer and float variables. The latter
/// two are used for inference of literal values (e.g. `100` could be one of
/// several integer types).
#[derive(Clone, Copy, PartialEq, Eq, Hash, Debug)]
pub enum InferTy {
    TypeVar(TypeVarId),
    IntVar(TypeVarId),
    FloatVar(TypeVarId),
}

impl InferTy {
    fn to_inner(self) -> TypeVarId {
        match self {
            InferTy::TypeVar(ty) | InferTy::IntVar(ty) | InferTy::FloatVar(ty) => ty,
        }
    }

    fn fallback_value(self) -> Ty {
        match self {
            InferTy::TypeVar(..) => Ty::Unknown,
            InferTy::IntVar(..) => {
                Ty::Int(primitive::UncertainIntTy::Signed(primitive::IntTy::I32))
            }
            InferTy::FloatVar(..) => {
                Ty::Float(primitive::UncertainFloatTy::Known(primitive::FloatTy::F64))
            }
        }
    }
}

/// When inferring an expression, we propagate downward whatever type hint we
/// are able in the form of an `Expectation`.
#[derive(Clone, PartialEq, Eq, Debug)]
struct Expectation {
    ty: Ty,
    // TODO: In some cases, we need to be aware whether the expectation is that
    // the type match exactly what we passed, or whether it just needs to be
    // coercible to the expected type. See Expectation::rvalue_hint in rustc.
}

impl Expectation {
    /// The expectation that the type of the expression needs to equal the given
    /// type.
    fn has_type(ty: Ty) -> Self {
        Expectation { ty }
    }

    /// This expresses no expectation on the type.
    fn none() -> Self {
        Expectation { ty: Ty::Unknown }
    }
}

/// A list of substitutions for generic parameters.
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct Substs(Arc<[Ty]>);

impl Substs {
    pub fn empty() -> Substs {
        Substs(Arc::new([]))
    }
}

/// A type. This is based on the `TyKind` enum in rustc (librustc/ty/sty.rs).
///
/// This should be cheap to clone.
#[derive(Clone, PartialEq, Eq, Debug)]
pub enum Ty {
    /// The primitive boolean type. Written as `bool`.
    Bool,

    /// The primitive character type; holds a Unicode scalar value
    /// (a non-surrogate code point). Written as `char`.
    Char,

    /// A primitive integer type. For example, `i32`.
    Int(primitive::UncertainIntTy),

    /// A primitive floating-point type. For example, `f64`.
    Float(primitive::UncertainFloatTy),

    /// Structures, enumerations and unions.
    Adt {
        /// The definition of the struct/enum.
        def_id: AdtDef,
        /// The name, for displaying.
        name: Name,
        /// Substitutions for the generic parameters of the type.
        substs: Substs,
    },

    /// The pointee of a string slice. Written as `str`.
    Str,

    /// The pointee of an array slice.  Written as `[T]`.
    Slice(Arc<Ty>),

    // An array with the given length. Written as `[T; n]`.
    Array(Arc<Ty>),

    /// A raw pointer. Written as `*mut T` or `*const T`
    RawPtr(Arc<Ty>, Mutability),

    /// A reference; a pointer with an associated lifetime. Written as
    /// `&'a mut T` or `&'a T`.
    Ref(Arc<Ty>, Mutability),

    /// The anonymous type of a function declaration/definition. Each
    /// function has a unique type, which is output (for a function
    /// named `foo` returning an `i32`) as `fn() -> i32 {foo}`.
    ///
    /// For example the type of `bar` here:
    ///
    /// ```rust
    /// fn foo() -> i32 { 1 }
    /// let bar = foo; // bar: fn() -> i32 {foo}
    /// ```
    FnDef {
        // Function definition
        def: Function,
        /// For display
        name: Name,
        /// Parameters and return type
        sig: Arc<FnSig>,
        /// Substitutions for the generic parameters of the type
        substs: Substs,
    },

    /// A pointer to a function.  Written as `fn() -> i32`.
    ///
    /// For example the type of `bar` here:
    ///
    /// ```rust
    /// fn foo() -> i32 { 1 }
    /// let bar: fn() -> i32 = foo;
    /// ```
    FnPtr(Arc<FnSig>),

    // rustc has a separate type for each function, which just coerces to the
    // above function pointer type. Once we implement generics, we will probably
    // need this as well.

    // A trait, defined with `dyn Trait`.
    // Dynamic(),

    // The anonymous type of a closure. Used to represent the type of
    // `|a| a`.
    // Closure(DefId, ClosureSubsts<'tcx>),

    // The anonymous type of a generator. Used to represent the type of
    // `|a| yield a`.
    // Generator(DefId, GeneratorSubsts<'tcx>, hir::GeneratorMovability),

    // A type representing the types stored inside a generator.
    // This should only appear in GeneratorInteriors.
    // GeneratorWitness(Binder<&'tcx List<Ty<'tcx>>>),
    /// The never type `!`.
    Never,

    /// A tuple type.  For example, `(i32, bool)`.
    Tuple(Arc<[Ty]>),

    // The projection of an associated type.  For example,
    // `<T as Trait<..>>::N`.pub
    // Projection(ProjectionTy),

    // Opaque (`impl Trait`) type found in a return type.
    // Opaque(DefId, Substs),
    /// A type parameter; for example, `T` in `fn f<T>(x: T) {}
    Param {
        /// The index of the parameter (starting with parameters from the
        /// surrounding impl, then the current function).
        idx: u32,
        /// The name of the parameter, for displaying.
        name: Name,
    },

    /// A type variable used during type checking. Not to be confused with a
    /// type parameter.
    Infer(InferTy),

    /// A placeholder for a type which could not be computed; this is propagated
    /// to avoid useless error messages. Doubles as a placeholder where type
    /// variables are inserted before type checking, since we want to try to
    /// infer a better type here anyway -- for the IDE use case, we want to try
    /// to infer as much as possible even in the presence of type errors.
    Unknown,
}

/// A function signature.
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct FnSig {
    input: Vec<Ty>,
    output: Ty,
}

impl Ty {
    pub(crate) fn from_hir(
        db: &impl HirDatabase,
        // TODO: the next three parameters basically describe the scope for name
        // resolution; this should be refactored into something like a general
        // resolver architecture
        module: &Module,
        impl_block: Option<&ImplBlock>,
        generics: &GenericParams,
        type_ref: &TypeRef,
    ) -> Self {
        match type_ref {
            TypeRef::Never => Ty::Never,
            TypeRef::Tuple(inner) => {
                let inner_tys = inner
                    .iter()
                    .map(|tr| Ty::from_hir(db, module, impl_block, generics, tr))
                    .collect::<Vec<_>>();
                Ty::Tuple(inner_tys.into())
            }
            TypeRef::Path(path) => Ty::from_hir_path(db, module, impl_block, generics, path),
            TypeRef::RawPtr(inner, mutability) => {
                let inner_ty = Ty::from_hir(db, module, impl_block, generics, inner);
                Ty::RawPtr(Arc::new(inner_ty), *mutability)
            }
            TypeRef::Array(inner) => {
                let inner_ty = Ty::from_hir(db, module, impl_block, generics, inner);
                Ty::Array(Arc::new(inner_ty))
            }
            TypeRef::Slice(inner) => {
                let inner_ty = Ty::from_hir(db, module, impl_block, generics, inner);
                Ty::Slice(Arc::new(inner_ty))
            }
            TypeRef::Reference(inner, mutability) => {
                let inner_ty = Ty::from_hir(db, module, impl_block, generics, inner);
                Ty::Ref(Arc::new(inner_ty), *mutability)
            }
            TypeRef::Placeholder => Ty::Unknown,
            TypeRef::Fn(params) => {
                let mut inner_tys = params
                    .iter()
                    .map(|tr| Ty::from_hir(db, module, impl_block, generics, tr))
                    .collect::<Vec<_>>();
                let return_ty = inner_tys
                    .pop()
                    .expect("TypeRef::Fn should always have at least return type");
                let sig = FnSig {
                    input: inner_tys,
                    output: return_ty,
                };
                Ty::FnPtr(Arc::new(sig))
            }
            TypeRef::Error => Ty::Unknown,
        }
    }

    pub(crate) fn from_hir_opt(
        db: &impl HirDatabase,
        module: &Module,
        impl_block: Option<&ImplBlock>,
        generics: &GenericParams,
        type_ref: Option<&TypeRef>,
    ) -> Self {
        type_ref.map_or(Ty::Unknown, |t| {
            Ty::from_hir(db, module, impl_block, generics, t)
        })
    }

    pub(crate) fn from_hir_path(
        db: &impl HirDatabase,
        module: &Module,
        impl_block: Option<&ImplBlock>,
        generics: &GenericParams,
        path: &Path,
    ) -> Self {
        if let Some(name) = path.as_ident() {
            if let Some(int_ty) = primitive::UncertainIntTy::from_name(name) {
                return Ty::Int(int_ty);
            } else if let Some(float_ty) = primitive::UncertainFloatTy::from_name(name) {
                return Ty::Float(float_ty);
            } else if name.as_known_name() == Some(KnownName::SelfType) {
                // TODO pass the impl block's generics?
                let generics = &GenericParams::default();
                return Ty::from_hir_opt(
                    db,
                    module,
                    None,
                    generics,
                    impl_block.map(|i| i.target_type()),
                );
            } else if let Some(known) = name.as_known_name() {
                match known {
                    KnownName::Bool => return Ty::Bool,
                    KnownName::Char => return Ty::Char,
                    KnownName::Str => return Ty::Str,
                    _ => {}
                }
            } else if let Some(generic_param) = generics.find_by_name(&name) {
                return Ty::Param {
                    idx: generic_param.idx,
                    name: generic_param.name.clone(),
                };
            }
        }

        // Resolve in module (in type namespace)
        let typable: TypableDef = match module
            .resolve_path(db, path)
            .take_types()
            .and_then(|it| it.into())
        {
            None => return Ty::Unknown,
            Some(it) => it,
        };
        let ty = db.type_for_def(typable);
        let substs = Ty::substs_from_path(db, module, impl_block, generics, path, typable);
        ty.apply_substs(substs)
    }

    /// Collect generic arguments from a path into a `Substs`. See also
    /// `create_substs_for_ast_path` and `def_to_ty` in rustc.
    fn substs_from_path(
        db: &impl HirDatabase,
        // the scope of the segment...
        module: &Module,
        impl_block: Option<&ImplBlock>,
        outer_generics: &GenericParams,
        path: &Path,
        resolved: TypableDef,
    ) -> Substs {
        let mut substs = Vec::new();
        let last = path
            .segments
            .last()
            .expect("path should have at least one segment");
        let (def_generics, segment) = match resolved {
            TypableDef::Function(func) => (func.generic_params(db), last),
            TypableDef::Struct(s) => (s.generic_params(db), last),
            TypableDef::Enum(e) => (e.generic_params(db), last),
            TypableDef::EnumVariant(var) => {
                // the generic args for an enum variant may be either specified
                // on the segment referring to the enum, or on the segment
                // referring to the variant. So `Option::<T>::None` and
                // `Option::None::<T>` are both allowed (though the former is
                // preferred). See also `def_ids_for_path_segments` in rustc.
                let len = path.segments.len();
                let segment = if len >= 2 && path.segments[len - 2].args_and_bindings.is_some() {
                    // Option::<T>::None
                    &path.segments[len - 2]
                } else {
                    // Option::None::<T>
                    last
                };
                (var.parent_enum(db).generic_params(db), segment)
            }
        };
        // substs_from_path
        if let Some(generic_args) = &segment.args_and_bindings {
            // if args are provided, it should be all of them, but we can't rely on that
            let param_count = def_generics.params.len();
            for arg in generic_args.args.iter().take(param_count) {
                match arg {
                    GenericArg::Type(type_ref) => {
                        let ty = Ty::from_hir(db, module, impl_block, outer_generics, type_ref);
                        substs.push(ty);
                    }
                }
            }
        }
        // add placeholders for args that were not provided
        // TODO: handle defaults
        let supplied_params = segment
            .args_and_bindings
            .as_ref()
            .map(|ga| ga.args.len())
            .unwrap_or(0);
        for _ in supplied_params..def_generics.params.len() {
            substs.push(Ty::Unknown);
        }
        assert_eq!(substs.len(), def_generics.params.len());
        Substs(substs.into())
    }

    pub fn unit() -> Self {
        Ty::Tuple(Arc::new([]))
    }

    fn walk_mut(&mut self, f: &mut impl FnMut(&mut Ty)) {
        f(self);
        match self {
            Ty::Slice(t) | Ty::Array(t) => Arc::make_mut(t).walk_mut(f),
            Ty::RawPtr(t, _) => Arc::make_mut(t).walk_mut(f),
            Ty::Ref(t, _) => Arc::make_mut(t).walk_mut(f),
            Ty::Tuple(ts) => {
                // Without an Arc::make_mut_slice, we can't avoid the clone here:
                let mut v: Vec<_> = ts.iter().cloned().collect();
                for t in &mut v {
                    t.walk_mut(f);
                }
                *ts = v.into();
            }
            Ty::FnPtr(sig) => {
                let sig_mut = Arc::make_mut(sig);
                for input in &mut sig_mut.input {
                    input.walk_mut(f);
                }
                sig_mut.output.walk_mut(f);
            }
            Ty::FnDef { substs, sig, .. } => {
                let sig_mut = Arc::make_mut(sig);
                for input in &mut sig_mut.input {
                    input.walk_mut(f);
                }
                sig_mut.output.walk_mut(f);
                // Without an Arc::make_mut_slice, we can't avoid the clone here:
                let mut v: Vec<_> = substs.0.iter().cloned().collect();
                for t in &mut v {
                    t.walk_mut(f);
                }
                substs.0 = v.into();
            }
            Ty::Adt { substs, .. } => {
                // Without an Arc::make_mut_slice, we can't avoid the clone here:
                let mut v: Vec<_> = substs.0.iter().cloned().collect();
                for t in &mut v {
                    t.walk_mut(f);
                }
                substs.0 = v.into();
            }
            _ => {}
        }
    }

    fn fold(mut self, f: &mut impl FnMut(Ty) -> Ty) -> Ty {
        self.walk_mut(&mut |ty_mut| {
            let ty = mem::replace(ty_mut, Ty::Unknown);
            *ty_mut = f(ty);
        });
        self
    }

    fn builtin_deref(&self) -> Option<Ty> {
        match self {
            Ty::Ref(t, _) => Some(Ty::clone(t)),
            Ty::RawPtr(t, _) => Some(Ty::clone(t)),
            _ => None,
        }
    }

    /// If this is a type with type parameters (an ADT or function), replaces
    /// the `Substs` for these type parameters with the given ones. (So e.g. if
    /// `self` is `Option<_>` and the substs contain `u32`, we'll have
    /// `Option<u32>` afterwards.)
    pub fn apply_substs(self, substs: Substs) -> Ty {
        match self {
            Ty::Adt { def_id, name, .. } => Ty::Adt {
                def_id,
                name,
                substs,
            },
            Ty::FnDef { def, name, sig, .. } => Ty::FnDef {
                def,
                name,
                sig,
                substs,
            },
            _ => self,
        }
    }

    /// Replaces type parameters in this type using the given `Substs`. (So e.g.
    /// if `self` is `&[T]`, where type parameter T has index 0, and the
    /// `Substs` contain `u32` at index 0, we'll have `&[u32]` afterwards.)
    pub fn subst(self, substs: &Substs) -> Ty {
        self.fold(&mut |ty| match ty {
            Ty::Param { idx, name } => {
                if (idx as usize) < substs.0.len() {
                    substs.0[idx as usize].clone()
                } else {
                    // TODO: does this indicate a bug? i.e. should we always
                    // have substs for all type params? (they might contain the
                    // params themselves again...)
                    Ty::Param { idx, name }
                }
            }
            ty => ty,
        })
    }

    /// Returns the type parameters of this type if it has some (i.e. is an ADT
    /// or function); so if `self` is `Option<u32>`, this returns the `u32`.
    fn substs(&self) -> Option<Substs> {
        match self {
            Ty::Adt { substs, .. } | Ty::FnDef { substs, .. } => Some(substs.clone()),
            _ => None,
        }
    }
}

impl fmt::Display for Ty {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        match self {
            Ty::Bool => write!(f, "bool"),
            Ty::Char => write!(f, "char"),
            Ty::Int(t) => write!(f, "{}", t.ty_to_string()),
            Ty::Float(t) => write!(f, "{}", t.ty_to_string()),
            Ty::Str => write!(f, "str"),
            Ty::Slice(t) | Ty::Array(t) => write!(f, "[{}]", t),
            Ty::RawPtr(t, m) => write!(f, "*{}{}", m.as_keyword_for_ptr(), t),
            Ty::Ref(t, m) => write!(f, "&{}{}", m.as_keyword_for_ref(), t),
            Ty::Never => write!(f, "!"),
            Ty::Tuple(ts) => {
                if ts.len() == 1 {
                    write!(f, "({},)", ts[0])
                } else {
                    join(ts.iter())
                        .surround_with("(", ")")
                        .separator(", ")
                        .to_fmt(f)
                }
            }
            Ty::FnPtr(sig) => {
                join(sig.input.iter())
                    .surround_with("fn(", ")")
                    .separator(", ")
                    .to_fmt(f)?;
                write!(f, " -> {}", sig.output)
            }
            Ty::FnDef {
                name, substs, sig, ..
            } => {
                write!(f, "fn {}", name)?;
                if substs.0.len() > 0 {
                    join(substs.0.iter())
                        .surround_with("<", ">")
                        .separator(", ")
                        .to_fmt(f)?;
                }
                join(sig.input.iter())
                    .surround_with("(", ")")
                    .separator(", ")
                    .to_fmt(f)?;
                write!(f, " -> {}", sig.output)
            }
            Ty::Adt { name, substs, .. } => {
                write!(f, "{}", name)?;
                if substs.0.len() > 0 {
                    join(substs.0.iter())
                        .surround_with("<", ">")
                        .separator(", ")
                        .to_fmt(f)?;
                }
                Ok(())
            }
            Ty::Param { name, .. } => write!(f, "{}", name),
            Ty::Unknown => write!(f, "[unknown]"),
            Ty::Infer(..) => write!(f, "_"),
        }
    }
}

// Functions returning declared types for items

/// Compute the declared type of a function. This should not need to look at the
/// function body.
fn type_for_fn(db: &impl HirDatabase, def: Function) -> Ty {
    let signature = def.signature(db);
    let module = def.module(db);
    let impl_block = def.impl_block(db);
    let generics = def.generic_params(db);
    let input = signature
        .params()
        .iter()
        .map(|tr| Ty::from_hir(db, &module, impl_block.as_ref(), &generics, tr))
        .collect::<Vec<_>>();
    let output = Ty::from_hir(
        db,
        &module,
        impl_block.as_ref(),
        &generics,
        signature.ret_type(),
    );
    let sig = Arc::new(FnSig { input, output });
    let substs = make_substs(&generics);
    let name = def.name(db);
    Ty::FnDef {
        def,
        sig,
        name,
        substs,
    }
}

fn make_substs(generics: &GenericParams) -> Substs {
    Substs(
        generics
            .params
            .iter()
            .map(|_p| Ty::Unknown)
            .collect::<Vec<_>>()
            .into(),
    )
}

fn type_for_struct(db: &impl HirDatabase, s: Struct) -> Ty {
    let generics = s.generic_params(db);
    Ty::Adt {
        def_id: s.into(),
        name: s.name(db).unwrap_or_else(Name::missing),
        substs: make_substs(&generics),
    }
}

pub(crate) fn type_for_enum(db: &impl HirDatabase, s: Enum) -> Ty {
    let generics = s.generic_params(db);
    Ty::Adt {
        def_id: s.into(),
        name: s.name(db).unwrap_or_else(Name::missing),
        substs: make_substs(&generics),
    }
}

pub(crate) fn type_for_enum_variant(db: &impl HirDatabase, ev: EnumVariant) -> Ty {
    let enum_parent = ev.parent_enum(db);

    type_for_enum(db, enum_parent)
}

#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
pub enum TypableDef {
    Function(Function),
    Struct(Struct),
    Enum(Enum),
    EnumVariant(EnumVariant),
}
impl_froms!(TypableDef: Function, Struct, Enum, EnumVariant);

impl From<ModuleDef> for Option<TypableDef> {
    fn from(def: ModuleDef) -> Option<TypableDef> {
        let res = match def {
            ModuleDef::Function(f) => f.into(),
            ModuleDef::Struct(s) => s.into(),
            ModuleDef::Enum(e) => e.into(),
            ModuleDef::EnumVariant(v) => v.into(),
            ModuleDef::Const(_)
            | ModuleDef::Static(_)
            | ModuleDef::Module(_)
            | ModuleDef::Trait(_)
            | ModuleDef::Type(_) => return None,
        };
        Some(res)
    }
}

pub(super) fn type_for_def(db: &impl HirDatabase, def: TypableDef) -> Ty {
    match def {
        TypableDef::Function(f) => type_for_fn(db, f),
        TypableDef::Struct(s) => type_for_struct(db, s),
        TypableDef::Enum(e) => type_for_enum(db, e),
        TypableDef::EnumVariant(v) => type_for_enum_variant(db, v),
    }
}

pub(super) fn type_for_field(db: &impl HirDatabase, field: StructField) -> Ty {
    let parent_def = field.parent_def(db);
    let (generics, module) = match parent_def {
        VariantDef::Struct(it) => (it.generic_params(db), it.module(db)),
        VariantDef::EnumVariant(it) => (it.parent_enum(db).generic_params(db), it.module(db)),
    };
    let var_data = parent_def.variant_data(db);
    let type_ref = &var_data.fields().unwrap()[field.id].type_ref;
    Ty::from_hir(db, &module, None, &generics, type_ref)
}

/// The result of type inference: A mapping from expressions and patterns to types.
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct InferenceResult {
    /// For each method call expr, records the function it resolves to.
    method_resolutions: FxHashMap<ExprId, Function>,
    /// For each field access expr, records the field it resolves to.
    field_resolutions: FxHashMap<ExprId, StructField>,
    type_of_expr: ArenaMap<ExprId, Ty>,
    type_of_pat: ArenaMap<PatId, Ty>,
}

impl InferenceResult {
    pub fn method_resolution(&self, expr: ExprId) -> Option<Function> {
        self.method_resolutions.get(&expr).map(|it| *it)
    }
    pub fn field_resolution(&self, expr: ExprId) -> Option<StructField> {
        self.field_resolutions.get(&expr).map(|it| *it)
    }
}

impl Index<ExprId> for InferenceResult {
    type Output = Ty;

    fn index(&self, expr: ExprId) -> &Ty {
        self.type_of_expr.get(expr).unwrap_or(&Ty::Unknown)
    }
}

impl Index<PatId> for InferenceResult {
    type Output = Ty;

    fn index(&self, pat: PatId) -> &Ty {
        self.type_of_pat.get(pat).unwrap_or(&Ty::Unknown)
    }
}

/// The inference context contains all information needed during type inference.
#[derive(Clone, Debug)]
struct InferenceContext<'a, D: HirDatabase> {
    db: &'a D,
    body: Arc<Body>,
    scopes: Arc<FnScopes>,
    module: Module,
    impl_block: Option<ImplBlock>,
    var_unification_table: InPlaceUnificationTable<TypeVarId>,
    method_resolutions: FxHashMap<ExprId, Function>,
    field_resolutions: FxHashMap<ExprId, StructField>,
    type_of_expr: ArenaMap<ExprId, Ty>,
    type_of_pat: ArenaMap<PatId, Ty>,
    /// The return type of the function being inferred.
    return_ty: Ty,
}

fn binary_op_return_ty(op: BinaryOp, rhs_ty: Ty) -> Ty {
    match op {
        BinaryOp::BooleanOr
        | BinaryOp::BooleanAnd
        | BinaryOp::EqualityTest
        | BinaryOp::LesserEqualTest
        | BinaryOp::GreaterEqualTest
        | BinaryOp::LesserTest
        | BinaryOp::GreaterTest => Ty::Bool,
        BinaryOp::Assignment
        | BinaryOp::AddAssign
        | BinaryOp::SubAssign
        | BinaryOp::DivAssign
        | BinaryOp::MulAssign
        | BinaryOp::RemAssign
        | BinaryOp::ShrAssign
        | BinaryOp::ShlAssign
        | BinaryOp::BitAndAssign
        | BinaryOp::BitOrAssign
        | BinaryOp::BitXorAssign => Ty::unit(),
        BinaryOp::Addition
        | BinaryOp::Subtraction
        | BinaryOp::Multiplication
        | BinaryOp::Division
        | BinaryOp::Remainder
        | BinaryOp::LeftShift
        | BinaryOp::RightShift
        | BinaryOp::BitwiseAnd
        | BinaryOp::BitwiseOr
        | BinaryOp::BitwiseXor => match rhs_ty {
            Ty::Int(..)
            | Ty::Float(..)
            | Ty::Infer(InferTy::IntVar(..))
            | Ty::Infer(InferTy::FloatVar(..)) => rhs_ty,
            _ => Ty::Unknown,
        },
        BinaryOp::RangeRightOpen | BinaryOp::RangeRightClosed => Ty::Unknown,
    }
}

fn binary_op_rhs_expectation(op: BinaryOp, lhs_ty: Ty) -> Ty {
    match op {
        BinaryOp::BooleanAnd | BinaryOp::BooleanOr => Ty::Bool,
        BinaryOp::Assignment | BinaryOp::EqualityTest => match lhs_ty {
            Ty::Int(..) | Ty::Float(..) | Ty::Str | Ty::Char | Ty::Bool => lhs_ty,
            _ => Ty::Unknown,
        },
        BinaryOp::LesserEqualTest
        | BinaryOp::GreaterEqualTest
        | BinaryOp::LesserTest
        | BinaryOp::GreaterTest
        | BinaryOp::AddAssign
        | BinaryOp::SubAssign
        | BinaryOp::DivAssign
        | BinaryOp::MulAssign
        | BinaryOp::RemAssign
        | BinaryOp::ShrAssign
        | BinaryOp::ShlAssign
        | BinaryOp::BitAndAssign
        | BinaryOp::BitOrAssign
        | BinaryOp::BitXorAssign
        | BinaryOp::Addition
        | BinaryOp::Subtraction
        | BinaryOp::Multiplication
        | BinaryOp::Division
        | BinaryOp::Remainder
        | BinaryOp::LeftShift
        | BinaryOp::RightShift
        | BinaryOp::BitwiseAnd
        | BinaryOp::BitwiseOr
        | BinaryOp::BitwiseXor => match lhs_ty {
            Ty::Int(..) | Ty::Float(..) => lhs_ty,
            _ => Ty::Unknown,
        },
        _ => Ty::Unknown,
    }
}

impl<'a, D: HirDatabase> InferenceContext<'a, D> {
    fn new(
        db: &'a D,
        body: Arc<Body>,
        scopes: Arc<FnScopes>,
        module: Module,
        impl_block: Option<ImplBlock>,
    ) -> Self {
        InferenceContext {
            method_resolutions: FxHashMap::default(),
            field_resolutions: FxHashMap::default(),
            type_of_expr: ArenaMap::default(),
            type_of_pat: ArenaMap::default(),
            var_unification_table: InPlaceUnificationTable::new(),
            return_ty: Ty::Unknown, // set in collect_fn_signature
            db,
            body,
            scopes,
            module,
            impl_block,
        }
    }

    fn resolve_all(mut self) -> InferenceResult {
        let mut tv_stack = Vec::new();
        let mut expr_types = mem::replace(&mut self.type_of_expr, ArenaMap::default());
        for ty in expr_types.values_mut() {
            let resolved = self.resolve_ty_completely(&mut tv_stack, mem::replace(ty, Ty::Unknown));
            *ty = resolved;
        }
        let mut pat_types = mem::replace(&mut self.type_of_pat, ArenaMap::default());
        for ty in pat_types.values_mut() {
            let resolved = self.resolve_ty_completely(&mut tv_stack, mem::replace(ty, Ty::Unknown));
            *ty = resolved;
        }
        InferenceResult {
            method_resolutions: mem::replace(&mut self.method_resolutions, Default::default()),
            field_resolutions: mem::replace(&mut self.field_resolutions, Default::default()),
            type_of_expr: expr_types,
            type_of_pat: pat_types,
        }
    }

    fn write_expr_ty(&mut self, expr: ExprId, ty: Ty) {
        self.type_of_expr.insert(expr, ty);
    }

    fn write_method_resolution(&mut self, expr: ExprId, func: Function) {
        self.method_resolutions.insert(expr, func);
    }

    fn write_field_resolution(&mut self, expr: ExprId, field: StructField) {
        self.field_resolutions.insert(expr, field);
    }

    fn write_pat_ty(&mut self, pat: PatId, ty: Ty) {
        self.type_of_pat.insert(pat, ty);
    }

    fn make_ty(&mut self, type_ref: &TypeRef) -> Ty {
        // TODO provide generics of function
        let generics = GenericParams::default();
        let ty = Ty::from_hir(
            self.db,
            &self.module,
            self.impl_block.as_ref(),
            &generics,
            type_ref,
        );
        let ty = self.insert_type_vars(ty);
        ty
    }

    fn unify_substs(&mut self, substs1: &Substs, substs2: &Substs) -> bool {
        substs1
            .0
            .iter()
            .zip(substs2.0.iter())
            .all(|(t1, t2)| self.unify(t1, t2))
    }

    fn unify(&mut self, ty1: &Ty, ty2: &Ty) -> bool {
        // try to resolve type vars first
        let ty1 = self.resolve_ty_shallow(ty1);
        let ty2 = self.resolve_ty_shallow(ty2);
        match (&*ty1, &*ty2) {
            (Ty::Unknown, ..) => true,
            (.., Ty::Unknown) => true,
            (Ty::Int(t1), Ty::Int(t2)) => match (t1, t2) {
                (primitive::UncertainIntTy::Unknown, _)
                | (_, primitive::UncertainIntTy::Unknown) => true,
                _ => t1 == t2,
            },
            (Ty::Float(t1), Ty::Float(t2)) => match (t1, t2) {
                (primitive::UncertainFloatTy::Unknown, _)
                | (_, primitive::UncertainFloatTy::Unknown) => true,
                _ => t1 == t2,
            },
            (Ty::Bool, _) | (Ty::Str, _) | (Ty::Never, _) | (Ty::Char, _) => ty1 == ty2,
            (
                Ty::Adt {
                    def_id: def_id1,
                    substs: substs1,
                    ..
                },
                Ty::Adt {
                    def_id: def_id2,
                    substs: substs2,
                    ..
                },
            ) if def_id1 == def_id2 => self.unify_substs(substs1, substs2),
            (Ty::Slice(t1), Ty::Slice(t2)) => self.unify(t1, t2),
            (Ty::RawPtr(t1, m1), Ty::RawPtr(t2, m2)) if m1 == m2 => self.unify(t1, t2),
            (Ty::Ref(t1, m1), Ty::Ref(t2, m2)) if m1 == m2 => self.unify(t1, t2),
            (Ty::FnPtr(sig1), Ty::FnPtr(sig2)) if sig1 == sig2 => true,
            (Ty::Tuple(ts1), Ty::Tuple(ts2)) if ts1.len() == ts2.len() => ts1
                .iter()
                .zip(ts2.iter())
                .all(|(t1, t2)| self.unify(t1, t2)),
            (Ty::Infer(InferTy::TypeVar(tv1)), Ty::Infer(InferTy::TypeVar(tv2)))
            | (Ty::Infer(InferTy::IntVar(tv1)), Ty::Infer(InferTy::IntVar(tv2)))
            | (Ty::Infer(InferTy::FloatVar(tv1)), Ty::Infer(InferTy::FloatVar(tv2))) => {
                // both type vars are unknown since we tried to resolve them
                self.var_unification_table.union(*tv1, *tv2);
                true
            }
            (Ty::Infer(InferTy::TypeVar(tv)), other)
            | (other, Ty::Infer(InferTy::TypeVar(tv)))
            | (Ty::Infer(InferTy::IntVar(tv)), other)
            | (other, Ty::Infer(InferTy::IntVar(tv)))
            | (Ty::Infer(InferTy::FloatVar(tv)), other)
            | (other, Ty::Infer(InferTy::FloatVar(tv))) => {
                // the type var is unknown since we tried to resolve it
                self.var_unification_table
                    .union_value(*tv, TypeVarValue::Known(other.clone()));
                true
            }
            _ => false,
        }
    }

    fn new_type_var(&mut self) -> Ty {
        Ty::Infer(InferTy::TypeVar(
            self.var_unification_table.new_key(TypeVarValue::Unknown),
        ))
    }

    fn new_integer_var(&mut self) -> Ty {
        Ty::Infer(InferTy::IntVar(
            self.var_unification_table.new_key(TypeVarValue::Unknown),
        ))
    }

    fn new_float_var(&mut self) -> Ty {
        Ty::Infer(InferTy::FloatVar(
            self.var_unification_table.new_key(TypeVarValue::Unknown),
        ))
    }

    /// Replaces Ty::Unknown by a new type var, so we can maybe still infer it.
    fn insert_type_vars_shallow(&mut self, ty: Ty) -> Ty {
        match ty {
            Ty::Unknown => self.new_type_var(),
            Ty::Int(primitive::UncertainIntTy::Unknown) => self.new_integer_var(),
            Ty::Float(primitive::UncertainFloatTy::Unknown) => self.new_float_var(),
            _ => ty,
        }
    }

    fn insert_type_vars(&mut self, ty: Ty) -> Ty {
        ty.fold(&mut |ty| self.insert_type_vars_shallow(ty))
    }

    /// Resolves the type as far as currently possible, replacing type variables
    /// by their known types. All types returned by the infer_* functions should
    /// be resolved as far as possible, i.e. contain no type variables with
    /// known type.
    fn resolve_ty_as_possible(&mut self, tv_stack: &mut Vec<TypeVarId>, ty: Ty) -> Ty {
        ty.fold(&mut |ty| match ty {
            Ty::Infer(tv) => {
                let inner = tv.to_inner();
                if tv_stack.contains(&inner) {
                    tested_by!(type_var_cycles_resolve_as_possible);
                    // recursive type
                    return tv.fallback_value();
                }
                if let Some(known_ty) = self.var_unification_table.probe_value(inner).known() {
                    // known_ty may contain other variables that are known by now
                    tv_stack.push(inner);
                    let result = self.resolve_ty_as_possible(tv_stack, known_ty.clone());
                    tv_stack.pop();
                    result
                } else {
                    ty
                }
            }
            _ => ty,
        })
    }

    /// If `ty` is a type variable with known type, returns that type;
    /// otherwise, return ty.
    fn resolve_ty_shallow<'b>(&mut self, ty: &'b Ty) -> Cow<'b, Ty> {
        match ty {
            Ty::Infer(tv) => {
                let inner = tv.to_inner();
                match self.var_unification_table.probe_value(inner).known() {
                    Some(known_ty) => {
                        // The known_ty can't be a type var itself
                        Cow::Owned(known_ty.clone())
                    }
                    _ => Cow::Borrowed(ty),
                }
            }
            _ => Cow::Borrowed(ty),
        }
    }

    /// Resolves the type completely; type variables without known type are
    /// replaced by Ty::Unknown.
    fn resolve_ty_completely(&mut self, tv_stack: &mut Vec<TypeVarId>, ty: Ty) -> Ty {
        ty.fold(&mut |ty| match ty {
            Ty::Infer(tv) => {
                let inner = tv.to_inner();
                if tv_stack.contains(&inner) {
                    tested_by!(type_var_cycles_resolve_completely);
                    // recursive type
                    return tv.fallback_value();
                }
                if let Some(known_ty) = self.var_unification_table.probe_value(inner).known() {
                    // known_ty may contain other variables that are known by now
                    tv_stack.push(inner);
                    let result = self.resolve_ty_completely(tv_stack, known_ty.clone());
                    tv_stack.pop();
                    result
                } else {
                    tv.fallback_value()
                }
            }
            _ => ty,
        })
    }

    fn infer_path_expr(&mut self, expr: ExprId, path: &Path) -> Option<Ty> {
        if path.is_ident() || path.is_self() {
            // resolve locally
            let name = path.as_ident().cloned().unwrap_or_else(Name::self_param);
            if let Some(scope_entry) = self.scopes.resolve_local_name(expr, name) {
                let ty = self.type_of_pat.get(scope_entry.pat())?;
                let ty = self.resolve_ty_as_possible(&mut vec![], ty.clone());
                return Some(ty);
            };
        };

        // resolve in module
        let typable: Option<TypableDef> = self
            .module
            .resolve_path(self.db, &path)
            .take_values()?
            .into();
        let typable = typable?;
        let ty = self.db.type_for_def(typable);
        let generics = GenericParams::default();
        let substs = Ty::substs_from_path(
            self.db,
            &self.module,
            self.impl_block.as_ref(),
            &generics,
            path,
            typable,
        );
        let ty = ty.apply_substs(substs);
        let ty = self.insert_type_vars(ty);

        Some(ty)
    }

    fn resolve_variant(&mut self, path: Option<&Path>) -> (Ty, Option<VariantDef>) {
        let path = match path {
            Some(path) => path,
            None => return (Ty::Unknown, None),
        };
        let typable: Option<TypableDef> = self
            .module
            .resolve_path(self.db, &path)
            .take_types()
            .and_then(|it| it.into());
        let def = match typable {
            None => return (Ty::Unknown, None),
            Some(it) => it,
        };
        // TODO remove the duplication between here and `Ty::from_path`?
        // TODO provide generics of function
        let generics = GenericParams::default();
        let substs = Ty::substs_from_path(
            self.db,
            &self.module,
            self.impl_block.as_ref(),
            &generics,
            path,
            def,
        );
        match def {
            TypableDef::Struct(s) => {
                let ty = type_for_struct(self.db, s);
                let ty = self.insert_type_vars(ty.apply_substs(substs));
                (ty, Some(s.into()))
            }
            TypableDef::EnumVariant(var) => {
                let ty = type_for_enum_variant(self.db, var);
                let ty = self.insert_type_vars(ty.apply_substs(substs));
                (ty, Some(var.into()))
            }
            TypableDef::Function(_) | TypableDef::Enum(_) => (Ty::Unknown, None),
        }
    }

    fn infer_tuple_struct_pat(
        &mut self,
        path: Option<&Path>,
        subpats: &[PatId],
        expected: &Ty,
    ) -> Ty {
        let (ty, def) = self.resolve_variant(path);

        self.unify(&ty, expected);

        let substs = ty.substs().unwrap_or_else(Substs::empty);

        for (i, &subpat) in subpats.iter().enumerate() {
            let expected_ty = def
                .and_then(|d| d.field(self.db, &Name::tuple_field_name(i)))
                .map_or(Ty::Unknown, |field| field.ty(self.db))
                .subst(&substs);
            self.infer_pat(subpat, &expected_ty);
        }

        ty
    }

    fn infer_struct_pat(&mut self, path: Option<&Path>, subpats: &[FieldPat], expected: &Ty) -> Ty {
        let (ty, def) = self.resolve_variant(path);

        self.unify(&ty, expected);

        let substs = ty.substs().unwrap_or_else(Substs::empty);

        for subpat in subpats {
            let matching_field = def.and_then(|it| it.field(self.db, &subpat.name));
            let expected_ty = matching_field
                .map_or(Ty::Unknown, |field| field.ty(self.db))
                .subst(&substs);
            self.infer_pat(subpat.pat, &expected_ty);
        }

        ty
    }

    fn infer_pat(&mut self, pat: PatId, expected: &Ty) -> Ty {
        let body = Arc::clone(&self.body); // avoid borrow checker problem

        let ty = match &body[pat] {
            Pat::Tuple(ref args) => {
                let expectations = match *expected {
                    Ty::Tuple(ref tuple_args) => &**tuple_args,
                    _ => &[],
                };
                let expectations_iter = expectations.into_iter().chain(repeat(&Ty::Unknown));

                let inner_tys = args
                    .iter()
                    .zip(expectations_iter)
                    .map(|(&pat, ty)| self.infer_pat(pat, ty))
                    .collect::<Vec<_>>()
                    .into();

                Ty::Tuple(inner_tys)
            }
            Pat::Ref { pat, mutability } => {
                let expectation = match *expected {
                    Ty::Ref(ref sub_ty, exp_mut) => {
                        if *mutability != exp_mut {
                            // TODO: emit type error?
                        }
                        &**sub_ty
                    }
                    _ => &Ty::Unknown,
                };
                let subty = self.infer_pat(*pat, expectation);
                Ty::Ref(subty.into(), *mutability)
            }
            Pat::TupleStruct {
                path: ref p,
                args: ref subpats,
            } => self.infer_tuple_struct_pat(p.as_ref(), subpats, expected),
            Pat::Struct {
                path: ref p,
                args: ref fields,
            } => self.infer_struct_pat(p.as_ref(), fields, expected),
            Pat::Path(path) => self
                .module
                .resolve_path(self.db, &path)
                .take_values()
                .and_then(|module_def| module_def.into())
                .map_or(Ty::Unknown, |resolved| self.db.type_for_def(resolved)),
            Pat::Bind {
                mode,
                name: _name,
                subpat,
            } => {
                let subty = if let Some(subpat) = subpat {
                    self.infer_pat(*subpat, expected)
                } else {
                    expected.clone()
                };

                match mode {
                    BindingAnnotation::Ref => Ty::Ref(subty.into(), Mutability::Shared),
                    BindingAnnotation::RefMut => Ty::Ref(subty.into(), Mutability::Mut),
                    BindingAnnotation::Mutable | BindingAnnotation::Unannotated => subty,
                }
            }
            _ => Ty::Unknown,
        };
        // use a new type variable if we got Ty::Unknown here
        let ty = self.insert_type_vars_shallow(ty);
        self.unify(&ty, expected);
        let ty = self.resolve_ty_as_possible(&mut vec![], ty);
        self.write_pat_ty(pat, ty.clone());
        ty
    }

    fn infer_expr(&mut self, tgt_expr: ExprId, expected: &Expectation) -> Ty {
        let body = Arc::clone(&self.body); // avoid borrow checker problem
        let ty = match &body[tgt_expr] {
            Expr::Missing => Ty::Unknown,
            Expr::If {
                condition,
                then_branch,
                else_branch,
            } => {
                // if let is desugared to match, so this is always simple if
                self.infer_expr(*condition, &Expectation::has_type(Ty::Bool));
                let then_ty = self.infer_expr(*then_branch, expected);
                match else_branch {
                    Some(else_branch) => {
                        self.infer_expr(*else_branch, expected);
                    }
                    None => {
                        // no else branch -> unit
                        self.unify(&then_ty, &Ty::unit()); // actually coerce
                    }
                };
                then_ty
            }
            Expr::Block { statements, tail } => self.infer_block(statements, *tail, expected),
            Expr::Loop { body } => {
                self.infer_expr(*body, &Expectation::has_type(Ty::unit()));
                // TODO handle break with value
                Ty::Never
            }
            Expr::While { condition, body } => {
                // while let is desugared to a match loop, so this is always simple while
                self.infer_expr(*condition, &Expectation::has_type(Ty::Bool));
                self.infer_expr(*body, &Expectation::has_type(Ty::unit()));
                Ty::unit()
            }
            Expr::For {
                iterable,
                body,
                pat,
            } => {
                let _iterable_ty = self.infer_expr(*iterable, &Expectation::none());
                self.infer_pat(*pat, &Ty::Unknown);
                self.infer_expr(*body, &Expectation::has_type(Ty::unit()));
                Ty::unit()
            }
            Expr::Lambda {
                body,
                args,
                arg_types,
            } => {
                assert_eq!(args.len(), arg_types.len());

                for (arg_pat, arg_type) in args.iter().zip(arg_types.iter()) {
                    let expected = if let Some(type_ref) = arg_type {
                        let ty = self.make_ty(type_ref);
                        ty
                    } else {
                        Ty::Unknown
                    };
                    self.infer_pat(*arg_pat, &expected);
                }

                // TODO: infer lambda type etc.
                let _body_ty = self.infer_expr(*body, &Expectation::none());
                Ty::Unknown
            }
            Expr::Call { callee, args } => {
                let callee_ty = self.infer_expr(*callee, &Expectation::none());
                let (param_tys, ret_ty) = match &callee_ty {
                    Ty::FnPtr(sig) => (sig.input.clone(), sig.output.clone()),
                    Ty::FnDef { substs, sig, .. } => {
                        let ret_ty = sig.output.clone().subst(&substs);
                        let param_tys = sig
                            .input
                            .iter()
                            .map(|ty| ty.clone().subst(&substs))
                            .collect();
                        (param_tys, ret_ty)
                    }
                    _ => {
                        // not callable
                        // TODO report an error?
                        (Vec::new(), Ty::Unknown)
                    }
                };
                let param_iter = param_tys.into_iter().chain(repeat(Ty::Unknown));
                for (arg, param) in args.iter().zip(param_iter) {
                    self.infer_expr(*arg, &Expectation::has_type(param));
                }
                ret_ty
            }
            Expr::MethodCall {
                receiver,
                args,
                method_name,
            } => {
                let receiver_ty = self.infer_expr(*receiver, &Expectation::none());
                let resolved = receiver_ty.clone().lookup_method(self.db, method_name);
                let method_ty = match resolved {
                    Some(func) => {
                        self.write_method_resolution(tgt_expr, func);
                        self.db.type_for_def(func.into())
                    }
                    None => Ty::Unknown,
                };
                let method_ty = self.insert_type_vars(method_ty);
                let (expected_receiver_ty, param_tys, ret_ty) = match &method_ty {
                    Ty::FnPtr(sig) => {
                        if sig.input.len() > 0 {
                            (
                                sig.input[0].clone(),
                                sig.input[1..].iter().cloned().collect(),
                                sig.output.clone(),
                            )
                        } else {
                            (Ty::Unknown, Vec::new(), sig.output.clone())
                        }
                    }
                    Ty::FnDef { substs, sig, .. } => {
                        let ret_ty = sig.output.clone().subst(&substs);

                        if sig.input.len() > 0 {
                            let mut arg_iter = sig.input.iter().map(|ty| ty.clone().subst(&substs));
                            let receiver_ty = arg_iter.next().unwrap();
                            (receiver_ty, arg_iter.collect(), ret_ty)
                        } else {
                            (Ty::Unknown, Vec::new(), ret_ty)
                        }
                    }
                    _ => (Ty::Unknown, Vec::new(), Ty::Unknown),
                };
                // TODO we would have to apply the autoderef/autoref steps here
                // to get the correct receiver type to unify...
                self.unify(&expected_receiver_ty, &receiver_ty);
                let param_iter = param_tys.into_iter().chain(repeat(Ty::Unknown));
                for (arg, param) in args.iter().zip(param_iter) {
                    self.infer_expr(*arg, &Expectation::has_type(param));
                }
                ret_ty
            }
            Expr::Match { expr, arms } => {
                let expected = if expected.ty == Ty::Unknown {
                    Expectation::has_type(self.new_type_var())
                } else {
                    expected.clone()
                };
                let input_ty = self.infer_expr(*expr, &Expectation::none());

                for arm in arms {
                    for &pat in &arm.pats {
                        let _pat_ty = self.infer_pat(pat, &input_ty);
                    }
                    // TODO type the guard
                    self.infer_expr(arm.expr, &expected);
                }

                expected.ty
            }
            Expr::Path(p) => self.infer_path_expr(tgt_expr, p).unwrap_or(Ty::Unknown),
            Expr::Continue => Ty::Never,
            Expr::Break { expr } => {
                if let Some(expr) = expr {
                    // TODO handle break with value
                    self.infer_expr(*expr, &Expectation::none());
                }
                Ty::Never
            }
            Expr::Return { expr } => {
                if let Some(expr) = expr {
                    self.infer_expr(*expr, &Expectation::has_type(self.return_ty.clone()));
                }
                Ty::Never
            }
            Expr::StructLit {
                path,
                fields,
                spread,
            } => {
                let (ty, def_id) = self.resolve_variant(path.as_ref());
                let substs = ty.substs().unwrap_or_else(Substs::empty);
                for field in fields {
                    let field_ty = def_id
                        .and_then(|it| it.field(self.db, &field.name))
                        .map_or(Ty::Unknown, |field| field.ty(self.db))
                        .subst(&substs);
                    self.infer_expr(field.expr, &Expectation::has_type(field_ty));
                }
                if let Some(expr) = spread {
                    self.infer_expr(*expr, &Expectation::has_type(ty.clone()));
                }
                ty
            }
            Expr::Field { expr, name } => {
                let receiver_ty = self.infer_expr(*expr, &Expectation::none());
                let ty = receiver_ty
                    .autoderef(self.db)
                    .find_map(|derefed_ty| match derefed_ty {
                        Ty::Tuple(fields) => {
                            let i = name.to_string().parse::<usize>().ok();
                            i.and_then(|i| fields.get(i).cloned())
                        }
                        Ty::Adt {
                            def_id: AdtDef::Struct(s),
                            ref substs,
                            ..
                        } => s.field(self.db, name).map(|field| {
                            self.write_field_resolution(tgt_expr, field);
                            field.ty(self.db).subst(substs)
                        }),
                        _ => None,
                    })
                    .unwrap_or(Ty::Unknown);
                self.insert_type_vars(ty)
            }
            Expr::Try { expr } => {
                let _inner_ty = self.infer_expr(*expr, &Expectation::none());
                Ty::Unknown
            }
            Expr::Cast { expr, type_ref } => {
                let _inner_ty = self.infer_expr(*expr, &Expectation::none());
                let cast_ty = self.make_ty(type_ref);
                // TODO check the cast...
                cast_ty
            }
            Expr::Ref { expr, mutability } => {
                // TODO pass the expectation down
                let inner_ty = self.infer_expr(*expr, &Expectation::none());
                // TODO reference coercions etc.
                Ty::Ref(Arc::new(inner_ty), *mutability)
            }
            Expr::UnaryOp { expr, op } => {
                let inner_ty = self.infer_expr(*expr, &Expectation::none());
                match op {
                    UnaryOp::Deref => {
                        if let Some(derefed_ty) = inner_ty.builtin_deref() {
                            derefed_ty
                        } else {
                            // TODO Deref::deref
                            Ty::Unknown
                        }
                    }
                    UnaryOp::Neg => {
                        match inner_ty {
                            Ty::Int(primitive::UncertainIntTy::Unknown)
                            | Ty::Int(primitive::UncertainIntTy::Signed(..))
                            | Ty::Infer(InferTy::IntVar(..))
                            | Ty::Infer(InferTy::FloatVar(..))
                            | Ty::Float(..) => inner_ty,
                            // TODO: resolve ops::Neg trait
                            _ => Ty::Unknown,
                        }
                    }
                    UnaryOp::Not => {
                        match inner_ty {
                            Ty::Bool | Ty::Int(_) | Ty::Infer(InferTy::IntVar(..)) => inner_ty,
                            // TODO: resolve ops::Not trait for inner_ty
                            _ => Ty::Unknown,
                        }
                    }
                }
            }
            Expr::BinaryOp { lhs, rhs, op } => match op {
                Some(op) => {
                    let lhs_expectation = match op {
                        BinaryOp::BooleanAnd | BinaryOp::BooleanOr => {
                            Expectation::has_type(Ty::Bool)
                        }
                        _ => Expectation::none(),
                    };
                    let lhs_ty = self.infer_expr(*lhs, &lhs_expectation);
                    // TODO: find implementation of trait corresponding to operation
                    // symbol and resolve associated `Output` type
                    let rhs_expectation = binary_op_rhs_expectation(*op, lhs_ty);
                    let rhs_ty = self.infer_expr(*rhs, &Expectation::has_type(rhs_expectation));

                    // TODO: similar as above, return ty is often associated trait type
                    binary_op_return_ty(*op, rhs_ty)
                }
                _ => Ty::Unknown,
            },
            Expr::Tuple { exprs } => {
                let mut ty_vec = Vec::with_capacity(exprs.len());
                for arg in exprs.iter() {
                    ty_vec.push(self.infer_expr(*arg, &Expectation::none()));
                }

                Ty::Tuple(Arc::from(ty_vec))
            }
            Expr::Array { exprs } => {
                let elem_ty = match &expected.ty {
                    Ty::Slice(inner) | Ty::Array(inner) => Ty::clone(&inner),
                    _ => self.new_type_var(),
                };

                for expr in exprs.iter() {
                    self.infer_expr(*expr, &Expectation::has_type(elem_ty.clone()));
                }

                Ty::Array(Arc::new(elem_ty))
            }
            Expr::Literal(lit) => match lit {
                Literal::Bool(..) => Ty::Bool,
                Literal::String(..) => Ty::Ref(Arc::new(Ty::Str), Mutability::Shared),
                Literal::ByteString(..) => {
                    let byte_type = Arc::new(Ty::Int(primitive::UncertainIntTy::Unsigned(
                        primitive::UintTy::U8,
                    )));
                    let slice_type = Arc::new(Ty::Slice(byte_type));
                    Ty::Ref(slice_type, Mutability::Shared)
                }
                Literal::Char(..) => Ty::Char,
                Literal::Int(_v, ty) => Ty::Int(*ty),
                Literal::Float(_v, ty) => Ty::Float(*ty),
            },
        };
        // use a new type variable if we got Ty::Unknown here
        let ty = self.insert_type_vars_shallow(ty);
        self.unify(&ty, &expected.ty);
        let ty = self.resolve_ty_as_possible(&mut vec![], ty);
        self.write_expr_ty(tgt_expr, ty.clone());
        ty
    }

    fn infer_block(
        &mut self,
        statements: &[Statement],
        tail: Option<ExprId>,
        expected: &Expectation,
    ) -> Ty {
        for stmt in statements {
            match stmt {
                Statement::Let {
                    pat,
                    type_ref,
                    initializer,
                } => {
                    let decl_ty = type_ref
                        .as_ref()
                        .map(|tr| self.make_ty(tr))
                        .unwrap_or(Ty::Unknown);
                    let decl_ty = self.insert_type_vars(decl_ty);
                    let ty = if let Some(expr) = initializer {
                        let expr_ty = self.infer_expr(*expr, &Expectation::has_type(decl_ty));
                        expr_ty
                    } else {
                        decl_ty
                    };

                    self.infer_pat(*pat, &ty);
                }
                Statement::Expr(expr) => {
                    self.infer_expr(*expr, &Expectation::none());
                }
            }
        }
        let ty = if let Some(expr) = tail {
            self.infer_expr(expr, expected)
        } else {
            Ty::unit()
        };
        ty
    }

    fn collect_fn_signature(&mut self, signature: &FnSignature) {
        let body = Arc::clone(&self.body); // avoid borrow checker problem
        for (type_ref, pat) in signature.params().iter().zip(body.params()) {
            let ty = self.make_ty(type_ref);

            self.infer_pat(*pat, &ty);
        }
        self.return_ty = self.make_ty(signature.ret_type());
    }

    fn infer_body(&mut self) {
        self.infer_expr(
            self.body.body_expr(),
            &Expectation::has_type(self.return_ty.clone()),
        );
    }
}

pub fn infer(db: &impl HirDatabase, func: Function) -> Arc<InferenceResult> {
    db.check_canceled();
    let body = func.body(db);
    let scopes = db.fn_scopes(func);
    let module = func.module(db);
    let impl_block = func.impl_block(db);
    let mut ctx = InferenceContext::new(db, body, scopes, module, impl_block);

    let signature = func.signature(db);
    ctx.collect_fn_signature(&signature);

    ctx.infer_body();

    Arc::new(ctx.resolve_all())
}