1 // Copyright 2020 The Go Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style
3 // license that can be found in the LICENSE file.
5 // This file implements type unification.
7 // Type unification attempts to make two types x and y structurally
8 // equivalent by determining the types for a given list of (bound)
9 // type parameters which may occur within x and y. If x and y are
10 // structurally different (say []T vs chan T), or conflicting
11 // types are determined for type parameters, unification fails.
12 // If unification succeeds, as a side-effect, the types of the
13 // bound type parameters may be determined.
15 // Unification typically requires multiple calls u.unify(x, y) to
16 // a given unifier u, with various combinations of types x and y.
17 // In each call, additional type parameter types may be determined
18 // as a side effect and recorded in u.
19 // If a call fails (returns false), unification fails.
21 // In the unification context, structural equivalence of two types
22 // ignores the difference between a defined type and its underlying
23 // type if one type is a defined type and the other one is not.
24 // It also ignores the difference between an (external, unbound)
25 // type parameter and its core type.
26 // If two types are not structurally equivalent, they cannot be Go
27 // identical types. On the other hand, if they are structurally
28 // equivalent, they may be Go identical or at least assignable, or
29 // they may be in the type set of a constraint.
30 // Whether they indeed are identical or assignable is determined
31 // upon instantiation and function argument passing.
43 // Upper limit for recursion depth. Used to catch infinite recursions
44 // due to implementation issues (e.g., see issues go.dev/issue/48619, go.dev/issue/48656).
45 unificationDepthLimit = 50
47 // Whether to panic when unificationDepthLimit is reached.
48 // If disabled, a recursion depth overflow results in a (quiet)
49 // unification failure.
50 panicAtUnificationDepthLimit = true
52 // If enableCoreTypeUnification is set, unification will consider
53 // the core types, if any, of non-local (unbound) type parameters.
54 enableCoreTypeUnification = true
56 // If enableInterfaceInference is set, type inference uses
57 // shared methods for improved type inference involving
59 enableInterfaceInference = true
61 // If traceInference is set, unification will print a trace of its operation.
62 // Interpretation of trace:
63 // x ≡ y attempt to unify types x and y
64 // p ➞ y type parameter p is set to type y (p is inferred to be y)
65 // p ⇄ q type parameters p and q match (p is inferred to be q and vice versa)
66 // x ≢ y types x and y cannot be unified
67 // [p, q, ...] ➞ [x, y, ...] mapping from type parameters to types
68 traceInference = false
71 // A unifier maintains a list of type parameters and
72 // corresponding types inferred for each type parameter.
73 // A unifier is created by calling newUnifier.
75 // handles maps each type parameter to its inferred type through
76 // an indirection *Type called (inferred type) "handle".
77 // Initially, each type parameter has its own, separate handle,
78 // with a nil (i.e., not yet inferred) type.
79 // After a type parameter P is unified with a type parameter Q,
80 // P and Q share the same handle (and thus type). This ensures
81 // that inferring the type for a given type parameter P will
82 // automatically infer the same type for all other parameters
83 // unified (joined) with P.
84 handles map[*TypeParam]*Type
85 depth int // recursion depth during unification
88 // newUnifier returns a new unifier initialized with the given type parameter
89 // and corresponding type argument lists. The type argument list may be shorter
90 // than the type parameter list, and it may contain nil types. Matching type
91 // parameters and arguments must have the same index.
92 func newUnifier(tparams []*TypeParam, targs []Type) *unifier {
93 assert(len(tparams) >= len(targs))
94 handles := make(map[*TypeParam]*Type, len(tparams))
95 // Allocate all handles up-front: in a correct program, all type parameters
96 // must be resolved and thus eventually will get a handle.
97 // Also, sharing of handles caused by unified type parameters is rare and
98 // so it's ok to not optimize for that case (and delay handle allocation).
99 for i, x := range tparams {
106 return &unifier{handles, 0}
109 // unifyMode controls the behavior of the unifier.
113 // If assign is set, we are unifying types involved in an assignment:
114 // they may match inexactly at the top, but element types must match
116 assign unifyMode = 1 << iota
118 // If exact is set, types unify if they are identical (or can be
119 // made identical with suitable arguments for type parameters).
120 // Otherwise, a named type and a type literal unify if their
121 // underlying types unify, channel directions are ignored, and
122 // if there is an interface, the other type must implement the
127 func (m unifyMode) String() string {
136 return "assign, exact"
138 return fmt.Sprintf("mode %d", m)
141 // unify attempts to unify x and y and reports whether it succeeded.
142 // As a side-effect, types may be inferred for type parameters.
143 // The mode parameter controls how types are compared.
144 func (u *unifier) unify(x, y Type, mode unifyMode) bool {
145 return u.nify(x, y, mode, nil)
148 func (u *unifier) tracef(format string, args ...interface{}) {
149 fmt.Println(strings.Repeat(". ", u.depth) + sprintf(nil, true, format, args...))
152 // String returns a string representation of the current mapping
153 // from type parameters to types.
154 func (u *unifier) String() string {
155 // sort type parameters for reproducible strings
156 tparams := make(typeParamsById, len(u.handles))
158 for tpar := range u.handles {
165 w := newTypeWriter(&buf, nil)
167 for i, x := range tparams {
179 type typeParamsById []*TypeParam
181 func (s typeParamsById) Len() int { return len(s) }
182 func (s typeParamsById) Less(i, j int) bool { return s[i].id < s[j].id }
183 func (s typeParamsById) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
185 // join unifies the given type parameters x and y.
186 // If both type parameters already have a type associated with them
187 // and they are not joined, join fails and returns false.
188 func (u *unifier) join(x, y *TypeParam) bool {
190 u.tracef("%s ⇄ %s", x, y)
192 switch hx, hy := u.handles[x], u.handles[y]; {
194 // Both type parameters already share the same handle. Nothing to do.
195 case *hx != nil && *hy != nil:
196 // Both type parameters have (possibly different) inferred types. Cannot join.
199 // Only type parameter x has an inferred type. Use handle of x.
201 // This case is treated like the default case.
203 // // Only type parameter y has an inferred type. Use handle of y.
204 // u.setHandle(x, hy)
206 // Neither type parameter has an inferred type. Use handle of y.
212 // asTypeParam returns x.(*TypeParam) if x is a type parameter recorded with u.
213 // Otherwise, the result is nil.
214 func (u *unifier) asTypeParam(x Type) *TypeParam {
215 if x, _ := x.(*TypeParam); x != nil {
216 if _, found := u.handles[x]; found {
223 // setHandle sets the handle for type parameter x
224 // (and all its joined type parameters) to h.
225 func (u *unifier) setHandle(x *TypeParam, h *Type) {
228 for y, hy := range u.handles {
235 // at returns the (possibly nil) type for type parameter x.
236 func (u *unifier) at(x *TypeParam) Type {
240 // set sets the type t for type parameter x;
241 // t must not be nil.
242 func (u *unifier) set(x *TypeParam, t Type) {
245 u.tracef("%s ➞ %s", x, t)
250 // unknowns returns the number of type parameters for which no type has been set yet.
251 func (u *unifier) unknowns() int {
253 for _, h := range u.handles {
261 // inferred returns the list of inferred types for the given type parameter list.
262 // The result is never nil and has the same length as tparams; result types that
263 // could not be inferred are nil. Corresponding type parameters and result types
264 // have identical indices.
265 func (u *unifier) inferred(tparams []*TypeParam) []Type {
266 list := make([]Type, len(tparams))
267 for i, x := range tparams {
273 // asInterface returns the underlying type of x as an interface if
274 // it is a non-type parameter interface. Otherwise it returns nil.
275 func asInterface(x Type) (i *Interface) {
276 if _, ok := x.(*TypeParam); !ok {
277 i, _ = under(x).(*Interface)
282 // nify implements the core unification algorithm which is an
283 // adapted version of Checker.identical. For changes to that
284 // code the corresponding changes should be made here.
285 // Must not be called directly from outside the unifier.
286 func (u *unifier) nify(x, y Type, mode unifyMode, p *ifacePair) (result bool) {
289 u.tracef("%s ≡ %s\t// %s", x, y, mode)
292 if traceInference && !result {
293 u.tracef("%s ≢ %s", x, y)
298 // nothing to do if x == y
303 // Stop gap for cases where unification fails.
304 if u.depth > unificationDepthLimit {
306 u.tracef("depth %d >= %d", u.depth, unificationDepthLimit)
308 if panicAtUnificationDepthLimit {
309 panic("unification reached recursion depth limit")
314 // Unification is symmetric, so we can swap the operands.
315 // Ensure that if we have at least one
316 // - defined type, make sure one is in y
317 // - type parameter recorded with u, make sure one is in x
318 if _, ok := x.(*Named); ok || u.asTypeParam(y) != nil {
320 u.tracef("%s ≡ %s\t// swap", y, x)
325 // Unification will fail if we match a defined type against a type literal.
326 // If we are matching types in an assignment, at the top-level, types with
327 // the same type structure are permitted as long as at least one of them
328 // is not a defined type. To accommodate for that possibility, we continue
329 // unification with the underlying type of a defined type if the other type
330 // is a type literal. This is controlled by the exact unification mode.
331 // We also continue if the other type is a basic type because basic types
332 // are valid underlying types and may appear as core types of type constraints.
333 // If we exclude them, inferred defined types for type parameters may not
334 // match against the core types of their constraints (even though they might
335 // correctly match against some of the types in the constraint's type set).
336 // Finally, if unification (incorrectly) succeeds by matching the underlying
337 // type of a defined type against a basic type (because we include basic types
338 // as type literals here), and if that leads to an incorrectly inferred type,
339 // we will fail at function instantiation or argument assignment time.
341 // If we have at least one defined type, there is one in y.
342 if ny, _ := y.(*Named); mode&exact == 0 && ny != nil && isTypeLit(x) && !(enableInterfaceInference && IsInterface(x)) {
344 u.tracef("%s ≡ under %s", x, ny)
347 // Per the spec, a defined type cannot have an underlying type
348 // that is a type parameter.
349 assert(!isTypeParam(y))
350 // x and y may be identical now
356 // Cases where at least one of x or y is a type parameter recorded with u.
357 // If we have at least one type parameter, there is one in x.
358 // If we have exactly one type parameter, because it is in x,
359 // isTypeLit(x) is false and y was not changed above. In other
360 // words, if y was a defined type, it is still a defined type
361 // (relevant for the logic below).
362 switch px, py := u.asTypeParam(x), u.asTypeParam(y); {
363 case px != nil && py != nil:
364 // both x and y are type parameters
368 // both x and y have an inferred type - they must match
369 return u.nify(u.at(px), u.at(py), mode, p)
372 // x is a type parameter, y is not
373 if x := u.at(px); x != nil {
374 // x has an inferred type which must match y
375 if u.nify(x, y, mode, p) {
376 // We have a match, possibly through underlying types.
381 // If we have two interfaces, what to do depends on
382 // whether they are named and their method sets.
383 if xi != nil && yi != nil {
384 // Both types are interfaces.
385 // If both types are defined types, they must be identical
386 // because unification doesn't know which type has the "right" name.
388 return Identical(x, y)
390 // In all other cases, the method sets must match.
391 // The types unified so we know that corresponding methods
392 // match and we can simply compare the number of methods.
393 // TODO(gri) We may be able to relax this rule and select
394 // the more general interface. But if one of them is a defined
395 // type, it's not clear how to choose and whether we introduce
396 // an order dependency or not. Requiring the same method set
398 if len(xi.typeSet().methods) != len(yi.typeSet().methods) {
401 } else if xi != nil || yi != nil {
402 // One but not both of them are interfaces.
403 // In this case, either x or y could be viable matches for the corresponding
404 // type parameter, which means choosing either introduces an order dependence.
405 // Therefore, we must fail unification (go.dev/issue/60933).
408 // If y is a defined type, make sure we record that type
409 // for type parameter x, which may have until now only
410 // recorded an underlying type (go.dev/issue/43056).
411 // Either both types are interfaces, or neither type is.
412 // If both are interfaces, they have the same methods.
414 // Note: Changing the recorded type for a type parameter to
415 // a defined type is only ok when unification is inexact.
416 // But in exact unification, if we have a match, x and y must
417 // be identical, so changing the recorded type for x is a no-op.
425 // otherwise, infer type from y
430 // x != y if we get here
433 // Type elements (array, slice, etc. elements) use emode for unification.
434 // Element types must match exactly if the types are used in an assignment.
436 if mode&assign != 0 {
440 // If EnableInterfaceInference is set and we don't require exact unification,
441 // if both types are interfaces, one interface must have a subset of the
442 // methods of the other and corresponding method signatures must unify.
443 // If only one type is an interface, all its methods must be present in the
444 // other type and corresponding method signatures must unify.
445 if enableInterfaceInference && mode&exact == 0 {
446 // One or both interfaces may be defined types.
447 // Look under the name, but not under type parameters (go.dev/issue/60564).
450 // If we have two interfaces, check the type terms for equivalence,
451 // and unify common methods if possible.
452 if xi != nil && yi != nil {
455 if xset.comparable != yset.comparable {
458 // For now we require terms to be equal.
459 // We should be able to relax this as well, eventually.
460 if !xset.terms.equal(yset.terms) {
463 // Interface types are the only types where cycles can occur
464 // that are not "terminated" via named types; and such cycles
465 // can only be created via method parameter types that are
466 // anonymous interfaces (directly or indirectly) embedding
467 // the current interface. Example:
469 // type T interface {
473 // If two such (differently named) interfaces are compared,
474 // endless recursion occurs if the cycle is not detected.
476 // If x and y were compared before, they must be equal
477 // (if they were not, the recursion would have stopped);
478 // search the ifacePair stack for the same pair.
480 // This is a quadratic algorithm, but in practice these stacks
481 // are extremely short (bounded by the nesting depth of interface
482 // type declarations that recur via parameter types, an extremely
483 // rare occurrence). An alternative implementation might use a
484 // "visited" map, but that is probably less efficient overall.
485 q := &ifacePair{xi, yi, p}
488 return true // same pair was compared before
492 // The method set of x must be a subset of the method set
493 // of y or vice versa, and the common methods must unify.
494 xmethods := xset.methods
495 ymethods := yset.methods
496 // The smaller method set must be the subset, if it exists.
497 if len(xmethods) > len(ymethods) {
498 xmethods, ymethods = ymethods, xmethods
500 // len(xmethods) <= len(ymethods)
501 // Collect the ymethods in a map for quick lookup.
502 ymap := make(map[string]*Func, len(ymethods))
503 for _, ym := range ymethods {
506 // All xmethods must exist in ymethods and corresponding signatures must unify.
507 for _, xm := range xmethods {
508 if ym := ymap[xm.Id()]; ym == nil || !u.nify(xm.typ, ym.typ, emode, p) {
515 // We don't have two interfaces. If we have one, make sure it's in xi.
521 // If we have one interface, at a minimum each of the interface methods
522 // must be implemented and thus unify with a corresponding method from
523 // the non-interface type, otherwise unification fails.
525 // All xi methods must exist in y and corresponding signatures must unify.
526 xmethods := xi.typeSet().methods
527 for _, xm := range xmethods {
528 obj, _, _ := LookupFieldOrMethod(y, false, xm.pkg, xm.name)
529 if ym, _ := obj.(*Func); ym == nil || !u.nify(xm.typ, ym.typ, emode, p) {
537 // Unless we have exact unification, neither x nor y are interfaces now.
538 // Except for unbound type parameters (see below), x and y must be structurally
539 // equivalent to unify.
541 // If we get here and x or y is a type parameter, they are unbound
542 // (not recorded with the unifier).
543 // Ensure that if we have at least one type parameter, it is in x
544 // (the earlier swap checks for _recorded_ type parameters only).
545 // This ensures that the switch switches on the type parameter.
547 // TODO(gri) Factor out type parameter handling from the switch.
550 u.tracef("%s ≡ %s\t// swap", y, x)
555 switch x := x.(type) {
557 // Basic types are singletons except for the rune and byte
558 // aliases, thus we cannot solely rely on the x == y check
559 // above. See also comment in TypeName.IsAlias.
560 if y, ok := y.(*Basic); ok {
561 return x.kind == y.kind
565 // Two array types unify if they have the same array length
566 // and their element types unify.
567 if y, ok := y.(*Array); ok {
568 // If one or both array lengths are unknown (< 0) due to some error,
569 // assume they are the same to avoid spurious follow-on errors.
570 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, emode, p)
574 // Two slice types unify if their element types unify.
575 if y, ok := y.(*Slice); ok {
576 return u.nify(x.elem, y.elem, emode, p)
580 // Two struct types unify if they have the same sequence of fields,
581 // and if corresponding fields have the same names, their (field) types unify,
582 // and they have identical tags. Two embedded fields are considered to have the same
583 // name. Lower-case field names from different packages are always different.
584 if y, ok := y.(*Struct); ok {
585 if x.NumFields() == y.NumFields() {
586 for i, f := range x.fields {
588 if f.embedded != g.embedded ||
589 x.Tag(i) != y.Tag(i) ||
590 !f.sameId(g.pkg, g.name) ||
591 !u.nify(f.typ, g.typ, emode, p) {
600 // Two pointer types unify if their base types unify.
601 if y, ok := y.(*Pointer); ok {
602 return u.nify(x.base, y.base, emode, p)
606 // Two tuples types unify if they have the same number of elements
607 // and the types of corresponding elements unify.
608 if y, ok := y.(*Tuple); ok {
609 if x.Len() == y.Len() {
611 for i, v := range x.vars {
613 if !u.nify(v.typ, w.typ, mode, p) {
623 // Two function types unify if they have the same number of parameters
624 // and result values, corresponding parameter and result types unify,
625 // and either both functions are variadic or neither is.
626 // Parameter and result names are not required to match.
627 // TODO(gri) handle type parameters or document why we can ignore them.
628 if y, ok := y.(*Signature); ok {
629 return x.variadic == y.variadic &&
630 u.nify(x.params, y.params, emode, p) &&
631 u.nify(x.results, y.results, emode, p)
635 assert(!enableInterfaceInference || mode&exact != 0) // handled before this switch
637 // Two interface types unify if they have the same set of methods with
638 // the same names, and corresponding function types unify.
639 // Lower-case method names from different packages are always different.
640 // The order of the methods is irrelevant.
641 if y, ok := y.(*Interface); ok {
644 if xset.comparable != yset.comparable {
647 if !xset.terms.equal(yset.terms) {
652 if len(a) == len(b) {
653 // Interface types are the only types where cycles can occur
654 // that are not "terminated" via named types; and such cycles
655 // can only be created via method parameter types that are
656 // anonymous interfaces (directly or indirectly) embedding
657 // the current interface. Example:
659 // type T interface {
663 // If two such (differently named) interfaces are compared,
664 // endless recursion occurs if the cycle is not detected.
666 // If x and y were compared before, they must be equal
667 // (if they were not, the recursion would have stopped);
668 // search the ifacePair stack for the same pair.
670 // This is a quadratic algorithm, but in practice these stacks
671 // are extremely short (bounded by the nesting depth of interface
672 // type declarations that recur via parameter types, an extremely
673 // rare occurrence). An alternative implementation might use a
674 // "visited" map, but that is probably less efficient overall.
675 q := &ifacePair{x, y, p}
678 return true // same pair was compared before
683 assertSortedMethods(a)
684 assertSortedMethods(b)
686 for i, f := range a {
688 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, emode, q) {
697 // Two map types unify if their key and value types unify.
698 if y, ok := y.(*Map); ok {
699 return u.nify(x.key, y.key, emode, p) && u.nify(x.elem, y.elem, emode, p)
703 // Two channel types unify if their value types unify
704 // and if they have the same direction.
705 // The channel direction is ignored for inexact unification.
706 if y, ok := y.(*Chan); ok {
707 return (mode&exact == 0 || x.dir == y.dir) && u.nify(x.elem, y.elem, emode, p)
711 // Two named types unify if their type names originate in the same type declaration.
712 // If they are instantiated, their type argument lists must unify.
713 if y, ok := y.(*Named); ok {
714 // Check type arguments before origins so they unify
715 // even if the origins don't match; for better error
716 // messages (see go.dev/issue/53692).
717 xargs := x.TypeArgs().list()
718 yargs := y.TypeArgs().list()
719 if len(xargs) != len(yargs) {
722 for i, xarg := range xargs {
723 if !u.nify(xarg, yargs[i], mode, p) {
727 return identicalOrigin(x, y)
731 // x must be an unbound type parameter (see comment above).
733 assert(u.asTypeParam(x) == nil)
735 // By definition, a valid type argument must be in the type set of
736 // the respective type constraint. Therefore, the type argument's
737 // underlying type must be in the set of underlying types of that
738 // constraint. If there is a single such underlying type, it's the
739 // constraint's core type. It must match the type argument's under-
740 // lying type, irrespective of whether the actual type argument,
741 // which may be a defined type, is actually in the type set (that
742 // will be determined at instantiation time).
743 // Thus, if we have the core type of an unbound type parameter,
744 // we know the structure of the possible types satisfying such
745 // parameters. Use that core type for further unification
746 // (see go.dev/issue/50755 for a test case).
747 if enableCoreTypeUnification {
748 // Because the core type is always an underlying type,
749 // unification will take care of matching against a
750 // defined or literal type automatically.
751 // If y is also an unbound type parameter, we will end
752 // up here again with x and y swapped, so we don't
753 // need to take care of that case separately.
754 if cx := coreType(x); cx != nil {
756 u.tracef("core %s ≡ %s", x, y)
758 // If y is a defined type, it may not match against cx which
759 // is an underlying type (incl. int, string, etc.). Use assign
760 // mode here so that the unifier automatically takes under(y)
762 return u.nify(cx, y, assign, p)
765 // x != y and there's nothing to do
768 // avoid a crash in case of nil type
771 panic(sprintf(nil, true, "u.nify(%s, %s, %d)", x, y, mode))