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 traceInference is set, unification will print a trace of its operation.
57 // Interpretation of trace:
58 // x ≡ y attempt to unify types x and y
59 // p ➞ y type parameter p is set to type y (p is inferred to be y)
60 // p ⇄ q type parameters p and q match (p is inferred to be q and vice versa)
61 // x ≢ y types x and y cannot be unified
62 // [p, q, ...] ➞ [x, y, ...] mapping from type parameters to types
63 traceInference = false
66 // A unifier maintains a list of type parameters and
67 // corresponding types inferred for each type parameter.
68 // A unifier is created by calling newUnifier.
70 // handles maps each type parameter to its inferred type through
71 // an indirection *Type called (inferred type) "handle".
72 // Initially, each type parameter has its own, separate handle,
73 // with a nil (i.e., not yet inferred) type.
74 // After a type parameter P is unified with a type parameter Q,
75 // P and Q share the same handle (and thus type). This ensures
76 // that inferring the type for a given type parameter P will
77 // automatically infer the same type for all other parameters
78 // unified (joined) with P.
79 handles map[*TypeParam]*Type
80 depth int // recursion depth during unification
81 enableInterfaceInference bool // use shared methods for better inference
84 // newUnifier returns a new unifier initialized with the given type parameter
85 // and corresponding type argument lists. The type argument list may be shorter
86 // than the type parameter list, and it may contain nil types. Matching type
87 // parameters and arguments must have the same index.
88 func newUnifier(tparams []*TypeParam, targs []Type, enableInterfaceInference bool) *unifier {
89 assert(len(tparams) >= len(targs))
90 handles := make(map[*TypeParam]*Type, len(tparams))
91 // Allocate all handles up-front: in a correct program, all type parameters
92 // must be resolved and thus eventually will get a handle.
93 // Also, sharing of handles caused by unified type parameters is rare and
94 // so it's ok to not optimize for that case (and delay handle allocation).
95 for i, x := range tparams {
102 return &unifier{handles, 0, enableInterfaceInference}
105 // unifyMode controls the behavior of the unifier.
109 // If assign is set, we are unifying types involved in an assignment:
110 // they may match inexactly at the top, but element types must match
112 assign unifyMode = 1 << iota
114 // If exact is set, types unify if they are identical (or can be
115 // made identical with suitable arguments for type parameters).
116 // Otherwise, a named type and a type literal unify if their
117 // underlying types unify, channel directions are ignored, and
118 // if there is an interface, the other type must implement the
123 func (m unifyMode) String() string {
132 return "assign, exact"
134 return fmt.Sprintf("mode %d", m)
137 // unify attempts to unify x and y and reports whether it succeeded.
138 // As a side-effect, types may be inferred for type parameters.
139 // The mode parameter controls how types are compared.
140 func (u *unifier) unify(x, y Type, mode unifyMode) bool {
141 return u.nify(x, y, mode, nil)
144 func (u *unifier) tracef(format string, args ...interface{}) {
145 fmt.Println(strings.Repeat(". ", u.depth) + sprintf(nil, true, format, args...))
148 // String returns a string representation of the current mapping
149 // from type parameters to types.
150 func (u *unifier) String() string {
151 // sort type parameters for reproducible strings
152 tparams := make(typeParamsById, len(u.handles))
154 for tpar := range u.handles {
161 w := newTypeWriter(&buf, nil)
163 for i, x := range tparams {
175 type typeParamsById []*TypeParam
177 func (s typeParamsById) Len() int { return len(s) }
178 func (s typeParamsById) Less(i, j int) bool { return s[i].id < s[j].id }
179 func (s typeParamsById) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
181 // join unifies the given type parameters x and y.
182 // If both type parameters already have a type associated with them
183 // and they are not joined, join fails and returns false.
184 func (u *unifier) join(x, y *TypeParam) bool {
186 u.tracef("%s ⇄ %s", x, y)
188 switch hx, hy := u.handles[x], u.handles[y]; {
190 // Both type parameters already share the same handle. Nothing to do.
191 case *hx != nil && *hy != nil:
192 // Both type parameters have (possibly different) inferred types. Cannot join.
195 // Only type parameter x has an inferred type. Use handle of x.
197 // This case is treated like the default case.
199 // // Only type parameter y has an inferred type. Use handle of y.
200 // u.setHandle(x, hy)
202 // Neither type parameter has an inferred type. Use handle of y.
208 // asTypeParam returns x.(*TypeParam) if x is a type parameter recorded with u.
209 // Otherwise, the result is nil.
210 func (u *unifier) asTypeParam(x Type) *TypeParam {
211 if x, _ := x.(*TypeParam); x != nil {
212 if _, found := u.handles[x]; found {
219 // setHandle sets the handle for type parameter x
220 // (and all its joined type parameters) to h.
221 func (u *unifier) setHandle(x *TypeParam, h *Type) {
224 for y, hy := range u.handles {
231 // at returns the (possibly nil) type for type parameter x.
232 func (u *unifier) at(x *TypeParam) Type {
236 // set sets the type t for type parameter x;
237 // t must not be nil.
238 func (u *unifier) set(x *TypeParam, t Type) {
241 u.tracef("%s ➞ %s", x, t)
246 // unknowns returns the number of type parameters for which no type has been set yet.
247 func (u *unifier) unknowns() int {
249 for _, h := range u.handles {
257 // inferred returns the list of inferred types for the given type parameter list.
258 // The result is never nil and has the same length as tparams; result types that
259 // could not be inferred are nil. Corresponding type parameters and result types
260 // have identical indices.
261 func (u *unifier) inferred(tparams []*TypeParam) []Type {
262 list := make([]Type, len(tparams))
263 for i, x := range tparams {
269 // asInterface returns the underlying type of x as an interface if
270 // it is a non-type parameter interface. Otherwise it returns nil.
271 func asInterface(x Type) (i *Interface) {
272 if _, ok := x.(*TypeParam); !ok {
273 i, _ = under(x).(*Interface)
278 // nify implements the core unification algorithm which is an
279 // adapted version of Checker.identical. For changes to that
280 // code the corresponding changes should be made here.
281 // Must not be called directly from outside the unifier.
282 func (u *unifier) nify(x, y Type, mode unifyMode, p *ifacePair) (result bool) {
285 u.tracef("%s ≡ %s\t// %s", x, y, mode)
288 if traceInference && !result {
289 u.tracef("%s ≢ %s", x, y)
294 // nothing to do if x == y
299 // Stop gap for cases where unification fails.
300 if u.depth > unificationDepthLimit {
302 u.tracef("depth %d >= %d", u.depth, unificationDepthLimit)
304 if panicAtUnificationDepthLimit {
305 panic("unification reached recursion depth limit")
310 // Unification is symmetric, so we can swap the operands.
311 // Ensure that if we have at least one
312 // - defined type, make sure one is in y
313 // - type parameter recorded with u, make sure one is in x
314 if asNamed(x) != nil || u.asTypeParam(y) != nil {
316 u.tracef("%s ≡ %s\t// swap", y, x)
321 // Unification will fail if we match a defined type against a type literal.
322 // If we are matching types in an assignment, at the top-level, types with
323 // the same type structure are permitted as long as at least one of them
324 // is not a defined type. To accommodate for that possibility, we continue
325 // unification with the underlying type of a defined type if the other type
326 // is a type literal. This is controlled by the exact unification mode.
327 // We also continue if the other type is a basic type because basic types
328 // are valid underlying types and may appear as core types of type constraints.
329 // If we exclude them, inferred defined types for type parameters may not
330 // match against the core types of their constraints (even though they might
331 // correctly match against some of the types in the constraint's type set).
332 // Finally, if unification (incorrectly) succeeds by matching the underlying
333 // type of a defined type against a basic type (because we include basic types
334 // as type literals here), and if that leads to an incorrectly inferred type,
335 // we will fail at function instantiation or argument assignment time.
337 // If we have at least one defined type, there is one in y.
338 if ny := asNamed(y); mode&exact == 0 && ny != nil && isTypeLit(x) && !(u.enableInterfaceInference && IsInterface(x)) {
340 u.tracef("%s ≡ under %s", x, ny)
343 // Per the spec, a defined type cannot have an underlying type
344 // that is a type parameter.
345 assert(!isTypeParam(y))
346 // x and y may be identical now
352 // Cases where at least one of x or y is a type parameter recorded with u.
353 // If we have at least one type parameter, there is one in x.
354 // If we have exactly one type parameter, because it is in x,
355 // isTypeLit(x) is false and y was not changed above. In other
356 // words, if y was a defined type, it is still a defined type
357 // (relevant for the logic below).
358 switch px, py := u.asTypeParam(x), u.asTypeParam(y); {
359 case px != nil && py != nil:
360 // both x and y are type parameters
364 // both x and y have an inferred type - they must match
365 return u.nify(u.at(px), u.at(py), mode, p)
368 // x is a type parameter, y is not
369 if x := u.at(px); x != nil {
370 // x has an inferred type which must match y
371 if u.nify(x, y, mode, p) {
372 // We have a match, possibly through underlying types.
375 xn := asNamed(x) != nil
376 yn := asNamed(y) != nil
377 // If we have two interfaces, what to do depends on
378 // whether they are named and their method sets.
379 if xi != nil && yi != nil {
380 // Both types are interfaces.
381 // If both types are defined types, they must be identical
382 // because unification doesn't know which type has the "right" name.
384 return Identical(x, y)
386 // In all other cases, the method sets must match.
387 // The types unified so we know that corresponding methods
388 // match and we can simply compare the number of methods.
389 // TODO(gri) We may be able to relax this rule and select
390 // the more general interface. But if one of them is a defined
391 // type, it's not clear how to choose and whether we introduce
392 // an order dependency or not. Requiring the same method set
394 if len(xi.typeSet().methods) != len(yi.typeSet().methods) {
397 } else if xi != nil || yi != nil {
398 // One but not both of them are interfaces.
399 // In this case, either x or y could be viable matches for the corresponding
400 // type parameter, which means choosing either introduces an order dependence.
401 // Therefore, we must fail unification (go.dev/issue/60933).
404 // If we have inexact unification and one of x or y is a defined type, select the
405 // defined type. This ensures that in a series of types, all matching against the
406 // same type parameter, we infer a defined type if there is one, independent of
407 // order. Type inference or assignment may fail, which is ok.
408 // Selecting a defined type, if any, ensures that we don't lose the type name;
409 // and since we have inexact unification, a value of equally named or matching
410 // undefined type remains assignable (go.dev/issue/43056).
412 // Similarly, if we have inexact unification and there are no defined types but
413 // channel types, select a directed channel, if any. This ensures that in a series
414 // of unnamed types, all matching against the same type parameter, we infer the
415 // directed channel if there is one, independent of order.
416 // Selecting a directional channel, if any, ensures that a value of another
417 // inexactly unifying channel type remains assignable (go.dev/issue/62157).
419 // If we have multiple defined channel types, they are either identical or we
420 // have assignment conflicts, so we can ignore directionality in this case.
422 // If we have defined and literal channel types, a defined type wins to avoid
423 // order dependencies.
427 // x is a defined type: nothing to do.
429 // x is not a defined type and y is a defined type: select y.
432 // Neither x nor y are defined types.
433 if yc, _ := under(y).(*Chan); yc != nil && yc.dir != SendRecv {
434 // y is a directed channel type: select y.
443 // otherwise, infer type from y
448 // x != y if we get here
451 // If u.EnableInterfaceInference is set and we don't require exact unification,
452 // if both types are interfaces, one interface must have a subset of the
453 // methods of the other and corresponding method signatures must unify.
454 // If only one type is an interface, all its methods must be present in the
455 // other type and corresponding method signatures must unify.
456 if u.enableInterfaceInference && mode&exact == 0 {
457 // One or both interfaces may be defined types.
458 // Look under the name, but not under type parameters (go.dev/issue/60564).
461 // If we have two interfaces, check the type terms for equivalence,
462 // and unify common methods if possible.
463 if xi != nil && yi != nil {
466 if xset.comparable != yset.comparable {
469 // For now we require terms to be equal.
470 // We should be able to relax this as well, eventually.
471 if !xset.terms.equal(yset.terms) {
474 // Interface types are the only types where cycles can occur
475 // that are not "terminated" via named types; and such cycles
476 // can only be created via method parameter types that are
477 // anonymous interfaces (directly or indirectly) embedding
478 // the current interface. Example:
480 // type T interface {
484 // If two such (differently named) interfaces are compared,
485 // endless recursion occurs if the cycle is not detected.
487 // If x and y were compared before, they must be equal
488 // (if they were not, the recursion would have stopped);
489 // search the ifacePair stack for the same pair.
491 // This is a quadratic algorithm, but in practice these stacks
492 // are extremely short (bounded by the nesting depth of interface
493 // type declarations that recur via parameter types, an extremely
494 // rare occurrence). An alternative implementation might use a
495 // "visited" map, but that is probably less efficient overall.
496 q := &ifacePair{xi, yi, p}
499 return true // same pair was compared before
503 // The method set of x must be a subset of the method set
504 // of y or vice versa, and the common methods must unify.
505 xmethods := xset.methods
506 ymethods := yset.methods
507 // The smaller method set must be the subset, if it exists.
508 if len(xmethods) > len(ymethods) {
509 xmethods, ymethods = ymethods, xmethods
511 // len(xmethods) <= len(ymethods)
512 // Collect the ymethods in a map for quick lookup.
513 ymap := make(map[string]*Func, len(ymethods))
514 for _, ym := range ymethods {
517 // All xmethods must exist in ymethods and corresponding signatures must unify.
518 for _, xm := range xmethods {
519 if ym := ymap[xm.Id()]; ym == nil || !u.nify(xm.typ, ym.typ, exact, p) {
526 // We don't have two interfaces. If we have one, make sure it's in xi.
532 // If we have one interface, at a minimum each of the interface methods
533 // must be implemented and thus unify with a corresponding method from
534 // the non-interface type, otherwise unification fails.
536 // All xi methods must exist in y and corresponding signatures must unify.
537 xmethods := xi.typeSet().methods
538 for _, xm := range xmethods {
539 obj, _, _ := LookupFieldOrMethod(y, false, xm.pkg, xm.name)
540 if ym, _ := obj.(*Func); ym == nil || !u.nify(xm.typ, ym.typ, exact, p) {
548 // Unless we have exact unification, neither x nor y are interfaces now.
549 // Except for unbound type parameters (see below), x and y must be structurally
550 // equivalent to unify.
552 // If we get here and x or y is a type parameter, they are unbound
553 // (not recorded with the unifier).
554 // Ensure that if we have at least one type parameter, it is in x
555 // (the earlier swap checks for _recorded_ type parameters only).
556 // This ensures that the switch switches on the type parameter.
558 // TODO(gri) Factor out type parameter handling from the switch.
561 u.tracef("%s ≡ %s\t// swap", y, x)
566 // Type elements (array, slice, etc. elements) use emode for unification.
567 // Element types must match exactly if the types are used in an assignment.
569 if mode&assign != 0 {
573 switch x := x.(type) {
575 // Basic types are singletons except for the rune and byte
576 // aliases, thus we cannot solely rely on the x == y check
577 // above. See also comment in TypeName.IsAlias.
578 if y, ok := y.(*Basic); ok {
579 return x.kind == y.kind
583 // Two array types unify if they have the same array length
584 // and their element types unify.
585 if y, ok := y.(*Array); ok {
586 // If one or both array lengths are unknown (< 0) due to some error,
587 // assume they are the same to avoid spurious follow-on errors.
588 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, emode, p)
592 // Two slice types unify if their element types unify.
593 if y, ok := y.(*Slice); ok {
594 return u.nify(x.elem, y.elem, emode, p)
598 // Two struct types unify if they have the same sequence of fields,
599 // and if corresponding fields have the same names, their (field) types unify,
600 // and they have identical tags. Two embedded fields are considered to have the same
601 // name. Lower-case field names from different packages are always different.
602 if y, ok := y.(*Struct); ok {
603 if x.NumFields() == y.NumFields() {
604 for i, f := range x.fields {
606 if f.embedded != g.embedded ||
607 x.Tag(i) != y.Tag(i) ||
608 !f.sameId(g.pkg, g.name) ||
609 !u.nify(f.typ, g.typ, emode, p) {
618 // Two pointer types unify if their base types unify.
619 if y, ok := y.(*Pointer); ok {
620 return u.nify(x.base, y.base, emode, p)
624 // Two tuples types unify if they have the same number of elements
625 // and the types of corresponding elements unify.
626 if y, ok := y.(*Tuple); ok {
627 if x.Len() == y.Len() {
629 for i, v := range x.vars {
631 if !u.nify(v.typ, w.typ, mode, p) {
641 // Two function types unify if they have the same number of parameters
642 // and result values, corresponding parameter and result types unify,
643 // and either both functions are variadic or neither is.
644 // Parameter and result names are not required to match.
645 // TODO(gri) handle type parameters or document why we can ignore them.
646 if y, ok := y.(*Signature); ok {
647 return x.variadic == y.variadic &&
648 u.nify(x.params, y.params, emode, p) &&
649 u.nify(x.results, y.results, emode, p)
653 assert(!u.enableInterfaceInference || mode&exact != 0) // handled before this switch
655 // Two interface types unify if they have the same set of methods with
656 // the same names, and corresponding function types unify.
657 // Lower-case method names from different packages are always different.
658 // The order of the methods is irrelevant.
659 if y, ok := y.(*Interface); ok {
662 if xset.comparable != yset.comparable {
665 if !xset.terms.equal(yset.terms) {
670 if len(a) == len(b) {
671 // Interface types are the only types where cycles can occur
672 // that are not "terminated" via named types; and such cycles
673 // can only be created via method parameter types that are
674 // anonymous interfaces (directly or indirectly) embedding
675 // the current interface. Example:
677 // type T interface {
681 // If two such (differently named) interfaces are compared,
682 // endless recursion occurs if the cycle is not detected.
684 // If x and y were compared before, they must be equal
685 // (if they were not, the recursion would have stopped);
686 // search the ifacePair stack for the same pair.
688 // This is a quadratic algorithm, but in practice these stacks
689 // are extremely short (bounded by the nesting depth of interface
690 // type declarations that recur via parameter types, an extremely
691 // rare occurrence). An alternative implementation might use a
692 // "visited" map, but that is probably less efficient overall.
693 q := &ifacePair{x, y, p}
696 return true // same pair was compared before
701 assertSortedMethods(a)
702 assertSortedMethods(b)
704 for i, f := range a {
706 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, exact, q) {
715 // Two map types unify if their key and value types unify.
716 if y, ok := y.(*Map); ok {
717 return u.nify(x.key, y.key, emode, p) && u.nify(x.elem, y.elem, emode, p)
721 // Two channel types unify if their value types unify
722 // and if they have the same direction.
723 // The channel direction is ignored for inexact unification.
724 if y, ok := y.(*Chan); ok {
725 return (mode&exact == 0 || x.dir == y.dir) && u.nify(x.elem, y.elem, emode, p)
729 // Two named types unify if their type names originate in the same type declaration.
730 // If they are instantiated, their type argument lists must unify.
731 if y := asNamed(y); y != nil {
732 // Check type arguments before origins so they unify
733 // even if the origins don't match; for better error
734 // messages (see go.dev/issue/53692).
735 xargs := x.TypeArgs().list()
736 yargs := y.TypeArgs().list()
737 if len(xargs) != len(yargs) {
740 for i, xarg := range xargs {
741 if !u.nify(xarg, yargs[i], mode, p) {
745 return identicalOrigin(x, y)
749 // x must be an unbound type parameter (see comment above).
751 assert(u.asTypeParam(x) == nil)
753 // By definition, a valid type argument must be in the type set of
754 // the respective type constraint. Therefore, the type argument's
755 // underlying type must be in the set of underlying types of that
756 // constraint. If there is a single such underlying type, it's the
757 // constraint's core type. It must match the type argument's under-
758 // lying type, irrespective of whether the actual type argument,
759 // which may be a defined type, is actually in the type set (that
760 // will be determined at instantiation time).
761 // Thus, if we have the core type of an unbound type parameter,
762 // we know the structure of the possible types satisfying such
763 // parameters. Use that core type for further unification
764 // (see go.dev/issue/50755 for a test case).
765 if enableCoreTypeUnification {
766 // Because the core type is always an underlying type,
767 // unification will take care of matching against a
768 // defined or literal type automatically.
769 // If y is also an unbound type parameter, we will end
770 // up here again with x and y swapped, so we don't
771 // need to take care of that case separately.
772 if cx := coreType(x); cx != nil {
774 u.tracef("core %s ≡ %s", x, y)
776 // If y is a defined type, it may not match against cx which
777 // is an underlying type (incl. int, string, etc.). Use assign
778 // mode here so that the unifier automatically takes under(y)
780 return u.nify(cx, y, assign, p)
783 // x != y and there's nothing to do
786 // avoid a crash in case of nil type
789 panic(sprintf(nil, true, "u.nify(%s, %s, %d)", x, y, mode))