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
83 // newUnifier returns a new unifier initialized with the given type parameter
84 // and corresponding type argument lists. The type argument list may be shorter
85 // than the type parameter list, and it may contain nil types. Matching type
86 // parameters and arguments must have the same index.
87 func newUnifier(tparams []*TypeParam, targs []Type) *unifier {
88 assert(len(tparams) >= len(targs))
89 handles := make(map[*TypeParam]*Type, len(tparams))
90 // Allocate all handles up-front: in a correct program, all type parameters
91 // must be resolved and thus eventually will get a handle.
92 // Also, sharing of handles caused by unified type parameters is rare and
93 // so it's ok to not optimize for that case (and delay handle allocation).
94 for i, x := range tparams {
101 return &unifier{handles, 0}
104 // unifyMode controls the behavior of the unifier.
108 // If assign is set, we are unifying types involved in an assignment:
109 // they may match inexactly at the top, but element types must match
111 assign unifyMode = 1 << iota
113 // If exact is set, types unify if they are identical (or can be
114 // made identical with suitable arguments for type parameters).
115 // Otherwise, a named type and a type literal unify if their
116 // underlying types unify, channel directions are ignored, and
117 // if there is an interface, the other type must implement the
122 func (m unifyMode) String() string {
131 return "assign, exact"
133 return fmt.Sprintf("mode %d", m)
136 // unify attempts to unify x and y and reports whether it succeeded.
137 // As a side-effect, types may be inferred for type parameters.
138 // The mode parameter controls how types are compared.
139 func (u *unifier) unify(x, y Type, mode unifyMode) bool {
140 return u.nify(x, y, mode, nil)
143 func (u *unifier) tracef(format string, args ...interface{}) {
144 fmt.Println(strings.Repeat(". ", u.depth) + sprintf(nil, true, format, args...))
147 // String returns a string representation of the current mapping
148 // from type parameters to types.
149 func (u *unifier) String() string {
150 // sort type parameters for reproducible strings
151 tparams := make(typeParamsById, len(u.handles))
153 for tpar := range u.handles {
160 w := newTypeWriter(&buf, nil)
162 for i, x := range tparams {
174 type typeParamsById []*TypeParam
176 func (s typeParamsById) Len() int { return len(s) }
177 func (s typeParamsById) Less(i, j int) bool { return s[i].id < s[j].id }
178 func (s typeParamsById) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
180 // join unifies the given type parameters x and y.
181 // If both type parameters already have a type associated with them
182 // and they are not joined, join fails and returns false.
183 func (u *unifier) join(x, y *TypeParam) bool {
185 u.tracef("%s ⇄ %s", x, y)
187 switch hx, hy := u.handles[x], u.handles[y]; {
189 // Both type parameters already share the same handle. Nothing to do.
190 case *hx != nil && *hy != nil:
191 // Both type parameters have (possibly different) inferred types. Cannot join.
194 // Only type parameter x has an inferred type. Use handle of x.
196 // This case is treated like the default case.
198 // // Only type parameter y has an inferred type. Use handle of y.
199 // u.setHandle(x, hy)
201 // Neither type parameter has an inferred type. Use handle of y.
207 // asTypeParam returns x.(*TypeParam) if x is a type parameter recorded with u.
208 // Otherwise, the result is nil.
209 func (u *unifier) asTypeParam(x Type) *TypeParam {
210 if x, _ := x.(*TypeParam); x != nil {
211 if _, found := u.handles[x]; found {
218 // setHandle sets the handle for type parameter x
219 // (and all its joined type parameters) to h.
220 func (u *unifier) setHandle(x *TypeParam, h *Type) {
223 for y, hy := range u.handles {
230 // at returns the (possibly nil) type for type parameter x.
231 func (u *unifier) at(x *TypeParam) Type {
235 // set sets the type t for type parameter x;
236 // t must not be nil.
237 func (u *unifier) set(x *TypeParam, t Type) {
240 u.tracef("%s ➞ %s", x, t)
245 // unknowns returns the number of type parameters for which no type has been set yet.
246 func (u *unifier) unknowns() int {
248 for _, h := range u.handles {
256 // inferred returns the list of inferred types for the given type parameter list.
257 // The result is never nil and has the same length as tparams; result types that
258 // could not be inferred are nil. Corresponding type parameters and result types
259 // have identical indices.
260 func (u *unifier) inferred(tparams []*TypeParam) []Type {
261 list := make([]Type, len(tparams))
262 for i, x := range tparams {
268 // asInterface returns the underlying type of x as an interface if
269 // it is a non-type parameter interface. Otherwise it returns nil.
270 func asInterface(x Type) (i *Interface) {
271 if _, ok := x.(*TypeParam); !ok {
272 i, _ = under(x).(*Interface)
277 // nify implements the core unification algorithm which is an
278 // adapted version of Checker.identical. For changes to that
279 // code the corresponding changes should be made here.
280 // Must not be called directly from outside the unifier.
281 func (u *unifier) nify(x, y Type, mode unifyMode, p *ifacePair) (result bool) {
284 u.tracef("%s ≡ %s\t// %s", x, y, mode)
287 if traceInference && !result {
288 u.tracef("%s ≢ %s", x, y)
293 // nothing to do if x == y
298 // Stop gap for cases where unification fails.
299 if u.depth > unificationDepthLimit {
301 u.tracef("depth %d >= %d", u.depth, unificationDepthLimit)
303 if panicAtUnificationDepthLimit {
304 panic("unification reached recursion depth limit")
309 // Unification is symmetric, so we can swap the operands.
310 // Ensure that if we have at least one
311 // - defined type, make sure one is in y
312 // - type parameter recorded with u, make sure one is in x
313 if _, ok := x.(*Named); ok || u.asTypeParam(y) != nil {
315 u.tracef("%s ≡ %s\t// swap", y, x)
320 // Unification will fail if we match a defined type against a type literal.
321 // If we are matching types in an assignment, at the top-level, types with
322 // the same type structure are permitted as long as at least one of them
323 // is not a defined type. To accommodate for that possibility, we continue
324 // unification with the underlying type of a defined type if the other type
325 // is a type literal. This is controlled by the exact unification mode.
326 // We also continue if the other type is a basic type because basic types
327 // are valid underlying types and may appear as core types of type constraints.
328 // If we exclude them, inferred defined types for type parameters may not
329 // match against the core types of their constraints (even though they might
330 // correctly match against some of the types in the constraint's type set).
331 // Finally, if unification (incorrectly) succeeds by matching the underlying
332 // type of a defined type against a basic type (because we include basic types
333 // as type literals here), and if that leads to an incorrectly inferred type,
334 // we will fail at function instantiation or argument assignment time.
336 // If we have at least one defined type, there is one in y.
337 if ny, _ := y.(*Named); mode&exact == 0 && ny != nil && isTypeLit(x) && !IsInterface(x) {
339 u.tracef("%s ≡ under %s", x, ny)
342 // Per the spec, a defined type cannot have an underlying type
343 // that is a type parameter.
344 assert(!isTypeParam(y))
345 // x and y may be identical now
351 // Cases where at least one of x or y is a type parameter recorded with u.
352 // If we have at least one type parameter, there is one in x.
353 // If we have exactly one type parameter, because it is in x,
354 // isTypeLit(x) is false and y was not changed above. In other
355 // words, if y was a defined type, it is still a defined type
356 // (relevant for the logic below).
357 switch px, py := u.asTypeParam(x), u.asTypeParam(y); {
358 case px != nil && py != nil:
359 // both x and y are type parameters
363 // both x and y have an inferred type - they must match
364 return u.nify(u.at(px), u.at(py), mode, p)
367 // x is a type parameter, y is not
368 if x := u.at(px); x != nil {
369 // x has an inferred type which must match y
370 if u.nify(x, y, mode, p) {
371 // We have a match, possibly through underlying types.
376 // If we have two interfaces, what to do depends on
377 // whether they are named and their method sets.
378 if xi != nil && yi != nil {
379 // Both types are interfaces.
380 // If both types are defined types, they must be identical
381 // because unification doesn't know which type has the "right" name.
383 return Identical(x, y)
385 // In all other cases, the method sets must match.
386 // The types unified so we know that corresponding methods
387 // match and we can simply compare the number of methods.
388 // TODO(gri) We may be able to relax this rule and select
389 // the more general interface. But if one of them is a defined
390 // type, it's not clear how to choose and whether we introduce
391 // an order dependency or not. Requiring the same method set
393 if len(xi.typeSet().methods) != len(yi.typeSet().methods) {
396 } else if xi != nil || yi != nil {
397 // One but not both of them are interfaces.
398 // In this case, either x or y could be viable matches for the corresponding
399 // type parameter, which means choosing either introduces an order dependence.
400 // Therefore, we must fail unification (go.dev/issue/60933).
403 // If y is a defined type, make sure we record that type
404 // for type parameter x, which may have until now only
405 // recorded an underlying type (go.dev/issue/43056).
406 // Either both types are interfaces, or neither type is.
407 // If both are interfaces, they have the same methods.
409 // Note: Changing the recorded type for a type parameter to
410 // a defined type is only ok when unification is inexact.
411 // But in exact unification, if we have a match, x and y must
412 // be identical, so changing the recorded type for x is a no-op.
420 // otherwise, infer type from y
425 // x != y if we get here
428 // If we don't require exact unification and both types are interfaces,
429 // one interface must have a subset of the methods of the other and
430 // corresponding method signatures must unify.
431 // If only one type is an interface, all its methods must be present in the
432 // other type and corresponding method signatures must unify.
434 // One or both interfaces may be defined types.
435 // Look under the name, but not under type parameters (go.dev/issue/60564).
438 // If we have two interfaces, check the type terms for equivalence,
439 // and unify common methods if possible.
440 if xi != nil && yi != nil {
443 if xset.comparable != yset.comparable {
446 // For now we require terms to be equal.
447 // We should be able to relax this as well, eventually.
448 if !xset.terms.equal(yset.terms) {
451 // Interface types are the only types where cycles can occur
452 // that are not "terminated" via named types; and such cycles
453 // can only be created via method parameter types that are
454 // anonymous interfaces (directly or indirectly) embedding
455 // the current interface. Example:
457 // type T interface {
461 // If two such (differently named) interfaces are compared,
462 // endless recursion occurs if the cycle is not detected.
464 // If x and y were compared before, they must be equal
465 // (if they were not, the recursion would have stopped);
466 // search the ifacePair stack for the same pair.
468 // This is a quadratic algorithm, but in practice these stacks
469 // are extremely short (bounded by the nesting depth of interface
470 // type declarations that recur via parameter types, an extremely
471 // rare occurrence). An alternative implementation might use a
472 // "visited" map, but that is probably less efficient overall.
473 q := &ifacePair{xi, yi, p}
476 return true // same pair was compared before
480 // The method set of x must be a subset of the method set
481 // of y or vice versa, and the common methods must unify.
482 xmethods := xset.methods
483 ymethods := yset.methods
484 // The smaller method set must be the subset, if it exists.
485 if len(xmethods) > len(ymethods) {
486 xmethods, ymethods = ymethods, xmethods
488 // len(xmethods) <= len(ymethods)
489 // Collect the ymethods in a map for quick lookup.
490 ymap := make(map[string]*Func, len(ymethods))
491 for _, ym := range ymethods {
494 // All xmethods must exist in ymethods and corresponding signatures must unify.
495 for _, xm := range xmethods {
496 if ym := ymap[xm.Id()]; ym == nil || !u.nify(xm.typ, ym.typ, exact, p) {
503 // We don't have two interfaces. If we have one, make sure it's in xi.
509 // If we have one interface, at a minimum each of the interface methods
510 // must be implemented and thus unify with a corresponding method from
511 // the non-interface type, otherwise unification fails.
513 // All xi methods must exist in y and corresponding signatures must unify.
514 xmethods := xi.typeSet().methods
515 for _, xm := range xmethods {
516 obj, _, _ := LookupFieldOrMethod(y, false, xm.pkg, xm.name)
517 if ym, _ := obj.(*Func); ym == nil || !u.nify(xm.typ, ym.typ, exact, p) {
525 // Unless we have exact unification, neither x nor y are interfaces now.
526 // Except for unbound type parameters (see below), x and y must be structurally
527 // equivalent to unify.
529 // If we get here and x or y is a type parameter, they are unbound
530 // (not recorded with the unifier).
531 // Ensure that if we have at least one type parameter, it is in x
532 // (the earlier swap checks for _recorded_ type parameters only).
533 // This ensures that the switch switches on the type parameter.
535 // TODO(gri) Factor out type parameter handling from the switch.
538 u.tracef("%s ≡ %s\t// swap", y, x)
543 // Type elements (array, slice, etc. elements) use emode for unification.
544 // Element types must match exactly if the types are used in an assignment.
546 if mode&assign != 0 {
550 switch x := x.(type) {
552 // Basic types are singletons except for the rune and byte
553 // aliases, thus we cannot solely rely on the x == y check
554 // above. See also comment in TypeName.IsAlias.
555 if y, ok := y.(*Basic); ok {
556 return x.kind == y.kind
560 // Two array types unify if they have the same array length
561 // and their element types unify.
562 if y, ok := y.(*Array); ok {
563 // If one or both array lengths are unknown (< 0) due to some error,
564 // assume they are the same to avoid spurious follow-on errors.
565 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, emode, p)
569 // Two slice types unify if their element types unify.
570 if y, ok := y.(*Slice); ok {
571 return u.nify(x.elem, y.elem, emode, p)
575 // Two struct types unify if they have the same sequence of fields,
576 // and if corresponding fields have the same names, their (field) types unify,
577 // and they have identical tags. Two embedded fields are considered to have the same
578 // name. Lower-case field names from different packages are always different.
579 if y, ok := y.(*Struct); ok {
580 if x.NumFields() == y.NumFields() {
581 for i, f := range x.fields {
583 if f.embedded != g.embedded ||
584 x.Tag(i) != y.Tag(i) ||
585 !f.sameId(g.pkg, g.name) ||
586 !u.nify(f.typ, g.typ, emode, p) {
595 // Two pointer types unify if their base types unify.
596 if y, ok := y.(*Pointer); ok {
597 return u.nify(x.base, y.base, emode, p)
601 // Two tuples types unify if they have the same number of elements
602 // and the types of corresponding elements unify.
603 if y, ok := y.(*Tuple); ok {
604 if x.Len() == y.Len() {
606 for i, v := range x.vars {
608 if !u.nify(v.typ, w.typ, mode, p) {
618 // Two function types unify if they have the same number of parameters
619 // and result values, corresponding parameter and result types unify,
620 // and either both functions are variadic or neither is.
621 // Parameter and result names are not required to match.
622 // TODO(gri) handle type parameters or document why we can ignore them.
623 if y, ok := y.(*Signature); ok {
624 return x.variadic == y.variadic &&
625 u.nify(x.params, y.params, emode, p) &&
626 u.nify(x.results, y.results, emode, p)
630 assert(mode&exact != 0) // inexact unification is handled before this switch
632 // Two interface types unify if they have the same set of methods with
633 // the same names, and corresponding function types unify.
634 // Lower-case method names from different packages are always different.
635 // The order of the methods is irrelevant.
636 if y, ok := y.(*Interface); ok {
639 if xset.comparable != yset.comparable {
642 if !xset.terms.equal(yset.terms) {
647 if len(a) == len(b) {
648 // Interface types are the only types where cycles can occur
649 // that are not "terminated" via named types; and such cycles
650 // can only be created via method parameter types that are
651 // anonymous interfaces (directly or indirectly) embedding
652 // the current interface. Example:
654 // type T interface {
658 // If two such (differently named) interfaces are compared,
659 // endless recursion occurs if the cycle is not detected.
661 // If x and y were compared before, they must be equal
662 // (if they were not, the recursion would have stopped);
663 // search the ifacePair stack for the same pair.
665 // This is a quadratic algorithm, but in practice these stacks
666 // are extremely short (bounded by the nesting depth of interface
667 // type declarations that recur via parameter types, an extremely
668 // rare occurrence). An alternative implementation might use a
669 // "visited" map, but that is probably less efficient overall.
670 q := &ifacePair{x, y, p}
673 return true // same pair was compared before
678 assertSortedMethods(a)
679 assertSortedMethods(b)
681 for i, f := range a {
683 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, exact, q) {
692 // Two map types unify if their key and value types unify.
693 if y, ok := y.(*Map); ok {
694 return u.nify(x.key, y.key, emode, p) && u.nify(x.elem, y.elem, emode, p)
698 // Two channel types unify if their value types unify
699 // and if they have the same direction.
700 // The channel direction is ignored for inexact unification.
701 if y, ok := y.(*Chan); ok {
702 return (mode&exact == 0 || x.dir == y.dir) && u.nify(x.elem, y.elem, emode, p)
706 // Two named types unify if their type names originate in the same type declaration.
707 // If they are instantiated, their type argument lists must unify.
708 if y, ok := y.(*Named); ok {
709 // Check type arguments before origins so they unify
710 // even if the origins don't match; for better error
711 // messages (see go.dev/issue/53692).
712 xargs := x.TypeArgs().list()
713 yargs := y.TypeArgs().list()
714 if len(xargs) != len(yargs) {
717 for i, xarg := range xargs {
718 if !u.nify(xarg, yargs[i], mode, p) {
722 return identicalOrigin(x, y)
726 // x must be an unbound type parameter (see comment above).
728 assert(u.asTypeParam(x) == nil)
730 // By definition, a valid type argument must be in the type set of
731 // the respective type constraint. Therefore, the type argument's
732 // underlying type must be in the set of underlying types of that
733 // constraint. If there is a single such underlying type, it's the
734 // constraint's core type. It must match the type argument's under-
735 // lying type, irrespective of whether the actual type argument,
736 // which may be a defined type, is actually in the type set (that
737 // will be determined at instantiation time).
738 // Thus, if we have the core type of an unbound type parameter,
739 // we know the structure of the possible types satisfying such
740 // parameters. Use that core type for further unification
741 // (see go.dev/issue/50755 for a test case).
742 if enableCoreTypeUnification {
743 // Because the core type is always an underlying type,
744 // unification will take care of matching against a
745 // defined or literal type automatically.
746 // If y is also an unbound type parameter, we will end
747 // up here again with x and y swapped, so we don't
748 // need to take care of that case separately.
749 if cx := coreType(x); cx != nil {
751 u.tracef("core %s ≡ %s", x, y)
753 // If y is a defined type, it may not match against cx which
754 // is an underlying type (incl. int, string, etc.). Use assign
755 // mode here so that the unifier automatically takes under(y)
757 return u.nify(cx, y, assign, p)
760 // x != y and there's nothing to do
763 // avoid a crash in case of nil type
766 panic(sprintf(nil, true, "u.nify(%s, %s, %d)", x, y, mode))