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 // unify attempts to unify x and y and reports whether it succeeded.
128 // As a side-effect, types may be inferred for type parameters.
129 // The mode parameter controls how types are compared.
130 func (u *unifier) unify(x, y Type, mode unifyMode) bool {
131 return u.nify(x, y, mode, nil)
134 func (u *unifier) tracef(format string, args ...interface{}) {
135 fmt.Println(strings.Repeat(". ", u.depth) + sprintf(nil, true, format, args...))
138 // String returns a string representation of the current mapping
139 // from type parameters to types.
140 func (u *unifier) String() string {
141 // sort type parameters for reproducible strings
142 tparams := make(typeParamsById, len(u.handles))
144 for tpar := range u.handles {
151 w := newTypeWriter(&buf, nil)
153 for i, x := range tparams {
165 type typeParamsById []*TypeParam
167 func (s typeParamsById) Len() int { return len(s) }
168 func (s typeParamsById) Less(i, j int) bool { return s[i].id < s[j].id }
169 func (s typeParamsById) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
171 // join unifies the given type parameters x and y.
172 // If both type parameters already have a type associated with them
173 // and they are not joined, join fails and returns false.
174 func (u *unifier) join(x, y *TypeParam) bool {
176 u.tracef("%s ⇄ %s", x, y)
178 switch hx, hy := u.handles[x], u.handles[y]; {
180 // Both type parameters already share the same handle. Nothing to do.
181 case *hx != nil && *hy != nil:
182 // Both type parameters have (possibly different) inferred types. Cannot join.
185 // Only type parameter x has an inferred type. Use handle of x.
187 // This case is treated like the default case.
189 // // Only type parameter y has an inferred type. Use handle of y.
190 // u.setHandle(x, hy)
192 // Neither type parameter has an inferred type. Use handle of y.
198 // asTypeParam returns x.(*TypeParam) if x is a type parameter recorded with u.
199 // Otherwise, the result is nil.
200 func (u *unifier) asTypeParam(x Type) *TypeParam {
201 if x, _ := x.(*TypeParam); x != nil {
202 if _, found := u.handles[x]; found {
209 // setHandle sets the handle for type parameter x
210 // (and all its joined type parameters) to h.
211 func (u *unifier) setHandle(x *TypeParam, h *Type) {
214 for y, hy := range u.handles {
221 // at returns the (possibly nil) type for type parameter x.
222 func (u *unifier) at(x *TypeParam) Type {
226 // set sets the type t for type parameter x;
227 // t must not be nil.
228 func (u *unifier) set(x *TypeParam, t Type) {
231 u.tracef("%s ➞ %s", x, t)
236 // unknowns returns the number of type parameters for which no type has been set yet.
237 func (u *unifier) unknowns() int {
239 for _, h := range u.handles {
247 // inferred returns the list of inferred types for the given type parameter list.
248 // The result is never nil and has the same length as tparams; result types that
249 // could not be inferred are nil. Corresponding type parameters and result types
250 // have identical indices.
251 func (u *unifier) inferred(tparams []*TypeParam) []Type {
252 list := make([]Type, len(tparams))
253 for i, x := range tparams {
259 // nify implements the core unification algorithm which is an
260 // adapted version of Checker.identical. For changes to that
261 // code the corresponding changes should be made here.
262 // Must not be called directly from outside the unifier.
263 func (u *unifier) nify(x, y Type, mode unifyMode, p *ifacePair) (result bool) {
266 u.tracef("%s ≡ %s (mode %d)", x, y, mode)
269 if traceInference && !result {
270 u.tracef("%s ≢ %s", x, y)
275 // nothing to do if x == y
280 // Stop gap for cases where unification fails.
281 if u.depth > unificationDepthLimit {
283 u.tracef("depth %d >= %d", u.depth, unificationDepthLimit)
285 if panicAtUnificationDepthLimit {
286 panic("unification reached recursion depth limit")
291 // Unification is symmetric, so we can swap the operands.
292 // Ensure that if we have at least one
293 // - defined type, make sure one is in y
294 // - type parameter recorded with u, make sure one is in x
295 if _, ok := x.(*Named); ok || u.asTypeParam(y) != nil {
297 u.tracef("%s ≡ %s (swap)", y, x)
302 // Unification will fail if we match a defined type against a type literal.
303 // If we are matching types in an assignment, at the top-level, types with
304 // the same type structure are permitted as long as at least one of them
305 // is not a defined type. To accommodate for that possibility, we continue
306 // unification with the underlying type of a defined type if the other type
307 // is a type literal. This is controlled by the exact unification mode.
308 // We also continue if the other type is a basic type because basic types
309 // are valid underlying types and may appear as core types of type constraints.
310 // If we exclude them, inferred defined types for type parameters may not
311 // match against the core types of their constraints (even though they might
312 // correctly match against some of the types in the constraint's type set).
313 // Finally, if unification (incorrectly) succeeds by matching the underlying
314 // type of a defined type against a basic type (because we include basic types
315 // as type literals here), and if that leads to an incorrectly inferred type,
316 // we will fail at function instantiation or argument assignment time.
318 // If we have at least one defined type, there is one in y.
319 if ny, _ := y.(*Named); mode&exact == 0 && ny != nil && isTypeLit(x) && !(enableInterfaceInference && IsInterface(x)) {
321 u.tracef("%s ≡ under %s", x, ny)
324 // Per the spec, a defined type cannot have an underlying type
325 // that is a type parameter.
326 assert(!isTypeParam(y))
327 // x and y may be identical now
333 // Cases where at least one of x or y is a type parameter recorded with u.
334 // If we have at least one type parameter, there is one in x.
335 // If we have exactly one type parameter, because it is in x,
336 // isTypeLit(x) is false and y was not changed above. In other
337 // words, if y was a defined type, it is still a defined type
338 // (relevant for the logic below).
339 switch px, py := u.asTypeParam(x), u.asTypeParam(y); {
340 case px != nil && py != nil:
341 // both x and y are type parameters
345 // both x and y have an inferred type - they must match
346 return u.nify(u.at(px), u.at(py), mode, p)
349 // x is a type parameter, y is not
350 if x := u.at(px); x != nil {
351 // x has an inferred type which must match y
352 if u.nify(x, y, mode, p) {
353 // If we have a match, possibly through underlying types,
354 // and y is a defined type, make sure we record that type
355 // for type parameter x, which may have until now only
356 // recorded an underlying type (go.dev/issue/43056).
357 if _, ok := y.(*Named); ok {
364 // otherwise, infer type from y
369 // x != y if we get here
372 // If we get here and x or y is a type parameter, they are unbound
373 // (not recorded with the unifier).
374 // Ensure that if we have at least one type parameter, it is in x
375 // (the earlier swap checks for _recorded_ type parameters only).
378 u.tracef("%s ≡ %s (swap)", y, x)
383 // Type elements (array, slice, etc. elements) use emode for unification.
384 // Element types must match exactly if the types are used in an assignment.
386 if mode&assign != 0 {
390 // If EnableInterfaceInference is set and we don't require exact unification,
391 // if both types are interfaces, one interface must have a subset of the
392 // methods of the other and corresponding method signatures must unify.
393 // If only one type is an interface, all its methods must be present in the
394 // other type and corresponding method signatures must unify.
395 if enableInterfaceInference && mode&exact == 0 {
396 xi, _ := x.(*Interface)
397 yi, _ := y.(*Interface)
398 // If we have two interfaces, check the type terms for equivalence,
399 // and unify common methods if possible.
400 if xi != nil && yi != nil {
403 if xset.comparable != yset.comparable {
406 // For now we require terms to be equal.
407 // We should be able to relax this as well, eventually.
408 if !xset.terms.equal(yset.terms) {
411 // Interface types are the only types where cycles can occur
412 // that are not "terminated" via named types; and such cycles
413 // can only be created via method parameter types that are
414 // anonymous interfaces (directly or indirectly) embedding
415 // the current interface. Example:
417 // type T interface {
421 // If two such (differently named) interfaces are compared,
422 // endless recursion occurs if the cycle is not detected.
424 // If x and y were compared before, they must be equal
425 // (if they were not, the recursion would have stopped);
426 // search the ifacePair stack for the same pair.
428 // This is a quadratic algorithm, but in practice these stacks
429 // are extremely short (bounded by the nesting depth of interface
430 // type declarations that recur via parameter types, an extremely
431 // rare occurrence). An alternative implementation might use a
432 // "visited" map, but that is probably less efficient overall.
433 q := &ifacePair{xi, yi, p}
436 return true // same pair was compared before
440 // The method set of x must be a subset of the method set
441 // of y or vice versa, and the common methods must unify.
442 xmethods := xset.methods
443 ymethods := yset.methods
444 // The smaller method set must be the subset, if it exists.
445 if len(xmethods) > len(ymethods) {
446 xmethods, ymethods = ymethods, xmethods
448 // len(xmethods) <= len(ymethods)
449 // Collect the ymethods in a map for quick lookup.
450 ymap := make(map[string]*Func, len(ymethods))
451 for _, ym := range ymethods {
454 // All xmethods must exist in ymethods and corresponding signatures must unify.
455 for _, xm := range xmethods {
456 if ym := ymap[xm.Id()]; ym == nil || !u.nify(xm.typ, ym.typ, emode, p) {
463 // We don't have two interfaces. If we have one, make sure it's in xi.
469 // If we have one interface, at a minimum each of the interface methods
470 // must be implemented and thus unify with a corresponding method from
471 // the non-interface type, otherwise unification fails.
473 // All xi methods must exist in y and corresponding signatures must unify.
474 xmethods := xi.typeSet().methods
475 for _, xm := range xmethods {
476 obj, _, _ := LookupFieldOrMethod(y, false, xm.pkg, xm.name)
477 if ym, _ := obj.(*Func); ym == nil || !u.nify(xm.typ, ym.typ, emode, p) {
484 // Neither x nor y are interface types.
485 // They must be structurally equivalent to unify.
488 switch x := x.(type) {
490 // Basic types are singletons except for the rune and byte
491 // aliases, thus we cannot solely rely on the x == y check
492 // above. See also comment in TypeName.IsAlias.
493 if y, ok := y.(*Basic); ok {
494 return x.kind == y.kind
498 // Two array types unify if they have the same array length
499 // and their element types unify.
500 if y, ok := y.(*Array); ok {
501 // If one or both array lengths are unknown (< 0) due to some error,
502 // assume they are the same to avoid spurious follow-on errors.
503 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, emode, p)
507 // Two slice types unify if their element types unify.
508 if y, ok := y.(*Slice); ok {
509 return u.nify(x.elem, y.elem, emode, p)
513 // Two struct types unify if they have the same sequence of fields,
514 // and if corresponding fields have the same names, their (field) types unify,
515 // and they have identical tags. Two embedded fields are considered to have the same
516 // name. Lower-case field names from different packages are always different.
517 if y, ok := y.(*Struct); ok {
518 if x.NumFields() == y.NumFields() {
519 for i, f := range x.fields {
521 if f.embedded != g.embedded ||
522 x.Tag(i) != y.Tag(i) ||
523 !f.sameId(g.pkg, g.name) ||
524 !u.nify(f.typ, g.typ, emode, p) {
533 // Two pointer types unify if their base types unify.
534 if y, ok := y.(*Pointer); ok {
535 return u.nify(x.base, y.base, emode, p)
539 // Two tuples types unify if they have the same number of elements
540 // and the types of corresponding elements unify.
541 if y, ok := y.(*Tuple); ok {
542 if x.Len() == y.Len() {
544 for i, v := range x.vars {
546 if !u.nify(v.typ, w.typ, mode, p) {
556 // Two function types unify if they have the same number of parameters
557 // and result values, corresponding parameter and result types unify,
558 // and either both functions are variadic or neither is.
559 // Parameter and result names are not required to match.
560 // TODO(gri) handle type parameters or document why we can ignore them.
561 if y, ok := y.(*Signature); ok {
562 return x.variadic == y.variadic &&
563 u.nify(x.params, y.params, emode, p) &&
564 u.nify(x.results, y.results, emode, p)
568 assert(!enableInterfaceInference || mode&exact != 0) // handled before this switch
570 // Two interface types unify if they have the same set of methods with
571 // the same names, and corresponding function types unify.
572 // Lower-case method names from different packages are always different.
573 // The order of the methods is irrelevant.
574 if y, ok := y.(*Interface); ok {
577 if xset.comparable != yset.comparable {
580 if !xset.terms.equal(yset.terms) {
585 if len(a) == len(b) {
586 // Interface types are the only types where cycles can occur
587 // that are not "terminated" via named types; and such cycles
588 // can only be created via method parameter types that are
589 // anonymous interfaces (directly or indirectly) embedding
590 // the current interface. Example:
592 // type T interface {
596 // If two such (differently named) interfaces are compared,
597 // endless recursion occurs if the cycle is not detected.
599 // If x and y were compared before, they must be equal
600 // (if they were not, the recursion would have stopped);
601 // search the ifacePair stack for the same pair.
603 // This is a quadratic algorithm, but in practice these stacks
604 // are extremely short (bounded by the nesting depth of interface
605 // type declarations that recur via parameter types, an extremely
606 // rare occurrence). An alternative implementation might use a
607 // "visited" map, but that is probably less efficient overall.
608 q := &ifacePair{x, y, p}
611 return true // same pair was compared before
616 assertSortedMethods(a)
617 assertSortedMethods(b)
619 for i, f := range a {
621 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, emode, q) {
630 // Two map types unify if their key and value types unify.
631 if y, ok := y.(*Map); ok {
632 return u.nify(x.key, y.key, emode, p) && u.nify(x.elem, y.elem, emode, p)
636 // Two channel types unify if their value types unify
637 // and if they have the same direction.
638 // The channel direction is ignored for inexact unification.
639 if y, ok := y.(*Chan); ok {
640 return (mode&exact == 0 || x.dir == y.dir) && u.nify(x.elem, y.elem, emode, p)
644 // Two named non-interface types unify if their type names originate
645 // in the same type declaration. If they are instantiated, their type
646 // argument lists must unify.
647 // If one or both named types are interfaces, the types unify if the
648 // respective methods unify (per the rules for interface unification).
649 if y, ok := y.(*Named); ok {
650 if enableInterfaceInference && mode&exact == 0 {
651 xi, _ := x.under().(*Interface)
652 yi, _ := y.under().(*Interface)
653 // If one or both of x and y are interfaces, use interface unification.
655 case xi != nil && yi != nil:
656 return u.nify(xi, yi, mode, p)
658 return u.nify(xi, y, mode, p)
660 return u.nify(x, yi, mode, p)
662 // In all other cases, the type arguments and origins must match.
665 // Check type arguments before origins so they unify
666 // even if the origins don't match; for better error
667 // messages (see go.dev/issue/53692).
668 xargs := x.TypeArgs().list()
669 yargs := y.TypeArgs().list()
670 if len(xargs) != len(yargs) {
673 for i, xarg := range xargs {
674 if !u.nify(xarg, yargs[i], mode, p) {
678 return indenticalOrigin(x, y)
682 // x must be an unbound type parameter (see comment above).
684 assert(u.asTypeParam(x) == nil)
686 // By definition, a valid type argument must be in the type set of
687 // the respective type constraint. Therefore, the type argument's
688 // underlying type must be in the set of underlying types of that
689 // constraint. If there is a single such underlying type, it's the
690 // constraint's core type. It must match the type argument's under-
691 // lying type, irrespective of whether the actual type argument,
692 // which may be a defined type, is actually in the type set (that
693 // will be determined at instantiation time).
694 // Thus, if we have the core type of an unbound type parameter,
695 // we know the structure of the possible types satisfying such
696 // parameters. Use that core type for further unification
697 // (see go.dev/issue/50755 for a test case).
698 if enableCoreTypeUnification {
699 // Because the core type is always an underlying type,
700 // unification will take care of matching against a
701 // defined or literal type automatically.
702 // If y is also an unbound type parameter, we will end
703 // up here again with x and y swapped, so we don't
704 // need to take care of that case separately.
705 if cx := coreType(x); cx != nil {
707 u.tracef("core %s ≡ %s", x, y)
709 return u.nify(cx, y, mode, p)
712 // x != y and there's nothing to do
715 // avoid a crash in case of nil type
718 panic(sprintf(nil, true, "u.nify(%s, %s, %d)", x, y, mode))