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.
14 // The unifier maintains two separate sets of type parameters x and y
15 // which are used to resolve type parameters in the x and y arguments
16 // provided to the unify call. For unidirectional unification, only
17 // one of these sets (say x) is provided, and then type parameters are
18 // only resolved for the x argument passed to unify, not the y argument
19 // (even if that also contains possibly the same type parameters). This
20 // is crucial to infer the type parameters of self-recursive calls:
22 // func f[P any](a P) { f(a) }
24 // For the call f(a) we want to infer that the type argument for P is P.
25 // During unification, the parameter type P must be resolved to the type
26 // parameter P ("x" side), but the argument type P must be left alone so
27 // that unification resolves the type parameter P to P.
29 // For bidirection unification, both sets are provided. This enables
30 // unification to go from argument to parameter type and vice versa.
31 // For constraint type inference, we use bidirectional unification
32 // where both the x and y type parameters are identical. This is done
33 // by setting up one of them (using init) and then assigning its value
36 // A unifier maintains the current type parameters for x and y
37 // and the respective types inferred for each type parameter.
38 // A unifier is created by calling newUnifier.
41 x, y tparamsList // x and y must initialized via tparamsList.init
42 types []Type // inferred types, shared by x and y
45 // newUnifier returns a new unifier.
46 // If exact is set, unification requires unified types to match
47 // exactly. If exact is not set, a named type's underlying type
48 // is considered if unification would fail otherwise, and the
49 // direction of channels is ignored.
50 func newUnifier(exact bool) *unifier {
51 u := &unifier{exact: exact}
57 // unify attempts to unify x and y and reports whether it succeeded.
58 func (u *unifier) unify(x, y Type) bool {
59 return u.nify(x, y, nil)
62 // A tparamsList describes a list of type parameters and the types inferred for them.
63 type tparamsList struct {
66 // For each tparams element, there is a corresponding type slot index in indices.
67 // index < 0: unifier.types[-index-1] == nil
68 // index == 0: no type slot allocated yet
69 // index > 0: unifier.types[index-1] == typ
70 // Joined tparams elements share the same type slot and thus have the same index.
71 // By using a negative index for nil types we don't need to check unifier.types
72 // to see if we have a type or not.
73 indices []int // len(d.indices) == len(d.tparams)
76 // String returns a string representation for a tparamsList. For debugging.
77 func (d *tparamsList) String() string {
80 for i, tname := range d.tparams {
84 writeType(&buf, tname.typ, nil, nil)
86 writeType(&buf, d.at(i), nil, nil)
92 // init initializes d with the given type parameters.
93 // The type parameters must be in the order in which they appear in their declaration
94 // (this ensures that the tparams indices match the respective type parameter index).
95 func (d *tparamsList) init(tparams []*TypeName) {
96 if len(tparams) == 0 {
100 for i, tpar := range tparams {
101 assert(i == tpar.typ.(*TypeParam).index)
105 d.indices = make([]int, len(tparams))
108 // join unifies the i'th type parameter of x with the j'th type parameter of y.
109 // If both type parameters already have a type associated with them and they are
110 // not joined, join fails and return false.
111 func (u *unifier) join(i, j int) bool {
115 case ti == 0 && tj == 0:
116 // Neither type parameter has a type slot associated with them.
117 // Allocate a new joined nil type slot (negative index).
118 u.types = append(u.types, nil)
119 u.x.indices[i] = -len(u.types)
120 u.y.indices[j] = -len(u.types)
122 // The type parameter for x has no type slot yet. Use slot of y.
125 // The type parameter for y has no type slot yet. Use slot of x.
128 // Both type parameters have a slot: ti != 0 && tj != 0.
130 // Both type parameters already share the same slot. Nothing to do.
132 case ti > 0 && tj > 0:
133 // Both type parameters have (possibly different) inferred types. Cannot join.
136 // Only the type parameter for x has an inferred type. Use x slot for y.
138 // This case is handled like the default case.
140 // // Only the type parameter for y has an inferred type. Use y slot for x.
141 // u.x.setIndex(i, tj)
143 // Neither type parameter has an inferred type. Use y slot for x
144 // (or x slot for y, it doesn't matter).
150 // If typ is a type parameter of d, index returns the type parameter index.
151 // Otherwise, the result is < 0.
152 func (d *tparamsList) index(typ Type) int {
153 if tpar, ok := typ.(*TypeParam); ok {
154 return tparamIndex(d.tparams, tpar)
159 // If tpar is a type parameter in list, tparamIndex returns the type parameter index.
160 // Otherwise, the result is < 0. tpar must not be nil.
161 func tparamIndex(list []*TypeName, tpar *TypeParam) int {
162 if i := tpar.index; i < len(list) && list[i].typ == tpar {
168 // setIndex sets the type slot index for the i'th type parameter
169 // (and all its joined parameters) to tj. The type parameter
170 // must have a (possibly nil) type slot associated with it.
171 func (d *tparamsList) setIndex(i, tj int) {
173 assert(ti != 0 && tj != 0)
174 for k, tk := range d.indices {
181 // at returns the type set for the i'th type parameter; or nil.
182 func (d *tparamsList) at(i int) Type {
183 if ti := d.indices[i]; ti > 0 {
184 return d.unifier.types[ti-1]
189 // set sets the type typ for the i'th type parameter;
190 // typ must not be nil and it must not have been set before.
191 func (d *tparamsList) set(i int, typ Type) {
194 switch ti := d.indices[i]; {
199 u.types = append(u.types, typ)
200 d.indices[i] = len(u.types)
202 panic("type already set")
206 // types returns the list of inferred types (via unification) for the type parameters
207 // described by d, and an index. If all types were inferred, the returned index is < 0.
208 // Otherwise, it is the index of the first type parameter which couldn't be inferred;
209 // i.e., for which list[index] is nil.
210 func (d *tparamsList) types() (list []Type, index int) {
211 list = make([]Type, len(d.tparams))
213 for i := range d.tparams {
216 if index < 0 && t == nil {
223 func (u *unifier) nifyEq(x, y Type, p *ifacePair) bool {
224 return x == y || u.nify(x, y, p)
227 // nify implements the core unification algorithm which is an
228 // adapted version of Checker.identical0. For changes to that
229 // code the corresponding changes should be made here.
230 // Must not be called directly from outside the unifier.
231 func (u *unifier) nify(x, y Type, p *ifacePair) bool {
232 // types must be expanded for comparison
237 // If exact unification is known to fail because we attempt to
238 // match a type name against an unnamed type literal, consider
239 // the underlying type of the named type.
240 // (Subtle: We use isNamed to include any type with a name (incl.
241 // basic types and type parameters. We use asNamed because we only
242 // want *Named types.)
244 case !isNamed(x) && y != nil && asNamed(y) != nil:
245 return u.nify(x, under(y), p)
246 case x != nil && asNamed(x) != nil && !isNamed(y):
247 return u.nify(under(x), y, p)
251 // Cases where at least one of x or y is a type parameter.
252 switch i, j := u.x.index(x), u.y.index(y); {
253 case i >= 0 && j >= 0:
254 // both x and y are type parameters
258 // both x and y have an inferred type - they must match
259 return u.nifyEq(u.x.at(i), u.y.at(j), p)
262 // x is a type parameter, y is not
263 if tx := u.x.at(i); tx != nil {
264 return u.nifyEq(tx, y, p)
266 // otherwise, infer type from y
271 // y is a type parameter, x is not
272 if ty := u.y.at(j); ty != nil {
273 return u.nifyEq(x, ty, p)
275 // otherwise, infer type from x
280 // For type unification, do not shortcut (x == y) for identical
281 // types. Instead keep comparing them element-wise to unify the
282 // matching (and equal type parameter types). A simple test case
283 // where this matters is: func f[P any](a P) { f(a) } .
285 switch x := x.(type) {
287 // Basic types are singletons except for the rune and byte
288 // aliases, thus we cannot solely rely on the x == y check
289 // above. See also comment in TypeName.IsAlias.
290 if y, ok := y.(*Basic); ok {
291 return x.kind == y.kind
295 // Two array types are identical if they have identical element types
296 // and the same array length.
297 if y, ok := y.(*Array); ok {
298 // If one or both array lengths are unknown (< 0) due to some error,
299 // assume they are the same to avoid spurious follow-on errors.
300 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, p)
304 // Two slice types are identical if they have identical element types.
305 if y, ok := y.(*Slice); ok {
306 return u.nify(x.elem, y.elem, p)
310 // Two struct types are identical if they have the same sequence of fields,
311 // and if corresponding fields have the same names, and identical types,
312 // and identical tags. Two embedded fields are considered to have the same
313 // name. Lower-case field names from different packages are always different.
314 if y, ok := y.(*Struct); ok {
315 if x.NumFields() == y.NumFields() {
316 for i, f := range x.fields {
318 if f.embedded != g.embedded ||
319 x.Tag(i) != y.Tag(i) ||
320 !f.sameId(g.pkg, g.name) ||
321 !u.nify(f.typ, g.typ, p) {
330 // Two pointer types are identical if they have identical base types.
331 if y, ok := y.(*Pointer); ok {
332 return u.nify(x.base, y.base, p)
336 // Two tuples types are identical if they have the same number of elements
337 // and corresponding elements have identical types.
338 if y, ok := y.(*Tuple); ok {
339 if x.Len() == y.Len() {
341 for i, v := range x.vars {
343 if !u.nify(v.typ, w.typ, p) {
353 // Two function types are identical if they have the same number of parameters
354 // and result values, corresponding parameter and result types are identical,
355 // and either both functions are variadic or neither is. Parameter and result
356 // names are not required to match.
357 // TODO(gri) handle type parameters or document why we can ignore them.
358 if y, ok := y.(*Signature); ok {
359 return x.variadic == y.variadic &&
360 u.nify(x.params, y.params, p) &&
361 u.nify(x.results, y.results, p)
365 panic("unimplemented: unification with type sets described by types")
368 // Two interface types are identical if they have the same set of methods with
369 // the same names and identical function types. Lower-case method names from
370 // different packages are always different. The order of the methods is irrelevant.
371 if y, ok := y.(*Interface); ok {
374 if !Identical(xset.types, yset.types) {
379 if len(a) == len(b) {
380 // Interface types are the only types where cycles can occur
381 // that are not "terminated" via named types; and such cycles
382 // can only be created via method parameter types that are
383 // anonymous interfaces (directly or indirectly) embedding
384 // the current interface. Example:
386 // type T interface {
390 // If two such (differently named) interfaces are compared,
391 // endless recursion occurs if the cycle is not detected.
393 // If x and y were compared before, they must be equal
394 // (if they were not, the recursion would have stopped);
395 // search the ifacePair stack for the same pair.
397 // This is a quadratic algorithm, but in practice these stacks
398 // are extremely short (bounded by the nesting depth of interface
399 // type declarations that recur via parameter types, an extremely
400 // rare occurrence). An alternative implementation might use a
401 // "visited" map, but that is probably less efficient overall.
402 q := &ifacePair{x, y, p}
405 return true // same pair was compared before
410 assertSortedMethods(a)
411 assertSortedMethods(b)
413 for i, f := range a {
415 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, q) {
424 // Two map types are identical if they have identical key and value types.
425 if y, ok := y.(*Map); ok {
426 return u.nify(x.key, y.key, p) && u.nify(x.elem, y.elem, p)
430 // Two channel types are identical if they have identical value types.
431 if y, ok := y.(*Chan); ok {
432 return (!u.exact || x.dir == y.dir) && u.nify(x.elem, y.elem, p)
436 // Two named types are identical if their type names originate
437 // in the same type declaration.
438 // if y, ok := y.(*Named); ok {
439 // return x.obj == y.obj
441 if y, ok := y.(*Named); ok {
442 // TODO(gri) This is not always correct: two types may have the same names
443 // in the same package if one of them is nested in a function.
444 // Extremely unlikely but we need an always correct solution.
445 if x.obj.pkg == y.obj.pkg && x.obj.name == y.obj.name {
446 assert(len(x.targs) == len(y.targs))
447 for i, x := range x.targs {
448 if !u.nify(x, y.targs[i], p) {
457 // Two type parameters (which are not part of the type parameters of the
458 // enclosing type as those are handled in the beginning of this function)
459 // are identical if they originate in the same declaration.
463 // unreachable since types are expanded
466 // avoid a crash in case of nil type
469 panic(fmt.Sprintf("### u.nify(%s, %s), u.x.tparams = %s", x, y, u.x.tparams))