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 {
79 w := newTypeWriter(&buf, nil)
81 for i, tpar := range d.tparams {
93 // init initializes d with the given type parameters.
94 // The type parameters must be in the order in which they appear in their declaration
95 // (this ensures that the tparams indices match the respective type parameter index).
96 func (d *tparamsList) init(tparams []*TypeParam) {
97 if len(tparams) == 0 {
101 for i, tpar := range tparams {
102 assert(i == tpar.index)
106 d.indices = make([]int, len(tparams))
109 // join unifies the i'th type parameter of x with the j'th type parameter of y.
110 // If both type parameters already have a type associated with them and they are
111 // not joined, join fails and returns false.
112 func (u *unifier) join(i, j int) bool {
116 case ti == 0 && tj == 0:
117 // Neither type parameter has a type slot associated with them.
118 // Allocate a new joined nil type slot (negative index).
119 u.types = append(u.types, nil)
120 u.x.indices[i] = -len(u.types)
121 u.y.indices[j] = -len(u.types)
123 // The type parameter for x has no type slot yet. Use slot of y.
126 // The type parameter for y has no type slot yet. Use slot of x.
129 // Both type parameters have a slot: ti != 0 && tj != 0.
131 // Both type parameters already share the same slot. Nothing to do.
133 case ti > 0 && tj > 0:
134 // Both type parameters have (possibly different) inferred types. Cannot join.
135 // TODO(gri) Should we check if types are identical? Investigate.
138 // Only the type parameter for x has an inferred type. Use x slot for y.
140 // This case is handled like the default case.
142 // // Only the type parameter for y has an inferred type. Use y slot for x.
143 // u.x.setIndex(i, tj)
145 // Neither type parameter has an inferred type. Use y slot for x
146 // (or x slot for y, it doesn't matter).
152 // If typ is a type parameter of d, index returns the type parameter index.
153 // Otherwise, the result is < 0.
154 func (d *tparamsList) index(typ Type) int {
155 if tpar, ok := typ.(*TypeParam); ok {
156 return tparamIndex(d.tparams, tpar)
161 // If tpar is a type parameter in list, tparamIndex returns the type parameter index.
162 // Otherwise, the result is < 0. tpar must not be nil.
163 func tparamIndex(list []*TypeParam, tpar *TypeParam) int {
164 // Once a type parameter is bound its index is >= 0. However, there are some
165 // code paths (namely tracing and type hashing) by which it is possible to
166 // arrive here with a type parameter that has not been bound, hence the check
168 // TODO(rfindley): investigate a better approach for guarding against using
169 // unbound type parameters.
170 if i := tpar.index; 0 <= i && i < len(list) && list[i] == tpar {
176 // setIndex sets the type slot index for the i'th type parameter
177 // (and all its joined parameters) to tj. The type parameter
178 // must have a (possibly nil) type slot associated with it.
179 func (d *tparamsList) setIndex(i, tj int) {
181 assert(ti != 0 && tj != 0)
182 for k, tk := range d.indices {
189 // at returns the type set for the i'th type parameter; or nil.
190 func (d *tparamsList) at(i int) Type {
191 if ti := d.indices[i]; ti > 0 {
192 return d.unifier.types[ti-1]
197 // set sets the type typ for the i'th type parameter;
198 // typ must not be nil and it must not have been set before.
199 func (d *tparamsList) set(i int, typ Type) {
202 switch ti := d.indices[i]; {
207 u.types = append(u.types, typ)
208 d.indices[i] = len(u.types)
210 panic("type already set")
214 // types returns the list of inferred types (via unification) for the type parameters
215 // described by d, and an index. If all types were inferred, the returned index is < 0.
216 // Otherwise, it is the index of the first type parameter which couldn't be inferred;
217 // i.e., for which list[index] is nil.
218 func (d *tparamsList) types() (list []Type, index int) {
219 list = make([]Type, len(d.tparams))
221 for i := range d.tparams {
224 if index < 0 && t == nil {
231 func (u *unifier) nifyEq(x, y Type, p *ifacePair) bool {
232 return x == y || u.nify(x, y, p)
235 // nify implements the core unification algorithm which is an
236 // adapted version of Checker.identical. For changes to that
237 // code the corresponding changes should be made here.
238 // Must not be called directly from outside the unifier.
239 func (u *unifier) nify(x, y Type, p *ifacePair) bool {
241 // If exact unification is known to fail because we attempt to
242 // match a type name against an unnamed type literal, consider
243 // the underlying type of the named type.
244 // (We use !hasName to exclude any type with a name, including
245 // basic types and type parameters; the rest are unamed types.)
246 if nx, _ := x.(*Named); nx != nil && !hasName(y) {
247 return u.nify(nx.under(), y, p)
248 } else if ny, _ := y.(*Named); ny != nil && !hasName(x) {
249 return u.nify(x, ny.under(), p)
253 // Cases where at least one of x or y is a type parameter.
254 switch i, j := u.x.index(x), u.y.index(y); {
255 case i >= 0 && j >= 0:
256 // both x and y are type parameters
260 // both x and y have an inferred type - they must match
261 return u.nifyEq(u.x.at(i), u.y.at(j), p)
264 // x is a type parameter, y is not
265 if tx := u.x.at(i); tx != nil {
266 return u.nifyEq(tx, y, p)
268 // otherwise, infer type from y
273 // y is a type parameter, x is not
274 if ty := u.y.at(j); ty != nil {
275 return u.nifyEq(x, ty, p)
277 // otherwise, infer type from x
282 // For type unification, do not shortcut (x == y) for identical
283 // types. Instead keep comparing them element-wise to unify the
284 // matching (and equal type parameter types). A simple test case
285 // where this matters is: func f[P any](a P) { f(a) } .
287 switch x := x.(type) {
289 // Basic types are singletons except for the rune and byte
290 // aliases, thus we cannot solely rely on the x == y check
291 // above. See also comment in TypeName.IsAlias.
292 if y, ok := y.(*Basic); ok {
293 return x.kind == y.kind
297 // Two array types are identical if they have identical element types
298 // and the same array length.
299 if y, ok := y.(*Array); ok {
300 // If one or both array lengths are unknown (< 0) due to some error,
301 // assume they are the same to avoid spurious follow-on errors.
302 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, p)
306 // Two slice types are identical if they have identical element types.
307 if y, ok := y.(*Slice); ok {
308 return u.nify(x.elem, y.elem, p)
312 // Two struct types are identical if they have the same sequence of fields,
313 // and if corresponding fields have the same names, and identical types,
314 // and identical tags. Two embedded fields are considered to have the same
315 // name. Lower-case field names from different packages are always different.
316 if y, ok := y.(*Struct); ok {
317 if x.NumFields() == y.NumFields() {
318 for i, f := range x.fields {
320 if f.embedded != g.embedded ||
321 x.Tag(i) != y.Tag(i) ||
322 !f.sameId(g.pkg, g.name) ||
323 !u.nify(f.typ, g.typ, p) {
332 // Two pointer types are identical if they have identical base types.
333 if y, ok := y.(*Pointer); ok {
334 return u.nify(x.base, y.base, p)
338 // Two tuples types are identical if they have the same number of elements
339 // and corresponding elements have identical types.
340 if y, ok := y.(*Tuple); ok {
341 if x.Len() == y.Len() {
343 for i, v := range x.vars {
345 if !u.nify(v.typ, w.typ, p) {
355 // Two function types are identical if they have the same number of parameters
356 // and result values, corresponding parameter and result types are identical,
357 // and either both functions are variadic or neither is. Parameter and result
358 // names are not required to match.
359 // TODO(gri) handle type parameters or document why we can ignore them.
360 if y, ok := y.(*Signature); ok {
361 return x.variadic == y.variadic &&
362 u.nify(x.params, y.params, p) &&
363 u.nify(x.results, y.results, p)
367 // Two interface types are identical if they have the same set of methods with
368 // the same names and identical function types. Lower-case method names from
369 // different packages are always different. The order of the methods is irrelevant.
370 if y, ok := y.(*Interface); ok {
373 if !xset.terms.equal(yset.terms) {
378 if len(a) == len(b) {
379 // Interface types are the only types where cycles can occur
380 // that are not "terminated" via named types; and such cycles
381 // can only be created via method parameter types that are
382 // anonymous interfaces (directly or indirectly) embedding
383 // the current interface. Example:
385 // type T interface {
389 // If two such (differently named) interfaces are compared,
390 // endless recursion occurs if the cycle is not detected.
392 // If x and y were compared before, they must be equal
393 // (if they were not, the recursion would have stopped);
394 // search the ifacePair stack for the same pair.
396 // This is a quadratic algorithm, but in practice these stacks
397 // are extremely short (bounded by the nesting depth of interface
398 // type declarations that recur via parameter types, an extremely
399 // rare occurrence). An alternative implementation might use a
400 // "visited" map, but that is probably less efficient overall.
401 q := &ifacePair{x, y, p}
404 return true // same pair was compared before
409 assertSortedMethods(a)
410 assertSortedMethods(b)
412 for i, f := range a {
414 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, q) {
423 // Two map types are identical if they have identical key and value types.
424 if y, ok := y.(*Map); ok {
425 return u.nify(x.key, y.key, p) && u.nify(x.elem, y.elem, p)
429 // Two channel types are identical if they have identical value types.
430 if y, ok := y.(*Chan); ok {
431 return (!u.exact || x.dir == y.dir) && u.nify(x.elem, y.elem, p)
435 // TODO(gri) This code differs now from the parallel code in Checker.identical. Investigate.
436 if y, ok := y.(*Named); ok {
437 xargs := x.targs.list()
438 yargs := y.targs.list()
440 // TODO(gri) This is not always correct: two types may have the same names
441 // in the same package if one of them is nested in a function.
442 // Extremely unlikely but we need an always correct solution.
443 if x.obj.pkg == y.obj.pkg && x.obj.name == y.obj.name {
444 assert(len(xargs) == len(yargs))
445 for i, x := range xargs {
446 if !u.nify(x, yargs[i], p) {
455 // Two type parameters (which are not part of the type parameters of the
456 // enclosing type as those are handled in the beginning of this function)
457 // are identical if they originate in the same declaration.
461 // avoid a crash in case of nil type
464 panic(fmt.Sprintf("### u.nify(%s, %s), u.x.tparams = %s", x, y, u.x.tparams))