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 t, ok := typ.(*TypeParam); ok {
154 if i := t.index; i < len(d.tparams) && d.tparams[i].typ == t {
161 // setIndex sets the type slot index for the i'th type parameter
162 // (and all its joined parameters) to tj. The type parameter
163 // must have a (possibly nil) type slot associated with it.
164 func (d *tparamsList) setIndex(i, tj int) {
166 assert(ti != 0 && tj != 0)
167 for k, tk := range d.indices {
174 // at returns the type set for the i'th type parameter; or nil.
175 func (d *tparamsList) at(i int) Type {
176 if ti := d.indices[i]; ti > 0 {
177 return d.unifier.types[ti-1]
182 // set sets the type typ for the i'th type parameter;
183 // typ must not be nil and it must not have been set before.
184 func (d *tparamsList) set(i int, typ Type) {
187 switch ti := d.indices[i]; {
192 u.types = append(u.types, typ)
193 d.indices[i] = len(u.types)
195 panic("type already set")
199 // types returns the list of inferred types (via unification) for the type parameters
200 // described by d, and an index. If all types were inferred, the returned index is < 0.
201 // Otherwise, it is the index of the first type parameter which couldn't be inferred;
202 // i.e., for which list[index] is nil.
203 func (d *tparamsList) types() (list []Type, index int) {
204 list = make([]Type, len(d.tparams))
206 for i := range d.tparams {
209 if index < 0 && t == nil {
216 func (u *unifier) nifyEq(x, y Type, p *ifacePair) bool {
217 return x == y || u.nify(x, y, p)
220 // nify implements the core unification algorithm which is an
221 // adapted version of Checker.identical0. For changes to that
222 // code the corresponding changes should be made here.
223 // Must not be called directly from outside the unifier.
224 func (u *unifier) nify(x, y Type, p *ifacePair) bool {
225 // types must be expanded for comparison
230 // If exact unification is known to fail because we attempt to
231 // match a type name against an unnamed type literal, consider
232 // the underlying type of the named type.
233 // (Subtle: We use isNamed to include any type with a name (incl.
234 // basic types and type parameters. We use asNamed because we only
235 // want *Named types.)
237 case !isNamed(x) && y != nil && asNamed(y) != nil:
238 return u.nify(x, under(y), p)
239 case x != nil && asNamed(x) != nil && !isNamed(y):
240 return u.nify(under(x), y, p)
244 // Cases where at least one of x or y is a type parameter.
245 switch i, j := u.x.index(x), u.y.index(y); {
246 case i >= 0 && j >= 0:
247 // both x and y are type parameters
251 // both x and y have an inferred type - they must match
252 return u.nifyEq(u.x.at(i), u.y.at(j), p)
255 // x is a type parameter, y is not
256 if tx := u.x.at(i); tx != nil {
257 return u.nifyEq(tx, y, p)
259 // otherwise, infer type from y
264 // y is a type parameter, x is not
265 if ty := u.y.at(j); ty != nil {
266 return u.nifyEq(x, ty, p)
268 // otherwise, infer type from x
273 // For type unification, do not shortcut (x == y) for identical
274 // types. Instead keep comparing them element-wise to unify the
275 // matching (and equal type parameter types). A simple test case
276 // where this matters is: func f[P any](a P) { f(a) } .
278 switch x := x.(type) {
280 // Basic types are singletons except for the rune and byte
281 // aliases, thus we cannot solely rely on the x == y check
282 // above. See also comment in TypeName.IsAlias.
283 if y, ok := y.(*Basic); ok {
284 return x.kind == y.kind
288 // Two array types are identical if they have identical element types
289 // and the same array length.
290 if y, ok := y.(*Array); ok {
291 // If one or both array lengths are unknown (< 0) due to some error,
292 // assume they are the same to avoid spurious follow-on errors.
293 return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, p)
297 // Two slice types are identical if they have identical element types.
298 if y, ok := y.(*Slice); ok {
299 return u.nify(x.elem, y.elem, p)
303 // Two struct types are identical if they have the same sequence of fields,
304 // and if corresponding fields have the same names, and identical types,
305 // and identical tags. Two embedded fields are considered to have the same
306 // name. Lower-case field names from different packages are always different.
307 if y, ok := y.(*Struct); ok {
308 if x.NumFields() == y.NumFields() {
309 for i, f := range x.fields {
311 if f.embedded != g.embedded ||
312 x.Tag(i) != y.Tag(i) ||
313 !f.sameId(g.pkg, g.name) ||
314 !u.nify(f.typ, g.typ, p) {
323 // Two pointer types are identical if they have identical base types.
324 if y, ok := y.(*Pointer); ok {
325 return u.nify(x.base, y.base, p)
329 // Two tuples types are identical if they have the same number of elements
330 // and corresponding elements have identical types.
331 if y, ok := y.(*Tuple); ok {
332 if x.Len() == y.Len() {
334 for i, v := range x.vars {
336 if !u.nify(v.typ, w.typ, p) {
346 // Two function types are identical if they have the same number of parameters
347 // and result values, corresponding parameter and result types are identical,
348 // and either both functions are variadic or neither is. Parameter and result
349 // names are not required to match.
350 // TODO(gri) handle type parameters or document why we can ignore them.
351 if y, ok := y.(*Signature); ok {
352 return x.variadic == y.variadic &&
353 u.nify(x.params, y.params, p) &&
354 u.nify(x.results, y.results, p)
358 // This should not happen with the current internal use of union types.
359 panic("type inference across union types not implemented")
362 // Two interface types are identical if they have the same set of methods with
363 // the same names and identical function types. Lower-case method names from
364 // different packages are always different. The order of the methods is irrelevant.
365 if y, ok := y.(*Interface); ok {
366 a := x.typeSet().methods
367 b := y.typeSet().methods
368 if len(a) == len(b) {
369 // Interface types are the only types where cycles can occur
370 // that are not "terminated" via named types; and such cycles
371 // can only be created via method parameter types that are
372 // anonymous interfaces (directly or indirectly) embedding
373 // the current interface. Example:
375 // type T interface {
379 // If two such (differently named) interfaces are compared,
380 // endless recursion occurs if the cycle is not detected.
382 // If x and y were compared before, they must be equal
383 // (if they were not, the recursion would have stopped);
384 // search the ifacePair stack for the same pair.
386 // This is a quadratic algorithm, but in practice these stacks
387 // are extremely short (bounded by the nesting depth of interface
388 // type declarations that recur via parameter types, an extremely
389 // rare occurrence). An alternative implementation might use a
390 // "visited" map, but that is probably less efficient overall.
391 q := &ifacePair{x, y, p}
394 return true // same pair was compared before
399 assertSortedMethods(a)
400 assertSortedMethods(b)
402 for i, f := range a {
404 if f.Id() != g.Id() || !u.nify(f.typ, g.typ, q) {
413 // Two map types are identical if they have identical key and value types.
414 if y, ok := y.(*Map); ok {
415 return u.nify(x.key, y.key, p) && u.nify(x.elem, y.elem, p)
419 // Two channel types are identical if they have identical value types.
420 if y, ok := y.(*Chan); ok {
421 return (!u.exact || x.dir == y.dir) && u.nify(x.elem, y.elem, p)
425 // Two named types are identical if their type names originate
426 // in the same type declaration.
427 // if y, ok := y.(*Named); ok {
428 // return x.obj == y.obj
430 if y, ok := y.(*Named); ok {
431 // TODO(gri) This is not always correct: two types may have the same names
432 // in the same package if one of them is nested in a function.
433 // Extremely unlikely but we need an always correct solution.
434 if x.obj.pkg == y.obj.pkg && x.obj.name == y.obj.name {
435 assert(len(x.targs) == len(y.targs))
436 for i, x := range x.targs {
437 if !u.nify(x, y.targs[i], p) {
446 // Two type parameters (which are not part of the type parameters of the
447 // enclosing type as those are handled in the beginning of this function)
448 // are identical if they originate in the same declaration.
452 // unreachable since types are expanded
455 // avoid a crash in case of nil type
458 panic(fmt.Sprintf("### u.nify(%s, %s), u.x.tparams = %s", x, y, u.x.tparams))