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// Copyright 2020 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// This file implements type unification.
//
// Type unification attempts to make two types x and y structurally
// equivalent by determining the types for a given list of (bound)
// type parameters which may occur within x and y. If x and y are
// structurally different (say []T vs chan T), or conflicting
// types are determined for type parameters, unification fails.
// If unification succeeds, as a side-effect, the types of the
// bound type parameters may be determined.
//
// Unification typically requires multiple calls u.unify(x, y) to
// a given unifier u, with various combinations of types x and y.
// In each call, additional type parameter types may be determined
// as a side effect and recorded in u.
// If a call fails (returns false), unification fails.
//
// In the unification context, structural equivalence of two types
// ignores the difference between a defined type and its underlying
// type if one type is a defined type and the other one is not.
// It also ignores the difference between an (external, unbound)
// type parameter and its core type.
// If two types are not structurally equivalent, they cannot be Go
// identical types. On the other hand, if they are structurally
// equivalent, they may be Go identical or at least assignable, or
// they may be in the type set of a constraint.
// Whether they indeed are identical or assignable is determined
// upon instantiation and function argument passing.
package types2
import (
"bytes"
"fmt"
"sort"
"strings"
)
const (
// Upper limit for recursion depth. Used to catch infinite recursions
// due to implementation issues (e.g., see issues go.dev/issue/48619, go.dev/issue/48656).
unificationDepthLimit = 50
// Whether to panic when unificationDepthLimit is reached.
// If disabled, a recursion depth overflow results in a (quiet)
// unification failure.
panicAtUnificationDepthLimit = true
// If enableCoreTypeUnification is set, unification will consider
// the core types, if any, of non-local (unbound) type parameters.
enableCoreTypeUnification = true
// If traceInference is set, unification will print a trace of its operation.
// Interpretation of trace:
// x ≡ y attempt to unify types x and y
// p ➞ y type parameter p is set to type y (p is inferred to be y)
// p ⇄ q type parameters p and q match (p is inferred to be q and vice versa)
// x ≢ y types x and y cannot be unified
// [p, q, ...] ➞ [x, y, ...] mapping from type parameters to types
traceInference = false
)
// A unifier maintains a list of type parameters and
// corresponding types inferred for each type parameter.
// A unifier is created by calling newUnifier.
type unifier struct {
// handles maps each type parameter to its inferred type through
// an indirection *Type called (inferred type) "handle".
// Initially, each type parameter has its own, separate handle,
// with a nil (i.e., not yet inferred) type.
// After a type parameter P is unified with a type parameter Q,
// P and Q share the same handle (and thus type). This ensures
// that inferring the type for a given type parameter P will
// automatically infer the same type for all other parameters
// unified (joined) with P.
handles map[*TypeParam]*Type
depth int // recursion depth during unification
enableInterfaceInference bool // use shared methods for better inference
}
// newUnifier returns a new unifier initialized with the given type parameter
// and corresponding type argument lists. The type argument list may be shorter
// than the type parameter list, and it may contain nil types. Matching type
// parameters and arguments must have the same index.
func newUnifier(tparams []*TypeParam, targs []Type, enableInterfaceInference bool) *unifier {
assert(len(tparams) >= len(targs))
handles := make(map[*TypeParam]*Type, len(tparams))
// Allocate all handles up-front: in a correct program, all type parameters
// must be resolved and thus eventually will get a handle.
// Also, sharing of handles caused by unified type parameters is rare and
// so it's ok to not optimize for that case (and delay handle allocation).
for i, x := range tparams {
var t Type
if i < len(targs) {
t = targs[i]
}
handles[x] = &t
}
return &unifier{handles, 0, enableInterfaceInference}
}
// unifyMode controls the behavior of the unifier.
type unifyMode uint
const (
// If assign is set, we are unifying types involved in an assignment:
// they may match inexactly at the top, but element types must match
// exactly.
assign unifyMode = 1 << iota
// If exact is set, types unify if they are identical (or can be
// made identical with suitable arguments for type parameters).
// Otherwise, a named type and a type literal unify if their
// underlying types unify, channel directions are ignored, and
// if there is an interface, the other type must implement the
// interface.
exact
)
func (m unifyMode) String() string {
switch m {
case 0:
return "inexact"
case assign:
return "assign"
case exact:
return "exact"
case assign | exact:
return "assign, exact"
}
return fmt.Sprintf("mode %d", m)
}
// unify attempts to unify x and y and reports whether it succeeded.
// As a side-effect, types may be inferred for type parameters.
// The mode parameter controls how types are compared.
func (u *unifier) unify(x, y Type, mode unifyMode) bool {
return u.nify(x, y, mode, nil)
}
func (u *unifier) tracef(format string, args ...interface{}) {
fmt.Println(strings.Repeat(". ", u.depth) + sprintf(nil, true, format, args...))
}
// String returns a string representation of the current mapping
// from type parameters to types.
func (u *unifier) String() string {
// sort type parameters for reproducible strings
tparams := make(typeParamsById, len(u.handles))
i := 0
for tpar := range u.handles {
tparams[i] = tpar
i++
}
sort.Sort(tparams)
var buf bytes.Buffer
w := newTypeWriter(&buf, nil)
w.byte('[')
for i, x := range tparams {
if i > 0 {
w.string(", ")
}
w.typ(x)
w.string(": ")
w.typ(u.at(x))
}
w.byte(']')
return buf.String()
}
type typeParamsById []*TypeParam
func (s typeParamsById) Len() int { return len(s) }
func (s typeParamsById) Less(i, j int) bool { return s[i].id < s[j].id }
func (s typeParamsById) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
// join unifies the given type parameters x and y.
// If both type parameters already have a type associated with them
// and they are not joined, join fails and returns false.
func (u *unifier) join(x, y *TypeParam) bool {
if traceInference {
u.tracef("%s ⇄ %s", x, y)
}
switch hx, hy := u.handles[x], u.handles[y]; {
case hx == hy:
// Both type parameters already share the same handle. Nothing to do.
case *hx != nil && *hy != nil:
// Both type parameters have (possibly different) inferred types. Cannot join.
return false
case *hx != nil:
// Only type parameter x has an inferred type. Use handle of x.
u.setHandle(y, hx)
// This case is treated like the default case.
// case *hy != nil:
// // Only type parameter y has an inferred type. Use handle of y.
// u.setHandle(x, hy)
default:
// Neither type parameter has an inferred type. Use handle of y.
u.setHandle(x, hy)
}
return true
}
// asTypeParam returns x.(*TypeParam) if x is a type parameter recorded with u.
// Otherwise, the result is nil.
func (u *unifier) asTypeParam(x Type) *TypeParam {
if x, _ := x.(*TypeParam); x != nil {
if _, found := u.handles[x]; found {
return x
}
}
return nil
}
// setHandle sets the handle for type parameter x
// (and all its joined type parameters) to h.
func (u *unifier) setHandle(x *TypeParam, h *Type) {
hx := u.handles[x]
assert(hx != nil)
for y, hy := range u.handles {
if hy == hx {
u.handles[y] = h
}
}
}
// at returns the (possibly nil) type for type parameter x.
func (u *unifier) at(x *TypeParam) Type {
return *u.handles[x]
}
// set sets the type t for type parameter x;
// t must not be nil.
func (u *unifier) set(x *TypeParam, t Type) {
assert(t != nil)
if traceInference {
u.tracef("%s ➞ %s", x, t)
}
*u.handles[x] = t
}
// unknowns returns the number of type parameters for which no type has been set yet.
func (u *unifier) unknowns() int {
n := 0
for _, h := range u.handles {
if *h == nil {
n++
}
}
return n
}
// inferred returns the list of inferred types for the given type parameter list.
// The result is never nil and has the same length as tparams; result types that
// could not be inferred are nil. Corresponding type parameters and result types
// have identical indices.
func (u *unifier) inferred(tparams []*TypeParam) []Type {
list := make([]Type, len(tparams))
for i, x := range tparams {
list[i] = u.at(x)
}
return list
}
// asInterface returns the underlying type of x as an interface if
// it is a non-type parameter interface. Otherwise it returns nil.
func asInterface(x Type) (i *Interface) {
if _, ok := x.(*TypeParam); !ok {
i, _ = under(x).(*Interface)
}
return i
}
// nify implements the core unification algorithm which is an
// adapted version of Checker.identical. For changes to that
// code the corresponding changes should be made here.
// Must not be called directly from outside the unifier.
func (u *unifier) nify(x, y Type, mode unifyMode, p *ifacePair) (result bool) {
u.depth++
if traceInference {
u.tracef("%s ≡ %s\t// %s", x, y, mode)
}
defer func() {
if traceInference && !result {
u.tracef("%s ≢ %s", x, y)
}
u.depth--
}()
x = Unalias(x)
y = Unalias(y)
// nothing to do if x == y
if x == y {
return true
}
// Stop gap for cases where unification fails.
if u.depth > unificationDepthLimit {
if traceInference {
u.tracef("depth %d >= %d", u.depth, unificationDepthLimit)
}
if panicAtUnificationDepthLimit {
panic("unification reached recursion depth limit")
}
return false
}
// Unification is symmetric, so we can swap the operands.
// Ensure that if we have at least one
// - defined type, make sure one is in y
// - type parameter recorded with u, make sure one is in x
if asNamed(x) != nil || u.asTypeParam(y) != nil {
if traceInference {
u.tracef("%s ≡ %s\t// swap", y, x)
}
x, y = y, x
}
// Unification will fail if we match a defined type against a type literal.
// If we are matching types in an assignment, at the top-level, types with
// the same type structure are permitted as long as at least one of them
// is not a defined type. To accommodate for that possibility, we continue
// unification with the underlying type of a defined type if the other type
// is a type literal. This is controlled by the exact unification mode.
// We also continue if the other type is a basic type because basic types
// are valid underlying types and may appear as core types of type constraints.
// If we exclude them, inferred defined types for type parameters may not
// match against the core types of their constraints (even though they might
// correctly match against some of the types in the constraint's type set).
// Finally, if unification (incorrectly) succeeds by matching the underlying
// type of a defined type against a basic type (because we include basic types
// as type literals here), and if that leads to an incorrectly inferred type,
// we will fail at function instantiation or argument assignment time.
//
// If we have at least one defined type, there is one in y.
if ny := asNamed(y); mode&exact == 0 && ny != nil && isTypeLit(x) && !(u.enableInterfaceInference && IsInterface(x)) {
if traceInference {
u.tracef("%s ≡ under %s", x, ny)
}
y = ny.under()
// Per the spec, a defined type cannot have an underlying type
// that is a type parameter.
assert(!isTypeParam(y))
// x and y may be identical now
if x == y {
return true
}
}
// Cases where at least one of x or y is a type parameter recorded with u.
// If we have at least one type parameter, there is one in x.
// If we have exactly one type parameter, because it is in x,
// isTypeLit(x) is false and y was not changed above. In other
// words, if y was a defined type, it is still a defined type
// (relevant for the logic below).
switch px, py := u.asTypeParam(x), u.asTypeParam(y); {
case px != nil && py != nil:
// both x and y are type parameters
if u.join(px, py) {
return true
}
// both x and y have an inferred type - they must match
return u.nify(u.at(px), u.at(py), mode, p)
case px != nil:
// x is a type parameter, y is not
if x := u.at(px); x != nil {
// x has an inferred type which must match y
if u.nify(x, y, mode, p) {
// We have a match, possibly through underlying types.
xi := asInterface(x)
yi := asInterface(y)
xn := asNamed(x) != nil
yn := asNamed(y) != nil
// If we have two interfaces, what to do depends on
// whether they are named and their method sets.
if xi != nil && yi != nil {
// Both types are interfaces.
// If both types are defined types, they must be identical
// because unification doesn't know which type has the "right" name.
if xn && yn {
return Identical(x, y)
}
// In all other cases, the method sets must match.
// The types unified so we know that corresponding methods
// match and we can simply compare the number of methods.
// TODO(gri) We may be able to relax this rule and select
// the more general interface. But if one of them is a defined
// type, it's not clear how to choose and whether we introduce
// an order dependency or not. Requiring the same method set
// is conservative.
if len(xi.typeSet().methods) != len(yi.typeSet().methods) {
return false
}
} else if xi != nil || yi != nil {
// One but not both of them are interfaces.
// In this case, either x or y could be viable matches for the corresponding
// type parameter, which means choosing either introduces an order dependence.
// Therefore, we must fail unification (go.dev/issue/60933).
return false
}
// If we have inexact unification and one of x or y is a defined type, select the
// defined type. This ensures that in a series of types, all matching against the
// same type parameter, we infer a defined type if there is one, independent of
// order. Type inference or assignment may fail, which is ok.
// Selecting a defined type, if any, ensures that we don't lose the type name;
// and since we have inexact unification, a value of equally named or matching
// undefined type remains assignable (go.dev/issue/43056).
//
// Similarly, if we have inexact unification and there are no defined types but
// channel types, select a directed channel, if any. This ensures that in a series
// of unnamed types, all matching against the same type parameter, we infer the
// directed channel if there is one, independent of order.
// Selecting a directional channel, if any, ensures that a value of another
// inexactly unifying channel type remains assignable (go.dev/issue/62157).
//
// If we have multiple defined channel types, they are either identical or we
// have assignment conflicts, so we can ignore directionality in this case.
//
// If we have defined and literal channel types, a defined type wins to avoid
// order dependencies.
if mode&exact == 0 {
switch {
case xn:
// x is a defined type: nothing to do.
case yn:
// x is not a defined type and y is a defined type: select y.
u.set(px, y)
default:
// Neither x nor y are defined types.
if yc, _ := under(y).(*Chan); yc != nil && yc.dir != SendRecv {
// y is a directed channel type: select y.
u.set(px, y)
}
}
}
return true
}
return false
}
// otherwise, infer type from y
u.set(px, y)
return true
}
// x != y if we get here
assert(x != y)
// If u.EnableInterfaceInference is set and we don't require exact unification,
// if both types are interfaces, one interface must have a subset of the
// methods of the other and corresponding method signatures must unify.
// If only one type is an interface, all its methods must be present in the
// other type and corresponding method signatures must unify.
if u.enableInterfaceInference && mode&exact == 0 {
// One or both interfaces may be defined types.
// Look under the name, but not under type parameters (go.dev/issue/60564).
xi := asInterface(x)
yi := asInterface(y)
// If we have two interfaces, check the type terms for equivalence,
// and unify common methods if possible.
if xi != nil && yi != nil {
xset := xi.typeSet()
yset := yi.typeSet()
if xset.comparable != yset.comparable {
return false
}
// For now we require terms to be equal.
// We should be able to relax this as well, eventually.
if !xset.terms.equal(yset.terms) {
return false
}
// Interface types are the only types where cycles can occur
// that are not "terminated" via named types; and such cycles
// can only be created via method parameter types that are
// anonymous interfaces (directly or indirectly) embedding
// the current interface. Example:
//
// type T interface {
// m() interface{T}
// }
//
// If two such (differently named) interfaces are compared,
// endless recursion occurs if the cycle is not detected.
//
// If x and y were compared before, they must be equal
// (if they were not, the recursion would have stopped);
// search the ifacePair stack for the same pair.
//
// This is a quadratic algorithm, but in practice these stacks
// are extremely short (bounded by the nesting depth of interface
// type declarations that recur via parameter types, an extremely
// rare occurrence). An alternative implementation might use a
// "visited" map, but that is probably less efficient overall.
q := &ifacePair{xi, yi, p}
for p != nil {
if p.identical(q) {
return true // same pair was compared before
}
p = p.prev
}
// The method set of x must be a subset of the method set
// of y or vice versa, and the common methods must unify.
xmethods := xset.methods
ymethods := yset.methods
// The smaller method set must be the subset, if it exists.
if len(xmethods) > len(ymethods) {
xmethods, ymethods = ymethods, xmethods
}
// len(xmethods) <= len(ymethods)
// Collect the ymethods in a map for quick lookup.
ymap := make(map[string]*Func, len(ymethods))
for _, ym := range ymethods {
ymap[ym.Id()] = ym
}
// All xmethods must exist in ymethods and corresponding signatures must unify.
for _, xm := range xmethods {
if ym := ymap[xm.Id()]; ym == nil || !u.nify(xm.typ, ym.typ, exact, p) {
return false
}
}
return true
}
// We don't have two interfaces. If we have one, make sure it's in xi.
if yi != nil {
xi = yi
y = x
}
// If we have one interface, at a minimum each of the interface methods
// must be implemented and thus unify with a corresponding method from
// the non-interface type, otherwise unification fails.
if xi != nil {
// All xi methods must exist in y and corresponding signatures must unify.
xmethods := xi.typeSet().methods
for _, xm := range xmethods {
obj, _, _ := LookupFieldOrMethod(y, false, xm.pkg, xm.name)
if ym, _ := obj.(*Func); ym == nil || !u.nify(xm.typ, ym.typ, exact, p) {
return false
}
}
return true
}
}
// Unless we have exact unification, neither x nor y are interfaces now.
// Except for unbound type parameters (see below), x and y must be structurally
// equivalent to unify.
// If we get here and x or y is a type parameter, they are unbound
// (not recorded with the unifier).
// Ensure that if we have at least one type parameter, it is in x
// (the earlier swap checks for _recorded_ type parameters only).
// This ensures that the switch switches on the type parameter.
//
// TODO(gri) Factor out type parameter handling from the switch.
if isTypeParam(y) {
if traceInference {
u.tracef("%s ≡ %s\t// swap", y, x)
}
x, y = y, x
}
// Type elements (array, slice, etc. elements) use emode for unification.
// Element types must match exactly if the types are used in an assignment.
emode := mode
if mode&assign != 0 {
emode |= exact
}
switch x := x.(type) {
case *Basic:
// Basic types are singletons except for the rune and byte
// aliases, thus we cannot solely rely on the x == y check
// above. See also comment in TypeName.IsAlias.
if y, ok := y.(*Basic); ok {
return x.kind == y.kind
}
case *Array:
// Two array types unify if they have the same array length
// and their element types unify.
if y, ok := y.(*Array); ok {
// If one or both array lengths are unknown (< 0) due to some error,
// assume they are the same to avoid spurious follow-on errors.
return (x.len < 0 || y.len < 0 || x.len == y.len) && u.nify(x.elem, y.elem, emode, p)
}
case *Slice:
// Two slice types unify if their element types unify.
if y, ok := y.(*Slice); ok {
return u.nify(x.elem, y.elem, emode, p)
}
case *Struct:
// Two struct types unify if they have the same sequence of fields,
// and if corresponding fields have the same names, their (field) types unify,
// and they have identical tags. Two embedded fields are considered to have the same
// name. Lower-case field names from different packages are always different.
if y, ok := y.(*Struct); ok {
if x.NumFields() == y.NumFields() {
for i, f := range x.fields {
g := y.fields[i]
if f.embedded != g.embedded ||
x.Tag(i) != y.Tag(i) ||
!f.sameId(g.pkg, g.name, false) ||
!u.nify(f.typ, g.typ, emode, p) {
return false
}
}
return true
}
}
case *Pointer:
// Two pointer types unify if their base types unify.
if y, ok := y.(*Pointer); ok {
return u.nify(x.base, y.base, emode, p)
}
case *Tuple:
// Two tuples types unify if they have the same number of elements
// and the types of corresponding elements unify.
if y, ok := y.(*Tuple); ok {
if x.Len() == y.Len() {
if x != nil {
for i, v := range x.vars {
w := y.vars[i]
if !u.nify(v.typ, w.typ, mode, p) {
return false
}
}
}
return true
}
}
case *Signature:
// Two function types unify if they have the same number of parameters
// and result values, corresponding parameter and result types unify,
// and either both functions are variadic or neither is.
// Parameter and result names are not required to match.
// TODO(gri) handle type parameters or document why we can ignore them.
if y, ok := y.(*Signature); ok {
return x.variadic == y.variadic &&
u.nify(x.params, y.params, emode, p) &&
u.nify(x.results, y.results, emode, p)
}
case *Interface:
assert(!u.enableInterfaceInference || mode&exact != 0) // handled before this switch
// Two interface types unify if they have the same set of methods with
// the same names, and corresponding function types unify.
// Lower-case method names from different packages are always different.
// The order of the methods is irrelevant.
if y, ok := y.(*Interface); ok {
xset := x.typeSet()
yset := y.typeSet()
if xset.comparable != yset.comparable {
return false
}
if !xset.terms.equal(yset.terms) {
return false
}
a := xset.methods
b := yset.methods
if len(a) == len(b) {
// Interface types are the only types where cycles can occur
// that are not "terminated" via named types; and such cycles
// can only be created via method parameter types that are
// anonymous interfaces (directly or indirectly) embedding
// the current interface. Example:
//
// type T interface {
// m() interface{T}
// }
//
// If two such (differently named) interfaces are compared,
// endless recursion occurs if the cycle is not detected.
//
// If x and y were compared before, they must be equal
// (if they were not, the recursion would have stopped);
// search the ifacePair stack for the same pair.
//
// This is a quadratic algorithm, but in practice these stacks
// are extremely short (bounded by the nesting depth of interface
// type declarations that recur via parameter types, an extremely
// rare occurrence). An alternative implementation might use a
// "visited" map, but that is probably less efficient overall.
q := &ifacePair{x, y, p}
for p != nil {
if p.identical(q) {
return true // same pair was compared before
}
p = p.prev
}
if debug {
assertSortedMethods(a)
assertSortedMethods(b)
}
for i, f := range a {
g := b[i]
if f.Id() != g.Id() || !u.nify(f.typ, g.typ, exact, q) {
return false
}
}
return true
}
}
case *Map:
// Two map types unify if their key and value types unify.
if y, ok := y.(*Map); ok {
return u.nify(x.key, y.key, emode, p) && u.nify(x.elem, y.elem, emode, p)
}
case *Chan:
// Two channel types unify if their value types unify
// and if they have the same direction.
// The channel direction is ignored for inexact unification.
if y, ok := y.(*Chan); ok {
return (mode&exact == 0 || x.dir == y.dir) && u.nify(x.elem, y.elem, emode, p)
}
case *Named:
// Two named types unify if their type names originate in the same type declaration.
// If they are instantiated, their type argument lists must unify.
if y := asNamed(y); y != nil {
// Check type arguments before origins so they unify
// even if the origins don't match; for better error
// messages (see go.dev/issue/53692).
xargs := x.TypeArgs().list()
yargs := y.TypeArgs().list()
if len(xargs) != len(yargs) {
return false
}
for i, xarg := range xargs {
if !u.nify(xarg, yargs[i], mode, p) {
return false
}
}
return identicalOrigin(x, y)
}
case *TypeParam:
// x must be an unbound type parameter (see comment above).
if debug {
assert(u.asTypeParam(x) == nil)
}
// By definition, a valid type argument must be in the type set of
// the respective type constraint. Therefore, the type argument's
// underlying type must be in the set of underlying types of that
// constraint. If there is a single such underlying type, it's the
// constraint's core type. It must match the type argument's under-
// lying type, irrespective of whether the actual type argument,
// which may be a defined type, is actually in the type set (that
// will be determined at instantiation time).
// Thus, if we have the core type of an unbound type parameter,
// we know the structure of the possible types satisfying such
// parameters. Use that core type for further unification
// (see go.dev/issue/50755 for a test case).
if enableCoreTypeUnification {
// Because the core type is always an underlying type,
// unification will take care of matching against a
// defined or literal type automatically.
// If y is also an unbound type parameter, we will end
// up here again with x and y swapped, so we don't
// need to take care of that case separately.
if cx := coreType(x); cx != nil {
if traceInference {
u.tracef("core %s ≡ %s", x, y)
}
// If y is a defined type, it may not match against cx which
// is an underlying type (incl. int, string, etc.). Use assign
// mode here so that the unifier automatically takes under(y)
// if necessary.
return u.nify(cx, y, assign, p)
}
}
// x != y and there's nothing to do
case nil:
// avoid a crash in case of nil type
default:
panic(sprintf(nil, true, "u.nify(%s, %s, %d)", x, y, mode))
}
return false
}