2018-06-03

tl;dr: I explain what co-, contra- and invariance are and what the implications for Go's type system would be. In particular, why it's impossible to have variance in slices.

A question that comes up relatively often with Go newcomers is "why can't I pass e.g. an []int to a func([]interface{}) "? In this post I want to explore this question and its implications for Go. But the concept of variance (which this is about) is also useful in other languages.

Variance describes what happens to subtype relationships, when they are used in composite types. In this context, "A is a subtype of B" means that a value of type A can always be used, where a value of type B is required. Go doesn't have explicit subtype relationships - the closest it has is assignability which mostly determines whether types can be used interchangeably. Probably the most important case of this is given by interfaces: If a type T (whether its a concrete type, or itself an interface) implements an interface I, then T can be viewed as a subtype of I. In that sense, *bytes.Buffer is a subtype of io.ReadWriter, which is a subtype of io.Reader. And every type is a subtype of interface{} .

The easiest way to understand what variance means, is to look at function types. Let's assume, we have a type and a subtype - for example, let's look at *bytes.Buffer as a subtype of io.Reader . Say, we have a func() *bytes.Buffer . We could also use this like a func() io.Reader - we just reinterpret the return value as an io.Reader . The reverse is not true: We can't treat a func() io.Reader as a func() *bytes.Buffer , because not every io.Reader is a *bytes.Buffer . So, function return values could preserve the direction of subtyping relationships: If A is a subtype of B, func() A could be a subtype of func() B . This is called covariance.

func F () io . Reader { return new ( bytes . Buffer ) } func G () * bytes . Buffer { return new ( bytes . Buffer ) } func Use ( f func () io . Reader ) { useReader ( f ()) } func main () { Use ( F ) // Works Use ( G ) // Doesn't work right now; but *could* be made equivalent to… Use ( func () io . Reader { return G () }) }

On the other hand, say we have a func(*bytes.Buffer) . Now we can't use that as a func(io.Reader) : You can't call it with an io.Reader . But we can do the reverse. If we have a *bytes.Buffer , we can call a func(io.Reader) with it. Thus, function arguments reverse the subtype relationship: If A is a subtype of B, then func(B) could be a subtype of func(A) . This is called contravariance.

func F ( r io . Reader ) { useReader ( r ) } func G ( r * bytes . Buffer ) { useReader ( r ) } func Use ( f func ( * bytes . Buffer )) { b := new ( bytes . Buffer ) f ( b ) } func main () { Use ( F ) // Doesn't work right now; but *could* be made equivalent to… Use ( func ( r * bytes . Buffer ) { F ( r ) }) Use ( G ) // Works }

So, func is contravariant for arguments and covariant for return values. Of course, we can combine the two: If A and C are subtypes of B and D respectively, we can make func(B) C a subtype of func(A) D , by converting like this:

// *os.PathError implements error func F ( r io . Reader ) * os . PathError { // ... } func Use ( f func ( * bytes . Buffer ) error ) { b := new ( bytes . Buffer ) err := f ( b ) useError ( err ) } func main () { Use ( F ) // Could be made to be equivalent to Use ( func ( r * bytes . Buffer ) error { return F ( r ) }) }

However, func(A) C and func(B) D are incompatible. Neither can be a subtype of the other:

func F ( r * bytes . Buffer ) * os . PathError { // ... } func UseF ( f func ( io . Reader ) error ) { b := strings . NewReader ( "foobar" ) err := f ( b ) useError ( err ) } func G ( r io . Reader ) error { // ... } func UseG ( f func ( * bytes . Buffer ) * os . PathErorr ) { b := new ( bytes . Buffer ) err := f () usePathError ( err ) } func main () { UseF ( F ) // Can't work, because: UseF ( func ( r io . Reader ) error { return F ( r ) // type-error: io.Reader is not *bytes.Buffer }) UseG ( G ) // Can't work, because: UseG ( func ( r * bytes . Buffer ) * os . PathError { return G ( r ) // type-error: error is not *os.PathError }) }

So in this case, there just is not relationship between the composite types. This is called invariance.

Now, we can get back to our opening question: Why can't you use []int as []interface{} ? This really is the question "Why are slice-types invariant"?. The questioner assumes that because int is a subtype of interface{} , we should also make []int a subtype of []interface{} . However, we can now see a simple problem with that. Slices support (among other things) two fundamental operations, that we can roughly translate into function calls:

as := make ([] A , 10 ) a := as [ 0 ] // func Get(as []A, i int) A as [ 1 ] = a // func Set(as []A, i int, a A)

This shows a clear problem: The type A appears both as an argument and as a return type. So it appears both covariantly and contravariantly. So while with functions there is a relatively clear-cut answer to how variance might work, it just doesn't make a lot of sense for slices. Reading from it would require covariance but writing to it would require contravariance. In other words: If you'd make []int a subtype of []interface{} you'd need to explain how this code would work:

func G () { v := [] int { 1 , 2 , 3 } F ( v ) fmt . Println ( v ) } func F ( v [] interface {}) { // string is a subtype of interface{}, so this should be valid v [ 0 ] = "Oops" }

Channels give another interesting perspective here. The bidirectional channel type has the same issue as slices: Receiving requires covariance, whereas sending requires contravariance. But you can restrict the directionality of a channel and only allow send- or receive-operations respectively. So while chan A and chan B would not be related, we could make <-chan A a subtype of <-chan B . And chan<- B a subtype of chan<- A .

In that sense, read-only types have the potential to at least theoretically allow variance for slices. While []int still wouldn't be a subtype of []interface{} , we could make ro []int a subtype of ro []interface{} (borrowing the syntax from the proposal).

Lastly, I want to emphasize that all of these are just the theoretical issues with adding variance to Go's type system. I consider them harder, but even if we could solve them we would still run into practical issues. The most pressing of which is that subtypes have different memory representations:

var ( // super pseudo-code to illustrate x * bytes . Buffer // unsafe.Pointer y io . ReadWriter // struct{ itable *itab; value unsafe.Pointer } // where itable has two entries z io . Reader // struct{ itable *itab; value unsafe.Pointer } // where itable has one entry )

So even though you might think that all interfaces have the same memory representation, they actually don't, because the method tables have a different assumed layout. So in code like this

func Do ( f func () io . Reader ) { r := f () r . Read ( buf ) } func F () io . Reader { return new ( bytes . Buffer ) } func G () io . ReadWriter { return new ( bytes . Buffer ) } func H () * bytes . Buffer { return new ( bytes . Buffer ) } func main () { // All of F, G, H should be subtypes of func() io.Reader Do ( F ) Do ( G ) Do ( H ) }

there still needs to be a place where the return value of H is wrapped into an io.Reader and there needs to be a place where the itable of the return value of G is transformed into the correct format expected for an io.Reader . This isn't a huge problem for func : The compiler can generate the appropriate wrappers at the call site in main . There is a performance overhead, but only code that actually uses this form of subtyping needs to pay it. However, it becomes significant problem for slices.