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Summary

The Fn traits should be modified to make the return type an associated type.

Motivation

The strongest reason is because it would permit impls like the following (example from @alexcrichton):

impl<R,F> Foo for F : FnMut() -> R { ... }

This impl is currently illegal because the parameter R is not constrained. (This also has an impact on my attempts to add variance, which would require a "phantom data" annotation for R for the same reason; but that RFC is not quite ready yet.)

Another related reason is that it often permits fewer type parameters. Rather than having a distinct type parameter for the return type, the associated type projection F::Output can be used. Consider the standard library Map type:

struct Map<A,B,I,F>
    where I : Iterator<Item=A>,
          F : FnMut(A) -> B,
{
    ...
}

impl<A,B,I,F> Iterator for Map<A,B,I,F>
    where I : Iterator<Item=A>,
          F : FnMut(A) -> B,
{
    type Item = B;
    ...
}

This type could be equivalently written:

struct Map<I,F>
    where I : Iterator, F : FnMut<(I::Item,)>
{
    ...
}

impl<I,F> Iterator for Map<I,F>,
    where I : Iterator,
          F : FnMut<(I::Item,)>,
{
    type Item = F::Output;
    ...
}

This example highlights one subtle point about the () notation, which is covered below.

Detailed design

The design has been implemented. You can see it in this pull request. The Fn trait is modified to read as follows:

trait Fn<A> {
    type Output;
    fn call(&self, args: A) -> Self::Output;
}

The other traits are modified in an analogous fashion.

Parentheses notation

The shorthand Foo(...) expands to Foo<(...), Output=()>. The shorthand Foo(..) -> B expands to Foo<(...), Output=B>. This implies that if you use the parenthetical notation, you must supply a return type (which could be a new type parameter). If you would prefer to leave the return type unspecified, you must use angle-bracket notation. (Note that using angle-bracket notation with the Fn traits is currently feature-gated, as described here.)

This can be seen in the In the Map example from the introduction. There the <> notation was used so that F::Output is left unbound:

struct Map<I,F>
    where I : Iterator, F : FnMut<(I::Item,)>

An alternative would be to retain the type parameter B:

struct Map<B,I,F>
    where I : Iterator, F : FnMut(I::Item) -> B

Or to remove the bound on F from the type definition and use it only in the impl:

struct Map<I,F>
    where I : Iterator
{
    ...
}

impl<B,I,F> Iterator for Map<I,F>,
    where I : Iterator,
          F : FnMut(I::Item) -> B
{
    type Item = F::Output;
    ...
}

Note that this final option is not legal without this change, because the type parameter B on the impl woudl be unconstrained.

Drawbacks

Cannot overload based on return type alone

This change means that you cannot overload indexing to "model" a trait like Default:

trait Default {
    fn default() -> Self;
}

That is, I can't do something like the following:

struct Defaulty;
impl<T:Default> Fn<()> for Defaulty {
    type Output = T;

    fn call(&self) -> T {
        Default::default()
    }
}

This is not possible because the impl type parameter T is not constrained.

This does not seem like a particularly strong limitation. Overloaded call notation is already less general than full traits in various ways (for example, it lacks the ability to define a closure that always panics; that is, the ! notation is not a type and hence something like FnMut() -> ! is not legal). The ability to overload based on return type is not removed, it is simply not something you can model using overloaded operators.

Alternatives

Special syntax to represent the lack of an Output binding

Rather than having people use angle-brackets to omit the Output binding, we could introduce some special syntax for this purpose. For example, FnMut() -> ? could desugar to FnMut<()> (whereas FnMut() alone desugars to FnMut<(), Output=()>). The first suggestion that is commonly made is FnMut() -> _, but that has an existing meaning in a function context (where _ represents a fresh type variable).

Change meaning of FnMut() to not bind the output

We could make FnMut() desugar to FnMut<()>, and hence require an explicit FnMut() -> () to bind the return type to unit. This feels suprising and inconsistent.

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