Make return type of the Fn traits an associated type

text/0000-fn-return-should-be-an-associated-type.md

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+- Start Date: (fill me in with today's date, YYYY-MM-DD)
+- RFC PR #: (leave this empty)
+- Rust Issue #: (leave this empty)
+
+# 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):
+
+```rust
+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:
+
+```rust
+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:
+
+```rust
+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:
+
+```rust
+trait Fn<A> {
+    type Output;
+    fn call(&self, args: A) -> Self::Output;
+}
+```
+
+The other traits are modified in an analogous fashion.
+
+[this pull request]: https://github.com/rust-lang/rust/pull/21019
+
+### 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][18875].)
+
+[18875]: https://github.com/rust-lang/rust/issues/18875
+
+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:
+
+```rust
+struct Map<I,F>
+    where I : Iterator, F : FnMut<(I::Item,)>
+```
+
+An alternative would be to retain the type parameter `B`:
+
+```rust
+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:
+
+```rust
+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`:
+
+```rust
+trait Default {
+    fn default() -> Self;
+}
+```
+
+That is, I can't do something like the following:
+
+```rust
+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.
+
+