Add `AsyncFn` family of traits
I'm proposing to add a new family of `async`hronous `Fn`-like traits to the standard library for experimentation purposes.
## Why do we need new traits?
On the user side, it is useful to be able to express `AsyncFn` trait bounds natively via the parenthesized sugar syntax, i.e. `x: impl AsyncFn(&str) -> String` when experimenting with async-closure code.
This also does not preclude `AsyncFn` becoming something else like a trait alias if a more fundamental desugaring (which can take many[^1] different[^2] forms) comes around. I think we should be able to play around with `AsyncFn` well before that, though.
I'm also not proposing stabilization of these trait names any time soon (we may even want to instead express them via new syntax, like `async Fn() -> ..`), but I also don't think we need to introduce an obtuse bikeshedding name, since `AsyncFn` just makes sense.
## The lending problem: why not add a more fundamental primitive of `LendingFn`/`LendingFnMut`?
Firstly, for `async` closures to be as flexible as possible, they must be allowed to return futures which borrow from the async closure's captures. This can be done by introducing `LendingFn`/`LendingFnMut` traits, or (equivalently) by adding a new generic associated type to `FnMut` which allows the return type to capture lifetimes from the `&mut self` argument of the trait. This was proposed in one of [Niko's blog posts](https://smallcultfollowing.com/babysteps/blog/2023/05/09/giving-lending-and-async-closures/).
Upon further experimentation, for the purposes of closure type- and borrow-checking, I've come to the conclusion that it's significantly harder to teach the compiler how to handle *general* lending closures which may borrow from their captures. This is, because unlike `Fn`/`FnMut`, the `LendingFn`/`LendingFnMut` traits don't form a simple "inheritance" hierarchy whose top trait is `FnOnce`.
```mermaid
flowchart LR
Fn
FnMut
FnOnce
LendingFn
LendingFnMut
Fn -- isa --> FnMut
FnMut -- isa --> FnOnce
LendingFn -- isa --> LendingFnMut
Fn -- isa --> LendingFn
FnMut -- isa --> LendingFnMut
```
For example:
```
fn main() {
let s = String::from("hello, world");
let f = move || &s;
let x = f(); // This borrows `f` for some lifetime `'1` and returns `&'1 String`.
```
That trait hierarchy means that in general for "lending" closures, like `f` above, there's not really a meaningful return type for `<typeof(f) as FnOnce>::Output` -- it can't return `&'static str`, for example.
### Special-casing this problem:
By splitting out these traits manually, and making sure that each trait has its own associated future type, we side-step the issue of having to answer the questions of a general `LendingFn`/`LendingFnMut` implementation, since the compiler knows how to generate built-in implementations for first-class constructs like async closures, including the required future types for the (by-move) `AsyncFnOnce` and (by-ref) `AsyncFnMut`/`AsyncFn` trait implementations.
[^1]: For example, with trait transformers, we may eventually be able to write: `trait AsyncFn = async Fn;`
[^2]: For example, via the introduction of a more fundamental "`LendingFn`" trait, plus a [special desugaring with augmented trait aliases](https://rust-lang.zulipchat.com/#narrow/stream/213817-t-lang/topic/Lending.20closures.20and.20Fn*.28.29.20-.3E.20impl.20Trait/near/408471480).
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