meaning of `impl Fn() -> impl Trait` (and potentially `impl Foo<Output = impl Bar>`

[nikomatsakis]

Motivation

As of 2023-04-10, the compiler permits impl Foo<Output = impl Bar> but not impl Fn() -> impl Bar. There have been proposals to permit impl Trait in the latter position -- but what should it mean?

Details

This issue exists to catalog the various options.

• In argument position:
  • fn something(f: impl Fn() -> impl Debug) could be equivalent to fn something<A,E>(f: A) where A: Fn() -> E, E: Debug, but this cannot accommodate higher-ranked signatures like impl Fn(&u32) -> impl Debug + '_.
  • fn something(f: impl Fn() -> impl Debug) could also be equivalent to fn something<A>(f: A) where A: Fn() -> _, A::Output: Debug (this is not legal syntax today, the -> _ is meant to mean "returns some type not specified). This would accommodate said signatures.
  • The same is relevant to impl Foo<Output = impl Bar>; for example to permit writing something like impl for<'a> Foo<Output<'a> = impl Bar + 'a> (not currently possible). Can we transition from current behavior to this? Not entirely backwards compatible, perhaps, but likely achievable. (Today, impl for<'a> Foo<Output<'a> = impl Bar> would assert that Output value is not dependent on 'a because the impl Bar desugars to a generic parameter outside the scope of the for.)
    cannot.
• In return position:
  • fn something() -> impl Fn() -> impl Debug could be equivalent to type A: Fn() -> B; type B: Debug; fn something() -> A