`deduce_closure_signature` fails in with ambiguous self-referential aliases

trait Foo<'a> {
    type Input;
}

impl<'a, F: Fn(&'a u32)> Foo<'a> for F {
    type Input = &'a u32;
}

fn needs_super<F: for<'a> Fn(<F as Foo<'a>>::Input) + for<'a> Foo<'a>>(_: F) {}

fn main() {
    needs_super(|_: &u32| {}); // doesn't need deduce sig rn
    needs_super(|_| {}); // fails with old solver
}

taken from https://github.com/rust-lang/trait-system-refactor-initiative/issues/191#issuecomment-3307163025

We currently don't decide the closure signature for needs_super even though we have a ?expectation: for<'a> Fn(<?expectation as Foo<'a>>::Input). Doing this properly relies on higher-kinded inference variables.

With higher-kinded infer vars, we could set the closure signature to ?inf[?expectation, 'a] and constrain that infer var via a Projection(<?expectation as Foo<'!a>>::Input, [?expectation, '!a]) goal (where '!a is a placeholder.

Start with the self-contained Rust reproducer around needs_super and confirm that the closure without an explicit parameter type fails during deduce_closure_signature. Read the linked trait-system refactor discussion and investigate the higher-kinded inference-variable requirement. Done means the ambiguous self-referential alias case can infer the closure signature successfully.