Can a CombinatorSystem be used as IntoSystem?

[focustense]

I normally don't have trouble with complex generics, but these system and system parameter types are proving too much for me.

I'm trying to consume an API that wants a particular system function. The signature looks like::

fn set_system<Params>(sys: impl IntoSystem<(Entity, Entity), bool, Params>) { ... }

Writing systems to pass into this involves a lot of repetitive boilerplate. So I thought I could abstract the boilerplate into its own function, and only have to keep rewriting the part that changes:

pub type Foo<A, B> = CombinatorSystem<FooMarker, A, B>;

pub struct FooMarker;

impl<A, B> Combine<A, B> for FooMarker
where
    A: System<In = Entity, Out = Option<Entity>>,
    B: System<In = (Entity, Entity, Entity), Out = bool>,
{
    type In = (Entity, Entity);
    type Out = bool;

    fn combine(
        input: Self::In,
        a: impl FnOnce(A::In) -> A::Out,
        b: impl FnOnce(B::In) -> B::Out
    ) -> Self::Out {
        let (entity, other_entity) = input;
        let Some(third_entity) = a(entity) else { return false; };
        b((entity, third_entity, other_entity))
    }
}

It's not really all that important what A and B actually do here (I think). To make things tangible, let's say that it's a Parent query, although in reality it's more involved.

I thought that the result of this combinator would have the correct type. It takes (Entity, Entity) as input, and emits bool as output. However, it's apparently not a compatible type, and as per #1519, the compiler error messages are of little help.

error[E0277]: the trait bound CombinatorSystem<FooMarker, for<'a, 'b, 'c, 'd> fn(bevy::prelude::In<bevy::prelude::Entity>, bevy::prelude::Res<'a, MyResource>, bevy::prelude::Query<'b, 'c, &'d mut SomeState>) {update_some_state}, for<'a, 'b, 'c> fn(bevy::prelude::In<(bevy::prelude::Entity, bevy::prelude::Entity)>, bevy::prelude::Res<'a, OtherResource>, OtherQuery) -> bool {common_fn::<CommonParams>}>: bevy::prelude::IntoSystem<(bevy::prelude::Entity, bevy::prelude::Entity, bevy::prelude::Entity), bool, _> is not satisfied

I elided some things in the error, so it might not be 100% true to form, but it's easily repro so I hope it's clear enough.

Interestingly, if I try to explicitly implement IntoSystem<...> on FooMarker, I get an error about a conflicting implementation. So it obviously implements some variant of IntoSystem... just not the one I'm expecting.

What am I getting wrong here, and is it even possible to do what I'm trying to do, or are systems just not designed to do this?

(P.S. Essentially what I want is just a pipe, except the pipe function requires that the origin be an open (no input) system, and in this case the origin system does have inputs. I'm guessing I'd be having the same problem even if pipe did accept an input-dependent system. Seems likely the disconnect has to do with the precise relationships between System, IntoSystem and the Fn types, which are not so easy to map out.)