fix: trait where clause check fixes

[asterite]

Description

Problem

Resolves #9367
Resolves #7024

Summary

First issue

The first issue has this code:

pub trait Foo<U> {}

pub trait Baz<T, U>
where
    T: Foo<U>,
{}

pub struct HasFoo1 {}
impl Foo<()> for HasFoo1 {}

pub struct HasBaz1 {}
impl Baz<HasFoo1, ()> for HasBaz1 {}

fn main() {}

• For impl Baz<HasFoo1, ()> for HasBaz1 {} we'll need to see if T: Foo<U> holds, where T is HasFoo1 and U is ().
• The constraint to solve, when debugging this, is T'3: Foo<U'4>
• We can also see that after binding the ordered generics in Baz<HasFoo1, ()> we end up with these bindings: '4: (), '3: HasFoo1
• We were correctly applying bindings to the constraint type (T) so it became HasFoo1, but we didn't do so for the entire constraint, meaning that the constraint remained as HasFoo1: Foo<U'4> and failed as there is no such generic impl.
• The fix was to also apply bindings (well, substitute) to the trait bound (and generally to the entire constraint) so that the constraint becomes HasFoo1: Foo<()> which now holds.

Second issue

This is the code:

pub trait BarTrait {}

pub trait Foo {
    type Bar;
}

pub trait Baz<T>
where
    T: Foo,
    <T as Foo>::Bar: BarTrait,
{}

pub struct HasBarTrait1 {}
impl BarTrait for HasBarTrait1 {}

pub struct HasFoo1 {}
impl Foo for HasFoo1 {
    type Bar = HasBarTrait1;
}

pub struct HasBaz1 {}
impl Baz<HasFoo1> for HasBaz1 {}

fn main() {}

• Here we start by checking Baz<HasFoo1>. For that we need to check that T: Foo and <T as Foo>::Bar: BarTrait hold.
• We first check T'4: Foo where we having '4: HasFoo1 in bindings, so we end up checking HasFoo1: Foo which succeeds
• Actually, because Foo has an associated type we check HasFoo1: Foo<Bar = <T as Foo>::Bar'6> where <T as Foo>::Bar'6 is an implicitly added named generic
• In a recent PR we started replacing these implicitly added named generics with type variables so that the trait impl lookup succeeds. In this case we end up replacing <T as Foo>::Bar'6 with '10, so we are really checking HasFoo1: Foo<Bar = '10>, which succeeds.
• Next we check the next constraint, <T as Foo>::Bar'6: BarTrait. The problem here is that this will fail as the constraint type is an unbound named generic. It's actually the implicitly added named generic!
• The solution here is to first remember that we replaced <T as Foo>::Bar'6 with '10. We do this by storing it in bindings: '6: '10.
• Next, after we check HasFoo1: Foo<Bar = '10>, try_lookup_trait_implementation will return these bindings: '10: HasBarTrait1. We were ignoring these returned bindings but not anymore: we add them to the existing bindings.
• Finally, when we need to solve <T as Foo>::Bar'6: BarTrait we apply bindings. Because we have '6: '10, '10: HasBarTrait1 we end up solving HasBarTrait1: BarTrait which now holds! 🎉

Sorry for the long explanation but since I'm starting to understand how bindings work I wanted to convince myself that the code I'm writing makes sense.

Additional Context

As a bonus, if the where clause has this order:

where
    <T as Foo>::Bar: BarTrait,
    T: Foo,

it would fail in Noir but actually succeed in Rust. I don't know how they do it but I implemented something for that here: we reorder the where clause so that "simpler" constraint types come before more complex ones. In this case T is simpler than <T as Foo>::Bar so we end up putting before it, and then it works.

Documentation

Check one:

• No documentation needed.
• Documentation included in this PR.
• [For Experimental Features] Documentation to be submitted in a separate PR.

PR Checklist

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[github-actions]

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'Test Suite Duration'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.20.

Benchmark suite	Current: 76a61e5	Previous: 9846e1e	Ratio
test_report_AztecProtocol_aztec-packages_noir-projects_aztec-nr	4 s	3 s	1.33
test_report_AztecProtocol_aztec-packages_noir-projects_noir-protocol-circuits_crates_rollup-lib	3 s	2 s	1.50

This comment was automatically generated by workflow using github-action-benchmark.

CC: @TomAFrench

[jfecher]

🎉