Chalk is an experimental trait solver for rust that is currently under development by the Traits Working Group. Its goal is to enable a lot of trait system features and bug fixes that are currently hard to implement (e.g. GATs or specialization). if you would like to help in hacking on the new solver, you will find instructions for getting involved in the Traits Working Group tracking issue.
The new-style trait solver is based on the work done in chalk. Chalk recasts Rust's trait system explicitly in terms of logic programming. It does this by "lowering" Rust code into a kind of logic program we can then execute queries against.
The key observation here is that the Rust trait system is basically a kind of logic, and it can be mapped onto standard logical inference rules. We can then look for solutions to those inference rules in a very similar fashion to how e.g. a Prolog solver works. It turns out that we can't quite use Prolog rules (also called Horn clauses) but rather need a somewhat more expressive variant.
You can read more about chalk itself in the Chalk book section.
The design of the new-style trait solving currently happens in two places:
chalk. The chalk repository is where we experiment with new ideas and designs for the trait system.
rustc. Once we are happy with the logical rules, we proceed to implementing them in rustc. We map our struct, trait, and impl declarations into logical inference rules in the lowering module in rustc.