Specialization
TODO: where does Chalk fit in? Should we mention/discuss it here?
Defined in the specialize
module.
The basic strategy is to build up a specialization graph during coherence checking (recall that coherence checking looks for overlapping impls). Insertion into the graph locates the right place to put an impl in the specialization hierarchy; if there is no right place (due to partial overlap but no containment), you get an overlap error. Specialization is consulted when selecting an impl (of course), and the graph is consulted when propagating defaults down the specialization hierarchy.
You might expect that the specialization graph would be used during selection – i.e. when actually performing specialization. This is not done for two reasons:

It's merely an optimization: given a set of candidates that apply, we can determine the most specialized one by comparing them directly for specialization, rather than consulting the graph. Given that we also cache the results of selection, the benefit of this optimization is questionable.

To build the specialization graph in the first place, we need to use selection (because we need to determine whether one impl specializes another). Dealing with this reentrancy would require some additional mode switch for selection. Given that there seems to be no strong reason to use the graph anyway, we stick with a simpler approach in selection, and use the graph only for propagating default implementations.
Trait impl selection can succeed even when multiple impls can apply,
as long as they are part of the same specialization family. In that
case, it returns a single impl on success – this is the most
specialized impl known to apply. However, if there are any inference
variables in play, the returned impl may not be the actual impl we
will use at trans time. Thus, we take special care to avoid projecting
associated types unless either (1) the associated type does not use
default
and thus cannot be overridden or (2) all input types are
known concretely.
Additional Resources
This talk by @sunjay may be useful. Keep in mind that the talk only gives a broad overview of the problem and the solution (it was presented about halfway through @sunjay's work). Also, it was given in June 2018, and some things may have changed by the time you watch it.