In my last Chalk post, I talked about an experimental, SLG-based solver that I wrote for Chalk. That particular design was based very closely on the excellent paper “Efficient top-down computation of queries under the well-founded semantics”, by W. Chen, T. Swift, and D. Warren. It followed a traditional Prolog execution model: this has a lot of strengths, but it probably wasn’t really suitable for use in rustc. The single biggest reason for this was that it didn’t really know when to stop: given a query like exists<T> { T: Sized }, it would happily try to enumerate all sized types in the system. It was also pretty non-obvious to me how to extend that system with things like co-inductive predicates (needed for auto traits) and a few other peculiarities of Rust.

For the last month or so, I’ve gotten kind of obsessed with exploring a new evaluation model for Chalk. Specifically, I’ve been looking at adapting the SLG algorithm, which is used in the XSB Prolog engine. I recently opened a PR that adds this SLG-based solver as an alternative, and this blog post is an effort to describe how that PR works, and explore some of the advantages and disadvantages I see in this approach relative to the current solver that I described in my previous post.

In my last post about chalk queries, I discussed how the query model in chalk. Since that writing, there have been some updates, and I thought it’d be nice to do a new post covering the current model. This post will also cover the tabling technique that scalexm implemented for handling cyclic relations and show how that enables us to implement implied bounds and other long-desired features in an elegant way. (Nice work, scalexm!)

For my next post discussing chalk, I want to take kind of a different turn. I want to talk about the general struct of chalk queries and how chalk handles them right now. (If you’ve never heard of chalk, it’s sort of “reference implementation” for Rust’s trait system, as well as an attempt to describe Rust’s trait system in terms of its logical underpinnings; see this post for an introduction to the big idea.)

In my previous post, I talked over the basics of how unification works and showed how that “mathematical version” winds up being expressed in chalk. I want to go a bit further now and extend that base system to cover associated types. These turn out to be a pretty non-trival extension.

What is an associated type?

If you’re not a Rust programmer, you may not be familiar with the term “associated type” (although many langages have equivalents). The basic idea is that traits can have type members associated with them. I find the most intuitive example to be the Iterator trait, which has an associated type Item. This type corresponds to kind of elements that are produced by the iterator:

So in my first post on chalk, I mentioned that unification and normalization of associated types were interesting topics. I’m going to write a two-part blog post series covering that. This first part begins with an overview of how ordinary type unification works during compilation. The next post will add in associated types and we can see what kinds of mischief they bring with them.

What is unification?

Let’s start with a brief overview of what unification is. When you are doing type-checking or trait-checking, it often happens that you wind up with types that you don’t know yet. For example, the user might write None – you know that this has type Option<T>, but you don’t know what that type T is. To handle this, the compiler will create a type variable. This basically represents an unknown, to-be-determined type. To denote this, I’ll write Option<?T>, where the leading question mark indicates a variable.

Over the last year or two (man, it’s scary how time flies), I’ve been doing quite a lot of thinking about Rust’s trait system. I’ve been looking for a way to correct a number of flaws and shortcomings in the current implementation, not the least of which is that it’s performance is not that great. But also, I’ve been wanting to get a relatively clear, normative definition of how the trait system works, so that we can better judge possible extensions. After a number of false starts, I think I’m finally getting somewhere, so I wanted to start writing about it.