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.

In the last few days, I’ve implemented a second SLG-based solver for Chalk. This one follows a rather different design. It’s kind of a hybrid of Chalk’s traditional “recursive” solver and the SLG-based one, with a lot of influence from MiniKanren. I think it’s getting a lot closer to the sort of solver we could use in Rustc.

One key aspect of its design is that it is “on-demand” – that is, it tries to only do as much as work as it needs to produce the next answer, and then stops. This means that we can generally stop it from doing silly things like iterating over every type in the system.

It also works in a “breadth-first fashion”. This means that, for example, it would rather produce a series of answers like [Vec<?T>, Rc<?T>, Box<?T>, ...] that to go deep and give answers like [Vec<?T>, Vec<Vec<?T>>, Vec<Vec<Vec<?T>>>, ...] . This is particularly useful when combined with on-demand solving, since it helps us to quickly see ambiguity and stop enumerating answers.

Details of how it works

As part of the PR, I wrote up a README that tries to walk through how query solving works in the new solver. I thought I’d paste that here into this blog post.

The basis of the solver is the Forest type. A forest stores a collection of tables as well as a stack. Each table represents the stored results of a particular query that is being performed, as well as the various strands, which are basically suspended computations that may be used to find more answers. Tables are interdependent: solving one query may require solving others.

Perhaps the easiest way to explain how the solver works is to walk through an example. Let’s imagine that we have the following program:

trait Debug { } struct u32 { } impl Debug for u32 { } struct Rc < T > { } impl < T : Debug > Debug for Rc < T > { } struct Vec < T > { } impl < T : Debug > Debug for Vec < T > { }

Now imagine that we want to find answers for the query exists<T> { Rc<T>: Debug } . The first step would be to u-canonicalize this query; this is the act of giving canonical names to all the unbound inference variables based on the order of their left-most appearance, as well as canonicalizing the universes of any universally bound names (e.g., the T in forall<T> { ... } ). In this case, there are no universally bound names, but the canonical form Q of the query might look something like:

Rc<?0>: Debug

where ?0 is a variable in the root universe U0. We would then go and look for a table with this as the key: since the forest is empty, this lookup will fail, and we will create a new table T0, corresponding to the u-canonical goal Q.

Creating a table. When we first create a table, we also initialize it with a set of initial strands. A “strand” is kind of like a “thread” for the solver: it contains a particular way to produce an answer. The initial set of strands for a goal like Rc<?0>: Debug (i.e., a “domain goal”) is determined by looking for clauses in the environment. In Rust, these clauses derive from impls, but also from where-clauses that are in scope. In the case of our example, there would be three clauses, each coming from the program. Using a Prolog-like notation, these look like:

(u32: Debug). (Rc<T>: Debug) :- (T: Debug). (Vec<T>: Debug) :- (T: Debug).

To create our initial strands, then, we will try to apply each of these clauses to our goal of Rc<?0>: Debug . The first and third clauses are inapplicable because u32 and Vec<?0> cannot be unified with Rc<?0> . The second clause, however, will work.

What is a strand? Let’s talk a bit more about what a strand is. In the code, a strand is the combination of an inference table, an X-clause, and (possibly) a selected subgoal from that X-clause. But what is an X-clause ( ExClause , in the code)? An X-clause pulls together a few things:

The current state of the goal we are trying to prove;

A set of subgoals that have yet to be proven;

A set of delayed literals that we will have to revisit later; (I’ll ignore these for now; they are only needed to handle loops between negative goals.)

A set of region constraints accumulated thus far. (I’ll ignore these too for now; we’ll cover regions later on.)



The general form of an X-clause is written much like a Prolog clause, but with somewhat different semantics:

G :- D | L

where G is a goal, D is a set of delayed literals, and L is the set of literals that must be proven (in the general case, these can be both a goal like G but also a negated goal like not { G } ). The idea is that – if we are able to prove L and D – then the goal G can be considered true.

In the case of our example, we would wind up creating one strand, with an X-clause like so:

(Rc<?T>: Debug) :- (?T: Debug)

Here, the ?T refers to one of the inference variables created in the inference table that accompanies the strand. (I’ll use named variables to refer to inference variables, and numbered variables like ?0 to refer to variables in a canonicalized goal; in the code, however, they are both represented with an index.)

For each strand, we also optionally store a selected subgoal. This is the literal after the turnstile ( :- ) that we are currently trying to prove in this strand. Initally, when a strand is first created, there is no selected subgoal.

Activating a strand. Now that we have created the table T0 and initialized it with strands, we have to actually try and produce an answer. We do this by invoking the ensure_answer operation on the table: specifically, we say ensure_answer(T0, A0) , meaning “ensure that there is a 0th answer”.

Remember that tables store not only strands, but also a vector of cached answers. The first thing that ensure_answer does is to check whether answer 0 is in this vector. If so, we can just return immediately. In this case, the vector will be empty, and hence that does not apply (this becomes important for cyclic checks later on).

When there is no cached answer, ensure_answer will try to produce one. It does this by selecting a strand from the set of active strands – the strands are stored in a VecDeque and hence processed in a round-robin fashion. Right now, we have only one strand, storing the following X-clause with no selected subgoal:

(Rc<?T>: Debug) :- (?T: Debug)

When we activate the strand, we see that we have no selected subgoal, and so we first pick one of the subgoals to process. Here, there is only one ( ?T: Debug ), so that becomes the selected subgoal, changing the state of the strand to:

(Rc<?T>: Debug) :- selected(?T: Debug, A0)

Here, we write selected(L, An) to indicate that (a) the literal L is the selected subgoal and (b) which answer An we are looking for. We start out looking for A0 .

Processing the selected subgoal. Next, we have to try and find an answer to this selected goal. To do that, we will u-canonicalize it and try to find an associated table. In this case, the u-canonical form of the subgoal is ?0: Debug : we don’t have a table yet for that, so we can create a new one, T1. As before, we’ll initialize T1 with strands. In this case, there will be three strands, because all the program clauses are potentially applicable. Those three strands will be:

(u32: Debug) :- , derived from the program clause (u32: Debug). . Note: This strand has no subgoals.

, derived from the program clause . (Vec<?U>: Debug) :- (?U: Debug) , derived from the Vec impl.

, derived from the impl. (Rc<?U>: Debug) :- (?U: Debug) , derived from the Rc impl.

We can thus summarize the state of the whole forest at this point as follows:

Table T0 [Rc<?0>: Debug] Strands: (Rc<?T>: Debug) :- selected(?T: Debug, A0) Table T1 [?0: Debug] Strands: (u32: Debug) :- (Vec<?U>: Debug) :- (?U: Debug) (Rc<?V>: Debug) :- (?V: Debug)

Delegation between tables. Now that the active strand from T0 has created the table T1, it can try to extract an answer. It does this via that same ensure_answer operation we saw before. In this case, the strand would invoke ensure_answer(T1, A0) , since we will start with the first answer. This will cause T1 to activate its first strand, u32: Debug :- .

This strand is somewhat special: it has no subgoals at all. This means that the goal is proven. We can therefore add u32: Debug to the set of answers for our table, calling it answer A0 (it is the first answer). The strand is then removed from the list of strands.

The state of table T1 is therefore:

Table T1 [?0: Debug] Answers: A0 = [?0 = u32] Strand: (Vec<?U>: Debug) :- (?U: Debug) (Rc<?V>: Debug) :- (?V: Debug)

Note that I am writing out the answer A0 as a substitution that can be applied to the table goal; actually, in the code, the goals for each X-clause are also represented as substitutions, but in this exposition I’ve chosen to write them as full goals, following NFTD.

Since we now have an answer, ensure_answer(T1, A0) will return Ok to the table T0, indicating that answer A0 is available. T0 now has the job of incorporating that result into its active strand. It does this in two ways. First, it creates a new strand that is looking for the next possible answer of T1. Next, it incorpoates the answer from A0 and removes the subgoal. The resulting state of table T0 is:

Table T0 [Rc<?0>: Debug] Strands: (Rc<?T>: Debug) :- selected(?T: Debug, A1) (Rc<u32>: Debug) :-

We then immediately activate the strand that incorporated the answer (the Rc<u32>: Debug one). In this case, that strand has no further subgoals, so it becomes an answer to the table T0. This answer can then be returned up to our caller, and the whole forest goes quiescent at this point (remember, we only do enough work to generate one answer). The ending state of the forest at this point will be:

Table T0 [Rc<?0>: Debug] Answer: A0 = [?0 = u32] Strands: (Rc<?T>: Debug) :- selected(?T: Debug, A1) Table T1 [?0: Debug] Answers: A0 = [?0 = u32] Strand: (Vec<?U>: Debug) :- (?U: Debug) (Rc<?V>: Debug) :- (?V: Debug)

Here you can see how the forest captures both the answers we have created thus far and the strands that will let us try to produce more answers later on.

Conclusions

Well, the README stops the story a bit short – it doesn’t explain, for example, what happens when there are cycles in the graph and so forth. Maybe you can piece it together, though.

The biggest question is: is this a suitable architecture for use in rustc? About this, I’m not sure yet. I feel like this route is quite promising, however, and it’s been an interesting journey for me in any case thus far.

One of the tricky things that I don’t yet know how to resolve: under the current setup, if our root query is generated a diverse set of answers, we can quite easily stop asking for more (e.g., to handle exists<T> { T: Sized } ). I think this is by far the more common scenario in Rust. However, it’s also possible to have a query which internally has to go through quite a few answers in order to produce any results at the root level. I’m imagining something like this:

impl<T> Foo for T where T: Bar, T: Baz,

Under the setup described here, one of these queries – let’s say T: Bar – gets chosen somewhat arbitrary to begin producing answers first. It might produce a very large number of answers, which will then get “fed” to the Baz trait, which will effectively filter them out. But maybe T: Baz is only implemented for a very few types, so if we had chosen the other order things would have been far more efficient. I can imagine some heuristics helping here – for example, we might take traits like Sized or Debug , or which have very open-ended impls – and prefer not to select them first. I suspect a few simple heuristics would get us quite far.

Currently, my biggest concern with this design is the “runaway internal query” aspect I just described. But I’m curious if there are other things I’m overlooking! As ever, I’ve created an internals thread, please leave comments there if you have thoughts (also suggestions for things I should go and read).