On Oct 14, 2021, at 11:59 AM, Benjamin Redelings <benjamin.redelings@gmail.com> wrote:

I asked about this on Haskell-Cafe, and was recommended to ask here instead. Any help is much appreciated!

I saw your post over there, but haven't had time to respond.... but this retelling of the story makes it easier to respond, so I'll do so here.

* The PolyKinds paper was the most helpful thing I've found, but it doesn't cover type classes. I'm also not sure that all implementers can follow algorithm descriptions that are laid out as inference rules, but maybe that could be fixed with a few hints about how to run the rules in reverse. Also, in practice I think an implementer would want to follow GHC in specifying the initial kind of a data type as k1 -> k2 -> ... kn -> *.

What is unique about type classes? It seems like you're worried about locally quantified type variables in method types, but (as far as kind inference is concerned) those are very much like existential variables in data constructors. So perhaps take the bit about existential variables from the PolyKinds part of that paper and combine it with the Haskell98 part.

It's true that many implementors may find the notation in that paper to be a barrier, but you just have to read the rules clockwise, starting from the bottom left and ending on the bottom right. :)

2. The following question (which I have maybe kind of answered now, but could use more advice on) is an example of what I am hoping such documentation would explain:

Q: How do you handle type variables that are present in class methods, but are not type class parameters? If there are multiple types/classes in a single recursive group, the kind of such type variables might not be fully resolved until a later type-or-class is processed. Is there a recommended approach?

I can see two ways to proceed:

i) First determine the kinds of all the data types, classes, and type synonyms. Then perform a second pass over each type or class to determine the kinds of type variables (in class methods) that are not type class parameters.

This won't work.

class C a where

meth :: a b -> b Int

You have to know the kind of local b to learn the kind of class-variable a. So you have to do it all at once.

ii) Alternatively, record the kind of each type variable as it is encountered -- even though such kinds may contain unification kind variables. After visiting all types-or-classes in the recursive group, replace any kind variables with their definition, or with a * if there is no definition.

I've currently implement approach i), which requires doing kind inference on class methods twice.

Further investigation revealed that GHC takes yet another approach (I think):

iii) Represent kinds with modifiable variables. Substitution can be implemented by modifying kind variables in-place. This is (I think) called "zonking" in the GHC sources.

I don't really see the difference between (ii) and (iii). Maybe (ii) records the kinds in a table somewhere, while (iii) records them "in" the kind variables themselves, but that's not so different, I think.

This solves a small mystery for me, since I previously thought that zonking was just replacing remaining kind variables with '*'. And indeed this seems to be an example of zonking, but not what zonking is (I think).

We can imagine that, instead of mutation, we build a substitution mapping unification variables to types (or kinds). This would be stored just as a simple mapping or dictionary structure. No mutation. As we learn about a unification variable, we just add to the mapping. If we did this, zonking would be the act of applying the substitution, replacing known unification variables with their values. It just so happens that GHC builds a mapping by using mutable cells in memory, but that's just an implementation detail: zonking is still just applying the substitution.

Zonking does not replace anything with *. Well, functions that have "zonk" in their name may do this. But it is not really logically part of the zonking operation. If you like, you can pretend that, after zonking a program, we take a separate pass replacing any yet-unfilled kind-level unification variables with *. Sometimes, this is called "zapping" in GHC, I believe.

Zonking looks painful to implement, but approach (i) might require multiple passes over types to update the kind of type variables, which might be worse...

Zonking is a bit laborious to implement, but not painful. Laborious, because it requires a full pass over the AST. Not painful, because all it's trying to do is replace type/kind variables with substitutions: each individual piece of the puzzle is quite simple.