Resources on how to implement (Haskell 98) kind checking?

Benjamin Redelings benjamin.redelings at
Wed Oct 27 13:42:33 UTC 2021

Oh, I forgot to add, would it make sense to put some of the information 
I discovered about implementing kind checking into the wiki somewhere?  
I am mostly thinking of a sequence of steps like:

1. Divide class, data/newtype, type synonym, and instance declarations 
into recursive groups.

1a) Record for each group which LOCAL typecons are mentioned in the 

1b) ... etc

2. Infer kinds within a recursive group

2a) Treat type classes as having kind k1 -> k2 -> ... -> kn -> Constraint

2b) Begin by recording a kind k1 -> k2 -> ... -> kn -> Constraint/* for 
each typecon

2c) etc...

2d) Substitute kind variables (zonking)

2e) Substitute * for remaining kind variables (zapping)

3. ...

I am not actually sure what to write yet, the above is just an illustration.

It might also help to reference the relevant papers (mostly the 
PolyKinds paper), and maybe also to mention papers like the THIH paper 
that don't actually implement kind checking.


On 10/15/21 1:37 PM, Richard Eisenberg wrote:
>> On Oct 14, 2021, at 11:59 AM, Benjamin Redelings 
>> <benjamin.redelings at> 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.
> I hope this is helpful!
> Richard
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