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

[Gergő Érdi]

Using mutable references for type metavariables is an implementation
optimization: unifying a metavariable with a kind can then be cheaply
implemented by replacing the metavar's content with the kind. After
you are done with unification, you don't need metavariables anymore.
If this were HM, you'd generalize remaining metavariables into type
variables. But for kinds, remaining metavariables are defaulted to *
in Haskell 98. (Of course, if you used PolyKinds, kind metavars would
also be generalized).

Zonking is the process of traversing a type / kind with these mutable
references and replacing each mutable reference with its value,
thereby "baking in" its current solution. If you encounter a mutable
reference that doesn't contain anything, it means the metavar it
represents hasn't been constrained in any way -- so you can just
choose * for them.

People seem to have upvoted my SO answer about GHC's zonking so you
might find it useful as well:
https://stackoverflow.com/a/31890743/477476

On Fri, Oct 15, 2021 at 12:01 AM Benjamin Redelings
<benjamin.redelings at gmail.com> wrote:
>
> Hi,
>
> I asked about this on Haskell-Cafe, and was recommended to ask here instead.  Any help is much appreciated!
>
> 1. I'm looking for resources that describe how to implement kind Haskell 98 checking.  Does anyone have any good suggestions?  So far, the papers that I've looked at all fall short in different ways:
>
> * Mark Jones's paper "A system of constructor classes":  This paper contains a kind-aware type-inference algorithm, but no kind inference algorithm.  The closest it comes is the rule:
>
>     C :: k' -> k   and   C' :: k'   =>   C C' :: k
>
> * The THIH paper doesn't have an algorithm for kind checking.  It assumes that every type variable already has a kind.
>
> * The 2010 Report helpfully mentions substituting any remaining kind variables with *.  But it refers to "A system of constructor classes" for an algorithm.
>
> * 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 -> *.
>
> * I've looked at the source code to GHC, and some of the longer notes were quite helpful.  However, it is hard to follow for a variety of reasons.  It isn't laid out like an algorithm description, and the complexity to handle options like PolyKinds and DataKinds makes the code harder to follow.
>
>
>
> 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.
>
> 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.
>
> 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).
>
> 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...
>
>
>
> 3. I'm curious now how many other pieces of software besides GHC have implemented kind inference...
>
>
> -BenRI
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