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.