How to model hierarchical data types in Haskell?

Question

I have a bunch of types where their hierarchy stores some useful information. I\'m trying to avoid having to bake in knowledge of the hierarchy of the types into the functio

Answer 1

Use typeclasses.

First define each of the concrete types as a seperate data declaration.

Then for each type with subtypes declare a typeclass with a constraint on its parent. An example of this sort of relationship is Functor => Applicative => Monad structure in prelude.

So to define the example structure:

class Root where
    ...

class Root => Dep where
    ...

class Dep => Aux where
    ...

class Aux => Auxpass where
    ...

class Aux => Cop where
    ...

class Dep => Arg where
    ...

class Arg => Agent where
    ...