I am working through the section on Functors in the Typeclassopedia.
A simple intuition is that a Functor represents a “container” of some sort, along with the ability to apply a function uniformly to every element in the container.
OK. So, functors appear pretty natural for inductive types like lists or trees.
Functors also appear pretty simple if the number of elements is fixed to a low number. For example, with Maybe you just have to be concerned about "Nothing" or "Just a" -- two things.
So, how would you make something like a graph, that could potentially have loops, an instance of Functor? I think a more generalized way to put it is, how do non-inductive types "fit into" Functors?
The more I think about it, the more I realize that inductive / non-inductive doesn't really matter. Inductive types are just easier to define fmap
for...
If I wanted to make a graph an instance of Functor, I would have to implement a graph traversal algorithm inside fmap; for example it would probably have to use a helper function that would keep track of the visited nodes. At this point, I am now wondering why bother defining it as a Functor instead of just writing this as a function itself? E.g. map vs fmap for lists...?
I hope someone with experience, war stories, and scars can shed some light. Thanks!