Deriving Functor - Haskell

Hi,
I see that it's possible to have deriving Functor after defining a type. While I can sortof guess what deriving Show do in general, I have trouble figuring how you can go from an ADT to a functor ? I mean wrapping/unwrapping constructor is not enough, the type of the parameter may change with function application

In what way do you see a problem with function application?
GHC analyzes every field and generates an fmap that applies the f argument to each of these, then reassembles the type

for a type

data A a = A (Maybe a) a

you'd get an fmap like

fmap f (A ma a) = A (fmap f ma) (f a)

if I have a type

data SomeType = A String | B Int | C Bool

then a functor would need to apply a function f to String, Int and Bool

you can't derive a functor for a type without a parameter!

SomeType isn’t a functor — functors must have at least one type argument.

ho yes right

in that case it would be id

well, it won't work, of course

Actually, that reminds me of something I run into occasionally. Sometimes I have a type wrapping a value, where that value is a specific type rather than a type variable. Often in this case I need to write some sort of mapping function, but of course I can’t use Functor as the type of the wrapped value is invariant, so I just end up with lots of mapping functions. Does anyone know of a good class I can use for such functions, or some other way of solving the problem? (I do know about MonoFunctor, but that requires a mono-traversables dependency…)

I'd say that's usually a case for lens

You could make the type an actual Functor and declare a type synonym which "fixes" the parameter.