Writing a generic functor instance across type constructors?

I'm learning basic type classes and have written my own implementation of functor for my type Test a (behaves just like Maybe):

data Test a = Test a | Emp

class FC c a where
  t :: (a -> b) -> c a -> c b

instance FC Test a where
  t f (Test a) = Test (f a) 
  t f (Emp) = Emp

instance FC Maybe a where
  t f (Just a) = Just (f a) 
  t f (Nothing) = Nothing

Is it possible to implement something like:

instance FC c where
  t f (c v) = c (f v)

Error:

Parse error in pattern: c

In other words, abstract away the type constructor, replace with c and v, therefore creating a general instance that can be applied to any value with a context?

Solution

As you've learned, c a is not a syntactically valid pattern. But reading your question instead as a feature proposal: How would that work? Not every Functor has a single-element constructor which can be mapped over according to your pattern. Some examples:

data Pair a = Pair a a  -- more than one element
instance Functor Pair where
    fmap f (Pair x y) = Pair (f x) (f y)

data Proxy a = Proxy  -- no elements
instance Functor Proxy where
    fmap f Proxy = Proxy

newtype Cont r a = Cont { runCont :: (a -> r) -> r }  -- element appears in a double-negative position
instance Functor (Cont r) where
    fmap f (Cont g) = Cont (g . (. f))

In any case, I don't think the idea of a "generic instance" really makes sense. The instance is where you put your type-specific code. (It has to go somewhere!)

If you want to exert less effort in writing Functor instances you can use GHC's DeriveFunctor extension.

{-# LANGUAGE DeriveFunctor #-}

data Pair a = Pair a a deriving Functor

data Proxy a = Proxy deriving Functor

newtype Cont r a = Cont { runCont :: (a -> r) -> r } deriving Functor