Three Laws of Functor Confusion

There's a conspiracy to prevent you from understanding functors, and the here are some of the tools used to keep you in the dark:

1. In explanations about functional programming, authors blithely use f to mean either a function or an object for which there's a functor, e.g.

  f      :: (a -> b -> c)
  fmap   :: Functor f => (d -> e) -> f d -> f e
  fmap f :: Functor f =>             f a -> f (b -> c)    -- Identify d with a, and e with (b -> c)

1. The word functor sometimes means a mapping between categories and other times means an object in a category for which such a mapping exists.
2. Back in OO land, people have been using the term functor since 1992 to mean an object used to encapsulate a function, i.e. pretty much any class with any method, as long as the intent is to fake a first class function. If the method is in C++ and called operator() or in scala and called apply() then it will even look like a function.

That bit about scala's apply() is a sub-annoyance. The use of the word here has nothing to do with applicative functors or with the way apply is used in lisp.