I'll be using pseudo code and skip over some technical details that are entirely irrelevant to this conversation in my answer. I hope I understood your question

I'll be using pseudo code and skip over some technical details that are entirely irrelevant to this conversation in my answer. I hope I understood your question correctly and not answering something else entirely. First, a functor doesn't go from A to F[B] but from F[A] to F[B]. A to F[B] looks suspiciously like something a monad does, a topic we don't want to get into. Your example is a functor that maps unary functions to unary functions by composing them. It's a good if slightly complicated example: unary functions have two type parameters (A and B in A => B), while the slide's Functor only takes one. That is, you want to write a Functor[A => B], but you cannot, or at least not directly. What you do is fix one of the parameters. You don't write a Functor for all unary functions, but a Functor for all unary functions whose parameter type is C (for concrete): Functor[C => A], where C is a concrete type and A the functor's type parameter. This functor's map method takes an instance of (C => A), a function f: A => B, and yields a function C => B. The only non-pathological implementation of this is composition: C => A => B What I just wrote makes it sound like you need to write a Functor implementation for all possible parameter types, but that luckily isn't true: writing a function that yields a Functor[C => A] for any given type parameter C is trivial. I'll put the code here just to show it is, but you don't really need to understand it: // I know the C => ? isn't standard Scala, I'm using kind-projector syntax to make this readable. implicit def functionFunctor[C] = new Functor[C => ?] { override def map[A, B](fa: C => A)(f: A => B): C => B = f compose fa } To go back to your concrete example: you just need to get functionFunctor[X] and call map on (x => x * 0.5) to get your function from X to double. Note that some technical details are skipped (partial application, calling the binary function map with a single parameter), but I arbitrarily deem them irrelevant to my point.