T. Morris

Hi Pho,
I have heard the term Functor used like that before. Also, I have seen a discussion on the Scala mailing list about it. FYI, I call it a misuse and so do many others, but let's not get hung up on that.

Instead, here is a more concise definition. A functor is any implementation of the following interface:
trait Functor[F[_]] { def fmap[A, B](f: A => B, fa: F[A]): F[B] }

...such that 2 laws satisfy:

identity. forall x. fmap(identity, x) == x

composition. forall f g x. fmap(f, fmap(g, x)) == fmap(f compose g, x)

Notice the kind of the type constructor argument F (* -> *). There are several type constructors that satisfy this kind. Just to name a few:

scala.List

scala.Option

scala.Stream

scala.Either.LeftProjection

scala.Either.RightProjection

scala.Function1#Apply[T] (i.e. curry the first type argument)

You might be keen to implement this interface with these type constructors just to observe each functor manifest

class ListFunctor extends Functor[List] { ...

You are mixing lazy evaluation with side-effects, which is a big no-no. As you have observed, reasoning about the correctness of your program becomes difficult.

Garrett, Look up "Abstract Algebraic Data Types". The use of an abstract ADT will resolve your issue.