While explaining to someone what a type class X is I struggle to find good examples of data structures which are exactly X.
So, I request examples for:
- A type constructor which is not a Functor.
- A type constructor which is a Functor, but not Applicative.
- A type constructor which is an Applicative, but is not a Monad.
- A type constructor which is a Monad.
I think there are plenty examples of Monad everywhere, but a good example of Monad with some relation to previous examples could complete the picture.
I look for examples which would be similar to each other, differing only in aspects important for belonging to the particular type class.
If one could manage to sneak up an example of Arrow somewhere in this hierarchy (is it between Applicative and Monad?), that would be great too!