On Mon, Apr 27, 2009 at 4:19 PM, Martijn van Steenbergen <martijn@van.steenbergen.nl> wrote:

They are in order of power: every monad is an applicative; every applicative is a functor; every functor is pointed.

Though I can't think of any non-functor pointiness at the moment.

Martijn.

On the other hand, here's an un-pure-able and un-point-able functor:

instance Functor ((,) m) where
  --fmap :: (n -> n') -> (m, n) -> (m, n')
    fmap f (m, n) = (m, f n)

n -> (m, n) is not a function you can write in general without bottom values (unless you specify that m is a monoid, using mempty). Nor is Pointed in the f () sense, since forall a. (a, ()) isn't something for which a value can be pulled out of thin non-bottom air. But... getting a bit off-topic >_>

—Gracenotes