On Sat, Oct 31, 2009 at 6:22 AM, Heinrich Apfelmus
Dan Weston wrote:
Can you elaborate on why Const is not a monad?
return x = Const x fmap f (Const x) = Const (f x) join (Const (Const x)) = Const x
This is not Const , this is the Identity monad.
The real Const looks like this:
newtype Const b a = Const b
instance Monoid b => Applicative (Const b) where pure x = Const mempty (Const b) <*> (Const b') = Const (b `mappend` b')
The only possible monad instance would be
return x = Const mempty fmap f (Const b) = Const b join (Const b) = Const b
but that's not just () turned into a monad.
This is inconsistent with the Applicative instance given above.
Const a <*> Const b = Const (a `mappend` b)
Const a `ap` Const b = Const a
In other words, Const has at least two Applicative instances, one of
which is not also a monad.
--
Dave Menendez