[Haskell-cafe] Re: Applicative but not Monad
apfelmus at quantentunnel.de
Sat Oct 31 06:22:59 EDT 2009
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.
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