[Haskell-cafe] Re: Applicative but not Monad
dave at zednenem.com
Sat Oct 31 11:38:18 EDT 2009
On Sat, Oct 31, 2009 at 6:22 AM, Heinrich Apfelmus
<apfelmus at quantentunnel.de> wrote:
> 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 <dave at zednenem.com>
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