Cont as Monoid

[David Menendez]

On 9/21/07, Iavor Diatchki <iavor.diatchki at gmail.com> wrote:
> Hi,
>
> On 9/18/07, Benjamin Franksen <benjamin.franksen at bessy.de> wrote:
> > Ashley Yakeley wrote:
> > > Monoid ought to be a type, in my view. And each of those wrapper classes
> > > can be replaced by a value in that type.
> >
> > Would you care to elaborate this idea? Do you mean a record with two
> > functions?
>
> Here is how you can do that:
>
> data Monoid a = Monoid { mempty :: a, mappend :: a -> a -> a }

Alternatively,

class Monoid a where
   type Carrier a
   mempty :: a -> Carrier a
   mappend :: a -> Carrier a -> Carrier a -> Carrier a

data Sum a
instance Num a => Monoid (Sum a) where
   type Carrier (Sum a) = a
   mempty _ = 0
   mappend _ = (+)

data Lift f a
instance (Monoid a, Applicative f) => Monoid (Lift f a) where
   type Carrier (Lift f a) = f (Carrier a)
   mempty _ = pure (mempty (undefined::a))
   mappend _ = liftA2 (mappend (undefined::a))

data Writer o a = Writer (Carrier o) a
instance (Monoid o) => Monad (Writer o) where
   return a = Writer (mempty (undefined::o)) a
   (Writer o1 a) >>= f =
       let Writer o2 b = f a in Writer (mappend (undefined::o) o1 o2) b

-- 
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>