While I personally prefer the (:*:) and (:+:) notation, both require an additional extension, TypeOperators, and to Ross's point (:+:) fails to be an Applicative/Monad transformers, so the scope of the package starts to stretch there.
That said, there are always ideal monad coproducts, but then you need the notion of ideal monads. ;)
data Ideal m a = Return a | Ideal (m a)
data Mutual m n a = Mutual (m (Mutual n m a))
data (m :+: n) a = Coproduct { runCoproduct :: Either (m a) (n a) }
type IdealCoproduct m n = Ideal (Mutual m n :+: Mutual n m)
given a definition for
class MonadIdeal m where
idealize :: m (Ideal m a) -> m a
which describes a monad, that has a separate return.
You can define
instance MonadIdeal m => Monad (Ideal m)
and then you can define an 'ideal monad coproduct' of any two ideal monads from there.
This covers, Maybe, Either, Identity, and a bunch of others. wherever the 'Return' constructor can be cleanly separated from the rest of the monad.
However, this drifts out of library/platform territory and into esoterica.
-Edward Kmett
On Mon, Mar 29, 2010 at 5:42 AM, Nicolas Pouillard
<nicolas.pouillard@gmail.com> wrote:
On Fri, 26 Mar 2010 19:28:18 +0000, Ross Paterson <
ross@soi.city.ac.uk> wrote:
> On Fri, Mar 26, 2010 at 05:24:18AM -0700, Nicolas Pouillard wrote:
> > Could we have functors products, sums, fixpoints as well? It would really
> > avoid to redefine them each time.
>
> Do you mean
>
> data Product f g a = Product (f a) (g a)
data (:*:) f g a = (:*:) (f a) (g a)
> with Functor, Foldable, Traversable and Applicative instances?
Yes.
> Not sure if the other two count as transformers.
Why not:
data (:+:) f g a = Inl (f a) | Inr (g a)
And sure, no applicative nor monad instance for this one.
And Fix like in category-extras:
http://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/Control-Functor-Fix.html
Best regards,