On Sat, Jan 8, 2011 at 12:05 PM, Conor McBride
On 8 Jan 2011, at 15:27, Henning Thielemann wrote:
On Sat, 8 Jan 2011, Conor McBride wrote:
On 8 Jan 2011, at 11:14, Henning Thielemann wrote:
For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
What has it to do with monads? There's no bind in sight.
I see a '>>=' in front of each of his expressions.
That'll teach me to wake up first. Sorry.
If you have some m (f x), and you make an (m x) from each inner x, then you do need something joiny.
Of course, there is an alternative generalisation.
[] and Maybe are both Foldable, hence so is their composition.
There's got to be a thing of type
collapse :: (Foldable f, Alternative a) => f x -> a x
which would do the job.
Something along these lines, I'd imagine. collapse = foldr (\a b -> pure a <|> b) empty Then, to get catMaybes you could either use composition, or just write it out manually: doubleCollapse = foldr (\a b -> foldr (\c d -> pure c <|> d) empty a <|> b) empty :: (Foldable f, Foldable g, Alternative h) => f (g a) -> h a For the generalized catMaybes, f ~ h.
Of course, anything which is both foldable and alternative certainly has a function with the type of join.
Right, that's doubleCollapse when f ~ g ~ h.
Alternative and Foldable are both specified rather loosely, so it's
not clear how closely doubleCollapse approximates join.
In particular, are <|> and empty expected to form a monoid? If not, we
could define a list- or stream-like structure that uses alternation
instead of appending for (<|>). That would not behave at all like
join.
Right now, I suspect any type which has with a monoidal structure,
pure, and a fold that respects the monoid has a join.
That is, if you have:
foldMap f mempty = mempty
foldMap f (a `mappend` b) = foldMap f a `mappend` foldMap f b
then when f = pure you can take a structure apart and put it back
together piece by piece. I think that's enough to get you join.
Naturally, if you also have pure and fmap, you also have a monad.
--
Dave Menendez