I've got a Partitionable class that I've been using for this purpose: https://github.com/mikeizbicki/ConstraintKinds/blob/master/src/Control/Const... The function called "parallel" in the HLearn library will automatically parallelize any homomorphism from a Partionable to a Monoid. I specifically use that to parallelize machine learning algorithms. I have two thoughts for better abstractions: 1) This Partitionable class is essentially a comonoid. By reversing the arrows of mappend, we get: comappend :: a -> (a,a) By itself, this works well if the number of processors you have is a power of two, but it needs some more fanciness to get things balanced properly for other numbers of processors. I bet there's another algebraic structure that would capture these other cases, but I'm not sure what it is. 2) I'm working with parallelizing tree structures right now (kd-trees, cover trees, oct-trees, etc.). The real problem is not splitting the number of data points equally (this is easy), but splitting the amount of work equally. Some points take longer to process than others, and this cannot be determined in advance. Therefore, an equal split of the data points can result in one processor getting 25% of the work load, and the second processor getting 75%. Some sort of lazy Partitionable class that was aware of processor loads and didn't split data points until they were needed would be ideal for this scenario. On Sat, Sep 28, 2013 at 6:46 PM, adam vogt wrote:

On Sat, Sep 28, 2013 at 1:09 PM, Ryan Newton wrote:

...

Hi all,

We all know and love Data.Foldable and are familiar with left folds and right folds. But what you want in a parallel program is a balanced fold over a tree. Fortunately, many of our datatypes (Sets, Maps) actually ARE balanced trees. Hmm, but how do we expose that?

Hi Ryan,

At least for Data.Map, the Foldable instance seems to have a reasonably balanced fold called fold (or foldMap):

...

fold t = go t where go (Bin _ _ v l r) = go l `mappend` (v `mappend` go r)

This doesn't seem to be guaranteed though. For example ghc's derived instance writes the foldr only, so fold would be right-associated for a:

...

data T a = B (T a) (T a) | L a deriving (Foldable)

Regards, Adam _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

Thanks, that's interesting to know (re: Fortress). Interestingly, in my Fortress days we looked at both using a split-like

interface and at a more foldMap / reduce - like interface, and it seemed like the latter worked better – it requires a lot less boilerplate for controlling recursion, and better matches the fanout of whatever structure you're actually using underneath.

Ok, we'll have to try that. I may be underestimating the power of a newtype and a monoid instance to expose the structure.. I was wrong about this before [1]. Here's the foldMap instance for Data.Map: foldMap _ Tip = mempty foldMap f (Bin _ _ v l r) = Foldable.foldMap f l `mappend` f v `mappend` Foldable.foldMap f r Simon Marlow in his recent Haxl talk also had a domain where they wanted a symmetric (non-monadic) parallel spawn operation... But it remains pretty hard for me to reason about the operational behavior of these things... especially since foldMap instances may vary. Thanks, -Ryan [1] For example, here is a non-allocating traverseWithKey_ that I failed to come up with: -- Version of traverseWithKey_ from Shachaf Ben-Kiki -- (See thread on Haskell-cafe.) -- Avoids O(N) allocation when traversing for side-effect. newtype Traverse_ f = Traverse_ { runTraverse_ :: f () } instance Applicative f => Monoid (Traverse_ f) where mempty = Traverse_ (pure ()) Traverse_ a `mappend` Traverse_ b = Traverse_ (a *> b) -- Since the Applicative used is Const (newtype Const m a = Const m), the -- structure is never built up. --(b) You can derive traverseWithKey_ from foldMapWithKey, e.g. as follows: traverseWithKey_ :: Applicative f => (k -> a -> f ()) -> M.Map k a -> f () traverseWithKey_ f = runTraverse_ . foldMapWithKey (\k x -> Traverse_ (void (f k x))) foldMapWithKey :: Monoid r => (k -> a -> r) -> M.Map k a -> r foldMapWithKey f = getConst . M.traverseWithKey (\k x -> Const (f k x))

Oops, this email got stuck in the pipe (flaky internet):

foldMap _ Tip = mempty foldMap f (Bin _ _ v l r) = Foldable.foldMap f l `mappend` f v `mappend` Foldable.foldMap f r

Btw, from my perspective, one problem with relying on foldMap is that it treats the whole structure uniformly, whereas the split approach would let one, for example, bottom out to a sequential implementation at a certain granularity. Perhaps that is the "boilerplate for controlling recursion" that you referred to... but isn't it sometimes necessary? -Ryan