Besides just partition balance, the ordering of the resulting partitions is important. For example, the most efficient way to partition a list is by taking an every-other-n approach, whereas the most efficient way to partition a vector is by using a slice. (This, BTW, might be a good alternative name for the class to avoid the conflict Edward mentioned.) These partitions are not necessarily usable in the same contexts. For example, Vector's slicing strategy is always usable (only requires associativity of the monoid to reduce over, which is guaranteed by the laws). But the List's strategy also requires commutativity. This is not guaranteed. I would guess that maintaining the partition ordering and balance will be at odds with each other in the Map and Set cases. On Sun, Sep 29, 2013 at 8:06 PM, Ryan Newton wrote:

Thanks Edward. Good point about Brent's 'split' package. That would be a really nice place to put the class. But it doesn't currently depend on containers or vector so I suppose the other instances would need to go somewhere else. (Assuming containers only exported monomorphic versions.)

Maybe a next step would be proposing some monomorphic variants for the containers package.

I think the complicated bit will be describing how "best-efforty" splitting variants are:

- Is it guaranteed O(1) time and allocation? - Is the provided Int an upper bound? Lower(ish) bound? Or just a hint?

With some data structures, there will be a trade-off between partition imbalance and the work required to achieve balance. But with some data structures it is happily not a problem (e.g. Vector)!

But whether there's one variant or a few, I'd be happy either way, as long as I get at least the cheap one (i.e. prefer imbalance to restructuring).

-Ryan

On Sun, Sep 29, 2013 at 8:20 AM, Edward Kmett wrote:

...

I don't know that it belongs in the "standard" libraries, but there could definitely be a package for something similar.

ConstraintKinds are a pretty hefty extension to throw at it, and the signature written there prevents it from being used on ByteString, Text, etc.

This can be implemented with much lighter weight types though!

class Partitionable t where

partition :: Int -> t -> [t]

Now ByteString, Text etc. can be instances and no real flexibility is lost, as with the class associated constraint on the argument, you'd already given up polymorphic recursion.

There still remain issues. partition is already established as the filterthat returns both the matching and unmatching elements, so the name is wrong.

This is a generalization of Data.List.splitEvery, perhaps it is worth seeing how many others can be generalized similarly and talk to Brent about adding, say, a Data.Split module to his split package in the platform?

-Edward

On Sun, Sep 29, 2013 at 4:21 AM, Ryan Newton wrote:

...

<subject change>

On Sun, Sep 29, 2013 at 3:31 AM, Mike Izbicki wrote:

...

I've got a Partitionable class that I've been using for this purpose:

https://github.com/mikeizbicki/ConstraintKinds/blob/master/src/Control/Const...

Mike -- Neat, that's a cool library!

Edward -- ideally, where in the standard libraries should the Partitionable comonoid go?

Btw, I'm not sure what the ideal return type for comappend is, given that it needs to be able to "bottom out". Mike, our partition function's list return type seems more reasonable. Or maybe something simple would be this:

*class Partitionable t where* * partition :: t -> Maybe (t,t)*

That is, at some point its not worth splitting and returns Nothing, and you'd better be able to deal with the 't' directly.

So what I really want is for the *containers package to please get some kind of Partitionable instances! * Johan & others, I would be happy to provide a patch if the class can be agreed on. This is important because currently the balanced tree structure of Data.Set/Map is an *amazing and beneficial property* that is *not* exposed at all through the API. For example, it would be great to have a parallel traverse_ for Maps and Sets in the Par monad. The particular impetus is that our new and enhanced Par monad makes extensive use of Maps and Sets, both the pure, balanced ones, and lockfree/inplace ones based on concurrent skip lists:

http://www.cs.indiana.edu/~rrnewton/haddock/lvish/

Alternatively, it would be ok if there were a "Data.Map.Internal" module that exposed the Bin/Tip, but I assume people would rather have a clean Partitionable instance...

Best, -Ryan

On Sun, Sep 29, 2013 at 3:31 AM, Mike Izbicki wrote:

...

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

Edward, The problem is that I need *something* more from the containers library to be able to construct this as a separate library. I don't think I can use foldMap to implement a Splittable/Partitionable instance for Data.Set, namely because I specifically want to do O(1) work instead of any kind of full traversal of the structure. Is the least possible disruption here to just have a Data.Map.Internal that exposes Tip and Bin? It can be marked with suitable warnings at the top of the module. Or would the preference to be to expose something more abstract of type "Map k a -> [Map k a]" that chops it into the "natural pieces"? [1] -Ryan [1] Btw, it seems like returning a tuple here might make deforestation more likely than returning a list... right? On Mon, Sep 30, 2013 at 9:52 AM, Edward Kmett wrote:

Upon consideration from a package management perspective this is probably easiest done by building a new small package to provide the functionality you want. That way we don't haphazardly change the transitive dependencies of a big chunk of the ecosystem and it can rest atop the various containers libraries. This also gives you a lot of opportunity to iterate on the API in public without incurring the instant rigidity of the Haskell Platform.

On Sun, Sep 29, 2013 at 11:06 PM, Ryan Newton wrote:

...

Thanks Edward. Good point about Brent's 'split' package. That would be a really nice place to put the class. But it doesn't currently depend on containers or vector so I suppose the other instances would need to go somewhere else. (Assuming containers only exported monomorphic versions.)

Maybe a next step would be proposing some monomorphic variants for the containers package.

I think the complicated bit will be describing how "best-efforty" splitting variants are:

- Is it guaranteed O(1) time and allocation? - Is the provided Int an upper bound? Lower(ish) bound? Or just a hint?

With some data structures, there will be a trade-off between partition imbalance and the work required to achieve balance. But with some data structures it is happily not a problem (e.g. Vector)!

But whether there's one variant or a few, I'd be happy either way, as long as I get at least the cheap one (i.e. prefer imbalance to restructuring).

-Ryan

On Sun, Sep 29, 2013 at 8:20 AM, Edward Kmett wrote:

...

I don't know that it belongs in the "standard" libraries, but there could definitely be a package for something similar.

ConstraintKinds are a pretty hefty extension to throw at it, and the signature written there prevents it from being used on ByteString, Text, etc.

This can be implemented with much lighter weight types though!

class Partitionable t where

partition :: Int -> t -> [t]

Now ByteString, Text etc. can be instances and no real flexibility is lost, as with the class associated constraint on the argument, you'd already given up polymorphic recursion.

There still remain issues. partition is already established as the filter that returns both the matching and unmatching elements, so the name is wrong.

This is a generalization of Data.List.splitEvery, perhaps it is worth seeing how many others can be generalized similarly and talk to Brent about adding, say, a Data.Split module to his split package in the platform?

-Edward

On Sun, Sep 29, 2013 at 4:21 AM, Ryan Newton wrote:

...

<subject change>

On Sun, Sep 29, 2013 at 3:31 AM, Mike Izbicki wrote:

...

I've got a Partitionable class that I've been using for this purpose:

https://github.com/mikeizbicki/ConstraintKinds/blob/master/src/Control/Const...

Mike -- Neat, that's a cool library!

Edward -- ideally, where in the standard libraries should the Partitionable comonoid go?

Btw, I'm not sure what the ideal return type for comappend is, given that it needs to be able to "bottom out". Mike, our partition function's list return type seems more reasonable. Or maybe something simple would be this:

*class Partitionable t where* * partition :: t -> Maybe (t,t)*

That is, at some point its not worth splitting and returns Nothing, and you'd better be able to deal with the 't' directly.

So what I really want is for the *containers package to please get some kind of Partitionable instances! * Johan & others, I would be happy to provide a patch if the class can be agreed on. This is important because currently the balanced tree structure of Data.Set/Map is an *amazing and beneficial property* that is *not* exposed at all through the API.

For example, it would be great to have a parallel traverse_ for Maps and Sets in the Par monad. The particular impetus is that our new and enhanced Par monad makes extensive use of Maps and Sets, both the pure, balanced ones, and lockfree/inplace ones based on concurrent skip lists:

http://www.cs.indiana.edu/~rrnewton/haddock/lvish/

Alternatively, it would be ok if there were a "Data.Map.Internal" module that exposed the Bin/Tip, but I assume people would rather have a clean Partitionable instance...

Best, -Ryan

On Sun, Sep 29, 2013 at 3:31 AM, Mike Izbicki wrote:

...

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

so the simple O(1) split would produce three submaps, the middle one having only one element. This operation would not be very parallelization-friendly.

Actually, I'm perfectly happy with that in this case! - A decent work-stealing system can tolerate a fairly large number of excessively small, trivial computations. It's having *only* those that's a big problem. (Which is what you often get if your parallel container ops spawn a task per element.) - Since Maps support O(1) size, the consumer of the split-up-map could choose to sequentially execute the singleton maps if desired. Personally, I'm most interested in set-like operations and don't need any order guarantees. But that's another dimension in which one could chop up the API... Maybe this does deserve its own module in the namespace, and maybe its own package, as Edward suggested. -Ryan