suggestion: use lazy pattern matching for Monoid instances of tuples
Petr Pudlák
petr.mvd at gmail.com
Mon Aug 19 16:47:02 CEST 2013
Just to be sure that I understand it correctly: If I take foldMap as the
basis and I run it on a binary tree with First/Last monoids, I get both
result in O(depth). But if I take foldl or foldr as the basis, either
searching for the first or for the last element will take O(size), am I
right?
Dne 08/19/2013 04:14 PM, Edward Kmett napsal(a):
> With foldMap one can have structures that get to explicitly reuse
> previous intermediate results.
>
> e.g.
> http://hackage.haskell.org/packages/archive/compressed/3.0.3/doc/html/Data-Compressed-Internal-LZ78.html
> gives you a list with a more efficient fold by using LZ78 to identify
> sharing with earlier parts of the list.
>
> With foldr you can't exploit such regularity as you can merely append
> one element at a time.
>
> Less drastically, with foldMap, you can binary search a tree structure
> if the foldMap preserves the original associativity of the structure.
>
> The lens package uses this to navigate to keys in a Zipper over a Map
> to a given key in O(log n) time borrowing the asymptotics from the
> balance of the underlying structure.
>
> In my current work I'm using "sequence-algebras" and "sequence-trees"
> to exploit even more structure than foldMap gives me.
>
> I'll probably write up an article at some point soon on the School of
> Haskell.
>
> -Edward
>
>
> On Mon, Aug 19, 2013 at 9:31 AM, Petr Pudlák <petr.mvd at gmail.com
> <mailto:petr.mvd at gmail.com>> wrote:
>
> This is exactly how I run into the Monoid problem. My original
> `foldr` version works fine, but when I saw this Gabriel's post:
> http://www.haskellforall.com/2013/08/composable-streaming-folds.html
> the monoid variant looked cleaner and nicer so I wanted to
> redesign my idea using monoids as well. And that was precisely
> when I realized that (,) isn't lazy enough.
>
> Could you elaborate a bit when/how the asymptotic difference occurs?
>
> Best regards,
> Petr
>
> Dne 08/19/2013 02:03 PM, Edward Kmett napsal(a):
>> If you are looking into a tackling lazy foldr, I'd recommend also
>> including or considering using foldMap as a basis. It can make an
>> asymptotic difference for some folds. I sent Gabriel a version in
>> that style. I'll dig up a copy and send it your way as well.
>>
>> -Edward
>>
>>
>> On Mon, Aug 19, 2013 at 3:29 AM, Petr Pudlák <petr.mvd at gmail.com
>> <mailto:petr.mvd at gmail.com>> wrote:
>>
>> Thank you all for the responses.
>>
>> Edward's objection is very serious, I didn't think of it.
>> Because of it I retract the proposal, this would indeed
>> create big problems. (I just wish someone invents an oracle
>> strictness analyzer...)
>>
>> Instead, as suggested, I'll make a package with `newtype`
>> wrappers for tuples that will provide the extra-lazy monoid
>> semantics. Any ideas for what other type classes except
>> `Monoid` (and `Semigroup`) could be included? Or perhaps even
>> other data types except tuples?
>>
>> Dne 08/18/2013 11:21 PM, Gabriel Gonzalez napsal(a):
>>> I'm guessing this proposal is related to this Stack Overflow
>>> answer you gave:
>>>
>>> http://stackoverflow.com/a/18289075/1026598
>>>
>>> Note that your solution is very similar to the solution in
>>> the `foldl` package I just released (also based off of the
>>> same blog post you got your solution from). The key
>>> differences are that:
>>>
>>> * The `foldl` solution is for left folds and uses a strict
>>> tuple internally to prevent space leaks
>>> * Your solution is for right folds and uses an extra-lazy
>>> tuple internally to promote laziness
>>>
>>> This suggests to me that it would be better to keep this
>>> extra-lazy tuple as an internal implementation detail of a
>>> right-fold package that would be the lazy analogy of
>>> `foldl`, rather than modifying the standard Haskell tuple.
>> Yes, this is how I encountered the problem. If I have time
>> I'll make a mirror package `foldr` based on extra-lazy
>> tuples. (Or perhaps we could merge the ideas into a single
>> package.)
>>
>> Best regards,
>> Petr
>>
>>
>
>
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