[Haskell-cafe] computation over containers, greatly simplified notation.

[Jason Dagit]

You might find this paper an interesting read: http://www.brics.dk/RS/01/10/

On Fri, Nov 30, 2012 at 4:43 PM, Takayuki Muranushi <muranushi at gmail.com>wrote:

> Dear everyone,
>
> After a number of attempts [1] I'm starting to think that my initial
> approach was ill-directed.
>
> After all, Functor, Applicative, Zip are three different classes.
> Functors are type constructors where you can map unary functions over them.
> Applicatives are those with map-over of zero-ary functions (pure,) unary
> functions, binary functions, ternary functions, ... etc.
> Zip are those with unary, binary, ternary ... mapover, but not zero-ary
> map-over.
>
> Repa Arrays and Vectors belong to Zip because there's no trivial unique
> way to implement pure.
>
> What the customer really needed [2] seems to be the following series of
> functions:
>
>
> forLiftZ1 :: Zip f => f a -> (a -> b) -> f b
>
> forLiftZ2 :: Zip f => f a -> f b -> (a -> b -> c) -> f c
>
>
> forLiftZ3 :: Zip f => f a -> f b -> f c -> (a -> b -> c -> d) -> f d
>
> Now I'm trying if it's possible to implement the series in a single shot
> [3] .
>
> I'm reporting my progress for anyone who might be still thinking for me.
> Thank you!!
>
> [1] https://github.com/nushio3/practice/tree/master/free-objects
> [2] http://www.projectcartoon.com/cartoon/3
> [3]
> https://github.com/nushio3/practice/blob/master/free-objects/printf6.hs
>
>
>
>
> 2012/11/29 Takayuki Muranushi <muranushi at gmail.com>
>
>> Dear all,
>>
>> I came up with an idea to greatly simplify some kinds of array
>> computations. It should work well with many kinds of arrays. Is this new?
>>
>> https://gist.github.com/4162375
>>
>>
>>
>> These few days, I've been trying to rewrite a hydrodynamic simulation
>> code that used Data.Vector (~250 lines), to Repa [1] . It seemed promising,
>> but soon I realized that I needed to use Repa.map and Repa.zipWith almost
>> everywhere. I need careful thinking to transform every lines (that used
>> vector's indexing) to Repa's point-free stile. Is there any better ways?
>>
>> Then I realized that I was the author of Paraiso [2], a DSL for stencil
>> computation. One of its feature is to write down array computation just as
>> if it were scalar computation.
>>
>> Basically what I need is ZipList-like Applicative instances for vectors
>> and Repa arrays. Why not they support ZipVector? Because 'pure' of zipList
>> was an infinite list and you can't do infinite vectors. Then I came up with
>> this idea.
>>
>> https://gist.github.com/4162375
>>
>> the wrapper W does several things: it represents the 'pure,' homogeneous
>> array in a space-efficient manner, and also serves as a newtype-wrapper of
>> Num (and possibly Fractional, Floating...) instances.
>>
>> Questions are: is this technology new? or promising? doomed?
>> It seems to me like a free-Applicative, like the free-Monad theory. Are
>> they related?
>> The function 'backend' helps to mix in the non-zip-like computations. How
>> can we remove the 'undefined' in the 'backend?'
>> Some of Repa computations are Monads. W needs to be a monad transformer
>> to incooperate this.
>>
>> Also I'm grateful to past cafe discussion on existing Zippable
>> implementations [3][4] .
>>
>> [1] hackage.haskell.org/package/repa
>> [2] http://hackage.haskell.org/package/Paraiso
>> [3] http://www.haskell.org/pipermail/haskell-cafe/2009-July/064403.html
>> [4]
>> http://hackage.haskell.org/packages/archive/category-extras/latest/doc/html/Control-Functor-Zip.html
>>
>>
>> --
>> Takayuki MURANUSHI
>> The Hakubi Center for Advanced Research, Kyoto University
>> http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html
>>
>
>
>
> --
> Takayuki MURANUSHI
> The Hakubi Center for Advanced Research, Kyoto University
> http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html
>
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>
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