On Fri, Nov 30, 2012 at 4:43 PM, Takayuki Muranushi <muranushi@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@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

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