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 <muranu...@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 <muranu...@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 > >
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