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
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