[Haskell-cafe] An ugly zip3 problem..

[Dan Weston]

There's an interesting blog post by Dan Piponi on the subject:

http://sigfpe.blogspot.com/2007/01/monads-hidden-behind-every-zipper.html

Summary: "convolution is comonadic"

Dan

Michael Feathers wrote:
> I'm working on something and it's looking rather ugly.. essentially, it 
> it's an application of a low pass filer to a dataset.
> 
> 
> type Dataset = [Double]
> type FilterWindow3 = (Double,Double,Double)
> 
> internalList :: [a] -> [a]
> internalList = tail . init
> 
> lowPass3 :: FilterWindow3 -> Double
> lowPass3 (i, j, k) = (i + 2 * j + k) / 4.0
> 
> filter3 :: (FilterWindow3 -> Double) -> Dataset -> Dataset
> filter3 f3 ds = [(f3 x) | x <- formWindows ds]
> 
> iterFilter :: (Dataset -> Dataset) -> Int -> Dataset -> Dataset
> iterFilter f n ds
>   | n > 0     = iterFilter f (n - 1) (f ds)
>   | otherwise = ds
> 
> smooth :: Int -> Dataset -> Dataset
> smooth = iterFilter $ filter3 lowPass3
> 
> formWindows :: Dataset -> [FilterWindow3]
> formWindows ds =
>   internalList $ zip3 x y z
>     where c0 = [head ds]
>           cn = [last ds]
>           x  = ds ++ cn ++ cn
>           y  = c0 ++ ds ++ cn
>           z  = c0 ++ c0 ++ ds
> 
> 
> The key idea is that I can take care of edge conditions with that last 
> function.  It lets me build a list of 3-tuples, each of which is reduced 
> to a single point in the next rewrite of the dataset.  I used zip3 to 
> build up that list, and I take care to keep the lists the same length by 
>  duplicating the head and last elements as necessary.  Has anyone done 
> this sort of thing before?
> 
> Any and all style advice welcome.
> 
> Thanks,
> 
> Michael Feathers
> 
>