Re: [Haskell-beginners] Creating beautiful code: can you make this divide-and-conquer implementation of the "tails" function beautiful?

I think using iterate expresses tails quite elegantly: tails = iterate tail But unfortunately "tail" is unsafe and throws an exception on a empty list: *Main> tails [1,2,3,4] [[1,2,3,4],[2,3,4],[3,4],[4],[],*** Exception: Prelude.tail: empty list To make this correct we can do something like: tails' l = take (length l) (iterate tail l) -- or the points free version -- import Control.Arrow -- tails' = uncurry take . (length &&& iterate tail) but that evaluates the entire list twice needlessly and is certainly not as elegant Seems to me that to do better than the Prelude definition what we really need is a exception safe tail function so "tails = iterate tail" works. -deech On Mon, Jun 27, 2011 at 8:16 PM, Michael Xavier wrote:

I'll bite. The source of tails is pretty elegant:

tails :: [a] -> [[a]] tails [] = [[]] tails xxs@(_:xs) = xxs : tails xs

On Mon, Jun 27, 2011 at 1:30 PM, Costello, Roger L. wrote:

...

Hi Folks,

Below is a divide-and-conquer implementation of the "tails" function.

Notice the two patterns (x:y:xs) and (x:[]). And notice that (x:y:xs) is used by the "length" function and again by the "splitAt" function. That doesn't seem elegant. Can the function be simplified and made beautiful?

/Roger

tails'               ::   [a] -> [[a]] tails' (x:y:xs)   =   map (++zs) (tails' ys) ++ tails' zs                           where m        =  length (x:y:xs)                                       n         =  m `div` 2                                      (ys,zs)  =  splitAt n (x:y:xs) tails' (x:[])      =    [[x]]

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-- Michael Xavier http://www.michaelxavier.net

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