[Haskell-cafe] another laziness blowup (this one unsolved)

[Thomas Hartman]

Is it possible to fix alternate' (the second version), or otherwise
define a fast stepwise alternate that doesn't blow up on long lists?

alternate just breaks up [1,2,3,4,5] into ([1,3,5],[2,4])

Thanks!

{-# LANGUAGE BangPatterns #-}
import Data.List
import Control.Arrow
import Control.Parallel.Strategies

t = (last *** last) $! alternate $ [1..(10^6)]
t' = (last *** last) $! alternate' $ [1..(10^6)]
t'' = (last *** last) $! alternate'' $ [1..(10^6)]


-- finishes reasonably fast, but does a separate computation for the
list and its tail rather than just rip through it
alternate x = (skip1 x,(skip1 $ tail x))
skip1 = skip 1
skip n xs =
  let (a,b) = splitAt (n+1) xs
  in case a of
     [] -> []
     x:_ -> x : skip n b



-- this one overflows on million element list, even after fiddling
with strictness on input args. can this be fixed?
alternate' xs =
  let f3 :: Int -> (([Int],[Int]),Int) -> (([Int],[Int]),Int)
      f3 x ((a,b),n) = -- rnf (x,((a,b),n)) `seq`
        let nxtn = n+1
        in if n `mod` 2 == 0
            then ((x:a,b),nxtn)
            else ((a,x:b),nxtn)
  in fst . foldr f3 (([],[]),0) $ xs

-- no overflow, goes through the list stepwise, but it's actually
slightly slower than the first alternate because of the reverses
alternate'' xs =
  let f3 ((a,b),n) x =
        (let nxtn = n+1
        in if n `mod` 2 == 0
            then ((x:a,b),nxtn)
            else ((a,x:b),nxtn) )
  in (reverse *** reverse) . fst . foldl' f3 (([],[]),0) $ xs