balanced fold for Data.List

[Henning Thielemann]

On Fri, 28 Jun 2013, Brent Yorgey wrote:

> How would people feel about adding a function
>
>  foldb :: (a -> a -> a) -> a -> [a] -> a
>
> to Data.List which performs a *balanced* fold of a list?  Right now I
> have this function in the Diagrams.Util module of diagrams-lib but it
> seems generally useful.  Here's a (strawman) implementation:
>
>  foldb :: (a -> a -> a) -> a -> [a] -> a
>  foldb _ z [] = z
>  foldb f _ as = foldb' as
>    where foldb' [x] = x
> 	  foldb' xs  = foldb' (go xs)
> 	  go []         = []
> 	  go [x]        = [x]
> 	  go (x1:x2:xs) = f x1 x2 : go xs
>
> I could also stick it in a separate package but it seems silly to have
> a whole package for such a small function.

For a commutative accumulation function I have an even more balanced fold:

foldNested :: (a -> a -> a) -> a -> [a] -> a
foldNested _ x [] = x
foldNested f _ xs@(_:rs) =
    let reduce (z0:z1:zs) = f z0 z1 : reduce zs
        reduce zs = zs
        ys = xs ++ zipWith (flip const) rs (reduce ys)
    in  last ys