[Haskell-cafe] Bifold: a simultaneous foldr and foldl

[Henning Thielemann]

Noah Easterly wrote:
> Somebody suggested I post this here if I wanted feedback.
> 
> So I was thinking about the ReverseState monad I saw mentioned on r/haskell a 
> couple days ago, and playing around with the concept of information flowing 
> two directions when I came up with this function:
> 
> bifold :: (l -> a -> r -> (r,l)) -> (l,r) -> [a] -> (r,l)
> bifold _ (l,r) [] = (r,l)
> bifold f (l,r) (a:as) = (ra,las)
>  where (ras,las) = bifold f (la,r) as
>          (ra,la) = f l a ras
> 
> (I'm sure someone else has come up with this before, so I'll just say I 
> discovered it, not invented it).
> 
> Basically, it's a simultaneous left and right fold, passing one value from 
> the start of the list toward the end, and one from the end toward the start.

I also needed a bidirectional fold in the past. See foldl'r in
   http://code.haskell.org/~thielema/utility/src/Data/List/HT/Private.hs

You can express it using foldr alone, since 'foldl' can be written as 'foldr':
    http://www.haskell.org/haskellwiki/Foldl_as_foldr

You may add your example to the Wiki.