[Haskell-cafe] A systematic method for deriving a defintion of
foldl using foldr?
aneumann at inf.fu-berlin.de
Wed Mar 11 14:33:47 EDT 2009
Read this excellent paper:
Am 11.03.2009 um 19:24 schrieb R J:
> foldl and foldr are defined as follows:
> foldr :: (a -> b -> b) -> b -> [a] -> b
> foldr f e  = e
> foldr f e (x : xs) = f x (foldr f e xs)
> foldl :: (b -> a -> b) -> b -> [a] -> b
> foldl f e  = e
> foldl f e (x : xs) = foldl f (f e x) xs
> 1. I understand how these definitions work, and yet I'm unable to
> implement foldl in terms of foldr. What's a systematic approach to
> identifying such an implementation, and what is the implementation?
> 2. I believe that the reverse implementation--namely, implementing
> foldr in terms of foldl--is impossible. What's the proof of that?
> 3. Any advice on how, aside from tons of practice, to develop the
> intuition for rapidly seeing solutions to questions like these
> would be much appreciated. The difficulty a newbie faces in
> answering seemingly simple questions like these is quite discouraging.
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