[Haskell-cafe] A systematic method for deriving a defintion of foldl using foldr?

[Adrian Neumann]

Read this excellent paper:

http://www.cs.nott.ac.uk/~gmh/fold.pdf


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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