[Haskell-cafe] beginner's problem about lists

[Henning Thielemann]

On Tue, 10 Oct 2006 falseep at gmail.com wrote:

> Hi all,
> 
> I'm trying to implement a function that returns the shorter one of two given
> lists,
> something like
> shorter :: [a] -> [a] -> [a]
> such that shorter [1..10] [1..5] returns [1..5],
> and it's okay for shorter [1..5] [2..6] to return either.
> 
> Simple, right?
> 
> However, it becomes difficult when dealing with infinite lists, for example,
> shorter [1..5] (shorter [2..] [3..])
> Could this evaluate to [1..5]? I haven't found a proper implementation.
> 
> Again it's ok for shorter [2..] [3..] to return whatever that can solve
> the above problem correctly.
> An infinite list could work, I guess, but I don't know how.

With PeanoNumbers,
   http://darcs.haskell.org/htam/src/Number/PeanoNumber.hs
 I would first attach a lazy length information to each list before any
call to 'shorter', then I would remove this information after the last
call to 'shorter'.

Untested code follows:

attachLength :: [a] -> (PeanoNumber.T, [a])
attachLength xs = (genericLength xs, xs)

detachLength :: (PeanoNumber.T, [a]) -> [a]
detachLength = snd 

shorter :: (PeanoNumber.T, [a]) -> (PeanoNumber.T, [a]) -> (PeanoNumber.T, [a])
shorter (xl,xs) (yl,ys) = (min xl yl, if xl < yl then xs else ys)


detachLength
   (shorter (attachLength [1..5])
       (shorter (attachLength [2..]) 
                (attachLength [3..])))


This will work with if one of the lists is finite. If all lists are
infinite, this solution fails. You can simulate the peano numbers also 
with [()].