I think this has the semantics you're looking for. (it would probably be somewhat prettier if "mappend" wasn't such an ugly identifier (compared to, say, (++)), but this is just me trying to sneak a shot in against the Monoid method's names ;)

ghci> let diag = foldr (curry (prod mappend fst snd . uncurry (coprod mappend (splitAt 2) (splitAt 1)))) []

ghci> diag [[1,2,3],[4,5,6],[7,8,9]]
[1,2,4,3,5,7,6,8,9]
ghci> diag [[1,2,3],[4],[5,6,7]]
[1,2,4,3,5,6,7]


On Wed, Apr 15, 2009 at 5:32 AM, Sebastian Fischer <sebf@informatik.uni-kiel.de> wrote:
Fancy some Codegolf?

I wrote the following function for list diagonalization:

> diag l = foldr (.) id ((sel l . flip sel) ((:[]).(:))) []
>  where
>   sel = foldr (\a b c -> id : mrg (a c) (b c)) (const []) . map (flip id)
>
>   mrg []     ys     = ys
>   mrg xs     []     = xs
>   mrg (x:xs) (y:ys) = (x.y) : mrg xs ys

Self explanatory, isn't it? Here is a test case:

   *Main> take 10 $ diag [[ (m,n) | n <- [1..]] | m <- [1..]]
   [(1,1),(1,2),(2,1),(1,3),(2,2),(3,1),(1,4),(2,3),(3,2),(4,1)]

I was trying to golf it down [^1] but my brain explodes. If you succeed in reducing keystrokes, I'd be happy to know!

Cheers,
Sebastian

[^1]: http://codegolf.com/
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