You are correct, my weave did hide the list in the explicit composition of closure(s). I can be even more declarative and let the closure construction be implicit in weave' below... (and this message should be literate Haskell) weave' uses a fixed point and pairs to tie the knot declaratively:
import Data.List
weave' :: [[a]] -> [a] weave' [] = [] weave' xss = let (ans,rest) = helper rest xss in ans where helper :: [[a]] -> [[a]] -> ([a],[[a]]) helper _rest ([]:_xss) = ([],[]) helper rest [] = (weave' rest,[]) helper rest ((x:xs):xss) = let (ans,rest') = helper rest xss in (x:ans,xs:rest')
The next case might be an optimization, since we know that nothing after the [] will be used in the next pass:
-- helper rest ((x:[]):xss) = let (ans,_) = helper rest xss -- in (x:ans,[]:[])
My previous weave, uses composition of (xs:) thunks instead of pairs:
weave :: [[a]] -> [a] weave [] = [] weave xss = helper id xss where helper :: ([[a]] -> [[a]]) -> [[a]] -> [a] helper _rest ([]:_xss) = [] -- done helper rest [] = weave (rest []) helper rest ((x:xs):xss) = x : helper (rest . (xs:)) xss
One might imagine an 'optimized' case like in weave':
-- helper rest ((x:[]):xss) = let yss = rest ([]:[]) -- in x : helper (const yss) xss
Some simple tests such that check should be True
check = (ans == test 20 weave) && (ans == test 20 weave')
test n w = map (take n . w) $ [] : [[]] : [[],[]] : [[1..10]] : [[1,3..10],[2,4..10]] : [[1..],[11..15],[301..],[11..15]] : [[1..],[11..15],[301..]] : [[1..],[11..15],[301..],[]] : [[1..],[11..15],[],[301..]] : [[1..],[],[11..15],[],[301..]] : [[],[1..],[11..15],[],[301..]] : testInf : [] testInf = map enumFrom [1..] ans = [[],[],[],[1,2,3,4,5,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10] ,[1,11,301,11,2,12,302,12,3,13,303,13,4,14,304,14,5,15,305,15] ,[1,11,301,2,12,302,3,13,303,4,14,304,5,15,305,6] ,[1,11,301],[1,11],[1],[] ,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]]