Lazy cartesian product in Haskell

Question

I would like to generate a rather large but finite Cartesian product in Haskell, which I need to then iterate on (think partition function of a mean-field model). The natural thing to do uses sequence, like this:

l = sequence $ replicate n [0,1,2]

Unfortunately, for large n, this does not fit in memory and I run out of heap as soon as I ask for length l for instance. I would need a way to do the same thing lazily. I ended up "rediscovering" base-3 arithmetics, like this,

nextConfig []     = []
nextConfig (0:xs) = 1:xs
nextConfig (1:xs) = 2:xs
nextConfig (2:xs) = 0:(nextConfig xs)

ll = take (3^n) $ iterate nextConfig $ replicate n 0

(which works) but it feels like reinventing the wheel, and besides it is much too specific. What would be a better lazy way to generate the product?

Answer 1

The more memory-friendly way is obtained by binding in reverse order compared to sequence,

foo 0 _ = [[]]
foo k xs = [h:t | t <- foo (k-1) xs, h <- xs]

It is slower due to less sharing, but since memory is your problem, maybe it's good enough for you.