How to zip multiple lists in Haskell?

Question

In python zip function accepts arbitrary number of lists and zips them together.

>>> l1 = [1,2,3]
>>> l2 = [5,6,7]
>>> l3 = [7,4,8]
>>> zip(l1,l2,l3)
[(1, 5, 7), (2, 6, 4), (3, 7, 8)]
>>> 

How can I zip together multiple lists in haskell?

Answer 1

A generalization of zip can be achieved using Applicative Notation. It's a bit unpleasant to use because of the newtype wrapping/unwrapping, but if you are doing something that can't be done with a zipWithn for reasonably small n, you are probably already at a high enough level of abstraction where the notational pains are absent anyway.

The type is ZipList a, and its applicative instance zips together lists. For example:

(+) <$> ZipList [1,2] <*> ZipList [3,4] == ZipList [4,6]

This generalizes to functions of arbitrary arity and type using partial application:

(+) <$> ZipList [1,2]  :: ZipList (Int -> Int)

See how (+) is partially applied here?

If you don't like adding ZipList and getZipList everywhere, you could recreate the notation easily enough:

(<$>) :: (a -> b) -> [a] -> [b]
(<$>) = map

(<*>) :: [a -> b] -> [a] -> [b]
(<*>) = zipWith ($)

Then the notation for zipWith f a b c d ... is:

f <$> a <*> b <*> c <*> d <*> ...

Applicative notation is a very powerful and general technique that has much wider scope than just generalized zipping. See the Typeclassopedia for more on Applicative notation.

Answer 2

You can transpose a list of lists:

>>> import Data.List
>>> transpose [l1,l2,l3]
[[1,5,7],[2,6,4],[3,7,8]]