Creating a list of all possible lists, given each element can take one of n values

Question

In Haskell I'm trying to create a function with the typing Int -> [a] -> [[a]], that generates a list such as: [[0, 0], [0, 1], [1, 0], [1, 1]] where each element in the smaller lists can take the value of either 1 or 0. Each of the smaller lists has the same size, which in this case is 2. If the size of the smaller lists was 3, I would expect to get the output [[0,0,0], [0,0,1], [0,1,0], [1,0,0], [1,1,0], [0,1,1], [1,0,1], [1,1,1]]

I've looked in to the permutations function, but this does not achieve exactly what I want. I believe there is also a variate function, but I cannot access this library.

Rather than the exact function (which would also be useful), what would be the process to generate such a list?

Answer 1

As oisdk mentions in a comment, a more general version of this exact function is already defined, with the name Control.Monad.replicateM:

Prelude> import Control.Monad (replicateM)
Prelude Control.Monad> replicateM 3 [0,1]
[[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]