What is going on in this function (haskell)?

Question

I have this haskell function that I don't quite understand.

ns :: [Integer]
ns = 0 : [n+k | (n, k) <- zip ns [1,3..]]

I am asked to "take 3 ns".

I thought ns was constant so it would only zip with the first element of the list, giving (0,1). Then when added gives an answer of 1. Then it says "take 3 ns" so I zipped 0 with the first 5 elements of the list, giving... (0,1),(0,3), (0,5) and then when added, I get a final answer of [1,3,5]. However this isn't the correct answer.

What is actually happening to ns? I'm struggling to understand...

Answer 1

haskell is lazy so you can have recursive definitions. Here it is laid out.

ns = 0 : something

(n,k) <- zip (0 : something ) [1,3,5,7...]
(n,k) <- [(0,1) : something )

ns = 0 : 1 : something

(n,k) <- zip ( 0 : 1 : something ) [3,5,7...]
(n,k) <- (0,1) : (1,3) : something

ns = 0 : 1 : 4 : something

(n,k) <- zip ( 0 : 1 : 4 : something ) [5,7...]
(n,k) <- (0,1) : (1,3) : (4,5) : something

ns = 0 : 1 : 4 : 9 : something

....

See how we determine what the next tuple is then add its two elements. This allows us to determine the next element.