Generating Fibonacci numbers in Haskell?

Question

In Haskell, how can I generate Fibonacci numbers based on the property that the nth Fibonacci number is equal to the (n-2)th Fibonacci number plus the (n-1)th Fibonacci numb

Answer 1

fibs :: [Integer]
fibs = 1 : 1 : zipWith (+) fibs (tail fibs)

at first, with fibs and tail fibs, we can get the 3rd element:

fibs                        : [1, 1, ?
tail fibs                   : [1, ?
zipWith (+) fibs (tail fibs): [2, ?

now, we know the 3rd is 2, we can get the 4th:

fibs                        : [1, 1, 2, ?
tail fibs                   : [1, 2, ?
zipWith (+) fibs (tail fibs): [2, 3, ?

now the 5th:

fibs                        : [1, 1, 2, 3, ?
tail fibs                   : [1, 2, 3, ?
zipWith (+) fibs (tail fibs): [2, 3, 5, ?

and so on ..