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I implemented the Fibonacci sequence using iterate.

import Data.List

fib :: Int -> Maybe Int
fib n 
 | n < 0     = Nothing
 | otherwise = (fmap (snd . fst)) $ find (\(_,i) -> n == i) (zip res [0..])

res :: [(Int, Int)]
res = iterate f (0,1)

f :: (Num a, Num b) => (a, a) -> (a, a)
f (x, y) = (y,x+y)

Testing

> fib (-1)
Nothing
> fib 0
Just 1
> fib 2
Just 2
> fib 3
Just 3
> fib 4
Just 5
> fib 5
Just 8
> fib 6
Just 13

Please review it.

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In my opinion, Maybe is too cumbersome here. I'd consider fib (-1) to be ill-defined, and I'd let it just crash with an error.

By your convention, the Fibonacci sequence is

1, 2, 3, 5, 8, 13, …

I would prefer to see it start earlier, such that fib 0 is 0:

0, 1, 1, 2, 3, 5, 8, 13, ….

The outputs can get pretty big. I suggest using Integer instead of Int.

You're using a very convoluted way to extract the nth item from a list.

Suggested solution

import Data.List (iterate)

fib :: Int -> Integer
fib n = fst $ sequence !! n
  where
    sequence = iterate (\(x, y) -> (y, x + y)) (0, 1)

You could also use the point-free style:

fib :: Int -> Integer
fib = (!!) $ map fst $ iterate (\(x, y) -> (y, x + y)) (0, 1)

For that matter, you could just define the infinite sequence

fibonacciSequence = map fst $ iterate (\(x, y) -> (y, x + y)) (0, 1)

… and let the caller do whatever they want with it, including extracting specific entries using !!.

Behaviour

*Main> fib (-1)
*** Exception: Prelude.!!: negative index
*Main> fib 0
0
*Main> fib 1
1
*Main> fib 2
1
*Main> fib 3
2
*Main> fib 4
3
*Main> fib 5
5
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