The Fibonacci sequence

Implementing the fibonacci sequence is considered the "Hello, world!" of Haskell programming. This page collects Haskell implementations of the sequence.

Naive solution

fib 0 = 0
fib 1 = 1
fib n = fib (n-1) + fib (n-2)

Canonical zipWith implementation

fib = 1 : 1 : zipWith (+) fib (tail fib)

With fix points

fix $ \fib -> 1 : 1 : zipWith (+) fib (tail fib)

With scanl

fib = fix ((1:) . scanl (+) 1)

Fastest Fib in the West

This was contributed by wli

import System.Environment
import Data.List

fib n = snd . foldl fib' (1, 0) . map (toEnum . fromIntegral) $ unfoldl divs n
    where
        unfoldl f x = case f x of
                Nothing     -> []
                Just (u, v) -> unfoldl f v ++ [u]

        divs 0 = Nothing
        divs k = Just (uncurry (flip (,)) (k `divMod` 2))

        fib' (f, g) p
            | p         = (f*(f+2*g), f^2 + g^2)
            | otherwise = (f^2+g^2,   g*(2*f-g))

main = getArgs >>= mapM_ (print . fib . read)