Fixed points

gistfile1.txt

Prelude> fix (\f c -> if null c then 0 else 1 + (f (tail c))) [1, 2, 3]
3
Prelude> fix (\f c -> if null c then head c  else 1 + (f (tail c))) [1, 2, 3]
*** Exception: Prelude.head: empty list
Prelude> fix (\f c -> if null c then 0 else 1 + (f (tail c))) [1, 2, 3]
3
Prelude> fix (\f c -> if null c then 0 else (head c) + (f (tail c))) [1, 2, 3]
6
Prelude> :t fix
fix :: (t -> t) -> t
Prelude> let fix f =  let  x = f x in x
Prelude> -- t :: ([Int] -> Int)
Prelude> -- fix' :: (([Int] -> Int) -> ([Int] -> Int)) -> [Int] -> Int
Prelude> -- fix' :: (([Int] -> Int) -> [Int] -> Int) -> [Int] -> Int