Haskell - Writing foldr recursively

Question

I am trying to write the library function foldr using recursion. However, I am getting syntax errors and not sure about the functional correctness. This is my code:

foldr :: (a -> b) -> [a] -> [b]
foldr f [] = []
foldr f xs = foldr f (init xs) : f (last xs)      

I would appreciate it if I can get some help on this

Answer 1

That is not the type of the foldr function. That is the type of the map function.

But that said, : concatenates one element to the front of a list. The way you are using it attempts to concatenate one element to the end of a list, which does not work.

The closest thing to what you mean -- which is still O(n^2) and deeply inefficient -- is to replace the last line with

foldr f xs = foldr f (init xs) ++ [f (last xs)]