Kata

The fix function can be defined as:

fix :: (a -> a) -> a
fix f = let x = f x in x

fix :: forall a b. ((a -> b) -> a -> b) -> a -> b
fix g v = g (fix g) v

If we regard this as a language primitive, any recursive function can be written without using recursion. Write foldr' and reverse' as non-recursive functions that can be 'fixed' to foldr and reverse as follows:

foldr = fix foldr'
reverse = fix reverse'

For a more detailed explanation of the fix function, see http://en.wikipedia.org/wiki/Fixed-point_combinator

Note: foldr is lazy, so your foldr' should be lazy too. Also, your foldr' need only work on lists - it does not have to work for an arbitrary Foldable functor.