[Haskell-cafe] defining last using foldr

[ok]

Let's start by reminding ourselves what foldr does.

foldr f z [x1,x2,...,xn] = f x1 (f x2 ... (f xn z) ...)

Now let's ask about last:

last [] = error ...
last [x1,...,xn] = xn

We're going to have to keep track of whether we have a last element
or not.  The obvious candidate for this is Maybe x.  Initially there
is no element, Nothing.
    f x Empty = Just x
    f x (Just y) = Just y
This picks up a new value (x) when there wasn't one (Nothing) and
keeps the old last element (Just y) when there was one (Just y).
But this gives us a Maybe x, when we want an x, so we'll have to finish
off with a fromJust.

last = fromJust . foldr f Nothing
   where f _ r@(Just _) = r
         f x Nothing    = Just x