On 8 Apr 2009, at 19:05, Josef Svenningsson wrote:

On Wed, Apr 8, 2009 at 4:57 PM, Thomas Davie <tom.davie@gmail.com> wrote:
>
> We have two possible definitions of an "iterateM" function:
>
> iterateM 0 _ _ = return []
> iterateM n f i = (i:) <$> (iterateM (n-1) f =<< f i)
>
> iterateM n f i = sequence . scanl (>>=) (return i) $ replicate n f
>
> The former uses primitive recursion, and I get the feeling it should be better written without it.  The latter is quadratic time – it builds up a list of monadic actions, and then runs them each in turn.
>
> Can anyone think of a version that combines the benefits of the two?

There seems to be a combinator missing in Control.Monad. Several people have suggested that iterateM should be implemented using a fold. But that seems very unnatural, we're trying to *build* a list, not *consume* it. This suggests that we should use an unfold function instead. Now, I haven't found one in the standard libraries that works for monads but arguably there should be one. So, let's pretend that the following function exists:
unfoldM :: Monad m => (b -> m (Maybe(a,b))) -> b -> m [a]

Then the implementation of iterateM becomes more natural:
\begin{code}
iterateM n f i = unfoldM g (n,i)
 where g (0,i) = return Nothing
      g (n,i) = do j <- f i
                   return (Just (i,(n-1,j)))
\end{code}
I'm not sure whether this version is to your satisfaction but it's quite intuitive IMHO.

That one certainly seems very natural to me, now if only unfoldM existed :)