[Haskell-cafe] A challenge

[Thomas Davie]

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

> On Wed, Apr 8, 2009 at 4:57 PM, Thomas Davie <tom.davie at 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 :)

Bob