On Wed, Apr 8, 2009 at 4:57 PM, Thomas Davie
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. Here's the function I used to test various versions of iterateM: \begin{code} test it = it 4 (\i -> putStrLn (show i) >> return (i+1)) 0 \end{code} Cheers, Josef