[Haskell-cafe] A challenge

[Jonathan Cast]

On Wed, 2009-04-08 at 16:57 +0200, Thomas Davie 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.

It's also quadratic in invocations of f, no?  If your monad's (>>=)
doesn't object to being left-associated (which is *not* the case for
free monads), then I think

iterateM n f i = foldl (>>=) (return i) $ replicate n f

would be both correct and linear.  If you're monad's (>>=) is itsef
quadratic in time when left-associated, you can try applying a CPS
transformation to fix the problem.[1]

jcc

[1] http://wwwtcs.inf.tu-dresden.de/~voigt/mpc08.pdf