[Haskell-cafe] Lazy Evaluation in Monads

[Antoine Latter]

On Tue, May 31, 2011 at 2:49 PM, Scott Lawrence <bytbox at gmail.com> wrote:
> I was under the impression that operations performed in monads (in this
> case, the IO monad) were lazy. (Certainly, every time I make the
> opposite assumption, my code fails :P .) Which doesn't explain why the
> following code fails to terminate:
>
>  iRecurse :: (Num a) => IO a
>  iRecurse = do
>    recurse <- iRecurse
>    return 1
>
>  main = (putStrLn . show) =<< iRecurse
>
> Any pointers to a good explanation of when the IO monad is lazy?
>
>
> === The long story ===
>
> I wrote a function unfold with type signature (([a] -> a) -> [a]), for
> generating a list in which each element can be calculated from all of
> the previous elements.
>
>  unfold :: ([a] -> a) -> [a]
>  unfold f = unfold1 f []
>
>  unfold1 :: ([a] -> a) -> [a] -> [a]
>  unfold1 f l = f l : unfold1 f (f l : l)
>
> Now I'm attempting to do the same thing, except where f returns a monad.
> (My use case is when f randomly selects the next element, i.e. text
> generation from markov chains.) So I want
>
>  unfoldM1 :: (Monad m) => ([a] -> m a) -> [a] -> m [a]
>
> My instinct, then, would be to do something like:
>
>  unfoldM1 f l = do
>    next <- f l
>    rest <- unfoldM1 f (next : l)
>    return (next : rest)
>
> But that, like iRecurse above, doesn't work.
>

You could use a different type:

> type IOStream a = (a, IO (IOStream a))

> unfold :: ([a] -> IO a) -> IO (IOStream a)
> unfold f =
>     let go prev = do
>           next <- f prev
>           return (next, go (next:prev))
>     in do
>       z <- f []
>       go [z]

> toList :: Int -> IOStream a -> IO [a]
> toList 0 _ = return []
> toList n (x,rest) = do
>   xs <- toList (n-1) rest
>   return (x:xs)

Antoine