# [Haskell-cafe] Is it possible to make lazy combinators for IO?

David Turner dct25-561bs at mythic-beasts.com
Tue Apr 19 06:30:14 UTC 2016

```I suspect you're looking for something like lazy IO (or a similarly unsafe
cousin like unsafeInterleaveIO as featured in the definition of fixIO)
although I still remain a bit confused.

The type of lazyMap :: (a -> b) -> IO a -> IO b is the same as for fmap,
but fmap is already as lazy as it can be without unsafeness:

fmap (const ()) (return undefined) = return ()
fmap (const ()) undefined = undefined

You can't (safely) define lazyMap where lazyMap f ma doesn't have all the
real-world effects of ma before returning. If ma has infinitely many
effects then it's not going to return, because if it did then you'd have
your hands on something of pure type 'b' which continues to have real-world
effects as you evaluate it. This is, roughly speaking, lazy IO.

On the other hand, you mention knot-tying and this is precisely what fixIO
is for. A slightly contrived example:

main :: IO ()
main = do
fibs <- fibsIO
print \$ fibs !! 10

fibsIO :: IO [Int]
fibsIO = mfix \$ \fibs -> do
fibs' <- forM [2..10] \$ \i -> do
putStrLn \$ "Calculating fibs !! " ++ show i
return \$ fibs !! (i-1) + fibs !! (i-2)
return \$ 0:1:fibs'

Note that I have to limit the number of actions for this to work - if it
said 'forM [2..] then there'd be infinitely many effects and it'd never
return.

Hope that helps,

David

On 19 April 2016 at 00:25, David Feuer <david.feuer at gmail.com> wrote:

> lazyMap :: (a -> b) -> IO a -> IO b, hypothetically.
>
> Let me take a step back. There are two ways I know of to use the result of
> an IO action. The most common way, by far, is to use >>= to send it on to
> the next computation. The other notable way is to use fixIO.
>
> No part of the result of an IO action becomes available until that action
> "completes" (in the shady case of lazy IO, this may be immediate, but I'm
> ignoring lazy IO for this discussion). This causes the well-known
> inefficiency of mapM in IO: individual results cannot be consed until the
> entire computation is complete. It seems to cause much more painful effects
> for fixIO--lazy programming techniques may simply be unavailable.
>
> For example, it's possible for a pure computation using a queue in a
> single-threaded fashion to represent that queue as a list, tying the knot
> to pass the list of all enqueued elements to the beginning. If an IO
> computation wants to use a queue, this technique does not seem to be
> available. The knot can be tied with fixIO, but conses are delayed until
> it's too late--attempting to dequeue an element will block forever.
>
> I'm wondering if there's some way to make this sort of thing work, either
> with plain Haskell IO or some thin layer built on top.
> On Apr 18, 2016 5:12 PM, "David Turner" <dct25-561bs at mythic-beasts.com>
> wrote:
>
>> Sorry, you've lost me. I suspect you're trying to give a minimal example
>> of the problem you're having, but you've stripped away too much context.
>> What are lazyMap and f? At least, what are their types?
>> On 18 Apr 2016 22:03, "David Feuer" <david.feuer at gmail.com> wrote:
>>
>>> Consider the implementation of `second` for pairs:
>>>
>>> second f ~(a,b) = (a, f b)
>>>
>>> Now
>>>
>>> fix \$ second (3 :)
>>>
>>> Will be (undefined, [3,3,....])
>>>
>>> Translating this to IO, I'd want
>>>
>>> lazyMap f undefined
>>>
>>> to produce as much as possible of the result, although it cannot produce
>>> the final State# RealWorld token.
>>> On Apr 18, 2016 4:47 PM, "David Turner" <dct25-561bs at mythic-beasts.com>
>>> wrote:
>>>
>>>> You can't know that the final result of the computation (x `seq`
>>>> (3:...)) will begin with 3, because sometimes it doesn't! More
>>>> specifically, it diverges (without yielding the 3) if x diverges.
>>>>
>>>> I don't think this is anything special about mfix: (let x = x `seq`
>>>> 3:... in x) also diverges for the same reason.
>>>>
>>>> Hope that helps,
>>>>
>>>> David
>>>> On 18 Apr 2016 21:19, "David Feuer" <david.feuer at gmail.com> wrote:
>>>>
>>>>> If
>>>>>
>>>>> f :: a -> IO a
>>>>>
>>>>> for some a, and I want to use
>>>>>
>>>>> mfix f
>>>>>
>>>>> then f must not inspect its argument in any way, or the computation
>>>>> will get stuck. In some cases, this seems a bit harsh. For example,
>>>>>
>>>>> mfix (\x -> fmap (3 :) (x `seq` readLn))
>>>>>
>>>>> looks perfectly reasonable. There is no need to inspect the return []
>>>>> action to know that the final result of the computation will begin
>>>>> with 3:. Is there a lazy IO mapping function somewhere that can work
>>>>> such magic?
>>>>> _______________________________________________