streaming: a free monad transformer optimized for streaming applications with an elementary streaming prelude

• The free stream on a streamable functor

Stream can be used wherever FreeT is used. The compiler's standard range of optimizations work better for operations written in terms of Stream. FreeT f m r / Stream f m r is of course extremely general, and many functor-general combinators are exported by the general module Streaming.

• The general idea of streaming

As soon as you consider the idea of an effectful stream of any kind whatsoever, for example, a stream of bytes from a handle, however constituted, you will inevitably be forced to contemplate the idea of a streaming succession of such streams. Thus, for example, however you imagine your bytes streaming from a handle, you will want to consider a succession of such streams divided on newlines. Similarly, suppose you have the idea the unfolding of some sort of stream from a Haskell value, a seed - a file name, as it might be. And suppose you also have some idea of a stream of such Haskell values - maybe a stream of file names coming from something like du, subjected to some filter. Then you will also have the idea of a streaming succession of such unfoldings linked together end to end in accordance with the initial succession of seed values.

Call those 5 sentences the ABCs. If you understood the ABCs you have a total comprehension of Stream f m r.

• Stream itself expresses what the word "succession" meant in the ABCs

• The general parameter f expresses what was meant by "such streams"

• m expresses the relevant form of "effect".

General combinators for working with this idea of succession irrespective of the form of succession are contained in the module Stream. They can be used, or example, to organize a succession of io-streams Generators or pipes Producers or the effectful bytestreams of the <https://hackage.haskell.org/package/streaming-bytestring streaming-bytestring> library, or whatever stream-form you can express in a Haskell functor.

• A freely generated stream of connected individual Haskell values is Producer, Generator or Source

But, of course, as soon as you grasp the general form of succession, you are already in possession of the most basic concrete form: a simple succession of individual Haskell values one after another. This is just Stream ((,) a) m r, or as we write it here, Stream (Of a) m r, strictifying the left element of the pair. The pairing just links the present element with the rest of the stream. The primitive yield statement just expresses the pairing of the yielded item with the rest of the stream; or rather it is itself the trivial singleton stream. Streaming.Prelude is focused on the manipulation of this all-important stream-form, which appears in the streaming IO libraries under titles like:

io-streams: Generator a r
pipes:      Producer a m r
conduit:    ConduitM () o m r
streaming:  Stream (Of a) m r

The only difference is that in streaming the simple Generator or Producer concept is formulated explicitly in terms of the general concept of successive connection. But this is a concept you need and already possess anyway, as your comprehension of the four sentences above showed.

The special case of a stream of individual Haskell values that simply comes to an end without a special result is variously expressed thus:

io-streams: InputStream a
pipes:      Producer a m ()
conduit:    Source m a
machines:   SourceT m a (= forall k. MachineT m k a)
streaming:  Stream (Of a) m ()

• Streaming.Prelude

Streaming.Prelude closely follows Pipes.Prelude. But since it restricts itself to use only of the general idea of streaming, it cleverly omits the pipes:

ghci> S.stdoutLn $ S.take 2 S.stdinLn
let's<Enter>
let's
stream<Enter>
stream

Here's a little connect and resume, as the streaming-io experts call it:

ghci> rest <- S.print $ S.splitAt 3 $ S.each [1..10]
1
2
3
ghci> S.sum rest
49

Somehow, we didn't even need a four-character operator for that, nor advice about best practices! - just ordinary Haskell common sense.

• Mother's Prelude vs. Streaming.Prelude

The effort of Streaming.Prelude is to leverage the intuition the user has acquired in mastering Prelude and Data.List and to elevate her understanding into a general comprehension of effectful streaming transformations. Unsurprisingly, it takes longer to type out the signatures. It cannot be emphasized enough, thought, that the transpositions are totally mechanical:

Data.List.Split.chunksOf :: Int -> [a]          -> [[a]]
Streaming.chunksOf       :: Int -> Stream f m r -> Stream (Stream f m) m r

Prelude.splitAt   :: Int -> [a]          -> ([a],[a])
Streaming.splitAt :: Int -> Stream f m r -> Stream f m (Stream f m r)

These concepts are "functor general", in the jargon used in the documentation, and are thus exported by the main Streaming module. Something like break requires us to inspect individual values for their properties, so it is found in the Streaming.Prelude

Prelude.break           :: (a -> Bool) -> [a]               -> ([a],[a])
Streaming.Prelude.break :: (a -> Bool) -> Stream (Of a) m r -> Stream (Of a) m (Stream (Of a) m r)

It is easy to prove that resistance to these types is resistance to effectful streaming itself. I will labor this point a bit more below, but you can also find it developed, with greater skill, in the documentation for the pipes libraries.

• How come there's not one of those fancy "ListT done right" implementations in here?

The use of the final return value appears to be a complication, but in fact it is essentially contained in the idea of effectful streaming. This is why this library does not export a ListT done right, which would be simple enough - following pipes, as usual:

newtype ListT m a = ListT (Stream (Of a) m ())

The associated monad instance would wrap

yield :: (Monad m)            => a -> Stream (Of a) m ()
for   :: (Monad m, Functor f) => Stream (Of a) m r -> (a -> Stream f m ()) -> Stream f m r

To see the trouble, consider this signature for splitting a ListT very much done right. Here's what becomes of chunksOf. As long as we are trapped in ListT, however much rightly implements, these operation can't be made to stream; something like a list must be accumulated. Similarly, try to imagine adding a splitAt or lines function to this API. It would accumulate strict text forever, just as this does and this doesn't and this doesn't The difference is simply that the latter libraries operate with the general concept of streaming, and the whole implementation is governed by it. The attractions of the various "ListT done right" implementations are superficial; the concept belongs to logic programming, not stream programming.

Note similarly that you can write a certain kind of take and drop with the machines library - as you can even with a "ListT done right". But I wish you luck writing splitAt! Similarly you can write a getContents; but I wish you luck dividing the resulting bytestream on its lines. This is - as usual! - because the library was not written with the general concept of effectful succession or streaming in view. Materials for sinking some elements of a stream in one way, and others in other ways - copying each line to a different file, as it might be, but without accumulation - are documented within. So are are myriad other elementary operations of streaming io.

• Didn't I hear that free monads are a real efficiency dog? Isn't Oleg working on this important problem?

We noted above that if we instantiate Stream f m r to Stream ((,) a) m r or the like, we get the standard idea of a producer or generator. If it is instantiated to Stream f Identity m r then we have the standard free monad construction. This construction is subject to certain familiar objections from an efficiency perspective; efforts have been made to substitute exotic cps-ed implementations and so forth. It is an interesting topic.

But in fact, the standard alarmist talk about retraversing binds and quadratic explosions and costly appends, and so on become transparent nonsense with Stream f m r in its streaming use. The conceptual power needed to see this is basically nil: Where m is read as IO, or some transformed IO, then the dreaded retraversing of the binds in a stream expression would involve repeating all the past actions. Don't worry, to get e.g. the second chunk of bytes from a handle, you won't need to start over and get the first one again! The first chunk has vanished into an unrepeatable past.

All of the difficulties a streaming library is attempting to avoid are concentrated in the deep irrationality of

sequence :: (Monad m, Traversable t) => t (m a) -> m (t a)

In the streaming context, this becomes

sequence :: Monad m, Functor f => Stream f m r -> Stream f m r
sequence = id

It is of course easy enough to define

accumulate :: Monad m, Functor f => Stream f m r -> m (Stream f Identity r)

or reifyBindsRetraversingWherePossible or _ICan'tTakeThisStreamingAnymore, as you might call it. The types themselves teach the user how to avoid or control the sort of accumulation characteristic of sequence in its various guises e.g. mapM f = sequence . map f and traverse f = sequence . fmap f and replicateM n = sequence . replicate n. See for example the types of

Control.Monad.replicateM :: Int -> m a -> m [a]
Streaming.Prelude.replicateM :: Int -> m a -> Stream (Of a) m ()

If you want to tempt fate and replicate the irrationality of Control.Monad.replicateM, then sure, you can define the hermaphroditic chimera

accumulate . Streaming.Prelude.replicateM :: Int -> m a -> m (Stream (Of a) Identity ())

which is what we find in our diseased base libraries. But once you know how to operate with a stream directly you will see less and less point in what is called extracting the (structured) value from IO. The distinction between

"getContents" :: String

and

getContents :: IO String

but, omitting consideration of eof, we might define getContents thus

getContents = sequence $ repeat getChar

There it is again! The very devil! By contrast there is no distinction between

"getContents" :: Stream (Of Char) m ()

and

getContents :: MonadIO m => Stream (Of Char) m ()

They unify just fine. That is, if I make the type synonym

type String m r = Stream (Of Char) m r

I get, for example:

"getLine"                              :: String m  ()
getLine                                :: String IO ()
"getLine" >> getLine                   :: String IO ()
splitAt 20 $ "getLine" >> getLine      :: String IO (String IO ())
length $ "getLine" >> getLine          :: IO Int

and can dispense with half the advice they will give you on #haskell. It is only a slight exaggeration to say that a stream should never be "extracted from IO".

With sequence and traverse, we accumulate a pure succession of pure values from a pure succession of monadic values. Why bother if you have intrinsically monadic conception of succession or traversal? Stream f m r gives you an immense body of such structures and a simple discipline for working with them. Spinkle id freely though your program if you get homesick.

Much of the discussion of the free monad concept is associated with the "algebraic effects" program. A leading advertisement for this approach is that we can toss generators into the soup without missing a beat. See for example this yield. concept

yield :: (Typeable a, Member (Yield a) r)                 => a   -> Eff r ()

With it I can over course write, e.g.

each  :: (Traversable t, Typeable a, Member (Yield a) r)  => t a -> Eff r ()
each = mapM_ yield

Once I have one of these "coroutine effects" on my hands, the fact that I am writing Haskell, not e.g. Python, will leave me with little trouble splitting it at the 20th element, and reserving the rest for later use. I invite you, though, to divide such a "coroutine effect" on its lines or into chunks of 500. There must be some sense in which these effects are "extensible". But it seems not as far as the ABCs.

• Interoperation with the streaming-io libraries

The simplest form of interoperation with pipes is accomplished with this isomorphism:

Pipes.unfoldr Streaming.next        :: Stream (Of a) m r   -> Producer a m r
Streaming.unfoldr Pipes.next        :: Producer a m r      -> Stream (Of a) m r

Of course, streaming can be mixed with pipes wherever pipes itself employs Control.Monad.Trans.Free; speedups are frequently appreciable. (This was the original purpose of the main Streaming module, which just mechanically transposes a simple optimization employed in Pipes.Internal.) Interoperation with io-streams is thus:

Streaming.reread IOStreams.read     :: InputStream a       -> Stream (Of a) IO ()
IOStreams.unfoldM Streaming.uncons  :: Stream (Of a) IO () -> IO (InputStream a)

A simple exit to conduit would be, e.g.:

Conduit.unfoldM Streaming.uncons    :: Stream (Of a) m ()  -> Source m a

These conversions should never be more expensive than a single >-> or =$=.

At a much more general level, we also of course have interoperation with free:

Free.iterTM  Stream.wrap              :: FreeT f m a -> Stream f m a
Stream.iterTM Free.wrap               :: Stream f m a -> FreeT f m a

• Examples

For some simple ghci examples, see the commentary throughout the Prelude module. For slightly more advanced usage see the commentary in the haddocks of streaming-bytestring and e.g. these replicas of shell-like programs from the io-streams tutorial. Here's a simple streaming GET request with intrinsically streaming byte streams.

• Problems

Questions about this library can be put as issues through the github site or on the pipes mailing list. (This library understands itself as part of the pipes "ecosystem.")

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