pipes-2.0.0: Compositional pipelines

Control.Pipe

Synopsis

# Types

This library represents streaming computations using a single data type: Pipe.

Pipe is a monad transformer that extends the base monad with the ability to await input from or yield output to other pipes. Pipes resemble enumeratees in other libraries because they receive an input stream and transform it into a new output stream.

I'll introduce our first Pipe, which is a verbose version of the Prelude's take function:

take' :: Int -> Pipe a a IO ()
take' n = do
replicateM_ n $do x <- await yield x lift$ putStrLn "You shall not pass!"

This pipe forwards the first n values it receives undisturbed, then it outputs a cute message.

Let's dissect the above pipe's type to learn a bit about how pipes work:

     | Input Type | Output Type | Base monad | Return value
Pipe   a            a             IO           ()

So take' awaits input values of type a from upstream pipes and yields output values of type a to downstream pipes. take' uses IO as its base monad because it invokes the putStrLn function. If we were to remove the call to putStrLn, the compiler would infer the following type instead, which is polymorphic in the base monad:

take' :: (Monad m) => Int -> Pipe a a m ()

Now let's create a function that converts a list into a pipe by yielding each element of the list:

fromList :: (Monad m) => [b] -> Pipe a b m ()
fromList = mapM_ yield

Note that fromList xs is polymorphic in its input. This is because it does not await any input. If we wanted, we could type-restrict it to:

fromList :: (Monad m) => [b] -> Pipe () b m ()

There is no type that forbids a pipe from awaiting, but you can guarantee that if it does await, the request is trivially satisfiable by supplying it with ().

A pipe that doesn't await (any useful input) can serve as the first stage in a Pipeline. I provide a type synonym for this common case:

type Producer b m r = Pipe () b m r

Producers resemble enumerators in other libraries because they function as data sources.

You can then use the Producer type synonym to rewrite the type signature for fromList as:

fromList :: (Monad m) => [b] -> Producer b m ()

Now let's create a pipe that prints every value delivered to it:

printer :: (Show b) => Pipe b c IO r
printer = forever $do x <- await lift$ print x

Here, printer is polymorphic in its output. We could type-restrict it to guarantee it will never yield by setting the output to Void, from Data.Void:

printer :: (Show a) => Pipe b Void IO r

A pipe that never yields can be the final stage in a Pipeline. Again, I provide a type synonym for this common case:

type Consumer b m r = Pipe b Void m r

So we could instead write printer's type as:

printer :: (Show b) => Consumer b IO r

Consumers resemble iteratees in other libraries because they function as data sinks.

# Composition

What distinguishes pipes from every other iteratee implementation is that they form a true Category. Because of this, you can literally compose pipes into Pipelines using ordinary composition:

newtype Lazy m r a b = Lazy { unLazy :: Pipe a b m r }
instance Category (Lazy m r) where ...

For example, you can compose the above pipes with:

pipeline :: Pipe () Void IO ()
pipeline = unLazy $Lazy printer . Lazy (take' 3) . Lazy (fromList [1..]) The compiler deduces that the final pipe must be blocked at both ends, meaning it will never await useful input and it will never yield any output. This represents a self-contained Pipeline and I provide a type synonym for this common case: type Pipeline m r = Pipe () Void m r Also, I provide <+< as a convenience operator for composing pipes without the burden of wrapping and unwrapping newtypes: p1 <+< p2 = unLazy$ Lazy p1 . Lazy p2

So you can rewrite pipeline as:

pipeline :: Pipeline IO ()
pipeline = printer <+< take' 3 <+< fromList [1..]

Like many other monad transformers, you convert the Pipe monad back to the base monad using some sort of "run..." function. In this case, it's the runPipe function:

runPipe :: (Monad m) => Pipeline m r -> m r

runPipe only works on self-contained Pipelines, but you don't need to worry about explicitly type-restricting any of your pipes. Self-contained pipelines will automatically have polymorphic input and output ends and they will type-check when you provide them to runPipe.

Let's try using runPipe:

>>> runPipe pipeline
1
2
3
You shall not pass!


Fascinating! Our pipe terminates even though printer never terminates and fromList never terminates when given an infinite list. To illustrate why our pipe terminates, let's outline the pipe flow control rules for composition:

• Pipes are lazy, so execution begins at the most downstream pipe (printer in our example).
• Upstream pipes only run if input is requested from them and they only run as long as necessary to yield back a value.
• If a pipe terminates, it terminates every other pipe composed with it.

Another way to think of this is like a stack where each pipe is a frame on that stack:

• If a pipe awaits input, it blocks and pushes the next pipe upstream onto the stack until that pipe yields back a value.
• If a pipe yields output, it pops itself off the stack and restores control to the original downstream pipe that was awaiting its input. This binds its result to the return value of the pending await command.

All of these flow control rules uniquely follow from the Category laws.

It might surprise you that termination brings down the entire pipeline until you realize that:

• Downstream pipes depending on the terminated pipe cannot proceed
• Upstream pipes won't be further evaluated because the terminated pipe will not request any further input from them

So in our previous example, the Pipeline terminated because take' 3 terminated and brought down the entire Pipeline with it.

Actually, these flow control rules will mislead you into thinking that composed pipes behave as a collection of sub-pipes with some sort of message passing architecture between them, but nothing could be further from the truth! When you compose pipes, they automatically fuse into a single pipe that corresponds to how you would have written the control flow by hand.

For example, if you compose printer and fromList:

printer <+< fromList [1..]

The result is indistinguishable from:

lift (mapM_ print [1..])

... which is what we would have written by hand if we had not used pipes at all! All runPipe does is just remove the lift!

# Modularity

Given a loop like:

loop :: IO r
loop = forever $do x <- dataSource y <- processData x dataSink y We could decompose it into three separate parts: stage1 :: Producer a IO r stage1 = forever$ do
x <- dataSource
yield x

stage2 :: Pipe a b IO r
stage2 = forever $do x <- await y <- processData x yield y stage3 :: Consumer b IO r stage3 = forever$ do
y <- await
dataSink

stage3 <+< stage2 <+< stage1 == lift loop

In other words, pipes let you decompose loops into modular components, which promotes loose coupling and allows you to freely mix and match those components.

To demonstrate this, let's define a new data source that indefinitely prompts the user for integers:

prompt :: Producer Int IO a
prompt = forever $do lift$ putStrLn "Enter a number: "
n <- read <$> lift getLine yield n Now we can use it as a drop-in replacement for fromList: >>> runPipe$ printer <+< take' 3 <+< prompt
Enter a number:
1<Enter>
1
Enter a number:
2<Enter>
2
Enter a number:
3<Enter>
3
You shall not pass!


# Vertical Concatenation

You can easily "vertically" concatenate pipes, Producers, and Consumers, all using simple monad sequencing: (>>). For example, here is how you concatenate Producers:

>>> runPipe $printer <+< (fromList [1..3] >> fromList [10..12]) 1 2 3 10 11 12  Here's how you would concatenate Consumers: >>> let print' n = printer <+< take' n :: (Show a) => Int -> Consumer a IO () >>> runPipe$ (print' 3 >> print' 4) <+< fromList [1..]
1
2
3
You shall not pass!
4
5
6
7
You shall not pass!


... but the above example is gratuitous because we could have just concatenated the intermediate take' pipe:

>>> runPipe $printer <+< (take' 3 >> take' 4) <+< fromList [1..] 1 2 3 You shall not pass! 4 5 6 7 You shall not pass!  # Return Values Pipe composition imposes an important requirement: You can only compose pipes that have the same return type. For example, I could write the following function: deliver :: (Monad m) => Int -> Consumer a m [a] deliver n = replicateM n await ... and I might try to compose it with fromList: >>> runPipe$ deliver 3 <+< fromList [1..10] -- wrong!


... but this wouldn't type-check, because fromList has a return type of () and deliver has a return type of [Int]. Composition requires that every pipe has a return value ready in case it terminates first.

Fortunately, we don't have to rewrite the fromList function because we can just add a return value using vertical concatenation:

>>> runPipe $deliver 3 <+< (fromList [1..10] >> return []) [1,2,3]  ... although a more idiomatic Haskell version would be: >>> runPipe$ (Just <$> deliver 3) <+< (fromList [1..10] *> pure Nothing) Just [1,2,3]  This forces you to cover all code paths by thinking about what return value you would provide if something were to go wrong. For example, let's say I were to make a mistake and request more input than fromList can deliver: >>> runPipe$ (Just <$> deliver 99) <+< (fromList [1..10] *> pure Nothing) Nothing  The type system saved me by forcing me to cover all corner cases and handle every way my program could terminate. # Termination Now what if you wanted to write a pipe that only reads from its input end (i.e. a Consumer) and returns a list of every value delivered to it when its input pipe terminates? toList :: (Monad m) => Consumer a m [a] toList = ??? You can't write such a pipe because if its input terminates then it brings down toList with it! This is correct because toList as defined is not compositional (yet!). To see why, let's say you somehow got toList to work and the following imaginary code sample worked: >>> runPipe$ toList <+< (fromList [1..5] >> return [])
[1,2,3,4,5]


toList is defined to return its value when the pipe immediately upstream (fromList in this case) terminates. This behavior immediately leads to a problem. What if I were to insert an "identity" pipe between toList and fromList:

identity = forever $await >>= yield -- This is how id is actually implemented! This pipe forwards every valued untouched, so we would expect it to not have any affect if we were to insert it in the middle: >>> runPipe$ toList <+< identity <+< (fromList [1..5] >> return [])
??? -- Oops! Something other than [1,2,3,4,5], perhaps even non-termination


The answer couldn't be [1,2,3,4,5] because toList would monitor identity instead of fromList and since identity never terminates toList never terminates. This is what I mean when I say that toList's specified behavior is non-compositional. It only works if it is coupled directly to the desired pipe and breaks when you introduce intermediate stages.

This was not an intentional design choice, but rather a direct consequence of enforcing the Category laws when I was implementing Pipe's Category instance. Satisfying the Category laws forces code to be compositional.

Note that a terminated pipe only brings down pipes composed with it. To illustrate this, let's use the following example:

p = do a <+< b
c

a, b, and c are pipes, and c shares the same input and output as the composite pipe a <+< b, otherwise we cannot combine them within the same monad. In the above example, either a or b could terminate and bring down the other one since they are composed, but c is guaranteed to continue after a <+< b terminates because it is not composed with them. Conceptually, we can think of this as c automatically taking over the pipe's channeling responsibilities when a <+< b can no longer continue. There is no need to "restart" the input or output manually as in some other iteratee libraries.

The pipes library, unlike other iteratee libraries, grounds its vertical and horizontal concatenation in category theory by deriving horizontal concatenation (.) from its Category instance and vertical concatenation (>>) from its Monad instance. This makes it easier to reason about pipes because you can leverage your intuition about Categorys and Monads to understand their behavior. The only Pipe-specific primitives are await and yield.

# Resource Management

Here's another problem with Pipe composition: resource finalization. Let's say we have the file "test.txt" with the following contents:

Line 1
Line 2
Line 3

.. and we wish to lazily read one line at a time from it:

readFile' :: Handle -> Producer Text IO ()
eof <- lift $hIsEOF h when (not eof)$ do
s <- lift $hGetLine h yield s readFile' h We could then try to be slick and write a lazy version that only reads as many lines as we request: read' :: FilePath -> Producer Text IO () read' = do lift$ putStrLn "Opening file ..."
h <- lift $openFile file ReadMode readFile' h lift$ putStrLn "Closing file ..."
lift $hClose h Now compose! >>> runPipe$ printer <+< read' "test.xt"
Opening file ...
"Line 1"
"Line 2"
"Line 3"
Closing file ...


So far, so good. Equally important, the file is never opened if we replace printer with a pipe that never demands input:

>>> runPipe $(lift$ putStrLn "I don't need input") <+< read' "test.txt"
I don't need input


There is still one problem, though. What if we wrote:

>>> runPipe $printer <+< take' 2 <+< read' "test.txt" Opening file ... "Line 1" "Line 2" You shall not pass!  Oh no! While it was lazy and only read two lines from the file, it was also too lazy to properly close our file! take' 2 terminated before read', preventing read' from properly closing "test.txt". This is why Pipe composition fails to guarantee deterministic finalization. # Frames So how could we implement finalization, then? The answer is to build a higher-order type on top of Pipe and define a new composition that permits prompt, deterministic finalization. To do this, we import Control.Pipe.Final, which exports the Frame type, analogous to the Pipe type, except more powerful. To demonstrate it in action, let's rewrite our take' function to be a Frame instead. take' :: Int -> Frame a a IO () take' n | n < 1 = Frame$ close $lift$ putStrLn "You shall not pass!"
| otherwise = Frame $do replicateM_ (n - 1)$ do
x <- awaitF
yieldF x
x <- awaitF
close $do lift$ putStrLn "You shall not pass!"
yieldF x

The type signature looks the same, except Pipe has been replaced with Frame. Also, now we have awaitF instead of await and yieldF instead of yield. However, you'll notice two new things: close and Frame.

close signals when we no longer need input from upstream. If you try to request input other than () after the close, you will get a type error. Whenever you close a frame, composition finalizes every upstream frame and removes them from the pipeline. The type error reflects the fact that if you awaitF past that point there is no longer anything upstream to request input from.

Frame is a newtype constructor that I use to give clearer type errors and abstract away the underlying implementation. The reason is that if you were to expand out the full type that Frame wraps you would get:

Frame a b m r ~ Pipe (Maybe a) (m (), b) m (Pipe (Maybe ()) (m (), b) m r)
-- Yuck!

Really, the only reason the type is that complicated is because I avoid using language extensions to implement Frames, otherwise it would look more like:

Pipe (Maybe a) (m (), b) m r

... which isn't so bad. In fact, it's not hard to understand what that type is doing. The Maybe is used to supply a Nothing to awaits when upstream terminates before yielding a value. The m () is the most recent finalizer which is yielded alongside every value so that downstream pipes can finalize you if they terminate before requesting another value. The finalization machinery uses these tricks behind the scene to guarantee that your finalizers get called. I provide a type synonym for this:

type Ensure a b m r = Pipe (Maybe a) (m (), b) m r

In other words, an Ensured pipe can intercept upstream termination and register finalizers for downstream to call in the event of premature termination. A good way to think about the distinction between Ensure and Frame is that Ensure is the Monad and Frame is the Category, unlike Pipe, which is both at the same time.

Using this type synonym, we can rewrite the type that Frame wraps:

Frame a b m r ~ Ensure a b m (Ensure () b m r)

The first half of the type is the part of the pipe before you call close, the second half of the type is the part of the pipe after you call close. Notice how the second half has a blocked input end.

However, I haven't yet shown you how to register finalizers. That's easy, though, since you just use catchP or finallyP, which are identical to their exception-handling counterparts, except they catch Frame terminations in either direction. Let's rewrite our read' function using finalizers:

readFile' :: Handle -> Ensure () Text IO ()
eof <- lift $hIsEOF h when (not eof)$ do
s <- lift $hGetLine h yieldF s readFile' h read' :: FilePath -> Frame () Text IO () read' = Frame$ close $do lift$ putStrLn "Opening file ..."
h <- lift $openFile file ReadMode finallyP (putStrLn "Closing file ..." >> hClose h) (readFile' h) Notice how read' closes its input end immediately because it never requires input. Also, the finallyP ensures that the finalizer is called both if read' terminates normally or is interrupted by another Frame terminating first. Now, all we need to do is rewrite printer to be a Frame: printer :: (Show b) => Frame b Void IO r printer = Frame$ forever $do x <- awaitF lift$ print x

This time we don't even need a close statement because printer never stops needing input. Any non-terminating Frame with a polymorphic return type can skip calling close altogether, and it will type-check.

# Frame Composition

Just like with Pipes, we can compose Frames, except now we use (<-<):

stack :: Frame Void () IO ()
stack = printer <-< take' 1 <-< read' "test.txt"

I call a complete set of Frames a Stack, to reflect the fact that Frame composition uses the exact same tricks stack-based programming uses to guarantee deterministic finalization. When a Frame terminates it finalizes upstream Frames as if they were a heap and it propagates an exceptional value (Nothing in this case) for downstream Frames to intercept. I provide a type synonym to reflect this:

type Stack m r = Frame Void () IO r

So we can rewrite the type of stack to be:

stack :: Stack IO ()

To run a Stack, we use runFrame, which is the Frame-based analog to runPipe:

>>> runFrame stack
Opening file ...
"Line 1"
Closing file ...
"Line 2"
You shall not pass!


Not only did it correctly finalize the file this time, but it did so as promptly as possible! I programmed take' so that it knew it would not need read' any longer before it yielded the second value, so it finalized the file before yielding the second value for printer. take' did this without knowing anything about the Frame upstream of it. One of the big advantages of Frames is that you can reason about the finalization behavior of each Frame in complete isolation from other Frames, allowing you to completely decouple their finalization behavior.

# Frame vs. Ensure

Unfortunately, in the absence of extensions I have to split the Monad and Category into two separate types. Ensure is the Monad, Frame is the Category.

However, you can achieve the best of both worlds by programming all your pipes in the Ensure monad, and then only adding close at the last minute when you are building your Stack. For example, if we wanted to read from multiple files, it would be much better to just remove the close function from the read' implementation, so it operates in the Ensure monad:

read' :: FilePath -> Ensure () Text IO ()

Then use close only after we've already concatenated our files:

files :: Frame () Text IO ()
files = close $do read' "test.txt" read' "dictionary.txt" read' "poem.txt" This is a more idiomatic Frame programming style that lets you take advantage of both the Monad and Category instances. The beauty of compositional finalization is we can decompose complicated problems into smaller ones. Imagine that we have a resource that needs a fine-grained finalization behavior like in our take' function which does a cute little optimization to finalize early. We can always decompose our frame into one that does the straight-forward thing (like read') and then just compose it with take' to get the cute optimization for free. In this way we've decomposed the problem into two separate problems: generating the resource and doing the cute optimization. # Folds Frames can actually do much more than manage finalization! Using Frames, we can now correctly implement folds like toList in a way that is truly compositional: toList :: (Monad m) => Frame a Void m [a] toList = Frame go where go = do x <- await case x of Nothing -> close$ pure []
Just a  -> fmap (fmap (a:)) go
-- the extra fmap is an unfortunate extra detail

This time I used an ordinary await, instead of awaitF, so I could access the underlying Maybe values that these Frames are passing around. Similarly, you could use yield instead of yieldF if you wanted to manually manage the finalizers passed downstream at each yield statement instead of using the catchP or finallyP convenience functions. Using these advanced features does not break any of the Category laws. I could expose every single internal of the library and you would not be able to break the Category laws because the Frames generated are still indistinguishable at the value level and fuse into the hand-written implementation. The compositionality of Frames is just as strong as the compositionality of Pipes.

Now let's use our toList function:

>>> runFrame $(Just <$> toList) <-< (Nothing <$fromList [1..3]) Just [1,2,3]  I still had to provide a return value for fromList (Nothing in this case), because when fromList terminates, it cannot guarantee that its return value will come from itself or from toList. When toList receives a Nothing from upstream, it can choose to terminate and over-ride the return value from upstream or await again and defer to the upstream return value (fromList in this case). It doesn't even have to immediately decide. It could just yield more values downstream and forget it had even received a Nothing and if downstream terminates then composition will still ensure that everything "just works" the way you would expect and no finalizers are missed or duplicated. Composition handles every single corner case of finalization. This directly follows from enforcing the Category laws, because categories have no corners! # Strictness We can go a step further and modify toList into something even cooler: strict :: (Monad m) => Frame a a m () strict = Frame$ do
xs <- go
close $mapM_ yieldF xs where go = do x <- await case x of Nothing -> pure [] Just a -> fmap (a:) go As the name suggests, strict is strict in its input. We can use strict to load the entire resource into memory immediately, allowing us to finalize it early. Let's use this to create a strict version of our file reader: >>> runFrame$ printer <-< take' 2 <-< strict <-< read' "test.txt"
Opening file ...
Closing file ...
"Line 1"
"Line 2"
You shall not pass!


Now we have a way to seamlessly switch from laziness to strictness all implemented entirely within Haskell without the use of artificial seq annotations.