java.util.stream.Stream: API for user-extensible intermediate operations

[Remi Forax]

> From: "Viktor Klang" <viktor.klang at oracle.com>
> To: "core-libs-dev" <core-libs-dev at openjdk.org>
> Sent: Tuesday, June 27, 2023 7:10:42 PM
> Subject: java.util.stream.Stream: API for user-extensible intermediate
> operations

> Hi core-libs-dev,

> Over the past 6+ months I've been thinking about, and tinkering with, how we'd
> be able to expose a user-facing API for extensible intermediate
> java.util.stream.Stream operations—a feature envisioned all the way back when
> Streams were created.

> I'm now at a point where I have a viable design and implementation, and so I'm
> turning to you for your feedback: on the direction taken; the API concepts;
> and, in particular, is there anything which I have overlooked/missed?

I think this API is overly generic and hard to reason about it, for users and IDEs. 

The main issue is that the same API is used for both stateless and stateful operations, which means that as a user, we have no idea if a call to stream.gather() is stateful or not. Which is a departure from the current API that cleanly separate stateless and staful operations. Here, we are left in the dark. In a sense, this API is too powerful, it can do too much thing, so as a user we can not reason about it. 

I like the idea of a Collector 2.0 i.e. using the Gatherer API at the end of the stream (not in the middle), but currently, the Gatherer API is not a Collector, so we now have two different APIs for doing partially the same job. I wonder if the Collector API can be retroffitted to act as a Gatherer API, avoiding to have to choose which one to use, a gatherer being the equivalent of a "flat-collector" + short-circuit. 

The idea of unsupportedCombiner() seems out of place, like a patch to be able to clobble different things together. I'm not sure to understand why it's needed for a Gatherer, and why it is not needed for Collectors ? 

So I would prefer that API to extends the current Collector API but not the intermediary operations. Yes, it's less powerful. 
It means that instead of using one stream with a collect like operation in the middle, users will have to use two streams, one after the other, but it makes the code easier to understand (also having two streams give users better control on which part should be in parallel). 

Rémi 

> (If you, like myself, prefer reading pre-rendered markdown, [
> https://cr.openjdk.org/~vklang/Gatherers.html |  click here ] )

> # Gathering the streams

> ## Introduction

> Java 8 introduced the `java.util.stream` API, which represents a lazily
> computed, potentially unbounded sequence of values (Streams was also the first
> designed-for-lambdas API in the JDK). Streams supports the ability to process
> the stream either sequentially or in parallel.

> A `Stream` pipeline consists of a source (collection, array, generator, etc),
> zero or more intermediate operations (`Stream` -> `Stream` transforms), and an
> eager terminal operation which produces a value or a side-effect.

> The Streams API come with a reasonably rich, but fixed set of built-in
> operations (mapping, filtering, reduction, sorting, etc), as well as an
> extensible terminal operation (`Stream::collect`) that enables the stream
> contents to be flexibly summarized in a variety of forms. The resulting API is
> rich enough that users have had good experience with streams, but there are
> repeated requests for "please add operation X to streams".

> In this document, we explore a corresponding extensible _intermediate_
> operation, called `Stream::gather`, which is able to address many of the
> requests we've gotten for additional operations.

> ## "Missing" intermediate operations

> Over the years, many new operations for streams have been proposed. Each of
> them may be useful in some situation, but many of them are too narrow to be
> included in the core `Stream` API. We'd like for people to be able to plug
> these operations in via an extension point, as with `Stream::collect`.

> Here are some examples of proposed intermediate operations that are not easily
> expressible as intermediate operations on `Stream` today.

> * **Folds**. Folding is a generalization of reduction. With reduction, the
> result type is the same as the element type, the combiner is associative, and
> the initial value is an identity for the combiner. For a fold, these
> conditions are not required, though we give up parallelizability.

> Example: `foldLeft("", (str,elem) -> str + " " + elem.toString())` over the
> values
> `[1,2,3]` yields `["1 2 3"]`.

> See https://bugs.openjdk.org/browse/JDK-8133680 &
> https://bugs.openjdk.org/browse/JDK-8292845

> * **Unfolds**. This takes an aggregate and decomposes it into elements. An
> `unfold` can reverse the operation of the above fold example using `Scanner`
> or `String::split`.

> Example: `unfold(e -> new Scanner(e), Scanner::hasNextInt, Scanner::nextInt)`
> `["1 2 3"]` yields `[1,2,3]`.

> See: https://bugs.openjdk.org/browse/JDK-8151408

> * **Barriers**. Usually all operations of a stream pipeline can run
> simultaneously as data is available. In some cases, we may wish to have a
> barrier that requires that the entirety of one operation is completed before
> providing any elements to the next operation.

> Example: `someStream.a(...).barrier(someEffect)...` would require that all
> effects from `a` are completed before executing `someEffect` or producing any
> downstream values.

> See: https://bugs.openjdk.org/browse/JDK-8294246

> * **Windowing**. Given a stream, we may wish to construct a stream which
> groups the original elements, either in overlapping or disjoint groups.

> Example: `fixedWindow(2)` over the values `[1,2,3,4,5]` yields
> `[[1,2],[3,4],[5]]`.
> Example: `slidingWindow(2)` over the values `[1,2,3]` yields
> `[[1,2],[2,3],[3,4]]`.

> See:
> https://stackoverflow.com/questions/34158634/how-to-transform-a-java-stream-into-a-sliding-window

> * **Prefix scans**. Prefix scans are a stream of incremental reductions.
> Perhaps surprisingly, some prefix scans are parallelizable, and we are exploring
> adding support for that beyond `Arrays.parallelPrefix()`.

> Example: `scan((sum, next) -> sum + next)` over values `[1,2,3,4]` yields
> `[1,3,6,10]`

> See:
> https://stackoverflow.com/questions/55265797/cumulative-sum-using-java-8-stream-api

> * **Duplicated elements**. The `distinct` operation will remove duplicates;
> sometimes we want only the elements that are duplicated.

> Example: `duplicates(Object::equals)` over values `[1,1,2,3,4]` yields `[1]`

> See:
> https://stackoverflow.com/questions/27677256/java-8-streams-to-find-the-duplicate-elements

> * **Running duplicate elimination**. Here, we want to eliminate adjacent
> repeated elements.

> Example: `collapseRuns(Object::equals)` over values `[1,1,2,3,3]` yields
> `[1,2,3]`

> These are just a few of the stream operations people have wished for—
> and while many operations are too specialized to include in the core library,
> all are things we'd like for people to be able to express with streams.

> ## Extending streams

> It was always desired for `java.util.stream.Stream` to have an extension point
> for intermediate operations; when the library was first built, this wish-list
> item was recorded: https://bugs.openjdk.org/browse/JDK-8132369. There were many
> reasons that this was not included in the initial version, the most important
> being that it was not at all obvious what the right API was.

> The set of intermediate operations on Streams carries the exact same trade-off
> as [CISC](Complex Instruction Set Computing) vs [RISC](Reduced Instruction Set
> Computing), namely: either you have to provide a rather sizeable set of
> specialized operations, or you provide a small set of general operations.

> For the **CISC**-strategy, the main drawback is that not all operations is
> equally useful, and having a large set of operations to choose from creates a
> barrier to effective usage by making the correct choice harder to identify.

> For the **RISC**-strategy, the main drawback is that it puts more effort on the
> user to encode more specialized operations over a set of generic operations,
> making code harder to read, and harder to maintain, for the user.

> However, one success story was `Collector`; this allowed us to extend _terminal_
> operations with a good balance of expressiveness, reuse, and API footprint. We
> would like to do the same for intermediate operations -- and we can draw some
> inspiration from `Collector` to get there.

> ## Requirements

> Breaking down operations into intermediate and terminal is a useful distinction,
> however,
> in reality there are many more characteristics we could use to describe
> operations,
> and relatively few operations use exactly the same subset of characteristics.
> The following is a curated set of characteristics of stream operations;
> if we want to enable generic, user-defineable, intermediate operations on
> streams,
> we probably have to provide for them all.

> | Ordinal | Feature | What this means in practice | Example operation(s) |
> |---------|--------------------------|-------------------------------------------------------------|-------------------------------------|
>| 1 | Intermediate operation | Add custom new operations to Stream pipelines |
> | *map*, *filter* |
>| 2 | Incremental operation | Evaluate the Stream pipeline depth-first | *map*,
> | *filter* |
>| 3 | Stateful operation | Remember information between processing elements |
> | *limit*, *foldLeft* |
>| 4 | N:M inputs-to-outputs | Encode a wide array of operations | *limit*,
> | *flatMap* |
>| 5 | Prefix consumption | An operation should consume only as much as needed |
> | *limit*, *takeWhile* |
>| 6 | Beginning-of-stream hook | Ability to have initialization logic |
> | *foldLeft*, *grouped* |
> | 7 | End-of-stream hook | Flush elements downstream | *sorted*, *grouped* |
>| 8 | Opt-in parallelizability | Speed up CPU-bound processing for parallelizable
> | operations | *reduce*, *map* |

> Now when we have a better idea of what we need to achieve, let's have a look at
> what our options are.

> ## Comparing existing operations

> Let's look at the operations we already have, to see if they would fit the bill
> as a generic extension point for intermediate `Stream`-operations.

> These are, in order, `Stream.map()`, `Stream.flatMap(…)` (`Stream.mapMulti(…)`
> is analogous), and `Collector` & `Stream.collect(…)`—and in the table below we
> see how they line up against our requirements.

>| Ordinal | Feature | Using Stream.map(…) | Using Stream.flatMap(…) | Using
> | Collector |
> |---------|--------------------------|---------------------------|---------------------------|-----------------|
> | 1 | Intermediate operation | Yes | Yes | No, terminal |
> | 2 | Incremental operation | Yes | Yes | No, terminal |
>| 3 | Stateful operation | Yes, via class or capture | Yes, via class or capture |
> | Yes |
> | 4 | N:M inputs-to-outputs | No, 1:1 | No, 1:M | No, N:1 |
> | 5 | Prefix consumption | No | No | No |
> | 6 | Beginning-of-stream hook | No | No | Yes |
> | 7 | End-of-stream hook | No | No | Yes |
> | 8 | Opt-in parallelizability | No, always on | No, always on | No, always on |

> Looking at the options above, none of them are going to, as-is, fit the bill as
> an extension point for generic intermediate `Stream` operations, but one of them
> has more promise than the others: `Collector`. Obvious needed upgrades are
> supporting short-circuiting and incremental generation of output; let's see what
> that looks like in practice.

> ## Collector 2.0

> Let's start with a clone of `Collector<T,A,R>` called `Gatherer<T,A,R>`:

> ```java
> /** @param <T> the element type
> * @param <A> the (mutable) intermediate accumulation type
> * @param <R> the (probably immutable) final accumulation type
> */
> interface Gatherer<T,A,R> {
> Supplier<A> supplier();
> BiConsumer<A, T> accumulator();
> BinaryOperator<A> combiner();
> Function<A, R> finisher();
> }
> ```

> Now, we need to make it output 0...M elements instead of strictly 1. In order
> to do that, we need a way to programmatically output elements from the
> `accumulator` to make it incremental (and has the added benefit that it would be
> able to run depth-first). Adding an additional argument, a downstream handle,
> to `accumulator` and `finisher` allows us to push elements downstream both for
> each input, and at the end of stream. As there exists no suitable pre-existing
> interface, we'll define a new interface named `Integrator` and rename
> `accumulator`
> to the more fitting `integrator`.
> Our `finisher` will also not have a useful return value, so we'll make it
> `void`:

> ```java
> /** @param <T> the element type
> * @param <A> the (mutable) intermediate accumulation type
> * @param <R> the (probably immutable) final accumulation type
> */
> interface Gatherer<T,A,R> {
> interface Integrator<A,T,R> {
> void integrate(A state, T element, Consumer<? super R> downstream);
> }
> Supplier<A> supplier();
> Integrator<A, T, R> integrator();
> BinaryOperator<A> combiner();
> BiConsumer<A, Consumer<? super> R> finisher();
> }
> ```

> Next, we need to tackle short-circuiting and add an upstream signal from each
> invocation of the `integrator` so we can detect when the integration does not
> want any more elements. We do this by returning a boolean from `integrate`:

> ```java
> /** @param <T> the element type
> * @param <A> the (mutable) intermediate accumulation type
> * @param <R> the (probably immutable) final accumulation type
> */
> interface Gatherer<T,A,R> {
> interface Integrator<A,T,R> {
> boolean integrate(A state, T element, Consumer<? super R> downstream);
> }
> Supplier<A> supplier();
> Integrator<A, T, R> integrator();
> BinaryOperator<A> combiner();
> BiConsumer<A, Consumer<? super> R> finisher();
> }
> ```

> Transitively supporting short-circuiting, i.e. that a downstream handle does
> not want to receive any more elements, requires us to make the same change as
> we did for `integrate`—return a `boolean` instead of `void`, and since the
> only built-in candidate would be `Predicate`, which is not supposed to have
> side-effects, let's introduce our own type `Sink`:

> ```java
> /** @param <T> the element type
> * @param <A> the (mutable) intermediate accumulation type
> * @param <R> the (probably immutable) final accumulation type
> */
> interface Gatherer<T,A,R> {
> interface Sink<R> {
> boolean flush(R element);
> }
> interface Integrator<A,T,R> {
> boolean integrate(A state, T element, Sink<? super R> downstream);
> }
> Supplier<A> supplier();
> Integrator<A, T, R> integrator();
> BinaryOperator<A> combiner();
> BiConsumer<A, Sink<? super R>> finisher();
> }
> ```

> Finally, we need to address parallelism. To opt-in to parallelism we can make
> the combiner optional -- we call it only for parallel executions, and if it is
> not present, execution is constrained to sequential.

> To demonstrate how all of the above fits together, we implement `fixedWindow(N)`
> where `fixedWindow(2)` over the values `[1,2,3,4,5]` yields `[[1,2],[3,4],[5]]`.

> ```java
> /**
> * Gathers elements into fixed-size windows. The last window can contain fewer
> elements.
> * @param windowSize the size of the windows
> * @return a new gatherer which gathers elements into fixed-size windows
> * @param <T> the type of elements this Gatherer gathers
> */
> public static <T> Gatherer<T, ?, List<T>> fixedWindow(int windowSize) {
> if (windowSize < 1)
> throw new IllegalArgumentException("'windowSize' must be greater than zero");
> else {
> Supplier<ArrayList<T>> supplier =
> () -> new ArrayList<T>(windowSize);

> Integrator<ArrayList<T>, T, List<T>> integrator =
> (openWindow, element, downstream) -> {
> if (openWindow.add(element) && openWindow.size() >= windowSize) {
> var closedWindow = List.copyOf(openWindow);
> openWindow.clear();
> return downstream.flush(closedWindow);
> } else
> return true;
> };

> // This combiner signals that we opt-out of parallelisation
> BinaryOperator<ArrayList<T>> combiner =
> Gatherer.unsupportedCombiner();

> BiConsumer<ArrayList<T>, Sink<? super List<T>>> finisher =
> (openWindow, downstream) -> {
> if(!openWindow.isEmpty()) {
> downstream.flush(List.copyOf(openWindow));
> openWindow.clear();
> }
> };

> return Gatherer.of(supplier, integrator, combiner, finisher);
> }
> }
> ```

> Or by implementing the `Gatherer` interface directly like so:

> ```java
> /**
> * Gathers elements into fixed-size windows. The last window can contain fewer
> elements.
> * @param windowSize the size of the windows
> * @return a new gatherer which gathers elements into fixed-size windows
> * @param <T> the type of elements this Gatherer gathers
> */
> public static <T> Gatherer<T, ?, List<T>> fixedWindow(int windowSize) {
> if (windowSize < 1)
> throw new IllegalArgumentException("'windowSize' must be greater than zero");
> class FixedWindowGatherer implements Gatherer<T,ArrayList<T>,List<T>> {
> @Override
> public Supplier<ArrayList<T>> initializer() {
> return () -> new ArrayList<>(windowSize);
> }

> @Override
> public Integrator<ArrayList<T>, T, List<T>> integrator() {
> return (openWindow, element, downstream) -> {
> if (openWindow.add(element) && openWindow.size() >= windowSize) {
> var closedWindow = List.copyOf(openWindow);
> openWindow.clear();
> return downstream.flush(closedWindow);
> } else
> return true;
> };
> }

> @Override
> public BinaryOperator<ArrayList<T>> combiner() {
> return Gatherer.unsupportedCombiner();
> }

> @Override
> public BiConsumer<ArrayList<T>, Sink<? super List<T>>> finisher() {
> return (openWindow, downstream) -> {
> if(!openWindow.isEmpty()) {
> downstream.flush(List.copyOf(openWindow));
> openWindow.clear();
> }
> };
> }
> }
> return new FixedWindowGatherer();
> }
> ```

> Compared to Collector, it would look like the following:

> | Ordinal | Feature | `Collector<T,A,R>` | `Gatherer<T,A,R>` |
> |---------|--------------------------|-----------------------------------|---------------------------------------|
> | 1 | Beginning-of-stream hook | `A supply()` | `A supply()` |
> | 2 | Per element | `void accept(A, T)` | `boolean integrate(A, T, Sink<R>)` |
> | 3 | End-of-stream hook | `R apply(A)` | `void accept(A, Sink<R>)` |
> | 4 | Parallelizability | `A apply(A, A)` | `A apply(A, A)` |

> To integrate it with `java.util.stream.Stream` we add the following method to
> it: `Stream<R> gather(Gatherer<T,?,R> gatherer)`

> Now we can use our `fixedWindow` Gatherer:

> ```java
> jshell> Stream.iterate(0, i -> i + 1).limit(10).gather(fixedWindow(2)).toList();
> $1 ==> [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]]
> ```

> Gatherer now provides all features:

> | Ordinal | Feature | Using Gatherer | Explanation |
> |---------|--------------------------|-------------------------|----------------------------------------------------------------------------------------|
>| 1 | Intermediate operation | Yes | A Gatherer's output is the following
> | operation's input |
>| 2 | Incremental operation | Yes | A Gatherer can produce elements in response to
> | consuming elements |
>| 3 | Stateful operation | Yes | A Gatherer supplies its own state, which can be
> | Void/null if stateless |
>| 4 | N:M inputs-to-outputs | Yes | A Gatherer can consume and produce any number
> | of elements |
>| 5 | Prefix consumption | Yes | A Gatherer can signal that it is done by
> | returning `false` from its `integrate`-method |
>| 6 | Beginning-of-stream hook | Yes | A Gatherer can run logic when creating its
> | initial state |
>| 7 | End-of-stream hook | Yes | A Gatherer's `finisher` is invoked at the end of
> | input |
> | 8 | Opt-in parallelizability | Yes | A Gatherer's `combiner` is optional |

> ## Summary

> None of the current candidates for a user-extensible API for generic
> intermediate stream operations fit the set of requirements, but `Collector`
> can form an excellent basis for a new construct, called `Gatherer`,
> which after a limited set of modifications checks all the boxes:

>| Ordinal | Feature | Using Stream.map(…) | Using Stream.flatMap(…) | Using
> | Collector | Using Gatherer |
> |---------|--------------------------|---------------------------|---------------------------|-----------------|----------------|
> | 1 | Intermediate operation | Yes | Yes | No, terminal | Yes |
> | 2 | Incremental operation | Yes | Yes | No, terminal | Yes |
>| 3 | Stateful operation | Yes, via class or capture | Yes, via class or capture |
> | Yes | Yes |
> | 4 | N:M inputs-to-outputs | No, 1:1 | No, 1:M | No, N:1 | Yes |
> | 5 | Prefix consumption | No | No | No | Yes |
> | 6 | Beginning-of-stream hook | No | No | Yes | Yes |
> | 7 | End-of-stream hook | No | No | Yes | Yes |
>| 8 | Opt-in parallelizability | No, always on | No, always on | No, always on |
> | Yes |

> As it turned out, we were a short hop away from a generic, stand-alone,
> reusable, parallelizable, API for intermediate operations all along!

> ## But wait … there's more

> While the aforementioned solution contains the bare-minimum to meet our
> requirements,
> the following will provide some significant quality-of-life improvements.

> ### Compositionality

> The astute reader may have noticed that by adding the `gather(Gatherer)`-method
> on `Stream`,
> one can in-effect **compose** `Gatherer`s together:

> ```java
> Gatherer<Integer,?,String> someGatherer = …;
> Gatherer<String,?,Long> someOtherGatherer = …;
> Stream<Long> stream =
> Stream.of(1).gather(someGatherer).gather(someOtherGatherer);
> ```

> As it turns out, it is possible to define a `default Gatherer
> andThen(Gatherer)`-method on `Gatherer` which composes `Gatherer`s:

> ```java
> Gatherer<Integer,?,String> someGatherer = …;
> Gatherer<String,?,Long> someOtherGatherer = …;
> Gatherer<Integer,?,Long> gatherer = someGatherer.andThen(someOtherGatherer);
> ```

> This makes it possible to both de-couple operations from their use-sites,
> as well as create more sophisticated `Gatherer`s from simple ones.

> But that's not all—by introducing a `default Collector
> collect(Collector)`-method
> it is also possible to compose a `Gatherer` with a `Collector`,
> and the result is another `Collector`:

> ```java
> Gatherer<Integer,?,String> someGatherer = …;
> Gatherer<String,?,Long> someOtherGatherer = …;
> Collector<Long,?,List<Long>>
> someGatherer.andThen(someOtherGatherer).collect(Collectors.toList());
> ```

> All of this together, it is now possible to build `Stream`-processing:
> "source-to-destination" using `Stream.gather(…).gather(…).gather(…)`;
> "intermediaries-first" using `gatherer.andThen(…).andThen(…);` and,
> "destination-to-source" using `gatherer.collect(otherGatherer.collect(…))`.

> ### Familiarity

> Since `Gatherer` is an evolution of `Collector` there's a clear on-ramp
> for any and all Java developers who are already familiar with `Collector`.

> ### Reusability

> `Gatherer`s, by virtue of being stand-alone, reusable, intermediaries,
> paired with compositionality and opt-in parallelization, allows for
> transformations
> to be created once and maintained in a single place, no matter if it is going to
> be
> used as a `Collector`, a `Gatherer`, or a `Stream`.

> ### Optimizability

> `Collector` has the notion of `Characteristics`, a `Set` of flags which
> describes them.
> This information can then be used by the underlying machinery which uses them
> to optimize their evaluation. The same approach can be used for `Gatherer`s.

> ### Summary 2.0

> Taking all of the above into consideration, we end up with a definition like the
> following:

> ```java
> /** @param <T> the element type
> * @param <A> the (mutable) intermediate accumulation type
> * @param <R> the (probably immutable) final accumulation type
> */
> interface Gatherer<T,A,R> {

> interface Sink<R> {
> boolean flush(R element);
> }
> interface Integrator<A,T,R> {
> boolean integrate(A state, T element, Sink<? super R> downstream);
> }

> enum Characteristics {
> GREEDY, // Never short-circuits
> SIZE_PRESERVING, // Emits exactly once per input element
> STATELESS; // No need to initialize or combine state
> }

> Supplier<A> supplier();
> Integrator<A, T, R> integrator();
> BinaryOperator<A> combiner();
> BiConsumer<A, Sink<? super R>> finisher();
> Set<Characteristics> characteristics();

> default <AA, RR> Gatherer<T,?,RR> andThen(Gatherer<R,AA,RR> that) {
> // Gatherers is analoguous to Collectors
> return Gatherers.Composite.of(this, that);
> }

> default <RR> Collector<T,?,RR> collect(Collector<R, ?, RR> collector) {
> // Gatherers is analoguous to Collectors
> return Gatherers.GathererCollector.of(this, collector);
> }
> }
> ```

> ## Appetizers

> The following examples showcase how `Gatherer` can be used to implement a
> diverse set
> of pre-existing, and future, intermediate operations for `Stream`s.

> ### How to implement `map(mapper)`

> ```java
> public final static <T,R> Gatherer<T, ?, R> map(Function<? super T, ? extends R>
> mapper) {
> return Gatherer.of(
> () -> (Void)null,
> (nothing, element, downstream) ->
> downstream.flush(mapper.apply(element)),
> (l,r) -> l,
> (nothing, downstream) -> {}
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(map(i -> i + 1)).toList()
> $1 ==> [2, 3, 4, 5]
> ```

> ### How to implement `flatMap(mapper)`

> ```java
> public final static <T,R> Gatherer<T, ?, R> flatMap(Function<? super T, ?
> extends Stream<R>> mapper) {
> return Gatherer.of(
> () -> (Void)null,
> (nothing, element, downstream) -> {
> try(Stream<? extends R> s = mapper.apply(element)) {
> return s == null || s.sequential().allMatch(downstream::flush);
> }
> },
> (l,r) -> l,
> (nothing, downstream) -> {}
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(flatMap(i -> Stream.of(i + 1))).toList()
> $1 ==> [2, 3, 4, 5]
> ```

> ### How to implement `takeWhile(predicate)`

> ```java
> public final static <T> Gatherer<T, ?, T> takeWhile(Predicate<? super T>
> predicate) {
> return Gatherer.of(
> () -> (Void)null,
> (nothing, element, downstream) ->
> predicate.test(element) && downstream.flush(element),
> (l, r) -> l,
> (nothing, downstream) -> {}
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(takeWhile(i -> i < 3)).toList()
> $1 ==> [1, 2]
> ```

> ### How to implement `limit(N)`

> ```java
> public static <M> Gatherer<M, ?, M> limit(long limit) {
> if (limit < 0)
> throw new IllegalArgumentException("'limit' has to be non-negative");

> class At { long n = 0; }
> return Gatherer.of(
> At::new,
> (at, element, downstream) ->
> at.n < limit && downstream.flush(element) && ++at.n < limit,
> Gatherer.unsupportedCombiner(),
> (at, downstream) -> {}
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(limit(2)).toList()
> $1 ==> [1, 2]
> ```

> ### How to implement prefix `scanLeft`

> ```java
> public static <T,R> Gatherer<T,?,R> scanLeft(R initial, BiFunction<R,T,R>
> scanner) {
> class State { R current = initial; }
> return Gatherer.of(
> State::new,
> (state, element, downstream) ->
> downstream.flush(state.current = scanner.apply(state.current, element)),
> Gatherer.unsupportedCombiner(),
> (state, downstream) -> {}
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(scanLeft("'", (acc, elem) -> acc + elem +
> "'")).toList()
> $1 ==> ['1', '1'2', '1'2'3', '1'2'3'4']
> ```

> ### How to implement `fold(initial, folder)`

> ```java
> public static <T> Gatherer<T,?,T> fold(T initial, BinaryOperator<T> folder) {
> class State { T current = initial; }
> return Gatherer.of(
> State::new,
> (state, element, downstream) -> {
> state.current = folder.apply(state.current, element);
> return true;
> },
> (l, r) -> {
> l.current = folder.apply(l.current, r.current);
> return l;
> },
> (state, downstream) -> downstream.flush(state.current)
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(fold(0, (acc, elem) -> acc + elem)).toList()
> $1 ==> [10]
> ```

> ### How to implement `foldLeft(initial, folder)`

> ```java
> public static <T,R> Gatherer<T,?,R> foldLeft(R initial, BiFunction<R,T,R>
> folder) {
> class State { R current = initial; }
> return Gatherer.of(
> State::new,
> (state, element, downstream) -> {
> state.current = folder.apply(state.current, element);
> return true;
> },
> Gatherer.unsupportedCombiner(),
> (state, downstream) -> downstream.flush(state.current)
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,3,4).gather(foldLeft(0L, (acc, elem) -> acc +
> elem)).toList()
> $1 ==> [10]
> ```

> ### How to implement `deduplicateAdjacent()`

> ```java
> public static <T> Gatherer<T,?,T> deduplicateAdjacent() {
> class State { T prev; boolean hasPrev; }
> return Gatherer.of(
> State::new,
> (state, element, downstream) -> {
> if (!state.hasPrev) {
> state.hasPrev = true;
> state.prev = element;
> return downstream.flush(element);
> } else if (!Objects.equals(state.prev, element)) {
> state.prev = element;
> return downstream.flush(element);
> } else {
> return true; // skip duplicate
> }
> },
> Gatherer.unsupportedCombiner(),
> (state, downstream) -> {}
> );
> }
> ```

> ```java
> jshell> Stream.of(1,2,2,3,2,4).gather(deduplicateAdjacent()).toList()
> $1 ==> [1, 2, 3, 2, 4]
> ```
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