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   * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   * This code is free software; you can redistribute it and/or modify it
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   *
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   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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  package java.util.stream;
  
  import java.nio.charset.Charset;
  import java.nio.file.Files;
  import java.nio.file.Path;
  import java.util.Arrays;
  import java.util.Collection;
  import java.util.Comparator;
  import java.util.Iterator;
  import java.util.Objects;
  import java.util.Optional;
  import java.util.Spliterator;
  import java.util.Spliterators;
  import java.util.concurrent.ConcurrentHashMap;
  import java.util.function.BiConsumer;
  import java.util.function.BiFunction;
  import java.util.function.BinaryOperator;
  import java.util.function.Consumer;
  import java.util.function.Function;
  import java.util.function.IntFunction;
  import java.util.function.Predicate;
  import java.util.function.Supplier;
  import java.util.function.ToDoubleFunction;
  import java.util.function.ToIntFunction;
  import java.util.function.ToLongFunction;
  import java.util.function.UnaryOperator;
  
  /**
   * A sequence of elements supporting sequential and parallel aggregate
   * operations.  The following example illustrates an aggregate operation using
   * {@link Stream} and {@link IntStream}:
   *
   * <pre>{@code
   *     int sum = widgets.stream()
   *                      .filter(w -> w.getColor() == RED)
   *                      .mapToInt(w -> w.getWeight())
   *                      .sum();
   * }</pre>
   *
   * In this example, {@code widgets} is a {@code Collection<Widget>}.  We create
   * a stream of {@code Widget} objects via {@link Collection#stream Collection.stream()},
   * filter it to produce a stream containing only the red widgets, and then
   * transform it into a stream of {@code int} values representing the weight of
   * each red widget. Then this stream is summed to produce a total weight.
   *
   * <p>In addition to {@code Stream}, which is a stream of object references,
   * there are primitive specializations for {@link IntStream}, {@link LongStream},
   * and {@link DoubleStream}, all of which are referred to as "streams" and
   * conform to the characteristics and restrictions described here.
   *
   * <p>To perform a computation, stream
   * <a href="package-summary.html#StreamOps">operations</a> are composed into a
   * <em>stream pipeline</em>.  A stream pipeline consists of a source (which
   * might be an array, a collection, a generator function, an I/O channel,
   * etc), zero or more <em>intermediate operations</em> (which transform a
   * stream into another stream, such as {@link Stream#filter(Predicate)}), and a
   * <em>terminal operation</em> (which produces a result or side-effect, such
   * as {@link Stream#count()} or {@link Stream#forEach(Consumer)}).
   * Streams are lazy; computation on the source data is only performed when the
   * terminal operation is initiated, and source elements are consumed only
   * as needed.
   *
   * <p>Collections and streams, while bearing some superficial similarities,
   * have different goals.  Collections are primarily concerned with the efficient
   * management of, and access to, their elements.  By contrast, streams do not
   * provide a means to directly access or manipulate their elements, and are
   * instead concerned with declaratively describing their source and the
   * computational operations which will be performed in aggregate on that source.
   * However, if the provided stream operations do not offer the desired
   * functionality, the {@link #iterator()} and {@link #spliterator()} operations
   * can be used to perform a controlled traversal.
   *
   * <p>A stream pipeline, like the "widgets" example above, can be viewed as
   * a <em>query</em> on the stream source.  Unless the source was explicitly
   * designed for concurrent modification (such as a {@link ConcurrentHashMap}),
   * unpredictable or erroneous behavior may result from modifying the stream
   * source while it is being queried.
   *
   * <p>Most stream operations accept parameters that describe user-specified
   * behavior, such as the lambda expression {@code w -> w.getWeight()} passed to
   * {@code mapToInt} in the example above.  To preserve correct behavior,
   * these <em>behavioral parameters</em>:
   * <ul>
   * <li>must be <a href="package-summary.html#NonInterference">non-interfering</a>
   * (they do not modify the stream source); and</li>
   * <li>in most cases must be <a href="package-summary.html#Statelessness">stateless</a>
   * (their result should not depend on any state that might change during execution
   * of the stream pipeline).</li>
   * </ul>
   *
   * <p>Such parameters are always instances of a
   * <a href="../function/package-summary.html">functional interface</a> such
   * as {@link Function}, and are often lambda expressions or
   * method references.  Unless otherwise specified these parameters must be
   * <em>non-null</em>.
   *
   * <p>A stream should be operated on (invoking an intermediate or terminal stream
   * operation) only once.  This rules out, for example, "forked" streams, where
   * the same source feeds two or more pipelines, or multiple traversals of the
   * same stream.  A stream implementation may throw {@link IllegalStateException}
   * if it detects that the stream is being reused. However, since some stream
   * operations may return their receiver rather than a new stream object, it may
   * not be possible to detect reuse in all cases.
   *
   * <p>Streams have a {@link #close()} method and implement {@link AutoCloseable},
   * but nearly all stream instances do not actually need to be closed after use.
   * Generally, only streams whose source is an IO channel (such as those returned
   * by {@link Files#lines(Path, Charset)}) will require closing.  Most streams
   * are backed by collections, arrays, or generating functions, which require no
   * special resource management.  (If a stream does require closing, it can be
   * declared as a resource in a {@code try}-with-resources statement.)
   *
   * <p>Stream pipelines may execute either sequentially or in
   * <a href="package-summary.html#Parallelism">parallel</a>.  This
   * execution mode is a property of the stream.  Streams are created
   * with an initial choice of sequential or parallel execution.  (For example,
   * {@link Collection#stream() Collection.stream()} creates a sequential stream,
   * and {@link Collection#parallelStream() Collection.parallelStream()} creates
   * a parallel one.)  This choice of execution mode may be modified by the
   * {@link #sequential()} or {@link #parallel()} methods, and may be queried with
   * the {@link #isParallel()} method.
   *
   * @param <T> the type of the stream elements
   * @since 1.8
   * @see IntStream
   * @see LongStream
   * @see DoubleStream
   * @see <a href="package-summary.html">java.util.stream</a>
   */
  public interface Stream<T> extends BaseStream<T, Stream<T>> {
  
      /**
       * Returns a stream consisting of the elements of this stream that match
       * the given predicate.
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                  <a href="package-summary.html#Statelessness">stateless</a>
       *                  predicate to apply to each element to determine if it
       *                  should be included
       * @return the new stream
       */
      Stream<T> filter(Predicate<? super T> predicate);
  
      /**
       * Returns a stream consisting of the results of applying the given
       * function to the elements of this stream.
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param <R> The element type of the new stream
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element
       * @return the new stream
       */
      <R> Stream<R> map(Function<? super T, ? extends R> mapper);
  
      /**
       * Returns an {@code IntStream} consisting of the results of applying the
       * given function to the elements of this stream.
       *
       * <p>This is an <a href="package-summary.html#StreamOps">
       *     intermediate operation</a>.
       *
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element
       * @return the new stream
       */
      IntStream mapToInt(ToIntFunction<? super T> mapper);
  
      /**
       * Returns a {@code LongStream} consisting of the results of applying the
       * given function to the elements of this stream.
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element
       * @return the new stream
       */
      LongStream mapToLong(ToLongFunction<? super T> mapper);
  
      /**
       * Returns a {@code DoubleStream} consisting of the results of applying the
       * given function to the elements of this stream.
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element
       * @return the new stream
       */
      DoubleStream mapToDouble(ToDoubleFunction<? super T> mapper);
  
      /**
       * Returns a stream consisting of the results of replacing each element of
       * this stream with the contents of a mapped stream produced by applying
       * the provided mapping function to each element.  Each mapped stream is
       * {@link BaseStream#close() closed} after its contents
       * have been placed into this stream.  (If a mapped stream is {@code null}
       * an empty stream is used, instead.)
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @apiNote
       * The {@code flatMap()} operation has the effect of applying a one-to-many
       * transformation to the elements of the stream, and then flattening the
       * resulting elements into a new stream.
       *
       * <p><b>Examples.</b>
       *
       * <p>If {@code orders} is a stream of purchase orders, and each purchase
       * order contains a collection of line items, then the following produces a
       * stream containing all the line items in all the orders:
       * <pre>{@code
       *     orders.flatMap(order -> order.getLineItems().stream())...
       * }</pre>
       *
       * <p>If {@code path} is the path to a file, then the following produces a
       * stream of the {@code words} contained in that file:
       * <pre>{@code
       *     Stream<String> lines = Files.lines(path, StandardCharsets.UTF_8);
       *     Stream<String> words = lines.flatMap(line -> Stream.of(line.split(" +")));
       * }</pre>
       * The {@code mapper} function passed to {@code flatMap} splits a line,
       * using a simple regular expression, into an array of words, and then
       * creates a stream of words from that array.
       *
       * @param <R> The element type of the new stream
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element which produces a stream
       *               of new values
       * @return the new stream
       */
      <R> Stream<R> flatMap(Function<? super T, ? extends Stream<? extends R>> mapper);
  
      /**
       * Returns an {@code IntStream} consisting of the results of replacing each
       * element of this stream with the contents of a mapped stream produced by
       * applying the provided mapping function to each element.  Each mapped
       * stream is {@link BaseStream#close() closed} after its
       * contents have been placed into this stream.  (If a mapped stream is
       * {@code null} an empty stream is used, instead.)
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element which produces a stream
       *               of new values
       * @return the new stream
       * @see #flatMap(Function)
       */
      IntStream flatMapToInt(Function<? super T, ? extends IntStream> mapper);
  
      /**
       * Returns an {@code LongStream} consisting of the results of replacing each
       * element of this stream with the contents of a mapped stream produced by
       * applying the provided mapping function to each element.  Each mapped
       * stream is {@link BaseStream#close() closed} after its
       * contents have been placed into this stream.  (If a mapped stream is
       * {@code null} an empty stream is used, instead.)
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element which produces a stream
       *               of new values
       * @return the new stream
       * @see #flatMap(Function)
       */
      LongStream flatMapToLong(Function<? super T, ? extends LongStream> mapper);
  
      /**
       * Returns an {@code DoubleStream} consisting of the results of replacing
       * each element of this stream with the contents of a mapped stream produced
       * by applying the provided mapping function to each element.  Each mapped
       * stream is {@link BaseStream#close() closed} after its
       * contents have placed been into this stream.  (If a mapped stream is
       * {@code null} an empty stream is used, instead.)
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *               <a href="package-summary.html#Statelessness">stateless</a>
       *               function to apply to each element which produces a stream
       *               of new values
       * @return the new stream
       * @see #flatMap(Function)
       */
      DoubleStream flatMapToDouble(Function<? super T, ? extends DoubleStream> mapper);
  
      /**
       * Returns a stream consisting of the distinct elements (according to
       * {@link Object#equals(Object)}) of this stream.
       *
       * <p>For ordered streams, the selection of distinct elements is stable
       * (for duplicated elements, the element appearing first in the encounter
       * order is preserved.)  For unordered streams, no stability guarantees
       * are made.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">stateful
       * intermediate operation</a>.
       *
       * @apiNote
       * Preserving stability for {@code distinct()} in parallel pipelines is
       * relatively expensive (requires that the operation act as a full barrier,
       * with substantial buffering overhead), and stability is often not needed.
       * Using an unordered stream source (such as {@link #generate(Supplier)})
       * or removing the ordering constraint with {@link #unordered()} may result
       * in significantly more efficient execution for {@code distinct()} in parallel
       * pipelines, if the semantics of your situation permit.  If consistency
       * with encounter order is required, and you are experiencing poor performance
       * or memory utilization with {@code distinct()} in parallel pipelines,
       * switching to sequential execution with {@link #sequential()} may improve
       * performance.
       *
       * @return the new stream
       */
      Stream<T> distinct();
  
      /**
       * Returns a stream consisting of the elements of this stream, sorted
       * according to natural order.  If the elements of this stream are not
       * {@code Comparable}, a {@code java.lang.ClassCastException} may be thrown
       * when the terminal operation is executed.
       *
       * <p>For ordered streams, the sort is stable.  For unordered streams, no
       * stability guarantees are made.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">stateful
       * intermediate operation</a>.
       *
       * @return the new stream
       */
      Stream<T> sorted();
  
      /**
       * Returns a stream consisting of the elements of this stream, sorted
       * according to the provided {@code Comparator}.
       *
       * <p>For ordered streams, the sort is stable.  For unordered streams, no
       * stability guarantees are made.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">stateful
       * intermediate operation</a>.
       *
       * @param comparator a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                   <a href="package-summary.html#Statelessness">stateless</a>
       *                   {@code Comparator} to be used to compare stream elements
       * @return the new stream
       */
      Stream<T> sorted(Comparator<? super T> comparator);
  
      /**
       * Returns a stream consisting of the elements of this stream, additionally
       * performing the provided action on each element as elements are consumed
       * from the resulting stream.
       *
       * <p>This is an <a href="package-summary.html#StreamOps">intermediate
       * operation</a>.
       *
       * <p>For parallel stream pipelines, the action may be called at
       * whatever time and in whatever thread the element is made available by the
       * upstream operation.  If the action modifies shared state,
       * it is responsible for providing the required synchronization.
       *
       * @apiNote This method exists mainly to support debugging, where you want
       * to see the elements as they flow past a certain point in a pipeline:
       * <pre>{@code
       *     Stream.of("one", "two", "three", "four")
       *         .filter(e -> e.length() > 3)
       *         .peek(e -> System.out.println("Filtered value: " + e))
       *         .map(String::toUpperCase)
       *         .peek(e -> System.out.println("Mapped value: " + e))
       *         .collect(Collectors.toList());
       * }</pre>
       *
       * @param action a <a href="package-summary.html#NonInterference">
       *                 non-interfering</a> action to perform on the elements as
       *                 they are consumed from the stream
       * @return the new stream
       */
      Stream<T> peek(Consumer<? super T> action);
  
      /**
       * Returns a stream consisting of the elements of this stream, truncated
       * to be no longer than {@code maxSize} in length.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
       * stateful intermediate operation</a>.
       *
       * @apiNote
       * While {@code limit()} is generally a cheap operation on sequential
       * stream pipelines, it can be quite expensive on ordered parallel pipelines,
       * especially for large values of {@code maxSize}, since {@code limit(n)}
       * is constrained to return not just any <em>n</em> elements, but the
       * <em>first n</em> elements in the encounter order.  Using an unordered
       * stream source (such as {@link #generate(Supplier)}) or removing the
       * ordering constraint with {@link #unordered()} may result in significant
       * speedups of {@code limit()} in parallel pipelines, if the semantics of
       * your situation permit.  If consistency with encounter order is required,
       * and you are experiencing poor performance or memory utilization with
       * {@code limit()} in parallel pipelines, switching to sequential execution
       * with {@link #sequential()} may improve performance.
       *
       * @param maxSize the number of elements the stream should be limited to
       * @return the new stream
       * @throws IllegalArgumentException if {@code maxSize} is negative
       */
      Stream<T> limit(long maxSize);
  
      /**
       * Returns a stream consisting of the remaining elements of this stream
       * after discarding the first {@code n} elements of the stream.
       * If this stream contains fewer than {@code n} elements then an
       * empty stream will be returned.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">stateful
       * intermediate operation</a>.
       *
       * @apiNote
       * While {@code skip()} is generally a cheap operation on sequential
       * stream pipelines, it can be quite expensive on ordered parallel pipelines,
       * especially for large values of {@code n}, since {@code skip(n)}
       * is constrained to skip not just any <em>n</em> elements, but the
       * <em>first n</em> elements in the encounter order.  Using an unordered
       * stream source (such as {@link #generate(Supplier)}) or removing the
       * ordering constraint with {@link #unordered()} may result in significant
       * speedups of {@code skip()} in parallel pipelines, if the semantics of
       * your situation permit.  If consistency with encounter order is required,
       * and you are experiencing poor performance or memory utilization with
       * {@code skip()} in parallel pipelines, switching to sequential execution
       * with {@link #sequential()} may improve performance.
       *
       * @param n the number of leading elements to skip
       * @return the new stream
       * @throws IllegalArgumentException if {@code n} is negative
       */
      Stream<T> skip(long n);
  
      /**
       * Performs an action for each element of this stream.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * <p>The behavior of this operation is explicitly nondeterministic.
       * For parallel stream pipelines, this operation does <em>not</em>
       * guarantee to respect the encounter order of the stream, as doing so
       * would sacrifice the benefit of parallelism.  For any given element, the
       * action may be performed at whatever time and in whatever thread the
       * library chooses.  If the action accesses shared state, it is
       * responsible for providing the required synchronization.
       *
       * @param action a <a href="package-summary.html#NonInterference">
       *               non-interfering</a> action to perform on the elements
       */
      void forEach(Consumer<? super T> action);
  
      /**
       * Performs an action for each element of this stream, in the encounter
       * order of the stream if the stream has a defined encounter order.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * <p>This operation processes the elements one at a time, in encounter
       * order if one exists.  Performing the action for one element
       * <a href="../concurrent/package-summary.html#MemoryVisibility"><i>happens-before</i></a>
       * performing the action for subsequent elements, but for any given element,
       * the action may be performed in whatever thread the library chooses.
       *
       * @param action a <a href="package-summary.html#NonInterference">
       *               non-interfering</a> action to perform on the elements
       * @see #forEach(Consumer)
       */
      void forEachOrdered(Consumer<? super T> action);
  
      /**
       * Returns an array containing the elements of this stream.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @return an array containing the elements of this stream
       */
      Object[] toArray();
  
      /**
       * Returns an array containing the elements of this stream, using the
       * provided {@code generator} function to allocate the returned array, as
       * well as any additional arrays that might be required for a partitioned
       * execution or for resizing.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @apiNote
       * The generator function takes an integer, which is the size of the
       * desired array, and produces an array of the desired size.  This can be
       * concisely expressed with an array constructor reference:
       * <pre>{@code
       *     Person[] men = people.stream()
       *                          .filter(p -> p.getGender() == MALE)
       *                          .toArray(Person[]::new);
       * }</pre>
       *
       * @param <A> the element type of the resulting array
       * @param generator a function which produces a new array of the desired
       *                  type and the provided length
       * @return an array containing the elements in this stream
       * @throws ArrayStoreException if the runtime type of the array returned
       * from the array generator is not a supertype of the runtime type of every
       * element in this stream
       */
      <A> A[] toArray(IntFunction<A[]> generator);
  
      /**
       * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
       * elements of this stream, using the provided identity value and an
       * <a href="package-summary.html#Associativity">associative</a>
       * accumulation function, and returns the reduced value.  This is equivalent
       * to:
       * <pre>{@code
       *     T result = identity;
       *     for (T element : this stream)
       *         result = accumulator.apply(result, element)
       *     return result;
       * }</pre>
       *
       * but is not constrained to execute sequentially.
       *
       * <p>The {@code identity} value must be an identity for the accumulator
       * function. This means that for all {@code t},
       * {@code accumulator.apply(identity, t)} is equal to {@code t}.
       * The {@code accumulator} function must be an
       * <a href="package-summary.html#Associativity">associative</a> function.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @apiNote Sum, min, max, average, and string concatenation are all special
       * cases of reduction. Summing a stream of numbers can be expressed as:
       *
       * <pre>{@code
       *     Integer sum = integers.reduce(0, (a, b) -> a+b);
       * }</pre>
       *
       * or:
       *
       * <pre>{@code
       *     Integer sum = integers.reduce(0, Integer::sum);
       * }</pre>
       *
       * <p>While this may seem a more roundabout way to perform an aggregation
       * compared to simply mutating a running total in a loop, reduction
       * operations parallelize more gracefully, without needing additional
       * synchronization and with greatly reduced risk of data races.
       *
       * @param identity the identity value for the accumulating function
       * @param accumulator an <a href="package-summary.html#Associativity">associative</a>,
       *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                    <a href="package-summary.html#Statelessness">stateless</a>
       *                    function for combining two values
       * @return the result of the reduction
       */
      T reduce(T identity, BinaryOperator<T> accumulator);
  
      /**
       * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
       * elements of this stream, using an
       * <a href="package-summary.html#Associativity">associative</a> accumulation
       * function, and returns an {@code Optional} describing the reduced value,
       * if any. This is equivalent to:
       * <pre>{@code
       *     boolean foundAny = false;
       *     T result = null;
       *     for (T element : this stream) {
       *         if (!foundAny) {
       *             foundAny = true;
       *             result = element;
       *         }
       *         else
       *             result = accumulator.apply(result, element);
       *     }
       *     return foundAny ? Optional.of(result) : Optional.empty();
       * }</pre>
       *
       * but is not constrained to execute sequentially.
       *
       * <p>The {@code accumulator} function must be an
       * <a href="package-summary.html#Associativity">associative</a> function.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @param accumulator an <a href="package-summary.html#Associativity">associative</a>,
       *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                    <a href="package-summary.html#Statelessness">stateless</a>
       *                    function for combining two values
       * @return an {@link Optional} describing the result of the reduction
       * @throws NullPointerException if the result of the reduction is null
       * @see #reduce(Object, BinaryOperator)
       * @see #min(Comparator)
       * @see #max(Comparator)
       */
      Optional<T> reduce(BinaryOperator<T> accumulator);
  
      /**
       * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
       * elements of this stream, using the provided identity, accumulation and
       * combining functions.  This is equivalent to:
       * <pre>{@code
       *     U result = identity;
       *     for (T element : this stream)
       *         result = accumulator.apply(result, element)
       *     return result;
       * }</pre>
       *
       * but is not constrained to execute sequentially.
       *
       * <p>The {@code identity} value must be an identity for the combiner
       * function.  This means that for all {@code u}, {@code combiner(identity, u)}
       * is equal to {@code u}.  Additionally, the {@code combiner} function
       * must be compatible with the {@code accumulator} function; for all
       * {@code u} and {@code t}, the following must hold:
       * <pre>{@code
       *     combiner.apply(u, accumulator.apply(identity, t)) == accumulator.apply(u, t)
       * }</pre>
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @apiNote Many reductions using this form can be represented more simply
       * by an explicit combination of {@code map} and {@code reduce} operations.
       * The {@code accumulator} function acts as a fused mapper and accumulator,
       * which can sometimes be more efficient than separate mapping and reduction,
       * such as when knowing the previously reduced value allows you to avoid
       * some computation.
       *
       * @param <U> The type of the result
       * @param identity the identity value for the combiner function
       * @param accumulator an <a href="package-summary.html#Associativity">associative</a>,
       *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                    <a href="package-summary.html#Statelessness">stateless</a>
       *                    function for incorporating an additional element into a result
       * @param combiner an <a href="package-summary.html#Associativity">associative</a>,
       *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                    <a href="package-summary.html#Statelessness">stateless</a>
       *                    function for combining two values, which must be
       *                    compatible with the accumulator function
       * @return the result of the reduction
       * @see #reduce(BinaryOperator)
       * @see #reduce(Object, BinaryOperator)
       */
      <U> U reduce(U identity,
                   BiFunction<U, ? super T, U> accumulator,
                   BinaryOperator<U> combiner);
  
      /**
       * Performs a <a href="package-summary.html#MutableReduction">mutable
       * reduction</a> operation on the elements of this stream.  A mutable
       * reduction is one in which the reduced value is a mutable result container,
       * such as an {@code ArrayList}, and elements are incorporated by updating
       * the state of the result rather than by replacing the result.  This
       * produces a result equivalent to:
       * <pre>{@code
       *     R result = supplier.get();
       *     for (T element : this stream)
       *         accumulator.accept(result, element);
       *     return result;
       * }</pre>
       *
       * <p>Like {@link #reduce(Object, BinaryOperator)}, {@code collect} operations
       * can be parallelized without requiring additional synchronization.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @apiNote There are many existing classes in the JDK whose signatures are
       * well-suited for use with method references as arguments to {@code collect()}.
       * For example, the following will accumulate strings into an {@code ArrayList}:
       * <pre>{@code
       *     List<String> asList = stringStream.collect(ArrayList::new, ArrayList::add,
       *                                                ArrayList::addAll);
       * }</pre>
       *
       * <p>The following will take a stream of strings and concatenates them into a
       * single string:
       * <pre>{@code
       *     String concat = stringStream.collect(StringBuilder::new, StringBuilder::append,
       *                                          StringBuilder::append)
       *                                 .toString();
       * }</pre>
       *
       * @param <R> type of the result
       * @param supplier a function that creates a new result container. For a
       *                 parallel execution, this function may be called
       *                 multiple times and must return a fresh value each time.
       * @param accumulator an <a href="package-summary.html#Associativity">associative</a>,
       *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                    <a href="package-summary.html#Statelessness">stateless</a>
       *                    function for incorporating an additional element into a result
       * @param combiner an <a href="package-summary.html#Associativity">associative</a>,
       *                    <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                    <a href="package-summary.html#Statelessness">stateless</a>
       *                    function for combining two values, which must be
       *                    compatible with the accumulator function
       * @return the result of the reduction
       */
      <R> R collect(Supplier<R> supplier,
                    BiConsumer<R, ? super T> accumulator,
                    BiConsumer<R, R> combiner);
  
      /**
       * Performs a <a href="package-summary.html#MutableReduction">mutable
       * reduction</a> operation on the elements of this stream using a
       * {@code Collector}.  A {@code Collector}
       * encapsulates the functions used as arguments to
       * {@link #collect(Supplier, BiConsumer, BiConsumer)}, allowing for reuse of
       * collection strategies and composition of collect operations such as
       * multiple-level grouping or partitioning.
       *
       * <p>If the stream is parallel, and the {@code Collector}
       * is {@link Collector.Characteristics#CONCURRENT concurrent}, and
       * either the stream is unordered or the collector is
       * {@link Collector.Characteristics#UNORDERED unordered},
       * then a concurrent reduction will be performed (see {@link Collector} for
       * details on concurrent reduction.)
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * <p>When executed in parallel, multiple intermediate results may be
       * instantiated, populated, and merged so as to maintain isolation of
       * mutable data structures.  Therefore, even when executed in parallel
       * with non-thread-safe data structures (such as {@code ArrayList}), no
       * additional synchronization is needed for a parallel reduction.
       *
       * @apiNote
       * The following will accumulate strings into an ArrayList:
       * <pre>{@code
       *     List<String> asList = stringStream.collect(Collectors.toList());
       * }</pre>
       *
       * <p>The following will classify {@code Person} objects by city:
       * <pre>{@code
       *     Map<String, List<Person>> peopleByCity
       *         = personStream.collect(Collectors.groupingBy(Person::getCity));
       * }</pre>
       *
       * <p>The following will classify {@code Person} objects by state and city,
       * cascading two {@code Collector}s together:
       * <pre>{@code
       *     Map<String, Map<String, List<Person>>> peopleByStateAndCity
       *         = personStream.collect(Collectors.groupingBy(Person::getState,
       *                                                      Collectors.groupingBy(Person::getCity)));
       * }</pre>
       *
       * @param <R> the type of the result
       * @param <A> the intermediate accumulation type of the {@code Collector}
       * @param collector the {@code Collector} describing the reduction
       * @return the result of the reduction
       * @see #collect(Supplier, BiConsumer, BiConsumer)
       * @see Collectors
       */
      <R, A> R collect(Collector<? super T, A, R> collector);
  
      /**
       * Returns the minimum element of this stream according to the provided
       * {@code Comparator}.  This is a special case of a
       * <a href="package-summary.html#Reduction">reduction</a>.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal operation</a>.
       *
       * @param comparator a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                   <a href="package-summary.html#Statelessness">stateless</a>
       *                   {@code Comparator} to compare elements of this stream
       * @return an {@code Optional} describing the minimum element of this stream,
       * or an empty {@code Optional} if the stream is empty
       * @throws NullPointerException if the minimum element is null
       */
      Optional<T> min(Comparator<? super T> comparator);
  
      /**
       * Returns the maximum element of this stream according to the provided
       * {@code Comparator}.  This is a special case of a
       * <a href="package-summary.html#Reduction">reduction</a>.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal
       * operation</a>.
       *
       * @param comparator a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                   <a href="package-summary.html#Statelessness">stateless</a>
       *                   {@code Comparator} to compare elements of this stream
       * @return an {@code Optional} describing the maximum element of this stream,
       * or an empty {@code Optional} if the stream is empty
       * @throws NullPointerException if the maximum element is null
       */
      Optional<T> max(Comparator<? super T> comparator);
  
      /**
       * Returns the count of elements in this stream.  This is a special case of
       * a <a href="package-summary.html#Reduction">reduction</a> and is
       * equivalent to:
       * <pre>{@code
       *     return mapToLong(e -> 1L).sum();
       * }</pre>
       *
       * <p>This is a <a href="package-summary.html#StreamOps">terminal operation</a>.
       *
       * @return the count of elements in this stream
       */
      long count();
  
      /**
       * Returns whether any elements of this stream match the provided
       * predicate.  May not evaluate the predicate on all elements if not
       * necessary for determining the result.  If the stream is empty then
       * {@code false} is returned and the predicate is not evaluated.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
       * terminal operation</a>.
       *
       * @apiNote
       * This method evaluates the <em>existential quantification</em> of the
       * predicate over the elements of the stream (for some x P(x)).
       *
       * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                  <a href="package-summary.html#Statelessness">stateless</a>
       *                  predicate to apply to elements of this stream
       * @return {@code true} if any elements of the stream match the provided
       * predicate, otherwise {@code false}
       */
      boolean anyMatch(Predicate<? super T> predicate);
  
      /**
       * Returns whether all elements of this stream match the provided predicate.
       * May not evaluate the predicate on all elements if not necessary for
       * determining the result.  If the stream is empty then {@code true} is
       * returned and the predicate is not evaluated.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
       * terminal operation</a>.
       *
       * @apiNote
       * This method evaluates the <em>universal quantification</em> of the
       * predicate over the elements of the stream (for all x P(x)).  If the
       * stream is empty, the quantification is said to be <em>vacuously
       * satisfied</em> and is always {@code true} (regardless of P(x)).
       *
       * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                  <a href="package-summary.html#Statelessness">stateless</a>
       *                  predicate to apply to elements of this stream
       * @return {@code true} if either all elements of the stream match the
       * provided predicate or the stream is empty, otherwise {@code false}
       */
      boolean allMatch(Predicate<? super T> predicate);
  
      /**
       * Returns whether no elements of this stream match the provided predicate.
       * May not evaluate the predicate on all elements if not necessary for
       * determining the result.  If the stream is empty then {@code true} is
       * returned and the predicate is not evaluated.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
       * terminal operation</a>.
       *
       * @apiNote
       * This method evaluates the <em>universal quantification</em> of the
       * negated predicate over the elements of the stream (for all x ~P(x)).  If
       * the stream is empty, the quantification is said to be vacuously satisfied
       * and is always {@code true}, regardless of P(x).
       *
       * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>,
       *                  <a href="package-summary.html#Statelessness">stateless</a>
       *                  predicate to apply to elements of this stream
       * @return {@code true} if either no elements of the stream match the
       * provided predicate or the stream is empty, otherwise {@code false}
       */
      boolean noneMatch(Predicate<? super T> predicate);
  
      /**
       * Returns an {@link Optional} describing the first element of this stream,
       * or an empty {@code Optional} if the stream is empty.  If the stream has
       * no encounter order, then any element may be returned.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
       * terminal operation</a>.
       *
       * @return an {@code Optional} describing the first element of this stream,
       * or an empty {@code Optional} if the stream is empty
       * @throws NullPointerException if the element selected is null
       */
      Optional<T> findFirst();
  
      /**
       * Returns an {@link Optional} describing some element of the stream, or an
       * empty {@code Optional} if the stream is empty.
       *
       * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
       * terminal operation</a>.
       *
       * <p>The behavior of this operation is explicitly nondeterministic; it is
       * free to select any element in the stream.  This is to allow for maximal
       * performance in parallel operations; the cost is that multiple invocations
       * on the same source may not return the same result.  (If a stable result
       * is desired, use {@link #findFirst()} instead.)
       *
       * @return an {@code Optional} describing some element of this stream, or an
       * empty {@code Optional} if the stream is empty
       * @throws NullPointerException if the element selected is null
       * @see #findFirst()
       */
      Optional<T> findAny();
  
      // Static factories
  
      /**
       * Returns a builder for a {@code Stream}.
       *
       * @param <T> type of elements
       * @return a stream builder
       */
      public static<T> Builder<T> builder() {
          return new Streams.StreamBuilderImpl<>();
      }
  
      /**
       * Returns an empty sequential {@code Stream}.
       *
       * @param <T> the type of stream elements
       * @return an empty sequential stream
       */
      public static<T> Stream<T> empty() {
          return StreamSupport.stream(Spliterators.<T>emptySpliterator(), false);
      }
  
      /**
       * Returns a sequential {@code Stream} containing a single element.
       *
       * @param t the single element
       * @param <T> the type of stream elements
       * @return a singleton sequential stream
       */
      public static<T> Stream<T> of(T t) {
          return StreamSupport.stream(new Streams.StreamBuilderImpl<>(t), false);
      }
  
      /**
       * Returns a sequential ordered stream whose elements are the specified values.
       *
       * @param <T> the type of stream elements
       * @param values the elements of the new stream
       * @return the new stream
       */
      @SafeVarargs
      @SuppressWarnings("varargs") // Creating a stream from an array is safe
      public static<T> Stream<T> of(T... values) {
          return Arrays.stream(values);
      }
  
      /**
       * Returns an infinite sequential ordered {@code Stream} produced by iterative
       * application of a function {@code f} to an initial element {@code seed},
       * producing a {@code Stream} consisting of {@code seed}, {@code f(seed)},
       * {@code f(f(seed))}, etc.
       *
       * <p>The first element (position {@code 0}) in the {@code Stream} will be
       * the provided {@code seed}.  For {@code n > 0}, the element at position
       * {@code n}, will be the result of applying the function {@code f} to the
       * element at position {@code n - 1}.
       *
       * @param <T> the type of stream elements
       * @param seed the initial element
       * @param f a function to be applied to to the previous element to produce
       *          a new element
       * @return a new sequential {@code Stream}
       */
      public static<T> Stream<T> iterate(final T seed, final UnaryOperator<T> f) {
          Objects.requireNonNull(f);
          final Iterator<T> iterator = new Iterator<T>() {
              @SuppressWarnings("unchecked")
              T t = (T) Streams.NONE;
  
              @Override
              public boolean hasNext() {
                  return true;
              }
  
              @Override
              public T next() {
                  return t = (t == Streams.NONE) ? seed : f.apply(t);
              }
          };
          return StreamSupport.stream(Spliterators.spliteratorUnknownSize(
                  iterator,
                  Spliterator.ORDERED | Spliterator.IMMUTABLE), false);
      }
  
      /**
       * Returns an infinite sequential unordered stream where each element is
       * generated by the provided {@code Supplier}.  This is suitable for
       * generating constant streams, streams of random elements, etc.
       *
       * @param <T> the type of stream elements
       * @param s the {@code Supplier} of generated elements
       * @return a new infinite sequential unordered {@code Stream}
       */
      public static<T> Stream<T> generate(Supplier<T> s) {
          Objects.requireNonNull(s);
          return StreamSupport.stream(
                  new StreamSpliterators.InfiniteSupplyingSpliterator.OfRef<>(Long.MAX_VALUE, s), false);
      }
  
      /**
       * Creates a lazily concatenated stream whose elements are all the
       * elements of the first stream followed by all the elements of the
       * second stream.  The resulting stream is ordered if both
       * of the input streams are ordered, and parallel if either of the input
       * streams is parallel.  When the resulting stream is closed, the close
       * handlers for both input streams are invoked.
       *
       * @implNote
       * Use caution when constructing streams from repeated concatenation.
       * Accessing an element of a deeply concatenated stream can result in deep
       * call chains, or even {@code StackOverflowException}.
       *
       * @param <T> The type of stream elements
       * @param a the first stream
       * @param b the second stream
       * @return the concatenation of the two input streams
       */
      public static <T> Stream<T> concat(Stream<? extends T> a, Stream<? extends T> b) {
          Objects.requireNonNull(a);
          Objects.requireNonNull(b);
  
          @SuppressWarnings("unchecked")
          Spliterator<T> split = new Streams.ConcatSpliterator.OfRef<>(
                  (Spliterator<T>) a.spliterator(), (Spliterator<T>) b.spliterator());
          Stream<T> stream = StreamSupport.stream(split, a.isParallel() || b.isParallel());
          return stream.onClose(Streams.composedClose(a, b));
      }
  
      /**
       * A mutable builder for a {@code Stream}.  This allows the creation of a
       * {@code Stream} by generating elements individually and adding them to the
       * {@code Builder} (without the copying overhead that comes from using
       * an {@code ArrayList} as a temporary buffer.)
       *
       * <p>A stream builder has a lifecycle, which starts in a building
       * phase, during which elements can be added, and then transitions to a built
       * phase, after which elements may not be added.  The built phase begins
       * when the {@link #build()} method is called, which creates an ordered
       * {@code Stream} whose elements are the elements that were added to the stream
       * builder, in the order they were added.
       *
       * @param <T> the type of stream elements
       * @see Stream#builder()
       * @since 1.8
       */
      public interface Builder<T> extends Consumer<T> {
  
          /**
           * Adds an element to the stream being built.
           *
           * @throws IllegalStateException if the builder has already transitioned to
           * the built state
           */
          @Override
          void accept(T t);
  
          /**
           * Adds an element to the stream being built.
           *
           * @implSpec
           * The default implementation behaves as if:
           * <pre>{@code
           *     accept(t)
           *     return this;
           * }</pre>
           *
           * @param t the element to add
           * @return {@code this} builder
           * @throws IllegalStateException if the builder has already transitioned to
           * the built state
           */
          default Builder<T> add(T t) {
              accept(t);
              return this;
          }
  
          /**
           * Builds the stream, transitioning this builder to the built state.
           * An {@code IllegalStateException} is thrown if there are further attempts
           * to operate on the builder after it has entered the built state.
           *
           * @return the built stream
           * @throws IllegalStateException if the builder has already transitioned to
           * the built state
           */
          Stream<T> build();
  
      }
  }
  