Map.java

/*
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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
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
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 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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package java.util;

import org.checkerframework.checker.index.qual.NonNegative;
import org.checkerframework.checker.lock.qual.GuardSatisfied;
import org.checkerframework.checker.lock.qual.ReleasesNoLocks;
import org.checkerframework.checker.nullness.qual.EnsuresKeyFor;
import org.checkerframework.checker.nullness.qual.EnsuresKeyForIf;
import org.checkerframework.checker.nullness.qual.KeyFor;
import org.checkerframework.checker.nullness.qual.NonNull;
import org.checkerframework.checker.nullness.qual.Nullable;
import org.checkerframework.checker.nullness.qual.PolyNull;
import org.checkerframework.checker.signedness.qual.UnknownSignedness;
import org.checkerframework.dataflow.qual.Pure;
import org.checkerframework.dataflow.qual.SideEffectFree;
import org.checkerframework.framework.qual.AnnotatedFor;
import org.checkerframework.framework.qual.CFComment;
import org.checkerframework.framework.qual.Covariant;

import java.util.function.BiConsumer;
import java.util.function.BiFunction;
import java.util.function.Function;
import java.io.Serializable;

/**
 * An object that maps keys to values.  A map cannot contain duplicate keys;
 * each key can map to at most one value.
 *
 * <p>This interface takes the place of the {@code Dictionary} class, which
 * was a totally abstract class rather than an interface.
 *
 * <p>The {@code Map} interface provides three <i>collection views</i>, which
 * allow a map's contents to be viewed as a set of keys, collection of values,
 * or set of key-value mappings.  The <i>order</i> of a map is defined as
 * the order in which the iterators on the map's collection views return their
 * elements.  Some map implementations, like the {@code TreeMap} class, make
 * specific guarantees as to their order; others, like the {@code HashMap}
 * class, do not.
 *
 * <p>Note: great care must be exercised if mutable objects are used as map
 * keys.  The behavior of a map is not specified if the value of an object is
 * changed in a manner that affects {@code equals} comparisons while the
 * object is a key in the map.  A special case of this prohibition is that it
 * is not permissible for a map to contain itself as a key.  While it is
 * permissible for a map to contain itself as a value, extreme caution is
 * advised: the {@code equals} and {@code hashCode} methods are no longer
 * well defined on such a map.
 *
 * <p>All general-purpose map implementation classes should provide two
 * "standard" constructors: a void (no arguments) constructor which creates an
 * empty map, and a constructor with a single argument of type {@code Map},
 * which creates a new map with the same key-value mappings as its argument.
 * In effect, the latter constructor allows the user to copy any map,
 * producing an equivalent map of the desired class.  There is no way to
 * enforce this recommendation (as interfaces cannot contain constructors) but
 * all of the general-purpose map implementations in the JDK comply.
 *
 * <p>The "destructive" methods contained in this interface, that is, the
 * methods that modify the map on which they operate, are specified to throw
 * {@code UnsupportedOperationException} if this map does not support the
 * operation.  If this is the case, these methods may, but are not required
 * to, throw an {@code UnsupportedOperationException} if the invocation would
 * have no effect on the map.  For example, invoking the {@link #putAll(Map)}
 * method on an unmodifiable map may, but is not required to, throw the
 * exception if the map whose mappings are to be "superimposed" is empty.
 *
 * <p>Some map implementations have restrictions on the keys and values they
 * may contain.  For example, some implementations prohibit null keys and
 * values, and some have restrictions on the types of their keys.  Attempting
 * to insert an ineligible key or value throws an unchecked exception,
 * typically {@code NullPointerException} or {@code ClassCastException}.
 * Attempting to query the presence of an ineligible key or value may throw an
 * exception, or it may simply return false; some implementations will exhibit
 * the former behavior and some will exhibit the latter.  More generally,
 * attempting an operation on an ineligible key or value whose completion
 * would not result in the insertion of an ineligible element into the map may
 * throw an exception or it may succeed, at the option of the implementation.
 * Such exceptions are marked as "optional" in the specification for this
 * interface.
 *
 * <p>Many methods in Collections Framework interfaces are defined
 * in terms of the {@link Object#equals(Object) equals} method.  For
 * example, the specification for the {@link #containsKey(Object)
 * containsKey(Object key)} method says: "returns {@code true} if and
 * only if this map contains a mapping for a key {@code k} such that
 * {@code (key==null ? k==null : key.equals(k))}." This specification should
 * <i>not</i> be construed to imply that invoking {@code Map.containsKey}
 * with a non-null argument {@code key} will cause {@code key.equals(k)} to
 * be invoked for any key {@code k}.  Implementations are free to
 * implement optimizations whereby the {@code equals} invocation is avoided,
 * for example, by first comparing the hash codes of the two keys.  (The
 * {@link Object#hashCode()} specification guarantees that two objects with
 * unequal hash codes cannot be equal.)  More generally, implementations of
 * the various Collections Framework interfaces are free to take advantage of
 * the specified behavior of underlying {@link Object} methods wherever the
 * implementor deems it appropriate.
 *
 * <p>Some map operations which perform recursive traversal of the map may fail
 * with an exception for self-referential instances where the map directly or
 * indirectly contains itself. This includes the {@code clone()},
 * {@code equals()}, {@code hashCode()} and {@code toString()} methods.
 * Implementations may optionally handle the self-referential scenario, however
 * most current implementations do not do so.
 *
 * <h2><a id="unmodifiable">Unmodifiable Maps</a></h2>
 * <p>The {@link Map#of() Map.of},
 * {@link Map#ofEntries(Map.Entry...) Map.ofEntries}, and
 * {@link Map#copyOf Map.copyOf}
 * static factory methods provide a convenient way to create unmodifiable maps.
 * The {@code Map}
 * instances created by these methods have the following characteristics:
 *
 * <ul>
 * <li>They are <a href="Collection.html#unmodifiable"><i>unmodifiable</i></a>. Keys and values
 * cannot be added, removed, or updated. Calling any mutator method on the Map
 * will always cause {@code UnsupportedOperationException} to be thrown.
 * However, if the contained keys or values are themselves mutable, this may cause the
 * Map to behave inconsistently or its contents to appear to change.
 * <li>They disallow {@code null} keys and values. Attempts to create them with
 * {@code null} keys or values result in {@code NullPointerException}.
 * <li>They are serializable if all keys and values are serializable.
 * <li>They reject duplicate keys at creation time. Duplicate keys
 * passed to a static factory method result in {@code IllegalArgumentException}.
 * <li>The iteration order of mappings is unspecified and is subject to change.
 * <li>They are <a href="../lang/doc-files/ValueBased.html">value-based</a>.
 * Programmers should treat instances that are {@linkplain #equals(Object) equal}
 * as interchangeable and should not use them for synchronization, or
 * unpredictable behavior may occur. For example, in a future release,
 * synchronization may fail. Callers should make no assumptions
 * about the identity of the returned instances. Factories are free to
 * create new instances or reuse existing ones.
 * <li>They are serialized as specified on the
 * <a href="{@docRoot}/serialized-form.html#java.util.CollSer">Serialized Form</a>
 * page.
 * </ul>
 *
 * <p>This interface is a member of the
 * <a href="{@docRoot}/java.base/java/util/package-summary.html#CollectionsFramework">
 * Java Collections Framework</a>.
 *
 * @param <K> the type of keys maintained by this map
 * @param <V> the type of mapped values
 *
 * @author  Josh Bloch
 * @see HashMap
 * @see TreeMap
 * @see Hashtable
 * @see SortedMap
 * @see Collection
 * @see Set
 * @since 1.2
 */
@CFComment({"lock/nullness: Subclasses of this interface/class may opt to prohibit null elements"})
@AnnotatedFor({"lock", "nullness", "index"})
public interface Map<K, V> {
    // Query Operations

    /**
     * Returns the number of key-value mappings in this map.  If the
     * map contains more than {@code Integer.MAX_VALUE} elements, returns
     * {@code Integer.MAX_VALUE}.
     *
     * @return the number of key-value mappings in this map
     */
    @Pure
    @NonNegative int size(@GuardSatisfied Map<K, V> this);

    /**
     * Returns {@code true} if this map contains no key-value mappings.
     *
     * @return {@code true} if this map contains no key-value mappings
     */
    @Pure
    boolean isEmpty(@GuardSatisfied Map<K, V> this);

    /**
     * Returns {@code true} if this map contains a mapping for the specified
     * key.  More formally, returns {@code true} if and only if
     * this map contains a mapping for a key {@code k} such that
     * {@code Objects.equals(key, k)}.  (There can be
     * at most one such mapping.)
     *
     * @param key key whose presence in this map is to be tested
     * @return {@code true} if this map contains a mapping for the specified
     *         key
     * @throws ClassCastException if the key is of an inappropriate type for
     *         this map
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key is null and this map
     *         does not permit null keys
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     */
    @CFComment("nullness: key is not @Nullable because this map might not permit null values")
    @EnsuresKeyForIf(expression={"#1"}, result=true, map={"this"})
    @Pure
    boolean containsKey(@GuardSatisfied Map<K, V> this, @GuardSatisfied @UnknownSignedness Object key);

    /**
     * Returns {@code true} if this map maps one or more keys to the
     * specified value.  More formally, returns {@code true} if and only if
     * this map contains at least one mapping to a value {@code v} such that
     * {@code Objects.equals(value, v)}.  This operation
     * will probably require time linear in the map size for most
     * implementations of the {@code Map} interface.
     *
     * @param value value whose presence in this map is to be tested
     * @return {@code true} if this map maps one or more keys to the
     *         specified value
     * @throws ClassCastException if the value is of an inappropriate type for
     *         this map
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified value is null and this
     *         map does not permit null values
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     */
    @Pure
    boolean containsValue(@GuardSatisfied Map<K, V> this, @GuardSatisfied @UnknownSignedness Object value);

    /**
     * Returns the value to which the specified key is mapped,
     * or {@code null} if this map contains no mapping for the key.
     *
     * <p>More formally, if this map contains a mapping from a key
     * {@code k} to a value {@code v} such that
     * {@code Objects.equals(key, k)},
     * then this method returns {@code v}; otherwise
     * it returns {@code null}.  (There can be at most one such mapping.)
     *
     * <p>If this map permits null values, then a return value of
     * {@code null} does not <i>necessarily</i> indicate that the map
     * contains no mapping for the key; it's also possible that the map
     * explicitly maps the key to {@code null}.  The {@link #containsKey
     * containsKey} operation may be used to distinguish these two cases.
     *
     * @param key the key whose associated value is to be returned
     * @return the value to which the specified key is mapped, or
     *         {@code null} if this map contains no mapping for the key
     * @throws ClassCastException if the key is of an inappropriate type for
     *         this map
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key is null and this map
     *         does not permit null keys
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     */
    @Pure
    @Nullable V get(@GuardSatisfied Map<K, V> this, @UnknownSignedness @GuardSatisfied Object key);

    // Modification Operations

    /**
     * Associates the specified value with the specified key in this map
     * (optional operation).  If the map previously contained a mapping for
     * the key, the old value is replaced by the specified value.  (A map
     * {@code m} is said to contain a mapping for a key {@code k} if and only
     * if {@link #containsKey(Object) m.containsKey(k)} would return
     * {@code true}.)
     *
     * @param key key with which the specified value is to be associated
     * @param value value to be associated with the specified key
     * @return the previous value associated with {@code key}, or
     *         {@code null} if there was no mapping for {@code key}.
     *         (A {@code null} return can also indicate that the map
     *         previously associated {@code null} with {@code key},
     *         if the implementation supports {@code null} values.)
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     * @throws ClassCastException if the class of the specified key or value
     *         prevents it from being stored in this map
     * @throws NullPointerException if the specified key or value is null
     *         and this map does not permit null keys or values
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     */
    @ReleasesNoLocks
    @EnsuresKeyFor(value={"#1"}, map={"this"})
    @Nullable V put(@GuardSatisfied Map<K, V> this, K key, V value);

    /**
     * Removes the mapping for a key from this map if it is present
     * (optional operation).   More formally, if this map contains a mapping
     * from key {@code k} to value {@code v} such that
     * {@code Objects.equals(key, k)}, that mapping
     * is removed.  (The map can contain at most one such mapping.)
     *
     * <p>Returns the value to which this map previously associated the key,
     * or {@code null} if the map contained no mapping for the key.
     *
     * <p>If this map permits null values, then a return value of
     * {@code null} does not <i>necessarily</i> indicate that the map
     * contained no mapping for the key; it's also possible that the map
     * explicitly mapped the key to {@code null}.
     *
     * <p>The map will not contain a mapping for the specified key once the
     * call returns.
     *
     * @param key key whose mapping is to be removed from the map
     * @return the previous value associated with {@code key}, or
     *         {@code null} if there was no mapping for {@code key}.
     * @throws UnsupportedOperationException if the {@code remove} operation
     *         is not supported by this map
     * @throws ClassCastException if the key is of an inappropriate type for
     *         this map
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key is null and this
     *         map does not permit null keys
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     */
    @CFComment("nullness: key is not @Nullable because this map might not permit null values")
    @Nullable V remove(@GuardSatisfied Map<K, V> this, @GuardSatisfied @UnknownSignedness Object key);


    // Bulk Operations

    /**
     * Copies all of the mappings from the specified map to this map
     * (optional operation).  The effect of this call is equivalent to that
     * of calling {@link #put(Object,Object) put(k, v)} on this map once
     * for each mapping from key {@code k} to value {@code v} in the
     * specified map.  The behavior of this operation is undefined if the
     * specified map is modified while the operation is in progress.
     *
     * @param m mappings to be stored in this map
     * @throws UnsupportedOperationException if the {@code putAll} operation
     *         is not supported by this map
     * @throws ClassCastException if the class of a key or value in the
     *         specified map prevents it from being stored in this map
     * @throws NullPointerException if the specified map is null, or if
     *         this map does not permit null keys or values, and the
     *         specified map contains null keys or values
     * @throws IllegalArgumentException if some property of a key or value in
     *         the specified map prevents it from being stored in this map
     */
    void putAll(@GuardSatisfied Map<K, V> this, Map<? extends K, ? extends V> m);

    /**
     * Removes all of the mappings from this map (optional operation).
     * The map will be empty after this call returns.
     *
     * @throws UnsupportedOperationException if the {@code clear} operation
     *         is not supported by this map
     */
    void clear(@GuardSatisfied Map<K, V> this);


    // Views

    /**
     * Returns a {@link Set} view of the keys contained in this map.
     * The set is backed by the map, so changes to the map are
     * reflected in the set, and vice-versa.  If the map is modified
     * while an iteration over the set is in progress (except through
     * the iterator's own {@code remove} operation), the results of
     * the iteration are undefined.  The set supports element removal,
     * which removes the corresponding mapping from the map, via the
     * {@code Iterator.remove}, {@code Set.remove},
     * {@code removeAll}, {@code retainAll}, and {@code clear}
     * operations.  It does not support the {@code add} or {@code addAll}
     * operations.
     *
     * @return a set view of the keys contained in this map
     */
    @SideEffectFree
    Set<@KeyFor({"this"}) K> keySet(@GuardSatisfied Map<K, V> this);

    /**
     * Returns a {@link Collection} view of the values contained in this map.
     * The collection is backed by the map, so changes to the map are
     * reflected in the collection, and vice-versa.  If the map is
     * modified while an iteration over the collection is in progress
     * (except through the iterator's own {@code remove} operation),
     * the results of the iteration are undefined.  The collection
     * supports element removal, which removes the corresponding
     * mapping from the map, via the {@code Iterator.remove},
     * {@code Collection.remove}, {@code removeAll},
     * {@code retainAll} and {@code clear} operations.  It does not
     * support the {@code add} or {@code addAll} operations.
     *
     * @return a collection view of the values contained in this map
     */
    @SideEffectFree
    Collection<V> values(@GuardSatisfied Map<K, V> this);

    /**
     * Returns a {@link Set} view of the mappings contained in this map.
     * The set is backed by the map, so changes to the map are
     * reflected in the set, and vice-versa.  If the map is modified
     * while an iteration over the set is in progress (except through
     * the iterator's own {@code remove} operation, or through the
     * {@code setValue} operation on a map entry returned by the
     * iterator) the results of the iteration are undefined.  The set
     * supports element removal, which removes the corresponding
     * mapping from the map, via the {@code Iterator.remove},
     * {@code Set.remove}, {@code removeAll}, {@code retainAll} and
     * {@code clear} operations.  It does not support the
     * {@code add} or {@code addAll} operations.
     *
     * @return a set view of the mappings contained in this map
     */
    @SideEffectFree
    Set<Map.Entry<@KeyFor({"this"}) K, V>> entrySet(@GuardSatisfied Map<K, V> this);

    /**
     * A map entry (key-value pair). The Entry may be unmodifiable, or the
     * value may be modifiable if the optional {@code setValue} method is
     * implemented. The Entry may be independent of any map, or it may represent
     * an entry of the entry-set view of a map.
     * <p>
     * Instances of the {@code Map.Entry} interface may be obtained by iterating
     * the entry-set view of a map. These instances maintain a connection to the
     * original, backing map. This connection to the backing map is valid
     * <i>only</i> for the duration of iteration over the entry-set view.
     * During iteration of the entry-set view, if supported by the backing map,
     * a change to a {@code Map.Entry}'s value via the
     * {@link Map.Entry#setValue setValue} method will be visible in the backing map.
     * The behavior of such a {@code Map.Entry} instance is undefined outside of
     * iteration of the map's entry-set view. It is also undefined if the backing
     * map has been modified after the {@code Map.Entry} was returned by the
     * iterator, except through the {@code Map.Entry.setValue} method. In particular,
     * a change to the value of a mapping in the backing map might or might not be
     * visible in the corresponding {@code Map.Entry} element of the entry-set view.
     *
     * @apiNote
     * It is possible to create a {@code Map.Entry} instance that is disconnected
     * from a backing map by using the {@link Map.Entry#copyOf copyOf} method. For example,
     * the following creates a snapshot of a map's entries that is guaranteed not to
     * change even if the original map is modified:
     * <pre> {@code
     * var entries = map.entrySet().stream().map(Map.Entry::copyOf).toList()
     * }</pre>
     *
     * @see Map#entrySet()
     * @since 1.2
     */
    @Covariant({0})
    interface Entry<K, V> {
        /**
         * Returns the key corresponding to this entry.
         *
         * @return the key corresponding to this entry
         * @throws IllegalStateException implementations may, but are not
         *         required to, throw this exception if the entry has been
         *         removed from the backing map.
         */
        @Pure
        K getKey(Map.@GuardSatisfied Entry<K, V> this);

        /**
         * Returns the value corresponding to this entry.  If the mapping
         * has been removed from the backing map (by the iterator's
         * {@code remove} operation), the results of this call are undefined.
         *
         * @return the value corresponding to this entry
         * @throws IllegalStateException implementations may, but are not
         *         required to, throw this exception if the entry has been
         *         removed from the backing map.
         */
        @Pure
        V getValue(Map.@GuardSatisfied Entry<K, V> this);

        /**
         * Replaces the value corresponding to this entry with the specified
         * value (optional operation).  (Writes through to the map.)  The
         * behavior of this call is undefined if the mapping has already been
         * removed from the map (by the iterator's {@code remove} operation).
         *
         * @param value new value to be stored in this entry
         * @return old value corresponding to the entry
         * @throws UnsupportedOperationException if the {@code put} operation
         *         is not supported by the backing map
         * @throws ClassCastException if the class of the specified value
         *         prevents it from being stored in the backing map
         * @throws NullPointerException if the backing map does not permit
         *         null values, and the specified value is null
         * @throws IllegalArgumentException if some property of this value
         *         prevents it from being stored in the backing map
         * @throws IllegalStateException implementations may, but are not
         *         required to, throw this exception if the entry has been
         *         removed from the backing map.
         */
        V setValue(Map.@GuardSatisfied Entry<K, V> this, V value);

        /**
         * Compares the specified object with this entry for equality.
         * Returns {@code true} if the given object is also a map entry and
         * the two entries represent the same mapping.  More formally, two
         * entries {@code e1} and {@code e2} represent the same mapping
         * if<pre>
         *     (e1.getKey()==null ?
         *      e2.getKey()==null : e1.getKey().equals(e2.getKey()))  &amp;&amp;
         *     (e1.getValue()==null ?
         *      e2.getValue()==null : e1.getValue().equals(e2.getValue()))
         * </pre>
         * This ensures that the {@code equals} method works properly across
         * different implementations of the {@code Map.Entry} interface.
         *
         * @param o object to be compared for equality with this map entry
         * @return {@code true} if the specified object is equal to this map
         *         entry
         */
        @Pure
        boolean equals(Map.@GuardSatisfied Entry<K, V> this, @GuardSatisfied @Nullable Object o);

        /**
         * Returns the hash code value for this map entry.  The hash code
         * of a map entry {@code e} is defined to be: <pre>
         *     (e.getKey()==null   ? 0 : e.getKey().hashCode()) ^
         *     (e.getValue()==null ? 0 : e.getValue().hashCode())
         * </pre>
         * This ensures that {@code e1.equals(e2)} implies that
         * {@code e1.hashCode()==e2.hashCode()} for any two Entries
         * {@code e1} and {@code e2}, as required by the general
         * contract of {@code Object.hashCode}.
         *
         * @return the hash code value for this map entry
         * @see Object#hashCode()
         * @see Object#equals(Object)
         * @see #equals(Object)
         */
        @Pure
        int hashCode(Map.@GuardSatisfied Entry<K, V> this);

        /**
         * Returns a comparator that compares {@link Map.Entry} in natural order on key.
         *
         * <p>The returned comparator is serializable and throws {@link
         * NullPointerException} when comparing an entry with a null key.
         *
         * @param  <K> the {@link Comparable} type of then map keys
         * @param  <V> the type of the map values
         * @return a comparator that compares {@link Map.Entry} in natural order on key.
         * @see Comparable
         * @since 1.8
         */
        @Pure
        public static <K extends Comparable<? super K>, V> Comparator<Map.Entry<K, V>> comparingByKey() {
            return (Comparator<Map.Entry<K, V>> & Serializable)
                (c1, c2) -> c1.getKey().compareTo(c2.getKey());
        }

        /**
         * Returns a comparator that compares {@link Map.Entry} in natural order on value.
         *
         * <p>The returned comparator is serializable and throws {@link
         * NullPointerException} when comparing an entry with null values.
         *
         * @param <K> the type of the map keys
         * @param <V> the {@link Comparable} type of the map values
         * @return a comparator that compares {@link Map.Entry} in natural order on value.
         * @see Comparable
         * @since 1.8
         */
        @Pure
        public static <K, V extends Comparable<? super V>> Comparator<Map.Entry<K, V>> comparingByValue() {
            return (Comparator<Map.Entry<K, V>> & Serializable)
                (c1, c2) -> c1.getValue().compareTo(c2.getValue());
        }

        /**
         * Returns a comparator that compares {@link Map.Entry} by key using the given
         * {@link Comparator}.
         *
         * <p>The returned comparator is serializable if the specified comparator
         * is also serializable.
         *
         * @param  <K> the type of the map keys
         * @param  <V> the type of the map values
         * @param  cmp the key {@link Comparator}
         * @return a comparator that compares {@link Map.Entry} by the key.
         * @since 1.8
         */
        @Pure
        public static <K, V> Comparator<Map.Entry<K, V>> comparingByKey(Comparator<? super K> cmp) {
            Objects.requireNonNull(cmp);
            return (Comparator<Map.Entry<K, V>> & Serializable)
                (c1, c2) -> cmp.compare(c1.getKey(), c2.getKey());
        }

        /**
         * Returns a comparator that compares {@link Map.Entry} by value using the given
         * {@link Comparator}.
         *
         * <p>The returned comparator is serializable if the specified comparator
         * is also serializable.
         *
         * @param  <K> the type of the map keys
         * @param  <V> the type of the map values
         * @param  cmp the value {@link Comparator}
         * @return a comparator that compares {@link Map.Entry} by the value.
         * @since 1.8
         */
        @Pure
        public static <K, V> Comparator<Map.Entry<K, V>> comparingByValue(Comparator<? super V> cmp) {
            Objects.requireNonNull(cmp);
            return (Comparator<Map.Entry<K, V>> & Serializable)
                (c1, c2) -> cmp.compare(c1.getValue(), c2.getValue());
        }

        /**
         * Returns a copy of the given {@code Map.Entry}. The returned instance is not
         * associated with any map. The returned instance has the same characteristics
         * as instances returned by the {@link Map#entry Map::entry} method.
         *
         * @apiNote
         * An instance obtained from a map's entry-set view has a connection to that map.
         * The {@code copyOf}  method may be used to create a {@code Map.Entry} instance,
         * containing the same key and value, that is independent of any map.
         *
         * @implNote
         * If the given entry was obtained from a call to {@code copyOf} or {@code Map::entry},
         * calling {@code copyOf} will generally not create another copy.
         *
         * @param <K> the type of the key
         * @param <V> the type of the value
         * @param e the entry to be copied
         * @return a map entry equal to the given entry
         * @throws NullPointerException if e is null or if either of its key or value is null
         * @since 17
         */
        @SuppressWarnings("unchecked")
        public static <K extends Object, V extends Object> Map.Entry<K, V> copyOf(Map.Entry<? extends K, ? extends V> e) {
            Objects.requireNonNull(e);
            if (e instanceof KeyValueHolder) {
                return (Map.Entry<K, V>) e;
            } else {
                return Map.entry(e.getKey(), e.getValue());
            }
        }
    }

    // Comparison and hashing

    /**
     * Compares the specified object with this map for equality.  Returns
     * {@code true} if the given object is also a map and the two maps
     * represent the same mappings.  More formally, two maps {@code m1} and
     * {@code m2} represent the same mappings if
     * {@code m1.entrySet().equals(m2.entrySet())}.  This ensures that the
     * {@code equals} method works properly across different implementations
     * of the {@code Map} interface.
     *
     * @param o object to be compared for equality with this map
     * @return {@code true} if the specified object is equal to this map
     */
    boolean equals(@GuardSatisfied Map<K, V> this, @GuardSatisfied @Nullable Object o);

    /**
     * Returns the hash code value for this map.  The hash code of a map is
     * defined to be the sum of the hash codes of each entry in the map's
     * {@code entrySet()} view.  This ensures that {@code m1.equals(m2)}
     * implies that {@code m1.hashCode()==m2.hashCode()} for any two maps
     * {@code m1} and {@code m2}, as required by the general contract of
     * {@link Object#hashCode}.
     *
     * @return the hash code value for this map
     * @see Map.Entry#hashCode()
     * @see Object#equals(Object)
     * @see #equals(Object)
     */
    int hashCode(@GuardSatisfied Map<K, V> this);

    // Defaultable methods

    /**
     * Returns the value to which the specified key is mapped, or
     * {@code defaultValue} if this map contains no mapping for the key.
     *
     * @implSpec
     * The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param key the key whose associated value is to be returned
     * @param defaultValue the default mapping of the key
     * @return the value to which the specified key is mapped, or
     * {@code defaultValue} if this map contains no mapping for the key
     * @throws ClassCastException if the key is of an inappropriate type for
     * this map
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key is null and this map
     * does not permit null keys
     * (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @since 1.8
     */
    @Pure
    @CFComment("nullness: We can't use @PolyNull V because the output can be null even when"
        + " defaultValue is not (namely, when the map contains a null value). "
        + "Map subclasses that forbid null values can use @PolyNull V.")
    default V getOrDefault(@GuardSatisfied @UnknownSignedness Object key, V defaultValue) {
        V v;
        return (((v = get(key)) != null) || containsKey(key))
            ? v
            : defaultValue;
    }

    /**
     * Performs the given action for each entry in this map until all entries
     * have been processed or the action throws an exception.   Unless
     * otherwise specified by the implementing class, actions are performed in
     * the order of entry set iteration (if an iteration order is specified.)
     * Exceptions thrown by the action are relayed to the caller.
     *
     * @implSpec
     * The default implementation is equivalent to, for this {@code map}:
     * <pre> {@code
     * for (Map.Entry<K, V> entry : map.entrySet())
     *     action.accept(entry.getKey(), entry.getValue());
     * }</pre>
     *
     * The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param action The action to be performed for each entry
     * @throws NullPointerException if the specified action is null
     * @throws ConcurrentModificationException if an entry is found to be
     * removed during iteration
     * @since 1.8
     */
    default void forEach(BiConsumer<? super K, ? super V> action) {
        Objects.requireNonNull(action);
        for (Map.Entry<K, V> entry : entrySet()) {
            K k;
            V v;
            try {
                k = entry.getKey();
                v = entry.getValue();
            } catch (IllegalStateException ise) {
                // this usually means the entry is no longer in the map.
                throw new ConcurrentModificationException(ise);
            }
            action.accept(k, v);
        }
    }

    /**
     * Replaces each entry's value with the result of invoking the given
     * function on that entry until all entries have been processed or the
     * function throws an exception.  Exceptions thrown by the function are
     * relayed to the caller.
     *
     * @implSpec
     * <p>The default implementation is equivalent to, for this {@code map}:
     * <pre> {@code
     * for (Map.Entry<K, V> entry : map.entrySet())
     *     entry.setValue(function.apply(entry.getKey(), entry.getValue()));
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param function the function to apply to each entry
     * @throws UnsupportedOperationException if the {@code set} operation
     * is not supported by this map's entry set iterator.
     * @throws ClassCastException if the class of a replacement value
     * prevents it from being stored in this map
     * @throws NullPointerException if the specified function is null, or the
     * specified replacement value is null, and this map does not permit null
     * values
     * @throws ClassCastException if a replacement value is of an inappropriate
     *         type for this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if function or a replacement value is null,
     *         and this map does not permit null keys or values
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of a replacement value
     *         prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ConcurrentModificationException if an entry is found to be
     * removed during iteration
     * @since 1.8
     */
    default void replaceAll(BiFunction<? super K, ? super V, ? extends V> function) {
        Objects.requireNonNull(function);
        for (Map.Entry<K, V> entry : entrySet()) {
            K k;
            V v;
            try {
                k = entry.getKey();
                v = entry.getValue();
            } catch (IllegalStateException ise) {
                // this usually means the entry is no longer in the map.
                throw new ConcurrentModificationException(ise);
            }

            // ise thrown from function is not a cme.
            v = function.apply(k, v);

            try {
                entry.setValue(v);
            } catch (IllegalStateException ise) {
                // this usually means the entry is no longer in the map.
                throw new ConcurrentModificationException(ise);
            }
        }
    }

    /**
     * If the specified key is not already associated with a value (or is mapped
     * to {@code null}) associates it with the given value and returns
     * {@code null}, else returns the current value.
     *
     * @implSpec
     * The default implementation is equivalent to, for this {@code map}:
     *
     * <pre> {@code
     * V v = map.get(key);
     * if (v == null)
     *     v = map.put(key, value);
     *
     * return v;
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param key key with which the specified value is to be associated
     * @param value value to be associated with the specified key
     * @return the previous value associated with the specified key, or
     *         {@code null} if there was no mapping for the key.
     *         (A {@code null} return can also indicate that the map
     *         previously associated {@code null} with the key,
     *         if the implementation supports null values.)
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the key or value is of an inappropriate
     *         type for this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key or value is null,
     *         and this map does not permit null keys or values
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @since 1.8
     */
    @EnsuresKeyFor(value={"#1"}, map={"this"})
    default @Nullable V putIfAbsent(K key, V value) {
        V v = get(key);
        if (v == null) {
            v = put(key, value);
        }

        return v;
    }

    /**
     * Removes the entry for the specified key only if it is currently
     * mapped to the specified value.
     *
     * @implSpec
     * The default implementation is equivalent to, for this {@code map}:
     *
     * <pre> {@code
     * if (map.containsKey(key) && Objects.equals(map.get(key), value)) {
     *     map.remove(key);
     *     return true;
     * } else
     *     return false;
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param key key with which the specified value is associated
     * @param value value expected to be associated with the specified key
     * @return {@code true} if the value was removed
     * @throws UnsupportedOperationException if the {@code remove} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the key or value is of an inappropriate
     *         type for this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key or value is null,
     *         and this map does not permit null keys or values
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @since 1.8
     */
    @CFComment("nullness: key and value are not @Nullable because this map might not permit null values")
    default boolean remove(@GuardSatisfied @UnknownSignedness Object key, @GuardSatisfied @UnknownSignedness Object value) {
        Object curValue = (key);
        if (!Objects.equals(curValue, value) ||
            (curValue == null && !containsKey(key))) {
            return false;
        }
        remove(key);
        return true;
    }

    /**
     * Replaces the entry for the specified key only if currently
     * mapped to the specified value.
     *
     * @implSpec
     * The default implementation is equivalent to, for this {@code map}:
     *
     * <pre> {@code
     * if (map.containsKey(key) && Objects.equals(map.get(key), oldValue)) {
     *     map.put(key, newValue);
     *     return true;
     * } else
     *     return false;
     * }</pre>
     *
     * The default implementation does not throw NullPointerException
     * for maps that do not support null values if oldValue is null unless
     * newValue is also null.
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param key key with which the specified value is associated
     * @param oldValue value expected to be associated with the specified key
     * @param newValue value to be associated with the specified key
     * @return {@code true} if the value was replaced
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the class of a specified key or value
     *         prevents it from being stored in this map
     * @throws NullPointerException if a specified key or newValue is null,
     *         and this map does not permit null keys or values
     * @throws NullPointerException if oldValue is null and this map does not
     *         permit null values
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of a specified key
     *         or value prevents it from being stored in this map
     * @since 1.8
     */
    default boolean replace(K key, V oldValue, V newValue) {
        Object curValue = get(key);
        if (!Objects.equals(curValue, oldValue) ||
            (curValue == null && !containsKey(key))) {
            return false;
        }
        put(key, newValue);
        return true;
    }

    /**
     * Replaces the entry for the specified key only if it is
     * currently mapped to some value.
     *
     * @implSpec
     * The default implementation is equivalent to, for this {@code map}:
     *
     * <pre> {@code
     * if (map.containsKey(key)) {
     *     return map.put(key, value);
     * } else
     *     return null;
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties.
     *
     * @param key key with which the specified value is associated
     * @param value value to be associated with the specified key
     * @return the previous value associated with the specified key, or
     *         {@code null} if there was no mapping for the key.
     *         (A {@code null} return can also indicate that the map
     *         previously associated {@code null} with the key,
     *         if the implementation supports null values.)
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the class of the specified key or value
     *         prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key or value is null,
     *         and this map does not permit null keys or values
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     * @since 1.8
     */
    default @Nullable V replace(K key, V value) {
        V curValue;
        if (((curValue = get(key)) != null) || containsKey(key)) {
            curValue = put(key, value);
        }
        return curValue;
    }

    /**
     * If the specified key is not already associated with a value (or is mapped
     * to {@code null}), attempts to compute its value using the given mapping
     * function and enters it into this map unless {@code null}.
     *
     * <p>If the mapping function returns {@code null}, no mapping is recorded.
     * If the mapping function itself throws an (unchecked) exception, the
     * exception is rethrown, and no mapping is recorded.  The most
     * common usage is to construct a new object serving as an initial
     * mapped value or memoized result, as in:
     *
     * <pre> {@code
     * map.computeIfAbsent(key, k -> new Value(f(k)));
     * }</pre>
     *
     * <p>Or to implement a multi-value map, {@code Map<K,Collection<V>>},
     * supporting multiple values per key:
     *
     * <pre> {@code
     * map.computeIfAbsent(key, k -> new HashSet<V>()).add(v);
     * }</pre>
     *
     * <p>The mapping function should not modify this map during computation.
     *
     * @implSpec
     * The default implementation is equivalent to the following steps for this
     * {@code map}, then returning the current value or {@code null} if now
     * absent:
     *
     * <pre> {@code
     * if (map.get(key) == null) {
     *     V newValue = mappingFunction.apply(key);
     *     if (newValue != null)
     *         map.put(key, newValue);
     * }
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about detecting if the
     * mapping function modifies this map during computation and, if
     * appropriate, reporting an error. Non-concurrent implementations should
     * override this method and, on a best-effort basis, throw a
     * {@code ConcurrentModificationException} if it is detected that the
     * mapping function modifies this map during computation. Concurrent
     * implementations should override this method and, on a best-effort basis,
     * throw an {@code IllegalStateException} if it is detected that the
     * mapping function modifies this map during computation and as a result
     * computation would never complete.
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties. In particular, all implementations of
     * subinterface {@link java.util.concurrent.ConcurrentMap} must document
     * whether the mapping function is applied once atomically only if the value
     * is not present.
     *
     * @param key key with which the specified value is to be associated
     * @param mappingFunction the mapping function to compute a value
     * @return the current (existing or computed) value associated with
     *         the specified key, or null if the computed value is null
     * @throws NullPointerException if the specified key is null and
     *         this map does not support null keys, or the mappingFunction
     *         is null
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the class of the specified key or value
     *         prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @since 1.8
     */
    default @PolyNull V computeIfAbsent(K key,
            Function<? super K, ? extends @PolyNull V> mappingFunction) {
        Objects.requireNonNull(mappingFunction);
        V v;
        if ((v = get(key)) == null) {
            V newValue;
            if ((newValue = mappingFunction.apply(key)) != null) {
                put(key, newValue);
                return newValue;
            }
        }

        return v;
    }

    /**
     * If the value for the specified key is present and non-null, attempts to
     * compute a new mapping given the key and its current mapped value.
     *
     * <p>If the remapping function returns {@code null}, the mapping is removed.
     * If the remapping function itself throws an (unchecked) exception, the
     * exception is rethrown, and the current mapping is left unchanged.
     *
     * <p>The remapping function should not modify this map during computation.
     *
     * @implSpec
     * The default implementation is equivalent to performing the following
     * steps for this {@code map}, then returning the current value or
     * {@code null} if now absent:
     *
     * <pre> {@code
     * if (map.get(key) != null) {
     *     V oldValue = map.get(key);
     *     V newValue = remappingFunction.apply(key, oldValue);
     *     if (newValue != null)
     *         map.put(key, newValue);
     *     else
     *         map.remove(key);
     * }
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about detecting if the
     * remapping function modifies this map during computation and, if
     * appropriate, reporting an error. Non-concurrent implementations should
     * override this method and, on a best-effort basis, throw a
     * {@code ConcurrentModificationException} if it is detected that the
     * remapping function modifies this map during computation. Concurrent
     * implementations should override this method and, on a best-effort basis,
     * throw an {@code IllegalStateException} if it is detected that the
     * remapping function modifies this map during computation and as a result
     * computation would never complete.
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties. In particular, all implementations of
     * subinterface {@link java.util.concurrent.ConcurrentMap} must document
     * whether the remapping function is applied once atomically only if the
     * value is not present.
     *
     * @param key key with which the specified value is to be associated
     * @param remappingFunction the remapping function to compute a value
     * @return the new value associated with the specified key, or null if none
     * @throws NullPointerException if the specified key is null and
     *         this map does not support null keys, or the
     *         remappingFunction is null
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the class of the specified key or value
     *         prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @since 1.8
     */
    default @PolyNull V computeIfPresent(K key,
            BiFunction<? super K, ? super @NonNull V, ? extends @PolyNull V> remappingFunction) {
        Objects.requireNonNull(remappingFunction);
        V oldValue;
        if ((oldValue = get(key)) != null) {
            V newValue = remappingFunction.apply(key, oldValue);
            if (newValue != null) {
                put(key, newValue);
                return newValue;
            } else {
                remove(key);
                return null;
            }
        } else {
            return null;
        }
    }

    /**
     * Attempts to compute a mapping for the specified key and its current
     * mapped value (or {@code null} if there is no current mapping). For
     * example, to either create or append a {@code String} msg to a value
     * mapping:
     *
     * <pre> {@code
     * map.compute(key, (k, v) -> (v == null) ? msg : v.concat(msg))}</pre>
     * (Method {@link #merge merge()} is often simpler to use for such purposes.)
     *
     * <p>If the remapping function returns {@code null}, the mapping is removed
     * (or remains absent if initially absent).  If the remapping function
     * itself throws an (unchecked) exception, the exception is rethrown, and
     * the current mapping is left unchanged.
     *
     * <p>The remapping function should not modify this map during computation.
     *
     * @implSpec
     * The default implementation is equivalent to performing the following
     * steps for this {@code map}:
     *
     * <pre> {@code
     * V oldValue = map.get(key);
     * V newValue = remappingFunction.apply(key, oldValue);
     * if (newValue != null) {
     *     map.put(key, newValue);
     * } else if (oldValue != null || map.containsKey(key)) {
     *     map.remove(key);
     * }
     * return newValue;
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about detecting if the
     * remapping function modifies this map during computation and, if
     * appropriate, reporting an error. Non-concurrent implementations should
     * override this method and, on a best-effort basis, throw a
     * {@code ConcurrentModificationException} if it is detected that the
     * remapping function modifies this map during computation. Concurrent
     * implementations should override this method and, on a best-effort basis,
     * throw an {@code IllegalStateException} if it is detected that the
     * remapping function modifies this map during computation and as a result
     * computation would never complete.
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties. In particular, all implementations of
     * subinterface {@link java.util.concurrent.ConcurrentMap} must document
     * whether the remapping function is applied once atomically only if the
     * value is not present.
     *
     * @param key key with which the specified value is to be associated
     * @param remappingFunction the remapping function to compute a value
     * @return the new value associated with the specified key, or null if none
     * @throws NullPointerException if the specified key is null and
     *         this map does not support null keys, or the
     *         remappingFunction is null
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the class of the specified key or value
     *         prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @since 1.8
     */
    default @PolyNull V compute(K key,
            BiFunction<? super K, ? super @Nullable V, ? extends @PolyNull V> remappingFunction) {
        Objects.requireNonNull(remappingFunction);
        V oldValue = get(key);

        V newValue = remappingFunction.apply(key, oldValue);
        if (newValue == null) {
            // delete mapping
            if (oldValue != null || containsKey(key)) {
                // something to remove
                remove(key);
                return null;
            } else {
                // nothing to do. Leave things as they were.
                return null;
            }
        } else {
            // add or replace old mapping
            put(key, newValue);
            return newValue;
        }
    }

    /**
     * If the specified key is not already associated with a value or is
     * associated with null, associates it with the given non-null value.
     * Otherwise, replaces the associated value with the results of the given
     * remapping function, or removes if the result is {@code null}. This
     * method may be of use when combining multiple mapped values for a key.
     * For example, to either create or append a {@code String msg} to a
     * value mapping:
     *
     * <pre> {@code
     * map.merge(key, msg, String::concat)
     * }</pre>
     *
     * <p>If the remapping function returns {@code null}, the mapping is removed.
     * If the remapping function itself throws an (unchecked) exception, the
     * exception is rethrown, and the current mapping is left unchanged.
     *
     * <p>The remapping function should not modify this map during computation.
     *
     * @implSpec
     * The default implementation is equivalent to performing the following
     * steps for this {@code map}, then returning the current value or
     * {@code null} if absent:
     *
     * <pre> {@code
     * V oldValue = map.get(key);
     * V newValue = (oldValue == null) ? value :
     *              remappingFunction.apply(oldValue, value);
     * if (newValue == null)
     *     map.remove(key);
     * else
     *     map.put(key, newValue);
     * }</pre>
     *
     * <p>The default implementation makes no guarantees about detecting if the
     * remapping function modifies this map during computation and, if
     * appropriate, reporting an error. Non-concurrent implementations should
     * override this method and, on a best-effort basis, throw a
     * {@code ConcurrentModificationException} if it is detected that the
     * remapping function modifies this map during computation. Concurrent
     * implementations should override this method and, on a best-effort basis,
     * throw an {@code IllegalStateException} if it is detected that the
     * remapping function modifies this map during computation and as a result
     * computation would never complete.
     *
     * <p>The default implementation makes no guarantees about synchronization
     * or atomicity properties of this method. Any implementation providing
     * atomicity guarantees must override this method and document its
     * concurrency properties. In particular, all implementations of
     * subinterface {@link java.util.concurrent.ConcurrentMap} must document
     * whether the remapping function is applied once atomically only if the
     * value is not present.
     *
     * @param key key with which the resulting value is to be associated
     * @param value the non-null value to be merged with the existing value
     *        associated with the key or, if no existing value or a null value
     *        is associated with the key, to be associated with the key
     * @param remappingFunction the remapping function to recompute a value if
     *        present
     * @return the new value associated with the specified key, or null if no
     *         value is associated with the key
     * @throws UnsupportedOperationException if the {@code put} operation
     *         is not supported by this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws ClassCastException if the class of the specified key or value
     *         prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws IllegalArgumentException if some property of the specified key
     *         or value prevents it from being stored in this map
     *         (<a href="{@docRoot}/java.base/java/util/Collection.html#optional-restrictions">optional</a>)
     * @throws NullPointerException if the specified key is null and this map
     *         does not support null keys or the value or remappingFunction is
     *         null
     * @since 1.8
     */
    default @PolyNull V merge(K key, @NonNull V value,
            BiFunction<? super @NonNull V, ? super @NonNull V, ? extends @PolyNull V> remappingFunction) {
        Objects.requireNonNull(remappingFunction);
        Objects.requireNonNull(value);
        V oldValue = get(key);
        V newValue = (oldValue == null) ? value :
                   remappingFunction.apply(oldValue, value);
        if (newValue == null) {
            remove(key);
        } else {
            put(key, newValue);
        }
        return newValue;
    }

    /**
     * Returns an unmodifiable map containing zero mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @return an empty {@code Map}
     *
     * @since 9
     */
    @SuppressWarnings("unchecked")
    static <K, V> Map<K, V> of() {
        return (Map<K,V>) ImmutableCollections.EMPTY_MAP;
    }

    /**
     * Returns an unmodifiable map containing a single mapping.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the mapping's key
     * @param v1 the mapping's value
     * @return a {@code Map} containing the specified mapping
     * @throws NullPointerException if the key or the value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1) {
        return new ImmutableCollections.Map1<>(k1, v1);
    }

    /**
     * Returns an unmodifiable map containing two mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if the keys are duplicates
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2);
    }

    /**
     * Returns an unmodifiable map containing three mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3);
    }

    /**
     * Returns an unmodifiable map containing four mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4);
    }

    /**
     * Returns an unmodifiable map containing five mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @param k5 the fifth mapping's key
     * @param v5 the fifth mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4, K k5, V v5) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4, k5, v5);
    }

    /**
     * Returns an unmodifiable map containing six mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @param k5 the fifth mapping's key
     * @param v5 the fifth mapping's value
     * @param k6 the sixth mapping's key
     * @param v6 the sixth mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4, K k5, V v5,
                               K k6, V v6) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4, k5, v5,
                                               k6, v6);
    }

    /**
     * Returns an unmodifiable map containing seven mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @param k5 the fifth mapping's key
     * @param v5 the fifth mapping's value
     * @param k6 the sixth mapping's key
     * @param v6 the sixth mapping's value
     * @param k7 the seventh mapping's key
     * @param v7 the seventh mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4, K k5, V v5,
                               K k6, V v6, K k7, V v7) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4, k5, v5,
                                               k6, v6, k7, v7);
    }

    /**
     * Returns an unmodifiable map containing eight mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @param k5 the fifth mapping's key
     * @param v5 the fifth mapping's value
     * @param k6 the sixth mapping's key
     * @param v6 the sixth mapping's value
     * @param k7 the seventh mapping's key
     * @param v7 the seventh mapping's value
     * @param k8 the eighth mapping's key
     * @param v8 the eighth mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4, K k5, V v5,
                               K k6, V v6, K k7, V v7, K k8, V v8) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4, k5, v5,
                                               k6, v6, k7, v7, k8, v8);
    }

    /**
     * Returns an unmodifiable map containing nine mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @param k5 the fifth mapping's key
     * @param v5 the fifth mapping's value
     * @param k6 the sixth mapping's key
     * @param v6 the sixth mapping's value
     * @param k7 the seventh mapping's key
     * @param v7 the seventh mapping's value
     * @param k8 the eighth mapping's key
     * @param v8 the eighth mapping's value
     * @param k9 the ninth mapping's key
     * @param v9 the ninth mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4, K k5, V v5,
                               K k6, V v6, K k7, V v7, K k8, V v8, K k9, V v9) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4, k5, v5,
                                               k6, v6, k7, v7, k8, v8, k9, v9);
    }

    /**
     * Returns an unmodifiable map containing ten mappings.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param k1 the first mapping's key
     * @param v1 the first mapping's value
     * @param k2 the second mapping's key
     * @param v2 the second mapping's value
     * @param k3 the third mapping's key
     * @param v3 the third mapping's value
     * @param k4 the fourth mapping's key
     * @param v4 the fourth mapping's value
     * @param k5 the fifth mapping's key
     * @param v5 the fifth mapping's value
     * @param k6 the sixth mapping's key
     * @param v6 the sixth mapping's value
     * @param k7 the seventh mapping's key
     * @param v7 the seventh mapping's value
     * @param k8 the eighth mapping's key
     * @param v8 the eighth mapping's value
     * @param k9 the ninth mapping's key
     * @param v9 the ninth mapping's value
     * @param k10 the tenth mapping's key
     * @param v10 the tenth mapping's value
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any key or value is {@code null}
     *
     * @since 9
     */
    static <K extends Object, V extends Object> Map<K, V> of(K k1, V v1, K k2, V v2, K k3, V v3, K k4, V v4, K k5, V v5,
                               K k6, V v6, K k7, V v7, K k8, V v8, K k9, V v9, K k10, V v10) {
        return new ImmutableCollections.MapN<>(k1, v1, k2, v2, k3, v3, k4, v4, k5, v5,
                                               k6, v6, k7, v7, k8, v8, k9, v9, k10, v10);
    }

    /**
     * Returns an unmodifiable map containing keys and values extracted from the given entries.
     * The entries themselves are not stored in the map.
     * See <a href="#unmodifiable">Unmodifiable Maps</a> for details.
     *
     * @apiNote
     * It is convenient to create the map entries using the {@link Map#entry Map.entry()} method.
     * For example,
     *
     * <pre>{@code
     *     import static java.util.Map.entry;
     *
     *     Map<Integer,String> map = Map.ofEntries(
     *         entry(1, "a"),
     *         entry(2, "b"),
     *         entry(3, "c"),
     *         ...
     *         entry(26, "z"));
     * }</pre>
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param entries {@code Map.Entry}s containing the keys and values from which the map is populated
     * @return a {@code Map} containing the specified mappings
     * @throws IllegalArgumentException if there are any duplicate keys
     * @throws NullPointerException if any entry, key, or value is {@code null}, or if
     *         the {@code entries} array is {@code null}
     *
     * @see Map#entry Map.entry()
     * @since 9
     */
    @SafeVarargs
    @SuppressWarnings("varargs")
    static <K extends Object, V extends Object> Map<K, V> ofEntries(Entry<? extends K, ? extends V>... entries) {
        if (entries.length == 0) { // implicit null check of entries array
            @SuppressWarnings("unchecked")
            var map = (Map<K,V>) ImmutableCollections.EMPTY_MAP;
            return map;
        } else if (entries.length == 1) {
            // implicit null check of the array slot
            return new ImmutableCollections.Map1<>(entries[0].getKey(),
                    entries[0].getValue());
        } else {
            Object[] kva = new Object[entries.length << 1];
            int a = 0;
            for (Entry<? extends K, ? extends V> entry : entries) {
                // implicit null checks of each array slot
                kva[a++] = entry.getKey();
                kva[a++] = entry.getValue();
            }
            return new ImmutableCollections.MapN<>(kva);
        }
    }

    /**
     * Returns an unmodifiable {@link Entry} containing the given key and value.
     * These entries are suitable for populating {@code Map} instances using the
     * {@link Map#ofEntries Map.ofEntries()} method.
     * The {@code Entry} instances created by this method have the following characteristics:
     *
     * <ul>
     * <li>They disallow {@code null} keys and values. Attempts to create them using a {@code null}
     * key or value result in {@code NullPointerException}.
     * <li>They are unmodifiable. Calls to {@link Entry#setValue Entry.setValue()}
     * on a returned {@code Entry} result in {@code UnsupportedOperationException}.
     * <li>They are not serializable.
     * <li>They are <a href="../lang/doc-files/ValueBased.html">value-based</a>.
     * Programmers should treat instances that are {@linkplain #equals(Object) equal}
     * as interchangeable and should not use them for synchronization, or
     * unpredictable behavior may occur. For example, in a future release,
     * synchronization may fail. Callers should make no assumptions
     * about the identity of the returned instances. This method is free to
     * create new instances or reuse existing ones.
     * </ul>
     *
     * @apiNote
     * For a serializable {@code Entry}, see {@link AbstractMap.SimpleEntry} or
     * {@link AbstractMap.SimpleImmutableEntry}.
     *
     * @param <K> the key's type
     * @param <V> the value's type
     * @param k the key
     * @param v the value
     * @return an {@code Entry} containing the specified key and value
     * @throws NullPointerException if the key or value is {@code null}
     *
     * @see Map#ofEntries Map.ofEntries()
     * @since 9
     */
    static <K extends Object, V extends Object> Entry<K, V> entry(K k, V v) {
        // KeyValueHolder checks for nulls
        return new KeyValueHolder<>(k, v);
    }

    /**
     * Returns an <a href="#unmodifiable">unmodifiable Map</a> containing the entries
     * of the given Map. The given Map must not be null, and it must not contain any
     * null keys or values. If the given Map is subsequently modified, the returned
     * Map will not reflect such modifications.
     *
     * @implNote
     * If the given Map is an <a href="#unmodifiable">unmodifiable Map</a>,
     * calling copyOf will generally not create a copy.
     *
     * @param <K> the {@code Map}'s key type
     * @param <V> the {@code Map}'s value type
     * @param map a {@code Map} from which entries are drawn, must be non-null
     * @return a {@code Map} containing the entries of the given {@code Map}
     * @throws NullPointerException if map is null, or if it contains any null keys or values
     * @since 10
     */
    @SuppressWarnings({"rawtypes","unchecked"})
    static <K extends Object, V extends Object> Map<K, V> copyOf(Map<? extends K, ? extends V> map) {
        if (map instanceof ImmutableCollections.AbstractImmutableMap) {
            return (Map<K,V>)map;
        } else {
            return (Map<K,V>)Map.ofEntries(map.entrySet().toArray(new Entry[0]));
        }
    }
}