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shoki's Introduction

Shōki (正気)

Build Status Shōki Shōki

Purely functional, persistent data structures for the JVM.

Table of Contents

Background

Shōki is a library offering purely functional, persistent data structures for the JVM.

So why another data structures library? Because writing correct code is hard, and it's especially hard if your data structures consistently advertise false interfaces. The data structures provided by Shōki are built on top of interfaces that promote type-checker participation by leveraging rich types, and encourage correct-by-construction software with obvious usage semantics.

Standard usage of Shōki interfaces should never throw: there are no IndexOutOfBoundsExceptions that result from seemingly innocuous get calls; no UnsupportedOperationExceptions because the interface you're presented with is an absolute fiction, and somewhere under the covers is an immutable collection masquerading as a mutable one; no ClassCastExceptions because a data structure that fundamentally only works in the presence of comparability fails to enforce this essential constraint at compile time. Any of these things happening is considered an error in Shōki, not in user code.

The constraints of the inputs and the outputs are also richly specified via their type signatures. If a lookup cannot be guaranteed to yield a value, it will return a Maybe rather than null so the type-checker can remind you that you may not have received what you wanted. If a value fundamentally cannot be zero, it will very likely be represented by a type that does not even include a "zero" term, so you don't waste mental energy writing code to handle impossible scenarios. If the total size of a collection can logically exceed Integer.MAX_VALUE, its sizeInfo will advertise a type that can realistically represent its size instead of one that might represent a negative value due to overflow.

The target audience for Shōki considers these characteristics not to be fine luxuries, but rather basic quality-of-life essentials. If you think your time is too valuable to be spent staring at four methods with four identical type signatures, trying to remember whether peek or poll throws or returns null, or element or remove alters its underlying structure or doesn't; then you're in good company. Welcome!

Installation

Shōki alpha releases are currently available in Maven Central. These alpha releases are meant to be of high enough quality as to be reliable in a production environment, while still allowing significant API changes to occur before a 1.0 release.

Add the following dependency to your:

pom.xml (Maven):

<dependency>
    <groupId>com.jnape.palatable</groupId>
    <artifactId>shoki</artifactId>
    <version>1.0-alpha-2</version>
</dependency>

build.gradle (Gradle):

compile group: 'com.jnape.palatable', name: 'shoki', version: '1.0-alpha-2'

Hierarchy

One of the core design tenants of Shōki's API is that a data structure is modeled as the incremental composition of its orthogonal capabilities and constraints.

Top-level orthogonal building blocks

  • Sequence<A>: an Iterable<A> interface that offers the methods Maybe<A> head() and Sequence<A> tail()
  • SizeInfo: a coproduct of Unknown or Known<N extends Number>, where Known<N> offers a method N getSize()
  • Sizable: an interface that offers a method SizeInfo sizeInfo()
  • Membership<A>: an interface that offers a membership test method boolean contains(A)
  • RandomAccess<Index, V>: Membership<Index> with an additional lookup method V get(Index)
  • Natural: a Number sum type of Zero or NonZero that never overflows and offers basic type-safe arithmetic

Refined data structure interfaces

  • Collection<Size extends Number, A>: a Sequence<A> that supports SizeInfo yielding a Known<Size>
  • OrderedCollection<Size extends Number, A>: a Collection<Size, A> that offers a reverse() method
  • SortedCollection<Size extends Number, A, Ordering>: an OrderedCollection<Size, A> that offers Maybe<A> min(), Maybe<A> max, and SortedCollection<Size, A, Ordering> sort(Comparator<? super Ordering> comparator) methods
  • Stack<Size extends Number, A>: an OrderedCollection<Size, A> with a method Stack<Size, A> cons(A) that adds an element to the top of the Stack<Size, A>
  • Queue<Size extends Number, A>: an OrderedCollection<Size, A> with a method Queue<Size, A> snoc(A) that adds an element to the bottom of the Queue<Size, A>
  • Set<Size extends Number, A>: a Collection<Size, A> that supports Membership<A>
  • MultiSet<A>: a Collection<Natural, A> of Tuple2<A, Natural.NonZero> that supports RandomAccess<A, Natural>
  • Map<Size extends Number, K, V>: a Collection<Size, Tuple2<K, V>> that supports RandomAccess<K, Maybe<V>>

Shōki is still very much in alpha development, so these specific interfaces are subject to change, but they should at least offer an intuition about the way in which the design is being approached.

Implementations

StrictStack<A>

A StrictStack<A> is a strictly-evaluated Stack<Natural, A> that offers worst-case O(1) space/time for cons, head, and tail.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.shoki.impl.StrictStack;

import static com.jnape.palatable.shoki.impl.StrictStack.strictStack;

public class Example {

    public static void main(String[] args) {
        StrictStack<String> empty     = strictStack();
        boolean             _true     = empty.isEmpty();
        Maybe<String>       nothing   = empty.head();
        StrictStack<String> alsoEmpty = empty.tail();

        StrictStack<String> fooBarBaz = empty.cons("baz").cons("bar").cons("foo");
        boolean             _false    = fooBarBaz.isEmpty();
        Maybe<String>       justFoo   = fooBarBaz.head();

        StrictStack<String> barBaz  = fooBarBaz.tail();
        Maybe<String>       justBar = barBaz.head();

        StrictStack<String> baz     = barBaz.tail();
        Maybe<String>       justBaz = baz.head();

        StrictStack<String> bazBarFooBaz = baz.consAll(fooBarBaz);
        boolean             __true       = bazBarFooBaz.equals(strictStack("baz", "bar", "foo", "baz"));
    }
}

StrictQueue<A>

A StrictQueue<A> is a strictly-evaluated Queue<Natural, A> and Stack<Natural, A> that offers worst-case O(1) space/time for cons, snoc, and head, and amortized O(1) for tail.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.shoki.impl.StrictQueue;

import static com.jnape.palatable.shoki.impl.StrictQueue.strictQueue;

public class Example {

    public static void main(String[] args) {
        StrictQueue<String> empty     = strictQueue();
        boolean             _true     = empty.isEmpty();
        Maybe<String>       nothing   = empty.head();
        StrictQueue<String> alsoEmpty = empty.tail();

        StrictQueue<String> fooBarBaz     = empty.snoc("foo").snoc("bar").snoc("baz");
        boolean             _false        = fooBarBaz.isEmpty();
        Maybe<String>       justFoo       = fooBarBaz.head();
        StrictQueue<String> alsoFooBarBaz = empty.cons("baz").cons("bar").cons("foo");

        StrictQueue<String> barBaz  = fooBarBaz.tail();
        Maybe<String>       justBar = barBaz.head();

        StrictQueue<String> baz     = barBaz.tail();
        Maybe<String>       justBaz = baz.head();

        StrictQueue<String> bazFooBarBaz = baz.snocAll(fooBarBaz);
        StrictQueue<String> bazBarFooBaz = baz.consAll(fooBarBaz);
        boolean             __true       = bazFooBarBaz.equals(strictQueue("baz", "foo", "bar", "baz"));
    }
}

HashMap<K, V>

A HashMap<K, V> is an ideal hash tree implementation of a Map<Natural, K, V> that offers amortized O(1) space/time for get, put, remove, and contains, and supports custom EquivalenceRelation<K>s and HashingAlgorithm<K>s.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.lambda.adt.hlist.Tuple2;
import com.jnape.palatable.shoki.impl.HashMap;
import com.jnape.palatable.shoki.impl.HashSet;
import com.jnape.palatable.shoki.impl.StrictQueue;

import static com.jnape.palatable.shoki.api.EquivalenceRelation.objectEquals;
import static com.jnape.palatable.shoki.api.HashingAlgorithm.objectHashCode;
import static com.jnape.palatable.shoki.impl.HashMap.hashMap;

public class Example {

    public static void main(String[] args) {
        // same as hashMap()
        HashMap<Integer, String> empty = hashMap(objectEquals(), objectHashCode());

        boolean                        _true     = empty.isEmpty();
        Maybe<Tuple2<Integer, String>> nothing   = empty.head();
        HashMap<Integer, String>       alsoEmpty = empty.tail();

        HashMap<Integer, String>       fooBarBaz     = empty.put(0, "foo").put(1, "bar").put(2, "baz");
        boolean                        _false        = fooBarBaz.isEmpty();
        Maybe<Tuple2<Integer, String>> just0Foo      = fooBarBaz.head();
        HashMap<Integer, String>       alsoFooBarBaz = empty.put(2, "baz").put(1, "bar").put(0, "foo");
        boolean                        __true        = fooBarBaz.contains(0);
        boolean                        __false       = fooBarBaz.contains(-1);

        // This HashSet uses the same EquivalenceRelation and HashingAlgorithm
        HashSet<Integer> keys = fooBarBaz.keys(); // HashSet[0, 1, 2]

        StrictQueue<String> values = fooBarBaz.values(); // StrictQueue["foo", "bar", "baz"]

        HashMap<Integer, String>       barBaz   = fooBarBaz.tail();
        Maybe<Tuple2<Integer, String>> just1Bar = barBaz.head();

        HashMap<Integer, String>       baz      = barBaz.tail();
        Maybe<Tuple2<Integer, String>> just2Baz = baz.head();

        // HashMap[(2=bazbaz)]
        HashMap<Integer, String> _2bazbaz = baz.merge(baz, (s1, s2) -> s1 + s2);
    }
}

HashSet<A>

A HashSet<A> is a Set<Natural, A> that is backed by a HashMap<A, Unit> and offers similar space/time complexities. Like HashMap, a HashSet supports custom EquivalenceRelation<K>s and HashingAlgorithm<K>s.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.shoki.impl.HashSet;

import static com.jnape.palatable.shoki.api.EquivalenceRelation.objectEquals;
import static com.jnape.palatable.shoki.api.HashingAlgorithm.objectHashCode;
import static com.jnape.palatable.shoki.impl.HashSet.hashSet;

public class Example {

    public static void main(String[] args) {
        // same as hashSet()
        HashSet<Integer> empty = hashSet(objectEquals(), objectHashCode());

        boolean          _true     = empty.isEmpty();
        Maybe<Integer>   nothing   = empty.head();
        HashSet<Integer> alsoEmpty = empty.tail();

        HashSet<Integer> _012    = empty.add(0).add(1).add(2);
        boolean          _false  = _012.isEmpty();
        Maybe<Integer>   just0   = _012.head();
        HashSet<Integer> also012 = empty.add(2).add(1).add(0);
        boolean          __true  = _012.contains(0);
        boolean          __false = _012.contains(-1);

        HashSet<Integer> _12   = _012.tail();
        Maybe<Integer>   just1 = _12.head();

        HashSet<Integer> _2    = _12.tail();
        Maybe<Integer>   just2 = _2.head();

        HashSet<Integer> _01234 = _012.union(hashSet(2, 3, 4));
        HashSet<Integer> _01    = _012.difference(hashSet(2, 3, 4));
        HashSet<Integer> _0134  = _012.symmetricDifference(hashSet(2, 3, 4));
        HashSet<Integer> __2    = _012.intersection(hashSet(2, 3, 4));
    }
}

HashMultiSet<A>

A HashMultiSet<A> is a MultiSet<A> that is backed by a HashMap<A, Natural.NonZero> and offers similar space/time complexities. Like HashMap, a HashMultiSet supports custom EquivalenceRelation<K>s and HashingAlgorithm<K>s.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.lambda.adt.hlist.Tuple2;
import com.jnape.palatable.shoki.api.Natural;
import com.jnape.palatable.shoki.api.Natural.NonZero;
import com.jnape.palatable.shoki.impl.HashMultiSet;
import com.jnape.palatable.shoki.impl.HashSet;

import static com.jnape.palatable.shoki.api.EquivalenceRelation.objectEquals;
import static com.jnape.palatable.shoki.api.HashingAlgorithm.objectHashCode;
import static com.jnape.palatable.shoki.impl.HashMultiSet.hashMultiSet;

public class Example {

    public static void main(String[] args) {
        // same as hashMultiSet()
        HashMultiSet<Integer> empty = hashMultiSet(objectEquals(), objectHashCode());

        boolean                         _true     = empty.isEmpty();
        Maybe<Tuple2<Integer, NonZero>> nothing   = empty.head();
        HashMultiSet<Integer>           alsoEmpty = empty.tail();

        HashMultiSet<Integer>           _0x1_1x2_2x1     = empty.inc(0).inc(1).inc(2).inc(1);
        boolean                         _false           = _0x1_1x2_2x1.isEmpty();
        Maybe<Tuple2<Integer, NonZero>> just0x1          = _0x1_1x2_2x1.head();
        HashMultiSet<Integer>           also_0x1_1x2_2x1 = empty.inc(1).inc(2).inc(1).inc(0);
        boolean                         __true           = _0x1_1x2_2x1.contains(0);
        boolean                         __false          = _0x1_1x2_2x1.contains(-1);

        Natural one = _0x1_1x2_2x1.get(0);
        Natural two = _0x1_1x2_2x1.get(1);

        HashMultiSet<Integer>           _1x2_2x1 = _0x1_1x2_2x1.tail();
        Maybe<Tuple2<Integer, NonZero>> just_1x2 = _1x2_2x1.head();

        HashMultiSet<Integer>           _2x1     = _1x2_2x1.tail();
        Maybe<Tuple2<Integer, NonZero>> just_2x1 = _2x1.head();

        HashMultiSet<Integer> _2x1_3x1_4x1         = hashMultiSet(2, 3, 4);
        HashMultiSet<Integer> _0x1_1x2_2x1_3x1_4x1 = _0x1_1x2_2x1.union(_2x1_3x1_4x1);
        HashMultiSet<Integer> _0x1_1x2             = _0x1_1x2_2x1.difference(_2x1_3x1_4x1);
        HashMultiSet<Integer> _0x1_1x2_3x1_4x1     = _0x1_1x2_2x1.symmetricDifference(_2x1_3x1_4x1);
        HashMultiSet<Integer> __2x1                = _0x1_1x2_2x1.intersection(_2x1_3x1_4x1);
        HashMultiSet<Integer> _0x1_1x2_2x2_3x1_4x1 = _0x1_1x2_2x1.sum(_2x1_3x1_4x1);

        HashSet<Integer> _012 = _0x1_1x2_2x1.unique();
    }
}

TreeMap<K, V>

A TreeMap<K, V> is a red-black tree implementation of a Map<Natural, K, V> that is also a SortedCollection<Natural, Tuple2<K, V>, K> offering amortized O(log(n)) space/time for get, put, remove, and contains, and supports custom Comparator<K>s.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.lambda.adt.hlist.Tuple2;
import com.jnape.palatable.shoki.impl.StrictQueue;
import com.jnape.palatable.shoki.impl.TreeMap;
import com.jnape.palatable.shoki.impl.TreeSet;

import static com.jnape.palatable.shoki.impl.TreeMap.treeMap;
import static java.util.Comparator.naturalOrder;

public class Example {

    public static void main(String[] args) {
        // same as treeMap()
        TreeMap<Integer, String> empty = treeMap(naturalOrder());

        boolean                        _true     = empty.isEmpty();
        Maybe<Tuple2<Integer, String>> nothing   = empty.head();
        TreeMap<Integer, String>       alsoEmpty = empty.tail();

        TreeMap<Integer, String>       fooBarBaz     = empty.put(0, "foo").put(1, "bar").put(2, "baz");
        boolean                        _false        = fooBarBaz.isEmpty();
        Maybe<Tuple2<Integer, String>> just0Foo      = fooBarBaz.head();
        Maybe<Tuple2<Integer, String>> alsoJust0Foo  = fooBarBaz.min();
        Maybe<Tuple2<Integer, String>> just2Baz      = fooBarBaz.max();
        TreeMap<Integer, String>       alsoFooBarBaz = empty.put(2, "baz").put(1, "bar").put(0, "foo");
        boolean                        __true        = fooBarBaz.contains(0);
        boolean                        __false       = fooBarBaz.contains(-1);

        // This TreeSet uses the same Comparator
        TreeSet<Integer> keys = fooBarBaz.keys(); // TreeSet[0, 1, 2]

        StrictQueue<String> values = fooBarBaz.values(); // StrictQueue["foo", "bar", "baz"]

        TreeMap<Integer, String>       barBaz   = fooBarBaz.tail();
        Maybe<Tuple2<Integer, String>> just1Bar = barBaz.head();

        TreeMap<Integer, String>       baz          = barBaz.tail();
        Maybe<Tuple2<Integer, String>> alsoJust2Baz = baz.head();

        // TreeMap[(2=bazbaz)]
        TreeMap<Integer, String> _2bazbaz = baz.merge(baz, (s1, s2) -> s1 + s2);
    }
}

TreeSet<A>

A TreeSet<A> is a Set<Natural, A> that is also a SortedCollection<Natural, A> and is backed by a TreeMap<A, Unit>, offering similar space/time complexities. Like TreeMap, a TreeSet supports custom Comparator<K>s.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.shoki.impl.TreeSet;

import static com.jnape.palatable.shoki.impl.TreeSet.treeSet;
import static java.util.Comparator.naturalOrder;

public class Example {

    public static void main(String[] args) {
        // same as treeSet()
        TreeSet<Integer> empty = treeSet(naturalOrder());

        boolean          _true     = empty.isEmpty();
        Maybe<Integer>   nothing   = empty.head();
        TreeSet<Integer> alsoEmpty = empty.tail();

        TreeSet<Integer> _012      = empty.add(0).add(1).add(2);
        boolean          _false    = _012.isEmpty();
        Maybe<Integer>   just0     = _012.head();
        Maybe<Integer>   alsoJust0 = _012.min();
        Maybe<Integer>   just2     = _012.max();
        TreeSet<Integer> also012   = empty.add(2).add(1).add(0);
        boolean          __true    = _012.contains(0);
        boolean          __false   = _012.contains(-1);

        TreeSet<Integer> _12   = _012.tail();
        Maybe<Integer>   just1 = _12.head();

        TreeSet<Integer> _2        = _12.tail();
        Maybe<Integer>   alsoJust2 = _2.head();

        TreeSet<Integer> _01234 = _012.union(treeSet(2, 3, 4));
        TreeSet<Integer> _01    = _012.difference(treeSet(2, 3, 4));
        TreeSet<Integer> _0134  = _012.symmetricDifference(treeSet(2, 3, 4));
        TreeSet<Integer> __2    = _012.intersection(treeSet(2, 3, 4));
    }
}

TreeMultiSet<A>

A TreeMultiSet<A> is a MultiSet<A> that is also a SortedCollection<Natural, Tuple2<A, NonZero>, A>, and is backed by a TreeMap<A, Natural.NonZero>, offering similar space/time complexities. Like TreeMap, a TreeMultiSet supports custom Comparator<K>s.

import com.jnape.palatable.lambda.adt.Maybe;
import com.jnape.palatable.lambda.adt.hlist.Tuple2;
import com.jnape.palatable.shoki.api.Natural;
import com.jnape.palatable.shoki.api.Natural.NonZero;
import com.jnape.palatable.shoki.impl.TreeMultiSet;
import com.jnape.palatable.shoki.impl.TreeSet;

import static com.jnape.palatable.shoki.impl.TreeMultiSet.treeMultiSet;
import static java.util.Comparator.naturalOrder;

public class Example {

    public static void main(String[] args) {
        // same as treeMultiSet()
        TreeMultiSet<Integer> empty = treeMultiSet(naturalOrder());

        boolean                         _true     = empty.isEmpty();
        Maybe<Tuple2<Integer, NonZero>> nothing   = empty.head();
        TreeMultiSet<Integer>           alsoEmpty = empty.tail();

        TreeMultiSet<Integer>           _0x1_1x2_2x1     = empty.inc(0).inc(1).inc(2).inc(1);
        boolean                         _false           = _0x1_1x2_2x1.isEmpty();
        Maybe<Tuple2<Integer, NonZero>> just0x1          = _0x1_1x2_2x1.head();
        Maybe<Tuple2<Integer, NonZero>> alsoJust0x1      = _0x1_1x2_2x1.min();
        Maybe<Tuple2<Integer, NonZero>> just2x1          = _0x1_1x2_2x1.max();
        TreeMultiSet<Integer>           also_0x1_1x2_2x1 = empty.inc(1).inc(2).inc(1).inc(0);
        boolean                         __true           = _0x1_1x2_2x1.contains(0);
        boolean                         __false          = _0x1_1x2_2x1.contains(-1);

        Natural one = _0x1_1x2_2x1.get(0);
        Natural two = _0x1_1x2_2x1.get(1);

        TreeMultiSet<Integer>           _1x2_2x1 = _0x1_1x2_2x1.tail();
        Maybe<Tuple2<Integer, NonZero>> just_1x2 = _1x2_2x1.head();

        TreeMultiSet<Integer>           _2x1     = _1x2_2x1.tail();
        Maybe<Tuple2<Integer, NonZero>> just_2x1 = _2x1.head();

        TreeMultiSet<Integer> _2x1_3x1_4x1         = treeMultiSet(2, 3, 4);
        TreeMultiSet<Integer> _0x1_1x2_2x1_3x1_4x1 = _0x1_1x2_2x1.union(_2x1_3x1_4x1);
        TreeMultiSet<Integer> _0x1_1x2             = _0x1_1x2_2x1.difference(_2x1_3x1_4x1);
        TreeMultiSet<Integer> _0x1_1x2_3x1_4x1     = _0x1_1x2_2x1.symmetricDifference(_2x1_3x1_4x1);
        TreeMultiSet<Integer> __2x1                = _0x1_1x2_2x1.intersection(_2x1_3x1_4x1);
        TreeMultiSet<Integer> _0x1_1x2_2x2_3x1_4x1 = _0x1_1x2_2x1.sum(_2x1_3x1_4x1);

        TreeSet<Integer> _012 = _0x1_1x2_2x1.unique();
    }
}

License

shōki is part of palatable, which is distributed under The MIT License.

shoki's People

Contributors

7h3kk1d avatar jnape avatar

Stargazers

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Watchers

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Forkers

andyglick sn-donbenjamin nomicflux daviddking 7h3kk1d kschuetz smagill dhaase corwintanner anlon-burke pdiaze

shoki's Issues

Heaps

min/max heaps seem like a reasonable next addition. Okasaki's binomial heap should translate nicely.

SortedCollection slices

SortedCollections should offer slice methods that rely on poset inequalities (e.g. java.util.NavigableMap#headMap/tailMap)

Shoki smart constructors support element type widening

Since shoki data structures are immutable, this should type-check:

interface Animal {}
class Dog implements Animal {}
class Cat implements Animal {}

StrictStack<Animal> animals = Shoki.strictStack(StrictStack.<Dog>strictStack());

...and perform no additional allocations.

Memoizable, computable sizes / hash codes

Computing the size and the hash code adds significant constant overhead for methods like StrictStack#cons, whereas if the size and hash code were computations that could be memoized, they would be amortized O(1) and have a negligible time cost on these hot path operations.

Shoki optics

Maybe as a separate library, but they're needed

LazyList

LazyLists, lists with lazy, memoized tail's, are generally useful and specifically useful as the backbone for RTDs.

sizes can still overflow

StrictStack#sizeInfo, for example, calls abs(size(this)); size returns long. This has to use an adder that auto-widens the numeric type; probably BigInteger to be safe.

StrictStack / StrictQueue sizeInfo time/space complexity

Currently both StrictStack and StrictQueue use an amortized O(1) time cost and O(1) space cost for their sizes. If StrictStack could gain an O(1) time/space complexity, and if StrictQueue delegated to StrictStack, it would achieve the same complexity. This should be doable with a single additional wrapper node in StrictStack that was carried the size along with the spine.

Safe, array-backed RandomAccess Sequence

An array-backed immutable sequence would natively support random access Natural -> Maybe a and would be very fast indeed, provided it could be made safe such that the array was fully encapsulated by the data type. This would mean that no public construction patterns should allow wrapping of an array: arrays should be fully existentialized behind a series of exported minimal interactions. As an example:

public static Vector<A> create(Consumer<Consumer<A>> withAdd) {
    // ...
}

This interface would receive a Consumer that would itself receive a Consumer representing an add invocation, so a valid argument might do something like:

Vector<Integer> ints = create(add -> {
    add.accept(1);
    add.accept(2);
    add.accept(3);
});

Each add would result in the internal array being updated, and after withAdd was finished, some flag would be flipped to specify the array is no longer candidate for update, so if someone did something accidental and caustic, like leaked add into an atomic reference, add could not be used after initialization to violate the immutable properties of the Vector.

This data type would likely be eventually supplanted by a BAMT, so it may or may not be worth adding in the short term.

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