java11-category-theory-set-coproduct

Reference: https://bartoszmilewski.com/2015/01/07/products-and-coproducts/
Reference: https://www.amazon.com/Category-Theory-Oxford-Logic-Guides/dp/0199237182
Reference: https://en.wikiversity.org/wiki/Introduction_to_Category_Theory/Products_and_Coproducts

definition

For product please refer my other github project: https://github.com/mtumilowicz/java11-category-theory-set-product

The coproduct of objects A and B is an object P together with morphisms (injections):

• i1 :: A -> P
• i2 :: B -> P that satisfy the following property:
• If X is any object in the category, and f1 :: A -> X and f2 :: B -> X are any morphisms, then there exists a unique morphism g :: X -> P such that:
• f1 = g . i1
• f2 = g . i2

disjoint union of sets is a coproduct in the Set category

Reference: https://en.wikipedia.org/wiki/Disjoint_union

let A + B := {(a, 1) | a e A} u {(b, 2) | b e B} be the coproduct with injections:

• i1(a) = (a, 1)
• i2(b) = (b, 2)

if there is other object X with injections f1 and f2 we define

g(x, delta) = f(x) if delta = 1 or g(x) if delta = 2

then

• g . i1 = f1
• g . i2 = f2

project description

We provide basic implementation of Either + tests:

public interface Either<L, R> {

    static <L, R> Either<L, R> right(R right) {
        return new Right<>(right);
    }

    static <L, R> Either<L, R> left(L left) {
        return new Left<>(left);
    }

    L getLeft();

    boolean isLeft();

    boolean isRight();

    R getRight();

    final class Left<L, R> implements Either<L, R> {

        private final L value;

        private Left(L value) {
            this.value = value;
        }

        @Override
        public R getRight() {
            throw new NoSuchElementException();
        }

        @Override
        public L getLeft() {
            return value;
        }

        @Override
        public boolean isLeft() {
            return true;
        }

        @Override
        public boolean isRight() {
            return false;
        }

        @Override
        public boolean equals(Object obj) {
            return (obj == this) || (obj instanceof Left && Objects.equals(value, ((Left) obj).value));
        }

        @Override
        public int hashCode() {
            return Objects.hashCode(value);
        }

        @Override
        public String toString() {
            return "Left" + "(" + value + ")";
        }
    }

    final class Right<L, R> implements Either<L, R> {

        private final R value;

        private Right(R value) {
            this.value = value;
        }

        @Override
        public R getRight() {
            return value;
        }

        @Override
        public L getLeft() {
            throw new NoSuchElementException();
        }

        @Override
        public boolean isLeft() {
            return false;
        }

        @Override
        public boolean isRight() {
            return true;
        }

        @Override
        public boolean equals(Object obj) {
            return (obj == this) || (obj instanceof Right && Objects.equals(value, ((Right) obj).value));
        }

        @Override
        public int hashCode() {
            return Objects.hashCode(value);
        }

        @Override
        public String toString() {
            return "Right" + "(" + value + ")";
        }
    }
}

full implementation could be found in VAVR: https://github.com/vavr-io/vavr/blob/master/vavr/src/main/java/io/vavr/control/Either.java