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
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 -> Pi2 :: B -> Pthat satisfy the following property:- If
Xis any object in the category, andf1 :: A -> Xandf2 :: B -> Xare any morphisms, then there exists a unique morphismg :: X -> Psuch that: f1 = g . i1f2 = g . i2
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 = f1g . i2 = f2
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