fold map

MonoidsFold.java

import java.util.Arrays;
import java.util.function.BiFunction;
import java.util.function.Function;

class Scratch {
    public static void main(String[] args) {
        Monoid<Integer> sum = Monoid.of(0, Integer::sum);
        Fold<String, Integer> sumStrings = Fold.of(Integer::parseInt, sum);
        Integer result = sumStrings.fold(Arrays.asList("1", "2", "3"));
        System.out.println(result);
    }

    interface Monoid<A> {
        A zero();

        A add(A a1, A a2);

        static <A> Monoid<A> of(A zero, BiFunction<A, A, A> add) {
            return new Monoid<A>() {
                @Override public A zero() {
                    return zero;
                }

                @Override public A add(A a1, A a2) {
                    return add.apply(a1, a2);
                }
            };
        }
    }

    interface Fold<A, B> {
        Function<A, B> toMonoid();

        Monoid<B> monoid();

        default B fold(Iterable<A> as) {
            B result = monoid().zero();
            for (A a : as) {
                result = monoid().add(result, toMonoid().apply(a));
            }
            return result;
        }

        static <A, B> Fold<A, B> of(Function<A, B> toMonoid, Monoid<B> monoid) {
            return new Fold<A, B>() {
                @Override public Function<A, B> toMonoid() {
                    return toMonoid;
                }

                @Override public Monoid<B> monoid() {
                    return monoid;
                }
            };
        }
    }
}