Monoid.java

package monoids;

public abstract class Monoid<T> {

        public abstract T combine(T one, T other);
        public abstract T identity();

        public T fold(Iterable<T> elements) {
                T result = identity();
                for (T i : elements) {
                        result = combine(result, i);
                }
                return result;
        }
}

NumberAddMonoid.java

package monoids;

import java.util.Arrays;
import java.util.List;

public class NumberAddMonoid extends Monoid<Integer>{
	
	@Override
	public Integer combine(Integer one, Integer other) {
		return one + other;
	}

	@Override
	public Integer identity() {
		return 0;
	}
	
	public static void main(String[] args) {
		NumberAddMonoid numMonoid = new NumberAddMonoid();
		Integer[] ints = new Integer[] {1, 2, 3, 4, 5};
		List<Integer> nums = Arrays.asList(ints);
		System.out.println(numMonoid.fold(nums));
	}
}

OptionalMonoid.java

package monoids;

import java.util.ArrayList;
import java.util.List;
import java.util.Optional;
import java.util.Random;

public class OptionalMonoid<T> extends Monoid<Optional<T>> {

	final Monoid<T> identity;
	
	public OptionalMonoid(Monoid<T> identity) {
		this.identity = identity;
	}
	
	@Override
	public Optional<T> combine(Optional<T> one, Optional<T> other) {
		if(one.isPresent() && other.isPresent()) 
			return Optional.of(identity.combine(one.get(), other.get()));
		else 
			return one.isPresent() ? one : other;			
	}

	@Override
	public Optional<T> identity() {
		return Optional.empty();
	}

	public static OptionalMonoid<Integer> intOptMonoid() {
		return new OptionalMonoid<>(new NumberAddMonoid());
	}
	
	public static void main(String[] args) {
		OptionalMonoid<Integer> optIntMonoid = OptionalMonoid.intOptMonoid();
		Random rand = new Random();
		List<Optional<Integer>> opts = new ArrayList<>();  
		for(int i=0; i<10; i++) {
			int randnumber = rand.nextInt(2);
			if(randnumber == 0)
				opts.add(Optional.ofNullable(10));
			else
				opts.add(Optional.ofNullable(null));
		}
		System.out.println(opts);
                System.out.println(optIntMonoid.fold(opts));

		//System.out.println(optIntMonoid.combine(Optional.ofNullable(12),  Optional.ofNullable(null)));
	}

}

OutputNumberAddMonoid.txt

15

OutputOptionalMonoidInt

[ Optional[10], 
  Optional[10], 
  Optional[10], 
  Optional[10], 
  Optional.empty, 
  Optional[10], 
  Optional[10], 
  Optional.empty, 
  Optional[10], 
  Optional[10] 
]

Optional[80]