SlangFizzBuzz.java

package fizzbuzz;

import javaslang.collection.Stream;
import javaslang.control.Option;

import static javaslang.control.Option.none;
import static javaslang.control.Option.some;

public class SlangFizzBuzz {
    public static void main(String[] args) {
        Stream<String>         nums    = Stream.from(1).map(Object::toString);
        Stream<Option<String>> fizz    = Stream.<Option<String>>of(none(), none(), some("Fizz")).cycle();
        Stream<Option<String>> buzz    = Stream.<Option<String>>of(none(), none(), none(), none(), some("Buzz")).cycle();
        Stream<Option<String>> pattern = fizz.zip(buzz).map(t -> t._1.flatMap(s -> t._2.map(s2 -> s + s2).orElse(t._1)).orElse(t._2));

        Stream<String> fizzbuzz        = pattern.zip(nums).map(t -> t._1.getOrElse(t._2));

        fizzbuzz.take(15).forEach(System.out::println);
    }
}

SlangFizzBuzzWithHelper.java

package fizzbuzz;

import javaslang.Tuple2;
import javaslang.collection.Stream;
import javaslang.control.Option;

import java.util.function.BinaryOperator;

import static javaslang.control.Option.none;
import static javaslang.control.Option.some;

public class SlangFizzBuzzWithHelper {
    public static void main(String[] args) {
        Stream<String>         nums    = Stream.from(1).map(Object::toString);
        Stream<Option<String>> fizz    = Stream.<Option<String>>of(none(), none(), some("Fizz")).cycle();
        Stream<Option<String>> buzz    = Stream.<Option<String>>of(none(), none(), none(), none(), some("Buzz")).cycle();
        Stream<Option<String>> pattern = fizz.zip(buzz).map(t -> eitherNeitherOrBoth(t, (a, b) -> a + b));

        Stream<String> fizzbuzz        = pattern.zip(nums).map(t -> t._1.getOrElse(t._2));

        fizzbuzz.take(15).forEach(System.out::println);
    }

    private static <T> Option<T> eitherNeitherOrBoth(Tuple2<Option<T>,Option<T>> tuple, BinaryOperator<T> combiner) {
        return tuple._1.flatMap(left -> tuple._2.map(right -> combiner.apply(left, right)).orElse(tuple._1)).orElse(tuple._2);
    }
}