java - In Stream reduce method, must the identity always be 0 for sum and 1 for multiplication?

Question

I proceed with java 8 learning.

I have found an interesting behavior:

let's see code sample:

// identity value and accumulator and combiner
Integer summaryAge = Person.getPersons().stream()
        //.parallel()  //will return surprising result
        .reduce(1,
                (intermediateResult, p) -> intermediateResult + p.age,
                (ir1, ir2) -> ir1 + ir2);
System.out.println(summaryAge);

and model class:

public class Person {

    String name;

    Integer age;
    ///...

    public static Collection<Person> getPersons() {
        List<Person> persons = new ArrayList<>();
        persons.add(new Person("Vasya", 12));
        persons.add(new Person("Petya", 32));
        persons.add(new Person("Serj", 10));
        persons.add(new Person("Onotole", 18));
        return persons;
   }
}

12+32+10+18 = 72. For sequential stream, this code always returns 73 which is 72 + 1 but for parallel, it always returns 76 which is 72 + 4*1 (4 is equal to stream elements count).

When I saw this result I thought that it is strange that parallel stream and sequential streams return different results.

Am I broke contract somewhere?

P.S.

for me, 73 is expected result but 76 is not.

Answer 1

The identity value is a value, such that x op identity = x. This is a concept which is not unique to Java Streams, see for example on Wikipedia.

It lists some examples of identity elements, some of them can be directly expressed in Java code, e.g.

• reduce("", String::concat)
• reduce(true, (a,b) -> a&&b)
• reduce(false, (a,b) -> a||b)
• reduce(Collections.emptySet(), (a,b)->{ Set<X> s=new HashSet<>(a); s.addAll(b); return s; })
• reduce(Double.POSITIVE_INFINITY, Math::min)
• reduce(Double.NEGATIVE_INFINITY, Math::max)

It should be clear that the expression x + y == x for arbitrary x can only be fulfilled when y==0, thus 0 is the identity element for the addition. Similarly, 1 is the identity element for the multiplication.

More complex examples are

• Reducing a stream of predicates

  reduce(x->true, Predicate::and)
  reduce(x->false, Predicate::or)
  

• Reducing a stream of functions

  reduce(Function.identity(), Function::andThen)