Working with streams - Java 8 in Action: Lambdas, Streams, and Functional-Style Programming - page 128

So far you saw reduction examples that produced an Integer: the sum of a stream, the maximum
of a stream, or the number of elements in a stream. You'll see in section 5.6 that built-in
methods such as sum and max are available as well to help you write slightly more concise code
for common reduction patterns. We investigate a more complex form of reductions using the
collect method in the next chapter. For example, instead of reducing a stream into an Integer,
you can also reduce it into a Map if you want to group dishes by types.
Stream operations: stateless vs. stateful
You've seen a lot of stream operations. An initial presentation can make them seem a panacea;
everything just works, and you get parallelism for free when you use parallelStream instead of
stream to get a stream from a collection.
Certainly for many applications this is the case, as you've seen in the previous examples. You can
turn a list of dishes into a stream, filter to select various dishes of a certain type, then map down
the resulting stream to add on the number of calories, and then reduce to produce the total
number of calories of the menu. You can even do such stream calculations in parallel. But these
operations have different characteristics. There are issues about what internal state they need to
operate.
Operations like map and filter take each element from the input stream and produce zero or one
result in the output stream. These operations are thus in general stateless : they don't have an
internal state (assuming the user-supplied lambda or method reference has no internal mutable
state).
But operations like reduce, sum, and max need to have internal state to accumulate the result.
In this case the internal state is small. In our example it consisted of an int or double. The
internal state is of bounded size no matter how many elements are in the stream being
processed.
By contrast, some operations such as sorted or distinct seem at first to behave like filter or
map—all take a stream and produce another stream (an intermediate operation), but there's a
crucial difference. Both sorting and removing duplicates from a stream require knowing the
previous history to do their job. For example, sorting requires all the elements to be buffered
before a single item can be added to the output stream; the storage requirement of the operation
is unbounded . This can be problematic if the data stream is large or infinite. (What should
reversing the stream of all prime numbers do? It should return the largest prime number, which
mathematics tells us doesn't exist.) We call these operations stateful operations .