Java 8 stream's .min() and .max(): why does this compile?

Let me explain what is happening here, because it isn't obvious!

First, Stream.max() accepts an instance of Comparator so that items in the stream can be compared against each other to find the minimum or maximum, in some optimal order that you don't need to worry too much about.

So the question is, of course, why is Integer::max accepted? After all it's not a comparator!

The answer is in the way that the new lambda functionality works in Java 8. It relies on a concept which is informally known as "single abstract method" interfaces, or "SAM" interfaces. The idea is that any interface with one abstract method can be automatically implemented by any lambda - or method reference - whose method signature is a match for the one method on the interface. So examining the Comparator interface (simple version):

public Comparator<T> {
    T compare(T o1, T o2);
}

If a method is looking for a Comparator<Integer>, then it's essentially looking for this signature:

int xxx(Integer o1, Integer o2);

I use "xxx" because the method name is not used for matching purposes.

Therefore, both Integer.min(int a, int b) and Integer.max(int a, int b) are close enough that autoboxing will allow this to appear as a Comparator<Integer> in a method context.

Comparator is a functional interface, and Integer::max complies with that interface (after autoboxing/unboxing is taken into consideration). It takes two int values and returns an int - just as you'd expect a Comparator<Integer> to (again, squinting to ignore the Integer/int difference).

However, I wouldn't expect it to do the right thing, given that Integer.max doesn't comply with the semantics of Comparator.compare. And indeed it doesn't really work in general. For example, make one small change:

for (int i = 1; i <= 20; i++)
    list.add(-i);

... and now the max value is -20 and the min value is -1.

Instead, both calls should use Integer::compare:

System.out.println(list.stream().max(Integer::compare).get());
System.out.println(list.stream().min(Integer::compare).get());

This works because Integer::min resolves to an implementation of the Comparator<Integer> interface.

The method reference of Integer::min resolves to Integer.min(int a, int b), resolved to IntBinaryOperator, and presumably autoboxing occurs somewhere making it a BinaryOperator<Integer>.

And the min() resp max() methods of the Stream<Integer> ask the Comparator<Integer> interface to be implemented.
Now this resolves to the single method Integer compareTo(Integer o1, Integer o2). Which is of type BinaryOperator<Integer>.

And thus the magic has happened as both methods are a BinaryOperator<Integer>.