Streamable Interface : How empty() method returns Iterable?

empty() returns a method reference Collections::emptyIterator.

In order for this code to pass compilation, that method reference must conform with the single abstract method of the Streamable<> interface.

Collections's emptyIterator() takes no arguments and returns an Iterator<T>.

Streamable<> extends both Iterable<T> and Supplier<Stream<T>>, which means it has to implement two methods (iterator() and get()), but one of them cannot be abstract (otherwise it wouldn't be a functional interface).

Collections's emptyIterator() can conform with Iterable<T>'s Iterator<T> iterator() signature.

So if Streamable<T> has a default implementation of Supplier<Stream<T>>'s get() method (if it doesn't, Streamable<T> cannot be a functional interface), Collections::emptyIterator can implement the Streamable<T> interface.

EDIT: If you were referring to org.springframework.data.util.Streamable, you can see that it does have a default implementation of get():

/*
 * (non-Javadoc)
 * @see java.util.function.Supplier#get()
 */
default Stream<T> get() {
    return stream();
}

Hence, any method reference that conforms with the single abstract method Iterator<T> iterator(), can implement that interface. Therefore Collections::emptyIterator can implement Streamable<T>.

For the record, this is the fully qualified name : org.springframework.data.util.Streamable.

The thing is that in the current context :

static <T> Streamable<T> empty() {    
    return Collections.emptyIterator();
}

is not the same thing than :

static <T> Streamable<T> empty() {    
    return Collections::emptyIterator;
}

return Collections.emptyIterator() returns an Iterator object while the method expects a Streamable. That indeed cannot compile as you supposed.

But return Collections::emptyIterator doesn't return an Iterator object. Instead, it defines the lambda body associated to the Streamable functional interface object returned by empty().

In fact this method reference :

return Collections::emptyIterator;

is equivalent to :

return () -> Collections.emptyIterator();

Why is it valid ?
Because Streamable is a functional interface defined as a function : ()-> Iterator<T> and emptyIterator() returns Iterator<T>.