Function definition: fun vs val

Kotlin is all about Java interoperability and defining a function as a val will produce a completely different result in terms of the interoperability. The following Kotlin class:

class A {
  fun f(x: Int) = 42
  val g = fun(x: Int) = 42
}

is effectively equivalent to:

public class A {
  private final Function1 gref = new Function1() {
    @Override
    public Integer invoke(final Integer integer) {
      return 42;
    }
  };

  public int f(final int value) {
    return 42;
  }

  public Function1 getG() {
    return gref;
  }
}

As you can see, the main differences are:

1. fun f is just a usual method, while val g in fact is a higher-order function that returns another function
2. val g involves creation of a new class which isn't good if you are targeting Android
3. val g requires unnecessary boxing and unboxing
4. val g cannot be easily invoked from java: A().g(42) in Kotlin vs new A().getG().invoke(42) in Java

UPDATE:

Regarding the A::f syntax. The compiler will generate an extra Function2 class for every A::f occurrence, so the following code results in two extra classes with 7 methods each:

val first = A::f
val second = A::f

Kotlin compiler isn't smart enough at the moment to optimize such kind of things. You can vote for the issue here https://youtrack.jetbrains.com/issue/KT-9831. In case you are interested, here is how each class looks in the bytecode: https://gist.github.com/nsk-mironov/fc13f2075bfa05d8a3c3