[java] How to specify function types for void (not Void) methods in Java8?

I feel you should be using the Consumer interface instead of Function<T, R>.

A Consumer is basically a functional interface designed to accept a value and return nothing (i.e void)

In your case, you can create a consumer elsewhere in your code like this:

Consumer<Integer> myFunction = x -> {
    System.out.println("processing value: " + x);    
    .... do some more things with "x" which returns nothing...
}

Then you can replace your myForEach code with below snippet:

public static void myForEach(List<Integer> list, Consumer<Integer> myFunction) 
{
  list.forEach(x->myFunction.accept(x));
}

You treat myFunction as a first-class object.