Frist of all, I read erickson's usefull reply to "Why can’t I define a static method in a Java interface?". This question is not about the "why" but about the "how then?".

So basically I want one Interface to provide both usual methods and e.g. a getSimilarObject method. For (a made up) example

public interface ParametricFunction {
  /** @return f(x) using the parameters */
  static abstract public double getValue(double x, double[] parameters);

  /** @return The function's name */
  static abstract public String getName();
}

and then

public class Parabola implements ParametricFunction {
  /** @return f(x) = parameters[0] * x² + parameters[1] * x + parameters[2] */
  static public double getValue(double x, double[] parameters) {
    return ( parameters[2] + x*(parameters[1] + x*parameters[0]));
  }
  static public String getName() { return "Parabola"; }
}

Since this is not allowed in the current Java standard, what is the closest thing to this?

The idea behind this is putting several ParametricFunction's in a package and use Reflection to list them all, allowing the user to pick e.g. which one to plot. Obviously one could provide a loader class containing an array of the available ParametricFunction's, but every time a new one is implemented one has to remember adding it there, too.