AngularJS passing function to directive recursively

Question

I have a problem passing a function as attribute to a directive, which implements itself recursivly (tree).

I reduced the code to make it easier to understand:

Controller:

vm.addNode = addNode;
vm.editNode = editNode;
vm.deleteNode = deleteNode;

function addNode(node) {
}

function editNode(node) {
}

function deleteNode(node) {
}

HTML:

<tree on-add="vm.addNode(node)"
      on-edit="vm.editNode(node)"
      on-delete="vm.deleteNode(node)"></tree>

So. If I don't delcare a function, for example on-add like:

<tree on-edit="vm.addNode(node)"
      on-delete="vm.editNode(node)"></tree>

the directive-attribute 'onAdd' will be undefined. This happens only at the first call of the directive. If the directive passes itself the on-add function (which should be undefined), the onAdd-attribute in the 'child-directives' is defined (function). Directive:

(function () {
  'use strict';

  angular
    .module('app')
    .directive('tree', Tree);

  function Tree() {
    return {
      restrict: 'E',
      templateUrl: 'tree.html',
      controller: TreeController,
      controllerAs: 'vm',
      bindToController: true,
      scope: {
        'onAdd': '&?',
        'onEdit': '&?',
        'onDelete': '&?'
      }
    };

   function TreeController() {
      var vm = this;  

      console.log(vm.onAdd); // Is undefined on first call (because of &? -> that's good)
                             // PROBLEM HERE: called recursiv, it will be a function again
   }
  }
})();

Directive-HTML:

<tree on-add="vm.onAdd({'node': node})"
      on-edit="vm.onEdit({'node': node})"
      on-delete="vm.onDelete({'node': node})"></tree>

// UPDATE:

I know why, because in the directive, I declare the on-add attribute. Angular wraps the vm.onAdd (which should be undefined) in a function. So the child-directive has onAdd as function and not as undefined.

Someone has a solution to pass it as undefined to each child-directive??

// UPDATE 2:

I made a workaround, doing a link-function and passing a dummy function in it, if any attribute (on-add, on-edit, on-delete) is not set. So I can fire the function without checking it.