Nested angular directives with typescript

Is it possible to use Typescript with nested angular directives?

http://jsfiddle.net/mrajcok/StXFK/

<div ng-controller="MyCtrl">
  <div screen>
    <div component>
        <div widget>
            <button ng-click="widgetIt()">Woo Hoo</button>
        </div>
    </div>
</div>
</div>

How would the following Javascript look as typescript code?

var myApp = angular.module('myApp',[])

.directive('screen', function() {
    return {
        scope: true,
        controller: function() {
            this.doSomethingScreeny = function() {
                alert("screeny!");
            }
        }
    }
})

.directive('component', function() {
    return {
        scope: true,
        require: '^screen',
        controller: function($scope) {
            this.componentFunction = function() {
                $scope.screenCtrl.doSomethingScreeny();
            }
        },
        link: function(scope, element, attrs, screenCtrl) {
            scope.screenCtrl = screenCtrl
        }
    }
})

.directive('widget', function() {
    return {
        scope: true,
        require: "^component",
        link: function(scope, element, attrs, componentCtrl) {
            scope.widgetIt = function() {
                componentCtrl.componentFunction();
            };
        }
    }
})


//myApp.directive('myDirective', function() {});
//myApp.factory('myService', function() {});

function MyCtrl($scope) {
    $scope.name = 'Superhero';
}