New Twiddle

application.controller.js

import Ember from 'ember';

export default Ember.Controller.extend({
  prop: 'a',
  
  actions: {
    setPropToA() {
      this.set('prop', 'a');
      this.notifyPropertyChange('prop');
    },
    
    setPropToZ() {
      this.set('prop', 'z');
      this.notifyPropertyChange('prop');
    }
  }
});

application.template.hbs

{{my-component prop=(readonly prop)}}
<br>
<br>
<button onclick={{action "setPropToA"}}>Set attrs.prop to A</button>
<br>
<button onclick={{action "setPropToZ"}}>Set attrs.prop to Z</button>

my-component.component.js

import Ember from 'ember';

export default Ember.Component.extend({
	prop: 'b',
  
  actions: {
    setPropToC() {
      this.set('prop', 'c');
    }
  }
});

my-component.template.hbs

<p>prop: {{prop}}</p>
<p>attrs.prop: {{attrs.prop}}</p>
<button onclick={{action "setPropToC"}}>Set prop to "c"</button>

twiddle.json

{
  "version": "0.4.17",
  "EmberENV": {
    "FEATURES": {}
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/2.2.0/ember.debug.js",
    "ember-data": "https://cdnjs.cloudflare.com/ajax/libs/ember-data.js/2.2.0/ember-data.js",
    "ember-template-compiler": "https://cdnjs.cloudflare.com/ajax/libs/ember.js/2.2.0/ember-template-compiler.js"
  }
}