connect react with redux.js

// Redux Code:
const ADD = 'ADD';

const addMessage = (message) => {
  return {
    type: ADD,
    message
  }
};

const messageReducer = (state = [], action) => {
  switch (action.type) {
    case ADD:
      return [
        ...state,
        action.message
      ];
    default:
      return state;
  }
};



const store = Redux.createStore(messageReducer);

// React Code:

class DisplayMessages extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      input: '',
      messages: []
    }
    this.handleChange = this.handleChange.bind(this);
    this.submitMessage = this.submitMessage.bind(this);
  }
  handleChange(event) {
    this.setState({
      input: event.target.value
    });
  }
  submitMessage() {
    const currentMessage = this.state.input;
    this.setState({
      input: '',
      messages: this.state.messages.concat(currentMessage)
    });
  }
  render() {
    return (
      <div>
        <h2>Type in a new Message:</h2>
        <input
          value={this.state.input}
          onChange={this.handleChange}/><br/>
        <button onClick={this.submitMessage}>Submit</button>
        <ul>
          {this.state.messages.map( (message, idx) => {
              return (
                 <li key={idx}>{message}</li>
              )
            })
          }
        </ul>
      </div>
    );
  }
};

const Provider = ReactRedux.Provider;

class AppWrapper extends React.Component {
  // render the Provider here
render(){
    return (
<Provider store={store}>
  <DisplayMessages/>
</Provider>
    );
}
};