Detecting that the browser has no mouse and is touch-only

I'm developing a webapp (not a website with pages of interesting text) with a very different interface for touch (your finger hides the screen when you click) and mouse (relies heavily on hover preview). How can I detect that my user has no mouse to present him the right interface? I plan to leave a switch for people with both mouse and touch (like some notebooks).

The touch event capability in the browser doesn't actually mean the user is using a touch device (for example, Modernizr doesn't cut it). The code that correctly answers the question should return false if the device has a mouse, true otherwise. For devices with mouse and touch, it should return false (not touch only)

As a side note, my touch interface might also be suitable for keyboard-only devices, so it's more the lack of mouse I'm looking to detect.

To make the need more clear, here is the API that I'm looking to implement:

// Level 1


// The current answers provide a way to do that.
hasTouch();

// Returns true if a mouse is expected.
// Note: as explained by the OP, this is not !hasTouch()
// I don't think we have this in the answers already, that why I offer a bounty
hasMouse();

// Level 2 (I don't think it's possible, but maybe I'm wrong, so why not asking)

// callback is called when the result of "hasTouch()" changes.
listenHasTouchChanges(callback);

// callback is called when the result of "hasMouse()" changes.
listenHasMouseChanges(callback);