For instance, a weakly consistent data structure could promise never to raise a merge conflict, and therefore be safe to compose. A stronger one could raise more precise merge exceptions depending on the exact error, which ripple up to the application.
An example of an application handling this sort of merge error is the Cuekeeper TODO manager (which is a pure JavaScript Irmin app that uses HTML5 Localstorage/IndexedDB). Try opening http://test.roscidus.com/CueKeeper/ in two tabs and creating conflicting changes, and see the Irmin merge error ripple up to the UI.
e.g. if you rename an action "orig" to "a" and to "b" and then merge, you'll end up with an action called "a" with a note saying the change to "b" was discarded.
BTW: it's easier to generate merge conflicts using this web interface, which lets you run two instances in one window:
http://roscidus.com/blog/blog/2015/04/28/cuekeeper-gitting-t...
Sure, conflicts need to be handled. That's a fundamental problem with reality!