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.