A file synchronizer restores consistency after multiple replicas of a filesystem have been changed independently. We present an algebra for reasoning about operations on filesystems and show that it is sound and complete with respect to a simple model. The algebra enables us to specify a file-synchronization algorithm that can be combined with several different conflict-resolution policies. By contrast, previous work builds the conflict-resolution policy into the specification, or worse, does not specify the synchronizer's behavior precisely. We classify synchronizers by asking whether conflicts can be resolved at a single disconnected replica and whether all replicas are identical after synchronization. We also discuss timestamps and argue that there is no good way to propagate timestamps when there is severe clock skew between replicas.