  Trees are fundamental data structure for many areas of computer science and
system engineering. In this report, we show how to ensure eventual consistency
of optimistically replicated trees. In optimistic replication, the different
replicas of a distributed system are allowed to diverge but should eventually
reach the same value if no more mutations occur. A new method to ensure
eventual consistency is to design Conflict-free Replicated Data Types (CRDT).
In this report, we design a collection of tree CRDT using existing set CRDTs.
The remaining concurrency problems particular to tree data structure are
resolved using one or two layers of correction algorithm. For each of these
layer, we propose different and independent policies. Any combination of set
CRDT and policies can be constructed, giving to the distributed application
programmer the entire control of the behavior of the shared data in face of
concurrent mutations. We also propose to order these trees by adding a
positioning layer which is also independent to obtain a collection of ordered
tree CRDTs.
