Ordered sets and maps play important roles as index structures in relational data models. When a shared index in a multi-user system is modified concurrently, the current state of the index will diverge into multiple versions containing the local modifications performed in each work flow. The confluent persistence problem arises when versions should be melded in commit and refresh operations so that modifications performed by different users become merged. Confluently Persistent Sets and Maps are functional binary search trees that support efficient set operations both when operands are disjoint and when they are overlapping. Treap properties with hash values as priorities are maintained and with hash-consing of nodes a unique representation is provided. Non-destructive set merge algorithms that skip inspection of equal subtrees and a conflict detecting meld algorithm based on set merges are presented. The meld algorithm is used in commit and refresh operations. With m modifications in one flow and n items in total, the expected cost of the operations is O(m log(n/m)).