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Dynamic trees, originally described by Sleator and Tarjan, have been studieddeeply for non persistent structures providing $\mathcal{O}(\log n)$ time forupdate and lookup operations as shown in theory and practice by Werneck.However, discussions on how the most common dynamic trees operations (i.e. linkand cut) are computed over a purely functional data structure have not beenstudied. Even more, asking whether vertices $u$ and $v$ are connected (i.e.within the same forest) assumes that corresponding indices or locations for $u$and $v$ are taken for granted in most of the literature, and not performed aspart of the whole computation for such a question. We present FunSeqSet, basedon the primitive version of finger trees, i.e. the de facto sequence datastructure for the purely functional programming language Haskell, augmentedwith variants of the collection (i.e. sets) data structures in order to manageefficiently $k$-ary trees for the linearisation case of the dynamic treesproblem. Different implementations are discussed, and the performance ismeasured.

FunSeqSet: Towards a Purely Functional Data Structure for the Linearisation Case of Dynamic Trees Problem