  Dynamic trees, originally described by Sleator and Tarjan, have been studied
deeply for non persistent structures providing $\mathcal{O}(\log n)$ time for
update and lookup operations as shown in theory and practice by Werneck.
However, discussions on how the most common dynamic trees operations (i.e. link
and cut) are computed over a purely functional data structure have not been
studied. 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 as
part of the whole computation for such a question. We present FunSeqSet, based
on the primitive version of finger trees, i.e. the de facto sequence data
structure for the purely functional programming language Haskell, augmented
with variants of the collection (i.e. sets) data structures in order to manage
efficiently $k$-ary trees for the linearisation case of the dynamic trees
problem. Different implementations are discussed, and the performance is
measured.
