Purely functional soft heap

Question

Are there any implementations of a purely functional soft heap data structure in any language?

Answer 1

A quick search of the ACM digital library indicates that Chazelle's soft heap structure, despite being very interesting, has received relatively little study, and that persistent/functional soft heaps are thus an open research topic.

So I would say no, there are no known approaches for persistent soft heaps. Describing one would be a publishable result (it may boil down to adding copying where you would mutate the original structure, and identifying sharing opportunities).