Is there a bidirectional multimap persistent data structure?

Question

In other words, can we model many to many relationships in a persistent data structure efficiently?

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A pair of unidirectional multimaps was suggested. However,

Answer 1

Proof by construction: the bimap package for Haskell.

A Bimap is essentially a bijection between subsets of its two argument types

And how is it implemented?

data Bimap a b = MkBimap !(M.Map a b) !(M.Map b a)

As a pair of unidirectional maps.