BiDict m n stores related value. Each value of one type has an associated set of the other type.
This is implemented using a pair of Dicts of values of one type to sets of values of the other type. One Dict in each direction.
There is also an EveryBiDict where you can store non-comparable values. It is based on EveryDict from eeue56/elm-all-dict, comparing values using a custom toString. You should make sure your values work correctly with it.