empty : Set k
single : k -> Set k
insert : Set k, k -> Set k
len : Set k -> Nat
remove : Set k, k -> Set k
contains : Set k, k -> Bool

# toList = \set -> Dict.keys (toDict set)
toList : Set k -> List k
fromList : List k -> Set k

union : Set k, Set k -> Set k
intersection : Set k, Set k -> Set k
difference : Set k, Set k -> Set k

toDict : Set k -> Dict k {}

walk : Set k, state, (state, k -> state) -> state
walk = \set, state, step ->
    Dict.walk (toDict set) state (\s, k, _ -> step s k)