A binary function is a function with two arguments and one value. Hence, it is a relation with three arguments.
(=> (Binary-Function ?F) (Forall (?List) (=> (Member ?List ?F) (Triple ?List)))) (=> (Binary-Function ?F) (Not (Empty ?F)))
(<=> (Binary-Function ?F) (And (Function ?F) (Not (Empty ?F)) (Forall (?List) (=> (Member ?List ?F) (Triple ?List)))))