A unary function is a function with a single argument and a single value. Hence, it is also a binary relation.
(<=> (Unary-Function ?F) (And (Function ?F) (Binary-Relation ?F)))
(=> (One-To-One-Relation@Frame-Ontology ?R) (Unary-Function ?R))
(<=> (One-To-One-Relation@Frame-Ontology ?R) (And (Unary-Function ?R) (Value-Type@Frame-Ontology ?R Inverse Function) (Value-Cardinality@Frame-Ontology ?R Inverse 1)))