Module Type TREE.
Parameter elt: Type.
Parameter elt_eq: forall (a b: elt), {a = b} + {a <> b}.
Parameter t: Type -> Type.
Parameter empty: forall (A: Type), t A.
Parameter get: forall (A: Type), elt -> t A -> option A.
Parameter set: forall (A: Type), elt -> A -> t A -> t A.
Parameter remove: forall (A: Type), elt -> t A -> t A.
(** Extensional equality between trees. *)
Parameter beq: forall (A: Type), (A -> A -> bool) -> t A -> t A -> bool.
(** Applying a function to all data of a tree. *)
Parameter map:
forall (A B: Type), (elt -> A -> B) -> t A -> t B.

Axiom gmap:
forall (A B: Type) (f: elt -> A -> B) (i: elt) (m: t A),
get i (map f m) = option_map (f i) (get i m).