OCaml Binary Tree Catamorphism

type 'a tree = Br of 'a * 'a tree * 'a tree | Lf

let a_tree =
    Br (
        (3, "three"),

        Br (
            (1, "one"), Lf, Br ((2, "two"), Lf, Lf)
        ),

        Br ((4, "four"), Lf, Lf)
    )

let rec cata f_lf f_br t =
    match t with
    | Lf -> f_lf ()
    | Br (x, l, r) ->
        f_br x (cata f_lf f_br l) (cata f_lf f_br r)

let fold_right op tree init = cata
    (fun unit -> init)
    (fun value l r -> op value l r)
    tree

let size (t : 'a tree) : int = fold_right (fun x y z -> x+y+z) t 0

let count = size a_tree
(* This expression has type (int * string) tree
   but an expression was expected of type int tree
   Type int * string is not compatible with type int *)