OCaml `Map.Make` input module

I am following the example here.

module IntPairs =struct  type t = int * int  let compare (x0,y0) (x1,y1) =    match Stdlib.compare x0 x1 with    | 0 -> Stdlib.compare y0 y1    | c -> cendmodule PairsMap = Map.Make(IntPairs)let m = PairsMap.(  empty   |> add (0,1) "hello"   |> add (1,0) "world")

My question is, why the code doesn't compile when I add : Map.OrderedType to the module IntPairs definition? Like this:

module IntPairs : Map.OrderedType =struct  type t = int * int  let compare (x0,y0) (x1,y1) =    match Stdlib.compare x0 x1 with    | 0 -> Stdlib.compare y0 y1    | c -> cendmodule PairsMap = Map.Make(IntPairs)let m = PairsMap.(  empty   |> add (0,1) "hello"   |> add (1,0) "world")

Error message:

64 | let m = PairsMap.(empty |> add (0, 1) "hello" |> add (1, 0) "world")                                    ^^^^^^Error: This expression has type 'a * 'b       but an expression was expected of type        key

Isn't IntPairs expected to implement the module type Map.OrderedType?