(** Unify 2 types and, if exists, returns the substitution *)
let rec unify ty1 ty2 =
  match ty1, ty2 with
  | Type.Product (p1_ty1, p1_ty2), Type.Product (p2_ty1, p2_ty2)
  | Type.Arrow (p1_ty1, p1_ty2), Type.Arrow (p2_ty1, p2_ty2) ->
    (match unify p1_ty1 p2_ty1 with
     | Some s1 ->
       (match
          unify (TypeSubstitution.apply s1 p1_ty2) (TypeSubstitution.apply s1 p2_ty2)
        with
        | Some s2 -> Some (TypeSubstitution.compose s2 s1)
        | None -> None)
     | None -> None)
  | ty1, ty2 when ty1 = ty2 -> Some TypeSubstitution.empty
  | _ -> None
;;