diff --git a/mqboost/objective.py b/mqboost/objective.py
index 3652a77..aa42bf2 100644
--- a/mqboost/objective.py
+++ b/mqboost/objective.py
@@ -9,9 +9,12 @@
 CHECK_LOSS: str = "check_loss"
 GradFnLike = Callable[[Any], np.ndarray]
 HessFnLike = Callable[[Any], np.ndarray]
-CallGradHessLike = Callable[
+ObjLike = Callable[
     [np.ndarray, DtrainLike, list[float], Any], tuple[np.ndarray, np.ndarray]
 ]
+EvalLike = Callable[
+    [np.ndarray, DtrainLike, list[float]], tuple[str, float, bool] | tuple[str, float]
+]
 
 
 # check loss
@@ -63,7 +66,7 @@ def _train_pred_reshape(
 
 
 # Compute gradient hessian logic
-def compute_grad_hess(grad_fn: GradFnLike, hess_fn: HessFnLike) -> CallGradHessLike:
+def compute_grad_hess(grad_fn: GradFnLike, hess_fn: HessFnLike) -> ObjLike:
     """Return computing gradient hessian function."""
 
     def _compute_grads_hess(
@@ -132,30 +135,32 @@ def _lgb_eval_loss(
     return CHECK_LOSS, loss, False
 
 
-def validate_parameters(objective: ObjectiveName, delta: float, epsilon: float):
+def validate_parameters(objective: ObjectiveName, delta: float, epsilon: float) -> None:
     if objective == ObjectiveName.huber:
         delta_validate(delta=delta)
     elif objective == ObjectiveName.approx:
         epsilon_validate(epsilon=epsilon)
 
 
-def get_fobj_function(objective, alphas, delta: float, epsilon: float):
-    objective_mapping = {
+def get_fobj_function(
+    objective: ObjectiveName, alphas: list[float], delta: float, epsilon: float
+) -> ObjLike:
+    objective_mapping: dict[ObjectiveName, ObjLike] = {
         ObjectiveName.check: partial(check_loss_grad_hess, alphas=alphas),
         ObjectiveName.huber: partial(huber_loss_grad_hess, alphas=alphas, delta=delta),
         ObjectiveName.approx: partial(
             approx_loss_grad_hess, alphas=alphas, epsilon=epsilon
         ),
     }
-    return objective_mapping.get(objective)
+    return objective_mapping[objective]
 
 
-def get_feval_function(model: ModelName, alphas):
-    model_mapping = {
+def get_feval_function(model: ModelName, alphas: list[float]) -> EvalLike:
+    model_mapping: dict[ModelName, EvalLike] = {
         ModelName.lightgbm: partial(_lgb_eval_loss, alphas=alphas),
         ModelName.xgboost: partial(_xgb_eval_loss, alphas=alphas),
     }
-    return model_mapping.get(model)
+    return model_mapping[model]
 
 
 class MQObjective: