diff --git a/src/frontend/src/optimizer/plan_rewriter/share_source_rewriter.rs b/src/frontend/src/optimizer/plan_rewriter/share_source_rewriter.rs
index db7ecd92c7aa5..9ab0d4d580ddc 100644
--- a/src/frontend/src/optimizer/plan_rewriter/share_source_rewriter.rs
+++ b/src/frontend/src/optimizer/plan_rewriter/share_source_rewriter.rs
@@ -109,8 +109,10 @@ impl PlanRewriter for ShareSourceRewriter {
     }
 }
 
-impl PlanVisitor<()> for SourceCounter {
-    type DefaultBehavior = impl DefaultBehavior<()>;
+impl PlanVisitor for SourceCounter {
+    type Result = ();
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         DefaultValue
diff --git a/src/frontend/src/optimizer/plan_visitor/cardinality_visitor.rs b/src/frontend/src/optimizer/plan_visitor/cardinality_visitor.rs
index 3b071ddaf3dfe..a9eb5639fcf85 100644
--- a/src/frontend/src/optimizer/plan_visitor/cardinality_visitor.rs
+++ b/src/frontend/src/optimizer/plan_visitor/cardinality_visitor.rs
@@ -83,8 +83,10 @@ impl CardinalityVisitor {
     }
 }
 
-impl PlanVisitor<Cardinality> for CardinalityVisitor {
-    type DefaultBehavior = impl DefaultBehavior<Cardinality>;
+impl PlanVisitor for CardinalityVisitor {
+    type Result = Cardinality;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         // returns unknown cardinality for default behavior, which is always correct
diff --git a/src/frontend/src/optimizer/plan_visitor/execution_mode_decider.rs b/src/frontend/src/optimizer/plan_visitor/execution_mode_decider.rs
index f1f3d4edfdc74..6eb7f7def64aa 100644
--- a/src/frontend/src/optimizer/plan_visitor/execution_mode_decider.rs
+++ b/src/frontend/src/optimizer/plan_visitor/execution_mode_decider.rs
@@ -28,8 +28,10 @@ impl ExecutionModeDecider {
     }
 }
 
-impl PlanVisitor<bool> for ExecutionModeDecider {
-    type DefaultBehavior = impl DefaultBehavior<bool>;
+impl PlanVisitor for ExecutionModeDecider {
+    type Result = bool;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         Merge(|a, b| a & b)
diff --git a/src/frontend/src/optimizer/plan_visitor/input_ref_validator.rs b/src/frontend/src/optimizer/plan_visitor/input_ref_validator.rs
index a8e48633d6a31..6911c6e8ce89a 100644
--- a/src/frontend/src/optimizer/plan_visitor/input_ref_validator.rs
+++ b/src/frontend/src/optimizer/plan_visitor/input_ref_validator.rs
@@ -103,8 +103,10 @@ macro_rules! visit_project {
     };
 }
 
-impl PlanVisitor<Option<String>> for InputRefValidator {
-    type DefaultBehavior = impl DefaultBehavior<Option<String>>;
+impl PlanVisitor for InputRefValidator {
+    type Result = Option<String>;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     visit_filter!(logical, batch, stream);
 
diff --git a/src/frontend/src/optimizer/plan_visitor/max_one_row_visitor.rs b/src/frontend/src/optimizer/plan_visitor/max_one_row_visitor.rs
index 32a6c874efe40..2a3a354674621 100644
--- a/src/frontend/src/optimizer/plan_visitor/max_one_row_visitor.rs
+++ b/src/frontend/src/optimizer/plan_visitor/max_one_row_visitor.rs
@@ -18,8 +18,10 @@ use crate::optimizer::plan_visitor::PlanVisitor;
 
 pub struct HasMaxOneRowApply();
 
-impl PlanVisitor<bool> for HasMaxOneRowApply {
-    type DefaultBehavior = impl DefaultBehavior<bool>;
+impl PlanVisitor for HasMaxOneRowApply {
+    type Result = bool;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         Merge(|a, b| a | b)
diff --git a/src/frontend/src/optimizer/plan_visitor/mod.rs b/src/frontend/src/optimizer/plan_visitor/mod.rs
index 7695128f255d4..4f8d5e0c2ade7 100644
--- a/src/frontend/src/optimizer/plan_visitor/mod.rs
+++ b/src/frontend/src/optimizer/plan_visitor/mod.rs
@@ -80,14 +80,15 @@ macro_rules! def_visitor {
     ($({ $convention:ident, $name:ident }),*) => {
         /// The visitor for plan nodes. visit all inputs and return the ret value of the left most input,
         /// and leaf node returns `R::default()`
-        pub trait PlanVisitor<R: Default> {
-            type DefaultBehavior: DefaultBehavior<R>;
+        pub trait PlanVisitor {
+            type Result: Default;
+            type DefaultBehavior: DefaultBehavior<Self::Result>;
 
             /// The behavior for the default implementations of `visit_xxx`.
             fn default_behavior() -> Self::DefaultBehavior;
 
             paste! {
-                fn visit(&mut self, plan: PlanRef) -> R{
+                fn visit(&mut self, plan: PlanRef) -> Self::Result {
                     match plan.node_type() {
                         $(
                             PlanNodeType::[<$convention $name>] => self.[<visit_ $convention:snake _ $name:snake>](plan.downcast_ref::<[<$convention $name>]>().unwrap()),
@@ -97,7 +98,7 @@ macro_rules! def_visitor {
 
                 $(
                     #[doc = "Visit [`" [<$convention $name>] "`] , the function should visit the inputs."]
-                    fn [<visit_ $convention:snake _ $name:snake>](&mut self, plan: &[<$convention $name>]) -> R {
+                    fn [<visit_ $convention:snake _ $name:snake>](&mut self, plan: &[<$convention $name>]) -> Self::Result {
                         let results = plan.inputs().into_iter().map(|input| self.visit(input));
                         Self::default_behavior().apply(results)
                     }
@@ -121,17 +122,18 @@ macro_rules! impl_has_variant {
                         pred: P,
                     }
 
-                    impl<P> PlanVisitor<bool> for HasWhere<P>
+                    impl<P> PlanVisitor for HasWhere<P>
                     where
                         P: FnMut(&$variant) -> bool,
                     {
-                        type DefaultBehavior = impl DefaultBehavior<bool>;
+                        type Result = bool;
+                        type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
                         fn default_behavior() -> Self::DefaultBehavior {
                             Merge(|a, b| a | b)
                         }
 
-                        fn [<visit_ $variant:snake>](&mut self, node: &$variant) -> bool {
+                        fn [<visit_ $variant:snake>](&mut self, node: &$variant) -> Self::Result {
                             (self.pred)(node)
                         }
                     }
diff --git a/src/frontend/src/optimizer/plan_visitor/plan_correlated_id_finder.rs b/src/frontend/src/optimizer/plan_visitor/plan_correlated_id_finder.rs
index e71497326a29a..7dd32e29b98bb 100644
--- a/src/frontend/src/optimizer/plan_visitor/plan_correlated_id_finder.rs
+++ b/src/frontend/src/optimizer/plan_visitor/plan_correlated_id_finder.rs
@@ -40,11 +40,13 @@ impl PlanCorrelatedIdFinder {
     }
 }
 
-impl PlanVisitor<()> for PlanCorrelatedIdFinder {
+impl PlanVisitor for PlanCorrelatedIdFinder {
     /// `correlated_input_ref` can only appear in `LogicalProject`, `LogicalFilter`,
     /// `LogicalJoin` or the `filter` clause of `PlanAggCall` of `LogicalAgg` now.
 
-    type DefaultBehavior = impl DefaultBehavior<()>;
+    type Result = ();
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         DefaultValue
diff --git a/src/frontend/src/optimizer/plan_visitor/relation_collector_visitor.rs b/src/frontend/src/optimizer/plan_visitor/relation_collector_visitor.rs
index 45fd2fdb90b14..a4b7102906c69 100644
--- a/src/frontend/src/optimizer/plan_visitor/relation_collector_visitor.rs
+++ b/src/frontend/src/optimizer/plan_visitor/relation_collector_visitor.rs
@@ -42,8 +42,10 @@ impl RelationCollectorVisitor {
     }
 }
 
-impl PlanVisitor<()> for RelationCollectorVisitor {
-    type DefaultBehavior = impl DefaultBehavior<()>;
+impl PlanVisitor for RelationCollectorVisitor {
+    type Result = ();
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         DefaultValue
diff --git a/src/frontend/src/optimizer/plan_visitor/share_parent_counter.rs b/src/frontend/src/optimizer/plan_visitor/share_parent_counter.rs
index 2b21f9d806e72..7d538392f9361 100644
--- a/src/frontend/src/optimizer/plan_visitor/share_parent_counter.rs
+++ b/src/frontend/src/optimizer/plan_visitor/share_parent_counter.rs
@@ -33,8 +33,10 @@ impl ShareParentCounter {
     }
 }
 
-impl PlanVisitor<()> for ShareParentCounter {
-    type DefaultBehavior = impl DefaultBehavior<()>;
+impl PlanVisitor for ShareParentCounter {
+    type Result = ();
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         DefaultValue
diff --git a/src/frontend/src/optimizer/plan_visitor/side_effect_visitor.rs b/src/frontend/src/optimizer/plan_visitor/side_effect_visitor.rs
index b7e87e656d58e..f36561d8d4457 100644
--- a/src/frontend/src/optimizer/plan_visitor/side_effect_visitor.rs
+++ b/src/frontend/src/optimizer/plan_visitor/side_effect_visitor.rs
@@ -19,8 +19,10 @@ use crate::optimizer::plan_node;
 /// eliminated trivially.
 pub struct SideEffectVisitor;
 
-impl PlanVisitor<bool> for SideEffectVisitor {
-    type DefaultBehavior = impl DefaultBehavior<bool>;
+impl PlanVisitor for SideEffectVisitor {
+    type Result = bool;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         Merge(|a, b| a | b)
diff --git a/src/frontend/src/optimizer/plan_visitor/sys_table_visitor.rs b/src/frontend/src/optimizer/plan_visitor/sys_table_visitor.rs
index 7b5210ca68db7..35f4a7246e49a 100644
--- a/src/frontend/src/optimizer/plan_visitor/sys_table_visitor.rs
+++ b/src/frontend/src/optimizer/plan_visitor/sys_table_visitor.rs
@@ -27,8 +27,10 @@ impl SysTableVisitor {
     }
 }
 
-impl PlanVisitor<bool> for SysTableVisitor {
-    type DefaultBehavior = impl DefaultBehavior<bool>;
+impl PlanVisitor for SysTableVisitor {
+    type Result = bool;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         Merge(|a, b| a | b)
diff --git a/src/frontend/src/optimizer/plan_visitor/temporal_join_validator.rs b/src/frontend/src/optimizer/plan_visitor/temporal_join_validator.rs
index 7fb0b1b49e309..d7da70b7a030b 100644
--- a/src/frontend/src/optimizer/plan_visitor/temporal_join_validator.rs
+++ b/src/frontend/src/optimizer/plan_visitor/temporal_join_validator.rs
@@ -29,8 +29,10 @@ impl TemporalJoinValidator {
     }
 }
 
-impl PlanVisitor<bool> for TemporalJoinValidator {
-    type DefaultBehavior = impl DefaultBehavior<bool>;
+impl PlanVisitor for TemporalJoinValidator {
+    type Result = bool;
+
+    type DefaultBehavior = impl DefaultBehavior<Self::Result>;
 
     fn default_behavior() -> Self::DefaultBehavior {
         Merge(|a, b| a | b)