diff --git a/kclvm/evaluator/src/node.rs b/kclvm/evaluator/src/node.rs
index 8d6c91424..01f8c2a7b 100644
--- a/kclvm/evaluator/src/node.rs
+++ b/kclvm/evaluator/src/node.rs
@@ -1208,10 +1208,22 @@ impl<'ctx> Evaluator<'ctx> {
                     // Lambda local variables.
                     } else if self.is_in_lambda() {
                         let value = right_value.clone().expect(kcl_error::INTERNAL_ERROR_MSG);
-                        // If variable exists in the scope and update it, if not, add it to the scope.
-                        if !self.store_variable_in_current_scope(name, value.clone()) {
-                            self.add_variable(name, self.undefined_value());
-                            self.store_variable(name, value);
+                        // schema frame in the lambda
+                        if self.is_schema_scope() {
+                            let is_local_var = self.is_local_var(name);
+                            let value = right_value.clone().expect(kcl_error::INTERNAL_ERROR_MSG);
+                            match (is_local_var, is_in_schema) {
+                                (false, true) => {
+                                    self.update_schema_or_rule_scope_value(name, Some(&value))
+                                }
+                                _ => self.add_variable(name, value),
+                            }
+                        } else {
+                            // If variable exists in the scope and update it, if not, add it to the scope.
+                            if !self.store_variable_in_current_scope(name, value.clone()) {
+                                self.add_variable(name, self.undefined_value());
+                                self.store_variable(name, value);
+                            }
                         }
                     } else {
                         let is_local_var = self.is_local_var(name);
diff --git a/kclvm/evaluator/src/schema.rs b/kclvm/evaluator/src/schema.rs
index ede41b97c..5a9ae3a7e 100644
--- a/kclvm/evaluator/src/schema.rs
+++ b/kclvm/evaluator/src/schema.rs
@@ -367,7 +367,7 @@ pub(crate) fn schema_body(
     };
     let schema_name = { ctx.borrow().node.name.node.to_string() };
     s.push_schema(crate::EvalContext::Schema(ctx.clone()));
-    s.enter_scope();
+    s.enter_schema_scope(true);
     // Evaluate arguments and keyword arguments and store values to local variables.
     s.walk_arguments(&ctx.borrow().node.args, args, kwargs);
     // Eval schema body and record schema instances.
diff --git a/kclvm/evaluator/src/scope.rs b/kclvm/evaluator/src/scope.rs
index 6507816f3..de1acc450 100644
--- a/kclvm/evaluator/src/scope.rs
+++ b/kclvm/evaluator/src/scope.rs
@@ -24,6 +24,8 @@ pub struct Scope {
     pub scalars: Vec<ValueRef>,
     /// schema_scalar_idx denotes whether a schema exists in the scalar list.
     pub schema_scalar_idx: usize,
+    /// is_schema denotes whether the scope is a schema.
+    pub is_schema: bool,
     /// Scope normal variables
     pub variables: IndexMap<String, ValueRef>,
     /// Potential arguments in the current scope, such as schema/lambda arguments.
@@ -107,16 +109,36 @@ impl<'ctx> Evaluator<'ctx> {
         scopes.len() - 1
     }
 
-    /// Enter scope
-    pub(crate) fn enter_scope(&self) {
+    /// Get the scope level
+    pub(crate) fn is_schema_scope(&self) -> bool {
+        let current_pkgpath = self.current_pkgpath();
+        let pkg_scopes = &self.pkg_scopes.borrow();
+        let msg = format!("pkgpath {} is not found", current_pkgpath);
+        let scopes = pkg_scopes.get(&current_pkgpath).expect(&msg);
+        if let Some(last_scope) = scopes.last() {
+            last_scope.is_schema
+        } else {
+            false
+        }
+    }
+
+    /// Enter a schema scope
+    pub(crate) fn enter_schema_scope(&self, is_schema: bool) {
         let current_pkgpath = self.current_pkgpath();
         let pkg_scopes = &mut self.pkg_scopes.borrow_mut();
         let msg = format!("pkgpath {} is not found", current_pkgpath);
         let scopes = pkg_scopes.get_mut(&current_pkgpath).expect(&msg);
-        let scope = Scope::default();
+        let mut scope = Scope::default();
+        scope.is_schema = is_schema;
         scopes.push(scope);
     }
 
+    /// Enter scope
+    #[inline]
+    pub(crate) fn enter_scope(&self) {
+        self.enter_schema_scope(false);
+    }
+
     /// Leave scope
     pub(crate) fn leave_scope(&self) {
         let current_pkgpath = self.current_pkgpath();
diff --git a/test/grammar/builtins/file/append/file_append.txt b/test/grammar/builtins/file/append/file_append.txt
deleted file mode 100644
index 719403733..000000000
--- a/test/grammar/builtins/file/append/file_append.txt
+++ /dev/null
@@ -1 +0,0 @@
-sample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample contentsample content
\ No newline at end of file
diff --git a/test/grammar/builtins/file/append/main.k b/test/grammar/builtins/file/append/main.k
deleted file mode 100644
index 4798753ca..000000000
--- a/test/grammar/builtins/file/append/main.k
+++ /dev/null
@@ -1,5 +0,0 @@
-import file
-
-file.append("file_append.txt", "sample content")
-
-file.append("", "sample content without path")
\ No newline at end of file
diff --git a/test/grammar/builtins/file/append/stderr.golden b/test/grammar/builtins/file/append/stderr.golden
deleted file mode 100644
index 7233d69b5..000000000
--- a/test/grammar/builtins/file/append/stderr.golden
+++ /dev/null
@@ -1,6 +0,0 @@
-error[E3M38]: EvaluationError
- --> ${CWD}/main.k:5:1
-  |
-5 | file.append("", "sample content without path")
-  |  Failed to open or create file '': No such file or directory (os error 2)
-  |
\ No newline at end of file
diff --git a/test/grammar/schema/optional_attr/inherit_4/main.k b/test/grammar/schema/optional_attr/inherit_4/main.k
new file mode 100644
index 000000000..04ac1fef2
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_4/main.k
@@ -0,0 +1,13 @@
+schema Name:
+    n1: str = "aa"
+    n2: str
+
+schema Sub[a: str](Name):
+    n2 = a
+
+schema Phase:
+    a: Sub
+
+a = lambda {
+    [[Phase{a = Sub("a")}.a]][0][0] | {}
+}()
diff --git a/test/grammar/schema/optional_attr/inherit_4/stdout.golden b/test/grammar/schema/optional_attr/inherit_4/stdout.golden
new file mode 100644
index 000000000..654f98b45
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_4/stdout.golden
@@ -0,0 +1,3 @@
+a:
+  n1: aa
+  n2: a
diff --git a/test/grammar/schema/optional_attr/inherit_5/main.k b/test/grammar/schema/optional_attr/inherit_5/main.k
new file mode 100644
index 000000000..e2fcc474e
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_5/main.k
@@ -0,0 +1,16 @@
+schema Name:
+    n1: str = "aa"
+    n2: str
+
+schema Sub[a: str](Name):
+    n2 = a
+
+schema Phase:
+    a: Sub
+
+schema Schema:
+    f = lambda {
+        [[Phase{a = Sub("a")}.a]][0][0] | {}
+    }()
+
+a = Schema{}
\ No newline at end of file
diff --git a/test/grammar/schema/optional_attr/inherit_5/stdout.golden b/test/grammar/schema/optional_attr/inherit_5/stdout.golden
new file mode 100644
index 000000000..d90f9ab82
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_5/stdout.golden
@@ -0,0 +1,4 @@
+a:
+  f:
+    n1: aa
+    n2: a
diff --git a/test/grammar/schema/optional_attr/inherit_6/main.k b/test/grammar/schema/optional_attr/inherit_6/main.k
new file mode 100644
index 000000000..9f27d96cc
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_6/main.k
@@ -0,0 +1,31 @@
+schema Name:
+    n1: str = "aa"
+    n2: str
+
+schema Sub[a: str](Name):
+    n2 = a
+
+schema Phase:
+    a: Sub
+
+schema Schema:
+    f0: () = lambda {
+        [[Phase{a = Sub("a")}.a]][0][0]
+    }
+    f1: () = lambda {
+        [[Phase{a = Sub("a")}.a]][0][0] | {}
+    }
+    f2: () = lambda {
+        s = [[Phase{a = Sub("a")}.a]][0][0] 
+        s | {}
+    }
+    ff: () -> () = lambda {
+        lambda {
+            [[Phase{a = Sub("a")}.a]][0] | [{}]
+        }
+    }
+
+a = Schema().f0()
+b = Schema().f1()
+c = Schema().f2()
+d = Schema().ff()()
diff --git a/test/grammar/schema/optional_attr/inherit_6/stdout.golden b/test/grammar/schema/optional_attr/inherit_6/stdout.golden
new file mode 100644
index 000000000..eaba9f398
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_6/stdout.golden
@@ -0,0 +1,12 @@
+a:
+  n1: aa
+  n2: a
+b:
+  n1: aa
+  n2: a
+c:
+  n1: aa
+  n2: a
+d:
+- n1: aa
+  n2: a
diff --git a/test/grammar/schema/optional_attr/inherit_7/main.k b/test/grammar/schema/optional_attr/inherit_7/main.k
new file mode 100644
index 000000000..0c53d54a8
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_7/main.k
@@ -0,0 +1,31 @@
+schema Name:
+    n1: str = "aa"
+    n2: str
+
+schema Sub[a: str](Name):
+    n2: str = a
+
+schema Phase:
+    a: Sub
+
+schema Schema:
+    f0: () = lambda {
+        [[Phase{a = Sub("a")}.a]][0][0]
+    }
+    f1: () = lambda {
+        [[Phase{a = Sub("a")}.a]][0][0] | {}
+    }
+    f2: () = lambda {
+        s = [[Phase{a = Sub("a")}.a]][0][0] 
+        s | {}
+    }
+    ff: () -> () = lambda {
+        lambda {
+            [[Phase{a = Sub("a")}.a]][0] | [{}]
+        }
+    }
+
+a = Schema().f0()
+b = Schema().f1()
+c = Schema().f2()
+d = Schema().ff()()
diff --git a/test/grammar/schema/optional_attr/inherit_7/stdout.golden b/test/grammar/schema/optional_attr/inherit_7/stdout.golden
new file mode 100644
index 000000000..eaba9f398
--- /dev/null
+++ b/test/grammar/schema/optional_attr/inherit_7/stdout.golden
@@ -0,0 +1,12 @@
+a:
+  n1: aa
+  n2: a
+b:
+  n1: aa
+  n2: a
+c:
+  n1: aa
+  n2: a
+d:
+- n1: aa
+  n2: a