diff --git a/datafusion/src/logical_plan/builder.rs b/datafusion/src/logical_plan/builder.rs
index 9515ac2ff373..c02555d63314 100644
--- a/datafusion/src/logical_plan/builder.rs
+++ b/datafusion/src/logical_plan/builder.rs
@@ -309,7 +309,7 @@ impl LogicalPlanBuilder {
         // FIXME: implement next
         // window_frame: Option<WindowFrame>,
     ) -> Result<Self> {
-        let window_expr = window_expr.into_iter().collect::<Vec<Expr>>();
+        let window_expr = window_expr.into_iter().collect::<Vec<_>>();
         // FIXME: implement next
         // let partition_by_expr = partition_by_expr.into_iter().collect::<Vec<Expr>>();
         // FIXME: implement next
diff --git a/datafusion/src/sql/planner.rs b/datafusion/src/sql/planner.rs
index a3027e589985..63499aa1abe2 100644
--- a/datafusion/src/sql/planner.rs
+++ b/datafusion/src/sql/planner.rs
@@ -17,10 +17,6 @@
 
 //! SQL Query Planner (produces logical plan from SQL AST)
 
-use std::str::FromStr;
-use std::sync::Arc;
-use std::{convert::TryInto, vec};
-
 use crate::catalog::TableReference;
 use crate::datasource::TableProvider;
 use crate::logical_plan::Expr::Alias;
@@ -28,6 +24,7 @@ use crate::logical_plan::{
     and, lit, DFSchema, Expr, LogicalPlan, LogicalPlanBuilder, Operator, PlanType,
     StringifiedPlan, ToDFSchema,
 };
+use crate::prelude::JoinType;
 use crate::scalar::ScalarValue;
 use crate::{
     error::{DataFusionError, Result},
@@ -38,11 +35,8 @@ use crate::{
     physical_plan::{aggregates, functions, window_functions},
     sql::parser::{CreateExternalTable, FileType, Statement as DFStatement},
 };
-
 use arrow::datatypes::*;
 use hashbrown::HashMap;
-
-use crate::prelude::JoinType;
 use sqlparser::ast::{
     BinaryOperator, DataType as SQLDataType, DateTimeField, Expr as SQLExpr, FunctionArg,
     Ident, Join, JoinConstraint, JoinOperator, ObjectName, Query, Select, SelectItem,
@@ -52,6 +46,9 @@ use sqlparser::ast::{
 use sqlparser::ast::{ColumnDef as SQLColumnDef, ColumnOption};
 use sqlparser::ast::{OrderByExpr, Statement};
 use sqlparser::parser::ParserError::ParserError;
+use std::str::FromStr;
+use std::sync::Arc;
+use std::{convert::TryInto, vec};
 
 use super::{
     parser::DFParser,
@@ -678,11 +675,11 @@ impl<'a, S: ContextProvider> SqlToRel<'a, S> {
         select_exprs: &[Expr],
     ) -> Result<(LogicalPlan, Vec<Expr>)> {
         let plan = LogicalPlanBuilder::from(input)
-            .window(window_exprs)?
+            .window(window_exprs.clone())?
             .build()?;
         let select_exprs = select_exprs
             .iter()
-            .map(|expr| expr_as_column_expr(&expr, &plan))
+            .map(|expr| rebase_expr(expr, &window_exprs, &plan))
             .into_iter()
             .collect::<Result<Vec<_>>>()?;
         Ok((plan, select_exprs))
@@ -2710,6 +2707,16 @@ mod tests {
         quick_test(sql, expected);
     }
 
+    #[test]
+    fn empty_over_with_alias() {
+        let sql = "SELECT order_id oid, MAX(order_id) OVER () max_oid from orders";
+        let expected = "\
+        Projection: #order_id AS oid, #MAX(order_id) AS max_oid\
+        \n  WindowAggr: windowExpr=[[MAX(#order_id)]] partitionBy=[], orderBy=[]\
+        \n    TableScan: orders projection=None";
+        quick_test(sql, expected);
+    }
+
     #[test]
     fn empty_over_plus() {
         let sql = "SELECT order_id, MAX(qty * 1.1) OVER () from orders";
diff --git a/integration-tests/sqls/simple_window_full_aggregation.sql b/integration-tests/sqls/simple_window_full_aggregation.sql
new file mode 100644
index 000000000000..94860bc3b183
--- /dev/null
+++ b/integration-tests/sqls/simple_window_full_aggregation.sql
@@ -0,0 +1,25 @@
+-- Licensed to the Apache Software Foundation (ASF) under one
+-- or more contributor license agreements.  See the NOTICE file
+-- distributed with this work for additional information
+-- regarding copyright ownership.  The ASF licenses this file
+-- to you under the Apache License, Version 2.0 (the
+-- "License"); you may not use this file except in compliance
+-- with the License.  You may obtain a copy of the License at
+
+-- http://www.apache.org/licenses/LICENSE-2.0
+
+-- Unless required by applicable law or agreed to in writing, software
+-- distributed under the License is distributed on an "AS IS" BASIS,
+-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+-- See the License for the specific language gOVERning permissions and
+-- limitations under the License.
+
+SELECT
+  row_number() OVER () AS row_number,
+  count(c3) OVER () AS count_c3,
+  avg(c3) OVER () AS avg,
+  sum(c3) OVER () AS sum,
+  max(c3) OVER () AS max,
+  min(c3) OVER () AS min
+FROM test
+ORDER BY row_number;
diff --git a/integration-tests/test_psql_parity.py b/integration-tests/test_psql_parity.py
index f4967b8457e4..5bd308180e59 100644
--- a/integration-tests/test_psql_parity.py
+++ b/integration-tests/test_psql_parity.py
@@ -74,7 +74,7 @@ class PsqlParityTest(unittest.TestCase):
     def test_parity(self):
         root = Path(os.path.dirname(__file__)) / "sqls"
         files = set(root.glob("*.sql"))
-        self.assertEqual(len(files), 4, msg="tests are missed")
+        self.assertEqual(len(files), 5, msg="tests are missed")
         for fname in files:
             with self.subTest(fname=fname):
                 datafusion_output = pd.read_csv(