alamb commented on code in PR #18970:
URL: https://github.com/apache/datafusion/pull/18970#discussion_r2577945355


##########
datafusion/physical-expr/src/simplifier/mod.rs:
##########
@@ -56,6 +57,11 @@ impl<'a> TreeNodeRewriter for PhysicalExprSimplifier<'a> {
     type Node = Arc<dyn PhysicalExpr>;
 
     fn f_up(&mut self, node: Self::Node) -> Result<Transformed<Self::Node>> {
+        // Apply NOT expression simplification first
+        let not_expr_simplified = simplify_not_expr(&node, self.schema)?;
+        let node = not_expr_simplified.data;
+        let transformed = not_expr_simplified.transformed;
+
         // Apply unwrap cast optimization
         #[cfg(test)]
         let original_type = node.data_type(self.schema).unwrap();

Review Comment:
   It would be nice to move the original type check before applying the not and 
the verification  after the not
   
   Somethg like 
   
   
   ```rust
   impl<'a> TreeNodeRewriter for PhysicalExprSimplifier<'a> {
       type Node = Arc<dyn PhysicalExpr>;
   
       fn f_up(&mut self, node: Self::Node) -> Result<Transformed<Self::Node>> {
           #[cfg(test)]
           let original_type = node.data_type(self.schema).unwrap();
   
           // Apply NOT expression simplification first
           let rewritten =
               simplify_not_expr(&node, self.schema)?.transform_data(|node| {
                   unwrap_cast::unwrap_cast_in_comparison(node, self.schema)
               })?;
   
           #[cfg(test)]
           assert_eq!(
               rewritten.data.data_type(self.schema).unwrap(),
               original_type,
               "Simplified expression should have the same data type as the 
original"
           );
   
           Ok(rewritten)
       }
   }
   ```
   



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {
+        let not_simplified = simplify_not_expr_impl(Arc::clone(&current_expr), 
schema)?;
+        if not_simplified.transformed {
+            overall_transformed = true;
+            current_expr = not_simplified.data;
+            continue;
+        }
+
+        if let Some(binary_expr) = 
current_expr.as_any().downcast_ref::<BinaryExpr>() {
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            if left_simplified.transformed || right_simplified.transformed {
+                let new_binary = Arc::new(BinaryExpr::new(
+                    left_simplified.data,
+                    *binary_expr.op(),
+                    right_simplified.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+        }
+
+        break;
+    }
+
+    if overall_transformed {
+        Ok(Transformed::yes(current_expr))
+    } else {
+        Ok(Transformed::no(current_expr))
+    }
+}
+
+/// Returns the negated version of a comparison operator, if possible
+fn negate_operator(op: &Operator) -> Option<Operator> {
+    match op {
+        Operator::Eq => Some(Operator::NotEq),
+        Operator::NotEq => Some(Operator::Eq),
+        Operator::Lt => Some(Operator::GtEq),
+        Operator::LtEq => Some(Operator::Gt),
+        Operator::Gt => Some(Operator::LtEq),
+        Operator::GtEq => Some(Operator::Lt),
+        Operator::IsDistinctFrom => Some(Operator::IsNotDistinctFrom),
+        Operator::IsNotDistinctFrom => Some(Operator::IsDistinctFrom),
+        // For other operators, we can't directly negate them
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::expressions::{col, in_list, lit, BinaryExpr, NotExpr};
+    use arrow::datatypes::{DataType, Field, Schema};
+    use datafusion_common::ScalarValue;
+    use datafusion_expr::Operator;
+
+    fn test_schema() -> Schema {
+        Schema::new(vec![
+            Field::new("a", DataType::Boolean, false),
+            Field::new("b", DataType::Int32, false),
+        ])
+    }
+
+    #[test]

Review Comment:
   Since this function is not really run in isolation (it is always run as part 
of `PhysicalExprSimplifier`) I think it would be better if these tests were in 
`datafusion/physical-expr/src/simplifier/mod.rs` rather than here.
   
   I don't think this change is required



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;

Review Comment:
   I think since `simplify_not_expr` is used in `PhysicalExprSimplifier` which 
is doing a walk up the plan (using `f_up`) there is no reason to also recurse 
explicitly in this rule. 
   
   You should be able to apply the rewrite rules only NOT(A OR B) --> NOT A AND 
NOT B rather than also changing the exprs



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {
+        let not_simplified = simplify_not_expr_impl(Arc::clone(&current_expr), 
schema)?;
+        if not_simplified.transformed {
+            overall_transformed = true;
+            current_expr = not_simplified.data;
+            continue;
+        }
+
+        if let Some(binary_expr) = 
current_expr.as_any().downcast_ref::<BinaryExpr>() {
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            if left_simplified.transformed || right_simplified.transformed {
+                let new_binary = Arc::new(BinaryExpr::new(
+                    left_simplified.data,
+                    *binary_expr.op(),
+                    right_simplified.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+        }
+
+        break;
+    }
+
+    if overall_transformed {
+        Ok(Transformed::yes(current_expr))
+    } else {
+        Ok(Transformed::no(current_expr))
+    }
+}
+
+/// Returns the negated version of a comparison operator, if possible
+fn negate_operator(op: &Operator) -> Option<Operator> {
+    match op {
+        Operator::Eq => Some(Operator::NotEq),
+        Operator::NotEq => Some(Operator::Eq),
+        Operator::Lt => Some(Operator::GtEq),
+        Operator::LtEq => Some(Operator::Gt),
+        Operator::Gt => Some(Operator::LtEq),
+        Operator::GtEq => Some(Operator::Lt),
+        Operator::IsDistinctFrom => Some(Operator::IsNotDistinctFrom),
+        Operator::IsNotDistinctFrom => Some(Operator::IsDistinctFrom),
+        // For other operators, we can't directly negate them
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::expressions::{col, in_list, lit, BinaryExpr, NotExpr};
+    use arrow::datatypes::{DataType, Field, Schema};
+    use datafusion_common::ScalarValue;
+    use datafusion_expr::Operator;
+
+    fn test_schema() -> Schema {
+        Schema::new(vec![
+            Field::new("a", DataType::Boolean, false),
+            Field::new("b", DataType::Int32, false),
+        ])
+    }
+
+    #[test]
+    fn test_double_negation_elimination() -> Result<()> {
+        let schema = test_schema();
+
+        // Create NOT(NOT(b > 5))
+        let inner_expr: Arc<dyn PhysicalExpr> = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Gt,
+            lit(ScalarValue::Int32(Some(5))),
+        ));
+        let inner_not = Arc::new(NotExpr::new(Arc::clone(&inner_expr)));
+        let double_not: Arc<dyn PhysicalExpr> = 
Arc::new(NotExpr::new(inner_not));
+
+        let result = simplify_not_expr(&double_not, &schema)?;
+
+        assert!(result.transformed);
+        // Should be simplified back to the original b > 5
+        assert_eq!(result.data.to_string(), inner_expr.to_string());

Review Comment:
   What is the reason for using `to_string()`? 
   
   I tried comparing the two directly and it seems to work
   ```rust
           assert_eq!(&result.data, &inner_expr);
   ```



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {
+        let not_simplified = simplify_not_expr_impl(Arc::clone(&current_expr), 
schema)?;
+        if not_simplified.transformed {
+            overall_transformed = true;
+            current_expr = not_simplified.data;
+            continue;
+        }
+
+        if let Some(binary_expr) = 
current_expr.as_any().downcast_ref::<BinaryExpr>() {
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            if left_simplified.transformed || right_simplified.transformed {
+                let new_binary = Arc::new(BinaryExpr::new(
+                    left_simplified.data,
+                    *binary_expr.op(),
+                    right_simplified.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+        }
+
+        break;
+    }
+
+    if overall_transformed {
+        Ok(Transformed::yes(current_expr))
+    } else {
+        Ok(Transformed::no(current_expr))
+    }
+}
+
+/// Returns the negated version of a comparison operator, if possible
+fn negate_operator(op: &Operator) -> Option<Operator> {
+    match op {
+        Operator::Eq => Some(Operator::NotEq),
+        Operator::NotEq => Some(Operator::Eq),
+        Operator::Lt => Some(Operator::GtEq),
+        Operator::LtEq => Some(Operator::Gt),
+        Operator::Gt => Some(Operator::LtEq),
+        Operator::GtEq => Some(Operator::Lt),
+        Operator::IsDistinctFrom => Some(Operator::IsNotDistinctFrom),
+        Operator::IsNotDistinctFrom => Some(Operator::IsDistinctFrom),
+        // For other operators, we can't directly negate them
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::expressions::{col, in_list, lit, BinaryExpr, NotExpr};
+    use arrow::datatypes::{DataType, Field, Schema};
+    use datafusion_common::ScalarValue;
+    use datafusion_expr::Operator;
+
+    fn test_schema() -> Schema {
+        Schema::new(vec![
+            Field::new("a", DataType::Boolean, false),
+            Field::new("b", DataType::Int32, false),
+        ])
+    }
+
+    #[test]
+    fn test_double_negation_elimination() -> Result<()> {
+        let schema = test_schema();
+
+        // Create NOT(NOT(b > 5))
+        let inner_expr: Arc<dyn PhysicalExpr> = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Gt,
+            lit(ScalarValue::Int32(Some(5))),
+        ));
+        let inner_not = Arc::new(NotExpr::new(Arc::clone(&inner_expr)));
+        let double_not: Arc<dyn PhysicalExpr> = 
Arc::new(NotExpr::new(inner_not));
+
+        let result = simplify_not_expr(&double_not, &schema)?;
+
+        assert!(result.transformed);
+        // Should be simplified back to the original b > 5
+        assert_eq!(result.data.to_string(), inner_expr.to_string());

Review Comment:
   It might also make these queries easier to read if you made a helper like
   ```rust
   fn assert_transformed(expr, expected_expr);
   ```
   
   and 
   ```rust
   fn assert_not_transformed(expr, expected_expr);
   ```



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {
+        let not_simplified = simplify_not_expr_impl(Arc::clone(&current_expr), 
schema)?;
+        if not_simplified.transformed {
+            overall_transformed = true;
+            current_expr = not_simplified.data;
+            continue;
+        }
+
+        if let Some(binary_expr) = 
current_expr.as_any().downcast_ref::<BinaryExpr>() {
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            if left_simplified.transformed || right_simplified.transformed {
+                let new_binary = Arc::new(BinaryExpr::new(
+                    left_simplified.data,
+                    *binary_expr.op(),
+                    right_simplified.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+        }
+
+        break;
+    }
+
+    if overall_transformed {
+        Ok(Transformed::yes(current_expr))
+    } else {
+        Ok(Transformed::no(current_expr))
+    }
+}
+
+/// Returns the negated version of a comparison operator, if possible
+fn negate_operator(op: &Operator) -> Option<Operator> {
+    match op {
+        Operator::Eq => Some(Operator::NotEq),
+        Operator::NotEq => Some(Operator::Eq),
+        Operator::Lt => Some(Operator::GtEq),
+        Operator::LtEq => Some(Operator::Gt),
+        Operator::Gt => Some(Operator::LtEq),
+        Operator::GtEq => Some(Operator::Lt),
+        Operator::IsDistinctFrom => Some(Operator::IsNotDistinctFrom),
+        Operator::IsNotDistinctFrom => Some(Operator::IsDistinctFrom),
+        // For other operators, we can't directly negate them
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::expressions::{col, in_list, lit, BinaryExpr, NotExpr};
+    use arrow::datatypes::{DataType, Field, Schema};
+    use datafusion_common::ScalarValue;
+    use datafusion_expr::Operator;
+
+    fn test_schema() -> Schema {
+        Schema::new(vec![
+            Field::new("a", DataType::Boolean, false),
+            Field::new("b", DataType::Int32, false),
+        ])
+    }
+
+    #[test]
+    fn test_double_negation_elimination() -> Result<()> {
+        let schema = test_schema();
+
+        // Create NOT(NOT(b > 5))
+        let inner_expr: Arc<dyn PhysicalExpr> = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Gt,
+            lit(ScalarValue::Int32(Some(5))),
+        ));
+        let inner_not = Arc::new(NotExpr::new(Arc::clone(&inner_expr)));
+        let double_not: Arc<dyn PhysicalExpr> = 
Arc::new(NotExpr::new(inner_not));
+
+        let result = simplify_not_expr(&double_not, &schema)?;
+
+        assert!(result.transformed);
+        // Should be simplified back to the original b > 5
+        assert_eq!(result.data.to_string(), inner_expr.to_string());
+        Ok(())
+    }
+
+    #[test]
+    fn test_not_literal() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(TRUE) -> FALSE
+        let not_true = 
Arc::new(NotExpr::new(lit(ScalarValue::Boolean(Some(true)))));
+        let result = simplify_not_expr_impl(not_true, &schema)?;
+        assert!(result.transformed);
+
+        if let Some(literal) = result.data.as_any().downcast_ref::<Literal>() {
+            assert_eq!(literal.value(), &ScalarValue::Boolean(Some(false)));
+        } else {
+            panic!("Expected literal result");
+        }
+
+        // NOT(FALSE) -> TRUE
+        let not_false: Arc<dyn PhysicalExpr> =
+            Arc::new(NotExpr::new(lit(ScalarValue::Boolean(Some(false)))));
+        let result = simplify_not_expr(&not_false, &schema)?;
+        assert!(result.transformed);
+
+        if let Some(literal) = result.data.as_any().downcast_ref::<Literal>() {
+            assert_eq!(literal.value(), &ScalarValue::Boolean(Some(true)));
+        } else {
+            panic!("Expected literal result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_negate_comparison() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(b = 5) -> b != 5
+        let eq_expr = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Eq,
+            lit(ScalarValue::Int32(Some(5))),
+        ));
+        let not_eq: Arc<dyn PhysicalExpr> = Arc::new(NotExpr::new(eq_expr));
+
+        let result = simplify_not_expr(&not_eq, &schema)?;
+        assert!(result.transformed);
+
+        if let Some(binary) = 
result.data.as_any().downcast_ref::<BinaryExpr>() {
+            assert_eq!(binary.op(), &Operator::NotEq);
+        } else {
+            panic!("Expected binary expression result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_demorgans_law_and() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(a AND b) -> NOT a OR NOT b
+        let and_expr = Arc::new(BinaryExpr::new(
+            col("a", &schema)?,
+            Operator::And,
+            col("b", &schema)?,
+        ));
+        let not_and: Arc<dyn PhysicalExpr> = Arc::new(NotExpr::new(and_expr));
+
+        let result = simplify_not_expr(&not_and, &schema)?;
+        assert!(result.transformed);
+
+        if let Some(binary) = 
result.data.as_any().downcast_ref::<BinaryExpr>() {
+            assert_eq!(binary.op(), &Operator::Or);
+            // Left and right should both be NOT expressions
+            
assert!(binary.left().as_any().downcast_ref::<NotExpr>().is_some());
+            
assert!(binary.right().as_any().downcast_ref::<NotExpr>().is_some());
+        } else {
+            panic!("Expected binary expression result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_demorgans_law_or() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(a OR b) -> NOT a AND NOT b
+        let or_expr = Arc::new(BinaryExpr::new(
+            col("a", &schema)?,
+            Operator::Or,
+            col("b", &schema)?,
+        ));
+        let not_or: Arc<dyn PhysicalExpr> = Arc::new(NotExpr::new(or_expr));
+
+        let result = simplify_not_expr(&not_or, &schema)?;
+        assert!(result.transformed);
+
+        if let Some(binary) = 
result.data.as_any().downcast_ref::<BinaryExpr>() {
+            assert_eq!(binary.op(), &Operator::And);
+            // Left and right should both be NOT expressions
+            
assert!(binary.left().as_any().downcast_ref::<NotExpr>().is_some());
+            
assert!(binary.right().as_any().downcast_ref::<NotExpr>().is_some());
+        } else {
+            panic!("Expected binary expression result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_demorgans_with_comparison_simplification() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(b = 1 AND b = 2) -> b != 1 OR b != 2
+        // This tests the combination of De Morgan's law and operator negation
+        let eq1 = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Eq,
+            lit(ScalarValue::Int32(Some(1))),
+        ));
+        let eq2 = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Eq,
+            lit(ScalarValue::Int32(Some(2))),
+        ));
+        let and_expr = Arc::new(BinaryExpr::new(eq1, Operator::And, eq2));
+        let not_and: Arc<dyn PhysicalExpr> = Arc::new(NotExpr::new(and_expr));
+
+        let result = simplify_not_expr(&not_and, &schema)?;
+        assert!(result.transformed, "Expression should be transformed");
+
+        // Verify the result is an OR expression
+        if let Some(or_binary) = 
result.data.as_any().downcast_ref::<BinaryExpr>() {
+            assert_eq!(or_binary.op(), &Operator::Or, "Top level should be 
OR");
+
+            // Verify left side is b != 1
+            if let Some(left_binary) =
+                or_binary.left().as_any().downcast_ref::<BinaryExpr>()
+            {
+                assert_eq!(left_binary.op(), &Operator::NotEq, "Left should be 
NotEq");
+            } else {
+                panic!("Expected left to be a binary expression with !=");
+            }
+
+            // Verify right side is b != 2
+            if let Some(right_binary) =
+                or_binary.right().as_any().downcast_ref::<BinaryExpr>()
+            {
+                assert_eq!(right_binary.op(), &Operator::NotEq, "Right should 
be NotEq");
+            } else {
+                panic!("Expected right to be a binary expression with !=");
+            }
+        } else {
+            panic!("Expected binary OR expression result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_not_of_not_and_not() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(NOT(a) AND NOT(b)) -> a OR b
+        // This tests the combination of De Morgan's law and double negation 
elimination
+        let not_a = Arc::new(NotExpr::new(col("a", &schema)?));
+        let not_b = Arc::new(NotExpr::new(col("b", &schema)?));
+        let and_expr = Arc::new(BinaryExpr::new(not_a, Operator::And, not_b));
+        let not_and: Arc<dyn PhysicalExpr> = Arc::new(NotExpr::new(and_expr));
+
+        let result = simplify_not_expr(&not_and, &schema)?;
+        assert!(result.transformed, "Expression should be transformed");
+
+        // Verify the result is an OR expression
+        if let Some(or_binary) = 
result.data.as_any().downcast_ref::<BinaryExpr>() {
+            assert_eq!(or_binary.op(), &Operator::Or, "Top level should be 
OR");
+
+            // Verify left side is just 'a'
+            
assert!(or_binary.left().as_any().downcast_ref::<NotExpr>().is_none(),
+                "Left should not be a NOT expression, it should be simplified 
to just 'a'");
+
+            // Verify right side is just 'b'
+            
assert!(or_binary.right().as_any().downcast_ref::<NotExpr>().is_none(),
+                "Right should not be a NOT expression, it should be simplified 
to just 'b'");
+        } else {
+            panic!("Expected binary OR expression result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_not_in_list() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(b IN (1, 2, 3)) -> b NOT IN (1, 2, 3)
+        let list = vec![
+            lit(ScalarValue::Int32(Some(1))),
+            lit(ScalarValue::Int32(Some(2))),
+            lit(ScalarValue::Int32(Some(3))),
+        ];
+        let in_list_expr = in_list(col("b", &schema)?, list, &false, &schema)?;
+        let not_in: Arc<dyn PhysicalExpr> = 
Arc::new(NotExpr::new(in_list_expr));
+
+        let result = simplify_not_expr(&not_in, &schema)?;
+        assert!(result.transformed, "Expression should be transformed");
+
+        // Verify the result is an InList expression with negated=true
+        if let Some(in_list_result) = 
result.data.as_any().downcast_ref::<InListExpr>() {
+            assert!(
+                in_list_result.negated(),
+                "InList should be negated (NOT IN)"
+            );
+            assert_eq!(
+                in_list_result.list().len(),
+                3,
+                "Should have 3 items in list"
+            );
+        } else {
+            panic!("Expected InListExpr result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_not_not_in_list() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(b NOT IN (1, 2, 3)) -> b IN (1, 2, 3)
+        let list = vec![
+            lit(ScalarValue::Int32(Some(1))),
+            lit(ScalarValue::Int32(Some(2))),
+            lit(ScalarValue::Int32(Some(3))),
+        ];
+        let not_in_list_expr = in_list(col("b", &schema)?, list, &true, 
&schema)?;
+        let not_not_in: Arc<dyn PhysicalExpr> = 
Arc::new(NotExpr::new(not_in_list_expr));
+
+        let result = simplify_not_expr(&not_not_in, &schema)?;
+        assert!(result.transformed, "Expression should be transformed");
+
+        // Verify the result is an InList expression with negated=false
+        if let Some(in_list_result) = 
result.data.as_any().downcast_ref::<InListExpr>() {
+            assert!(
+                !in_list_result.negated(),
+                "InList should not be negated (IN)"
+            );
+            assert_eq!(
+                in_list_result.list().len(),
+                3,
+                "Should have 3 items in list"
+            );
+        } else {
+            panic!("Expected InListExpr result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_double_not_in_list() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(NOT(b IN (1, 2, 3))) -> b IN (1, 2, 3)
+        let list = vec![
+            lit(ScalarValue::Int32(Some(1))),
+            lit(ScalarValue::Int32(Some(2))),
+            lit(ScalarValue::Int32(Some(3))),
+        ];
+        let in_list_expr = in_list(col("b", &schema)?, list, &false, &schema)?;
+        let not_in = Arc::new(NotExpr::new(in_list_expr));
+        let double_not: Arc<dyn PhysicalExpr> = Arc::new(NotExpr::new(not_in));
+
+        let result = simplify_not_expr(&double_not, &schema)?;
+        assert!(result.transformed, "Expression should be transformed");
+
+        // After double negation elimination, we should get back the original 
IN expression
+        if let Some(in_list_result) = 
result.data.as_any().downcast_ref::<InListExpr>() {
+            assert!(
+                !in_list_result.negated(),
+                "InList should not be negated (IN)"
+            );
+            assert_eq!(
+                in_list_result.list().len(),
+                3,
+                "Should have 3 items in list"
+            );
+        } else {
+            panic!("Expected InListExpr result");
+        }
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_deeply_nested_not() -> Result<()> {
+        let schema = test_schema();
+
+        // Create a deeply nested NOT expression: NOT(NOT(NOT(...NOT(b > 
5)...)))
+        // This tests that we don't get stack overflow with many nested NOTs

Review Comment:
   👍 



##########
datafusion/physical-expr/src/simplifier/mod.rs:
##########
@@ -66,7 +72,12 @@ impl<'a> TreeNodeRewriter for PhysicalExprSimplifier<'a> {
             original_type,
             "Simplified expression should have the same data type as the 
original"
         );
-        Ok(unwrapped)
+        // Combine transformation results
+        let final_transformed = transformed || unwrapped.transformed;

Review Comment:
   I think you can use `transform_data` here instead: 
https://docs.rs/datafusion/latest/datafusion/common/tree_node/struct.Transformed.html#method.transform_data
   
   
   So something like
   
   ```rust
           // Apply NOT expression simplification first
           let rewritten =
               simplify_not_expr(&node, self.schema)?.transform_data(|node| {
                   unwrap_cast::unwrap_cast_in_comparison(node, self.schema)
               })?;
   ```
   
   That handles combining the transformed flag for you



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {
+        let not_simplified = simplify_not_expr_impl(Arc::clone(&current_expr), 
schema)?;
+        if not_simplified.transformed {
+            overall_transformed = true;
+            current_expr = not_simplified.data;
+            continue;
+        }
+
+        if let Some(binary_expr) = 
current_expr.as_any().downcast_ref::<BinaryExpr>() {
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            if left_simplified.transformed || right_simplified.transformed {
+                let new_binary = Arc::new(BinaryExpr::new(
+                    left_simplified.data,
+                    *binary_expr.op(),
+                    right_simplified.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+        }
+
+        break;
+    }
+
+    if overall_transformed {
+        Ok(Transformed::yes(current_expr))
+    } else {
+        Ok(Transformed::no(current_expr))
+    }
+}
+
+/// Returns the negated version of a comparison operator, if possible
+fn negate_operator(op: &Operator) -> Option<Operator> {
+    match op {
+        Operator::Eq => Some(Operator::NotEq),
+        Operator::NotEq => Some(Operator::Eq),
+        Operator::Lt => Some(Operator::GtEq),
+        Operator::LtEq => Some(Operator::Gt),
+        Operator::Gt => Some(Operator::LtEq),
+        Operator::GtEq => Some(Operator::Lt),
+        Operator::IsDistinctFrom => Some(Operator::IsNotDistinctFrom),
+        Operator::IsNotDistinctFrom => Some(Operator::IsDistinctFrom),
+        // For other operators, we can't directly negate them
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::expressions::{col, in_list, lit, BinaryExpr, NotExpr};
+    use arrow::datatypes::{DataType, Field, Schema};
+    use datafusion_common::ScalarValue;
+    use datafusion_expr::Operator;
+
+    fn test_schema() -> Schema {
+        Schema::new(vec![
+            Field::new("a", DataType::Boolean, false),
+            Field::new("b", DataType::Int32, false),
+        ])
+    }
+
+    #[test]
+    fn test_double_negation_elimination() -> Result<()> {
+        let schema = test_schema();
+
+        // Create NOT(NOT(b > 5))
+        let inner_expr: Arc<dyn PhysicalExpr> = Arc::new(BinaryExpr::new(
+            col("b", &schema)?,
+            Operator::Gt,
+            lit(ScalarValue::Int32(Some(5))),
+        ));
+        let inner_not = Arc::new(NotExpr::new(Arc::clone(&inner_expr)));
+        let double_not: Arc<dyn PhysicalExpr> = 
Arc::new(NotExpr::new(inner_not));
+
+        let result = simplify_not_expr(&double_not, &schema)?;
+
+        assert!(result.transformed);
+        // Should be simplified back to the original b > 5
+        assert_eq!(result.data.to_string(), inner_expr.to_string());
+        Ok(())
+    }
+
+    #[test]
+    fn test_not_literal() -> Result<()> {
+        let schema = test_schema();
+
+        // NOT(TRUE) -> FALSE
+        let not_true = 
Arc::new(NotExpr::new(lit(ScalarValue::Boolean(Some(true)))));
+        let result = simplify_not_expr_impl(not_true, &schema)?;
+        assert!(result.transformed);
+
+        if let Some(literal) = result.data.as_any().downcast_ref::<Literal>() {
+            assert_eq!(literal.value(), &ScalarValue::Boolean(Some(false)));
+        } else {
+            panic!("Expected literal result");
+        }

Review Comment:
   You could potentially make this a function to make the tests easier to read 
- something like
   
   ```rust
   let literal = as_literal(&result);
   ```
   
   And handle the panic internally in `as_literal` 
   
   That way the mechics of the test wouldn't obscure the test logic so much
   
   
    I think you could do something similar with `BinaryExpr`



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {
+        let not_simplified = simplify_not_expr_impl(Arc::clone(&current_expr), 
schema)?;
+        if not_simplified.transformed {
+            overall_transformed = true;
+            current_expr = not_simplified.data;
+            continue;
+        }
+
+        if let Some(binary_expr) = 
current_expr.as_any().downcast_ref::<BinaryExpr>() {
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            if left_simplified.transformed || right_simplified.transformed {
+                let new_binary = Arc::new(BinaryExpr::new(
+                    left_simplified.data,
+                    *binary_expr.op(),
+                    right_simplified.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+        }
+
+        break;
+    }
+
+    if overall_transformed {
+        Ok(Transformed::yes(current_expr))
+    } else {
+        Ok(Transformed::no(current_expr))
+    }
+}
+
+/// Returns the negated version of a comparison operator, if possible
+fn negate_operator(op: &Operator) -> Option<Operator> {

Review Comment:
   This looks the same as `Operator::negate`: 
https://docs.rs/datafusion/latest/datafusion/logical_expr/enum.Operator.html#method.negate
   
   I recommend using that code, or if there is a reason not to use 
`Operator::negate` add a comment explaining why it is not used



##########
datafusion/physical-expr/src/simplifier/not.rs:
##########
@@ -0,0 +1,570 @@
+// 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.
+
+//! Simplify NOT expressions in physical expressions
+//!
+//! This module provides optimizations for NOT expressions such as:
+//! - Double negation elimination: NOT(NOT(expr)) -> expr
+//! - NOT with binary comparisons: NOT(a = b) -> a != b
+//! - NOT with IN expressions: NOT(a IN (list)) -> a NOT IN (list)
+//! - De Morgan's laws: NOT(A AND B) -> NOT A OR NOT B
+//! - Constant folding: NOT(TRUE) -> FALSE, NOT(FALSE) -> TRUE
+
+use std::sync::Arc;
+
+use arrow::datatypes::Schema;
+use datafusion_common::{tree_node::Transformed, Result, ScalarValue};
+use datafusion_expr::Operator;
+
+use crate::expressions::{in_list, lit, BinaryExpr, InListExpr, Literal, 
NotExpr};
+use crate::PhysicalExpr;
+
+/// Attempts to simplify NOT expressions
+pub(crate) fn simplify_not_expr_impl(
+    expr: Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    // Check if this is a NOT expression
+    let not_expr = match expr.as_any().downcast_ref::<NotExpr>() {
+        Some(not_expr) => not_expr,
+        None => return Ok(Transformed::no(expr)),
+    };
+
+    let inner_expr = not_expr.arg();
+
+    // Handle NOT(NOT(expr)) -> expr (double negation elimination)
+    if let Some(inner_not) = inner_expr.as_any().downcast_ref::<NotExpr>() {
+        // We eliminated double negation, so always return transformed=true
+        return Ok(Transformed::yes(Arc::clone(inner_not.arg())));
+    }
+
+    // Handle NOT(literal) -> !literal
+    if let Some(literal) = inner_expr.as_any().downcast_ref::<Literal>() {
+        if let ScalarValue::Boolean(Some(val)) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(Some(!val)))));
+        }
+        if let ScalarValue::Boolean(None) = literal.value() {
+            return Ok(Transformed::yes(lit(ScalarValue::Boolean(None))));
+        }
+    }
+
+    // Handle NOT(IN list) -> NOT IN list
+    if let Some(in_list_expr) = 
inner_expr.as_any().downcast_ref::<InListExpr>() {
+        // Create a new InList expression with negated flag flipped
+        let negated = !in_list_expr.negated();
+        let new_in_list = in_list(
+            Arc::clone(in_list_expr.expr()),
+            in_list_expr.list().to_vec(),
+            &negated,
+            schema,
+        )?;
+        return Ok(Transformed::yes(new_in_list));
+    }
+
+    // Handle NOT(binary_expr) where we can flip the operator
+    if let Some(binary_expr) = 
inner_expr.as_any().downcast_ref::<BinaryExpr>() {
+        if let Some(negated_op) = negate_operator(binary_expr.op()) {
+            // Recursively simplify the left and right expressions first
+            let left_simplified = simplify_not_expr(binary_expr.left(), 
schema)?;
+            let right_simplified = simplify_not_expr(binary_expr.right(), 
schema)?;
+
+            let new_binary = Arc::new(BinaryExpr::new(
+                left_simplified.data,
+                negated_op,
+                right_simplified.data,
+            ));
+            // We flipped the operator, so always return transformed=true
+            return Ok(Transformed::yes(new_binary));
+        }
+
+        // Handle De Morgan's laws for AND/OR
+        match binary_expr.op() {
+            Operator::And => {
+                // NOT(A AND B) -> NOT A OR NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::Or,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            Operator::Or => {
+                // NOT(A OR B) -> NOT A AND NOT B
+                let not_left: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.left())));
+                let not_right: Arc<dyn PhysicalExpr> =
+                    Arc::new(NotExpr::new(Arc::clone(binary_expr.right())));
+
+                // Recursively simplify the NOT expressions
+                let simplified_left = simplify_not_expr(&not_left, schema)?;
+                let simplified_right = simplify_not_expr(&not_right, schema)?;
+
+                let new_binary = Arc::new(BinaryExpr::new(
+                    simplified_left.data,
+                    Operator::And,
+                    simplified_right.data,
+                ));
+                return Ok(Transformed::yes(new_binary));
+            }
+            _ => {}
+        }
+    }
+
+    // If no simplification possible, return the original expression
+    Ok(Transformed::no(expr))
+}
+
+pub fn simplify_not_expr(
+    expr: &Arc<dyn PhysicalExpr>,
+    schema: &Schema,
+) -> Result<Transformed<Arc<dyn PhysicalExpr>>> {
+    let mut current_expr = Arc::clone(expr);
+    let mut overall_transformed = false;
+
+    loop {

Review Comment:
   I am also somewhat concerned about this loop -- it seems like it may be 
trying to handle a non complete recursion and it could potentially lead to 
infinite recursion if a rewrite flip/flopped 
   
   If the loop is needed I suggest:
   1. Put it in the higher level PhysicalExprSimplifier
   2. add a counter that breaks after some number of iterations (e.g. 5 or 
something)



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