diff --git a/vortex-array/src/arrays/scalar_fn/vtable/mod.rs b/vortex-array/src/arrays/scalar_fn/vtable/mod.rs
index fa98bdb9683..bb597bc6bb8 100644
--- a/vortex-array/src/arrays/scalar_fn/vtable/mod.rs
+++ b/vortex-array/src/arrays/scalar_fn/vtable/mod.rs
@@ -38,6 +38,7 @@ use crate::dtype::DType;
 use crate::executor::ExecutionCtx;
 use crate::executor::ExecutionResult;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::matcher::Matcher;
 use crate::scalar_fn;
 use crate::scalar_fn::Arity;
@@ -309,7 +310,7 @@ impl scalar_fn::ScalarFnVTable for ArrayExpr {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        _expr: &Expression,
+        _expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "{}", options.0.encoding_id())
diff --git a/vortex-array/src/expr/bound_expression.rs b/vortex-array/src/expr/bound_expression.rs
index 3a35757068a..26173171d91 100644
--- a/vortex-array/src/expr/bound_expression.rs
+++ b/vortex-array/src/expr/bound_expression.rs
@@ -228,7 +228,10 @@ impl BoundExpression {
 
 impl Display for BoundExpression {
     fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
-        Display::fmt(&self.unbind(), f)
+        match self.kind() {
+            BoundKind::Scalar { scalar_fn, .. } => scalar_fn.fmt_sql(self, f),
+            BoundKind::Root => f.write_str("$"),
+        }
     }
 }
 
@@ -333,9 +336,10 @@ mod tests {
     }
 
     #[test]
-    fn bound_tree_display_matches_unbound() -> VortexResult<()> {
+    fn bound_display_matches_unbound() -> VortexResult<()> {
         for expr in [root(), col("a"), eq(col("a"), lit(1_i32)), lit(true)] {
             let bound = expr.bind_scope(&scope())?;
+            assert_eq!(bound.to_string(), expr.to_string());
             assert_eq!(
                 bound.display_tree().to_string(),
                 expr.display_tree().to_string()
diff --git a/vortex-array/src/expr/display.rs b/vortex-array/src/expr/display.rs
index 685af718134..d542f7d35b3 100644
--- a/vortex-array/src/expr/display.rs
+++ b/vortex-array/src/expr/display.rs
@@ -16,6 +16,38 @@ pub enum DisplayFormat {
     Tree,
 }
 
+/// Read-only expression-tree interface used by scalar functions for SQL-style formatting.
+///
+/// Both [`Expression`] and [`BoundExpression`] implement this interface, allowing scalar
+/// functions to format either representation without converting between them.
+pub trait ExprDisplay: Display {
+    /// Return the child at `index`.
+    fn display_child(&self, index: usize) -> &dyn ExprDisplay;
+
+    /// Return the number of children in this node.
+    fn display_children_count(&self) -> usize;
+}
+
+impl ExprDisplay for Expression {
+    fn display_child(&self, index: usize) -> &dyn ExprDisplay {
+        Expression::child(self, index)
+    }
+
+    fn display_children_count(&self) -> usize {
+        self.children().len()
+    }
+}
+
+impl ExprDisplay for BoundExpression {
+    fn display_child(&self, index: usize) -> &dyn ExprDisplay {
+        &self.children()[index]
+    }
+
+    fn display_children_count(&self) -> usize {
+        self.children().len()
+    }
+}
+
 trait DisplayTreeNode: Sized {
     fn tree_children(&self) -> &[Self];
 
diff --git a/vortex-array/src/scalar_fn/erased.rs b/vortex-array/src/scalar_fn/erased.rs
index 6e0011c297a..f4c8136ad26 100644
--- a/vortex-array/src/scalar_fn/erased.rs
+++ b/vortex-array/src/scalar_fn/erased.rs
@@ -20,6 +20,7 @@ use crate::ArrayRef;
 use crate::ExecutionCtx;
 use crate::dtype::DType;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::EmptyOptions;
 use crate::scalar_fn::ExecutionArgs;
 use crate::scalar_fn::ReduceCtx;
@@ -160,8 +161,12 @@ impl ScalarFnRef {
     // Expression-taking methods — used by expr/ module via pub(crate)
     // ------------------------------------------------------------------
 
-    /// Format this expression in SQL-style format.
-    pub(crate) fn fmt_sql(&self, expr: &Expression, f: &mut Formatter<'_>) -> std::fmt::Result {
+    /// Format an expression tree in SQL-style format.
+    pub(crate) fn fmt_sql(
+        &self,
+        expr: &dyn ExprDisplay,
+        f: &mut Formatter<'_>,
+    ) -> std::fmt::Result {
         self.0.fmt_sql(expr, f)
     }
 
diff --git a/vortex-array/src/scalar_fn/fns/between/mod.rs b/vortex-array/src/scalar_fn/fns/between/mod.rs
index 1a2e038b2fb..c3131dbd342 100644
--- a/vortex-array/src/scalar_fn/fns/between/mod.rs
+++ b/vortex-array/src/scalar_fn/fns/between/mod.rs
@@ -25,6 +25,7 @@ use crate::arrays::Primitive;
 use crate::builtins::ArrayBuiltins;
 use crate::dtype::DType;
 use crate::dtype::DType::Bool;
+use crate::expr::display::ExprDisplay;
 use crate::expr::expression::Expression;
 use crate::scalar::Scalar;
 use crate::scalar_fn::Arity;
@@ -224,7 +225,7 @@ impl ScalarFnVTable for Between {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         let lower_op = if options.lower_strict.is_strict() {
@@ -240,11 +241,11 @@ impl ScalarFnVTable for Between {
         write!(
             f,
             "({} {} {} {} {})",
-            expr.child(1),
+            expr.display_child(1),
             lower_op,
-            expr.child(0),
+            expr.display_child(0),
             upper_op,
-            expr.child(2)
+            expr.display_child(2)
         )
     }
 
diff --git a/vortex-array/src/scalar_fn/fns/binary/mod.rs b/vortex-array/src/scalar_fn/fns/binary/mod.rs
index 8a986c079a0..a5b9fe70539 100644
--- a/vortex-array/src/scalar_fn/fns/binary/mod.rs
+++ b/vortex-array/src/scalar_fn/fns/binary/mod.rs
@@ -1,6 +1,7 @@
 // SPDX-License-Identifier: Apache-2.0
 // SPDX-FileCopyrightText: Copyright the Vortex contributors
 
+use std::fmt::Display;
 use std::fmt::Formatter;
 
 #[expect(deprecated)]
@@ -19,6 +20,7 @@ use crate::ExecutionCtx;
 use crate::dtype::DType;
 use crate::dtype::Nullability;
 use crate::expr::and;
+use crate::expr::display::ExprDisplay;
 use crate::expr::expression::Expression;
 use crate::expr::lit;
 use crate::scalar_fn::Arity;
@@ -89,13 +91,13 @@ impl ScalarFnVTable for Binary {
     fn fmt_sql(
         &self,
         operator: &Operator,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "(")?;
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, " {} ", operator)?;
-        expr.child(1).fmt_sql(f)?;
+        Display::fmt(expr.display_child(1), f)?;
         write!(f, ")")
     }
 
diff --git a/vortex-array/src/scalar_fn/fns/case_when.rs b/vortex-array/src/scalar_fn/fns/case_when.rs
index 189556c1fdb..8779e0a179c 100644
--- a/vortex-array/src/scalar_fn/fns/case_when.rs
+++ b/vortex-array/src/scalar_fn/fns/case_when.rs
@@ -35,6 +35,7 @@ use crate::builders::builder_with_capacity;
 use crate::builtins::ArrayBuiltins;
 use crate::dtype::DType;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar::Scalar;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
@@ -136,7 +137,7 @@ impl ScalarFnVTable for CaseWhen {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> fmt::Result {
         write!(f, "CASE")?;
@@ -144,13 +145,13 @@ impl ScalarFnVTable for CaseWhen {
             write!(
                 f,
                 " WHEN {} THEN {}",
-                expr.child(i * 2),
-                expr.child(i * 2 + 1)
+                expr.display_child(i * 2),
+                expr.display_child(i * 2 + 1)
             )?;
         }
         if options.has_else {
             let else_idx = options.num_when_then_pairs as usize * 2;
-            write!(f, " ELSE {}", expr.child(else_idx))?;
+            write!(f, " ELSE {}", expr.display_child(else_idx))?;
         }
         write!(f, " END")
     }
diff --git a/vortex-array/src/scalar_fn/fns/cast/mod.rs b/vortex-array/src/scalar_fn/fns/cast/mod.rs
index 8df6accece3..7a9f1356647 100644
--- a/vortex-array/src/scalar_fn/fns/cast/mod.rs
+++ b/vortex-array/src/scalar_fn/fns/cast/mod.rs
@@ -3,6 +3,7 @@
 
 mod kernel;
 
+use std::fmt::Display;
 use std::fmt::Formatter;
 
 pub use kernel::*;
@@ -33,6 +34,7 @@ use crate::arrays::VarBinView;
 use crate::arrays::struct_::compute::cast::struct_cast;
 use crate::builtins::ArrayBuiltins;
 use crate::dtype::DType;
+use crate::expr::display::ExprDisplay;
 use crate::expr::expression::Expression;
 use crate::expr::lit;
 use crate::scalar_fn::Arity;
@@ -91,9 +93,14 @@ impl ScalarFnVTable for Cast {
         }
     }
 
-    fn fmt_sql(&self, dtype: &DType, expr: &Expression, f: &mut Formatter<'_>) -> std::fmt::Result {
+    fn fmt_sql(
+        &self,
+        dtype: &DType,
+        expr: &dyn ExprDisplay,
+        f: &mut Formatter<'_>,
+    ) -> std::fmt::Result {
         write!(f, "cast(")?;
-        expr.children()[0].fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, " as {}", dtype)?;
         write!(f, ")")
     }
diff --git a/vortex-array/src/scalar_fn/fns/dynamic.rs b/vortex-array/src/scalar_fn/fns/dynamic.rs
index a741fcd9217..00e59796e05 100644
--- a/vortex-array/src/scalar_fn/fns/dynamic.rs
+++ b/vortex-array/src/scalar_fn/fns/dynamic.rs
@@ -20,6 +20,7 @@ use crate::IntoArray;
 use crate::arrays::ConstantArray;
 use crate::dtype::DType;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::expr::traversal::NodeExt;
 use crate::expr::traversal::NodeVisitor;
 use crate::expr::traversal::TraversalOrder;
@@ -64,10 +65,10 @@ impl ScalarFnVTable for DynamicComparison {
     fn fmt_sql(
         &self,
         dynamic: &DynamicComparisonExpr,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, " {} dynamic(", dynamic.operator)?;
         match dynamic.scalar() {
             None => write!(f, "scalar=<none>")?,
diff --git a/vortex-array/src/scalar_fn/fns/get_item.rs b/vortex-array/src/scalar_fn/fns/get_item.rs
index af319ecf742..bbbc15de479 100644
--- a/vortex-array/src/scalar_fn/fns/get_item.rs
+++ b/vortex-array/src/scalar_fn/fns/get_item.rs
@@ -1,6 +1,7 @@
 // SPDX-License-Identifier: Apache-2.0
 // SPDX-FileCopyrightText: Copyright the Vortex contributors
 
+use std::fmt::Display;
 use std::fmt::Formatter;
 
 use prost::Message;
@@ -20,6 +21,7 @@ use crate::dtype::DType;
 use crate::dtype::FieldName;
 use crate::dtype::Nullability;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::expr::lit;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
@@ -78,10 +80,10 @@ impl ScalarFnVTable for GetItem {
     fn fmt_sql(
         &self,
         field_name: &FieldName,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
-        expr.children()[0].fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, ".{}", field_name)
     }
 
diff --git a/vortex-array/src/scalar_fn/fns/is_not_null.rs b/vortex-array/src/scalar_fn/fns/is_not_null.rs
index acb3b9e0f35..dcf00f62c08 100644
--- a/vortex-array/src/scalar_fn/fns/is_not_null.rs
+++ b/vortex-array/src/scalar_fn/fns/is_not_null.rs
@@ -1,6 +1,7 @@
 // SPDX-License-Identifier: Apache-2.0
 // SPDX-FileCopyrightText: Copyright the Vortex contributors
 
+use std::fmt::Display;
 use std::fmt::Formatter;
 
 use vortex_error::VortexResult;
@@ -13,7 +14,7 @@ use crate::IntoArray;
 use crate::arrays::ConstantArray;
 use crate::dtype::DType;
 use crate::dtype::Nullability;
-use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
 use crate::scalar_fn::EmptyOptions;
@@ -60,11 +61,11 @@ impl ScalarFnVTable for IsNotNull {
     fn fmt_sql(
         &self,
         _options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "is_not_null(")?;
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, ")")
     }
 
diff --git a/vortex-array/src/scalar_fn/fns/like/mod.rs b/vortex-array/src/scalar_fn/fns/like/mod.rs
index 3637e0384a3..c947ce461b2 100644
--- a/vortex-array/src/scalar_fn/fns/like/mod.rs
+++ b/vortex-array/src/scalar_fn/fns/like/mod.rs
@@ -31,6 +31,7 @@ use crate::dtype::DType;
 use crate::dtype::Nullability;
 use crate::expr::Expression;
 use crate::expr::and;
+use crate::expr::display::ExprDisplay;
 use crate::scalar::Scalar;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
@@ -107,10 +108,10 @@ impl ScalarFnVTable for Like {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         if options.negated {
             write!(f, " not")?;
         }
@@ -119,7 +120,7 @@ impl ScalarFnVTable for Like {
         } else {
             write!(f, " like ")?;
         }
-        expr.child(1).fmt_sql(f)
+        Display::fmt(expr.display_child(1), f)
     }
 
     fn return_dtype(&self, _options: &Self::Options, arg_dtypes: &[DType]) -> VortexResult<DType> {
diff --git a/vortex-array/src/scalar_fn/fns/literal.rs b/vortex-array/src/scalar_fn/fns/literal.rs
index 0449ae27e29..4c95fd3172d 100644
--- a/vortex-array/src/scalar_fn/fns/literal.rs
+++ b/vortex-array/src/scalar_fn/fns/literal.rs
@@ -16,6 +16,7 @@ use crate::IntoArray;
 use crate::arrays::ConstantArray;
 use crate::dtype::DType;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar::Scalar;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
@@ -74,7 +75,7 @@ impl ScalarFnVTable for Literal {
     fn fmt_sql(
         &self,
         scalar: &Scalar,
-        _expr: &Expression,
+        _expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "{}", scalar)
diff --git a/vortex-array/src/scalar_fn/fns/pack.rs b/vortex-array/src/scalar_fn/fns/pack.rs
index 84983d9d55e..60eb5b1c2c4 100644
--- a/vortex-array/src/scalar_fn/fns/pack.rs
+++ b/vortex-array/src/scalar_fn/fns/pack.rs
@@ -23,6 +23,7 @@ use crate::dtype::FieldNames;
 use crate::dtype::Nullability;
 use crate::dtype::StructFields;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::expr::lit;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
@@ -105,13 +106,13 @@ impl ScalarFnVTable for Pack {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "pack(")?;
-        for (i, (name, child)) in options.names.iter().zip(expr.children().iter()).enumerate() {
+        for (i, name) in options.names.iter().enumerate() {
             write!(f, "{}: ", name)?;
-            child.fmt_sql(f)?;
+            Display::fmt(expr.display_child(i), f)?;
             if i + 1 < options.names.len() {
                 write!(f, ", ")?;
             }
diff --git a/vortex-array/src/scalar_fn/fns/root.rs b/vortex-array/src/scalar_fn/fns/root.rs
index 646bed19a1b..0831e5b8585 100644
--- a/vortex-array/src/scalar_fn/fns/root.rs
+++ b/vortex-array/src/scalar_fn/fns/root.rs
@@ -11,7 +11,7 @@ use vortex_session::registry::CachedId;
 use crate::ArrayRef;
 use crate::ExecutionCtx;
 use crate::dtype::DType;
-use crate::expr::expression::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
 use crate::scalar_fn::EmptyOptions;
@@ -58,7 +58,7 @@ impl ScalarFnVTable for Root {
     fn fmt_sql(
         &self,
         _options: &Self::Options,
-        _expr: &Expression,
+        _expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "$")
diff --git a/vortex-array/src/scalar_fn/fns/select.rs b/vortex-array/src/scalar_fn/fns/select.rs
index 2e0bbd02975..d6d30c5547b 100644
--- a/vortex-array/src/scalar_fn/fns/select.rs
+++ b/vortex-array/src/scalar_fn/fns/select.rs
@@ -24,6 +24,7 @@ use crate::arrays::struct_::StructArrayExt;
 use crate::dtype::DType;
 use crate::dtype::FieldName;
 use crate::dtype::FieldNames;
+use crate::expr::display::ExprDisplay;
 use crate::expr::expression::Expression;
 use crate::expr::field::DisplayFieldNames;
 use crate::expr::get_item;
@@ -104,10 +105,10 @@ impl ScalarFnVTable for Select {
     fn fmt_sql(
         &self,
         selection: &FieldSelection,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         match selection {
             FieldSelection::Include(fields) => {
                 write!(f, "{{{}}}", DisplayFieldNames(fields))
diff --git a/vortex-array/src/scalar_fn/fns/stat.rs b/vortex-array/src/scalar_fn/fns/stat.rs
index 612298424e4..c961ac10d53 100644
--- a/vortex-array/src/scalar_fn/fns/stat.rs
+++ b/vortex-array/src/scalar_fn/fns/stat.rs
@@ -20,7 +20,7 @@ use crate::aggregate_fn::fns::all_non_null::AllNonNull;
 use crate::aggregate_fn::fns::all_null::AllNull;
 use crate::arrays::ConstantArray;
 use crate::dtype::DType;
-use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::expr::stats::Precision;
 use crate::expr::stats::Stat;
 use crate::expr::stats::StatsProvider;
@@ -101,11 +101,11 @@ impl ScalarFnVTable for StatFn {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "stat(")?;
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, ", {})", options.aggregate_fn())
     }
 
diff --git a/vortex-array/src/scalar_fn/fns/variant_get/mod.rs b/vortex-array/src/scalar_fn/fns/variant_get/mod.rs
index d939235d24f..593ecb9c1db 100644
--- a/vortex-array/src/scalar_fn/fns/variant_get/mod.rs
+++ b/vortex-array/src/scalar_fn/fns/variant_get/mod.rs
@@ -25,7 +25,7 @@ use crate::builders::builder_with_capacity_in;
 use crate::dtype::DType;
 use crate::dtype::FieldName;
 use crate::dtype::Nullability;
-use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar::Scalar;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
@@ -92,11 +92,11 @@ impl ScalarFnVTable for VariantGet {
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> fmt::Result {
         write!(f, "variant_get(")?;
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         let path = options.path().to_string();
         write!(f, ", \"{}\"", StringEscape(&path))?;
         if let Some(dtype) = options.dtype() {
diff --git a/vortex-array/src/scalar_fn/fns/zip/mod.rs b/vortex-array/src/scalar_fn/fns/zip/mod.rs
index 5cb84bc737e..9b591cbdf0d 100644
--- a/vortex-array/src/scalar_fn/fns/zip/mod.rs
+++ b/vortex-array/src/scalar_fn/fns/zip/mod.rs
@@ -3,6 +3,7 @@
 
 mod kernel;
 
+use std::fmt::Display;
 use std::fmt::Formatter;
 
 pub use kernel::*;
@@ -24,6 +25,7 @@ use crate::builders::builder_with_capacity;
 use crate::builtins::ArrayBuiltins;
 use crate::dtype::DType;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
 use crate::scalar_fn::EmptyOptions;
@@ -80,15 +82,15 @@ impl ScalarFnVTable for Zip {
     fn fmt_sql(
         &self,
         _options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "zip(")?;
-        expr.child(0).fmt_sql(f)?;
+        Display::fmt(expr.display_child(0), f)?;
         write!(f, ", ")?;
-        expr.child(1).fmt_sql(f)?;
+        Display::fmt(expr.display_child(1), f)?;
         write!(f, ", ")?;
-        expr.child(2).fmt_sql(f)?;
+        Display::fmt(expr.display_child(2), f)?;
         write!(f, ")")
     }
 
diff --git a/vortex-array/src/scalar_fn/foreign.rs b/vortex-array/src/scalar_fn/foreign.rs
index 94fd75b08f1..667b4756c1c 100644
--- a/vortex-array/src/scalar_fn/foreign.rs
+++ b/vortex-array/src/scalar_fn/foreign.rs
@@ -13,7 +13,7 @@ use crate::ArrayRef;
 use crate::ExecutionCtx;
 use crate::dtype::DType;
 use crate::dtype::Nullability;
-use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
 use crate::scalar_fn::ExecutionArgs;
@@ -93,15 +93,15 @@ impl ScalarFnVTable for ForeignScalarFnVTable {
     fn fmt_sql(
         &self,
         _options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> fmt::Result {
         write!(f, "{}(", self.id)?;
-        for i in 0..expr.children().len() {
+        for i in 0..expr.display_children_count() {
             if i > 0 {
                 write!(f, ", ")?;
             }
-            expr.child(i).fmt_sql(f)?;
+            Display::fmt(expr.display_child(i), f)?;
         }
         write!(f, ")")
     }
diff --git a/vortex-array/src/scalar_fn/internal/row_count.rs b/vortex-array/src/scalar_fn/internal/row_count.rs
index 7f78acbef64..290378c30a7 100644
--- a/vortex-array/src/scalar_fn/internal/row_count.rs
+++ b/vortex-array/src/scalar_fn/internal/row_count.rs
@@ -11,7 +11,7 @@ use vortex_array::arrays::scalar_fn::ScalarFnArrayExt;
 use vortex_array::dtype::DType;
 use vortex_array::dtype::Nullability;
 use vortex_array::dtype::PType;
-use vortex_array::expr::Expression;
+use vortex_array::expr::display::ExprDisplay;
 use vortex_array::scalar_fn::Arity;
 use vortex_array::scalar_fn::ChildName;
 use vortex_array::scalar_fn::EmptyOptions;
@@ -64,7 +64,7 @@ impl ScalarFnVTable for RowCount {
     fn fmt_sql(
         &self,
         _options: &Self::Options,
-        _expr: &Expression,
+        _expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "row_count()")
diff --git a/vortex-array/src/scalar_fn/typed.rs b/vortex-array/src/scalar_fn/typed.rs
index a6620735ff2..9c9225c7737 100644
--- a/vortex-array/src/scalar_fn/typed.rs
+++ b/vortex-array/src/scalar_fn/typed.rs
@@ -24,6 +24,7 @@ use crate::ArrayRef;
 use crate::ExecutionCtx;
 use crate::dtype::DType;
 use crate::expr::Expression;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::Arity;
 use crate::scalar_fn::ChildName;
 use crate::scalar_fn::ExecutionArgs;
@@ -92,8 +93,8 @@ pub(super) trait DynScalarFn: 'static + Send + Sync + super::sealed::Sealed {
     fn is_strict(&self) -> bool;
     fn is_fallible(&self) -> bool;
 
-    // Expression methods — take &Expression for tree traversal
-    fn fmt_sql(&self, expression: &Expression, f: &mut Formatter<'_>) -> fmt::Result;
+    // Expression methods — take expressions for tree traversal
+    fn fmt_sql(&self, expression: &dyn ExprDisplay, f: &mut Formatter<'_>) -> fmt::Result;
     fn simplify(
         &self,
         expression: &Expression,
@@ -192,7 +193,7 @@ impl<V: ScalarFnVTable> DynScalarFn for TypedScalarFnInstance<V> {
         V::is_fallible(&self.vtable, &self.options)
     }
 
-    fn fmt_sql(&self, expression: &Expression, f: &mut Formatter<'_>) -> fmt::Result {
+    fn fmt_sql(&self, expression: &dyn ExprDisplay, f: &mut Formatter<'_>) -> fmt::Result {
         V::fmt_sql(&self.vtable, &self.options, expression, f)
     }
 
diff --git a/vortex-array/src/scalar_fn/vtable.rs b/vortex-array/src/scalar_fn/vtable.rs
index ece52f6c4b4..55c897ce1a1 100644
--- a/vortex-array/src/scalar_fn/vtable.rs
+++ b/vortex-array/src/scalar_fn/vtable.rs
@@ -20,7 +20,7 @@ use crate::ArrayRef;
 use crate::ExecutionCtx;
 use crate::dtype::DType;
 use crate::expr::Expression;
-use crate::expr::traversal::Node;
+use crate::expr::display::ExprDisplay;
 use crate::scalar_fn::ScalarFnId;
 use crate::scalar_fn::ScalarFnRef;
 use crate::scalar_fn::TypedScalarFnInstance;
@@ -67,20 +67,20 @@ pub trait ScalarFnVTable: 'static + Sized + Clone + Send + Sync {
     /// Returns the name of the nth child of the expr.
     fn child_name(&self, options: &Self::Options, child_idx: usize) -> ChildName;
 
-    /// Format this expression in a nice human-readable SQL-style format
+    /// Format an expression tree in a human-readable SQL-style format.
     ///
-    /// The implementation should recursively format child expressions by calling
-    /// `expr.child(i).fmt_sql(f)`.
+    /// The expression may be either an [`Expression`] or a
+    /// [`bound expression`](crate::expr::BoundExpression).
     fn fmt_sql(
         &self,
         options: &Self::Options,
-        expr: &Expression,
+        expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> fmt::Result {
         write!(f, "{}(", self.id())?;
-        let nchildren = expr.children_count();
-        for (i, child) in expr.children().iter().enumerate() {
-            child.fmt_sql(f)?;
+        let nchildren = expr.display_children_count();
+        for i in 0..nchildren {
+            Display::fmt(expr.display_child(i), f)?;
             if i + 1 < nchildren {
                 write!(f, ", ")?;
             }
diff --git a/vortex-layout/src/layouts/row_idx/expr.rs b/vortex-layout/src/layouts/row_idx/expr.rs
index c0043542f93..31dbbd4d47e 100644
--- a/vortex-layout/src/layouts/row_idx/expr.rs
+++ b/vortex-layout/src/layouts/row_idx/expr.rs
@@ -8,6 +8,7 @@ use vortex_array::dtype::DType;
 use vortex_array::dtype::Nullability;
 use vortex_array::dtype::PType;
 use vortex_array::expr::Expression;
+use vortex_array::expr::display::ExprDisplay;
 use vortex_array::scalar_fn::Arity;
 use vortex_array::scalar_fn::ChildName;
 use vortex_array::scalar_fn::EmptyOptions;
@@ -41,7 +42,7 @@ impl ScalarFnVTable for RowIdx {
     fn fmt_sql(
         &self,
         _options: &Self::Options,
-        _expr: &Expression,
+        _expr: &dyn ExprDisplay,
         f: &mut Formatter<'_>,
     ) -> std::fmt::Result {
         write!(f, "#row_idx")