diff --git a/src/evaluator.rs b/src/evaluator.rs
index 6b45263..ac7c0b1 100644
--- a/src/evaluator.rs
+++ b/src/evaluator.rs
@@ -289,6 +289,7 @@ impl<'a> Evaluator<'a> {
         Ok(Value::Function(Function::UserDefined {
           body: body.clone(),
           environment: self.environment.clone(),
+          identity: Rc::new(()),
           name: None,
           parameters: parameters.clone(),
         }))
@@ -447,6 +448,7 @@ impl<'a> Evaluator<'a> {
         let function = Function::UserDefined {
           body: body.clone(),
           environment: self.environment.clone(),
+          identity: Rc::new(()),
           name: Some(name.clone()),
           parameters: params.clone(),
         };
diff --git a/src/function.rs b/src/function.rs
index d1736da..a94d9fd 100644
--- a/src/function.rs
+++ b/src/function.rs
@@ -10,6 +10,7 @@ pub enum Function<'src> {
   UserDefined {
     body: Vec<Spanned<Statement>>,
     environment: Environment<'src>,
+    identity: Rc<()>,
     name: Option<String>,
     parameters: Vec<String>,
   },
@@ -37,6 +38,7 @@ impl<'src> Function<'src> {
         environment,
         name,
         parameters,
+        ..
       } => {
         let call_environment = Environment::with_parent(environment.clone());
 
@@ -98,9 +100,9 @@ impl PartialEq for Function<'_> {
     match (self, other) {
       (Self::Builtin { name: a, .. }, Self::Builtin { name: b, .. }) => a == b,
       (
-        Self::UserDefined { name: Some(a), .. },
-        Self::UserDefined { name: Some(b), .. },
-      ) => a == b,
+        Self::UserDefined { identity: a, .. },
+        Self::UserDefined { identity: b, .. },
+      ) => Rc::ptr_eq(a, b),
       _ => false,
     }
   }
diff --git a/tests/integration.rs b/tests/integration.rs
index bc913d3..6b3841d 100644
--- a/tests/integration.rs
+++ b/tests/integration.rs
@@ -1354,6 +1354,35 @@ fn function_calling_builtin() -> Result {
     .run()
 }
 
+#[test]
+fn function_equality_uses_identity() -> Result {
+  Test::new()?
+    .program(indoc! {
+      "
+      anonymous = fn() {}
+      alias = anonymous
+
+      println(anonymous == anonymous)
+      println(anonymous == alias)
+      println(anonymous == fn() {})
+
+      fn foo() {
+        return 1
+      }
+
+      original = foo
+
+      fn foo() {
+        return 2
+      }
+
+      println(original == foo)
+      "
+    })
+    .expected_stdout(Exact("true\ntrue\nfalse\nfalse\n"))
+    .run()
+}
+
 #[test]
 fn function_modifying_outer_scope() -> Result {
   Test::new()?