diff --git a/jit-compiler/src/codegen.rs b/jit-compiler/src/codegen.rs
index aec7ea37f..a359b3e07 100644
--- a/jit-compiler/src/codegen.rs
+++ b/jit-compiler/src/codegen.rs
@@ -29,18 +29,26 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
         }
     }
 
-    pub fn request_symbol(&mut self, name: &str) -> Result<(), String> {
+    /// Requests code for the symbol to be generated and returns the
+    /// code that returns the value of the symbol, which is either
+    /// the escaped name of the symbol or a dereferenced name of a lazy static.
+    pub fn request_symbol(&mut self, name: &str) -> Result<String, String> {
         if let Some(err) = self.failed.get(name) {
             return Err(err.clone());
         }
+        let reference = if self.symbol_needs_deref(name) {
+            format!("(*{})", escape_symbol(name))
+        } else {
+            escape_symbol(name)
+        };
         if self.requested.contains(name) {
-            return Ok(());
+            return Ok(reference);
         }
         self.requested.insert(name.to_string());
         match self.generate_code(name) {
             Ok(code) => {
                 self.symbols.insert(name.to_string(), code);
-                Ok(())
+                Ok(reference)
             }
             Err(err) => {
                 let err = format!("Failed to compile {name}: {err}");
@@ -60,7 +68,7 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
     }
 
     fn generate_code(&mut self, symbol: &str) -> Result<String, String> {
-        if let Some(code) = self.try_generate_builtin(symbol) {
+        if let Some(code) = try_generate_builtin::<T>(symbol) {
             return Ok(code);
         }
 
@@ -74,22 +82,28 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
 
         let type_scheme = value.type_scheme.clone().unwrap();
 
-        Ok(match type_scheme {
-            TypeScheme {
-                vars,
-                ty:
-                    Type::Function(FunctionType {
-                        params: param_types,
-                        value: return_type,
-                    }),
-            } => {
+        Ok(match (&value.e, type_scheme) {
+            (
+                Expression::LambdaExpression(..),
+                TypeScheme {
+                    vars,
+                    ty:
+                        Type::Function(FunctionType {
+                            params: param_types,
+                            value: return_type,
+                        }),
+                },
+            ) => {
                 assert!(vars.is_empty());
                 self.try_format_function(symbol, &param_types, return_type.as_ref(), &value.e)?
             }
-            TypeScheme {
-                vars,
-                ty: Type::Col,
-            } => {
+            (
+                Expression::LambdaExpression(..),
+                TypeScheme {
+                    vars,
+                    ty: Type::Col,
+                },
+            ) => {
                 assert!(vars.is_empty());
                 // TODO we assume it is an int -> int function.
                 // The type inference algorithm should store the derived type.
@@ -97,14 +111,26 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
                 // in the trait vars.
                 self.try_format_function(symbol, &[Type::Int], &Type::Fe, &value.e)?
             }
-            _ => format!(
-                "lazy_static::lazy_static! {{\n\
-                static ref {}: {} = {};\n\
-                }}\n",
-                escape_symbol(symbol),
-                map_type(&value.type_scheme.as_ref().unwrap().ty),
-                self.format_expr(&value.e)?
-            ),
+            _ => {
+                let type_scheme = value.type_scheme.as_ref().unwrap();
+                assert!(type_scheme.vars.is_empty());
+                let ty = if type_scheme.ty == Type::Col {
+                    Type::Function(FunctionType {
+                        params: vec![Type::Int],
+                        value: Box::new(Type::Fe),
+                    })
+                } else {
+                    type_scheme.ty.clone()
+                };
+                format!(
+                    "lazy_static::lazy_static! {{\n\
+                    static ref {}: {} = {};\n\
+                    }}\n",
+                    escape_symbol(symbol),
+                    map_type(&ty),
+                    self.format_expr(&value.e)?
+                )
+            }
         })
     }
 
@@ -116,7 +142,7 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
         expr: &Expression,
     ) -> Result<String, String> {
         let Expression::LambdaExpression(_, LambdaExpression { params, body, .. }) = expr else {
-            return Err(format!("Expected lambda expression for {name}, got {expr}",));
+            panic!();
         };
         Ok(format!(
             "fn {}({}) -> {} {{ {} }}\n",
@@ -131,31 +157,14 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
         ))
     }
 
-    fn try_generate_builtin(&self, symbol: &str) -> Option<String> {
-        let code = match symbol {
-            "std::array::len" => "<T>(a: Vec<T>) -> ibig::IBig { ibig::IBig::from(a.len()) }".to_string(),
-            "std::check::panic" => "(s: &str) -> ! { panic!(\"{s}\"); }".to_string(),
-            "std::field::modulus" => {
-                let modulus = T::modulus();
-                format!("() -> ibig::IBig {{ ibig::IBig::from(\"{modulus}\") }}")
-            }
-            "std::convert::fe" => "(n: ibig::IBig) -> FieldElement {\n    <FieldElement as PrimeField>::BigInt::try_from(n.to_biguint().unwrap()).unwrap().into()\n}"
-                .to_string(),
-            _ => return None,
-        };
-
-        Some(format!("fn {}{code}", escape_symbol(symbol)))
-    }
-
     fn format_expr(&mut self, e: &Expression) -> Result<String, String> {
         Ok(match e {
             Expression::Reference(_, Reference::LocalVar(_id, name)) => name.clone(),
             Expression::Reference(_, Reference::Poly(PolynomialReference { name, type_args })) => {
-                self.request_symbol(name)?;
+                let reference = self.request_symbol(name)?;
                 let ta = type_args.as_ref().unwrap();
                 format!(
-                    "{}{}",
-                    escape_symbol(name),
+                    "{reference}{}",
                     (!ta.is_empty())
                         .then(|| format!("::<{}>", ta.iter().map(map_type).join(", ")))
                         .unwrap_or_default()
@@ -279,6 +288,19 @@ impl<'a, T: FieldElement> CodeGenerator<'a, T> {
     fn format_statement(&mut self, s: &StatementInsideBlock<Expression>) -> Result<String, String> {
         Err(format!("Implement {s}"))
     }
+
+    /// Returns true if a reference to the symbol needs a deref operation or not.
+    fn symbol_needs_deref(&self, symbol: &str) -> bool {
+        if is_builtin(symbol) {
+            return false;
+        }
+        let (_, def) = self.analyzed.definitions.get(symbol).as_ref().unwrap();
+        if let Some(FunctionValueDefinition::Expression(typed_expr)) = def {
+            matches!(typed_expr.e, Expression::LambdaExpression(..))
+        } else {
+            false
+        }
+    }
 }
 
 pub fn escape_symbol(s: &str) -> String {
@@ -295,7 +317,11 @@ fn map_type(ty: &Type) -> String {
         Type::Expr => "Expr".to_string(),
         Type::Array(ArrayType { base, length: _ }) => format!("Vec<{}>", map_type(base)),
         Type::Tuple(_) => todo!(),
-        Type::Function(ft) => todo!("Type {ft}"),
+        Type::Function(ft) => format!(
+            "fn({}) -> {}",
+            ft.params.iter().map(map_type).join(", "),
+            map_type(&ft.value)
+        ),
         Type::TypeVar(tv) => tv.to_string(),
         Type::NamedType(path, type_args) => {
             if type_args.is_some() {
@@ -307,6 +333,28 @@ fn map_type(ty: &Type) -> String {
     }
 }
 
+fn is_builtin(symbol: &str) -> bool {
+    matches!(
+        symbol,
+        "std::array::len" | "std::check::panic" | "std::field::modulus" | "std::convert::fe"
+    )
+}
+
+fn try_generate_builtin<T: FieldElement>(symbol: &str) -> Option<String> {
+    let code = match symbol {
+        "std::array::len" => Some("<T>(a: Vec<T>) -> ibig::IBig { ibig::IBig::from(a.len()) }".to_string()),
+        "std::check::panic" => Some("(s: &str) -> ! { panic!(\"{s}\"); }".to_string()),
+        "std::field::modulus" => {
+            let modulus = T::modulus();
+            Some(format!("() -> ibig::IBig {{ ibig::IBig::from(\"{modulus}\") }}"))
+        }
+        "std::convert::fe" => Some("(n: ibig::IBig) -> FieldElement {\n    <FieldElement as PrimeField>::BigInt::try_from(n.to_biguint().unwrap()).unwrap().into()\n}"
+            .to_string()),
+        _ => None,
+    }?;
+    Some(format!("fn {}{code}", escape_symbol(symbol)))
+}
+
 #[cfg(test)]
 mod test {
     use powdr_number::GoldilocksField;
diff --git a/jit-compiler/tests/execution.rs b/jit-compiler/tests/execution.rs
index debc2ae66..3ce6115f0 100644
--- a/jit-compiler/tests/execution.rs
+++ b/jit-compiler/tests/execution.rs
@@ -44,6 +44,29 @@ fn sqrt() {
     assert_eq!(f(0), 0);
 }
 
+#[test]
+fn assigned_functions() {
+    let input = r#"
+        namespace std::array;
+            let len = 8;
+        namespace main;
+            let a: int -> int = |i| i + 1;
+            let b: int -> int = |i| i + 2;
+            let t: bool = "" == "";
+            let c = if t { a } else { b };
+            let d = |i| c(i);
+        "#;
+    let c = compile(input, "main::c");
+
+    assert_eq!(c(0), 1);
+    assert_eq!(c(1), 2);
+    assert_eq!(c(2), 3);
+    assert_eq!(c(3), 4);
+
+    let d = compile(input, "main::d");
+    assert_eq!(d(0), 1);
+}
+
 #[test]
 fn simple_field() {
     let f = compile(