diff --git a/crates/cross/src/compound/list/flat.rs b/crates/cross/src/compound/list/flat.rs
index 2784fb7..205504e 100644
--- a/crates/cross/src/compound/list/flat.rs
+++ b/crates/cross/src/compound/list/flat.rs
@@ -309,6 +309,7 @@ pub trait SplitHead {
     type Head;
     type Tail;
     fn split(self) -> (Self::Head, Self::Tail);
+    fn split_ref<'a>(&'a self) -> (&'a Self::Head, &'a Self::Tail);
 }
 impl<H, T> SplitHead for Node<H, T> {
     type Head = H;
@@ -316,6 +317,9 @@ impl<H, T> SplitHead for Node<H, T> {
     fn split(self) -> (Self::Head, Self::Tail) {
         (self.head, self.tail)
     }
+    fn split_ref<'a>(&'a self) -> (&'a Self::Head, &'a Self::Tail) {
+        (&self.head, &self.tail)
+    }
 }
 
 /// these are exported for the convenience of potential consumers: not needed internally
diff --git a/crates/cross/src/compound/list/mod.rs b/crates/cross/src/compound/list/mod.rs
index 6b2d531..2fe3923 100644
--- a/crates/cross/src/compound/list/mod.rs
+++ b/crates/cross/src/compound/list/mod.rs
@@ -97,7 +97,7 @@ where
 // - [x] map (calls into fold, with the accumulator being Appendable::append)
 // - [ ] visit (calls into fold, with a no-op accumulator)
 // - [ ] visit_ref, visit_mut (calls as_ref/as_mut, then visit)
-// - [ ] enumerate (calls fold, with the accumulator being a Peano counter + value copy)
+// - [x] enumerate (calls fold, with the accumulator being a Peano counter + value copy)
 
 pub trait ListConsumer<L> {
     type Output;
@@ -113,6 +113,7 @@ pub trait FoldOp<State, V> {
 
 pub struct FoldImpl<Op, State>(Op, State);
 
+//////// fold by-value
 impl<Op, State> ListConsumer<Empty> for FoldImpl<Op, State> {
     type Output = State;
     fn consume(self, _l: Empty) -> Self::Output {
@@ -134,6 +135,28 @@ where
     }
 }
 
+//////// fold by-ref
+impl<Op, State> ListConsumer<&Empty> for FoldImpl<Op, State> {
+    type Output = State;
+    fn consume(self, _l: &Empty) -> Self::Output {
+        self.1
+    }
+}
+
+impl<'a, H, T, Op, State> ListConsumer<&'a Node<H, T>> for FoldImpl<Op, State>
+where
+    Op: FoldOp<State, &'a H>,
+    FoldImpl<Op, Op::Output>: ListConsumer<&'a T>,
+{
+    type Output = <FoldImpl<Op, Op::Output> as ListConsumer<&'a T>>::Output;
+    fn consume(self, l: &'a Node<H, T>) -> Self::Output {
+        let FoldImpl(op, state) = self;
+        let (head, tail) = l.split_ref();
+        let next_state = op.feed(state, head);
+        FoldImpl(op, next_state).consume(tail)
+    }
+}
+
 pub trait Fold<Op, Init> {
     type Output;
     fn fold(self, op: Op, init: Init) -> Self::Output;
@@ -309,6 +332,32 @@ mod test {
         assert_eq!(list.fold(Sum, 2i32), 28f32);
     }
 
+
+    #[derive(PartialEq)]
+    struct NotCopy(i32);
+
+    struct SumRef;
+    impl FoldOp<i32, &NotCopy> for SumRef {
+        type Output = i32;
+        fn feed(&self, prev: i32, next: &NotCopy) -> Self::Output {
+            prev + next.0
+        }
+    }
+    impl FoldOp<i32, &i32> for SumRef {
+        type Output = i32;
+        fn feed(&self, prev: i32, next: &i32) -> Self::Output {
+            prev + *next
+        }
+    }
+
+    #[test]
+    fn fold_ref() {
+        let list = &(3i32, NotCopy(4i32), 5i32).into_list();
+        assert_eq!(list.fold(SumRef, 2i32), 14i32);
+        assert!(list == list); // just check that it wasn't consumed
+    }
+
+
     #[test]
     fn reverse_empty() {
         assert!(Empty::default().reverse() == Empty::default());