diff --git a/compiler/gen/src/llvm/build.rs b/compiler/gen/src/llvm/build.rs
index 7dd9a2d1cb..1bede26857 100644
--- a/compiler/gen/src/llvm/build.rs
+++ b/compiler/gen/src/llvm/build.rs
@@ -881,17 +881,23 @@ pub fn build_exp_call<'a, 'ctx, 'env>(
                 .unwrap_or_else(|| panic!("LLVM error: Invalid call by pointer."))
         }
 
-        CallType::LowLevel {
+        CallType::LowLevel { op } => {
+            run_low_level(env, layout_ids, scope, parent, layout, *op, arguments)
+        }
+
+        CallType::HigherOrderLowLevel {
             op,
-            opt_closure_layout,
-        } => run_low_level(
+            closure_layout,
+            function_owns_closure_data,
+        } => run_higher_order_low_level(
             env,
             layout_ids,
             scope,
             parent,
             layout,
             *op,
-            *opt_closure_layout,
+            *closure_layout,
+            *function_owns_closure_data,
             arguments,
         ),
 
@@ -2157,6 +2163,10 @@ pub fn build_exp_stmt<'a, 'ctx, 'env>(
             CallType::LowLevel { .. } => {
                 unreachable!("lowlevel itself never throws exceptions")
             }
+
+            CallType::HigherOrderLowLevel { .. } => {
+                unreachable!("lowlevel itself never throws exceptions")
+            }
         },
 
         Rethrow => {
@@ -3577,22 +3587,24 @@ pub static FAST_CALL_CONV: u32 = 8;
 pub static COLD_CALL_CONV: u32 = 9;
 
 #[allow(clippy::too_many_arguments)]
-fn run_low_level<'a, 'ctx, 'env>(
+fn run_higher_order_low_level<'a, 'ctx, 'env>(
     env: &Env<'a, 'ctx, 'env>,
     layout_ids: &mut LayoutIds<'a>,
     scope: &Scope<'a, 'ctx>,
     parent: FunctionValue<'ctx>,
     layout: &Layout<'a>,
     op: LowLevel,
-    opt_closure_layout: Option<Layout<'a>>,
+    function_layout: Layout<'a>,
+    function_owns_closure_data: bool,
     args: &[Symbol],
 ) -> BasicValueEnum<'ctx> {
     use LowLevel::*;
 
+    debug_assert!(op.is_higher_order());
+
     // macros because functions cause lifetime issues related to the `env` or `layout_ids`
     macro_rules! passed_function_at_index {
         ($index:expr) => {{
-            let function_layout = opt_closure_layout.unwrap();
             let function_symbol = args[$index];
 
             let fn_name = layout_ids
@@ -3616,7 +3628,6 @@ fn run_low_level<'a, 'ctx, 'env>(
 
             let (default, default_layout) = load_symbol_and_layout(scope, &args[1]);
 
-            let function_layout = opt_closure_layout.unwrap();
             let function = passed_function_at_index!(2);
 
             let (closure, closure_layout) = load_symbol_and_layout(scope, &args[3]);
@@ -3643,6 +3654,285 @@ fn run_low_level<'a, 'ctx, 'env>(
             }
         }};
     }
+    match op {
+        ListMap => {
+            // List.map : List before, (before -> after) -> List after
+            debug_assert_eq!(args.len(), 3);
+
+            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
+
+            let function = passed_function_at_index!(1);
+
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            match list_layout {
+                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
+                Layout::Builtin(Builtin::List(_, element_layout)) => list_map(
+                    env,
+                    function,
+                    function_layout,
+                    closure,
+                    *closure_layout,
+                    list,
+                    element_layout,
+                ),
+                _ => unreachable!("invalid list layout"),
+            }
+        }
+        ListMap2 => {
+            debug_assert_eq!(args.len(), 4);
+
+            let (list1, list1_layout) = load_symbol_and_layout(scope, &args[0]);
+            let (list2, list2_layout) = load_symbol_and_layout(scope, &args[1]);
+
+            let function = passed_function_at_index!(2);
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[3]);
+
+            match (list1_layout, list2_layout) {
+                (
+                    Layout::Builtin(Builtin::List(_, element1_layout)),
+                    Layout::Builtin(Builtin::List(_, element2_layout)),
+                ) => list_map2(
+                    env,
+                    layout_ids,
+                    function,
+                    function_layout,
+                    closure,
+                    *closure_layout,
+                    list1,
+                    list2,
+                    element1_layout,
+                    element2_layout,
+                ),
+                (Layout::Builtin(Builtin::EmptyList), _)
+                | (_, Layout::Builtin(Builtin::EmptyList)) => empty_list(env),
+                _ => unreachable!("invalid list layout"),
+            }
+        }
+        ListMap3 => {
+            debug_assert_eq!(args.len(), 5);
+
+            let (list1, list1_layout) = load_symbol_and_layout(scope, &args[0]);
+            let (list2, list2_layout) = load_symbol_and_layout(scope, &args[1]);
+            let (list3, list3_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            let function = passed_function_at_index!(3);
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[4]);
+
+            match (list1_layout, list2_layout, list3_layout) {
+                (
+                    Layout::Builtin(Builtin::List(_, element1_layout)),
+                    Layout::Builtin(Builtin::List(_, element2_layout)),
+                    Layout::Builtin(Builtin::List(_, element3_layout)),
+                ) => list_map3(
+                    env,
+                    layout_ids,
+                    function,
+                    function_layout,
+                    closure,
+                    *closure_layout,
+                    list1,
+                    list2,
+                    list3,
+                    element1_layout,
+                    element2_layout,
+                    element3_layout,
+                ),
+                (Layout::Builtin(Builtin::EmptyList), _, _)
+                | (_, Layout::Builtin(Builtin::EmptyList), _)
+                | (_, _, Layout::Builtin(Builtin::EmptyList)) => empty_list(env),
+                _ => unreachable!("invalid list layout"),
+            }
+        }
+        ListMapWithIndex => {
+            // List.mapWithIndex : List before, (Nat, before -> after) -> List after
+            debug_assert_eq!(args.len(), 3);
+
+            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
+
+            let function = passed_function_at_index!(1);
+
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            match list_layout {
+                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
+                Layout::Builtin(Builtin::List(_, element_layout)) => list_map_with_index(
+                    env,
+                    function,
+                    function_layout,
+                    closure,
+                    *closure_layout,
+                    list,
+                    element_layout,
+                ),
+                _ => unreachable!("invalid list layout"),
+            }
+        }
+        ListKeepIf => {
+            // List.keepIf : List elem, (elem -> Bool) -> List elem
+            debug_assert_eq!(args.len(), 3);
+
+            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
+
+            let function = passed_function_at_index!(1);
+
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            match list_layout {
+                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
+                Layout::Builtin(Builtin::List(_, element_layout)) => list_keep_if(
+                    env,
+                    layout_ids,
+                    function,
+                    closure,
+                    *closure_layout,
+                    list,
+                    element_layout,
+                ),
+                _ => unreachable!("invalid list layout"),
+            }
+        }
+        ListKeepOks => {
+            // List.keepOks : List before, (before -> Result after *) -> List after
+            debug_assert_eq!(args.len(), 3);
+
+            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
+
+            let function = passed_function_at_index!(1);
+
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            match (list_layout, layout) {
+                (_, Layout::Builtin(Builtin::EmptyList))
+                | (Layout::Builtin(Builtin::EmptyList), _) => empty_list(env),
+                (
+                    Layout::Builtin(Builtin::List(_, before_layout)),
+                    Layout::Builtin(Builtin::List(_, after_layout)),
+                ) => list_keep_oks(
+                    env,
+                    layout_ids,
+                    function,
+                    function_layout,
+                    closure,
+                    *closure_layout,
+                    list,
+                    before_layout,
+                    after_layout,
+                ),
+                (other1, other2) => {
+                    unreachable!("invalid list layouts:\n{:?}\n{:?}", other1, other2)
+                }
+            }
+        }
+        ListKeepErrs => {
+            // List.keepErrs : List before, (before -> Result * after) -> List after
+            debug_assert_eq!(args.len(), 3);
+
+            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
+
+            let function = passed_function_at_index!(1);
+
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            match (list_layout, layout) {
+                (_, Layout::Builtin(Builtin::EmptyList))
+                | (Layout::Builtin(Builtin::EmptyList), _) => empty_list(env),
+                (
+                    Layout::Builtin(Builtin::List(_, before_layout)),
+                    Layout::Builtin(Builtin::List(_, after_layout)),
+                ) => list_keep_errs(
+                    env,
+                    layout_ids,
+                    function,
+                    function_layout,
+                    closure,
+                    *closure_layout,
+                    list,
+                    before_layout,
+                    after_layout,
+                ),
+                (other1, other2) => {
+                    unreachable!("invalid list layouts:\n{:?}\n{:?}", other1, other2)
+                }
+            }
+        }
+        ListWalk => {
+            list_walk!(crate::llvm::build_list::ListWalk::Walk)
+        }
+        ListWalkUntil => {
+            list_walk!(crate::llvm::build_list::ListWalk::WalkUntil)
+        }
+        ListWalkBackwards => {
+            list_walk!(crate::llvm::build_list::ListWalk::WalkBackwards)
+        }
+        ListSortWith => {
+            // List.sortWith : List a, (a, a -> Ordering) -> List a
+            debug_assert_eq!(args.len(), 3);
+
+            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
+
+            let function = passed_function_at_index!(1);
+
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
+
+            match list_layout {
+                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
+                Layout::Builtin(Builtin::List(_, element_layout)) => list_sort_with(
+                    env,
+                    function,
+                    closure,
+                    *closure_layout,
+                    list,
+                    element_layout,
+                ),
+                _ => unreachable!("invalid list layout"),
+            }
+        }
+        DictWalk => {
+            debug_assert_eq!(args.len(), 4);
+
+            let (dict, dict_layout) = load_symbol_and_layout(scope, &args[0]);
+            let (default, default_layout) = load_symbol_and_layout(scope, &args[1]);
+            let function = passed_function_at_index!(2);
+            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[3]);
+
+            match dict_layout {
+                Layout::Builtin(Builtin::EmptyDict) => {
+                    // no elements, so `key` is not in here
+                    panic!("key type unknown")
+                }
+                Layout::Builtin(Builtin::Dict(key_layout, value_layout)) => dict_walk(
+                    env,
+                    layout_ids,
+                    dict,
+                    function,
+                    closure,
+                    *closure_layout,
+                    default,
+                    key_layout,
+                    value_layout,
+                    default_layout,
+                ),
+                _ => unreachable!("invalid dict layout"),
+            }
+        }
+        _ => unreachable!(),
+    }
+}
+
+#[allow(clippy::too_many_arguments)]
+fn run_low_level<'a, 'ctx, 'env>(
+    env: &Env<'a, 'ctx, 'env>,
+    layout_ids: &mut LayoutIds<'a>,
+    scope: &Scope<'a, 'ctx>,
+    parent: FunctionValue<'ctx>,
+    layout: &Layout<'a>,
+    op: LowLevel,
+    args: &[Symbol],
+) -> BasicValueEnum<'ctx> {
+    use LowLevel::*;
+
+    debug_assert!(!op.is_higher_order());
 
     match op {
         StrConcat => {
@@ -3784,213 +4074,6 @@ fn run_low_level<'a, 'ctx, 'env>(
 
             list_concat(env, inplace, parent, first_list, second_list, list_layout)
         }
-        ListMap => {
-            // List.map : List before, (before -> after) -> List after
-            debug_assert_eq!(args.len(), 3);
-
-            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
-
-            let function_layout = opt_closure_layout.unwrap();
-            let function = passed_function_at_index!(1);
-
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            match list_layout {
-                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
-                Layout::Builtin(Builtin::List(_, element_layout)) => list_map(
-                    env,
-                    function,
-                    function_layout,
-                    closure,
-                    *closure_layout,
-                    list,
-                    element_layout,
-                ),
-                _ => unreachable!("invalid list layout"),
-            }
-        }
-        ListMap2 => {
-            debug_assert_eq!(args.len(), 4);
-
-            let (list1, list1_layout) = load_symbol_and_layout(scope, &args[0]);
-            let (list2, list2_layout) = load_symbol_and_layout(scope, &args[1]);
-
-            let function_layout = opt_closure_layout.unwrap();
-            let function = passed_function_at_index!(2);
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[3]);
-
-            match (list1_layout, list2_layout) {
-                (
-                    Layout::Builtin(Builtin::List(_, element1_layout)),
-                    Layout::Builtin(Builtin::List(_, element2_layout)),
-                ) => list_map2(
-                    env,
-                    layout_ids,
-                    function,
-                    function_layout,
-                    closure,
-                    *closure_layout,
-                    list1,
-                    list2,
-                    element1_layout,
-                    element2_layout,
-                ),
-                (Layout::Builtin(Builtin::EmptyList), _)
-                | (_, Layout::Builtin(Builtin::EmptyList)) => empty_list(env),
-                _ => unreachable!("invalid list layout"),
-            }
-        }
-        ListMap3 => {
-            debug_assert_eq!(args.len(), 5);
-
-            let (list1, list1_layout) = load_symbol_and_layout(scope, &args[0]);
-            let (list2, list2_layout) = load_symbol_and_layout(scope, &args[1]);
-            let (list3, list3_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            let function_layout = opt_closure_layout.unwrap();
-            let function = passed_function_at_index!(3);
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[4]);
-
-            match (list1_layout, list2_layout, list3_layout) {
-                (
-                    Layout::Builtin(Builtin::List(_, element1_layout)),
-                    Layout::Builtin(Builtin::List(_, element2_layout)),
-                    Layout::Builtin(Builtin::List(_, element3_layout)),
-                ) => list_map3(
-                    env,
-                    layout_ids,
-                    function,
-                    function_layout,
-                    closure,
-                    *closure_layout,
-                    list1,
-                    list2,
-                    list3,
-                    element1_layout,
-                    element2_layout,
-                    element3_layout,
-                ),
-                (Layout::Builtin(Builtin::EmptyList), _, _)
-                | (_, Layout::Builtin(Builtin::EmptyList), _)
-                | (_, _, Layout::Builtin(Builtin::EmptyList)) => empty_list(env),
-                _ => unreachable!("invalid list layout"),
-            }
-        }
-        ListMapWithIndex => {
-            // List.mapWithIndex : List before, (Nat, before -> after) -> List after
-            debug_assert_eq!(args.len(), 3);
-
-            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
-
-            let function_layout = opt_closure_layout.unwrap();
-            let function = passed_function_at_index!(1);
-
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            match list_layout {
-                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
-                Layout::Builtin(Builtin::List(_, element_layout)) => list_map_with_index(
-                    env,
-                    function,
-                    function_layout,
-                    closure,
-                    *closure_layout,
-                    list,
-                    element_layout,
-                ),
-                _ => unreachable!("invalid list layout"),
-            }
-        }
-        ListKeepIf => {
-            // List.keepIf : List elem, (elem -> Bool) -> List elem
-            debug_assert_eq!(args.len(), 3);
-
-            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
-
-            let function = passed_function_at_index!(1);
-
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            match list_layout {
-                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
-                Layout::Builtin(Builtin::List(_, element_layout)) => list_keep_if(
-                    env,
-                    layout_ids,
-                    function,
-                    closure,
-                    *closure_layout,
-                    list,
-                    element_layout,
-                ),
-                _ => unreachable!("invalid list layout"),
-            }
-        }
-        ListKeepOks => {
-            // List.keepOks : List before, (before -> Result after *) -> List after
-            debug_assert_eq!(args.len(), 3);
-
-            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
-
-            let function_layout = opt_closure_layout.unwrap();
-            let function = passed_function_at_index!(1);
-
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            match (list_layout, layout) {
-                (_, Layout::Builtin(Builtin::EmptyList))
-                | (Layout::Builtin(Builtin::EmptyList), _) => empty_list(env),
-                (
-                    Layout::Builtin(Builtin::List(_, before_layout)),
-                    Layout::Builtin(Builtin::List(_, after_layout)),
-                ) => list_keep_oks(
-                    env,
-                    layout_ids,
-                    function,
-                    function_layout,
-                    closure,
-                    *closure_layout,
-                    list,
-                    before_layout,
-                    after_layout,
-                ),
-                (other1, other2) => {
-                    unreachable!("invalid list layouts:\n{:?}\n{:?}", other1, other2)
-                }
-            }
-        }
-        ListKeepErrs => {
-            // List.keepErrs : List before, (before -> Result * after) -> List after
-            debug_assert_eq!(args.len(), 3);
-
-            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
-
-            let function_layout = opt_closure_layout.unwrap();
-            let function = passed_function_at_index!(1);
-
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            match (list_layout, layout) {
-                (_, Layout::Builtin(Builtin::EmptyList))
-                | (Layout::Builtin(Builtin::EmptyList), _) => empty_list(env),
-                (
-                    Layout::Builtin(Builtin::List(_, before_layout)),
-                    Layout::Builtin(Builtin::List(_, after_layout)),
-                ) => list_keep_errs(
-                    env,
-                    layout_ids,
-                    function,
-                    function_layout,
-                    closure,
-                    *closure_layout,
-                    list,
-                    before_layout,
-                    after_layout,
-                ),
-                (other1, other2) => {
-                    unreachable!("invalid list layouts:\n{:?}\n{:?}", other1, other2)
-                }
-            }
-        }
         ListContains => {
             // List.contains : List elem, elem -> Bool
             debug_assert_eq!(args.len(), 2);
@@ -4015,15 +4098,6 @@ fn run_low_level<'a, 'ctx, 'env>(
 
             list_range(env, *builtin, low.into_int_value(), high.into_int_value())
         }
-        ListWalk => {
-            list_walk!(crate::llvm::build_list::ListWalk::Walk)
-        }
-        ListWalkUntil => {
-            list_walk!(crate::llvm::build_list::ListWalk::WalkUntil)
-        }
-        ListWalkBackwards => {
-            list_walk!(crate::llvm::build_list::ListWalk::WalkBackwards)
-        }
         ListAppend => {
             // List.append : List elem, elem -> List elem
             debug_assert_eq!(args.len(), 2);
@@ -4056,29 +4130,6 @@ fn run_low_level<'a, 'ctx, 'env>(
 
             list_join(env, inplace, parent, list, outer_list_layout)
         }
-        ListSortWith => {
-            // List.sortWith : List a, (a, a -> Ordering) -> List a
-            debug_assert_eq!(args.len(), 3);
-
-            let (list, list_layout) = load_symbol_and_layout(scope, &args[0]);
-
-            let function = passed_function_at_index!(1);
-
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[2]);
-
-            match list_layout {
-                Layout::Builtin(Builtin::EmptyList) => empty_list(env),
-                Layout::Builtin(Builtin::List(_, element_layout)) => list_sort_with(
-                    env,
-                    function,
-                    closure,
-                    *closure_layout,
-                    list,
-                    element_layout,
-                ),
-                _ => unreachable!("invalid list layout"),
-            }
-        }
         NumAbs | NumNeg | NumRound | NumSqrtUnchecked | NumLogUnchecked | NumSin | NumCos
         | NumCeiling | NumFloor | NumToFloat | NumIsFinite | NumAtan | NumAcos | NumAsin => {
             debug_assert_eq!(args.len(), 1);
@@ -4512,34 +4563,6 @@ fn run_low_level<'a, 'ctx, 'env>(
                 _ => unreachable!("invalid dict layout"),
             }
         }
-        DictWalk => {
-            debug_assert_eq!(args.len(), 4);
-
-            let (dict, dict_layout) = load_symbol_and_layout(scope, &args[0]);
-            let (default, default_layout) = load_symbol_and_layout(scope, &args[1]);
-            let function = passed_function_at_index!(2);
-            let (closure, closure_layout) = load_symbol_and_layout(scope, &args[3]);
-
-            match dict_layout {
-                Layout::Builtin(Builtin::EmptyDict) => {
-                    // no elements, so `key` is not in here
-                    panic!("key type unknown")
-                }
-                Layout::Builtin(Builtin::Dict(key_layout, value_layout)) => dict_walk(
-                    env,
-                    layout_ids,
-                    dict,
-                    function,
-                    closure,
-                    *closure_layout,
-                    default,
-                    key_layout,
-                    value_layout,
-                    default_layout,
-                ),
-                _ => unreachable!("invalid dict layout"),
-            }
-        }
         SetFromList => {
             debug_assert_eq!(args.len(), 1);
 
@@ -4581,6 +4604,10 @@ fn run_low_level<'a, 'ctx, 'env>(
 
             cond
         }
+
+        ListMap | ListMap2 | ListMap3 | ListMapWithIndex | ListKeepIf | ListWalk
+        | ListWalkUntil | ListWalkBackwards | ListKeepOks | ListKeepErrs | ListSortWith
+        | DictWalk => unreachable!("these are higher order, and are handled elsewhere"),
     }
 }
 
diff --git a/compiler/gen_dev/src/lib.rs b/compiler/gen_dev/src/lib.rs
index 7b2cd79057..36255ffc2a 100644
--- a/compiler/gen_dev/src/lib.rs
+++ b/compiler/gen_dev/src/lib.rs
@@ -211,10 +211,9 @@ where
                         }
                     }
 
-                    CallType::LowLevel {
-                        op: lowlevel,
-                        opt_closure_layout: _,
-                    } => self.build_run_low_level(sym, lowlevel, arguments, layout),
+                    CallType::LowLevel { op: lowlevel } => {
+                        self.build_run_low_level(sym, lowlevel, arguments, layout)
+                    }
                     x => Err(format!("the call type, {:?}, is not yet implemented", x)),
                 }
             }
@@ -524,6 +523,7 @@ where
                 self.set_last_seen(*sym, stmt);
             }
             CallType::LowLevel { .. } => {}
+            CallType::HigherOrderLowLevel { .. } => {}
             CallType::Foreign { .. } => {}
         }
     }
diff --git a/compiler/module/src/low_level.rs b/compiler/module/src/low_level.rs
index bd31c5031d..517c8bd01b 100644
--- a/compiler/module/src/low_level.rs
+++ b/compiler/module/src/low_level.rs
@@ -102,7 +102,9 @@ pub enum LowLevel {
 }
 
 impl LowLevel {
-    pub fn is_higher_order_function(&self) -> bool {
+    /// is one of the arguments always a function?
+    /// An example is List.map.
+    pub fn is_higher_order(&self) -> bool {
         use LowLevel::*;
 
         match self {
diff --git a/compiler/mono/src/borrow.rs b/compiler/mono/src/borrow.rs
index 11faa80aa7..ca1596ab57 100644
--- a/compiler/mono/src/borrow.rs
+++ b/compiler/mono/src/borrow.rs
@@ -407,29 +407,36 @@ impl<'a> BorrowInfState<'a> {
                 self.own_args(arguments);
             }
 
-            LowLevel {
-                op,
-                opt_closure_layout,
+            LowLevel { op } => {
+                debug_assert!(!op.is_higher_order());
+
+                self.own_var(z);
+
+                let ps = lowlevel_borrow_signature(self.arena, *op);
+
+                self.own_args_using_bools(arguments, ps);
+            }
+
+            HigherOrderLowLevel {
+                op, closure_layout, ..
             } => {
                 use roc_module::low_level::LowLevel::*;
-                match op {
-                    ListMap => {
-                        match self
-                            .param_map
-                            .get_symbol(arguments[1], opt_closure_layout.unwrap())
-                        {
-                            Some(ps) => {
-                                if !ps[0].borrow {
-                                    self.own_var(arguments[0]);
-                                }
 
-                                if ps.len() > 1 && !ps[1].borrow {
-                                    self.own_var(arguments[2]);
-                                }
+                debug_assert!(op.is_higher_order());
+
+                match op {
+                    ListMap => match self.param_map.get_symbol(arguments[1], *closure_layout) {
+                        Some(ps) => {
+                            if !ps[0].borrow {
+                                self.own_var(arguments[0]);
+                            }
+
+                            if ps.len() > 1 && !ps[1].borrow {
+                                self.own_var(arguments[2]);
                             }
-                            None => unreachable!(),
                         }
-                    }
+                        None => unreachable!(),
+                    },
                     _ => {
                         // very unsure what demand RunLowLevel should place upon its arguments
                         self.own_var(z);
diff --git a/compiler/mono/src/decision_tree.rs b/compiler/mono/src/decision_tree.rs
index baa0ed17f5..d3bc2753d8 100644
--- a/compiler/mono/src/decision_tree.rs
+++ b/compiler/mono/src/decision_tree.rs
@@ -1405,10 +1405,7 @@ fn compile_test_help<'a>(
     };
 
     let test = Expr::Call(crate::ir::Call {
-        call_type: crate::ir::CallType::LowLevel {
-            op: LowLevel::Eq,
-            opt_closure_layout: None,
-        },
+        call_type: crate::ir::CallType::LowLevel { op: LowLevel::Eq },
         arguments: arena.alloc([lhs, rhs]),
     });
 
diff --git a/compiler/mono/src/inc_dec.rs b/compiler/mono/src/inc_dec.rs
index fe70d8e26b..4c5fa80d5b 100644
--- a/compiler/mono/src/inc_dec.rs
+++ b/compiler/mono/src/inc_dec.rs
@@ -441,15 +441,23 @@ impl<'a> Context<'a> {
         use crate::ir::CallType::*;
 
         match &call_type {
-            LowLevel {
-                op,
-                opt_closure_layout,
+            LowLevel { op } => {
+                let ps = crate::borrow::lowlevel_borrow_signature(self.arena, *op);
+                let b = self.add_dec_after_lowlevel(arguments, ps, b, b_live_vars);
+
+                let v = Expr::Call(crate::ir::Call {
+                    call_type,
+                    arguments,
+                });
+
+                &*self.arena.alloc(Stmt::Let(z, v, l, b))
+            }
+
+            HigherOrderLowLevel {
+                op, closure_layout, ..
             } => match op {
                 roc_module::low_level::LowLevel::ListMap => {
-                    match self
-                        .param_map
-                        .get_symbol(arguments[1], opt_closure_layout.unwrap())
-                    {
+                    match self.param_map.get_symbol(arguments[1], *closure_layout) {
                         Some(ps) => {
                             let b = if ps[0].borrow {
                                 let ps = [BORROWED, BORROWED, BORROWED];
@@ -463,6 +471,18 @@ impl<'a> Context<'a> {
                                 ))
                             };
 
+                            let call_type = {
+                                if ps[1].borrow {
+                                    call_type
+                                } else {
+                                    HigherOrderLowLevel {
+                                        op: *op,
+                                        closure_layout: *closure_layout,
+                                        function_owns_closure_data: true,
+                                    }
+                                }
+                            };
+
                             let v = Expr::Call(crate::ir::Call {
                                 call_type,
                                 arguments,
@@ -790,14 +810,15 @@ impl<'a> Context<'a> {
 
                 use crate::ir::CallType;
                 let stmt = match &call.call_type {
-                    CallType::LowLevel {
-                        op,
-                        opt_closure_layout: _,
-                    } => {
+                    CallType::LowLevel { op } => {
                         let ps = crate::borrow::lowlevel_borrow_signature(self.arena, *op);
                         self.add_dec_after_lowlevel(call.arguments, ps, cont, &invoke_live_vars)
                     }
 
+                    CallType::HigherOrderLowLevel { .. } => {
+                        todo!("copy the code for normal calls over to here");
+                    }
+
                     CallType::Foreign { .. } => {
                         let ps = crate::borrow::foreign_borrow_signature(
                             self.arena,
diff --git a/compiler/mono/src/ir.rs b/compiler/mono/src/ir.rs
index 5cd3c6925a..5b88903ff1 100644
--- a/compiler/mono/src/ir.rs
+++ b/compiler/mono/src/ir.rs
@@ -1047,10 +1047,14 @@ impl<'a> Call<'a> {
                     .text("CallByPointer ")
                     .append(alloc.intersperse(it, " "))
             }
-            LowLevel {
-                op: lowlevel,
-                opt_closure_layout: _,
-            } => {
+            LowLevel { op: lowlevel } => {
+                let it = arguments.iter().map(|s| symbol_to_doc(alloc, *s));
+
+                alloc
+                    .text(format!("lowlevel {:?} ", lowlevel))
+                    .append(alloc.intersperse(it, " "))
+            }
+            HigherOrderLowLevel { op: lowlevel, .. } => {
                 let it = arguments.iter().map(|s| symbol_to_doc(alloc, *s));
 
                 alloc
@@ -1092,8 +1096,13 @@ pub enum CallType<'a> {
     },
     LowLevel {
         op: LowLevel,
+    },
+    HigherOrderLowLevel {
+        op: LowLevel,
         /// the layout of the closure argument, if any
-        opt_closure_layout: Option<Layout<'a>>,
+        closure_layout: Layout<'a>,
+        /// does the function need to own the closure data
+        function_owns_closure_data: bool,
     },
 }
 
@@ -2654,7 +2663,11 @@ macro_rules! match_on_closure_argument {
                     lambda_set,
                     $closure_data_symbol,
                     |top_level_function, closure_data, function_layout| self::Call {
-                        call_type: CallType::LowLevel { op: $op, opt_closure_layout: Some(function_layout) },
+                        call_type: CallType::HigherOrderLowLevel {
+                            op: $op,
+                            closure_layout: function_layout,
+                            function_owns_closure_data: false
+                        },
                         arguments: arena.alloc([$($x,)* top_level_function, closure_data]),
                     },
                     arena.alloc(top_level).full(),
@@ -4345,10 +4358,7 @@ pub fn with_hole<'a>(
                 }
                 _ => {
                     let call = self::Call {
-                        call_type: CallType::LowLevel {
-                            op,
-                            opt_closure_layout: None,
-                        },
+                        call_type: CallType::LowLevel { op },
                         arguments: arg_symbols,
                     };
 
@@ -4568,7 +4578,6 @@ pub fn from_can<'a>(
 
             let call_type = CallType::LowLevel {
                 op: LowLevel::ExpectTrue,
-                opt_closure_layout: None,
             };
             let arguments = env.arena.alloc([cond_symbol]);
             let call = self::Call {
@@ -5339,6 +5348,7 @@ fn substitute_in_call<'a>(
         }),
         CallType::Foreign { .. } => None,
         CallType::LowLevel { .. } => None,
+        CallType::HigherOrderLowLevel { .. } => None,
     };
 
     let mut did_change = false;
@@ -6052,6 +6062,12 @@ fn can_throw_exception(call: &Call) -> bool {
 
         CallType::LowLevel { .. } => {
             // lowlevel operations themselves don't throw
+            // TODO except for on allocation?
+            false
+        }
+        CallType::HigherOrderLowLevel { .. } => {
+            // TODO throwing is based on whether the HOF can throw
+            // or if there is (potentially) allocation in the lowlevel
             false
         }
     }