Merge pull request #64 from AeneasVerif/son/merge_back

Merge the forward/backward functions

17 files changed, 1896 insertions, 2749 deletions

diff --git a/tests/lean/Array.lean b/tests/lean/Array.lean
index 25dad3cf..7785a208 100644
--- a/tests/lean/Array.lean
+++ b/tests/lean/Array.lean
@@ -11,99 +11,91 @@ inductive AB :=
 | A : AB
 | B : AB
 
-/- [array::incr]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::incr]:
    Source: 'src/array.rs', lines 8:0-8:24 -/
 def incr (x : U32) : Result U32 :=
   x + 1#u32
 
-/- [array::array_to_shared_slice_]: forward function
+/- [array::array_to_shared_slice_]:
    Source: 'src/array.rs', lines 16:0-16:53 -/
 def array_to_shared_slice_
   (T : Type) (s : Array T 32#usize) : Result (Slice T) :=
   Array.to_slice T 32#usize s
 
-/- [array::array_to_mut_slice_]: forward function
+/- [array::array_to_mut_slice_]:
    Source: 'src/array.rs', lines 21:0-21:58 -/
-def array_to_mut_slice_ (T : Type) (s : Array T 32#usize) : Result (Slice T) :=
-  Array.to_slice T 32#usize s
-
-/- [array::array_to_mut_slice_]: backward function 0
-   Source: 'src/array.rs', lines 21:0-21:58 -/
-def array_to_mut_slice__back
-  (T : Type) (s : Array T 32#usize) (ret : Slice T) :
-  Result (Array T 32#usize)
+def array_to_mut_slice_
+  (T : Type) (s : Array T 32#usize) :
+  Result ((Slice T) × (Slice T → Result (Array T 32#usize)))
   :=
-  Array.from_slice T 32#usize s ret
+  do
+  let (s1, to_slice_mut_back) ← Array.to_slice_mut T 32#usize s
+  Result.ret (s1, to_slice_mut_back)
 
-/- [array::array_len]: forward function
+/- [array::array_len]:
    Source: 'src/array.rs', lines 25:0-25:40 -/
 def array_len (T : Type) (s : Array T 32#usize) : Result Usize :=
   do
-    let s0 ← Array.to_slice T 32#usize s
-    let i := Slice.len T s0
-    Result.ret i
+  let s1 ← Array.to_slice T 32#usize s
+  let i := Slice.len T s1
+  Result.ret i
 
-/- [array::shared_array_len]: forward function
+/- [array::shared_array_len]:
    Source: 'src/array.rs', lines 29:0-29:48 -/
 def shared_array_len (T : Type) (s : Array T 32#usize) : Result Usize :=
   do
-    let s0 ← Array.to_slice T 32#usize s
-    let i := Slice.len T s0
-    Result.ret i
+  let s1 ← Array.to_slice T 32#usize s
+  let i := Slice.len T s1
+  Result.ret i
 
-/- [array::shared_slice_len]: forward function
+/- [array::shared_slice_len]:
    Source: 'src/array.rs', lines 33:0-33:44 -/
 def shared_slice_len (T : Type) (s : Slice T) : Result Usize :=
   let i := Slice.len T s
   Result.ret i
 
-/- [array::index_array_shared]: forward function
+/- [array::index_array_shared]:
    Source: 'src/array.rs', lines 37:0-37:57 -/
 def index_array_shared
   (T : Type) (s : Array T 32#usize) (i : Usize) : Result T :=
   Array.index_usize T 32#usize s i
 
-/- [array::index_array_u32]: forward function
+/- [array::index_array_u32]:
    Source: 'src/array.rs', lines 44:0-44:53 -/
 def index_array_u32 (s : Array U32 32#usize) (i : Usize) : Result U32 :=
   Array.index_usize U32 32#usize s i
 
-/- [array::index_array_copy]: forward function
+/- [array::index_array_copy]:
    Source: 'src/array.rs', lines 48:0-48:45 -/
 def index_array_copy (x : Array U32 32#usize) : Result U32 :=
   Array.index_usize U32 32#usize x 0#usize
 
-/- [array::index_mut_array]: forward function
+/- [array::index_mut_array]:
    Source: 'src/array.rs', lines 52:0-52:62 -/
-def index_mut_array (T : Type) (s : Array T 32#usize) (i : Usize) : Result T :=
-  Array.index_usize T 32#usize s i
-
-/- [array::index_mut_array]: backward function 0
-   Source: 'src/array.rs', lines 52:0-52:62 -/
-def index_mut_array_back
-  (T : Type) (s : Array T 32#usize) (i : Usize) (ret : T) :
-  Result (Array T 32#usize)
+def index_mut_array
+  (T : Type) (s : Array T 32#usize) (i : Usize) :
+  Result (T × (T → Result (Array T 32#usize)))
   :=
-  Array.update_usize T 32#usize s i ret
+  do
+  let (t, index_mut_back) ← Array.index_mut_usize T 32#usize s i
+  Result.ret (t, index_mut_back)
 
-/- [array::index_slice]: forward function
+/- [array::index_slice]:
    Source: 'src/array.rs', lines 56:0-56:46 -/
 def index_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
   Slice.index_usize T s i
 
-/- [array::index_mut_slice]: forward function
+/- [array::index_mut_slice]:
    Source: 'src/array.rs', lines 60:0-60:58 -/
-def index_mut_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
-  Slice.index_usize T s i
-
-/- [array::index_mut_slice]: backward function 0
-   Source: 'src/array.rs', lines 60:0-60:58 -/
-def index_mut_slice_back
-  (T : Type) (s : Slice T) (i : Usize) (ret : T) : Result (Slice T) :=
-  Slice.update_usize T s i ret
+def index_mut_slice
+  (T : Type) (s : Slice T) (i : Usize) :
+  Result (T × (T → Result (Slice T)))
+  :=
+  do
+  let (t, index_mut_back) ← Slice.index_mut_usize T s i
+  Result.ret (t, index_mut_back)
 
-/- [array::slice_subslice_shared_]: forward function
+/- [array::slice_subslice_shared_]:
    Source: 'src/array.rs', lines 64:0-64:70 -/
 def slice_subslice_shared_
   (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
@@ -111,41 +103,35 @@ def slice_subslice_shared_
     (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
     { start := y, end_ := z }
 
-/- [array::slice_subslice_mut_]: forward function
+/- [array::slice_subslice_mut_]:
    Source: 'src/array.rs', lines 68:0-68:75 -/
 def slice_subslice_mut_
-  (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
-  core.slice.index.Slice.index_mut U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
-    { start := y, end_ := z }
-
-/- [array::slice_subslice_mut_]: backward function 0
-   Source: 'src/array.rs', lines 68:0-68:75 -/
-def slice_subslice_mut__back
-  (x : Slice U32) (y : Usize) (z : Usize) (ret : Slice U32) :
-  Result (Slice U32)
+  (x : Slice U32) (y : Usize) (z : Usize) :
+  Result ((Slice U32) × (Slice U32 → Result (Slice U32)))
   :=
-  core.slice.index.Slice.index_mut_back U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
-    { start := y, end_ := z } ret
+  do
+  let (s, index_mut_back) ←
+    core.slice.index.Slice.index_mut U32 (core.ops.range.Range Usize)
+      (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
+      { start := y, end_ := z }
+  Result.ret (s, index_mut_back)
 
-/- [array::array_to_slice_shared_]: forward function
+/- [array::array_to_slice_shared_]:
    Source: 'src/array.rs', lines 72:0-72:54 -/
 def array_to_slice_shared_ (x : Array U32 32#usize) : Result (Slice U32) :=
   Array.to_slice U32 32#usize x
 
-/- [array::array_to_slice_mut_]: forward function
+/- [array::array_to_slice_mut_]:
    Source: 'src/array.rs', lines 76:0-76:59 -/
-def array_to_slice_mut_ (x : Array U32 32#usize) : Result (Slice U32) :=
-  Array.to_slice U32 32#usize x
-
-/- [array::array_to_slice_mut_]: backward function 0
-   Source: 'src/array.rs', lines 76:0-76:59 -/
-def array_to_slice_mut__back
-  (x : Array U32 32#usize) (ret : Slice U32) : Result (Array U32 32#usize) :=
-  Array.from_slice U32 32#usize x ret
+def array_to_slice_mut_
+  (x : Array U32 32#usize) :
+  Result ((Slice U32) × (Slice U32 → Result (Array U32 32#usize)))
+  :=
+  do
+  let (s, to_slice_mut_back) ← Array.to_slice_mut U32 32#usize x
+  Result.ret (s, to_slice_mut_back)
 
-/- [array::array_subslice_shared_]: forward function
+/- [array::array_subslice_shared_]:
    Source: 'src/array.rs', lines 80:0-80:74 -/
 def array_subslice_shared_
   (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
@@ -154,311 +140,294 @@ def array_subslice_shared_
     (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
     { start := y, end_ := z }
 
-/- [array::array_subslice_mut_]: forward function
+/- [array::array_subslice_mut_]:
    Source: 'src/array.rs', lines 84:0-84:79 -/
 def array_subslice_mut_
-  (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
-  core.array.Array.index_mut U32 (core.ops.range.Range Usize) 32#usize
-    (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
-    { start := y, end_ := z }
-
-/- [array::array_subslice_mut_]: backward function 0
-   Source: 'src/array.rs', lines 84:0-84:79 -/
-def array_subslice_mut__back
-  (x : Array U32 32#usize) (y : Usize) (z : Usize) (ret : Slice U32) :
-  Result (Array U32 32#usize)
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) :
+  Result ((Slice U32) × (Slice U32 → Result (Array U32 32#usize)))
   :=
-  core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 32#usize
-    (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
-    { start := y, end_ := z } ret
-
-/- [array::index_slice_0]: forward function
+  do
+  let (s, index_mut_back) ←
+    core.array.Array.index_mut U32 (core.ops.range.Range Usize) 32#usize
+      (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
+      (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
+      { start := y, end_ := z }
+  Result.ret (s, index_mut_back)
+
+/- [array::index_slice_0]:
    Source: 'src/array.rs', lines 88:0-88:38 -/
 def index_slice_0 (T : Type) (s : Slice T) : Result T :=
   Slice.index_usize T s 0#usize
 
-/- [array::index_array_0]: forward function
+/- [array::index_array_0]:
    Source: 'src/array.rs', lines 92:0-92:42 -/
 def index_array_0 (T : Type) (s : Array T 32#usize) : Result T :=
   Array.index_usize T 32#usize s 0#usize
 
-/- [array::index_index_array]: forward function
+/- [array::index_index_array]:
    Source: 'src/array.rs', lines 103:0-103:71 -/
 def index_index_array
   (s : Array (Array U32 32#usize) 32#usize) (i : Usize) (j : Usize) :
   Result U32
   :=
   do
-    let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
-    Array.index_usize U32 32#usize a j
+  let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
+  Array.index_usize U32 32#usize a j
 
-/- [array::update_update_array]: forward function
+/- [array::update_update_array]:
    Source: 'src/array.rs', lines 114:0-114:70 -/
 def update_update_array
   (s : Array (Array U32 32#usize) 32#usize) (i : Usize) (j : Usize) :
   Result Unit
   :=
   do
-    let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
-    let a0 ← Array.update_usize U32 32#usize a j 0#u32
-    let _ ← Array.update_usize (Array U32 32#usize) 32#usize s i a0
-    Result.ret ()
+  let (a, index_mut_back) ←
+    Array.index_mut_usize (Array U32 32#usize) 32#usize s i
+  let (_, index_mut_back1) ← Array.index_mut_usize U32 32#usize a j
+  let a1 ← index_mut_back1 0#u32
+  let _ ← index_mut_back a1
+  Result.ret ()
 
-/- [array::array_local_deep_copy]: forward function
+/- [array::array_local_deep_copy]:
    Source: 'src/array.rs', lines 118:0-118:43 -/
 def array_local_deep_copy (x : Array U32 32#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::take_array]: forward function
+/- [array::take_array]:
    Source: 'src/array.rs', lines 122:0-122:30 -/
 def take_array (a : Array U32 2#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::take_array_borrow]: forward function
+/- [array::take_array_borrow]:
    Source: 'src/array.rs', lines 123:0-123:38 -/
 def take_array_borrow (a : Array U32 2#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::take_slice]: forward function
+/- [array::take_slice]:
    Source: 'src/array.rs', lines 124:0-124:28 -/
 def take_slice (s : Slice U32) : Result Unit :=
   Result.ret ()
 
-/- [array::take_mut_slice]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::take_mut_slice]:
    Source: 'src/array.rs', lines 125:0-125:36 -/
 def take_mut_slice (s : Slice U32) : Result (Slice U32) :=
   Result.ret s
 
-/- [array::const_array]: forward function
+/- [array::const_array]:
    Source: 'src/array.rs', lines 127:0-127:32 -/
 def const_array : Result (Array U32 2#usize) :=
   Result.ret (Array.make U32 2#usize [ 0#u32, 0#u32 ])
 
-/- [array::const_slice]: forward function
+/- [array::const_slice]:
    Source: 'src/array.rs', lines 131:0-131:20 -/
 def const_slice : Result Unit :=
   do
-    let _ ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    Result.ret ()
+  let _ ←
+    Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  Result.ret ()
 
-/- [array::take_all]: forward function
+/- [array::take_all]:
    Source: 'src/array.rs', lines 141:0-141:17 -/
 def take_all : Result Unit :=
   do
-    let _ ← take_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let _ ← take_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let s ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let _ ← take_slice s
-    let s0 ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let s1 ← take_mut_slice s0
-    let _ ←
-      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
-    Result.ret ()
-
-/- [array::index_array]: forward function
+  let _ ← take_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let _ ← take_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let _ ← take_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let s ←
+    Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let _ ← take_slice s
+  let (s1, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let s2 ← take_mut_slice s1
+  let _ ← to_slice_mut_back s2
+  Result.ret ()
+
+/- [array::index_array]:
    Source: 'src/array.rs', lines 155:0-155:38 -/
 def index_array (x : Array U32 2#usize) : Result U32 :=
   Array.index_usize U32 2#usize x 0#usize
 
-/- [array::index_array_borrow]: forward function
+/- [array::index_array_borrow]:
    Source: 'src/array.rs', lines 158:0-158:46 -/
 def index_array_borrow (x : Array U32 2#usize) : Result U32 :=
   Array.index_usize U32 2#usize x 0#usize
 
-/- [array::index_slice_u32_0]: forward function
+/- [array::index_slice_u32_0]:
    Source: 'src/array.rs', lines 162:0-162:42 -/
 def index_slice_u32_0 (x : Slice U32) : Result U32 :=
   Slice.index_usize U32 x 0#usize
 
-/- [array::index_mut_slice_u32_0]: forward function
+/- [array::index_mut_slice_u32_0]:
    Source: 'src/array.rs', lines 166:0-166:50 -/
-def index_mut_slice_u32_0 (x : Slice U32) : Result U32 :=
-  Slice.index_usize U32 x 0#usize
-
-/- [array::index_mut_slice_u32_0]: backward function 0
-   Source: 'src/array.rs', lines 166:0-166:50 -/
-def index_mut_slice_u32_0_back (x : Slice U32) : Result (Slice U32) :=
+def index_mut_slice_u32_0 (x : Slice U32) : Result (U32 × (Slice U32)) :=
   do
-    let _ ← Slice.index_usize U32 x 0#usize
-    Result.ret x
+  let i ← Slice.index_usize U32 x 0#usize
+  Result.ret (i, x)
 
-/- [array::index_all]: forward function
+/- [array::index_all]:
    Source: 'src/array.rs', lines 170:0-170:25 -/
 def index_all : Result U32 :=
   do
-    let i ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let i0 ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let i1 ← i + i0
-    let i2 ← index_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let i3 ← i1 + i2
-    let s ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let i4 ← index_slice_u32_0 s
-    let i5 ← i3 + i4
-    let s0 ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let i6 ← index_mut_slice_u32_0 s0
-    let i7 ← i5 + i6
-    let s1 ← index_mut_slice_u32_0_back s0
-    let _ ←
-      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
-    Result.ret i7
-
-/- [array::update_array]: forward function
+  let i ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i1 ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i2 ← i + i1
+  let i3 ← index_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i4 ← i2 + i3
+  let s ←
+    Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i5 ← index_slice_u32_0 s
+  let i6 ← i4 + i5
+  let (s1, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (i7, s2) ← index_mut_slice_u32_0 s1
+  let i8 ← i6 + i7
+  let _ ← to_slice_mut_back s2
+  Result.ret i8
+
+/- [array::update_array]:
    Source: 'src/array.rs', lines 184:0-184:36 -/
 def update_array (x : Array U32 2#usize) : Result Unit :=
   do
-    let _ ← Array.update_usize U32 2#usize x 0#usize 1#u32
-    Result.ret ()
+  let (_, index_mut_back) ← Array.index_mut_usize U32 2#usize x 0#usize
+  let _ ← index_mut_back 1#u32
+  Result.ret ()
 
-/- [array::update_array_mut_borrow]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::update_array_mut_borrow]:
    Source: 'src/array.rs', lines 187:0-187:48 -/
 def update_array_mut_borrow
   (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
-  Array.update_usize U32 2#usize x 0#usize 1#u32
+  do
+  let (_, index_mut_back) ← Array.index_mut_usize U32 2#usize x 0#usize
+  index_mut_back 1#u32
 
-/- [array::update_mut_slice]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::update_mut_slice]:
    Source: 'src/array.rs', lines 190:0-190:38 -/
 def update_mut_slice (x : Slice U32) : Result (Slice U32) :=
-  Slice.update_usize U32 x 0#usize 1#u32
+  do
+  let (_, index_mut_back) ← Slice.index_mut_usize U32 x 0#usize
+  index_mut_back 1#u32
 
-/- [array::update_all]: forward function
+/- [array::update_all]:
    Source: 'src/array.rs', lines 194:0-194:19 -/
 def update_all : Result Unit :=
   do
-    let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let x ← update_array_mut_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let s ← Array.to_slice U32 2#usize x
-    let s0 ← update_mut_slice s
-    let _ ← Array.from_slice U32 2#usize x s0
-    Result.ret ()
-
-/- [array::range_all]: forward function
+  let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let a ← update_array_mut_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (s, to_slice_mut_back) ← Array.to_slice_mut U32 2#usize a
+  let s1 ← update_mut_slice s
+  let _ ← to_slice_mut_back s1
+  Result.ret ()
+
+/- [array::range_all]:
    Source: 'src/array.rs', lines 205:0-205:18 -/
 def range_all : Result Unit :=
   do
-    let s ←
-      core.array.Array.index_mut U32 (core.ops.range.Range Usize) 4#usize
-        (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-        (core.slice.index.SliceIndexRangeUsizeSliceTInst U32))
-        (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
-        { start := 1#usize, end_ := 3#usize }
-    let s0 ← update_mut_slice s
-    let _ ←
-      core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 4#usize
-        (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-        (core.slice.index.SliceIndexRangeUsizeSliceTInst U32))
-        (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
-        { start := 1#usize, end_ := 3#usize } s0
-    Result.ret ()
-
-/- [array::deref_array_borrow]: forward function
+  let (s, index_mut_back) ←
+    core.array.Array.index_mut U32 (core.ops.range.Range Usize) 4#usize
+      (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
+      (core.slice.index.SliceIndexRangeUsizeSliceTInst U32))
+      (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
+      { start := 1#usize, end_ := 3#usize }
+  let s1 ← update_mut_slice s
+  let _ ← index_mut_back s1
+  Result.ret ()
+
+/- [array::deref_array_borrow]:
    Source: 'src/array.rs', lines 214:0-214:46 -/
 def deref_array_borrow (x : Array U32 2#usize) : Result U32 :=
   Array.index_usize U32 2#usize x 0#usize
 
-/- [array::deref_array_mut_borrow]: forward function
-   Source: 'src/array.rs', lines 219:0-219:54 -/
-def deref_array_mut_borrow (x : Array U32 2#usize) : Result U32 :=
-  Array.index_usize U32 2#usize x 0#usize
-
-/- [array::deref_array_mut_borrow]: backward function 0
+/- [array::deref_array_mut_borrow]:
    Source: 'src/array.rs', lines 219:0-219:54 -/
-def deref_array_mut_borrow_back
-  (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
+def deref_array_mut_borrow
+  (x : Array U32 2#usize) : Result (U32 × (Array U32 2#usize)) :=
   do
-    let _ ← Array.index_usize U32 2#usize x 0#usize
-    Result.ret x
+  let i ← Array.index_usize U32 2#usize x 0#usize
+  Result.ret (i, x)
 
-/- [array::take_array_t]: forward function
+/- [array::take_array_t]:
    Source: 'src/array.rs', lines 227:0-227:31 -/
 def take_array_t (a : Array AB 2#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::non_copyable_array]: forward function
+/- [array::non_copyable_array]:
    Source: 'src/array.rs', lines 229:0-229:27 -/
 def non_copyable_array : Result Unit :=
   do
-    let _ ← take_array_t (Array.make AB 2#usize [ AB.A, AB.B ])
-    Result.ret ()
+  let _ ← take_array_t (Array.make AB 2#usize [ AB.A, AB.B ])
+  Result.ret ()
 
-/- [array::sum]: loop 0: forward function
+/- [array::sum]: loop 0:
    Source: 'src/array.rs', lines 242:0-250:1 -/
-divergent def sum_loop (s : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
-  let i0 := Slice.len U32 s
-  if i < i0
+divergent def sum_loop (s : Slice U32) (sum1 : U32) (i : Usize) : Result U32 :=
+  let i1 := Slice.len U32 s
+  if i < i1
   then
     do
-      let i1 ← Slice.index_usize U32 s i
-      let sum1 ← sum0 + i1
-      let i2 ← i + 1#usize
-      sum_loop s sum1 i2
-  else Result.ret sum0
+    let i2 ← Slice.index_usize U32 s i
+    let sum3 ← sum1 + i2
+    let i3 ← i + 1#usize
+    sum_loop s sum3 i3
+  else Result.ret sum1
 
-/- [array::sum]: forward function
+/- [array::sum]:
    Source: 'src/array.rs', lines 242:0-242:28 -/
 def sum (s : Slice U32) : Result U32 :=
   sum_loop s 0#u32 0#usize
 
-/- [array::sum2]: loop 0: forward function
+/- [array::sum2]: loop 0:
    Source: 'src/array.rs', lines 252:0-261:1 -/
 divergent def sum2_loop
-  (s : Slice U32) (s2 : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
-  let i0 := Slice.len U32 s
-  if i < i0
+  (s : Slice U32) (s2 : Slice U32) (sum1 : U32) (i : Usize) : Result U32 :=
+  let i1 := Slice.len U32 s
+  if i < i1
   then
     do
-      let i1 ← Slice.index_usize U32 s i
-      let i2 ← Slice.index_usize U32 s2 i
-      let i3 ← i1 + i2
-      let sum1 ← sum0 + i3
-      let i4 ← i + 1#usize
-      sum2_loop s s2 sum1 i4
-  else Result.ret sum0
-
-/- [array::sum2]: forward function
+    let i2 ← Slice.index_usize U32 s i
+    let i3 ← Slice.index_usize U32 s2 i
+    let i4 ← i2 + i3
+    let sum3 ← sum1 + i4
+    let i5 ← i + 1#usize
+    sum2_loop s s2 sum3 i5
+  else Result.ret sum1
+
+/- [array::sum2]:
    Source: 'src/array.rs', lines 252:0-252:41 -/
 def sum2 (s : Slice U32) (s2 : Slice U32) : Result U32 :=
   let i := Slice.len U32 s
-  let i0 := Slice.len U32 s2
-  if not (i = i0)
+  let i1 := Slice.len U32 s2
+  if not (i = i1)
   then Result.fail .panic
   else sum2_loop s s2 0#u32 0#usize
 
-/- [array::f0]: forward function
+/- [array::f0]:
    Source: 'src/array.rs', lines 263:0-263:11 -/
 def f0 : Result Unit :=
   do
-    let s ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
-    let s0 ← Slice.update_usize U32 s 0#usize 1#u32
-    let _ ←
-      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ]) s0
-    Result.ret ()
-
-/- [array::f1]: forward function
+  let (s, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+  let (_, index_mut_back) ← Slice.index_mut_usize U32 s 0#usize
+  let s1 ← index_mut_back 1#u32
+  let _ ← to_slice_mut_back s1
+  Result.ret ()
+
+/- [array::f1]:
    Source: 'src/array.rs', lines 268:0-268:11 -/
 def f1 : Result Unit :=
   do
-    let _ ←
-      Array.update_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
-        0#usize 1#u32
-    Result.ret ()
+  let (_, index_mut_back) ←
+    Array.index_mut_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+      0#usize
+  let _ ← index_mut_back 1#u32
+  Result.ret ()
 
-/- [array::f2]: forward function
+/- [array::f2]:
    Source: 'src/array.rs', lines 273:0-273:17 -/
 def f2 (i : U32) : Result Unit :=
   Result.ret ()
 
-/- [array::f4]: forward function
+/- [array::f4]:
    Source: 'src/array.rs', lines 282:0-282:54 -/
 def f4 (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
   core.array.Array.index U32 (core.ops.range.Range Usize) 32#usize
@@ -466,44 +435,42 @@ def f4 (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
     (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
     { start := y, end_ := z }
 
-/- [array::f3]: forward function
+/- [array::f3]:
    Source: 'src/array.rs', lines 275:0-275:18 -/
 def f3 : Result U32 :=
   do
-    let i ←
-      Array.index_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
-        0#usize
-    let _ ← f2 i
-    let b := Array.repeat U32 32#usize 0#u32
-    let s ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
-    let s0 ← f4 b 16#usize 18#usize
-    sum2 s s0
+  let i ←
+    Array.index_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+      0#usize
+  let _ ← f2 i
+  let b := Array.repeat U32 32#usize 0#u32
+  let s ←
+    Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+  let s1 ← f4 b 16#usize 18#usize
+  sum2 s s1
 
 /- [array::SZ]
    Source: 'src/array.rs', lines 286:0-286:19 -/
 def sz_body : Result Usize := Result.ret 32#usize
 def sz_c : Usize := eval_global sz_body (by simp)
 
-/- [array::f5]: forward function
+/- [array::f5]:
    Source: 'src/array.rs', lines 289:0-289:31 -/
 def f5 (x : Array U32 32#usize) : Result U32 :=
   Array.index_usize U32 32#usize x 0#usize
 
-/- [array::ite]: forward function
+/- [array::ite]:
    Source: 'src/array.rs', lines 294:0-294:12 -/
 def ite : Result Unit :=
   do
-    let s ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let s0 ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    let s1 ← index_mut_slice_u32_0_back s0
-    let _ ←
-      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
-    let s2 ← index_mut_slice_u32_0_back s
-    let _ ←
-      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s2
-    Result.ret ()
+  let (s, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (_, s1) ← index_mut_slice_u32_0 s
+  let (s2, to_slice_mut_back1) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (_, s3) ← index_mut_slice_u32_0 s2
+  let _ ← to_slice_mut_back1 s3
+  let _ ← to_slice_mut_back s1
+  Result.ret ()
 
 end array
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
index 0d7cb984..96daa197 100644
--- a/tests/lean/BetreeMain/Funs.lean
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -7,7 +7,7 @@ open Primitives
 
 namespace betree_main
 
-/- [betree_main::betree::load_internal_node]: forward function
+/- [betree_main::betree::load_internal_node]:
    Source: 'src/betree.rs', lines 36:0-36:52 -/
 def betree.load_internal_node
   (id : U64) (st : State) :
@@ -15,65 +15,53 @@ def betree.load_internal_node
   :=
   betree_utils.load_internal_node id st
 
-/- [betree_main::betree::store_internal_node]: forward function
+/- [betree_main::betree::store_internal_node]:
    Source: 'src/betree.rs', lines 41:0-41:60 -/
 def betree.store_internal_node
   (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← betree_utils.store_internal_node id content st
-    Result.ret (st0, ())
+  let (st1, _) ← betree_utils.store_internal_node id content st
+  Result.ret (st1, ())
 
-/- [betree_main::betree::load_leaf_node]: forward function
+/- [betree_main::betree::load_leaf_node]:
    Source: 'src/betree.rs', lines 46:0-46:44 -/
 def betree.load_leaf_node
   (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) :=
   betree_utils.load_leaf_node id st
 
-/- [betree_main::betree::store_leaf_node]: forward function
+/- [betree_main::betree::store_leaf_node]:
    Source: 'src/betree.rs', lines 51:0-51:52 -/
 def betree.store_leaf_node
   (id : U64) (content : betree.List (U64 × U64)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← betree_utils.store_leaf_node id content st
-    Result.ret (st0, ())
+  let (st1, _) ← betree_utils.store_leaf_node id content st
+  Result.ret (st1, ())
 
-/- [betree_main::betree::fresh_node_id]: forward function
+/- [betree_main::betree::fresh_node_id]:
    Source: 'src/betree.rs', lines 55:0-55:48 -/
-def betree.fresh_node_id (counter : U64) : Result U64 :=
+def betree.fresh_node_id (counter : U64) : Result (U64 × U64) :=
   do
-    let _ ← counter + 1#u64
-    Result.ret counter
+  let counter1 ← counter + 1#u64
+  Result.ret (counter, counter1)
 
-/- [betree_main::betree::fresh_node_id]: backward function 0
-   Source: 'src/betree.rs', lines 55:0-55:48 -/
-def betree.fresh_node_id_back (counter : U64) : Result U64 :=
-  counter + 1#u64
-
-/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]:
    Source: 'src/betree.rs', lines 206:4-206:20 -/
 def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
   Result.ret { next_node_id := 0#u64 }
 
-/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]:
    Source: 'src/betree.rs', lines 210:4-210:36 -/
-def betree.NodeIdCounter.fresh_id (self : betree.NodeIdCounter) : Result U64 :=
+def betree.NodeIdCounter.fresh_id
+  (self : betree.NodeIdCounter) : Result (U64 × betree.NodeIdCounter) :=
   do
-    let _ ← self.next_node_id + 1#u64
-    Result.ret self.next_node_id
+  let i ← self.next_node_id + 1#u64
+  Result.ret (self.next_node_id, { next_node_id := i })
 
-/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
-   Source: 'src/betree.rs', lines 210:4-210:36 -/
-def betree.NodeIdCounter.fresh_id_back
-  (self : betree.NodeIdCounter) : Result betree.NodeIdCounter :=
-  do
-    let i ← self.next_node_id + 1#u64
-    Result.ret { next_node_id := i }
-
-/- [betree_main::betree::upsert_update]: forward function
+/- [betree_main::betree::upsert_update]:
    Source: 'src/betree.rs', lines 234:0-234:70 -/
 def betree.upsert_update
   (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
@@ -81,30 +69,30 @@ def betree.upsert_update
   | none =>
     match st with
     | betree.UpsertFunState.Add v => Result.ret v
-    | betree.UpsertFunState.Sub i => Result.ret 0#u64
-  | some prev0 =>
+    | betree.UpsertFunState.Sub _ => Result.ret 0#u64
+  | some prev1 =>
     match st with
     | betree.UpsertFunState.Add v =>
       do
-        let margin ← core_u64_max - prev0
-        if margin >= v
-        then prev0 + v
-        else Result.ret core_u64_max
+      let margin ← core_u64_max - prev1
+      if margin >= v
+      then prev1 + v
+      else Result.ret core_u64_max
     | betree.UpsertFunState.Sub v =>
-      if prev0 >= v
-      then prev0 - v
+      if prev1 >= v
+      then prev1 - v
       else Result.ret 0#u64
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::len]:
    Source: 'src/betree.rs', lines 276:4-276:24 -/
 divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 :=
   match self with
-  | betree.List.Cons t tl => do
-                               let i ← betree.List.len T tl
-                               1#u64 + i
+  | betree.List.Cons _ tl => do
+                             let i ← betree.List.len T tl
+                             1#u64 + i
   | betree.List.Nil => Result.ret 0#u64
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]:
    Source: 'src/betree.rs', lines 284:4-284:51 -/
 divergent def betree.List.split_at
   (T : Type) (self : betree.List T) (n : U64) :
@@ -116,56 +104,45 @@ divergent def betree.List.split_at
     match self with
     | betree.List.Cons hd tl =>
       do
-        let i ← n - 1#u64
-        let p ← betree.List.split_at T tl i
-        let (ls0, ls1) := p
-        let l := ls0
-        Result.ret (betree.List.Cons hd l, ls1)
+      let i ← n - 1#u64
+      let p ← betree.List.split_at T tl i
+      let (ls0, ls1) := p
+      Result.ret (betree.List.Cons hd ls0, ls1)
     | betree.List.Nil => Result.fail .panic
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]:
    Source: 'src/betree.rs', lines 299:4-299:34 -/
 def betree.List.push_front
   (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
-  let tl := core.mem.replace (betree.List T) self betree.List.Nil
-  let l := tl
-  Result.ret (betree.List.Cons x l)
-
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
-   Source: 'src/betree.rs', lines 306:4-306:32 -/
-def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
-  let ls := core.mem.replace (betree.List T) self betree.List.Nil
-  match ls with
-  | betree.List.Cons x tl => Result.ret x
-  | betree.List.Nil => Result.fail .panic
+  let (tl, _) := core.mem.replace (betree.List T) self betree.List.Nil
+  Result.ret (betree.List.Cons x tl)
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]:
    Source: 'src/betree.rs', lines 306:4-306:32 -/
-def betree.List.pop_front_back
-  (T : Type) (self : betree.List T) : Result (betree.List T) :=
-  let ls := core.mem.replace (betree.List T) self betree.List.Nil
+def betree.List.pop_front
+  (T : Type) (self : betree.List T) : Result (T × (betree.List T)) :=
+  let (ls, _) := core.mem.replace (betree.List T) self betree.List.Nil
   match ls with
-  | betree.List.Cons x tl => Result.ret tl
+  | betree.List.Cons x tl => Result.ret (x, tl)
   | betree.List.Nil => Result.fail .panic
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::hd]:
    Source: 'src/betree.rs', lines 318:4-318:22 -/
 def betree.List.hd (T : Type) (self : betree.List T) : Result T :=
   match self with
-  | betree.List.Cons hd l => Result.ret hd
+  | betree.List.Cons hd _ => Result.ret hd
   | betree.List.Nil => Result.fail .panic
 
-/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]:
    Source: 'src/betree.rs', lines 327:4-327:44 -/
 def betree.ListTupleU64T.head_has_key
   (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool :=
   match self with
-  | betree.List.Cons hd l => let (i, _) := hd
+  | betree.List.Cons hd _ => let (i, _) := hd
                              Result.ret (i = key)
   | betree.List.Nil => Result.ret false
 
-/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]:
    Source: 'src/betree.rs', lines 339:4-339:73 -/
 divergent def betree.ListTupleU64T.partition_at_pivot
   (T : Type) (self : betree.List (U64 × T)) (pivot : U64) :
@@ -178,334 +155,186 @@ divergent def betree.ListTupleU64T.partition_at_pivot
     then Result.ret (betree.List.Nil, betree.List.Cons (i, t) tl)
     else
       do
-        let p ← betree.ListTupleU64T.partition_at_pivot T tl pivot
-        let (ls0, ls1) := p
-        let l := ls0
-        Result.ret (betree.List.Cons (i, t) l, ls1)
+      let p ← betree.ListTupleU64T.partition_at_pivot T tl pivot
+      let (ls0, ls1) := p
+      Result.ret (betree.List.Cons (i, t) ls0, ls1)
   | betree.List.Nil => Result.ret (betree.List.Nil, betree.List.Nil)
 
-/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]:
    Source: 'src/betree.rs', lines 359:4-364:17 -/
 def betree.Leaf.split
   (self : betree.Leaf) (content : betree.List (U64 × U64))
   (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
-  Result (State × betree.Internal)
+  Result (State × (betree.Internal × betree.NodeIdCounter))
   :=
   do
-    let p ← betree.List.split_at (U64 × U64) content params.split_size
-    let (content0, content1) := p
-    let p0 ← betree.List.hd (U64 × U64) content1
-    let (pivot, _) := p0
-    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
-    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
-    let (st0, _) ← betree.store_leaf_node id0 content0 st
-    let (st1, _) ← betree.store_leaf_node id1 content1 st0
-    let n := betree.Node.Leaf { id := id0, size := params.split_size }
-    let n0 := betree.Node.Leaf { id := id1, size := params.split_size }
-    Result.ret (st1, betree.Internal.mk self.id pivot n n0)
-
-/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
-   Source: 'src/betree.rs', lines 359:4-364:17 -/
-def betree.Leaf.split_back
-  (self : betree.Leaf) (content : betree.List (U64 × U64))
-  (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
-  Result betree.NodeIdCounter
-  :=
-  do
-    let p ← betree.List.split_at (U64 × U64) content params.split_size
-    let (content0, content1) := p
-    let _ ← betree.List.hd (U64 × U64) content1
-    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
-    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
-    let (st0, _) ← betree.store_leaf_node id0 content0 st
-    let _ ← betree.store_leaf_node id1 content1 st0
-    betree.NodeIdCounter.fresh_id_back node_id_cnt0
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+  let p ← betree.List.split_at (U64 × U64) content params.split_size
+  let (content0, content1) := p
+  let p1 ← betree.List.hd (U64 × U64) content1
+  let (pivot, _) := p1
+  let (id0, nic) ← betree.NodeIdCounter.fresh_id node_id_cnt
+  let (id1, nic1) ← betree.NodeIdCounter.fresh_id nic
+  let (st1, _) ← betree.store_leaf_node id0 content0 st
+  let (st2, _) ← betree.store_leaf_node id1 content1 st1
+  let n := betree.Node.Leaf { id := id0, size := params.split_size }
+  let n1 := betree.Node.Leaf { id := id1, size := params.split_size }
+  Result.ret (st2, (betree.Internal.mk self.id pivot n n1, nic1))
+
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]:
    Source: 'src/betree.rs', lines 789:4-792:34 -/
 divergent def betree.Node.lookup_first_message_for_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
+  Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 ×
+    betree.Message) → Result (betree.List (U64 × betree.Message))))
   :=
   match msgs with
   | betree.List.Cons x next_msgs =>
     let (i, m) := x
     if i >= key
-    then Result.ret (betree.List.Cons (i, m) next_msgs)
-    else betree.Node.lookup_first_message_for_key key next_msgs
-  | betree.List.Nil => Result.ret betree.List.Nil
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
-   Source: 'src/betree.rs', lines 789:4-792:34 -/
-divergent def betree.Node.lookup_first_message_for_key_back
-  (key : U64) (msgs : betree.List (U64 × betree.Message))
-  (ret : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
-  :=
-  match msgs with
-  | betree.List.Cons x next_msgs =>
-    let (i, m) := x
-    if i >= key
-    then Result.ret ret
+    then Result.ret (betree.List.Cons (i, m) next_msgs, Result.ret)
     else
       do
-        let next_msgs0 ←
-          betree.Node.lookup_first_message_for_key_back key next_msgs ret
-        Result.ret (betree.List.Cons (i, m) next_msgs0)
-  | betree.List.Nil => Result.ret ret
+      let (l, lookup_first_message_for_key_back) ←
+        betree.Node.lookup_first_message_for_key key next_msgs
+      let back_'a :=
+        fun ret =>
+          do
+          let next_msgs1 ← lookup_first_message_for_key_back ret
+          Result.ret (betree.List.Cons (i, m) next_msgs1)
+      Result.ret (l, back_'a)
+  | betree.List.Nil => Result.ret (betree.List.Nil, Result.ret)
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]:
    Source: 'src/betree.rs', lines 636:4-636:80 -/
 divergent def betree.Node.lookup_in_bindings
   (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) :=
   match bindings with
   | betree.List.Cons hd tl =>
-    let (i, i0) := hd
+    let (i, i1) := hd
     if i = key
-    then Result.ret (some i0)
+    then Result.ret (some i1)
     else
       if i > key
       then Result.ret none
       else betree.Node.lookup_in_bindings key tl
   | betree.List.Nil => Result.ret none
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]:
    Source: 'src/betree.rs', lines 819:4-819:90 -/
 divergent def betree.Node.apply_upserts
   (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
   (st : State) :
-  Result (State × U64)
+  Result (State × (U64 × (betree.List (U64 × betree.Message))))
   :=
   do
-    let b ← betree.ListTupleU64T.head_has_key betree.Message msgs key
-    if b
-    then
-      do
-        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
-        let (_, m) := msg
-        match m with
-        | betree.Message.Insert i => Result.fail .panic
-        | betree.Message.Delete => Result.fail .panic
-        | betree.Message.Upsert s =>
-          do
-            let v ← betree.upsert_update prev s
-            let msgs0 ←
-              betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts msgs0 (some v) key st
-    else
-      do
-        let (st0, v) ← core.option.Option.unwrap U64 prev st
-        let _ ←
-          betree.List.push_front (U64 × betree.Message) msgs (key,
-            betree.Message.Insert v)
-        Result.ret (st0, v)
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
-   Source: 'src/betree.rs', lines 819:4-819:90 -/
-divergent def betree.Node.apply_upserts_back
-  (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
-  (st : State) :
-  Result (betree.List (U64 × betree.Message))
-  :=
-  do
-    let b ← betree.ListTupleU64T.head_has_key betree.Message msgs key
-    if b
-    then
-      do
-        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
-        let (_, m) := msg
-        match m with
-        | betree.Message.Insert i => Result.fail .panic
-        | betree.Message.Delete => Result.fail .panic
-        | betree.Message.Upsert s =>
-          do
-            let v ← betree.upsert_update prev s
-            let msgs0 ←
-              betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts_back msgs0 (some v) key st
-    else
+  let b ← betree.ListTupleU64T.head_has_key betree.Message msgs key
+  if b
+  then
+    do
+    let (msg, l) ← betree.List.pop_front (U64 × betree.Message) msgs
+    let (_, m) := msg
+    match m with
+    | betree.Message.Insert _ => Result.fail .panic
+    | betree.Message.Delete => Result.fail .panic
+    | betree.Message.Upsert s =>
       do
-        let (_, v) ← core.option.Option.unwrap U64 prev st
-        betree.List.push_front (U64 × betree.Message) msgs (key,
-          betree.Message.Insert v)
+      let v ← betree.upsert_update prev s
+      betree.Node.apply_upserts l (some v) key st
+  else
+    do
+    let (st1, v) ← core.option.Option.unwrap U64 prev st
+    let l ←
+      betree.List.push_front (U64 × betree.Message) msgs (key,
+        betree.Message.Insert v)
+    Result.ret (st1, (v, l))
 
-/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]:
    Source: 'src/betree.rs', lines 395:4-395:63 -/
 mutual divergent def betree.Internal.lookup_in_children
   (self : betree.Internal) (key : U64) (st : State) :
-  Result (State × (Option U64))
+  Result (State × ((Option U64) × betree.Internal))
   :=
-  let ⟨ _, i, n, n0 ⟩ := self
-  if key < i
-  then betree.Node.lookup n key st
-  else betree.Node.lookup n0 key st
-
-/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
-   Source: 'src/betree.rs', lines 395:4-395:63 -/
-divergent def betree.Internal.lookup_in_children_back
-  (self : betree.Internal) (key : U64) (st : State) : Result betree.Internal :=
-  let ⟨ i, i0, n, n0 ⟩ := self
-  if key < i0
+  let ⟨ i, i1, n, n1 ⟩ := self
+  if key < i1
   then
     do
-      let n1 ← betree.Node.lookup_back n key st
-      Result.ret (betree.Internal.mk i i0 n1 n0)
+    let (st1, (o, n2)) ← betree.Node.lookup n key st
+    Result.ret (st1, (o, betree.Internal.mk i i1 n2 n1))
   else
     do
-      let n1 ← betree.Node.lookup_back n0 key st
-      Result.ret (betree.Internal.mk i i0 n n1)
+    let (st1, (o, n2)) ← betree.Node.lookup n1 key st
+    Result.ret (st1, (o, betree.Internal.mk i i1 n n2))
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]:
    Source: 'src/betree.rs', lines 709:4-709:58 -/
 divergent def betree.Node.lookup
   (self : betree.Node) (key : U64) (st : State) :
-  Result (State × (Option U64))
+  Result (State × ((Option U64) × betree.Node))
   :=
   match self with
   | betree.Node.Internal node =>
     do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, msgs) ← betree.load_internal_node i st
-      let pending ← betree.Node.lookup_first_message_for_key key msgs
-      match pending with
-      | betree.List.Cons p l =>
-        let (k, msg) := p
-        if k != key
-        then
-          do
-            let (st1, o) ←
-              betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
-                key st0
-            let _ ←
-              betree.Node.lookup_first_message_for_key_back key msgs
-                (betree.List.Cons (k, msg) l)
-            Result.ret (st1, o)
-        else
-          match msg with
-          | betree.Message.Insert v =>
-            do
-              let _ ←
-                betree.Node.lookup_first_message_for_key_back key msgs
-                  (betree.List.Cons (k, betree.Message.Insert v) l)
-              Result.ret (st0, some v)
-          | betree.Message.Delete =>
-            do
-              let _ ←
-                betree.Node.lookup_first_message_for_key_back key msgs
-                  (betree.List.Cons (k, betree.Message.Delete) l)
-              Result.ret (st0, none)
-          | betree.Message.Upsert ufs =>
-            do
-              let (st1, v) ←
-                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
-                  n0) key st0
-              let (st2, v0) ←
-                betree.Node.apply_upserts (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let node0 ←
-                betree.Internal.lookup_in_children_back (betree.Internal.mk i
-                  i0 n n0) key st0
-              let ⟨ i1, _, _, _ ⟩ := node0
-              let pending0 ←
-                betree.Node.apply_upserts_back (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let msgs0 ←
-                betree.Node.lookup_first_message_for_key_back key msgs pending0
-              let (st3, _) ← betree.store_internal_node i1 msgs0 st2
-              Result.ret (st3, some v0)
-      | betree.List.Nil =>
+    let ⟨ i, i1, n, n1 ⟩ := node
+    let (st1, msgs) ← betree.load_internal_node i st
+    let (pending, lookup_first_message_for_key_back) ←
+      betree.Node.lookup_first_message_for_key key msgs
+    match pending with
+    | betree.List.Cons p l =>
+      let (k, msg) := p
+      if k != key
+      then
         do
-          let (st1, o) ←
-            betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
-              key st0
+        let (st2, (o, i2)) ←
+          betree.Internal.lookup_in_children (betree.Internal.mk i i1 n n1) key
+            st1
+        let _ ←
+          lookup_first_message_for_key_back (betree.List.Cons (k, msg) l)
+        Result.ret (st2, (o, betree.Node.Internal i2))
+      else
+        match msg with
+        | betree.Message.Insert v =>
+          do
           let _ ←
-            betree.Node.lookup_first_message_for_key_back key msgs
-              betree.List.Nil
-          Result.ret (st1, o)
-  | betree.Node.Leaf node =>
-    do
-      let (st0, bindings) ← betree.load_leaf_node node.id st
-      let o ← betree.Node.lookup_in_bindings key bindings
-      Result.ret (st0, o)
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]: backward function 0
-   Source: 'src/betree.rs', lines 709:4-709:58 -/
-divergent def betree.Node.lookup_back
-  (self : betree.Node) (key : U64) (st : State) : Result betree.Node :=
-  match self with
-  | betree.Node.Internal node =>
-    do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, msgs) ← betree.load_internal_node i st
-      let pending ← betree.Node.lookup_first_message_for_key key msgs
-      match pending with
-      | betree.List.Cons p l =>
-        let (k, msg) := p
-        if k != key
-        then
+            lookup_first_message_for_key_back (betree.List.Cons (k,
+              betree.Message.Insert v) l)
+          Result.ret (st1, (some v, betree.Node.Internal (betree.Internal.mk i
+            i1 n n1)))
+        | betree.Message.Delete =>
           do
-            let _ ←
-              betree.Node.lookup_first_message_for_key_back key msgs
-                (betree.List.Cons (k, msg) l)
-            let node0 ←
-              betree.Internal.lookup_in_children_back (betree.Internal.mk i i0
-                n n0) key st0
-            Result.ret (betree.Node.Internal node0)
-        else
-          match msg with
-          | betree.Message.Insert v =>
-            do
-              let _ ←
-                betree.Node.lookup_first_message_for_key_back key msgs
-                  (betree.List.Cons (k, betree.Message.Insert v) l)
-              Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
-          | betree.Message.Delete =>
-            do
-              let _ ←
-                betree.Node.lookup_first_message_for_key_back key msgs
-                  (betree.List.Cons (k, betree.Message.Delete) l)
-              Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
-          | betree.Message.Upsert ufs =>
-            do
-              let (st1, v) ←
-                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
-                  n0) key st0
-              let (st2, _) ←
-                betree.Node.apply_upserts (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let node0 ←
-                betree.Internal.lookup_in_children_back (betree.Internal.mk i
-                  i0 n n0) key st0
-              let ⟨ i1, i2, n1, n2 ⟩ := node0
-              let pending0 ←
-                betree.Node.apply_upserts_back (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let msgs0 ←
-                betree.Node.lookup_first_message_for_key_back key msgs pending0
-              let _ ← betree.store_internal_node i1 msgs0 st2
-              Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1
-                n2))
-      | betree.List.Nil =>
-        do
           let _ ←
-            betree.Node.lookup_first_message_for_key_back key msgs
-              betree.List.Nil
-          let node0 ←
-            betree.Internal.lookup_in_children_back (betree.Internal.mk i i0 n
-              n0) key st0
-          Result.ret (betree.Node.Internal node0)
+            lookup_first_message_for_key_back (betree.List.Cons (k,
+              betree.Message.Delete) l)
+          Result.ret (st1, (none, betree.Node.Internal (betree.Internal.mk i i1
+            n n1)))
+        | betree.Message.Upsert ufs =>
+          do
+          let (st2, (v, i2)) ←
+            betree.Internal.lookup_in_children (betree.Internal.mk i i1 n n1)
+              key st1
+          let (st3, (v1, l1)) ←
+            betree.Node.apply_upserts (betree.List.Cons (k,
+              betree.Message.Upsert ufs) l) v key st2
+          let ⟨ i3, i4, n2, n3 ⟩ := i2
+          let msgs1 ← lookup_first_message_for_key_back l1
+          let (st4, _) ← betree.store_internal_node i3 msgs1 st3
+          Result.ret (st4, (some v1, betree.Node.Internal (betree.Internal.mk
+            i3 i4 n2 n3)))
+    | betree.List.Nil =>
+      do
+      let (st2, (o, i2)) ←
+        betree.Internal.lookup_in_children (betree.Internal.mk i i1 n n1) key
+          st1
+      let _ ← lookup_first_message_for_key_back betree.List.Nil
+      Result.ret (st2, (o, betree.Node.Internal i2))
   | betree.Node.Leaf node =>
     do
-      let (_, bindings) ← betree.load_leaf_node node.id st
-      let _ ← betree.Node.lookup_in_bindings key bindings
-      Result.ret (betree.Node.Leaf node)
+    let (st1, bindings) ← betree.load_leaf_node node.id st
+    let o ← betree.Node.lookup_in_bindings key bindings
+    Result.ret (st1, (o, betree.Node.Leaf node))
 
 end
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]:
    Source: 'src/betree.rs', lines 674:4-674:77 -/
 divergent def betree.Node.filter_messages_for_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
@@ -517,33 +346,19 @@ divergent def betree.Node.filter_messages_for_key
     if k = key
     then
       do
-        let msgs0 ←
-          betree.List.pop_front_back (U64 × betree.Message) (betree.List.Cons
-            (k, m) l)
-        betree.Node.filter_messages_for_key key msgs0
+      let (_, l1) ←
+        betree.List.pop_front (U64 × betree.Message) (betree.List.Cons (k, m)
+          l)
+      betree.Node.filter_messages_for_key key l1
     else Result.ret (betree.List.Cons (k, m) l)
   | betree.List.Nil => Result.ret betree.List.Nil
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]:
    Source: 'src/betree.rs', lines 689:4-692:34 -/
 divergent def betree.Node.lookup_first_message_after_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
-  :=
-  match msgs with
-  | betree.List.Cons p next_msgs =>
-    let (k, m) := p
-    if k = key
-    then betree.Node.lookup_first_message_after_key key next_msgs
-    else Result.ret (betree.List.Cons (k, m) next_msgs)
-  | betree.List.Nil => Result.ret betree.List.Nil
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
-   Source: 'src/betree.rs', lines 689:4-692:34 -/
-divergent def betree.Node.lookup_first_message_after_key_back
-  (key : U64) (msgs : betree.List (U64 × betree.Message))
-  (ret : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
+  Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 ×
+    betree.Message) → Result (betree.List (U64 × betree.Message))))
   :=
   match msgs with
   | betree.List.Cons p next_msgs =>
@@ -551,14 +366,18 @@ divergent def betree.Node.lookup_first_message_after_key_back
     if k = key
     then
       do
-        let next_msgs0 ←
-          betree.Node.lookup_first_message_after_key_back key next_msgs ret
-        Result.ret (betree.List.Cons (k, m) next_msgs0)
-    else Result.ret ret
-  | betree.List.Nil => Result.ret ret
+      let (l, lookup_first_message_after_key_back) ←
+        betree.Node.lookup_first_message_after_key key next_msgs
+      let back_'a :=
+        fun ret =>
+          do
+          let next_msgs1 ← lookup_first_message_after_key_back ret
+          Result.ret (betree.List.Cons (k, m) next_msgs1)
+      Result.ret (l, back_'a)
+    else Result.ret (betree.List.Cons (k, m) next_msgs, Result.ret)
+  | betree.List.Nil => Result.ret (betree.List.Nil, Result.ret)
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]:
    Source: 'src/betree.rs', lines 521:4-521:89 -/
 def betree.Node.apply_to_internal
   (msgs : betree.List (U64 × betree.Message)) (key : U64)
@@ -566,66 +385,63 @@ def betree.Node.apply_to_internal
   Result (betree.List (U64 × betree.Message))
   :=
   do
-    let msgs0 ← betree.Node.lookup_first_message_for_key key msgs
-    let b ← betree.ListTupleU64T.head_has_key betree.Message msgs0 key
-    if b
-    then
-      match new_msg with
-      | betree.Message.Insert i =>
+  let (msgs1, lookup_first_message_for_key_back) ←
+    betree.Node.lookup_first_message_for_key key msgs
+  let b ← betree.ListTupleU64T.head_has_key betree.Message msgs1 key
+  if b
+  then
+    match new_msg with
+    | betree.Message.Insert i =>
+      do
+      let l ← betree.Node.filter_messages_for_key key msgs1
+      let l1 ←
+        betree.List.push_front (U64 × betree.Message) l (key,
+          betree.Message.Insert i)
+      lookup_first_message_for_key_back l1
+    | betree.Message.Delete =>
+      do
+      let l ← betree.Node.filter_messages_for_key key msgs1
+      let l1 ←
+        betree.List.push_front (U64 × betree.Message) l (key,
+          betree.Message.Delete)
+      lookup_first_message_for_key_back l1
+    | betree.Message.Upsert s =>
+      do
+      let p ← betree.List.hd (U64 × betree.Message) msgs1
+      let (_, m) := p
+      match m with
+      | betree.Message.Insert prev =>
         do
-          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
-          let msgs2 ←
-            betree.List.push_front (U64 × betree.Message) msgs1 (key,
-              betree.Message.Insert i)
-          betree.Node.lookup_first_message_for_key_back key msgs msgs2
+        let v ← betree.upsert_update (some prev) s
+        let (_, l) ← betree.List.pop_front (U64 × betree.Message) msgs1
+        let l1 ←
+          betree.List.push_front (U64 × betree.Message) l (key,
+            betree.Message.Insert v)
+        lookup_first_message_for_key_back l1
       | betree.Message.Delete =>
         do
-          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
-          let msgs2 ←
-            betree.List.push_front (U64 × betree.Message) msgs1 (key,
-              betree.Message.Delete)
-          betree.Node.lookup_first_message_for_key_back key msgs msgs2
-      | betree.Message.Upsert s =>
+        let (_, l) ← betree.List.pop_front (U64 × betree.Message) msgs1
+        let v ← betree.upsert_update none s
+        let l1 ←
+          betree.List.push_front (U64 × betree.Message) l (key,
+            betree.Message.Insert v)
+        lookup_first_message_for_key_back l1
+      | betree.Message.Upsert _ =>
         do
-          let p ← betree.List.hd (U64 × betree.Message) msgs0
-          let (_, m) := p
-          match m with
-          | betree.Message.Insert prev =>
-            do
-              let v ← betree.upsert_update (some prev) s
-              let msgs1 ←
-                betree.List.pop_front_back (U64 × betree.Message) msgs0
-              let msgs2 ←
-                betree.List.push_front (U64 × betree.Message) msgs1 (key,
-                  betree.Message.Insert v)
-              betree.Node.lookup_first_message_for_key_back key msgs msgs2
-          | betree.Message.Delete =>
-            do
-              let v ← betree.upsert_update none s
-              let msgs1 ←
-                betree.List.pop_front_back (U64 × betree.Message) msgs0
-              let msgs2 ←
-                betree.List.push_front (U64 × betree.Message) msgs1 (key,
-                  betree.Message.Insert v)
-              betree.Node.lookup_first_message_for_key_back key msgs msgs2
-          | betree.Message.Upsert ufs =>
-            do
-              let msgs1 ←
-                betree.Node.lookup_first_message_after_key key msgs0
-              let msgs2 ←
-                betree.List.push_front (U64 × betree.Message) msgs1 (key,
-                  betree.Message.Upsert s)
-              let msgs3 ←
-                betree.Node.lookup_first_message_after_key_back key msgs0 msgs2
-              betree.Node.lookup_first_message_for_key_back key msgs msgs3
-    else
-      do
-        let msgs1 ←
-          betree.List.push_front (U64 × betree.Message) msgs0 (key, new_msg)
-        betree.Node.lookup_first_message_for_key_back key msgs msgs1
+        let (msgs2, lookup_first_message_after_key_back) ←
+          betree.Node.lookup_first_message_after_key key msgs1
+        let l ←
+          betree.List.push_front (U64 × betree.Message) msgs2 (key,
+            betree.Message.Upsert s)
+        let msgs3 ← lookup_first_message_after_key_back l
+        lookup_first_message_for_key_back msgs3
+  else
+    do
+    let l ←
+      betree.List.push_front (U64 × betree.Message) msgs1 (key, new_msg)
+    lookup_first_message_for_key_back l
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]:
    Source: 'src/betree.rs', lines 502:4-505:5 -/
 divergent def betree.Node.apply_messages_to_internal
   (msgs : betree.List (U64 × betree.Message))
@@ -635,45 +451,36 @@ divergent def betree.Node.apply_messages_to_internal
   match new_msgs with
   | betree.List.Cons new_msg new_msgs_tl =>
     do
-      let (i, m) := new_msg
-      let msgs0 ← betree.Node.apply_to_internal msgs i m
-      betree.Node.apply_messages_to_internal msgs0 new_msgs_tl
+    let (i, m) := new_msg
+    let l ← betree.Node.apply_to_internal msgs i m
+    betree.Node.apply_messages_to_internal l new_msgs_tl
   | betree.List.Nil => Result.ret msgs
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]:
    Source: 'src/betree.rs', lines 653:4-656:32 -/
 divergent def betree.Node.lookup_mut_in_bindings
   (key : U64) (bindings : betree.List (U64 × U64)) :
-  Result (betree.List (U64 × U64))
-  :=
-  match bindings with
-  | betree.List.Cons hd tl =>
-    let (i, i0) := hd
-    if i >= key
-    then Result.ret (betree.List.Cons (i, i0) tl)
-    else betree.Node.lookup_mut_in_bindings key tl
-  | betree.List.Nil => Result.ret betree.List.Nil
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
-   Source: 'src/betree.rs', lines 653:4-656:32 -/
-divergent def betree.Node.lookup_mut_in_bindings_back
-  (key : U64) (bindings : betree.List (U64 × U64))
-  (ret : betree.List (U64 × U64)) :
-  Result (betree.List (U64 × U64))
+  Result ((betree.List (U64 × U64)) × (betree.List (U64 × U64) → Result
+    (betree.List (U64 × U64))))
   :=
   match bindings with
   | betree.List.Cons hd tl =>
-    let (i, i0) := hd
+    let (i, i1) := hd
     if i >= key
-    then Result.ret ret
+    then Result.ret (betree.List.Cons (i, i1) tl, Result.ret)
     else
       do
-        let tl0 ← betree.Node.lookup_mut_in_bindings_back key tl ret
-        Result.ret (betree.List.Cons (i, i0) tl0)
-  | betree.List.Nil => Result.ret ret
+      let (l, lookup_mut_in_bindings_back) ←
+        betree.Node.lookup_mut_in_bindings key tl
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← lookup_mut_in_bindings_back ret
+          Result.ret (betree.List.Cons (i, i1) tl1)
+      Result.ret (l, back_'a)
+  | betree.List.Nil => Result.ret (betree.List.Nil, Result.ret)
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]:
    Source: 'src/betree.rs', lines 460:4-460:87 -/
 def betree.Node.apply_to_leaf
   (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message)
@@ -681,49 +488,39 @@ def betree.Node.apply_to_leaf
   Result (betree.List (U64 × U64))
   :=
   do
-    let bindings0 ← betree.Node.lookup_mut_in_bindings key bindings
-    let b ← betree.ListTupleU64T.head_has_key U64 bindings0 key
-    if b
-    then
+  let (bindings1, lookup_mut_in_bindings_back) ←
+    betree.Node.lookup_mut_in_bindings key bindings
+  let b ← betree.ListTupleU64T.head_has_key U64 bindings1 key
+  if b
+  then
+    do
+    let (hd, l) ← betree.List.pop_front (U64 × U64) bindings1
+    match new_msg with
+    | betree.Message.Insert v =>
       do
-        let hd ← betree.List.pop_front (U64 × U64) bindings0
-        match new_msg with
-        | betree.Message.Insert v =>
-          do
-            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
-            let bindings2 ←
-              betree.List.push_front (U64 × U64) bindings1 (key, v)
-            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
-        | betree.Message.Delete =>
-          do
-            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
-            betree.Node.lookup_mut_in_bindings_back key bindings bindings1
-        | betree.Message.Upsert s =>
-          do
-            let (_, i) := hd
-            let v ← betree.upsert_update (some i) s
-            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
-            let bindings2 ←
-              betree.List.push_front (U64 × U64) bindings1 (key, v)
-            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
-    else
-      match new_msg with
-      | betree.Message.Insert v =>
-        do
-          let bindings1 ←
-            betree.List.push_front (U64 × U64) bindings0 (key, v)
-          betree.Node.lookup_mut_in_bindings_back key bindings bindings1
-      | betree.Message.Delete =>
-        betree.Node.lookup_mut_in_bindings_back key bindings bindings0
-      | betree.Message.Upsert s =>
-        do
-          let v ← betree.upsert_update none s
-          let bindings1 ←
-            betree.List.push_front (U64 × U64) bindings0 (key, v)
-          betree.Node.lookup_mut_in_bindings_back key bindings bindings1
+      let l1 ← betree.List.push_front (U64 × U64) l (key, v)
+      lookup_mut_in_bindings_back l1
+    | betree.Message.Delete => lookup_mut_in_bindings_back l
+    | betree.Message.Upsert s =>
+      do
+      let (_, i) := hd
+      let v ← betree.upsert_update (some i) s
+      let l1 ← betree.List.push_front (U64 × U64) l (key, v)
+      lookup_mut_in_bindings_back l1
+  else
+    match new_msg with
+    | betree.Message.Insert v =>
+      do
+      let l ← betree.List.push_front (U64 × U64) bindings1 (key, v)
+      lookup_mut_in_bindings_back l
+    | betree.Message.Delete => lookup_mut_in_bindings_back bindings1
+    | betree.Message.Upsert s =>
+      do
+      let v ← betree.upsert_update none s
+      let l ← betree.List.push_front (U64 × U64) bindings1 (key, v)
+      lookup_mut_in_bindings_back l
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]:
    Source: 'src/betree.rs', lines 444:4-447:5 -/
 divergent def betree.Node.apply_messages_to_leaf
   (bindings : betree.List (U64 × U64))
@@ -733,337 +530,182 @@ divergent def betree.Node.apply_messages_to_leaf
   match new_msgs with
   | betree.List.Cons new_msg new_msgs_tl =>
     do
-      let (i, m) := new_msg
-      let bindings0 ← betree.Node.apply_to_leaf bindings i m
-      betree.Node.apply_messages_to_leaf bindings0 new_msgs_tl
+    let (i, m) := new_msg
+    let l ← betree.Node.apply_to_leaf bindings i m
+    betree.Node.apply_messages_to_leaf l new_msgs_tl
   | betree.List.Nil => Result.ret bindings
 
-/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]:
    Source: 'src/betree.rs', lines 410:4-415:26 -/
 mutual divergent def betree.Internal.flush
   (self : betree.Internal) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
   (content : betree.List (U64 × betree.Message)) (st : State) :
-  Result (State × (betree.List (U64 × betree.Message)))
+  Result (State × ((betree.List (U64 × betree.Message)) × (betree.Internal
+    × betree.NodeIdCounter)))
   :=
   do
-    let ⟨ _, i, n, n0 ⟩ := self
-    let p ← betree.ListTupleU64T.partition_at_pivot betree.Message content i
-    let (msgs_left, msgs_right) := p
-    let len_left ← betree.List.len (U64 × betree.Message) msgs_left
-    if len_left >= params.min_flush_size
+  let ⟨ i, i1, n, n1 ⟩ := self
+  let p ← betree.ListTupleU64T.partition_at_pivot betree.Message content i1
+  let (msgs_left, msgs_right) := p
+  let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+  if len_left >= params.min_flush_size
+  then
+    do
+    let (st1, p1) ←
+      betree.Node.apply_messages n params node_id_cnt msgs_left st
+    let (n2, node_id_cnt1) := p1
+    let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+    if len_right >= params.min_flush_size
     then
       do
-        let (st0, _) ←
-          betree.Node.apply_messages n params node_id_cnt msgs_left st
-        let (_, node_id_cnt0) ←
-          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
-        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
-        if len_right >= params.min_flush_size
-        then
-          do
-            let (st1, _) ←
-              betree.Node.apply_messages n0 params node_id_cnt0 msgs_right st0
-            let _ ←
-              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
-                st0
-            Result.ret (st1, betree.List.Nil)
-        else Result.ret (st0, msgs_right)
+      let (st2, p2) ←
+        betree.Node.apply_messages n1 params node_id_cnt1 msgs_right st1
+      let (n3, node_id_cnt2) := p2
+      Result.ret (st2, (betree.List.Nil, (betree.Internal.mk i i1 n2 n3,
+        node_id_cnt2)))
     else
-      do
-        let (st0, _) ←
-          betree.Node.apply_messages n0 params node_id_cnt msgs_right st
-        let _ ←
-          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
-        Result.ret (st0, msgs_left)
-
-/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
-   Source: 'src/betree.rs', lines 410:4-415:26 -/
-divergent def betree.Internal.flush_back
-  (self : betree.Internal) (params : betree.Params)
-  (node_id_cnt : betree.NodeIdCounter)
-  (content : betree.List (U64 × betree.Message)) (st : State) :
-  Result (betree.Internal × betree.NodeIdCounter)
-  :=
-  do
-    let ⟨ i, i0, n, n0 ⟩ := self
-    let p ← betree.ListTupleU64T.partition_at_pivot betree.Message content i0
-    let (msgs_left, msgs_right) := p
-    let len_left ← betree.List.len (U64 × betree.Message) msgs_left
-    if len_left >= params.min_flush_size
-    then
-      do
-        let (st0, _) ←
-          betree.Node.apply_messages n params node_id_cnt msgs_left st
-        let (n1, node_id_cnt0) ←
-          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
-        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
-        if len_right >= params.min_flush_size
-        then
-          do
-            let (n2, node_id_cnt1) ←
-              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
-                st0
-            Result.ret (betree.Internal.mk i i0 n1 n2, node_id_cnt1)
-        else Result.ret (betree.Internal.mk i i0 n1 n0, node_id_cnt0)
-    else
-      do
-        let (n1, node_id_cnt0) ←
-          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
-        Result.ret (betree.Internal.mk i i0 n n1, node_id_cnt0)
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
-   Source: 'src/betree.rs', lines 588:4-593:5 -/
-divergent def betree.Node.apply_messages
-  (self : betree.Node) (params : betree.Params)
-  (node_id_cnt : betree.NodeIdCounter)
-  (msgs : betree.List (U64 × betree.Message)) (st : State) :
-  Result (State × Unit)
-  :=
-  match self with
-  | betree.Node.Internal node =>
-    do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, content) ← betree.load_internal_node i st
-      let content0 ← betree.Node.apply_messages_to_internal content msgs
-      let num_msgs ← betree.List.len (U64 × betree.Message) content0
-      if num_msgs >= params.min_flush_size
-      then
-        do
-          let (st1, content1) ←
-            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let (node0, _) ←
-            betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let ⟨ i1, _, _, _ ⟩ := node0
-          let (st2, _) ← betree.store_internal_node i1 content1 st1
-          Result.ret (st2, ())
-      else
-        do
-          let (st1, _) ← betree.store_internal_node i content0 st0
-          Result.ret (st1, ())
-  | betree.Node.Leaf node =>
+      Result.ret (st1, (msgs_right, (betree.Internal.mk i i1 n2 n1,
+        node_id_cnt1)))
+  else
     do
-      let (st0, content) ← betree.load_leaf_node node.id st
-      let content0 ← betree.Node.apply_messages_to_leaf content msgs
-      let len ← betree.List.len (U64 × U64) content0
-      let i ← 2#u64 * params.split_size
-      if len >= i
-      then
-        do
-          let (st1, _) ←
-            betree.Leaf.split node content0 params node_id_cnt st0
-          let (st2, _) ← betree.store_leaf_node node.id betree.List.Nil st1
-          Result.ret (st2, ())
-      else
-        do
-          let (st1, _) ← betree.store_leaf_node node.id content0 st0
-          Result.ret (st1, ())
+    let (st1, p1) ←
+      betree.Node.apply_messages n1 params node_id_cnt msgs_right st
+    let (n2, node_id_cnt1) := p1
+    Result.ret (st1, (msgs_left, (betree.Internal.mk i i1 n n2, node_id_cnt1)))
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]:
    Source: 'src/betree.rs', lines 588:4-593:5 -/
-divergent def betree.Node.apply_messages_back
+divergent def betree.Node.apply_messages
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
   (msgs : betree.List (U64 × betree.Message)) (st : State) :
-  Result (betree.Node × betree.NodeIdCounter)
+  Result (State × (betree.Node × betree.NodeIdCounter))
   :=
   match self with
   | betree.Node.Internal node =>
     do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, content) ← betree.load_internal_node i st
-      let content0 ← betree.Node.apply_messages_to_internal content msgs
-      let num_msgs ← betree.List.len (U64 × betree.Message) content0
-      if num_msgs >= params.min_flush_size
-      then
-        do
-          let (st1, content1) ←
-            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let (node0, node_id_cnt0) ←
-            betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let ⟨ i1, i2, n1, n2 ⟩ := node0
-          let _ ← betree.store_internal_node i1 content1 st1
-          Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1 n2),
-            node_id_cnt0)
-      else
-        do
-          let _ ← betree.store_internal_node i content0 st0
-          Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0),
-            node_id_cnt)
+    let ⟨ i, i1, n, n1 ⟩ := node
+    let (st1, content) ← betree.load_internal_node i st
+    let l ← betree.Node.apply_messages_to_internal content msgs
+    let num_msgs ← betree.List.len (U64 × betree.Message) l
+    if num_msgs >= params.min_flush_size
+    then
+      do
+      let (st2, (content1, p)) ←
+        betree.Internal.flush (betree.Internal.mk i i1 n n1) params node_id_cnt
+          l st1
+      let (node1, node_id_cnt1) := p
+      let ⟨ i2, i3, n2, n3 ⟩ := node1
+      let (st3, _) ← betree.store_internal_node i2 content1 st2
+      Result.ret (st3, (betree.Node.Internal (betree.Internal.mk i2 i3 n2 n3),
+        node_id_cnt1))
+    else
+      do
+      let (st2, _) ← betree.store_internal_node i l st1
+      Result.ret (st2, (betree.Node.Internal (betree.Internal.mk i i1 n n1),
+        node_id_cnt))
   | betree.Node.Leaf node =>
     do
-      let (st0, content) ← betree.load_leaf_node node.id st
-      let content0 ← betree.Node.apply_messages_to_leaf content msgs
-      let len ← betree.List.len (U64 × U64) content0
-      let i ← 2#u64 * params.split_size
-      if len >= i
-      then
-        do
-          let (st1, new_node) ←
-            betree.Leaf.split node content0 params node_id_cnt st0
-          let _ ← betree.store_leaf_node node.id betree.List.Nil st1
-          let node_id_cnt0 ←
-            betree.Leaf.split_back node content0 params node_id_cnt st0
-          Result.ret (betree.Node.Internal new_node, node_id_cnt0)
-      else
-        do
-          let _ ← betree.store_leaf_node node.id content0 st0
-          Result.ret (betree.Node.Leaf { node with size := len }, node_id_cnt)
+    let (st1, content) ← betree.load_leaf_node node.id st
+    let l ← betree.Node.apply_messages_to_leaf content msgs
+    let len ← betree.List.len (U64 × U64) l
+    let i ← 2#u64 * params.split_size
+    if len >= i
+    then
+      do
+      let (st2, (new_node, nic)) ←
+        betree.Leaf.split node l params node_id_cnt st1
+      let (st3, _) ← betree.store_leaf_node node.id betree.List.Nil st2
+      Result.ret (st3, (betree.Node.Internal new_node, nic))
+    else
+      do
+      let (st2, _) ← betree.store_leaf_node node.id l st1
+      Result.ret (st2, (betree.Node.Leaf { node with size := len },
+        node_id_cnt))
 
 end
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply]:
    Source: 'src/betree.rs', lines 576:4-582:5 -/
 def betree.Node.apply
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
   (st : State) :
-  Result (State × Unit)
+  Result (State × (betree.Node × betree.NodeIdCounter))
   :=
   do
-    let l := betree.List.Nil
-    let (st0, _) ←
-      betree.Node.apply_messages self params node_id_cnt (betree.List.Cons
-        (key, new_msg) l) st
-    let _ ←
-      betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
-        (key, new_msg) l) st
-    Result.ret (st0, ())
+  let (st1, p) ←
+    betree.Node.apply_messages self params node_id_cnt (betree.List.Cons (key,
+      new_msg) betree.List.Nil) st
+  let (self1, node_id_cnt1) := p
+  Result.ret (st1, (self1, node_id_cnt1))
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
-   Source: 'src/betree.rs', lines 576:4-582:5 -/
-def betree.Node.apply_back
-  (self : betree.Node) (params : betree.Params)
-  (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
-  (st : State) :
-  Result (betree.Node × betree.NodeIdCounter)
-  :=
-  let l := betree.List.Nil
-  betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
-    (key, new_msg) l) st
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::new]:
    Source: 'src/betree.rs', lines 849:4-849:60 -/
 def betree.BeTree.new
   (min_flush_size : U64) (split_size : U64) (st : State) :
   Result (State × betree.BeTree)
   :=
   do
-    let node_id_cnt ← betree.NodeIdCounter.new
-    let id ← betree.NodeIdCounter.fresh_id node_id_cnt
-    let (st0, _) ← betree.store_leaf_node id betree.List.Nil st
-    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    Result.ret (st0,
-      {
-        params :=
-          { min_flush_size := min_flush_size, split_size := split_size },
-        node_id_cnt := node_id_cnt0,
-        root := (betree.Node.Leaf { id := id, size := 0#u64 })
-      })
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+  let node_id_cnt ← betree.NodeIdCounter.new
+  let (id, nic) ← betree.NodeIdCounter.fresh_id node_id_cnt
+  let (st1, _) ← betree.store_leaf_node id betree.List.Nil st
+  Result.ret (st1,
+    {
+      params := { min_flush_size := min_flush_size, split_size := split_size },
+      node_id_cnt := nic,
+      root := (betree.Node.Leaf { id := id, size := 0#u64 })
+    })
+
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]:
    Source: 'src/betree.rs', lines 868:4-868:47 -/
 def betree.BeTree.apply
   (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree.Node.apply self.root self.params self.node_id_cnt key msg st
-    let _ ←
-      betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
-   Source: 'src/betree.rs', lines 868:4-868:47 -/
-def betree.BeTree.apply_back
-  (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
-  Result betree.BeTree
+  Result (State × betree.BeTree)
   :=
   do
-    let (n, nic) ←
-      betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
-    Result.ret { self with node_id_cnt := nic, root := n }
+  let (st1, p) ←
+    betree.Node.apply self.root self.params self.node_id_cnt key msg st
+  let (n, nic) := p
+  Result.ret (st1, { self with node_id_cnt := nic, root := n })
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]:
    Source: 'src/betree.rs', lines 874:4-874:52 -/
 def betree.BeTree.insert
   (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree.BeTree.apply self key (betree.Message.Insert value) st
-    let _ ←
-      betree.BeTree.apply_back self key (betree.Message.Insert value) st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
-   Source: 'src/betree.rs', lines 874:4-874:52 -/
-def betree.BeTree.insert_back
-  (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
-  Result betree.BeTree
+  Result (State × betree.BeTree)
   :=
-  betree.BeTree.apply_back self key (betree.Message.Insert value) st
+  betree.BeTree.apply self key (betree.Message.Insert value) st
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]:
    Source: 'src/betree.rs', lines 880:4-880:38 -/
 def betree.BeTree.delete
-  (self : betree.BeTree) (key : U64) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← betree.BeTree.apply self key betree.Message.Delete st
-    let _ ← betree.BeTree.apply_back self key betree.Message.Delete st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: backward function 0
-   Source: 'src/betree.rs', lines 880:4-880:38 -/
-def betree.BeTree.delete_back
-  (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
-  betree.BeTree.apply_back self key betree.Message.Delete st
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
-   Source: 'src/betree.rs', lines 886:4-886:59 -/
-def betree.BeTree.upsert
-  (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
-  :
-  Result (State × Unit)
+  (self : betree.BeTree) (key : U64) (st : State) :
+  Result (State × betree.BeTree)
   :=
-  do
-    let (st0, _) ←
-      betree.BeTree.apply self key (betree.Message.Upsert upd) st
-    let _ ← betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
-    Result.ret (st0, ())
+  betree.BeTree.apply self key betree.Message.Delete st
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]:
    Source: 'src/betree.rs', lines 886:4-886:59 -/
-def betree.BeTree.upsert_back
+def betree.BeTree.upsert
   (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
   :
-  Result betree.BeTree
+  Result (State × betree.BeTree)
   :=
-  betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
+  betree.BeTree.apply self key (betree.Message.Upsert upd) st
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]:
    Source: 'src/betree.rs', lines 895:4-895:62 -/
 def betree.BeTree.lookup
   (self : betree.BeTree) (key : U64) (st : State) :
-  Result (State × (Option U64))
+  Result (State × ((Option U64) × betree.BeTree))
   :=
-  betree.Node.lookup self.root key st
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
-   Source: 'src/betree.rs', lines 895:4-895:62 -/
-def betree.BeTree.lookup_back
-  (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
   do
-    let n ← betree.Node.lookup_back self.root key st
-    Result.ret { self with root := n }
+  let (st1, (o, n)) ← betree.Node.lookup self.root key st
+  Result.ret (st1, (o, { self with root := n }))
 
-/- [betree_main::main]: forward function
+/- [betree_main::main]:
    Source: 'src/betree_main.rs', lines 5:0-5:9 -/
 def main : Result Unit :=
   Result.ret ()
diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean
index 95f88873..eaa4b6c2 100644
--- a/tests/lean/BetreeMain/FunsExternal_Template.lean
+++ b/tests/lean/BetreeMain/FunsExternal_Template.lean
@@ -6,29 +6,29 @@ import BetreeMain.Types
 open Primitives
 open betree_main
 
-/- [betree_main::betree_utils::load_internal_node]: forward function
+/- [betree_main::betree_utils::load_internal_node]:
    Source: 'src/betree_utils.rs', lines 98:0-98:63 -/
 axiom betree_utils.load_internal_node
   : U64 → State → Result (State × (betree.List (U64 × betree.Message)))
 
-/- [betree_main::betree_utils::store_internal_node]: forward function
+/- [betree_main::betree_utils::store_internal_node]:
    Source: 'src/betree_utils.rs', lines 115:0-115:71 -/
 axiom betree_utils.store_internal_node
   :
   U64 → betree.List (U64 × betree.Message) → State → Result (State ×
     Unit)
 
-/- [betree_main::betree_utils::load_leaf_node]: forward function
+/- [betree_main::betree_utils::load_leaf_node]:
    Source: 'src/betree_utils.rs', lines 132:0-132:55 -/
 axiom betree_utils.load_leaf_node
   : U64 → State → Result (State × (betree.List (U64 × U64)))
 
-/- [betree_main::betree_utils::store_leaf_node]: forward function
+/- [betree_main::betree_utils::store_leaf_node]:
    Source: 'src/betree_utils.rs', lines 145:0-145:63 -/
 axiom betree_utils.store_leaf_node
   : U64 → betree.List (U64 × U64) → State → Result (State × Unit)
 
-/- [core::option::{core::option::Option<T>}::unwrap]: forward function
+/- [core::option::{core::option::Option<T>}::unwrap]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 -/
 axiom core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T)
diff --git a/tests/lean/Bitwise.lean b/tests/lean/Bitwise.lean
index c8538aa2..7c47e3dd 100644
--- a/tests/lean/Bitwise.lean
+++ b/tests/lean/Bitwise.lean
@@ -5,31 +5,31 @@ open Primitives
 
 namespace bitwise
 
-/- [bitwise::shift_u32]: forward function
+/- [bitwise::shift_u32]:
    Source: 'src/bitwise.rs', lines 3:0-3:31 -/
 def shift_u32 (a : U32) : Result U32 :=
   do
-    let t ← a >>> 16#usize
-    t <<< 16#usize
+  let t ← a >>> 16#usize
+  t <<< 16#usize
 
-/- [bitwise::shift_i32]: forward function
+/- [bitwise::shift_i32]:
    Source: 'src/bitwise.rs', lines 10:0-10:31 -/
 def shift_i32 (a : I32) : Result I32 :=
   do
-    let t ← a >>> 16#isize
-    t <<< 16#isize
+  let t ← a >>> 16#isize
+  t <<< 16#isize
 
-/- [bitwise::xor_u32]: forward function
+/- [bitwise::xor_u32]:
    Source: 'src/bitwise.rs', lines 17:0-17:37 -/
 def xor_u32 (a : U32) (b : U32) : Result U32 :=
   Result.ret (a ^^^ b)
 
-/- [bitwise::or_u32]: forward function
+/- [bitwise::or_u32]:
    Source: 'src/bitwise.rs', lines 21:0-21:36 -/
 def or_u32 (a : U32) (b : U32) : Result U32 :=
   Result.ret (a ||| b)
 
-/- [bitwise::and_u32]: forward function
+/- [bitwise::and_u32]:
    Source: 'src/bitwise.rs', lines 25:0-25:37 -/
 def and_u32 (a : U32) (b : U32) : Result U32 :=
   Result.ret (a &&& b)
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
index 80864427..2912805f 100644
--- a/tests/lean/Constants.lean
+++ b/tests/lean/Constants.lean
@@ -20,7 +20,7 @@ def x1_c : U32 := eval_global x1_body (by simp)
 def x2_body : Result U32 := Result.ret 3#u32
 def x2_c : U32 := eval_global x2_body (by simp)
 
-/- [constants::incr]: forward function
+/- [constants::incr]:
    Source: 'src/constants.rs', lines 17:0-17:32 -/
 def incr (n : U32) : Result U32 :=
   n + 1#u32
@@ -30,7 +30,7 @@ def incr (n : U32) : Result U32 :=
 def x3_body : Result U32 := incr 32#u32
 def x3_c : U32 := eval_global x3_body (by simp)
 
-/- [constants::mk_pair0]: forward function
+/- [constants::mk_pair0]:
    Source: 'src/constants.rs', lines 23:0-23:51 -/
 def mk_pair0 (x : U32) (y : U32) : Result (U32 × U32) :=
   Result.ret (x, y)
@@ -41,7 +41,7 @@ structure Pair (T1 T2 : Type) where
   x : T1
   y : T2
 
-/- [constants::mk_pair1]: forward function
+/- [constants::mk_pair1]:
    Source: 'src/constants.rs', lines 27:0-27:55 -/
 def mk_pair1 (x : U32) (y : U32) : Result (Pair U32 U32) :=
   Result.ret { x := x, y := y }
@@ -71,7 +71,7 @@ def p3_c : Pair U32 U32 := eval_global p3_body (by simp)
 structure Wrap (T : Type) where
   value : T
 
-/- [constants::{constants::Wrap<T>}::new]: forward function
+/- [constants::{constants::Wrap<T>}::new]:
    Source: 'src/constants.rs', lines 54:4-54:41 -/
 def Wrap.new (T : Type) (value : T) : Result (Wrap T) :=
   Result.ret { value := value }
@@ -81,7 +81,7 @@ def Wrap.new (T : Type) (value : T) : Result (Wrap T) :=
 def y_body : Result (Wrap I32) := Wrap.new I32 2#i32
 def y_c : Wrap I32 := eval_global y_body (by simp)
 
-/- [constants::unwrap_y]: forward function
+/- [constants::unwrap_y]:
    Source: 'src/constants.rs', lines 43:0-43:30 -/
 def unwrap_y : Result I32 :=
   Result.ret y_c.value
@@ -96,12 +96,12 @@ def yval_c : I32 := eval_global yval_body (by simp)
 def get_z1_z1_body : Result I32 := Result.ret 3#i32
 def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
 
-/- [constants::get_z1]: forward function
+/- [constants::get_z1]:
    Source: 'src/constants.rs', lines 61:0-61:28 -/
 def get_z1 : Result I32 :=
   Result.ret get_z1_z1_c
 
-/- [constants::add]: forward function
+/- [constants::add]:
    Source: 'src/constants.rs', lines 66:0-66:39 -/
 def add (a : I32) (b : I32) : Result I32 :=
   a + b
@@ -121,13 +121,13 @@ def q2_c : I32 := eval_global q2_body (by simp)
 def q3_body : Result I32 := add q2_c 3#i32
 def q3_c : I32 := eval_global q3_body (by simp)
 
-/- [constants::get_z2]: forward function
+/- [constants::get_z2]:
    Source: 'src/constants.rs', lines 70:0-70:28 -/
 def get_z2 : Result I32 :=
   do
-    let i ← get_z1
-    let i0 ← add i q3_c
-    add q1_c i0
+  let i ← get_z1
+  let i1 ← add i q3_c
+  add q1_c i1
 
 /- [constants::S1]
    Source: 'src/constants.rs', lines 80:0-80:18 -/
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
index 48ec6ad5..db15aacc 100644
--- a/tests/lean/External/Funs.lean
+++ b/tests/lean/External/Funs.lean
@@ -7,92 +7,58 @@ open Primitives
 
 namespace external
 
-/- [external::swap]: forward function
+/- [external::swap]:
    Source: 'src/external.rs', lines 6:0-6:46 -/
-def swap (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← core.mem.swap T x y st
-    let (st1, _) ← core.mem.swap_back0 T x y st st0
-    let (st2, _) ← core.mem.swap_back1 T x y st st1
-    Result.ret (st2, ())
-
-/- [external::swap]: backward function 0
-   Source: 'src/external.rs', lines 6:0-6:46 -/
-def swap_back
-  (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
-  Result (State × (T × T))
-  :=
-  do
-    let (st1, _) ← core.mem.swap T x y st
-    let (st2, x0) ← core.mem.swap_back0 T x y st st1
-    let (_, y0) ← core.mem.swap_back1 T x y st st2
-    Result.ret (st0, (x0, y0))
+def swap
+  (T : Type) (x : T) (y : T) (st : State) : Result (State × (T × T)) :=
+  core.mem.swap T x y st
 
-/- [external::test_new_non_zero_u32]: forward function
+/- [external::test_new_non_zero_u32]:
    Source: 'src/external.rs', lines 11:0-11:60 -/
 def test_new_non_zero_u32
   (x : U32) (st : State) : Result (State × core.num.nonzero.NonZeroU32) :=
   do
-    let (st0, o) ← core.num.nonzero.NonZeroU32.new x st
-    core.option.Option.unwrap core.num.nonzero.NonZeroU32 o st0
+  let (st1, o) ← core.num.nonzero.NonZeroU32.new x st
+  core.option.Option.unwrap core.num.nonzero.NonZeroU32 o st1
 
-/- [external::test_vec]: forward function
+/- [external::test_vec]:
    Source: 'src/external.rs', lines 17:0-17:17 -/
 def test_vec : Result Unit :=
   do
-    let v := alloc.vec.Vec.new U32
-    let _ ← alloc.vec.Vec.push U32 v 0#u32
-    Result.ret ()
+  let _ ← alloc.vec.Vec.push U32 (alloc.vec.Vec.new U32) 0#u32
+  Result.ret ()
 
 /- Unit test for [external::test_vec] -/
 #assert (test_vec == Result.ret ())
 
-/- [external::custom_swap]: forward function
+/- [external::custom_swap]:
    Source: 'src/external.rs', lines 24:0-24:66 -/
 def custom_swap
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
-  do
-    let (st0, _) ← core.mem.swap T x y st
-    let (st1, x0) ← core.mem.swap_back0 T x y st st0
-    let (st2, _) ← core.mem.swap_back1 T x y st st1
-    Result.ret (st2, x0)
-
-/- [external::custom_swap]: backward function 0
-   Source: 'src/external.rs', lines 24:0-24:66 -/
-def custom_swap_back
-  (T : Type) (x : T) (y : T) (st : State) (ret : T) (st0 : State) :
-  Result (State × (T × T))
+  (T : Type) (x : T) (y : T) (st : State) :
+  Result (State × (T × (T → State → Result (State × (T × T)))))
   :=
   do
-    let (st1, _) ← core.mem.swap T x y st
-    let (st2, _) ← core.mem.swap_back0 T x y st st1
-    let (_, y0) ← core.mem.swap_back1 T x y st st2
-    Result.ret (st0, (ret, y0))
+  let (st1, (t, t1)) ← core.mem.swap T x y st
+  let back_'a := fun ret st2 => Result.ret (st2, (ret, t1))
+  Result.ret (st1, (t, back_'a))
 
-/- [external::test_custom_swap]: forward function
+/- [external::test_custom_swap]:
    Source: 'src/external.rs', lines 29:0-29:59 -/
 def test_custom_swap
-  (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
+  (x : U32) (y : U32) (st : State) : Result (State × (U32 × U32)) :=
   do
-    let (st0, _) ← custom_swap U32 x y st
-    Result.ret (st0, ())
-
-/- [external::test_custom_swap]: backward function 0
-   Source: 'src/external.rs', lines 29:0-29:59 -/
-def test_custom_swap_back
-  (x : U32) (y : U32) (st : State) (st0 : State) :
-  Result (State × (U32 × U32))
-  :=
-  custom_swap_back U32 x y st 1#u32 st0
+  let (st1, (_, custom_swap_back)) ← custom_swap U32 x y st
+  let (_, (x1, y1)) ← custom_swap_back 1#u32 st1
+  Result.ret (st1, (x1, y1))
 
-/- [external::test_swap_non_zero]: forward function
+/- [external::test_swap_non_zero]:
    Source: 'src/external.rs', lines 35:0-35:44 -/
 def test_swap_non_zero (x : U32) (st : State) : Result (State × U32) :=
   do
-    let (st0, _) ← swap U32 x 0#u32 st
-    let (st1, (x0, _)) ← swap_back U32 x 0#u32 st st0
-    if x0 = 0#u32
-    then Result.fail .panic
-    else Result.ret (st1, x0)
+  let (st1, p) ← swap U32 x 0#u32 st
+  let (x1, _) := p
+  if x1 = 0#u32
+  then Result.fail .panic
+  else Result.ret (st1, x1)
 
 end external
diff --git a/tests/lean/External/FunsExternal.lean b/tests/lean/External/FunsExternal.lean
index aae11ba1..63830abc 100644
--- a/tests/lean/External/FunsExternal.lean
+++ b/tests/lean/External/FunsExternal.lean
@@ -8,22 +8,11 @@ open external
 
 /- [core::mem::swap] -/
 def core.mem.swap
-  (T : Type) : T → T → State → Result (State × Unit) :=
-  fun _x _y s => .ret (s, ())
-
-/- [core::mem::swap] -/
-def core.mem.swap_back0
-  (T : Type) : T → T → State → State → Result (State × T) :=
-  fun _x y _s0 s1 => .ret (s1, y)
-
-/- [core::mem::swap] -/
-def core.mem.swap_back1
-  (T : Type) : T → T → State → State → Result (State × T) :=
-  fun x _y _s0 s1 => .ret (s1, x)
+  (T : Type) : T → T → State → Result (State × (T × T)) :=
+  fun x y s => .ret (s, (y, x))
 
 /- [core::num::nonzero::NonZeroU32::{14}::new] -/
-def core.num.nonzero.NonZeroU32.new
-  :
+def core.num.nonzero.NonZeroU32.new :
   U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t)) :=
   fun _ _ => .fail .panic
 
diff --git a/tests/lean/External/FunsExternal_Template.lean b/tests/lean/External/FunsExternal_Template.lean
index 55cd6bb5..7e237369 100644
--- a/tests/lean/External/FunsExternal_Template.lean
+++ b/tests/lean/External/FunsExternal_Template.lean
@@ -6,26 +6,17 @@ import External.Types
 open Primitives
 open external
 
-/- [core::mem::swap]: forward function
+/- [core::mem::swap]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 -/
-axiom core.mem.swap (T : Type) : T → T → State → Result (State × Unit)
+axiom core.mem.swap
+  (T : Type) : T → T → State → Result (State × (T × T))
 
-/- [core::mem::swap]: backward function 0
-   Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 -/
-axiom core.mem.swap_back0
-  (T : Type) : T → T → State → State → Result (State × T)
-
-/- [core::mem::swap]: backward function 1
-   Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 -/
-axiom core.mem.swap_back1
-  (T : Type) : T → T → State → State → Result (State × T)
-
-/- [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+/- [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 -/
 axiom core.num.nonzero.NonZeroU32.new
   : U32 → State → Result (State × (Option core.num.nonzero.NonZeroU32))
 
-/- [core::option::{core::option::Option<T>}::unwrap]: forward function
+/- [core::option::{core::option::Option<T>}::unwrap]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 -/
 axiom core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T)
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index e03981a2..3978bfc7 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -6,12 +6,12 @@ open Primitives
 
 namespace hashmap
 
-/- [hashmap::hash_key]: forward function
+/- [hashmap::hash_key]:
    Source: 'src/hashmap.rs', lines 27:0-27:32 -/
 def hash_key (k : Usize) : Result Usize :=
   Result.ret k
 
-/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0:
    Source: 'src/hashmap.rs', lines 50:4-56:5 -/
 divergent def HashMap.allocate_slots_loop
   (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) :
@@ -20,12 +20,12 @@ divergent def HashMap.allocate_slots_loop
   if n > 0#usize
   then
     do
-      let slots0 ← alloc.vec.Vec.push (List T) slots List.Nil
-      let n0 ← n - 1#usize
-      HashMap.allocate_slots_loop T slots0 n0
+    let v ← alloc.vec.Vec.push (List T) slots List.Nil
+    let n1 ← n - 1#usize
+    HashMap.allocate_slots_loop T v n1
   else Result.ret slots
 
-/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
    Source: 'src/hashmap.rs', lines 50:4-50:76 -/
 def HashMap.allocate_slots
   (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) :
@@ -33,7 +33,7 @@ def HashMap.allocate_slots
   :=
   HashMap.allocate_slots_loop T slots n
 
-/- [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::new_with_capacity]:
    Source: 'src/hashmap.rs', lines 59:4-63:13 -/
 def HashMap.new_with_capacity
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
@@ -41,252 +41,220 @@ def HashMap.new_with_capacity
   Result (HashMap T)
   :=
   do
-    let v := alloc.vec.Vec.new (List T)
-    let slots ← HashMap.allocate_slots T v capacity
-    let i ← capacity * max_load_dividend
-    let i0 ← i / max_load_divisor
-    Result.ret
-      {
-        num_entries := 0#usize,
-        max_load_factor := (max_load_dividend, max_load_divisor),
-        max_load := i0,
-        slots := slots
-      }
-
-/- [hashmap::{hashmap::HashMap<T>}::new]: forward function
+  let slots ← HashMap.allocate_slots T (alloc.vec.Vec.new (List T)) capacity
+  let i ← capacity * max_load_dividend
+  let i1 ← i / max_load_divisor
+  Result.ret
+    {
+      num_entries := 0#usize,
+      max_load_factor := (max_load_dividend, max_load_divisor),
+      max_load := i1,
+      slots := slots
+    }
+
+/- [hashmap::{hashmap::HashMap<T>}::new]:
    Source: 'src/hashmap.rs', lines 75:4-75:24 -/
 def HashMap.new (T : Type) : Result (HashMap T) :=
   HashMap.new_with_capacity T 32#usize 4#usize 5#usize
 
-/- [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::clear]: loop 0:
    Source: 'src/hashmap.rs', lines 80:4-88:5 -/
 divergent def HashMap.clear_loop
   (T : Type) (slots : alloc.vec.Vec (List T)) (i : Usize) :
   Result (alloc.vec.Vec (List T))
   :=
-  let i0 := alloc.vec.Vec.len (List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (List T) slots
+  if i < i1
   then
     do
-      let i1 ← i + 1#usize
-      let slots0 ←
-        alloc.vec.Vec.index_mut_back (List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
-          List.Nil
-      HashMap.clear_loop T slots0 i1
+    let (_, index_mut_back) ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back List.Nil
+    HashMap.clear_loop T slots1 i2
   else Result.ret slots
 
-/- [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::clear]:
    Source: 'src/hashmap.rs', lines 80:4-80:27 -/
 def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
-    let v ← HashMap.clear_loop T self.slots 0#usize
-    Result.ret { self with num_entries := 0#usize, slots := v }
+  let back ← HashMap.clear_loop T self.slots 0#usize
+  Result.ret { self with num_entries := 0#usize, slots := back }
 
-/- [hashmap::{hashmap::HashMap<T>}::len]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::len]:
    Source: 'src/hashmap.rs', lines 90:4-90:30 -/
 def HashMap.len (T : Type) (self : HashMap T) : Result Usize :=
   Result.ret self.num_entries
 
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 97:4-114:5 -/
 divergent def HashMap.insert_in_list_loop
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
-  match ls with
-  | List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret false
-    else HashMap.insert_in_list_loop T key value tl
-  | List.Nil => Result.ret true
-
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def HashMap.insert_in_list
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
-  HashMap.insert_in_list_loop T key value ls
-
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 97:4-114:5 -/
-divergent def HashMap.insert_in_list_loop_back
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
+  (T : Type) (key : Usize) (value : T) (ls : List T) :
+  Result (Bool × (List T))
+  :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (List.Cons ckey value tl)
+    then Result.ret (false, List.Cons ckey value tl)
     else
       do
-        let tl0 ← HashMap.insert_in_list_loop_back T key value tl
-        Result.ret (List.Cons ckey cvalue tl0)
-  | List.Nil => let l := List.Nil
-                Result.ret (List.Cons key value l)
+      let (b, back) ← HashMap.insert_in_list_loop T key value tl
+      Result.ret (b, List.Cons ckey cvalue back)
+  | List.Nil => Result.ret (true, List.Cons key value List.Nil)
 
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
+/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
    Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def HashMap.insert_in_list_back
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
-  HashMap.insert_in_list_loop_back T key value ls
+def HashMap.insert_in_list
+  (T : Type) (key : Usize) (value : T) (ls : List T) :
+  Result (Bool × (List T))
+  :=
+  HashMap.insert_in_list_loop T key value ls
 
-/- [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::insert_no_resize]:
    Source: 'src/hashmap.rs', lines 117:4-117:54 -/
 def HashMap.insert_no_resize
   (T : Type) (self : HashMap T) (key : Usize) (value : T) :
   Result (HashMap T)
   :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let inserted ← HashMap.insert_in_list T key value l
-    if inserted
-    then
-      do
-        let i0 ← self.num_entries + 1#usize
-        let l0 ← HashMap.insert_in_list_back T key value l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with num_entries := i0, slots := v }
-    else
-      do
-        let l0 ← HashMap.insert_in_list_back T key value l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with slots := v }
-
-/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  let (inserted, l1) ← HashMap.insert_in_list T key value l
+  if inserted
+  then
+    do
+    let i1 ← self.num_entries + 1#usize
+    let v ← index_mut_back l1
+    Result.ret { self with num_entries := i1, slots := v }
+  else do
+       let v ← index_mut_back l1
+       Result.ret { self with slots := v }
+
+/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 183:4-196:5 -/
 divergent def HashMap.move_elements_from_list_loop
   (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
   match ls with
   | List.Cons k v tl =>
     do
-      let ntable0 ← HashMap.insert_no_resize T ntable k v
-      HashMap.move_elements_from_list_loop T ntable0 tl
+    let hm ← HashMap.insert_no_resize T ntable k v
+    HashMap.move_elements_from_list_loop T hm tl
   | List.Nil => Result.ret ntable
 
-/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]:
    Source: 'src/hashmap.rs', lines 183:4-183:72 -/
 def HashMap.move_elements_from_list
   (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
   HashMap.move_elements_from_list_loop T ntable ls
 
-/- [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0:
    Source: 'src/hashmap.rs', lines 171:4-180:5 -/
 divergent def HashMap.move_elements_loop
   (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize)
   :
   Result ((HashMap T) × (alloc.vec.Vec (List T)))
   :=
-  let i0 := alloc.vec.Vec.len (List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (List T) slots
+  if i < i1
   then
     do
-      let l ←
-        alloc.vec.Vec.index_mut (List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
-      let ls := core.mem.replace (List T) l List.Nil
-      let ntable0 ← HashMap.move_elements_from_list T ntable ls
-      let i1 ← i + 1#usize
-      let l0 := core.mem.replace_back (List T) l List.Nil
-      let slots0 ←
-        alloc.vec.Vec.index_mut_back (List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i l0
-      HashMap.move_elements_loop T ntable0 slots0 i1
+    let (l, index_mut_back) ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
+    let (ls, l1) := core.mem.replace (List T) l List.Nil
+    let hm ← HashMap.move_elements_from_list T ntable ls
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back l1
+    let back_'a ← HashMap.move_elements_loop T hm slots1 i2
+    let (hm1, v) := back_'a
+    Result.ret (hm1, v)
   else Result.ret (ntable, slots)
 
-/- [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::move_elements]:
    Source: 'src/hashmap.rs', lines 171:4-171:95 -/
 def HashMap.move_elements
   (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize)
   :
   Result ((HashMap T) × (alloc.vec.Vec (List T)))
   :=
-  HashMap.move_elements_loop T ntable slots i
+  do
+  let back_'a ← HashMap.move_elements_loop T ntable slots i
+  let (hm, v) := back_'a
+  Result.ret (hm, v)
 
-/- [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::try_resize]:
    Source: 'src/hashmap.rs', lines 140:4-140:28 -/
 def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
-    let max_usize ← Scalar.cast .Usize core_u32_max
-    let capacity := alloc.vec.Vec.len (List T) self.slots
-    let n1 ← max_usize / 2#usize
-    let (i, i0) := self.max_load_factor
-    let i1 ← n1 / i
-    if capacity <= i1
-    then
-      do
-        let i2 ← capacity * 2#usize
-        let ntable ← HashMap.new_with_capacity T i2 i i0
-        let (ntable0, _) ← HashMap.move_elements T ntable self.slots 0#usize
-        Result.ret
-          {
-            ntable0
-              with
-              num_entries := self.num_entries, max_load_factor := (i, i0)
-          }
-    else Result.ret { self with max_load_factor := (i, i0) }
-
-/- [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  let max_usize ← Scalar.cast .Usize core_u32_max
+  let capacity := alloc.vec.Vec.len (List T) self.slots
+  let n1 ← max_usize / 2#usize
+  let (i, i1) := self.max_load_factor
+  let i2 ← n1 / i
+  if capacity <= i2
+  then
+    do
+    let i3 ← capacity * 2#usize
+    let ntable ← HashMap.new_with_capacity T i3 i i1
+    let p ← HashMap.move_elements T ntable self.slots 0#usize
+    let (ntable1, _) := p
+    Result.ret
+      {
+        ntable1
+          with
+          num_entries := self.num_entries, max_load_factor := (i, i1)
+      }
+  else Result.ret { self with max_load_factor := (i, i1) }
+
+/- [hashmap::{hashmap::HashMap<T>}::insert]:
    Source: 'src/hashmap.rs', lines 129:4-129:48 -/
 def HashMap.insert
   (T : Type) (self : HashMap T) (key : Usize) (value : T) :
   Result (HashMap T)
   :=
   do
-    let self0 ← HashMap.insert_no_resize T self key value
-    let i ← HashMap.len T self0
-    if i > self0.max_load
-    then HashMap.try_resize T self0
-    else Result.ret self0
+  let hm ← HashMap.insert_no_resize T self key value
+  let i ← HashMap.len T hm
+  if i > hm.max_load
+  then HashMap.try_resize T hm
+  else Result.ret hm
 
-/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 206:4-219:5 -/
 divergent def HashMap.contains_key_in_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result Bool :=
   match ls with
-  | List.Cons ckey t tl =>
+  | List.Cons ckey _ tl =>
     if ckey = key
     then Result.ret true
     else HashMap.contains_key_in_list_loop T key tl
   | List.Nil => Result.ret false
 
-/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]:
    Source: 'src/hashmap.rs', lines 206:4-206:68 -/
 def HashMap.contains_key_in_list
   (T : Type) (key : Usize) (ls : List T) : Result Bool :=
   HashMap.contains_key_in_list_loop T key ls
 
-/- [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::contains_key]:
    Source: 'src/hashmap.rs', lines 199:4-199:49 -/
 def HashMap.contains_key
   (T : Type) (self : HashMap T) (key : Usize) : Result Bool :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    HashMap.contains_key_in_list T key l
-
-/- [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  HashMap.contains_key_in_list T key l
+
+/- [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 224:4-237:5 -/
 divergent def HashMap.get_in_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result T :=
@@ -297,231 +265,170 @@ divergent def HashMap.get_in_list_loop
     else HashMap.get_in_list_loop T key tl
   | List.Nil => Result.fail .panic
 
-/- [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::get_in_list]:
    Source: 'src/hashmap.rs', lines 224:4-224:70 -/
 def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T :=
   HashMap.get_in_list_loop T key ls
 
-/- [hashmap::{hashmap::HashMap<T>}::get]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::get]:
    Source: 'src/hashmap.rs', lines 239:4-239:55 -/
 def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    HashMap.get_in_list T key l
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  HashMap.get_in_list T key l
+
+/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 245:4-254:5 -/
 divergent def HashMap.get_mut_in_list_loop
-  (T : Type) (ls : List T) (key : Usize) : Result T :=
-  match ls with
-  | List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret cvalue
-    else HashMap.get_mut_in_list_loop T tl key
-  | List.Nil => Result.fail .panic
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def HashMap.get_mut_in_list
-  (T : Type) (ls : List T) (key : Usize) : Result T :=
-  HashMap.get_mut_in_list_loop T ls key
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 245:4-254:5 -/
-divergent def HashMap.get_mut_in_list_loop_back
-  (T : Type) (ls : List T) (key : Usize) (ret : T) : Result (List T) :=
+  (T : Type) (ls : List T) (key : Usize) :
+  Result (T × (T → Result (List T)))
+  :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (List.Cons ckey ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ckey ret tl)
+      Result.ret (cvalue, back_'a)
     else
       do
-        let tl0 ← HashMap.get_mut_in_list_loop_back T tl key ret
-        Result.ret (List.Cons ckey cvalue tl0)
+      let (t, back_'a) ← HashMap.get_mut_in_list_loop T tl key
+      let back_'a1 :=
+        fun ret =>
+          do
+          let tl1 ← back_'a ret
+          Result.ret (List.Cons ckey cvalue tl1)
+      Result.ret (t, back_'a1)
   | List.Nil => Result.fail .panic
 
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]:
    Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def HashMap.get_mut_in_list_back
-  (T : Type) (ls : List T) (key : Usize) (ret : T) : Result (List T) :=
-  HashMap.get_mut_in_list_loop_back T ls key ret
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
-   Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+def HashMap.get_mut_in_list
+  (T : Type) (ls : List T) (key : Usize) :
+  Result (T × (T → Result (List T)))
+  :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    HashMap.get_mut_in_list T l key
+  let (t, back_'a) ← HashMap.get_mut_in_list_loop T ls key
+  Result.ret (t, back_'a)
 
-/- [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+/- [hashmap::{hashmap::HashMap<T>}::get_mut]:
    Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def HashMap.get_mut_back
-  (T : Type) (self : HashMap T) (key : Usize) (ret : T) : Result (HashMap T) :=
+def HashMap.get_mut
+  (T : Type) (self : HashMap T) (key : Usize) :
+  Result (T × (T → Result (HashMap T)))
+  :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let l0 ← HashMap.get_mut_in_list_back T l key ret
-    let v ←
-      alloc.vec.Vec.index_mut_back (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod l0
-    Result.ret { self with slots := v }
-
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
-   Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def HashMap.remove_from_list_loop
-  (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
-  match ls with
-  | List.Cons ckey t tl =>
-    if ckey = key
-    then
-      let mv_ls := core.mem.replace (List T) (List.Cons ckey t tl) List.Nil
-      match mv_ls with
-      | List.Cons i cvalue tl0 => Result.ret (some cvalue)
-      | List.Nil => Result.fail .panic
-    else HashMap.remove_from_list_loop T key tl
-  | List.Nil => Result.ret none
-
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
-   Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def HashMap.remove_from_list
-  (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
-  HashMap.remove_from_list_loop T key ls
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  let (t, get_mut_in_list_back) ← HashMap.get_mut_in_list T l key
+  let back_'a :=
+    fun ret =>
+      do
+      let l1 ← get_mut_in_list_back ret
+      let v ← index_mut_back l1
+      Result.ret { self with slots := v }
+  Result.ret (t, back_'a)
 
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def HashMap.remove_from_list_loop_back
-  (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
+divergent def HashMap.remove_from_list_loop
+  (T : Type) (key : Usize) (ls : List T) : Result ((Option T) × (List T)) :=
   match ls with
   | List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls := core.mem.replace (List T) (List.Cons ckey t tl) List.Nil
+      let (mv_ls, _) :=
+        core.mem.replace (List T) (List.Cons ckey t tl) List.Nil
       match mv_ls with
-      | List.Cons i cvalue tl0 => Result.ret tl0
+      | List.Cons _ cvalue tl1 => Result.ret (some cvalue, tl1)
       | List.Nil => Result.fail .panic
     else
       do
-        let tl0 ← HashMap.remove_from_list_loop_back T key tl
-        Result.ret (List.Cons ckey t tl0)
-  | List.Nil => Result.ret List.Nil
+      let (o, back) ← HashMap.remove_from_list_loop T key tl
+      Result.ret (o, List.Cons ckey t back)
+  | List.Nil => Result.ret (none, List.Nil)
 
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
+/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
    Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def HashMap.remove_from_list_back
-  (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
-  HashMap.remove_from_list_loop_back T key ls
+def HashMap.remove_from_list
+  (T : Type) (key : Usize) (ls : List T) : Result ((Option T) × (List T)) :=
+  HashMap.remove_from_list_loop T key ls
 
-/- [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::remove]:
    Source: 'src/hashmap.rs', lines 294:4-294:52 -/
 def HashMap.remove
-  (T : Type) (self : HashMap T) (key : Usize) : Result (Option T) :=
-  do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let x ← HashMap.remove_from_list T key l
-    match x with
-    | none => Result.ret none
-    | some x0 => do
-                   let _ ← self.num_entries - 1#usize
-                   Result.ret (some x0)
-
-/- [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
-   Source: 'src/hashmap.rs', lines 294:4-294:52 -/
-def HashMap.remove_back
-  (T : Type) (self : HashMap T) (key : Usize) : Result (HashMap T) :=
+  (T : Type) (self : HashMap T) (key : Usize) :
+  Result ((Option T) × (HashMap T))
+  :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let x ← HashMap.remove_from_list T key l
-    match x with
-    | none =>
-      do
-        let l0 ← HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with slots := v }
-    | some x0 =>
-      do
-        let i0 ← self.num_entries - 1#usize
-        let l0 ← HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with num_entries := i0, slots := v }
-
-/- [hashmap::test1]: forward function
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  let (x, l1) ← HashMap.remove_from_list T key l
+  match x with
+  | none =>
+    do
+    let v ← index_mut_back l1
+    Result.ret (none, { self with slots := v })
+  | some x1 =>
+    do
+    let i1 ← self.num_entries - 1#usize
+    let v ← index_mut_back l1
+    Result.ret (some x1, { self with num_entries := i1, slots := v })
+
+/- [hashmap::test1]:
    Source: 'src/hashmap.rs', lines 315:0-315:10 -/
 def test1 : Result Unit :=
   do
-    let hm ← HashMap.new U64
-    let hm0 ← HashMap.insert U64 hm 0#usize 42#u64
-    let hm1 ← HashMap.insert U64 hm0 128#usize 18#u64
-    let hm2 ← HashMap.insert U64 hm1 1024#usize 138#u64
-    let hm3 ← HashMap.insert U64 hm2 1056#usize 256#u64
-    let i ← HashMap.get U64 hm3 128#usize
-    if not (i = 18#u64)
+  let hm ← HashMap.new U64
+  let hm1 ← HashMap.insert U64 hm 0#usize 42#u64
+  let hm2 ← HashMap.insert U64 hm1 128#usize 18#u64
+  let hm3 ← HashMap.insert U64 hm2 1024#usize 138#u64
+  let hm4 ← HashMap.insert U64 hm3 1056#usize 256#u64
+  let i ← HashMap.get U64 hm4 128#usize
+  if not (i = 18#u64)
+  then Result.fail .panic
+  else
+    do
+    let (_, get_mut_back) ← HashMap.get_mut U64 hm4 1024#usize
+    let hm5 ← get_mut_back 56#u64
+    let i1 ← HashMap.get U64 hm5 1024#usize
+    if not (i1 = 56#u64)
     then Result.fail .panic
     else
       do
-        let hm4 ← HashMap.get_mut_back U64 hm3 1024#usize 56#u64
-        let i0 ← HashMap.get U64 hm4 1024#usize
-        if not (i0 = 56#u64)
+      let (x, hm6) ← HashMap.remove U64 hm5 1024#usize
+      match x with
+      | none => Result.fail .panic
+      | some x1 =>
+        if not (x1 = 56#u64)
         then Result.fail .panic
         else
           do
-            let x ← HashMap.remove U64 hm4 1024#usize
-            match x with
-            | none => Result.fail .panic
-            | some x0 =>
-              if not (x0 = 56#u64)
+          let i2 ← HashMap.get U64 hm6 0#usize
+          if not (i2 = 42#u64)
+          then Result.fail .panic
+          else
+            do
+            let i3 ← HashMap.get U64 hm6 128#usize
+            if not (i3 = 18#u64)
+            then Result.fail .panic
+            else
+              do
+              let i4 ← HashMap.get U64 hm6 1056#usize
+              if not (i4 = 256#u64)
               then Result.fail .panic
-              else
-                do
-                  let hm5 ← HashMap.remove_back U64 hm4 1024#usize
-                  let i1 ← HashMap.get U64 hm5 0#usize
-                  if not (i1 = 42#u64)
-                  then Result.fail .panic
-                  else
-                    do
-                      let i2 ← HashMap.get U64 hm5 128#usize
-                      if not (i2 = 18#u64)
-                      then Result.fail .panic
-                      else
-                        do
-                          let i3 ← HashMap.get U64 hm5 1056#usize
-                          if not (i3 = 256#u64)
-                          then Result.fail .panic
-                          else Result.ret ()
+              else Result.ret ()
 
 end hashmap
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
index e79c422d..7215e286 100644
--- a/tests/lean/Hashmap/Properties.lean
+++ b/tests/lean/Hashmap/Properties.lean
@@ -55,71 +55,6 @@ theorem match_lawful_beq [BEq α] [LawfulBEq α] [DecidableEq α] (x y : α) :
   (x == y) = (if x = y then true else false) := by
   split <;> simp_all
 
-@[pspec]
-theorem insert_in_list_spec0 {α : Type} (key: Usize) (value: α) (ls: List α) :
-  ∃ b,
-    insert_in_list α key value ls = ret b ∧
-    (b ↔ ls.lookup key = none)
-  := match ls with
-  | .Nil => by simp [insert_in_list, insert_in_list_loop]
-  | .Cons k v tl =>
-    if h: k = key then -- TODO: The order of k/key matters
-      by
-        simp [insert_in_list]
-        rw [insert_in_list_loop]
-        simp [h]
-    else
-      have ⟨ b, hi ⟩ := insert_in_list_spec0 key value tl
-      by
-        exists b
-        simp [insert_in_list]
-        rw [insert_in_list_loop] -- TODO: Using simp leads to infinite recursion
-        simp only [insert_in_list] at hi
-        simp [*]
-
--- Variation: use progress
-theorem insert_in_list_spec1 {α : Type} (key: Usize) (value: α) (ls: List α) :
-  ∃ b,
-    insert_in_list α key value ls = ret b ∧
-    (b ↔ ls.lookup key = none)
-  := match ls with
-  | .Nil => by simp [insert_in_list, insert_in_list_loop]
-  | .Cons k v tl =>
-    if h: k = key then -- TODO: The order of k/key matters
-      by
-        simp [insert_in_list]
-        rw [insert_in_list_loop]
-        simp [h]
-    else
-      by
-        simp only [insert_in_list]
-        rw [insert_in_list_loop]
-        conv => rhs; ext; simp [*]
-        progress keep heq as ⟨ b, hi ⟩
-        simp only [insert_in_list] at heq
-        exists b
-
--- Variation: use tactics from the beginning
-theorem insert_in_list_spec2 {α : Type} (key: Usize) (value: α) (ls: List α) :
-  ∃ b,
-    insert_in_list α key value ls = ret b ∧
-    (b ↔ (ls.lookup key = none))
-  := by
-  induction ls
-  case Nil => simp [insert_in_list, insert_in_list_loop]
-  case Cons k v tl ih =>
-    simp only [insert_in_list]
-    rw [insert_in_list_loop]
-    simp only
-    if h: k = key then
-     simp [h]
-    else
-     conv => rhs; ext; left; simp [h] -- TODO: Simplify
-     simp only [insert_in_list] at ih;
-     -- TODO: give the possibility of using underscores
-     progress as ⟨ b, h ⟩
-     simp [*]
-
 def distinct_keys (ls : Core.List (Usize × α)) := ls.pairwise_rel (λ x y => x.fst ≠ y.fst)
 
 def hash_mod_key (k : Usize) (l : Int) : Int :=
@@ -175,11 +110,16 @@ def inv (hm : HashMap α) : Prop :=
   base_inv hm
   -- TODO: either the hashmap is not overloaded, or we can't resize it
 
-theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+-- This rewriting lemma is problematic below
+attribute [-simp] Bool.exists_bool
+
+theorem insert_in_list_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
   (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
   (hdk : distinct_keys l0.v) :
-  ∃ l1,
-    insert_in_list_back α key value l0 = ret l1 ∧
+  ∃ b l1,
+    insert_in_list α key value l0 = ret (b, l1) ∧
+    -- The boolean is true ↔ we inserted a new binding
+    (b ↔ (l0.lookup key = none)) ∧
     -- We update the binding
     l1.lookup key = value ∧
     (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
@@ -193,16 +133,19 @@ theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value:
     distinct_keys l1.v ∧
     -- We need this auxiliary property to prove that the keys distinct properties is preserved
     (∀ k, k ≠ key → l0.v.allP (λ (k1, _) => k ≠ k1) → l1.v.allP (λ (k1, _) => k ≠ k1))
-  := match l0 with
-  | .Nil => by checkpoint
+  :=
+  match l0 with
+  | .Nil => by
+    exists true -- TODO: why do we need to do this?
     simp (config := {contextual := true})
-      [insert_in_list_back, insert_in_list_loop_back,
+      [insert_in_list, insert_in_list_loop,
        List.v, slot_s_inv_hash, distinct_keys, List.pairwise_rel]
   | .Cons k v tl0 =>
-     if h: k = key then by checkpoint
-       simp [insert_in_list_back]
-       rw [insert_in_list_loop_back]
+     if h: k = key then by
+       rw [insert_in_list]
+       rw [insert_in_list_loop]
        simp [h]
+       exists false; simp -- TODO: why do we need to do this?
        split_conjs
        . intros; simp [*]
        . simp [List.v, slot_s_inv_hash] at *
@@ -210,17 +153,17 @@ theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value:
        . simp [*, distinct_keys] at *
          apply hdk
        . tauto
-     else by checkpoint
-       simp [insert_in_list_back]
-       rw [insert_in_list_loop_back]
+     else by
+       rw [insert_in_list]
+       rw [insert_in_list_loop]
        simp [h]
        have : slot_s_inv_hash l (hash_mod_key key l) (List.v tl0) := by checkpoint
          simp_all [List.v, slot_s_inv_hash]
        have : distinct_keys (List.v tl0) := by checkpoint
          simp [distinct_keys] at hdk
          simp [hdk, distinct_keys]
-       progress keep heq as ⟨ tl1 .. ⟩
-       simp only [insert_in_list_back] at heq
+       progress keep heq as ⟨ b, tl1 .. ⟩
+       simp only [insert_in_list] at heq
        have : slot_s_inv_hash l (hash_mod_key key l) (List.v (List.Cons k v tl1)) := by checkpoint
          simp [List.v, slot_s_inv_hash] at *
          simp [*]
@@ -228,14 +171,16 @@ theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value:
          simp [distinct_keys] at *
          simp [*]
        -- TODO: canonize addition by default?
+       exists b
        simp_all [Int.add_assoc, Int.add_comm, Int.add_left_comm]
 
 @[pspec]
-theorem insert_in_list_back_spec {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+theorem insert_in_list_spec {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
   (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
   (hdk : distinct_keys l0.v) :
-  ∃ l1,
-    insert_in_list_back α key value l0 = ret l1 ∧
+  ∃ b l1,
+    insert_in_list α key value l0 = ret (b, l1) ∧
+    (b ↔ (l0.lookup key = none)) ∧
     -- We update the binding
     l1.lookup key = value ∧
     (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
@@ -248,7 +193,8 @@ theorem insert_in_list_back_spec {α : Type} (l : Int) (key: Usize) (value: α)
     -- The keys are distinct
     distinct_keys l1.v
   := by
-  progress with insert_in_list_back_spec_aux as ⟨ l1 .. ⟩
+  progress with insert_in_list_spec_aux as ⟨ b, l1 .. ⟩
+  exists b
   exists l1
 
 @[simp]
@@ -286,7 +232,7 @@ set_option pp.coercions false -- do not print coercions with ↑ (this doesn't p
 
 -- The proof below is a bit expensive, so we need to increase the maximum number
 -- of heart beats
-set_option maxHeartbeats 400000
+set_option maxHeartbeats 1000000
 
 theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value : α)
   (hinv : hm.inv) (hnsat : hm.lookup key = none → hm.len_s < Usize.max) :
@@ -315,9 +261,19 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
       simp [hinv]
     -- TODO: we want to automate that
     simp [*, Int.emod_lt_of_pos]
-  progress as ⟨ l, h_leq ⟩
-  -- TODO: make progress use the names written in the goal
-  progress as ⟨ inserted ⟩
+  progress as ⟨ l, index_mut_back, h_leq, h_index_mut_back ⟩
+  simp [h_index_mut_back] at *; clear h_index_mut_back index_mut_back
+  have h_slot :
+    slot_s_inv_hash hm.slots.length (hash_mod_key key hm.slots.length) l.v := by
+    simp [inv] at hinv
+    have h := (hinv.right.left hash_mod.val (by assumption) (by assumption)).right
+    simp [slot_t_inv, hhm] at h
+    simp [h, hhm, h_leq]
+  have hd : distinct_keys l.v := by
+    simp [inv, slots_t_inv, slot_t_inv] at hinv
+    have h := hinv.right.left hash_mod.val (by assumption) (by assumption)
+    simp [h, h_leq]
+  progress as ⟨ inserted, l0, _, _, _, _, hlen .. ⟩
   rw [if_update_eq] -- TODO: necessary because we don't have a join
   -- TODO: progress to ...
   have hipost :
@@ -336,20 +292,9 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
     else
       simp [*, Pure.pure]
   progress as ⟨ i0 ⟩
-  have h_slot : slot_s_inv_hash hm.slots.length (hash_mod_key key hm.slots.length) l.v
-    := by
-    simp [inv] at hinv
-    have h := (hinv.right.left hash_mod.val (by assumption) (by assumption)).right
-    simp [slot_t_inv, hhm] at h
-    simp [h, hhm, h_leq]
-  have hd : distinct_keys l.v := by checkpoint
-    simp [inv, slots_t_inv, slot_t_inv] at hinv
-    have h := hinv.right.left hash_mod.val (by assumption) (by assumption)
-    simp [h, h_leq]
   -- TODO: hide the variables and only keep the props
   -- TODO: allow providing terms to progress to instantiate the meta variables
   -- which are not propositions
-  progress as ⟨ l0, _, _, _, hlen .. ⟩
   progress keep hv as ⟨ v, h_veq ⟩
   -- TODO: update progress to automate that
   -- TODO: later I don't want to inline nhm - we need to control simp: deactivate
@@ -428,8 +373,7 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
         simp [*]
       else
         simp [*]
-    . -- TODO: simp[*] fails: "(deterministic) timeout at 'whnf'"
-      simp [hinv, h_veq, nhm_eq]
+    . simp [hinv, h_veq, nhm_eq]
   simp_all
 
 end HashMap
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index f87ad355..ebed2570 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -7,12 +7,12 @@ open Primitives
 
 namespace hashmap_main
 
-/- [hashmap_main::hashmap::hash_key]: forward function
+/- [hashmap_main::hashmap::hash_key]:
    Source: 'src/hashmap.rs', lines 27:0-27:32 -/
 def hashmap.hash_key (k : Usize) : Result Usize :=
   Result.ret k
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0:
    Source: 'src/hashmap.rs', lines 50:4-56:5 -/
 divergent def hashmap.HashMap.allocate_slots_loop
   (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) :
@@ -21,12 +21,12 @@ divergent def hashmap.HashMap.allocate_slots_loop
   if n > 0#usize
   then
     do
-      let slots0 ← alloc.vec.Vec.push (hashmap.List T) slots hashmap.List.Nil
-      let n0 ← n - 1#usize
-      hashmap.HashMap.allocate_slots_loop T slots0 n0
+    let v ← alloc.vec.Vec.push (hashmap.List T) slots hashmap.List.Nil
+    let n1 ← n - 1#usize
+    hashmap.HashMap.allocate_slots_loop T v n1
   else Result.ret slots
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]:
    Source: 'src/hashmap.rs', lines 50:4-50:76 -/
 def hashmap.HashMap.allocate_slots
   (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) :
@@ -34,7 +34,7 @@ def hashmap.HashMap.allocate_slots
   :=
   hashmap.HashMap.allocate_slots_loop T slots n
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]:
    Source: 'src/hashmap.rs', lines 59:4-63:13 -/
 def hashmap.HashMap.new_with_capacity
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
@@ -42,136 +42,106 @@ def hashmap.HashMap.new_with_capacity
   Result (hashmap.HashMap T)
   :=
   do
-    let v := alloc.vec.Vec.new (hashmap.List T)
-    let slots ← hashmap.HashMap.allocate_slots T v capacity
-    let i ← capacity * max_load_dividend
-    let i0 ← i / max_load_divisor
-    Result.ret
-      {
-        num_entries := 0#usize,
-        max_load_factor := (max_load_dividend, max_load_divisor),
-        max_load := i0,
-        slots := slots
-      }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+  let slots ←
+    hashmap.HashMap.allocate_slots T (alloc.vec.Vec.new (hashmap.List T))
+      capacity
+  let i ← capacity * max_load_dividend
+  let i1 ← i / max_load_divisor
+  Result.ret
+    {
+      num_entries := 0#usize,
+      max_load_factor := (max_load_dividend, max_load_divisor),
+      max_load := i1,
+      slots := slots
+    }
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
    Source: 'src/hashmap.rs', lines 75:4-75:24 -/
 def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) :=
   hashmap.HashMap.new_with_capacity T 32#usize 4#usize 5#usize
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0:
    Source: 'src/hashmap.rs', lines 80:4-88:5 -/
 divergent def hashmap.HashMap.clear_loop
   (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
   Result (alloc.vec.Vec (hashmap.List T))
   :=
-  let i0 := alloc.vec.Vec.len (hashmap.List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (hashmap.List T) slots
+  if i < i1
   then
     do
-      let i1 ← i + 1#usize
-      let slots0 ←
-        alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
-          hashmap.List.Nil
-      hashmap.HashMap.clear_loop T slots0 i1
+    let (_, index_mut_back) ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back hashmap.List.Nil
+    hashmap.HashMap.clear_loop T slots1 i2
   else Result.ret slots
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]:
    Source: 'src/hashmap.rs', lines 80:4-80:27 -/
 def hashmap.HashMap.clear
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
-    let v ← hashmap.HashMap.clear_loop T self.slots 0#usize
-    Result.ret { self with num_entries := 0#usize, slots := v }
+  let back ← hashmap.HashMap.clear_loop T self.slots 0#usize
+  Result.ret { self with num_entries := 0#usize, slots := back }
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]:
    Source: 'src/hashmap.rs', lines 90:4-90:30 -/
 def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize :=
   Result.ret self.num_entries
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 97:4-114:5 -/
 divergent def hashmap.HashMap.insert_in_list_loop
-  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
-  match ls with
-  | hashmap.List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret false
-    else hashmap.HashMap.insert_in_list_loop T key value tl
-  | hashmap.List.Nil => Result.ret true
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def hashmap.HashMap.insert_in_list
-  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
-  hashmap.HashMap.insert_in_list_loop T key value ls
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 97:4-114:5 -/
-divergent def hashmap.HashMap.insert_in_list_loop_back
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
-  Result (hashmap.List T)
+  Result (Bool × (hashmap.List T))
   :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (hashmap.List.Cons ckey value tl)
+    then Result.ret (false, hashmap.List.Cons ckey value tl)
     else
       do
-        let tl0 ← hashmap.HashMap.insert_in_list_loop_back T key value tl
-        Result.ret (hashmap.List.Cons ckey cvalue tl0)
+      let (b, back) ← hashmap.HashMap.insert_in_list_loop T key value tl
+      Result.ret (b, hashmap.List.Cons ckey cvalue back)
   | hashmap.List.Nil =>
-    let l := hashmap.List.Nil
-    Result.ret (hashmap.List.Cons key value l)
+    Result.ret (true, hashmap.List.Cons key value hashmap.List.Nil)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]:
    Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def hashmap.HashMap.insert_in_list_back
+def hashmap.HashMap.insert_in_list
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
-  Result (hashmap.List T)
+  Result (Bool × (hashmap.List T))
   :=
-  hashmap.HashMap.insert_in_list_loop_back T key value ls
+  hashmap.HashMap.insert_in_list_loop T key value ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]:
    Source: 'src/hashmap.rs', lines 117:4-117:54 -/
 def hashmap.HashMap.insert_no_resize
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let inserted ← hashmap.HashMap.insert_in_list T key value l
-    if inserted
-    then
-      do
-        let i0 ← self.num_entries + 1#usize
-        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with num_entries := i0, slots := v }
-    else
-      do
-        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with slots := v }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  let (inserted, l1) ← hashmap.HashMap.insert_in_list T key value l
+  if inserted
+  then
+    do
+    let i1 ← self.num_entries + 1#usize
+    let v ← index_mut_back l1
+    Result.ret { self with num_entries := i1, slots := v }
+  else do
+       let v ← index_mut_back l1
+       Result.ret { self with slots := v }
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 183:4-196:5 -/
 divergent def hashmap.HashMap.move_elements_from_list_loop
   (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
@@ -180,12 +150,11 @@ divergent def hashmap.HashMap.move_elements_from_list_loop
   match ls with
   | hashmap.List.Cons k v tl =>
     do
-      let ntable0 ← hashmap.HashMap.insert_no_resize T ntable k v
-      hashmap.HashMap.move_elements_from_list_loop T ntable0 tl
+    let hm ← hashmap.HashMap.insert_no_resize T ntable k v
+    hashmap.HashMap.move_elements_from_list_loop T hm tl
   | hashmap.List.Nil => Result.ret ntable
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]:
    Source: 'src/hashmap.rs', lines 183:4-183:72 -/
 def hashmap.HashMap.move_elements_from_list
   (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
@@ -193,114 +162,111 @@ def hashmap.HashMap.move_elements_from_list
   :=
   hashmap.HashMap.move_elements_from_list_loop T ntable ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0:
    Source: 'src/hashmap.rs', lines 171:4-180:5 -/
 divergent def hashmap.HashMap.move_elements_loop
   (T : Type) (ntable : hashmap.HashMap T)
   (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
   Result ((hashmap.HashMap T) × (alloc.vec.Vec (hashmap.List T)))
   :=
-  let i0 := alloc.vec.Vec.len (hashmap.List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (hashmap.List T) slots
+  if i < i1
   then
     do
-      let l ←
-        alloc.vec.Vec.index_mut (hashmap.List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
-      let ls := core.mem.replace (hashmap.List T) l hashmap.List.Nil
-      let ntable0 ← hashmap.HashMap.move_elements_from_list T ntable ls
-      let i1 ← i + 1#usize
-      let l0 := core.mem.replace_back (hashmap.List T) l hashmap.List.Nil
-      let slots0 ←
-        alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
-          l0
-      hashmap.HashMap.move_elements_loop T ntable0 slots0 i1
+    let (l, index_mut_back) ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
+    let (ls, l1) := core.mem.replace (hashmap.List T) l hashmap.List.Nil
+    let hm ← hashmap.HashMap.move_elements_from_list T ntable ls
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back l1
+    let back_'a ← hashmap.HashMap.move_elements_loop T hm slots1 i2
+    let (hm1, v) := back_'a
+    Result.ret (hm1, v)
   else Result.ret (ntable, slots)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]:
    Source: 'src/hashmap.rs', lines 171:4-171:95 -/
 def hashmap.HashMap.move_elements
   (T : Type) (ntable : hashmap.HashMap T)
   (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
   Result ((hashmap.HashMap T) × (alloc.vec.Vec (hashmap.List T)))
   :=
-  hashmap.HashMap.move_elements_loop T ntable slots i
+  do
+  let back_'a ← hashmap.HashMap.move_elements_loop T ntable slots i
+  let (hm, v) := back_'a
+  Result.ret (hm, v)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]:
    Source: 'src/hashmap.rs', lines 140:4-140:28 -/
 def hashmap.HashMap.try_resize
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
-    let max_usize ← Scalar.cast .Usize core_u32_max
-    let capacity := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let n1 ← max_usize / 2#usize
-    let (i, i0) := self.max_load_factor
-    let i1 ← n1 / i
-    if capacity <= i1
-    then
-      do
-        let i2 ← capacity * 2#usize
-        let ntable ← hashmap.HashMap.new_with_capacity T i2 i i0
-        let (ntable0, _) ←
-          hashmap.HashMap.move_elements T ntable self.slots 0#usize
-        Result.ret
-          {
-            ntable0
-              with
-              num_entries := self.num_entries, max_load_factor := (i, i0)
-          }
-    else Result.ret { self with max_load_factor := (i, i0) }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  let max_usize ← Scalar.cast .Usize core_u32_max
+  let capacity := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let n1 ← max_usize / 2#usize
+  let (i, i1) := self.max_load_factor
+  let i2 ← n1 / i
+  if capacity <= i2
+  then
+    do
+    let i3 ← capacity * 2#usize
+    let ntable ← hashmap.HashMap.new_with_capacity T i3 i i1
+    let p ← hashmap.HashMap.move_elements T ntable self.slots 0#usize
+    let (ntable1, _) := p
+    Result.ret
+      {
+        ntable1
+          with
+          num_entries := self.num_entries, max_load_factor := (i, i1)
+      }
+  else Result.ret { self with max_load_factor := (i, i1) }
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
    Source: 'src/hashmap.rs', lines 129:4-129:48 -/
 def hashmap.HashMap.insert
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let self0 ← hashmap.HashMap.insert_no_resize T self key value
-    let i ← hashmap.HashMap.len T self0
-    if i > self0.max_load
-    then hashmap.HashMap.try_resize T self0
-    else Result.ret self0
+  let hm ← hashmap.HashMap.insert_no_resize T self key value
+  let i ← hashmap.HashMap.len T hm
+  if i > hm.max_load
+  then hashmap.HashMap.try_resize T hm
+  else Result.ret hm
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 206:4-219:5 -/
 divergent def hashmap.HashMap.contains_key_in_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
   match ls with
-  | hashmap.List.Cons ckey t tl =>
+  | hashmap.List.Cons ckey _ tl =>
     if ckey = key
     then Result.ret true
     else hashmap.HashMap.contains_key_in_list_loop T key tl
   | hashmap.List.Nil => Result.ret false
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]:
    Source: 'src/hashmap.rs', lines 206:4-206:68 -/
 def hashmap.HashMap.contains_key_in_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
   hashmap.HashMap.contains_key_in_list_loop T key ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]:
    Source: 'src/hashmap.rs', lines 199:4-199:49 -/
 def hashmap.HashMap.contains_key
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    hashmap.HashMap.contains_key_in_list T key l
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  hashmap.HashMap.contains_key_in_list T key l
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 224:4-237:5 -/
 divergent def hashmap.HashMap.get_in_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
@@ -311,259 +277,193 @@ divergent def hashmap.HashMap.get_in_list_loop
     else hashmap.HashMap.get_in_list_loop T key tl
   | hashmap.List.Nil => Result.fail .panic
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]:
    Source: 'src/hashmap.rs', lines 224:4-224:70 -/
 def hashmap.HashMap.get_in_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
   hashmap.HashMap.get_in_list_loop T key ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]:
    Source: 'src/hashmap.rs', lines 239:4-239:55 -/
 def hashmap.HashMap.get
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    hashmap.HashMap.get_in_list T key l
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  hashmap.HashMap.get_in_list T key l
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 245:4-254:5 -/
 divergent def hashmap.HashMap.get_mut_in_list_loop
-  (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
-  match ls with
-  | hashmap.List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret cvalue
-    else hashmap.HashMap.get_mut_in_list_loop T tl key
-  | hashmap.List.Nil => Result.fail .panic
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def hashmap.HashMap.get_mut_in_list
-  (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
-  hashmap.HashMap.get_mut_in_list_loop T ls key
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 245:4-254:5 -/
-divergent def hashmap.HashMap.get_mut_in_list_loop_back
-  (T : Type) (ls : hashmap.List T) (key : Usize) (ret : T) :
-  Result (hashmap.List T)
+  (T : Type) (ls : hashmap.List T) (key : Usize) :
+  Result (T × (T → Result (hashmap.List T)))
   :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (hashmap.List.Cons ckey ret tl)
+    then
+      let back_'a := fun ret => Result.ret (hashmap.List.Cons ckey ret tl)
+      Result.ret (cvalue, back_'a)
     else
       do
-        let tl0 ← hashmap.HashMap.get_mut_in_list_loop_back T tl key ret
-        Result.ret (hashmap.List.Cons ckey cvalue tl0)
+      let (t, back_'a) ← hashmap.HashMap.get_mut_in_list_loop T tl key
+      let back_'a1 :=
+        fun ret =>
+          do
+          let tl1 ← back_'a ret
+          Result.ret (hashmap.List.Cons ckey cvalue tl1)
+      Result.ret (t, back_'a1)
   | hashmap.List.Nil => Result.fail .panic
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]:
    Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def hashmap.HashMap.get_mut_in_list_back
-  (T : Type) (ls : hashmap.List T) (key : Usize) (ret : T) :
-  Result (hashmap.List T)
+def hashmap.HashMap.get_mut_in_list
+  (T : Type) (ls : hashmap.List T) (key : Usize) :
+  Result (T × (T → Result (hashmap.List T)))
   :=
-  hashmap.HashMap.get_mut_in_list_loop_back T ls key ret
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
-   Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def hashmap.HashMap.get_mut
-  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    hashmap.HashMap.get_mut_in_list T l key
+  let (t, back_'a) ← hashmap.HashMap.get_mut_in_list_loop T ls key
+  Result.ret (t, back_'a)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
    Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def hashmap.HashMap.get_mut_back
-  (T : Type) (self : hashmap.HashMap T) (key : Usize) (ret : T) :
-  Result (hashmap.HashMap T)
+def hashmap.HashMap.get_mut
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) :
+  Result (T × (T → Result (hashmap.HashMap T)))
   :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let l0 ← hashmap.HashMap.get_mut_in_list_back T l key ret
-    let v ←
-      alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod l0
-    Result.ret { self with slots := v }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
-   Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def hashmap.HashMap.remove_from_list_loop
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
-  match ls with
-  | hashmap.List.Cons ckey t tl =>
-    if ckey = key
-    then
-      let mv_ls :=
-        core.mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
-          hashmap.List.Nil
-      match mv_ls with
-      | hashmap.List.Cons i cvalue tl0 => Result.ret (some cvalue)
-      | hashmap.List.Nil => Result.fail .panic
-    else hashmap.HashMap.remove_from_list_loop T key tl
-  | hashmap.List.Nil => Result.ret none
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
-   Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def hashmap.HashMap.remove_from_list
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
-  hashmap.HashMap.remove_from_list_loop T key ls
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  let (t, get_mut_in_list_back) ← hashmap.HashMap.get_mut_in_list T l key
+  let back_'a :=
+    fun ret =>
+      do
+      let l1 ← get_mut_in_list_back ret
+      let v ← index_mut_back l1
+      Result.ret { self with slots := v }
+  Result.ret (t, back_'a)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def hashmap.HashMap.remove_from_list_loop_back
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
+divergent def hashmap.HashMap.remove_from_list_loop
+  (T : Type) (key : Usize) (ls : hashmap.List T) :
+  Result ((Option T) × (hashmap.List T))
+  :=
   match ls with
   | hashmap.List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls :=
+      let (mv_ls, _) :=
         core.mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
           hashmap.List.Nil
       match mv_ls with
-      | hashmap.List.Cons i cvalue tl0 => Result.ret tl0
+      | hashmap.List.Cons _ cvalue tl1 => Result.ret (some cvalue, tl1)
       | hashmap.List.Nil => Result.fail .panic
     else
       do
-        let tl0 ← hashmap.HashMap.remove_from_list_loop_back T key tl
-        Result.ret (hashmap.List.Cons ckey t tl0)
-  | hashmap.List.Nil => Result.ret hashmap.List.Nil
+      let (o, back) ← hashmap.HashMap.remove_from_list_loop T key tl
+      Result.ret (o, hashmap.List.Cons ckey t back)
+  | hashmap.List.Nil => Result.ret (none, hashmap.List.Nil)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]:
    Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def hashmap.HashMap.remove_from_list_back
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
-  hashmap.HashMap.remove_from_list_loop_back T key ls
+def hashmap.HashMap.remove_from_list
+  (T : Type) (key : Usize) (ls : hashmap.List T) :
+  Result ((Option T) × (hashmap.List T))
+  :=
+  hashmap.HashMap.remove_from_list_loop T key ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]:
    Source: 'src/hashmap.rs', lines 294:4-294:52 -/
 def hashmap.HashMap.remove
-  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result (Option T) :=
-  do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let x ← hashmap.HashMap.remove_from_list T key l
-    match x with
-    | none => Result.ret none
-    | some x0 => do
-                   let _ ← self.num_entries - 1#usize
-                   Result.ret (some x0)
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
-   Source: 'src/hashmap.rs', lines 294:4-294:52 -/
-def hashmap.HashMap.remove_back
   (T : Type) (self : hashmap.HashMap T) (key : Usize) :
-  Result (hashmap.HashMap T)
+  Result ((Option T) × (hashmap.HashMap T))
   :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let x ← hashmap.HashMap.remove_from_list T key l
-    match x with
-    | none =>
-      do
-        let l0 ← hashmap.HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with slots := v }
-    | some x0 =>
-      do
-        let i0 ← self.num_entries - 1#usize
-        let l0 ← hashmap.HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with num_entries := i0, slots := v }
-
-/- [hashmap_main::hashmap::test1]: forward function
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  let (x, l1) ← hashmap.HashMap.remove_from_list T key l
+  match x with
+  | none =>
+    do
+    let v ← index_mut_back l1
+    Result.ret (none, { self with slots := v })
+  | some x1 =>
+    do
+    let i1 ← self.num_entries - 1#usize
+    let v ← index_mut_back l1
+    Result.ret (some x1, { self with num_entries := i1, slots := v })
+
+/- [hashmap_main::hashmap::test1]:
    Source: 'src/hashmap.rs', lines 315:0-315:10 -/
 def hashmap.test1 : Result Unit :=
   do
-    let hm ← hashmap.HashMap.new U64
-    let hm0 ← hashmap.HashMap.insert U64 hm 0#usize 42#u64
-    let hm1 ← hashmap.HashMap.insert U64 hm0 128#usize 18#u64
-    let hm2 ← hashmap.HashMap.insert U64 hm1 1024#usize 138#u64
-    let hm3 ← hashmap.HashMap.insert U64 hm2 1056#usize 256#u64
-    let i ← hashmap.HashMap.get U64 hm3 128#usize
-    if not (i = 18#u64)
+  let hm ← hashmap.HashMap.new U64
+  let hm1 ← hashmap.HashMap.insert U64 hm 0#usize 42#u64
+  let hm2 ← hashmap.HashMap.insert U64 hm1 128#usize 18#u64
+  let hm3 ← hashmap.HashMap.insert U64 hm2 1024#usize 138#u64
+  let hm4 ← hashmap.HashMap.insert U64 hm3 1056#usize 256#u64
+  let i ← hashmap.HashMap.get U64 hm4 128#usize
+  if not (i = 18#u64)
+  then Result.fail .panic
+  else
+    do
+    let (_, get_mut_back) ← hashmap.HashMap.get_mut U64 hm4 1024#usize
+    let hm5 ← get_mut_back 56#u64
+    let i1 ← hashmap.HashMap.get U64 hm5 1024#usize
+    if not (i1 = 56#u64)
     then Result.fail .panic
     else
       do
-        let hm4 ← hashmap.HashMap.get_mut_back U64 hm3 1024#usize 56#u64
-        let i0 ← hashmap.HashMap.get U64 hm4 1024#usize
-        if not (i0 = 56#u64)
+      let (x, hm6) ← hashmap.HashMap.remove U64 hm5 1024#usize
+      match x with
+      | none => Result.fail .panic
+      | some x1 =>
+        if not (x1 = 56#u64)
         then Result.fail .panic
         else
           do
-            let x ← hashmap.HashMap.remove U64 hm4 1024#usize
-            match x with
-            | none => Result.fail .panic
-            | some x0 =>
-              if not (x0 = 56#u64)
+          let i2 ← hashmap.HashMap.get U64 hm6 0#usize
+          if not (i2 = 42#u64)
+          then Result.fail .panic
+          else
+            do
+            let i3 ← hashmap.HashMap.get U64 hm6 128#usize
+            if not (i3 = 18#u64)
+            then Result.fail .panic
+            else
+              do
+              let i4 ← hashmap.HashMap.get U64 hm6 1056#usize
+              if not (i4 = 256#u64)
               then Result.fail .panic
-              else
-                do
-                  let hm5 ← hashmap.HashMap.remove_back U64 hm4 1024#usize
-                  let i1 ← hashmap.HashMap.get U64 hm5 0#usize
-                  if not (i1 = 42#u64)
-                  then Result.fail .panic
-                  else
-                    do
-                      let i2 ← hashmap.HashMap.get U64 hm5 128#usize
-                      if not (i2 = 18#u64)
-                      then Result.fail .panic
-                      else
-                        do
-                          let i3 ← hashmap.HashMap.get U64 hm5 1056#usize
-                          if not (i3 = 256#u64)
-                          then Result.fail .panic
-                          else Result.ret ()
-
-/- [hashmap_main::insert_on_disk]: forward function
+              else Result.ret ()
+
+/- [hashmap_main::insert_on_disk]:
    Source: 'src/hashmap_main.rs', lines 7:0-7:43 -/
 def insert_on_disk
   (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
   do
-    let (st0, hm) ← hashmap_utils.deserialize st
-    let hm0 ← hashmap.HashMap.insert U64 hm key value
-    let (st1, _) ← hashmap_utils.serialize hm0 st0
-    Result.ret (st1, ())
+  let (st1, hm) ← hashmap_utils.deserialize st
+  let hm1 ← hashmap.HashMap.insert U64 hm key value
+  let (st2, _) ← hashmap_utils.serialize hm1 st1
+  Result.ret (st2, ())
 
-/- [hashmap_main::main]: forward function
+/- [hashmap_main::main]:
    Source: 'src/hashmap_main.rs', lines 16:0-16:13 -/
 def main : Result Unit :=
   Result.ret ()
diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean
index 02ca5b0e..c09edbd2 100644
--- a/tests/lean/HashmapMain/FunsExternal_Template.lean
+++ b/tests/lean/HashmapMain/FunsExternal_Template.lean
@@ -6,12 +6,12 @@ import HashmapMain.Types
 open Primitives
 open hashmap_main
 
-/- [hashmap_main::hashmap_utils::deserialize]: forward function
+/- [hashmap_main::hashmap_utils::deserialize]:
    Source: 'src/hashmap_utils.rs', lines 10:0-10:43 -/
 axiom hashmap_utils.deserialize
   : State → Result (State × (hashmap.HashMap U64))
 
-/- [hashmap_main::hashmap_utils::serialize]: forward function
+/- [hashmap_main::hashmap_utils::serialize]:
    Source: 'src/hashmap_utils.rs', lines 5:0-5:42 -/
 axiom hashmap_utils.serialize
   : hashmap.HashMap U64 → State → Result (State × Unit)
diff --git a/tests/lean/Loops.lean b/tests/lean/Loops.lean
index 08aa08a5..fbb4616f 100644
--- a/tests/lean/Loops.lean
+++ b/tests/lean/Loops.lean
@@ -5,73 +5,72 @@ open Primitives
 
 namespace loops
 
-/- [loops::sum]: loop 0: forward function
+/- [loops::sum]: loop 0:
    Source: 'src/loops.rs', lines 4:0-14:1 -/
 divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
   if i < max
   then do
-         let s0 ← s + i
-         let i0 ← i + 1#u32
-         sum_loop max i0 s0
+       let s1 ← s + i
+       let i1 ← i + 1#u32
+       sum_loop max i1 s1
   else s * 2#u32
 
-/- [loops::sum]: forward function
+/- [loops::sum]:
    Source: 'src/loops.rs', lines 4:0-4:27 -/
 def sum (max : U32) : Result U32 :=
   sum_loop max 0#u32 0#u32
 
-/- [loops::sum_with_mut_borrows]: loop 0: forward function
+/- [loops::sum_with_mut_borrows]: loop 0:
    Source: 'src/loops.rs', lines 19:0-31:1 -/
 divergent def sum_with_mut_borrows_loop
   (max : U32) (mi : U32) (ms : U32) : Result U32 :=
   if mi < max
   then
     do
-      let ms0 ← ms + mi
-      let mi0 ← mi + 1#u32
-      sum_with_mut_borrows_loop max mi0 ms0
+    let ms1 ← ms + mi
+    let mi1 ← mi + 1#u32
+    sum_with_mut_borrows_loop max mi1 ms1
   else ms * 2#u32
 
-/- [loops::sum_with_mut_borrows]: forward function
+/- [loops::sum_with_mut_borrows]:
    Source: 'src/loops.rs', lines 19:0-19:44 -/
 def sum_with_mut_borrows (max : U32) : Result U32 :=
   sum_with_mut_borrows_loop max 0#u32 0#u32
 
-/- [loops::sum_with_shared_borrows]: loop 0: forward function
+/- [loops::sum_with_shared_borrows]: loop 0:
    Source: 'src/loops.rs', lines 34:0-48:1 -/
 divergent def sum_with_shared_borrows_loop
   (max : U32) (i : U32) (s : U32) : Result U32 :=
   if i < max
   then
     do
-      let i0 ← i + 1#u32
-      let s0 ← s + i0
-      sum_with_shared_borrows_loop max i0 s0
+    let i1 ← i + 1#u32
+    let s1 ← s + i1
+    sum_with_shared_borrows_loop max i1 s1
   else s * 2#u32
 
-/- [loops::sum_with_shared_borrows]: forward function
+/- [loops::sum_with_shared_borrows]:
    Source: 'src/loops.rs', lines 34:0-34:47 -/
 def sum_with_shared_borrows (max : U32) : Result U32 :=
   sum_with_shared_borrows_loop max 0#u32 0#u32
 
-/- [loops::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [loops::clear]: loop 0:
    Source: 'src/loops.rs', lines 52:0-58:1 -/
 divergent def clear_loop
   (v : alloc.vec.Vec U32) (i : Usize) : Result (alloc.vec.Vec U32) :=
-  let i0 := alloc.vec.Vec.len U32 v
-  if i < i0
+  let i1 := alloc.vec.Vec.len U32 v
+  if i < i1
   then
     do
-      let i1 ← i + 1#usize
-      let v0 ←
-        alloc.vec.Vec.index_mut_back U32 Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst U32) v i 0#u32
-      clear_loop v0 i1
+    let (_, index_mut_back) ←
+      alloc.vec.Vec.index_mut U32 Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst U32) v i
+    let i2 ← i + 1#usize
+    let v1 ← index_mut_back 0#u32
+    clear_loop v1 i2
   else Result.ret v
 
-/- [loops::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [loops::clear]:
    Source: 'src/loops.rs', lines 52:0-52:30 -/
 def clear (v : alloc.vec.Vec U32) : Result (alloc.vec.Vec U32) :=
   clear_loop v 0#usize
@@ -82,7 +81,7 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [loops::list_mem]: loop 0: forward function
+/- [loops::list_mem]: loop 0:
    Source: 'src/loops.rs', lines 66:0-75:1 -/
 divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
   match ls with
@@ -91,51 +90,41 @@ divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
                       else list_mem_loop x tl
   | List.Nil => Result.ret false
 
-/- [loops::list_mem]: forward function
+/- [loops::list_mem]:
    Source: 'src/loops.rs', lines 66:0-66:52 -/
 def list_mem (x : U32) (ls : List U32) : Result Bool :=
   list_mem_loop x ls
 
-/- [loops::list_nth_mut_loop]: loop 0: forward function
+/- [loops::list_nth_mut_loop]: loop 0:
    Source: 'src/loops.rs', lines 78:0-88:1 -/
 divergent def list_nth_mut_loop_loop
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut_loop_loop T tl i0
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop]: forward function
-   Source: 'src/loops.rs', lines 78:0-78:71 -/
-def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_mut_loop_loop T ls i
-
-/- [loops::list_nth_mut_loop]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 78:0-88:1 -/
-divergent def list_nth_mut_loop_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret : T) : Result (List T) :=
+  (T : Type) (ls : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match ls with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, back) ← list_nth_mut_loop_loop T tl i1
+      let back1 :=
+        fun ret => do
+                   let tl1 ← back ret
+                   Result.ret (List.Cons x tl1)
+      Result.ret (t, back1)
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop]: backward function 0
+/- [loops::list_nth_mut_loop]:
    Source: 'src/loops.rs', lines 78:0-78:71 -/
-def list_nth_mut_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret : T) : Result (List T) :=
-  list_nth_mut_loop_loop_back T ls i ret
+def list_nth_mut_loop
+  (T : Type) (ls : List T) (i : U32) : Result (T × (T → Result (List T))) :=
+  do
+  let (t, back) ← list_nth_mut_loop_loop T ls i
+  Result.ret (t, back)
 
-/- [loops::list_nth_shared_loop]: loop 0: forward function
+/- [loops::list_nth_shared_loop]: loop 0:
    Source: 'src/loops.rs', lines 91:0-101:1 -/
 divergent def list_nth_shared_loop_loop
   (T : Type) (ls : List T) (i : U32) : Result T :=
@@ -144,64 +133,54 @@ divergent def list_nth_shared_loop_loop
     if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - 1#u32
-           list_nth_shared_loop_loop T tl i0
+         let i1 ← i - 1#u32
+         list_nth_shared_loop_loop T tl i1
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop]: forward function
+/- [loops::list_nth_shared_loop]:
    Source: 'src/loops.rs', lines 91:0-91:66 -/
 def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
   list_nth_shared_loop_loop T ls i
 
-/- [loops::get_elem_mut]: loop 0: forward function
+/- [loops::get_elem_mut]: loop 0:
    Source: 'src/loops.rs', lines 103:0-117:1 -/
-divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret y
-                      else get_elem_mut_loop x tl
-  | List.Nil => Result.fail .panic
-
-/- [loops::get_elem_mut]: forward function
-   Source: 'src/loops.rs', lines 103:0-103:73 -/
-def get_elem_mut
-  (slots : alloc.vec.Vec (List Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ←
-      alloc.vec.Vec.index_mut (List Usize) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-    get_elem_mut_loop x l
-
-/- [loops::get_elem_mut]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 103:0-117:1 -/
-divergent def get_elem_mut_loop_back
-  (x : Usize) (ls : List Usize) (ret : Usize) : Result (List Usize) :=
+divergent def get_elem_mut_loop
+  (x : Usize) (ls : List Usize) :
+  Result (Usize × (Usize → Result (List Usize)))
+  :=
   match ls with
   | List.Cons y tl =>
     if y = x
-    then Result.ret (List.Cons ret tl)
+    then
+      let back := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (y, back)
     else
       do
-        let tl0 ← get_elem_mut_loop_back x tl ret
-        Result.ret (List.Cons y tl0)
+      let (i, back) ← get_elem_mut_loop x tl
+      let back1 :=
+        fun ret => do
+                   let tl1 ← back ret
+                   Result.ret (List.Cons y tl1)
+      Result.ret (i, back1)
   | List.Nil => Result.fail .panic
 
-/- [loops::get_elem_mut]: backward function 0
+/- [loops::get_elem_mut]:
    Source: 'src/loops.rs', lines 103:0-103:73 -/
-def get_elem_mut_back
-  (slots : alloc.vec.Vec (List Usize)) (x : Usize) (ret : Usize) :
-  Result (alloc.vec.Vec (List Usize))
+def get_elem_mut
+  (slots : alloc.vec.Vec (List Usize)) (x : Usize) :
+  Result (Usize × (Usize → Result (alloc.vec.Vec (List Usize))))
   :=
   do
-    let l ←
-      alloc.vec.Vec.index_mut (List Usize) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-    let l0 ← get_elem_mut_loop_back x l ret
-    alloc.vec.Vec.index_mut_back (List Usize) Usize
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List Usize) Usize
       (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-      l0
+  let (i, back) ← get_elem_mut_loop x l
+  let back1 := fun ret => do
+                          let l1 ← back ret
+                          index_mut_back l1
+  Result.ret (i, back1)
 
-/- [loops::get_elem_shared]: loop 0: forward function
+/- [loops::get_elem_shared]: loop 0:
    Source: 'src/loops.rs', lines 119:0-133:1 -/
 divergent def get_elem_shared_loop
   (x : Usize) (ls : List Usize) : Result Usize :=
@@ -211,76 +190,63 @@ divergent def get_elem_shared_loop
                       else get_elem_shared_loop x tl
   | List.Nil => Result.fail .panic
 
-/- [loops::get_elem_shared]: forward function
+/- [loops::get_elem_shared]:
    Source: 'src/loops.rs', lines 119:0-119:68 -/
 def get_elem_shared
   (slots : alloc.vec.Vec (List Usize)) (x : Usize) : Result Usize :=
   do
-    let l ←
-      alloc.vec.Vec.index (List Usize) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-    get_elem_shared_loop x l
-
-/- [loops::id_mut]: forward function
-   Source: 'src/loops.rs', lines 135:0-135:50 -/
-def id_mut (T : Type) (ls : List T) : Result (List T) :=
-  Result.ret ls
+  let l ←
+    alloc.vec.Vec.index (List Usize) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
+  get_elem_shared_loop x l
 
-/- [loops::id_mut]: backward function 0
+/- [loops::id_mut]:
    Source: 'src/loops.rs', lines 135:0-135:50 -/
-def id_mut_back (T : Type) (ls : List T) (ret : List T) : Result (List T) :=
-  Result.ret ret
+def id_mut
+  (T : Type) (ls : List T) :
+  Result ((List T) × (List T → Result (List T)))
+  :=
+  Result.ret (ls, Result.ret)
 
-/- [loops::id_shared]: forward function
+/- [loops::id_shared]:
    Source: 'src/loops.rs', lines 139:0-139:45 -/
 def id_shared (T : Type) (ls : List T) : Result (List T) :=
   Result.ret ls
 
-/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function
+/- [loops::list_nth_mut_loop_with_id]: loop 0:
    Source: 'src/loops.rs', lines 144:0-155:1 -/
 divergent def list_nth_mut_loop_with_id_loop
-  (T : Type) (i : U32) (ls : List T) : Result T :=
+  (T : Type) (i : U32) (ls : List T) : Result (T × (T → Result (List T))) :=
   match ls with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut_loop_with_id_loop T i0 tl
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_with_id]: forward function
-   Source: 'src/loops.rs', lines 144:0-144:75 -/
-def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_mut T ls
-    list_nth_mut_loop_with_id_loop T i ls0
-
-/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 144:0-155:1 -/
-divergent def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : U32) (ls : List T) (ret : T) : Result (List T) :=
-  match ls with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, back) ← list_nth_mut_loop_with_id_loop T i1 tl
+      let back1 :=
+        fun ret => do
+                   let tl1 ← back ret
+                   Result.ret (List.Cons x tl1)
+      Result.ret (t, back1)
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop_with_id]: backward function 0
+/- [loops::list_nth_mut_loop_with_id]:
    Source: 'src/loops.rs', lines 144:0-144:75 -/
-def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : List T) (i : U32) (ret : T) : Result (List T) :=
+def list_nth_mut_loop_with_id
+  (T : Type) (ls : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   do
-    let ls0 ← id_mut T ls
-    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret
-    id_mut_back T ls l
-
-/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+  let (ls1, id_mut_back) ← id_mut T ls
+  let (t, back) ← list_nth_mut_loop_with_id_loop T i ls1
+  let back1 := fun ret => do
+                          let l ← back ret
+                          id_mut_back l
+  Result.ret (t, back1)
+
+/- [loops::list_nth_shared_loop_with_id]: loop 0:
    Source: 'src/loops.rs', lines 158:0-169:1 -/
 divergent def list_nth_shared_loop_with_id_loop
   (T : Type) (i : U32) (ls : List T) : Result T :=
@@ -289,97 +255,60 @@ divergent def list_nth_shared_loop_with_id_loop
     if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - 1#u32
-           list_nth_shared_loop_with_id_loop T i0 tl
+         let i1 ← i - 1#u32
+         list_nth_shared_loop_with_id_loop T i1 tl
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop_with_id]: forward function
+/- [loops::list_nth_shared_loop_with_id]:
    Source: 'src/loops.rs', lines 158:0-158:70 -/
 def list_nth_shared_loop_with_id
   (T : Type) (ls : List T) (i : U32) : Result T :=
   do
-    let ls0 ← id_shared T ls
-    list_nth_shared_loop_with_id_loop T i ls0
+  let ls1 ← id_shared T ls
+  list_nth_shared_loop_with_id_loop T i ls1
 
-/- [loops::list_nth_mut_loop_pair]: loop 0: forward function
+/- [loops::list_nth_mut_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 174:0-195:1 -/
 divergent def list_nth_mut_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (x0, x1)
-      else do
-             let i0 ← i - 1#u32
-             list_nth_mut_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_pair]: forward function
-   Source: 'src/loops.rs', lines 174:0-178:27 -/
-def list_nth_mut_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 174:0-195:1 -/
-divergent def list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)) × (T → Result (List T)))
   :=
   match ls0 with
   | List.Cons x0 tl0 =>
     match ls1 with
     | List.Cons x1 tl1 =>
       if i = 0#u32
-      then Result.ret (List.Cons ret tl0)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl0)
+        let back_'b := fun ret => Result.ret (List.Cons ret tl1)
+        Result.ret ((x0, x1), back_'a, back_'b)
       else
         do
-          let i0 ← i - 1#u32
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00)
+        let i1 ← i - 1#u32
+        let (p, back_'a, back_'b) ← list_nth_mut_loop_pair_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl01 ← back_'a ret
+                     Result.ret (List.Cons x0 tl01)
+        let back_'b1 :=
+          fun ret => do
+                     let tl11 ← back_'b ret
+                     Result.ret (List.Cons x1 tl11)
+        Result.ret (p, back_'a1, back_'b1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop_pair]: backward function 0
+/- [loops::list_nth_mut_loop_pair]:
    Source: 'src/loops.rs', lines 174:0-178:27 -/
-def list_nth_mut_loop_pair_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1
-   Source: 'src/loops.rs', lines 174:0-195:1 -/
-divergent def list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (List.Cons ret tl1)
-      else
-        do
-          let i0 ← i - 1#u32
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_pair]: backward function 1
-   Source: 'src/loops.rs', lines 174:0-178:27 -/
-def list_nth_mut_loop_pair_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)) × (T → Result (List T)))
   :=
-  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret
+  do
+  let (p, back_'a, back_'b) ← list_nth_mut_loop_pair_loop T ls0 ls1 i
+  Result.ret (p, back_'a, back_'b)
 
-/- [loops::list_nth_shared_loop_pair]: loop 0: forward function
+/- [loops::list_nth_shared_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 198:0-219:1 -/
 divergent def list_nth_shared_loop_pair_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
@@ -390,71 +319,58 @@ divergent def list_nth_shared_loop_pair_loop
       if i = 0#u32
       then Result.ret (x0, x1)
       else do
-             let i0 ← i - 1#u32
-             list_nth_shared_loop_pair_loop T tl0 tl1 i0
+           let i1 ← i - 1#u32
+           list_nth_shared_loop_pair_loop T tl0 tl1 i1
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop_pair]: forward function
+/- [loops::list_nth_shared_loop_pair]:
    Source: 'src/loops.rs', lines 198:0-202:19 -/
 def list_nth_shared_loop_pair
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   list_nth_shared_loop_pair_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 223:0-238:1 -/
 divergent def list_nth_mut_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - 1#u32
-          list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_pair_merge]: forward function
-   Source: 'src/loops.rs', lines 223:0-227:27 -/
-def list_nth_mut_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 223:0-238:1 -/
-divergent def list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : (T × T)) :
-  Result ((List T) × (List T))
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × ((T × T) → Result ((List T) × (List T))))
   :=
   match ls0 with
   | List.Cons x0 tl0 =>
     match ls1 with
     | List.Cons x1 tl1 =>
       if i = 0#u32
-      then let (t, t0) := ret
-           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
+      then
+        let back_'a :=
+          fun ret =>
+            let (t, t1) := ret
+            Result.ret (List.Cons t tl0, List.Cons t1 tl1)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ← list_nth_mut_loop_pair_merge_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret =>
+            do
+            let (tl01, tl11) ← back_'a ret
+            Result.ret (List.Cons x0 tl01, List.Cons x1 tl11)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop_pair_merge]: backward function 0
+/- [loops::list_nth_mut_loop_pair_merge]:
    Source: 'src/loops.rs', lines 223:0-227:27 -/
-def list_nth_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : (T × T)) :
-  Result ((List T) × (List T))
+def list_nth_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × ((T × T) → Result ((List T) × (List T))))
   :=
-  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
-/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_shared_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 241:0-256:1 -/
 divergent def list_nth_shared_loop_pair_merge_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
@@ -466,221 +382,161 @@ divergent def list_nth_shared_loop_pair_merge_loop
       then Result.ret (x0, x1)
       else
         do
-          let i0 ← i - 1#u32
-          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
+        let i1 ← i - 1#u32
+        list_nth_shared_loop_pair_merge_loop T tl0 tl1 i1
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop_pair_merge]: forward function
+/- [loops::list_nth_shared_loop_pair_merge]:
    Source: 'src/loops.rs', lines 241:0-245:19 -/
 def list_nth_shared_loop_pair_merge
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 259:0-274:1 -/
 divergent def list_nth_mut_shared_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - 1#u32
-          list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_shared_loop_pair]: forward function
-   Source: 'src/loops.rs', lines 259:0-263:23 -/
-def list_nth_mut_shared_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 259:0-274:1 -/
-divergent def list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
   match ls0 with
   | List.Cons x0 tl0 =>
     match ls1 with
     | List.Cons x1 tl1 =>
       if i = 0#u32
-      then Result.ret (List.Cons ret tl0)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl0)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let tl00 ← list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ← list_nth_mut_shared_loop_pair_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl01 ← back_'a ret
+                     Result.ret (List.Cons x0 tl01)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_shared_loop_pair]: backward function 0
+/- [loops::list_nth_mut_shared_loop_pair]:
    Source: 'src/loops.rs', lines 259:0-263:23 -/
-def list_nth_mut_shared_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_mut_shared_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
-/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 278:0-293:1 -/
 divergent def list_nth_mut_shared_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - 1#u32
-          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function
-   Source: 'src/loops.rs', lines 278:0-282:23 -/
-def list_nth_mut_shared_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 278:0-293:1 -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
   match ls0 with
   | List.Cons x0 tl0 =>
     match ls1 with
     | List.Cons x1 tl1 =>
       if i = 0#u32
-      then Result.ret (List.Cons ret tl0)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl0)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ←
+          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl01 ← back_'a ret
+                     Result.ret (List.Cons x0 tl01)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0
+/- [loops::list_nth_mut_shared_loop_pair_merge]:
    Source: 'src/loops.rs', lines 278:0-282:23 -/
-def list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_mut_shared_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
-/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 297:0-312:1 -/
 divergent def list_nth_shared_mut_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - 1#u32
-          list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_shared_mut_loop_pair]: forward function
-   Source: 'src/loops.rs', lines 297:0-301:23 -/
-def list_nth_shared_mut_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1
-   Source: 'src/loops.rs', lines 297:0-312:1 -/
-divergent def list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
   match ls0 with
   | List.Cons x0 tl0 =>
     match ls1 with
     | List.Cons x1 tl1 =>
       if i = 0#u32
-      then Result.ret (List.Cons ret tl1)
+      then
+        let back_'b := fun ret => Result.ret (List.Cons ret tl1)
+        Result.ret ((x0, x1), back_'b)
       else
         do
-          let i0 ← i - 1#u32
-          let tl10 ← list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x1 tl10)
+        let i1 ← i - 1#u32
+        let (p, back_'b) ← list_nth_shared_mut_loop_pair_loop T tl0 tl1 i1
+        let back_'b1 :=
+          fun ret => do
+                     let tl11 ← back_'b ret
+                     Result.ret (List.Cons x1 tl11)
+        Result.ret (p, back_'b1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_mut_loop_pair]: backward function 1
+/- [loops::list_nth_shared_mut_loop_pair]:
    Source: 'src/loops.rs', lines 297:0-301:23 -/
-def list_nth_shared_mut_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_shared_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'b) ← list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
+  Result.ret (p, back_'b)
 
-/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 316:0-331:1 -/
 divergent def list_nth_shared_mut_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = 0#u32
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - 1#u32
-          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function
-   Source: 'src/loops.rs', lines 316:0-320:23 -/
-def list_nth_shared_mut_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 316:0-331:1 -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
   match ls0 with
   | List.Cons x0 tl0 =>
     match ls1 with
     | List.Cons x1 tl1 =>
       if i = 0#u32
-      then Result.ret (List.Cons ret tl1)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl1)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x1 tl10)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ←
+          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl11 ← back_'a ret
+                     Result.ret (List.Cons x1 tl11)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0
+/- [loops::list_nth_shared_mut_loop_pair_merge]:
    Source: 'src/loops.rs', lines 316:0-320:23 -/
-def list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_shared_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
 end loops
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index 0bce3a64..0dd29429 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -43,98 +43,98 @@ inductive Sum (T1 T2 : Type) :=
 | Left : T1 → Sum T1 T2
 | Right : T2 → Sum T1 T2
 
-/- [no_nested_borrows::neg_test]: forward function
+/- [no_nested_borrows::neg_test]:
    Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 -/
 def neg_test (x : I32) : Result I32 :=
   - x
 
-/- [no_nested_borrows::add_u32]: forward function
+/- [no_nested_borrows::add_u32]:
    Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 -/
 def add_u32 (x : U32) (y : U32) : Result U32 :=
   x + y
 
-/- [no_nested_borrows::subs_u32]: forward function
+/- [no_nested_borrows::subs_u32]:
    Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 -/
 def subs_u32 (x : U32) (y : U32) : Result U32 :=
   x - y
 
-/- [no_nested_borrows::div_u32]: forward function
+/- [no_nested_borrows::div_u32]:
    Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 -/
 def div_u32 (x : U32) (y : U32) : Result U32 :=
   x / y
 
-/- [no_nested_borrows::div_u32_const]: forward function
+/- [no_nested_borrows::div_u32_const]:
    Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 -/
 def div_u32_const (x : U32) : Result U32 :=
   x / 2#u32
 
-/- [no_nested_borrows::rem_u32]: forward function
+/- [no_nested_borrows::rem_u32]:
    Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 -/
 def rem_u32 (x : U32) (y : U32) : Result U32 :=
   x % y
 
-/- [no_nested_borrows::mul_u32]: forward function
+/- [no_nested_borrows::mul_u32]:
    Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 -/
 def mul_u32 (x : U32) (y : U32) : Result U32 :=
   x * y
 
-/- [no_nested_borrows::add_i32]: forward function
+/- [no_nested_borrows::add_i32]:
    Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 -/
 def add_i32 (x : I32) (y : I32) : Result I32 :=
   x + y
 
-/- [no_nested_borrows::subs_i32]: forward function
+/- [no_nested_borrows::subs_i32]:
    Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 -/
 def subs_i32 (x : I32) (y : I32) : Result I32 :=
   x - y
 
-/- [no_nested_borrows::div_i32]: forward function
+/- [no_nested_borrows::div_i32]:
    Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 -/
 def div_i32 (x : I32) (y : I32) : Result I32 :=
   x / y
 
-/- [no_nested_borrows::div_i32_const]: forward function
+/- [no_nested_borrows::div_i32_const]:
    Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 -/
 def div_i32_const (x : I32) : Result I32 :=
   x / 2#i32
 
-/- [no_nested_borrows::rem_i32]: forward function
+/- [no_nested_borrows::rem_i32]:
    Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 -/
 def rem_i32 (x : I32) (y : I32) : Result I32 :=
   x % y
 
-/- [no_nested_borrows::mul_i32]: forward function
+/- [no_nested_borrows::mul_i32]:
    Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 -/
 def mul_i32 (x : I32) (y : I32) : Result I32 :=
   x * y
 
-/- [no_nested_borrows::mix_arith_u32]: forward function
+/- [no_nested_borrows::mix_arith_u32]:
    Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 -/
 def mix_arith_u32 (x : U32) (y : U32) (z : U32) : Result U32 :=
   do
-    let i ← x + y
-    let i0 ← x / y
-    let i1 ← i * i0
-    let i2 ← z % y
-    let i3 ← x - i2
-    let i4 ← i1 + i3
-    let i5 ← x + y
-    let i6 ← i5 + z
-    i4 % i6
-
-/- [no_nested_borrows::mix_arith_i32]: forward function
+  let i ← x + y
+  let i1 ← x / y
+  let i2 ← i * i1
+  let i3 ← z % y
+  let i4 ← x - i3
+  let i5 ← i2 + i4
+  let i6 ← x + y
+  let i7 ← i6 + z
+  i5 % i7
+
+/- [no_nested_borrows::mix_arith_i32]:
    Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 -/
 def mix_arith_i32 (x : I32) (y : I32) (z : I32) : Result I32 :=
   do
-    let i ← x + y
-    let i0 ← x / y
-    let i1 ← i * i0
-    let i2 ← z % y
-    let i3 ← x - i2
-    let i4 ← i1 + i3
-    let i5 ← x + y
-    let i6 ← i5 + z
-    i4 % i6
+  let i ← x + y
+  let i1 ← x / y
+  let i2 ← i * i1
+  let i3 ← z % y
+  let i4 ← x - i3
+  let i5 ← i2 + i4
+  let i6 ← x + y
+  let i7 ← i6 + z
+  i5 % i7
 
 /- [no_nested_borrows::CONST0]
    Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 -/
@@ -146,65 +146,65 @@ def const0_c : Usize := eval_global const0_body (by simp)
 def const1_body : Result Usize := 2#usize * 2#usize
 def const1_c : Usize := eval_global const1_body (by simp)
 
-/- [no_nested_borrows::cast_u32_to_i32]: forward function
+/- [no_nested_borrows::cast_u32_to_i32]:
    Source: 'src/no_nested_borrows.rs', lines 128:0-128:37 -/
 def cast_u32_to_i32 (x : U32) : Result I32 :=
   Scalar.cast .I32 x
 
-/- [no_nested_borrows::cast_bool_to_i32]: forward function
+/- [no_nested_borrows::cast_bool_to_i32]:
    Source: 'src/no_nested_borrows.rs', lines 132:0-132:39 -/
 def cast_bool_to_i32 (x : Bool) : Result I32 :=
   Scalar.cast_bool .I32 x
 
-/- [no_nested_borrows::cast_bool_to_bool]: forward function
+/- [no_nested_borrows::cast_bool_to_bool]:
    Source: 'src/no_nested_borrows.rs', lines 137:0-137:41 -/
 def cast_bool_to_bool (x : Bool) : Result Bool :=
   Result.ret x
 
-/- [no_nested_borrows::test2]: forward function
+/- [no_nested_borrows::test2]:
    Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 -/
 def test2 : Result Unit :=
   do
-    let _ ← 23#u32 + 44#u32
-    Result.ret ()
+  let _ ← 23#u32 + 44#u32
+  Result.ret ()
 
 /- Unit test for [no_nested_borrows::test2] -/
 #assert (test2 == Result.ret ())
 
-/- [no_nested_borrows::get_max]: forward function
+/- [no_nested_borrows::get_max]:
    Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 -/
 def get_max (x : U32) (y : U32) : Result U32 :=
   if x >= y
   then Result.ret x
   else Result.ret y
 
-/- [no_nested_borrows::test3]: forward function
+/- [no_nested_borrows::test3]:
    Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 -/
 def test3 : Result Unit :=
   do
-    let x ← get_max 4#u32 3#u32
-    let y ← get_max 10#u32 11#u32
-    let z ← x + y
-    if not (z = 15#u32)
-    then Result.fail .panic
-    else Result.ret ()
+  let x ← get_max 4#u32 3#u32
+  let y ← get_max 10#u32 11#u32
+  let z ← x + y
+  if not (z = 15#u32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test3] -/
 #assert (test3 == Result.ret ())
 
-/- [no_nested_borrows::test_neg1]: forward function
+/- [no_nested_borrows::test_neg1]:
    Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 -/
 def test_neg1 : Result Unit :=
   do
-    let y ← - 3#i32
-    if not (y = (-(3:Int))#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let y ← - 3#i32
+  if not (y = (-(3:Int))#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_neg1] -/
 #assert (test_neg1 == Result.ret ())
 
-/- [no_nested_borrows::refs_test1]: forward function
+/- [no_nested_borrows::refs_test1]:
    Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 -/
 def refs_test1 : Result Unit :=
   if not (1#i32 = 1#i32)
@@ -214,7 +214,7 @@ def refs_test1 : Result Unit :=
 /- Unit test for [no_nested_borrows::refs_test1] -/
 #assert (refs_test1 == Result.ret ())
 
-/- [no_nested_borrows::refs_test2]: forward function
+/- [no_nested_borrows::refs_test2]:
    Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 -/
 def refs_test2 : Result Unit :=
   if not (2#i32 = 2#i32)
@@ -232,7 +232,7 @@ def refs_test2 : Result Unit :=
 /- Unit test for [no_nested_borrows::refs_test2] -/
 #assert (refs_test2 == Result.ret ())
 
-/- [no_nested_borrows::test_list1]: forward function
+/- [no_nested_borrows::test_list1]:
    Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 -/
 def test_list1 : Result Unit :=
   Result.ret ()
@@ -240,128 +240,123 @@ def test_list1 : Result Unit :=
 /- Unit test for [no_nested_borrows::test_list1] -/
 #assert (test_list1 == Result.ret ())
 
-/- [no_nested_borrows::test_box1]: forward function
+/- [no_nested_borrows::test_box1]:
    Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 -/
 def test_box1 : Result Unit :=
   do
-    let b := 0#i32
-    let b0 ← alloc.boxed.Box.deref_mut_back I32 b 1#i32
-    let x ← alloc.boxed.Box.deref I32 b0
-    if not (x = 1#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let (_, deref_mut_back) ← alloc.boxed.Box.deref_mut I32 0#i32
+  let b ← deref_mut_back 1#i32
+  let x ← alloc.boxed.Box.deref I32 b
+  if not (x = 1#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_box1] -/
 #assert (test_box1 == Result.ret ())
 
-/- [no_nested_borrows::copy_int]: forward function
+/- [no_nested_borrows::copy_int]:
    Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 -/
 def copy_int (x : I32) : Result I32 :=
   Result.ret x
 
-/- [no_nested_borrows::test_unreachable]: forward function
+/- [no_nested_borrows::test_unreachable]:
    Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 -/
 def test_unreachable (b : Bool) : Result Unit :=
   if b
   then Result.fail .panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_panic]: forward function
+/- [no_nested_borrows::test_panic]:
    Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 -/
 def test_panic (b : Bool) : Result Unit :=
   if b
   then Result.fail .panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_copy_int]: forward function
+/- [no_nested_borrows::test_copy_int]:
    Source: 'src/no_nested_borrows.rs', lines 239:0-239:22 -/
 def test_copy_int : Result Unit :=
   do
-    let y ← copy_int 0#i32
-    if not (0#i32 = y)
-    then Result.fail .panic
-    else Result.ret ()
+  let y ← copy_int 0#i32
+  if not (0#i32 = y)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_copy_int] -/
 #assert (test_copy_int == Result.ret ())
 
-/- [no_nested_borrows::is_cons]: forward function
+/- [no_nested_borrows::is_cons]:
    Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 -/
 def is_cons (T : Type) (l : List T) : Result Bool :=
   match l with
-  | List.Cons t l0 => Result.ret true
+  | List.Cons _ _ => Result.ret true
   | List.Nil => Result.ret false
 
-/- [no_nested_borrows::test_is_cons]: forward function
+/- [no_nested_borrows::test_is_cons]:
    Source: 'src/no_nested_borrows.rs', lines 253:0-253:21 -/
 def test_is_cons : Result Unit :=
   do
-    let l := List.Nil
-    let b ← is_cons I32 (List.Cons 0#i32 l)
-    if not b
-    then Result.fail .panic
-    else Result.ret ()
+  let b ← is_cons I32 (List.Cons 0#i32 List.Nil)
+  if not b
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_is_cons] -/
 #assert (test_is_cons == Result.ret ())
 
-/- [no_nested_borrows::split_list]: forward function
+/- [no_nested_borrows::split_list]:
    Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 -/
 def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
   match l with
   | List.Cons hd tl => Result.ret (hd, tl)
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::test_split_list]: forward function
+/- [no_nested_borrows::test_split_list]:
    Source: 'src/no_nested_borrows.rs', lines 267:0-267:24 -/
 def test_split_list : Result Unit :=
   do
-    let l := List.Nil
-    let p ← split_list I32 (List.Cons 0#i32 l)
-    let (hd, _) := p
-    if not (hd = 0#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let p ← split_list I32 (List.Cons 0#i32 List.Nil)
+  let (hd, _) := p
+  if not (hd = 0#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_split_list] -/
 #assert (test_split_list == Result.ret ())
 
-/- [no_nested_borrows::choose]: forward function
+/- [no_nested_borrows::choose]:
    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 -/
-def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+def choose
+  (T : Type) (b : Bool) (x : T) (y : T) :
+  Result (T × (T → Result (T × T)))
+  :=
   if b
-  then Result.ret x
-  else Result.ret y
+  then let back_'a := fun ret => Result.ret (ret, y)
+       Result.ret (x, back_'a)
+  else let back_'a := fun ret => Result.ret (x, ret)
+       Result.ret (y, back_'a)
 
-/- [no_nested_borrows::choose]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret : T) : Result (T × T) :=
-  if b
-  then Result.ret (ret, y)
-  else Result.ret (x, ret)
-
-/- [no_nested_borrows::choose_test]: forward function
+/- [no_nested_borrows::choose_test]:
    Source: 'src/no_nested_borrows.rs', lines 282:0-282:20 -/
 def choose_test : Result Unit :=
   do
-    let z ← choose I32 true 0#i32 0#i32
-    let z0 ← z + 1#i32
-    if not (z0 = 1#i32)
+  let (z, choose_back) ← choose I32 true 0#i32 0#i32
+  let z1 ← z + 1#i32
+  if not (z1 = 1#i32)
+  then Result.fail .panic
+  else
+    do
+    let (x, y) ← choose_back z1
+    if not (x = 1#i32)
     then Result.fail .panic
-    else
-      do
-        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
-        if not (x = 1#i32)
-        then Result.fail .panic
-        else if not (y = 0#i32)
-             then Result.fail .panic
-             else Result.ret ()
+    else if not (y = 0#i32)
+         then Result.fail .panic
+         else Result.ret ()
 
 /- Unit test for [no_nested_borrows::choose_test] -/
 #assert (choose_test == Result.ret ())
 
-/- [no_nested_borrows::test_char]: forward function
+/- [no_nested_borrows::test_char]:
    Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 -/
 def test_char : Result Char :=
   Result.ret 'a'
@@ -382,16 +377,16 @@ inductive NodeElem (T : Type) :=
 
 end
 
-/- [no_nested_borrows::list_length]: forward function
+/- [no_nested_borrows::list_length]:
    Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 -/
 divergent def list_length (T : Type) (l : List T) : Result U32 :=
   match l with
-  | List.Cons t l1 => do
-                        let i ← list_length T l1
-                        1#u32 + i
+  | List.Cons _ l1 => do
+                      let i ← list_length T l1
+                      1#u32 + i
   | List.Nil => Result.ret 0#u32
 
-/- [no_nested_borrows::list_nth_shared]: forward function
+/- [no_nested_borrows::list_nth_shared]:
    Source: 'src/no_nested_borrows.rs', lines 347:0-347:62 -/
 divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
@@ -399,38 +394,33 @@ divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
     if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - 1#u32
-           list_nth_shared T tl i0
+         let i1 ← i - 1#u32
+         list_nth_shared T tl i1
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::list_nth_mut]: forward function
+/- [no_nested_borrows::list_nth_mut]:
    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 -/
-divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+divergent def list_nth_mut
+  (T : Type) (l : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match l with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut T tl i0
-  | List.Nil => Result.fail .panic
-
-/- [no_nested_borrows::list_nth_mut]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 -/
-divergent def list_nth_mut_back
-  (T : Type) (l : List T) (i : U32) (ret : T) : Result (List T) :=
-  match l with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back_'a)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, list_nth_mut_back) ← list_nth_mut T tl i1
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← list_nth_mut_back ret
+          Result.ret (List.Cons x tl1)
+      Result.ret (t, back_'a)
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::list_rev_aux]: forward function
+/- [no_nested_borrows::list_rev_aux]:
    Source: 'src/no_nested_borrows.rs', lines 379:0-379:63 -/
 divergent def list_rev_aux
   (T : Type) (li : List T) (lo : List T) : Result (List T) :=
@@ -438,136 +428,113 @@ divergent def list_rev_aux
   | List.Cons hd tl => list_rev_aux T tl (List.Cons hd lo)
   | List.Nil => Result.ret lo
 
-/- [no_nested_borrows::list_rev]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [no_nested_borrows::list_rev]:
    Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 -/
 def list_rev (T : Type) (l : List T) : Result (List T) :=
-  let li := core.mem.replace (List T) l List.Nil
+  let (li, _) := core.mem.replace (List T) l List.Nil
   list_rev_aux T li List.Nil
 
-/- [no_nested_borrows::test_list_functions]: forward function
+/- [no_nested_borrows::test_list_functions]:
    Source: 'src/no_nested_borrows.rs', lines 398:0-398:28 -/
 def test_list_functions : Result Unit :=
   do
-    let l := List.Nil
-    let l0 := List.Cons 2#i32 l
-    let l1 := List.Cons 1#i32 l0
-    let i ← list_length I32 (List.Cons 0#i32 l1)
-    if not (i = 3#u32)
+  let l := List.Cons 2#i32 List.Nil
+  let l1 := List.Cons 1#i32 l
+  let i ← list_length I32 (List.Cons 0#i32 l1)
+  if not (i = 3#u32)
+  then Result.fail .panic
+  else
+    do
+    let i1 ← list_nth_shared I32 (List.Cons 0#i32 l1) 0#u32
+    if not (i1 = 0#i32)
     then Result.fail .panic
     else
       do
-        let i0 ← list_nth_shared I32 (List.Cons 0#i32 l1) 0#u32
-        if not (i0 = 0#i32)
+      let i2 ← list_nth_shared I32 (List.Cons 0#i32 l1) 1#u32
+      if not (i2 = 1#i32)
+      then Result.fail .panic
+      else
+        do
+        let i3 ← list_nth_shared I32 (List.Cons 0#i32 l1) 2#u32
+        if not (i3 = 2#i32)
         then Result.fail .panic
         else
           do
-            let i1 ← list_nth_shared I32 (List.Cons 0#i32 l1) 1#u32
-            if not (i1 = 1#i32)
+          let (_, list_nth_mut_back) ←
+            list_nth_mut I32 (List.Cons 0#i32 l1) 1#u32
+          let ls ← list_nth_mut_back 3#i32
+          let i4 ← list_nth_shared I32 ls 0#u32
+          if not (i4 = 0#i32)
+          then Result.fail .panic
+          else
+            do
+            let i5 ← list_nth_shared I32 ls 1#u32
+            if not (i5 = 3#i32)
             then Result.fail .panic
             else
               do
-                let i2 ← list_nth_shared I32 (List.Cons 0#i32 l1) 2#u32
-                if not (i2 = 2#i32)
-                then Result.fail .panic
-                else
-                  do
-                    let ls ←
-                      list_nth_mut_back I32 (List.Cons 0#i32 l1) 1#u32 3#i32
-                    let i3 ← list_nth_shared I32 ls 0#u32
-                    if not (i3 = 0#i32)
-                    then Result.fail .panic
-                    else
-                      do
-                        let i4 ← list_nth_shared I32 ls 1#u32
-                        if not (i4 = 3#i32)
-                        then Result.fail .panic
-                        else
-                          do
-                            let i5 ← list_nth_shared I32 ls 2#u32
-                            if not (i5 = 2#i32)
-                            then Result.fail .panic
-                            else Result.ret ()
+              let i6 ← list_nth_shared I32 ls 2#u32
+              if not (i6 = 2#i32)
+              then Result.fail .panic
+              else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_list_functions] -/
 #assert (test_list_functions == Result.ret ())
 
-/- [no_nested_borrows::id_mut_pair1]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 -/
-def id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair1]: backward function 0
+/- [no_nested_borrows::id_mut_pair1]:
    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 -/
-def id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 -/
-def id_mut_pair2 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2]: backward function 0
+def id_mut_pair1
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  Result ((T1 × T2) × ((T1 × T2) → Result (T1 × T2)))
+  :=
+  let back_'a := fun ret => let (t, t1) := ret
+                            Result.ret (t, t1)
+  Result.ret ((x, y), back_'a)
+
+/- [no_nested_borrows::id_mut_pair2]:
    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 -/
-def id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair3]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair3]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : Result T1 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair3]: backward function 1
+def id_mut_pair2
+  (T1 T2 : Type) (p : (T1 × T2)) :
+  Result ((T1 × T2) × ((T1 × T2) → Result (T1 × T2)))
+  :=
+  let (t, t1) := p
+  let back_'a := fun ret => let (t2, t3) := ret
+                            Result.ret (t2, t3)
+  Result.ret ((t, t1), back_'a)
+
+/- [no_nested_borrows::id_mut_pair3]:
    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : Result T2 :=
-  Result.ret ret
+def id_mut_pair3
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  Result ((T1 × T2) × (T1 → Result T1) × (T2 → Result T2))
+  :=
+  Result.ret ((x, y), Result.ret, Result.ret)
 
-/- [no_nested_borrows::id_mut_pair4]: forward function
+/- [no_nested_borrows::id_mut_pair4]:
    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair4]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : T1) : Result T1 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair4]: backward function 1
-   Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : T2) : Result T2 :=
-  Result.ret ret
+def id_mut_pair4
+  (T1 T2 : Type) (p : (T1 × T2)) :
+  Result ((T1 × T2) × (T1 → Result T1) × (T2 → Result T2))
+  :=
+  let (t, t1) := p
+  Result.ret ((t, t1), Result.ret, Result.ret)
 
 /- [no_nested_borrows::StructWithTuple]
    Source: 'src/no_nested_borrows.rs', lines 433:0-433:34 -/
 structure StructWithTuple (T1 T2 : Type) where
   p : (T1 × T2)
 
-/- [no_nested_borrows::new_tuple1]: forward function
+/- [no_nested_borrows::new_tuple1]:
    Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 -/
 def new_tuple1 : Result (StructWithTuple U32 U32) :=
   Result.ret { p := (1#u32, 2#u32) }
 
-/- [no_nested_borrows::new_tuple2]: forward function
+/- [no_nested_borrows::new_tuple2]:
    Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 -/
 def new_tuple2 : Result (StructWithTuple I16 I16) :=
   Result.ret { p := (1#i16, 2#i16) }
 
-/- [no_nested_borrows::new_tuple3]: forward function
+/- [no_nested_borrows::new_tuple3]:
    Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 -/
 def new_tuple3 : Result (StructWithTuple U64 I64) :=
   Result.ret { p := (1#u64, 2#i64) }
@@ -577,42 +544,42 @@ def new_tuple3 : Result (StructWithTuple U64 I64) :=
 structure StructWithPair (T1 T2 : Type) where
   p : Pair T1 T2
 
-/- [no_nested_borrows::new_pair1]: forward function
+/- [no_nested_borrows::new_pair1]:
    Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 -/
 def new_pair1 : Result (StructWithPair U32 U32) :=
   Result.ret { p := { x := 1#u32, y := 2#u32 } }
 
-/- [no_nested_borrows::test_constants]: forward function
+/- [no_nested_borrows::test_constants]:
    Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 -/
 def test_constants : Result Unit :=
   do
-    let swt ← new_tuple1
-    let (i, _) := swt.p
-    if not (i = 1#u32)
+  let swt ← new_tuple1
+  let (i, _) := swt.p
+  if not (i = 1#u32)
+  then Result.fail .panic
+  else
+    do
+    let swt1 ← new_tuple2
+    let (i1, _) := swt1.p
+    if not (i1 = 1#i16)
     then Result.fail .panic
     else
       do
-        let swt0 ← new_tuple2
-        let (i0, _) := swt0.p
-        if not (i0 = 1#i16)
+      let swt2 ← new_tuple3
+      let (i2, _) := swt2.p
+      if not (i2 = 1#u64)
+      then Result.fail .panic
+      else
+        do
+        let swp ← new_pair1
+        if not (swp.p.x = 1#u32)
         then Result.fail .panic
-        else
-          do
-            let swt1 ← new_tuple3
-            let (i1, _) := swt1.p
-            if not (i1 = 1#u64)
-            then Result.fail .panic
-            else
-              do
-                let swp ← new_pair1
-                if not (swp.p.x = 1#u32)
-                then Result.fail .panic
-                else Result.ret ()
+        else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_constants] -/
 #assert (test_constants == Result.ret ())
 
-/- [no_nested_borrows::test_weird_borrows1]: forward function
+/- [no_nested_borrows::test_weird_borrows1]:
    Source: 'src/no_nested_borrows.rs', lines 471:0-471:28 -/
 def test_weird_borrows1 : Result Unit :=
   Result.ret ()
@@ -620,65 +587,80 @@ def test_weird_borrows1 : Result Unit :=
 /- Unit test for [no_nested_borrows::test_weird_borrows1] -/
 #assert (test_weird_borrows1 == Result.ret ())
 
-/- [no_nested_borrows::test_mem_replace]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [no_nested_borrows::test_mem_replace]:
    Source: 'src/no_nested_borrows.rs', lines 481:0-481:37 -/
 def test_mem_replace (px : U32) : Result U32 :=
-  let y := core.mem.replace U32 px 1#u32
+  let (y, _) := core.mem.replace U32 px 1#u32
   if not (y = 0#u32)
   then Result.fail .panic
   else Result.ret 2#u32
 
-/- [no_nested_borrows::test_shared_borrow_bool1]: forward function
+/- [no_nested_borrows::test_shared_borrow_bool1]:
    Source: 'src/no_nested_borrows.rs', lines 488:0-488:47 -/
 def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
   if b
   then Result.ret 0#u32
   else Result.ret 1#u32
 
-/- [no_nested_borrows::test_shared_borrow_bool2]: forward function
+/- [no_nested_borrows::test_shared_borrow_bool2]:
    Source: 'src/no_nested_borrows.rs', lines 501:0-501:40 -/
 def test_shared_borrow_bool2 : Result U32 :=
   Result.ret 0#u32
 
-/- [no_nested_borrows::test_shared_borrow_enum1]: forward function
+/- [no_nested_borrows::test_shared_borrow_enum1]:
    Source: 'src/no_nested_borrows.rs', lines 516:0-516:52 -/
 def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
   match l with
-  | List.Cons i l0 => Result.ret 1#u32
+  | List.Cons _ _ => Result.ret 1#u32
   | List.Nil => Result.ret 0#u32
 
-/- [no_nested_borrows::test_shared_borrow_enum2]: forward function
+/- [no_nested_borrows::test_shared_borrow_enum2]:
    Source: 'src/no_nested_borrows.rs', lines 528:0-528:40 -/
 def test_shared_borrow_enum2 : Result U32 :=
   Result.ret 0#u32
 
-/- [no_nested_borrows::Tuple]
+/- [no_nested_borrows::incr]:
    Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 -/
+def incr (x : U32) : Result U32 :=
+  x + 1#u32
+
+/- [no_nested_borrows::call_incr]:
+   Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 -/
+def call_incr (x : U32) : Result U32 :=
+  incr x
+
+/- [no_nested_borrows::read_then_incr]:
+   Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 -/
+def read_then_incr (x : U32) : Result (U32 × U32) :=
+  do
+  let x1 ← x + 1#u32
+  Result.ret (x, x1)
+
+/- [no_nested_borrows::Tuple]
+   Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 -/
 def Tuple (T1 T2 : Type) := T1 × T2
 
-/- [no_nested_borrows::use_tuple_struct]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
-   Source: 'src/no_nested_borrows.rs', lines 541:0-541:48 -/
+/- [no_nested_borrows::use_tuple_struct]:
+   Source: 'src/no_nested_borrows.rs', lines 556:0-556:48 -/
 def use_tuple_struct (x : Tuple U32 U32) : Result (Tuple U32 U32) :=
   Result.ret (1#u32, x.1)
 
-/- [no_nested_borrows::create_tuple_struct]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 545:0-545:61 -/
+/- [no_nested_borrows::create_tuple_struct]:
+   Source: 'src/no_nested_borrows.rs', lines 560:0-560:61 -/
 def create_tuple_struct (x : U32) (y : U64) : Result (Tuple U32 U64) :=
   Result.ret (x, y)
 
 /- [no_nested_borrows::IdType]
-   Source: 'src/no_nested_borrows.rs', lines 550:0-550:20 -/
+   Source: 'src/no_nested_borrows.rs', lines 565:0-565:20 -/
 @[reducible] def IdType (T : Type) := T
 
-/- [no_nested_borrows::use_id_type]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 552:0-552:40 -/
+/- [no_nested_borrows::use_id_type]:
+   Source: 'src/no_nested_borrows.rs', lines 567:0-567:40 -/
 def use_id_type (T : Type) (x : IdType T) : Result T :=
   Result.ret x
 
-/- [no_nested_borrows::create_id_type]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 556:0-556:43 -/
+/- [no_nested_borrows::create_id_type]:
+   Source: 'src/no_nested_borrows.rs', lines 571:0-571:43 -/
 def create_id_type (T : Type) (x : T) : Result (IdType T) :=
   Result.ret x
 
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
index 08386bb7..a35c8db0 100644
--- a/tests/lean/Paper.lean
+++ b/tests/lean/Paper.lean
@@ -5,55 +5,51 @@ open Primitives
 
 namespace paper
 
-/- [paper::ref_incr]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [paper::ref_incr]:
    Source: 'src/paper.rs', lines 4:0-4:28 -/
 def ref_incr (x : I32) : Result I32 :=
   x + 1#i32
 
-/- [paper::test_incr]: forward function
+/- [paper::test_incr]:
    Source: 'src/paper.rs', lines 8:0-8:18 -/
 def test_incr : Result Unit :=
   do
-    let x ← ref_incr 0#i32
-    if not (x = 1#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let i ← ref_incr 0#i32
+  if not (i = 1#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [paper::test_incr] -/
 #assert (test_incr == Result.ret ())
 
-/- [paper::choose]: forward function
-   Source: 'src/paper.rs', lines 15:0-15:70 -/
-def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
-  if b
-  then Result.ret x
-  else Result.ret y
-
-/- [paper::choose]: backward function 0
+/- [paper::choose]:
    Source: 'src/paper.rs', lines 15:0-15:70 -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret : T) : Result (T × T) :=
+def choose
+  (T : Type) (b : Bool) (x : T) (y : T) :
+  Result (T × (T → Result (T × T)))
+  :=
   if b
-  then Result.ret (ret, y)
-  else Result.ret (x, ret)
+  then let back_'a := fun ret => Result.ret (ret, y)
+       Result.ret (x, back_'a)
+  else let back_'a := fun ret => Result.ret (x, ret)
+       Result.ret (y, back_'a)
 
-/- [paper::test_choose]: forward function
+/- [paper::test_choose]:
    Source: 'src/paper.rs', lines 23:0-23:20 -/
 def test_choose : Result Unit :=
   do
-    let z ← choose I32 true 0#i32 0#i32
-    let z0 ← z + 1#i32
-    if not (z0 = 1#i32)
+  let (z, choose_back) ← choose I32 true 0#i32 0#i32
+  let z1 ← z + 1#i32
+  if not (z1 = 1#i32)
+  then Result.fail .panic
+  else
+    do
+    let (x, y) ← choose_back z1
+    if not (x = 1#i32)
     then Result.fail .panic
-    else
-      do
-        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
-        if not (x = 1#i32)
-        then Result.fail .panic
-        else if not (y = 0#i32)
-             then Result.fail .panic
-             else Result.ret ()
+    else if not (y = 0#i32)
+         then Result.fail .panic
+         else Result.ret ()
 
 /- Unit test for [paper::test_choose] -/
 #assert (test_choose == Result.ret ())
@@ -64,68 +60,62 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [paper::list_nth_mut]: forward function
+/- [paper::list_nth_mut]:
    Source: 'src/paper.rs', lines 42:0-42:67 -/
-divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+divergent def list_nth_mut
+  (T : Type) (l : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match l with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut T tl i0
-  | List.Nil => Result.fail .panic
-
-/- [paper::list_nth_mut]: backward function 0
-   Source: 'src/paper.rs', lines 42:0-42:67 -/
-divergent def list_nth_mut_back
-  (T : Type) (l : List T) (i : U32) (ret : T) : Result (List T) :=
-  match l with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back_'a)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, list_nth_mut_back) ← list_nth_mut T tl i1
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← list_nth_mut_back ret
+          Result.ret (List.Cons x tl1)
+      Result.ret (t, back_'a)
   | List.Nil => Result.fail .panic
 
-/- [paper::sum]: forward function
+/- [paper::sum]:
    Source: 'src/paper.rs', lines 57:0-57:32 -/
 divergent def sum (l : List I32) : Result I32 :=
   match l with
   | List.Cons x tl => do
-                        let i ← sum tl
-                        x + i
+                      let i ← sum tl
+                      x + i
   | List.Nil => Result.ret 0#i32
 
-/- [paper::test_nth]: forward function
+/- [paper::test_nth]:
    Source: 'src/paper.rs', lines 68:0-68:17 -/
 def test_nth : Result Unit :=
   do
-    let l := List.Nil
-    let l0 := List.Cons 3#i32 l
-    let l1 := List.Cons 2#i32 l0
-    let x ← list_nth_mut I32 (List.Cons 1#i32 l1) 2#u32
-    let x0 ← x + 1#i32
-    let l2 ← list_nth_mut_back I32 (List.Cons 1#i32 l1) 2#u32 x0
-    let i ← sum l2
-    if not (i = 7#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let l := List.Cons 3#i32 List.Nil
+  let l1 := List.Cons 2#i32 l
+  let (x, list_nth_mut_back) ← list_nth_mut I32 (List.Cons 1#i32 l1) 2#u32
+  let x1 ← x + 1#i32
+  let l2 ← list_nth_mut_back x1
+  let i ← sum l2
+  if not (i = 7#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [paper::test_nth] -/
 #assert (test_nth == Result.ret ())
 
-/- [paper::call_choose]: forward function
+/- [paper::call_choose]:
    Source: 'src/paper.rs', lines 76:0-76:44 -/
 def call_choose (p : (U32 × U32)) : Result U32 :=
   do
-    let (px, py) := p
-    let pz ← choose U32 true px py
-    let pz0 ← pz + 1#u32
-    let (px0, _) ← choose_back U32 true px py pz0
-    Result.ret px0
+  let (px, py) := p
+  let (pz, choose_back) ← choose U32 true px py
+  let pz1 ← pz + 1#u32
+  let (px1, _) ← choose_back pz1
+  Result.ret px1
 
 end paper
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
index 37f0dffb..59c557a0 100644
--- a/tests/lean/PoloniusList.lean
+++ b/tests/lean/PoloniusList.lean
@@ -11,28 +11,25 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [polonius_list::get_list_at_x]: forward function
+/- [polonius_list::get_list_at_x]:
    Source: 'src/polonius_list.rs', lines 13:0-13:76 -/
-divergent def get_list_at_x (ls : List U32) (x : U32) : Result (List U32) :=
+divergent def get_list_at_x
+  (ls : List U32) (x : U32) :
+  Result ((List U32) × (List U32 → Result (List U32)))
+  :=
   match ls with
   | List.Cons hd tl =>
     if hd = x
-    then Result.ret (List.Cons hd tl)
-    else get_list_at_x tl x
-  | List.Nil => Result.ret List.Nil
-
-/- [polonius_list::get_list_at_x]: backward function 0
-   Source: 'src/polonius_list.rs', lines 13:0-13:76 -/
-divergent def get_list_at_x_back
-  (ls : List U32) (x : U32) (ret : List U32) : Result (List U32) :=
-  match ls with
-  | List.Cons hd tl =>
-    if hd = x
-    then Result.ret ret
+    then Result.ret (List.Cons hd tl, Result.ret)
     else
       do
-        let tl0 ← get_list_at_x_back tl x ret
-        Result.ret (List.Cons hd tl0)
-  | List.Nil => Result.ret ret
+      let (l, get_list_at_x_back) ← get_list_at_x tl x
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← get_list_at_x_back ret
+          Result.ret (List.Cons hd tl1)
+      Result.ret (l, back_'a)
+  | List.Nil => Result.ret (List.Nil, Result.ret)
 
 end polonius_list
diff --git a/tests/lean/Traits.lean b/tests/lean/Traits.lean
index 17118203..35f9e5bf 100644
--- a/tests/lean/Traits.lean
+++ b/tests/lean/Traits.lean
@@ -10,7 +10,7 @@ namespace traits
 structure BoolTrait (Self : Type) where
   get_bool : Self → Result Bool
 
-/- [traits::{bool}::get_bool]: forward function
+/- [traits::{bool}::get_bool]:
    Source: 'src/traits.rs', lines 12:4-12:30 -/
 def Bool.get_bool (self : Bool) : Result Bool :=
   Result.ret self
@@ -21,27 +21,27 @@ def traits.BoolTraitBoolInst : BoolTrait Bool := {
   get_bool := Bool.get_bool
 }
 
-/- [traits::BoolTrait::ret_true]: forward function
+/- [traits::BoolTrait::ret_true]:
    Source: 'src/traits.rs', lines 6:4-6:30 -/
 def BoolTrait.ret_true
   {Self : Type} (self_clause : BoolTrait Self) (self : Self) : Result Bool :=
   Result.ret true
 
-/- [traits::test_bool_trait_bool]: forward function
+/- [traits::test_bool_trait_bool]:
    Source: 'src/traits.rs', lines 17:0-17:44 -/
 def test_bool_trait_bool (x : Bool) : Result Bool :=
   do
-    let b ← Bool.get_bool x
-    if b
-    then BoolTrait.ret_true traits.BoolTraitBoolInst x
-    else Result.ret false
+  let b ← Bool.get_bool x
+  if b
+  then BoolTrait.ret_true traits.BoolTraitBoolInst x
+  else Result.ret false
 
-/- [traits::{core::option::Option<T>#1}::get_bool]: forward function
+/- [traits::{core::option::Option<T>#1}::get_bool]:
    Source: 'src/traits.rs', lines 23:4-23:30 -/
 def Option.get_bool (T : Type) (self : Option T) : Result Bool :=
   match self with
   | none => Result.ret false
-  | some t => Result.ret true
+  | some _ => Result.ret true
 
 /- Trait implementation: [traits::{core::option::Option<T>#1}]
    Source: 'src/traits.rs', lines 22:0-22:31 -/
@@ -50,16 +50,16 @@ def traits.BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait (Option T)
   get_bool := Option.get_bool T
 }
 
-/- [traits::test_bool_trait_option]: forward function
+/- [traits::test_bool_trait_option]:
    Source: 'src/traits.rs', lines 31:0-31:54 -/
 def test_bool_trait_option (T : Type) (x : Option T) : Result Bool :=
   do
-    let b ← Option.get_bool T x
-    if b
-    then BoolTrait.ret_true (traits.BoolTraitcoreoptionOptionTInst T) x
-    else Result.ret false
+  let b ← Option.get_bool T x
+  if b
+  then BoolTrait.ret_true (traits.BoolTraitcoreoptionOptionTInst T) x
+  else Result.ret false
 
-/- [traits::test_bool_trait]: forward function
+/- [traits::test_bool_trait]:
    Source: 'src/traits.rs', lines 35:0-35:50 -/
 def test_bool_trait
   (T : Type) (BoolTraitTInst : BoolTrait T) (x : T) : Result Bool :=
@@ -70,7 +70,7 @@ def test_bool_trait
 structure ToU64 (Self : Type) where
   to_u64 : Self → Result U64
 
-/- [traits::{u64#2}::to_u64]: forward function
+/- [traits::{u64#2}::to_u64]:
    Source: 'src/traits.rs', lines 44:4-44:26 -/
 def U64.to_u64 (self : U64) : Result U64 :=
   Result.ret self
@@ -81,15 +81,15 @@ def traits.ToU64U64Inst : ToU64 U64 := {
   to_u64 := U64.to_u64
 }
 
-/- [traits::{(A, A)#3}::to_u64]: forward function
+/- [traits::{(A, A)#3}::to_u64]:
    Source: 'src/traits.rs', lines 50:4-50:26 -/
 def Pair.to_u64
   (A : Type) (ToU64AInst : ToU64 A) (self : (A × A)) : Result U64 :=
   do
-    let (t, t0) := self
-    let i ← ToU64AInst.to_u64 t
-    let i0 ← ToU64AInst.to_u64 t0
-    i + i0
+  let (t, t1) := self
+  let i ← ToU64AInst.to_u64 t
+  let i1 ← ToU64AInst.to_u64 t1
+  i + i1
 
 /- Trait implementation: [traits::{(A, A)#3}]
    Source: 'src/traits.rs', lines 49:0-49:31 -/
@@ -98,18 +98,18 @@ def traits.ToU64TupleAAInst (A : Type) (ToU64AInst : ToU64 A) : ToU64 (A × A)
   to_u64 := Pair.to_u64 A ToU64AInst
 }
 
-/- [traits::f]: forward function
+/- [traits::f]:
    Source: 'src/traits.rs', lines 55:0-55:36 -/
 def f (T : Type) (ToU64TInst : ToU64 T) (x : (T × T)) : Result U64 :=
   Pair.to_u64 T ToU64TInst x
 
-/- [traits::g]: forward function
+/- [traits::g]:
    Source: 'src/traits.rs', lines 59:0-61:18 -/
 def g
   (T : Type) (ToU64TupleTTInst : ToU64 (T × T)) (x : (T × T)) : Result U64 :=
   ToU64TupleTTInst.to_u64 x
 
-/- [traits::h0]: forward function
+/- [traits::h0]:
    Source: 'src/traits.rs', lines 66:0-66:24 -/
 def h0 (x : U64) : Result U64 :=
   U64.to_u64 x
@@ -119,7 +119,7 @@ def h0 (x : U64) : Result U64 :=
 structure Wrapper (T : Type) where
   x : T
 
-/- [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+/- [traits::{traits::Wrapper<T>#4}::to_u64]:
    Source: 'src/traits.rs', lines 75:4-75:26 -/
 def Wrapper.to_u64
   (T : Type) (ToU64TInst : ToU64 T) (self : Wrapper T) : Result U64 :=
@@ -132,12 +132,12 @@ def traits.ToU64traitsWrapperTInst (T : Type) (ToU64TInst : ToU64 T) : ToU64
   to_u64 := Wrapper.to_u64 T ToU64TInst
 }
 
-/- [traits::h1]: forward function
+/- [traits::h1]:
    Source: 'src/traits.rs', lines 80:0-80:33 -/
 def h1 (x : Wrapper U64) : Result U64 :=
   Wrapper.to_u64 U64 traits.ToU64U64Inst x
 
-/- [traits::h2]: forward function
+/- [traits::h2]:
    Source: 'src/traits.rs', lines 84:0-84:41 -/
 def h2 (T : Type) (ToU64TInst : ToU64 T) (x : Wrapper T) : Result U64 :=
   Wrapper.to_u64 T ToU64TInst x
@@ -147,7 +147,7 @@ def h2 (T : Type) (ToU64TInst : ToU64 T) (x : Wrapper T) : Result U64 :=
 structure ToType (Self T : Type) where
   to_type : Self → Result T
 
-/- [traits::{u64#5}::to_type]: forward function
+/- [traits::{u64#5}::to_type]:
    Source: 'src/traits.rs', lines 93:4-93:28 -/
 def U64.to_type (self : U64) : Result Bool :=
   Result.ret (self > 0#u64)
@@ -164,7 +164,7 @@ structure OfType (Self : Type) where
   of_type : forall (T : Type) (ToTypeTSelfInst : ToType T Self), T → Result
     Self
 
-/- [traits::h3]: forward function
+/- [traits::h3]:
    Source: 'src/traits.rs', lines 104:0-104:50 -/
 def h3
   (T1 T2 : Type) (OfTypeT1Inst : OfType T1) (ToTypeT2T1Inst : ToType T2 T1)
@@ -179,7 +179,7 @@ structure OfTypeBis (Self T : Type) where
   ToTypeTSelfInst : ToType T Self
   of_type : T → Result Self
 
-/- [traits::h4]: forward function
+/- [traits::h4]:
    Source: 'src/traits.rs', lines 118:0-118:57 -/
 def h4
   (T1 T2 : Type) (OfTypeBisT1T2Inst : OfTypeBis T1 T2) (ToTypeT2T1Inst : ToType
@@ -201,7 +201,7 @@ def h4
 structure TestType.test.TestTrait (Self : Type) where
   test : Self → Result Bool
 
-/- [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+/- [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]:
    Source: 'src/traits.rs', lines 139:12-139:34 -/
 def TestType.test.TestType1.test
   (self : TestType.test.TestType1) : Result Bool :=
@@ -214,23 +214,23 @@ def traits.TestType.test.TestTraittraitstraitsTestTypeTtestTestType1Inst :
   test := TestType.test.TestType1.test
 }
 
-/- [traits::{traits::TestType<T>#6}::test]: forward function
+/- [traits::{traits::TestType<T>#6}::test]:
    Source: 'src/traits.rs', lines 126:4-126:36 -/
 def TestType.test
   (T : Type) (ToU64TInst : ToU64 T) (self : TestType T) (x : T) :
   Result Bool
   :=
   do
-    let x0 ← ToU64TInst.to_u64 x
-    if x0 > 0#u64
-    then TestType.test.TestType1.test 0#u64
-    else Result.ret false
+  let x1 ← ToU64TInst.to_u64 x
+  if x1 > 0#u64
+  then TestType.test.TestType1.test 0#u64
+  else Result.ret false
 
 /- [traits::BoolWrapper]
    Source: 'src/traits.rs', lines 150:0-150:22 -/
 @[reducible] def BoolWrapper := Bool
 
-/- [traits::{traits::BoolWrapper#7}::to_type]: forward function
+/- [traits::{traits::BoolWrapper#7}::to_type]:
    Source: 'src/traits.rs', lines 156:4-156:25 -/
 def BoolWrapper.to_type
   (T : Type) (ToTypeBoolTInst : ToType Bool T) (self : BoolWrapper) :
@@ -266,8 +266,7 @@ structure WithConstTy (Self : Type) (LEN : Usize) where
 def bool_len1_body : Result Usize := Result.ret 12#usize
 def bool_len1_c : Usize := eval_global bool_len1_body (by simp)
 
-/- [traits::{bool#8}::f]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [traits::{bool#8}::f]:
    Source: 'src/traits.rs', lines 180:4-180:39 -/
 def Bool.f (i : U64) (a : Array U8 32#usize) : Result U64 :=
   Result.ret i
@@ -283,16 +282,15 @@ def traits.WithConstTyBool32Inst : WithConstTy Bool 32#usize := {
   f := Bool.f
 }
 
-/- [traits::use_with_const_ty1]: forward function
+/- [traits::use_with_const_ty1]:
    Source: 'src/traits.rs', lines 183:0-183:75 -/
 def use_with_const_ty1
   (H : Type) (LEN : Usize) (WithConstTyHLENInst : WithConstTy H LEN) :
   Result Usize
   :=
-  let i := WithConstTyHLENInst.LEN1
-  Result.ret i
+  Result.ret WithConstTyHLENInst.LEN1
 
-/- [traits::use_with_const_ty2]: forward function
+/- [traits::use_with_const_ty2]:
    Source: 'src/traits.rs', lines 187:0-187:73 -/
 def use_with_const_ty2
   (H : Type) (LEN : Usize) (WithConstTyHLENInst : WithConstTy H LEN)
@@ -301,7 +299,7 @@ def use_with_const_ty2
   :=
   Result.ret ()
 
-/- [traits::use_with_const_ty3]: forward function
+/- [traits::use_with_const_ty3]:
    Source: 'src/traits.rs', lines 189:0-189:80 -/
 def use_with_const_ty3
   (H : Type) (LEN : Usize) (WithConstTyHLENInst : WithConstTy H LEN)
@@ -310,12 +308,12 @@ def use_with_const_ty3
   :=
   WithConstTyHLENInst.W_clause_0.to_u64 x
 
-/- [traits::test_where1]: forward function
+/- [traits::test_where1]:
    Source: 'src/traits.rs', lines 193:0-193:40 -/
 def test_where1 (T : Type) (_x : T) : Result Unit :=
   Result.ret ()
 
-/- [traits::test_where2]: forward function
+/- [traits::test_where2]:
    Source: 'src/traits.rs', lines 194:0-194:57 -/
 def test_where2
   (T : Type) (WithConstTyT32Inst : WithConstTy T 32#usize) (_x : U32) :
@@ -340,22 +338,30 @@ structure ChildTrait (Self : Type) where
   ParentTrait0SelfInst : ParentTrait0 Self
   ParentTrait1SelfInst : ParentTrait1 Self
 
-/- [traits::test_child_trait1]: forward function
-   Source: 'src/traits.rs', lines 209:0-209:56 -/
+/- [traits::test_parent_trait0]:
+   Source: 'src/traits.rs', lines 208:0-208:57 -/
+def test_parent_trait0
+  (T : Type) (ParentTrait0TInst : ParentTrait0 T) (x : T) :
+  Result ParentTrait0TInst.W
+  :=
+  ParentTrait0TInst.get_w x
+
+/- [traits::test_child_trait1]:
+   Source: 'src/traits.rs', lines 213:0-213:56 -/
 def test_child_trait1
   (T : Type) (ChildTraitTInst : ChildTrait T) (x : T) : Result String :=
   ChildTraitTInst.ParentTrait0SelfInst.get_name x
 
-/- [traits::test_child_trait2]: forward function
-   Source: 'src/traits.rs', lines 213:0-213:54 -/
+/- [traits::test_child_trait2]:
+   Source: 'src/traits.rs', lines 217:0-217:54 -/
 def test_child_trait2
   (T : Type) (ChildTraitTInst : ChildTrait T) (x : T) :
   Result ChildTraitTInst.ParentTrait0SelfInst.W
   :=
   ChildTraitTInst.ParentTrait0SelfInst.get_w x
 
-/- [traits::order1]: forward function
-   Source: 'src/traits.rs', lines 219:0-219:59 -/
+/- [traits::order1]:
+   Source: 'src/traits.rs', lines 223:0-223:59 -/
 def order1
   (T U : Type) (ParentTrait0TInst : ParentTrait0 T) (ParentTrait0UInst :
   ParentTrait0 U) :
@@ -364,28 +370,28 @@ def order1
   Result.ret ()
 
 /- Trait declaration: [traits::ChildTrait1]
-   Source: 'src/traits.rs', lines 222:0-222:35 -/
+   Source: 'src/traits.rs', lines 226:0-226:35 -/
 structure ChildTrait1 (Self : Type) where
   ParentTrait1SelfInst : ParentTrait1 Self
 
 /- Trait implementation: [traits::{usize#9}]
-   Source: 'src/traits.rs', lines 224:0-224:27 -/
+   Source: 'src/traits.rs', lines 228:0-228:27 -/
 def traits.ParentTrait1UsizeInst : ParentTrait1 Usize := {
 }
 
 /- Trait implementation: [traits::{usize#10}]
-   Source: 'src/traits.rs', lines 225:0-225:26 -/
+   Source: 'src/traits.rs', lines 229:0-229:26 -/
 def traits.ChildTrait1UsizeInst : ChildTrait1 Usize := {
   ParentTrait1SelfInst := traits.ParentTrait1UsizeInst
 }
 
 /- Trait declaration: [traits::Iterator]
-   Source: 'src/traits.rs', lines 229:0-229:18 -/
+   Source: 'src/traits.rs', lines 233:0-233:18 -/
 structure Iterator (Self : Type) where
   Item : Type
 
 /- Trait declaration: [traits::IntoIterator]
-   Source: 'src/traits.rs', lines 233:0-233:22 -/
+   Source: 'src/traits.rs', lines 237:0-237:22 -/
 structure IntoIterator (Self : Type) where
   Item : Type
   IntoIter : Type
@@ -393,76 +399,86 @@ structure IntoIterator (Self : Type) where
   into_iter : Self → Result IntoIter
 
 /- Trait declaration: [traits::FromResidual]
-   Source: 'src/traits.rs', lines 250:0-250:21 -/
+   Source: 'src/traits.rs', lines 254:0-254:21 -/
 structure FromResidual (Self T : Type) where
 
 /- Trait declaration: [traits::Try]
-   Source: 'src/traits.rs', lines 246:0-246:48 -/
+   Source: 'src/traits.rs', lines 250:0-250:48 -/
 structure Try (Self : Type) where
   Residual : Type
   FromResidualSelftraitsTrySelfResidualInst : FromResidual Self Residual
 
 /- Trait declaration: [traits::WithTarget]
-   Source: 'src/traits.rs', lines 252:0-252:20 -/
+   Source: 'src/traits.rs', lines 256:0-256:20 -/
 structure WithTarget (Self : Type) where
   Target : Type
 
 /- Trait declaration: [traits::ParentTrait2]
-   Source: 'src/traits.rs', lines 256:0-256:22 -/
+   Source: 'src/traits.rs', lines 260:0-260:22 -/
 structure ParentTrait2 (Self : Type) where
   U : Type
   U_clause_0 : WithTarget U
 
 /- Trait declaration: [traits::ChildTrait2]
-   Source: 'src/traits.rs', lines 260:0-260:35 -/
+   Source: 'src/traits.rs', lines 264:0-264:35 -/
 structure ChildTrait2 (Self : Type) where
   ParentTrait2SelfInst : ParentTrait2 Self
   convert : ParentTrait2SelfInst.U → Result
     ParentTrait2SelfInst.U_clause_0.Target
 
 /- Trait implementation: [traits::{u32#11}]
-   Source: 'src/traits.rs', lines 264:0-264:23 -/
+   Source: 'src/traits.rs', lines 268:0-268:23 -/
 def traits.WithTargetU32Inst : WithTarget U32 := {
   Target := U32
 }
 
 /- Trait implementation: [traits::{u32#12}]
-   Source: 'src/traits.rs', lines 268:0-268:25 -/
+   Source: 'src/traits.rs', lines 272:0-272:25 -/
 def traits.ParentTrait2U32Inst : ParentTrait2 U32 := {
   U := U32
   U_clause_0 := traits.WithTargetU32Inst
 }
 
-/- [traits::{u32#13}::convert]: forward function
-   Source: 'src/traits.rs', lines 273:4-273:29 -/
+/- [traits::{u32#13}::convert]:
+   Source: 'src/traits.rs', lines 277:4-277:29 -/
 def U32.convert (x : U32) : Result U32 :=
   Result.ret x
 
 /- Trait implementation: [traits::{u32#13}]
-   Source: 'src/traits.rs', lines 272:0-272:24 -/
+   Source: 'src/traits.rs', lines 276:0-276:24 -/
 def traits.ChildTrait2U32Inst : ChildTrait2 U32 := {
   ParentTrait2SelfInst := traits.ParentTrait2U32Inst
   convert := U32.convert
 }
 
 /- Trait declaration: [traits::CFnOnce]
-   Source: 'src/traits.rs', lines 286:0-286:23 -/
+   Source: 'src/traits.rs', lines 290:0-290:23 -/
 structure CFnOnce (Self Args : Type) where
   Output : Type
   call_once : Self → Args → Result Output
 
 /- Trait declaration: [traits::CFnMut]
-   Source: 'src/traits.rs', lines 292:0-292:37 -/
+   Source: 'src/traits.rs', lines 296:0-296:37 -/
 structure CFnMut (Self Args : Type) where
   CFnOnceSelfArgsInst : CFnOnce Self Args
-  call_mut : Self → Args → Result CFnOnceSelfArgsInst.Output
-  call_mut_back : Self → Args → CFnOnceSelfArgsInst.Output → Result Self
+  call_mut : Self → Args → Result (CFnOnceSelfArgsInst.Output × Self)
 
 /- Trait declaration: [traits::CFn]
-   Source: 'src/traits.rs', lines 296:0-296:33 -/
+   Source: 'src/traits.rs', lines 300:0-300:33 -/
 structure CFn (Self Args : Type) where
   CFnMutSelfArgsInst : CFnMut Self Args
-  call_mut : Self → Args → Result
-    CFnMutSelfArgsInst.CFnOnceSelfArgsInst.Output
+  call : Self → Args → Result CFnMutSelfArgsInst.CFnOnceSelfArgsInst.Output
+
+/- Trait declaration: [traits::GetTrait]
+   Source: 'src/traits.rs', lines 304:0-304:18 -/
+structure GetTrait (Self : Type) where
+  W : Type
+  get_w : Self → Result W
+
+/- [traits::test_get_trait]:
+   Source: 'src/traits.rs', lines 309:0-309:49 -/
+def test_get_trait
+  (T : Type) (GetTraitTInst : GetTrait T) (x : T) : Result GetTraitTInst.W :=
+  GetTraitTInst.get_w x
 
 end traits