Merge pull request #64 from AeneasVerif/son/merge_back

Merge the forward/backward functions

7 files changed, 411 insertions, 707 deletions

diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar-split/hashmap/Hashmap.Properties.fst
index def520f0..def520f0 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fst
+++ b/tests/fstar-split/hashmap/Hashmap.Properties.fst
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fsti b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
index 26c0ec06..26c0ec06 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fsti
+++ b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
index e6cd1411..447f9b49 100644
--- a/tests/fstar/hashmap/Hashmap.Funs.fst
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -7,12 +7,12 @@ include Hashmap.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap::hash_key]: forward function
+(** [hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 let hash_key (k : usize) : result usize =
   Return 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 *)
 let rec hashMap_allocate_slots_loop
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
@@ -21,12 +21,12 @@ let rec hashMap_allocate_slots_loop
   =
   if n > 0
   then
-    let* slots0 = alloc_vec_Vec_push (list_t t) slots List_Nil in
-    let* n0 = usize_sub n 1 in
-    hashMap_allocate_slots_loop t slots0 n0
+    let* v = alloc_vec_Vec_push (list_t t) slots List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashMap_allocate_slots_loop t v n1
   else Return slots
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
     Source: 'src/hashmap.rs', lines 50:4-50:76 *)
 let hashMap_allocate_slots
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
@@ -34,107 +34,85 @@ let 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 *)
 let hashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
   result (hashMap_t t)
   =
-  let v = alloc_vec_Vec_new (list_t t) in
-  let* slots = hashMap_allocate_slots t v capacity in
+  let* slots = hashMap_allocate_slots t (alloc_vec_Vec_new (list_t t)) capacity
+    in
   let* i = usize_mul capacity max_load_dividend in
-  let* i0 = usize_div i max_load_divisor in
+  let* i1 = usize_div i max_load_divisor in
   Return
     {
       num_entries = 0;
       max_load_factor = (max_load_dividend, max_load_divisor);
-      max_load = i0;
+      max_load = i1;
       slots = slots
     }
 
-(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 let hashMap_new (t : Type0) : result (hashMap_t t) =
   hashMap_new_with_capacity t 32 4 5
 
-(** [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 *)
 let rec hashMap_clear_loop
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
   Tot (result (alloc_vec_Vec (list_t t)))
   (decreases (hashMap_clear_loop_decreases t slots i))
   =
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
   then
-    let* i1 = usize_add i 1 in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i
-        List_Nil in
-    hashMap_clear_loop t slots0 i1
+    let* (_, index_mut_back) =
+      alloc_vec_Vec_index_mut (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back List_Nil in
+    hashMap_clear_loop t slots1 i2
   else Return 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 *)
 let hashMap_clear (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
-  let* v = hashMap_clear_loop t self.slots 0 in
-  Return { self with num_entries = 0; slots = v }
+  let* back = hashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = back }
 
-(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::len]:
     Source: 'src/hashmap.rs', lines 90:4-90:30 *)
 let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
   Return 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 *)
 let rec hashMap_insert_in_list_loop
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Tot (result bool)
+  Tot (result (bool & (list_t t)))
   (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
   | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return false
-    else hashMap_insert_in_list_loop t key value tl
-  | List_Nil -> Return true
+    then Return (false, List_Cons ckey value tl)
+    else
+      let* (b, back) = hashMap_insert_in_list_loop t key value tl in
+      Return (b, List_Cons ckey cvalue back)
+  | List_Nil -> Return (true, List_Cons key value List_Nil)
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
 let hashMap_insert_in_list
-  (t : Type0) (key : usize) (value : t) (ls : list_t 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 *)
-let rec hashMap_insert_in_list_loop_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Tot (result (list_t t))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  result (bool & (list_t t))
   =
-  begin match ls with
-  | List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return (List_Cons ckey value tl)
-    else
-      let* tl0 = hashMap_insert_in_list_loop_back t key value tl in
-      Return (List_Cons ckey cvalue tl0)
-  | List_Nil -> let l = List_Nil in Return (List_Cons key value l)
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashMap_insert_in_list_back
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
-  hashMap_insert_in_list_loop_back t key value ls
+  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 *)
 let hashMap_insert_no_resize
   (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
@@ -143,30 +121,19 @@ let hashMap_insert_no_resize
   let* hash = hash_key key in
   let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* inserted = hashMap_insert_in_list t key value l in
+  let* (inserted, l1) = hashMap_insert_in_list t key value l in
   if inserted
   then
-    let* i0 = usize_add self.num_entries 1 in
-    let* l0 = hashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
-  else
-    let* l0 = hashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { 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* i1 = usize_add self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return { self with num_entries = i1; slots = v }
+  else let* v = index_mut_back l1 in Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 183:4-196:5 *)
 let rec hashMap_move_elements_from_list_loop
   (t : Type0) (ntable : hashMap_t t) (ls : list_t t) :
@@ -175,20 +142,18 @@ let rec hashMap_move_elements_from_list_loop
   =
   begin match ls with
   | List_Cons k v tl ->
-    let* ntable0 = hashMap_insert_no_resize t ntable k v in
-    hashMap_move_elements_from_list_loop t ntable0 tl
+    let* hm = hashMap_insert_no_resize t ntable k v in
+    hashMap_move_elements_from_list_loop t hm tl
   | List_Nil -> Return ntable
   end
 
-(** [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 *)
 let hashMap_move_elements_from_list
   (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : result (hashMap_t 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 *)
 let rec hashMap_move_elements_loop
   (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
@@ -196,64 +161,63 @@ let rec hashMap_move_elements_loop
   Tot (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
   (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
   =
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
   then
-    let* l =
+    let* (l, index_mut_back) =
       alloc_vec_Vec_index_mut (list_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
-    let ls = core_mem_replace (list_t t) l List_Nil in
-    let* ntable0 = hashMap_move_elements_from_list t ntable ls in
-    let* i1 = usize_add i 1 in
-    let l0 = core_mem_replace_back (list_t t) l List_Nil in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i l0 in
-    hashMap_move_elements_loop t ntable0 slots0 i1
+    let (ls, l1) = core_mem_replace (list_t t) l List_Nil in
+    let* hm = hashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back l1 in
+    let* back_'a = hashMap_move_elements_loop t hm slots1 i2 in
+    let (hm1, v) = back_'a in
+    Return (hm1, v)
   else Return (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 *)
 let hashMap_move_elements
   (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
   (i : usize) :
   result ((hashMap_t t) & (alloc_vec_Vec (list_t t)))
   =
-  hashMap_move_elements_loop t ntable slots i
+  let* back_'a = hashMap_move_elements_loop t ntable slots i in
+  let (hm, v) = back_'a in
+  Return (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 *)
 let hashMap_try_resize
   (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
   let* max_usize = scalar_cast U32 Usize core_u32_max in
   let capacity = alloc_vec_Vec_len (list_t t) self.slots in
   let* n1 = usize_div max_usize 2 in
-  let (i, i0) = self.max_load_factor in
-  let* i1 = usize_div n1 i in
-  if capacity <= i1
+  let (i, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
   then
-    let* i2 = usize_mul capacity 2 in
-    let* ntable = hashMap_new_with_capacity t i2 i i0 in
-    let* (ntable0, _) = hashMap_move_elements t ntable self.slots 0 in
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashMap_new_with_capacity t i3 i i1 in
+    let* p = hashMap_move_elements t ntable self.slots 0 in
+    let (ntable1, _) = p in
     Return
-      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
       }
-  else Return { self with max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i1) }
 
-(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 let hashMap_insert
   (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   result (hashMap_t t)
   =
-  let* self0 = hashMap_insert_no_resize t self key value in
-  let* i = hashMap_len t self0 in
-  if i > self0.max_load then hashMap_try_resize t self0 else Return self0
+  let* hm = hashMap_insert_no_resize t self key value in
+  let* i = hashMap_len t hm in
+  if i > hm.max_load then hashMap_try_resize t hm else Return 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 *)
 let rec hashMap_contains_key_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
@@ -261,20 +225,20 @@ let rec hashMap_contains_key_in_list_loop
   (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | List_Cons ckey x tl ->
+  | List_Cons ckey _ tl ->
     if ckey = key
     then Return true
     else hashMap_contains_key_in_list_loop t key tl
   | List_Nil -> Return false
   end
 
-(** [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 *)
 let hashMap_contains_key_in_list
   (t : Type0) (key : usize) (ls : list_t 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 *)
 let hashMap_contains_key
   (t : Type0) (self : hashMap_t t) (key : usize) : result bool =
@@ -287,7 +251,7 @@ let hashMap_contains_key
       hash_mod in
   hashMap_contains_key_in_list t key l
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 let rec hashMap_get_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
@@ -299,12 +263,12 @@ let rec hashMap_get_in_list_loop
   | List_Nil -> Fail Failure
   end
 
-(** [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 *)
 let hashMap_get_in_list (t : Type0) (key : usize) (ls : list_t 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 *)
 let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
   let* hash = hash_key key in
@@ -316,214 +280,146 @@ let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
       hash_mod in
   hashMap_get_in_list t key l
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 let rec hashMap_get_mut_in_list_loop
   (t : Type0) (ls : list_t t) (key : usize) :
-  Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
-  =
-  begin match ls with
-  | List_Cons ckey cvalue tl ->
-    if ckey = key then Return cvalue else hashMap_get_mut_in_list_loop t tl key
-  | List_Nil -> Fail Failure
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list
-  (t : Type0) (ls : list_t 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 *)
-let rec hashMap_get_mut_in_list_loop_back
-  (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
-  Tot (result (list_t t))
+  Tot (result (t & (t -> result (list_t t))))
   (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
   | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (List_Cons ckey ret tl)
+    then
+      let back_'a = fun ret -> Return (List_Cons ckey ret tl) in
+      Return (cvalue, back_'a)
     else
-      let* tl0 = hashMap_get_mut_in_list_loop_back t tl key ret in
-      Return (List_Cons ckey cvalue tl0)
+      let* (x, back_'a) = hashMap_get_mut_in_list_loop t tl key in
+      let back_'a1 =
+        fun ret -> let* tl1 = back_'a ret in Return (List_Cons ckey cvalue tl1)
+        in
+      Return (x, back_'a1)
   | List_Nil -> Fail Failure
   end
 
-(** [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 *)
-let hashMap_get_mut_in_list_back
-  (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t 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 *)
-let hashMap_get_mut (t : Type0) (self : hashMap_t t) (key : usize) : result t =
-  let* hash = hash_key key in
-  let i = alloc_vec_Vec_len (list_t t) self.slots in
-  let* hash_mod = usize_rem hash i in
-  let* l =
-    alloc_vec_Vec_index_mut (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod in
-  hashMap_get_mut_in_list t l key
+let hashMap_get_mut_in_list
+  (t : Type0) (ls : list_t t) (key : usize) :
+  result (t & (t -> result (list_t t)))
+  =
+  let* (x, back_'a) = hashMap_get_mut_in_list_loop t ls key in
+  Return (x, 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 *)
-let hashMap_get_mut_back
-  (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
-  result (hashMap_t t)
+let hashMap_get_mut
+  (t : Type0) (self : hashMap_t t) (key : usize) :
+  result (t & (t -> result (hashMap_t t)))
   =
   let* hash = hash_key key in
   let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* l0 = hashMap_get_mut_in_list_back t l key ret in
-  let* v =
-    alloc_vec_Vec_index_mut_back (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod l0 in
-  Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let* (x, get_mut_in_list_back) = hashMap_get_mut_in_list t l key in
+  let back_'a =
+    fun ret ->
+      let* l1 = get_mut_in_list_back ret in
+      let* v = index_mut_back l1 in
+      Return { self with slots = v } in
+  Return (x, back_'a)
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 let rec hashMap_remove_from_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result (option t))
+  Tot (result ((option t) & (list_t t)))
   (decreases (hashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
   | List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      let (mv_ls, _) =
+        core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | List_Cons i cvalue tl0 -> Return (Some cvalue)
+      | List_Cons _ cvalue tl1 -> Return (Some cvalue, tl1)
       | List_Nil -> Fail Failure
       end
-    else hashMap_remove_from_list_loop t key tl
-  | List_Nil -> Return None
+    else
+      let* (o, back) = hashMap_remove_from_list_loop t key tl in
+      Return (o, List_Cons ckey x back)
+  | List_Nil -> Return (None, List_Nil)
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
     Source: 'src/hashmap.rs', lines 265:4-265:69 *)
 let hashMap_remove_from_list
-  (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
-  hashMap_remove_from_list_loop t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-let rec hashMap_remove_from_list_loop_back
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result (list_t t))
-  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  result ((option t) & (list_t t))
   =
-  begin match ls with
-  | List_Cons ckey x tl ->
-    if ckey = key
-    then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
-      begin match mv_ls with
-      | List_Cons i cvalue tl0 -> Return tl0
-      | List_Nil -> Fail Failure
-      end
-    else
-      let* tl0 = hashMap_remove_from_list_loop_back t key tl in
-      Return (List_Cons ckey x tl0)
-  | List_Nil -> Return List_Nil
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashMap_remove_from_list_back
-  (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
-  hashMap_remove_from_list_loop_back t key ls
+  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 *)
 let hashMap_remove
-  (t : Type0) (self : hashMap_t t) (key : usize) : result (option t) =
-  let* hash = hash_key key in
-  let i = alloc_vec_Vec_len (list_t t) self.slots in
-  let* hash_mod = usize_rem hash i in
-  let* l =
-    alloc_vec_Vec_index_mut (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod in
-  let* x = hashMap_remove_from_list t key l in
-  begin match x with
-  | None -> Return None
-  | Some x0 -> let* _ = usize_sub self.num_entries 1 in Return (Some x0)
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashMap_remove_back
-  (t : Type0) (self : hashMap_t t) (key : usize) : result (hashMap_t t) =
+  (t : Type0) (self : hashMap_t t) (key : usize) :
+  result ((option t) & (hashMap_t t))
+  =
   let* hash = hash_key key in
   let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* x = hashMap_remove_from_list t key l in
+  let* (x, l1) = hashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    let* l0 = hashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with slots = v }
-  | Some x0 ->
-    let* i0 = usize_sub self.num_entries 1 in
-    let* l0 = hashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
+    let* v = index_mut_back l1 in Return (None, { self with slots = v })
+  | Some x1 ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return (Some x1, { self with num_entries = i1; slots = v })
   end
 
-(** [hashmap::test1]: forward function
+(** [hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 let test1 : result unit =
   let* hm = hashMap_new u64 in
-  let* hm0 = hashMap_insert u64 hm 0 42 in
-  let* hm1 = hashMap_insert u64 hm0 128 18 in
-  let* hm2 = hashMap_insert u64 hm1 1024 138 in
-  let* hm3 = hashMap_insert u64 hm2 1056 256 in
-  let* i = hashMap_get u64 hm3 128 in
+  let* hm1 = hashMap_insert u64 hm 0 42 in
+  let* hm2 = hashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashMap_insert u64 hm3 1056 256 in
+  let* i = hashMap_get u64 hm4 128 in
   if not (i = 18)
   then Fail Failure
   else
-    let* hm4 = hashMap_get_mut_back u64 hm3 1024 56 in
-    let* i0 = hashMap_get u64 hm4 1024 in
-    if not (i0 = 56)
+    let* (_, get_mut_back) = hashMap_get_mut u64 hm4 1024 in
+    let* hm5 = get_mut_back 56 in
+    let* i1 = hashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
     then Fail Failure
     else
-      let* x = hashMap_remove u64 hm4 1024 in
+      let* (x, hm6) = hashMap_remove u64 hm5 1024 in
       begin match x with
       | None -> Fail Failure
-      | Some x0 ->
-        if not (x0 = 56)
+      | Some x1 ->
+        if not (x1 = 56)
         then Fail Failure
         else
-          let* hm5 = hashMap_remove_back u64 hm4 1024 in
-          let* i1 = hashMap_get u64 hm5 0 in
-          if not (i1 = 42)
+          let* i2 = hashMap_get u64 hm6 0 in
+          if not (i2 = 42)
           then Fail Failure
           else
-            let* i2 = hashMap_get u64 hm5 128 in
-            if not (i2 = 18)
+            let* i3 = hashMap_get u64 hm6 128 in
+            if not (i3 = 18)
             then Fail Failure
             else
-              let* i3 = hashMap_get u64 hm5 1056 in
-              if not (i3 = 256) then Fail Failure else Return ()
+              let* i4 = hashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
       end
 
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -55,8 +55,7 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
-let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // Trait declaration: [core::ops::index::IndexMut]
 noeq type core_ops_index_IndexMut (self idx : Type0) = {
   indexInst : core_ops_index_Index self idx;
-  index_mut : self → idx → result indexInst.output;
-  index_mut_back : self → idx → indexInst.output → result self;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // Trait declaration [core::ops::deref::DerefMut]
 noeq type core_ops_deref_DerefMut (self : Type0) = {
   derefInst : core_ops_deref_Deref self;
-  deref_mut : self → result derefInst.target;
-  deref_mut_back : self → derefInst.target → result self;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [alloc] *)
 
 let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
   derefInst = alloc_boxed_Box_coreopsDerefInst self;
   deref_mut = alloc_boxed_Box_deref_mut self;
-  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
 }
 
 (*** Array *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) :
+  result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
 let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     end
   else Fail Failure
 
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
 let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
@@ -619,13 +636,11 @@ noeq type core_slice_index_SliceIndex (self t : Type0) = {
   sealedInst : core_slice_index_private_slice_index_Sealed self;
   output : Type0;
   get : self → t → result (option output);
-  get_mut : self → t → result (option output);
-  get_mut_back : self → t → option output → result t;
+  get_mut : self → t → result (option output & (option output -> result t));
   get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
   get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
   index : self → t → result output;
-  index_mut : self → t → result output;
-  index_mut_back : self → t → output → result t;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_get_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
-  admit () // TODO
-
-// [core::slice::index::Range::get_mut]: backward function 0
-let core_slice_index_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_index_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::Range::index_mut]: backward function 0
-let core_slice_index_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (slice t & (slice t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::[T]::index_mut]: forward function
 let core_slice_index_Slice_index_mut
   (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → result inst.output =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   admit () // 
 
-// [core::slice::index::[T]::index_mut]: backward function 0
-let core_slice_index_Slice_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → inst.output → result (slice t) =
-  admit () // TODO
-
 // [core::array::[T; N]::index]: forward function
 let core_array_Array_index
   (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [core::array::[T; N]::index_mut]: forward function
 let core_array_Array_index_mut
   (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) : result inst.indexInst.output =
-  admit () // TODO
-
-// [core::array::[T; N]::index_mut]: backward function 0
-let core_array_Array_index_mut_back
-  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst t idx inst;
   index_mut = core_slice_index_Slice_index_mut t idx inst;
-  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
 }
 
 // Trait implementation: [core::array::[T; N]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
   index_mut = core_array_Array_index_mut t idx n inst;
-  index_mut_back = core_array_Array_index_mut_back t idx n inst;
 }
 
 // [core::slice::index::usize::get]: forward function
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   admit () // TODO
 
 // [core::slice::index::usize::get_mut]: forward function
-let core_slice_index_usize_get_mut
-  (t : Type0) : usize → slice t → result (option t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_mut]: backward function 0
-let core_slice_index_usize_get_mut_back
-  (t : Type0) : usize → slice t → option t → result (slice t) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
   admit () // TODO
 
 // [core::slice::index::usize::index_mut]: forward function
-let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
-  admit () // TODO
-
-// [core::slice::index::usize::index_mut]: backward function 0
-let core_slice_index_usize_index_mut_back
-  (t : Type0) : usize → slice t → t → result (slice t) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   output = t;
   get = core_slice_index_usize_get t;
   get_mut = core_slice_index_usize_get_mut t;
-  get_mut_back = core_slice_index_usize_get_mut_back t;
   get_unchecked = core_slice_index_usize_get_unchecked t;
   get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
   index = core_slice_index_usize_index t;
   index_mut = core_slice_index_usize_index_mut t;
-  index_mut_back = core_slice_index_usize_index_mut_back t;
 }
 
 // [alloc::vec::Vec::index]: forward function
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [alloc::vec::Vec::index_mut]: forward function
 let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
-  admit () // TODO
-
-// [alloc::vec::Vec::index_mut]: backward function 0
-let alloc_vec_Vec_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
   indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
   index_mut = alloc_vec_Vec_index_mut t idx inst;
-  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
 }
 
 (*** Theorems *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
   Lemma (
     alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
   =
   admit()
-
-let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
-  Lemma (
-    alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
index f2d09a38..b16dcada 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
@@ -8,12 +8,12 @@ include HashmapMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap_main::hashmap::hash_key]: forward function
+(** [hashmap_main::hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 let hashmap_hash_key (k : usize) : result usize =
   Return 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 *)
 let rec hashmap_HashMap_allocate_slots_loop
   (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) :
@@ -22,13 +22,12 @@ let rec hashmap_HashMap_allocate_slots_loop
   =
   if n > 0
   then
-    let* slots0 = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil
-      in
-    let* n0 = usize_sub n 1 in
-    hashmap_HashMap_allocate_slots_loop t slots0 n0
+    let* v = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashmap_HashMap_allocate_slots_loop t v n1
   else Return 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 *)
 let hashmap_HashMap_allocate_slots
   (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) :
@@ -36,112 +35,90 @@ let 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 *)
 let hashmap_HashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
   result (hashmap_HashMap_t t)
   =
-  let v = alloc_vec_Vec_new (hashmap_List_t t) in
-  let* slots = hashmap_HashMap_allocate_slots t v capacity in
+  let* slots =
+    hashmap_HashMap_allocate_slots t (alloc_vec_Vec_new (hashmap_List_t t))
+      capacity in
   let* i = usize_mul capacity max_load_dividend in
-  let* i0 = usize_div i max_load_divisor in
+  let* i1 = usize_div i max_load_divisor in
   Return
     {
       num_entries = 0;
       max_load_factor = (max_load_dividend, max_load_divisor);
-      max_load = i0;
+      max_load = i1;
       slots = slots
     }
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 let hashmap_HashMap_new (t : Type0) : result (hashmap_HashMap_t t) =
   hashmap_HashMap_new_with_capacity t 32 4 5
 
-(** [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 *)
 let rec hashmap_HashMap_clear_loop
   (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) :
   Tot (result (alloc_vec_Vec (hashmap_List_t t)))
   (decreases (hashmap_HashMap_clear_loop_decreases t slots i))
   =
-  let i0 = alloc_vec_Vec_len (hashmap_List_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in
+  if i < i1
   then
-    let* i1 = usize_add i 1 in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+    let* (_, index_mut_back) =
+      alloc_vec_Vec_index_mut (hashmap_List_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
-        Hashmap_List_Nil in
-    hashmap_HashMap_clear_loop t slots0 i1
+      in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back Hashmap_List_Nil in
+    hashmap_HashMap_clear_loop t slots1 i2
   else Return 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 *)
 let hashmap_HashMap_clear
   (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) =
-  let* v = hashmap_HashMap_clear_loop t self.slots 0 in
-  Return { self with num_entries = 0; slots = v }
+  let* back = hashmap_HashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; 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 *)
 let hashmap_HashMap_len
   (t : Type0) (self : hashmap_HashMap_t t) : result usize =
   Return 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 *)
 let rec hashmap_HashMap_insert_in_list_loop
   (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
-  Tot (result bool)
+  Tot (result (bool & (hashmap_List_t t)))
   (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
   | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return false
-    else hashmap_HashMap_insert_in_list_loop t key value tl
-  | Hashmap_List_Nil -> Return true
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashmap_HashMap_insert_in_list
-  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t 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 *)
-let rec hashmap_HashMap_insert_in_list_loop_back
-  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
-  Tot (result (hashmap_List_t t))
-  (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls))
-  =
-  begin match ls with
-  | Hashmap_List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return (Hashmap_List_Cons ckey value tl)
+    then Return (false, Hashmap_List_Cons ckey value tl)
     else
-      let* tl0 = hashmap_HashMap_insert_in_list_loop_back t key value tl in
-      Return (Hashmap_List_Cons ckey cvalue tl0)
+      let* (b, back) = hashmap_HashMap_insert_in_list_loop t key value tl in
+      Return (b, Hashmap_List_Cons ckey cvalue back)
   | Hashmap_List_Nil ->
-    let l = Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
+    Return (true, Hashmap_List_Cons key value Hashmap_List_Nil)
   end
 
-(** [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 *)
-let hashmap_HashMap_insert_in_list_back
+let hashmap_HashMap_insert_in_list
   (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
-  result (hashmap_List_t t)
+  result (bool & (hashmap_List_t 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 *)
 let hashmap_HashMap_insert_no_resize
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
@@ -150,30 +127,19 @@ let hashmap_HashMap_insert_no_resize
   let* hash = hashmap_hash_key key in
   let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (hashmap_List_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
       self.slots hash_mod in
-  let* inserted = hashmap_HashMap_insert_in_list t key value l in
+  let* (inserted, l1) = hashmap_HashMap_insert_in_list t key value l in
   if inserted
   then
-    let* i0 = usize_add self.num_entries 1 in
-    let* l0 = hashmap_HashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
-  else
-    let* l0 = hashmap_HashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { 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* i1 = usize_add self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return { self with num_entries = i1; slots = v }
+  else let* v = index_mut_back l1 in Return { 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 *)
 let rec hashmap_HashMap_move_elements_from_list_loop
   (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) :
@@ -183,13 +149,12 @@ let rec hashmap_HashMap_move_elements_from_list_loop
   =
   begin match ls with
   | Hashmap_List_Cons k v tl ->
-    let* ntable0 = hashmap_HashMap_insert_no_resize t ntable k v in
-    hashmap_HashMap_move_elements_from_list_loop t ntable0 tl
+    let* hm = hashmap_HashMap_insert_no_resize t ntable k v in
+    hashmap_HashMap_move_elements_from_list_loop t hm tl
   | Hashmap_List_Nil -> Return ntable
   end
 
-(** [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 *)
 let hashmap_HashMap_move_elements_from_list
   (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) :
@@ -197,8 +162,7 @@ let 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 *)
 let rec hashmap_HashMap_move_elements_loop
   (t : Type0) (ntable : hashmap_HashMap_t t)
@@ -206,68 +170,64 @@ let rec hashmap_HashMap_move_elements_loop
   Tot (result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t))))
   (decreases (hashmap_HashMap_move_elements_loop_decreases t ntable slots i))
   =
-  let i0 = alloc_vec_Vec_len (hashmap_List_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in
+  if i < i1
   then
-    let* l =
+    let* (l, index_mut_back) =
       alloc_vec_Vec_index_mut (hashmap_List_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
       in
-    let ls = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in
-    let* ntable0 = hashmap_HashMap_move_elements_from_list t ntable ls in
-    let* i1 = usize_add i 1 in
-    let l0 = core_mem_replace_back (hashmap_List_t t) l Hashmap_List_Nil in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
-        l0 in
-    hashmap_HashMap_move_elements_loop t ntable0 slots0 i1
+    let (ls, l1) = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in
+    let* hm = hashmap_HashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back l1 in
+    let* back_'a = hashmap_HashMap_move_elements_loop t hm slots1 i2 in
+    let (hm1, v) = back_'a in
+    Return (hm1, v)
   else Return (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 *)
 let hashmap_HashMap_move_elements
   (t : Type0) (ntable : hashmap_HashMap_t t)
   (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) :
   result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t)))
   =
-  hashmap_HashMap_move_elements_loop t ntable slots i
+  let* back_'a = hashmap_HashMap_move_elements_loop t ntable slots i in
+  let (hm, v) = back_'a in
+  Return (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 *)
 let hashmap_HashMap_try_resize
   (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) =
   let* max_usize = scalar_cast U32 Usize core_u32_max in
   let capacity = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* n1 = usize_div max_usize 2 in
-  let (i, i0) = self.max_load_factor in
-  let* i1 = usize_div n1 i in
-  if capacity <= i1
+  let (i, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
   then
-    let* i2 = usize_mul capacity 2 in
-    let* ntable = hashmap_HashMap_new_with_capacity t i2 i i0 in
-    let* (ntable0, _) = hashmap_HashMap_move_elements t ntable self.slots 0 in
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashmap_HashMap_new_with_capacity t i3 i i1 in
+    let* p = hashmap_HashMap_move_elements t ntable self.slots 0 in
+    let (ntable1, _) = p in
     Return
-      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
       }
-  else Return { self with max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i1) }
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 let hashmap_HashMap_insert
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
   result (hashmap_HashMap_t t)
   =
-  let* self0 = hashmap_HashMap_insert_no_resize t self key value in
-  let* i = hashmap_HashMap_len t self0 in
-  if i > self0.max_load
-  then hashmap_HashMap_try_resize t self0
-  else Return self0
+  let* hm = hashmap_HashMap_insert_no_resize t self key value in
+  let* i = hashmap_HashMap_len t hm in
+  if i > hm.max_load then hashmap_HashMap_try_resize t hm else Return 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 *)
 let rec hashmap_HashMap_contains_key_in_list_loop
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
@@ -275,20 +235,20 @@ let rec hashmap_HashMap_contains_key_in_list_loop
   (decreases (hashmap_HashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | Hashmap_List_Cons ckey x tl ->
+  | Hashmap_List_Cons ckey _ tl ->
     if ckey = key
     then Return true
     else hashmap_HashMap_contains_key_in_list_loop t key tl
   | Hashmap_List_Nil -> Return false
   end
 
-(** [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 *)
 let hashmap_HashMap_contains_key_in_list
   (t : Type0) (key : usize) (ls : hashmap_List_t 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 *)
 let hashmap_HashMap_contains_key
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result bool =
@@ -301,7 +261,7 @@ let hashmap_HashMap_contains_key
       self.slots hash_mod in
   hashmap_HashMap_contains_key_in_list t key l
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 let rec hashmap_HashMap_get_in_list_loop
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
@@ -316,13 +276,13 @@ let rec hashmap_HashMap_get_in_list_loop
   | Hashmap_List_Nil -> Fail Failure
   end
 
-(** [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 *)
 let hashmap_HashMap_get_in_list
   (t : Type0) (key : usize) (ls : hashmap_List_t 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 *)
 let hashmap_HashMap_get
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t =
@@ -335,241 +295,161 @@ let hashmap_HashMap_get
       self.slots hash_mod in
   hashmap_HashMap_get_in_list t key l
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 let rec hashmap_HashMap_get_mut_in_list_loop
   (t : Type0) (ls : hashmap_List_t t) (key : usize) :
-  Tot (result t)
-  (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
-  =
-  begin match ls with
-  | Hashmap_List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return cvalue
-    else hashmap_HashMap_get_mut_in_list_loop t tl key
-  | Hashmap_List_Nil -> Fail Failure
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashmap_HashMap_get_mut_in_list
-  (t : Type0) (ls : hashmap_List_t 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 *)
-let rec hashmap_HashMap_get_mut_in_list_loop_back
-  (t : Type0) (ls : hashmap_List_t t) (key : usize) (ret : t) :
-  Tot (result (hashmap_List_t t))
+  Tot (result (t & (t -> result (hashmap_List_t t))))
   (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
   | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (Hashmap_List_Cons ckey ret tl)
+    then
+      let back_'a = fun ret -> Return (Hashmap_List_Cons ckey ret tl) in
+      Return (cvalue, back_'a)
     else
-      let* tl0 = hashmap_HashMap_get_mut_in_list_loop_back t tl key ret in
-      Return (Hashmap_List_Cons ckey cvalue tl0)
+      let* (x, back_'a) = hashmap_HashMap_get_mut_in_list_loop t tl key in
+      let back_'a1 =
+        fun ret ->
+          let* tl1 = back_'a ret in Return (Hashmap_List_Cons ckey cvalue tl1)
+        in
+      Return (x, back_'a1)
   | Hashmap_List_Nil -> Fail Failure
   end
 
-(** [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 *)
-let hashmap_HashMap_get_mut_in_list_back
-  (t : Type0) (ls : hashmap_List_t t) (key : usize) (ret : t) :
-  result (hashmap_List_t t)
+let hashmap_HashMap_get_mut_in_list
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) :
+  result (t & (t -> result (hashmap_List_t t)))
   =
-  hashmap_HashMap_get_mut_in_list_loop_back t ls key ret
+  let* (x, back_'a) = hashmap_HashMap_get_mut_in_list_loop t ls key in
+  Return (x, back_'a)
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
     Source: 'src/hashmap.rs', lines 257:4-257:67 *)
 let hashmap_HashMap_get_mut
-  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t =
-  let* hash = hashmap_hash_key key in
-  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
-  let* hash_mod = usize_rem hash i in
-  let* l =
-    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-      self.slots hash_mod in
-  hashmap_HashMap_get_mut_in_list t l key
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
-    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashmap_HashMap_get_mut_back
-  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (ret : t) :
-  result (hashmap_HashMap_t t)
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) :
+  result (t & (t -> result (hashmap_HashMap_t t)))
   =
   let* hash = hashmap_hash_key key in
   let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (hashmap_List_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
       self.slots hash_mod in
-  let* l0 = hashmap_HashMap_get_mut_in_list_back t l key ret in
-  let* v =
-    alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-      self.slots hash_mod l0 in
-  Return { self with slots = v }
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let* (x, get_mut_in_list_back) = hashmap_HashMap_get_mut_in_list t l key in
+  let back_'a =
+    fun ret ->
+      let* l1 = get_mut_in_list_back ret in
+      let* v = index_mut_back l1 in
+      Return { self with slots = v } in
+  Return (x, back_'a)
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 let rec hashmap_HashMap_remove_from_list_loop
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
-  Tot (result (option t))
+  Tot (result ((option t) & (hashmap_List_t t)))
   (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
   | Hashmap_List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls =
+      let (mv_ls, _) =
         core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
           Hashmap_List_Nil in
       begin match mv_ls with
-      | Hashmap_List_Cons i cvalue tl0 -> Return (Some cvalue)
-      | Hashmap_List_Nil -> Fail Failure
-      end
-    else hashmap_HashMap_remove_from_list_loop t key tl
-  | Hashmap_List_Nil -> Return None
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashmap_HashMap_remove_from_list
-  (t : Type0) (key : usize) (ls : hashmap_List_t t) : result (option t) =
-  hashmap_HashMap_remove_from_list_loop t key ls
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-let rec hashmap_HashMap_remove_from_list_loop_back
-  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
-  Tot (result (hashmap_List_t t))
-  (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls))
-  =
-  begin match ls with
-  | Hashmap_List_Cons ckey x tl ->
-    if ckey = key
-    then
-      let mv_ls =
-        core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
-          Hashmap_List_Nil in
-      begin match mv_ls with
-      | Hashmap_List_Cons i cvalue tl0 -> Return tl0
+      | Hashmap_List_Cons _ cvalue tl1 -> Return (Some cvalue, tl1)
       | Hashmap_List_Nil -> Fail Failure
       end
     else
-      let* tl0 = hashmap_HashMap_remove_from_list_loop_back t key tl in
-      Return (Hashmap_List_Cons ckey x tl0)
-  | Hashmap_List_Nil -> Return Hashmap_List_Nil
+      let* (o, back) = hashmap_HashMap_remove_from_list_loop t key tl in
+      Return (o, Hashmap_List_Cons ckey x back)
+  | Hashmap_List_Nil -> Return (None, Hashmap_List_Nil)
   end
 
-(** [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 *)
-let hashmap_HashMap_remove_from_list_back
+let hashmap_HashMap_remove_from_list
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
-  result (hashmap_List_t t)
+  result ((option t) & (hashmap_List_t t))
   =
-  hashmap_HashMap_remove_from_list_loop_back t key ls
+  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 *)
 let hashmap_HashMap_remove
-  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result (option t) =
-  let* hash = hashmap_hash_key key in
-  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
-  let* hash_mod = usize_rem hash i in
-  let* l =
-    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-      self.slots hash_mod in
-  let* x = hashmap_HashMap_remove_from_list t key l in
-  begin match x with
-  | None -> Return None
-  | Some x0 -> let* _ = usize_sub self.num_entries 1 in Return (Some x0)
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashmap_HashMap_remove_back
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) :
-  result (hashmap_HashMap_t t)
+  result ((option t) & (hashmap_HashMap_t t))
   =
   let* hash = hashmap_hash_key key in
   let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (hashmap_List_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
       self.slots hash_mod in
-  let* x = hashmap_HashMap_remove_from_list t key l in
+  let* (x, l1) = hashmap_HashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    let* l0 = hashmap_HashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with slots = v }
-  | Some x0 ->
-    let* i0 = usize_sub self.num_entries 1 in
-    let* l0 = hashmap_HashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
+    let* v = index_mut_back l1 in Return (None, { self with slots = v })
+  | Some x1 ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return (Some x1, { self with num_entries = i1; slots = v })
   end
 
-(** [hashmap_main::hashmap::test1]: forward function
+(** [hashmap_main::hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 let hashmap_test1 : result unit =
   let* hm = hashmap_HashMap_new u64 in
-  let* hm0 = hashmap_HashMap_insert u64 hm 0 42 in
-  let* hm1 = hashmap_HashMap_insert u64 hm0 128 18 in
-  let* hm2 = hashmap_HashMap_insert u64 hm1 1024 138 in
-  let* hm3 = hashmap_HashMap_insert u64 hm2 1056 256 in
-  let* i = hashmap_HashMap_get u64 hm3 128 in
+  let* hm1 = hashmap_HashMap_insert u64 hm 0 42 in
+  let* hm2 = hashmap_HashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashmap_HashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashmap_HashMap_insert u64 hm3 1056 256 in
+  let* i = hashmap_HashMap_get u64 hm4 128 in
   if not (i = 18)
   then Fail Failure
   else
-    let* hm4 = hashmap_HashMap_get_mut_back u64 hm3 1024 56 in
-    let* i0 = hashmap_HashMap_get u64 hm4 1024 in
-    if not (i0 = 56)
+    let* (_, get_mut_back) = hashmap_HashMap_get_mut u64 hm4 1024 in
+    let* hm5 = get_mut_back 56 in
+    let* i1 = hashmap_HashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
     then Fail Failure
     else
-      let* x = hashmap_HashMap_remove u64 hm4 1024 in
+      let* (x, hm6) = hashmap_HashMap_remove u64 hm5 1024 in
       begin match x with
       | None -> Fail Failure
-      | Some x0 ->
-        if not (x0 = 56)
+      | Some x1 ->
+        if not (x1 = 56)
         then Fail Failure
         else
-          let* hm5 = hashmap_HashMap_remove_back u64 hm4 1024 in
-          let* i1 = hashmap_HashMap_get u64 hm5 0 in
-          if not (i1 = 42)
+          let* i2 = hashmap_HashMap_get u64 hm6 0 in
+          if not (i2 = 42)
           then Fail Failure
           else
-            let* i2 = hashmap_HashMap_get u64 hm5 128 in
-            if not (i2 = 18)
+            let* i3 = hashmap_HashMap_get u64 hm6 128 in
+            if not (i3 = 18)
             then Fail Failure
             else
-              let* i3 = hashmap_HashMap_get u64 hm5 1056 in
-              if not (i3 = 256) then Fail Failure else Return ()
+              let* i4 = hashmap_HashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
       end
 
-(** [hashmap_main::insert_on_disk]: forward function
+(** [hashmap_main::insert_on_disk]:
     Source: 'src/hashmap_main.rs', lines 7:0-7:43 *)
 let insert_on_disk
   (key : usize) (value : u64) (st : state) : result (state & unit) =
-  let* (st0, hm) = hashmap_utils_deserialize st in
-  let* hm0 = hashmap_HashMap_insert u64 hm key value in
-  let* (st1, _) = hashmap_utils_serialize hm0 st0 in
-  Return (st1, ())
+  let* (st1, hm) = hashmap_utils_deserialize st in
+  let* hm1 = hashmap_HashMap_insert u64 hm key value in
+  let* (st2, _) = hashmap_utils_serialize hm1 st1 in
+  Return (st2, ())
 
-(** [hashmap_main::main]: forward function
+(** [hashmap_main::main]:
     Source: 'src/hashmap_main.rs', lines 16:0-16:13 *)
 let main : result unit =
   Return ()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti
index b00bbcde..50a6509f 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti
@@ -6,12 +6,12 @@ include HashmapMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap_main::hashmap_utils::deserialize]: forward function
+(** [hashmap_main::hashmap_utils::deserialize]:
     Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
 val hashmap_utils_deserialize
   : state -> result (state & (hashmap_HashMap_t u64))
 
-(** [hashmap_main::hashmap_utils::serialize]: forward function
+(** [hashmap_main::hashmap_utils::serialize]:
     Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
 val hashmap_utils_serialize
   : hashmap_HashMap_t u64 -> state -> result (state & unit)
diff --git a/tests/fstar/hashmap_on_disk/Primitives.fst b/tests/fstar/hashmap_on_disk/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/hashmap_on_disk/Primitives.fst
+++ b/tests/fstar/hashmap_on_disk/Primitives.fst
@@ -55,8 +55,7 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
-let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // Trait declaration: [core::ops::index::IndexMut]
 noeq type core_ops_index_IndexMut (self idx : Type0) = {
   indexInst : core_ops_index_Index self idx;
-  index_mut : self → idx → result indexInst.output;
-  index_mut_back : self → idx → indexInst.output → result self;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // Trait declaration [core::ops::deref::DerefMut]
 noeq type core_ops_deref_DerefMut (self : Type0) = {
   derefInst : core_ops_deref_Deref self;
-  deref_mut : self → result derefInst.target;
-  deref_mut_back : self → derefInst.target → result self;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [alloc] *)
 
 let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
   derefInst = alloc_boxed_Box_coreopsDerefInst self;
   deref_mut = alloc_boxed_Box_deref_mut self;
-  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
 }
 
 (*** Array *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) :
+  result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
 let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     end
   else Fail Failure
 
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
 let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
@@ -619,13 +636,11 @@ noeq type core_slice_index_SliceIndex (self t : Type0) = {
   sealedInst : core_slice_index_private_slice_index_Sealed self;
   output : Type0;
   get : self → t → result (option output);
-  get_mut : self → t → result (option output);
-  get_mut_back : self → t → option output → result t;
+  get_mut : self → t → result (option output & (option output -> result t));
   get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
   get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
   index : self → t → result output;
-  index_mut : self → t → result output;
-  index_mut_back : self → t → output → result t;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_get_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
-  admit () // TODO
-
-// [core::slice::index::Range::get_mut]: backward function 0
-let core_slice_index_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_index_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::Range::index_mut]: backward function 0
-let core_slice_index_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (slice t & (slice t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::[T]::index_mut]: forward function
 let core_slice_index_Slice_index_mut
   (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → result inst.output =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   admit () // 
 
-// [core::slice::index::[T]::index_mut]: backward function 0
-let core_slice_index_Slice_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → inst.output → result (slice t) =
-  admit () // TODO
-
 // [core::array::[T; N]::index]: forward function
 let core_array_Array_index
   (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [core::array::[T; N]::index_mut]: forward function
 let core_array_Array_index_mut
   (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) : result inst.indexInst.output =
-  admit () // TODO
-
-// [core::array::[T; N]::index_mut]: backward function 0
-let core_array_Array_index_mut_back
-  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst t idx inst;
   index_mut = core_slice_index_Slice_index_mut t idx inst;
-  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
 }
 
 // Trait implementation: [core::array::[T; N]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
   index_mut = core_array_Array_index_mut t idx n inst;
-  index_mut_back = core_array_Array_index_mut_back t idx n inst;
 }
 
 // [core::slice::index::usize::get]: forward function
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   admit () // TODO
 
 // [core::slice::index::usize::get_mut]: forward function
-let core_slice_index_usize_get_mut
-  (t : Type0) : usize → slice t → result (option t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_mut]: backward function 0
-let core_slice_index_usize_get_mut_back
-  (t : Type0) : usize → slice t → option t → result (slice t) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
   admit () // TODO
 
 // [core::slice::index::usize::index_mut]: forward function
-let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
-  admit () // TODO
-
-// [core::slice::index::usize::index_mut]: backward function 0
-let core_slice_index_usize_index_mut_back
-  (t : Type0) : usize → slice t → t → result (slice t) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   output = t;
   get = core_slice_index_usize_get t;
   get_mut = core_slice_index_usize_get_mut t;
-  get_mut_back = core_slice_index_usize_get_mut_back t;
   get_unchecked = core_slice_index_usize_get_unchecked t;
   get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
   index = core_slice_index_usize_index t;
   index_mut = core_slice_index_usize_index_mut t;
-  index_mut_back = core_slice_index_usize_index_mut_back t;
 }
 
 // [alloc::vec::Vec::index]: forward function
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [alloc::vec::Vec::index_mut]: forward function
 let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
-  admit () // TODO
-
-// [alloc::vec::Vec::index_mut]: backward function 0
-let alloc_vec_Vec_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
   indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
   index_mut = alloc_vec_Vec_index_mut t idx inst;
-  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
 }
 
 (*** Theorems *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
   Lemma (
     alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
   =
   admit()
-
-let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
-  Lemma (
-    alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()