Merge pull request #64 from AeneasVerif/son/merge_back

Merge the forward/backward functions

3 files changed, 228 insertions, 289 deletions

diff --git a/tests/fstar/array/Array.Clauses.Template.fst b/tests/fstar/array/Array.Clauses.Template.fst
index 84347ab9..b2f2649c 100644
--- a/tests/fstar/array/Array.Clauses.Template.fst
+++ b/tests/fstar/array/Array.Clauses.Template.fst
@@ -9,13 +9,13 @@ open Array.Types
 (** [array::sum]: decreases clause
     Source: 'src/array.rs', lines 242:0-250:1 *)
 unfold
-let sum_loop_decreases (s : slice u32) (sum0 : u32) (i : usize) : nat =
+let sum_loop_decreases (s : slice u32) (sum1 : u32) (i : usize) : nat =
   admit ()
 
 (** [array::sum2]: decreases clause
     Source: 'src/array.rs', lines 252:0-261:1 *)
 unfold
-let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum0 : u32)
+let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum1 : u32)
   (i : usize) : nat =
   admit ()
 
diff --git a/tests/fstar/array/Array.Funs.fst b/tests/fstar/array/Array.Funs.fst
index 935bd9c9..4193ba7d 100644
--- a/tests/fstar/array/Array.Funs.fst
+++ b/tests/fstar/array/Array.Funs.fst
@@ -7,86 +7,79 @@ include Array.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [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 *)
 let incr (x : u32) : result u32 =
   u32_add x 1
 
-(** [array::array_to_shared_slice_]: forward function
+(** [array::array_to_shared_slice_]:
     Source: 'src/array.rs', lines 16:0-16:53 *)
 let array_to_shared_slice_ (t : Type0) (s : array t 32) : result (slice t) =
   array_to_slice t 32 s
 
-(** [array::array_to_mut_slice_]: forward function
+(** [array::array_to_mut_slice_]:
     Source: 'src/array.rs', lines 21:0-21:58 *)
-let array_to_mut_slice_ (t : Type0) (s : array t 32) : result (slice t) =
-  array_to_slice t 32 s
-
-(** [array::array_to_mut_slice_]: backward function 0
-    Source: 'src/array.rs', lines 21:0-21:58 *)
-let array_to_mut_slice__back
-  (t : Type0) (s : array t 32) (ret : slice t) : result (array t 32) =
-  array_from_slice t 32 s ret
+let array_to_mut_slice_
+  (t : Type0) (s : array t 32) :
+  result ((slice t) & (slice t -> result (array t 32)))
+  =
+  let* (s1, to_slice_mut_back) = array_to_slice_mut t 32 s in
+  Return (s1, to_slice_mut_back)
 
-(** [array::array_len]: forward function
+(** [array::array_len]:
     Source: 'src/array.rs', lines 25:0-25:40 *)
 let array_len (t : Type0) (s : array t 32) : result usize =
-  let* s0 = array_to_slice t 32 s in let i = slice_len t s0 in Return i
+  let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i
 
-(** [array::shared_array_len]: forward function
+(** [array::shared_array_len]:
     Source: 'src/array.rs', lines 29:0-29:48 *)
 let shared_array_len (t : Type0) (s : array t 32) : result usize =
-  let* s0 = array_to_slice t 32 s in let i = slice_len t s0 in Return i
+  let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i
 
-(** [array::shared_slice_len]: forward function
+(** [array::shared_slice_len]:
     Source: 'src/array.rs', lines 33:0-33:44 *)
 let shared_slice_len (t : Type0) (s : slice t) : result usize =
   let i = slice_len t s in Return i
 
-(** [array::index_array_shared]: forward function
+(** [array::index_array_shared]:
     Source: 'src/array.rs', lines 37:0-37:57 *)
 let index_array_shared (t : Type0) (s : array t 32) (i : usize) : result t =
   array_index_usize t 32 s i
 
-(** [array::index_array_u32]: forward function
+(** [array::index_array_u32]:
     Source: 'src/array.rs', lines 44:0-44:53 *)
 let index_array_u32 (s : array u32 32) (i : usize) : result u32 =
   array_index_usize u32 32 s i
 
-(** [array::index_array_copy]: forward function
+(** [array::index_array_copy]:
     Source: 'src/array.rs', lines 48:0-48:45 *)
 let index_array_copy (x : array u32 32) : result u32 =
   array_index_usize u32 32 x 0
 
-(** [array::index_mut_array]: forward function
+(** [array::index_mut_array]:
     Source: 'src/array.rs', lines 52:0-52:62 *)
-let index_mut_array (t : Type0) (s : array t 32) (i : usize) : result t =
-  array_index_usize t 32 s i
-
-(** [array::index_mut_array]: backward function 0
-    Source: 'src/array.rs', lines 52:0-52:62 *)
-let index_mut_array_back
-  (t : Type0) (s : array t 32) (i : usize) (ret : t) : result (array t 32) =
-  array_update_usize t 32 s i ret
+let index_mut_array
+  (t : Type0) (s : array t 32) (i : usize) :
+  result (t & (t -> result (array t 32)))
+  =
+  let* (x, index_mut_back) = array_index_mut_usize t 32 s i in
+  Return (x, index_mut_back)
 
-(** [array::index_slice]: forward function
+(** [array::index_slice]:
     Source: 'src/array.rs', lines 56:0-56:46 *)
 let index_slice (t : Type0) (s : slice t) (i : usize) : result t =
   slice_index_usize t s i
 
-(** [array::index_mut_slice]: forward function
-    Source: 'src/array.rs', lines 60:0-60:58 *)
-let index_mut_slice (t : Type0) (s : slice t) (i : usize) : result t =
-  slice_index_usize t s i
-
-(** [array::index_mut_slice]: backward function 0
+(** [array::index_mut_slice]:
     Source: 'src/array.rs', lines 60:0-60:58 *)
-let index_mut_slice_back
-  (t : Type0) (s : slice t) (i : usize) (ret : t) : result (slice t) =
-  slice_update_usize t s i ret
+let index_mut_slice
+  (t : Type0) (s : slice t) (i : usize) :
+  result (t & (t -> result (slice t)))
+  =
+  let* (x, index_mut_back) = slice_index_mut_usize t s i in
+  Return (x, index_mut_back)
 
-(** [array::slice_subslice_shared_]: forward function
+(** [array::slice_subslice_shared_]:
     Source: 'src/array.rs', lines 64:0-64:70 *)
 let slice_subslice_shared_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) =
@@ -94,41 +87,33 @@ let 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 *)
 let 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 *)
-let 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
+  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 } in
+  Return (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 *)
 let array_to_slice_shared_ (x : array u32 32) : result (slice u32) =
   array_to_slice u32 32 x
 
-(** [array::array_to_slice_mut_]: forward function
+(** [array::array_to_slice_mut_]:
     Source: 'src/array.rs', lines 76:0-76:59 *)
-let array_to_slice_mut_ (x : array u32 32) : result (slice u32) =
-  array_to_slice u32 32 x
-
-(** [array::array_to_slice_mut_]: backward function 0
-    Source: 'src/array.rs', lines 76:0-76:59 *)
-let array_to_slice_mut__back
-  (x : array u32 32) (ret : slice u32) : result (array u32 32) =
-  array_from_slice u32 32 x ret
+let array_to_slice_mut_
+  (x : array u32 32) :
+  result ((slice u32) & (slice u32 -> result (array u32 32)))
+  =
+  let* (s, to_slice_mut_back) = array_to_slice_mut u32 32 x in
+  Return (s, to_slice_mut_back)
 
-(** [array::array_subslice_shared_]: forward function
+(** [array::array_subslice_shared_]:
     Source: 'src/array.rs', lines 80:0-80:74 *)
 let array_subslice_shared_
   (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
@@ -137,274 +122,262 @@ let 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 *)
 let array_subslice_mut_
-  (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
-  core_array_Array_index_mut u32 (core_ops_range_Range usize) 32
-    (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 *)
-let array_subslice_mut__back
-  (x : array u32 32) (y : usize) (z : usize) (ret : slice u32) :
-  result (array u32 32)
+  (x : array u32 32) (y : usize) (z : usize) :
+  result ((slice u32) & (slice u32 -> result (array u32 32)))
   =
-  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32
-    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
-    { start = y; end_ = z } ret
+  let* (s, index_mut_back) =
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 32
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+      { start = y; end_ = z } in
+  Return (s, index_mut_back)
 
-(** [array::index_slice_0]: forward function
+(** [array::index_slice_0]:
     Source: 'src/array.rs', lines 88:0-88:38 *)
 let index_slice_0 (t : Type0) (s : slice t) : result t =
   slice_index_usize t s 0
 
-(** [array::index_array_0]: forward function
+(** [array::index_array_0]:
     Source: 'src/array.rs', lines 92:0-92:42 *)
 let index_array_0 (t : Type0) (s : array t 32) : result t =
   array_index_usize t 32 s 0
 
-(** [array::index_index_array]: forward function
+(** [array::index_index_array]:
     Source: 'src/array.rs', lines 103:0-103:71 *)
 let index_index_array
   (s : array (array u32 32) 32) (i : usize) (j : usize) : result u32 =
   let* a = array_index_usize (array u32 32) 32 s i in
   array_index_usize u32 32 a j
 
-(** [array::update_update_array]: forward function
+(** [array::update_update_array]:
     Source: 'src/array.rs', lines 114:0-114:70 *)
 let update_update_array
   (s : array (array u32 32) 32) (i : usize) (j : usize) : result unit =
-  let* a = array_index_usize (array u32 32) 32 s i in
-  let* a0 = array_update_usize u32 32 a j 0 in
-  let* _ = array_update_usize (array u32 32) 32 s i a0 in
+  let* (a, index_mut_back) = array_index_mut_usize (array u32 32) 32 s i in
+  let* (_, index_mut_back1) = array_index_mut_usize u32 32 a j in
+  let* a1 = index_mut_back1 0 in
+  let* _ = index_mut_back a1 in
   Return ()
 
-(** [array::array_local_deep_copy]: forward function
+(** [array::array_local_deep_copy]:
     Source: 'src/array.rs', lines 118:0-118:43 *)
 let array_local_deep_copy (x : array u32 32) : result unit =
   Return ()
 
-(** [array::take_array]: forward function
+(** [array::take_array]:
     Source: 'src/array.rs', lines 122:0-122:30 *)
 let take_array (a : array u32 2) : result unit =
   Return ()
 
-(** [array::take_array_borrow]: forward function
+(** [array::take_array_borrow]:
     Source: 'src/array.rs', lines 123:0-123:38 *)
 let take_array_borrow (a : array u32 2) : result unit =
   Return ()
 
-(** [array::take_slice]: forward function
+(** [array::take_slice]:
     Source: 'src/array.rs', lines 124:0-124:28 *)
 let take_slice (s : slice u32) : result unit =
   Return ()
 
-(** [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 *)
 let take_mut_slice (s : slice u32) : result (slice u32) =
   Return s
 
-(** [array::const_array]: forward function
+(** [array::const_array]:
     Source: 'src/array.rs', lines 127:0-127:32 *)
 let const_array : result (array u32 2) =
   Return (mk_array u32 2 [ 0; 0 ])
 
-(** [array::const_slice]: forward function
+(** [array::const_slice]:
     Source: 'src/array.rs', lines 131:0-131:20 *)
 let const_slice : result unit =
   let* _ = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in Return ()
 
-(** [array::take_all]: forward function
+(** [array::take_all]:
     Source: 'src/array.rs', lines 141:0-141:17 *)
 let take_all : result unit =
   let* _ = take_array (mk_array u32 2 [ 0; 0 ]) in
+  let* _ = take_array (mk_array u32 2 [ 0; 0 ]) in
   let* _ = take_array_borrow (mk_array u32 2 [ 0; 0 ]) in
   let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
   let* _ = take_slice s in
-  let* s0 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* s1 = take_mut_slice s0 in
-  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+  let* (s1, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s2 = take_mut_slice s1 in
+  let* _ = to_slice_mut_back s2 in
   Return ()
 
-(** [array::index_array]: forward function
+(** [array::index_array]:
     Source: 'src/array.rs', lines 155:0-155:38 *)
 let index_array (x : array u32 2) : result u32 =
   array_index_usize u32 2 x 0
 
-(** [array::index_array_borrow]: forward function
+(** [array::index_array_borrow]:
     Source: 'src/array.rs', lines 158:0-158:46 *)
 let index_array_borrow (x : array u32 2) : result u32 =
   array_index_usize u32 2 x 0
 
-(** [array::index_slice_u32_0]: forward function
+(** [array::index_slice_u32_0]:
     Source: 'src/array.rs', lines 162:0-162:42 *)
 let index_slice_u32_0 (x : slice u32) : result u32 =
   slice_index_usize u32 x 0
 
-(** [array::index_mut_slice_u32_0]: forward function
-    Source: 'src/array.rs', lines 166:0-166:50 *)
-let index_mut_slice_u32_0 (x : slice u32) : result u32 =
-  slice_index_usize u32 x 0
-
-(** [array::index_mut_slice_u32_0]: backward function 0
+(** [array::index_mut_slice_u32_0]:
     Source: 'src/array.rs', lines 166:0-166:50 *)
-let index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) =
-  let* _ = slice_index_usize u32 x 0 in Return x
+let index_mut_slice_u32_0 (x : slice u32) : result (u32 & (slice u32)) =
+  let* i = slice_index_usize u32 x 0 in Return (i, x)
 
-(** [array::index_all]: forward function
+(** [array::index_all]:
     Source: 'src/array.rs', lines 170:0-170:25 *)
 let index_all : result u32 =
   let* i = index_array (mk_array u32 2 [ 0; 0 ]) in
-  let* i0 = index_array (mk_array u32 2 [ 0; 0 ]) in
-  let* i1 = u32_add i i0 in
-  let* i2 = index_array_borrow (mk_array u32 2 [ 0; 0 ]) in
-  let* i3 = u32_add i1 i2 in
+  let* i1 = index_array (mk_array u32 2 [ 0; 0 ]) in
+  let* i2 = u32_add i i1 in
+  let* i3 = index_array_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* i4 = u32_add i2 i3 in
   let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* i4 = index_slice_u32_0 s in
-  let* i5 = u32_add i3 i4 in
-  let* s0 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* i6 = index_mut_slice_u32_0 s0 in
-  let* i7 = u32_add i5 i6 in
-  let* s1 = index_mut_slice_u32_0_back s0 in
-  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
-  Return i7
-
-(** [array::update_array]: forward function
+  let* i5 = index_slice_u32_0 s in
+  let* i6 = u32_add i4 i5 in
+  let* (s1, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* (i7, s2) = index_mut_slice_u32_0 s1 in
+  let* i8 = u32_add i6 i7 in
+  let* _ = to_slice_mut_back s2 in
+  Return i8
+
+(** [array::update_array]:
     Source: 'src/array.rs', lines 184:0-184:36 *)
 let update_array (x : array u32 2) : result unit =
-  let* _ = array_update_usize u32 2 x 0 1 in Return ()
+  let* (_, index_mut_back) = array_index_mut_usize u32 2 x 0 in
+  let* _ = index_mut_back 1 in
+  Return ()
 
-(** [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 *)
 let update_array_mut_borrow (x : array u32 2) : result (array u32 2) =
-  array_update_usize u32 2 x 0 1
+  let* (_, index_mut_back) = array_index_mut_usize u32 2 x 0 in
+  index_mut_back 1
 
-(** [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 *)
 let update_mut_slice (x : slice u32) : result (slice u32) =
-  slice_update_usize u32 x 0 1
+  let* (_, index_mut_back) = slice_index_mut_usize u32 x 0 in index_mut_back 1
 
-(** [array::update_all]: forward function
+(** [array::update_all]:
     Source: 'src/array.rs', lines 194:0-194:19 *)
 let update_all : result unit =
   let* _ = update_array (mk_array u32 2 [ 0; 0 ]) in
-  let* x = update_array_mut_borrow (mk_array u32 2 [ 0; 0 ]) in
-  let* s = array_to_slice u32 2 x in
-  let* s0 = update_mut_slice s in
-  let* _ = array_from_slice u32 2 x s0 in
+  let* _ = update_array (mk_array u32 2 [ 0; 0 ]) in
+  let* a = update_array_mut_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* (s, to_slice_mut_back) = array_to_slice_mut u32 2 a in
+  let* s1 = update_mut_slice s in
+  let* _ = to_slice_mut_back s1 in
   Return ()
 
-(** [array::range_all]: forward function
+(** [array::range_all]:
     Source: 'src/array.rs', lines 205:0-205:18 *)
 let range_all : result unit =
-  let* s =
+  let* (s, index_mut_back) =
     core_array_Array_index_mut u32 (core_ops_range_Range usize) 4
       (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
       (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
       (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } in
-  let* s0 = update_mut_slice s in
-  let* _ =
-    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4
-      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
-      (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } s0 in
+  let* s1 = update_mut_slice s in
+  let* _ = index_mut_back s1 in
   Return ()
 
-(** [array::deref_array_borrow]: forward function
+(** [array::deref_array_borrow]:
     Source: 'src/array.rs', lines 214:0-214:46 *)
 let deref_array_borrow (x : array u32 2) : result u32 =
   array_index_usize u32 2 x 0
 
-(** [array::deref_array_mut_borrow]: forward function
+(** [array::deref_array_mut_borrow]:
     Source: 'src/array.rs', lines 219:0-219:54 *)
-let deref_array_mut_borrow (x : array u32 2) : result u32 =
-  array_index_usize u32 2 x 0
+let deref_array_mut_borrow (x : array u32 2) : result (u32 & (array u32 2)) =
+  let* i = array_index_usize u32 2 x 0 in Return (i, x)
 
-(** [array::deref_array_mut_borrow]: backward function 0
-    Source: 'src/array.rs', lines 219:0-219:54 *)
-let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) =
-  let* _ = array_index_usize u32 2 x 0 in Return x
-
-(** [array::take_array_t]: forward function
+(** [array::take_array_t]:
     Source: 'src/array.rs', lines 227:0-227:31 *)
 let take_array_t (a : array aB_t 2) : result unit =
   Return ()
 
-(** [array::non_copyable_array]: forward function
+(** [array::non_copyable_array]:
     Source: 'src/array.rs', lines 229:0-229:27 *)
 let non_copyable_array : result unit =
   let* _ = take_array_t (mk_array aB_t 2 [ AB_A; AB_B ]) in Return ()
 
-(** [array::sum]: loop 0: forward function
+(** [array::sum]: loop 0:
     Source: 'src/array.rs', lines 242:0-250:1 *)
 let rec sum_loop
-  (s : slice u32) (sum0 : u32) (i : usize) :
-  Tot (result u32) (decreases (sum_loop_decreases s sum0 i))
+  (s : slice u32) (sum1 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum_loop_decreases s sum1 i))
   =
-  let i0 = slice_len u32 s in
-  if i < i0
+  let i1 = slice_len u32 s in
+  if i < i1
   then
-    let* i1 = slice_index_usize u32 s i in
-    let* sum1 = u32_add sum0 i1 in
-    let* i2 = usize_add i 1 in
-    sum_loop s sum1 i2
-  else Return sum0
+    let* i2 = slice_index_usize u32 s i in
+    let* sum3 = u32_add sum1 i2 in
+    let* i3 = usize_add i 1 in
+    sum_loop s sum3 i3
+  else Return sum1
 
-(** [array::sum]: forward function
+(** [array::sum]:
     Source: 'src/array.rs', lines 242:0-242:28 *)
 let sum (s : slice u32) : result u32 =
   sum_loop s 0 0
 
-(** [array::sum2]: loop 0: forward function
+(** [array::sum2]: loop 0:
     Source: 'src/array.rs', lines 252:0-261:1 *)
 let rec sum2_loop
-  (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
-  Tot (result u32) (decreases (sum2_loop_decreases s s2 sum0 i))
+  (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum2_loop_decreases s s2 sum1 i))
   =
-  let i0 = slice_len u32 s in
-  if i < i0
+  let i1 = slice_len u32 s in
+  if i < i1
   then
-    let* i1 = slice_index_usize u32 s i in
-    let* i2 = slice_index_usize u32 s2 i in
-    let* i3 = u32_add i1 i2 in
-    let* sum1 = u32_add sum0 i3 in
-    let* i4 = usize_add i 1 in
-    sum2_loop s s2 sum1 i4
-  else Return sum0
-
-(** [array::sum2]: forward function
+    let* i2 = slice_index_usize u32 s i in
+    let* i3 = slice_index_usize u32 s2 i in
+    let* i4 = u32_add i2 i3 in
+    let* sum3 = u32_add sum1 i4 in
+    let* i5 = usize_add i 1 in
+    sum2_loop s s2 sum3 i5
+  else Return sum1
+
+(** [array::sum2]:
     Source: 'src/array.rs', lines 252:0-252:41 *)
 let sum2 (s : slice u32) (s2 : slice u32) : result u32 =
   let i = slice_len u32 s in
-  let i0 = slice_len u32 s2 in
-  if not (i = i0) then Fail Failure else sum2_loop s s2 0 0
+  let i1 = slice_len u32 s2 in
+  if not (i = i1) then Fail Failure else sum2_loop s s2 0 0
 
-(** [array::f0]: forward function
+(** [array::f0]:
     Source: 'src/array.rs', lines 263:0-263:11 *)
 let f0 : result unit =
-  let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in
-  let* s0 = slice_update_usize u32 s 0 1 in
-  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 1; 2 ]) s0 in
+  let* (s, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 1; 2 ]) in
+  let* (_, index_mut_back) = slice_index_mut_usize u32 s 0 in
+  let* s1 = index_mut_back 1 in
+  let* _ = to_slice_mut_back s1 in
   Return ()
 
-(** [array::f1]: forward function
+(** [array::f1]:
     Source: 'src/array.rs', lines 268:0-268:11 *)
 let f1 : result unit =
-  let* _ = array_update_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in Return ()
+  let* (_, index_mut_back) =
+    array_index_mut_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 in
+  let* _ = index_mut_back 1 in
+  Return ()
 
-(** [array::f2]: forward function
+(** [array::f2]:
     Source: 'src/array.rs', lines 273:0-273:17 *)
 let f2 (i : u32) : result unit =
   Return ()
 
-(** [array::f4]: forward function
+(** [array::f4]:
     Source: 'src/array.rs', lines 282:0-282:54 *)
 let f4 (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
   core_array_Array_index u32 (core_ops_range_Range usize) 32
@@ -412,34 +385,36 @@ let f4 (x : array u32 32) (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 *)
 let f3 : result u32 =
   let* i = array_index_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 in
   let* _ = f2 i in
   let b = array_repeat u32 32 0 in
   let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in
-  let* s0 = f4 b 16 18 in
-  sum2 s s0
+  let* s1 = f4 b 16 18 in
+  sum2 s s1
 
 (** [array::SZ]
     Source: 'src/array.rs', lines 286:0-286:19 *)
 let sz_body : result usize = Return 32
 let sz_c : usize = eval_global sz_body
 
-(** [array::f5]: forward function
+(** [array::f5]:
     Source: 'src/array.rs', lines 289:0-289:31 *)
 let f5 (x : array u32 32) : result u32 =
   array_index_usize u32 32 x 0
 
-(** [array::ite]: forward function
+(** [array::ite]:
     Source: 'src/array.rs', lines 294:0-294:12 *)
 let ite : result unit =
-  let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* s0 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* s1 = index_mut_slice_u32_0_back s0 in
-  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
-  let* s2 = index_mut_slice_u32_0_back s in
-  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  let* (s, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* (_, s1) = index_mut_slice_u32_0 s in
+  let* (s2, to_slice_mut_back1) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* (_, s3) = index_mut_slice_u32_0 s2 in
+  let* _ = to_slice_mut_back1 s3 in
+  let* _ = to_slice_mut_back s1 in
   Return ()
 
diff --git a/tests/fstar/array/Primitives.fst b/tests/fstar/array/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/array/Primitives.fst
+++ b/tests/fstar/array/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()