Merge pull request #44 from AeneasVerif/son_traits_types

Add support for traits

4 files changed, 690 insertions, 379 deletions

diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index 657d5590..eac78186 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -13,656 +13,668 @@ Import HashmapMain_Opaque.
 Module HashmapMain_Funs.
 
 (** [hashmap_main::hashmap::hash_key]: forward function *)
-Definition hashmap_hash_key_fwd (k : usize) : result usize :=
+Definition hashmap_hash_key (k : usize) : result usize :=
   Return k.
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
-  result (vec (Hashmap_list_t T))
+Fixpoint hashmap_HashMap_allocate_slots_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s> 0%usize
     then (
-      slots0 <- vec_push_back (Hashmap_list_t T) slots HashmapListNil;
+      slots0 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
       n2 <- usize_sub n0 1%usize;
-      hashmap_hash_map_allocate_slots_loop_fwd T n1 slots0 n2)
+      hashmap_HashMap_allocate_slots_loop T n1 slots0 n2)
     else Return slots
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
-Definition hashmap_hash_map_allocate_slots_fwd
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
-  result (vec (Hashmap_list_t T))
+Definition hashmap_HashMap_allocate_slots
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
-  hashmap_hash_map_allocate_slots_loop_fwd T n slots n0
+  hashmap_HashMap_allocate_slots_loop T n slots n0
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-Definition hashmap_hash_map_new_with_capacity_fwd
+Definition hashmap_HashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (Hashmap_hash_map_t T)
+  result (hashmap_HashMap_t T)
   :=
-  let v := vec_new (Hashmap_list_t T) in
-  slots <- hashmap_hash_map_allocate_slots_fwd T n v capacity;
+  let v := alloc_vec_Vec_new (hashmap_List_t T) in
+  slots <- hashmap_HashMap_allocate_slots T n v capacity;
   i <- usize_mul capacity max_load_dividend;
   i0 <- usize_div i max_load_divisor;
   Return
     {|
-      Hashmap_hash_map_num_entries := 0%usize;
-      Hashmap_hash_map_max_load_factor := (max_load_dividend, max_load_divisor);
-      Hashmap_hash_map_max_load := i0;
-      Hashmap_hash_map_slots := slots
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor);
+      hashmap_HashMap_max_load := i0;
+      hashmap_HashMap_slots := slots
     |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
-Definition hashmap_hash_map_new_fwd
-  (T : Type) (n : nat) : result (Hashmap_hash_map_t T) :=
-  hashmap_hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
+Definition hashmap_HashMap_new
+  (T : Type) (n : nat) : result (hashmap_HashMap_t T) :=
+  hashmap_HashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_clear_loop_fwd_back
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result (vec (Hashmap_list_t T))
+Fixpoint hashmap_HashMap_clear_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (Hashmap_list_t T) slots in
+    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      slots0 <- vec_index_mut_back (Hashmap_list_t T) slots i HashmapListNil;
-      hashmap_hash_map_clear_loop_fwd_back T n0 slots0 i1)
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+          T)) slots i Hashmap_List_Nil;
+      hashmap_HashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_clear_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_clear
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  v <-
-    hashmap_hash_map_clear_loop_fwd_back T n self.(Hashmap_hash_map_slots)
-      0%usize;
+  v <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
   Return
     {|
-      Hashmap_hash_map_num_entries := 0%usize;
-      Hashmap_hash_map_max_load_factor :=
-        self.(Hashmap_hash_map_max_load_factor);
-      Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-      Hashmap_hash_map_slots := v
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := v
     |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
-Definition hashmap_hash_map_len_fwd
-  (T : Type) (self : Hashmap_hash_map_t T) : result usize :=
-  Return self.(Hashmap_hash_map_num_entries)
+Definition hashmap_HashMap_len
+  (T : Type) (self : hashmap_HashMap_t T) : result usize :=
+  Return self.(hashmap_HashMap_num_entries)
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
+Fixpoint hashmap_HashMap_insert_in_list_loop
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return false
-      else hashmap_hash_map_insert_in_list_loop_fwd T n0 key value tl
-    | HashmapListNil => Return true
+      else hashmap_HashMap_insert_in_list_loop T n0 key value tl
+    | Hashmap_List_Nil => Return true
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
-Definition hashmap_hash_map_insert_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
+Definition hashmap_HashMap_insert_in_list
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
   :=
-  hashmap_hash_map_insert_in_list_loop_fwd T n key value ls
+  hashmap_HashMap_insert_in_list_loop T n key value ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-Fixpoint hashmap_hash_map_insert_in_list_loop_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Fixpoint hashmap_HashMap_insert_in_list_loop_back
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (HashmapListCons ckey value tl)
+      then Return (Hashmap_List_Cons ckey value tl)
       else (
-        tl0 <- hashmap_hash_map_insert_in_list_loop_back T n0 key value tl;
-        Return (HashmapListCons ckey cvalue tl0))
-    | HashmapListNil =>
-      let l := HashmapListNil in Return (HashmapListCons key value l)
+        tl0 <- hashmap_HashMap_insert_in_list_loop_back T n0 key value tl;
+        Return (Hashmap_List_Cons ckey cvalue tl0))
+    | Hashmap_List_Nil =>
+      let l := Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-Definition hashmap_hash_map_insert_in_list_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Definition hashmap_HashMap_insert_in_list_back
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_insert_in_list_loop_back T n key value ls
+  hashmap_HashMap_insert_in_list_loop_back T n key value ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_insert_no_resize_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
-  :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_insert_no_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  inserted <- hashmap_hash_map_insert_in_list_fwd T n key value l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  inserted <- hashmap_HashMap_insert_in_list T n key value l;
   if inserted
   then (
-    i0 <- usize_add self.(Hashmap_hash_map_num_entries) 1%usize;
-    l0 <- hashmap_hash_map_insert_in_list_back T n key value l;
+    i0 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
+    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := i0;
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |})
   else (
-    l0 <- hashmap_hash_map_insert_in_list_back T n key value l;
+    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |})
 .
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
-  :
-  result (Hashmap_hash_map_t T)
+Fixpoint hashmap_HashMap_move_elements_from_list_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons k v tl =>
-      ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T n0 ntable k v;
-      hashmap_hash_map_move_elements_from_list_loop_fwd_back T n0 ntable0 tl
-    | HashmapListNil => Return ntable
+    | Hashmap_List_Cons k v tl =>
+      ntable0 <- hashmap_HashMap_insert_no_resize T n0 ntable k v;
+      hashmap_HashMap_move_elements_from_list_loop T n0 ntable0 tl
+    | Hashmap_List_Nil => Return ntable
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_move_elements_from_list_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
-  :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_move_elements_from_list
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  hashmap_hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
+  hashmap_HashMap_move_elements_from_list_loop T n ntable ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
-  (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result ((Hashmap_hash_map_t T) * (vec (Hashmap_list_t T)))
+Fixpoint hashmap_HashMap_move_elements_loop
+  (T : Type) (n : nat) (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)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (Hashmap_list_t T) slots in
+    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
     if i s< i0
     then (
-      l <- vec_index_mut_fwd (Hashmap_list_t T) slots i;
-      let ls := mem_replace_fwd (Hashmap_list_t T) l HashmapListNil in
-      ntable0 <-
-        hashmap_hash_map_move_elements_from_list_fwd_back T n0 ntable ls;
+      l <-
+        alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+          T)) slots i;
+      let ls := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
+      ntable0 <- hashmap_HashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
-      let l0 := mem_replace_back (Hashmap_list_t T) l HashmapListNil in
-      slots0 <- vec_index_mut_back (Hashmap_list_t T) slots i l0;
-      hashmap_hash_map_move_elements_loop_fwd_back T n0 ntable0 slots0 i1)
+      let l0 := core_mem_replace_back (hashmap_List_t T) l Hashmap_List_Nil in
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+          T)) slots i l0;
+      hashmap_HashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_move_elements_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
-  (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result ((Hashmap_hash_map_t T) * (vec (Hashmap_list_t T)))
+Definition hashmap_HashMap_move_elements
+  (T : Type) (n : nat) (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_hash_map_move_elements_loop_fwd_back T n ntable slots i
+  hashmap_HashMap_move_elements_loop T n ntable slots i
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_try_resize_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_try_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
-  let capacity := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  max_usize <- scalar_cast U32 Usize core_u32_max;
+  let capacity :=
+    alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   n1 <- usize_div max_usize 2%usize;
-  let (i, i0) := self.(Hashmap_hash_map_max_load_factor) in
+  let (i, i0) := self.(hashmap_HashMap_max_load_factor) in
   i1 <- usize_div n1 i;
   if capacity s<= i1
   then (
     i2 <- usize_mul capacity 2%usize;
-    ntable <- hashmap_hash_map_new_with_capacity_fwd T n i2 i i0;
+    ntable <- hashmap_HashMap_new_with_capacity T n i2 i i0;
     p <-
-      hashmap_hash_map_move_elements_fwd_back T n ntable
-        self.(Hashmap_hash_map_slots) 0%usize;
+      hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots)
+        0%usize;
     let (ntable0, _) := p in
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor := (i, i0);
-        Hashmap_hash_map_max_load := ntable0.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := ntable0.(Hashmap_hash_map_slots)
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load := ntable0.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := ntable0.(hashmap_HashMap_slots)
       |})
   else
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor := (i, i0);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := self.(Hashmap_hash_map_slots)
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := self.(hashmap_HashMap_slots)
       |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_insert_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
-  :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_insert
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
   :=
-  self0 <- hashmap_hash_map_insert_no_resize_fwd_back T n self key value;
-  i <- hashmap_hash_map_len_fwd T self0;
-  if i s> self0.(Hashmap_hash_map_max_load)
-  then hashmap_hash_map_try_resize_fwd_back T n self0
+  self0 <- hashmap_HashMap_insert_no_resize T n self key value;
+  i <- hashmap_HashMap_len T self0;
+  if i s> self0.(hashmap_HashMap_max_load)
+  then hashmap_HashMap_try_resize T n self0
   else Return self0
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
+Fixpoint hashmap_HashMap_contains_key_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then Return true
-      else hashmap_hash_map_contains_key_in_list_loop_fwd T n0 key tl
-    | HashmapListNil => Return false
+      else hashmap_HashMap_contains_key_in_list_loop T n0 key tl
+    | Hashmap_List_Nil => Return false
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-Definition hashmap_hash_map_contains_key_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
-  hashmap_hash_map_contains_key_in_list_loop_fwd T n key ls
+Definition hashmap_HashMap_contains_key_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
+  hashmap_HashMap_contains_key_in_list_loop T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
-Definition hashmap_hash_map_contains_key_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
+Definition hashmap_HashMap_contains_key
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result bool
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_contains_key_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_contains_key_in_list T n key l
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_get_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
+Fixpoint hashmap_HashMap_get_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_hash_map_get_in_list_loop_fwd T n0 key tl
-    | HashmapListNil => Fail_ Failure
+      else hashmap_HashMap_get_in_list_loop T n0 key tl
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
-Definition hashmap_hash_map_get_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
-  hashmap_hash_map_get_in_list_loop_fwd T n key ls
+Definition hashmap_HashMap_get_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
+  hashmap_HashMap_get_in_list_loop T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
-Definition hashmap_hash_map_get_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result T
-  :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+Definition hashmap_HashMap_get
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_get_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_in_list T n key l
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
+Fixpoint hashmap_HashMap_get_mut_in_list_loop
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_hash_map_get_mut_in_list_loop_fwd T n0 tl key
-    | HashmapListNil => Fail_ Failure
+      else hashmap_HashMap_get_mut_in_list_loop T n0 tl key
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-Definition hashmap_hash_map_get_mut_in_list_fwd
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
-  hashmap_hash_map_get_mut_in_list_loop_fwd T n ls key
+Definition hashmap_HashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
+  hashmap_HashMap_get_mut_in_list_loop T n ls key
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
-  result (Hashmap_list_t T)
+Fixpoint hashmap_HashMap_get_mut_in_list_loop_back
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (HashmapListCons ckey ret tl)
+      then Return (Hashmap_List_Cons ckey ret tl)
       else (
-        tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (HashmapListCons ckey cvalue tl0))
-    | HashmapListNil => Fail_ Failure
+        tl0 <- hashmap_HashMap_get_mut_in_list_loop_back T n0 tl key ret;
+        Return (Hashmap_List_Cons ckey cvalue tl0))
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-Definition hashmap_hash_map_get_mut_in_list_back
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
-  result (Hashmap_list_t T)
+Definition hashmap_HashMap_get_mut_in_list_back
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_get_mut_in_list_loop_back T n ls key ret
+  hashmap_HashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
-Definition hashmap_hash_map_get_mut_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result T
-  :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+Definition hashmap_HashMap_get_mut
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_get_mut_in_list_fwd T n l key
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_mut_in_list T n l key
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-Definition hashmap_hash_map_get_mut_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (ret : T) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_get_mut_back
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (ret : T) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  l0 <- hashmap_hash_map_get_mut_in_list_back T n l key ret;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  l0 <- hashmap_HashMap_get_mut_in_list_back T n l key ret;
   v <-
-    vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-      hash_mod l0;
+    alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod l0;
   Return
     {|
-      Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-      Hashmap_hash_map_max_load_factor :=
-        self.(Hashmap_hash_map_max_load_factor);
-      Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-      Hashmap_hash_map_slots := v
+      hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := v
     |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
+Fixpoint hashmap_HashMap_remove_from_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
         let mv_ls :=
-          mem_replace_fwd (Hashmap_list_t T) (HashmapListCons ckey t tl)
-            HashmapListNil in
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
         match mv_ls with
-        | HashmapListCons i cvalue tl0 => Return (Some cvalue)
-        | HashmapListNil => Fail_ Failure
+        | Hashmap_List_Cons i cvalue tl0 => Return (Some cvalue)
+        | Hashmap_List_Nil => Fail_ Failure
         end
-      else hashmap_hash_map_remove_from_list_loop_fwd T n0 key tl
-    | HashmapListNil => Return None
+      else hashmap_HashMap_remove_from_list_loop T n0 key tl
+    | Hashmap_List_Nil => Return None
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
-Definition hashmap_hash_map_remove_from_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
+Definition hashmap_HashMap_remove_from_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
   :=
-  hashmap_hash_map_remove_from_list_loop_fwd T n key ls
+  hashmap_HashMap_remove_from_list_loop T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-Fixpoint hashmap_hash_map_remove_from_list_loop_back
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Fixpoint hashmap_HashMap_remove_from_list_loop_back
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
         let mv_ls :=
-          mem_replace_fwd (Hashmap_list_t T) (HashmapListCons ckey t tl)
-            HashmapListNil in
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
         match mv_ls with
-        | HashmapListCons i cvalue tl0 => Return tl0
-        | HashmapListNil => Fail_ Failure
+        | Hashmap_List_Cons i cvalue tl0 => Return tl0
+        | Hashmap_List_Nil => Fail_ Failure
         end
       else (
-        tl0 <- hashmap_hash_map_remove_from_list_loop_back T n0 key tl;
-        Return (HashmapListCons ckey t tl0))
-    | HashmapListNil => Return HashmapListNil
+        tl0 <- hashmap_HashMap_remove_from_list_loop_back T n0 key tl;
+        Return (Hashmap_List_Cons ckey t tl0))
+    | Hashmap_List_Nil => Return Hashmap_List_Nil
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-Definition hashmap_hash_map_remove_from_list_back
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Definition hashmap_HashMap_remove_from_list_back
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_remove_from_list_loop_back T n key ls
+  hashmap_HashMap_remove_from_list_loop_back T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
-Definition hashmap_hash_map_remove_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
+Definition hashmap_HashMap_remove
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result (option T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  x <- hashmap_hash_map_remove_from_list_fwd T n key l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
   | None => Return None
   | Some x0 =>
-    _ <- usize_sub self.(Hashmap_hash_map_num_entries) 1%usize;
-    Return (Some x0)
+    _ <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize; Return (Some x0)
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
-Definition hashmap_hash_map_remove_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_remove_back
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  x <- hashmap_hash_map_remove_from_list_fwd T n key l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
   | None =>
-    l0 <- hashmap_hash_map_remove_from_list_back T n key l;
+    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |}
   | Some x0 =>
-    i0 <- usize_sub self.(Hashmap_hash_map_num_entries) 1%usize;
-    l0 <- hashmap_hash_map_remove_from_list_back T n key l;
+    i0 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize;
+    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := i0;
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |}
   end
 .
 
 (** [hashmap_main::hashmap::test1]: forward function *)
-Definition hashmap_test1_fwd (n : nat) : result unit :=
-  hm <- hashmap_hash_map_new_fwd u64 n;
-  hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
-  hm1 <- hashmap_hash_map_insert_fwd_back u64 n hm0 128%usize 18%u64;
-  hm2 <- hashmap_hash_map_insert_fwd_back u64 n hm1 1024%usize 138%u64;
-  hm3 <- hashmap_hash_map_insert_fwd_back u64 n hm2 1056%usize 256%u64;
-  i <- hashmap_hash_map_get_fwd u64 n hm3 128%usize;
+Definition hashmap_test1 (n : nat) : result unit :=
+  hm <- hashmap_HashMap_new u64 n;
+  hm0 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64;
+  hm1 <- hashmap_HashMap_insert u64 n hm0 128%usize 18%u64;
+  hm2 <- hashmap_HashMap_insert u64 n hm1 1024%usize 138%u64;
+  hm3 <- hashmap_HashMap_insert u64 n hm2 1056%usize 256%u64;
+  i <- hashmap_HashMap_get u64 n hm3 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    hm4 <- hashmap_hash_map_get_mut_back u64 n hm3 1024%usize 56%u64;
-    i0 <- hashmap_hash_map_get_fwd u64 n hm4 1024%usize;
+    hm4 <- hashmap_HashMap_get_mut_back u64 n hm3 1024%usize 56%u64;
+    i0 <- hashmap_HashMap_get u64 n hm4 1024%usize;
     if negb (i0 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashmap_hash_map_remove_fwd u64 n hm4 1024%usize;
+      x <- hashmap_HashMap_remove u64 n hm4 1024%usize;
       match x with
       | None => Fail_ Failure
       | Some x0 =>
         if negb (x0 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hashmap_hash_map_remove_back u64 n hm4 1024%usize;
-          i1 <- hashmap_hash_map_get_fwd u64 n hm5 0%usize;
+          hm5 <- hashmap_HashMap_remove_back u64 n hm4 1024%usize;
+          i1 <- hashmap_HashMap_get u64 n hm5 0%usize;
           if negb (i1 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashmap_hash_map_get_fwd u64 n hm5 128%usize;
+            i2 <- hashmap_HashMap_get u64 n hm5 128%usize;
             if negb (i2 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashmap_hash_map_get_fwd u64 n hm5 1056%usize;
+              i3 <- hashmap_HashMap_get u64 n hm5 1056%usize;
               if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
 (** [hashmap_main::insert_on_disk]: forward function *)
-Definition insert_on_disk_fwd
+Definition insert_on_disk
   (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
-  p <- hashmap_utils_deserialize_fwd st;
+  p <- hashmap_utils_deserialize st;
   let (st0, hm) := p in
-  hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm key value;
-  p0 <- hashmap_utils_serialize_fwd hm0 st0;
+  hm0 <- hashmap_HashMap_insert u64 n hm key value;
+  p0 <- hashmap_utils_serialize hm0 st0;
   let (st1, _) := p0 in
   Return (st1, tt)
 .
 
 (** [hashmap_main::main]: forward function *)
-Definition main_fwd : result unit :=
+Definition main : result unit :=
   Return tt.
 
-(** Unit test for [hashmap_main::main] *)
-Check (main_fwd )%return.
-
 End HashmapMain_Funs .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
index 2d17cc29..5e376239 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
@@ -11,13 +11,13 @@ Import HashmapMain_Types.
 Module HashmapMain_Opaque.
 
 (** [hashmap_main::hashmap_utils::deserialize]: forward function *)
-Axiom hashmap_utils_deserialize_fwd
-  : state -> result (state * (Hashmap_hash_map_t u64))
+Axiom hashmap_utils_deserialize
+  : state -> result (state * (hashmap_HashMap_t u64))
 .
 
 (** [hashmap_main::hashmap_utils::serialize]: forward function *)
-Axiom hashmap_utils_serialize_fwd
-  : Hashmap_hash_map_t u64 -> state -> result (state * unit)
+Axiom hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state * unit)
 .
 
 End HashmapMain_Opaque .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Types.v b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
index 36aaaf25..95e5f35b 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Types.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
@@ -9,29 +9,29 @@ Local Open Scope Primitives_scope.
 Module HashmapMain_Types.
 
 (** [hashmap_main::hashmap::List] *)
-Inductive Hashmap_list_t (T : Type) :=
-| HashmapListCons : usize -> T -> Hashmap_list_t T -> Hashmap_list_t T
-| HashmapListNil : Hashmap_list_t T
+Inductive hashmap_List_t (T : Type) :=
+| Hashmap_List_Cons : usize -> T -> hashmap_List_t T -> hashmap_List_t T
+| Hashmap_List_Nil : hashmap_List_t T
 .
 
-Arguments HashmapListCons {T} _ _ _.
-Arguments HashmapListNil {T}.
+Arguments Hashmap_List_Cons { _ }.
+Arguments Hashmap_List_Nil { _ }.
 
 (** [hashmap_main::hashmap::HashMap] *)
-Record Hashmap_hash_map_t (T : Type) :=
-mkHashmap_hash_map_t {
-  Hashmap_hash_map_num_entries : usize;
-  Hashmap_hash_map_max_load_factor : (usize * usize);
-  Hashmap_hash_map_max_load : usize;
-  Hashmap_hash_map_slots : vec (Hashmap_list_t T);
+Record hashmap_HashMap_t (T : Type) :=
+mkhashmap_HashMap_t {
+  hashmap_HashMap_num_entries : usize;
+  hashmap_HashMap_max_load_factor : (usize * usize);
+  hashmap_HashMap_max_load : usize;
+  hashmap_HashMap_slots : alloc_vec_Vec (hashmap_List_t T);
 }
 .
 
-Arguments mkHashmap_hash_map_t {T} _ _ _ _.
-Arguments Hashmap_hash_map_num_entries {T}.
-Arguments Hashmap_hash_map_max_load_factor {T}.
-Arguments Hashmap_hash_map_max_load {T}.
-Arguments Hashmap_hash_map_slots {T}.
+Arguments mkhashmap_HashMap_t { _ }.
+Arguments hashmap_HashMap_num_entries { _ }.
+Arguments hashmap_HashMap_max_load_factor { _ }.
+Arguments hashmap_HashMap_max_load { _ }.
+Arguments hashmap_HashMap_slots { _ }.
 
 (** The state type used in the state-error monad *)
 Axiom state : Type.
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.