Regenerate the test files and add the fstar-split tests

2 files changed, 152 insertions, 138 deletions

diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/traits/Primitives.v
+++ b/tests/coq/traits/Primitives.v
@@ -67,8 +67,7 @@ Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self));
 }.
 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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ Axiom slice_len : forall (T : Type) (s : slice T), usize.
 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** Subslices *)
 
 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | right _ => Fail_ Failure
   end.
 
-(* The **forward** function shouldn't be used *)
-Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
-
 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 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 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
index 2448e8f3..7055e25d 100644
--- a/tests/coq/traits/Traits.v
+++ b/tests/coq/traits/Traits.v
@@ -17,7 +17,7 @@ Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
 Arguments mkBoolTrait_t { _ }.
 Arguments BoolTrait_t_get_bool { _ }.
 
-(** [traits::{bool}::get_bool]: forward function
+(** [traits::{bool}::get_bool]:
     Source: 'src/traits.rs', lines 12:4-12:30 *)
 Definition bool_get_bool (self : bool) : result bool :=
   Return self.
@@ -28,24 +28,24 @@ Definition traits_BoolTraitBoolInst : BoolTrait_t bool := {|
   BoolTrait_t_get_bool := bool_get_bool;
 |}.
 
-(** [traits::BoolTrait::ret_true]: forward function
+(** [traits::BoolTrait::ret_true]:
     Source: 'src/traits.rs', lines 6:4-6:30 *)
 Definition boolTrait_ret_true
   {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool :=
   Return true
 .
 
-(** [traits::test_bool_trait_bool]: forward function
+(** [traits::test_bool_trait_bool]:
     Source: 'src/traits.rs', lines 17:0-17:44 *)
 Definition test_bool_trait_bool (x : bool) : result bool :=
   b <- bool_get_bool x;
   if b then boolTrait_ret_true traits_BoolTraitBoolInst x else Return false
 .
 
-(** [traits::{core::option::Option<T>#1}::get_bool]: forward function
+(** [traits::{core::option::Option<T>#1}::get_bool]:
     Source: 'src/traits.rs', lines 23:4-23:30 *)
 Definition option_get_bool (T : Type) (self : option T) : result bool :=
-  match self with | None => Return false | Some t => Return true end
+  match self with | None => Return false | Some _ => Return true end
 .
 
 (** Trait implementation: [traits::{core::option::Option<T>#1}]
@@ -55,7 +55,7 @@ Definition traits_BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait_t
   BoolTrait_t_get_bool := option_get_bool T;
 |}.
 
-(** [traits::test_bool_trait_option]: forward function
+(** [traits::test_bool_trait_option]:
     Source: 'src/traits.rs', lines 31:0-31:54 *)
 Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
   b <- option_get_bool T x;
@@ -64,7 +64,7 @@ Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
   else Return false
 .
 
-(** [traits::test_bool_trait]: forward function
+(** [traits::test_bool_trait]:
     Source: 'src/traits.rs', lines 35:0-35:50 *)
 Definition test_bool_trait
   (T : Type) (boolTraitTInst : BoolTrait_t T) (x : T) : result bool :=
@@ -80,7 +80,7 @@ Record ToU64_t (Self : Type) := mkToU64_t {
 Arguments mkToU64_t { _ }.
 Arguments ToU64_t_to_u64 { _ }.
 
-(** [traits::{u64#2}::to_u64]: forward function
+(** [traits::{u64#2}::to_u64]:
     Source: 'src/traits.rs', lines 44:4-44:26 *)
 Definition u64_to_u64 (self : u64) : result u64 :=
   Return self.
@@ -91,14 +91,14 @@ Definition traits_ToU64U64Inst : ToU64_t u64 := {|
   ToU64_t_to_u64 := u64_to_u64;
 |}.
 
-(** [traits::{(A, A)#3}::to_u64]: forward function
+(** [traits::{(A, A)#3}::to_u64]:
     Source: 'src/traits.rs', lines 50:4-50:26 *)
 Definition pair_to_u64
   (A : Type) (toU64AInst : ToU64_t A) (self : (A * A)) : result u64 :=
-  let (t, t0) := self in
+  let (t, t1) := self in
   i <- toU64AInst.(ToU64_t_to_u64) t;
-  i0 <- toU64AInst.(ToU64_t_to_u64) t0;
-  u64_add i i0
+  i1 <- toU64AInst.(ToU64_t_to_u64) t1;
+  u64_add i i1
 .
 
 (** Trait implementation: [traits::{(A, A)#3}]
@@ -108,20 +108,20 @@ Definition traits_ToU64TupleAAInst (A : Type) (toU64AInst : ToU64_t A) :
   ToU64_t_to_u64 := pair_to_u64 A toU64AInst;
 |}.
 
-(** [traits::f]: forward function
+(** [traits::f]:
     Source: 'src/traits.rs', lines 55:0-55:36 *)
 Definition f (T : Type) (toU64TInst : ToU64_t T) (x : (T * T)) : result u64 :=
   pair_to_u64 T toU64TInst x
 .
 
-(** [traits::g]: forward function
+(** [traits::g]:
     Source: 'src/traits.rs', lines 59:0-61:18 *)
 Definition g
   (T : Type) (toU64TupleTTInst : ToU64_t (T * T)) (x : (T * T)) : result u64 :=
   toU64TupleTTInst.(ToU64_t_to_u64) x
 .
 
-(** [traits::h0]: forward function
+(** [traits::h0]:
     Source: 'src/traits.rs', lines 66:0-66:24 *)
 Definition h0 (x : u64) : result u64 :=
   u64_to_u64 x.
@@ -133,7 +133,7 @@ Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }.
 Arguments mkWrapper_t { _ }.
 Arguments wrapper_x { _ }.
 
-(** [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+(** [traits::{traits::Wrapper<T>#4}::to_u64]:
     Source: 'src/traits.rs', lines 75:4-75:26 *)
 Definition wrapper_to_u64
   (T : Type) (toU64TInst : ToU64_t T) (self : Wrapper_t T) : result u64 :=
@@ -147,13 +147,13 @@ Definition traits_ToU64traitsWrapperTInst (T : Type) (toU64TInst : ToU64_t T) :
   ToU64_t_to_u64 := wrapper_to_u64 T toU64TInst;
 |}.
 
-(** [traits::h1]: forward function
+(** [traits::h1]:
     Source: 'src/traits.rs', lines 80:0-80:33 *)
 Definition h1 (x : Wrapper_t u64) : result u64 :=
   wrapper_to_u64 u64 traits_ToU64U64Inst x
 .
 
-(** [traits::h2]: forward function
+(** [traits::h2]:
     Source: 'src/traits.rs', lines 84:0-84:41 *)
 Definition h2
   (T : Type) (toU64TInst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
@@ -169,7 +169,7 @@ Record ToType_t (Self T : Type) := mkToType_t {
 Arguments mkToType_t { _ _ }.
 Arguments ToType_t_to_type { _ _ }.
 
-(** [traits::{u64#5}::to_type]: forward function
+(** [traits::{u64#5}::to_type]:
     Source: 'src/traits.rs', lines 93:4-93:28 *)
 Definition u64_to_type (self : u64) : result bool :=
   Return (self s> 0%u64).
@@ -190,7 +190,7 @@ Record OfType_t (Self : Type) := mkOfType_t {
 Arguments mkOfType_t { _ }.
 Arguments OfType_t_of_type { _ }.
 
-(** [traits::h3]: forward function
+(** [traits::h3]:
     Source: 'src/traits.rs', lines 104:0-104:50 *)
 Definition h3
   (T1 T2 : Type) (ofTypeT1Inst : OfType_t T1) (toTypeT2T1Inst : ToType_t T2 T1)
@@ -211,7 +211,7 @@ Arguments mkOfTypeBis_t { _ _ }.
 Arguments OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst { _ _ }.
 Arguments OfTypeBis_t_of_type { _ _ }.
 
-(** [traits::h4]: forward function
+(** [traits::h4]:
     Source: 'src/traits.rs', lines 118:0-118:57 *)
 Definition h4
   (T1 T2 : Type) (ofTypeBisT1T2Inst : OfTypeBis_t T1 T2) (toTypeT2T1Inst :
@@ -238,7 +238,7 @@ Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
 Arguments mkTestType_test_TestTrait_t { _ }.
 Arguments TestType_test_TestTrait_t_test { _ }.
 
-(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]:
     Source: 'src/traits.rs', lines 139:12-139:34 *)
 Definition testType_test_TestType1_test
   (self : TestType_test_TestType1_t) : result bool :=
@@ -252,21 +252,21 @@ Definition traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst
   TestType_test_TestTrait_t_test := testType_test_TestType1_test;
 |}.
 
-(** [traits::{traits::TestType<T>#6}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test]:
     Source: 'src/traits.rs', lines 126:4-126:36 *)
 Definition testType_test
   (T : Type) (toU64TInst : ToU64_t T) (self : TestType_t T) (x : T) :
   result bool
   :=
-  x0 <- toU64TInst.(ToU64_t_to_u64) x;
-  if x0 s> 0%u64 then testType_test_TestType1_test 0%u64 else Return false
+  x1 <- toU64TInst.(ToU64_t_to_u64) x;
+  if x1 s> 0%u64 then testType_test_TestType1_test 0%u64 else Return false
 .
 
 (** [traits::BoolWrapper]
     Source: 'src/traits.rs', lines 150:0-150:22 *)
 Definition BoolWrapper_t : Type := bool.
 
-(** [traits::{traits::BoolWrapper#7}::to_type]: forward function
+(** [traits::{traits::BoolWrapper#7}::to_type]:
     Source: 'src/traits.rs', lines 156:4-156:25 *)
 Definition boolWrapper_to_type
   (T : Type) (toTypeBoolTInst : ToType_t bool T) (self : BoolWrapper_t) :
@@ -312,8 +312,7 @@ Arguments WithConstTy_t_f { _ _ }.
 Definition bool_len1_body : result usize := Return 12%usize.
 Definition bool_len1_c : usize := bool_len1_body%global.
 
-(** [traits::{bool#8}::f]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [traits::{bool#8}::f]:
     Source: 'src/traits.rs', lines 180:4-180:39 *)
 Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
   Return i.
@@ -329,7 +328,7 @@ Definition traits_WithConstTyBool32Inst : WithConstTy_t bool 32%usize := {|
   WithConstTy_t_f := bool_f;
 |}.
 
-(** [traits::use_with_const_ty1]: forward function
+(** [traits::use_with_const_ty1]:
     Source: 'src/traits.rs', lines 183:0-183:75 *)
 Definition use_with_const_ty1
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) :
@@ -338,7 +337,7 @@ Definition use_with_const_ty1
   let i := withConstTyHLENInst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
 .
 
-(** [traits::use_with_const_ty2]: forward function
+(** [traits::use_with_const_ty2]:
     Source: 'src/traits.rs', lines 187:0-187:73 *)
 Definition use_with_const_ty2
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
@@ -348,7 +347,7 @@ Definition use_with_const_ty2
   Return tt
 .
 
-(** [traits::use_with_const_ty3]: forward function
+(** [traits::use_with_const_ty3]:
     Source: 'src/traits.rs', lines 189:0-189:80 *)
 Definition use_with_const_ty3
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
@@ -359,12 +358,12 @@ Definition use_with_const_ty3
     x
 .
 
-(** [traits::test_where1]: forward function
+(** [traits::test_where1]:
     Source: 'src/traits.rs', lines 193:0-193:40 *)
 Definition test_where1 (T : Type) (_x : T) : result unit :=
   Return tt.
 
-(** [traits::test_where2]: forward function
+(** [traits::test_where2]:
     Source: 'src/traits.rs', lines 194:0-194:57 *)
 Definition test_where2
   (T : Type) (withConstTyT32Inst : WithConstTy_t T 32%usize) (_x : u32) :
@@ -403,16 +402,25 @@ Arguments mkChildTrait_t { _ }.
 Arguments ChildTrait_tChildTrait_t_ParentTrait0SelfInst { _ }.
 Arguments ChildTrait_tChildTrait_t_ParentTrait1SelfInst { _ }.
 
-(** [traits::test_child_trait1]: forward function
-    Source: 'src/traits.rs', lines 209:0-209:56 *)
+(** [traits::test_parent_trait0]:
+    Source: 'src/traits.rs', lines 208:0-208:57 *)
+Definition test_parent_trait0
+  (T : Type) (parentTrait0TInst : ParentTrait0_t T) (x : T) :
+  result parentTrait0TInst.(ParentTrait0_tParentTrait0_t_W)
+  :=
+  parentTrait0TInst.(ParentTrait0_t_get_w) x
+.
+
+(** [traits::test_child_trait1]:
+    Source: 'src/traits.rs', lines 213:0-213:56 *)
 Definition test_child_trait1
   (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) : result string :=
   childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_t_get_name)
     x
 .
 
-(** [traits::test_child_trait2]: forward function
-    Source: 'src/traits.rs', lines 213:0-213:54 *)
+(** [traits::test_child_trait2]:
+    Source: 'src/traits.rs', lines 217:0-217:54 *)
 Definition test_child_trait2
   (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) :
   result
@@ -422,8 +430,8 @@ Definition test_child_trait2
     x
 .
 
-(** [traits::order1]: forward function
-    Source: 'src/traits.rs', lines 219:0-219:59 *)
+(** [traits::order1]:
+    Source: 'src/traits.rs', lines 223:0-223:59 *)
 Definition order1
   (T U : Type) (parentTrait0TInst : ParentTrait0_t T) (parentTrait0UInst :
   ParentTrait0_t U) :
@@ -433,7 +441,7 @@ Definition order1
 .
 
 (** Trait declaration: [traits::ChildTrait1]
-    Source: 'src/traits.rs', lines 222:0-222:35 *)
+    Source: 'src/traits.rs', lines 226:0-226:35 *)
 Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
   ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst : ParentTrait1_t Self;
 }.
@@ -442,19 +450,19 @@ Arguments mkChildTrait1_t { _ }.
 Arguments ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst { _ }.
 
 (** Trait implementation: [traits::{usize#9}]
-    Source: 'src/traits.rs', lines 224:0-224:27 *)
+    Source: 'src/traits.rs', lines 228:0-228:27 *)
 Definition traits_ParentTrait1UsizeInst : ParentTrait1_t usize
   := mkParentTrait1_t.
 
 (** Trait implementation: [traits::{usize#10}]
-    Source: 'src/traits.rs', lines 225:0-225:26 *)
+    Source: 'src/traits.rs', lines 229:0-229:26 *)
 Definition traits_ChildTrait1UsizeInst : ChildTrait1_t usize := {|
   ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst :=
     traits_ParentTrait1UsizeInst;
 |}.
 
 (** Trait declaration: [traits::Iterator]
-    Source: 'src/traits.rs', lines 229:0-229:18 *)
+    Source: 'src/traits.rs', lines 233:0-233:18 *)
 Record Iterator_t (Self : Type) := mkIterator_t {
   Iterator_tIterator_t_Item : Type;
 }.
@@ -463,7 +471,7 @@ Arguments mkIterator_t { _ }.
 Arguments Iterator_tIterator_t_Item { _ }.
 
 (** Trait declaration: [traits::IntoIterator]
-    Source: 'src/traits.rs', lines 233:0-233:22 *)
+    Source: 'src/traits.rs', lines 237:0-237:22 *)
 Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
   IntoIterator_tIntoIterator_t_Item : Type;
   IntoIterator_tIntoIterator_t_IntoIter : Type;
@@ -480,13 +488,13 @@ Arguments IntoIterator_tIntoIterator_t_IntoIter_clause_0 { _ }.
 Arguments IntoIterator_t_into_iter { _ }.
 
 (** Trait declaration: [traits::FromResidual]
-    Source: 'src/traits.rs', lines 250:0-250:21 *)
+    Source: 'src/traits.rs', lines 254:0-254:21 *)
 Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
 
 Arguments mkFromResidual_t { _ _ }.
 
 (** Trait declaration: [traits::Try]
-    Source: 'src/traits.rs', lines 246:0-246:48 *)
+    Source: 'src/traits.rs', lines 250:0-250:48 *)
 Record Try_t (Self : Type) := mkTry_t {
   Try_tTry_t_Residual : Type;
   Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst : FromResidual_t Self
@@ -498,7 +506,7 @@ Arguments Try_tTry_t_Residual { _ }.
 Arguments Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst { _ }.
 
 (** Trait declaration: [traits::WithTarget]
-    Source: 'src/traits.rs', lines 252:0-252:20 *)
+    Source: 'src/traits.rs', lines 256:0-256:20 *)
 Record WithTarget_t (Self : Type) := mkWithTarget_t {
   WithTarget_tWithTarget_t_Target : Type;
 }.
@@ -507,7 +515,7 @@ Arguments mkWithTarget_t { _ }.
 Arguments WithTarget_tWithTarget_t_Target { _ }.
 
 (** Trait declaration: [traits::ParentTrait2]
-    Source: 'src/traits.rs', lines 256:0-256:22 *)
+    Source: 'src/traits.rs', lines 260:0-260:22 *)
 Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
   ParentTrait2_tParentTrait2_t_U : Type;
   ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
@@ -519,7 +527,7 @@ Arguments ParentTrait2_tParentTrait2_t_U { _ }.
 Arguments ParentTrait2_tParentTrait2_t_U_clause_0 { _ }.
 
 (** Trait declaration: [traits::ChildTrait2]
-    Source: 'src/traits.rs', lines 260:0-260:35 *)
+    Source: 'src/traits.rs', lines 264:0-264:35 *)
 Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
   ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst : ParentTrait2_t Self;
   ChildTrait2_t_convert :
@@ -533,25 +541,25 @@ Arguments ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst { _ }.
 Arguments ChildTrait2_t_convert { _ }.
 
 (** Trait implementation: [traits::{u32#11}]
-    Source: 'src/traits.rs', lines 264:0-264:23 *)
+    Source: 'src/traits.rs', lines 268:0-268:23 *)
 Definition traits_WithTargetU32Inst : WithTarget_t u32 := {|
   WithTarget_tWithTarget_t_Target := u32;
 |}.
 
 (** Trait implementation: [traits::{u32#12}]
-    Source: 'src/traits.rs', lines 268:0-268:25 *)
+    Source: 'src/traits.rs', lines 272:0-272:25 *)
 Definition traits_ParentTrait2U32Inst : ParentTrait2_t u32 := {|
   ParentTrait2_tParentTrait2_t_U := u32;
   ParentTrait2_tParentTrait2_t_U_clause_0 := traits_WithTargetU32Inst;
 |}.
 
-(** [traits::{u32#13}::convert]: forward function
-    Source: 'src/traits.rs', lines 273:4-273:29 *)
+(** [traits::{u32#13}::convert]:
+    Source: 'src/traits.rs', lines 277:4-277:29 *)
 Definition u32_convert (x : u32) : result u32 :=
   Return x.
 
 (** Trait implementation: [traits::{u32#13}]
-    Source: 'src/traits.rs', lines 272:0-272:24 *)
+    Source: 'src/traits.rs', lines 276:0-276:24 *)
 Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
   ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst :=
     traits_ParentTrait2U32Inst;
@@ -559,7 +567,7 @@ Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
 |}.
 
 (** Trait declaration: [traits::CFnOnce]
-    Source: 'src/traits.rs', lines 286:0-286:23 *)
+    Source: 'src/traits.rs', lines 290:0-290:23 *)
 Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
   CFnOnce_tCFnOnce_t_Output : Type;
   CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
@@ -570,31 +578,48 @@ Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
 Arguments CFnOnce_t_call_once { _ _ }.
 
 (** Trait declaration: [traits::CFnMut]
-    Source: 'src/traits.rs', lines 292:0-292:37 *)
+    Source: 'src/traits.rs', lines 296:0-296:37 *)
 Record CFnMut_t (Self Args : Type) := mkCFnMut_t {
   CFnMut_tCFnMut_t_CFnOnceSelfArgsInst : CFnOnce_t Self Args;
   CFnMut_t_call_mut : Self -> Args -> result
-    (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output);
-  CFnMut_t_call_mut_back : Self -> Args ->
-    (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) ->
-    result Self;
+    ((CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) *
+    Self);
 }.
 
 Arguments mkCFnMut_t { _ _ }.
 Arguments CFnMut_tCFnMut_t_CFnOnceSelfArgsInst { _ _ }.
 Arguments CFnMut_t_call_mut { _ _ }.
-Arguments CFnMut_t_call_mut_back { _ _ }.
 
 (** Trait declaration: [traits::CFn]
-    Source: 'src/traits.rs', lines 296:0-296:33 *)
+    Source: 'src/traits.rs', lines 300:0-300:33 *)
 Record CFn_t (Self Args : Type) := mkCFn_t {
   CFn_tCFn_t_CFnMutSelfArgsInst : CFnMut_t Self Args;
-  CFn_t_call_mut : Self -> Args -> result
+  CFn_t_call : Self -> Args -> result
     (CFn_tCFn_t_CFnMutSelfArgsInst).(CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output);
 }.
 
 Arguments mkCFn_t { _ _ }.
 Arguments CFn_tCFn_t_CFnMutSelfArgsInst { _ _ }.
-Arguments CFn_t_call_mut { _ _ }.
+Arguments CFn_t_call { _ _ }.
+
+(** Trait declaration: [traits::GetTrait]
+    Source: 'src/traits.rs', lines 304:0-304:18 *)
+Record GetTrait_t (Self : Type) := mkGetTrait_t {
+  GetTrait_tGetTrait_t_W : Type;
+  GetTrait_t_get_w : Self -> result GetTrait_tGetTrait_t_W;
+}.
+
+Arguments mkGetTrait_t { _ }.
+Arguments GetTrait_tGetTrait_t_W { _ }.
+Arguments GetTrait_t_get_w { _ }.
+
+(** [traits::test_get_trait]:
+    Source: 'src/traits.rs', lines 309:0-309:49 *)
+Definition test_get_trait
+  (T : Type) (getTraitTInst : GetTrait_t T) (x : T) :
+  result getTraitTInst.(GetTrait_tGetTrait_t_W)
+  :=
+  getTraitTInst.(GetTrait_t_get_w) x
+.
 
 End Traits.