(*moved to compcert_rmaps
Definition funsig := (list (ident*type) * type)%type. (* argument and result signature *)

Definition strict_bool_val (v: val) (t: type) : option bool :=
   match v, t with
   | Vint n, Tint _ _ _ => Some (negb (Int.eq n Int.zero))
   | Vlong n, Tlong _ _ => Some (negb (Int64.eq n Int64.zero))
   | (Vint n), (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _ ) =>
             if Archi.ptr64 then None else if Int.eq n Int.zero then Some false else None
   | Vlong n, (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _ ) =>
            if Archi.ptr64 then if Int64.eq n Int64.zero then Some false else None else None
   | Vptr b ofs, (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _ ) => Some true
   | Vfloat f, Tfloat F64 _ => Some (negb(Float.cmp Ceq f Float.zero))
   | Vsingle f, Tfloat F32 _ => Some (negb(Float32.cmp Ceq f Float32.zero))
   | _, _ => None
   end.
*)

(*moved to mpred
(* TWO ALTERNATE WAYS OF DOING LIFTING *)
(* LIFTING METHOD ONE: *)
Definition lift0 {B} (P: B) : environ -> B := fun _ => P.
Definition lift1 {A1 B} (P: A1 -> B) (f1: environ -> A1) : environ -> B := fun rho => P (f1 rho).
Definition lift2 {A1 A2 B} (P: A1 -> A2 -> B) (f1: environ -> A1) (f2: environ -> A2):
   environ -> B := fun rho => P (f1 rho) (f2 rho).
Definition lift3 {A1 A2 A3 B} (P: A1 -> A2 -> A3 -> B)
     (f1: environ -> A1) (f2: environ -> A2) (f3: environ -> A3) :  environ -> B :=
     fun rho => P (f1 rho) (f2 rho) (f3 rho).
Definition lift4 {A1 A2 A3 A4 B} (P: A1 -> A2 -> A3 -> A4 -> B)
     (f1: environ -> A1) (f2: environ -> A2) (f3: environ -> A3)(f4: environ -> A4):  environ -> B :=
     fun rho => P (f1 rho) (f2 rho) (f3 rho) (f4 rho).

(* LIFTING METHOD TWO: *)
Set Warnings "-projection-no-head-constant,-redundant-canonical-projection".
Canonical Structure LiftEnviron := Tend environ.
Set Warnings "+projection-no-head-constant,+redundant-canonical-projection".

Ltac super_unfold_lift :=
  cbv delta [liftx LiftEnviron Tarrow Tend lift_S lift_T lift_prod
  lift_last lifted lift_uncurry_open lift_curry lift lift0 lift1 lift2 lift3] beta iota in *.

Definition eval_id (id: ident) (rho: environ) := force_val (Map.get (te_of rho) id).

 *)

(** Functions for evaluating expressions in environments,
these return vundef if something goes wrong, meaning they always return some value **)

Definition eval_unop (op: Cop.unary_operation) (t1 : type) :=
       force_val1 (Clight_Cop2.sem_unary_operation op t1).Definition op_to_cmp cop :=
match cop with
| Cop.Oeq => Ceq | Cop.One =>  Cne
| Cop.Olt => Clt | Cop.Ogt =>  Cgt
| Cop.Ole => Cle | Cop.Oge =>  Cge
| _ => Ceq (*doesn't matter*)
end.Definition is_comparison op :=
match op with
  | Cop.Oeq | Cop.One | Cop.Olt | Cop.Ogt | Cop.Ole | Cop.Oge => true
  | _ => false
end.Definition eval_binop {CS:compspecs} (op: Cop.binary_operation) (t1 t2 : type) :=
       force_val2 (Clight_Cop2.sem_binary_operation'  op t1 t2).Definition eval_cast (t1 t2 : type) :=
  force_val1 (sem_cast t1 t2).Definition eval_var (id:ident) (ty: type) (rho: environ) : val :=
                         match Map.get (ve_of rho) id with
                         | Some (b,ty') => if eqb_type ty ty'
                                                    then Vptr b Ptrofs.zero
                                                    else Vundef
                         | None =>
                            match Map.get (ge_of rho) id with
                            | Some b => Vptr b Ptrofs.zero
                            | None => Vundef
                            end
                        end.Definition deref_noload (ty: type) : val -> val :=
 match access_mode ty with
 | By_reference => Datatypes.id
 | _ => always Vundef
 end.(** Beginning of typechecking **)

Definition bool_type (t: type) : bool :=
  match t with
  | Tpointer _ _ => negb (eqb_type t int_or_ptr_type)
  | Tint _ _ _ | Tlong _ _ | Tarray _ _ _ | Tfunction _ _ _ | Tfloat _ _ =>  true
  | _ => false
  end.Definition is_scalar_type (ty:type) : bool :=
match ty with
| Tint _ _ _ => true
| Tfloat _ _ => true
| _ => false
end.Definition is_int_type ty :=
match ty with
| Tint _ _ _ => true
| _ => false
end.Definition is_int32_type ty :=
match ty with
| Tint I32 _ _ => true
| _ => false
end.Definition is_long_type ty :=
match ty with
| Tlong _ _ => true
| _ => false
end.Definition is_ptrofs_type :=
 if Archi.ptr64 then is_long_type else is_int32_type.Definition is_float_type ty :=
match ty with
| Tfloat F64 _ => true
| _ => false
end.Definition is_single_type ty :=
match ty with
| Tfloat F32 _ => true
| _ => false
end.Definition is_anyfloat_type ty :=
match ty with
| Tfloat F64 _ => true
| Tfloat F32 _ => true
| _ => false
end.Definition is_pointer_type ty :=
match ty with
| (Tpointer _ _ 
   | Tarray _ _ _ | Tfunction _ _ _
   | Tstruct _ _  | Tunion _ _) => 
    negb (eqb_type ty int_or_ptr_type)
| _ => false
end.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_error :=
| op_result_type : expr -> tc_error
| arg_type : expr -> tc_error
| pp_compare_size_0 : type -> tc_error
| pp_compare_size_exceed : type -> tc_error
| invalid_cast : type -> type -> tc_error
| invalid_cast_result : type -> type -> tc_error
| invalid_expression : expr -> tc_error
| var_not_in_tycontext : tycontext -> positive  -> tc_error
| mismatch_context_type : type -> type -> tc_error
| deref_byvalue : type -> tc_error
| volatile_load : type -> tc_error
| invalid_field_access : expr -> tc_error
| invalid_composite_name: ident -> tc_error
| invalid_struct_field : ident (* field name *) -> ident (* struct name *) -> tc_error
| invalid_lvalue : expr -> tc_error
| wrong_signature : tc_error
| int_or_ptr_type_error : tc_error
| miscellaneous_typecheck_error : tc_error.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Inductive tc_assert :=
| tc_FF: tc_error -> tc_assert
| tc_TT : tc_assert
| tc_andp': tc_assert -> tc_assert -> tc_assert
| tc_orp' : tc_assert -> tc_assert -> tc_assert
| tc_nonzero': expr -> tc_assert
| tc_iszero': expr -> tc_assert
| tc_isptr: expr -> tc_assert
| tc_isint: expr -> tc_assert
| tc_islong: expr -> tc_assert
| tc_test_eq': expr -> expr -> tc_assert
| tc_test_order': expr -> expr -> tc_assert
| tc_ilt': expr -> int -> tc_assert
| tc_llt': expr -> int64 -> tc_assert
| tc_Zle: expr -> Z -> tc_assert
| tc_Zge: expr -> Z -> tc_assert
| tc_samebase: expr -> expr -> tc_assert
| tc_nodivover': expr -> expr -> tc_assert
| tc_initialized: PTree.elt -> type -> tc_assert
| tc_nosignedover: (Z->Z->Z) -> expr -> expr -> tc_assert.Definition tc_noproof := tc_FF miscellaneous_typecheck_error.Definition tc_iszero {CS: compspecs} (e: expr) : tc_assert :=
  match eval_expr e any_environ with
  | Vint i => if Int.eq i Int.zero then tc_TT else tc_FF (pp_compare_size_0 Tvoid)
  | Vlong i => if Int64.eq i Int64.zero then tc_TT else tc_FF (pp_compare_size_0 Tvoid)
  | _ => tc_iszero' e
  end.Definition tc_nonzero {CS: compspecs} (e: expr) : tc_assert :=
  match eval_expr e any_environ with
   | Vint i => if negb (Int.eq i Int.zero) then tc_TT else tc_nonzero' e
   | Vlong i => if negb (Int64.eq i Int64.zero) then tc_TT else tc_nonzero' e
   | _ => tc_nonzero' e
   end.Definition tc_test_eq {CS: compspecs} (e1 e2: expr) : tc_assert :=
 match eval_expr e1 any_environ, eval_expr e2 any_environ with
 | Vint i, Vint j => if andb (negb Archi.ptr64)
                             (andb (Int.eq i Int.zero) (Int.eq j Int.zero))
                             then tc_TT else tc_test_eq' e1 e2
 | Vlong i, Vlong j => if andb Archi.ptr64
                             (andb (Int64.eq i Int64.zero) (Int64.eq j Int64.zero))
                             then tc_TT else tc_test_eq' e1 e2
 | _, _ => tc_test_eq' e1 e2
 end.Definition tc_test_order {CS: compspecs} (e1 e2: expr) : tc_assert :=
 match eval_expr e1 any_environ, eval_expr e2 any_environ with
 | Vint i, Vint j => if  andb (negb Archi.ptr64)
                                  (andb (Int.eq i Int.zero) (Int.eq j Int.zero))
                             then tc_TT else tc_test_order' e1 e2
 | Vlong i, Vlong j => if  andb Archi.ptr64
                                  (andb (Int64.eq i Int64.zero) (Int64.eq j Int64.zero))
                             then tc_TT else tc_test_order' e1 e2
 | _, _ => tc_test_order' e1 e2
 end.Definition tc_nodivover {CS: compspecs} (e1 e2: expr) : tc_assert :=
 match eval_expr e1 any_environ, eval_expr e2 any_environ with
                           | Vint n1, Vint n2 => if (negb
                                   (Int.eq n1 (Int.repr Int.min_signed)
                                    && Int.eq n2 Int.mone))
                                     then tc_TT else tc_nodivover' e1 e2
                           | Vlong n1, Vlong n2 => if (negb
                                   (Int64.eq n1 (Int64.repr Int64.min_signed)
                                    && Int64.eq n2 Int64.mone))
                                     then tc_TT else tc_nodivover' e1 e2
                           | Vint n1, Vlong n2 => tc_TT
                           | Vlong n1, Vint n2 => if (negb
                                   (Int64.eq n1 (Int64.repr Int64.min_signed)
                                    && Int.eq n2 Int.mone))
                                     then tc_TT else tc_nodivover' e1 e2
                           | _ , _ => tc_nodivover' e1 e2
                          end.Definition if_expr_signed (e: expr) (tc: tc_assert) : tc_assert :=
 match typeof e with
 | Tint _ Signed _ => tc
 | Tlong Signed _ => tc
 | _ => tc_TT
 end.Definition tc_nobinover (op: Z->Z->Z) {CS: compspecs} (e1 e2: expr) : tc_assert :=
 if_expr_signed e1
 match eval_expr e1 any_environ, eval_expr e2 any_environ with
 | Vint n1, Vint n2 => 
    if range_s32 (op (Int.signed n1) (Int.signed n2))
     then tc_TT else tc_nosignedover op e1 e2
 | Vlong n1, Vlong n2 => 
    if range_s64 (op (Int64.signed n1) (Int64.signed n2))
     then tc_TT else tc_nosignedover op e1 e2
 | Vint n1, Vlong n2 =>
    if range_s64 (op (Int.signed n1) (Int64.signed n2))
     then tc_TT else tc_nosignedover op e1 e2
 | Vlong n1, Vint n2 =>
    if range_s64 (op (Int64.signed n1) (Int.signed n2))
     then tc_TT else tc_nosignedover op e1 e2
 | _ , _ => tc_nosignedover op e1 e2
 end.Definition tc_andp (a1: tc_assert) (a2 : tc_assert) : tc_assert :=
match a1 with
| tc_TT => a2
| tc_FF e => tc_FF e
| _ => match a2 with
      | tc_TT => a1
      | tc_FF e => tc_FF e
      | _ => tc_andp' a1 a2
      end
end.Definition tc_orp (a1: tc_assert) (a2 : tc_assert) : tc_assert :=
match a1 with
| tc_TT => tc_TT
| tc_FF _ => a2
| _ => match a2 with
       | tc_TT => tc_TT
       | tc_FF _ => a1
       | _ => tc_orp' a1 a2
       end
end.Definition tc_bool (b : bool) (e: tc_error) :=
if b then tc_TT else tc_FF e.Definition check_pp_int {CS: compspecs} e1 e2 op t e :=
  match op with
  | Cop.Oeq | Cop.One =>
      tc_andp
        (tc_test_eq e1 e2)
        (tc_bool (is_int_type t) (op_result_type e))
  | Cop.Ole | Cop.Olt | Cop.Oge | Cop.Ogt =>
      tc_andp
        (tc_test_order e1 e2)
        (tc_bool (is_int_type t) (op_result_type e))
  | _ => tc_noproof
  end.Definition binarithType t1 t2 ty deferr reterr : tc_assert :=
  match Cop.classify_binarith t1 t2 with
  | Cop.bin_case_i sg =>  tc_bool (is_int32_type ty) reterr
  | Cop.bin_case_l sg => tc_bool (is_long_type ty) reterr
  | Cop.bin_case_f   => tc_bool (is_float_type ty) reterr
  | Cop.bin_case_s   => tc_bool (is_single_type ty) reterr
  | Cop.bin_default => tc_FF deferr
  end.Definition is_numeric_type t :=
match t with Tint _ _ _ | Tlong _ _ | Tfloat _ _ => true | _ => false end.Definition tc_ilt {CS: compspecs} (e: expr) (j: int) :=
    match eval_expr e any_environ with
    | Vint i => if Int.ltu i j then tc_TT else tc_ilt' e j
    | _ => tc_ilt' e j
    end.Definition tc_llt {CS: compspecs} (e: expr) (j: int64) :=
    match eval_expr e any_environ with
    | Vlong i => if Int64.ltu i j then tc_TT else tc_llt' e j
    | _ => tc_llt' e j
    end.Definition tc_int_or_ptr_type (t: type) : tc_assert :=
 tc_bool (negb (eqb_type t int_or_ptr_type)) int_or_ptr_type_error.Definition isUnOpResultType {CS: compspecs} op a ty : tc_assert :=
match op with
  | Cop.Onotbool => match typeof a with
                        | Tint _ _ _ | Tlong _ _ | Tfloat _ _ =>
                                        tc_bool (is_int_type ty) (op_result_type a)
                        | Tpointer _ _ => 
                             tc_andp (tc_int_or_ptr_type (typeof a))
                             (tc_andp (tc_bool (is_int_type ty) (op_result_type a))
                              (tc_test_eq a 
                                (if Archi.ptr64 
                                 then Econst_long Int64.zero (Tlong Signed noattr)
                                 else Econst_int Int.zero (Tint I32 Signed noattr))))
                        | _ => tc_FF (op_result_type a)
                        end
  | Cop.Onotint => match Cop.classify_notint (typeof a) with
                        | Cop.notint_default => tc_FF (op_result_type a)
                        | Cop.notint_case_i _ => tc_bool (is_int32_type ty) (op_result_type a)
                        | Cop.notint_case_l _ => tc_bool (is_long_type ty) (op_result_type a)
                        end
  | Cop.Oneg => match Cop.classify_neg (typeof a) with
                    | Cop.neg_case_i sg => 
                          tc_andp (tc_bool (is_int32_type ty) (op_result_type a))
                          match (typeof a) with
                          | Tint _ Signed _ => tc_nosignedover Z.sub (Econst_int Int.zero (typeof a)) a
                          | Tlong Signed _ => tc_nosignedover Z.sub (Econst_long Int64.zero (typeof a)) a
                          | _ => tc_TT
                          end
                    | Cop.neg_case_f => tc_bool (is_float_type ty) (op_result_type a)
                    | Cop.neg_case_s => tc_bool (is_single_type ty) (op_result_type a)
                    | _ => tc_FF (op_result_type a)
                    end
  | Cop.Oabsfloat =>match Cop.classify_neg (typeof a) with
                    | Cop.neg_case_i sg => tc_bool (is_float_type ty) (op_result_type a)
                    | Cop.neg_case_l _ => tc_bool (is_float_type ty) (op_result_type a)
                    | Cop.neg_case_f => tc_bool (is_float_type ty) (op_result_type a)
                    | Cop.neg_case_s => tc_bool (is_float_type ty) (op_result_type a)
                    | _ => tc_FF (op_result_type a)
                    end
end.(*Moved to Cop2.
  Definition size_t := if Archi.ptr64 then tulong else tuint.*)

Definition isBinOpResultType {CS: compspecs} op a1 a2 ty : tc_assert :=
let e := (Ebinop op a1 a2 ty) in
let reterr := op_result_type e in
let deferr := arg_type e in
match op with
  | Cop.Oadd => match Cop.classify_add (typeof a1) (typeof a2) with
                    | Cop.add_case_pi t si => tc_andp (tc_andp (tc_andp (tc_isptr a1)
                                           (tc_bool (complete_type cenv_cs t) reterr))
                                            (tc_int_or_ptr_type (typeof a1)))
                                            (tc_bool (is_pointer_type ty) reterr)
                    | Cop.add_case_ip si t => tc_andp (tc_andp (tc_andp (tc_isptr a2)
                                           (tc_bool (complete_type cenv_cs t) reterr))
                                            (tc_int_or_ptr_type (typeof a2)))
                                            (tc_bool (is_pointer_type ty) reterr)
                    | Cop.add_case_pl t => tc_andp (tc_andp (tc_andp (tc_isptr a1)
                                           (tc_bool (complete_type cenv_cs t) reterr))
                                            (tc_int_or_ptr_type (typeof a1)))
                                            (tc_bool (is_pointer_type ty) reterr)
                    | Cop.add_case_lp t => tc_andp (tc_andp (tc_andp (tc_isptr a2)
                                           (tc_bool (complete_type cenv_cs t) reterr))
                                            (tc_int_or_ptr_type (typeof a2)))
                                            (tc_bool (is_pointer_type ty) reterr)
                    | Cop.add_default => tc_andp 
                                           (binarithType (typeof a1) (typeof a2) ty deferr reterr)
                                           (tc_nobinover Z.add a1 a2)
            end
  | Cop.Osub => match Cop.classify_sub (typeof a1) (typeof a2) with
                    | Cop.sub_case_pi t si => tc_andp (tc_andp (tc_andp (tc_isptr a1)
                                           (tc_bool (complete_type cenv_cs t) reterr))
                                            (tc_int_or_ptr_type (typeof a1)))
                                            (tc_bool (is_pointer_type ty) reterr)
                    | Cop.sub_case_pl t => tc_andp (tc_andp (tc_andp (tc_isptr a1)
                                           (tc_bool (complete_type cenv_cs t) reterr))
                                            (tc_int_or_ptr_type (typeof a1)))
                                            (tc_bool (is_pointer_type ty) reterr)
                    | Cop.sub_case_pp t =>
                             tc_andp (tc_andp (tc_andp (tc_andp (tc_andp (tc_andp (tc_andp 
                               (tc_andp (tc_samebase a1 a2)
                             (tc_isptr a1))
                              (tc_isptr a2))
                               (tc_int_or_ptr_type (typeof a1)))
                               (tc_int_or_ptr_type (typeof a2)))
                               (tc_bool (is_ptrofs_type ty) reterr))
			        (tc_bool (negb (Z.eqb (sizeof t) 0))
                                      (pp_compare_size_0 t)))
                                 (tc_bool (complete_type cenv_cs t) reterr))
                                   (tc_bool (Z.leb (sizeof t) Ptrofs.max_signed)
                                          (pp_compare_size_exceed t))
                    | Cop.sub_default => tc_andp 
                                    (binarithType (typeof a1) (typeof a2) ty deferr reterr)
                                    (tc_nobinover Z.sub a1 a2)
            end
  | Cop.Omul => tc_andp (binarithType (typeof a1) (typeof a2) ty deferr reterr)
                                    (tc_nobinover Z.mul a1 a2)
  | Cop.Omod => match Cop.classify_binarith (typeof a1) (typeof a2) with
                    | Cop.bin_case_i Unsigned =>
                           tc_andp (tc_nonzero a2)
                           (tc_bool (is_int32_type ty) reterr)
                    | Cop.bin_case_l Unsigned =>
                           tc_andp (tc_nonzero a2)
                           (tc_bool (is_long_type ty) reterr)
                    | Cop.bin_case_i Signed => tc_andp (tc_andp (tc_nonzero a2)
                                                      (tc_nodivover a1 a2))
                                                     (tc_bool (is_int32_type ty) reterr)
                    | Cop.bin_case_l Signed => tc_andp (tc_andp (tc_nonzero a2)
                                                      (tc_nodivover a1 a2))
                                                     (tc_bool (is_long_type ty) reterr)
                    | _ => tc_FF deferr
            end
  | Cop.Odiv => match Cop.classify_binarith (typeof a1) (typeof a2) with
                    | Cop.bin_case_i Unsigned => tc_andp (tc_nonzero a2) (tc_bool (is_int32_type ty) reterr)
                    | Cop.bin_case_l Unsigned => tc_andp (tc_nonzero a2) (tc_bool (is_long_type ty) reterr)
                    | Cop.bin_case_i Signed => tc_andp (tc_andp (tc_nonzero a2) (tc_nodivover a1 a2))
                                                        (tc_bool (is_int32_type ty) reterr)
                    | Cop.bin_case_l Signed => tc_andp (tc_andp (tc_nonzero a2) (tc_nodivover a1 a2))
                                                        (tc_bool (is_long_type ty) reterr)
                    | Cop.bin_case_f  =>  tc_bool (is_float_type ty) reterr
                    | Cop.bin_case_s  =>  tc_bool (is_single_type ty) reterr
                    | Cop.bin_default => tc_FF deferr
            end
  | Cop.Oshl | Cop.Oshr => match Cop.classify_shift (typeof a1) (typeof a2) with
                    | Cop.shift_case_ii _ =>  tc_andp (tc_ilt a2 Int.iwordsize) (tc_bool (is_int32_type ty)
                                                                                         reterr)
                    | Cop.shift_case_il _ =>  tc_andp (tc_llt a2 (Int64.repr 32)) (tc_bool (is_int32_type ty)
                                                                                         reterr)
                    | Cop.shift_case_li _ =>  tc_andp (tc_ilt a2 Int64.iwordsize') (tc_bool (is_long_type ty)
                                                                                         reterr)
                    | Cop.shift_case_ll _ =>  tc_andp (tc_llt a2 Int64.iwordsize) (tc_bool (is_long_type ty)
                                                                                         reterr)
                    | Cop.shift_default => tc_FF deferr
                   end
  | Cop.Oand | Cop.Oor | Cop.Oxor =>
                   match Cop.classify_binarith (typeof a1) (typeof a2) with
                    | Cop.bin_case_i _ =>tc_bool (is_int32_type ty) reterr
                    | Cop.bin_case_l _ =>tc_bool (is_long_type ty) reterr
                    | Cop.bin_case_f => tc_FF deferr
                    | Cop.bin_case_s => tc_FF deferr
                    | Cop.bin_default => tc_FF deferr
                   end
  | Cop.Oeq | Cop.One | Cop.Olt | Cop.Ogt | Cop.Ole | Cop.Oge =>
         match Cop.classify_cmp (typeof a1) (typeof a2) with
              | Cop.cmp_default =>
                           tc_bool (is_numeric_type (typeof a1)
                                         && is_numeric_type (typeof a2)
                                          && is_int_type ty)
                                             deferr
	            | Cop.cmp_case_pp => 
                     tc_andp (tc_andp (tc_int_or_ptr_type (typeof a1)) 
                                      (tc_int_or_ptr_type (typeof a2)))
                       (check_pp_int a1 a2 op ty e)
              | Cop.cmp_case_pi si =>
                     tc_andp (tc_int_or_ptr_type (typeof a1))
                       (check_pp_int a1 (Ecast a2 size_t) op ty e)
              | Cop.cmp_case_ip si => 
                     tc_andp (tc_int_or_ptr_type (typeof a2))
                    (check_pp_int (Ecast a1 size_t) a2 op ty e)
              | Cop.cmp_case_pl => 
                     tc_andp (tc_int_or_ptr_type (typeof a1))
                       (check_pp_int a1 (Ecast a2 size_t) op ty e)
              | Cop.cmp_case_lp => 
                     tc_andp (tc_int_or_ptr_type (typeof a2))
                    (check_pp_int (Ecast a1 size_t) a2 op ty e)
              end
  end.Definition isCastResultType {CS: compspecs} tfrom tto a : tc_assert :=
  (* missing casts from f2s and s2f *)
match classify_cast tfrom tto with
| Cop.cast_case_default => tc_FF (invalid_cast tfrom tto)
| Cop.cast_case_f2i _ Signed => tc_andp (tc_Zge a Int.min_signed ) (tc_Zle a Int.max_signed)
| Cop.cast_case_s2i _ Signed => tc_andp (tc_Zge a Int.min_signed ) (tc_Zle a Int.max_signed)
| Cop.cast_case_f2i _ Unsigned => tc_andp (tc_Zge a 0) (tc_Zle a Int.max_unsigned)
| Cop.cast_case_s2i _ Unsigned => tc_andp (tc_Zge a 0) (tc_Zle a Int.max_unsigned)
| Cop.cast_case_i2l _ => 
           tc_andp (tc_bool (is_int_type tfrom) (invalid_cast_result tfrom tto))
             (if is_pointer_type tto then tc_iszero a else tc_TT)
| Cop.cast_case_l2i _ _ => 
           tc_andp (tc_bool (is_long_type tfrom) (invalid_cast_result tfrom tto))
             (if is_pointer_type tto then tc_iszero a else tc_TT)
| Cop.cast_case_pointer  => 
           if eqb_type tfrom tto then tc_TT else
           if orb  (andb (is_pointer_type tto) (is_pointer_type tfrom))
                       (if Archi.ptr64
                        then (andb (is_long_type tto) (is_long_type tfrom)) 
                        else (andb (is_int_type tto) (is_int_type tfrom)))
           then tc_TT else 
           if (andb (eqb_type tto int_or_ptr_type) ((if Archi.ptr64 then is_long_type else is_int_type) tfrom))
           then tc_TT else
           if (andb (eqb_type tto int_or_ptr_type) (is_pointer_type tfrom))
           then tc_TT else
           if (andb (eqb_type tfrom int_or_ptr_type) (is_pointer_type tto))
           then tc_isptr a else
           if (andb (eqb_type tfrom int_or_ptr_type) ((if Archi.ptr64 then is_long_type else is_int_type) tto))
           then (if Archi.ptr64 then tc_islong else tc_isint) a
           else tc_iszero a
| Cop.cast_case_l2l => tc_bool (is_long_type tfrom && is_long_type tto) (invalid_cast_result tto tto)
| Cop.cast_case_void => tc_noproof
| Cop.cast_case_f2bool => tc_bool (is_float_type tfrom) (invalid_cast_result tfrom tto)
| Cop.cast_case_s2bool => tc_bool (is_single_type tfrom) (invalid_cast_result tfrom tto)
(*| Cop.cast_case_p2bool => tc_andp (tc_test_eq a (Econst_int Int.zero (Tint I32 Signed noattr)))
                                                (tc_bool (orb (is_int_type tfrom) (is_pointer_type tfrom)) (invalid_cast_result tfrom tto))
*)
      (* before CompCert 2.5: tc_bool (orb (is_int_type tfrom) (is_pointer_type tfrom)) (invalid_cast_result tfrom tto) *)
| Cop.cast_case_l2bool => 
      if is_pointer_type tfrom
      then tc_test_eq a (Econst_long Int64.zero (Tlong Unsigned noattr))
      else tc_TT
| Cop.cast_case_i2bool =>
      if is_pointer_type tfrom
      then tc_test_eq a (Econst_int Int.zero (Tint I32 Unsigned noattr))
      else tc_TT
| _ => match tto with
      | Tint _ _ _  => tc_bool (is_int_type tfrom) (invalid_cast_result tto tto)
      | Tfloat F64 _  => tc_bool (is_anyfloat_type tfrom) (invalid_cast_result tto tto)
      | Tfloat F32 _  => tc_bool (is_anyfloat_type tfrom) (invalid_cast_result tto tto)
      | _ => tc_FF (invalid_cast tfrom tto)
      end
end.(* A "neutral cast" from t1 to t2 is such that
  it satisfies the neutral_cast_lemma, i.e. if v already typechecks as t1
  then it will not be modified by casting to t2. *)
Definition is_neutral_cast t1 t2 :=
 match t1, t2 with
 | Tint IBool _ _, Tint _ _ _ => true
 | Tint I8 Signed _, Tint I8 Signed _ => true
 | Tint I8 Signed _, Tint I16 Signed _ => true
 | Tint I16 Signed _, Tint I16 Signed _ => true
 | Tint I8 Unsigned _, Tint I8 Unsigned _ => true
 | Tint I8 Unsigned _, Tint I16 Unsigned _ => true
 | Tint I16 Unsigned _, Tint I16 Unsigned _ => true
 | Tint _ _ _, Tint I32 _ _ => true
 | Tlong _ _, Tlong _ _ => true
 | Tfloat F64 _, Tfloat F64 _ => true
 | Tfloat F32 _, Tfloat F32 _ => true
 | Tpointer _ _, Tpointer _ _ => eqb_type t1 t2 
                    || negb (eqb_type t1 int_or_ptr_type) 
                     && negb (eqb_type t2 int_or_ptr_type)
 | _, _ => false
 end.Definition same_base_type t1 t2 : bool :=
match t1, t2 with
| (Tarray _ _ _ | Tfunction _ _ _),
   (Tpointer _ _ | Tarray _ _ _ | Tfunction _ _ _) =>
     Bool.eqb (eqb_type t1 int_or_ptr_type)
              (eqb_type t2 int_or_ptr_type)
| (Tstruct _ _ | Tunion _ _), (Tstruct _ _ | Tunion _ _ ) => true
| _, _ => false
end.Definition implicit_deref (t: type) : type :=
  match t with
  | Tarray t' _ _ => Tpointer t' noattr
  | _ => t
  end.Fixpoint tc_might_be_true (asn : tc_assert) :=
match asn with
 | tc_FF _ => false
 | tc_andp' a1 a2 => tc_might_be_true a1 && tc_might_be_true a2
 | _ => true
end.Fixpoint tc_always_true (asn : tc_assert) :=
match asn with
 | tc_TT => true
 | tc_andp' a1 a2 => tc_always_true a1 && tc_always_true a2
 | _ => false
end.(* A more standard typechecker, should approximate the c typechecker,
might need to add a tc_noproof for nested loads*)
Definition typecheck_b {CS: compspecs}Delta e :=  tc_might_be_true (typecheck_expr Delta e).(*Definition of the original *pure* typechecker where true means the expression
will always evaluate, may not be useful since tc_denote will just compute to true
on these assertions*)
Definition typecheck_pure_b {CS: compspecs}Delta e := tc_always_true (typecheck_expr Delta e).Fixpoint typecheck_exprlist {CS: compspecs}(Delta : tycontext) (tl : list type) (el : list expr) : tc_assert :=
match tl,el with
| t::tl', e:: el' => tc_andp (typecheck_expr Delta (Ecast e t))
                      (typecheck_exprlist Delta tl' el')
| nil, nil => tc_TT
| _, _ => tc_FF wrong_signature
end.(*
Definition specs_types (Delta: tycontext) :=
  forall id s, (glob_specs Delta) ! id = Some s ->
                (glob_types Delta) ! id = Some (type_of_funspec s).
*)
(*
Definition same_mode (ge: genviron) (ve:venviron)
                     (gt : PTree.t global_spec) (vt : PTree.t type) id  :=
match (vt ! id), (gt ! id), ve id  with
| None, Some _, Some _ => false
| _, _, _  => true
end.

Fixpoint same_env  (rho : environ) (Delta : tycontext) (ids : list positive) : bool :=
match ids with
| h::t => same_mode (ge_of rho) (ve_of rho) (glob_types Delta) (var_types Delta) h && same_env rho Delta t
| nil => true
end.

Definition all_var_ids (Delta : tycontext) : list positive :=
(fst (split (PTree.elements (glob_types Delta)))).
*)

Definition typecheck_environ (Delta: tycontext) (rho : environ) :=
typecheck_temp_environ (te_of rho) (temp_types Delta) /\
typecheck_var_environ  (ve_of rho) (var_types Delta) /\
typecheck_glob_environ (ge_of rho) (glob_types Delta).Ltac _destruct_var_types i Heq_vt Heq_ve t b :=
  let HH := fresh "H" in
  match goal with
  | H: typecheck_var_environ _ _ |- _ =>
      pose proof WARNING___________you_should_use_tactic___destruct_var_types___instead _ _ H i as HH
  | H: typecheck_environ _ _ |- _ =>
      pose proof WARNING___________you_should_use_tactic___destruct_var_types___instead _ _ (proj1 (proj2 H)) i as HH
  end;
  match type of HH with
  | match ?o with _ => _ end =>
      match goal with
      | H: o = Some _ |- _ =>
          rewrite H in HH
      | H: Some _ = o |- _ =>
          rewrite <- H in HH
      | H: o = None |- _ =>
          rewrite H in HH
      | H: None = o |- _ =>
          rewrite <- H in HH
      | _ =>
          let HH' := fresh "H" in
          pose proof eq_refl o as HH';
          destruct o as [t |] in HH, HH' at 2;
          pose proof HH' as Heq_vt; clear HH'
      end
  end;
  match type of HH with
  | ex _ =>
      pose proof HH as [b Heq_ve]
  | _ =>
      pose proof HH as Heq_ve
  end;
  clear HH.Ltac _destruct_glob_types i Heq_gt Heq_ge t b :=
  let HH := fresh "H" in
  match goal with
  | H: typecheck_glob_environ _ _ |- _ =>
      pose proof WARNING___________you_should_use_tactic___destruct_glob_types___instead _ _ H i as HH
  | H: typecheck_environ _ _ |- _ =>
      pose proof WARNING___________you_should_use_tactic___destruct_glob_types___instead _ _ (proj2 (proj2 H)) i as HH
  end;
  match type of HH with
  | match ?o with _ => _ end =>
      match goal with
      | H: o = Some _ |- _ =>
          rewrite H in HH
      | H: Some _ = o |- _ =>
          rewrite <- H in HH
      | H: o = None |- _ =>
          rewrite H in HH
      | H: None = o |- _ =>
          rewrite <- H in HH
      | _ =>
          let HH' := fresh "H" in
          pose proof eq_refl o as HH';
          destruct o as [t |] in HH, HH' at 2;
          pose proof HH' as Heq_gt; clear HH'
      end
  end;
  match type of HH with
  | ex _ =>
      pose proof HH as [b Heq_ge]
  | _ =>
      idtac
  end;
  clear HH.(** Type-checking of function parameters **)

Fixpoint match_fsig_aux (bl: list expr) (tl: list (ident*type)) : bool :=
 match bl, tl with
 | b::bl', (_,t'):: tl' => if eqb_type (typeof b) t' then match_fsig_aux bl' tl' else false
 | nil, nil => true
 | nil, _::_ => false
 | _::_, nil => false
 end.Definition match_fsig (fs: funsig) (bl: list expr) (ret: option ident) : bool :=
  andb (match_fsig_aux bl (fst fs))
          (match snd fs, ret with
            | Tvoid , None => true
            | Tvoid, Some _ => false
            | _, None => false
            | _, Some _ => true
            end).

(* Specifications: *)
Lemma match_fsig_e: forall fs bl ret, match_fsig fs bl ret = true -> map typeof bl = map (@snd _ _) (fst fs) /\ (snd fs=Tvoid <-> ret=None).