Definition log2_sizeof_pointer : N := 
  ltac:(let n := eval compute in 
  (N.log2 (Z.to_N (@sizeof (PTree.empty _) (Tpointer Tvoid noattr))))
   in exact (n)).Definition int_or_ptr_type : type :=
  Tpointer Tvoid {| attr_volatile := false; attr_alignas := Some log2_sizeof_pointer |}.(** The following describes types that can be interpreted as a boolean:
  integers, floats, pointers.  It is used for the semantics of
  the [!] and [?] operators, as well as the [if], [while], [for] statements. *)

(** Interpretation of values as truth values.
  Non-zero integers, non-zero floats and non-null pointers are
  considered as true.  The integer zero (which also represents
  the null pointer) and the float 0.0 are false. *)

Definition bool_val_i (v : val) : option bool :=
match v with
      | Vint n => Some (negb (Int.eq n Int.zero))
      | _ => None
      end.Definition bool_val_p (v : val) : option bool :=
match v with
      | Vint n => if Archi.ptr64 then None else Some (negb (Int.eq n Int.zero))
      | Vlong n => if Archi.ptr64 then Some (negb (Int64.eq n Int64.zero)) else None
      | Vptr b ofs => Some true
      | _ => None
      end.Definition bool_val_s (v : val) : option bool :=
 match v with
      | Vsingle f => Some (negb (Float32.cmp Ceq f Float32.zero))
      | _ => None
      end.Definition bool_val_f (v : val) : option bool :=
 match v with
      | Vfloat f => Some (negb (Float.cmp Ceq f Float.zero))
      | _ => None
      end.Definition bool_val_l (v : val) : option bool :=
 match v with
      | Vlong n => Some (negb (Int64.eq n Int64.zero))
      | Vptr b ofs =>
          if negb Archi.ptr64 then None else Some true
      | _ => None
      end.Definition bool_val (t: type) : val -> option bool :=
  match t with
  | Tint _ _ _ => bool_val_i
  | Tpointer _ _ => if  eqb_type t int_or_ptr_type then (fun _ => None) else bool_val_p
  | Tfloat F64 _ => bool_val_f
  | Tfloat F32 _ => bool_val_s
  | Tlong _ _ => bool_val_l
  | _ => fun v => None
  end.(*************** from veric.expr.v   **********************)

Definition size_t := if Archi.ptr64 then Tlong Unsigned noattr else Tint I32 Unsigned noattr.Definition is_int (sz: intsize) (sg: signedness) (v: val) :=
  match v with
  | Vint i =>
    match sz, sg with
    | I8, Signed => Byte.min_signed <= Int.signed i <= Byte.max_signed
    | I8, Unsigned => Int.unsigned i <= Byte.max_unsigned
    | I16, Signed => -two_p (16-1) <= Int.signed i <= two_p (16-1) -1
    | I16, Unsigned => Int.unsigned i <= two_p 16 - 1
    | I32, _ => True
    | IBool, _ => i = Int.zero \/ i = Int.one
    end
  | _ => False
  end.Definition tc_val (ty: type) : val -> Prop :=
 match ty with
 | Tint sz sg _ => is_int sz sg
 | Tlong _ _ => is_long
 | Tfloat F64 _ => is_float
 | Tfloat F32 _ => is_single
 | Tpointer _ _ => if eqb_type ty int_or_ptr_type then is_pointer_or_integer else is_pointer_or_null
 | Tarray _ _ _ | Tfunction _ _ _ => is_pointer_or_null
 | Tstruct _ _ => isptr
 | Tunion _ _ => isptr
 | _ => fun _ => False
 end.Definition tc_val' t v := v <> Vundef -> tc_val t v.Fixpoint tc_vals (ty: list type) (v: list val) : Prop :=
 match v, ty with
 | v1::vs , t1::ts => tc_val t1 v1 /\ tc_vals ts vs
 | nil, nil => True
 | _, _ => False
end.

(* Specifications: *)
Lemma tc_val_Vundef: forall t, ~tc_val t Vundef.
Lemma tc_val'_Vundef: forall t, tc_val' t Vundef.
Lemma tc_val_tc_val': forall t v, tc_val t v -> tc_val' t v.
Lemma tc_val_has_type (ty : type) (v : val) : tc_val ty v -> Val.has_type v (typ_of_type ty).