(** Extract the attributes of a type. *)

Definition attr_of_type (ty: type) :=
  match ty with
  | Tvoid => noattr
  | Tint sz si a => a
  | Tlong si a => a
  | Tfloat sz a => a
  | Tpointer elt a => a
  | Tarray elt sz a => a
  | Tfunction args res cc => noattr
  | Tstruct id a => a
  | Tunion id a => a
  end.(** Change the top-level attributes of a type *)

Definition change_attributes (f: attr -> attr) (ty: type) : type :=
  match ty with
  | Tvoid => ty
  | Tint sz si a => Tint sz si (f a)
  | Tlong si a => Tlong si (f a)
  | Tfloat sz a => Tfloat sz (f a)
  | Tpointer elt a => Tpointer elt (f a)
  | Tarray elt sz a => Tarray elt sz (f a)
  | Tfunction args res cc => ty
  | Tstruct id a => Tstruct id (f a)
  | Tunion id a => Tunion id (f a)
  end.(** Erase the top-level attributes of a type *)

Definition remove_attributes (ty: type) : type :=
  change_attributes (fun _ => noattr) ty.(** Add extra attributes to the top-level attributes of a type *)

Definition attr_union (a1 a2: attr) : attr :=
  {| attr_volatile := a1.(attr_volatile) || a2.(attr_volatile);
     attr_alignas :=
       match a1.(attr_alignas), a2.(attr_alignas) with
       | None, al => al
       | al, None => al
       | Some n1, Some n2 => Some (N.max n1 n2)
       end
  |}.Definition merge_attributes (ty: type) (a: attr) : type :=
  change_attributes (attr_union a) ty.(** Syntax for [struct] and [union] definitions.  [struct] and [union]
  are collectively called "composites".  Each compilation unit
  comes with a list of top-level definitions of composites. *)

Inductive struct_or_union : Type := Struct | Union.(** Syntax for [struct] and [union] definitions.  [struct] and [union]
  are collectively called "composites".  Each compilation unit
  comes with a list of top-level definitions of composites. *)

Inductive struct_or_union : Type := Struct | Union.(** Syntax for [struct] and [union] definitions.  [struct] and [union]
  are collectively called "composites".  Each compilation unit
  comes with a list of top-level definitions of composites. *)

Inductive struct_or_union : Type := Struct | Union.Definition members : Type := list (ident * type).Inductive composite_definition : Type :=
  Composite (id: ident) (su: struct_or_union) (m: members) (a: attr).Inductive composite_definition : Type :=
  Composite (id: ident) (su: struct_or_union) (m: members) (a: attr).Definition name_composite_def (c: composite_definition) : ident :=
  match c with Composite id su m a => id end.Definition composite_def_eq (x y: composite_definition): {x=y} + {x<>y}.Definition composite_env : Type := PTree.t composite.(** * Operations over types *)

(** ** Conversions *)

Definition type_int32s := Tint I32 Signed noattr.Definition type_bool := Tint IBool Signed noattr.(** The usual unary conversion.  Promotes small integer types to [signed int32]
  and degrades array types and function types to pointer types.
  Attributes are erased. *)

Definition typeconv (ty: type) : type :=
  match ty with
  | Tint (I8 | I16 | IBool) _ _ => Tint I32 Signed noattr
  | Tarray t sz a       => Tpointer t noattr
  | Tfunction _ _ _     => Tpointer ty noattr
  | _                   => remove_attributes ty
  end.(** Default conversion for arguments to an unprototyped or variadic function.
  Like [typeconv] but also converts single floats to double floats. *)

Definition default_argument_conversion (ty: type) : type :=
  match ty with
  | Tint (I8 | I16 | IBool) _ _ => Tint I32 Signed noattr
  | Tfloat _ _          => Tfloat F64 noattr
  | Tarray t sz a       => Tpointer t noattr
  | Tfunction _ _ _     => Tpointer ty noattr
  | _                   => remove_attributes ty
  end.Definition complete_or_function_type (env: composite_env) (t: type) : bool :=
  match t with
  | Tfunction _ _ _ => true
  | _ => complete_type env t
  end.(** ** Alignment of a type *)

(** Adjust the natural alignment [al] based on the attributes [a] attached
  to the type.  If an "alignas" attribute is given, use it as alignment
  in preference to [al]. *)

Definition align_attr (a: attr) (al: Z) : Z :=
  match attr_alignas a with
  | Some l => two_p (Z.of_N l)
  | None => al
  end.Remark align_attr_two_p:
  forall al a,
  (exists n, al = two_power_nat n) ->
  (exists n, align_attr a al = two_power_nat n).

Lemma sizeof_pos: forall env t, sizeof env t >= 0.