(** The size of a type is an integral multiple of its alignment,
  unless the alignment was artificially increased with the [__Alignas]
  attribute. *)

Fixpoint naturally_aligned (t: type) : Prop :=
  attr_alignas (attr_of_type t) = None /\
  match t with
  | Tarray t' _ _ => naturally_aligned t'
  | _ => True
  end.(** ** Size and alignment for composite definitions *)

(** The alignment for a structure or union is the max of the alignment
  of its members. *)

Fixpoint alignof_composite (env: composite_env) (m: members) : Z :=
  match m with
  | nil => 1
  | (id, t) :: m' => Z.max (alignof env t) (alignof_composite env m')
  end.(** The size of a structure corresponds to its layout: fields are
  laid out consecutively, and padding is inserted to align
  each field to the alignment for its type. *)

Fixpoint sizeof_struct (env: composite_env) (cur: Z) (m: members) : Z :=
  match m with
  | nil => cur
  | (id, t) :: m' => sizeof_struct env (align cur (alignof env t) + sizeof env t) m'
  end.(** The size of an union is the max of the sizes of its members. *)

Fixpoint sizeof_union (env: composite_env) (m: members) : Z :=
  match m with
  | nil => 0
  | (id, t) :: m' => Z.max (sizeof env t) (sizeof_union env m')
  end.

(* Specifications: *)
Lemma alignof_composite_two_p: forall env m, exists n, alignof_composite env m = two_power_nat n.
Lemma alignof_composite_pos: forall env m a, align_attr a (alignof_composite env m) > 0.
Lemma sizeof_struct_incr: forall env m cur, cur <= sizeof_struct env cur m.
Lemma sizeof_union_pos: forall env m, 0 <= sizeof_union env m.
Lemma alignof_composite_two_p: forall env m, exists n, alignof_composite env m = two_power_nat n.
Lemma alignof_composite_pos: forall env m a, align_attr a (alignof_composite env m) > 0.
Lemma sizeof_struct_incr: forall env m cur, cur <= sizeof_struct env cur m.
Lemma sizeof_union_pos: forall env m, 0 <= sizeof_union env m.