Section WITH_SHARE.
Variable sh: share.
Definition data_at_rec: forall t, reptype t -> val -> mpred :=
type_func (fun t => reptype t -> val -> mpred)
(fun t v p =>
if type_is_volatile t
then memory_block sh (sizeof t) p
else mapsto sh t p (repinject t v))
(fun t n a P v => array_pred 0 (Z.max 0 n) (fun i v => at_offset (P v) (sizeof t * i)) (unfold_reptype v))
(fun id a P v => struct_data_at_rec_aux sh (co_members (get_co id)) (co_members (get_co id)) (co_sizeof (get_co id)) P (unfold_reptype v))
(fun id a P v => union_data_at_rec_aux sh (co_members (get_co id)) (co_members (get_co id)) (co_sizeof (get_co id)) P (unfold_reptype v)).
End WITH_SHARE.
(************************************************  Transformation between data_at/data_at_ and mapsto.  ************************************************)

Lemma by_value_data_at_rec_default_val: forall sh t p,
type_is_by_value t = true ->
size_compatible t p ->
align_compatible t p ->
data_at_rec sh t (default_val t) p = memory_block sh (sizeof t) p.