Section TypeRecFunctions.
Context {cs: compspecs}.
Definition reptype_gen: type -> (sigT (fun x => x)) :=
type_func (fun _ => (sigT (fun x => x)))
(fun t =>
match t with
| Tint => existT (fun x => x) val Vundef
| Tstruct _ => existT (fun x => x) unit tt
end)
(fun id TVs => existT (fun x => x) (list_prod_sigT_type (decay TVs)) (list_prod_sigT_value (decay TVs))).
Definition reptype t: Type := match reptype_gen t with existT t _ => t end.
Definition default_val t: reptype t :=
match reptype_gen t as tv
return match tv with existT t _ => t end
with existT t v => v end.

(* Specifications: *)
Lemma reptype_gen_eq: forall t,
reptype_gen t =
match t with
| Tstruct id => existT (fun x => x)
(list_prod_sigT_type (map reptype_gen (map (fun it => field_type (fst it) (co_members (get_co id))) (co_members (get_co id)))))
(list_prod_sigT_value (map reptype_gen (map (fun it => field_type (fst it) (co_members (get_co id))) (co_members (get_co id)))))
| Tint => existT (fun x => x) val Vundef
end.