Definition f_res : functor := Functor ff_res.
Inductive res_join (PRED : Type) : f_res PRED -> f_res PRED -> f_res PRED -> Prop :=
| res_join_NO1 : forall sh1 nsh1 sh2 nsh2 sh3 nsh3,
join sh1 sh2 sh3 ->
res_join PRED (NO' PRED sh1 nsh1) (NO' PRED sh2 nsh2)
(NO' PRED sh3 nsh3)
| res_join_NO2 : forall sh1 nsh1 sh2 rsh2 sh3 rsh3 k p,
join sh1 sh2 sh3 ->
res_join PRED (NO' PRED sh1 nsh1) (YES' PRED sh2 rsh2 k p)
(YES' PRED sh3 rsh3 k p)
| res_join_NO3 : forall sh1 rsh1 sh2 nsh2 sh3 rsh3 k p,
join sh1 sh2 sh3 ->
res_join PRED (YES' PRED sh1 rsh1 k p) (NO' PRED sh2 nsh2)
(YES' PRED sh3 rsh3 k p)
| res_join_YES : forall sh1 rsh1 sh2 rsh2 sh3 rsh3 k p,
join sh1 sh2 sh3 ->
res_join PRED (YES' PRED sh1 rsh1 k p) (YES' PRED sh2 rsh2 k p) (YES' PRED sh3 rsh3 k p)
| res_join_PURE : forall k p, res_join PRED (PURE' PRED k p) (PURE' PRED k p) (PURE' PRED k p).
Instance Join_res (PRED: Type) : Join (res PRED) := res_join PRED.
Instance pa_rj : forall PRED, @Perm_alg _ (res_join PRED).
Instance sa_rj : forall PRED, @Sep_alg _ (res_join PRED).
Definition res_option (PRED : Type) (r: res PRED) : option (rshare * kind):=
match r with
| NO' _ _ => None
| YES' sh rsh k _ => Some (readable_part rsh,k)
| PURE' _ _ => None (* PUREs cannot be split in any interesting way, which is what valid is about. *)
end.
Definition ghost (PRED : Type) : Type :=
list (option ({g: Ghost & {a: @G g | ghost.valid a}} * fpreds PRED)%type).
Definition ghost_fmap (A B:Type) (f:A->B) (g:B->A)(x:ghost A) : ghost B :=
fmap (flist (foption (fpair (fconst _) fpreds))) f g x.

(* Specifications: *)
Lemma ff_ghost : functorFacts ghost ghost_fmap.
Definition f_ghost : functor := Functor ff_ghost.