(****** Specific specs  ****************)

(* Memory predicates need to explicitly not capture any ghost state. *)
Definition VALspec : spec :=
       fun (sh: Share.t) (l: address) =>
          allp (jam (eq_dec l)
                                  (fun l' => EX v: memval, 
                                                yesat NoneP (VAL v) sh l')
                                  noat) && noghost.Definition VALspec_range (n: Z) : spec :=
     fun (sh: Share.t) (l: address) =>
          andp (allp (jam (adr_range_dec l n)
                                  (fun l' => EX v: memval, 
                                                yesat NoneP (VAL v) sh l')
                                  noat)) noghost.Definition nonlock_permission_bytes (sh: share) (a: address) (n: Z) : pred rmap :=
  andp (allp (jam (adr_range_dec a n) (fun i => shareat i sh && nonlockat i) noat)) noghost.Definition nthbyte (n: Z) (l: list memval) : memval :=
     nth (nat_of_Z n) l Undef.(*  Unfortunately address_mapsto_old, while a more elegant definition than
   address_mapsto, is not quite right.  For example, it doesn't uniquely determine v *)
Definition address_mapsto_old (ch: memory_chunk) (v: val) : spec :=
        fun (sh: Share.t) (l: AV.address)  => 
             allp (jam (adr_range_dec l (size_chunk ch)) 
                              (fun l' => yesat NoneP (VAL (nthbyte (snd l' - snd l) (encode_val ch v))) sh l')
                           noat).Definition LKspec lock_size (R: pred rmap) : spec :=
   fun (sh: Share.t) (l: AV.address)  =>
    allp (jam (adr_range_dec l lock_size)
               (fun l' => yesat (SomeP Mpred (fun _ => R)) (LK lock_size (snd l' - snd l)) sh l')
               noat) && noghost.(*Lenb: moved to veric/seplog.v
Definition packPQ {A: rmaps.TypeTree}
  (P Q: forall ts, dependent_type_functor_rec ts (AssertTT A) (pred rmap)):
  forall ts, dependent_type_functor_rec ts (SpecTT A) (pred rmap) :=
  fun ts a b => if b then P ts a else Q ts a.
*)
Definition TTat (l: address) : pred rmap := TT.

(* Specifications: *)
Lemma address_mapsto_old_parametric: forall ch v, spec_parametric (fun l sh l' => yesat NoneP (VAL (nthbyte (snd l' - snd l) (encode_val ch v))) sh l').
Lemma VALspec_parametric: spec_parametric (fun l sh l' => EX v: memval, yesat NoneP (VAL v) sh l').
Lemma LKspec_parametric lock_size: forall R: pred rmap, spec_parametric (fun l sh l' => yesat (SomeP Mpred (fun _ => R)) (LK lock_size (snd l' - snd l)) sh l').