Commit 5cfe326f authored by Ralf Jung's avatar Ralf Jung
Browse files

fix indentation and various nits

parent b0da646d
......@@ -66,11 +66,14 @@ Section ofe.
dyn_reservation_map_data_proj x {n} dyn_reservation_map_data_proj y
dyn_reservation_map_token_proj x = dyn_reservation_map_token_proj y.
Global Instance DynReservationMap_ne : NonExpansive2 (@DynReservationMap A).
Global Instance DynReservationMap_ne :
NonExpansive2 (@DynReservationMap A).
Proof. by split. Qed.
Global Instance DynReservationMap_proper : Proper (() ==> (=) ==> ()) (@DynReservationMap A).
Global Instance DynReservationMap_proper :
Proper (() ==> (=) ==> ()) (@DynReservationMap A).
Proof. by split. Qed.
Global Instance dyn_reservation_map_data_proj_ne: NonExpansive (@dyn_reservation_map_data_proj A).
Global Instance dyn_reservation_map_data_proj_ne :
NonExpansive (@dyn_reservation_map_data_proj A).
Proof. by destruct 1. Qed.
Global Instance dyn_reservation_map_data_proj_proper :
Proper (() ==> ()) (@dyn_reservation_map_data_proj A).
......@@ -151,198 +154,195 @@ Section cmra.
| CoPsetBot => False
end := eq_refl _.
Lemma dyn_reservation_map_included x y :
x y
dyn_reservation_map_data_proj x dyn_reservation_map_data_proj y
dyn_reservation_map_token_proj x dyn_reservation_map_token_proj y.
Proof.
split; [intros [[z1 z2] Hz]; split; [exists z1|exists z2]; apply Hz|].
intros [[z1 Hz1] [z2 Hz2]]; exists (DynReservationMap z1 z2); split; auto.
Qed.
Lemma dyn_reservation_map_included x y :
x y
dyn_reservation_map_data_proj x dyn_reservation_map_data_proj y
dyn_reservation_map_token_proj x dyn_reservation_map_token_proj y.
Proof.
split; [intros [[z1 z2] Hz]; split; [exists z1|exists z2]; apply Hz|].
intros [[z1 Hz1] [z2 Hz2]]; exists (DynReservationMap z1 z2); split; auto.
Qed.
Lemma dyn_reservation_map_data_proj_validN n x : {n} x {n} dyn_reservation_map_data_proj x.
Proof. by destruct x as [? [?|]]=> // -[??]. Qed.
Lemma dyn_reservation_map_token_proj_validN n x : {n} x {n} dyn_reservation_map_token_proj x.
Proof. by destruct x as [? [?|]]=> // -[??]. Qed.
Lemma dyn_reservation_map_data_proj_validN n x : {n} x {n} dyn_reservation_map_data_proj x.
Proof. by destruct x as [? [?|]]=> // -[??]. Qed.
Lemma dyn_reservation_map_token_proj_validN n x : {n} x {n} dyn_reservation_map_token_proj x.
Proof. by destruct x as [? [?|]]=> // -[??]. Qed.
Lemma dyn_reservation_map_cmra_mixin : CmraMixin (dyn_reservation_map A).
Proof.
apply (iso_cmra_mixin_restrict from_reservation_map to_reservation_map); try done.
- intros n [m [E|]];
rewrite dyn_reservation_map_validN_eq reservation_map_validN_eq /=;
naive_solver.
- intros n [m1 [E1|]] [m2 [E2|]] [Hm ?]=> // -[?[??]]; split; simplify_eq/=.
+ by rewrite -Hm.
+ split; first done. intros i. by rewrite -(dist_None n) -Hm dist_None.
- intros [m [E|]]; rewrite dyn_reservation_map_valid_eq dyn_reservation_map_validN_eq /=
?cmra_valid_validN; naive_solver eauto using O.
- intros n [m [E|]]; rewrite dyn_reservation_map_validN_eq /=;
naive_solver eauto using cmra_validN_S.
- intros n [m1 [E1|]] [m2 [E2|]]=> //=; rewrite dyn_reservation_map_validN_eq /=.
rewrite {1}/op /cmra_op /=. case_decide; last done.
intros [Hm [Hinf Hdisj]]; split; first by eauto using cmra_validN_op_l.
split.
+ rewrite ->difference_union_distr_r in Hinf.
eapply set_infinite_subseteq; last done.
set_solver.
+ intros i. move: (Hdisj i). rewrite lookup_op.
case: (m1 !! i)=> [a|]; last auto.
move=> [].
{ by case: (m2 !! i). }
set_solver.
Qed.
Lemma dyn_reservation_map_cmra_mixin : CmraMixin (dyn_reservation_map A).
Proof.
apply (iso_cmra_mixin_restrict from_reservation_map to_reservation_map); try done.
- intros n [m [E|]];
rewrite dyn_reservation_map_validN_eq reservation_map_validN_eq /=;
naive_solver.
- intros n [m1 [E1|]] [m2 [E2|]] [Hm ?]=> // -[?[??]]; split; simplify_eq/=.
+ by rewrite -Hm.
+ split; first done. intros i. by rewrite -(dist_None n) -Hm dist_None.
- intros [m [E|]]; rewrite dyn_reservation_map_valid_eq dyn_reservation_map_validN_eq /=
?cmra_valid_validN; naive_solver eauto using O.
- intros n [m [E|]]; rewrite dyn_reservation_map_validN_eq /=;
naive_solver eauto using cmra_validN_S.
- intros n [m1 [E1|]] [m2 [E2|]]=> //=; rewrite dyn_reservation_map_validN_eq /=.
rewrite {1}/op /cmra_op /=. case_decide; last done.
intros [Hm [Hinf Hdisj]]; split; first by eauto using cmra_validN_op_l.
split.
+ rewrite ->difference_union_distr_r_L in Hinf.
eapply set_infinite_subseteq, Hinf. set_solver.
+ intros i. move: (Hdisj i). rewrite lookup_op.
case: (m1 !! i); case: (m2 !! i); set_solver.
Qed.
Canonical Structure dyn_reservation_mapR :=
Cmra (dyn_reservation_map A) dyn_reservation_map_cmra_mixin.
Canonical Structure dyn_reservation_mapR :=
Cmra (dyn_reservation_map A) dyn_reservation_map_cmra_mixin.
Global Instance dyn_reservation_map_cmra_discrete :
CmraDiscrete A CmraDiscrete dyn_reservation_mapR.
Proof.
split; first apply _.
intros [m [E|]]; rewrite dyn_reservation_map_validN_eq dyn_reservation_map_valid_eq //=.
by intros [?%cmra_discrete_valid ?].
Qed.
Global Instance dyn_reservation_map_cmra_discrete :
CmraDiscrete A CmraDiscrete dyn_reservation_mapR.
Proof.
split; first apply _.
intros [m [E|]]; rewrite dyn_reservation_map_validN_eq dyn_reservation_map_valid_eq //=.
by intros [?%cmra_discrete_valid ?].
Qed.
Local Instance dyn_reservation_map_empty_instance : Unit (dyn_reservation_map A) :=
DynReservationMap ε ε.
Lemma dyn_reservation_map_ucmra_mixin : UcmraMixin (dyn_reservation_map A).
Proof.
split; simpl.
- rewrite dyn_reservation_map_valid_eq /=. split; [apply ucmra_unit_valid|]. split.
+ rewrite difference_empty. apply top_infinite.
+ set_solver.
- split; simpl; [by rewrite left_id|by rewrite left_id_L].
- do 2 constructor; [apply (core_id_core _)|done].
Qed.
Canonical Structure dyn_reservation_mapUR :=
Ucmra (dyn_reservation_map A) dyn_reservation_map_ucmra_mixin.
Local Instance dyn_reservation_map_empty_instance : Unit (dyn_reservation_map A) :=
DynReservationMap ε ε.
Lemma dyn_reservation_map_ucmra_mixin : UcmraMixin (dyn_reservation_map A).
Proof.
split; simpl.
- rewrite dyn_reservation_map_valid_eq /=. split; [apply ucmra_unit_valid|]. split.
+ rewrite difference_empty_L. apply top_infinite.
+ set_solver.
- split; simpl; [by rewrite left_id|by rewrite left_id_L].
- do 2 constructor; [apply (core_id_core _)|done].
Qed.
Canonical Structure dyn_reservation_mapUR :=
Ucmra (dyn_reservation_map A) dyn_reservation_map_ucmra_mixin.
Global Instance dyn_reservation_map_data_core_id N a :
CoreId a CoreId (dyn_reservation_map_data N a).
Proof. do 2 constructor; simpl; auto. apply core_id_core, _. Qed.
Global Instance dyn_reservation_map_data_core_id N a :
CoreId a CoreId (dyn_reservation_map_data N a).
Proof. do 2 constructor; simpl; auto. apply core_id_core, _. Qed.
Lemma dyn_reservation_map_data_valid N a :
(dyn_reservation_map_data N a) a.
Proof.
rewrite dyn_reservation_map_valid_eq /= singleton_valid.
split; first naive_solver. intros Ha.
split; first done. split; last set_solver.
rewrite difference_empty. apply top_infinite.
Qed.
Lemma dyn_reservation_map_token_valid E :
(dyn_reservation_map_token E) set_infinite ( E).
Proof.
rewrite dyn_reservation_map_valid_eq /=. split; first naive_solver.
intros Hinf. do 2 (split; first done). by left.
Qed.
Lemma dyn_reservation_map_data_op N a b :
dyn_reservation_map_data N (a b) = dyn_reservation_map_data N a dyn_reservation_map_data N b.
Proof.
by rewrite {2}/op /dyn_reservation_map_op_instance /dyn_reservation_map_data /= singleton_op left_id_L.
Qed.
Lemma dyn_reservation_map_data_mono N a b :
a b dyn_reservation_map_data N a dyn_reservation_map_data N b.
Proof. intros [c ->]. rewrite dyn_reservation_map_data_op. apply cmra_included_l. Qed.
Global Instance dyn_reservation_map_data_is_op N a b1 b2 :
IsOp a b1 b2
IsOp' (dyn_reservation_map_data N a) (dyn_reservation_map_data N b1) (dyn_reservation_map_data N b2).
Proof. rewrite /IsOp' /IsOp=> ->. by rewrite dyn_reservation_map_data_op. Qed.
Lemma dyn_reservation_map_data_valid N a :
(dyn_reservation_map_data N a) a.
Proof.
rewrite dyn_reservation_map_valid_eq /= singleton_valid.
split; first naive_solver. intros Ha.
split; first done. split; last set_solver.
rewrite difference_empty_L. apply top_infinite.
Qed.
Lemma dyn_reservation_map_token_valid E :
(dyn_reservation_map_token E) set_infinite ( E).
Proof.
rewrite dyn_reservation_map_valid_eq /=. split; first naive_solver.
intros Hinf. do 2 (split; first done). by left.
Qed.
Lemma dyn_reservation_map_data_op N a b :
dyn_reservation_map_data N (a b) = dyn_reservation_map_data N a dyn_reservation_map_data N b.
Proof.
by rewrite {2}/op /dyn_reservation_map_op_instance /dyn_reservation_map_data /= singleton_op left_id_L.
Qed.
Lemma dyn_reservation_map_data_mono N a b :
a b dyn_reservation_map_data N a dyn_reservation_map_data N b.
Proof. intros [c ->]. rewrite dyn_reservation_map_data_op. apply cmra_included_l. Qed.
Global Instance dyn_reservation_map_data_is_op N a b1 b2 :
IsOp a b1 b2
IsOp' (dyn_reservation_map_data N a) (dyn_reservation_map_data N b1) (dyn_reservation_map_data N b2).
Proof. rewrite /IsOp' /IsOp=> ->. by rewrite dyn_reservation_map_data_op. Qed.
Lemma dyn_reservation_map_token_union E1 E2 :
E1 ## E2
dyn_reservation_map_token (E1 E2) = dyn_reservation_map_token E1 dyn_reservation_map_token E2.
Proof.
intros. by rewrite /op /dyn_reservation_map_op_instance
/dyn_reservation_map_token /= coPset_disj_union // left_id_L.
Qed.
Lemma dyn_reservation_map_token_difference E1 E2 :
E1 E2
dyn_reservation_map_token E2 = dyn_reservation_map_token E1 dyn_reservation_map_token (E2 E1).
Proof.
intros. rewrite -dyn_reservation_map_token_union; last set_solver.
by rewrite -union_difference_L.
Qed.
Lemma dyn_reservation_map_token_valid_op E1 E2 :
(dyn_reservation_map_token E1 dyn_reservation_map_token E2)
E1 ## E2 set_infinite ( (E1 E2)).
Proof.
split.
- rewrite dyn_reservation_map_valid_eq /= {1}/op /cmra_op /=. case_decide; last done.
naive_solver.
- intros [Hdisj Hinf]. rewrite -dyn_reservation_map_token_union //.
apply dyn_reservation_map_token_valid. done.
Qed.
Lemma dyn_reservation_map_token_union E1 E2 :
E1 ## E2
dyn_reservation_map_token (E1 E2) = dyn_reservation_map_token E1 dyn_reservation_map_token E2.
Proof.
intros. by rewrite /op /dyn_reservation_map_op_instance
/dyn_reservation_map_token /= coPset_disj_union // left_id_L.
Qed.
Lemma dyn_reservation_map_token_difference E1 E2 :
E1 E2
dyn_reservation_map_token E2 = dyn_reservation_map_token E1 dyn_reservation_map_token (E2 E1).
Proof.
intros. rewrite -dyn_reservation_map_token_union; last set_solver.
by rewrite -union_difference_L.
Qed.
Lemma dyn_reservation_map_token_valid_op E1 E2 :
(dyn_reservation_map_token E1 dyn_reservation_map_token E2)
E1 ## E2 set_infinite ( (E1 E2)).
Proof.
split.
- rewrite dyn_reservation_map_valid_eq /= {1}/op /cmra_op /=. case_decide; last done.
naive_solver.
- intros [Hdisj Hinf]. rewrite -dyn_reservation_map_token_union //.
apply dyn_reservation_map_token_valid. done.
Qed.
Lemma dyn_reservation_map_reserve (Q : dyn_reservation_map A Prop) :
( E, set_infinite E Q (dyn_reservation_map_token E))
ε ~~>: Q.
Proof.
intros HQ. apply cmra_total_updateP=> n [mf [Ef|]];
rewrite left_id {1}dyn_reservation_map_validN_eq /=; last done.
intros [Hmap [Hinf Hdisj]].
(* Pick a fresh set disjoint from the existing tokens [Ef] and map [mf],
such that both that set [E1] and the remainder [E2] are infinite. *)
edestruct (coPset_split_infinite ( (Ef dom coPset mf))) as
Lemma dyn_reservation_map_reserve (Q : dyn_reservation_map A Prop) :
( E, set_infinite E Q (dyn_reservation_map_token E))
ε ~~>: Q.
Proof.
intros HQ. apply cmra_total_updateP=> n [mf [Ef|]];
rewrite left_id {1}dyn_reservation_map_validN_eq /=; last done.
intros [Hmap [Hinf Hdisj]].
(* Pick a fresh set disjoint from the existing tokens [Ef] and map [mf],
such that both that set [E1] and the remainder [E2] are infinite. *)
edestruct (coPset_split_infinite ( (Ef dom coPset mf))) as
(E1 & E2 & HEunion & HEdisj & HE1inf & HE2inf).
{ rewrite -difference_difference.
apply difference_infinite; first done.
apply gset_to_coPset_finite. }
exists (dyn_reservation_map_token E1).
split; first by apply HQ. clear HQ.
rewrite dyn_reservation_map_validN_eq /=.
rewrite coPset_disj_union; last set_solver.
split; first by rewrite left_id. split.
- eapply set_infinite_subseteq; last by apply HE2inf. set_solver.
- intros i. rewrite left_id_L. destruct (Hdisj i) as [?|Hi]; first by left.
destruct (mf !! i) as [p|] eqn:Hp; last by left.
apply elem_of_dom_2 in Hp. right. set_solver.
Qed.
Lemma dyn_reservation_map_reserve' :
ε ~~>: (λ x, E, set_infinite E x = dyn_reservation_map_token E).
Proof. eauto using dyn_reservation_map_reserve. Qed.
{ rewrite -difference_difference_L.
by apply difference_infinite, dom_finite. }
exists (dyn_reservation_map_token E1).
split; first by apply HQ. clear HQ.
rewrite dyn_reservation_map_validN_eq /=.
rewrite coPset_disj_union; last set_solver.
split; first by rewrite left_id_L. split.
- eapply set_infinite_subseteq, HE2inf. set_solver.
- intros i. rewrite left_id_L. destruct (Hdisj i) as [?|Hi]; first by left.
destruct (mf !! i) as [p|] eqn:Hp; last by left.
apply elem_of_dom_2 in Hp. right. set_solver.
Qed.
Lemma dyn_reservation_map_reserve' :
ε ~~>: (λ x, E, set_infinite E x = dyn_reservation_map_token E).
Proof. eauto using dyn_reservation_map_reserve. Qed.
Lemma dyn_reservation_map_alloc E k a :
k E a dyn_reservation_map_token E ~~> dyn_reservation_map_data k a.
Proof.
intros ??. apply cmra_total_update=> n [mf [Ef|]] //.
rewrite dyn_reservation_map_validN_eq /= {1}/op /cmra_op /=. case_decide; last done.
rewrite left_id_L {1}left_id. intros [Hmf [Hinf Hdisj]]; split; last split.
- destruct (Hdisj (k)) as [Hmfi|]; last set_solver.
move: Hmfi. rewrite lookup_op lookup_empty left_id_L=> Hmfi.
intros j. rewrite lookup_op.
destruct (decide (k = j)) as [<-|].
+ rewrite Hmfi lookup_singleton right_id_L. by apply cmra_valid_validN.
+ by rewrite lookup_singleton_ne // left_id_L.
- eapply set_infinite_subseteq; last done. set_solver.
- intros j. destruct (decide (k = j)); first set_solver.
rewrite lookup_op lookup_singleton_ne //.
destruct (Hdisj j) as [Hmfi|?]; last set_solver.
move: Hmfi. rewrite lookup_op lookup_empty; auto.
Qed.
Lemma dyn_reservation_map_updateP P (Q : dyn_reservation_map A Prop) k a :
a ~~>: P
( a', P a' Q (dyn_reservation_map_data k a')) dyn_reservation_map_data k a ~~>: Q.
Proof.
intros Hup HP. apply cmra_total_updateP=> n [mf [Ef|]] //.
rewrite dyn_reservation_map_validN_eq /= left_id_L. intros [Hmf [Hinf Hdisj]].
destruct (Hup n (mf !! k)) as (a'&?&?).
{ move: (Hmf (k)).
by rewrite lookup_op lookup_singleton Some_op_opM. }
exists (dyn_reservation_map_data k a'); split; first by eauto.
rewrite /= left_id_L. split; last split.
- intros j. destruct (decide (k = j)) as [<-|].
+ by rewrite lookup_op lookup_singleton Some_op_opM.
+ rewrite lookup_op lookup_singleton_ne // left_id_L.
move: (Hmf j). rewrite lookup_op. eauto using cmra_validN_op_r.
- done.
- intros j. move: (Hdisj j).
rewrite !lookup_op !op_None !lookup_singleton_None. naive_solver.
Qed.
Lemma dyn_reservation_map_update k a b :
a ~~> b dyn_reservation_map_data k a ~~> dyn_reservation_map_data k b.
Proof.
rewrite !cmra_update_updateP. eauto using dyn_reservation_map_updateP with subst.
Qed.
Lemma dyn_reservation_map_alloc E k a :
k E a dyn_reservation_map_token E ~~> dyn_reservation_map_data k a.
Proof.
intros ??. apply cmra_total_update=> n [mf [Ef|]] //.
rewrite dyn_reservation_map_validN_eq /= {1}/op /cmra_op /=. case_decide; last done.
rewrite left_id_L {1}left_id. intros [Hmf [Hinf Hdisj]]; split; last split.
- destruct (Hdisj k) as [Hmfi|]; last set_solver.
move: Hmfi. rewrite lookup_op lookup_empty left_id_L=> Hmfi.
intros j. rewrite lookup_op.
destruct (decide (k = j)) as [<-|].
+ rewrite Hmfi lookup_singleton right_id_L. by apply cmra_valid_validN.
+ by rewrite lookup_singleton_ne // left_id_L.
- eapply set_infinite_subseteq, Hinf. set_solver.
- intros j. destruct (decide (k = j)); first set_solver.
rewrite lookup_op lookup_singleton_ne //.
destruct (Hdisj j) as [Hmfi|?]; last set_solver.
move: Hmfi. rewrite lookup_op lookup_empty; auto.
Qed.
Lemma dyn_reservation_map_updateP P (Q : dyn_reservation_map A Prop) k a :
a ~~>: P
( a', P a' Q (dyn_reservation_map_data k a'))
dyn_reservation_map_data k a ~~>: Q.
Proof.
intros Hup HP. apply cmra_total_updateP=> n [mf [Ef|]] //.
rewrite dyn_reservation_map_validN_eq /= left_id_L. intros [Hmf [Hinf Hdisj]].
destruct (Hup n (mf !! k)) as (a'&?&?).
{ move: (Hmf (k)).
by rewrite lookup_op lookup_singleton Some_op_opM. }
exists (dyn_reservation_map_data k a'); split; first by eauto.
rewrite /= left_id_L. split; last split.
- intros j. destruct (decide (k = j)) as [<-|].
+ by rewrite lookup_op lookup_singleton Some_op_opM.
+ rewrite lookup_op lookup_singleton_ne // left_id_L.
move: (Hmf j). rewrite lookup_op. eauto using cmra_validN_op_r.
- done.
- intros j. move: (Hdisj j).
rewrite !lookup_op !op_None !lookup_singleton_None. naive_solver.
Qed.
Lemma dyn_reservation_map_update k a b :
a ~~> b
dyn_reservation_map_data k a ~~> dyn_reservation_map_data k b.
Proof.
rewrite !cmra_update_updateP. eauto using dyn_reservation_map_updateP with subst.
Qed.
End cmra.
Global Arguments dyn_reservation_mapR : clear implicits.
......
......@@ -41,259 +41,261 @@ Global Instance: Params (@reservation_map_data) 2 := {}.
(* Ofe *)
Section ofe.
Context {A : ofe}.
Implicit Types x y : reservation_map A.
Context {A : ofe}.
Implicit Types x y : reservation_map A.
Local Instance reservation_map_equiv : Equiv (reservation_map A) := λ x y,
reservation_map_data_proj x reservation_map_data_proj y
reservation_map_token_proj x = reservation_map_token_proj y.
Local Instance reservation_map_dist : Dist (reservation_map A) := λ n x y,
reservation_map_data_proj x {n} reservation_map_data_proj y
reservation_map_token_proj x = reservation_map_token_proj y.
Local Instance reservation_map_equiv : Equiv (reservation_map A) := λ x y,
reservation_map_data_proj x reservation_map_data_proj y
reservation_map_token_proj x = reservation_map_token_proj y.
Local Instance reservation_map_dist : Dist (reservation_map A) := λ n x y,
reservation_map_data_proj x {n} reservation_map_data_proj y
reservation_map_token_proj x = reservation_map_token_proj y.
Global Instance ReservationMap_ne : NonExpansive2 (@ReservationMap A).
Proof. by split. Qed.
Global Instance ReservationMap_proper : Proper (() ==> (=) ==> ()) (@ReservationMap A).
Proof. by split. Qed.
Global Instance reservation_map_data_proj_ne: NonExpansive (@reservation_map_data_proj A).
Proof. by destruct 1. Qed.
Global Instance reservation_map_data_proj_proper :
Proper (() ==> ()) (@reservation_map_data_proj A).
Proof. by destruct 1. Qed.
Global Instance ReservationMap_ne :
NonExpansive2 (@ReservationMap A).
Proof. by split. Qed.
Global Instance ReservationMap_proper :
Proper (() ==> (=) ==> ()) (@ReservationMap A).
Proof. by split. Qed.
Global Instance reservation_map_data_proj_ne :
NonExpansive (@reservation_map_data_proj A).
Proof. by destruct 1. Qed.
Global Instance reservation_map_data_proj_proper :
Proper (() ==> ()) (@reservation_map_data_proj A).
Proof. by destruct 1. Qed.
Definition reservation_map_ofe_mixin : OfeMixin (reservation_map A).
Proof.
by apply (iso_ofe_mixin
(λ x, (reservation_map_data_proj x, reservation_map_token_proj x))).
Qed.
Canonical Structure reservation_mapO :=
Ofe (reservation_map A) reservation_map_ofe_mixin.
Definition reservation_map_ofe_mixin : OfeMixin (reservation_map A).
Proof.
by apply (iso_ofe_mixin
(λ x, (reservation_map_data_proj x, reservation_map_token_proj x))).
Qed.
Canonical Structure reservation_mapO :=
Ofe (reservation_map A) reservation_map_ofe_mixin.
Global Instance ReservationMap_discrete a b :
Discrete a Discrete b Discrete (ReservationMap a b).
Proof. intros ?? [??] [??]; split; unfold_leibniz; by eapply discrete. Qed.
Global Instance reservation_map_ofe_discrete :
OfeDiscrete A OfeDiscrete reservation_mapO.
Proof. intros ? [??]; apply _. Qed.
Global Instance ReservationMap_discrete a b :
Discrete a Discrete b Discrete (ReservationMap a b).
Proof. intros ?? [??] [??]; split; unfold_leibniz; by eapply discrete. Qed.
Global Instance reservation_map_ofe_discrete :
OfeDiscrete A OfeDiscrete reservation_mapO.
Proof. intros ? [??]; apply _. Qed.
End ofe.
Global Arguments reservation_mapO : clear implicits.
(* Camera *)
Section cmra.
Context {A : cmra}.
Implicit Types a b : A.
Implicit Types x y : reservation_map A.
Implicit Types k : positive.
Context {A : cmra}.
Implicit Types a b : A.
Implicit Types x y : reservation_map A.
Implicit Types k : positive.
Global Instance reservation_map_data_ne i : NonExpansive (@reservation_map_data A i).
Proof. solve_proper. Qed.
Global Instance reservation_map_data_proper N :
Proper (() ==> ()) (@reservation_map_data A N).
Proof. solve_proper. Qed.
Global Instance reservation_map_data_discrete N a :
Discrete a Discrete (reservation_map_data N a).
Proof. intros. apply ReservationMap_discrete; apply _. Qed.
Global Instance reservation_map_token_discrete E : Discrete (@reservation_map_token A E).
Proof. intros. apply ReservationMap_discrete; apply _. Qed.
Global Instance reservation_map_data_ne i : NonExpansive (@reservation_map_data A i).
Proof. solve_proper. Qed.
Global Instance reservation_map_data_proper N :
Proper (() ==> ()) (@reservation_map_data A N).
Proof. solve_proper. Qed.
Global Instance reservation_map_data_discrete N a :
Discrete a Discrete (reservation_map_data N a).
Proof. intros. apply ReservationMap_discrete; apply _. Qed.
Global Instance reservation_map_token_discrete E : Discrete (@reservation_map_token A E).
Proof. intros. apply ReservationMap_discrete; apply _. Qed.
Local Instance reservation_map_valid_instance : Valid (reservation_map A) := λ x,
match reservation_map_token_proj x with
| CoPset E =>
(reservation_map_data_proj x)
(* dom (reservation_map_data_proj x) ⊥ E *)
i, reservation_map_data_proj x !! i = None i E
| CoPsetBot => False
end.
Global Arguments reservation_map_valid_instance !_ /.
Local Instance reservation_map_validN_instance : ValidN (reservation_map A) := λ n x,
match reservation_map_token_proj x with
| CoPset E =>
{n} (reservation_map_data_proj x)
(* dom (reservation_map_data_proj x) ⊥ E *)
i, reservation_map_data_proj x !! i = None i E
| CoPsetBot => False
end.
Global Arguments reservation_map_validN_instance !_ /.
Local Instance reservation_map_pcore_instance : PCore (reservation_map A) := λ x,
Some (ReservationMap (core (reservation_map_data_proj x)) ε).
Local Instance reservation_map_op_instance : Op (reservation_map A) := λ x y,
ReservationMap (reservation_map_data_proj x reservation_map_data_proj y)
(reservation_map_token_proj x reservation_map_token_proj y).
Local Instance reservation_map_valid_instance : Valid (reservation_map A) := λ x,
match reservation_map_token_proj x with
| CoPset E =>
(reservation_map_data_proj x)
(* dom (reservation_map_data_proj x) ⊥ E *)