Commit 30394154 authored by Ralf Jung's avatar Ralf Jung
Browse files

introduce a notion oflocal updates (up for discussion) and use it to formulate the auth rules

parent 0b7e25c2
Require Export algebra.excl.
Require Import algebra.functor.
Require Import algebra.functor algebra.option.
Local Arguments validN _ _ _ !_ /.
Record auth (A : Type) : Type := Auth { authoritative : excl A ; own : A }.
......@@ -169,6 +169,18 @@ Qed.
Lemma auth_update_op_r a a' b :
(a b) a a' ~~> (a b) (a' b).
Proof. rewrite -!(commutative _ b); apply auth_update_op_l. Qed.
Lemma auth_local_update (L : LocalUpdate A) `{!LocalUpdateSpec L} a a' b :
L a = Some b (b a')
(a a') a ~~> (b a') b.
intros Hlv Hv. apply auth_update=>n af Hab EQ.
split; last done.
apply (injective (R:=()) Some).
rewrite !Some_op -Hlv.
rewrite -!local_update_spec //; eauto; last by rewrite -EQ; [].
by rewrite EQ.
End cmra.
Arguments authRA : clear implicits.
......@@ -384,6 +384,7 @@ Section cmra_monotone.
Proof. rewrite !cmra_valid_validN; eauto using validN_preserving. Qed.
End cmra_monotone.
(** * Transporting a CMRA equality *)
Definition cmra_transport {A B : cmraT} (H : A = B) (x : A) : B :=
eq_rect A id x _ H.
Require Export algebra.cmra.
Require Import algebra.functor.
Require Import algebra.functor algebra.option.
Local Arguments validN _ _ _ !_ /.
Local Arguments valid _ _ !_ /.
......@@ -143,6 +143,18 @@ Lemma excl_update (x : A) y : ✓ y → Excl x ~~> y.
Proof. by destruct y; intros ? [?| |]. Qed.
Lemma excl_updateP (P : excl A Prop) x y : y P y Excl x ~~>: P.
Proof. intros ?? z n ?; exists y. by destruct y, z as [?| |]. Qed.
Definition excl_local_update_to (b : A) : LocalUpdate exclRA :=
λ a, if a is Excl _ then Some (Excl b) else None.
Global Instance excl_local_update_to_spec b :
LocalUpdateSpec (excl_local_update_to b).
- move=>? a a' EQ. destruct EQ; done.
- move=>a a' n [b' Hlv] Hv /=. destruct a; try discriminate Hlv; [].
destruct a'; try contradiction Hv; []. reflexivity.
End excl.
Arguments exclC : clear implicits.
......@@ -263,6 +263,7 @@ Lemma map_singleton_updateP_empty' `{Empty A, !CMRAIdentity A} (P: A → Prop) i
~~>: P ~~>: λ m, y, m = {[ i y ]} P y.
Proof. eauto using map_singleton_updateP_empty. Qed.
Section freshness.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Lemma map_updateP_alloc (Q : gmap K A Prop) m x :
x ( i, m !! i = None Q (<[i:=x]>m)) m ~~>: Q.
......@@ -277,6 +278,49 @@ Qed.
Lemma map_updateP_alloc' m x :
x m ~~>: λ m', i, m' = <[i:=x]>m m !! i = None.
Proof. eauto using map_updateP_alloc. Qed.
End freshness.
Section local.
Definition map_local_alloc i x : LocalUpdate (mapRA K A) :=
local_update_op {[ i x ]}.
(* Deallocation is not a local update. The trouble is that if we own {[ i ↦ x ]},
then the frame could always own "unit x", and prevent deallocation. *)
Context (L : LocalUpdate A) `{!LocalUpdateSpec L}.
Definition map_local_update i : LocalUpdate (mapRA K A) :=
λ m, x m !! i; y L x; Some (<[i:=y]>m).
Global Instance map_local_update_spec i : LocalUpdateSpec (map_local_update i).
rewrite /map_local_update. split.
- (* FIXME Oh wow, this is harder than expected... *)
move=>n f g EQ. move:(EQ i).
case _:(f !! i)=>[fi|]; case _:(g !! i)=>[gi|]; move=>EQi;
inversion EQi; subst; simpl; last done.
assert (EQL : L fi {n} L gi) by (by apply local_update_ne). move: EQL.
case _:(L fi)=>[Lfi|] /=; case _:(L gi)=>[Lgi|]; move=>EQL;
inversion EQL; subst; simpl; last done.
apply Some_ne, insert_ne; done.
- move=>f g n [b Hlv] Hv. rewrite lookup_op. move:Hlv.
case EQf:(f !! i)=>[fi|]; simpl; last discriminate.
case EQL:(L fi)=>[Lfi|]; simpl; last discriminate.
case=>?. subst b.
case EQg:(g !! i)=>[gi|]; simpl.
+ assert (L (fi gi) {n} L fi Some gi) as EQLi.
{ apply local_update_spec; first by eauto.
move:(Hv i). rewrite lookup_op EQf EQg -Some_op. done. }
rewrite EQL -Some_op in EQLi.
destruct (L (fi gi)) as [Lfgi|]; inversion EQLi; subst; simpl.
rewrite -Some_op. apply Some_ne. move=>j. rewrite lookup_op.
destruct (decide (i = j)); simplify_map_equality; last by rewrite lookup_op.
rewrite EQg -Some_op. apply Some_ne. done.
+ rewrite EQL /=.
rewrite -Some_op. apply Some_ne. move=>j. rewrite lookup_op.
destruct (decide (i = j)); simplify_map_equality; last by rewrite lookup_op.
by rewrite EQg.
End local.
End properties.
(** Functor *)
......@@ -314,3 +358,4 @@ Next Obligation.
intros K ?? Σ A B C f g x. rewrite /= -map_fmap_compose.
apply map_fmap_setoid_ext=> ? y _; apply ifunctor_map_compose.
......@@ -82,6 +82,7 @@ Lemma None_includedN n (mx : option A) : None ≼{n} mx.
Proof. rewrite option_includedN; auto. Qed.
Lemma Some_Some_includedN n (x y : A) : x {n} y Some x {n} Some y.
Proof. rewrite option_includedN; eauto 10. Qed.
Definition Some_op a b : Some (a b) = Some a Some b := eq_refl.
Definition option_cmra_mixin : CMRAMixin (option A).
......@@ -186,3 +187,28 @@ Next Obligation.
intros Σ A B C f g x. rewrite /= -option_fmap_compose.
apply option_fmap_setoid_ext=>y; apply ifunctor_map_compose.
(** * Local CMRA Updates *)
(* FIXME: These need the CMRA structure on option, hence they are defined here. Or maybe moe option to cmra.v? *)
(* TODO: Probably needs some more magic flags. What about notation? *)
Section local_update.
Context {A : cmraT}.
(* Do we need more step-indexing here? *)
Definition LocalUpdate := A option A.
Class LocalUpdateSpec (L : LocalUpdate) := {
local_update_ne n :> Proper ((dist n) ==> (dist n)) L;
local_update_spec a b n : is_Some (L a) {n}(a b) L (a b) {n} (L a) Some b
Definition local_update_op (b : A) : LocalUpdate
:= λ a, Some (b a).
Global Instance local_update_op_spec b : LocalUpdateSpec (local_update_op b).
rewrite /local_update_op. split.
- move=>? ? ? EQ /=. by rewrite EQ.
- move=>a a' n Hlv Hv /=. by rewrite associative.
End local_update.
Arguments LocalUpdate : clear implicits.
......@@ -58,16 +58,17 @@ Section auth.
by rewrite sep_elim_l.
Lemma auth_closing a a' b γ :
auth_step (a a') a (b a') b
Context (L : LocalUpdate A) `{!LocalUpdateSpec L}.
Lemma auth_closing a a' b γ :
L a = Some b (b a')
(φ (b a') own AuthI γ ( (a a') a))
pvs N N (auth_inv γ auth_own γ b).
intros Hstep. rewrite /auth_inv /auth_own -(exist_intro (b a')).
intros HL Hv. rewrite /auth_inv /auth_own -(exist_intro (b a')).
rewrite [(_ φ _)%I]commutative -associative.
rewrite -pvs_frame_l. apply sep_mono; first done.
rewrite -own_op. apply own_update.
by apply auth_update.
by apply (auth_local_update L).
End auth.
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