Commit 2299d5e8 authored by Dan Frumin's avatar Dan Frumin

A wee bit of cleanup

parent 79e07b5f
......@@ -3,7 +3,6 @@
theories/lib/list.v
theories/lib/mset.v
theories/lib/spin_lock.v
theories/lib/flock.v
theories/lib/locking_heap.v
theories/lib/U.v
......
From iris.heap_lang Require Export proofmode notation.
From iris.heap_lang Require Import spin_lock.
(* From iris_c.lib Require Export spin_lock. *)
From iris.base_logic.lib Require Import cancelable_invariants auth saved_prop.
From iris.algebra Require Import auth agree excl frac gmap gset.
From iris.bi.lib Require Import fractional.
......@@ -38,7 +37,7 @@ Instance lockstate_inhabited : Inhabited lockstate := populate Unlocked.
Finally, the actual propositional content of the resources is
shared via cancellable invariants. Each proposition (active or
pending) is stored in a cancellable invariant associated with it:
C(X) = X.prop ∗ X.token₁ ∨ X.token₂
The exclusive tokens allow the thread to take out the proposition
......@@ -46,12 +45,12 @@ Instance lockstate_inhabited : Inhabited lockstate := populate Unlocked.
Record flock_name := {
(** ghost name for the actual spin lock invariant *)
flock_lock_name : gname;
flock_lock_name : gname;
(** -//- for keeping the track of the state of the flock *)
flock_state_name : gname;
(** -//- for keeping track of all propositions in the flock *)
flock_props_name : gname;
(** -//- for keeping track of the "active" propositions,
(** -//- for keeping track of the "active" propositions,
once you relase the lock you need to know that the set of the active propositions
has not changed since you have acquired it *)
flock_props_active_name : gname
......@@ -125,11 +124,11 @@ Section flock.
(* Tokens that allow you to get all the propositions from `A` out of the invariants *)
Definition all_tokens (P : gmap prop_id lock_res_name) : iProp Σ :=
([ map] i X P, token X)%I.
(** For active propositions we also need to know the fraction which was used to access it *)
Definition from_active (A : gmap prop_id (frac * lock_res_name))
:= fmap snd A.
Definition flock_res (γ : flock_name) (s : prop_id) (X : lock_res) : iProp Σ :=
(own (flock_props_name γ) ( {[s := (res_frac X, to_agree (res_name X))]})
cinv (resN.@s) (flock_cinv_name (res_name X)) (C (res_prop X) (res_name X))
......@@ -207,7 +206,7 @@ Section flock.
(* Global Instance flock_res_as_fractional γ s R π : *)
(* AsFractional (flock_res γ s R π) (flock_res γ s R) π. *)
(* Proof. split. done. apply _. Qed. *)
Lemma to_props_map_singleton_included fp i q ρ:
{[i := (q, to_agree ρ)]} to_props_map fp fp !! i = Some ρ.
Proof.
......@@ -219,7 +218,7 @@ Section flock.
Lemma to_props_map_delete fp i:
delete i (to_props_map fp) = to_props_map (delete i fp).
Proof.
by rewrite /to_props_map fmap_delete.
by rewrite /to_props_map fmap_delete.
Qed.
(** ** Spectral and physical operations *)
......@@ -236,7 +235,7 @@ Section flock.
"(>% & >Hstate & >Haprops & >Haactive & >Htokens & Hst)" "Hcl".
pose (i := (fresh ((dom (gset prop_id) (fp from_active fa)) X))).
assert (i (dom (gset prop_id) (fp from_active fa)) X) as Hs.
{ apply is_fresh. }
{ apply is_fresh. }
apply not_elem_of_union in Hs. destruct Hs as [Hi1 Hi2].
(* Alloc all the data for the resource *)
......@@ -248,7 +247,7 @@ Section flock.
{| flock_cinv_name := γc;
flock_token1_name := γt;
flock_token2_name := γt |}).
(* Put it in the map of flock resources *)
iMod (own_update with "Haprops") as "Haprops".
{ apply (auth_update_alloc _ (to_props_map (<[i := ρ]> fp from_active fa))
......@@ -267,7 +266,7 @@ Section flock.
set_solver. }
iFrame. iPureIntro.
apply map_disjoint_insert_l_2; eauto.
eapply (not_elem_of_dom (D:=gset prop_id)).
eapply (not_elem_of_dom (D:=gset prop_id)).
intros Hi; apply Hi1. rewrite dom_union_L elem_of_union. eauto.
}
iModIntro; iExists i, ρ; iSplit; eauto.
......@@ -307,8 +306,8 @@ Section flock.
{ apply lookup_union_Some in Hfoo; last done.
destruct Hfoo as [? | Hfoo]; first done.
exfalso. revert Hfoo. by rewrite /from_active lookup_fmap Hbar.
}
}
iMod (own_update_2 with "Haprops Hi") as "Haprops".
{ apply auth_update_dealloc, (delete_singleton_local_update _ i _). }
rewrite /all_tokens (big_sepM_delete _ fp i ρ) //.
......@@ -317,7 +316,7 @@ Section flock.
rewrite /C /=. iDestruct "HC" as "[[HR >T1] | >T2']"; last first.
{ iDestruct (own_valid_2 with "T2 T2'") as %?. done. }
iFrame "HR".
(* Now that the resource is cancelled we close the flock invariant *)
iApply "Hcl". iNext.
iExists Locked,fa,(delete i fp). iFrame.
......@@ -386,7 +385,7 @@ Section flock.
iApply wp_fupd.
iApply (acquire_spec with "Hlk").
iNext. iIntros "[Hlocked Hunlk]".
iInv invN as ([|] fa fp)
iInv invN as ([|] fa fp)
"(>% & >Hstate & >Haprops & >Haactive & >Htokens & Hst)" "Hcl".
- iDestruct "Hst" as "(>Hlocked2 & ?)".
iExFalso. iApply (locked_exclusive with "Hlocked Hlocked2").
......@@ -412,7 +411,7 @@ Section flock.
(* move (i,ρ) to the set of active propositions *)
rewrite /all_tokens (big_sepM_delete _ fp i ρ) //.
iDestruct "Htokens" as "[T2 Htokens]".
iMod (own_update_2 with "Haactive Hfactive") as "[Haactive Hfactive]".
{ apply (auth_update _ _ (Excl' {[ i := (π, ρ) ]})
(Excl' {[ i := (π, ρ) ]})).
......@@ -536,178 +535,43 @@ Section flock.
rewrite -lookup_fmap HJ' //.
Qed.
(* Lemma big_sepM_own_frag {A B : Type} `{EqDecision A, Countable A} *)
(* `{inG Σ (authR (gmapUR A C))} (f : B → C) (m : gmap A B) (γ : gname) : *)
(* own γ (◯ ∅) -∗ *)
(* own γ (◯ (f <$> m)) ∗-∗ [∗ map] i↦x ∈ m, own γ (◯ {[ i := f x ]}). *)
(* Proof. *)
(* simple refine (map_ind (λ m, _)%I _ _ m); simpl. *)
(* - iIntros "He". rewrite fmap_empty big_sepM_empty. iSplit; eauto. *)
(* - iIntros (i x m' Hi IH) "He". *)
(* rewrite fmap_insert insert_union_singleton_l. *)
(* assert (({[i := f x]} ∪ (f <$> m')) = {[i := f x]} ⋅ (f <$> m')) as ->. *)
(* { rewrite /op /cmra_op /= /gmap_op. *)
(* apply map_eq. intros j. destruct (decide (i = j)) as [->|?]. *)
(* - etransitivity. eapply lookup_union_Some_l. apply lookup_insert. *)
(* symmetry. rewrite lookup_merge lookup_insert. *)
(* rewrite lookup_fmap Hi /=. done. *)
(* - remember (m' !! j) as mj. *)
(* destruct mj; simplify_eq/=. *)
(* + etransitivity. apply lookup_union_Some_raw. *)
(* right. split; first by rewrite lookup_insert_ne. *)
(* by rewrite lookup_fmap -Heqmj. *)
(* symmetry. rewrite lookup_merge lookup_singleton_ne; eauto. *)
(* rewrite lookup_fmap -Heqmj. done. *)
(* + etransitivity. apply lookup_union_None. *)
(* split; first by rewrite lookup_singleton_ne. *)
(* rewrite lookup_fmap -Heqmj //. *)
(* symmetry. *)
(* rewrite lookup_merge lookup_singleton_ne // lookup_fmap -Heqmj //. } *)
(* rewrite auth_frag_op own_op IH big_sepM_insert; last eauto. *)
(* iSplit; iIntros "[$ Hm']"; by iApply "He". *)
(* Qed. *)
Lemma big_sepM_own_frag {A B : Type} {C} `{EqDecision A, Countable A}
`{inG Σ (authR (gmapUR A C))} (f : B C) (m : gmap A B) (γ : gname) :
own γ ( ) -
own γ ( (f <$> m)) - [ map] ix m, own γ ( {[ i := f x ]}).
Proof.
simple refine (map_ind (λ m, _)%I _ _ m); simpl.
- iIntros "He". rewrite fmap_empty big_sepM_empty. iSplit; eauto.
- iIntros (i x m' Hi IH) "He".
rewrite fmap_insert insert_union_singleton_l.
assert (({[i := f x]} (f <$> m')) = {[i := f x]} (f <$> m')) as ->.
{ rewrite /op /cmra_op /= /gmap_op.
apply map_eq. intros j. destruct (decide (i = j)) as [->|?].
- etransitivity. eapply lookup_union_Some_l. apply lookup_insert.
symmetry. rewrite lookup_merge lookup_insert.
rewrite lookup_fmap Hi /=. done.
- remember (m' !! j) as mj.
destruct mj; simplify_eq/=.
+ etransitivity. apply lookup_union_Some_raw.
right. split; first by rewrite lookup_insert_ne.
by rewrite lookup_fmap -Heqmj.
symmetry. rewrite lookup_merge lookup_singleton_ne; eauto.
rewrite lookup_fmap -Heqmj. done.
+ etransitivity. apply lookup_union_None.
split; first by rewrite lookup_singleton_ne.
rewrite lookup_fmap -Heqmj //.
symmetry.
rewrite lookup_merge lookup_singleton_ne // lookup_fmap -Heqmj //. }
rewrite auth_frag_op own_op IH big_sepM_insert; last eauto.
iSplit; iIntros "[$ Hm']"; by iApply "He".
Qed.
(* (* here it is crucial that we use a gmap: *)
(* that way there is at most one flock_res associated with a prop_id *) *)
(* Lemma acquire_cancel_spec γ lk (I : gmap prop_id (iProp Σ * frac)) : *)
(* {{{ is_flock γ lk ∗ [∗ map] i ↦ p ∈ I, flock_res γ i p.1 p.2 }}} *)
(* acquire lk *)
(* {{{ RET #(); *)
(* (▷ [∗ map] p ∈ I, p.1) *)
(* ∗ ((▷ [∗ map] p ∈ I, p.1) ={⊤}=∗ flocked γ ∅ *)
(* ∗ [∗ map] i ↦ p ∈ I, flock_res γ i p.1 p.2) }}}. *)
(* Proof. *)
(* iIntros (Φ) "(Hl & HRres) HΦ". *)
(* rewrite /is_flock. iDestruct "Hl" as "(#Hinv & #Hlk)". *)
(* iApply (acquire_spec with "Hlk"). *)
(* iNext. iIntros "[Hlocked Hunlk]". *)
(* iInv (flockN.@"inv") as ([|] fp fa) "(>% & >Hstate & >Hauth & >Hfactive & Hfp & Hrest)" "Hcl". *)
(* - iDestruct "Hrest" as "(>Hlocked2 & Htokens)". *)
(* iExFalso. iApply (locked_exclusive with "Hlocked Hlocked2"). *)
(* - iDestruct "Hrest" as ">Haactive". *)
(* iAssert (⌜fa = ∅⌝)%I with "[-]" as %->. *)
(* { iDestruct (own_valid_2 with "Haactive Hfactive") *)
(* as %[Hfoo%Excl_included _]%auth_valid_discrete_2. *)
(* iPureIntro. by unfold_leibniz. } *)
(* rewrite from_active_empty right_id. *)
(* (* Unlocked ~~> Locked *) *)
(* iMod (own_update_2 with "Hstate Hunlk") as "Hstate". *)
(* { apply (auth_update _ _ (Excl' Locked) (Excl' Locked)). *)
(* apply option_local_update. *)
(* by apply exclusive_local_update. } *)
(* iDestruct "Hstate" as "[Hstate Hflkd]". *)
(* iDestruct (extract_existential with "HRres") as (J HJ) "HRres". *)
(* iAssert (([∗ map] a↦bc ∈ J, own (flock_props_name γ) (◯ {[a := (bc.1.2, to_agree bc.2)]})) ∗ ([∗ map] a↦bc ∈ J, saved_prop_own bc.2.1 bc.1.1 ∗ own bc.2.2 bc.1.2))%I with "[HRres]" as "[Hfs HJ]". *)
(* { rewrite -big_sepM_sepM. iApply (big_sepM_mono with "HRres"). *)
(* iIntros (k x Hk) "(? & ? & ?)". eauto with iFrame. } *)
(* pose (fs := fmap (λ bc, {| prop_perm := bc.1.2; prop_saved_name := bc.2.1; prop_perm_name := bc.2.2 |}) J). *)
(* iMod (own_update _ _ (● to_props_map fp ⋅ ◯ ∅) with "Hauth") as "[Hauth He]". *)
(* { by apply auth_update_alloc. } *)
(* iAssert (own (flock_props_name γ) (◯ to_props_map_ fs))%I with "[Hfs He]" as "Hfs". *)
(* { unfold fs. iApply (big_sepM_own_frag with "He"). *)
(* rewrite big_sepM_fmap /=. iApply (big_sepM_mono with "Hfs"). *)
(* iIntros (k x Hk) "H /=". by destruct (x.2). } *)
(* (* fs ≤ fp *) *)
(* iDestruct (own_valid_2 with "Hauth Hfs") *)
(* as %[Hfoo _]%auth_valid_discrete_2. *)
(* assert (∃ fo : gmap prop_id PropPerm, *)
(* to_props_map fp = to_props_map_ fs ⋅ to_props_map_ fo) *)
(* as [fo Hfo]. *)
(* { admit. } *)
(* rewrite (all_props_to_props_map_ fp fs fo); last done. *)
(* iDestruct "Hfp" as "[Hfs_props Hfo]". *)
(* iMod (own_update_2 with "Haactive Hfactive") as "[Haactive Hfactive]". *)
(* { apply (auth_update _ _ (Excl' fs) *)
(* (Excl' fs)). *)
(* by apply option_local_update, exclusive_local_update. } *)
(* rewrite (big_sepM_sepM _ _ J). *)
(* iDestruct "HJ" as "[#HJ Htokens]". *)
(* iMod ("Hcl" with "[-HΦ Haactive Hflkd Hfs_props Hfs HJ]") as "_". *)
(* { iNext. iExists Locked,(from_active fo),fs. *)
(* iFrame. iSplitR. admit. (* TODO: map_disjoint *) *)
(* iSplitL "Hauth". *)
(* - admit. (* fp = from_active fo ∪ from_active fs *) *)
(* - rewrite /all_tokens /fs big_sepM_fmap /= //. } *)
(* iAssert (▷▷ [∗ map] p ∈ I, p.1)%I with "[Hfs_props]" as "Hfs_props". *)
(* { iNext. rewrite /all_props /fs -HJ !big_sepM_fmap big_sepM_later /=. *)
(* (* TODO: why is big_sepM_mono not formulated with the persistence modality? *) *)
(* iCombine "HJ Hfs_props" as "Hfs". *)
(* rewrite -big_sepM_sepM. *)
(* iApply (big_sepM_mono with "Hfs"). *)
(* iIntros (k ρ Hk) "[#Hsaved HR]". *)
(* iDestruct "HR" as (R') "[Hsaved' HR']". *)
(* iDestruct (saved_prop_agree with "Hsaved Hsaved'") as "#Hfoo". *)
(* iNext. iRewrite -"Hfoo" in "HR'". done. *)
(* (* TODO: iRewrite "Hfoo" didn't work *) } *)
(* iModIntro. iApply "HΦ". *)
(* iNext. iFrame "Hfs_props". iIntros "Hfs_props". *)
(* clear Hfoo H1 Hfo fp. rewrite /flocked /flock_res. *)
(* iInv (flockN.@"inv") as ([|] fp fa) "(>% & >Hstate & >Hauth & >Hfactive & Hfp & Hrest)" "Hcl"; last first. *)
(* + iDestruct (own_valid_2 with "Hstate Hflkd") *)
(* as %[Hfoo%Excl_included _]%auth_valid_discrete_2. *)
(* fold_leibniz. inversion Hfoo. *)
(* + iDestruct "Hrest" as ">[Hlocked Htokens]". *)
(* iDestruct (own_valid_2 with "Haactive Hfactive") *)
(* as %[Hfoo%Excl_included _]%auth_valid_discrete_2. *)
(* fold_leibniz. simplify_eq/=. *)
(* iMod (own_update_2 with "Haactive Hfactive") as "[Haactive Hfactive]". *)
(* { apply (auth_update _ _ (Excl' ∅) (Excl' ∅)). *)
(* by apply option_local_update, exclusive_local_update. } *)
(* (* fs ≤ fp *) *)
(* iDestruct (own_valid_2 with "Hauth Hfs") *)
(* as %[Hfoo _]%auth_valid_discrete_2. *)
(* iMod (own_update _ _ (● to_props_map _ ⋅ ◯ ∅) with "Hauth") as "[Hauth He]". *)
(* { by apply auth_update_alloc. } *)
(* iMod ("Hcl" with "[Hlocked Hstate Hauth Hfactive Hfp Hfs_props]") as "_". *)
(* { iNext. iExists Locked,(fp ∪ from_active fs),∅. iFrame. *)
(* iSplitR. *)
(* { rewrite from_active_empty. iPureIntro. apply map_disjoint_empty_r. } *)
(* iSplitL "Hauth". *)
(* - by rewrite from_active_empty right_id. *)
(* - iSplitL; last first. *)
(* { by rewrite /all_tokens big_sepM_empty. } *)
(* rewrite big_sepM_fmap. *)
(* rewrite /fs /from_active. *)
(* (* TODO: need all_props union lemma *) *)
(* admit. } *)
(* iModIntro. iFrame. rewrite /all_props from_active_empty big_sepM_empty. *)
(* iSplitR; first done. rewrite /all_tokens big_sepM_fmap. *)
(* rewrite {1}/fs /to_props_map_ -map_fmap_compose /=. *)
(* iAssert ([∗ map] k↦y ∈ J, own (flock_props_name γ) (◯ {[k := (y.1.2, to_agree y.2)]}))%I with "[Hfs He]" as "Hfs". *)
(* { iApply (big_sepM_own_frag with "He"); simpl. *)
(* assert (((λ y, (y.1.2, to_agree y.2)) <$> J) = ((λ x : PropPerm, (prop_perm x, *)
(* to_agree (prop_saved_name x, prop_perm_name x))) *)
(* ∘ (λ bc : iProp Σ * Qp * (gname * gname), *)
(* {| *)
(* prop_perm := bc.1.2; *)
(* prop_saved_name := bc.2.1; *)
(* prop_perm_name := bc.2.2 |}) <$> J)) as Hh. *)
(* { apply map_eq=>i /=. rewrite !lookup_fmap /=. *)
(* destruct (J !! i);eauto. simpl. by destruct (p.2). } *)
(* rewrite Hh. done. } *)
(* iCombine "Hfs Htokens" as "Hm". *)
(* rewrite /fs big_sepM_fmap -big_sepM_sepM. *)
(* iCombine "HJ Hm" as "Hm". rewrite -big_sepM_sepM. *)
(* iApply (big_sepM_mono with "Hm"). *)
(* iIntros (k x Hk) "(Hsaved & Hx & Hperm)". simpl. *)
(* iExists x.2. iFrame. *)
(* Admitted. *)
Lemma acquire_flock_spec γ lk (I : gmap prop_id lock_res) :
{{{ is_flock γ lk [ map] i X I, flock_res γ i X }}}
acquire lk
{{{ RET #();
([ map] i X I, (res_prop X))
(([ map] i X I, (res_prop X)) ={}= flocked γ I) }}}.
Proof. Abort.
End flock.
From iris.program_logic Require Export weakestpre.
From iris.heap_lang Require Export lang.
From iris.proofmode Require Import tactics.
From iris.heap_lang Require Import proofmode notation.
From iris.algebra Require Import excl.
From iris.heap_lang.lib Require Import lock.
Set Default Proof Using "Type".
Definition newlock : val := λ: <>, ref #false.
Definition try_acquire : val := λ: "l", CAS "l" #false #true.
Definition acquire : val :=
rec: "acquire" "l" := if: try_acquire "l" then #() else "acquire" "l".
Definition release : val := λ: "l", "l" <- #false.
(** The CMRA we need. *)
(* Not bundling heapG, as it may be shared with other users. *)
Class lockG Σ := LockG { lock_tokG :> inG Σ (exclR unitC) }.
Definition lockΣ : gFunctors := #[GFunctor (exclR unitC)].
Instance subG_lockΣ {Σ} : subG lockΣ Σ lockG Σ.
Proof. solve_inG. Qed.
Section proof.
Context `{!heapG Σ, !lockG Σ} (N : namespace).
Definition lock_inv (γ : gname) (l : loc) (R : iProp Σ) : iProp Σ :=
( b : bool, l #b if b then True else own γ (Excl ()) R)%I.
Definition is_lock (γ : gname) (lk : val) (R : iProp Σ) : iProp Σ :=
( l: loc, lk = #l inv N (lock_inv γ l R))%I.
Definition locked (γ : gname) : iProp Σ := own γ (Excl ()).
Lemma locked_exclusive (γ : gname) : locked γ - locked γ - False.
Proof. iIntros "H1 H2". by iDestruct (own_valid_2 with "H1 H2") as %?. Qed.
Global Instance lock_inv_ne γ l : NonExpansive (lock_inv γ l).
Proof. solve_proper. Qed.
Global Instance is_lock_ne γ l : NonExpansive (is_lock γ l).
Proof. solve_proper. Qed.
(** The main proofs. *)
Global Instance is_lock_persistent γ l R : Persistent (is_lock γ l R).
Proof. apply _. Qed.
Global Instance locked_timeless γ : Timeless (locked γ).
Proof. apply _. Qed.
Lemma newlock_spec (R : iProp Σ):
{{{ R }}} newlock #() {{{ lk γ, RET lk; is_lock γ lk R }}}.
Proof.
iIntros (Φ) "HR HΦ". rewrite -wp_fupd /newlock /=.
wp_lam. wp_alloc l as "Hl".
iMod (own_alloc (Excl ())) as (γ) "Hγ"; first done.
iMod (inv_alloc N _ (lock_inv γ l R) with "[-HΦ]") as "#?".
{ iIntros "!>". iExists false. by iFrame. }
iModIntro. iApply "HΦ". iExists l. eauto.
Qed.
Lemma try_acquire_spec γ lk R :
{{{ is_lock γ lk R }}} try_acquire lk
{{{ b, RET #b; if b is true then locked γ R else True }}}.
Proof.
iIntros (Φ) "#Hl HΦ". iDestruct "Hl" as (l ->) "#Hinv".
wp_rec. iInv N as ([]) "[Hl HR]" "Hclose".
- wp_cas_fail. iMod ("Hclose" with "[Hl]"); first (iNext; iExists true; eauto).
iModIntro. iApply ("HΦ" $! false). done.
- wp_cas_suc. iDestruct "HR" as "[Hγ HR]".
iMod ("Hclose" with "[Hl]"); first (iNext; iExists true; eauto).
iModIntro. rewrite /locked. by iApply ("HΦ" $! true with "[$Hγ $HR]").
Qed.
Lemma acquire_spec γ lk R :
( Φ,
is_lock γ lk R - (locked γ R - |={}=> Φ #()%V) - WP acquire lk {{ Φ }})%I.
Proof.
iIntros (Φ) "#Hl HΦ". iLöb as "IH". wp_rec.
wp_apply (try_acquire_spec with "Hl"). iIntros ([]).
- iIntros "[Hlked HR]". iMod ("HΦ" with "[$Hlked $HR]"). wp_if. done.
- iIntros "_". wp_if. iApply ("IH" with "[HΦ]"). auto.
Qed.
Lemma release_spec γ lk R :
{{{ is_lock γ lk R locked γ R }}} release lk {{{ RET #(); True }}}.
Proof.
iIntros (Φ) "(Hlock & Hlocked & HR) HΦ".
iDestruct "Hlock" as (l ->) "#Hinv".
rewrite /release /=. wp_let. iInv N as (b) "[Hl _]" "Hclose".
wp_store. iApply "HΦ". iApply "Hclose". iNext. iExists false. by iFrame.
Qed.
End proof.
Typeclasses Opaque is_lock locked.
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