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proof_rcu_simple.v
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proof_rcu_simple.v
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From iris.base_logic.lib Require Import invariants ghost_map.
From smr.program_logic Require Import atomic.
From smr.lang Require Import proofmode notation.
From smr Require Import ebr.spec_rcu_base ebr.spec_rcu_simple helpers logic.reclamation.
From iris.prelude Require Import options.
Set Printing Projections.
Section ebr.
Context `{!heapGS Σ, !reclamationG Σ}.
Context (N : namespace).
Context (base : spec_rcu_base.rcu_base_spec Σ (mgmtN N) (ptrsN N)).
Implicit Types
(γd γb γdata γ_p : gname)
(i : positive)
(R : resource Σ).
Definition Managed γd (p : blk) (γ_p : gname) (sz : nat) R : iProp Σ :=
∃ γb γdata i,
⌜γd = encode (γb, γdata)⌝ ∗
i ↪[γdata]□ γ_p ∗
base.(BaseManaged) γb p i sz (wrap_resource γdata R γ_p).
Definition Guard γd (g : loc) (st : guard_state) : iProp Σ :=
∃ γb γdata,
⌜γd = encode (γb, γdata)⌝ ∗
match st with
| Deactivated => base.(BaseInactive) γb g
| Activated γg => ∃ Syn G Gb,
base.(BaseGuard) γb γg g Syn Gb ∗
[∗ map] p ↦ γ_p; i ∈ G; Gb,
i ↪[γdata]□ γ_p
end.
Definition RCUInv γb γdata Im Dm Rs : iProp Σ :=
ghost_map_auth γdata 1 Dm ∗
base.(RCUAuth) γb Im Rs ∗
⌜dom Im = dom Dm⌝.
Definition IsRCUDomain γd d : iProp Σ :=
∃ γb γdata,
⌜γd = encode (γb, γdata)⌝ ∗
base.(spec_rcu_base.IsRCUDomain) γb d ∗
inv ((mgmtN N).@"simpl") (∃ Im Dm Rs, RCUInv γb γdata Im Dm Rs).
Definition NodeInfo γd γg p γ_p size_i R : iProp Σ :=
∃ γb γdata i,
⌜γd = encode (γb, γdata)⌝ ∗
i ↪[γdata]□ γ_p ∗
base.(BaseGuardedNodeInfo) γb γg p i size_i (wrap_resource γdata R γ_p).
Global Instance IsRCUDomain_Persistent γd d : Persistent (IsRCUDomain γd d).
Proof. apply _. Qed.
Global Instance NodeInfo_Persistent γd γg p γ_p size_i R : Persistent (NodeInfo γd γg p γ_p size_i R).
Proof. apply _. Qed.
Lemma rcu_domain_new_spec :
rcu_domain_new_spec' N base.(rcu_domain_new) IsRCUDomain.
Proof.
intros ?.
iIntros (Φ) "_ HΦ".
iApply wp_fupd.
wp_apply (spec_rcu_base.rcu_domain_new_spec with "[//]") as (γb d) "[#BIRD BR]".
iMod (ghost_map_alloc ∅) as (γdata) "[data _]".
remember (encode (γb,γdata)) as γd eqn:Hγd.
iMod (inv_alloc ((mgmtN N).@"simpl") _ (∃ Im Dm Rs, RCUInv γb γdata Im Dm Rs) with "[data BR]") as "#?".
{ iNext. repeat iExists _. iFrame. by rewrite !dom_empty_L. }
iApply "HΦ". repeat iExists _. by iFrame (Hγd) "∗#".
Qed.
Lemma rcu_domain_register :
rcu_domain_register' N IsRCUDomain Managed.
Proof.
intros ????????.
iIntros "#IRD (p↦ & †p & R)".
iDestruct "IRD" as (γb γdata Hγd) "(BIRD & RI)".
iInv "RI" as (???) ">(data & BRA & %Hdom)".
iMod (spec_rcu_base.rcu_domain_register base (λ p lv i, i ↪[γdata]□ γ_p ∗ R p lv γ_p)%I
(dom Dm)
(λ i, ghost_map_auth γdata 1 (<[i := γ_p]> Dm) ∗ i ↪[γdata]□ γ_p)%I
with "BIRD BRA p↦ †p [data $R]") as "OUT"; [solve_ndisj..| |].
{ iIntros (i Hi).
by iMod (ghost_map_insert_persist i γ_p with "data") as "[$ #$]"; [by apply not_elem_of_dom|].
}
iDestruct "OUT" as (i Hi) "(BRA & BM & [data #i↪□])".
iModIntro. iSplitL "BRA data".
{ iNext. repeat iExists _. iFrame.
iPureIntro. rewrite !dom_insert_L. set_solver.
}
iModIntro. repeat iExists _. iFrame (Hγd) "∗#".
Qed.
Lemma guard_new_spec :
guard_new_spec' N base.(guard_new) IsRCUDomain Guard.
Proof.
intros ????.
iIntros "#IRD" (Φ) "!> _ HΦ".
iDestruct "IRD" as (γb γdata Hγd) "(BIRD & RI)".
wp_apply (spec_rcu_base.guard_new_spec with "BIRD [//]") as (g) "BG"; [solve_ndisj|].
iApply "HΦ".
repeat iExists _. iFrame (Hγd) "∗".
Qed.
Lemma guard_activate_spec :
guard_activate_spec' N base.(guard_activate) IsRCUDomain Guard.
Proof.
intros ?????.
iIntros "#IRD" (Φ) "!> G HΦ".
iDestruct "IRD" as (γb γdata Hγd) "(BIRD & RI)".
iDestruct "G" as (???) "BG". encode_agree Hγd.
wp_apply (spec_rcu_base.guard_activate_spec with "BIRD BG") as (γg Syn) "BG"; [solve_ndisj|].
iApply "HΦ".
repeat iExists _. iFrame (Hγd) "∗".
repeat iExists _. by iFrame "∗".
Qed.
Lemma guard_managed_agree :
guard_managed_agree' N Managed Guard NodeInfo.
Proof.
intros ??????????.
iIntros "#Info G M".
iDestruct "Info" as (??? Hγd) "[#i↪□' BInfo]".
iDestruct "G" as (??? Syn G Gb) "[BG #GInfo]".
iDestruct "M" as (????) "[#i↪□ BM]". do 2 encode_agree Hγd.
iDestruct (spec_rcu_base.guard_managed_agree with "BInfo BG BM") as %<-.
by iDestruct (ghost_map_elem_agree with "i↪□ i↪□'") as %?.
Qed.
Lemma guard_protect :
guard_protect' N IsRCUDomain Managed Guard NodeInfo.
Proof.
intros ??????????.
iIntros "#IRD M G".
iDestruct "IRD" as (?? Hγd) "(BIRD & RI)".
iDestruct "G" as (??? Syn G Gb) "[BG #GInfo]".
iDestruct "M" as (????) "[#i↪□ BM]". do 2 encode_agree Hγd.
iMod (spec_rcu_base.guard_protect with "BIRD BM BG") as "(BM & BG & %NotIn & %LookUp)"; [solve_ndisj|].
iDestruct (spec_rcu_base.managed_get_node_info with "BM") as "#BInfo".
iMod (spec_rcu_base.guard_protect_node_info with "BIRD BInfo BG") as "(BG & #BGInfo & _)"; [solve_ndisj|done|].
rewrite insert_insert.
iModIntro. iSplitL "BM".
{ repeat iExists _; iFrame (Hγd) "∗#". }
iDestruct (big_sepM2_dom with "GInfo") as %Hdom.
destruct (decide (is_Some (Gb !! p))) as [Hp|Hp%eq_None_not_Some]; last first.
{ assert (G !! p = None).
{ by rewrite -not_elem_of_dom Hdom not_elem_of_dom. }
iSplit; repeat iExists _; iFrame (Hγd) "∗#".
iExists _,(<[ p:= _ ]> G),_. iFrame.
rewrite (big_sepM2_insert _ _ _ p); [|done..].
iFrame "#".
}
specialize (LookUp Hp) as HGbp.
rewrite insert_id //.
iDestruct (big_sepM2_lookup_r with "GInfo") as (? HGp) "#i↪□'"; [exact HGbp|].
iDestruct (ghost_map_elem_agree with "i↪□ i↪□'") as %<-.
iSplit; repeat iExists _; iFrame (Hγd) "∗#".
repeat iExists _. iFrame "∗#".
Qed.
Lemma guard_acc :
guard_acc' N Guard NodeInfo.
Proof.
intros ?????????.
iIntros "#Info G".
iDestruct "Info" as (??? Hγd) "[i↪□ BInfo]".
iDestruct "G" as (??? Syn G Gb) "[BG #GInfo]".
encode_agree Hγd.
iMod (spec_rcu_base.guard_acc with "BInfo BG") as (lv) "(%Hlv & p↦ & [_ R] & BG & Close1)"; [solve_ndisj|].
iApply fupd_mask_intro; [solve_ndisj|]. iIntros "Close2".
iExists lv. iFrame "∗%".
iSplitL "BG".
{ repeat iExists _. iFrame (Hγd) "∗#". repeat iExists _. iFrame "∗#". }
iIntros (lv') "(%Hlv' & p↦ & R)".
iMod "Close2".
iMod ("Close1" with "[$p↦ R]"). { iFrame (Hlv') "∗#". }
done.
Qed.
Lemma managed_acc :
managed_acc' N Managed.
Proof.
intros ???????.
iDestruct 1 as (??? Hγd) "[#i↪ BM]".
iMod (spec_rcu_base.managed_acc with "BM") as (lv) "(% & p↦ & [_ R] & BM & Close1)"; [solve_ndisj|].
iApply fupd_mask_intro; [solve_ndisj|]. iIntros "Close2".
iExists lv. iFrame "∗%".
iSplitL "BM".
{ repeat iExists _. iFrame (Hγd) "∗#". }
iIntros (lv') "(%Hlv' & p↦ & R)".
iMod "Close2".
iMod ("Close1" with "[$p↦ R]"). { iFrame (Hlv') "∗#". }
done.
Qed.
Lemma managed_exclusive :
managed_exclusive' N Managed.
Proof.
iDestruct 1 as (??? Hγd) "[#i↪ BM1]".
iDestruct 1 as (??? ?) "[#i↪' BM2]".
encode_agree Hγd.
iApply (spec_rcu_base.managed_exclusive with "BM1 BM2").
Qed.
Lemma guard_deactivate_spec :
guard_deactivate_spec' N base.(guard_deactivate) IsRCUDomain Guard.
Proof.
intros ??????.
iIntros "#IRD" (Φ) "!> G HΦ".
iDestruct "IRD" as (γb γdata Hγd) "(BIRD & RI)".
iDestruct "G" as (??????) "[BG #GInfo]". encode_agree Hγd.
wp_apply (spec_rcu_base.guard_deactivate_spec with "BIRD BG") as "BG"; [solve_ndisj|].
iApply "HΦ".
repeat iExists _. iFrame (Hγd) "∗".
Qed.
Lemma guard_drop_spec :
guard_drop_spec' N base.(guard_drop) IsRCUDomain Guard.
Proof.
intros ??????.
iIntros "#IRD" (Φ) "!> G HΦ".
iDestruct "IRD" as (γb γdata Hγd) "(BIRD & RI)".
iDestruct "G" as (???) "BG". encode_agree Hγd.
destruct gs.
- wp_apply (spec_rcu_base.guard_drop_inactive_spec with "BIRD BG"); [solve_ndisj|]. done.
- iDestruct "BG" as (???) "[BG #GInfo]".
wp_apply (spec_rcu_base.guard_drop_spec with "BIRD BG"); [solve_ndisj|]. done.
Qed.
Lemma rcu_domain_retire_spec :
rcu_domain_retire_spec' N base.(rcu_domain_retire) IsRCUDomain Managed.
Proof.
intros ????????.
iIntros "#IRD" (Φ) "!> M HΦ".
iDestruct "IRD" as (γb γdata Hγd) "(BIRD & RI)".
iDestruct "M" as (????) "[#i↪ BM]". encode_agree Hγd.
iApply (wp_step_fupd _ E E _ (_ -∗ _)%I with "[$HΦ]"); [done..|].
awp_apply (spec_rcu_base.rcu_domain_retire_spec with "BIRD BM"); [solve_ndisj|].
iInv "RI" as (???) ">(data & BRA & %Hdom)".
iAaccIntro with "BRA".
{ iIntros. iModIntro. iSplit; last done. iNext. repeat iExists _. iFrame. done. }
iIntros "BRA".
iModIntro. iSplitL "BRA data".
{ iNext. repeat iExists _. iFrame. done. }
iIntros "_ HΦ !>". iApply "HΦ". done.
Qed.
Lemma rcu_domain_do_reclamation_spec :
rcu_domain_do_reclamation_spec' N base.(rcu_domain_do_reclamation) IsRCUDomain.
Proof.
intros ????. iIntros "#IRD" (Φ) "!> _ HΦ".
iDestruct "IRD" as (??) "(%Hγ & #BIRD & #RI)".
wp_apply (spec_rcu_base.rcu_domain_do_reclamation_spec with "BIRD [//]"); [solve_ndisj|].
iFrame "HΦ".
Qed.
End ebr.
#[export] Typeclasses Opaque IsRCUDomain Guard Managed NodeInfo.