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Commit ade8f525 authored by Zhen Zhang's avatar Zhen Zhang
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Unfix f in flat combiner; Unifies atomic_triple

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atomic.v
View file @ ade8f525
......@@ -5,38 +5,21 @@ From iris.proofmode Require Import tactics.
Import uPred.
Section atomic.
Context `{irisG Λ Σ} {A: Type}.
Context `{irisG Λ Σ} (A: Type).
(* logically atomic triple: <x, α> e @ E_i, E_o <v, β x v> *)
Definition atomic_triple
(α: A → iProp Σ)
(β: A → val _ → iProp Σ)
(Ei Eo: coPset)
(e: expr _) : iProp Σ :=
(∀ P Q, (P ={Eo, Ei}=> ∃ x:A,
α x ★
((α x ={Ei, Eo}=★ P) ∧
(∀ v, β x v ={Ei, Eo}=★ Q x v))
) -★ {{ P }} e @ ⊤ {{ v, (∃ x: A, Q x v) }})%I.
(* Weakest-pre version of the above one. Also weaker in some sense *)
Definition atomic_triple_wp
Definition atomic_triple_base
(α: A → iProp Σ)
(β: A → val _ → iProp Σ)
(Ei Eo: coPset)
(e: expr _) : iProp Σ :=
(∀ P Q, (P ={Eo, Ei}=> ∃ x,
α x ★
((α x ={Ei, Eo}=★ P) ∧
(∀ v, β x v ={Ei, Eo}=★ Q x v))
) -★ P -★ WP e @ ⊤ {{ v, (∃ x, Q x v) }})%I.
(e: expr _) P Q : iProp Σ :=
((P ={Eo, Ei}=> ∃ x:A,
α x ★
((α x ={Ei, Eo}=★ P) ∧
(∀ v, β x v ={Ei, Eo}=★ Q x v))
) -★ {{ P }} e @ ⊤ {{ v, (∃ x: A, Q x v) }})%I.
Lemma atomic_triple_weaken α β Ei Eo e:
atomic_triple α β Ei Eo e ⊢ atomic_triple_wp α β Ei Eo e.
Proof.
iIntros "H". iIntros (P Q) "Hvs Hp".
by iApply ("H" $! P Q with "Hvs").
Qed.
(* logically atomic triple: <x, α> e @ E_i, E_o <v, β x v> *)
Definition atomic_triple α β Ei Eo e := (∀ P Q, atomic_triple_base α β Ei Eo e P Q)%I.
Arguments atomic_triple {_} _ _ _ _.
End atomic.
......@@ -57,11 +40,11 @@ Section incr.
(* TODO: Can we have a more WP-style definition and avoid the equality? *)
Definition incr_triple (l: loc) :=
atomic_triple (fun (v: Z) => l ↦ #v)%I
(fun v ret => ret = #v ★ l ↦ #(v + 1))%I
(nclose heapN)
⊤
(incr #l).
atomic_triple _ (fun (v: Z) => l ↦ #v)%I
(fun v ret => ret = #v ★ l ↦ #(v + 1))%I
(nclose heapN)
⊤
(incr #l).
Lemma incr_atomic_spec: ∀ (l: loc), heapN ⊥ N → heap_ctx ⊢ incr_triple l.
Proof.
......
atomic_sync.v
View file @ ade8f525
......@@ -13,9 +13,7 @@ Instance subG_syncΣ {Σ} : subG syncΣ Σ → syncG Σ.
Proof. by intros ?%subG_inG. Qed.
Section atomic_sync.
Context `{!heapG Σ, !lockG Σ, !inG Σ (prodR fracR (dec_agreeR val))} (N : namespace).
Definition A := val. (* FIXME: can't use a general A instead of val *)
Context `{EqDecision A, !heapG Σ, !lockG Σ, !inG Σ (prodR fracR (dec_agreeR A))} (N : namespace).
Definition gHalf (γ: gname) g : iProp Σ := own γ ((1/2)%Qp, DecAgree g).
......@@ -24,15 +22,16 @@ Section atomic_sync.
(β: val → A → A → val → iProp Σ)
(Ei Eo: coPset)
(f x: val) γ : iProp Σ :=
(∀ P Q, (∀ g, (P x ={Eo, Ei}=> gHalf γ g ★ □ α x) ★
(gHalf γ g ★ □ α x ={Ei, Eo}=> P x) ★
(∀ g' r, gHalf γ g' ★ β x g g' r ={Ei, Eo}=> Q x r))
-★ {{ P x }} f x {{ v, Q x v }})%I.
Definition sync (syncer: val) : val :=
(∀ P Q, atomic_triple_base A (fun g => gHalf γ g ★ □ α x)
(fun g v => ∃ g':A, gHalf γ g' ★ β x g g' v)
Ei Eo
(f x) (P x) (fun _ => Q x))%I.
Definition sync (mk_syncer: val) : val :=
λ: "f_cons" "f_seq",
let: "l" := "f_cons" #() in
syncer ("f_seq" "l").
let: "l" := "f_cons" #() in
let: "s" := mk_syncer #() in
"s" ("f_seq" "l").
Definition seq_spec (f: val) (ϕ: val → A → iProp Σ) α β (E: coPset) :=
∀ (Φ: val → iProp Σ) (l: val),
......@@ -48,55 +47,66 @@ Section atomic_sync.
⊢ WP f #() {{ Φ }}.
Definition synced R (f' f: val) :=
(∀ P Q (x: val), ({{ R ★ P x }} f x {{ v, R ★ Q x v }}) → ({{ P x }} f' x {{ v, Q x v }}))%I.
(□ ∀ P Q (x: val), ({{ R ★ P x }} f x {{ v, R ★ Q x v }}) → ({{ P x }} f' x {{ v, Q x v }}))%I.
Definition is_syncer (R: iProp Σ) (s: val) :=
(∀ (f : val), WP s f {{ f', synced R f' f }})%I.
Definition mk_sync_spec (syncer: val) :=
∀ f R (Φ: val → iProp Σ),
heapN ⊥ N →
heap_ctx ★ R ★ (∀ f', □ synced R f' f -★ Φ f') ⊢ WP syncer f {{ Φ }}.
Definition mk_syncer_spec (mk_syncer: val) :=
∀ (R: iProp Σ) (Φ: val -> iProp Σ),
heapN ⊥ N →
heap_ctx ★ R ★ (∀ s, □ (is_syncer R s) -★ Φ s) ⊢ WP mk_syncer #() {{ Φ }}.
Lemma atomic_spec (syncer f_cons f_seq: val) (ϕ: val → A → iProp Σ) α β Ei:
Lemma atomic_spec (mk_syncer f_cons f_seq: val) (ϕ: val → A → iProp Σ) α β Ei:
∀ (g0: A),
heapN ⊥ N → seq_spec f_seq ϕ α β ⊤ → cons_spec f_cons g0 ϕ →
mk_sync_spec syncer →
mk_syncer_spec mk_syncer →
heap_ctx
⊢ WP (sync syncer) f_cons f_seq {{ f, ∃ γ, gHalf γ g0 ★ ∀ x, □ atomic_triple' α β Ei ⊤ f x γ }}.
⊢ WP (sync mk_syncer) f_cons f_seq {{ f, ∃ γ, gHalf γ g0 ★ ∀ x, □ atomic_triple' α β Ei ⊤ f x γ }}.
Proof.
iIntros (g0 HN Hseq Hcons Hsync) "#Hh". repeat wp_let.
wp_bind (f_cons _). iApply Hcons=>//. iFrame "Hh".
iIntros (l γ) "Hϕ HFull HFrag".
wp_let. wp_bind (f_seq _)%E.
iApply wp_wand_r. iSplitR; first by iApply (Hseq with "[]")=>//.
iIntros (f Hf). iApply (Hsync f (∃ g: A, ϕ l g ★ gHalf γ g)%I)=>//.
iFrame "#". iSplitL "HFull Hϕ".
wp_let. wp_bind (mk_syncer _).
iApply (Hsync (∃ g: A, ϕ l g ★ gHalf γ g)%I)=>//. iFrame "Hh".
iSplitL "HFull Hϕ".
{ iExists g0. by iFrame. }
iIntros (f') "#Hflatten".
iIntros (s) "#Hsyncer".
wp_let. wp_bind (f_seq _). iApply wp_wand_r.
iSplitR; first by iApply (Hseq with "[]")=>//.
iIntros (f) "%".
iApply wp_wand_r.
iSplitR; first iApply "Hsyncer".
iIntros (f') "#Hsynced".
iExists γ. iFrame.
iIntros (x). iAlways.
rewrite /atomic_triple'.
iIntros (P Q) "#Hvss".
rewrite /synced.
iSpecialize ("Hflatten" $! P Q).
iApply ("Hflatten" with "[]").
iAlways. iIntros "[HR HP]". iDestruct "HR" as (g) "[Hϕ HgFull]".
(* we should view shift at this point *)
iDestruct ("Hvss" $! g) as "[Hvs1 [Hvs2 Hvs3]]".
iApply pvs_wp.
iVs ("Hvs1" with "HP") as "[HgFrag #Hα]".
iVs ("Hvs2" with "[HgFrag]") as "HP"; first by iFrame.
iVsIntro. iApply Hf=>//.
iFrame "Hh Hϕ". iSplitR; first done. iIntros (ret g') "Hϕ' Hβ".
iVs ("Hvs1" with "HP") as "[HgFrag _]".
iCombine "HgFull" "HgFrag" as "Hg".
rewrite /gHalf.
iAssert (|=r=> own γ (((1 / 2)%Qp, DecAgree g') ⋅ ((1 / 2)%Qp, DecAgree g')))%I with "[Hg]" as "Hupd".
{ iApply (own_update); last by iAssumption. apply pair_l_frac_update. }
iVs "Hupd" as "[HgFull HgFrag]".
iVs ("Hvs3" $! g' ret with "[HgFrag Hβ]"); first by iFrame.
iVsIntro.
iSplitL "HgFull Hϕ'".
- iExists g'. by iFrame.
- done.
iSpecialize ("Hsynced" $! P Q x).
iIntros "!# HP". iApply wp_wand_r. iSplitL "HP".
- iApply ("Hsynced" with "[]")=>//.
iAlways. iIntros "[HR HP]". iDestruct "HR" as (g) "[Hϕ Hg1]".
(* we should view shift at this point *)
iDestruct ("Hvss" with "HP") as "Hvss'". iApply pvs_wp.
iVs "Hvss'". iDestruct "Hvss'" as (?) "[[Hg2 #Hα] [Hvs1 _]]".
iVs ("Hvs1" with "[Hg2]") as "HP"; first by iFrame.
iVsIntro. iApply H=>//.
iFrame "Hh Hϕ". iSplitR; first done. iIntros (ret g') "Hϕ' Hβ".
iVs ("Hvss" with "HP") as (g'') "[[Hg'' _] [_ Hvs2]]".
iSpecialize ("Hvs2" $! ret).
iDestruct (m_frag_agree' with "[Hg'' Hg1]") as "[Hg %]"; first iFrame. subst.
rewrite Qp_div_2.
iAssert (|=r=> own γ (((1 / 2)%Qp, DecAgree g') ⋅ ((1 / 2)%Qp, DecAgree g')))%I
with "[Hg]" as "==>[Hg1 Hg2]".
{ iApply own_update; last by iAssumption.
apply cmra_update_exclusive. by rewrite pair_op dec_agree_idemp. }
iVs ("Hvs2" with "[Hg1 Hβ]").
{ iExists g'. iFrame. }
iVsIntro. iSplitL "Hg2 Hϕ'".
* iExists g'. by iFrame.
* done.
- iIntros (?) "?". by iExists g0.
Qed.
End atomic_sync.
flat.v
View file @ ade8f525
......@@ -6,50 +6,42 @@ From iris.algebra Require Import auth upred frac agree excl dec_agree upred_big_
From iris_atomic Require Import misc atomic treiber atomic_sync evmap.
Definition doOp : val :=
λ: "f" "p",
match: !"p" with
InjL "x" => "p" <- InjR ("f" "x")
| InjR "_" => #()
end.
Definition doOp' (f:val) : val :=
λ: "p",
match: !"p" with
InjL "x" => "p" <- InjR (f "x")
InjL "req" => "p" <- InjR ((Fst "req") (Snd "req"))
| InjR "_" => #()
end.
Definition try_srv : val :=
λ: "lk" "s" "f",
λ: "lk" "s",
if: try_acquire "lk"
then let: "hd" := !"s" in
let: "f'" := doOp "f" in
iter "hd" "f'";;
iter "hd" doOp;;
release "lk"
else #().
Definition loop: val :=
rec: "loop" "f" "p" "s" "lk" :=
rec: "loop" "p" "s" "lk" :=
match: !"p" with
InjL "_" =>
try_srv "lk" "s" "f";;
"loop" "f" "p" "s" "lk"
try_srv "lk" "s";;
"loop" "p" "s" "lk"
| InjR "r" => "r"
end.
Definition install : val :=
λ: "x" "s",
let: "p" := ref (InjL "x") in
λ: "f" "x" "s",
let: "p" := ref (InjL ("f", "x")) in
push "s" "p";;
"p".
Definition mk_flat : val :=
λ: "f",
λ: <>,
let: "lk" := newlock #() in
let: "s" := new_stack #() in
λ: "x",
let: "p" := install "x" "s" in
let: "r" := loop "f" "p" "s" "lk" in
λ: "f" "x",
let: "p" := install "f" "x" "s" in
let: "r" := loop "p" "s" "lk" in
"r".
Global Opaque doOp try_srv install loop mk_flat.
......@@ -74,15 +66,15 @@ Proof. intros [?%subG_inG [?%subG_inG [? _]%subG_inv]%subG_inv]%subG_inv. split;
Section proof.
Context `{!heapG Σ, !lockG Σ, !evidenceG loc val unitR Σ, !flatG Σ} (N : namespace).
Context (R: iProp Σ).
Definition init_s (ts: toks) :=
let '(_, γ1, γ3, _, _) := ts in (own γ1 (Excl ()) ★ own γ3 (Excl ()))%I.
Definition installed_s (ts: toks) (f x: val) :=
Definition installed_s R (ts: toks) (f x: val) :=
let '(γx, γ1, _, γ4, γq) := ts in
(∃ (P: val → iProp Σ) Q, own γx ((1/2)%Qp, DecAgree x) ★ P x ★ ({{ R ★ P x }} f x {{ v, R ★ Q x v }}) ★
saved_prop_own γq (Q x) ★ own γ1 (Excl ()) ★ own γ4 (Excl ()))%I.
(∃ (P: val → iProp Σ) Q,
own γx ((1/2)%Qp, DecAgree x) ★ P x ★ ({{ R ★ P x }} f x {{ v, R ★ Q x v }}) ★
saved_prop_own γq (Q x) ★ own γ1 (Excl ()) ★ own γ4 (Excl ()))%I.
Definition received_s (ts: toks) (x: val) γr :=
let '(γx, _, _, γ4, _) := ts in
......@@ -97,39 +89,38 @@ Section proof.
Definition evm := ev loc toks.
(* p slot invariant *)
Definition p_inv (γm γr: gname) (f v: val) :=
Definition p_inv R (γm γr: gname) (v: val) :=
(∃ (ts: toks) (p : loc),
v = #p ★ evm γm p ts ★
((* INIT *)
(∃ y: val, p ↦{1/2} InjRV y ★ init_s ts)∨
(* INSTALLED *)
(∃ x: val, p ↦{1/2} InjLV x ★ installed_s ts f x) ∨
(∃ f x: val, p ↦{1/2} InjLV (f, x) ★ installed_s R ts f x) ∨
(* RECEIVED *)
(∃ x: val, p ↦{1/2} InjLV x ★ received_s ts x γr) ∨
(∃ f x: val, p ↦{1/2} InjLV (f, x) ★ received_s ts x γr) ∨
(* FINISHED *)
(∃ x y: val, p ↦{1/2} InjRV y ★ finished_s ts x y)))%I.
Definition srv_stack_inv γs γm γr s f := (∃ xs, is_stack' (p_inv γm γr f) γs xs s)%I.
Definition srv_stack_inv R γs γm γr s := (∃ xs, is_stack' (p_inv R γm γr) γs xs s)%I.
Definition srv_tokm_inv γm := (∃ m : tokmR, own γm (● m) ★ [★ map] p ↦ _ ∈ m, ∃ v, p ↦{1/2} v)%I.
Lemma install_push_spec
(Φ: val → iProp Σ)
Lemma install_push_spec R
(p: loc) (γs γm γr: gname) (ts: toks)
(s: loc) (f x: val) :
(s: loc) (f x: val) (Φ: val → iProp Σ) :
heapN ⊥ N →
heap_ctx ★ inv N (srv_stack_inv γs γm γr s f ★ srv_tokm_inv γm) ★
evm γm p ts ★ installed_s ts f x ★
p ↦{1/2} InjLV x ★ ((∃ hd, evs γs hd #p) -★ Φ #())
heap_ctx ★ inv N (srv_stack_inv R γs γm γr s ★ srv_tokm_inv γm) ★
evm γm p ts ★ installed_s R ts f x ★
p ↦{1/2} InjLV (f, x) ★ ((∃ hd, evs γs hd #p) -★ Φ #())
⊢ WP push #s #p {{ Φ }}.
Proof.
iIntros (HN) "(#Hh & #? & Hpm & Hs & Hp & HΦ)".
rewrite /srv_stack_inv.
iDestruct (push_spec N (p_inv γm γr f) (fun v => (∃ hd, evs γs hd #p) ★ v = #())%I
iDestruct (push_spec N (p_inv R γm γr) (fun v => (∃ hd, evs γs hd #p) ★ v = #())%I
with "[-HΦ]") as "Hpush"=>//.
- iFrame "Hh". iSplitL "Hp Hs Hpm"; last eauto.
iExists ts. iExists p. iSplit=>//. iFrame "Hpm".
iRight. iLeft. iExists x. iFrame.
iRight. iLeft. iExists f, x. iFrame.
- iApply wp_wand_r.
iSplitL "Hpush"; first done.
iIntros (?) "[? %]". subst.
......@@ -141,15 +132,17 @@ Section proof.
(own γ3 (Excl ()) ★ own γx ((1/2)%Qp, DecAgree x) ★ saved_prop_own γq (Q x))%I.
Lemma install_spec
(Φ: val → iProp Σ) P Q
(f x: val) (γs γm γr: gname) (s: loc):
R P Q
(f x: val) (γs γm γr: gname) (s: loc)
(Φ: val → iProp Σ):
heapN ⊥ N →
heap_ctx ★ inv N (srv_stack_inv γs γm γr s f ★ srv_tokm_inv γm) ★ P x ★ ({{ R ★ P x }} f x {{ v, R ★ Q x v }}) ★
heap_ctx ★ inv N (srv_stack_inv R γs γm γr s ★ srv_tokm_inv γm) ★
P x ★ ({{ R ★ P x }} f x {{ v, R ★ Q x v }}) ★
(∀ (p: loc) (ts: toks), installed_recp ts x Q -★ evm γm p ts -★(∃ hd, evs γs hd #p) -★ Φ #p)
⊢ WP install x #s {{ Φ }}.
⊢ WP install f x #s {{ Φ }}.
Proof.
iIntros (HN) "(#Hh & #? & Hpx & Hf & HΦ)".
wp_seq. wp_let. wp_alloc p as "Hl".
wp_seq. wp_let. wp_let. wp_alloc p as "Hl".
iApply pvs_wp.
iVs (own_alloc (Excl ())) as (γ1) "Ho1"; first done.
iVs (own_alloc (Excl ())) as (γ3) "Ho3"; first done.
......@@ -181,20 +174,20 @@ Section proof.
by iApply ("HΦ" with "[]").
Qed.
Lemma loop_iter_list_spec Φ (f: val) (s hd: loc) (γs γm γr: gname) xs:
Lemma loop_iter_doOp_spec R (s hd: loc) (γs γm γr: gname) xs Φ:
heapN ⊥ N →
heap_ctx ★ inv N (srv_stack_inv γs γm γr s f ★ srv_tokm_inv γm) ★ own γr (Excl ()) ★ R ★
heap_ctx ★ inv N (srv_stack_inv R γs γm γr s ★ srv_tokm_inv γm) ★ own γr (Excl ()) ★ R ★
is_list' γs hd xs ★ (own γr (Excl ()) -★ R -★ Φ #())
⊢ WP doOp f {{ f', WP iter #hd f' {{ Φ }} }}.
⊢ WP iter #hd doOp {{ Φ }}.
Proof.
iIntros (HN) "(#Hf & #? & Ho2 & HR & Hlist' & HΦ)".
iApply pvs_wp.
iDestruct (dup_is_list' with "[Hlist']") as "==>[Hl1 Hl2]"; first by iFrame.
iDestruct (dup_is_list' with "[Hl2]") as "==>[Hl2 Hl3]"; first by iFrame.
iVsIntro. wp_seq.
iDestruct (iter_spec _ (p_inv γm γr f) (fun v => v = #() ★ own γr (Excl ()) ★ R)%I γs s
iVsIntro.
iDestruct (iter_spec _ (p_inv R γm γr) (fun v => v = #() ★ own γr (Excl ()) ★ R)%I γs s
(is_list' γs hd xs ★ own γr (Excl ()) ★ R)%I (srv_tokm_inv γm) xs hd
(doOp' f) (doOp' f)
doOp doOp
with "[-Hl1 HΦ]") as "Hiter"=>//.
- rewrite /f_spec.
iIntros (Φ' p _ Hin) "(#Hh & #? & (Hls & Ho2 & HR) & HΦ')".
......@@ -214,9 +207,9 @@ Section proof.
iFrame. iExists #p''. iSplitR; first done. iExists ts, p''.
iSplitR; first done. iFrame "#". iLeft. iExists y. iFrame. }
iVsIntro. wp_match. iApply "HΦ'". by iFrame.
+ iDestruct "Hp" as (x') "(Hp & Hs)".
+ iDestruct "Hp" as (f' x') "(Hp & Hs)".
wp_load. destruct ts as [[[[γx γ1] γ3] γ4] γq].
iDestruct "Hs" as (P Q) "(Hx & Hpx & Hf & HoQ& Ho1 & Ho4)".
iDestruct "Hs" as (P Q) "(Hx & Hpx & Hf & HoQ& Ho1 & Ho4)".
iAssert (|=r=> own γx (((1/2/2)%Qp, DecAgree x') ⋅
((1/2/2)%Qp, DecAgree x')))%I with "[Hx]" as "==>[Hx1 Hx2]".
{ iDestruct (own_update with "Hx") as "?"; last by iAssumption.
......@@ -228,9 +221,10 @@ Section proof.
iFrame "Hom". iDestruct (big_sepM_delete _ m with "[-]") as "?"=>//.
simpl. iFrame. iExists #p''. iSplitR; auto. rewrite /allocated.
iExists (γx, γ1, γ3, γ4, γq), p''. iSplitR; auto.
iFrame "#". iRight. iRight. iLeft. iExists x'. iFrame. }
iFrame "#". iRight. iRight. iLeft. iExists f', x'. iFrame. }
iVsIntro. wp_match.
wp_bind (f _). iApply wp_wand_r. iSplitL "Hpx Hf HR".
wp_proj. wp_proj.
wp_bind (f' _). iApply wp_wand_r. iSplitL "Hpx Hf HR".
{ iApply "Hf". iFrame. }
iIntros (v) "[HR HQ]".
wp_value. iVsIntro. iInv N as "[Hs >Hm]" "Hclose".
......@@ -246,9 +240,9 @@ Section proof.
iDestruct "Hps" as "[Hp | [Hp | [Hp | Hp]]]".
* iDestruct "Hp" as (?) "(_ & >Ho1' & _)".
iApply excl_falso. iFrame.
* iDestruct "Hp" as (?) "[>? Hs]". iDestruct "Hs" as (? ?) "(_ & _ & _ & _ & >Ho1' & _)".
* iDestruct "Hp" as (? ?) "[>? Hs]". iDestruct "Hs" as (? ?) "(_ & _ & _ & _ & >Ho1' & _)".
iApply excl_falso. iFrame.
* iDestruct "Hp" as (x5) ">(Hp & Hx & Ho2 & Ho4)".
* iDestruct "Hp" as (? x5) ">(Hp & Hx & Ho2 & Ho4)".
iDestruct "Hm" as (m2) "[Hom2 HRm]".
destruct (m2 !! p'''') eqn:Heqn.
{
......@@ -257,7 +251,7 @@ Section proof.
iDestruct (heap_mapsto_op_1 with "[HRk Hp]") as "[% Hp]"; first by iFrame.
rewrite Qp_div_2. wp_store.
(* now close the invariant *)
iDestruct (m_frag_agree with "[Hx Hx2]") as "==>[Hx %]"; first iFrame.
iDestruct (m_frag_agree' with "[Hx Hx2]") as "[Hx %]"; first iFrame.
subst. rewrite Qp_div_2. iVs ("Hclose" with "[-HΦ' Ho2 HR Hls3]").
{ iNext. iDestruct "Hp" as "[Hp1 Hp2]".
iAssert (srv_tokm_inv γm) with "[Hp1 HRm Hom2]" as "HRm".
......@@ -281,7 +275,7 @@ Section proof.
}
{ iDestruct (evmap_frag_agree_split with "[]") as "%"; first iFrame "Hevm Hevm2".
inversion H4. subst. by contradiction Hneq. }
+ destruct ts as [[[[γx γ1] γ3] γ4] γq]. iDestruct "Hp" as (y) "(_ & _ & >Ho2' & _)".
+ destruct ts as [[[[γx γ1] γ3] γ4] γq]. iDestruct "Hp" as (? x) "(_ & _ & >Ho2' & _)".
iApply excl_falso. iFrame.
+ destruct ts as [[[[γx γ1] γ3] γ4] γq]. iDestruct "Hp" as (x' y) "[Hp Hs]".
iDestruct "Hs" as (Q) "(>Hx & HoQ & HQxy & >Ho1 & >Ho4)".
......@@ -304,15 +298,14 @@ Section proof.
let '(γx, _, _, _, γq) := ts in
(∃ Q, own γx ((1 / 2)%Qp, DecAgree x) ★ saved_prop_own γq (Q x) ★ Q x y)%I.
Lemma try_srv_spec Φ (s: loc) (lk: val) (f: val)
(γs γr γm γlk: gname):
Lemma try_srv_spec R (s: loc) (lk: val) (γs γr γm γlk: gname) Φ :
heapN ⊥ N →
heap_ctx ★ inv N (srv_stack_inv γs γm γr s f ★ srv_tokm_inv γm) ★
heap_ctx ★ inv N (srv_stack_inv R γs γm γr s ★ srv_tokm_inv γm) ★
is_lock N γlk lk (own γr (Excl ()) ★ R) ★ Φ #()
⊢ WP try_srv lk #s f {{ Φ }}.
⊢ WP try_srv lk #s {{ Φ }}.
Proof.
iIntros (?) "(#? & #? & #? & HΦ)".
wp_seq. wp_let. wp_let.
wp_seq. wp_let.
wp_bind (try_acquire _). iApply try_acquire_spec.
iFrame "#". iSplit; last by wp_if.
(* acquired the lock *)
......@@ -323,26 +316,24 @@ Section proof.
wp_load. iDestruct (dup_is_list' with "[Hxs]") as "==>[Hxs1 Hxs2]"; first by iFrame.
iVs ("Hclose" with "[Hs Hxs1 HRs Hm]").
{ iNext. iFrame. iExists xs', hd'. by iFrame. }
iVsIntro. wp_let. wp_bind (doOp f).
iVsIntro. wp_let.
wp_bind (iter _ _).
iApply wp_wand_r. iSplitL "HR Ho2 Hxs2".
{ iApply (loop_iter_list_spec (fun v => own γr (Excl ()) ★ R ★ v = #()))%I=>//.
{ iApply (loop_iter_doOp_spec R _ _ _ _ _ _ (fun v => own γr (Excl ()) ★ R ★ v = #()))%I=>//.
iFrame "#". iFrame. iIntros "? ?". by iFrame. }
iIntros (f') "Hf'".
wp_let. wp_bind ((iter _) _).
iApply wp_wand_r. iSplitL "Hf'"; first iApply "Hf'".
iIntros (?) "[Ho2 [HR %]]". subst.
wp_seq. iApply release_spec.
iFrame "#". iFrame.
iIntros (f') "[Ho [HR %]]". subst.
wp_let. iApply release_spec. iFrame "#".
iFrame.
Qed.
Lemma loop_spec Φ (p s: loc) (lk: val) (f: val)
(γs γr γm γlk: gname) (ts: toks):
Lemma loop_spec R (p s: loc) (lk: val)
(γs γr γm γlk: gname) (ts: toks) Φ:
heapN ⊥ N →
heap_ctx ★ inv N (srv_stack_inv γs γm γr s f ★ srv_tokm_inv γm) ★
heap_ctx ★ inv N (srv_stack_inv R γs γm γr s ★ srv_tokm_inv γm) ★
is_lock N γlk lk (own γr (Excl ()) ★ R) ★
own_γ3 ts ★ evm γm p ts ★
(∃ hd, evs γs hd #p) ★ (∀ x y, finished_recp ts x y -★ Φ y)
⊢ WP loop f #p #s lk {{ Φ }}.
⊢ WP loop #p #s lk {{ Φ }}.
Proof.
iIntros (HN) "(#Hh & #? & #? & Ho3 & #Hev & Hhd & HΦ)".
iLöb as "IH". wp_rec. repeat wp_let.
......@@ -361,28 +352,28 @@ Section proof.
iDestruct "Hp" as "[Hp | [Hp | [ Hp | Hp]]]".
+ iDestruct "Hp" as (?) "(_ & _ & >Ho3')".
iApply excl_falso. iFrame.
+ iDestruct "Hp" as (x) "(>Hp & Hs')".
+ iDestruct "Hp" as (f x) "(>Hp & Hs')".
wp_load. iVs ("Hclose" with "[-Ho3 HΦ Hhd]").
{ iNext. iFrame. iExists xs, hd. iFrame. iExists m. iFrame.
iDestruct (big_sepM_delete _ m with "[-]") as "?"=>//.
iFrame. iExists #p'. iSplitR; first auto. iExists (γx, γ1, γ3, γ4, γq), p'.
iSplitR; first auto. iFrame.
iRight. iLeft. iExists x. iFrame. }
iRight. iLeft. iExists f, x. iFrame. }
iVsIntro. wp_match.
wp_bind (try_srv _ _ _). iApply try_srv_spec=>//.
wp_bind (try_srv _ _). iApply try_srv_spec=>//.
iFrame "#". wp_seq.
iAssert (∃ hd, evs γs hd #p')%I with "[Hhd]" as "Hhd"; eauto.
by iApply ("IH" with "Ho3 Hhd").
+ iDestruct "Hp" as (x) "(Hp & Hx & Ho2 & Ho4)".
+ iDestruct "Hp" as (f x) "(Hp & Hx & Ho2 & Ho4)".
wp_load.
iVs ("Hclose" with "[-Ho3 HΦ Hhd]").
{ iNext. iFrame. iExists xs, hd. iFrame. iExists m. iFrame.
iDestruct (big_sepM_delete _ m with "[-]") as "?"=>//.
iFrame. iExists #p'. iSplitR; auto. iExists (γx, γ1, γ3, γ4, γq), p'.
iSplitR; first auto. iFrame.
iRight. iRight. iLeft. iExists x. iFrame. }
iRight. iRight. iLeft. iExists f, x. iFrame. }
iVsIntro. wp_match.
wp_bind (try_srv _ _ _). iApply try_srv_spec=>//.
wp_bind (try_srv _ _). iApply try_srv_spec=>//.
iFrame "#". wp_seq.
iAssert (∃ hd, evs γs hd #p')%I with "[Hhd]" as "Hhd"; eauto.
by iApply ("IH" with "Ho3 Hhd").
......@@ -399,12 +390,9 @@ Section proof.
rewrite /ev. eauto.
Qed.
Lemma mk_flat_spec (f: val) :
∀ (Φ: val → iProp Σ),
heapN ⊥ N →
heap_ctx ★ R ★ (∀ f', □ synced R f' f -★ Φ f') ⊢ WP mk_flat f {{ Φ }}.
Lemma mk_flat_spec: mk_syncer_spec N mk_flat.
Proof.
iIntros (Φ HN) "(#Hh & HR & HΦ)".
iIntros (R Φ HN) "(#Hh & HR & HΦ)".
iVs (own_alloc (Excl ())) as (γr) "Ho2"; first done.
iVs (own_alloc (● (∅: tokmR) ⋅ ◯ ∅)) as (γm) "[Hm _]"; first by rewrite -auth_both_op.
iAssert (srv_tokm_inv γm) with "[Hm]" as "Hm"; first eauto.
......@@ -413,16 +401,18 @@ Section proof.
iApply (newlock_spec _ (own γr (Excl ()) ★ R))%I=>//.
iFrame "Hh Ho2 HR". iIntros (lk γlk) "#Hlk".
wp_let. wp_bind (new_stack _).
iApply (new_stack_spec' _ (p_inv γm γr f))=>//.
iApply (new_stack_spec' _ (p_inv _ γm γr))=>//.
iFrame "Hh Hm". iIntros (γ s) "#Hss".
wp_let. iVsIntro. iApply "HΦ". rewrite /synced.
iAlways. iIntros (P Q x) "#Hf".
iAlways.
iIntros (f). wp_let. iVsIntro. iAlways.
iIntros (P Q x) "#Hf".
iIntros "!# Hp". wp_let.
wp_bind ((install _) _).
iApply (install_spec _ P Q)=>//.
wp_bind (install _ _ _).
iApply (install_spec R P Q)=>//.
iFrame "#". iFrame "Hp". iSplitR; first iApply "Hf".
iIntros (p [[[[γx γ1] γ3] γ4] γq]) "(Ho3 & Hx & HoQ) Hev Hhd".
wp_let. wp_bind (loop _ _ _ _).
wp_let. wp_bind (loop _ _ _).
iApply loop_spec=>//.
iFrame "#". iFrame.