Commit 45ad940f authored by Ralf Jung's avatar Ralf Jung

restructure snapshot to not actually have a protocol on the y location

parent c67a9a51
......@@ -11,44 +11,27 @@ Set Default Proof Using "Type".
(** Specifying snapshots with histories
Implementing atomic pair snapshot data structure from Sergey et al. (ESOP 2015) *)
(** The CMRA & functor we need. *)
Definition timestampUR := gmapUR Z $ agreeR valC.
Class atomic_snapshotG Σ := AtomicSnapshotG {
atomic_snapshot_stateG :> inG Σ $ authR $ optionUR $ exclR $ prodC valC valC;
atomic_snapshot_timestampG :> inG Σ $ authR $ timestampUR
}.
Definition atomic_snapshotΣ : gFunctors :=
#[GFunctor (authR $ optionUR $ exclR $ prodC valC valC); GFunctor (authR timestampUR)].
Instance subG_atomic_snapshotΣ {Σ} : subG atomic_snapshotΣ Σ atomic_snapshotG Σ.
Proof. solve_inG. Qed.
Section atomic_snapshot.
Context {Σ} `{!heapG Σ, !atomic_snapshotG Σ}.
(*
(*
newPair x y :=
(ref (ref (x, 0)), ref y)
*)
Definition newPair : val :=
Definition newPair : val :=
λ: "args",
let: "x" := Fst "args" in
let: "y" := Snd "args" in
(ref (ref ("x", #0)), ref "y").
(*
(*
writeY (xp, yp) y :=
yp <- y
*)
Definition writeY : val :=
Definition writeY : val :=
λ: "args",
let: "p" := Fst "args" in
Snd "p" <- Snd "args".
(*
(*
writeX (xp, yp) x :=
let xp1 = !xp in
let v = (!xp1).2
......@@ -57,7 +40,7 @@ Section atomic_snapshot.
then ()
else writeX (xp, yp) x
*)
Definition writeX : val :=
Definition writeX : val :=
rec: "writeX" "args" :=
let: "p" := Fst "args" in
let: "x" := Snd "args" in
......@@ -69,21 +52,21 @@ Section atomic_snapshot.
then #()
else "writeX" "args".
(*
(*
readX (xp, yp) :=
!!xp
*)
Definition readX : val :=
Definition readX : val :=
λ: "p",
let: "xp" := Fst "p" in
!(!"xp").
Definition readY : val :=
Definition readY : val :=
λ: "p",
let: "yp" := Snd "p" in
!"yp".
(*
(*
readPair l :=
let (x, v) = readX l in
let y = readY l in
......@@ -92,7 +75,7 @@ Section atomic_snapshot.
then (x, y)
else readPair l
*)
Definition readPair : val :=
Definition readPair : val :=
rec: "readPair" "l" :=
let: "x" := readX "l" in
let: "y" := readY "l" in
......@@ -101,7 +84,7 @@ Section atomic_snapshot.
then (Fst "x", Fst "y")
else "readPair" "l".
Definition readPair_proph : val :=
Definition readPair_proph : val :=
rec: "readPair" "l" :=
let: "xv1" := readX "l" in
let: "proph" := NewProph in
......@@ -114,35 +97,54 @@ Section atomic_snapshot.
then (Fst "xv1", "y")
else "readPair" "l".
(** The CMRA & functor we need. *)
Definition timestampUR := gmapUR Z $ agreeR valC.
Class atomic_snapshotG Σ := AtomicSnapshotG {
atomic_snapshot_stateG :> inG Σ $ authR $ optionUR $ exclR $ valC;
atomic_snapshot_timestampG :> inG Σ $ authR $ timestampUR
}.
Definition atomic_snapshotΣ : gFunctors :=
#[GFunctor (authR $ optionUR $ exclR $ valC); GFunctor (authR timestampUR)].
Instance subG_atomic_snapshotΣ {Σ} : subG atomic_snapshotΣ Σ atomic_snapshotG Σ.
Proof. solve_inG. Qed.
Section atomic_snapshot.
Context {Σ} `{!heapG Σ, !atomic_snapshotG Σ}.
Variable N: namespace.
Definition gmap_to_UR T : timestampUR := to_agree <$> T.
Definition pair_inv γ1 γ2 l1 l2 : iProp Σ :=
( q (l1':loc) (T : gmap Z val) x y (t : Z),
Definition pair_inv γ1 γ2 l1 : iProp Σ :=
( q (l1':loc) (T : gmap Z val) x (t : Z),
(* we add the q to make the l1' map fractional. that way,
we can take a fraction of the l1' map out of the invariant
and do a case analysis on whether the pointer is the same
throughout invariant openings *)
l1 #l1' l1' {q} (x, #t) l2 y
own γ1 ( Excl' (x, y)) own γ2 ( gmap_to_UR T)
l1 #l1' l1' {q} (x, #t)
own γ1 ( Excl' x) own γ2 ( gmap_to_UR T)
T !! t = Some x
forall (t' : Z), t' dom (gset Z) T (t' <= t)%Z)%I.
Definition is_pair (γs: gname * gname) (p : val) :=
( (l1 l2 : loc), p = (#l1, #l2)%V inv N (pair_inv γs.1 γs.2 l1 l2))%I.
Definition is_pair (γs: gname * gname * loc) (p : val) :=
( (l1 : loc), p = (#l1, #γs.2)%V inv N (pair_inv γs.1.1 γs.1.2 l1))%I.
Global Instance is_pair_persistent γs p : Persistent (is_pair γs p) := _.
Definition pair_content (γs : gname * gname) (a : val * val) :=
(own γs.1 ( Excl' a))%I.
Definition pair_content (γs : gname * gname * loc) (a : val * val) :=
(own γs.1.1 ( Excl' a.1) γs.2 a.2)%I.
Global Instance pair_content_timeless γs a : Timeless (pair_content γs a) := _.
Lemma pair_content_exclusive γs a1 a2 :
pair_content γs a1 - pair_content γs a2 - False.
Proof.
iIntros "H1 H2". iDestruct (own_valid_2 with "H1 H2") as %[].
iIntros "[H1 _] [H2 _]". iDestruct (own_valid_2 with "H1 H2") as %[].
Qed.
Definition new_timestamp t v : gmap Z val := {[ t := v ]}.
......@@ -152,14 +154,14 @@ Section atomic_snapshot.
newPair (v1, v2)%V
{{{ γs p, RET p; is_pair γs p pair_content γs (v1, v2) }}}.
Proof.
iIntros (Φ _) "Hp". rewrite /newPair. wp_lam.
iIntros (Φ _) "Hx". rewrite /newPair. wp_lam.
repeat (wp_proj; wp_let).
iApply wp_fupd.
wp_alloc ly as "Hly".
wp_alloc lx' as "Hlx'".
wp_alloc lx as "Hlx".
wp_alloc ly as "Hly".
set (Excl' (v1, v2)) as p.
iMod (own_alloc ( p p)) as (γ1) "[Hp⚫ Hp◯]". {
set (Excl' v1) as p.
iMod (own_alloc ( p p)) as (γ1) "[Hx⚫ Hx◯]". {
rewrite /p. apply auth_both_valid. split; done.
}
set (new_timestamp 0 v1) as t.
......@@ -167,14 +169,14 @@ Section atomic_snapshot.
rewrite /t /new_timestamp. apply auth_both_valid.
split; first done. rewrite /gmap_to_UR map_fmap_singleton. apply singleton_valid. done.
}
wp_pures. iApply ("Hp" $! (γ1, γ2)).
iMod (inv_alloc N _ (pair_inv γ1 γ2 _ _) with "[-Hp◯ Ht◯]") as "#Hinv". {
iNext. rewrite /pair_inv. iExists _, _, _, _, _. iExists 0. iFrame.
wp_pures. iApply ("Hx" $! (γ1, γ2, ly)).
iMod (inv_alloc N _ (pair_inv γ1 γ2 _) with "[-Hx◯ Ht◯ Hly]") as "#Hinv". {
iNext. rewrite /pair_inv. iExists _, _, _, _, 0. iFrame.
iPureIntro. split; first done. intros ?. subst t. rewrite /new_timestamp dom_singleton.
rewrite elem_of_singleton. lia.
}
iModIntro. iSplitR. rewrite /is_pair. repeat (iExists _). iSplitL; eauto.
rewrite /pair_content. rewrite /p. iApply "Hp◯".
iModIntro. rewrite /is_pair /pair_content. iFrame. iExists _.
iSplitL; first done. done.
Qed.
Lemma excl_update γ n' n m :
......@@ -239,20 +241,15 @@ Section atomic_snapshot.
@ ∖↑N
<<< pair_content γ (x, y2), RET #() >>>.
Proof.
iIntros "Hp". iIntros (Φ) "AU".
iDestruct "Hp" as (l1 l2 ->) "#Hinv". wp_pures.
iIntros "Hx". iIntros (Φ) "AU".
iDestruct "Hx" as (l1 ->) "#Hinv". wp_pures.
wp_lam. wp_pures.
iApply wp_fupd.
iInv N as (q l1' T x) "Hinvp".
iDestruct "Hinvp" as (y v') "[Hl1 [Hl1' [Hl2 [Hp⚫ Htime]]]]".
iMod "AU" as (xv yv) "[[Hx Hy] [_ Hclose]]".
wp_store.
iMod "AU" as (xv yv) "[Hpair [_ Hclose]]".
rewrite /pair_content.
iDestruct (excl_sync with "Hp⚫ Hpair") as %[= -> ->].
iMod (excl_update _ (x, y2) with "Hp⚫ Hpair") as "[Hp⚫ Hp◯]".
iMod ("Hclose" with "Hp◯") as "HΦ".
iModIntro. iSplitR "HΦ"; last done.
iNext. unfold pair_inv. eauto 7 with iFrame.
iMod ("Hclose" with "[Hx Hy]") as "HΦ".
{ rewrite /pair_content. iFrame. }
eauto.
Qed.
Lemma writeX_spec γ (x2: val) p :
......@@ -262,12 +259,11 @@ Section atomic_snapshot.
@ ∖↑N
<<< pair_content γ (x2, y), RET #() >>>.
Proof.
iIntros "Hp". iIntros (Φ) "AU". iLöb as "IH".
iDestruct "Hp" as (l1 l2 ->) "#Hinv". wp_pures. wp_lam. wp_pures.
iIntros "Hx". iIntros (Φ) "AU". iLöb as "IH".
iDestruct "Hx" as (l1 ->) "#Hinv". wp_pures. wp_lam. wp_pures.
(* first read *)
(* open invariant *)
wp_bind (!_)%E. iInv N as (q l1' T x) "Hinvp".
iDestruct "Hinvp" as (y v') "[Hl1 [Hl1' [Hl2 [Hp⚫ Htime]]]]".
wp_bind (!_)%E. iInv N as (q l1' T x v') "[Hl1 [Hl1' [Hx⚫ Htime]]]".
wp_load.
iDestruct "Hl1'" as "[Hl1'frac1 Hl1'frac2]".
iModIntro. iSplitR "AU Hl1'frac2".
......@@ -279,19 +275,19 @@ Section atomic_snapshot.
(* CAS *)
wp_bind (CAS _ _ _)%E.
(* open invariant *)
iInv N as (q' l1'' T x') ">Hinvp".
iDestruct "Hinvp" as (y' v'') "[Hl1 [Hl1'' [Hl2 [Hp⚫ [Ht● Ht]]]]]".
iInv N as (q' l1'' T x' v'') ">[Hl1 [Hl1'' [Hx⚫ [Ht● Ht]]]]".
iDestruct "Ht" as %[Ht Hvt].
destruct (decide (l1'' = l1')) as [-> | Hn].
- wp_cas_suc.
iDestruct (mapsto_agree with "Hl1'frac2 Hl1''") as %[= -> ->]. iClear "Hl1'frac2".
(* open AU *)
iMod "AU" as (xv yv) "[Hpair [_ Hclose]]".
iMod "AU" as (xv yv) "[[Hx Hy] [_ Hclose]]".
(* update pair ghost state to (x2, y') *)
iDestruct (excl_sync with "Hp⚫ Hpair") as %[= -> ->].
iMod (excl_update _ (x2, y') with "Hp⚫ Hpair") as "[Hp⚫ Hp◯]".
iDestruct (excl_sync with "Hx⚫ Hx") as %[= ->].
iMod (excl_update _ x2 with "Hx⚫ Hx") as "[Hx⚫ Hx◯]".
(* close AU *)
iMod ("Hclose" with "Hp◯") as "HΦ".
iMod ("Hclose" with "[Hx◯ Hy]") as "HΦ".
{ rewrite /pair_content. iFrame. }
(* update timestamp *)
iMod (timestamp_update _ T (v'' + 1)%Z x2 with "[Ht●]") as "Ht".
{ eapply (not_elem_of_dom (D:=gset Z) T). intros Hd. specialize (Hvt _ Hd). omega. }
......@@ -300,7 +296,7 @@ Section atomic_snapshot.
iModIntro. iSplitR "HΦ".
+ iNext. rewrite /pair_inv.
set (<[ v'' + 1 := x2]> T) as T'.
iExists 1%Qp, l1'new, T', x2, y', (v'' + 1).
iExists 1%Qp, l1'new, T', x2, (v'' + 1).
iFrame.
iPureIntro. split.
* apply: lookup_insert.
......@@ -324,19 +320,15 @@ Section atomic_snapshot.
@ ∖↑N
<<< pair_content γ (v1, v2), RET v2 >>>.
Proof.
iIntros "Hp". iIntros (Φ) "AU".
iDestruct "Hp" as (l1 l2 ->) "#Hinv".
iIntros "Hx". iIntros (Φ) "AU".
iDestruct "Hx" as (l1 ->) "#Hinv".
repeat (wp_lam; wp_proj). wp_let.
iApply wp_fupd.
iInv N as (q l1' T x) "Hinvp".
iDestruct "Hinvp" as (y v') "[Hl1 [Hl1' [Hl2 [Hp⚫ Htime]]]]".
iMod "AU" as (xv yv) "[[Hx Hy] [_ Hclose]]".
wp_load.
iMod "AU" as (xv yv) "[Hpair [_ Hclose]]".
rewrite /pair_content.
iDestruct (excl_sync with "Hp⚫ Hpair") as %[= -> ->].
iMod ("Hclose" with "Hpair") as "HΦ".
iModIntro. iSplitR "HΦ"; last done.
iNext. unfold pair_inv. eauto 7 with iFrame.
iMod ("Hclose" with "[$Hx $Hy]") as "HΦ".
iModIntro. done.
Qed.
Lemma readX_spec γ p :
......@@ -346,23 +338,22 @@ Section atomic_snapshot.
@ ∖↑N
<<< (t: Z), pair_content γ (v1, v2), RET (v1, #t) >>>.
Proof.
iIntros "Hp". iIntros (Φ) "AU".
iDestruct "Hp" as (l1 l2 ->) "#Hinv".
iIntros "Hx". iIntros (Φ) "AU".
iDestruct "Hx" as (l1 ->) "#Hinv".
repeat (wp_lam; wp_proj). wp_let. wp_bind (! #l1)%E.
(* open invariant for 1st read *)
iInv N as (q l1' T x) ">Hinvp".
iDestruct "Hinvp" as (y v') "[Hl1 [Hl1' [Hl2 [Hp⚫ Htime]]]]".
iInv N as (q l1' T x v') ">[Hl1 [Hl1' [Hx⚫ Htime]]]".
wp_load.
iDestruct "Hl1'" as "[Hl1' Hl1'frac]".
iMod "AU" as (xv yv) "[Hpair [_ Hclose]]".
iDestruct (excl_sync with "Hp⚫ Hpair") as %[= -> ->].
iMod ("Hclose" with "Hpair") as "HΦ".
iMod "AU" as (xv yv) "[[Hx Hy] [_ Hclose]]".
iDestruct (excl_sync with "Hx⚫ Hx") as %[= ->].
iMod ("Hclose" with "[Hx Hy]") as "HΦ".
{ rewrite /pair_content. iFrame. }
(* close invariant *)
iModIntro. iSplitR "HΦ Hl1'". {
iNext. unfold pair_inv. eauto 7 with iFrame.
}
iApply wp_fupd. clear T y.
wp_load. eauto.
iApply wp_fupd. wp_load. eauto.
Qed.
Definition prophecy_to_bool (v : list (val * val)) : bool :=
......@@ -378,20 +369,20 @@ Section atomic_snapshot.
@ ∖↑N
<<< pair_content γ (v1, v2), RET (v1, v2) >>>.
Proof.
iIntros "Hp". iIntros (Φ) "AU". iLöb as "IH".
iIntros "Hx". iIntros (Φ) "AU". iLöb as "IH".
wp_pures.
(* ************ 1st readX ********** *)
iDestruct "Hp" as (l1 l2 ->) "#Hinv". repeat (wp_lam; wp_pures).
iDestruct "Hx" as (l1 ->) "#Hinv". repeat (wp_lam; wp_pures).
wp_bind (! #l1)%E.
(* open invariant for 1st read *)
iInv N as (q_x1 l1' T_x x1) ">Hinvp".
iDestruct "Hinvp" as (y_x1 v_x1) "[Hl1 [Hl1' [Hl2 [Hp⚫ [Ht_x Htime_x]]]]]".
iInv N as (q_x1 l1' T_x x1 v_x1) ">[Hl1 [Hl1' [Hx⚫ [Ht_x Htime_x]]]]".
iDestruct "Htime_x" as %[Hlookup_x Hdom_x].
wp_load.
iDestruct "Hl1'" as "[Hl1' Hl1'frac]".
iMod "AU" as (xv yv) "[Hpair [Hclose _]]".
iDestruct (excl_sync with "Hp⚫ Hpair") as %[= -> ->].
iMod ("Hclose" with "Hpair") as "AU".
iMod "AU" as (xv yv) "[[Hx Hy] [Hclose _]]".
iDestruct (excl_sync with "Hx⚫ Hx") as %[= ->].
iMod ("Hclose" with "[Hx Hy]") as "AU".
{ rewrite /pair_content. iFrame. }
(* duplicate timestamp T_x1 *)
iMod (timestamp_dupl with "Ht_x") as "[Ht_x1⚫ Ht_x1◯]".
(* close invariant *)
......@@ -405,24 +396,24 @@ Section atomic_snapshot.
wp_let.
(* ************ readY ********** *)
repeat (wp_lam; wp_pures). wp_bind (!_)%E.
iInv N as (q_y l1'_y T_y x_y) ">Hinvp".
iDestruct "Hinvp" as (y_y v_y) "[Hl1 [Hl1'_y [Hl2 [Hp⚫ [Ht_y Htime_y]]]]]".
iInv N as (q_y l1'_y T_y x_y v_y) ">[Hl1 [Hl1'_y [Hx⚫ [Ht_y Htime_y]]]]".
iDestruct "Htime_y" as %[Hlookup_y Hdom_y].
wp_load.
(* linearization point *)
iMod "AU" as (xv yv) "[Hpair Hclose]".
clear yv.
iMod "AU" as (xv yv) "[[Hx Hy] Hclose]".
wp_load.
rewrite /pair_content.
iDestruct (excl_sync with "Hp⚫ Hpair") as %[= -> ->].
iDestruct (excl_sync with "Hx⚫ Hx") as %[= ->].
destruct (prophecy_to_bool proph_val) eqn:Hproph.
- (* prophecy value is predicting that timestamp has not changed, so we commit *)
(* committing AU *)
iMod ("Hclose" with "Hpair") as "HΦ".
iMod ("Hclose" with "[$Hx $Hy]") as "HΦ".
(* duplicate timestamp T_y *)
iMod (timestamp_dupl with "Ht_y") as "[Ht_y● Ht_y◯]".
(* show that T_x <= T_y *)
iDestruct (timestamp_sub with "[Ht_y● Ht_x1◯]") as "#Hs"; first by iFrame.
iDestruct "Hs" as %Hs.
iModIntro.
iModIntro. iModIntro.
(* closing invariant *)
iSplitR "HΦ Hl1' Ht_x1◯ Ht_y◯ Hpr".
{ iNext. unfold pair_inv. eauto 10 with iFrame. }
......@@ -430,8 +421,7 @@ Section atomic_snapshot.
(* ************ 2nd readX ********** *)
repeat (wp_lam; wp_pures). wp_bind (! #l1)%E.
(* open invariant *)
iInv N as (q_x2 l1'_x2 T_x2 x2) ">Hinvp".
iDestruct "Hinvp" as (y_x2 v_x2) "[Hl1 [Hl1'_x2 [Hl2 [Hp⚫ [Ht_x2 Htime_x2]]]]]".
iInv N as (q_x2 l1'_x2 T_x2 x2 v_x2) ">[Hl1 [Hl1'_x2 [Hx⚫ [Ht_x2 Htime_x2]]]]".
iDestruct "Htime_x2" as %[Hlookup_x2 Hdom_x2].
iDestruct "Hl1'_x2" as "[Hl1'_x2 Hl1'_x2_frag]".
wp_load.
......@@ -461,8 +451,8 @@ Section atomic_snapshot.
}
done.
+ inversion Hproph.
- iDestruct "Hclose" as "[Hclose _]". iMod ("Hclose" with "Hpair") as "AU".
iModIntro.
- iDestruct "Hclose" as "[Hclose _]". iMod ("Hclose" with "[$Hx $Hy]") as "AU".
iModIntro. iModIntro.
(* closing invariant *)
iSplitR "AU Hpr".
{ iNext. unfold pair_inv. eauto 10 with iFrame. }
......@@ -470,8 +460,7 @@ Section atomic_snapshot.
(* ************ 2nd readX ********** *)
repeat (wp_lam; wp_proj). wp_let. wp_bind (! #l1)%E.
(* open invariant *)
iInv N as (q_x2 l1'_x2 T_x2 x2) ">Hinvp".
iDestruct "Hinvp" as (y_x2 v_x2) "[Hl1 [Hl1'_x2 [Hl2 [Hp⚫ [Ht_x2 Htime_x2]]]]]".
iInv N as (q_x2 l1'_x2 T_x2 x2 v_x2) "[Hl1 [Hl1'_x2 [Hx⚫ [Ht_x2 Htime_x2]]]]".
iDestruct "Hl1'_x2" as "[Hl1'_x2 Hl1'_x2_frag]".
wp_load.
iModIntro. iSplitR "AU Hl1'_x2_frag Hpr". {
......
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