Commit efc93d9c authored by Robbert Krebbers's avatar Robbert Krebbers

Simplify the ticket lock proofs a bit.

parent b7a055bf
Pipeline #2548 passed with stage
in 3 minutes and 56 seconds
......@@ -2,7 +2,6 @@ From iris.program_logic Require Export global_functor auth.
From iris.proofmode Require Import invariants ghost_ownership.
From iris.heap_lang Require Import proofmode notation.
From iris.algebra Require Import gset.
From iris.prelude Require Import set.
Import uPred.
Definition wait_loop: val :=
......@@ -25,18 +24,18 @@ Definition release : val :=
let: "oldl" := !"l" in
if: CAS "l" "oldl" (Fst "oldl" + #1, Snd "oldl")
then #()
else "release" "l".
else "release" "l".
Global Opaque newlock acquire release wait_loop.
(** The CMRA we need. *)
(** The CMRAs we need. *)
Class tlockG Σ := TlockG {
tlock_G :> authG heap_lang Σ (gset_disjUR nat);
tlock_exclG :> inG heap_lang Σ (exclR unitC)
}.
Definition tlockGF : gFunctorList := [ authGF (gset_disjUR nat)
; GFunctor (constRF (exclR unitC))].
Definition tlockGF : gFunctorList :=
[authGF (gset_disjUR nat); GFunctor (constRF (exclR unitC))].
Instance inGF_tlockG `{H : inGFs heap_lang Σ tlockGF} : tlockG Σ.
Proof. destruct H as (? & ? & ?). split. apply _. apply: inGF_inG. Qed.
......@@ -44,70 +43,24 @@ Section proof.
Context `{!heapG Σ, !tlockG Σ} (N : namespace).
Local Notation iProp := (iPropG heap_lang Σ).
Section natstuff.
Open Scope nat_scope.
Fixpoint natset (s len: nat) : gset nat :=
match len with
| O =>
| S len' => natset s len' {[ s + len' ]}
end.
Lemma natset_range: (len s x: nat), x natset s len -> x < (s + len).
Proof.
intros len.
elim len.
+ intros. simpl in H. set_solver.
+ intros. simpl in H0. apply elem_of_union in H0.
destruct H0.
- apply H in H0.
omega.
- assert (x = s + n).
set_solver.
omega.
Qed.
Lemma natset_not_in: x, x natset 0 x.
Proof.
intros x H.
apply natset_range in H.
omega.
Qed.
Lemma natset_incr: x, {[x]} natset 0 x = natset 0 (x + 1).
Proof.
intros.
rewrite Nat.add_1_r.
simpl.
set_solver.
Qed.
Lemma natset_disj: x, {[x]} natset 0 x.
Proof.
intros.
assert (x natset 0 x).
apply natset_not_in.
set_solver.
Qed.
End natstuff.
Definition tickets_inv (n: nat) (gs: gset_disjUR nat) :iProp :=
( gs', GSet gs' = gs gs' = natset 0 n)%I.
Definition tickets_inv (n: nat) (gs: gset_disjUR nat) : iProp :=
(gs = GSet (seq_set 0 n))%I.
Definition lock_inv (γ1 γ2: gname) (l : loc) (R : iProp) : iProp :=
( (o n: nat), l (#o, #n)
( o n: nat, l (#o, #n)
auth_inv γ1 (tickets_inv n)
((own γ2 (Excl ()) R)
auth_own γ1 (GSet {[ o ]})))%I.
((own γ2 (Excl ()) R) auth_own γ1 (GSet {[ o ]})))%I.
Definition is_lock (l: loc) (R: iProp) : iProp :=
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R))%I.
Definition issued (l : loc) (x: nat) (R : iProp) : iProp :=
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R) auth_own γ1 (GSet {[ x ]}))%I.
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R)
auth_own γ1 (GSet {[ x ]}))%I.
Definition locked (l : loc) (R : iProp) : iProp :=
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R) own γ2 (Excl ()))%I.
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R)
own γ2 (Excl ()))%I.
Global Instance lock_inv_ne n γ1 γ2 l : Proper (dist n ==> dist n) (lock_inv γ1 γ2 l).
Proof. solve_proper. Qed.
......@@ -134,13 +87,9 @@ Proof.
iSplitL "Hγ1".
{ rewrite /auth_inv.
iExists (GSet ).
iFrame.
rewrite /tickets_inv.
iExists ; by iSplit.
}
by iFrame. }
iLeft.
by iFrame.
}
by iFrame. }
iPvsIntro.
iApply "HΦ".
iExists γ1, γ2.
......@@ -162,18 +111,16 @@ Proof.
iExists o, n.
iFrame.
by iRight.
* wp_proj. wp_let. wp_op=>Ho; last by contradiction Ho. clear Ho.
* wp_proj. wp_let. wp_op=>[_|[]] //.
  • Can you explain a bit about how this wp_op pattern work? Thanks :)

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wp_if. iPvsIntro.
iApply ("HΦ" with "[-HR] HR"). iExists γ1, γ2; eauto.
+ iExFalso. iCombine "Ht" "Haown" as "Haown".
iDestruct (auth_own_valid with "Haown") as "%".
apply gset_disj_valid_op in H0.
iDestruct (auth_own_valid with "Haown") as % ?%gset_disj_valid_op.
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set_solver.
- iSplitL "Hl Ha".
+ iNext. iExists o, n. by iFrame.
+ wp_proj. wp_let. wp_op=>?.
* subst. contradiction Hneq. omega.
* wp_if. by iApply ("IH" with "Ht").
+ wp_proj. wp_let. wp_op=>?; first omega.
wp_if. by iApply ("IH" with "Ht").
Qed.
Lemma acquire_spec l R (Φ : val iProp) :
......@@ -185,46 +132,29 @@ Proof.
wp_load. iPvsIntro.
iSplitL "Hl Ha".
- iNext. iExists o, n. by iFrame.
- wp_let.
- wp_let. wp_proj. wp_proj. wp_op.
wp_focus (CAS _ _ _).
wp_proj. wp_proj.
wp_op.
iInv N as (o' n') "[Hl [Hainv Haown]]".
destruct (decide ((#o', #n')%V = (#o, #n)%V)) as [Heq | Hneq].
iInv N as (o' n') "[Hl [Hainv Haown]]".
destruct (decide ((#o', #n') = (#o, #n)))%V
as [[= ->%Nat2Z.inj ->%Nat2Z.inj] | Hneq].
+ wp_cas_suc.
inversion Heq; subst.
iDestruct "Hainv" as (s) "[Ho Ht]".
iDestruct (own_valid with "#Ho") as "Hvalid".
iDestruct (auth_validI _ with "Hvalid") as "[_ %]"; simpl; iClear "Hvalid".
destruct s as [s|]; last by contradiction.
iDestruct "Ht" as (gs) "[% %]".
inversion H3. subst. subst. clear H3.
iDestruct "Hainv" as (s) "[Ho %]"; subst.
iPvs (own_update with "Ho") as "Ho".
{ eapply auth_update_no_frag, gset_alloc_empty_local_update.
eapply natset_not_in. }
{ eapply auth_update_no_frag, (gset_alloc_empty_local_update n).
rewrite elem_of_seq_set; omega. }
iDestruct "Ho" as "[Hofull Hofrag]".
iSplitL "Hl Haown Hofull".
* replace (GSet {[n']} GSet (natset 0 n')) with (GSet (natset 0 (n' + 1))).
{ iPvsIntro. iNext.
iExists o', (n' + 1)%nat.
rewrite Nat2Z.inj_add.
iFrame. iExists (GSet (natset 0 (n' + 1))).
iFrame. iExists (natset 0 (n' + 1)).
by auto.
}
{ rewrite gset_disj_union.
replace (natset 0 (n' + 1)) with ({[n']} natset 0 n').
- auto.
- apply natset_incr.
- apply natset_disj.
}
* rewrite gset_disj_union; last by apply (seq_set_S_disjoint 0).
rewrite -(seq_set_S_union_L 0).
iPvsIntro. iNext.
iExists o, (S n)%nat.
rewrite Nat2Z.inj_succ -Z.add_1_r.
iFrame. iExists (GSet (seq_set 0 (S n))).
by iFrame.
* iPvsIntro. wp_if. wp_proj.
iApply wait_loop_spec.
iSplitR "HΦ"; last by done.
iExists γ1, γ2.
(* FIXME: iFrame should be able to make progress here. *)
repeat (iSplit; first by auto).
by rewrite /auth_own.
rewrite /issued /auth_own; eauto 10.
  • Also this eauto 10. I've seen it used at other places, but I have no idea how it works :/

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+ wp_cas_fail.
iPvsIntro.
iSplitL "Hl Hainv Haown".
......@@ -244,15 +174,14 @@ Proof.
- wp_let. wp_focus (CAS _ _ _ ).
wp_proj. wp_op. wp_proj.
iInv N as (o' n') "[Hl Hr]".
destruct (decide ((#o', #n')%V = (#o, #n)%V)) as [Heq | Hneq].
+ inversion Heq; subst.
wp_cas_suc.
destruct (decide ((#o', #n') = (#o, #n)))%V
as [[= ->%Nat2Z.inj ->%Nat2Z.inj] | Hneq].
+ wp_cas_suc.
iDestruct "Hr" as "[Hainv [[Ho _] | Hown]]".
* iExFalso. iCombine "Hγ" "Ho" as "Ho".
iDestruct (own_valid with "#Ho") as "Hvalid".
by iDestruct (excl_validI _ with "Hvalid") as "%".
iDestruct (own_valid with "#Ho") as %[].
* iSplitL "Hl HR Hγ Hainv".
{ iPvsIntro. iNext. iExists (o' + 1)%nat, n'%nat.
{ iPvsIntro. iNext. iExists (o + 1)%nat, n%nat.
iFrame. rewrite Nat2Z.inj_add.
iFrame. iLeft; by iFrame. }
{ iPvsIntro. by wp_if. }
......@@ -265,4 +194,3 @@ Qed.
End proof.
Typeclasses Opaque is_lock issued locked.
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