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proof_retired_list.v
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proof_retired_list.v
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From iris.base_logic Require Import lib.invariants.
From smr.program_logic Require Import atomic.
From smr Require Import helpers.
From smr.lang Require Import proofmode notation.
From iris.prelude Require Import options.
From smr Require Import spec_retired_list code_retired_list.
Set Printing Projections.
Section retired_list.
Context `{!heapGS Σ}.
Notation iProp := (iProp Σ).
(* hd is the head of a linked list representing xs *)
Fixpoint phys_list (hd : base_lit) (xs : list (blk * nat * nat)) : iProp :=
match xs with
| [] => ⌜hd = LitLoc NULL⌝
| (x, size, epoch) :: xs =>
∃ (p : loc) (nxt : option loc), ⌜hd = LitLoc p⌝ ∗
(p +ₗ rNodeNext) ↦ #(oloc_to_lit nxt) ∗
(p +ₗ rNodePtr) ↦ #x ∗
(p +ₗ rNodePtrSize) ↦ #size ∗
(p +ₗ rNodeEpoch) ↦ #epoch ∗
†p…rNodeSize ∗
phys_list (oloc_to_lit nxt) xs
end.
Definition RetiredNode (rNode ptr : loc) (next : option loc) (size : nat) (epoch : nat) : iProp :=
(rNode +ₗ rNodeNext) ↦ #(oloc_to_lit next) ∗
(rNode +ₗ rNodePtr) ↦ #ptr ∗
(rNode +ₗ rNodePtrSize) ↦ #size ∗
(rNode +ₗ rNodeEpoch) ↦ #epoch ∗
†rNode…rNodeSize.
Definition RetiredList (rList : loc) (rs : list (blk * nat * nat)) : iProp :=
∃ (hd : option loc),
(rList +ₗ rSetHead) ↦ #(oloc_to_lit hd) ∗
phys_list (oloc_to_lit hd) rs.
Definition RetiredNodes (rNode : option loc) (rs : list (blk * nat * nat)) : iProp :=
phys_list (oloc_to_lit rNode) rs.
Global Instance phys_list_timeless hd xs: Timeless (phys_list hd xs).
Proof.
revert hd. induction xs; simpl; [apply _|].
intros. repeat case_match. subst. apply _.
Qed.
Global Instance RetiredNode_Timeless rNode ptr next size epoch:
Timeless (RetiredNode rNode ptr next size epoch).
Proof. apply _. Qed.
Global Instance RetiredList_Timeless rList rs: Timeless (RetiredList rList rs).
Proof. apply _. Qed.
Global Instance RetiredNodes_Timeless rNode rs: Timeless (RetiredNodes rNode rs).
Proof. apply _. Qed.
Lemma retired_node_new_spec :
retired_node_new_spec' RetiredNode.
Proof.
iIntros (?????) "_ HΦ".
wp_rec. wp_pures. wp_alloc r as "r↦" "†r".
wp_pures.
repeat (wp_apply (wp_store_offset with "r↦") as "r↦"; [by simplify_list_eq|]; wp_pures).
iApply "HΦ". simpl. iFrame. rewrite !array_cons 3!Loc.add_assoc Loc.add_0.
by iDestruct "r↦" as "($ & $ & $ & $ & _)".
Qed.
Lemma retired_node_next_spec :
retired_node_next_spec' RetiredNode.
Proof.
iIntros (???????) "[r.next↦ ?] HΦ".
wp_rec. wp_pures. wp_load. iModIntro.
iApply "HΦ"; iFrame.
Qed.
Lemma retired_node_ptr_spec :
retired_node_ptr_spec' RetiredNode.
Proof.
iIntros (???????) "(? & r.ptr↦ & ?) HΦ".
wp_rec. wp_pures. wp_load. iModIntro.
iApply "HΦ"; iFrame.
Qed.
Lemma retired_node_size_spec :
retired_node_size_spec' RetiredNode.
Proof.
iIntros (???????) "(? & ? & r.size↦ & ?) HΦ".
wp_rec. wp_pures. wp_load. iModIntro.
iApply "HΦ"; iFrame.
Qed.
Lemma retired_node_epoch_spec :
retired_node_epoch_spec' RetiredNode.
Proof.
iIntros (???????) "(? & ? & ? & r.epoch↦ & ?) HΦ".
wp_rec. wp_pures. wp_load. iModIntro.
iApply "HΦ"; iFrame.
Qed.
Lemma retired_node_drop_spec :
retired_node_drop_spec' RetiredNode.
Proof.
iIntros (???????) "(r.next↦ & r.ptr↦ & r.size↦ & r.epoch↦ & †r) HΦ".
rewrite -!array_singleton Loc.add_0.
iCombine "r.next↦ r.ptr↦" as "r↦".
rewrite -array_app.
(* rewrite -heap_pointsto_vec_app /=. *)
iCombine "r↦ r.size↦" as "r↦".
rewrite -array_app.
iCombine "r↦ r.epoch↦" as "r↦".
rewrite -array_app /=.
wp_rec. wp_free; [done|by iApply "HΦ"].
Qed.
Lemma retired_list_new_spec :
retired_list_new_spec' RetiredList.
Proof.
iIntros (??) "_ HΦ". wp_rec. wp_alloc r as "r↦" "†r".
wp_pures. rewrite Loc.add_0 array_singleton. wp_store.
iModIntro. iApply "HΦ".
iExists None. rewrite Loc.add_0. by iFrame.
Qed.
Lemma retired_list_push_spec :
retired_list_push_spec' RetiredNode RetiredList.
Proof.
iIntros (???????) "r↦ % AU". iDestruct "r↦" as "(r.next↦ & r.ptr↦ & r.size↦ & r.epoch↦ & †r)".
iLöb as "IH" forall (next).
wp_rec. wp_pures.
wp_bind (! _)%E.
iMod "AU" as (xs1) "[[%hd1 [>Hrs Hphys]] [Abort _]]".
wp_load.
iMod ("Abort" with "[Hrs Hphys]") as "AU".
{ iNext. iExists hd1; iFrame. }
iModIntro. clear.
wp_pures. wp_store. wp_pures.
wp_bind (CmpXchg _ _ _)%E.
iMod "AU" as (xs2) "[[%hd2 [>Hrs Hphys]] AU]".
destruct (decide (hd1 = hd2)) as [?|NE]; subst.
- (* success *)
iDestruct "AU" as "[_ Commit]".
wp_cmpxchg_suc.
iMod ("Commit" with "[-]") as "HΦ".
{ iExists (Some rNode); iFrame. done. }
iModIntro. wp_pures. by iApply "HΦ".
- (* fail *)
iDestruct "AU" as "[Abort _]".
wp_cmpxchg_fail.
iMod ("Abort" with "[Hrs Hphys]") as "AU".
{ iNext. iExists hd2; iFrame. }
iModIntro. wp_pures.
iApply ("IH" with "r.next↦ r.ptr↦ r.size↦ r.epoch↦ †r AU").
Qed.
Lemma retired_list_pop_all_spec :
retired_list_pop_all_spec' RetiredList RetiredNodes.
Proof.
iIntros (???) "AU".
wp_rec. wp_pures.
iMod "AU" as (?) "[Hrl [_ Commit]]".
iDestruct "Hrl" as (?) "[>Hrl Hphys]".
iApply (wp_xchg with "Hrl").
iNext. iIntros "Hrl".
iMod ("Commit" with "[-]") as "HΦ"; last by iApply "HΦ".
iSplitL "Hrl"; auto. iExists None; auto.
Qed.
Lemma retired_nodes_cons :
retired_nodes_cons' RetiredNode RetiredNodes.
Proof.
iIntros (rNode rs). iSplit.
- iIntros "RNodes". rewrite /RetiredNodes /=.
destruct rs as [|[[r e] p] rs]; simpl.
+ iDestruct "RNodes" as %[= ?].
+ iDestruct "RNodes" as (? nxt [= <-]) "(?&?&?&?&?&?)".
repeat iExists _. by iFrame.
- iDestruct 1 as (r rs' next size epoch ->) "(RNode & RNodes)".
rewrite /RetiredNodes /RetiredNode /=. repeat iExists _. by iFrame.
Qed.
End retired_list.
Definition retired_list_impl Σ `{!heapGS Σ} : spec_retired_list.retired_list_spec Σ := {|
spec_retired_list.RetiredNode := RetiredNode;
spec_retired_list.RetiredList := RetiredList;
spec_retired_list.RetiredNodes := RetiredNodes;
spec_retired_list.RetiredNode_Timeless := RetiredNode_Timeless;
spec_retired_list.RetiredList_Timeless := RetiredList_Timeless;
spec_retired_list.RetiredNodes_Timeless := RetiredNodes_Timeless;
spec_retired_list.retired_node_new_spec := retired_node_new_spec;
spec_retired_list.retired_node_next_spec := retired_node_next_spec;
spec_retired_list.retired_node_ptr_spec := retired_node_ptr_spec;
spec_retired_list.retired_node_size_spec := retired_node_size_spec;
spec_retired_list.retired_node_epoch_spec := retired_node_epoch_spec;
spec_retired_list.retired_node_drop_spec := retired_node_drop_spec;
spec_retired_list.retired_list_new_spec := retired_list_new_spec;
spec_retired_list.retired_list_push_spec := retired_list_push_spec;
spec_retired_list.retired_list_pop_all_spec := retired_list_pop_all_spec;
spec_retired_list.retired_nodes_cons := retired_nodes_cons;
|}.