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From iris.program_logic Require Export auth weakestpre.
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From iris.proofmode Require Import invariants ghost_ownership.
From iris.heap_lang Require Export lang.
From iris.heap_lang Require Import proofmode notation.
From iris.heap_lang.lib Require Import spin_lock.
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From iris.algebra Require Import frac excl dec_agree upred_big_op gset gmap.
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From iris.tests Require Import atomic treiber_stack.
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From flatcomb Require Import misc.
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Definition doOp : val :=
  λ: "f" "p",
     match: !"p" with
       InjL "x" => "p" <- InjR ("f" "x")
     | InjR "_" => #()
     end.
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Definition loop : val :=
  rec: "loop" "p" "f" "s" "lk" :=
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    match: !"p" with
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      InjL "_" =>
        if: CAS "lk" #false #true
          then iter (doOp "f") "s"
          else "loop" "p" "f" "s" "lk"
    | InjR "r" => "r"
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    end.

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(* Naive implementation *)
Definition install : val :=
  λ: "x" "s",
     let: "p" := ref (InjL "x") in
     push "s" "p";;
     "p".
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Definition flat : val :=
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  λ: "f",
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     let: "lk" := ref (#false) in
     let: "s" := new_stack #() in
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     λ: "x",
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        let: "p" := install "x" "s" in
        loop "p" "f" "s" "lk".

Global Opaque doOp install loop flat.
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Definition hdset := gset loc.
Definition gnmap := gmap loc (dec_agree (gname * gname * gname * gname * gname)).

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Definition srvR := prodR fracR (dec_agreeR val).
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Definition hdsetR := gset_disjUR loc.
Definition gnmapR := gmapUR loc (dec_agreeR (gname * gname * gname * gname * gname)).

Class srvG Σ :=
  SrvG {
      srv_tokG :> inG Σ srvR;
      hd_G :> inG Σ (authR hdsetR);
      gn_G :> inG Σ (authR gnmapR)
    }.

Definition srvΣ : gFunctors :=
  #[ GFunctor (constRF srvR);
     GFunctor (constRF (authR hdsetR));
     GFunctor (constRF (authR gnmapR))
   ].
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Instance subG_srvΣ {Σ} : subG srvΣ Σ  srvG Σ.
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Proof. intros [?%subG_inG [?subG_inG [?subG_inG _]%subG_inv]%subG_inv]%subG_inv. split; apply _. Qed.
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Section proof.
  Context `{!heapG Σ, !lockG Σ, !srvG Σ} (N : namespace).
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  Definition p_inv
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             (γx γ1 γ2 γ3 γ4: gname) (p: loc)
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             (Q: val  val  Prop): iProp Σ :=
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    (( (y: val), p  InjRV y  own γ1 (Excl ())  own γ3 (Excl ())) 
     ( (x: val), p  InjLV x  own γx ((1/2)%Qp, DecAgree x)  own γ1 (Excl ())  own γ4 (Excl ())) 
     ( (x: val), p  InjLV x  own γx ((1/4)%Qp, DecAgree x)  own γ2 (Excl ())  own γ4 (Excl ())) 
     ( (x y: val), p  InjRV y  own γx ((1/2)%Qp, DecAgree x)   Q x y  own γ1 (Excl ())  own γ4 (Excl ())))%I.
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  Definition p_inv' (γs: dec_agree (gname * gname * gname * gname * gname)) p Q :=
    match γs with
      | DecAgreeBot => False%I
      | DecAgree (γx, γ1, γ2, γ3, γ4) => p_inv γx γ1 γ2 γ3 γ4 p Q
    end.

  Definition srv_inv (γhd γgn: gname) (s: loc) (Q: val  val  Prop) : iProp Σ :=
    ( (hds: hdset) (gnm: gnmap),
       own γhd ( GSet hds)  own γgn ( gnm) 
       ( xs: list loc, is_stack s (map (fun x => # (LitLoc x)) xs) 
                        [ list] k  x  xs,  (x  dom (gset loc) gnm)) 
       ([ set] hd  hds,  xs, is_list hd (map (fun x => # (LitLoc x)) xs) 
                                [ list] k  x  xs,  (x  dom (gset loc) gnm)) 
       ([ map] p  γs  gnm, p_inv' γs p Q)
    )%I.

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  Instance p_inv_timeless γx γ1 γ2 γ3 γ4 p Q: TimelessP (p_inv γx γ1 γ2 γ3 γ4 p Q).  
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  Proof. apply _. Qed.

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  Instance p_inv'_timeless γs p Q: TimelessP (p_inv' γs p Q).
  Proof.
    rewrite /p_inv'. destruct γs as [γs|].
    - repeat (destruct γs as [γs ?]). apply _.
    - apply _.
  Qed.

  Instance srv_inv_timeless γhd γgn s Q: TimelessP (srv_inv γhd γgn s Q).
  Proof. apply _. Qed.

  Lemma push_spec
        (Φ: val  iProp Σ) (Q: val  val  Prop)
        (p: loc) (γx γ1 γ2 γ3 γ4: gname)
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        (γhd γgn: gname) (s: loc) (x: val) :
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    heapN  N 
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    heap_ctx  inv N (srv_inv γhd γgn s Q)  own γx ((1/2)%Qp, DecAgree x) 
    p  InjLV x  own γ1 (Excl ())  own γ4 (Excl ())  (True - Φ #())
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     WP push #s #p {{ Φ }}.
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  Proof.
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    iIntros (HN) "(#Hh & #Hsrv & Hp & Hx & Ho1 & Ho4 & HΦ)".    
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    iDestruct (push_atomic_spec N s #p with "Hh") as "Hpush"=>//.
    rewrite /push_triple /atomic_triple.
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    iSpecialize ("Hpush" $! (p  InjLV x  own γ1 (Excl ())  own γ4 (Excl ()) 
                             own γx ((1/2)%Qp, DecAgree x))%I
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                            (fun _ ret => ret = #())%I with "[]").
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    - iIntros "!#". iIntros "(Hp & Hx & Ho1 & Ho4)".
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      (* open the invariant *)
      iInv N as (hds gnm) ">(Hohd & Hogn & Hxs & Hhd & Hps)" "Hclose".
      iDestruct "Hxs" as (xs) "(Hs & Hgn)".
      (* mask magic *)
      iApply pvs_intro'.
      { apply ndisj_subseteq_difference; auto. }
      iIntros "Hvs".
      iExists (map (λ x : loc, #x) xs).
      iFrame "Hs". iSplit.
      + (* provide a way to rollback *)
        iIntros "Hl'".
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        iVs "Hvs". iVs ("Hclose" with "[-Hp Hx Ho1 Ho4]"); last by iFrame.
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        iNext. rewrite /srv_inv. iExists hds, gnm.
        iFrame. iExists xs. by iFrame.
      + (* provide a way to commit *)
        iIntros (?) "[% Hs]". subst.
        iVs "Hvs". iVs ("Hclose" with "[-]"); last done.
        iNext. rewrite /srv_inv. iExists hds, (gnm  {[ p := DecAgree (γx, γ1, γ2, γ3, γ4) ]}).
        iFrame.
        iClear "Hogn".
        iAssert (own γgn ( (gnm  {[p := DecAgree (γx, γ1, γ2, γ3, γ4)]})) 
                 own γgn ( {[ p := DecAgree (γx, γ1, γ2, γ3, γ4) ]}))%I as "[Hogn' Hfrag]".
        { admit. }
        iFrame. iSplitL "Hs Hgn".
        { iExists (p::xs).
          iFrame. admit. }
        iSplitL "Hhd".
        { admit. }
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        iAssert (p_inv' (DecAgree (γx, γ1, γ2, γ3, γ4)) p Q)  with "[Hp Hx Ho1 Ho4]" as "Hinvp".
        { rewrite /p_inv' /p_inv. iRight. iLeft. iExists x. by iFrame. }
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        admit.
    - iApply wp_wand_r. iSplitR "HΦ".
      + iApply "Hpush". by iFrame.
      + iIntros (?) "H". iDestruct "H" as (?) "%". subst. by iApply "HΦ".
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  Admitted.
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  Lemma install_spec
        (Φ: val  iProp Σ) (Q: val  val  Prop)
        (x: val) (γhd γgn: gname) (s: loc):
    heapN  N 
    heap_ctx  inv N (srv_inv γhd γgn s Q) 
    ( (p: loc) (γx γ1 γ2 γ3 γ4: gname),
       own γ2 (Excl ()) - own γ3 (Excl ()) - own γgn ( {[ p := DecAgree (γx, γ1, γ2, γ3, γ4) ]}) -
       own γx ((1/2)%Qp, DecAgree x) - Φ #p)
     WP install x #s {{ Φ }}.
  Proof.
    iIntros (HN) "(#Hh & #Hsrv & HΦ)".
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    wp_seq. wp_let. wp_alloc p as "Hl".
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    iVs (own_alloc (Excl ())) as (γ1) "Ho1"; first done.
    iVs (own_alloc (Excl ())) as (γ2) "Ho2"; first done.
    iVs (own_alloc (Excl ())) as (γ3) "Ho3"; first done.
    iVs (own_alloc (Excl ())) as (γ4) "Ho4"; first done.
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    iVs (own_alloc (1%Qp, DecAgree x)) as (γx) "Hx"; first done.
    iDestruct (own_update with "Hx") as "==>[Hx1 Hx2]".
    { by apply pair_l_frac_op_1'. }
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    wp_let. wp_bind ((push _) _).
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    iApply push_spec=>//.
    iFrame "Hh Hsrv Hx1 Hl Ho1 Ho4".
    iIntros "_". wp_seq. iVsIntro.
    iSpecialize ("HΦ" $! p γx γ1 γ2 γ3 γ4).
    iAssert (own γgn ( {[p := DecAgree (γx, γ1, γ2, γ3, γ4)]})) as "Hfrag".
    { admit. }
    iApply ("HΦ" with "Ho2 Ho3 Hfrag Hx2").
  Admitted.
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  Definition pinv_sub RI γx γ1 γ2 γ3 γ4 p Q := (RI ⊣⊢  Rf, Rf  p_inv γx γ1 γ2 γ3 γ4 p Q)%I.

  Lemma doOp_spec Φ (f: val) (RI: iProp Σ) γx γ1 γ2 γ3 γ4 p Q `{TimelessP _ RI}:
    heapN  N  pinv_sub RI γx γ1 γ2 γ3 γ4 p Q 
    heap_ctx  inv N RI  own γ2 (Excl ()) 
     ( x:val, WP f x {{ v,  Q x v }})%I  (own γ2 (Excl ()) - Φ #())
     WP doOp f #p {{ Φ }}.
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  Proof.
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    iIntros (HN Hsub) "(#Hh & #HRI & Ho2 & #Hf & HΦ)".
    wp_seq. wp_let. wp_bind (! _)%E.
    iInv N as ">H" "Hclose".
    iDestruct (Hsub with "H") as (Rf) "[HRf [Hp | [Hp | [Hp | Hp]]]]".
    - iDestruct "Hp" as (y) "(Hp & Ho1 & Ho3)".
      wp_load. iVs ("Hclose" with "[HRf Hp Ho1 Ho3]").
      { iNext. iApply Hsub. iExists Rf. iFrame "HRf".
        iLeft. iExists y. by iFrame. }
      iVsIntro. wp_match. by iApply "HΦ".
    - iDestruct "Hp" as (x) "(Hp & Hx & Ho1 & Ho4)".
      wp_load.
      iAssert (|=r=> own γx (((1 / 4)%Qp, DecAgree x)  ((1 / 4)%Qp, DecAgree x)))%I with "[Hx]" as "==>[Hx1 Hx2]".
      { iDestruct (own_update with "Hx") as "Hx"; last by iAssumption.
        replace ((1 / 2)%Qp) with (1/4 + 1/4)%Qp; last by apply Qp_div_S.
        by apply pair_l_frac_op'. }
      iVs ("Hclose" with "[HRf Hp Hx1 Ho2 Ho4]").
      { iNext. iApply Hsub. iExists Rf. iFrame "HRf".
        iRight. iRight. iLeft. iExists x. by iFrame. }
      iVsIntro. wp_match.
      wp_bind (f _). iApply wp_wand_r.
      iSplitR; first by iApply "Hf".
      iIntros (y) "%".
      iInv N as ">H" "Hclose".
      iDestruct (Hsub with "H") as (Rf') "[HRf [Hp | [Hp | [Hp | Hp]]]]".
      + admit.
      + admit.
      + iDestruct "Hp" as (x') "(Hp & Hx & Ho2 & Ho4)".
        destruct (decide (x = x')) as [->|Hneq]; last by admit.
        iCombine "Hx2" "Hx" as "Hx".
        iDestruct (own_update with "Hx") as "==>Hx"; first by apply pair_l_frac_op.
        rewrite Qp_div_S.
        wp_store. iVs ("Hclose" with "[HRf Hp Hx Ho1 Ho4]").
        { iNext. iApply Hsub. iExists Rf'. iFrame "HRf".
          iRight. iRight. iRight. iExists x', y.
          by iFrame. }
        iVsIntro. by iApply "HΦ".
      + admit.
    - admit.
    - admit.
  Admitted.