Delete pcas example (which is redundant)

pcas.v

-From iris.program_logic Require Export weakestpre hoare.
-From iris.heap_lang Require Export lang.
-From iris.heap_lang Require Import proofmode notation.
-From iris.heap_lang.lib Require Import spin_lock.
-From iris.algebra Require Import excl.
-Require Import iris_atomic.simple_sync.
-Import uPred.
-
-(* CAS, load and store to pair of locations *)
-(* TODO: Make it mroe realistic by taking two parameters rather than sharing one for both locations*)
-(* TODO: Eliminate the duplication of spec code *)
-(* TODO: release spec of lock user *)
-
-Definition casp_seq' (l1 l2: loc) : val :=
-  λ: "vp",
-     let: "oldv" := Fst "vp" in
-     let: "newv" := Snd "vp" in
-     if: !(Fst (#l1, #l2)) = "oldv"
-       then if: !(Snd (#l1, #l2)) = "oldv"
-              then (Fst (#l1, #l2)) <- "newv";; (Snd (#l1, #l2)) <- "newv";; #true
-              else #false
-       else #false.
-
-Definition casp_seq: val :=
-    λ: "lp" "vp",
-       let: "oldv" := Fst "vp" in
-       let: "newv" := Snd "vp" in
-       if: !(Fst "lp") = "oldv"
-         then if: !(Snd "lp") = "oldv"
-                then (Fst "lp") <- "newv";; (Snd "lp") <- "newv";; #true
-                else #false
-         else #false.
-
-Definition loadp_seq' (l1 l2: loc) : val := λ: "x", (!(Fst (#l1, #l2)), !(Snd (#l1, #l2))).
-
-Definition loadp_seq: val := λ: "lp" "x", (!(Fst "lp"), !(Snd "lp")).
-
-Definition storep_seq: val :=
-  λ: "lp" "x",
-     Fst "lp" <- "x";;
-     Snd "lp" <- "x".
-
-Definition storep_seq' (l1 l2: loc) : val :=
-  λ: "x",
-     Fst (#l1, #l2) <- "x";;
-     Snd (#l1, #l2) <- "x".
-
-(* constructor that returns operations bound to the same two-locations *)
-Definition make_pair: val :=
-  λ: "v1" "v2",
-     let: "l1" := ref "v1" in
-     let: "l2" := ref "v2" in
-     let: "s" := mk_sync #() in
-     ("s" (casp_seq ("l1", "l2")),
-      "s" (loadp_seq ("l1", "l2")),
-      "s" (storep_seq ("l1", "l2"))).
-
-Definition casp: val := λ: "s", Fst (Fst "s").
-Definition loadp: val := λ: "s", Snd (Fst "s").
-Definition storep: val := λ: "s", Snd "s".
-
-Global Opaque casp_seq storep_seq loadp_seq.
-
-(* Instantiate a (stupid) lock of a pair of resource *)
-
-Definition newplock : val := λ: <>, make_pair #false #false.
-
-Definition pacquire : val :=
-  rec: "pacquire" "p" :=
-    if: casp "p" (#false, #true) then #() else "pacquire" "p".
-
-Definition prelease : val :=
-    λ: "p", storep "p" #false.
-
-Section proof.
-  Context `{!heapG Σ, !lockG Σ} (N: namespace).
-
-  Definition plocked : iProp Σ :=
-    (∃ (γ1 γ2: gname),
-       heapN ⊥ N ∧ heap_ctx ∧
-       own γ1 (Excl ()) ∧ own γ2 (Excl ()))%I.
-
-  Definition plock_inv (γ1 γ2 : gname) (R1 R2: iProp Σ) (l1 l2: loc) : iProp Σ :=
-    (∃ (b1 b2: bool),
-       l1 ↦ #b1 ★ l2 ↦ #b2 ★
-       (if b1 then True else own γ1 (Excl ()) ★ R1) ★
-       (if b2 then True else own γ2 (Excl ()) ★ R2))%I.
-
-  Definition is_plock (fs: val) (R1 R2 : iProp Σ) : iProp Σ :=
-    (∃ (l1 l2: loc) (f1 f2 f3: val) (γ1 γ2: gname),
-       heapN ⊥ N ∧ heap_ctx ∧ fs = (f1, f2, f3)%V ∧
-       synced f1 (casp_seq' l1 l2) (plock_inv γ1 γ2 R1 R2 l1 l2) ∧
-       synced f2 (loadp_seq' l1 l2) (plock_inv γ1 γ2 R1 R2 l1 l2) ∧
-       synced f3 (storep_seq' l1 l2) (plock_inv γ1 γ2 R1 R2 l1 l2))%I.
-
-  Global Instance is_plock_persistent p R1 R2: PersistentP (is_plock p R1 R2).
-  Proof. apply _. Qed.
-
-  Lemma not_false_is_true: ∀ b: bool, b ≠ false -> b = true.
-  Proof. intros b H. destruct (Sumbool.sumbool_of_bool b); by (try contradiction). Qed.
-
-  Lemma newplock_spec (R1 R2: iProp Σ) (Φ: val → iProp Σ):
-    heapN ⊥ N →
-    heap_ctx ★ R1 ★ R2 ★ (∀ p, is_plock p R1 R2 -★ Φ p)
-    ⊢ WP newplock #() {{ Φ }}.
-  Proof.
-    iIntros (HN) "(#? & HR1 & HR2 & HΦ)".
-    wp_seq. wp_let. wp_let.
-    wp_alloc l1 as "Hl1". wp_let.
-    iVs (own_alloc (Excl ())) as (γ1) "Hγ1"; first done.
-    wp_alloc l2 as "Hl2". wp_let.
-    iVs (own_alloc (Excl ())) as (γ2) "Hγ2"; first done.
-    wp_bind (mk_sync _).
-    iApply (mk_sync_spec_wp _ (plock_inv γ1 γ2 R1 R2 l1 l2)); try by auto.
-    iSplit; first by auto.
-    iSplitR "HΦ".
-    + rewrite /plock_inv.
-      iExists false, false.
-      by iFrame.
-    + iIntros (s) "#Hs".
-      wp_let. wp_bind (s _).
-      iApply wp_wand_r.
-      iSplitR "HΦ".
-      { wp_let. wp_bind (λ: _, _)%E. wp_value. iApply "Hs". }
-      iIntros (v) "HRcas".
-      wp_bind (s _)%E.
-      iApply wp_wand_r.
-      iSplitR "HRcas HΦ".
-      { wp_let. wp_bind (λ: _, _)%E.
-        wp_value. (* XXX: manually force lambda to be value *)
-        iApply "Hs". }
-      iIntros (v0) "HRload".
-      wp_bind (s _)%E.
-      iApply wp_wand_r.
-      iSplitR "HRcas HRload HΦ".
-      { wp_let. wp_bind (λ: _, _)%E. wp_value. iApply "Hs". }
-      iIntros (v1) "HRstore".
-      wp_value.
-      iApply "HΦ".
-      rewrite /is_plock. iExists l1, l2, _, _, _, γ1, γ2.
-      repeat (iSplit; first by auto).
-      rewrite /casp_seq'.
-      iApply "HRstore".
-  Qed.
-
-  Lemma pacquire_spec (p: val) (R1 R2: iProp Σ) (Φ : val → iProp Σ):
-    is_plock p R1 R2 ★ (plocked -★ R1 -★ R2 -★ Φ #()) ⊢ WP pacquire p {{ Φ }}.
-  Proof.
-    iIntros "(#Hp & HΦ)".
-    iLöb as "Hl".
-    wp_rec. wp_let.
-    rewrite /is_plock /synced.
-    iDestruct "Hp" as (l1 l2 casp loadp storep γ1 γ2) "(#? & #? & % & #HRcas & _ & #HRstore)".
-    subst. wp_proj. wp_proj. wp_bind (casp _).
-    iAssert ({{ True }} casp (#false%V, #true%V)%E {{ z, z = #false ∨ (z =#true ★ plocked ★ R1 ★ R2)}})%I as "#HP".
-    (* prove the contextual property of casp closure returned from constructor *)
-    {
-      iApply ("HRcas" with "[]")=>//.
-      iIntros "!# [Hplk _]".
-      repeat (try (wp_let); try wp_proj).
-      iDestruct "Hplk" as (b1 b2) "(Hl1 & Hl2 & Hdisj1 & Hdisj2)".
-      wp_load.
-      destruct b1.
-      - wp_op=>[|_]//.
-        destruct b2; wp_if.
-        + iSplitL; last by iLeft.
-          iExists true, true. by iFrame.
-        + iSplitL; last by auto.
-          iExists true, false. by iFrame.
-      - wp_op=>[_|]//.
-        destruct b2; wp_if; wp_proj; wp_load.
-        + wp_op=>[_|]// _; wp_if.
-          iSplitL; last by iLeft.
-          iExists false, true. by iFrame.
-        + wp_op=>[_|]//. wp_if.
-          wp_proj. wp_store. wp_proj. wp_store.
-          iSplitL "Hl1 Hl2".
-          { rewrite /plock_inv. iExists true, true.
-            iFrame. iSplitL; done. }
-          iRight.
-          iDestruct "Hdisj1" as "[Ho1 HR1]".
-          iDestruct "Hdisj2" as "[Ho2 HR2]".
-          iFrame. iSplitR; first by auto.
-          iExists γ1, γ2. iFrame.
-          iVsIntro. iSplit; by auto.
-    }
-    iApply wp_wand_r.
-    iSplitR; first by iApply "HP".
-    iIntros (v) "[%|(% & Hlocked & HR1 & HR2)]"; subst.
-    - wp_if. iApply "Hl". iApply "HΦ".
-    - wp_if. iVsIntro. iApply ("HΦ" with "Hlocked HR1 HR2").
-  Qed.
-
-End proof.