Commit d1d67a37 by Ralf Jung

### turn CAS into compare-and-swap instead of compare-and-set: make it return the old value

parent 4a85888c
 ... @@ -15,7 +15,7 @@ Section tests. ... @@ -15,7 +15,7 @@ Section tests. vals_cas_compare_safe v1 v1 → vals_cas_compare_safe v1 v1 → {{{ proph p vs ∗ ▷ l ↦ v1 }}} {{{ proph p vs ∗ ▷ l ↦ v1 }}} CAS_resolve #l v1 v2 #p v @ s; E CAS_resolve #l v1 v2 #p v @ s; E {{{ RET #true ; ∃ vs', ⌜vs = (#true, v)::vs'⌝ ∗ proph p vs' ∗ l ↦ v2 }}}. {{{ RET v1 ; ∃ vs', ⌜vs = (v1, v)::vs'⌝ ∗ proph p vs' ∗ l ↦ v2 }}}. Proof. Proof. iIntros (Hcmp Φ) "[Hp Hl] HΦ". iIntros (Hcmp Φ) "[Hp Hl] HΦ". wp_apply (wp_resolve with "Hp"); first done. wp_apply (wp_resolve with "Hp"); first done. ... @@ -28,7 +28,7 @@ Section tests. ... @@ -28,7 +28,7 @@ Section tests. val_for_compare v' ≠ val_for_compare v1 → vals_cas_compare_safe v' v1 → val_for_compare v' ≠ val_for_compare v1 → vals_cas_compare_safe v' v1 → {{{ proph p vs ∗ ▷ l ↦ v' }}} {{{ proph p vs ∗ ▷ l ↦ v' }}} CAS_resolve #l v1 v2 #p v @ s; E CAS_resolve #l v1 v2 #p v @ s; E {{{ RET #false ; ∃ vs', ⌜vs = (#false, v)::vs'⌝ ∗ proph p vs' ∗ l ↦ v' }}}. {{{ RET v' ; ∃ vs', ⌜vs = (v', v)::vs'⌝ ∗ proph p vs' ∗ l ↦ v' }}}. Proof. Proof. iIntros (NEq Hcmp Φ) "[Hp Hl] HΦ". iIntros (NEq Hcmp Φ) "[Hp Hl] HΦ". wp_apply (wp_resolve with "Hp"); first done. wp_apply (wp_resolve with "Hp"); first done. ... @@ -39,7 +39,7 @@ Section tests. ... @@ -39,7 +39,7 @@ Section tests. Lemma test_resolve1 E (l : loc) (n : Z) (p : proph_id) (vs : list (val * val)) (v : val) : Lemma test_resolve1 E (l : loc) (n : Z) (p : proph_id) (vs : list (val * val)) (v : val) : l ↦ #n -∗ l ↦ #n -∗ proph p vs -∗ proph p vs -∗ WP Resolve (CAS #l #n (#n + #1)) #p v @ E {{ v, ⌜v = #true⌝ ∗ ∃vs, proph p vs ∗ l ↦ #(n+1) }}%I. WP Resolve (CAS #l #n (#n + #1)) #p v @ E {{ v, ⌜v = #n⌝ ∗ ∃vs, proph p vs ∗ l ↦ #(n+1) }}%I. Proof. Proof. iIntros "Hl Hp". wp_pures. wp_apply (wp_resolve with "Hp"); first done. iIntros "Hl Hp". wp_pures. wp_apply (wp_resolve with "Hp"); first done. wp_cas_suc. iIntros (ws ->) "Hp". eauto with iFrame. wp_cas_suc. iIntros (ws ->) "Hp". eauto with iFrame. ... ...
 ... @@ -121,7 +121,7 @@ Definition newcounter : val := λ: <>, ref #0. ... @@ -121,7 +121,7 @@ Definition newcounter : val := λ: <>, ref #0. Definition incr : val := Definition incr : val := rec: "incr" "l" := rec: "incr" "l" := let: "n" := !"l" in let: "n" := !"l" in if: CAS "l" "n" (#1 + "n") then #() else "incr" "l". if: CAS "l" "n" (#1 + "n") = "n" then #() else "incr" "l". Definition read : val := λ: "l", !"l". Definition read : val := λ: "l", !"l". (** The CMRA we need. *) (** The CMRA we need. *) ... @@ -231,10 +231,11 @@ Section counter_proof. ... @@ -231,10 +231,11 @@ Section counter_proof. rewrite (auth_frag_op (S n) (S c)); last lia; iDestruct "Hγ" as "[Hγ Hγf]". rewrite (auth_frag_op (S n) (S c)); last lia; iDestruct "Hγ" as "[Hγ Hγf]". wp_cas_suc. iSplitL "Hl Hγ". wp_cas_suc. iSplitL "Hl Hγ". { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. } { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. } wp_if. rewrite {3}/C; eauto 10. wp_op. rewrite bool_decide_true //. wp_if. rewrite {3}/C; eauto 10. - wp_cas_fail; first (intros [=]; abstract omega). - assert (#c ≠ #c') by (intros [=]; abstract omega). wp_cas_fail. iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|]. iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|]. wp_if. iApply ("IH" with "[Hγf]"). rewrite {3}/C; eauto 10. wp_op. rewrite bool_decide_false //. wp_if. iApply ("IH" with "[Hγf]"). rewrite {3}/C; eauto 10. Qed. Qed. Check "read_spec". Check "read_spec". ... ...
 ... @@ -9,7 +9,7 @@ Set Default Proof Using "Type". ... @@ -9,7 +9,7 @@ Set Default Proof Using "Type". Definition one_shot_example : val := λ: <>, Definition one_shot_example : val := λ: <>, let: "x" := ref NONE in ( let: "x" := ref NONE in ( (* tryset *) (λ: "n", (* tryset *) (λ: "n", CAS "x" NONE (SOME "n")), CAS "x" NONE (SOME "n") = NONE), (* check *) (λ: <>, (* check *) (λ: <>, let: "y" := !"x" in λ: <>, let: "y" := !"x" in λ: <>, match: "y" with match: "y" with ... @@ -49,13 +49,15 @@ Proof. ... @@ -49,13 +49,15 @@ Proof. iMod (inv_alloc N _ (one_shot_inv γ l) with "[Hl Hγ]") as "#HN". iMod (inv_alloc N _ (one_shot_inv γ l) with "[Hl Hγ]") as "#HN". { iNext. iLeft. by iSplitL "Hl". } { iNext. iLeft. by iSplitL "Hl". } wp_pures. iModIntro. iApply "Hf"; iSplit. wp_pures. iModIntro. iApply "Hf"; iSplit. - iIntros (n) "!#". wp_lam. wp_pures. - iIntros (n) "!#". wp_lam. wp_pures. wp_bind (CAS _ _ _). iInv N as ">[[Hl Hγ]|H]"; last iDestruct "H" as (m) "[Hl Hγ]". iInv N as ">[[Hl Hγ]|H]"; last iDestruct "H" as (m) "[Hl Hγ]". + iMod (own_update with "Hγ") as "Hγ". + iMod (own_update with "Hγ") as "Hγ". { by apply cmra_update_exclusive with (y:=Shot n). } { by apply cmra_update_exclusive with (y:=Shot n). } wp_cas_suc. iSplitL; last eauto. wp_cas_suc. iSplitL; iModIntro; last first. iModIntro. iNext; iRight; iExists n; by iFrame. { wp_pures. eauto. } + wp_cas_fail. iSplitL; last eauto. iNext; iRight; iExists n; by iFrame. + wp_cas_fail. iSplitL; iModIntro; last first. { wp_pures. eauto. } rewrite /one_shot_inv; eauto 10. rewrite /one_shot_inv; eauto 10. - iIntros "!# /=". wp_lam. wp_bind (! _)%E. - iIntros "!# /=". wp_lam. wp_bind (! _)%E. iInv N as ">Hγ". iInv N as ">Hγ". ... ...
 ... @@ -97,8 +97,8 @@ Inductive expr := ... @@ -97,8 +97,8 @@ Inductive expr := | AllocN (e1 e2 : expr) (* array length (positive number), initial value *) | AllocN (e1 e2 : expr) (* array length (positive number), initial value *) | Load (e : expr) | Load (e : expr) | Store (e1 : expr) (e2 : expr) | Store (e1 : expr) (e2 : expr) | CAS (e0 : expr) (e1 : expr) (e2 : expr) | CAS (e0 : expr) (e1 : expr) (e2 : expr) (* Compare-and-swap (NOT compare-and-set!) *) | FAA (e1 : expr) (e2 : expr) | FAA (e1 : expr) (e2 : expr) (* Fetch-and-add *) (* Prophecy *) (* Prophecy *) | NewProph | NewProph | Resolve (e0 : expr) (e1 : expr) (e2 : expr) (* wrapped expr, proph, val *) | Resolve (e0 : expr) (e1 : expr) (e2 : expr) (* wrapped expr, proph, val *) ... @@ -518,6 +518,7 @@ Definition bin_op_eval_bool (op : bin_op) (b1 b2 : bool) : option base_lit := ... @@ -518,6 +518,7 @@ Definition bin_op_eval_bool (op : bin_op) (b1 b2 : bool) : option base_lit := Definition bin_op_eval (op : bin_op) (v1 v2 : val) : option val := Definition bin_op_eval (op : bin_op) (v1 v2 : val) : option val := if decide (op = EqOp) then if decide (op = EqOp) then (* Crucially, this compares the same way as [CAS]! *) Some \$ LitV \$ LitBool \$ bool_decide (val_for_compare v1 = val_for_compare v2) Some \$ LitV \$ LitBool \$ bool_decide (val_for_compare v1 = val_for_compare v2) else else match v1, v2 with match v1, v2 with ... @@ -633,19 +634,13 @@ Inductive head_step : expr → state → list observation → expr → state → ... @@ -633,19 +634,13 @@ Inductive head_step : expr → state → list observation → expr → state → [] [] (Val \$ LitV LitUnit) (state_upd_heap <[l:=v]> σ) (Val \$ LitV LitUnit) (state_upd_heap <[l:=v]> σ) [] [] | CasFailS l v1 v2 vl σ : | CasS l v1 v2 vl σ : vals_cas_compare_safe vl v1 → vals_cas_compare_safe vl v1 → σ.(heap) !! l = Some vl → σ.(heap) !! l = Some vl → val_for_compare vl ≠ val_for_compare v1 → head_step (CAS (Val \$ LitV \$ LitLoc l) (Val v1) (Val v2)) σ [] (Val \$ LitV \$ LitBool false) σ [] | CasSucS l v1 v2 vl σ : vals_cas_compare_safe vl v1 → σ.(heap) !! l = Some vl → val_for_compare vl = val_for_compare v1 → head_step (CAS (Val \$ LitV \$ LitLoc l) (Val v1) (Val v2)) σ head_step (CAS (Val \$ LitV \$ LitLoc l) (Val v1) (Val v2)) σ [] [] (Val \$ LitV \$ LitBool true) (state_upd_heap <[l:=v2]> σ) (* Crucially, this compares the same way as [EqOp]! *) (Val vl) (if decide (val_for_compare vl = val_for_compare v1) then state_upd_heap <[l:=v2]> σ else σ) [] [] | FaaS l i1 i2 σ : | FaaS l i1 i2 σ : σ.(heap) !! l = Some (LitV (LitInt i1)) → σ.(heap) !! l = Some (LitV (LitInt i1)) → ... ...
 ... @@ -36,7 +36,7 @@ Class atomic_heap {Σ} `{!heapG Σ} := AtomicHeap { ... @@ -36,7 +36,7 @@ Class atomic_heap {Σ} `{!heapG Σ} := AtomicHeap { val_is_unboxed w1 → val_is_unboxed w1 → <<< ∀ v, mapsto l 1 v >>> cas #l w1 w2 @ ⊤ <<< ∀ v, mapsto l 1 v >>> cas #l w1 w2 @ ⊤ <<< if decide (val_for_compare v = val_for_compare w1) then mapsto l 1 w2 else mapsto l 1 v, <<< if decide (val_for_compare v = val_for_compare w1) then mapsto l 1 w2 else mapsto l 1 v, RET #(if decide (val_for_compare v = val_for_compare w1) then true else false) >>>; RET v >>>; }. }. Arguments atomic_heap _ {_}. Arguments atomic_heap _ {_}. ... @@ -100,7 +100,7 @@ Section proof. ... @@ -100,7 +100,7 @@ Section proof. <<< ∀ (v : val), l ↦ v >>> <<< ∀ (v : val), l ↦ v >>> primitive_cas #l w1 w2 @ ⊤ primitive_cas #l w1 w2 @ ⊤ <<< if decide (val_for_compare v = val_for_compare w1) then l ↦ w2 else l ↦ v, <<< if decide (val_for_compare v = val_for_compare w1) then l ↦ w2 else l ↦ v, RET #(if decide (val_for_compare v = val_for_compare w1) then true else false) >>>. RET v >>>. Proof. Proof. iIntros (? Φ) "AU". wp_lam. wp_let. wp_let. iIntros (? Φ) "AU". wp_lam. wp_let. wp_let. iMod "AU" as (v) "[H↦ [_ Hclose]]". iMod "AU" as (v) "[H↦ [_ Hclose]]". ... ...
 ... @@ -9,7 +9,7 @@ Set Default Proof Using "Type". ... @@ -9,7 +9,7 @@ Set Default Proof Using "Type". Definition newcounter : val := λ: <>, ref #0. Definition newcounter : val := λ: <>, ref #0. Definition incr : val := rec: "incr" "l" := Definition incr : val := rec: "incr" "l" := let: "n" := !"l" in let: "n" := !"l" in if: CAS "l" "n" (#1 + "n") then #() else "incr" "l". if: CAS "l" "n" (#1 + "n") = "n" then #() else "incr" "l". Definition read : val := λ: "l", !"l". Definition read : val := λ: "l", !"l". (** Monotone counter *) (** Monotone counter *) ... @@ -59,13 +59,16 @@ Section mono_proof. ... @@ -59,13 +59,16 @@ Section mono_proof. { apply auth_update, (mnat_local_update _ _ (S c)); auto. } { apply auth_update, (mnat_local_update _ _ (S c)); auto. } wp_cas_suc. iModIntro. iSplitL "Hl Hγ". wp_cas_suc. iModIntro. iSplitL "Hl Hγ". { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. } { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. } wp_if. iApply "HΦ"; iExists γ; repeat iSplit; eauto. wp_op. rewrite bool_decide_true //. wp_if. iApply "HΦ"; iExists γ; repeat iSplit; eauto. iApply (own_mono with "Hγf"). iApply (own_mono with "Hγf"). (* FIXME: FIXME(Coq #6294): needs new unification *) (* FIXME: FIXME(Coq #6294): needs new unification *) apply: auth_frag_mono. by apply mnat_included, le_n_S. apply: auth_frag_mono. by apply mnat_included, le_n_S. - wp_cas_fail; first (by intros [= ?%Nat2Z.inj]). iModIntro. - assert (#c ≠ #c') by by intros [= ?%Nat2Z.inj]. wp_cas_fail. iModIntro. iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|]. iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|]. wp_if. iApply ("IH" with "[Hγf] [HΦ]"); last by auto. wp_op. rewrite bool_decide_false //. wp_if. iApply ("IH" with "[Hγf] [HΦ]"); last by auto. rewrite {3}/mcounter; eauto 10. rewrite {3}/mcounter; eauto 10. Qed. Qed. ... @@ -136,10 +139,11 @@ Section contrib_spec. ... @@ -136,10 +139,11 @@ Section contrib_spec. { apply frac_auth_update, (nat_local_update _ _ (S c) (S n)); lia. } { apply frac_auth_update, (nat_local_update _ _ (S c) (S n)); lia. } wp_cas_suc. iModIntro. iSplitL "Hl Hγ". wp_cas_suc. iModIntro. iSplitL "Hl Hγ". { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. } { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. } wp_if. by iApply "HΦ". wp_op. rewrite bool_decide_true //. wp_if. by iApply "HΦ". - wp_cas_fail; first (by intros [= ?%Nat2Z.inj]). - assert (#c ≠ #c') by by intros [= ?%Nat2Z.inj]. wp_cas_fail. iModIntro. iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|]. iModIntro. iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|]. wp_if. by iApply ("IH" with "[Hγf] [HΦ]"); auto. wp_op. rewrite bool_decide_false //. wp_if. by iApply ("IH" with "[Hγf] [HΦ]"); auto. Qed. Qed. Lemma read_contrib_spec γ l q n : Lemma read_contrib_spec γ l q n : ... ...
 ... @@ -16,7 +16,7 @@ Section increment_physical. ... @@ -16,7 +16,7 @@ Section increment_physical. Definition incr_phy : val := Definition incr_phy : val := rec: "incr" "l" := rec: "incr" "l" := let: "oldv" := !"l" in let: "oldv" := !"l" in if: CAS "l" "oldv" ("oldv" + #1) if: CAS "l" "oldv" ("oldv" + #1) = "oldv" then "oldv" (* return old value if success *) then "oldv" (* return old value if success *) else "incr" "l". else "incr" "l". ... @@ -29,9 +29,9 @@ Section increment_physical. ... @@ -29,9 +29,9 @@ Section increment_physical. wp_pures. wp_bind (CAS _ _ _)%E. iMod "AU" as (w) "[Hl Hclose]". wp_pures. wp_bind (CAS _ _ _)%E. iMod "AU" as (w) "[Hl Hclose]". destruct (decide (#v = #w)) as [[= ->]|Hx]. destruct (decide (#v = #w)) as [[= ->]|Hx]. - wp_cas_suc. iDestruct "Hclose" as "[_ Hclose]". iMod ("Hclose" with "Hl") as "HΦ". - wp_cas_suc. iDestruct "Hclose" as "[_ Hclose]". iMod ("Hclose" with "Hl") as "HΦ". iModIntro. wp_if. done. iModIntro. wp_op. rewrite bool_decide_true //. wp_if. done. - wp_cas_fail. iDestruct "Hclose" as "[Hclose _]". iMod ("Hclose" with "Hl") as "AU". - wp_cas_fail. iDestruct "Hclose" as "[Hclose _]". iMod ("Hclose" with "Hl") as "AU". iModIntro. wp_if. iApply "IH". done. iModIntro. wp_op. rewrite bool_decide_false //. wp_if. iApply "IH". done. Qed. Qed. End increment_physical. End increment_physical. ... @@ -45,7 +45,7 @@ Section increment. ... @@ -45,7 +45,7 @@ Section increment. Definition incr : val := Definition incr : val := rec: "incr" "l" := rec: "incr" "l" := let: "oldv" := !"l" in let: "oldv" := !"l" in if: CAS "l" "oldv" ("oldv" + #1) if: CAS "l" "oldv" ("oldv" + #1) = "oldv" then "oldv" (* return old value if success *) then "oldv" (* return old value if success *) else "incr" "l". else "incr" "l". ... @@ -70,9 +70,9 @@ Section increment. ... @@ -70,9 +70,9 @@ Section increment. { (* abort case *) iDestruct "Hclose" as "[? _]". done. } { (* abort case *) iDestruct "Hclose" as "[? _]". done. } iIntros "Hl". simpl. destruct (decide (#w = #v)) as [[= ->]|Hx]. iIntros "Hl". simpl. destruct (decide (#w = #v)) as [[= ->]|Hx]. - iDestruct "Hclose" as "[_ Hclose]". iMod ("Hclose" with "Hl") as "HΦ". - iDestruct "Hclose" as "[_ Hclose]". iMod ("Hclose" with "Hl") as "HΦ". iIntros "!>". wp_if. by iApply "HΦ". iIntros "!>". wp_op. rewrite bool_decide_true //. wp_if. by iApply "HΦ". - iDestruct "Hclose" as "[Hclose _]". iMod ("Hclose" with "Hl") as "AU". - iDestruct "Hclose" as "[Hclose _]". iMod ("Hclose" with "Hl") as "AU". iIntros "!>". wp_if. iApply "IH". done. iIntros "!>". wp_op. rewrite bool_decide_false //. wp_if. iApply "IH". done. Qed. Qed. (** A proof of the incr specification that uses lemmas to avoid reasining (** A proof of the incr specification that uses lemmas to avoid reasining ... @@ -94,9 +94,9 @@ Section increment. ... @@ -94,9 +94,9 @@ Section increment. iIntros "H↦ !>". iIntros "H↦ !>". simpl. destruct (decide (#x' = #x)) as [[= ->]|Hx]. simpl. destruct (decide (#x' = #x)) as [[= ->]|Hx]. - iRight. iFrame. iIntros "HΦ !>". - iRight. iFrame. iIntros "HΦ !>". wp_if. by iApply "HΦ". wp_op. rewrite bool_decide_true //. wp_if. by iApply "HΦ". - iLeft. iFrame. iIntros "AU !>". - iLeft. iFrame. iIntros "AU !>". wp_if. iApply "IH". done. wp_op. rewrite bool_decide_false //. wp_if. iApply "IH". done. Qed. Qed. (** A "weak increment": assumes that there is no race *) (** A "weak increment": assumes that there is no race *) ... ...
 ... @@ -7,7 +7,7 @@ From iris.heap_lang.lib Require Import lock. ... @@ -7,7 +7,7 @@ From iris.heap_lang.lib Require Import lock. Set Default Proof Using "Type". Set Default Proof Using "Type". Definition newlock : val := λ: <>, ref #false. Definition newlock : val := λ: <>, ref #false. Definition try_acquire : val := λ: "l", CAS "l" #false #true. Definition try_acquire : val := λ: "l", CAS "l" #false #true = #false. Definition acquire : val := Definition acquire : val := rec: "acquire" "l" := if: try_acquire "l" then #() else "acquire" "l". rec: "acquire" "l" := if: try_acquire "l" then #() else "acquire" "l". Definition release : val := λ: "l", "l" <- #false. Definition release : val := λ: "l", "l" <- #false. ... @@ -61,12 +61,12 @@ Section proof. ... @@ -61,12 +61,12 @@ Section proof. {{{ b, RET #b; if b is true then locked γ ∗ R else True }}}. {{{ b, RET #b; if b is true then locked γ ∗ R else True }}}. Proof. Proof. iIntros (Φ) "#Hl HΦ". iDestruct "Hl" as (l ->) "#Hinv". iIntros (Φ) "#Hl HΦ". iDestruct "Hl" as (l ->) "#Hinv". wp_rec. iInv N as ([]) "[Hl HR]". wp_rec. wp_bind (CAS _ _ _). iInv N as ([]) "[Hl HR]". - wp_cas_fail. iModIntro. iSplitL "Hl"; first (iNext; iExists true; eauto). - wp_cas_fail. iModIntro. iSplitL "Hl"; first (iNext; iExists true; eauto). iApply ("HΦ" \$! false). done. wp_pures. iApply ("HΦ" \$! false). done. - wp_cas_suc. iDestruct "HR" as "[Hγ HR]". - wp_cas_suc. iDestruct "HR" as "[Hγ HR]". iModIntro. iSplitL "Hl"; first (iNext; iExists true; eauto). iModIntro. iSplitL "Hl"; first (iNext; iExists true; eauto). rewrite /locked. by iApply ("HΦ" \$! true with "[\$Hγ \$HR]"). rewrite /locked. wp_pures. by iApply ("HΦ" \$! true with "[\$Hγ \$HR]"). Qed. Qed. Lemma acquire_spec γ lk R : Lemma acquire_spec γ lk R : ... ...
 ... @@ -20,7 +20,7 @@ Definition newlock : val := ... @@ -20,7 +20,7 @@ Definition newlock : val := Definition acquire : val := Definition acquire : val := rec: "acquire" "lk" := rec: "acquire" "lk" := let: "n" := !(Snd "lk") in let: "n" := !(Snd "lk") in if: CAS (Snd "lk") "n" ("n" + #1) if: CAS (Snd "lk") "n" ("n" + #1) = "n" then wait_loop "n" "lk" then wait_loop "n" "lk" else "acquire" "lk". else "acquire" "lk". ... @@ -122,14 +122,14 @@ Section proof. ... @@ -122,14 +122,14 @@ Section proof. wp_cas_suc. iModIntro. iSplitL "Hlo' Hln' Haown Hauth". wp_cas_suc. iModIntro. iSplitL "Hlo' Hln' Haown Hauth". { iNext. iExists o', (S n). { iNext. iExists o', (S n). rewrite Nat2Z.inj_succ -Z.add_1_r. by iFrame. } rewrite Nat2Z.inj_succ -Z.add_1_r. by iFrame. } wp_if. wp_op. rewrite bool_decide_true //. wp_if. iApply (wait_loop_spec γ (#lo, #ln) with "[-HΦ]"). iApply (wait_loop_spec γ (#lo, #ln) with "[-HΦ]"). + iFrame. rewrite /is_lock; eauto 10. + iFrame. rewrite /is_lock; eauto 10. + by iNext. + by iNext. - wp_cas_fail. iModIntro. - wp_cas_fail. iModIntro. iSplitL "Hlo' Hln' Hauth Haown". iSplitL "Hlo' Hln' Hauth Haown". { iNext. iExists o', n'. by iFrame. } { iNext. iExists o', n'. by iFrame. } wp_if. by iApply "IH"; auto. wp_op. rewrite bool_decide_false //. wp_if. by iApply "IH"; auto. Qed. Qed. Lemma release_spec γ lk R : Lemma release_spec γ lk R : ... ...