one_shot_once.v 5.91 KB
 Jacques-Henri Jourdan committed Sep 13, 2019 1 2 ``````From iris.proofmode Require Import tactics. From iris.algebra Require Import frac agree csum. `````` Ralf Jung committed Aug 09, 2019 3 4 5 6 7 8 ``````From iris.program_logic Require Export weakestpre hoare. From iris.heap_lang Require Export lang. From iris.heap_lang Require Import assert proofmode notation adequacy. From iris.heap_lang.lib Require Import par. Set Default Proof Using "Type". `````` Ralf Jung committed Aug 12, 2019 9 10 11 ``````(** This is the introductory example from Ralf's PhD thesis. The difference to [one_shot] is that [set] asserts to be called only once. *) `````` Ralf Jung committed Aug 09, 2019 12 13 14 15 16 17 ``````Definition one_shot_example : val := λ: <>, let: "x" := ref NONE in ( (* set *) (λ: "n", assert: CAS "x" NONE (SOME "n")), (* check *) (λ: <>, let: "y" := !"x" in λ: <>, `````` Ralf Jung committed Aug 14, 2019 18 19 20 21 22 `````` let: "y'" := !"x" in match: "y" with NONE => #() | SOME <> => assert: "y" = "y'" end)). `````` Ralf Jung committed Aug 09, 2019 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 `````` Definition one_shotR := csumR fracR (agreeR ZO). Definition Pending (q : Qp) : one_shotR := Cinl q. Definition Shot (n : Z) : one_shotR := Cinr (to_agree n). Class one_shotG Σ := { one_shot_inG :> inG Σ one_shotR }. Definition one_shotΣ : gFunctors := #[GFunctor one_shotR]. Instance subG_one_shotΣ {Σ} : subG one_shotΣ Σ → one_shotG Σ. Proof. solve_inG. Qed. Section proof. Local Set Default Proof Using "Type*". Context `{!heapG Σ, !one_shotG Σ}. Definition one_shot_inv (γ : gname) (l : loc) : iProp Σ := (l ↦ NONEV ∗ own γ (Pending (1/2)%Qp) ∨ ∃ n : Z, l ↦ SOMEV #n ∗ own γ (Shot n))%I. `````` Ralf Jung committed Aug 14, 2019 41 42 ``````Local Hint Extern 0 (environments.envs_entails _ (one_shot_inv _ _)) => unfold one_shot_inv. `````` Ralf Jung committed Aug 09, 2019 43 44 45 ``````Lemma pending_split γ q : own γ (Pending q) ⊣⊢ own γ (Pending (q/2)) ∗ own γ (Pending (q/2)). Proof. `````` Paolo G. Giarrusso committed Aug 13, 2019 46 `````` rewrite /Pending. rewrite -own_op -Cinl_op. rewrite frac_op' Qp_div_2 //. `````` Ralf Jung committed Aug 09, 2019 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 ``````Qed. Lemma pending_shoot γ n : own γ (Pending 1%Qp) ==∗ own γ (Shot n). Proof. iIntros "Hγ". iMod (own_update with "Hγ") as "\$"; last done. by apply cmra_update_exclusive with (y:=Shot n). Qed. Lemma wp_one_shot (Φ : val → iProp Σ) : (∀ (f1 f2 : val) (T : iProp Σ), T ∗ □ (∀ n : Z, T -∗ WP f1 #n {{ w, True }}) ∗ □ WP f2 #() {{ g, □ WP g #() {{ _, True }} }} -∗ Φ (f1,f2)%V) ⊢ WP one_shot_example #() {{ Φ }}. Proof. iIntros "Hf /=". pose proof (nroot .@ "N") as N. rewrite -wp_fupd. wp_lam. wp_alloc l as "Hl". iMod (own_alloc (Pending 1%Qp)) as (γ) "Hγ"; first done. iDestruct (pending_split with "Hγ") as "[Hγ1 Hγ2]". iMod (inv_alloc N _ (one_shot_inv γ l) with "[Hl Hγ2]") as "#HN". { iNext. iLeft. by iFrame. } wp_pures. iModIntro. iApply ("Hf" \$! _ _ (own γ (Pending (1/2)%Qp))). iSplitL; first done. iSplit. - iIntros (n) "!# Hγ1". wp_pures. iApply wp_assert. wp_pures. wp_bind (CmpXchg _ _ _). iInv N as ">[[Hl Hγ2]|H]"; last iDestruct "H" as (m) "[Hl Hγ']". + iDestruct (pending_split with "[\$Hγ1 \$Hγ2]") as "Hγ". iMod (pending_shoot _ n with "Hγ") as "Hγ". wp_cmpxchg_suc. iModIntro. iSplitL; last (wp_pures; by eauto). iNext; iRight; iExists n; by iFrame. + by iDestruct (own_valid_2 with "Hγ1 Hγ'") as %?. - iIntros "!# /=". wp_lam. wp_bind (! _)%E. iInv N as ">Hγ". iAssert (∃ v, l ↦ v ∗ (⌜v = NONEV⌝ ∗ own γ (Pending (1/2)%Qp) ∨ ∃ n : Z, ⌜v = SOMEV #n⌝ ∗ own γ (Shot n)))%I with "[Hγ]" as "Hv". { iDestruct "Hγ" as "[[Hl Hγ]|Hl]"; last iDestruct "Hl" as (m) "[Hl Hγ]". + iExists NONEV. iFrame. eauto. + iExists (SOMEV #m). iFrame. eauto. } iDestruct "Hv" as (v) "[Hl Hv]". wp_load. iAssert (one_shot_inv γ l ∗ (⌜v = NONEV⌝ ∨ ∃ n : Z, ⌜v = SOMEV #n⌝ ∗ own γ (Shot n)))%I with "[Hl Hv]" as "[Hinv #Hv]". { iDestruct "Hv" as "[[% ?]|Hv]"; last iDestruct "Hv" as (m) "[% ?]"; subst. + Show. iSplit. iLeft; by iSplitL "Hl". eauto. + iSplit. iRight; iExists m; by iSplitL "Hl". eauto. } iSplitL "Hinv"; first by eauto. `````` Ralf Jung committed Aug 14, 2019 92 93 94 95 96 97 98 99 100 101 102 103 `````` iModIntro. wp_pures. iIntros "!#". wp_lam. wp_bind (! _)%E. iInv N as "Hinv". iDestruct "Hv" as "[%|Hv]"; last iDestruct "Hv" as (m) "[% Hγ']"; subst. + iDestruct "Hinv" as "[[Hl >Hγ]|H]"; last iDestruct "H" as (m') "[Hl Hγ]"; wp_load; iModIntro; (iSplitL "Hl Hγ"; first by eauto with iFrame); wp_pures; done. + iDestruct "Hinv" as "[[Hl >Hγ]|H]"; last iDestruct "H" as (m') "[Hl Hγ]". { by iDestruct (own_valid_2 with "Hγ Hγ'") as %?. } wp_load. Show. iDestruct (own_valid_2 with "Hγ Hγ'") as %?%agree_op_invL'; subst. iModIntro. iSplitL "Hl Hγ"; first by eauto with iFrame. wp_pures. iApply wp_assert. wp_op. by case_bool_decide. `````` Ralf Jung committed Aug 09, 2019 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 ``````Qed. Lemma ht_one_shot (Φ : val → iProp Σ) : {{ True }} one_shot_example #() {{ ff, ∃ T, T ∗ (∀ n : Z, {{ T }} Fst ff #n {{ _, True }}) ∗ {{ True }} Snd ff #() {{ g, {{ True }} g #() {{ _, True }} }} }}. Proof. iIntros "!# _". iApply wp_one_shot. iIntros (f1 f2 T) "(HT & #Hf1 & #Hf2)". iExists T. iFrame "HT". iSplit. - iIntros (n) "!# HT". wp_apply "Hf1". done. - iIntros "!# _". wp_apply (wp_wand with "Hf2"). by iIntros (v) "#? !# _". Qed. End proof. (* Have a client with a closed proof. *) Definition client : expr := let: "ff" := one_shot_example #() in (Fst "ff" #5 ||| let: "check" := Snd "ff" #() in "check" #()). Section client. Context `{!heapG Σ, !one_shotG Σ, !spawnG Σ}. Lemma client_safe : WP client {{ _, True }}%I. Proof using Type*. rewrite /client. wp_apply wp_one_shot. iIntros (f1 f2 T) "(HT & #Hf1 & #Hf2)". wp_let. wp_apply (wp_par with "[HT]"). - wp_apply "Hf1". done. - wp_proj. wp_bind (f2 _)%E. iApply wp_wand; first by iExact "Hf2". iIntros (check) "Hcheck". wp_pures. iApply "Hcheck". - auto. Qed. End client. (** Put together all library functors. *) Definition clientΣ : gFunctors := #[ heapΣ; one_shotΣ; spawnΣ ]. (** This lemma implicitly shows that these functors are enough to meet all library assumptions. *) Lemma client_adequate σ : adequate NotStuck client σ (λ _ _, True). Proof. apply (heap_adequacy clientΣ)=> ?. apply client_safe. Qed.``````