From iris.algebra Require Import dec_agree csum. From iris.program_logic Require Import hoare. From iris.heap_lang Require Import assert proofmode notation. From iris.proofmode Require Import invariants ghost_ownership. Import uPred. Definition one_shot_example : val := λ: <>, let: "x" := ref NONE in ( (* tryset *) (λ: "n", CAS "x" NONE (SOME "n")), (* check *) (λ: <>, let: "y" := !"x" in λ: <>, match: "y" with NONE => #() | SOME "n" => match: !"x" with NONE => assert: #false | SOME "m" => assert: "n" = "m" end end)). Global Opaque one_shot_example. Definition one_shotR := csumR (exclR unitC) (dec_agreeR Z). Definition Pending : one_shotR := (Cinl (Excl ()) : one_shotR). Definition Shot (n : Z) : one_shotR := (Cinr (DecAgree n) : one_shotR). Class one_shotG Σ := one_shot_inG :> inG heap_lang Σ one_shotR. Definition one_shotGF : gFunctorList := [GFunctor (constRF one_shotR)]. Instance inGF_one_shotG Σ : inGFs heap_lang Σ one_shotGF → one_shotG Σ. Proof. intros [? _]; apply: inGF_inG. Qed. Section proof. Context `{!heapG Σ, !one_shotG Σ} (N : namespace) (HN : heapN ⊥ N). Local Notation iProp := (iPropG heap_lang Σ). Definition one_shot_inv (γ : gname) (l : loc) : iProp := (l ↦ NONEV ★ own γ Pending ∨ ∃ n : Z, l ↦ SOMEV #n ★ own γ (Shot n))%I. Lemma wp_one_shot (Φ : val → iProp) : heap_ctx ★ (∀ f1 f2 : val, (∀ n : Z, □ WP f1 #n {{ w, w = #true ∨ w = #false }}) ★ □ WP f2 #() {{ g, □ WP g #() {{ _, True }} }} -★ Φ (f1,f2)%V) ⊢ WP one_shot_example #() {{ Φ }}. Proof. iIntros "[#? Hf] /=". rewrite /one_shot_example. wp_seq. wp_alloc l as "Hl". wp_let. iPvs (own_alloc Pending) as (γ) "Hγ"; first done. iPvs (inv_alloc N _ (one_shot_inv γ l) with "[Hl Hγ]") as "#HN"; first done. { iNext. iLeft. by iSplitL "Hl". } iPvsIntro. iApply "Hf"; iSplit. - iIntros (n) "!". wp_let. iInv> N as "[[Hl Hγ]|H]"; last iDestruct "H" as (m) "[Hl Hγ]". + wp_cas_suc. iSplitL; [|by iLeft]. iPvs (own_update with "Hγ") as "Hγ". { by apply cmra_update_exclusive with (y:=Shot n). } iPvsIntro; iRight; iExists n; by iSplitL "Hl". + wp_cas_fail. rewrite /one_shot_inv; eauto 10. - iIntros "!". wp_seq. wp_focus (! _)%E. iInv> N as "Hγ". iAssert (∃ v, l ↦ v ★ ((v = NONEV ★ own γ Pending) ∨ ∃ n : Z, v = SOMEV #n ★ own γ (Shot n)))%I with "[-]" 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; iPvsIntro. iAssert (one_shot_inv γ l ★ (v = NONEV ∨ ∃ n : Z, v = SOMEV #n ★ own γ (Shot n)))%I with "[-]" as "[\$ #Hv]". { iDestruct "Hv" as "[[% ?]|Hv]"; last iDestruct "Hv" as (m) "[% ?]"; subst. + iSplit. iLeft; by iSplitL "Hl". eauto. + iSplit. iRight; iExists m; by iSplitL "Hl". eauto. } wp_let. iPvsIntro. iIntros "!". wp_seq. iDestruct "Hv" as "[%|Hv]"; last iDestruct "Hv" as (m) "[% Hγ']"; subst. { by wp_match. } wp_match. wp_focus (! _)%E. iInv> N as "[[Hl Hγ]|Hinv]"; last iDestruct "Hinv" as (m') "[Hl Hγ]". { iCombine "Hγ" "Hγ'" as "Hγ". by iDestruct (own_valid with "Hγ") as %?. } wp_load; iPvsIntro. iCombine "Hγ" "Hγ'" as "Hγ". iDestruct (own_valid with "#Hγ") as %[=->]%dec_agree_op_inv. iSplitL "Hl"; [iRight; by eauto|]. wp_match. iApply wp_assert. wp_op=>?; simplify_eq/=; eauto. Qed. Lemma hoare_one_shot (Φ : val → iProp) : heap_ctx ⊢ {{ True }} one_shot_example #() {{ ff, (∀ n : Z, {{ True }} Fst ff #n {{ w, w = #true ∨ w = #false }}) ★ {{ True }} Snd ff #() {{ g, {{ True }} g #() {{ _, True }} }} }}. Proof. iIntros "#? ! _". iApply wp_one_shot. iSplit; first done. iIntros (f1 f2) "[#Hf1 #Hf2]"; iSplit. - iIntros (n) "! _". wp_proj. iApply "Hf1". - iIntros "! _". wp_proj. iApply wp_wand_l; iFrame "Hf2". by iIntros (v) "#? ! _". Qed. End proof.