par.v 1.74 KB
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From iris.heap_lang Require Export spawn.
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From iris.heap_lang Require Import proofmode notation.
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Import uPred.
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Definition par {X} : expr X :=
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  λ: "fs",
    let: "handle" := ^spawn (Fst '"fs") in
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    let: "v2" := Snd '"fs" #() in
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    let: "v1" := ^join '"handle" in
    Pair '"v1" '"v2".
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Notation Par e1 e2 := (par (Pair (λ: <>, e1) (λ: <>, e2)))%E.
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Infix "||" := Par : expr_scope.
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Instance do_wexpr_par {X Y} (H : X `included` Y) : WExpr H par par := _.
Instance do_wsubst_par {X Y} x es (H : X `included` x :: Y) :
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  WSubst x es H par par := do_wsubst_closed _ x es H _.
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Global Opaque par.
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Section proof.
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Context {Σ : gFunctors} `{!heapG Σ, !spawnG Σ}.
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Context (heapN N : namespace).
Local Notation iProp := (iPropG heap_lang Σ).

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Lemma par_spec (Ψ1 Ψ2 : val  iProp) e (f1 f2 : val) (Φ : val  iProp) :
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  heapN  N  to_val e = Some (f1,f2)%V 
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  (heap_ctx heapN  WP f1 #() {{ Ψ1 }}  WP f2 #() {{ Ψ2 }} 
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    v1 v2, Ψ1 v1  Ψ2 v2 -  Φ (v1,v2)%V)
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   WP par e {{ Φ }}.
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Proof.
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  iIntros (??) "(#Hh&Hf1&Hf2&HΦ)".
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  rewrite /par. wp_value. iPvsIntro. wp_let. wp_proj.
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  wp_apply spawn_spec; try wp_done. iFrame "Hf1 Hh".
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  iIntros (l) "Hl". wp_let. wp_proj. wp_focus (f2 _).
  iApply wp_wand_l; iFrame "Hf2"; iIntros (v) "H2". wp_let.
  wp_apply join_spec; iFrame "Hl". iIntros (w) "H1".
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  iSpecialize ("HΦ" with "* [-]"); first by iSplitL "H1". by wp_let.
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Qed.
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Lemma wp_par (Ψ1 Ψ2 : val  iProp) (e1 e2 : expr []) (Φ : val  iProp) :
  heapN  N 
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  (heap_ctx heapN  WP e1 {{ Ψ1 }}  WP e2 {{ Ψ2 }} 
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    v1 v2, Ψ1 v1  Ψ2 v2 -  Φ (v1,v2)%V)
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   WP e1 || e2 {{ Φ }}.
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Proof.
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  iIntros (?) "(#Hh&H1&H2&H)". iApply (par_spec Ψ1 Ψ2); auto.
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  iFrame "Hh H". iSplitL "H1"; by wp_let.
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Qed.
End proof.