Commit 0e48566f by Robbert Krebbers

### Notation for PairV.

parent bfdeefd3
 ... ... @@ -32,6 +32,7 @@ Notation "^ v" := (of_val' v%V) (at level 8, format "^ v") : expr_scope. (** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come first. *) Notation "( e1 , e2 , .. , en )" := (Pair .. (Pair e1 e2) .. en) : expr_scope. Notation "( e1 , e2 , .. , en )" := (PairV .. (PairV e1 e2) .. en) : val_scope. Notation "'match:' e0 'with' 'InjL' x1 => e1 | 'InjR' x2 => e2 'end'" := (Match e0 x1 e1 x2 e2) (e0, x1, e1, x2, e2 at level 200) : expr_scope. ... ...
 ... ... @@ -20,21 +20,21 @@ Context (heapN N : namespace). Local Notation iProp := (iPropG heap_lang Σ). Lemma par_spec (Ψ1 Ψ2 : val → iProp) e (f1 f2 : val) (Φ : val → iProp) : heapN ⊥ N → to_val e = Some (PairV f1 f2) → heapN ⊥ N → to_val e = Some (f1,f2)%V → (heap_ctx heapN ★ #> f1 #() {{ Ψ1 }} ★ #> f2 #() {{ Ψ2 }} ★ ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ Φ (PairV v1 v2)) ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ Φ (v1,v2)%V) ⊑ #> par e {{ Φ }}. Proof. intros. rewrite /par. wp_focus e. etransitivity; last by eapply wp_value. wp_let. (* FIXME: wp_proj should not spawn these goals. *) wp_proj; eauto using to_of_val. (ewp eapply spawn_spec); eauto using to_of_val. ewp eapply spawn_spec; eauto using to_of_val. apply sep_mono_r. apply sep_mono_r. apply forall_intro=>h. apply wand_intro_l. wp_let. wp_proj; eauto using to_of_val. wp_focus (f2 _). rewrite wp_frame_r wp_frame_l. apply wp_mono=>v2. wp_let. (ewp eapply join_spec); eauto using to_of_val. apply sep_mono_r. ewp eapply join_spec; eauto using to_of_val. apply sep_mono_r. apply forall_intro=>v1. apply wand_intro_l. wp_let. etransitivity; last by (eapply wp_value, to_val_Pair; eapply to_of_val). rewrite (forall_elim v1) (forall_elim v2). rewrite assoc. ... ... @@ -44,7 +44,7 @@ Qed. Lemma wp_par (Ψ1 Ψ2 : val → iProp) (e1 e2 : expr []) (Φ : val → iProp) : heapN ⊥ N → (heap_ctx heapN ★ #> e1 {{ Ψ1 }} ★ #> e2 {{ Ψ2 }} ★ ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ Φ (PairV v1 v2)) ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ Φ (v1,v2)%V) ⊑ #> ParV e1 e2 {{ Φ }}. Proof. intros. rewrite -par_spec //. apply sep_mono_r. ... ...
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