Commit 961b94c1 by Ralf Jung

### un-curry "par"; add wp_tactics for case and projections

parent b83e7a10
 ... ... @@ -3,12 +3,12 @@ From heap_lang Require Import wp_tactics notation. Import uPred. Definition par : val := λ: "f1" "f2", let: "handle" := ^spawn '"f1" in let: "v2" := '"f2" #() in let: "v1" := ^join '"handle" in Pair '"v1" '"v2". Notation Par e1 e2 := (^par (λ: <>, e1) (λ: <>, e2))%E. Notation ParV e1 e2 := (par (λ: <>, e1) (λ: <>, e2))%E. λ: "fs", let: "handle" := ^spawn (Fst '"fs") in let: "v2" := Snd '"fs" #() in let: "v1" := ^join '"handle" in Pair '"v1" '"v2". Notation Par e1 e2 := (^par (Pair (λ: <>, e1) (λ: <>, e2)))%E. Notation ParV e1 e2 := (par (Pair (λ: <>, e1) (λ: <>, e2)))%E. (* We want both par and par^ to print like this. *) Infix "||" := ParV : expr_scope. Infix "||" := Par : expr_scope. ... ... @@ -18,21 +18,21 @@ Context {Σ : rFunctorG} `{!heapG Σ, !spawnG Σ}. Context (heapN N : namespace). Local Notation iProp := (iPropG heap_lang Σ). Lemma par_spec (Ψ1 Ψ2 : val → iProp) e1 e2 (f1 f2 : val) (Φ : val → iProp) : heapN ⊥ N → to_val e1 = Some f1 → to_val e2 = Some f2 → (* TODO like in spawn.v -- wp about e or f? *) (heap_ctx heapN ★ #> e1 #() {{ Ψ1 }} ★ #> e2 #() {{ Ψ2 }} ★ Lemma par_spec (Ψ1 Ψ2 : val → iProp) e (f1 f2 : val) (Φ : val → iProp) : heapN ⊥ N → to_val e = Some (PairV f1 f2) → (heap_ctx heapN ★ #> f1 #() {{ Ψ1 }} ★ #> f2 #() {{ Ψ2 }} ★ ∀ v1 v2, Ψ1 v1 ★ Ψ2 v2 -★ Φ (PairV v1 v2)) ⊑ #> par e1 e2 {{ Φ }}. ⊑ #> par e {{ Φ }}. Proof. intros. rewrite /par. wp_focus e1. etransitivity; last by eapply wp_value. wp_let. wp_focus e2. etransitivity; last by eapply wp_value. wp_let. 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. apply sep_mono_r. rewrite (of_to_val e1) //. apply sep_mono_r. apply sep_mono_r. apply sep_mono_r. apply forall_intro=>h. apply wand_intro_l. wp_let. wp_focus (f2 _). rewrite wp_frame_r wp_frame_l. rewrite (of_to_val e2) //. apply wp_mono=>v2. 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. apply forall_intro=>v1. apply wand_intro_l. wp_let. etransitivity; last by (eapply wp_value, to_val_Pair; eapply to_of_val). ... ...
 ... ... @@ -45,8 +45,7 @@ Proof. solve_proper. Qed. Lemma spawn_spec (Ψ : val → iProp) e (f : val) (Φ : val → iProp) : to_val e = Some f → heapN ⊥ N → (* TODO: Not sure whether the wp should be about [e] or [f]. Both work. *) (heap_ctx heapN ★ #> e #() {{ Ψ }} ★ ∀ l, join_handle l Ψ -★ Φ (%l)) (heap_ctx heapN ★ #> f #() {{ Ψ }} ★ ∀ l, join_handle l Ψ -★ Φ (%l)) ⊑ #> spawn e {{ Φ }}. Proof. intros Hval Hdisj. rewrite /spawn. ... ... @@ -60,7 +59,7 @@ Proof. rewrite !pvs_frame_r. eapply wp_strip_pvs. rewrite !sep_exist_r. apply exist_elim=>γ. (* TODO: Figure out a better way to say "I want to establish ▷ spawn_inv". *) trans (heap_ctx heapN ★ #> e #() {{ Ψ }} ★ (join_handle l Ψ -★ Φ (%l)%V) ★ trans (heap_ctx heapN ★ #> f #() {{ Ψ }} ★ (join_handle l Ψ -★ Φ (%l)%V) ★ own γ (Excl ()) ★ ▷ (spawn_inv γ l Ψ))%I. { ecancel [ #> _ {{ _ }}; _ -★ _; heap_ctx _; own _ _]%I. rewrite -later_intro /spawn_inv -(exist_intro (InjLV #0)). ... ... @@ -101,7 +100,7 @@ Proof. cancel [l ↦ lv]%I. rewrite sep_or_r. apply or_elim. - (* Case 1 : nothing sent yet, we wait. *) rewrite -or_intro_l. apply const_elim_sep_l=>-> {lv}. do 2 rewrite const_equiv // left_id. (ewp eapply wp_case_inl); eauto. do 2 rewrite const_equiv // left_id. wp_case; eauto. wp_seq. rewrite -always_wand_impl always_elim. rewrite !assoc. eapply wand_apply_r'; first done. rewrite -(exist_intro γ). solve_sep_entails. ... ... @@ -112,7 +111,7 @@ Proof. rewrite [(heap_ctx _ ★ _)%I]sep_elim_r !assoc. rewrite -own_op own_valid_l. rewrite -!assoc discrete_valid. apply const_elim_sep_l=>-[]. } rewrite -or_intro_r. ecancel [own _ _]. (ewp apply: wp_case_inr); eauto using to_of_val. wp_case; eauto using to_of_val. wp_let. etransitivity; last by eapply wp_value, to_of_val. rewrite (forall_elim v). rewrite !assoc. eapply wand_apply_r'; eauto with I. Qed. ... ...
 ... ... @@ -62,23 +62,45 @@ Tactic Notation "wp_op" ">" := | BinOp LeOp _ _ => wp_bind K; apply wp_le; wp_finish | BinOp EqOp _ _ => wp_bind K; apply wp_eq; wp_finish | BinOp _ _ _ => wp_bind K; etrans; [|fast_by eapply wp_bin_op]; wp_finish wp_bind K; etrans; [|eapply wp_bin_op; try fast_done]; wp_finish | UnOp _ _ => wp_bind K; etrans; [|fast_by eapply wp_un_op]; wp_finish wp_bind K; etrans; [|eapply wp_un_op; try fast_done]; wp_finish end) end. Tactic Notation "wp_op" := wp_op>; try strip_later. Tactic Notation "wp_proj" ">" := match goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => match eval hnf in e' with | Fst _ => wp_bind K; etrans; [|eapply wp_fst; try fast_done]; wp_finish | Snd _ => wp_bind K; etrans; [|eapply wp_snd; try fast_done]; wp_finish end) end. Tactic Notation "wp_proj" := wp_proj>; try strip_later. Tactic Notation "wp_if" ">" := match goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => match eval hnf in e' with If _ _ _ => wp_bind K; etrans; [|apply wp_if_true || apply wp_if_false]; wp_finish etrans; [|eapply wp_if_true || eapply wp_if_false]; wp_finish end) end. Tactic Notation "wp_if" := wp_if>; try strip_later. Tactic Notation "wp_case" ">" := match goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => match eval hnf in e' with Case _ _ _ => wp_bind K; etrans; [|eapply wp_case_inl || eapply wp_case_inr]; wp_finish end) end. Tactic Notation "wp_case" := wp_case>; try strip_later. Tactic Notation "wp_focus" open_constr(efoc) := match goal with | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => ... ...
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