Commit 961b94c1 authored by Ralf Jung's avatar Ralf Jung

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

parent b83e7a10
Pipeline #258 passed with stage
......@@ -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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