Commit 6428df91 authored by Ralf Jung's avatar Ralf Jung
Browse files

write a tactic to strip away laters

parent 77769756
......@@ -214,10 +214,8 @@ Section proof.
apply forall_intro=>-[p I]. apply wand_intro_l. rewrite -!assoc.
apply const_elim_sep_l=>Hs. destruct p; last done.
rewrite {1}/barrier_inv =>/={Hs}. rewrite later_sep.
eapply wp_store; eauto with I ndisj.
rewrite -!assoc. apply sep_mono_r. etrans; last eapply later_mono.
{ (* Is this really the best way to strip the later? *)
erewrite later_sep. apply sep_mono_r. apply later_intro. }
eapply wp_store; eauto with I ndisj.
rewrite -!assoc. apply sep_mono_r. u_strip_later.
apply wand_intro_l. rewrite -(exist_intro (State High I)).
rewrite -(exist_intro ). rewrite const_equiv /=; last first.
{ apply rtc_once. constructor; first constructor;
......@@ -249,9 +247,7 @@ Section proof.
apply const_elim_sep_l=>Hs.
rewrite {1}/barrier_inv =>/=. rewrite later_sep.
eapply wp_load; eauto with I ndisj.
rewrite -!assoc. apply sep_mono_r. etrans; last eapply later_mono.
{ (* Is this really the best way to strip the later? *)
erewrite later_sep. apply sep_mono_r, later_intro. }
rewrite -!assoc. apply sep_mono_r. u_strip_later.
apply wand_intro_l. destruct p.
{ (* a Low state. The comparison fails, and we recurse. *)
rewrite -(exist_intro (State Low I)) -(exist_intro {[ Change i ]}).
......@@ -261,7 +257,8 @@ Section proof.
wp_op; first done. intros _. wp_if. rewrite !assoc.
rewrite -{2}pvs_wp. apply pvs_wand_r.
rewrite -(exist_intro γ) -(exist_intro P) -(exist_intro Q) -(exist_intro i).
rewrite !assoc. do 3 (rewrite -pvs_frame_r; apply sep_mono_l).
rewrite !assoc.
do 3 (rewrite -pvs_frame_r; apply sep_mono; last (try apply later_intro; reflexivity)).
rewrite [(_ heap_ctx _)%I]comm -!assoc -pvs_frame_l. apply sep_mono_r.
rewrite comm -pvs_frame_l. apply sep_mono_r.
apply sts_ownS_weaken; eauto using sts.up_subseteq. }
......@@ -285,11 +282,7 @@ Section proof.
apply wand_intro_l. rewrite [(heap_ctx _ _)%I]sep_elim_r.
rewrite [(sts_own _ _ _ _)%I]sep_elim_r [(sts_ctx _ _ _ _)%I]sep_elim_r.
rewrite !assoc [(_ saved_prop_own i Q)%I]comm !assoc saved_prop_agree.
wp_op>; last done. intros _.
etrans; last eapply later_mono.
{ (* Is this really the best way to strip the later? *)
erewrite later_sep. apply sep_mono; last apply later_intro.
rewrite ->later_sep. apply sep_mono_l. rewrite ->later_sep. done. }
wp_op>; last done. intros _. u_strip_later.
wp_if.
eapply wand_apply_r; [done..|]. eapply wand_apply_r; [done..|].
apply: (eq_rewrite Q' Q (λ x, x)%I); last by eauto with I.
......
From heap_lang Require Export tactics substitution.
Import uPred.
(* TODO: The next 6 tactics are not wp-specific at all. They should move elsewhere. *)
Ltac revert_intros tac :=
lazymatch goal with
| |- _, _ => let H := fresh in intro H; revert_intros tac; revert H
......@@ -15,17 +17,36 @@ Ltac wp_strip_later :=
end
in revert_intros ltac:(etrans; [|go]).
(** Assumes a goal of the shape P ⊑ ▷ Q.
Will get rid of ▷ in P below ★, ∧ and ∨. *)
Ltac u_strip_later :=
let rec strip :=
match goal with
| |- (_ _) _ =>
etrans; last (eapply equiv_spec, later_sep);
apply sep_mono; strip
| |- (_ _) _ =>
etrans; last (eapply equiv_spec, later_and);
apply sep_mono; strip
| |- (_ _) _ =>
etrans; last (eapply equiv_spec, later_or);
apply sep_mono; strip
| |- _ _ => apply later_mono; reflexivity
| |- _ _ => apply later_intro; reflexivity
end
in etrans; last eapply later_mono; first solve [ strip ].
(* ssreflect-locks the part after the ⊑ *)
(* FIXME: I tried doing a lazymatch to only apply the tactic if the goal has shape ⊑,
bit the match is executed *before* doing the recursion... WTF? *)
Ltac uLock_goal := revert_intros ltac:(apply uPred_lock_conclusion).
Ltac u_lock_goal := revert_intros ltac:(apply uPred_lock_conclusion).
(** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
the moves all the assumptions back. *)
Ltac uRevert_all :=
Ltac u_revert_all :=
lazymatch goal with
| |- _, _ => let H := fresh in intro H; uRevert_all;
| |- _, _ => let H := fresh in intro H; u_revert_all;
(* TODO: Really, we should distinguish based on whether this is a
dependent function type or not. Right now, we distinguish based
on the sort of the argument, which is suboptimal. *)
......@@ -41,8 +62,8 @@ Ltac uRevert_all :=
assumptions, then moves all the Coq assumptions back out to the context,
applies [tac] on the goal (now of the form _ ⊑ _), and then reverts the Coq
assumption so that we end up with the same shape as where we started. *)
Ltac uLöb tac :=
uLock_goal; uRevert_all;
Ltac u_löb tac :=
u_lock_goal; u_revert_all;
(* We now have a goal for the form True ⊑ P, with the "original" conclusion
being locked. *)
apply löb_strong; etransitivity;
......@@ -81,7 +102,7 @@ Ltac wp_finish :=
end in simpl; revert_intros go.
Tactic Notation "wp_rec" :=
uLöb ltac:((* Find the redex and apply wp_rec *)
u_löb ltac:((* Find the redex and apply wp_rec *)
match goal with
| |- _ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
match eval cbv in e' with
......
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