diff --git a/algebra/upred_tactics.v b/algebra/upred_tactics.v
index 0540bf34f381da70d418a3c14e2db24c95178a4d..4e82798c749fe424ff4fafe55cc7e629f8821a0f 100644
--- a/algebra/upred_tactics.v
+++ b/algebra/upred_tactics.v
@@ -151,19 +151,19 @@ Tactic Notation "ecancel" open_constr(Ps) :=
Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
Ltac strip_later :=
let rec strip :=
- lazymatch goal with
- | |- (_ ★ _) ⊑ ▷ _ =>
- etrans; last (eapply equiv_entails_sym, later_sep);
- apply sep_mono; strip
- | |- (_ ∧ _) ⊑ ▷ _ =>
- etrans; last (eapply equiv_entails_sym, later_and);
- apply sep_mono; strip
- | |- (_ ∨ _) ⊑ ▷ _ =>
- etrans; last (eapply equiv_entails_sym, later_or);
- apply sep_mono; strip
- | |- ▷ _ ⊑ ▷ _ => apply later_mono; reflexivity
- | |- _ ⊑ ▷ _ => apply later_intro; reflexivity
- end
+ lazymatch goal with
+ | |- (_ ★ _) ⊑ ▷ _ =>
+ etrans; last (eapply equiv_entails_sym, later_sep);
+ apply sep_mono; strip
+ | |- (_ ∧ _) ⊑ ▷ _ =>
+ etrans; last (eapply equiv_entails_sym, later_and);
+ apply sep_mono; strip
+ | |- (_ ∨ _) ⊑ ▷ _ =>
+ etrans; last (eapply equiv_entails_sym, later_or);
+ apply sep_mono; strip
+ | |- ▷ _ ⊑ ▷ _ => apply later_mono; reflexivity
+ | |- _ ⊑ ▷ _ => apply later_intro; reflexivity
+ end
in let rec shape_Q :=
lazymatch goal with
| |- _ ⊑ (_ ★ _) =>
@@ -190,13 +190,14 @@ Ltac strip_later :=
(* TODO: this name may be a big too general *)
Ltac revert_all :=
lazymatch goal with
- | |- ∀ _, _ => let H := fresh in intro H; 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. *)
- first [ apply (const_intro_impl _ _ _ H); clear H
- | revert H; apply forall_elim']
- | |- ?C ⊑ _ => apply impl_entails
+ | |- ∀ _, _ =>
+ let H := fresh in intro H; 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. *)
+ first [ apply (const_intro_impl _ _ _ H); clear H
+ | revert H; apply forall_elim']
+ | |- _ ⊑ _ => apply impl_entails
end.
(** This starts on a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2.
@@ -217,16 +218,15 @@ Ltac löb tac :=
(* Now introduce again all the things that we reverted, and at the bottom,
do the work *)
let rec go :=
- lazymatch goal with
- | |- _ ⊑ (∀ _, _) => apply forall_intro;
- let H := fresh in intro H; go; revert H
- | |- _ ⊑ (■_ → _) => apply impl_intro_l, const_elim_l;
- let H := fresh in intro H; go; revert H
- (* This is the "bottom" of the goal, where we see the impl introduced
- by uPred_revert_all as well as the ▷ from löb_strong and the □ we added. *)
- | |- ▷ □ ?R ⊑ (?L → _) => apply impl_intro_l;
- trans (L ★ ▷ □ R)%I;
- first (eapply equiv_entails, always_and_sep_r, _; reflexivity);
- tac
- end
+ lazymatch goal with
+ | |- _ ⊑ (∀ _, _) =>
+ apply forall_intro; let H := fresh in intro H; go; revert H
+ | |- _ ⊑ (■_ → _) =>
+ apply impl_intro_l, const_elim_l; let H := fresh in intro H; go; revert H
+ (* This is the "bottom" of the goal, where we see the impl introduced
+ by uPred_revert_all as well as the ▷ from löb_strong and the □ we added. *)
+ | |- ▷ □ ?R ⊑ (?L → _) => apply impl_intro_l;
+ trans (L ★ ▷ □ R)%I;
+ [eapply equiv_entails, always_and_sep_r, _; reflexivity | tac]
+ end
in go.
diff --git a/heap_lang/wp_tactics.v b/heap_lang/wp_tactics.v
index 85a186b186067fcbb917e9b7e130c9fe8cfe30d3..1eb190fb3bb218a635b6e1158e32673d84041ce7 100644
--- a/heap_lang/wp_tactics.v
+++ b/heap_lang/wp_tactics.v
@@ -5,14 +5,6 @@ Import uPred.
(** wp-specific helper tactics *)
(* First try to productively strip off laters; if that fails, at least
cosmetically get rid of laters in the conclusion. *)
-Ltac wp_strip_later :=
- let rec go :=
- lazymatch goal with
- | |- _ ⊑ (_ ★ _) => apply sep_mono; go
- | |- _ ⊑ ▷ _ => apply later_intro
- | |- _ ⊑ _ => reflexivity
- end
- in intros_revert ltac:(first [ strip_later | etrans; [|go] ] ).
Ltac wp_bind K :=
lazymatch eval hnf in K with
| [] => idtac
@@ -23,26 +15,26 @@ Ltac wp_finish :=
match goal with
| |- _ ⊑ ▷ _ => etrans; [|apply later_mono; go; reflexivity]
| |- _ ⊑ wp _ _ _ =>
- etrans; [|eapply wp_value_pvs; reflexivity];
- (* sometimes, we will have to do a final view shift, so only apply
- wp_value if we obtain a consecutive wp *)
- try (eapply pvs_intro;
- match goal with |- _ ⊑ wp _ _ _ => simpl | _ => fail end)
+ etrans; [|eapply wp_value_pvs; reflexivity];
+ (* sometimes, we will have to do a final view shift, so only apply
+ pvs_intro if we obtain a consecutive wp *)
+ try (eapply pvs_intro;
+ match goal with |- _ ⊑ wp _ _ _ => simpl | _ => fail end)
| _ => idtac
end in simpl; intros_revert go.
Tactic Notation "wp_rec" ">" :=
- löb ltac:((* Find the redex and apply wp_rec *)
- idtac; (* <https://coq.inria.fr/bugs/show_bug.cgi?id=4584> *)
- lazymatch goal with
- | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
- match eval cbv in e' with
- | App (Rec _ _ _) _ =>
- wp_bind K; etrans; [|eapply wp_rec; reflexivity];
- wp_finish
- end)
- end).
-Tactic Notation "wp_rec" := wp_rec>; wp_strip_later.
+ löb ltac:(
+ (* Find the redex and apply wp_rec *)
+ idtac; (* <https://coq.inria.fr/bugs/show_bug.cgi?id=4584> *)
+ lazymatch goal with
+ | |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' =>
+ match eval cbv in e' with
+ | App (Rec _ _ _) _ =>
+ wp_bind K; etrans; [|eapply wp_rec; reflexivity]; wp_finish
+ end)
+ end).
+Tactic Notation "wp_rec" := wp_rec>; try strip_later.
Tactic Notation "wp_lam" ">" :=
match goal with
@@ -52,7 +44,7 @@ Tactic Notation "wp_lam" ">" :=
wp_bind K; etrans; [|eapply wp_lam; reflexivity]; wp_finish
end)
end.
-Tactic Notation "wp_lam" := wp_lam>; wp_strip_later.
+Tactic Notation "wp_lam" := wp_lam>; try strip_later.
Tactic Notation "wp_let" ">" := wp_lam>.
Tactic Notation "wp_let" := wp_lam.
@@ -72,7 +64,7 @@ Tactic Notation "wp_op" ">" :=
wp_bind K; etrans; [|eapply wp_un_op; reflexivity]; wp_finish
end)
end.
-Tactic Notation "wp_op" := wp_op>; wp_strip_later.
+Tactic Notation "wp_op" := wp_op>; try strip_later.
Tactic Notation "wp_if" ">" :=
match goal with
@@ -83,7 +75,7 @@ Tactic Notation "wp_if" ">" :=
etrans; [|apply wp_if_true || apply wp_if_false]; wp_finish
end)
end.
-Tactic Notation "wp_if" := wp_if>; wp_strip_later.
+Tactic Notation "wp_if" := wp_if>; try strip_later.
Tactic Notation "wp_focus" open_constr(efoc) :=
match goal with
@@ -95,7 +87,7 @@ Tactic Notation "wp" ">" tactic(tac) :=
match goal with
| |- _ ⊑ wp ?E ?e ?Q => reshape_expr e ltac:(fun K e' => wp_bind K; tac)
end.
-Tactic Notation "wp" tactic(tac) := (wp> tac); [wp_strip_later|..].
+Tactic Notation "wp" tactic(tac) := (wp> tac); [try strip_later|..].
(* In case the precondition does not match.
TODO: Have one tactic unifying wp and ewp. *)