Move and rename some tactics.

algebra/upred_tactics.v

@@ -146,19 +146,10 @@ Tactic Notation "ecancel" open_constr(Ps) :=
        close Ps (@nil (uPred M)) ltac:(fun Qs => cancel Qs)
     end. 
 
-(* Some more generic uPred tactics.
-   TODO: Naming. *)
-
-Ltac revert_intros tac :=
-  lazymatch goal with
-  | |- ∀ _, _ => let H := fresh in intro H; revert_intros tac; revert H
-  | |- _ => tac
-  end.
-
 (** Assumes a goal of the shape P ⊑ ▷ Q. Alterantively, if Q
     is built of ★, ∧, ∨ with ▷ in all branches; that will work, too.
     Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
-Ltac u_strip_later :=
+Ltac strip_later :=
   let rec strip :=
       lazymatch goal with
       | |- (_ ★ _) ⊑ ▷ _  =>
@@ -190,23 +181,22 @@ Ltac u_strip_later :=
     | |- _ ⊑ ▷ _ => apply later_mono; reflexivity
     (* We fail if we don't find laters in all branches. *)
     end
-  in revert_intros ltac:(etrans; [|shape_Q];
+  in intros_revert ltac:(etrans; [|shape_Q];
                          etrans; last eapply later_mono; first solve [ strip ]).
 
 (** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
     into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
     the moves all the assumptions back. *)
-Ltac u_revert_all :=
+(* TODO: this name may be a big too general *)
+Ltac revert_all :=
   lazymatch goal with
-  | |- ∀ _, _ => let H := fresh in intro H; u_revert_all;
+  | |- ∀ _, _ => 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 ⊑ _ => trans (True ∧ C)%I;
-           first (apply equiv_entails_sym, left_id, _; reflexivity);
-           apply impl_elim_l'
+  | |- ?C ⊑ _ => apply impl_entails
   end.
 
 (** This starts on a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2.
@@ -215,8 +205,8 @@ Ltac u_revert_all :=
    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,
    but with an additional assumption ★-ed to the context *)
-Ltac u_löb tac :=
-  u_revert_all;
+Ltac löb tac :=
+  revert_all;
   (* Add a box *)
   etrans; last (eapply always_elim; reflexivity);
   (* We now have a goal for the form True ⊑ P, with the "original" conclusion
@@ -233,7 +223,7 @@ Ltac u_löb tac :=
       | |- _ ⊑ (■ _ → _) => 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 u_revert_all as well as the ▷ from löb_strong and the □ we added. *)
+         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);

barrier/proof.v

@@ -81,7 +81,7 @@ Proof.
   do 4 (rewrite big_sepS_insert; last set_solver).
   rewrite !fn_lookup_insert fn_lookup_insert_ne // !fn_lookup_insert.
   rewrite 3!assoc. apply sep_mono.
-  - rewrite saved_prop_agree. u_strip_later.
+  - rewrite saved_prop_agree. strip_later.
     apply wand_intro_l. rewrite [(_ ★ (_ -★ Π★{set _} _))%I]comm !assoc wand_elim_r.
     rewrite (big_sepS_delete _ I i) //.
     rewrite [(_ ★ Π★{set _} _)%I]comm [(_ ★ Π★{set _} _)%I]comm -!assoc.
@@ -116,8 +116,7 @@ Proof.
   rewrite [(▷ _ ★ _)%I]comm -!assoc. eapply wand_apply_l.
   { by rewrite <-later_wand, <-later_intro. }
   { by rewrite later_sep. }
-  u_strip_later.
-  apply: (eq_rewrite R Q (λ x, x)%I); eauto with I.
+  strip_later. apply: (eq_rewrite R Q (λ x, x)%I); eauto with I.
 Qed.
 
 (** Actual proofs *)
@@ -181,7 +180,7 @@ Proof.
   apply const_elim_sep_l=>Hs. destruct p; last done.
   rewrite {1}/barrier_inv =>/={Hs}. rewrite later_sep.
   eapply wp_store with (v' := '0); eauto with I ndisj. 
-  u_strip_later. cancel [l ↦ '0]%I.
+  strip_later. cancel [l ↦ '0]%I.
   apply wand_intro_l. rewrite -(exist_intro (State High I)).
   rewrite -(exist_intro ∅). rewrite const_equiv /=; last by eauto using signal_step.
   rewrite left_id -later_intro {2}/barrier_inv -!assoc. apply sep_mono_r.
@@ -212,7 +211,7 @@ 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. u_strip_later.
+  rewrite -!assoc. apply sep_mono_r. 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 ]}).
@@ -242,8 +241,7 @@ 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 _. u_strip_later.
-  wp_if. 
+  wp_op; [|done]=> _. 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.
   rewrite eq_sym. eauto with I.

heap_lang/wp_tactics.v

@@ -12,7 +12,7 @@ Ltac wp_strip_later :=
     | |- _ ⊑ ▷ _ => apply later_intro
     | |- _ ⊑ _ => reflexivity
     end
-  in revert_intros ltac:(first [ u_strip_later | etrans; [|go] ] ).
+  in intros_revert ltac:(first [ strip_later | etrans; [|go] ] ).
 Ltac wp_bind K :=
   lazymatch eval hnf in K with
   | [] => idtac
@@ -29,10 +29,10 @@ Ltac wp_finish :=
      try (eapply pvs_intro;
           match goal with |- _ ⊑ wp _ _ _ => simpl | _ => fail end)
   | _ => idtac
-  end in simpl; revert_intros go.
+  end in simpl; intros_revert go.
 
 Tactic Notation "wp_rec" ">" :=
-  u_löb ltac:((* Find the redex and apply 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' =>

prelude/tactics.v

@@ -228,6 +228,14 @@ Ltac setoid_subst :=
   | H : @equiv ?A ?e _ ?x |- _ => symmetry in H; setoid_subst_aux (@equiv A e) x
   end.
 
+(** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac,
+and then reverts them. *)
+Ltac intros_revert tac :=
+  lazymatch goal with
+  | |- ∀ _, _ => let H := fresh in intro H; intros_revert tac; revert H
+  | |- _ => tac
+  end.
+
 (** Given a tactic [tac2] generating a list of terms, [iter tac1 tac2]
 runs [tac x] for each element [x] until [tac x] succeeds. If it does not
 suceed for any element of the generated list, the whole tactic wil fail. *)