Also keep track of whether a hypothesis is persistent in IntoWand.

This enables things like `iSpecialize ("H2" with "H1") in the below:

  "H1" : P
  ---------□
  "H2" : □ P -∗ Q
  ---------∗
  R

theories/base_logic/lib/fancy_updates.v

@@ -155,7 +155,8 @@ Section proofmode_classes.
   Proof. rewrite /FromAssumption=>->. apply bupd_fupd. Qed.
 
   Global Instance wand_weaken_fupd E1 E2 P Q P' Q' :
-    WandWeaken P Q P' Q' → WandWeaken' P Q (|={E1,E2}=> P') (|={E1,E2}=> Q').
+    WandWeaken false P Q P' Q' →
+    WandWeaken' false P Q (|={E1,E2}=> P') (|={E1,E2}=> Q').
   Proof.
     rewrite /WandWeaken' /WandWeaken=>->. apply wand_intro_l. by rewrite fupd_wand_r.
   Qed.

theories/proofmode/class_instances.v

@@ -248,57 +248,66 @@ Global Instance from_later_exist {A} n (Φ Ψ : A → uPred M) :
 Proof. intros ?. rewrite /FromLaterN laterN_exist=> ?. by apply exist_mono. Qed.
 
 (* IntoWand *)
-Global Instance wand_weaken_assumption P1 P2 Q :
-  FromAssumption false P2 P1 → WandWeaken P1 Q P2 Q | 0.
+Global Instance wand_weaken_assumption p P1 P2 Q :
+  FromAssumption p P2 P1 → WandWeaken p P1 Q P2 Q | 0.
 Proof. by rewrite /WandWeaken /FromAssumption /= =>->. Qed.
-Global Instance wand_weaken_later P Q P' Q' :
-  WandWeaken P Q P' Q' → WandWeaken' P Q (▷ P') (▷ Q').
+Global Instance wand_weaken_later p P Q P' Q' :
+  WandWeaken p P Q P' Q' → WandWeaken' p P Q (▷ P') (▷ Q').
 Proof.
-  rewrite /WandWeaken' /WandWeaken=> ->. by rewrite -later_wand -later_intro.
+  rewrite /WandWeaken' /WandWeaken=> ->.
+  by rewrite always_if_later -later_wand -later_intro.
 Qed.
-Global Instance wand_weaken_laterN n P Q P' Q' :
-  WandWeaken P Q P' Q' → WandWeaken' P Q (▷^n P') (▷^n Q').
+Global Instance wand_weaken_laterN p n P Q P' Q' :
+  WandWeaken p P Q P' Q' → WandWeaken' p P Q (▷^n P') (▷^n Q').
 Proof.
-  rewrite /WandWeaken' /WandWeaken=> ->. by rewrite -laterN_wand -laterN_intro.
+  rewrite /WandWeaken' /WandWeaken=> ->.
+  by rewrite always_if_laterN -laterN_wand -laterN_intro.
 Qed.
-Global Instance bupd_weaken_laterN P Q P' Q' :
-  WandWeaken P Q P' Q' → WandWeaken' P Q (|==> P') (|==> Q').
+Global Instance bupd_weaken_laterN p P Q P' Q' :
+  WandWeaken false P Q P' Q' → WandWeaken' p P Q (|==> P') (|==> Q').
 Proof.
   rewrite /WandWeaken' /WandWeaken=> ->.
-  apply wand_intro_l. by rewrite bupd_wand_r.
+  apply wand_intro_l. by rewrite always_if_elim bupd_wand_r.
 Qed.
 
-Global Instance into_wand_wand P P' Q Q' :
-  WandWeaken P Q P' Q' → IntoWand (P -∗ Q) P' Q'.
+Global Instance into_wand_wand p P P' Q Q' :
+  WandWeaken p P Q P' Q' → IntoWand p (P -∗ Q) P' Q'.
 Proof. done. Qed.
-Global Instance into_wand_impl P P' Q Q' :
-  WandWeaken P Q P' Q' → IntoWand (P → Q) P' Q'.
+Global Instance into_wand_impl p P P' Q Q' :
+  WandWeaken p P Q P' Q' → IntoWand p (P → Q) P' Q'.
 Proof. rewrite /WandWeaken /IntoWand /= => <-. apply impl_wand. Qed.
 
-Global Instance into_wand_iff_l P P' Q Q' :
-  WandWeaken P Q P' Q' → IntoWand (P ↔ Q) P' Q'.
+Global Instance into_wand_iff_l p P P' Q Q' :
+  WandWeaken p P Q P' Q' → IntoWand p (P ↔ Q) P' Q'.
 Proof. rewrite /WandWeaken /IntoWand=> <-. apply and_elim_l', impl_wand. Qed.
-Global Instance into_wand_iff_r P P' Q Q' :
-  WandWeaken Q P Q' P' → IntoWand (P ↔ Q) Q' P'.
+Global Instance into_wand_iff_r p P P' Q Q' :
+  WandWeaken p Q P Q' P' → IntoWand p (P ↔ Q) Q' P'.
 Proof. rewrite /WandWeaken /IntoWand=> <-. apply and_elim_r', impl_wand. Qed.
 
-Global Instance into_wand_forall {A} (Φ : A → uPred M) P Q x :
-  IntoWand (Φ x) P Q → IntoWand (∀ x, Φ x) P Q.
+Global Instance into_wand_forall {A} p (Φ : A → uPred M) P Q x :
+  IntoWand p (Φ x) P Q → IntoWand p (∀ x, Φ x) P Q.
 Proof. rewrite /IntoWand=> <-. apply forall_elim. Qed.
-Global Instance into_wand_always R P Q : IntoWand R P Q → IntoWand (□ R) P Q.
+Global Instance into_wand_always p R P Q :
+  IntoWand p R P Q → IntoWand p (□ R) P Q.
 Proof. rewrite /IntoWand=> ->. apply always_elim. Qed.
 
-Global Instance into_wand_later R P Q :
-  IntoWand R P Q → IntoWand (▷ R) (▷ P) (▷ Q).
-Proof. rewrite /IntoWand=> ->. by rewrite -later_wand. Qed.
-Global Instance into_wand_laterN n R P Q :
-  IntoWand R P Q → IntoWand (▷^n R) (▷^n P) (▷^n Q).
-Proof. rewrite /IntoWand=> ->. by rewrite -laterN_wand. Qed.
+Global Instance into_wand_later p R P Q :
+  IntoWand p R P Q → IntoWand p (▷ R) (▷ P) (▷ Q).
+Proof. rewrite /IntoWand=> ->. by rewrite always_if_later -later_wand. Qed.
+Global Instance into_wand_laterN p n R P Q :
+  IntoWand p R P Q → IntoWand p (▷^n R) (▷^n P) (▷^n Q).
+Proof. rewrite /IntoWand=> ->. by rewrite always_if_laterN -laterN_wand. Qed.
+
 Global Instance into_wand_bupd R P Q :
-  IntoWand R P Q → IntoWand (|==> R) (|==> P) (|==> Q).
+  IntoWand false R P Q → IntoWand false (|==> R) (|==> P) (|==> Q).
 Proof.
   rewrite /IntoWand=> ->. apply wand_intro_l. by rewrite bupd_sep wand_elim_r.
 Qed.
+Global Instance into_wand_bupd_persistent R P Q :
+  IntoWand true R P Q → IntoWand true (|==> R) P (|==> Q).
+Proof.
+  rewrite /IntoWand=>->. apply wand_intro_l. by rewrite bupd_frame_l wand_elim_r.
+Qed.
 
 (* FromAnd *)
 Global Instance from_and_and p P1 P2 : FromAnd p (P1 ∧ P2) P1 P2 | 100.

theories/proofmode/classes.v

@@ -71,17 +71,18 @@ Class FromLaterN {M} (n : nat) (P Q : uPred M) := from_laterN : ▷^n Q ⊢ P.
 Arguments from_laterN {_} _ _ _ {_}.
 Hint Mode FromLaterN + - ! - : typeclass_instances.
 
-Class WandWeaken {M} (P Q P' Q' : uPred M) := wand_weaken : (P -∗ Q) ⊢ (P' -∗ Q').
-Hint Mode WandWeaken + - - - - : typeclass_instances.
-
-Class WandWeaken' {M} (P Q P' Q' : uPred M) :=
-  wand_weaken' :> WandWeaken P Q P' Q'.
-Hint Mode WandWeaken' + - - ! - : typeclass_instances.
-Hint Mode WandWeaken' + - - - ! : typeclass_instances.
-
-Class IntoWand {M} (R P Q : uPred M) := into_wand : R ⊢ P -∗ Q.
-Arguments into_wand {_} _ _ _ {_}.
-Hint Mode IntoWand + ! - - : typeclass_instances.
+Class WandWeaken {M} (p : bool) (P Q P' Q' : uPred M) :=
+  wand_weaken : (P -∗ Q) ⊢ (□?p P' -∗ Q').
+Hint Mode WandWeaken + + - - - - : typeclass_instances.
+
+Class WandWeaken' {M} (p : bool) (P Q P' Q' : uPred M) :=
+  wand_weaken' :> WandWeaken p P Q P' Q'.
+Hint Mode WandWeaken' + + - - ! - : typeclass_instances.
+Hint Mode WandWeaken' + + - - - ! : typeclass_instances.
+
+Class IntoWand {M} (p : bool) (R P Q : uPred M) := into_wand : R ⊢ □?p P -∗ Q.
+Arguments into_wand {_} _ _ _ _ {_}.
+Hint Mode IntoWand + + ! - - : typeclass_instances.
 
 Class FromAnd {M} (p : bool) (P Q1 Q2 : uPred M) :=
   from_and : (if p then Q1 ∧ Q2 else Q1 ∗ Q2) ⊢ P.

theories/proofmode/coq_tactics.v

@@ -542,7 +542,7 @@ but it is doing some work to keep the order of hypotheses preserved. *)
 Lemma tac_specialize Δ Δ' Δ'' i p j q P1 P2 R Q :
   envs_lookup_delete i Δ = Some (p, P1, Δ') →
   envs_lookup j (if p then Δ else Δ') = Some (q, R) →
-  IntoWand R P1 P2 →
+  IntoWand p R P1 P2 →
   match p with
   | true  => envs_simple_replace j q (Esnoc Enil j P2) Δ
   | false => envs_replace j q false (Esnoc Enil j P2) Δ'
@@ -552,16 +552,17 @@ Lemma tac_specialize Δ Δ' Δ'' i p j q P1 P2 R Q :
 Proof.
   intros [? ->]%envs_lookup_delete_Some ??? <-. destruct p.
   - rewrite envs_lookup_persistent_sound // envs_simple_replace_sound //; simpl.
-    rewrite assoc (into_wand R) (always_elim_if q) -always_if_sep wand_elim_r.
-    by rewrite right_id wand_elim_r.
+    rewrite right_id assoc (into_wand _ R) /=. destruct q; simpl.
+    + by rewrite always_wand always_always !wand_elim_r.
+    + by rewrite !wand_elim_r.
   - rewrite envs_lookup_sound //; simpl.
     rewrite envs_lookup_sound // (envs_replace_sound' _ Δ'') //; simpl.
-    by rewrite right_id assoc (into_wand R) always_if_elim wand_elim_r wand_elim_r.
+    by rewrite right_id assoc (into_wand _ R) always_if_elim wand_elim_r wand_elim_r.
 Qed.
 
 Lemma tac_specialize_assert Δ Δ' Δ1 Δ2' j q lr js R P1 P2 P1' Q :
   envs_lookup_delete j Δ = Some (q, R, Δ') →
-  IntoWand R P1 P2 → ElimModal P1' P1 Q Q →
+  IntoWand false R P1 P2 → ElimModal P1' P1 Q Q →
   ('(Δ1,Δ2) ← envs_split lr js Δ';
     Δ2' ← envs_app false (Esnoc Enil j P2) Δ2;
     Some (Δ1,Δ2')) = Some (Δ1,Δ2') → (* does not preserve position of [j] *)
@@ -572,7 +573,7 @@ Proof.
     destruct (envs_app _ _ _) eqn:?; simplify_eq/=.
   rewrite envs_lookup_sound // envs_split_sound //.
   rewrite (envs_app_sound Δ2) //; simpl.
-  rewrite right_id (into_wand R) HP1 assoc -(comm _ P1') -assoc.
+  rewrite right_id (into_wand _ R) HP1 assoc -(comm _ P1') -assoc.
   rewrite -(elim_modal P1' P1 Q Q). apply sep_mono_r, wand_intro_l.
   by rewrite always_if_elim assoc !wand_elim_r.
 Qed.
@@ -582,7 +583,7 @@ Proof. by unlock. Qed.
 
 Lemma tac_specialize_frame Δ Δ' j q R P1 P2 P1' Q Q' :
   envs_lookup_delete j Δ = Some (q, R, Δ') →
-  IntoWand R P1 P2 →
+  IntoWand false R P1 P2 →
   ElimModal P1' P1 Q Q →
   (Δ' ⊢ P1' ∗ locked Q') →
   Q' = (P2 -∗ Q)%I →
@@ -590,25 +591,25 @@ Lemma tac_specialize_frame Δ Δ' j q R P1 P2 P1' Q Q' :
 Proof.
   intros [? ->]%envs_lookup_delete_Some ?? HPQ ->.
   rewrite envs_lookup_sound //. rewrite HPQ -lock.
-  rewrite (into_wand R) assoc -(comm _ P1') -assoc always_if_elim.
+  rewrite (into_wand _ R) assoc -(comm _ P1') -assoc always_if_elim.
   rewrite -{2}(elim_modal P1' P1 Q Q). apply sep_mono_r, wand_intro_l.
   by rewrite assoc !wand_elim_r.
 Qed.
 
 Lemma tac_specialize_assert_pure Δ Δ' j q R P1 P2 φ Q :
   envs_lookup j Δ = Some (q, R) →
-  IntoWand R P1 P2 → FromPure P1 φ →
+  IntoWand false R P1 P2 → FromPure P1 φ →
   envs_simple_replace j q (Esnoc Enil j P2) Δ = Some Δ' →
   φ → (Δ' ⊢ Q) → Δ ⊢ Q.
 Proof.
   intros. rewrite envs_simple_replace_sound //; simpl.
-  rewrite right_id (into_wand R) -(from_pure P1) pure_True //.
+  rewrite right_id (into_wand _ R) -(from_pure P1) pure_True //.
   by rewrite wand_True wand_elim_r.
 Qed.
 
 Lemma tac_specialize_assert_persistent Δ Δ' Δ'' j q P1 P2 R Q :
   envs_lookup_delete j Δ = Some (q, R, Δ') →
-  IntoWand R P1 P2 → PersistentP P1 →
+  IntoWand false R P1 P2 → PersistentP P1 →
   envs_simple_replace j q (Esnoc Enil j P2) Δ = Some Δ'' →
   (Δ' ⊢ P1) → (Δ'' ⊢ Q) → Δ ⊢ Q.
 Proof.
@@ -617,7 +618,7 @@ Proof.
   rewrite -(idemp uPred_and (envs_delete _ _ _)).
   rewrite {1}HP1 (persistentP P1) always_and_sep_l assoc.
   rewrite envs_simple_replace_sound' //; simpl.
-  rewrite right_id (into_wand R) (always_elim_if q) -always_if_sep wand_elim_l.
+  rewrite right_id (into_wand _ R) (always_elim_if q) -always_if_sep wand_elim_l.
   by rewrite wand_elim_r.
 Qed.
 
@@ -704,11 +705,11 @@ Proof.
 Qed.
 
 Lemma tac_apply Δ Δ' i p R P1 P2 :
-  envs_lookup_delete i Δ = Some (p, R, Δ') → IntoWand R P1 P2 →
+  envs_lookup_delete i Δ = Some (p, R, Δ') → IntoWand false R P1 P2 →
   (Δ' ⊢ P1) → Δ ⊢ P2.
 Proof.
   intros ?? HP1. rewrite envs_lookup_delete_sound' //.
-  by rewrite (into_wand R) HP1 wand_elim_l.
+  by rewrite (into_wand _ R) HP1 wand_elim_l.
 Qed.
 
 (** * Rewriting *)

theories/tests/proofmode.v

@@ -176,4 +176,7 @@ Lemma test_split_box (P Q : uPred M) :
   □ P -∗ □ (P ∗ P).
 Proof. iIntros "#?". by iSplit. Qed.
 
+Lemma test_specialize_persistent (P Q : uPred M) :
+  □ P -∗ (□ P -∗ Q) -∗ Q.
+Proof. iIntros "#HP HPQ". by iSpecialize ("HPQ" with "HP"). Qed.
 End tests.