Use more informative tags `Strong` and `Weak` for the modalities.

theories/base_logic/big_op.v

@@ -126,7 +126,7 @@ Section list.
   Proof. apply (big_opL_commute _). Qed.
 
   Lemma big_sepL_forall Φ l :
-    (∀ k x, PersistentP true (Φ k x)) →
+    (∀ k x, PersistentP Weak (Φ k x)) →
     ([∗ list] k↦x ∈ l, Φ k x) ⊣⊢ (∀ k x, ⌜l !! k = Some x⌝ → Φ k x).
   Proof.
     intros HΦ. apply (anti_symm _).
@@ -316,7 +316,7 @@ Section gmap.
   Proof. apply (big_opM_commute _). Qed.
 
   Lemma big_sepM_forall Φ m :
-    (∀ k x, PersistentP true (Φ k x)) →
+    (∀ k x, PersistentP Weak (Φ k x)) →
     ([∗ map] k↦x ∈ m, Φ k x) ⊣⊢ (∀ k x, ⌜m !! k = Some x⌝ → Φ k x).
   Proof.
     intros. apply (anti_symm _).
@@ -468,7 +468,7 @@ Section gset.
   Proof. apply (big_opS_commute _). Qed.
 
   Lemma big_sepS_forall Φ X :
-    (∀ x, PersistentP true (Φ x)) → ([∗ set] x ∈ X, Φ x) ⊣⊢ (∀ x, ⌜x ∈ X⌝ → Φ x).
+    (∀ x, PersistentP Weak (Φ x)) → ([∗ set] x ∈ X, Φ x) ⊣⊢ (∀ x, ⌜x ∈ X⌝ → Φ x).
   Proof.
     intros. apply (anti_symm _).
     { apply forall_intro=> x.

theories/base_logic/derived.v

@@ -16,13 +16,13 @@ Notation "▷? p P" := (uPred_laterN (Nat.b2n p) P)
   (at level 20, p at level 9, P at level 20,
    format "▷? p  P") : uPred_scope.
 
-Definition uPred_always_if {M} (c p : bool) (P : uPred M) : uPred M :=
+Definition uPred_always_if {M} (c : strength) (p : bool) (P : uPred M) : uPred M :=
   (if p then □{c} P else P)%I.
 Instance: Params (@uPred_always_if) 2.
 Arguments uPred_always_if _ _ !_ _/.
 Notation "□{ c }? p P" := (uPred_always_if c p P)
   (at level 20, c at next level, p at level 9, P at level 20, format "□{ c }? p  P").
-Notation "□? p P" := (uPred_always_if true p P)
+Notation "□? p P" := (uPred_always_if Weak p P)
   (at level 20, p at level 9, P at level 20, format "□? p  P").
 
 Definition uPred_except_0 {M} (P : uPred M) : uPred M := ▷ False ∨ P.
@@ -36,7 +36,7 @@ Arguments timelessP {_} _ {_}.
 Hint Mode TimelessP + ! : typeclass_instances.
 Instance: Params (@TimelessP) 1.
 
-Class PersistentP {M} (c : bool) (P : uPred M) := persistentP : P ⊢ □{c} P.
+Class PersistentP {M} (c : strength) (P : uPred M) := persistentP : P ⊢ □{c} P.
 Arguments persistentP {_} _ _ {_}.
 Hint Mode PersistentP + + ! : typeclass_instances.
 Instance: Params (@PersistentP) 2.
@@ -743,7 +743,7 @@ Lemma except_0_sep P Q : ◇ (P ∗ Q) ⊣⊢ ◇ P ∗ ◇ Q.
 Proof.
   rewrite /uPred_except_0. apply (anti_symm _).
   - apply or_elim; last by auto.
-    by rewrite -!or_intro_l -(always_pure true) -always_later -always_sep_dup'.
+    by rewrite -!or_intro_l -(always_pure Weak) -always_later -always_sep_dup'.
   - rewrite sep_or_r sep_elim_l sep_or_l; auto.
 Qed.
 Lemma except_0_forall {A} (Φ : A → uPred M) : ◇ (∀ a, Φ a) ⊢ ∀ a, ◇ Φ a.
@@ -840,7 +840,7 @@ Proof.
   apply or_mono, wand_intro_l; first done.
   rewrite -{2}(löb Q); apply impl_intro_l.
   rewrite HQ /uPred_except_0 !and_or_r. apply or_elim; last auto.
-  rewrite -(always_pure true) -always_later always_and_sep_l'.
+  rewrite -(always_pure Weak) -always_later always_and_sep_l'.
   by rewrite assoc (comm _ _ P) -assoc -always_and_sep_l' impl_elim_r wand_elim_r.
 Qed.
 Global Instance forall_timeless {A} (Ψ : A → uPred M) :
@@ -885,7 +885,7 @@ Global Instance limit_preserving_PersistentP
   NonExpansive Φ → LimitPreserving (λ x, PersistentP c (Φ x)).
 Proof. intros. apply limit_preserving_entails; solve_proper. Qed.
 
-Lemma persistent_mask_weaken P : PersistentP false P → PersistentP true P.
+Lemma persistent_strength_weaken P : PersistentP Strong P → PersistentP Weak P.
 Proof. rewrite /PersistentP=> HP. by rewrite {1}HP always_mask_mono. Qed.
 
 Lemma always_always c P `{!PersistentP c P} : □{c} P ⊣⊢ P.
@@ -894,43 +894,43 @@ Lemma always_if_always c p P `{!PersistentP c P} : □{c}?p P ⊣⊢ P.
 Proof. destruct p; simpl; auto using always_always. Qed.
 Lemma always_intro c P Q `{!PersistentP c P} : (P ⊢ Q) → P ⊢ □{c} Q.
 Proof. rewrite -(always_always c P); apply always_intro'. Qed.
-Lemma always_and_sep_l P Q `{!PersistentP true P} : P ∧ Q ⊣⊢ P ∗ Q.
-Proof. by rewrite -(always_always true P) always_and_sep_l'. Qed.
-Lemma always_and_sep_r P Q `{!PersistentP true Q} : P ∧ Q ⊣⊢ P ∗ Q.
-Proof. by rewrite -(always_always true Q) always_and_sep_r'. Qed.
-Lemma always_sep_dup P `{!PersistentP true P} : P ⊣⊢ P ∗ P.
-Proof. by rewrite -(always_always true P) -always_sep_dup'. Qed.
-Lemma always_entails_l P Q `{!PersistentP true Q} : (P ⊢ Q) → P ⊢ Q ∗ P.
-Proof. by rewrite -(always_always true Q); apply always_entails_l'. Qed.
-Lemma always_entails_r P Q `{!PersistentP true Q} : (P ⊢ Q) → P ⊢ P ∗ Q.
-Proof. by rewrite -(always_always true Q); apply always_entails_r'. Qed.
-Lemma always_impl_wand P `{!PersistentP true P} Q : (P → Q) ⊣⊢ (P -∗ Q).
+Lemma always_and_sep_l P Q `{!PersistentP Weak P} : P ∧ Q ⊣⊢ P ∗ Q.
+Proof. by rewrite -(always_always Weak P) always_and_sep_l'. Qed.
+Lemma always_and_sep_r P Q `{!PersistentP Weak Q} : P ∧ Q ⊣⊢ P ∗ Q.
+Proof. by rewrite -(always_always Weak Q) always_and_sep_r'. Qed.
+Lemma always_sep_dup P `{!PersistentP Weak P} : P ⊣⊢ P ∗ P.
+Proof. by rewrite -(always_always Weak P) -always_sep_dup'. Qed.
+Lemma always_entails_l P Q `{!PersistentP Weak Q} : (P ⊢ Q) → P ⊢ Q ∗ P.
+Proof. by rewrite -(always_always Weak Q); apply always_entails_l'. Qed.
+Lemma always_entails_r P Q `{!PersistentP Weak Q} : (P ⊢ Q) → P ⊢ P ∗ Q.
+Proof. by rewrite -(always_always Weak Q); apply always_entails_r'. Qed.
+Lemma always_impl_wand P `{!PersistentP Weak P} Q : (P → Q) ⊣⊢ (P -∗ Q).
 Proof.
   apply (anti_symm _); auto using impl_wand.
   apply impl_intro_l. by rewrite always_and_sep_l wand_elim_r.
 Qed.
 
-Lemma bupd_persistent P `{!PersistentP false P} : (|==> P) ⊢ P.
-Proof. by rewrite -{1}(always_always false P) bupd_always. Qed.
+Lemma bupd_persistent P `{!PersistentP Strong P} : (|==> P) ⊢ P.
+Proof. by rewrite -{1}(always_always Strong P) bupd_always. Qed.
 
 (* Persistence *)
 Global Instance pure_persistent c φ : PersistentP c (⌜φ⌝ : uPred M)%I.
 Proof. by rewrite /PersistentP always_pure. Qed.
 Global Instance impl_persistent c P Q :
-  PersistentP false P → PersistentP c Q → PersistentP c (P → Q).
+  PersistentP Strong P → PersistentP c Q → PersistentP c (P → Q).
 Proof.
   rewrite /PersistentP=> HP HQ.
   rewrite {2}HP -always_impl_always. by rewrite -HQ always_elim.
 Qed.
 Global Instance wand_persistent c P Q :
-  PersistentP false P → PersistentP c Q → PersistentP c (P -∗ Q)%I.
+  PersistentP Strong P → PersistentP c Q → PersistentP c (P -∗ Q)%I.
 Proof.
   rewrite /PersistentP=> HP HQ.
-  by rewrite {2}HP -{1}(always_elim false P) !wand_impl_always -always_impl_always -HQ.
+  by rewrite {2}HP -{1}(always_elim Strong P) !wand_impl_always -always_impl_always -HQ.
 Qed.
 Global Instance always_persistent c P : PersistentP c (□{c} P).
 Proof. by apply always_intro'. Qed.
-Global Instance always_persistent' c P : PersistentP true (□{c} P).
+Global Instance always_persistent' c P : PersistentP Weak (□{c} P).
 Proof. by rewrite /PersistentP always_idemp'. Qed.
 Global Instance and_persistent c P Q :
   PersistentP c P → PersistentP c Q → PersistentP c (P ∧ Q).
@@ -959,7 +959,7 @@ Global Instance except_0_persistent c P : PersistentP c P → PersistentP c (◇
 Proof. by intros; rewrite /PersistentP -except_0_always; apply except_0_mono. Qed.
 Global Instance laterN_persistent c n P : PersistentP c P → PersistentP c (▷^n P).
 Proof. induction n; apply _. Qed.
-Global Instance ownM_persistent : Persistent a → PersistentP true (@uPred_ownM M a).
+Global Instance ownM_persistent : Persistent a → PersistentP Weak (@uPred_ownM M a).
 Proof. intros. by rewrite /PersistentP always_ownM. Qed.
 Global Instance from_option_persistent {A} c P (Ψ : A → uPred M) (mx : option A) :
   (∀ x, PersistentP c (Ψ x)) → PersistentP c P → PersistentP c (from_option Ψ P mx).
@@ -1033,4 +1033,4 @@ the instance at any node in the proof search tree.
 To avoid that, we declare it using a [Hint Immediate], so that it will only be
 used at the leaves of the proof search tree, i.e. when the premise of the hint
 can be derived from just the current context. *)
-Hint Immediate uPred.persistent_mask_weaken : typeclass_instances.
+Hint Immediate uPred.persistent_strength_weaken : typeclass_instances.

theories/base_logic/lib/auth.v

@@ -33,7 +33,7 @@ Section definitions.
   Global Instance auth_own_timeless a : TimelessP (auth_own a).
   Proof. apply _. Qed.
   Global Instance auth_own_persistent a :
-    Persistent a → PersistentP true (auth_own a).
+    Persistent a → PersistentP Weak (auth_own a).
   Proof. apply _. Qed.
 
   Global Instance auth_inv_ne n :
@@ -52,7 +52,7 @@ Section definitions.
     Proper (pointwise_relation T (≡) ==>
             pointwise_relation T (⊣⊢) ==> (⊣⊢)) (auth_ctx N).
   Proof. solve_proper. Qed.
-  Global Instance auth_ctx_persistent N f φ : PersistentP true (auth_ctx N f φ).
+  Global Instance auth_ctx_persistent N f φ : PersistentP Weak (auth_ctx N f φ).
   Proof. apply _. Qed.
 End definitions.
 

theories/base_logic/lib/boxes.v

@@ -65,7 +65,7 @@ Proof. solve_contractive. Qed.
 Global Instance slice_proper γ : Proper ((≡) ==> (≡)) (slice N γ).
 Proof. apply ne_proper, _. Qed.
 
-Global Instance slice_persistent γ P : PersistentP true (slice N γ P).
+Global Instance slice_persistent γ P : PersistentP Weak (slice N γ P).
 Proof. apply _. Qed.
 
 Global Instance box_contractive f : Contractive (box N f).

theories/base_logic/lib/cancelable_invariants.v

@@ -34,7 +34,7 @@ Section proofs.
   Global Instance cinv_proper N γ : Proper ((≡) ==> (≡)) (cinv N γ).
   Proof. exact: ne_proper. Qed.
 
-  Global Instance cinv_persistent N γ P : PersistentP true (cinv N γ P).
+  Global Instance cinv_persistent N γ P : PersistentP Weak (cinv N γ P).
   Proof. rewrite /cinv; apply _. Qed.
 
   Global Instance cinv_own_fractionnal γ : Fractional (cinv_own γ).

theories/base_logic/lib/core.v

@@ -5,7 +5,7 @@ Import uPred.
 
 (** The "core" of an assertion is its maximal persistent part. *)
 Definition coreP {M : ucmraT} (P : uPred M) : uPred M :=
-  (∀ Q, □{false} (Q → □ Q) → □{false} (P → Q) → Q)%I.
+  (∀ Q, □{Strong} (Q → □ Q) → □{Strong} (P → Q) → Q)%I.
 Instance: Params (@coreP) 1.
 Typeclasses Opaque coreP.
 
@@ -16,7 +16,7 @@ Section core.
   Lemma coreP_intro P : P -∗ coreP P.
   Proof. iIntros "HP". iIntros (Q) "_ HPQ". by iApply "HPQ". Qed.
 
-  Global Instance coreP_persistent P : PersistentP true (coreP P).
+  Global Instance coreP_persistent P : PersistentP Weak (coreP P).
   Proof.
     rewrite /coreP /PersistentP. iIntros "HC".
     iApply always_forall. iIntros (Q). (* FIXME: iIntros should apply always_forall automatically. *)
@@ -36,7 +36,7 @@ Section core.
     iApply ("H" $! Q with "[]"); first done. by rewrite HP.
   Qed.
 
-  Lemma coreP_elim P : PersistentP true P → coreP P -∗ P.
+  Lemma coreP_elim P : PersistentP Weak P → coreP P -∗ P.
   Proof. rewrite /coreP. iIntros (?) "HCP". iApply ("HCP" $! P); auto. Qed.
 
   Lemma coreP_wand P Q : (coreP P ⊢ Q) ↔ (P ⊢ □ Q).

theories/base_logic/lib/counter_examples.v

@@ -12,7 +12,7 @@ Module savedprop. Section savedprop.
 
   (** Saved Propositions and the update modality *)
   Context (sprop : Type) (saved : sprop → iProp → iProp).
-  Hypothesis sprop_persistent : ∀ i P, PersistentP true (saved i P).
+  Hypothesis sprop_persistent : ∀ i P, PersistentP Weak (saved i P).
   Hypothesis sprop_alloc_dep :
     ∀ (P : sprop → iProp), (|==> (∃ i, saved i (P i)))%I.
   Hypothesis sprop_agree : ∀ i P Q, saved i P ∧ saved i Q ⊢ □ (P ↔ Q).
@@ -67,7 +67,7 @@ Module inv. Section inv.
 
   (** We have invariants *)
   Context (name : Type) (inv : name → iProp → iProp).
-  Hypothesis inv_persistent : ∀ i P, PersistentP true (inv i P).
+  Hypothesis inv_persistent : ∀ i P, PersistentP Weak (inv i P).
   Hypothesis inv_alloc : ∀ P, P ⊢ fupd M1 (∃ i, inv i P).
   Hypothesis inv_open :
     ∀ i P Q R, (P ∗ Q ⊢ fupd M0 (P ∗ R)) → (inv i P ∗ Q ⊢ fupd M1 R).
@@ -130,7 +130,7 @@ Module inv. Section inv.
   (** Now to the actual counterexample. We start with a weird form of saved propositions. *)
   Definition saved (γ : gname) (P : iProp) : iProp :=
     ∃ i, inv i (start γ ∨ (finished γ ∗ □ P)).
-  Global Instance saved_persistent γ P : PersistentP true (saved γ P) := _.
+  Global Instance saved_persistent γ P : PersistentP Weak (saved γ P) := _.
 
   Lemma saved_alloc (P : gname → iProp) : fupd M1 (∃ γ, saved γ (P γ)).
   Proof.
@@ -163,7 +163,7 @@ Module inv. Section inv.
   (** And now we tie a bad knot. *)
   Notation "¬ P" := (□ (P -∗ fupd M1 False))%I : uPred_scope.
   Definition A i : iProp := ∃ P, ¬P ∗ saved i P.
-  Global Instance A_persistent i : PersistentP true (A i) := _.
+  Global Instance A_persistent i : PersistentP Weak (A i) := _.
 
   Lemma A_alloc : fupd M1 (∃ i, saved i (A i)).
   Proof. by apply saved_alloc. Qed.

theories/base_logic/lib/fancy_updates.v

@@ -141,7 +141,7 @@ Proof.
   intros P1 P2 HP Q1 Q2 HQ. by rewrite HP HQ -fupd_sep.
 Qed.
 
-Lemma fupd_persistent' {E1 E2 E2'} P Q `{!PersistentP false P} :
+Lemma fupd_persistent' {E1 E2 E2'} P Q `{!PersistentP Strong P} :
   E1 ⊆ E2 →
   (Q ={E1, E2'}=∗ P) → (|={E1, E2}=> Q) ⊢ |={E1}=> ((|={E1, E2}=> Q) ∗ P).
 Proof.
@@ -159,7 +159,7 @@ Proof.
   iModIntro; iFrame; auto.
 Qed.
 
-Lemma fupd_plain {E1 E2} P Q `{!PersistentP false P} :
+Lemma fupd_plain {E1 E2} P Q `{!PersistentP Strong P} :
   E1 ⊆ E2 → (Q ⊢ P) → (|={E1, E2}=> Q) ⊢ |={E1}=> ((|={E1, E2}=> Q) ∗ P).
 Proof.
   iIntros (HE HQP) "HQ".
@@ -167,7 +167,7 @@ Proof.
   by iIntros "?"; iApply fupd_intro; iApply HQP.
 Qed.
 
-Lemma later_fupd_plain {E} P `{Hpl: !PersistentP false P} :
+Lemma later_fupd_plain {E} P `{Hpl: !PersistentP Strong P} :
   (▷ |={E}=> P) ⊢ |={E}=> ▷ ◇ P.
 Proof.
   iIntros "HP". rewrite fupd_eq /fupd_def.

theories/base_logic/lib/fancy_updates_from_vs.v

@@ -13,7 +13,7 @@ Notation "P ={ E1 , E2 }=> Q" := (vs E1 E2 P Q)
    format "P  ={ E1 , E2 }=>  Q") : uPred_scope.
 
 Context (vs_ne : ∀ E1 E2, NonExpansive2 (vs E1 E2)).
-Context (vs_persistent : ∀ E1 E2 P Q, PersistentP true (P ={E1,E2}=> Q)).
+Context (vs_persistent : ∀ E1 E2 P Q, PersistentP Weak (P ={E1,E2}=> Q)).
 
 Context (vs_impl : ∀ E P Q, □ (P → Q) ⊢ P ={E,E}=> Q).
 Context (vs_transitive : ∀ E1 E2 E3 P Q R,
@@ -24,7 +24,7 @@ Context (vs_frame_r : ∀ E1 E2 P Q R, (P ={E1,E2}=> Q) ⊢ P ∗ R ={E1,E2}=> Q
 Context (vs_exists : ∀ {A} E1 E2 (Φ : A → uPred M) Q,
   (∀ x, Φ x ={E1,E2}=> Q) ⊢ (∃ x, Φ x) ={E1,E2}=> Q).
 Context (vs_persistent_intro_r : ∀ E1 E2 P Q R,
-  PersistentP true R →
+  PersistentP Weak R →
   (R -∗ (P ={E1,E2}=> Q)) ⊢ P ∗ R ={E1,E2}=> Q).
 
 Definition fupd (E1 E2 : coPset) (P : uPred M) : uPred M :=

theories/base_logic/lib/fractional.v

@@ -50,7 +50,7 @@ Section fractional.
 
   (** Fractional and logical connectives *)
   Global Instance persistent_fractional P :
-    PersistentP true P → Fractional (λ _, P).
+    PersistentP Weak P → Fractional (λ _, P).
   Proof. intros HP q q'. by apply uPred.always_sep_dup. Qed.
 
   Global Instance fractional_sep Φ Ψ :

theories/base_logic/lib/invariants.v

@@ -31,7 +31,7 @@ Proof. apply contractive_ne, _. Qed.
 Global Instance inv_Proper N : Proper ((⊣⊢) ==> (⊣⊢)) (inv N).
 Proof. apply ne_proper, _. Qed.
 
-Global Instance inv_persistent N P : PersistentP true (inv N P).
+Global Instance inv_persistent N P : PersistentP Weak (inv N P).
 Proof. rewrite inv_eq /inv; apply _. Qed.
 
 Lemma fresh_inv_name (E : gset positive) N : ∃ i, i ∉ E ∧ i ∈ (↑N:coPset).

theories/base_logic/lib/na_invariants.v

@@ -40,7 +40,7 @@ Section proofs.
   Global Instance na_inv_proper p N : Proper ((≡) ==> (≡)) (na_inv p N).
   Proof. apply (ne_proper _). Qed.
 
-  Global Instance na_inv_persistent p N P : PersistentP true (na_inv p N P).
+  Global Instance na_inv_persistent p N P : PersistentP Weak (na_inv p N P).
   Proof. rewrite /na_inv; apply _. Qed.
 
   Lemma na_alloc : (|==> ∃ p, na_own p ⊤)%I.

theories/base_logic/lib/own.v

@@ -108,7 +108,7 @@ Proof. by rewrite comm -own_valid_r. Qed.
 
 Global Instance own_timeless γ a : Timeless a → TimelessP (own γ a).
 Proof. rewrite !own_eq /own_def; apply _. Qed.
-Global Instance own_core_persistent γ a : Persistent a → PersistentP true (own γ a).
+Global Instance own_core_persistent γ a : Persistent a → PersistentP Weak (own γ a).
 Proof. rewrite !own_eq /own_def; apply _. Qed.
 
 (** ** Allocation *)

theories/base_logic/lib/saved_prop.v

@@ -24,7 +24,7 @@ Section saved_prop.
   Implicit Types γ : gname.
 
   Global Instance saved_prop_persistent γ x :
-    PersistentP true (saved_prop_own γ x).
+    PersistentP Weak (saved_prop_own γ x).
   Proof. rewrite /saved_prop_own; apply _. Qed.
 
   Lemma saved_prop_alloc_strong x (G : gset gname) :

theories/base_logic/lib/sts.v

@@ -43,11 +43,11 @@ Section definitions.
   Global Instance sts_ctx_proper `{!invG Σ} N :
     Proper (pointwise_relation _ (≡) ==> (⊣⊢)) (sts_ctx N).
   Proof. solve_proper. Qed.
-  Global Instance sts_ctx_persistent `{!invG Σ} N φ : PersistentP true (sts_ctx N φ).
+  Global Instance sts_ctx_persistent `{!invG Σ} N φ : PersistentP Weak (sts_ctx N φ).
   Proof. apply _. Qed.
-  Global Instance sts_own_persistent s : PersistentP true (sts_own s ∅).
+  Global Instance sts_own_persistent s : PersistentP Weak (sts_own s ∅).
   Proof. apply _. Qed.
-  Global Instance sts_ownS_persistent S : PersistentP true (sts_ownS S ∅).
+  Global Instance sts_ownS_persistent S : PersistentP Weak (sts_ownS S ∅).
   Proof. apply _. Qed.
 End definitions.
 

theories/base_logic/lib/wsat.v

@@ -49,7 +49,7 @@ Instance invariant_unfold_contractive : Contractive (@invariant_unfold Σ).
 Proof. solve_contractive. Qed.
 Global Instance ownI_contractive i : Contractive (@ownI Σ _ i).
 Proof. solve_contractive. Qed.
-Global Instance ownI_persistent i P : PersistentP true (ownI i P).
+Global Instance ownI_persistent i P : PersistentP Weak (ownI i P).
 Proof. rewrite /ownI. apply _. Qed.
 
 Lemma ownE_empty : (|==> ownE ∅)%I.

theories/base_logic/primitive.v

@@ -97,8 +97,9 @@ Definition uPred_wand {M} := unseal uPred_wand_aux M.
 Definition uPred_wand_eq :
   @uPred_wand = @uPred_wand_def := seal_eq uPred_wand_aux.
 
-Program Definition uPred_always_def {M} (c : bool) (P : uPred M) : uPred M :=
-  {| uPred_holds n x := P n (if c then core x else ε) |}.
+Inductive strength := Weak | Strong.
+Program Definition uPred_always_def {M} (c : strength) (P : uPred M) : uPred M :=
+  {| uPred_holds n x := P n (if c is Weak return _ then core x else ε) |}.
 Next Obligation.
   intros M []; naive_solver eauto using uPred_mono, @cmra_core_monoN.
 Qed.
@@ -181,10 +182,8 @@ Notation "∃ x .. y , P" :=
   (at level 200, x binder, y binder, right associativity) : uPred_scope.
 Notation "□{ c } P" := (uPred_always c P)
   (at level 20, c at next level, right associativity, format "□{ c }  P") : uPred_scope.
-
-Notation "□ P" := (□{true} P)%I
+Notation "□ P" := (□{Weak} P)%I
   (at level 20, right associativity) : uPred_scope.
-
 Notation "▷ P" := (uPred_later P)
   (at level 20, right associativity) : uPred_scope.
 Infix "≡" := uPred_internal_eq : uPred_scope.
@@ -436,7 +435,7 @@ Proof.
   intros HP; unseal; split=> n x ? /=.
   apply HP; destruct c; auto using ucmra_unit_validN, cmra_core_validN.
 Qed.
-Lemma always_mask_mono P : □{false} P ⊢ □ P.
+Lemma always_mask_mono P : □{Strong} P ⊢ □ P.
 Proof. unseal; split; simpl; eauto using uPred_mono, @ucmra_unit_leastN. Qed.
 Lemma always_elim' P : □ P ⊢ P.
 Proof.
@@ -451,19 +450,19 @@ Proof. by unseal. Qed.
 Lemma always_exist_1 {A} c (Ψ : A → uPred M) : (□{c} ∃ a, Ψ a) ⊢ (∃ a, □{c} Ψ a).
 Proof. by unseal. Qed.
 
-Lemma prop_ext P Q : □{false} ((P → Q) ∧ (Q → P)) ⊢ P ≡ Q.
+Lemma prop_ext P Q : □{Strong} ((P → Q) ∧ (Q → P)) ⊢ P ≡ Q.
 Proof.
   unseal; split=> n x ? /= HPQ; split=> n' x' ? HP;
     split; eapply HPQ; eauto using @ucmra_unit_least.
 Qed.
 
-Lemma always_and_sep_l_1' P Q : □{true} P ∧ Q ⊢ □{true} P ∗ Q.
+Lemma always_and_sep_l_1' P Q : □ P ∧ Q ⊢ □ P ∗ Q.
 Proof.
   unseal; split=> n x ? [??]; exists (core x), x; simpl in *.
   by rewrite cmra_core_l cmra_core_idemp.
 Qed.
 
-Lemma always_impl_always c P Q : (□{false} P → □{c} Q) ⊢ □{c} (□{false} P → Q).
+Lemma always_impl_always c P Q : (□{Strong} P → □{c} Q) ⊢ □{c} (□{Strong} P → Q).
 Proof.
   unseal; split=> /= n x ? HPQ n' x' ????. destruct c.
   - eapply uPred_mono with (core x), cmra_included_includedN; auto.
@@ -541,7 +540,7 @@ Lemma cmra_valid_intro {A : cmraT} (a : A) : ✓ a → uPred_valid (M:=M) (✓ a
 Proof. unseal=> ?; split=> n x ? _ /=; by apply cmra_valid_validN. Qed.
 Lemma cmra_valid_elim {A : cmraT} (a : A) : ¬ ✓{0} a → ✓ a ⊢ False.
 Proof. unseal=> Ha; split=> n x ??; apply Ha, cmra_validN_le with n; auto. Qed.
-Lemma always_cmra_valid_1' {A : cmraT} (a : A) : ✓ a ⊢ □{false} ✓ a.
+Lemma always_cmra_valid_1' {A : cmraT} (a : A) : ✓ a ⊢ □{Strong} ✓ a.
 Proof. by unseal. Qed.
 Lemma cmra_valid_weaken {A : cmraT} (a b : A) : ✓ (a ⋅ b) ⊢ ✓ a.
 Proof. unseal; split=> n x _; apply cmra_validN_op_l. Qed.
@@ -578,7 +577,7 @@ Proof.
   exists (y ⋅ x3); split; first by rewrite -assoc.
   exists y; eauto using cmra_includedN_l.
 Qed.
-Lemma bupd_always P : (|==> □{false} P) ⊢ P.
+Lemma bupd_always P : (|==> □{Strong} P) ⊢ P.
 Proof.
   unseal; split => n x Hnx /= Hng.
   destruct (Hng n ε) as [? [_ Hng']]; try rewrite right_id; auto.

theories/heap_lang/lib/counter.v

@@ -29,7 +29,7 @@ Section mono_proof.
     (∃ γ, inv N (mcounter_inv γ l) ∧ own γ (◯ (n : mnat)))%I.
 
   (** The main proofs. *)
-  Global Instance mcounter_persistent l n : PersistentP true (mcounter l n).
+  Global Instance mcounter_persistent l n : PersistentP Weak (mcounter l n).
   Proof. apply _. Qed.
 
   Lemma newcounter_mono_spec :

theories/heap_lang/lib/lock.v

@@ -14,7 +14,7 @@ Structure lock Σ `{!heapG Σ} := Lock {
   locked (γ: name) : iProp Σ;
   (* -- general properties -- *)
   is_lock_ne N γ lk : NonExpansive (is_lock N γ lk);
-  is_lock_persistent N γ lk R : PersistentP true (is_lock N γ lk R);
+  is_lock_persistent N γ lk R : PersistentP Weak (is_lock N γ lk R);
   locked_timeless γ : TimelessP (locked γ);
   locked_exclusive γ : locked γ -∗ locked γ -∗ False;
   (* -- operation specs -- *)

theories/heap_lang/lib/spin_lock.v

@@ -40,7 +40,7 @@ Section proof.
   Proof. solve_proper. Qed.
 
   (** The main proofs. *)
-  Global Instance is_lock_persistent γ l R : PersistentP true (is_lock γ l R).
+  Global Instance is_lock_persistent γ l R : PersistentP Weak (is_lock γ l R).
   Proof. apply _. Qed.
   Global Instance locked_timeless γ : TimelessP (locked γ).
   Proof. apply _. Qed.