change frac_auth notation

CHANGELOG.md

@@ -143,6 +143,7 @@ Changes in Coq:
 * Add the camera `ufrac` for unbounded fractions (i.e. without fractions that
   can be `> 1`) and the camera `ufrac_auth` for a variant of the authoritative
   fractional camera (`frac_auth`) with unbounded fractions.
+* Changed `frac_auth` notation from `●!`/`◯!` to `●F`/`◯F`.
 
 ## Iris 3.1.0 (released 2017-12-19)
 

theories/algebra/frac_auth.v

@@ -24,9 +24,9 @@ Typeclasses Opaque frac_auth_auth frac_auth_frag.
 Instance: Params (@frac_auth_auth) 1 := {}.
 Instance: Params (@frac_auth_frag) 2 := {}.
 
-Notation "●! a" := (frac_auth_auth a) (at level 10).
-Notation "◯!{ q } a" := (frac_auth_frag q a) (at level 10, format "◯!{ q }  a").
-Notation "◯! a" := (frac_auth_frag 1 a) (at level 10).
+Notation "●F a" := (frac_auth_auth a) (at level 10).
+Notation "◯F{ q } a" := (frac_auth_frag q a) (at level 10, format "◯F{ q }  a").
+Notation "◯F a" := (frac_auth_frag 1 a) (at level 10).
 
 Section frac_auth.
   Context {A : cmraT}.
@@ -41,79 +41,79 @@ Section frac_auth.
   Global Instance frac_auth_frag_proper q : Proper ((≡) ==> (≡)) (@frac_auth_frag A q).
   Proof. solve_proper. Qed.
 
-  Global Instance frac_auth_auth_discrete a : Discrete a → Discrete (●! a).
+  Global Instance frac_auth_auth_discrete a : Discrete a → Discrete (●F a).
   Proof. intros; apply auth_auth_discrete; [apply Some_discrete|]; apply _. Qed.
-  Global Instance frac_auth_frag_discrete q a : Discrete a → Discrete (◯!{q} a).
+  Global Instance frac_auth_frag_discrete q a : Discrete a → Discrete (◯F{q} a).
   Proof. intros; apply auth_frag_discrete, Some_discrete; apply _. Qed.
 
-  Lemma frac_auth_validN n a : ✓{n} a → ✓{n} (●! a ⋅ ◯! a).
+  Lemma frac_auth_validN n a : ✓{n} a → ✓{n} (●F a ⋅ ◯F a).
   Proof. by rewrite auth_both_validN. Qed.
-  Lemma frac_auth_valid a : ✓ a → ✓ (●! a ⋅ ◯! a).
+  Lemma frac_auth_valid a : ✓ a → ✓ (●F a ⋅ ◯F a).
   Proof. intros. by apply auth_both_valid_2. Qed.
 
-  Lemma frac_auth_agreeN n a b : ✓{n} (●! a ⋅ ◯! b) → a ≡{n}≡ b.
+  Lemma frac_auth_agreeN n a b : ✓{n} (●F a ⋅ ◯F b) → a ≡{n}≡ b.
   Proof.
     rewrite auth_both_validN /= => -[Hincl Hvalid].
     by move: Hincl=> /Some_includedN_exclusive /(_ Hvalid ) [??].
   Qed.
-  Lemma frac_auth_agree a b : ✓ (●! a ⋅ ◯! b) → a ≡ b.
+  Lemma frac_auth_agree a b : ✓ (●F a ⋅ ◯F b) → a ≡ b.
   Proof.
     intros. apply equiv_dist=> n. by apply frac_auth_agreeN, cmra_valid_validN.
   Qed.
-  Lemma frac_auth_agreeL `{!LeibnizEquiv A} a b : ✓ (●! a ⋅ ◯! b) → a = b.
+  Lemma frac_auth_agreeL `{!LeibnizEquiv A} a b : ✓ (●F a ⋅ ◯F b) → a = b.
   Proof. intros. by apply leibniz_equiv, frac_auth_agree. Qed.
 
-  Lemma frac_auth_includedN n q a b : ✓{n} (●! a ⋅ ◯!{q} b) → Some b ≼{n} Some a.
+  Lemma frac_auth_includedN n q a b : ✓{n} (●F a ⋅ ◯F{q} b) → Some b ≼{n} Some a.
   Proof. by rewrite auth_both_validN /= => -[/Some_pair_includedN [_ ?] _]. Qed.
   Lemma frac_auth_included `{CmraDiscrete A} q a b :
-    ✓ (●! a ⋅ ◯!{q} b) → Some b ≼ Some a.
+    ✓ (●F a ⋅ ◯F{q} b) → Some b ≼ Some a.
   Proof. by rewrite auth_both_valid /= => -[/Some_pair_included [_ ?] _]. Qed.
   Lemma frac_auth_includedN_total `{CmraTotal A} n q a b :
-    ✓{n} (●! a ⋅ ◯!{q} b) → b ≼{n} a.
+    ✓{n} (●F a ⋅ ◯F{q} b) → b ≼{n} a.
   Proof. intros. by eapply Some_includedN_total, frac_auth_includedN. Qed.
   Lemma frac_auth_included_total `{CmraDiscrete A, CmraTotal A} q a b :
-    ✓ (●! a ⋅ ◯!{q} b) → b ≼ a.
+    ✓ (●F a ⋅ ◯F{q} b) → b ≼ a.
   Proof. intros. by eapply Some_included_total, frac_auth_included. Qed.
 
-  Lemma frac_auth_auth_validN n a : ✓{n} (●! a) ↔ ✓{n} a.
+  Lemma frac_auth_auth_validN n a : ✓{n} (●F a) ↔ ✓{n} a.
   Proof.
     rewrite auth_auth_frac_validN Some_validN. split.
     by intros [?[]]. intros. by split.
   Qed.
-  Lemma frac_auth_auth_valid a : ✓ (●! a) ↔ ✓ a.
+  Lemma frac_auth_auth_valid a : ✓ (●F a) ↔ ✓ a.
   Proof. rewrite !cmra_valid_validN. by setoid_rewrite frac_auth_auth_validN. Qed.
 
-  Lemma frac_auth_frag_validN n q a : ✓{n} (◯!{q} a) ↔ ✓{n} q ∧ ✓{n} a.
+  Lemma frac_auth_frag_validN n q a : ✓{n} (◯F{q} a) ↔ ✓{n} q ∧ ✓{n} a.
   Proof. done. Qed.
-  Lemma frac_auth_frag_valid q a : ✓ (◯!{q} a) ↔ ✓ q ∧ ✓ a.
+  Lemma frac_auth_frag_valid q a : ✓ (◯F{q} a) ↔ ✓ q ∧ ✓ a.
   Proof. done. Qed.
 
-  Lemma frac_auth_frag_op q1 q2 a1 a2 : ◯!{q1+q2} (a1 ⋅ a2) ≡ ◯!{q1} a1 ⋅ ◯!{q2} a2.
+  Lemma frac_auth_frag_op q1 q2 a1 a2 : ◯F{q1+q2} (a1 ⋅ a2) ≡ ◯F{q1} a1 ⋅ ◯F{q2} a2.
   Proof. done. Qed.
 
-  Lemma frac_auth_frag_validN_op_1_l n q a b : ✓{n} (◯!{1} a ⋅ ◯!{q} b) → False.
+  Lemma frac_auth_frag_validN_op_1_l n q a b : ✓{n} (◯F{1} a ⋅ ◯F{q} b) → False.
   Proof. rewrite -frac_auth_frag_op frac_auth_frag_validN=> -[/exclusiveN_l []]. Qed.
-  Lemma frac_auth_frag_valid_op_1_l q a b : ✓ (◯!{1} a ⋅ ◯!{q} b) → False.
+  Lemma frac_auth_frag_valid_op_1_l q a b : ✓ (◯F{1} a ⋅ ◯F{q} b) → False.
   Proof. rewrite -frac_auth_frag_op frac_auth_frag_valid=> -[/exclusive_l []]. Qed.
 
   Global Instance is_op_frac_auth (q q1 q2 : frac) (a a1 a2 : A) :
-    IsOp q q1 q2 → IsOp a a1 a2 → IsOp' (◯!{q} a) (◯!{q1} a1) (◯!{q2} a2).
+    IsOp q q1 q2 → IsOp a a1 a2 → IsOp' (◯F{q} a) (◯F{q1} a1) (◯F{q2} a2).
   Proof. by rewrite /IsOp' /IsOp=> /leibniz_equiv_iff -> ->. Qed.
 
   Global Instance is_op_frac_auth_core_id (q q1 q2 : frac) (a  : A) :
-    CoreId a → IsOp q q1 q2 → IsOp' (◯!{q} a) (◯!{q1} a) (◯!{q2} a).
+    CoreId a → IsOp q q1 q2 → IsOp' (◯F{q} a) (◯F{q1} a) (◯F{q2} a).
   Proof.
     rewrite /IsOp' /IsOp=> ? /leibniz_equiv_iff ->.
     by rewrite -frac_auth_frag_op -core_id_dup.
   Qed.
 
   Lemma frac_auth_update q a b a' b' :
-    (a,b) ~l~> (a',b') → ●! a ⋅ ◯!{q} b ~~> ●! a' ⋅ ◯!{q} b'.
+    (a,b) ~l~> (a',b') → ●F a ⋅ ◯F{q} b ~~> ●F a' ⋅ ◯F{q} b'.
   Proof.
     intros. by apply auth_update, option_local_update, prod_local_update_2.
   Qed.
 
-  Lemma frac_auth_update_1 a b a' : ✓ a' → ●! a ⋅ ◯! b ~~> ●! a' ⋅ ◯! a'.
+  Lemma frac_auth_update_1 a b a' : ✓ a' → ●F a ⋅ ◯F b ~~> ●F a' ⋅ ◯F a'.
   Proof.
     intros. by apply auth_update, option_local_update, exclusive_local_update.
   Qed.

theories/heap_lang/lib/counter.v

@@ -97,13 +97,13 @@ Section contrib_spec.
   Context `{!heapG Σ, !ccounterG Σ} (N : namespace).
 
   Definition ccounter_inv (γ : gname) (l : loc) : iProp Σ :=
-    (∃ n, own γ (●! n) ∗ l ↦ #n)%I.
+    (∃ n, own γ (●F n) ∗ l ↦ #n)%I.
 
   Definition ccounter_ctx (γ : gname) (l : loc) : iProp Σ :=
     inv N (ccounter_inv γ l).
 
   Definition ccounter (γ : gname) (q : frac) (n : nat) : iProp Σ :=
-    own γ (◯!{q} n).
+    own γ (◯F{q} n).
 
   (** The main proofs. *)
   Lemma ccounter_op γ q1 q2 n1 n2 :
@@ -115,7 +115,7 @@ Section contrib_spec.
     {{{ γ l, RET #l; ccounter_ctx γ l ∗ ccounter γ 1 0 }}}.
   Proof.
     iIntros (Φ) "_ HΦ". rewrite -wp_fupd /newcounter /=. wp_lam. wp_alloc l as "Hl".
-    iMod (own_alloc (●! O%nat ⋅ ◯! 0%nat)) as (γ) "[Hγ Hγ']";
+    iMod (own_alloc (●F O%nat ⋅ ◯F 0%nat)) as (γ) "[Hγ Hγ']";
       first by apply auth_both_valid.
     iMod (inv_alloc N _ (ccounter_inv γ l) with "[Hl Hγ]").
     { iNext. iExists 0%nat. by iFrame. }