Change some names related to the global ghost CMRA around

globalC -> globalF
New notation: iPropG, iFunctorG

program_logic/auth.v

@@ -4,11 +4,10 @@ Import uPred.
 
 Section auth.
   Context {A : cmraT} `{Empty A, !CMRAIdentity A} `{!∀ a : A, Timeless a}.
-  Context {Λ : language} {Σ : gid → iFunctor} (AuthI : gid) `{!InG Λ Σ AuthI (authRA A)}.
-  (* TODO: Come up with notation for "iProp Λ (globalC Σ)". *)
-  Context (N : namespace) (φ : A → iProp Λ (globalC Σ)).
+  Context {Λ : language} {Σ : iFunctorG} (AuthI : gid) `{!InG Λ Σ AuthI (authRA A)}.
+  Context (N : namespace) (φ : A → iPropG Λ Σ).
 
-  Implicit Types P Q R : iProp Λ (globalC Σ).
+  Implicit Types P Q R : iPropG Λ Σ.
   Implicit Types a b : A.
   Implicit Types γ : gname.
 
@@ -23,12 +22,12 @@ Section auth.
   (* TODO: Need this to be proven somewhere. *)
   (* FIXME ✓ binds too strong, I need parenthesis here. *)
   Hypothesis auth_valid :
-    forall a b, (✓ (Auth (Excl a) b) : iProp Λ (globalC Σ)) ⊑ (∃ b', a ≡ b ⋅ b').
+    forall a b, (✓ (Auth (Excl a) b) : iPropG Λ Σ) ⊑ (∃ b', a ≡ b ⋅ b').
 
-  Definition auth_inv (γ : gname) : iProp Λ (globalC Σ) :=
+  Definition auth_inv (γ : gname) : iPropG Λ Σ :=
     (∃ a, own AuthI γ (● a) ★ φ a)%I.
-  Definition auth_own (γ : gname) (a : A) : iProp Λ (globalC Σ) := own AuthI γ (◯ a).
-  Definition auth_ctx (γ : gname) : iProp Λ (globalC Σ) := inv N (auth_inv γ).
+  Definition auth_own (γ : gname) (a : A) : iPropG Λ Σ := own AuthI γ (◯ a).
+  Definition auth_ctx (γ : gname) : iPropG Λ Σ := inv N (auth_inv γ).
 
   Lemma auth_alloc a :
     ✓a → φ a ⊑ pvs N N (∃ γ, auth_ctx γ ∧ auth_own γ a).
@@ -78,7 +77,7 @@ Section auth.
      step-indices. However, since A is timeless, that should not be
      a restriction.  *)
   Lemma auth_fsa {X : Type} {FSA} (FSAs : FrameShiftAssertion (A:=X) FSA)
-        `{!LocalUpdate Lv L} E P (Q : X → iProp Λ (globalC Σ)) γ a :
+        `{!LocalUpdate Lv L} E P (Q : X → iPropG Λ Σ) γ a :
     nclose N ⊆ E →
     (auth_ctx γ ★ auth_own γ a ★ (∀ a', ▷φ (a ⋅ a') -★
         FSA (E ∖ nclose N) (λ x, ■(Lv a ∧ ✓(L a⋅a')) ★ ▷φ (L a ⋅ a') ★ (auth_own γ (L a) -★ Q x))))

program_logic/ghost_ownership.v

@@ -7,52 +7,55 @@ Definition gid := nat.
 (** Name of one instance of a particular CMRA in the ghost state. *)
 Definition gname := positive.
 (** The global CMRA: Indexed product over a gid i to (gname --fin--> Σ i) *)
-Definition globalC (Σ : gid → iFunctor) : iFunctor :=
+Definition globalF (Σ : gid → iFunctor) : iFunctor :=
   iprodF (λ i, mapF gname (Σ i)).
 
 Class InG (Λ : language) (Σ : gid → iFunctor) (i : gid) (A : cmraT) :=
-  inG : A = Σ i (laterC (iPreProp Λ (globalC Σ))).
+  inG : A = Σ i (laterC (iPreProp Λ (globalF Σ))).
 
-Definition to_globalC {Λ Σ A}
-    (i : gid) `{!InG Λ Σ i A} (γ : gname) (a : A) : iGst Λ (globalC Σ) :=
+Definition to_globalF {Λ Σ A}
+    (i : gid) `{!InG Λ Σ i A} (γ : gname) (a : A) : iGst Λ (globalF Σ) :=
   iprod_singleton i {[ γ ↦ cmra_transport inG a ]}.
 Definition own {Λ Σ A}
-    (i : gid) `{!InG Λ Σ i A} (γ : gname) (a : A) : iProp Λ (globalC Σ) :=
-  ownG (to_globalC i γ a).
-Instance: Params (@to_globalC) 6.
+    (i : gid) `{!InG Λ Σ i A} (γ : gname) (a : A) : iProp Λ (globalF Σ) :=
+  ownG (to_globalF i γ a).
+Instance: Params (@to_globalF) 6.
 Instance: Params (@own) 6.
-Typeclasses Opaque to_globalC own.
+Typeclasses Opaque to_globalF own.
+
+Notation iPropG Λ Σ := (iProp Λ (globalF Σ)).
+Notation iFunctorG := (gid → iFunctor).
 
 Section global.
-Context {Λ : language} {Σ : gid → iFunctor} (i : gid) `{!InG Λ Σ i A}.
+Context {Λ : language} {Σ : iFunctorG} (i : gid) `{!InG Λ Σ i A}.
 Implicit Types a : A.
 
 (** * Properties of to_globalC *)
-Instance to_globalC_ne γ n : Proper (dist n ==> dist n) (to_globalC i γ).
+Instance to_globalF_ne γ n : Proper (dist n ==> dist n) (to_globalF i γ).
 Proof. by intros a a' Ha; apply iprod_singleton_ne; rewrite Ha. Qed.
-Lemma to_globalC_validN n γ a : ✓{n} (to_globalC i γ a) ↔ ✓{n} a.
+Lemma to_globalF_validN n γ a : ✓{n} (to_globalF i γ a) ↔ ✓{n} a.
 Proof.
-  by rewrite /to_globalC
+  by rewrite /to_globalF
     iprod_singleton_validN map_singleton_validN cmra_transport_validN.
 Qed.
-Lemma to_globalC_op γ a1 a2 :
-  to_globalC i γ (a1 ⋅ a2) ≡ to_globalC i γ a1 ⋅ to_globalC i γ a2.
+Lemma to_globalF_op γ a1 a2 :
+  to_globalF i γ (a1 ⋅ a2) ≡ to_globalF i γ a1 ⋅ to_globalF i γ a2.
 Proof.
-  by rewrite /to_globalC iprod_op_singleton map_op_singleton cmra_transport_op.
+  by rewrite /to_globalF iprod_op_singleton map_op_singleton cmra_transport_op.
 Qed.
-Lemma to_globalC_unit γ a : unit (to_globalC i γ a) ≡ to_globalC i γ (unit a).
+Lemma to_globalF_unit γ a : unit (to_globalF i γ a) ≡ to_globalF i γ (unit a).
 Proof.
-  by rewrite /to_globalC
+  by rewrite /to_globalF
     iprod_unit_singleton map_unit_singleton cmra_transport_unit.
 Qed.
-Instance to_globalC_timeless γ m : Timeless m → Timeless (to_globalC i γ m).
-Proof. rewrite /to_globalC; apply _. Qed.
+Instance to_globalF_timeless γ m : Timeless m → Timeless (to_globalF i γ m).
+Proof. rewrite /to_globalF; apply _. Qed.
 
 (** * Transport empty *)
-Instance inG_empty `{Empty A} : Empty (Σ i (laterC (iPreProp Λ (globalC Σ)))) :=
+Instance inG_empty `{Empty A} : Empty (Σ i (laterC (iPreProp Λ (globalF Σ)))) :=
   cmra_transport inG ∅.
 Instance inG_empty_spec `{Empty A} :
-  CMRAIdentity A → CMRAIdentity (Σ i (laterC (iPreProp Λ (globalC Σ)))).
+  CMRAIdentity A → CMRAIdentity (Σ i (laterC (iPreProp Λ (globalF Σ)))).
 Proof.
   split.
   * apply cmra_transport_valid, cmra_empty_valid.
@@ -66,12 +69,12 @@ Proof. by intros m m' Hm; rewrite /own Hm. Qed.
 Global Instance own_proper γ : Proper ((≡) ==> (≡)) (own i γ) := ne_proper _.
 
 Lemma own_op γ a1 a2 : own i γ (a1 ⋅ a2) ≡ (own i γ a1 ★ own i γ a2)%I.
-Proof. by rewrite /own -ownG_op to_globalC_op. Qed.
+Proof. by rewrite /own -ownG_op to_globalF_op. Qed.
 Lemma always_own_unit γ a : (□ own i γ (unit a))%I ≡ own i γ (unit a).
-Proof. by rewrite /own -to_globalC_unit always_ownG_unit. Qed.
+Proof. by rewrite /own -to_globalF_unit always_ownG_unit. Qed.
 Lemma own_valid γ a : own i γ a ⊑ ✓ a.
 Proof.
-  rewrite /own ownG_valid; apply valid_mono=> ?; apply to_globalC_validN.
+  rewrite /own ownG_valid; apply valid_mono=> ?; apply to_globalF_validN.
 Qed.
 Lemma own_valid_r γ a : own i γ a ⊑ (own i γ a ★ ✓ a).
 Proof. apply (uPred.always_entails_r' _ _), own_valid. Qed.
@@ -83,7 +86,7 @@ Proof. unfold own; apply _. Qed.
 Lemma own_alloc a E : ✓ a → True ⊑ pvs E E (∃ γ, own i γ a).
 Proof.
   intros Ha.
-  rewrite -(pvs_mono _ _ (∃ m, ■ (∃ γ, m = to_globalC i γ a) ∧ ownG m)%I).
+  rewrite -(pvs_mono _ _ (∃ m, ■ (∃ γ, m = to_globalF i γ a) ∧ ownG m)%I).
   * eapply pvs_ownG_updateP_empty, (iprod_singleton_updateP_empty i);
       first (eapply map_updateP_alloc', cmra_transport_valid, Ha); naive_solver.
   * apply exist_elim=>m; apply const_elim_l=>-[γ ->].
@@ -94,7 +97,7 @@ Lemma own_updateP γ a P E :
   a ~~>: P → own i γ a ⊑ pvs E E (∃ a', ■ P a' ∧ own i γ a').
 Proof.
   intros Ha.
-  rewrite -(pvs_mono _ _ (∃ m, ■ (∃ a', m = to_globalC i γ a' ∧ P a') ∧ ownG m)%I).
+  rewrite -(pvs_mono _ _ (∃ m, ■ (∃ a', m = to_globalF i γ a' ∧ P a') ∧ ownG m)%I).
   * eapply pvs_ownG_updateP, iprod_singleton_updateP;
       first by (eapply map_singleton_updateP', cmra_transport_updateP', Ha).
     naive_solver.
@@ -106,7 +109,7 @@ Lemma own_updateP_empty `{Empty A, !CMRAIdentity A} γ a P E :
   ∅ ~~>: P → True ⊑ pvs E E (∃ a, ■ P a ∧ own i γ a).
 Proof.
   intros Hemp.
-  rewrite -(pvs_mono _ _ (∃ m, ■ (∃ a', m = to_globalC i γ a' ∧ P a') ∧ ownG m)%I).
+  rewrite -(pvs_mono _ _ (∃ m, ■ (∃ a', m = to_globalF i γ a' ∧ P a') ∧ ownG m)%I).
   * eapply pvs_ownG_updateP_empty, iprod_singleton_updateP_empty;
       first eapply map_singleton_updateP_empty', cmra_transport_updateP', Hemp.
     naive_solver.

program_logic/viewshifts.v

@@ -105,9 +105,9 @@ Proof. by intros; apply vs_alt, inv_alloc. Qed.
 End vs.
 
 Section vs_ghost.
-Context {Λ : language} {Σ : gid → iFunctor} (i : gid) `{!InG Λ Σ i A}.
+Context {Λ : language} {Σ : iFunctorG} (i : gid) `{!InG Λ Σ i A}.
 Implicit Types a : A.
-Implicit Types P Q R : iProp Λ (globalC Σ).
+Implicit Types P Q R : iPropG Λ Σ.
 
 Lemma vs_own_updateP E γ a φ :
   a ~~>: φ → own i γ a ={E}=> ∃ a', ■ φ a' ∧ own i γ a'.