Rename `Timeless` → `Discrete` (discrete OFE elements).

theories/algebra/agree.v

@@ -149,12 +149,12 @@ Proof. rewrite /CMRATotal; eauto. Qed.
 Global Instance agree_persistent (x : agree A) : Persistent x.
 Proof. by constructor. Qed.
 
-Global Instance agree_ofe_discrete : OFEDiscrete A → CMRADiscrete agreeR.
+Global Instance agree_cmra_discrete : OFEDiscrete A → CMRADiscrete agreeR.
 Proof.
   intros HD. split.
-  - intros x y [H H'] n; split=> a; setoid_rewrite <-(timeless_iff_0 _ _); auto.
+  - intros x y [H H'] n; split=> a; setoid_rewrite <-(discrete_iff_0 _ _); auto.
   - intros x; rewrite agree_validN_def=> Hv n. apply agree_validN_def=> a b ??.
-    apply timeless_iff_0; auto.
+    apply discrete_iff_0; auto.
 Qed.
 
 Program Definition to_agree (a : A) : agree A :=

theories/algebra/auth.v

@@ -49,9 +49,9 @@ Proof.
     (λ x, (authoritative x, auth_own x))); by repeat intro.
 Qed.
 
-Global Instance Auth_timeless a b :
-  Timeless a → Timeless b → Timeless (Auth a b).
-Proof. by intros ?? [??] [??]; split; apply: timeless. Qed.
+Global Instance Auth_discrete a b :
+  Discrete a → Discrete b → Discrete (Auth a b).
+Proof. by intros ?? [??] [??]; split; apply: discrete. Qed.
 Global Instance auth_ofe_discrete : OFEDiscrete A → OFEDiscrete authC.
 Proof. intros ? [??]; apply _. Qed.
 Global Instance auth_leibniz : LeibnizEquiv A → LeibnizEquiv (auth A).

theories/algebra/cmra.v

@@ -530,22 +530,22 @@ Section total_core.
   Qed.
 End total_core.
 
-(** ** Timeless *)
-Lemma cmra_timeless_included_l x y : Timeless x → ✓{0} y → x ≼{0} y → x ≼ y.
+(** ** Discrete *)
+Lemma cmra_discrete_included_l x y : Discrete x → ✓{0} y → x ≼{0} y → x ≼ y.
 Proof.
   intros ?? [x' ?].
   destruct (cmra_extend 0 y x x') as (z&z'&Hy&Hz&Hz'); auto; simpl in *.
-  by exists z'; rewrite Hy (timeless x z).
+  by exists z'; rewrite Hy (discrete x z).
 Qed.
-Lemma cmra_timeless_included_r x y : Timeless y → x ≼{0} y → x ≼ y.
-Proof. intros ? [x' ?]. exists x'. by apply (timeless y). Qed.
-Lemma cmra_op_timeless x1 x2 :
-  ✓ (x1 ⋅ x2) → Timeless x1 → Timeless x2 → Timeless (x1 ⋅ x2).
+Lemma cmra_discrete_included_r x y : Discrete y → x ≼{0} y → x ≼ y.
+Proof. intros ? [x' ?]. exists x'. by apply (discrete y). Qed.
+Lemma cmra_op_discrete x1 x2 :
+  ✓ (x1 ⋅ x2) → Discrete x1 → Discrete x2 → Discrete (x1 ⋅ x2).
 Proof.
   intros ??? z Hz.
   destruct (cmra_extend 0 z x1 x2) as (y1&y2&Hz'&?&?); auto; simpl in *.
   { rewrite -?Hz. by apply cmra_valid_validN. }
-  by rewrite Hz' (timeless x1 y1) // (timeless x2 y2).
+  by rewrite Hz' (discrete x1 y1) // (discrete x2 y2).
 Qed.
 
 (** ** Discrete *)
@@ -557,7 +557,7 @@ Qed.
 Lemma cmra_discrete_included_iff `{OFEDiscrete A} n x y : x ≼ y ↔ x ≼{n} y.
 Proof.
   split; first by apply cmra_included_includedN.
-  intros [z ->%(timeless_iff _ _)]; eauto using cmra_included_l.
+  intros [z ->%(discrete_iff _ _)]; eauto using cmra_included_l.
 Qed.
 
 (** Cancelable elements  *)
@@ -567,7 +567,7 @@ Lemma cancelable x `{!Cancelable x} y z : ✓(x ⋅ y) → x ⋅ y ≡ x ⋅ z
 Proof. rewrite !equiv_dist cmra_valid_validN. intros. by apply (cancelableN x). Qed.
 Lemma discrete_cancelable x `{CMRADiscrete A}:
   (∀ y z, ✓(x ⋅ y) → x ⋅ y ≡ x ⋅ z → y ≡ z) → Cancelable x.
-Proof. intros ????. rewrite -!timeless_iff -cmra_discrete_valid_iff. auto. Qed.
+Proof. intros ????. rewrite -!discrete_iff -cmra_discrete_valid_iff. auto. Qed.
 Global Instance cancelable_op x y :
   Cancelable x → Cancelable y → Cancelable (x ⋅ y).
 Proof.
@@ -598,7 +598,7 @@ Proof. rewrite comm. eauto using id_free_r. Qed.
 Lemma discrete_id_free x `{CMRADiscrete A}:
   (∀ y, ✓ x → x ⋅ y ≡ x → False) → IdFree x.
 Proof.
-  intros Hx y ??. apply (Hx y), (timeless _); eauto using cmra_discrete_valid.
+  intros Hx y ??. apply (Hx y), (discrete _); eauto using cmra_discrete_valid.
 Qed.
 Global Instance id_free_op_r x y : IdFree y → Cancelable x → IdFree (x ⋅ y).
 Proof.
@@ -845,7 +845,7 @@ Section cmra_transport.
   Proof. by destruct H. Qed.
   Lemma cmra_transport_valid x : ✓ T x ↔ ✓ x.
   Proof. by destruct H. Qed.
-  Global Instance cmra_transport_timeless x : Timeless x → Timeless (T x).
+  Global Instance cmra_transport_discrete x : Discrete x → Discrete (T x).
   Proof. by destruct H. Qed.
   Global Instance cmra_transport_persistent x : Persistent x → Persistent (T x).
   Proof. by destruct H. Qed.

theories/algebra/csum.v

@@ -97,15 +97,15 @@ Next Obligation.
 Qed.
 
 Global Instance csum_ofe_discrete : OFEDiscrete A → OFEDiscrete B → OFEDiscrete csumC.
-Proof. by inversion_clear 3; constructor; apply (timeless _). Qed.
+Proof. by inversion_clear 3; constructor; apply (discrete _). Qed.
 Global Instance csum_leibniz :
   LeibnizEquiv A → LeibnizEquiv B → LeibnizEquiv (csumC A B).
 Proof. by destruct 3; f_equal; apply leibniz_equiv. Qed.
 
-Global Instance Cinl_timeless a : Timeless a → Timeless (Cinl a).
-Proof. by inversion_clear 2; constructor; apply (timeless _). Qed.
-Global Instance Cinr_timeless b : Timeless b → Timeless (Cinr b).
-Proof. by inversion_clear 2; constructor; apply (timeless _). Qed.
+Global Instance Cinl_discrete a : Discrete a → Discrete (Cinl a).
+Proof. by inversion_clear 2; constructor; apply (discrete _). Qed.
+Global Instance Cinr_discrete b : Discrete b → Discrete (Cinr b).
+Proof. by inversion_clear 2; constructor; apply (discrete _). Qed.
 End cofe.
 
 Arguments csumC : clear implicits.

theories/algebra/excl.v

@@ -60,13 +60,13 @@ Proof.
 Qed.
 
 Global Instance excl_ofe_discrete : OFEDiscrete A → OFEDiscrete exclC.
-Proof. by inversion_clear 2; constructor; apply (timeless _). Qed.
+Proof. by inversion_clear 2; constructor; apply (discrete _). Qed.
 Global Instance excl_leibniz : LeibnizEquiv A → LeibnizEquiv (excl A).
 Proof. by destruct 2; f_equal; apply leibniz_equiv. Qed.
 
-Global Instance Excl_timeless a : Timeless a → Timeless (Excl a).
-Proof. by inversion_clear 2; constructor; apply (timeless _). Qed.
-Global Instance ExclBot_timeless : Timeless (@ExclBot A).
+Global Instance Excl_discrete a : Discrete a → Discrete (Excl a).
+Proof. by inversion_clear 2; constructor; apply (discrete _). Qed.
+Global Instance ExclBot_discrete : Discrete (@ExclBot A).
 Proof. by inversion_clear 1; constructor. Qed.
 
 (* CMRA *)

theories/algebra/frac_auth.v

@@ -34,10 +34,10 @@ 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_timeless a : Timeless a → Timeless (●! a).
-  Proof. intros; apply Auth_timeless; apply _. Qed.
-  Global Instance frac_auth_frag_timeless a : Timeless a → Timeless (◯! a).
-  Proof. intros; apply Auth_timeless, Some_timeless; apply _. Qed.
+  Global Instance frac_auth_auth_discrete a : Discrete a → Discrete (●! a).
+  Proof. intros; apply Auth_discrete; apply _. Qed.
+  Global Instance frac_auth_frag_discrete a : Discrete a → Discrete (◯! a).
+  Proof. intros; apply Auth_discrete, Some_discrete; apply _. Qed.
 
   Lemma frac_auth_validN n a : ✓{n} a → ✓{n} (●! a ⋅ ◯! a).
   Proof. done. Qed.

theories/algebra/gmap.v

@@ -38,7 +38,7 @@ Next Obligation.
 Qed.
 
 Global Instance gmap_ofe_discrete : OFEDiscrete A → OFEDiscrete gmapC.
-Proof. intros ? m m' ? i. by apply (timeless _). Qed.
+Proof. intros ? m m' ? i. by apply (discrete _). Qed.
 (* why doesn't this go automatic? *)
 Global Instance gmapC_leibniz: LeibnizEquiv A → LeibnizEquiv gmapC.
 Proof. intros; change (LeibnizEquiv (gmap K A)); apply _. Qed.
@@ -70,27 +70,27 @@ Proof.
     [by constructor|by apply lookup_ne].
 Qed.
 
-Global Instance gmap_empty_timeless : Timeless (∅ : gmap K A).
+Global Instance gmap_empty_discrete : Discrete (∅ : gmap K A).
 Proof.
   intros m Hm i; specialize (Hm i); rewrite lookup_empty in Hm |- *.
   inversion_clear Hm; constructor.
 Qed.
-Global Instance gmap_lookup_timeless m i : Timeless m → Timeless (m !! i).
+Global Instance gmap_lookup_discrete m i : Discrete m → Discrete (m !! i).
 Proof.
-  intros ? [x|] Hx; [|by symmetry; apply: timeless].
+  intros ? [x|] Hx; [|by symmetry; apply: discrete].
   assert (m ≡{0}≡ <[i:=x]> m)
     by (by symmetry in Hx; inversion Hx; ofe_subst; rewrite insert_id).
-  by rewrite (timeless m (<[i:=x]>m)) // lookup_insert.
+  by rewrite (discrete m (<[i:=x]>m)) // lookup_insert.
 Qed.
-Global Instance gmap_insert_timeless m i x :
-  Timeless x → Timeless m → Timeless (<[i:=x]>m).
+Global Instance gmap_insert_discrete m i x :
+  Discrete x → Discrete m → Discrete (<[i:=x]>m).
 Proof.
   intros ?? m' Hm j; destruct (decide (i = j)); simplify_map_eq.
-  { by apply: timeless; rewrite -Hm lookup_insert. }
-  by apply: timeless; rewrite -Hm lookup_insert_ne.
+  { by apply: discrete; rewrite -Hm lookup_insert. }
+  by apply: discrete; rewrite -Hm lookup_insert_ne.
 Qed.
-Global Instance gmap_singleton_timeless i x :
-  Timeless x → Timeless ({[ i := x ]} : gmap K A) := _.
+Global Instance gmap_singleton_discrete i x :
+  Discrete x → Discrete ({[ i := x ]} : gmap K A) := _.
 End cofe.
 
 Arguments gmapC _ {_ _} _.

theories/algebra/iprod.v

@@ -61,22 +61,22 @@ Section iprod_cofe.
     x ≠ x' → (iprod_insert x y f) x' = f x'.
   Proof. by rewrite /iprod_insert; destruct (decide _). Qed.
 
-  Global Instance iprod_lookup_timeless f x : Timeless f → Timeless (f x).
+  Global Instance iprod_lookup_discrete f x : Discrete f → Discrete (f x).
   Proof.
     intros ? y ?.
     cut (f ≡ iprod_insert x y f).
     { by move=> /(_ x)->; rewrite iprod_lookup_insert. }
-    apply (timeless _)=> x'; destruct (decide (x = x')) as [->|];
+    apply (discrete _)=> x'; destruct (decide (x = x')) as [->|];
       by rewrite ?iprod_lookup_insert ?iprod_lookup_insert_ne.
   Qed.
-  Global Instance iprod_insert_timeless f x y :
-    Timeless f → Timeless y → Timeless (iprod_insert x y f).
+  Global Instance iprod_insert_discrete f x y :
+    Discrete f → Discrete y → Discrete (iprod_insert x y f).
   Proof.
     intros ?? g Heq x'; destruct (decide (x = x')) as [->|].
     - rewrite iprod_lookup_insert.
-      apply: timeless. by rewrite -(Heq x') iprod_lookup_insert.
+      apply: discrete. by rewrite -(Heq x') iprod_lookup_insert.
     - rewrite iprod_lookup_insert_ne //.
-      apply: timeless. by rewrite -(Heq x') iprod_lookup_insert_ne.
+      apply: discrete. by rewrite -(Heq x') iprod_lookup_insert_ne.
   Qed.
 End iprod_cofe.
 
@@ -140,9 +140,9 @@ Section iprod_cmra.
   Qed.
   Canonical Structure iprodUR := UCMRAT (iprod B) iprod_ucmra_mixin.
 
-  Global Instance iprod_empty_timeless :
-    (∀ i, Timeless (ε : B i)) → Timeless (ε : iprod B).
-  Proof. intros ? f Hf x. by apply: timeless. Qed.
+  Global Instance iprod_empty_discrete :
+    (∀ i, Discrete (ε : B i)) → Discrete (ε : iprod B).
+  Proof. intros ? f Hf x. by apply: discrete. Qed.
 
   (** Internalized properties *)
   Lemma iprod_equivI {M} g1 g2 : g1 ≡ g2 ⊣⊢ (∀ i, g1 i ≡ g2 i : uPred M).
@@ -198,8 +198,8 @@ Section iprod_singleton.
     x ≠ x' → (iprod_singleton x y) x' = ε.
   Proof. intros; by rewrite /iprod_singleton iprod_lookup_insert_ne. Qed.
 
-  Global Instance iprod_singleton_timeless x (y : B x) :
-    (∀ i, Timeless (ε : B i)) →  Timeless y → Timeless (iprod_singleton x y).
+  Global Instance iprod_singleton_discrete x (y : B x) :
+    (∀ i, Discrete (ε : B i)) →  Discrete y → Discrete (iprod_singleton x y).
   Proof. apply _. Qed.
 
   Lemma iprod_singleton_validN n x (y : B x) : ✓{n} iprod_singleton x y ↔ ✓{n} y.

theories/algebra/list.v

@@ -78,12 +78,12 @@ Next Obligation.
 Qed.
 
 Global Instance list_ofe_discrete : OFEDiscrete A → OFEDiscrete listC.
-Proof. induction 2; constructor; try apply (timeless _); auto. Qed.
+Proof. induction 2; constructor; try apply (discrete _); auto. Qed.
 
-Global Instance nil_timeless : Timeless (@nil A).
+Global Instance nil_discrete : Discrete (@nil A).
 Proof. inversion_clear 1; constructor. Qed.
-Global Instance cons_timeless x l : Timeless x → Timeless l → Timeless (x :: l).
-Proof. intros ??; inversion_clear 1; constructor; by apply timeless. Qed.
+Global Instance cons_discrete x l : Discrete x → Discrete l → Discrete (x :: l).
+Proof. intros ??; inversion_clear 1; constructor; by apply discrete. Qed.
 End cofe.
 
 Arguments listC : clear implicits.

theories/algebra/local_updates.v

@@ -56,8 +56,8 @@ Section updates.
     (x,y) ~l~> (x',y') ↔ ∀ mz, ✓ x → x ≡ y ⋅? mz → ✓ x' ∧ x' ≡ y' ⋅? mz.
   Proof.
     rewrite /local_update /=. setoid_rewrite <-cmra_discrete_valid_iff.
-    setoid_rewrite <-(λ n, timeless_iff n x).
-    setoid_rewrite <-(λ n, timeless_iff n x'). naive_solver eauto using 0.
+    setoid_rewrite <-(λ n, discrete_iff n x).
+    setoid_rewrite <-(λ n, discrete_iff n x'). naive_solver eauto using 0.
   Qed.
 
   Lemma local_update_valid0 x y x' y' :
@@ -76,7 +76,7 @@ Section updates.
     (✓ x → ✓ y → x ≡ y ∨ y ≼ x → (x,y) ~l~> (x',y')) → (x,y) ~l~> (x',y').
   Proof.
     rewrite !(cmra_discrete_valid_iff 0)
-      (cmra_discrete_included_iff 0) (timeless_iff 0).
+      (cmra_discrete_included_iff 0) (discrete_iff 0).
     apply local_update_valid0.
   Qed.
 

theories/algebra/ofe.v

@@ -99,15 +99,13 @@ End ofe_mixin.
 
 Hint Extern 1 (_ ≡{_}≡ _) => apply equiv_dist; assumption.
 
-(** Discrete OFEs and Timeless elements *)
-(* TODO: On paper, We called these "discrete elements". I think that makes
-   more sense. *)
-Class Timeless {A : ofeT} (x : A) := timeless y : x ≡{0}≡ y → x ≡ y.
-Arguments timeless {_} _ {_} _ _.
-Hint Mode Timeless + ! : typeclass_instances.
-Instance: Params (@Timeless) 1.
-
-Class OFEDiscrete (A : ofeT) := ofe_discrete_timeless (x : A) :> Timeless x.
+(** Discrete OFEs and discrete OFE elements *)
+Class Discrete {A : ofeT} (x : A) := discrete y : x ≡{0}≡ y → x ≡ y.
+Arguments discrete {_} _ {_} _ _.
+Hint Mode Discrete + ! : typeclass_instances.
+Instance: Params (@Discrete) 1.
+
+Class OFEDiscrete (A : ofeT) := ofe_discrete_discrete (x : A) :> Discrete x.
 Hint Mode OFEDiscrete ! : typeclass_instances.
 
 (** OFEs with a completion *)
@@ -165,8 +163,8 @@ Section ofe.
   Qed.
   Global Instance dist_proper_2 n x : Proper ((≡) ==> iff) (dist n x).
   Proof. by apply dist_proper. Qed.
-  Global Instance Timeless_proper : Proper ((≡) ==> iff) (@Timeless A).
-  Proof. intros x y Hxy. rewrite /Timeless. by setoid_rewrite Hxy. Qed.
+  Global Instance Discrete_proper : Proper ((≡) ==> iff) (@Discrete A).
+  Proof. intros x y Hxy. rewrite /Discrete. by setoid_rewrite Hxy. Qed.
 
   Lemma dist_le n n' x y : x ≡{n}≡ y → n' ≤ n → x ≡{n'}≡ y.
   Proof. induction 2; eauto using dist_S. Qed.
@@ -188,13 +186,13 @@ Section ofe.
     apply chain_cauchy. omega.
   Qed.
 
-  Lemma timeless_iff n (x : A) `{!Timeless x} y : x ≡ y ↔ x ≡{n}≡ y.
+  Lemma discrete_iff n (x : A) `{!Discrete x} y : x ≡ y ↔ x ≡{n}≡ y.
   Proof.
-    split; intros; auto. apply (timeless _), dist_le with n; auto with lia.
+    split; intros; auto. apply (discrete _), dist_le with n; auto with lia.
   Qed.
-  Lemma timeless_iff_0 n (x : A) `{!Timeless x} y : x ≡{0}≡ y ↔ x ≡{n}≡ y.
+  Lemma discrete_iff_0 n (x : A) `{!Discrete x} y : x ≡{0}≡ y ↔ x ≡{n}≡ y.
   Proof.
-    split=> ?. by apply equiv_dist, (timeless _). eauto using dist_le with lia.
+    split=> ?. by apply equiv_dist, (discrete _). eauto using dist_le with lia.
   Qed.
 End ofe.
 
@@ -273,7 +271,7 @@ Section limit_preserving.
   Global Instance limit_preserving_const (P : Prop) : LimitPreserving (λ _, P).
   Proof. intros c HP. apply (HP 0). Qed.
 
-  Lemma limit_preserving_timeless (P : A → Prop) :
+  Lemma limit_preserving_discrete (P : A → Prop) :
     Proper (dist 0 ==> impl) P → LimitPreserving P.
   Proof. intros PH c Hc. by rewrite (conv_compl 0). Qed.
 
@@ -683,9 +681,9 @@ Section product.
     apply (conv_compl n (chain_map snd c)).
   Qed.
 
-  Global Instance prod_timeless (x : A * B) :
-    Timeless (x.1) → Timeless (x.2) → Timeless x.
-  Proof. by intros ???[??]; split; apply (timeless _). Qed.
+  Global Instance prod_discrete (x : A * B) :
+    Discrete (x.1) → Discrete (x.2) → Discrete x.
+  Proof. by intros ???[??]; split; apply (discrete _). Qed.
   Global Instance prod_ofe_discrete : OFEDiscrete A → OFEDiscrete B → OFEDiscrete prodC.
   Proof. intros ?? [??]; apply _. Qed.
 End product.
@@ -864,10 +862,10 @@ Section sum.
     - rewrite (conv_compl n (inr_chain c _)) /=. destruct (c n); naive_solver.
   Qed.
 
-  Global Instance inl_timeless (x : A) : Timeless x → Timeless (inl x).
-  Proof. inversion_clear 2; constructor; by apply (timeless _). Qed.
-  Global Instance inr_timeless (y : B) : Timeless y → Timeless (inr y).
-  Proof. inversion_clear 2; constructor; by apply (timeless _). Qed.
+  Global Instance inl_discrete (x : A) : Discrete x → Discrete (inl x).
+  Proof. inversion_clear 2; constructor; by apply (discrete _). Qed.
+  Global Instance inr_discrete (y : B) : Discrete y → Discrete (inr y).
+  Proof. inversion_clear 2; constructor; by apply (discrete _). Qed.
   Global Instance sum_ofe_discrete : OFEDiscrete A → OFEDiscrete B → OFEDiscrete sumC.
   Proof. intros ?? [?|?]; apply _. Qed.
 End sum.
@@ -993,7 +991,7 @@ Section option.
   Qed.
 
   Global Instance option_ofe_discrete : OFEDiscrete A → OFEDiscrete optionC.
-  Proof. destruct 2; constructor; by apply (timeless _). Qed.
+  Proof. destruct 2; constructor; by apply (discrete _). Qed.
 
   Global Instance Some_ne : NonExpansive (@Some A).
   Proof. by constructor. Qed.
@@ -1005,10 +1003,10 @@ Section option.
     Proper (dist n ==> R) f → Proper (R ==> dist n ==> R) (from_option f).
   Proof. destruct 3; simpl; auto. Qed.
 
-  Global Instance None_timeless : Timeless (@None A).
+  Global Instance None_discrete : Discrete (@None A).
   Proof. inversion_clear 1; constructor. Qed.
-  Global Instance Some_timeless x : Timeless x → Timeless (Some x).
-  Proof. by intros ?; inversion_clear 1; constructor; apply timeless. Qed.
+  Global Instance Some_discrete x : Discrete x → Discrete (Some x).
+  Proof. by intros ?; inversion_clear 1; constructor; apply discrete. Qed.
 
   Lemma dist_None n mx : mx ≡{n}≡ None ↔ mx = None.
   Proof. split; [by inversion_clear 1|by intros ->]. Qed.
@@ -1224,8 +1222,8 @@ Section sigma.
   Global Instance sig_cofe `{Cofe A, !LimitPreserving P} : Cofe sigC.
   Proof. apply (iso_cofe_subtype' P (exist P) proj1_sig)=> //. by intros []. Qed.
 
-  Global Instance sig_timeless (x : sig P) :  Timeless (`x) → Timeless x.
-  Proof. intros ? y. rewrite sig_dist_alt sig_equiv_alt. apply (timeless _). Qed.
+  Global Instance sig_discrete (x : sig P) :  Discrete (`x) → Discrete x.
+  Proof. intros ? y. rewrite sig_dist_alt sig_equiv_alt. apply (discrete _). Qed.
   Global Instance sig_ofe_discrete : OFEDiscrete A → OFEDiscrete sigC.
   Proof. intros ??. apply _. Qed.
 End sigma.

theories/algebra/vector.v

@@ -21,13 +21,13 @@ Section ofe.
     - intros c. by rewrite (conv_compl 0 (chain_map _ c)) /= vec_to_list_length.
   Qed.
 
-  Global Instance vnil_timeless : Timeless (@vnil A).
+  Global Instance vnil_discrete : Discrete (@vnil A).
   Proof. intros v _. by inv_vec v. Qed.
-  Global Instance vcons_timeless n x (v : vec A n) :
-    Timeless x → Timeless v → Timeless (x ::: v).
+  Global Instance vcons_discrete n x (v : vec A n) :
+    Discrete x → Discrete v → Discrete (x ::: v).
   Proof.
     intros ?? v' ?. inv_vec v'=>x' v'. inversion_clear 1.
-    constructor. by apply timeless. change (v ≡ v'). by apply timeless.
+    constructor. by apply discrete. change (v ≡ v'). by apply discrete.
   Qed.
   Global Instance vec_ofe_discrete m : OFEDiscrete A → OFEDiscrete (vecC m).
   Proof. intros ? v. induction v; apply _. Qed.

theories/base_logic/derived.v

@@ -794,7 +794,7 @@ Proof.
   by rewrite -bupd_intro -or_intro_l.
 Qed.
 
-(* Timeless instances *)
+(* Discrete instances *)
 Global Instance TimelessP_proper : Proper ((≡) ==> iff) (@TimelessP M).
 Proof. solve_proper. Qed.
 Global Instance pure_timeless φ : TimelessP (⌜φ⌝ : uPred M)%I.
@@ -848,9 +848,9 @@ Proof. intros; rewrite /TimelessP except_0_always -always_later; auto. Qed.
 Global Instance always_if_timeless p P : TimelessP P → TimelessP (□?p P).
 Proof. destruct p; apply _. Qed.
 Global Instance eq_timeless {A : ofeT} (a b : A) :
-  Timeless a → TimelessP (a ≡ b : uPred M)%I.
-Proof. intros. rewrite /TimelessP !timeless_eq. apply (timelessP _). Qed.
-Global Instance ownM_timeless (a : M) : Timeless a → TimelessP (uPred_ownM a).
+  Discrete a → TimelessP (a ≡ b : uPred M)%I.
+Proof. intros. rewrite /TimelessP !discrete_eq. apply (timelessP _). Qed.
+Global Instance ownM_timeless (a : M) : Discrete a → TimelessP (uPred_ownM a).
 Proof.
   intros ?. rewrite /TimelessP later_ownM. apply exist_elim=> b.
   rewrite (timelessP (a≡b)) (except_0_intro (uPred_ownM b)) -except_0_and.

theories/base_logic/lib/own.v

@@ -106,7 +106,7 @@ Proof. apply: uPred.always_entails_r. apply own_valid. Qed.
 Lemma own_valid_l γ a : own γ a ⊢ ✓ a ∗ own γ a.
 Proof. by rewrite comm -own_valid_r. Qed.
 
-Global Instance own_timeless γ a : Timeless a → TimelessP (own γ a).
+Global Instance own_timeless γ a : Discrete a → TimelessP (own γ a).
 Proof. rewrite !own_eq /own_def; apply _. Qed.
 Global Instance own_core_persistent γ a : Persistent a → PersistentP (own γ a).
 Proof. rewrite !own_eq /own_def; apply _. Qed.

theories/base_logic/primitive.v

@@ -563,9 +563,9 @@ Proof. by unseal. Qed.
 (* Discrete *)
 Lemma discrete_valid {A : cmraT} `{!CMRADiscrete A} (a : A) : ✓ a ⊣⊢ ⌜✓ a⌝.
 Proof. unseal; split=> n x _. by rewrite /= -cmra_discrete_valid_iff. Qed.
-Lemma timeless_eq {A : ofeT} (a b : A) : Timeless a → a ≡ b ⊣⊢ ⌜a ≡ b⌝.
+Lemma discrete_eq {A : ofeT} (a b : A) : Discrete a → a ≡ b ⊣⊢ ⌜a ≡ b⌝.
 Proof.
-  unseal=> ?. apply (anti_symm (⊢)); split=> n x ?; by apply (timeless_iff n).
+  unseal=> ?. apply (anti_symm (⊢)); split=> n x ?; by apply (discrete_iff n).
 Qed.
 
 (* Option *)

theories/proofmode/class_instances.v

@@ -42,8 +42,8 @@ Proof. rewrite /FromAssumption=> <-. by rewrite forall_elim. Qed.
 Global Instance into_pure_pure φ : @IntoPure M ⌜φ⌝ φ.
 Proof. done. Qed.
 Global Instance into_pure_eq {A : ofeT} (a b : A) :
-  Timeless a → @IntoPure M (a ≡ b) (a ≡ b).
-Proof. intros. by rewrite /IntoPure timeless_eq. Qed.
+  Discrete a → @IntoPure M (a ≡ b) (a ≡ b).
+Proof. intros. by rewrite /IntoPure discrete_eq. Qed.
 Global Instance into_pure_cmra_valid `{CMRADiscrete A} (a : A) :
   @IntoPure M (✓ a) (✓ a).
 Proof. by rewrite /IntoPure discrete_valid. Qed.