rename CMRA unit -> core

algebra/agree.v

@@ -60,7 +60,7 @@ Program Instance agree_op : Op (agree A) := λ x y,
   {| agree_car := x;
      agree_is_valid n := agree_is_valid x n ∧ agree_is_valid y n ∧ x ≡{n}≡ y |}.
 Next Obligation. naive_solver eauto using agree_valid_S, dist_S. Qed.
-Instance agree_unit : Unit (agree A) := id.
+Instance agree_core : Core (agree A) := id.
 Instance agree_div : Div (agree A) := λ x y, x.
 
 Instance: Comm (≡) (@op (agree A) _).

algebra/auth.v

@@ -85,8 +85,8 @@ Instance auth_validN : ValidN (auth A) := λ n x,
   | ExclBot => False
   end.
 Global Arguments auth_validN _ !_ /.
-Instance auth_unit : Unit (auth A) := λ x,
-  Auth (unit (authoritative x)) (unit (own x)).
+Instance auth_core : Core (auth A) := λ x,
+  Auth (core (authoritative x)) (core (own x)).
 Instance auth_op : Op (auth A) := λ x y,
   Auth (authoritative x ⋅ authoritative y) (own x ⋅ own y).
 Instance auth_div : Div (auth A) := λ x y,
@@ -117,10 +117,10 @@ Proof.
   - intros n [[] ?] ?; naive_solver eauto using cmra_includedN_S, cmra_validN_S.
   - by split; simpl; rewrite assoc.
   - by split; simpl; rewrite comm.
-  - by split; simpl; rewrite ?cmra_unit_l.
-  - by split; simpl; rewrite ?cmra_unit_idemp.
+  - by split; simpl; rewrite ?cmra_core_l.
+  - by split; simpl; rewrite ?cmra_core_idemp.
   - intros ??; rewrite! auth_included; intros [??].
-    by split; simpl; apply cmra_unit_preserving.
+    by split; simpl; apply cmra_core_preserving.
   - assert (∀ n (a b1 b2 : A), b1 ⋅ b2 ≼{n} a → b1 ≼{n} a).
     { intros n a b1 b2 <-; apply cmra_includedN_l. }
    intros n [[a1| |] b1] [[a2| |] b2];

algebra/cmra.v

 From algebra Require Export cofe.
 
-Class Unit (A : Type) := unit : A → A.
-Instance: Params (@unit) 2.
+Class Core (A : Type) := core : A → A.
+Instance: Params (@core) 2.
 
 Class Op (A : Type) := op : A → A → A.
 Instance: Params (@op) 2.
@@ -34,10 +34,10 @@ Instance: Params (@includedN) 4.
 Hint Extern 0 (_ ≼{_} _) => reflexivity.
 
 Record CMRAMixin A
-    `{Dist A, Equiv A, Unit A, Op A, Valid A, ValidN A, Div A} := {
+    `{Dist A, Equiv A, Core A, Op A, Valid A, ValidN A, Div A} := {
   (* setoids *)
   mixin_cmra_op_ne n (x : A) : Proper (dist n ==> dist n) (op x);
-  mixin_cmra_unit_ne n : Proper (dist n ==> dist n) unit;
+  mixin_cmra_core_ne n : Proper (dist n ==> dist n) core;
   mixin_cmra_validN_ne n : Proper (dist n ==> impl) (validN n);
   mixin_cmra_div_ne n : Proper (dist n ==> dist n ==> dist n) div;
   (* valid *)
@@ -46,9 +46,9 @@ Record CMRAMixin A
   (* monoid *)
   mixin_cmra_assoc : Assoc (≡) (⋅);
   mixin_cmra_comm : Comm (≡) (⋅);
-  mixin_cmra_unit_l x : unit x ⋅ x ≡ x;
-  mixin_cmra_unit_idemp x : unit (unit x) ≡ unit x;
-  mixin_cmra_unit_preserving x y : x ≼ y → unit x ≼ unit y;
+  mixin_cmra_core_l x : core x ⋅ x ≡ x;
+  mixin_cmra_core_idemp x : core (core x) ≡ core x;
+  mixin_cmra_core_preserving x y : x ≼ y → core x ≼ core y;
   mixin_cmra_validN_op_l n x y : ✓{n} (x ⋅ y) → ✓{n} x;
   mixin_cmra_op_div x y : x ≼ y → x ⋅ y ÷ x ≡ y;
   mixin_cmra_extend n x y1 y2 :
@@ -62,7 +62,7 @@ Structure cmraT := CMRAT {
   cmra_equiv : Equiv cmra_car;
   cmra_dist : Dist cmra_car;
   cmra_compl : Compl cmra_car;
-  cmra_unit : Unit cmra_car;
+  cmra_core : Core cmra_car;
   cmra_op : Op cmra_car;
   cmra_valid : Valid cmra_car;
   cmra_validN : ValidN cmra_car;
@@ -75,7 +75,7 @@ Arguments cmra_car : simpl never.
 Arguments cmra_equiv : simpl never.
 Arguments cmra_dist : simpl never.
 Arguments cmra_compl : simpl never.
-Arguments cmra_unit : simpl never.
+Arguments cmra_core : simpl never.
 Arguments cmra_op : simpl never.
 Arguments cmra_valid : simpl never.
 Arguments cmra_validN : simpl never.
@@ -83,7 +83,7 @@ Arguments cmra_div : simpl never.
 Arguments cmra_cofe_mixin : simpl never.
 Arguments cmra_mixin : simpl never.
 Add Printing Constructor cmraT.
-Existing Instances cmra_unit cmra_op cmra_valid cmra_validN cmra_div.
+Existing Instances cmra_core cmra_op cmra_valid cmra_validN cmra_div.
 Coercion cmra_cofeC (A : cmraT) : cofeT := CofeT (cmra_cofe_mixin A).
 Canonical Structure cmra_cofeC.
 
@@ -93,8 +93,8 @@ Section cmra_mixin.
   Implicit Types x y : A.
   Global Instance cmra_op_ne n (x : A) : Proper (dist n ==> dist n) (op x).
   Proof. apply (mixin_cmra_op_ne _ (cmra_mixin A)). Qed.
-  Global Instance cmra_unit_ne n : Proper (dist n ==> dist n) (@unit A _).
-  Proof. apply (mixin_cmra_unit_ne _ (cmra_mixin A)). Qed.
+  Global Instance cmra_core_ne n : Proper (dist n ==> dist n) (@core A _).
+  Proof. apply (mixin_cmra_core_ne _ (cmra_mixin A)). Qed.
   Global Instance cmra_validN_ne n : Proper (dist n ==> impl) (@validN A _ n).
   Proof. apply (mixin_cmra_validN_ne _ (cmra_mixin A)). Qed.
   Global Instance cmra_div_ne n :
@@ -108,12 +108,12 @@ Section cmra_mixin.
   Proof. apply (mixin_cmra_assoc _ (cmra_mixin A)). Qed.
   Global Instance cmra_comm : Comm (≡) (@op A _).
   Proof. apply (mixin_cmra_comm _ (cmra_mixin A)). Qed.
-  Lemma cmra_unit_l x : unit x ⋅ x ≡ x.
-  Proof. apply (mixin_cmra_unit_l _ (cmra_mixin A)). Qed.
-  Lemma cmra_unit_idemp x : unit (unit x) ≡ unit x.
-  Proof. apply (mixin_cmra_unit_idemp _ (cmra_mixin A)). Qed.
-  Lemma cmra_unit_preserving x y : x ≼ y → unit x ≼ unit y.
-  Proof. apply (mixin_cmra_unit_preserving _ (cmra_mixin A)). Qed.
+  Lemma cmra_core_l x : core x ⋅ x ≡ x.
+  Proof. apply (mixin_cmra_core_l _ (cmra_mixin A)). Qed.
+  Lemma cmra_core_idemp x : core (core x) ≡ core x.
+  Proof. apply (mixin_cmra_core_idemp _ (cmra_mixin A)). Qed.
+  Lemma cmra_core_preserving x y : x ≼ y → core x ≼ core y.
+  Proof. apply (mixin_cmra_core_preserving _ (cmra_mixin A)). Qed.
   Lemma cmra_validN_op_l n x y : ✓{n} (x ⋅ y) → ✓{n} x.
   Proof. apply (mixin_cmra_validN_op_l _ (cmra_mixin A)). Qed.
   Lemma cmra_op_div x y : x ≼ y → x ⋅ y ÷ x ≡ y.
@@ -175,7 +175,7 @@ Implicit Types x y z : A.
 Implicit Types xs ys zs : list A.
 
 (** ** Setoids *)
-Global Instance cmra_unit_proper : Proper ((≡) ==> (≡)) (@unit A _).
+Global Instance cmra_core_proper : Proper ((≡) ==> (≡)) (@core A _).
 Proof. apply (ne_proper _). Qed.
 Global Instance cmra_op_ne' n : Proper (dist n ==> dist n ==> dist n) (@op A _).
 Proof.
@@ -236,15 +236,15 @@ Proof. rewrite (comm _ x); apply cmra_validN_op_l. Qed.
 Lemma cmra_valid_op_r x y : ✓ (x ⋅ y) → ✓ y.
 Proof. rewrite !cmra_valid_validN; eauto using cmra_validN_op_r. Qed.
 
-(** ** Units *)
-Lemma cmra_unit_r x : x ⋅ unit x ≡ x.
-Proof. by rewrite (comm _ x) cmra_unit_l. Qed.
-Lemma cmra_unit_unit x : unit x ⋅ unit x ≡ unit x.
-Proof. by rewrite -{2}(cmra_unit_idemp x) cmra_unit_r. Qed.
-Lemma cmra_unit_validN n x : ✓{n} x → ✓{n} unit x.
-Proof. rewrite -{1}(cmra_unit_l x); apply cmra_validN_op_l. Qed.
-Lemma cmra_unit_valid x : ✓ x → ✓ unit x.
-Proof. rewrite -{1}(cmra_unit_l x); apply cmra_valid_op_l. Qed.
+(** ** Core *)
+Lemma cmra_core_r x : x ⋅ core x ≡ x.
+Proof. by rewrite (comm _ x) cmra_core_l. Qed.
+Lemma cmra_core_core x : core x ⋅ core x ≡ core x.
+Proof. by rewrite -{2}(cmra_core_idemp x) cmra_core_r. Qed.
+Lemma cmra_core_validN n x : ✓{n} x → ✓{n} core x.
+Proof. rewrite -{1}(cmra_core_l x); apply cmra_validN_op_l. Qed.
+Lemma cmra_core_valid x : ✓ x → ✓ core x.
+Proof. rewrite -{1}(cmra_core_l x); apply cmra_valid_op_l. Qed.
 
 (** ** Div *)
 Lemma cmra_op_div' n x y : x ≼{n} y → x ⋅ y ÷ x ≡{n}≡ y.
@@ -260,7 +260,7 @@ Qed.
 Global Instance cmra_includedN_preorder n : PreOrder (@includedN A _ _ n).
 Proof.
   split.
-  - by intros x; exists (unit x); rewrite cmra_unit_r.
+  - by intros x; exists (core x); rewrite cmra_core_r.
   - intros x y z [z1 Hy] [z2 Hz]; exists (z1 ⋅ z2).
     by rewrite assoc -Hy -Hz.
 Qed.
@@ -288,13 +288,13 @@ Proof. rewrite (comm op); apply cmra_includedN_l. Qed.
 Lemma cmra_included_r x y : y ≼ x ⋅ y.
 Proof. rewrite (comm op); apply cmra_included_l. Qed.
 
-Lemma cmra_unit_preservingN n x y : x ≼{n} y → unit x ≼{n} unit y.
+Lemma cmra_core_preservingN n x y : x ≼{n} y → core x ≼{n} core y.
 Proof.
   intros [z ->].
-  apply cmra_included_includedN, cmra_unit_preserving, cmra_included_l.
+  apply cmra_included_includedN, cmra_core_preserving, cmra_included_l.
 Qed.
-Lemma cmra_included_unit x : unit x ≼ x.
-Proof. by exists x; rewrite cmra_unit_l. Qed.
+Lemma cmra_included_core x : core x ≼ x.
+Proof. by exists x; rewrite cmra_core_l. Qed.
 Lemma cmra_preservingN_l n x y z : x ≼{n} y → z ⋅ x ≼{n} z ⋅ y.
 Proof. by intros [z1 Hz1]; exists z1; rewrite Hz1 (assoc op). Qed.
 Lemma cmra_preserving_l x y z : x ≼ y → z ⋅ x ≼ z ⋅ y.
@@ -358,8 +358,8 @@ Section identity.
   Proof. by exists x; rewrite left_id. Qed.
   Global Instance cmra_empty_right_id : RightId (≡) ∅ (⋅).
   Proof. by intros x; rewrite (comm op) left_id. Qed.
-  Lemma cmra_unit_empty : unit ∅ ≡ ∅.
-  Proof. by rewrite -{2}(cmra_unit_l ∅) right_id. Qed.
+  Lemma cmra_core_empty : core ∅ ≡ ∅.
+  Proof. by rewrite -{2}(cmra_core_l ∅) right_id. Qed.
 End identity.
 
 (** ** Local updates *)
@@ -468,7 +468,7 @@ Section cmra_transport.
   Proof. by intros ???; destruct H. Qed.
   Lemma cmra_transport_op x y : T (x ⋅ y) = T x ⋅ T y.
   Proof. by destruct H. Qed.
-  Lemma cmra_transport_unit x : T (unit x) = unit (T x).
+  Lemma cmra_transport_core x : T (core x) = core (T x).
   Proof. by destruct H. Qed.
   Lemma cmra_transport_validN n x : ✓{n} T x ↔ ✓{n} x.
   Proof. by destruct H. Qed.
@@ -486,25 +486,25 @@ End cmra_transport.
 
 (** * Instances *)
 (** ** Discrete CMRA *)
-Class RA A `{Equiv A, Unit A, Op A, Valid A, Div A} := {
+Class RA A `{Equiv A, Core A, Op A, Valid A, Div A} := {
   (* setoids *)
   ra_op_ne (x : A) : Proper ((≡) ==> (≡)) (op x);
-  ra_unit_ne :> Proper ((≡) ==> (≡)) unit;
+  ra_core_ne :> Proper ((≡) ==> (≡)) core;
   ra_validN_ne :> Proper ((≡) ==> impl) valid;
   ra_div_ne :> Proper ((≡) ==> (≡) ==> (≡)) div;
   (* monoid *)
   ra_assoc :> Assoc (≡) (⋅);
   ra_comm :> Comm (≡) (⋅);
-  ra_unit_l x : unit x ⋅ x ≡ x;
-  ra_unit_idemp x : unit (unit x) ≡ unit x;
-  ra_unit_preserving x y : x ≼ y → unit x ≼ unit y;
+  ra_core_l x : core x ⋅ x ≡ x;
+  ra_core_idemp x : core (core x) ≡ core x;
+  ra_core_preserving x y : x ≼ y → core x ≼ core y;
   ra_valid_op_l x y : ✓ (x ⋅ y) → ✓ x;
   ra_op_div x y : x ≼ y → x ⋅ y ÷ x ≡ y
 }.
 
 Section discrete.
   Context {A : cofeT} `{Discrete A}.
-  Context `{Unit A, Op A, Valid A, Div A} (ra : RA A).
+  Context `{Core A, Op A, Valid A, Div A} (ra : RA A).
 
   Instance discrete_validN : ValidN A := λ n x, ✓ x.
   Definition discrete_cmra_mixin : CMRAMixin A.
@@ -523,7 +523,7 @@ End discrete.
 (** ** CMRA for the unit type *)
 Section unit.
   Instance unit_valid : Valid () := λ x, True.
-  Instance unit_unit : Unit () := λ x, x.
+  Instance unit_core : Core () := λ x, x.
   Instance unit_op : Op () := λ x y, ().
   Instance unit_div : Div () := λ x y, ().
   Global Instance unit_empty : Empty () := ().
@@ -541,7 +541,7 @@ Section prod.
   Context {A B : cmraT}.
   Instance prod_op : Op (A * B) := λ x y, (x.1 ⋅ y.1, x.2 ⋅ y.2).
   Global Instance prod_empty `{Empty A, Empty B} : Empty (A * B) := (∅, ∅).
-  Instance prod_unit : Unit (A * B) := λ x, (unit (x.1), unit (x.2)).
+  Instance prod_core : Core (A * B) := λ x, (core (x.1), core (x.2)).
   Instance prod_valid : Valid (A * B) := λ x, ✓ x.1 ∧ ✓ x.2.
   Instance prod_validN : ValidN (A * B) := λ n x, ✓{n} x.1 ∧ ✓{n} x.2.
   Instance prod_div : Div (A * B) := λ x y, (x.1 ÷ y.1, x.2 ÷ y.2).
@@ -569,10 +569,10 @@ Section prod.
     - by intros n x [??]; split; apply cmra_validN_S.
     - by split; rewrite /= assoc.
     - by split; rewrite /= comm.
-    - by split; rewrite /= cmra_unit_l.
-    - by split; rewrite /= cmra_unit_idemp.
+    - by split; rewrite /= cmra_core_l.
+    - by split; rewrite /= cmra_core_idemp.
     - intros x y; rewrite !prod_included.
-      by intros [??]; split; apply cmra_unit_preserving.
+      by intros [??]; split; apply cmra_core_preserving.
     - intros n x y [??]; split; simpl in *; eauto using cmra_validN_op_l.
     - intros x y; rewrite prod_included; intros [??].
       by split; apply cmra_op_div.

algebra/dec_agree.v

@@ -2,7 +2,7 @@ From algebra Require Export cmra.
 Local Arguments validN _ _ _ !_ /.
 Local Arguments valid _ _  !_ /.
 Local Arguments op _ _ _ !_ /.
-Local Arguments unit _ _ !_ /.
+Local Arguments core _ _ !_ /.
 
 (* This is isomorphic to option, but has a very different RA structure. *)
 Inductive dec_agree (A : Type) : Type := 
@@ -26,7 +26,7 @@ Instance dec_agree_op : Op (dec_agree A) := λ x y,
   | DecAgree a, DecAgree b => if decide (a = b) then DecAgree a else DecAgreeBot
   | _, _ => DecAgreeBot
   end.
-Instance dec_agree_unit : Unit (dec_agree A) := id.
+Instance dec_agree_core : Core (dec_agree A) := id.
 Instance dec_agree_div : Div (dec_agree A) := λ x y, x.
 
 Definition dec_agree_ra : RA (dec_agree A).

algebra/dra.v

@@ -18,17 +18,17 @@ Definition dra_included `{Equiv A, Valid A, Disjoint A, Op A} := λ x y,
 Instance: Params (@dra_included) 4.
 Local Infix "≼" := dra_included.
 
-Class DRA A `{Equiv A, Valid A, Unit A, Disjoint A, Op A, Div A} := {
+Class DRA A `{Equiv A, Valid A, Core A, Disjoint A, Op A, Div A} := {
   (* setoids *)
   dra_equivalence :> Equivalence ((≡) : relation A);
   dra_op_proper :> Proper ((≡) ==> (≡) ==> (≡)) (⋅);
-  dra_unit_proper :> Proper ((≡) ==> (≡)) unit;
+  dra_core_proper :> Proper ((≡) ==> (≡)) core;
   dra_valid_proper :> Proper ((≡) ==> impl) valid;
   dra_disjoint_proper :> ∀ x, Proper ((≡) ==> impl) (disjoint x);
   dra_div_proper :> Proper ((≡) ==> (≡) ==> (≡)) div;
   (* validity *)
   dra_op_valid x y : ✓ x → ✓ y → x ⊥ y → ✓ (x ⋅ y);
-  dra_unit_valid x : ✓ x → ✓ unit x;
+  dra_core_valid x : ✓ x → ✓ core x;
   dra_div_valid x y : ✓ x → ✓ y → x ≼ y → ✓ (y ÷ x);
   (* monoid *)
   dra_assoc :> Assoc (≡) (⋅);
@@ -36,10 +36,10 @@ Class DRA A `{Equiv A, Valid A, Unit A, Disjoint A, Op A, Div A} := {
   dra_disjoint_move_l x y z : ✓ x → ✓ y → ✓ z → x ⊥ y → x ⋅ y ⊥ z → x ⊥ y ⋅ z;
   dra_symmetric :> Symmetric (@disjoint A _);
   dra_comm x y : ✓ x → ✓ y → x ⊥ y → x ⋅ y ≡ y ⋅ x;
-  dra_unit_disjoint_l x : ✓ x → unit x ⊥ x;
-  dra_unit_l x : ✓ x → unit x ⋅ x ≡ x;
-  dra_unit_idemp x : ✓ x → unit (unit x) ≡ unit x;
-  dra_unit_preserving x y : ✓ x → ✓ y → x ≼ y → unit x ≼ unit y;
+  dra_core_disjoint_l x : ✓ x → core x ⊥ x;
+  dra_core_l x : ✓ x → core x ⋅ x ≡ x;
+  dra_core_idemp x : ✓ x → core (core x) ≡ core x;
+  dra_core_preserving x y : ✓ x → ✓ y → x ≼ y → core x ≼ core y;
   dra_disjoint_div x y : ✓ x → ✓ y → x ≼ y → x ⊥ y ÷ x;
   dra_op_div x y : ✓ x → ✓ y → x ≼ y → x ⋅ y ÷ x ≡ y
 }.
@@ -88,9 +88,9 @@ Hint Unfold dra_included.
 Lemma validity_valid_car_valid (z : T) : ✓ z → ✓ validity_car z.
 Proof. apply validity_prf. Qed.
 Hint Resolve validity_valid_car_valid.
-Program Instance validity_unit : Unit T := λ x,
-  Validity (unit (validity_car x)) (✓ x) _.
-Solve Obligations with naive_solver auto using dra_unit_valid.
+Program Instance validity_core : Core T := λ x,
+  Validity (core (validity_car x)) (✓ x) _.
+Solve Obligations with naive_solver auto using dra_core_valid.
 Program Instance validity_op : Op T := λ x y,
   Validity (validity_car x ⋅ validity_car y)
            (✓ x ∧ ✓ y ∧ validity_car x ⊥ validity_car y) _.
@@ -118,14 +118,14 @@ Proof.
       |by intros; rewrite assoc].
   - intros [x px ?] [y py ?]; split; naive_solver eauto using dra_comm.
   - intros [x px ?]; split;
-      naive_solver eauto using dra_unit_l, dra_unit_disjoint_l.
-  - intros [x px ?]; split; naive_solver eauto using dra_unit_idemp.
-  - intros x y Hxy; exists (unit y ÷ unit x).
+      naive_solver eauto using dra_core_l, dra_core_disjoint_l.
+  - intros [x px ?]; split; naive_solver eauto using dra_core_idemp.
+  - intros x y Hxy; exists (core y ÷ core x).
     destruct x as [x px ?], y as [y py ?], Hxy as [[z pz ?] [??]]; simpl in *.
-    assert (py → unit x ≼ unit y)
-      by intuition eauto 10 using dra_unit_preserving.
+    assert (py → core x ≼ core y)
+      by intuition eauto 10 using dra_core_preserving.
     constructor; [|symmetry]; simpl in *;
-      intuition eauto using dra_op_div, dra_disjoint_div, dra_unit_valid.
+      intuition eauto using dra_op_div, dra_disjoint_div, dra_core_valid.
   - by intros [x px ?] [y py ?] (?&?&?).
   - intros [x px ?] [y py ?] [[z pz ?] [??]]; split; simpl in *;
       intuition eauto 10 using dra_disjoint_div, dra_op_div.

algebra/excl.v

@@ -91,7 +91,7 @@ Instance excl_valid : Valid (excl A) := λ x,
 Instance excl_validN : ValidN (excl A) := λ n x,
   match x with Excl _ | ExclUnit => True | ExclBot => False end.
 Global Instance excl_empty : Empty (excl A) := ExclUnit.
-Instance excl_unit : Unit (excl A) := λ _, ∅.
+Instance excl_core : Core (excl A) := λ _, ∅.
 Instance excl_op : Op (excl A) := λ x y,
   match x, y with
   | Excl a, ExclUnit | ExclUnit, Excl a => Excl a

algebra/fin_maps.v

@@ -93,7 +93,7 @@ Context `{Countable K} {A : cmraT}.
 Implicit Types m : gmap K A.
 
 Instance map_op : Op (gmap K A) := merge op.
-Instance map_unit : Unit (gmap K A) := fmap unit.
+Instance map_core : Core (gmap K A) := fmap core.
 Instance map_valid : Valid (gmap K A) := λ m, ∀ i, ✓ (m !! i).
 Instance map_validN : ValidN (gmap K A) := λ n m, ∀ i, ✓{n} (m !! i).
 Instance map_div : Div (gmap K A) := merge div.
@@ -102,7 +102,7 @@ Lemma lookup_op m1 m2 i : (m1 ⋅ m2) !! i = m1 !! i ⋅ m2 !! i.
 Proof. by apply lookup_merge. Qed.
 Lemma lookup_div m1 m2 i : (m1 ÷ m2) !! i = m1 !! i ÷ m2 !! i.
 Proof. by apply lookup_merge. Qed.
-Lemma lookup_unit m i : unit m !! i = unit (m !! i).
+Lemma lookup_core m i : core m !! i = core (m !! i).
 Proof. by apply lookup_fmap. Qed.
 
 Lemma map_included_spec (m1 m2 : gmap K A) : m1 ≼ m2 ↔ ∀ i, m1 !! i ≼ m2 !! i.
@@ -125,7 +125,7 @@ Definition map_cmra_mixin : CMRAMixin (gmap K A).
 Proof.
   split.
   - by intros n m1 m2 m3 Hm i; rewrite !lookup_op (Hm i).
-  - by intros n m1 m2 Hm i; rewrite !lookup_unit (Hm i).
+  - by intros n m1 m2 Hm i; rewrite !lookup_core (Hm i).
   - by intros n m1 m2 Hm ? i; rewrite -(Hm i).
   - by intros n m1 m1' Hm1 m2 m2' Hm2 i; rewrite !lookup_div (Hm1 i) (Hm2 i).
   - intros m; split.
@@ -134,10 +134,10 @@ Proof.
   - intros n m Hm i; apply cmra_validN_S, Hm.
   - by intros m1 m2 m3 i; rewrite !lookup_op assoc.
   - by intros m1 m2 i; rewrite !lookup_op comm.
-  - by intros m i; rewrite lookup_op !lookup_unit cmra_unit_l.
-  - by intros m i; rewrite !lookup_unit cmra_unit_idemp.
+  - by intros m i; rewrite lookup_op !lookup_core cmra_core_l.
+  - by intros m i; rewrite !lookup_core cmra_core_idemp.
   - intros x y; rewrite !map_included_spec; intros Hm i.
-    by rewrite !lookup_unit; apply cmra_unit_preserving.
+    by rewrite !lookup_core; apply cmra_core_preserving.
   - intros n m1 m2 Hm i; apply cmra_validN_op_l with (m2 !! i).
     by rewrite -lookup_op.
   - intros x y; rewrite map_included_spec=> ? i.
@@ -201,21 +201,21 @@ Lemma map_singleton_valid i x : ✓ ({[ i := x ]} : gmap K A) ↔ ✓ x.
 Proof. rewrite !cmra_valid_validN. by setoid_rewrite map_singleton_validN. Qed.
 
 Lemma map_insert_singleton_opN n m i x :
-  m !! i = None ∨ m !! i ≡{n}≡ Some (unit x) → <[i:=x]> m ≡{n}≡ {[ i := x ]} ⋅ m.
+  m !! i = None ∨ m !! i ≡{n}≡ Some (core x) → <[i:=x]> m ≡{n}≡ {[ i := x ]} ⋅ m.
 Proof.
   intros Hi j; destruct (decide (i = j)) as [->|];
     [|by rewrite lookup_op lookup_insert_ne // lookup_singleton_ne // left_id].
   rewrite lookup_op lookup_insert lookup_singleton.
-  by destruct Hi as [->| ->]; constructor; rewrite ?cmra_unit_r.
+  by destruct Hi as [->| ->]; constructor; rewrite ?cmra_core_r.
 Qed.
 Lemma map_insert_singleton_op m i x :
-  m !! i = None ∨ m !! i ≡ Some (unit x) → <[i:=x]> m ≡ {[ i := x ]} ⋅ m.
+  m !! i = None ∨ m !! i ≡ Some (core x) → <[i:=x]> m ≡ {[ i := x ]} ⋅ m.
 Proof.
   rewrite !equiv_dist; naive_solver eauto using map_insert_singleton_opN.
 Qed.
 
-Lemma map_unit_singleton (i : K) (x : A) :
-  unit ({[ i := x ]} : gmap K A) = {[ i := unit x ]}.
+Lemma map_core_singleton (i : K) (x : A) :
+  core ({[ i := x ]} : gmap K A) = {[ i := core x ]}.
 Proof. apply map_fmap_singleton. Qed.
 Lemma map_op_singleton (i : K) (x y : A) :
   {[ i := x ]} ⋅ {[ i := y ]} = ({[ i := x ⋅ y ]} : gmap K A).
@@ -315,7 +315,7 @@ End freshness.
 
 (* Allocation is a local update: Just use composition with a singleton map. *)
 (* Deallocation is *not* a local update. The trouble is that if we
-   own {[ i ↦ x ]}, then the frame could always own "unit x", and prevent
+   own {[ i ↦ x ]}, then the frame could always own "core x", and prevent
    deallocation. *)
 
 (* Applying a local update at a position we own is a local update. *)

algebra/frac.v

@@ -122,7 +122,7 @@ Instance frac_valid : Valid (frac A) := λ x,
 Instance frac_validN : ValidN (frac A) := λ n x,
   match x with Frac q a => (q ≤ 1)%Qc ∧ ✓{n} a | FracUnit => True end.
 Global Instance frac_empty : Empty (frac A) := FracUnit.
-Instance frac_unit : Unit (frac A) := λ _, ∅.
+Instance frac_core : Core (frac A) := λ _, ∅.
 Instance frac_op : Op (frac A) := λ x y,
   match x, y with
   | Frac q1 a, Frac q2 b => Frac (q1 + q2) (a ⋅ b)
@@ -225,7 +225,7 @@ Qed.
 Lemma frac_update (a1 a2 : A) p : a1 ~~> a2 → Frac p a1 ~~> Frac p a2.
 Proof.
   intros Ha n [q b|] [??]; split; auto.
-  apply cmra_validN_op_l with (unit a1), Ha. by rewrite cmra_unit_r.
+  apply cmra_validN_op_l with (core a1), Ha. by rewrite cmra_core_r.
 Qed.
 End cmra.
 

algebra/iprod.v

@@ -117,13 +117,13 @@ Section iprod_cmra.
   Implicit Types f g : iprod B.
 
   Instance iprod_op : Op (iprod B) := λ f g x, f x ⋅ g x.
-  Instance iprod_unit : Unit (iprod B) := λ f x, unit (f x).
+  Instance iprod_core : Core (iprod B) := λ f x, core (f x).
   Instance iprod_valid : Valid (iprod B) := λ f, ∀ x, ✓ f x.
   Instance iprod_validN : ValidN (iprod B) := λ n f, ∀ x, ✓{n} f x.
   Instance iprod_div : Div (iprod B) := λ f g x, f x ÷ g x.
 
   Definition iprod_lookup_op f g x : (f ⋅ g) x = f x ⋅ g x := eq_refl.
-  Definition iprod_lookup_unit f x : (unit f) x = unit (f x) := eq_refl.
+  Definition iprod_lookup_core f x : (core f) x = core (f x) := eq_refl.
   Definition iprod_lookup_div f g x : (f ÷ g) x = f x ÷ g x := eq_refl.
 
   Lemma iprod_included_spec (f g : iprod B) : f ≼ g ↔ ∀ x, f x ≼ g x.
@@ -138,7 +138,7 @@ Section iprod_cmra.
   Proof.
     split.
     - by intros n f1 f2 f3 Hf x; rewrite iprod_lookup_op (Hf x).
-    - by intros n f1 f2 Hf x; rewrite iprod_lookup_unit (Hf x).
+    - by intros n f1 f2 Hf x; rewrite iprod_lookup_core (Hf x).
     - by intros n f1 f2 Hf ? x; rewrite -(Hf x).
     - by intros n f f' Hf g g' Hg i; rewrite iprod_lookup_div (Hf i) (Hg i).
     - intros g; split.
@@ -147,10 +147,10 @@ Section iprod_cmra.
     - intros n f Hf x; apply cmra_validN_S, Hf.
     - by intros f1 f2 f3 x; rewrite iprod_lookup_op assoc.
     - by intros f1 f2 x; rewrite iprod_lookup_op comm.
-    - by intros f x; rewrite iprod_lookup_op iprod_lookup_unit cmra_unit_l.
-    - by intros f x; rewrite iprod_lookup_unit cmra_unit_idemp.
+    - by intros f x; rewrite iprod_lookup_op iprod_lookup_core cmra_core_l.
+    - by intros f x; rewrite iprod_lookup_core cmra_core_idemp.
     - intros f1 f2; rewrite !iprod_included_spec=> Hf x.
-      by rewrite iprod_lookup_unit; apply cmra_unit_preserving, Hf.
+      by rewrite iprod_lookup_core; apply cmra_core_preserving, Hf.
     - intros n f1 f2 Hf x; apply cmra_validN_op_l with (f2 x), Hf.
     - intros f1 f2; rewrite iprod_included_spec=> Hf x.
       by rewrite iprod_lookup_op iprod_lookup_div cmra_op_div; try apply Hf.
@@ -211,12 +211,12 @@ Section iprod_cmra.
     by apply cmra_empty_validN.
   Qed.
 
-  Lemma iprod_unit_singleton x (y : B x) :
-    unit (iprod_singleton x y) ≡ iprod_singleton x (unit y).
+  Lemma iprod_core_singleton x (y : B x) :
+    core (iprod_singleton x y) ≡ iprod_singleton x (core y).
   Proof.
     by move=>x'; destruct (decide (x = x')) as [->|];
-      rewrite iprod_lookup_unit ?iprod_lookup_singleton
-      ?iprod_lookup_singleton_ne // cmra_unit_empty.
+      rewrite iprod_lookup_core ?iprod_lookup_singleton
+      ?iprod_lookup_singleton_ne // cmra_core_empty.
   Qed.