Rename absolutely → objectively and relatively → subjectively.

sed -i 's/absolute/objective/g; s/relative/subjective/g; s/Absolute/Objective/g; s/Relative/Subjective/g' $(find ./ -name \*.v)

ProofMode.md

@@ -117,7 +117,7 @@ Modalities
 - `iModIntro mod` : introduction of a modality. The type class `FromModal` is
   used to specify which modalities this tactic should introduce. Instances of
   that type class include: later, except 0, basic update and fancy update,
-  persistently, affinely, plainly, absorbingly, absolutely, and relatively.
+  persistently, affinely, plainly, absorbingly, objectively, and subjectively.
   The optional argument `mod` can be used to specify what modality to introduce
   in case of ambiguity, e.g. `⎡|==> P⎤`.
 - `iAlways` : a deprecated alias of `iModIntro`.

theories/bi/embedding.v

@@ -233,6 +233,6 @@ End sbi_embed.
 
 (* Not defined using an ordinary [Instance] because the default
 [class_apply @bi_embed_plainly] shelves the [BiPlainly] premise, making proof
-search for the other premises fail. See the proof of [monPred_absolutely_plain]
+search for the other premises fail. See the proof of [monPred_objectively_plain]
 for an example where it would fail with a regular [Instance].*)
 Hint Extern 4 (Plain ⎡_⎤) => eapply @embed_plain : typeclass_instances.

theories/proofmode/classes.v

@@ -98,7 +98,7 @@ introduce, [sel] should be an evar.
 For modalities [N] that do not need to augment the proof mode environment, one
 can define an instance [FromModal modality_id (N P) P]. Defining such an
 instance only imposes the proof obligation [P ⊢ N P]. Examples of such
-modalities [N] are [bupd], [fupd], [except_0], [monPred_relatively] and
+modalities [N] are [bupd], [fupd], [except_0], [monPred_subjectively] and
 [bi_absorbingly]. *)
 Class FromModal {PROP1 PROP2 : bi} {A}
     (M : modality PROP1 PROP2) (sel : A) (P : PROP2) (Q : PROP1) :=

theories/proofmode/modalities.v

@@ -154,7 +154,7 @@ End modality1.
 [P ⊢ M P]. This is done by defining an instance [FromModal modality_id (M P) P],
 which will instruct [iModIntro] to introduce the modality without modifying the
 proof mode context. Examples of such modalities are [bupd], [fupd], [except_0],
-[monPred_relatively] and [bi_absorbingly]. *)
+[monPred_subjectively] and [bi_absorbingly]. *)
 Lemma modality_id_mixin {PROP : bi} : modality_mixin (@id PROP) MIEnvId MIEnvId.
 Proof. split; simpl; eauto. Qed.
 Definition modality_id {PROP : bi} := Modality (@id PROP) modality_id_mixin.

theories/proofmode/monpred.v

@@ -18,18 +18,18 @@ Hint Extern 1 (IsBiIndexRel _ _) => unfold IsBiIndexRel; assumption
 Section modalities.
   Context {I : biIndex} {PROP : bi}.
 
-  Lemma modality_absolutely_mixin :
-    modality_mixin (@monPred_absolutely I PROP)
-      (MIEnvFilter Absolute) (MIEnvFilter Absolute).
+  Lemma modality_objectively_mixin :
+    modality_mixin (@monPred_objectively I PROP)
+      (MIEnvFilter Objective) (MIEnvFilter Objective).
   Proof.
     split; simpl; split_and?; intros;
       try match goal with H : TCDiag _ _ _ |- _ => destruct H end;
-      eauto using bi.equiv_entails_sym, absolute_absolutely,
-        monPred_absolutely_mono, monPred_absolutely_and,
-        monPred_absolutely_sep_2 with typeclass_instances.
+      eauto using bi.equiv_entails_sym, objective_objectively,
+        monPred_objectively_mono, monPred_objectively_and,
+        monPred_objectively_sep_2 with typeclass_instances.
   Qed.
-  Definition modality_absolutely :=
-    Modality _ modality_absolutely_mixin.
+  Definition modality_objectively :=
+    Modality _ modality_objectively_mixin.
 End modalities.
 
 Section bi.
@@ -42,12 +42,12 @@ Implicit Types 𝓟 𝓠 𝓡 : PROP.
 Implicit Types φ : Prop.
 Implicit Types i j : I.
 
-Global Instance from_modal_absolutely P :
-  FromModal modality_absolutely (∀ᵢ P) (∀ᵢ P) P | 1.
+Global Instance from_modal_objectively P :
+  FromModal modality_objectively (∀ᵢ P) (∀ᵢ P) P | 1.
 Proof. by rewrite /FromModal. Qed.
-Global Instance from_modal_relatively P :
+Global Instance from_modal_subjectively P :
   FromModal modality_id (∃ᵢ P) (∃ᵢ P) P | 1.
-Proof. by rewrite /FromModal /= -monPred_relatively_intro. Qed.
+Proof. by rewrite /FromModal /= -monPred_subjectively_intro. Qed.
 
 Global Instance from_modal_affinely_monPred_at `(sel : A) P Q 𝓠 i :
   FromModal modality_affinely sel P Q → MakeMonPredAt i Q 𝓠 →
@@ -135,12 +135,12 @@ Proof.
   apply  bi.affinely_persistently_if_elim.
 Qed.
 
-Global Instance from_assumption_make_monPred_absolutely P Q :
+Global Instance from_assumption_make_monPred_objectively P Q :
   FromAssumption p P Q → FromAssumption p (∀ᵢ P) Q.
-Proof. intros ?. by rewrite /FromAssumption monPred_absolutely_elim. Qed.
-Global Instance from_assumption_make_monPred_relatively P Q :
+Proof. intros ?. by rewrite /FromAssumption monPred_objectively_elim. Qed.
+Global Instance from_assumption_make_monPred_subjectively P Q :
   FromAssumption p P Q → FromAssumption p P (∃ᵢ Q).
-Proof. intros ?. by rewrite /FromAssumption -monPred_relatively_intro. Qed.
+Proof. intros ?. by rewrite /FromAssumption -monPred_subjectively_intro. Qed.
 
 Global Instance as_valid_monPred_at φ P (Φ : I → PROP) :
   AsValid0 φ P → (∀ i, MakeMonPredAt i P (Φ i)) → AsValid φ (∀ i, Φ i) | 100.
@@ -292,26 +292,26 @@ Proof.
   by rewrite monPred_at_exist.
 Qed.
 
-Global Instance from_forall_monPred_at_absolutely P (Φ : I → PROP) i :
+Global Instance from_forall_monPred_at_objectively P (Φ : I → PROP) i :
   (∀ i, MakeMonPredAt i P (Φ i)) → FromForall ((∀ᵢ P) i)%I Φ.
 Proof.
-  rewrite /FromForall /MakeMonPredAt monPred_at_absolutely=>H. by setoid_rewrite <- H.
+  rewrite /FromForall /MakeMonPredAt monPred_at_objectively=>H. by setoid_rewrite <- H.
 Qed.
-Global Instance into_forall_monPred_at_absolutely P (Φ : I → PROP) i :
+Global Instance into_forall_monPred_at_objectively P (Φ : I → PROP) i :
   (∀ i, MakeMonPredAt i P (Φ i)) → IntoForall ((∀ᵢ P) i) Φ.
 Proof.
-  rewrite /IntoForall /MakeMonPredAt monPred_at_absolutely=>H. by setoid_rewrite <- H.
+  rewrite /IntoForall /MakeMonPredAt monPred_at_objectively=>H. by setoid_rewrite <- H.
 Qed.
 
 Global Instance from_exist_monPred_at_ex P (Φ : I → PROP) i :
   (∀ i, MakeMonPredAt i P (Φ i)) → FromExist ((∃ᵢ P) i) Φ.
 Proof.
-  rewrite /FromExist /MakeMonPredAt monPred_at_relatively=>H. by setoid_rewrite <- H.
+  rewrite /FromExist /MakeMonPredAt monPred_at_subjectively=>H. by setoid_rewrite <- H.
 Qed.
 Global Instance into_exist_monPred_at_ex P (Φ : I → PROP) i :
   (∀ i, MakeMonPredAt i P (Φ i)) → IntoExist ((∃ᵢ P) i) Φ.
 Proof.
-  rewrite /IntoExist /MakeMonPredAt monPred_at_relatively=>H. by setoid_rewrite <- H.
+  rewrite /IntoExist /MakeMonPredAt monPred_at_subjectively=>H. by setoid_rewrite <- H.
 Qed.
 
 Global Instance from_forall_monPred_at {A} P (Φ : A → monPred) (Ψ : A → PROP) i :
@@ -346,11 +346,11 @@ Proof.
                          ?monPred_at_persistently monPred_at_embed.
 Qed.
 
-Global Instance into_embed_absolute P :
-  Absolute P → IntoEmbed P (∀ i, P i).
+Global Instance into_embed_objective P :
+  Objective P → IntoEmbed P (∀ i, P i).
 Proof.
   rewrite /IntoEmbed=> ?.
-  by rewrite {1}(absolute_absolutely P) monPred_absolutely_unfold.
+  by rewrite {1}(objective_objectively P) monPred_objectively_unfold.
 Qed.
 
 Global Instance elim_modal_at_bupd_goal `{BiBUpd PROP} φ 𝓟 𝓟' Q Q' i :

theories/tests/proofmode_monpred.v

@@ -69,14 +69,14 @@ Section tests.
     iIntros "H HP". by iApply "H".
   Qed.
 
-  Lemma test_absolutely P Q : ∀ᵢ emp -∗ ∀ᵢ P -∗ ∀ᵢ Q -∗ ∀ᵢ (P ∗ Q).
+  Lemma test_objectively P Q : ∀ᵢ emp -∗ ∀ᵢ P -∗ ∀ᵢ Q -∗ ∀ᵢ (P ∗ Q).
   Proof. iIntros "#? HP HQ". iAlways. by iSplitL "HP". Qed.
 
-  Lemma test_absolutely_absorbing P Q R `{!Absorbing P} :
+  Lemma test_objectively_absorbing P Q R `{!Absorbing P} :
     ∀ᵢ emp -∗ ∀ᵢ P -∗ ∀ᵢ Q -∗ R -∗ ∀ᵢ (P ∗ Q).
   Proof. iIntros "#? HP HQ HR". iAlways. by iSplitL "HP". Qed.
 
-  Lemma test_absolutely_affine P Q R `{!Affine R} :
+  Lemma test_objectively_affine P Q R `{!Affine R} :
     ∀ᵢ emp -∗ ∀ᵢ P -∗ ∀ᵢ Q -∗ R -∗ ∀ᵢ (P ∗ Q).
   Proof. iIntros "#? HP HQ HR". iAlways. by iSplitL "HP". Qed.
 
@@ -84,7 +84,7 @@ Section tests.
     □ P -∗ Q -∗ ⎡𝓟⎤ -∗ ⎡𝓠⎤ -∗ ⎡ 𝓟 ∗ 𝓠 ⎤.
   Proof. iIntros "#H1 _ H2 H3". iAlways. iFrame. Qed.
 
-  Lemma test_iModIntro_embed_absolute P `{!Absolute Q} 𝓟 𝓠 :
+  Lemma test_iModIntro_embed_objective P `{!Objective Q} 𝓟 𝓠 :
     □ P -∗ Q -∗ ⎡𝓟⎤ -∗ ⎡𝓠⎤ -∗ ⎡ ∀ i, 𝓟 ∗ 𝓠 ∗ Q i ⎤.
   Proof. iIntros "#H1 H2 H3 H4". iAlways. iFrame. Qed.