Split the MakeXXX typeclasses into two, and add Hint Modes for them.

They are split into:
1- KnownMakeXXX , which only works if the parameter is not an evar. Hence, it will never force this evar to becomes e.g., emp or True.
2- MakeXXX, which works even if this is an evar, but it only has instances that will not instanciate arbitrarilly this evar.

theories/proofmode/class_instances.v

@@ -871,16 +871,13 @@ Proof.
   rewrite /FromPure /Frame=> <-. by rewrite affinely_persistently_if_elim sep_elim_l.
 Qed.
 
-Class MakeEmbed `{BiEmbedding PROP PROP'} P (Q : PROP') :=
-  make_embed : ⎡P⎤ ⊣⊢ Q.
-Arguments MakeEmbed {_ _ _} _%I _%I.
 Global Instance make_embed_pure `{BiEmbedding PROP PROP'} φ :
-  MakeEmbed ⌜φ⌝ ⌜φ⌝.
-Proof. by rewrite /MakeEmbed bi_embed_pure. Qed.
+  KnownMakeEmbed ⌜φ⌝ ⌜φ⌝.
+Proof. apply bi_embed_pure. Qed.
 Global Instance make_embed_emp `{BiEmbedding PROP PROP'} :
-  MakeEmbed emp emp.
-Proof. by rewrite /MakeEmbed bi_embed_emp. Qed.
-Global Instance make_embed_default `{BiEmbedding PROP PROP'} :
+  KnownMakeEmbed emp emp.
+Proof. apply bi_embed_emp. Qed.
+Global Instance make_embed_default `{BiEmbedding PROP PROP'} P :
   MakeEmbed P ⎡P⎤ | 100.
 Proof. by rewrite /MakeEmbed. Qed.
 
@@ -894,20 +891,18 @@ Global Instance frame_pure_embed `{BiEmbedding PROP PROP'} p P Q (Q' : PROP') φ
   Frame p ⌜φ⌝ P Q → MakeEmbed Q Q' → Frame p ⌜φ⌝ ⎡P⎤ Q'.
 Proof. rewrite /Frame /MakeEmbed -bi_embed_pure. apply (frame_embed p P Q). Qed.
 
-Class MakeSep (P Q PQ : PROP) := make_sep : P ∗ Q ⊣⊢ PQ.
-Arguments MakeSep _%I _%I _%I.
-Global Instance make_sep_emp_l P : MakeSep emp P P.
-Proof. by rewrite /MakeSep left_id. Qed.
-Global Instance make_sep_emp_r P : MakeSep P emp P.
-Proof. by rewrite /MakeSep right_id. Qed.
-Global Instance make_sep_true_l P : Absorbing P → MakeSep True P P.
-Proof. intros. by rewrite /MakeSep True_sep. Qed.
-Global Instance make_and_emp_l_absorbingly P : MakeSep True P (bi_absorbingly P) | 10.
-Proof. intros. by rewrite /MakeSep. Qed.
-Global Instance make_sep_true_r P : Absorbing P → MakeSep P True P.
-Proof. intros. by rewrite /MakeSep sep_True. Qed.
-Global Instance make_and_emp_r_absorbingly P : MakeSep P True (bi_absorbingly P) | 10.
-Proof. intros. by rewrite /MakeSep comm. Qed.
+Global Instance make_sep_emp_l P : KnownLMakeSep emp P P.
+Proof. apply left_id, _. Qed.
+Global Instance make_sep_emp_r P : KnownRMakeSep P emp P.
+Proof. apply right_id, _. Qed.
+Global Instance make_sep_true_l P : Absorbing P → KnownLMakeSep True P P.
+Proof. intros. apply True_sep, _. Qed.
+Global Instance make_and_emp_l_absorbingly P : KnownLMakeSep True P (bi_absorbingly P) | 10.
+Proof. intros. by rewrite /KnownLMakeSep /MakeSep. Qed.
+Global Instance make_sep_true_r P : Absorbing P → KnownRMakeSep P True P.
+Proof. intros. by rewrite /KnownRMakeSep /MakeSep sep_True. Qed.
+Global Instance make_and_emp_r_absorbingly P : KnownRMakeSep P True (bi_absorbingly P) | 10.
+Proof. intros. by rewrite /KnownRMakeSep /MakeSep comm. Qed.
 Global Instance make_sep_default P Q : MakeSep P Q (P ∗ Q) | 100.
 Proof. by rewrite /MakeSep. Qed.
 
@@ -937,20 +932,18 @@ Global Instance frame_big_sepL_app {A} p (Φ : nat → A → PROP) R Q l l1 l2 :
   Frame p R ([∗ list] k ↦ y ∈ l, Φ k y) Q.
 Proof. rewrite /IsApp=>->. by rewrite /Frame big_opL_app. Qed.
 
-Class MakeAnd (P Q PQ : PROP) := make_and : P ∧ Q ⊣⊢ PQ.
-Arguments MakeAnd _%I _%I _%I.
-Global Instance make_and_true_l P : MakeAnd True P P.
-Proof. by rewrite /MakeAnd left_id. Qed.
-Global Instance make_and_true_r P : MakeAnd P True P.
-Proof. by rewrite /MakeAnd right_id. Qed.
-Global Instance make_and_emp_l P : Affine P → MakeAnd emp P P.
-Proof. intros. by rewrite /MakeAnd emp_and. Qed.
-Global Instance make_and_emp_l_affinely P : MakeAnd emp P (bi_affinely P) | 10.
-Proof. intros. by rewrite /MakeAnd. Qed.
-Global Instance make_and_emp_r P : Affine P → MakeAnd P emp P.
-Proof. intros. by rewrite /MakeAnd and_emp. Qed.
-Global Instance make_and_emp_r_affinely P : MakeAnd P emp (bi_affinely P) | 10.
-Proof. intros. by rewrite /MakeAnd comm. Qed.
+Global Instance make_and_true_l P : KnownLMakeAnd True P P.
+Proof. apply left_id, _. Qed.
+Global Instance make_and_true_r P : KnownRMakeAnd P True P.
+Proof. by rewrite /KnownRMakeAnd /MakeAnd right_id. Qed.
+Global Instance make_and_emp_l P : Affine P → KnownLMakeAnd emp P P.
+Proof. intros. by rewrite /KnownLMakeAnd /MakeAnd emp_and. Qed.
+Global Instance make_and_emp_l_affinely P : KnownLMakeAnd emp P (bi_affinely P) | 10.
+Proof. intros. by rewrite /KnownLMakeAnd /MakeAnd. Qed.
+Global Instance make_and_emp_r P : Affine P → KnownRMakeAnd P emp P.
+Proof. intros. by rewrite /KnownRMakeAnd /MakeAnd and_emp. Qed.
+Global Instance make_and_emp_r_affinely P : KnownRMakeAnd P emp (bi_affinely P) | 10.
+Proof. intros. by rewrite /KnownRMakeAnd /MakeAnd comm. Qed.
 Global Instance make_and_default P Q : MakeAnd P Q (P ∧ Q) | 100.
 Proof. by rewrite /MakeAnd. Qed.
 
@@ -965,16 +958,14 @@ Proof.
   [rewrite and_elim_l|rewrite and_elim_r]; done.
 Qed.
 
-Class MakeOr (P Q PQ : PROP) := make_or : P ∨ Q ⊣⊢ PQ.
-Arguments MakeOr _%I _%I _%I.
-Global Instance make_or_true_l P : MakeOr True P True.
-Proof. by rewrite /MakeOr left_absorb. Qed.
-Global Instance make_or_true_r P : MakeOr P True True.
-Proof. by rewrite /MakeOr right_absorb. Qed.
-Global Instance make_or_emp_l P : Affine P → MakeOr emp P emp.
-Proof. intros. by rewrite /MakeOr emp_or. Qed.
-Global Instance make_or_emp_r P : Affine P → MakeOr P emp emp.
-Proof. intros. by rewrite /MakeOr or_emp. Qed.
+Global Instance make_or_true_l P : KnownLMakeOr True P True.
+Proof. apply left_absorb, _. Qed.
+Global Instance make_or_true_r P : KnownRMakeOr P True True.
+Proof. by rewrite /KnownRMakeOr /MakeOr right_absorb. Qed.
+Global Instance make_or_emp_l P : Affine P → KnownLMakeOr emp P emp.
+Proof. intros. by rewrite /KnownLMakeOr /MakeOr emp_or. Qed.
+Global Instance make_or_emp_r P : Affine P → KnownRMakeOr P emp emp.
+Proof. intros. by rewrite /KnownRMakeOr /MakeOr or_emp. Qed.
 Global Instance make_or_default P Q : MakeOr P Q (P ∨ Q) | 100.
 Proof. by rewrite /MakeOr. Qed.
 
@@ -1013,12 +1004,10 @@ Proof.
   by rewrite assoc (comm _ P1) -assoc wand_elim_r.
 Qed.
 
-Class MakeAffinely (P Q : PROP) := make_affinely : bi_affinely P ⊣⊢ Q.
-Arguments MakeAffinely _%I _%I.
-Global Instance make_affinely_True : MakeAffinely True emp | 0.
-Proof. by rewrite /MakeAffinely affinely_True_emp affinely_emp. Qed.
-Global Instance make_affinely_affine P : Affine P → MakeAffinely P P | 1.
-Proof. intros. by rewrite /MakeAffinely affine_affinely. Qed.
+Global Instance make_affinely_True : @KnownMakeAffinely PROP True emp | 0.
+Proof. by rewrite /KnownMakeAffinely /MakeAffinely affinely_True_emp affinely_emp. Qed.
+Global Instance make_affinely_affine P : Affine P → KnownMakeAffinely P P | 1.
+Proof. intros. by rewrite /KnownMakeAffinely /MakeAffinely affine_affinely. Qed.
 Global Instance make_affinely_default P : MakeAffinely P (bi_affinely P) | 100.
 Proof. by rewrite /MakeAffinely. Qed.
 
@@ -1029,10 +1018,11 @@ Proof.
   by rewrite -{1}affinely_idemp affinely_sep_2.
 Qed.
 
-Class MakeAbsorbingly (P Q : PROP) := make_absorbingly : bi_absorbingly P ⊣⊢ Q.
-Arguments MakeAbsorbingly _%I _%I.
-Global Instance make_absorbingly_emp : MakeAbsorbingly emp True | 0.
-Proof. by rewrite /MakeAbsorbingly -absorbingly_True_emp absorbingly_pure. Qed.
+Global Instance make_absorbingly_emp : @KnownMakeAbsorbingly PROP emp True | 0.
+Proof.
+  by rewrite /KnownMakeAbsorbingly /MakeAbsorbingly
+     -absorbingly_True_emp absorbingly_pure.
+Qed.
 (* Note: there is no point in having an instance `Absorbing P → MakeAbsorbingly P P`
 because framing will never turn a proposition that is not absorbing into
 something that is absorbing. *)
@@ -1043,12 +1033,13 @@ Global Instance frame_absorbingly p R P Q Q' :
   Frame p R P Q → MakeAbsorbingly Q Q' → Frame p R (bi_absorbingly P) Q'.
 Proof. rewrite /Frame /MakeAbsorbingly=> <- <- /=. by rewrite absorbingly_sep_r. Qed.
 
-Class MakePersistently (P Q : PROP) := make_persistently : bi_persistently P ⊣⊢ Q.
-Arguments MakePersistently _%I _%I.
-Global Instance make_persistently_true : MakePersistently True True.
-Proof. by rewrite /MakePersistently persistently_pure. Qed.
-Global Instance make_persistently_emp : MakePersistently emp True.
-Proof. by rewrite /MakePersistently -persistently_True_emp persistently_pure. Qed.
+Global Instance make_persistently_true : @KnownMakePersistently PROP True True.
+Proof. by rewrite /KnownMakePersistently /MakePersistently persistently_pure. Qed.
+Global Instance make_persistently_emp : @KnownMakePersistently PROP emp True.
+Proof.
+  by rewrite /KnownMakePersistently /MakePersistently
+     -persistently_True_emp persistently_pure.
+Qed.
 Global Instance make_persistently_default P :
   MakePersistently P (bi_persistently P) | 100.
 Proof. by rewrite /MakePersistently. Qed.
@@ -1536,10 +1527,8 @@ Global Instance frame_eq_embed `{SbiEmbedding PROP PROP'} p P Q (Q' : PROP')
   Frame p (a ≡ b) P Q → MakeEmbed Q Q' → Frame p (a ≡ b) ⎡P⎤ Q'.
 Proof. rewrite /Frame /MakeEmbed -sbi_embed_internal_eq. apply (frame_embed p P Q). Qed.
 
-Class MakeLaterN (n : nat) (P lP : PROP) := make_laterN : ▷^n P ⊣⊢ lP.
-Arguments MakeLaterN _%nat _%I _%I.
-Global Instance make_laterN_true n : MakeLaterN n True True | 0.
-Proof. by rewrite /MakeLaterN laterN_True. Qed.
+Global Instance make_laterN_true n : @KnownMakeLaterN PROP n True True | 0.
+Proof. by rewrite /KnownMakeLaterN /MakeLaterN laterN_True. Qed.
 Global Instance make_laterN_0 P : MakeLaterN 0 P P | 0.
 Proof. by rewrite /MakeLaterN. Qed.
 Global Instance make_laterN_1 P : MakeLaterN 1 P (▷ P) | 2.
@@ -1569,11 +1558,8 @@ Global Instance frame_fupd `{FUpdFacts PROP} p E1 E2 R P Q :
   Frame p R P Q → Frame p R (|={E1,E2}=> P) (|={E1,E2}=> Q).
 Proof. rewrite /Frame=><-. by rewrite fupd_frame_l. Qed.
 
-Class MakeExcept0 (P Q : PROP) := make_except_0 : ◇ P ⊣⊢ Q.
-Arguments MakeExcept0 _%I _%I.
-
-Global Instance make_except_0_True : MakeExcept0 True True.
-Proof. by rewrite /MakeExcept0 except_0_True. Qed.
+Global Instance make_except_0_True : @KnownMakeExcept0 PROP True True.
+Proof. by rewrite /KnownMakeExcept0 /MakeExcept0 except_0_True. Qed.
 Global Instance make_except_0_default P : MakeExcept0 P (◇ P) | 100.
 Proof. by rewrite /MakeExcept0. Qed.
 

theories/proofmode/classes.v

@@ -389,6 +389,94 @@ Instance maybe_frame_default {PROP : bi} (R P : PROP) :
   TCOr (Affine R) (Absorbing P) → MaybeFrame false R P P false | 100.
 Proof. intros. rewrite /MaybeFrame /=. apply: sep_elim_r. Qed.
 
+(* For each of the [MakeXxxx] class, there is a [KnownMakeXxxx] variant,
+   that only succeeds if the parameter(s) is not an evar. In the case
+   the parameter(s) is an evar, then [MakeXxxx] will not instantiate
+   it arbitrarily. *)
+Class MakeEmbed `{BiEmbedding PROP PROP'} (P : PROP) (Q : PROP') :=
+  make_embed : ⎡P⎤ ⊣⊢ Q.
+Arguments MakeEmbed {_ _ _ _} _%I _%I.
+Hint Mode MakeEmbed + + + + - - : typeclass_instances.
+Class KnownMakeEmbed `{BiEmbedding PROP PROP'} (P : PROP) (Q : PROP') :=
+  go_make_embed :> MakeEmbed P Q.
+Arguments KnownMakeEmbed {_ _ _ _} _%I _%I.
+Hint Mode KnownMakeEmbed + + + + ! - : typeclass_instances.
+
+Class MakeSep {PROP : bi} (P Q PQ : PROP) := make_sep : P ∗ Q ⊣⊢ PQ .
+Arguments MakeSep {_} _%I _%I _%I.
+Hint Mode MakeSep + - - - : typeclass_instances.
+Class KnownLMakeSep {PROP : bi} (P Q PQ : PROP) := gol_make_sep :> MakeSep P Q PQ.
+Arguments KnownLMakeSep {_} _%I _%I _%I.
+Hint Mode KnownLMakeSep + ! - - : typeclass_instances.
+Class KnownRMakeSep {PROP : bi} (P Q PQ : PROP) := gor_make_sep :> MakeSep P Q PQ.
+Arguments KnownRMakeSep {_} _%I _%I _%I.
+Hint Mode KnownRMakeSep + - ! - : typeclass_instances.
+
+Class MakeAnd {PROP : bi} (P Q PQ : PROP) :=  make_and_l : P ∧ Q ⊣⊢ PQ.
+Arguments MakeAnd {_} _%I _%I _%I.
+Hint Mode MakeAnd + - - - : typeclass_instances.
+Class KnownLMakeAnd {PROP : bi} (P Q PQ : PROP) := gol_make_and :> MakeAnd P Q PQ.
+Arguments KnownLMakeAnd {_} _%I _%I _%I.
+Hint Mode KnownLMakeAnd + ! - - : typeclass_instances.
+Class KnownRMakeAnd {PROP : bi} (P Q PQ : PROP) := gor_make_and :> MakeAnd P Q PQ.
+Arguments KnownRMakeAnd {_} _%I _%I _%I.
+Hint Mode KnownRMakeAnd + - ! - : typeclass_instances.
+
+Class MakeOr {PROP : bi} (P Q PQ : PROP) := make_or_l : P ∨ Q ⊣⊢ PQ.
+Arguments MakeOr {_} _%I _%I _%I.
+Hint Mode MakeOr + - - - : typeclass_instances.
+Class KnownLMakeOr {PROP : bi} (P Q PQ : PROP) := gol_make_or :> MakeOr P Q PQ.
+Arguments KnownLMakeOr {_} _%I _%I _%I.
+Hint Mode KnownLMakeOr + ! - - : typeclass_instances.
+Class KnownRMakeOr {PROP : bi} (P Q PQ : PROP) := gor_make_or :> MakeOr P Q PQ.
+Arguments KnownRMakeOr {_} _%I _%I _%I.
+Hint Mode KnownRMakeOr + - ! - : typeclass_instances.
+
+Class MakeAffinely {PROP : bi} (P Q : PROP) :=
+  make_affinely :> bi_affinely P ⊣⊢ Q.
+Arguments MakeAffinely {_} _%I _%I.
+Hint Mode MakeAffinely + - - : typeclass_instances.
+Class KnownMakeAffinely {PROP : bi} (P Q : PROP) :=
+  go_make_affinely : MakeAffinely P Q.
+Arguments KnownMakeAffinely {_} _%I _%I.
+Hint Mode KnownMakeAffinely + ! - : typeclass_instances.
+
+Class MakeAbsorbingly {PROP : bi} (P Q : PROP) :=
+  make_absorbingly : bi_absorbingly P ⊣⊢ Q.
+Arguments MakeAbsorbingly {_} _%I _%I.
+Hint Mode MakeAbsorbingly + - - : typeclass_instances.
+Class KnownMakeAbsorbingly {PROP : bi} (P Q : PROP) :=
+  go_make_absorbingly :> MakeAbsorbingly P Q.
+Arguments KnownMakeAbsorbingly {_} _%I _%I.
+Hint Mode KnownMakeAbsorbingly + ! - : typeclass_instances.
+
+Class MakePersistently {PROP : bi} (P Q : PROP) :=
+  make_persistently : bi_persistently P ⊣⊢ Q.
+Arguments MakePersistently {_} _%I _%I.
+Hint Mode MakePersistently + - - : typeclass_instances.
+Class KnownMakePersistently {PROP : bi} (P Q : PROP) :=
+  go_make_persistently :> MakePersistently P Q.
+Arguments KnownMakePersistently {_} _%I _%I.
+Hint Mode KnownMakePersistently + ! - : typeclass_instances.
+
+Class MakeLaterN {PROP : sbi} (n : nat) (P lP : PROP) :=
+  make_laterN : ▷^n P ⊣⊢ lP.
+Arguments MakeLaterN {_} _%nat _%I _%I.
+Hint Mode MakeLaterN + + - - : typeclass_instances.
+Class KnownMakeLaterN {PROP : sbi} (n : nat) (P lP : PROP) :=
+  go_make_laterN :> MakeLaterN n P lP.
+Arguments KnownMakeLaterN {_} _%nat _%I _%I.
+Hint Mode KnownMakeLaterN + + ! - : typeclass_instances.
+
+Class MakeExcept0 {PROP : sbi} (P Q : PROP) :=
+  make_except_0 : sbi_except_0 P ⊣⊢ Q.
+Arguments MakeExcept0 {_} _%I _%I.
+Hint Mode MakeExcept0 + - - : typeclass_instances.
+Class KnownMakeExcept0 {PROP : sbi} (P Q : PROP) :=
+  go_make_except_0 :> MakeExcept0 P Q.
+Arguments KnownMakeExcept0 {_} _%I _%I.
+Hint Mode KnownMakeExcept0 + ! - : typeclass_instances.
+
 Class IntoExcept0 {PROP : sbi} (P Q : PROP) := into_except_0 : P ⊢ ◇ Q.
 Arguments IntoExcept0 {_} _%I _%I : simpl never.
 Arguments into_except_0 {_} _%I _%I {_}.

theories/tests/proofmode.v

@@ -369,4 +369,15 @@ Proof.
   iMatchHyp (fun H _ =>
     iApply ("H" with [spec_patterns.SIdent H; spec_patterns.SIdent "HQ"])).
 Qed.
+
+Lemma iFrame_with_evar_r P Q :
+  P -∗ Q -∗ ∃ R, P ∗ R.
+Proof.
+  iIntros "HP HQ". iExists _. iFrame. iApply "HQ".
+Qed.
+Lemma iFrame_with_evar_l P Q :
+  P -∗ Q -∗ ∃ R, R ∗ P.
+Proof.
+  iIntros "HP HQ". iExists _. iFrame. iApply "HQ".
+Qed.
 End tests.