More missing `Hint Mode`s.

theories/base.v

@@ -460,14 +460,18 @@ Proof. auto. Qed.
 relation [R] instead of [⊆] to support multiple orders on the same type. *)
 Definition strict {A} (R : relation A) : relation A := λ X Y, R X Y ∧ ¬R Y X.
 Global Instance: Params (@strict) 2 := {}.
+
 Class PartialOrder {A} (R : relation A) : Prop := {
   partial_order_pre :> PreOrder R;
   partial_order_anti_symm :> AntiSymm (=) R
 }.
+Global Hint Mode PartialOrder ! + : typeclass_instances.
+
 Class TotalOrder {A} (R : relation A) : Prop := {
   total_order_partial :> PartialOrder R;
   total_order_trichotomy :> Trichotomy (strict R)
 }.
+Global Hint Mode TotalOrder ! + : typeclass_instances.
 
 (** * Logic *)
 Global Instance prop_inhabited : Inhabited Prop := populate True.
@@ -1007,18 +1011,27 @@ class with the monad laws). *)
 Class MRet (M : Type → Type) := mret: ∀ {A}, A → M A.
 Global Arguments mret {_ _ _} _ : assert.
 Global Instance: Params (@mret) 3 := {}.
+Global Hint Mode MRet ! : typeclass_instances.
+
 Class MBind (M : Type → Type) := mbind : ∀ {A B}, (A → M B) → M A → M B.
 Global Arguments mbind {_ _ _ _} _ !_ / : assert.
 Global Instance: Params (@mbind) 4 := {}.
+Global Hint Mode MBind ! : typeclass_instances.
+
 Class MJoin (M : Type → Type) := mjoin: ∀ {A}, M (M A) → M A.
 Global Arguments mjoin {_ _ _} !_ / : assert.
 Global Instance: Params (@mjoin) 3 := {}.
+Global Hint Mode MJoin ! : typeclass_instances.
+
 Class FMap (M : Type → Type) := fmap : ∀ {A B}, (A → B) → M A → M B.
 Global Arguments fmap {_ _ _ _} _ !_ / : assert.
 Global Instance: Params (@fmap) 4 := {}.
+Global Hint Mode FMap ! : typeclass_instances.
+
 Class OMap (M : Type → Type) := omap: ∀ {A B}, (A → option B) → M A → M B.
 Global Arguments omap {_ _ _ _} _ !_ / : assert.
 Global Instance: Params (@omap) 4 := {}.
+Global Hint Mode OMap ! : typeclass_instances.
 
 Notation "m ≫= f" := (mbind f m) (at level 60, right associativity) : stdpp_scope.
 Notation "( m ≫=.)" := (λ f, mbind f m) (only parsing) : stdpp_scope.
@@ -1044,6 +1057,7 @@ Notation "ps .*2" := (fmap (M:=list) snd ps)
 Class MGuard (M : Type → Type) :=
   mguard: ∀ P {dec : Decision P} {A}, (P → M A) → M A.
 Global Arguments mguard _ _ _ !_ _ _ / : assert.
+Global Hint Mode MGuard ! : typeclass_instances.
 Notation "'guard' P ; z" := (mguard P (λ _, z))
   (at level 20, z at level 200, only parsing, right associativity) : stdpp_scope.
 Notation "'guard' P 'as' H ; z" := (mguard P (λ H, z))
@@ -1283,18 +1297,23 @@ Class SemiSet A C `{ElemOf A C,
   elem_of_singleton (x y : A) : x ∈@{C} {[ y ]} ↔ x = y;
   elem_of_union (X Y : C) (x : A) : x ∈ X ∪ Y ↔ x ∈ X ∨ x ∈ Y
 }.
+Global Hint Mode SemiSet - ! - - - - : typeclass_instances.
+
 Class Set_ A C `{ElemOf A C, Empty C, Singleton A C,
     Union C, Intersection C, Difference C} : Prop := {
   set_semi_set :> SemiSet A C;
   elem_of_intersection (X Y : C) (x : A) : x ∈ X ∩ Y ↔ x ∈ X ∧ x ∈ Y;
   elem_of_difference (X Y : C) (x : A) : x ∈ X ∖ Y ↔ x ∈ X ∧ x ∉ Y
 }.
+Global Hint Mode Set_ - ! - - - - - - : typeclass_instances.
+
 Class TopSet A C `{ElemOf A C, Empty C, Top C, Singleton A C,
     Union C, Intersection C, Difference C} : Prop := {
   top_set_set :> Set_ A C;
   elem_of_top' (x : A) : x ∈@{C} ⊤; (* We prove [elem_of_top : x ∈@{C} ⊤ ↔ True]
   in [sets.v], which is more convenient for rewriting. *)
 }.
+Global Hint Mode TopSet - ! - - - - - - - : typeclass_instances.
 
 (** We axiomative a finite set as a set whose elements can be
 enumerated as a list. These elements, given by the [elements] function, may be
@@ -1386,6 +1405,7 @@ Class Infinite A := {
   infinite_is_fresh (xs : list A) : fresh xs ∉ xs;
   infinite_fresh_Permutation :> Proper (@Permutation A ==> (=)) fresh;
 }.
+Global Hint Mode Infinite ! : typeclass_instances.
 Global Arguments infinite_fresh : simpl never.
 
 (** * Miscellaneous *)

theories/coGset.v

@@ -138,7 +138,7 @@ End infinite.
 Definition coGpick `{Countable A, Infinite A} (X : coGset A) : A :=
   fresh (match X with FinGSet _ => ∅ | CoFinGset X => X end).
 
-Lemma coGpick_elem_of `{Countable A, Infinite A} X :
+Lemma coGpick_elem_of `{Countable A, Infinite A} (X : coGset A) :
   ¬set_finite X → coGpick X ∈ X.
 Proof.
   unfold coGpick.

theories/fin_maps.v

@@ -316,7 +316,7 @@ Proof.
     destruct (decide (Exists (λ ix, m1 !! ix.1 = None) (map_to_list m2)))
       as [[[i x] [?%elem_of_map_to_list ?]]%Exists_exists
          |Hm%(not_Exists_Forall _)]; [eauto|].
-    destruct Heq; apply (anti_symm _), map_subseteq_spec; [done|intros i x Hi].
+    destruct Heq; apply (anti_symm (⊆)), map_subseteq_spec; [done|intros i x Hi].
     assert (is_Some (m1 !! i)) as [x' ?].
     { by apply not_eq_None_Some,
         (proj1 (Forall_forall _ _) Hm (i,x)), elem_of_map_to_list. }
@@ -689,24 +689,25 @@ Lemma lookup_omap_id_Some {A} (m : M (option A)) i x :
   omap id m !! i = Some x ↔ m !! i = Some (Some x).
 Proof. rewrite lookup_omap_Some. naive_solver. Qed.
 
-Lemma fmap_empty {A B} (f : A → B) : f <$> ∅ = ∅.
+Lemma fmap_empty {A B} (f : A → B) : f <$> ∅ =@{M B} ∅.
 Proof. apply map_empty; intros i. by rewrite lookup_fmap, lookup_empty. Qed.
-Lemma omap_empty {A B} (f : A → option B) : omap f ∅ = ∅.
+Lemma omap_empty {A B} (f : A → option B) : omap f ∅ =@{M B} ∅.
 Proof. apply map_empty; intros i. by rewrite lookup_omap, lookup_empty. Qed.
 
-Lemma fmap_empty_inv {A B} (f : A → B) m : f <$> m = ∅ → m = ∅.
+Lemma fmap_empty_inv {A B} (f : A → B) m : f <$> m =@{M B} ∅ → m = ∅.
 Proof.
   intros Hm. apply map_eq; intros i. generalize (f_equal (lookup i) Hm).
   by rewrite lookup_fmap, !lookup_empty, fmap_None.
 Qed.
 
-Lemma fmap_insert {A B} (f: A → B) m i x: f <$> <[i:=x]>m = <[i:=f x]>(f <$> m).
+Lemma fmap_insert {A B} (f: A → B) (m : M A) i x :
+  f <$> <[i:=x]>m = <[i:=f x]>(f <$> m).
 Proof.
   apply map_eq; intros i'; destruct (decide (i' = i)) as [->|].
   - by rewrite lookup_fmap, !lookup_insert.
   - by rewrite lookup_fmap, !lookup_insert_ne, lookup_fmap by done.
 Qed.
-Lemma omap_insert {A B} (f : A → option B) m i x :
+Lemma omap_insert {A B} (f : A → option B) (m : M A) i x :
   omap f (<[i:=x]>m) =
     (match f x with Some y => <[i:=y]> | None => delete i end) (omap f m).
 Proof.
@@ -719,20 +720,21 @@ Proof.
     + by rewrite lookup_insert_ne, lookup_omap by done.
     + by rewrite lookup_delete_ne, lookup_omap by done.
 Qed.
-Lemma omap_insert_Some {A B} (f : A → option B) m i x y :
+Lemma omap_insert_Some {A B} (f : A → option B) (m : M A) i x y :
   f x = Some y → omap f (<[i:=x]>m) = <[i:=y]>(omap f m).
 Proof. intros Hx. by rewrite omap_insert, Hx. Qed.
-Lemma omap_insert_None {A B} (f : A → option B) m i x :
+Lemma omap_insert_None {A B} (f : A → option B) (m : M A) i x :
   f x = None → omap f (<[i:=x]>m) = delete i (omap f m).
 Proof. intros Hx. by rewrite omap_insert, Hx. Qed.
 
-Lemma fmap_delete {A B} (f: A → B) m i: f <$> delete i m = delete i (f <$> m).
+Lemma fmap_delete {A B} (f: A → B) (m : M A) i :
+  f <$> delete i m = delete i (f <$> m).
 Proof.
   apply map_eq; intros i'; destruct (decide (i' = i)) as [->|].
   - by rewrite lookup_fmap, !lookup_delete.
   - by rewrite lookup_fmap, !lookup_delete_ne, lookup_fmap by done.
 Qed.
-Lemma omap_delete {A B} (f: A → option B) m i :
+Lemma omap_delete {A B} (f: A → option B) (m : M A) i :
   omap f (delete i m) = delete i (omap f m).
 Proof.
   apply map_eq; intros i'; destruct (decide (i' = i)) as [->|].
@@ -740,22 +742,23 @@ Proof.
   - by rewrite lookup_omap, !lookup_delete_ne, lookup_omap by done.
 Qed.
 
-Lemma map_fmap_singleton {A B} (f : A → B) i x : f <$> {[i := x]} = {[i := f x]}.
+Lemma map_fmap_singleton {A B} (f : A → B) i x :
+  f <$> {[i := x]} =@{M B} {[i := f x]}.
 Proof.
   by unfold singletonM, map_singleton; rewrite fmap_insert, fmap_empty.
 Qed.
 Lemma omap_singleton {A B} (f : A → option B) i x :
-  omap f {[ i := x ]} = match f x with Some y => {[ i:=y ]} | None => ∅ end.
+  omap f {[ i := x ]} =@{M B} match f x with Some y => {[ i:=y ]} | None => ∅ end.
 Proof.
   rewrite <-insert_empty, omap_insert, omap_empty. destruct (f x) as [y|]; simpl.
   - by rewrite insert_empty.
   - by rewrite delete_empty.
 Qed.
 Lemma omap_singleton_Some {A B} (f : A → option B) i x y :
-  f x = Some y → omap f {[ i := x ]} = {[ i := y ]}.
+  f x = Some y → omap f {[ i := x ]} =@{M B} {[ i := y ]}.
 Proof. intros Hx. by rewrite omap_singleton, Hx. Qed.
 Lemma omap_singleton_None {A B} (f : A → option B) i x :
-  f x = None → omap f {[ i := x ]} = ∅.
+  f x = None → omap f {[ i := x ]} =@{M B} ∅.
 Proof. intros Hx. by rewrite omap_singleton, Hx. Qed.
 
 Lemma map_fmap_id {A} (m : M A) : id <$> m = m.
@@ -1608,14 +1611,14 @@ Section more_merge.
     <[i:=x]>(merge f m1 m2) = merge f m1 (<[i:=z]>m2).
   Proof. by intros; apply partial_alter_merge_r. Qed.
 
-  Lemma fmap_merge {D} (g : C → D) m1 m2 :
+  Lemma fmap_merge {D} (g : C → D) (m1 : M A) (m2 : M B) :
     g <$> merge f m1 m2 = merge (λ mx1 mx2, g <$> f mx1 mx2) m1 m2.
   Proof.
     assert (DiagNone (λ mx1 mx2, g <$> f mx1 mx2)).
     { unfold DiagNone. by rewrite diag_none. }
     apply map_eq; intros i. by rewrite lookup_fmap, !lookup_merge by done.
   Qed.
-  Lemma omap_merge {D} (g : C → option D) m1 m2 :
+  Lemma omap_merge {D} (g : C → option D) (m1 : M A) (m2 : M B) :
     omap g (merge f m1 m2) = merge (λ mx1 mx2, f mx1 mx2 ≫= g) m1 m2.
   Proof.
     assert (DiagNone (λ mx1 mx2, f mx1 mx2 ≫= g)).
@@ -1682,7 +1685,8 @@ Proof.
   rewrite <- (map_fmap_id m1) at 1. by rewrite map_zip_with_fmap.
 Qed.
 
-Lemma map_fmap_zip_with {A B C D} (f : A → B → C) (g : C → D) m1 m2 :
+Lemma map_fmap_zip_with {A B C D} (f : A → B → C) (g : C → D)
+    (m1 : M A) (m2 : M B) :
   g <$> map_zip_with f m1 m2 = map_zip_with (λ x y, g (f x y)) m1 m2.
 Proof.
   apply map_eq; intro i. rewrite lookup_fmap, !map_lookup_zip_with.
@@ -2533,7 +2537,7 @@ Section map_seq.
   Qed.
 
   Lemma fmap_map_seq {B} (f : A → B) start xs :
-    f <$> map_seq start xs = map_seq start (f <$> xs).
+    f <$> map_seq start xs =@{M B} map_seq start (f <$> xs).
   Proof.
     revert start. induction xs as [|x xs IH]; intros start; csimpl.
     { by rewrite fmap_empty. }

theories/list.v

@@ -3558,7 +3558,7 @@ Section fmap.
     Proper ((≡) ==> (≡)) f → Proper ((≡) ==> (≡)) (fmap f).
   Proof. induction 2; simpl; [constructor|solve_proper]. Qed.
 
-  Global Instance fmap_inj: Inj (=) (=) f → Inj (=) (=) (fmap f).
+  Global Instance fmap_inj: Inj (=) (=) f → Inj (=@{list A}) (=) (fmap f).
   Proof.
     intros ? l1. induction l1 as [|x l1 IH]; [by intros [|??]|].
     intros [|??]; intros; f_equal/=; simplify_eq; auto.

theories/natmap.v

@@ -190,7 +190,7 @@ Global Instance natmap_to_list {A} : FinMapToList nat A (natmap A) := λ m,
   let (l,_) := m in natmap_to_list_raw 0 l.
 
 Definition natmap_map_raw {A B} (f : A → B) : natmap_raw A → natmap_raw B :=
-  fmap (fmap f).
+  fmap (fmap (M:=option) f).
 Lemma natmap_map_wf {A B} (f : A → B) l :
   natmap_wf l → natmap_wf (natmap_map_raw f l).
 Proof.

theories/numbers.v

@@ -853,7 +853,7 @@ Global Instance Qp_mul_inj_r p : Inj (=) (=) (Qp_mul p).
 Proof.
   destruct p as [p ?]. intros [q1 ?] [q2 ?]. rewrite <-!Qp_to_Qc_inj_iff; simpl.
   intros Hpq.
-  apply (anti_symm _); apply (Qcmult_le_mono_pos_l _ _ p); by rewrite ?Hpq.
+  apply (anti_symm Qcle); apply (Qcmult_le_mono_pos_l _ _ p); by rewrite ?Hpq.
 Qed.
 Global Instance Qp_mul_inj_l p : Inj (=) (=) (λ q, q * p).
 Proof.

theories/option.v

@@ -205,10 +205,10 @@ Lemma fmap_None {A B} (f : A → B) mx : f <$> mx = None ↔ mx = None.
 Proof. by destruct mx. Qed.
 Lemma option_fmap_id {A} (mx : option A) : id <$> mx = mx.
 Proof. by destruct mx. Qed.
-Lemma option_fmap_compose {A B} (f : A → B) {C} (g : B → C) mx :
+Lemma option_fmap_compose {A B} (f : A → B) {C} (g : B → C) (mx : option A) :
   g ∘ f <$> mx = g <$> (f <$> mx).
 Proof. by destruct mx. Qed.
-Lemma option_fmap_ext {A B} (f g : A → B) mx :
+Lemma option_fmap_ext {A B} (f g : A → B) (mx : option A) :
   (∀ x, f x = g x) → f <$> mx = g <$> mx.
 Proof. intros; destruct mx; f_equal/=; auto. Qed.
 Lemma option_fmap_equiv_ext {A} `{Equiv B} (f g : A → B) (mx : option A) :

theories/orders.v

@@ -13,7 +13,7 @@ Section orders.
   Lemma reflexive_eq `{!Reflexive R} X Y : X = Y → X ⊆ Y.
   Proof. by intros <-. Qed.
   Lemma anti_symm_iff `{!PartialOrder R} X Y : X = Y ↔ R X Y ∧ R Y X.
-  Proof. split; [by intros ->|]. by intros [??]; apply (anti_symm _). Qed.
+  Proof. split; [by intros ->|]. by intros [??]; apply (anti_symm R). Qed.
   Lemma strict_spec X Y : X ⊂ Y ↔ X ⊆ Y ∧ Y ⊈ X.
   Proof. done. Qed.
   Lemma strict_include X Y : X ⊂ Y → X ⊆ Y.