Remove PropHolds type class.

prelude/base.v

@@ -90,21 +90,6 @@ Hint Extern 0 (_ ≡ _) => symmetry; assumption.
 
 
 (** * Type classes *)
-(** ** Provable propositions *)
-(** This type class collects provable propositions. It is useful to constraint
-type classes by arbitrary propositions. *)
-Class PropHolds (P : Prop) := prop_holds: P.
-
-Hint Extern 0 (PropHolds _) => assumption : typeclass_instances.
-Instance: Proper (iff ==> iff) PropHolds.
-Proof. repeat intro; trivial. Qed.
-
-Ltac solve_propholds :=
-  match goal with
-  | |- PropHolds (?P) => apply _
-  | |- ?P => change (PropHolds P); apply _
-  end.
-
 (** ** Decidable propositions *)
 (** This type class by (Spitters/van der Weegen, 2011) collects decidable
 propositions. For example to declare a parameter expressing decidable equality
@@ -176,22 +161,6 @@ Arguments total {_} _ {_} _ _.
 Arguments trichotomy {_} _ {_} _ _.
 Arguments trichotomyT {_} _ {_} _ _.
 
-Instance left_id_propholds {A} (R : relation A) i f :
-  LeftId R i f → ∀ x, PropHolds (R (f i x) x).
-Proof. red. trivial. Qed.
-Instance right_id_propholds {A} (R : relation A) i f :
-  RightId R i f → ∀ x, PropHolds (R (f x i) x).
-Proof. red. trivial. Qed.
-Instance left_absorb_propholds {A} (R : relation A) i f :
-  LeftAbsorb R i f → ∀ x, PropHolds (R (f i x) i).
-Proof. red. trivial. Qed.
-Instance right_absorb_propholds {A} (R : relation A) i f :
-  RightAbsorb R i f → ∀ x, PropHolds (R (f x i) i).
-Proof. red. trivial. Qed.
-Instance idem_propholds {A} (R : relation A) f :
-  IdemP R f → ∀ x, PropHolds (R (f x x) x).
-Proof. red. trivial. Qed.
-
 Lemma not_symmetry `{R : relation A, !Symmetric R} x y : ¬R x y → ¬R y x.
 Proof. intuition. Qed.
 Lemma symmetry_iff `(R : relation A) `{!Symmetric R} x y : R x y ↔ R y x.

prelude/fin_maps.v

@@ -39,8 +39,7 @@ Class FinMap K M `{FMap M, ∀ A, Lookup K A (M A), ∀ A, Empty (M A), ∀ A,
   elem_of_map_to_list {A} (m : M A) i x :
     (i,x) ∈ map_to_list m ↔ m !! i = Some x;
   lookup_omap {A B} (f : A → option B) m i : omap f m !! i = m !! i ≫= f;
-  lookup_merge {A B C} (f : option A → option B → option C)
-      `{!PropHolds (f None None = None)} m1 m2 i :
+  lookup_merge {A B C} (f: option A → option B → option C) `{!DiagNone f} m1 m2 i :
     merge f m1 m2 !! i = f (m1 !! i) (m2 !! i)
 }.
 
@@ -150,8 +149,7 @@ Section setoid.
     intros ?? Hf; apply partial_alter_proper.
     by destruct 1; constructor; apply Hf.
   Qed.
-  Lemma merge_ext f g
-      `{!PropHolds (f None None = None), !PropHolds (g None None = None)} :
+  Lemma merge_ext f g `{!DiagNone f, !DiagNone g} :
     ((≡) ==> (≡) ==> (≡))%signature f g →
     ((≡) ==> (≡) ==> (≡))%signature (merge (M:=M) f) (merge g).
   Proof.
@@ -825,8 +823,7 @@ End map_Forall.
 
 (** ** Properties of the [merge] operation *)
 Section merge.
-Context {A} (f : option A → option A → option A).
-Context `{!PropHolds (f None None = None)}.
+Context {A} (f : option A → option A → option A) `{!DiagNone f}.
 Global Instance: LeftId (=) None f → LeftId (=) ∅ (merge f).
 Proof.
   intros ??. apply map_eq. intros.
@@ -841,29 +838,25 @@ Lemma merge_comm m1 m2 :
   (∀ i, f (m1 !! i) (m2 !! i) = f (m2 !! i) (m1 !! i)) →
   merge f m1 m2 = merge f m2 m1.
 Proof. intros. apply map_eq. intros. by rewrite !(lookup_merge f). Qed.
-Global Instance: Comm (=) f → Comm (=) (merge f).
-Proof.
-  intros ???. apply merge_comm. intros. by apply (comm f).
-Qed.
+Global Instance merge_comm' : Comm (=) f → Comm (=) (merge f).
+Proof. intros ???. apply merge_comm. intros. by apply (comm f). Qed.
 Lemma merge_assoc m1 m2 m3 :
   (∀ i, f (m1 !! i) (f (m2 !! i) (m3 !! i)) =
         f (f (m1 !! i) (m2 !! i)) (m3 !! i)) →
   merge f m1 (merge f m2 m3) = merge f (merge f m1 m2) m3.
 Proof. intros. apply map_eq. intros. by rewrite !(lookup_merge f). Qed.
-Global Instance: Assoc (=) f → Assoc (=) (merge f).
-Proof.
-  intros ????. apply merge_assoc. intros. by apply (assoc_L f).
-Qed.
+Global Instance merge_assoc' : Assoc (=) f → Assoc (=) (merge f).
+Proof. intros ????. apply merge_assoc. intros. by apply (assoc_L f). Qed.
 Lemma merge_idemp m1 :
   (∀ i, f (m1 !! i) (m1 !! i) = m1 !! i) → merge f m1 m1 = m1.
 Proof. intros. apply map_eq. intros. by rewrite !(lookup_merge f). Qed.
-Global Instance: IdemP (=) f → IdemP (=) (merge f).
+Global Instance merge_idemp' : IdemP (=) f → IdemP (=) (merge f).
 Proof. intros ??. apply merge_idemp. intros. by apply (idemp f). Qed.
 End merge.
 
 Section more_merge.
-Context {A B C} (f : option A → option B → option C).
-Context `{!PropHolds (f None None = None)}.
+Context {A B C} (f : option A → option B → option C) `{!DiagNone f}.
+
 Lemma merge_Some m1 m2 m :
   (∀ i, m !! i = f (m1 !! i) (m2 !! i)) ↔ merge f m1 m2 = m.
 Proof.
@@ -983,7 +976,7 @@ Proof.
   split; [|naive_solver].
   intros [i[(x&y&?&?&?)|[(x&?&?&[])|(y&?&?&[])]]]; naive_solver.
 Qed.
-Global Instance: Symmetric (map_disjoint : relation (M A)).
+Global Instance map_disjoint_sym : Symmetric (map_disjoint : relation (M A)).
 Proof. intros A m1 m2. rewrite !map_disjoint_spec. naive_solver. Qed.
 Lemma map_disjoint_empty_l {A} (m : M A) : ∅ ⊥ₘ m.
 Proof. rewrite !map_disjoint_spec. intros i x y. by rewrite lookup_empty. Qed.

prelude/list.v

@@ -3668,5 +3668,3 @@ Ltac solve_suffix_of := by intuition (repeat
   | |- suffix_of _ (_ ++ _) => apply suffix_of_app_r
   | H : suffix_of _ _ → False |- _ => destruct H
   end).
-Hint Extern 0 (PropHolds (suffix_of _ _)) =>
-  unfold PropHolds; solve_suffix_of : typeclass_instances.

prelude/option.v

@@ -257,23 +257,33 @@ Lemma option_union_Some {A} (mx my : option A) z :
   mx ∪ my = Some z → mx = Some z ∨ my = Some z.
 Proof. destruct mx, my; naive_solver. Qed.
 
-Section option_union_intersection_difference.
+Class DiagNone {A B C} (f : option A → option B → option C) :=
+  diag_none : f None None = None.
+
+Section union_intersection_difference.
   Context {A} (f : A → A → option A).
-  Global Instance: LeftId (=) None (union_with f).
+
+  Global Instance union_with_diag_none : DiagNone (union_with f).
+  Proof. reflexivity. Qed.
+  Global Instance intersection_with_diag_none : DiagNone (intersection_with f).
+  Proof. reflexivity. Qed.
+  Global Instance difference_with_diag_none : DiagNone (difference_with f).
+  Proof. reflexivity. Qed.
+  Global Instance union_with_left_id : LeftId (=) None (union_with f).
   Proof. by intros [?|]. Qed.
-  Global Instance: RightId (=) None (union_with f).
+  Global Instance union_with_right_id : RightId (=) None (union_with f).
   Proof. by intros [?|]. Qed.
-  Global Instance: Comm (=) f → Comm (=) (union_with f).
+  Global Instance union_with_comm : Comm (=) f → Comm (=) (union_with f).
   Proof. by intros ? [?|] [?|]; compute; rewrite 1?(comm f). Qed.
-  Global Instance: LeftAbsorb (=) None (intersection_with f).
+  Global Instance intersection_with_left_ab : LeftAbsorb (=) None (intersection_with f).
   Proof. by intros [?|]. Qed.
-  Global Instance: RightAbsorb (=) None (intersection_with f).
+  Global Instance intersection_with_right_ab : RightAbsorb (=) None (intersection_with f).
   Proof. by intros [?|]. Qed.
-  Global Instance: Comm (=) f → Comm (=) (intersection_with f).
+  Global Instance difference_with_comm : Comm (=) f → Comm (=) (intersection_with f).
   Proof. by intros ? [?|] [?|]; compute; rewrite 1?(comm f). Qed.
-  Global Instance: RightId (=) None (difference_with f).
+  Global Instance difference_with_right_id : RightId (=) None (difference_with f).
   Proof. by intros [?|]. Qed.
-End option_union_intersection_difference.
+End union_intersection_difference.
 
 (** * Tactics *)
 Tactic Notation "case_option_guard" "as" ident(Hx) :=