Commit d7643649 authored by Robbert Krebbers's avatar Robbert Krebbers

Remove CollectionOps class.

This class whose name is horrible and purpose is arbitrary seems to be a
leftover of some experiment with ch2o, a long time a ago.
parent f511129c
......@@ -908,13 +908,6 @@ Class Collection A C `{ElemOf A C, Empty C, Singleton A C,
elem_of_intersection X Y (x : A) : x X Y x X x Y;
elem_of_difference X Y (x : A) : x X Y x X x Y
}.
Class CollectionOps A C `{ElemOf A C, Empty C, Singleton A C, Union C,
Intersection C, Difference C, IntersectionWith A C, Filter A C} : Prop := {
collection_ops :>> Collection A C;
elem_of_intersection_with (f : A A option A) X Y (x : A) :
x intersection_with f X Y x1 x2, x1 X x2 Y f x1 x2 = Some x;
elem_of_filter X P `{ x, Decision (P x)} x : x filter P X P x x X
}.
(** We axiomative a finite collection as a collection whose elements can be
enumerated as a list. These elements, given by the [elements] function, may be
......
......@@ -467,35 +467,6 @@ Section collection.
End dec.
End collection.
Section collection_ops.
Context `{CollectionOps A C}.
Lemma elem_of_intersection_with_list (f : A A option A) Xs Y x :
x intersection_with_list f Y Xs xs y,
Forall2 () xs Xs y Y foldr (λ x, (= f x)) (Some y) xs = Some x.
Proof.
split.
- revert x. induction Xs; simpl; intros x HXs; [eexists [], x; intuition|].
rewrite elem_of_intersection_with in HXs; destruct HXs as (x1&x2&?&?&?).
destruct (IHXs x2) as (xs & y & hy & ? & ?); trivial.
eexists (x1 :: xs), y. intuition (simplify_option_eq; auto).
- intros (xs & y & Hxs & ? & Hx). revert x Hx.
induction Hxs; intros; simplify_option_eq; [done |].
rewrite elem_of_intersection_with. naive_solver.
Qed.
Lemma intersection_with_list_ind (P Q : A Prop) f Xs Y :
( y, y Y P y)
Forall (λ X, x, x X Q x) Xs
( x y z, Q x P y f x y = Some z P z)
x, x intersection_with_list f Y Xs P x.
Proof.
intros HY HXs Hf. induction Xs; simplify_option_eq; [done |].
intros x Hx. rewrite elem_of_intersection_with in Hx.
decompose_Forall. destruct Hx as (? & ? & ? & ? & ?). eauto.
Qed.
End collection_ops.
(** * Sets without duplicates up to an equivalence *)
Section NoDup.
Context `{SimpleCollection A B} (R : relation A) `{!Equivalence R}.
......
......@@ -42,10 +42,6 @@ Instance listset_intersection: Intersection (listset A) := λ l k,
let (l') := l in let (k') := k in Listset (list_intersection l' k').
Instance listset_difference: Difference (listset A) := λ l k,
let (l') := l in let (k') := k in Listset (list_difference l' k').
Instance listset_intersection_with: IntersectionWith A (listset A) := λ f l k,
let (l') := l in let (k') := k in Listset (list_intersection_with f l' k').
Instance listset_filter: Filter A (listset A) := λ P _ l,
let (l') := l in Listset (filter P l').
Instance: Collection A (listset A).
Proof.
......@@ -62,13 +58,6 @@ Proof.
- intros. apply elem_of_remove_dups.
- intros. apply NoDup_remove_dups.
Qed.
Global Instance: CollectionOps A (listset A).
Proof.
split.
- apply _.
- intros ? [?] [?]. apply elem_of_list_intersection_with.
- intros [?] ??. apply elem_of_list_filter.
Qed.
End listset.
(** These instances are declared using [Hint Extern] to avoid too
......@@ -83,14 +72,10 @@ Hint Extern 1 (Union (listset _)) =>
eapply @listset_union : typeclass_instances.
Hint Extern 1 (Intersection (listset _)) =>
eapply @listset_intersection : typeclass_instances.
Hint Extern 1 (IntersectionWith _ (listset _)) =>
eapply @listset_intersection_with : typeclass_instances.
Hint Extern 1 (Difference (listset _)) =>
eapply @listset_difference : typeclass_instances.
Hint Extern 1 (Elements _ (listset _)) =>
eapply @listset_elems : typeclass_instances.
Hint Extern 1 (Filter _ (listset _)) =>
eapply @listset_filter : typeclass_instances.
Instance listset_ret: MRet listset := λ A x, {[ x ]}.
Instance listset_fmap: FMap listset := λ A B f l,
......
......@@ -29,12 +29,6 @@ Instance listset_nodup_intersection: Intersection C := λ l k,
Instance listset_nodup_difference: Difference C := λ l k,
let (l',Hl) := l in let (k',Hk) := k
in ListsetNoDup _ (NoDup_list_difference _ k' Hl).
Instance listset_nodup_intersection_with: IntersectionWith A C := λ f l k,
let (l',Hl) := l in let (k',Hk) := k
in ListsetNoDup
(remove_dups (list_intersection_with f l' k')) (NoDup_remove_dups _).
Instance listset_nodup_filter: Filter A C := λ P _ l,
let (l',Hl) := l in ListsetNoDup _ (NoDup_filter P _ Hl).
Instance: Collection A C.
Proof.
......@@ -49,15 +43,6 @@ Qed.
Global Instance listset_nodup_elems: Elements A C := listset_nodup_car.
Global Instance: FinCollection A C.
Proof. split. apply _. done. by intros [??]. Qed.
Global Instance: CollectionOps A C.
Proof.
split.
- apply _.
- intros ? [??] [??] ?. unfold intersection_with, elem_of,
listset_nodup_intersection_with, listset_nodup_elem_of; simpl.
rewrite elem_of_remove_dups. by apply elem_of_list_intersection_with.
- intros [??] ???. apply elem_of_list_filter.
Qed.
End list_collection.
Hint Extern 1 (ElemOf _ (listset_nodup _)) =>
......@@ -74,5 +59,3 @@ Hint Extern 1 (Difference (listset_nodup _)) =>
eapply @listset_nodup_difference : typeclass_instances.
Hint Extern 1 (Elements _ (listset_nodup _)) =>
eapply @listset_nodup_elems : typeclass_instances.
Hint Extern 1 (Filter _ (listset_nodup _)) =>
eapply @listset_nodup_filter : typeclass_instances.
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