listset_nodup.v 2.52 KB
Newer Older
Robbert Krebbers's avatar
Robbert Krebbers committed
1
2
3
4
5
(* Copyright (c) 2012-2015, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements finite as unordered lists without duplicates.
Although this implementation is slow, it is very useful as decidable equality
is the only constraint on the carrier set. *)
6
From iris.prelude Require Export collections list.
Robbert Krebbers's avatar
Robbert Krebbers committed
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35

Record listset_nodup A := ListsetNoDup {
  listset_nodup_car : list A; listset_nodup_prf : NoDup listset_nodup_car
}.
Arguments ListsetNoDup {_} _ _.
Arguments listset_nodup_car {_} _.
Arguments listset_nodup_prf {_} _.

Section list_collection.
Context {A : Type} `{ x y : A, Decision (x = y)}.
Notation C := (listset_nodup A).

Instance listset_nodup_elem_of: ElemOf A C := λ x l, x  listset_nodup_car l.
Instance listset_nodup_empty: Empty C := ListsetNoDup [] (@NoDup_nil_2 _).
Instance listset_nodup_singleton: Singleton A C := λ x,
  ListsetNoDup [x] (NoDup_singleton x).
Instance listset_nodup_union: Union C := λ l k,
  let (l',Hl) := l in let (k',Hk) := k
  in ListsetNoDup _ (NoDup_list_union _ _ Hl Hk).
Instance listset_nodup_intersection: Intersection C := λ l k,
  let (l',Hl) := l in let (k',Hk) := k
  in ListsetNoDup _ (NoDup_list_intersection _ k' Hl).
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: Collection A C.
Proof.
  split; [split | | ].
36
37
38
39
40
  - by apply not_elem_of_nil.
  - by apply elem_of_list_singleton.
  - intros [??] [??] ?. apply elem_of_list_union.
  - intros [??] [??] ?. apply elem_of_list_intersection.
  - intros [??] [??] ?. apply elem_of_list_difference.
Robbert Krebbers's avatar
Robbert Krebbers committed
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
Qed.

Global Instance listset_nodup_elems: Elements A C := listset_nodup_car.
Global Instance: FinCollection A C.
Proof. split. apply _. done. by intros [??]. Qed.
End list_collection.

Hint Extern 1 (ElemOf _ (listset_nodup _)) =>
  eapply @listset_nodup_elem_of : typeclass_instances.
Hint Extern 1 (Empty (listset_nodup _)) =>
  eapply @listset_nodup_empty : typeclass_instances.
Hint Extern 1 (Singleton _ (listset_nodup _)) =>
  eapply @listset_nodup_singleton : typeclass_instances.
Hint Extern 1 (Union (listset_nodup _)) =>
  eapply @listset_nodup_union : typeclass_instances.
Hint Extern 1 (Intersection (listset_nodup _)) =>
  eapply @listset_nodup_intersection : typeclass_instances.
Hint Extern 1 (Difference (listset_nodup _)) =>
  eapply @listset_nodup_difference : typeclass_instances.
Hint Extern 1 (Elements _ (listset_nodup _)) =>
  eapply @listset_nodup_elems : typeclass_instances.