Forked from
Iris / stdpp
1802 commits behind the upstream repository.
-
Robbert Krebbers authored
Get rid of using `Collection` and favor `set` everywhere. Also, prefer conversion functions that are called `X_to_Y`. The following sed script performs most of the renaming, with the exception of: - `set`, which has been renamed into `propset`. I couldn't do this rename using `sed` since it's too context sensitive. - There was a spurious rename of `Vec.of_list`, which I correctly manually. - Updating some section names and comments. ``` sed ' s/SimpleCollection/SemiSet/g; s/FinCollection/FinSet/g; s/CollectionMonad/MonadSet/g; s/Collection/Set\_/g; s/collection\_simple/set\_semi\_set/g; s/fin\_collection/fin\_set/g; s/collection\_monad\_simple/monad\_set\_semi\_set/g; s/collection\_equiv/set\_equiv/g; s/\bbset/boolset/g; s/mkBSet/BoolSet/g; s/mkSet/PropSet/g; s/set\_equivalence/set\_equiv\_equivalence/g; s/collection\_subseteq/set\_subseteq/g; s/collection\_disjoint/set\_disjoint/g; s/collection\_fold/set\_fold/g; s/collection\_map/set\_map/g; s/collection\_size/set\_size/g; s/collection\_filter/set\_filter/g; s/collection\_guard/set\_guard/g; s/collection\_choose/set\_choose/g; s/collection\_ind/set\_ind/g; s/collection\_wf/set\_wf/g; s/map\_to\_collection/map\_to\_set/g; s/map\_of\_collection/set\_to\_map/g; s/map\_of\_list/list\_to\_map/g; s/map\_of\_to_list/list\_to\_map\_to\_list/g; s/map\_to\_of\_list/map\_to\_list\_to\_map/g; s/\bof\_list/list\_to\_set/g; s/\bof\_option/option\_to\_set/g; s/elem\_of\_of\_list/elem\_of\_list\_to\_set/g; s/elem\_of\_of\_option/elem\_of\_option\_to\_set/g; s/collection\_not\_subset\_inv/set\_not\_subset\_inv/g; s/seq\_set/set\_seq/g; s/collections/sets/g; s/collection/set/g; ' -i $(find -name "*.v") ```
Robbert Krebbers authoredGet rid of using `Collection` and favor `set` everywhere. Also, prefer conversion functions that are called `X_to_Y`. The following sed script performs most of the renaming, with the exception of: - `set`, which has been renamed into `propset`. I couldn't do this rename using `sed` since it's too context sensitive. - There was a spurious rename of `Vec.of_list`, which I correctly manually. - Updating some section names and comments. ``` sed ' s/SimpleCollection/SemiSet/g; s/FinCollection/FinSet/g; s/CollectionMonad/MonadSet/g; s/Collection/Set\_/g; s/collection\_simple/set\_semi\_set/g; s/fin\_collection/fin\_set/g; s/collection\_monad\_simple/monad\_set\_semi\_set/g; s/collection\_equiv/set\_equiv/g; s/\bbset/boolset/g; s/mkBSet/BoolSet/g; s/mkSet/PropSet/g; s/set\_equivalence/set\_equiv\_equivalence/g; s/collection\_subseteq/set\_subseteq/g; s/collection\_disjoint/set\_disjoint/g; s/collection\_fold/set\_fold/g; s/collection\_map/set\_map/g; s/collection\_size/set\_size/g; s/collection\_filter/set\_filter/g; s/collection\_guard/set\_guard/g; s/collection\_choose/set\_choose/g; s/collection\_ind/set\_ind/g; s/collection\_wf/set\_wf/g; s/map\_to\_collection/map\_to\_set/g; s/map\_of\_collection/set\_to\_map/g; s/map\_of\_list/list\_to\_map/g; s/map\_of\_to_list/list\_to\_map\_to\_list/g; s/map\_to\_of\_list/map\_to\_list\_to\_map/g; s/\bof\_list/list\_to\_set/g; s/\bof\_option/option\_to\_set/g; s/elem\_of\_of\_list/elem\_of\_list\_to\_set/g; s/elem\_of\_of\_option/elem\_of\_option\_to\_set/g; s/collection\_not\_subset\_inv/set\_not\_subset\_inv/g; s/seq\_set/set\_seq/g; s/collections/sets/g; s/collection/set/g; ' -i $(find -name "*.v") ```
boolset.v 1.76 KiB
(* Copyright (c) 2012-2019, Coq-std++ developers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This file implements boolsets as functions into Prop. *)
From stdpp Require Export prelude.
Set Default Proof Using "Type".
Record boolset (A : Type) : Type := BoolSet { boolset_car : A → bool }.
Arguments BoolSet {_} _ : assert.
Arguments boolset_car {_} _ _ : assert.
Instance boolset_top {A} : Top (boolset A) := BoolSet (λ _, true).
Instance boolset_empty {A} : Empty (boolset A) := BoolSet (λ _, false).
Instance boolset_singleton `{EqDecision A} : Singleton A (boolset A) := λ x,
BoolSet (λ y, bool_decide (y = x)).
Instance boolset_elem_of {A} : ElemOf A (boolset A) := λ x X, boolset_car X x.
Instance boolset_union {A} : Union (boolset A) := λ X1 X2,
BoolSet (λ x, boolset_car X1 x || boolset_car X2 x).
Instance boolset_intersection {A} : Intersection (boolset A) := λ X1 X2,
BoolSet (λ x, boolset_car X1 x && boolset_car X2 x).
Instance boolset_difference {A} : Difference (boolset A) := λ X1 X2,
BoolSet (λ x, boolset_car X1 x && negb (boolset_car X2 x)).
Instance boolset_set `{EqDecision A} : Set_ A (boolset A).
Proof.
split; [split| |].
- by intros x ?.
- by intros x y; rewrite <-(bool_decide_spec (x = y)).
- split. apply orb_prop_elim. apply orb_prop_intro.
- split. apply andb_prop_elim. apply andb_prop_intro.
- intros X Y x; unfold elem_of, boolset_elem_of; simpl.
destruct (boolset_car X x), (boolset_car Y x); simpl; tauto.
Qed.
Instance boolset_elem_of_dec {A} : RelDecision (∈@{boolset A}).
Proof. refine (λ x X, cast_if (decide (boolset_car X x))); done. Defined.
Typeclasses Opaque boolset_elem_of.
Global Opaque boolset_empty boolset_singleton boolset_union
boolset_intersection boolset_difference.