Commit 2af4573e authored by Robbert Krebbers's avatar Robbert Krebbers
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More documentation of [coPset].

parent ef823867
(* Copyright (c) 2012-2015, Robbert Krebbers. *)
(* This file is distributed under the terms of the BSD license. *)
(** This files implements an efficient implementation of finite/cofinite sets
of positive binary naturals [positive]. *)
(** This files implements the type [coPset] of efficient finite/cofinite sets
of positive binary naturals [positive]. These sets are:
- Closed under union, intersection and set complement.
- Closed under splitting of cofinite sets.
Also, they enjoy various nice properties, such as decidable equality and set
membership, as well as extensional equality (i.e. [X = Y ↔ ∀ x, x ∈ X ↔ x ∈ Y]).
Since [positive]s are bitstrings, we encode [coPset]s as trees that correspond
to the decision function that map bitstrings to bools. *)
From stdpp Require Export collections.
From stdpp Require Import pmap gmap mapset.
Local Open Scope positive_scope.
......@@ -228,9 +237,9 @@ Proof.
refine (cast_if (decide (coPset_finite (`X)))); by rewrite coPset_finite_spec.
(** * Pick element from infitinite sets *)
(* just depth-first search: using this to pick elements results in very
unbalanced trees. *)
(** * Pick element from infinite sets *)
(* Implemented using depth-first search, which results in very unbalanced
trees. *)
Fixpoint coPpick_raw (t : coPset_raw) : option positive :=
match t with
| coPLeaf true | coPNode true _ _ => Some 1
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