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97e8a9de
Commit
97e8a9de
authored
Jul 25, 2016
by
Robbert Krebbers
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More documentation of [coPset].
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#2378
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prelude/coPset.v
prelude/coPset.v
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prelude/coPset.v
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97e8a9de
(* Copyright (c) 20122015, 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
iris
.
prelude
Require
Export
collections
.
From
iris
.
prelude
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
.
Defined
.
(** * Pick element from infi
ti
nite sets *)
(*
just depthfirst search: using this to pick elements results in very
unbalanced
trees. *)
(** * Pick element from infinite sets *)
(*
Implemented using depthfirst 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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