NAME
Set::Infinite  Sets of intervals
SYNOPSIS
use Set::Infinite;
$set = Set::Infinite>new(1,2); # [1..2]
print $set>union(5,6); # [1..2],[5..6]
DESCRIPTION
Set::Infinite is a Set Theory module for infinite sets.
A set is a collection of objects. The objects that belong to a set are called its members, or "elements".
As objects we allow (almost) anything: reals, integers, and objects (such as dates).
We allow sets to be infinite.
There is no account for the order of elements. For example, {1,2} = {2,1}.
There is no account for repetition of elements. For example, {1,2,2} = {1,1,1,2} = {1,2}.
CONSTRUCTOR
new
Creates a new set object:
$set = Set::Infinite>new; # empty set
$set = Set::Infinite>new( 10 ); # single element
$set = Set::Infinite>new( 10, 20 ); # single range
$set = Set::Infinite>new(
[ 10, 20 ], [ 50, 70 ] ); # two ranges
 empty set

$set = Set::Infinite>new;
 set with a single element

$set = Set::Infinite>new( 10 ); $set = Set::Infinite>new( [ 10 ] );
 set with a single span

$set = Set::Infinite>new( 10, 20 ); $set = Set::Infinite>new( [ 10, 20 ] ); # 10 <= x <= 20
 set with a single, open span

$set = Set::Infinite>new( { a => 10, open_begin => 0, b => 20, open_end => 1, } ); # 10 <= x < 20
 set with multiple spans

$set = Set::Infinite>new( 10, 20, 100, 200 ); $set = Set::Infinite>new( [ 10, 20 ], [ 100, 200 ] ); $set = Set::Infinite>new( { a => 10, open_begin => 0, b => 20, open_end => 0, }, { a => 100, open_begin => 0, b => 200, open_end => 0, } );
The new()
method expects ordered parameters.
If you have unordered ranges, you can build the set using union
:
@ranges = ( [ 10, 20 ], [ 10, 1 ] );
$set = Set::Infinite>new;
$set = $set>union( @$_ ) for @ranges;
The data structures passed to new
must be immutable. So this is not good practice:
$set = Set::Infinite>new( $object_a, $object_b );
$object_a>set_value( 10 );
This is the recommended way to do it:
$set = Set::Infinite>new( $object_a>clone, $object_b>clone );
$object_a>set_value( 10 );
clone / copy
Creates a new object, and copy the object data.
empty_set
Creates an empty set.
If called from an existing set, the empty set inherits the "type" and "density" characteristics.
universal_set
Creates a set containing "all" possible elements.
If called from an existing set, the universal set inherits the "type" and "density" characteristics.
SET FUNCTIONS
union
$set = $set>union($b);
Returns the set of all elements from both sets.
This function behaves like an "OR" operation.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
$set2 = new Set::Infinite( [ 7, 20 ] );
print $set1>union( $set2 );
# output: [1..4],[7..20]
intersection
$set = $set>intersection($b);
Returns the set of elements common to both sets.
This function behaves like an "AND" operation.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
$set2 = new Set::Infinite( [ 7, 20 ] );
print $set1>intersection( $set2 );
# output: [8..12]
complement
minus
difference
$set = $set>complement;
Returns the set of all elements that don't belong to the set.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
print $set1>complement;
# output: (inf..1),(4..8),(12..inf)
The complement function might take a parameter:
$set = $set>minus($b);
Returns the setdifference, that is, the elements that don't belong to the given set.
$set1 = new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );
$set2 = new Set::Infinite( [ 7, 20 ] );
print $set1>minus( $set2 );
# output: [1..4]
symmetric_difference
Returns a set containing elements that are in either set, but not in both. This is the "set" version of "XOR".
DENSITY METHODS
real
$set1 = $set>real;
Returns a set with density "0".
integer
$set1 = $set>integer;
Returns a set with density "1".
LOGIC FUNCTIONS
intersects
$logic = $set>intersects($b);
contains
$logic = $set>contains($b);
is_empty
is_null
$logic = $set>is_null;
is_nonempty
This set that has at least 1 element.
is_span
This set that has a single span or interval.
is_singleton
This set that has a single element.
is_subset( $set )
Every element of this set is a member of the given set.
is_proper_subset( $set )
Every element of this set is a member of the given set. Some members of the given set are not elements of this set.
is_disjoint( $set )
The given set has no elements in common with this set.
is_too_complex
Sometimes a set might be too complex to enumerate or print.
This happens with sets that represent infinite recurrences, such as when you ask for a quantization on a set bounded by inf or inf.
See also: count
method.
SCALAR FUNCTIONS
min
$i = $set>min;
max
$i = $set>max;
size
$i = $set>size;
count
$i = $set>count;
OVERLOADED OPERATORS
stringification
print $set;
$str = "$set";
See also: as_string
.
comparison
sort
> < == >= <= <=>
See also: spaceship
method.
CLASS METHODS
Set::Infinite>separators(@i)
chooses the interval separators for stringification.
default are [ ] ( ) '..' ','.
inf
returns an 'Infinity' number.
minus_inf
returns 'Infinity' number.
type
type( "My::Class::Name" )
Chooses a default object data type.
Default is none (a normal Perl SCALAR).
SPECIAL SET FUNCTIONS
span
$set1 = $set>span;
Returns the set span.
until
Extends a set until another:
0,5,7 > until 2,6,10
gives
[0..2), [5..6), [7..10)
start_set
end_set
These methods do the inverse of the "until" method.
Given:
[0..2), [5..6), [7..10)
start_set is:
0,5,7
end_set is:
2,6,10
intersected_spans
$set = $set1>intersected_spans( $set2 );
The method returns a new set, containing all spans that are intersected by the given set.
Unlike the intersection
method, the spans are not modified. See diagram below:
set1 [....] [....] [....] [....]
set2 [................]
intersection [.] [....] [.]
intersected_spans [....] [....] [....]
quantize
quantize( parameters )
Makes equalsized subsets.
Returns an ordered set of equalsized subsets.
Example:
$set = Set::Infinite>new([1,3]);
print join (" ", $set>quantize( quant => 1 ) );
Gives:
[1..2) [2..3) [3..4)
select
select( parameters )
Selects set spans based on their ordered positions
select
has a behaviour similar to an array slice
.
by  default=All
count  default=Infinity
0 1 2 3 4 5 6 7 8 # original set
0 1 2 # count => 3
1 6 # by => [ 2, 1 ]
offset
offset ( parameters )
Offsets the subsets. Parameters:
value  default=[0,0]
mode  default='offset'. Possible values are: 'offset', 'begin', 'end'.
unit  type of value. Can be 'days', 'weeks', 'hours', 'minutes', 'seconds'.
iterate
iterate ( sub { } , @args )
Iterates on the set spans, over a callback subroutine. Returns the union of all partial results.
The callback argument $_[0]
is a span. If there are additional arguments they are passed to the callback.
The callback can return a span, a hashref (see Set::Infinite::Basic
), a scalar, an object, or undef
.
[EXPERIMENTAL] iterate
accepts an optional backtrack_callback
argument. The purpose of the backtrack_callback
is to reverse the iterate() function, overcoming the limitations of the internal backtracking algorithm. The syntax is:
iterate ( sub { } , backtrack_callback => sub { }, @args )
The backtrack_callback
can return a span, a hashref, a scalar, an object, or undef
.
For example, the following snippet adds a constant to each element of an unbounded set:
$set1 = $set>iterate(
sub { $_[0]>min + 54, $_[0]>max + 54 },
backtrack_callback =>
sub { $_[0]>min  54, $_[0]>max  54 },
);
first / last
first / last
In scalar context returns the first or last interval of a set.
In list context returns the first or last interval of a set, and the remaining set (the 'tail').
See also: min
, max
, min_a
, max_a
methods.
type
type( "My::Class::Name" )
Chooses a default object data type.
default is none (a normal perl SCALAR).
INTERNAL FUNCTIONS
_backtrack
$set>_backtrack( 'intersection', $b );
Internal function to evaluate recurrences.
numeric
$set>numeric;
Internal function to ignore the set "type". It is used in some internal optimizations, when it is possible to use scalar values instead of objects.
fixtype
$set>fixtype;
Internal function to fix the result of operations that use the numeric() function.
tolerance
$set = $set>tolerance(0) # defaults to real sets (default)
$set = $set>tolerance(1) # defaults to integer sets
Internal function for changing the set "density".
min_a
($min, $min_is_open) = $set>min_a;
max_a
($max, $max_is_open) = $set>max_a;
as_string
Implements the "stringification" operator.
Stringification of unbounded recurrences is not implemented.
Unbounded recurrences are stringified as "function descriptions", if the class variable $PRETTY_PRINT is set.
spaceship
Implements the "comparison" operator.
Comparison of unbounded recurrences is not implemented.
CAVEATS
constructor "span" notation
$set = Set::Infinite>new(10,1);
Will be interpreted as [1..10]
constructor "multiplespan" notation
$set = Set::Infinite>new(1,2,3,4);
Will be interpreted as [1..2],[3..4] instead of [1,2,3,4]. You probably want >new([1],[2],[3],[4]) instead, or maybe >new(1,4)
"range operator"
$set = Set::Infinite>new(1..3);
Will be interpreted as [1..2],3 instead of [1,2,3]. You probably want >new(1,3) instead.
INTERNALS
The base set object, without recurrences, is a Set::Infinite::Basic
.
A recurrenceset is represented by a method name, one or two parent objects, and extra arguments. The list
key is set to an empty array, and the too_complex
key is set to 1
.
This is a structure that holds the union of two "complex sets":
{
too_complex => 1, # "this is a recurrence"
list => [ ], # not used
method => 'union', # function name
parent => [ $set1, $set2 ], # "leaves" in the syntaxtree
param => [ ] # optional arguments for the function
}
This is a structure that holds the complement of a "complex set":
{
too_complex => 1, # "this is a recurrence"
list => [ ], # not used
method => 'complement', # function name
parent => $set, # "leaf" in the syntaxtree
param => [ ] # optional arguments for the function
}
SEE ALSO
See modules DateTime::Set, DateTime::Event::Recurrence, DateTime::Event::ICal, DateTime::Event::Cron for uptodate information on datesets.
The perldatetime project <http://datetime.perl.org>
AUTHOR
Flavio S. Glock <fglock@gmail.com>
COPYRIGHT
Copyright (c) 2003 Flavio Soibelmann Glock. All rights reserved. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
The full text of the license can be found in the LICENSE file included with this module.