Set::Infinite - Sets of intervals
use Set::Infinite; $set = Set::Infinite->new(1,2); # [1..2] print $set->union(5,6); # [1..2],[5..6]
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}.
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
$set = Set::Infinite->new;
$set = Set::Infinite->new( 10 ); $set = Set::Infinite->new( [ 10 ] );
$set = Set::Infinite->new( 10, 20 ); $set = Set::Infinite->new( [ 10, 20 ] ); # 10 <= x <= 20
$set = Set::Infinite->new( { a => 10, open_begin => 0, b => 20, open_end => 1, } ); # 10 <= x < 20
$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 );
Creates a new object, and copy the object data.
Creates an empty set.
If called from an existing set, the empty set inherits the "type" and "density" characteristics.
Creates a set containing "all" possible elements.
If called from an existing set, the universal set inherits the "type" and "density" characteristics.
$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]
$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]
$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 set-difference, 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]
Returns a set containing elements that are in either set, but not in both. This is the "set" version of "XOR".
$set1 = $set->real;
Returns a set with density "0".
$set1 = $set->integer;
Returns a set with density "1".
$logic = $set->intersects($b);
$logic = $set->contains($b);
$logic = $set->is_null;
This set that has at least 1 element.
This set that has a single span or interval.
This set that has a single element.
Every element of this set is a member of the given 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.
The given set has no elements in common with this set.
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.
$i = $set->min;
$i = $set->max;
$i = $set->size;
$i = $set->count;
print $set; $str = "$set";
See also: as_string
.
sort > < == >= <= <=>
See also: spaceship
method.
Set::Infinite->separators(@i) chooses the interval separators for stringification. default are [ ] ( ) '..' ','. inf returns an 'Infinity' number. minus_inf returns '-Infinity' number.
type( "My::Class::Name" )
Chooses a default object data type.
Default is none (a normal Perl SCALAR).
$set1 = $set->span;
Returns the set span.
Extends a set until another:
0,5,7 -> until 2,6,10
gives
[0..2), [5..6), [7..10)
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
$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( parameters ) Makes equal-sized subsets. Returns an ordered set of equal-sized subsets. Example: $set = Set::Infinite->new([1,3]); print join (" ", $set->quantize( quant => 1 ) ); Gives: [1..2) [2..3) [3..4)
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 ( 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 ( 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
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( "My::Class::Name" )
Chooses a default object data type.
default is none (a normal perl SCALAR).
$set->_backtrack( 'intersection', $b );
Internal function to evaluate recurrences.
$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.
$set->fixtype;
Internal function to fix the result of operations that use the numeric() function.
$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, $min_is_open) = $set->min_a;
($max, $max_is_open) = $set->max_a;
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.
Implements the "comparison" operator.
Comparison of unbounded recurrences is not implemented.
constructor "span" notation
$set = Set::Infinite->new(10,1);
Will be interpreted as [1..10]
constructor "multiple-span" 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.
The base set object, without recurrences, is a Set::Infinite::Basic
.
A recurrence-set 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 syntax-tree 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 syntax-tree param => [ ] # optional arguments for the function }
See modules DateTime::Set, DateTime::Event::Recurrence, DateTime::Event::ICal, DateTime::Event::Cron for up-to-date information on date-sets.
The perl-date-time project <http://datetime.perl.org>
Flavio S. Glock <fglock@gmail.com>
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.