NAME
Set::Infinite - Sets of intervals
SYNOPSIS
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 ] );$set1->union($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 ] );$set1->intersection($set2);# output: [8..12]
complement
minus
difference
$set=$set->complement;
Returns the set of all elements that don't belong to the set.
$set1= new Set::Infinite( [ 1, 4 ], [ 8, 12 ] );$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 ] );$set1->minus($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
$set;$str="$set";
See also: as_string.
comparison
sort> < == >= <= <=>
See also: spaceship method.
CLASS METHODS
Set::Infinite->separators(@i)chooses the interval separatorsforstringification.defaultare [ ] ( )'..'','.infreturns an'Infinity'number.minus_infreturns'-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 ->until2,6,10
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($set2);
The method returns a new set, containing all spans that are intersected by the given set.
Unlike the intersection method, the spans are not modified. See diagram below:
set1 [....] [....] [....] [....]set2 [................]intersection [.] [....] [.]intersected_spans [....] [....] [....]
quantize
quantize( parameters )Makes equal-sized subsets.Returns an ordered set of equal-sized subsets.Example:$set= Set::Infinite->new([1,3]);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=Allcount -default=Infinity0 1 2 3 4 5 6 7 8# original set0 1 2# count => 31 6# by => [ -2, 1 ]
offset
offset ( parameters )
Offsets the subsets. Parameters:
value -default=[0,0]mode -default='offset'. Possiblevaluesare:'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 "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"
$set= Set::Infinite->new(1..3);Will be interpreted as [1..2],3 instead of [1,2,3]. You probably want ->new(1,3) instead.
INTERNALS
The base set object, without recurrences, is a Set::Infinite::Basic.
A recurrence-set is represented by a method name, one or two parent objects, and extra arguments. The list key is set to an empty array, and the too_complex key is set to 1.
This is a structure that holds the union of two "complex sets":
{too_complex=> 1,# "this is a recurrence"list=> [ ],# not usedmethod=>'union',# function nameparent=> [$set1,$set2],# "leaves" in the syntax-treeparam=> [ ]# optional arguments for the function}
This is a structure that holds the complement of a "complex set":
{too_complex=> 1,# "this is a recurrence"list=> [ ],# not usedmethod=>'complement',# function nameparent=>$set,# "leaf" in the syntax-treeparam=> [ ]# optional arguments for the function}
SEE ALSO
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>
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.