Provided by: libset-infinite-perl_0.65-1_all #### 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.

```

#### SETFUNCTIONS

```   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 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]

symmetric_difference
Returns a set containing elements that are in either set, but not in both. This is the
"set" version of "XOR".

```

#### DENSITYMETHODS

```   real
\$set1 = \$set->real;

Returns a set with density "0".

integer
\$set1 = \$set->integer;

Returns a set with density "1".

```

#### LOGICFUNCTIONS

```   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.

```

#### SCALARFUNCTIONS

```   min
\$i = \$set->min;

max
\$i = \$set->max;

size
\$i = \$set->size;

count
\$i = \$set->count;

```

```   stringification
print \$set;

\$str = "\$set";

comparison
sort

> < == >= <= <=>

```

#### CLASSMETHODS

```           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).

```

#### SPECIALSETFUNCTIONS

```   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 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
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 \$_ 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 { \$_->min + 54, \$_->max + 54 },
backtrack_callback =>
sub { \$_->min - 54, \$_->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').

type
type( "My::Class::Name" )

Chooses a default object data type.

default is none (a normal perl SCALAR).

```

#### INTERNALFUNCTIONS

```   _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

·   "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)

```

#### 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 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
}

```

#### SEEALSO

```       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 (c) 2003 Flavio Soibelmann Glock.  All rights reserved.  This program is free