.. _library_sets:

``sets``
========

This library provides a set protocol and two implementations of this
protocol using *ordered lists*, one of them a parametric object that
takes the type of the set elements as a parameter. Although representing
sets as ordered lists is a common representation, is best practice to
regard sets as opaque terms and only access them using the library
predicates.

API documentation
-----------------

Open the
`../../docs/library_index.html#sets <../../docs/library_index.html#sets>`__
link in a web browser.

Loading
-------

To load all entities in this library, load the ``loader.lgt`` file:

::

   | ?- logtalk_load(sets(loader)).

Testing
-------

To test this library predicates, load the ``tester.lgt`` file:

::

   | ?- logtalk_load(sets(tester)).

Usage
-----

First, select a set implementation. Use the ``set(Type)`` object if you
want to type-check the set elements. Otherwise, use the ``set`` object.

To create a new set, you can use the ``new/1`` predicate. For example:

::

   | ?- set::new(Set).
   Set = []
   yes

You can also create a new set with all unique elements from a list of
terms by using the ``as_set/2`` predicate. For example:

::

   | ?- set::as_set([1,3,2,1,2], Set).
   Set = [1, 2, 3]
   yes

Predicates are provided for the most common set operations. For example:

::

   | ?- set::(
           as_set([1,3,2,1,2], Set1),
           as_set([7,4,2,5,1], Set2),
           intersection(Set1, Set2, Intersection),
           symdiff(Set1, Set2, Difference)
       ).
   Set1 = [1, 2, 3],
   Set2 = [1, 2, 4, 5, 7],
   Intersection = [1, 2],
   Difference = [3, 4, 5, 7]
   yes

When working with a custom type of set elements, the corresponding
object must implement the ``comparingp`` protocol. For example:

::

   :- object(rainbow_colors,
       implements(comparingp)).

       order(red,    1).
       order(orange, 2).
       order(yellow, 3).
       order(green,  4).
       order(blue,   5).
       order(indigo, 6).
       order(violet, 7).

       Color1 < Color2 :-
           order(Color1, N1),
           order(Color2, N2),
           {N1 < N2}.

       Color1 =< Color2 :-
           order(Color1, N1),
           order(Color2, N2),
           {N1 =< N2}.

       ...

   :- end_object.

We can then use this object with the ``set/1`` parametric object. For
example:

::

   | ?- set(rainbow_colors)::as_set([blue, yellow, violet], Set).
   Set = [yellow, blue, violet]
   yes

For details on these and other provided predicates, consult the library
API documentation.

Credits
-------

Some predicates adapted from code authored by Richard O'Keefe.
