.. _library_sets:

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

This library provides a set protocol, 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), and an
implementation using *treaps* (tree heaps).

The set representations should be regarded as *opaque terms* and only
constructed, accessed, and updated them using the library predicates.

For small sets, the ordered list implementations are likely to provide
the best performance. For larger sets, the treap implementation likely
provides better performance, notably for the ``memberchk/2``,
``insert/3``, and ``delete/3`` operations. Benchmark both
implementations to select the best one for your application.

The current implementations use ``==/2`` for element comparison and
standard term ordering. This allows non-ground set elements. But
requires caution with later unifications with output arguments and when
using the ``member/2`` and ``select/3`` predicates, which can break the
ordered representation. Note also that, per the ISO Prolog Core
Standard, variable ordering is implementation dependent. This can result
in unexpected results and portability issues.

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

Open the
`../../apis/library_index.html#sets <../../apis/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 and the ordered list
representation, 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.
