# `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 solution, the best practice is to regard sets as opaque terms and only construct, access, and update them using the library predicates. For better performance when handling large sets, alternative implementations of the protocol can always be written.

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 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.