# `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 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_protocol.

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.