`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 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.

sets