.. index:: single: combinations_protocol
.. _combinations_protocol/0:

.. rst-class:: right

**protocol**

``combinations_protocol``
=========================

Protocol for combinations operations over lists.

| **Availability:** 
|    ``logtalk_load(combinations(loader))``

| **Author:** Paulo Moura
| **Version:** 1:0:0
| **Date:** 2026-02-26

| **Compilation flags:**
|    ``static``


| **Dependencies:**
|   (none)


| **Remarks:**
|    (none)

| **Inherited public predicates:**
|    (none)

.. contents::
   :local:
   :backlinks: top

Public predicates
-----------------

.. index:: combinations/3
.. _combinations_protocol/0::combinations/3:

``combinations/3``
^^^^^^^^^^^^^^^^^^

Generates all K-element combinations of a list.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combinations(K,List,Combinations)``
| **Mode and number of proofs:**
|    ``combinations(+integer,+list,-list)`` - ``one``


------------

.. index:: combination/3
.. _combinations_protocol/0::combination/3:

``combination/3``
^^^^^^^^^^^^^^^^^

True iff the third argument is a K-element combination of a list.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combination(K,List,Combination)``
| **Mode and number of proofs:**
|    ``combination(+integer,+list,-list)`` - ``one_or_more``


------------

.. index:: combinations/4
.. _combinations_protocol/0::combinations/4:

``combinations/4``
^^^^^^^^^^^^^^^^^^

Generates all K-element combinations with the given order: ``default``, ``lexicographic``, or ``shortlex``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combinations(K,List,Order,Combinations)``
| **Mode and number of proofs:**
|    ``combinations(+integer,+list,+atom,-list)`` - ``one``


------------

.. index:: combination/4
.. _combinations_protocol/0::combination/4:

``combination/4``
^^^^^^^^^^^^^^^^^

True iff the fourth argument is a K-element combination with the given order: ``default``, ``lexicographic``, or ``shortlex``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combination(K,List,Order,Combination)``
| **Mode and number of proofs:**
|    ``combination(+integer,+list,+atom,-list)`` - ``one_or_more``


------------

.. index:: combinations_with_replacement/3
.. _combinations_protocol/0::combinations_with_replacement/3:

``combinations_with_replacement/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Generates all K-element combinations with replacement.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combinations_with_replacement(K,List,Combinations)``
| **Mode and number of proofs:**
|    ``combinations_with_replacement(+integer,+list,-list)`` - ``one``


------------

.. index:: combinations_with_replacement/4
.. _combinations_protocol/0::combinations_with_replacement/4:

``combinations_with_replacement/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Generates all K-element combinations with replacement with the given order: ``default``, ``lexicographic``, or ``shortlex``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combinations_with_replacement(K,List,Order,Combinations)``
| **Mode and number of proofs:**
|    ``combinations_with_replacement(+integer,+list,+atom,-list)`` - ``one``


------------

.. index:: combination_with_replacement/3
.. _combinations_protocol/0::combination_with_replacement/3:

``combination_with_replacement/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

True iff the third argument is a K-element combination with replacement.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combination_with_replacement(K,List,Combination)``
| **Mode and number of proofs:**
|    ``combination_with_replacement(+integer,+list,-list)`` - ``one_or_more``


------------

.. index:: combination_with_replacement/4
.. _combinations_protocol/0::combination_with_replacement/4:

``combination_with_replacement/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

True iff the fourth argument is a K-element combination with replacement with the given order: ``default``, ``lexicographic``, or ``shortlex``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combination_with_replacement(K,List,Order,Combination)``
| **Mode and number of proofs:**
|    ``combination_with_replacement(+integer,+list,+atom,-list)`` - ``one_or_more``


------------

.. index:: distinct_combinations/3
.. _combinations_protocol/0::distinct_combinations/3:

``distinct_combinations/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Generates all distinct K-element combinations of a list (deduplicating equal-valued combinations).

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``distinct_combinations(K,List,Combinations)``
| **Mode and number of proofs:**
|    ``distinct_combinations(+integer,+list,-list)`` - ``one``


------------

.. index:: distinct_combination/3
.. _combinations_protocol/0::distinct_combination/3:

``distinct_combination/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^

True iff the third argument is a distinct K-element combination of a list.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``distinct_combination(K,List,Combination)``
| **Mode and number of proofs:**
|    ``distinct_combination(+integer,+list,-list)`` - ``one_or_more``


------------

.. index:: distinct_combinations/4
.. _combinations_protocol/0::distinct_combinations/4:

``distinct_combinations/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Generates all distinct K-element combinations with the given order: ``default``, ``lexicographic``, or ``shortlex``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``distinct_combinations(K,List,Order,Combinations)``
| **Mode and number of proofs:**
|    ``distinct_combinations(+integer,+list,+atom,-list)`` - ``one``


------------

.. index:: distinct_combination/4
.. _combinations_protocol/0::distinct_combination/4:

``distinct_combination/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^

True iff the fourth argument is a distinct K-element combination with the given order: ``default``, ``lexicographic``, or ``shortlex``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``distinct_combination(K,List,Order,Combination)``
| **Mode and number of proofs:**
|    ``distinct_combination(+integer,+list,+atom,-list)`` - ``one_or_more``


------------

.. index:: nth_combination/4
.. _combinations_protocol/0::nth_combination/4:

``nth_combination/4``
^^^^^^^^^^^^^^^^^^^^^

Returns the combination at a given zero-based index.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``nth_combination(K,List,Index,Combination)``
| **Mode and number of proofs:**
|    ``nth_combination(+integer,+list,+integer,-list)`` - ``zero_or_one``


------------

.. index:: combination_index/4
.. _combinations_protocol/0::combination_index/4:

``combination_index/4``
^^^^^^^^^^^^^^^^^^^^^^^

Returns the zero-based index of a combination.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``combination_index(K,List,Combination,Index)``
| **Mode and number of proofs:**
|    ``combination_index(+integer,+list,+list,-integer)`` - ``zero_or_one``


------------

.. index:: count_combinations/3
.. _combinations_protocol/0::count_combinations/3:

``count_combinations/3``
^^^^^^^^^^^^^^^^^^^^^^^^

Counts the number of K-element combinations of a list.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``count_combinations(K,List,Count)``
| **Mode and number of proofs:**
|    ``count_combinations(+integer,+list,-integer)`` - ``one``


------------

.. index:: count_combinations_with_replacement/3
.. _combinations_protocol/0::count_combinations_with_replacement/3:

``count_combinations_with_replacement/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Counts the number of K-element combinations with replacement of a list.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``count_combinations_with_replacement(K,List,Count)``
| **Mode and number of proofs:**
|    ``count_combinations_with_replacement(+integer,+list,-integer)`` - ``one``


------------

.. index:: random_combination/3
.. _combinations_protocol/0::random_combination/3:

``random_combination/3``
^^^^^^^^^^^^^^^^^^^^^^^^

Returns a random K-element combination of a list.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``random_combination(K,List,Combination)``
| **Mode and number of proofs:**
|    ``random_combination(+integer,+list,-list)`` - ``zero_or_one``


------------

Protected predicates
--------------------

(none)

Private predicates
------------------

(none)

Operators
---------

(none)