.. index:: single: multisets_protocol
.. _multisets_protocol/0:

.. rst-class:: right

**protocol**

``multisets_protocol``
======================

Protocol for multiset operations over lists.

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

| **Author:** Paulo Moura
| **Version:** 1:0:0
| **Date:** 2026-05-12

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


| **Dependencies:**
|   (none)


| **Remarks:**
|    (none)

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

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

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

.. index:: multisets/3
.. _multisets_protocol/0::multisets/3:

``multisets/3``
^^^^^^^^^^^^^^^

Generates all K-multisets (unordered K-element selections with replacement) of a list using default order.

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

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


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

.. index:: multiset/3
.. _multisets_protocol/0::multiset/3:

``multiset/3``
^^^^^^^^^^^^^^

True iff the third argument is a K-multiset with replacement of a list using default order.

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

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


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

.. index:: multisets/4
.. _multisets_protocol/0::multisets/4:

``multisets/4``
^^^^^^^^^^^^^^^

Generates all K-multisets with the given order: ``default`` or ``lexicographic``.

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

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


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

.. index:: multiset/4
.. _multisets_protocol/0::multiset/4:

``multiset/4``
^^^^^^^^^^^^^^

True iff the fourth argument is a K-multiset with replacement with the given order: ``default`` or ``lexicographic``.

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

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


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

.. index:: distinct_multisets/3
.. _multisets_protocol/0::distinct_multisets/3:

``distinct_multisets/3``
^^^^^^^^^^^^^^^^^^^^^^^^

Generates all distinct K-multisets (deduplicating repeated values in the input list) using default order.

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

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


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

.. index:: distinct_multiset/3
.. _multisets_protocol/0::distinct_multiset/3:

``distinct_multiset/3``
^^^^^^^^^^^^^^^^^^^^^^^

True iff the third argument is a distinct K-multiset with replacement of a list using default order.

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

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


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

.. index:: distinct_multisets/4
.. _multisets_protocol/0::distinct_multisets/4:

``distinct_multisets/4``
^^^^^^^^^^^^^^^^^^^^^^^^

Generates all distinct K-multisets with the given order: ``default`` or ``lexicographic``.

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

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


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

.. index:: distinct_multiset/4
.. _multisets_protocol/0::distinct_multiset/4:

``distinct_multiset/4``
^^^^^^^^^^^^^^^^^^^^^^^

True iff the fourth argument is a distinct K-multiset with replacement with the given order: ``default`` or ``lexicographic``.

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

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


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

.. index:: nth_multiset/4
.. _multisets_protocol/0::nth_multiset/4:

``nth_multiset/4``
^^^^^^^^^^^^^^^^^^

Returns the K-multiset at a given zero-based index using default order.

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

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


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

.. index:: nth_multiset/5
.. _multisets_protocol/0::nth_multiset/5:

``nth_multiset/5``
^^^^^^^^^^^^^^^^^^

Returns the K-multiset at a given zero-based index in the given order: ``default`` or ``lexicographic``.

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

| **Template:**
|    ``nth_multiset(K,List,Order,Index,Multiset)``
| **Mode and number of proofs:**
|    ``nth_multiset(+integer,+list,+atom,+integer,-list)`` - ``zero_or_one``


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

.. index:: multiset_index/4
.. _multisets_protocol/0::multiset_index/4:

``multiset_index/4``
^^^^^^^^^^^^^^^^^^^^

Returns the zero-based index of a K-multiset using default order.

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

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


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

.. index:: multiset_index/5
.. _multisets_protocol/0::multiset_index/5:

``multiset_index/5``
^^^^^^^^^^^^^^^^^^^^

Returns the zero-based index of a K-multiset in the given order: ``default`` or ``lexicographic``.

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

| **Template:**
|    ``multiset_index(K,List,Order,Multiset,Index)``
| **Mode and number of proofs:**
|    ``multiset_index(+integer,+list,+atom,+list,-integer)`` - ``zero_or_one``


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

.. index:: count_multisets/3
.. _multisets_protocol/0::count_multisets/3:

``count_multisets/3``
^^^^^^^^^^^^^^^^^^^^^

Counts the number of K-multisets with replacement of a list.

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

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


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

.. index:: count_distinct_multisets/3
.. _multisets_protocol/0::count_distinct_multisets/3:

``count_distinct_multisets/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Counts the number of distinct K-multisets with replacement of a list (deduplicating repeated values in the input list).

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

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


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

.. index:: nth_distinct_multiset/4
.. _multisets_protocol/0::nth_distinct_multiset/4:

``nth_distinct_multiset/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Returns the distinct K-multiset at a given zero-based index in default generation order.

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

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


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

.. index:: distinct_multiset_index/4
.. _multisets_protocol/0::distinct_multiset_index/4:

``distinct_multiset_index/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Returns the zero-based index of a distinct K-multiset in default generation order.

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

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


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

.. index:: random_multiset/3
.. _multisets_protocol/0::random_multiset/3:

``random_multiset/3``
^^^^^^^^^^^^^^^^^^^^^

Returns a random K-multiset with replacement of a list.

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

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


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

.. index:: sample_multisets/4
.. _multisets_protocol/0::sample_multisets/4:

``sample_multisets/4``
^^^^^^^^^^^^^^^^^^^^^^

Returns SampleCount random K-multisets with replacement of a list, sampled with replacement.

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

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


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

.. index:: random_distinct_multiset/3
.. _multisets_protocol/0::random_distinct_multiset/3:

``random_distinct_multiset/3``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Returns a random distinct K-multiset with replacement of a list (deduplicating repeated values in the input list).

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

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


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

.. index:: sample_distinct_multisets/4
.. _multisets_protocol/0::sample_distinct_multisets/4:

``sample_distinct_multisets/4``
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Returns SampleCount random distinct K-multisets with replacement of a list, sampled with replacement after deduplicating repeated values in the input list.

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

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


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

.. index:: next_multiset/3
.. _multisets_protocol/0::next_multiset/3:

``next_multiset/3``
^^^^^^^^^^^^^^^^^^^

Returns the next distinct multiset value in lexicographic order induced by the first argument.

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

| **Template:**
|    ``next_multiset(List,Multiset,Next)``
| **Mode and number of proofs:**
|    ``next_multiset(+list,+list,-list)`` - ``zero_or_one``


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

.. index:: previous_multiset/3
.. _multisets_protocol/0::previous_multiset/3:

``previous_multiset/3``
^^^^^^^^^^^^^^^^^^^^^^^

Returns the previous distinct multiset value in lexicographic order induced by the first argument.

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

| **Template:**
|    ``previous_multiset(List,Multiset,Previous)``
| **Mode and number of proofs:**
|    ``previous_multiset(+list,+list,-list)`` - ``zero_or_one``


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

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

(none)

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

(none)

Operators
---------

(none)