.. ## Copyright (c) Lawrence Livermore National Security, LLC and other
.. ## Axom Project Contributors. See top-level LICENSE and COPYRIGHT
.. ## files for dates and other details.
.. ##
.. ## SPDX-License-Identifier: (BSD-3-Clause)

.. _srm-label:

=============
Core concepts
=============

Describe Slam concepts, what they mean, how they are used, etc.

.. figure:: figs/set_relation_map.png
   :figwidth: 400px
   :alt: Sets, relations and maps in slam
   :align: center

   A **relation** (blue lines) between two **sets** (ovals with red and green dots, as elements)
   and a **map** of scalar values (brown) on the second set.

.. _set-concept-label:

Set
===

* Taxonomy of set types (OrderedSet, IndirectionSet, Subset, static vs. dynamic)
* Simple API (including semantics of operator[] and iterators )
* Example to show how we iterate through a set

.. Future
   Discuss different indexing schemes for ProductSets


.. _relation-concept-label:

Relation
========

* Relational operator (from element of Set A to set of elements in Set B)
* Taxonomy:
    * Cardinality: Fixed vs Variable number of elements per relation
    * Mutability: Static vs. Dynamic relation
    * Storage: Implicit vs. Explicit (e.g. product set)
* Simple API (including semantics of operator[] )
* Three ways to iterate through a relations
    * Double subscript
    * Separate subscripts
    * Iterators


.. _map-concept-label:

Map
===

* Data associated with all members of a set
* Simple API (including semantics of operator[] )