Editing Associative array (section)

===Properties===

The operations of the associative array should satisfy various properties:<ref name="Black">{{cite web |last1=Black |first1=Paul E. |last2=Stewart |first2=Rob |title=dictionary |url=https://xlinux.nist.gov/dads/HTML/dictionary.html |website=Dictionary of Algorithms and Data Structures |access-date=26 January 2022 |date=2 November 2020}}</ref>
* <code>lookup(k, insert(j, v, D)) = if k == j then v else lookup(k, D)</code>
* <code>lookup(k, new()) = fail</code>, where <code>fail</code> is an exception or default value
* <code>remove(k, insert(j, v, D)) = if k == j then remove(k, D) else insert(j, v, remove(k, D))</code>
* <code>remove(k, new()) = new()</code>
where <code>k</code> and <code>j</code> are keys, <code>v</code> is a value, <code>D</code> is an associative array, and <code>new()</code> creates a new, empty associative array.