I'm looking for the formal specification for the Abstract Data Type Algebra for the Associative Array, Associative List (AKA multimap), and other similar ADT to cite for use in a data specification similar to Binary JSON. The Wikipedia Associative Array entry uses non-standard math terminology and their sources are all secondary sources with no original sources. There is an algebra for the Dictionary and it starts with Let x be a set and it defines operations on that set. Who invented the dictionary and when? It should be pretty old, possible from the Journal of the Association of Computer Machinery or similar publication.
The consensus from the available information I've found points to SNOBOL4, released in 1967, as the earliest implementation of "associative arrays".
This post on the Software Engineering community is very similar to your question and has some great info.
Associative arrays were first used in the programming language Snobol4 in the mid-1960s. They are a very common data structure in the Unix environment, being provided as the major data structure by languages like Awk, Perl, etc.