Formalized description of data structures - how?

Question

Mathematics

There is an impressive number of data structures that programmers and mathematicians have to work with.
For each type of data structure, mankind has already come up with many ways to formalize the description of a particular data model, ranging from XML schema and SQL DDL to JSON. However, it is absolutely incomprehensible how to mathematically define the structure itself so that it is competent and understandable to the reader. How to show that the data will be organized in a stack or a red-black tree, besides writing these terms or drawing a picture?
I would be grateful for any ideas or tips where such descriptions are used.

Answer 1

Not sure if this will work, but