Elements of the Theory of Nested Named Sets
Mark Burgin · Journal Plus Education · 2020
The goal of this paper is exploration of an important phenomenon called nesting, which plays a weighty role in many areas including mathematics and computer science. In mathematics, we can see nesting in algebraic and arithmetical expressions, in functions on rings of functions, in simplicial complexes, in various formulas, and other mathematical constructions. In computer science and technology, there are nested calls; nesting of several levels of subroutines; nesting in recursive calls; nested levels of parentheses in arithmetical expressions; nested blocks of imperative source code such as nested if-clauses, while-clauses or repeat-until clauses; nesting in information hiding; and nested data structures such as records, objects, classes, etc. Here we elaborate mathematical foundations for modeling and study of the systems with nesting as well as for measuring different attributes of nesting.