Formal Notation & Symbol Conventions

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Abstractions about notational and symbolic conventions in formal systems, including comparison and grouping symbols such as the much-greater-than relation and symbols of grouping, programming-language operators like the null coalescing operator and weak symbol, and formal axiomatic encodings of arithmetic such as typographical number theory.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Much-Greater-Than Relation — These relations are known as strict inequalities, meaning that a is strictly less than or strictly greater than b.
• Null coalescing operator — While its behavior differs between implementations, the null coalescing operator generally returns the result of its left-most operand if it exists and is not null, and otherwise returns the right-most operand.
• Symbols of Grouping — Symbols of grouping are paired mathematical delimiters that bind subexpressions, establish scope, and control the order in which an expression is parsed or evaluated.
• Typographical Number Theory — Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher, Bach.
• Weak Symbol — A weak symbol denotes a specially annotated symbol during linking of Executable and Linkable Format (ELF) object files.