What Does This Notation Mean Anyway?
David Feller, Joe B. Wells, Fairouz Kamareddine (ULTRA), Sebastien, Carlier

TL;DR
This paper explores the ambiguous notation of Math-BNF (MBNF), illustrating its differences from BNF, and proposes a definition of syntactic math text (SMT) to clarify its usage and structure.
Contribution
It provides examples of MBNF, highlights its differences from BNF, and introduces a formal definition of SMT to improve understanding and application.
Findings
MBNF differs from BNF in entities and operations
A set of examples illustrating MBNF usage
Proposed definition of SMT for better clarity
Abstract
Following the introduction of BNF notation by Backus for the Algol 60 report and subsequent notational variants, a metalanguage involving formal "grammars" has developed for discussing structured objects in Computer Science and Mathematical Logic. We refer to this offspring of BNF as Math-BNF or MBNF, to the original BNF and its notational variants just as BNF, and to aspects common to both as BNF-style. What all BNF-style notations share is the use of production rules roughly of this form: Normally, such a rule says "every instance of for is also an in stance of ". MBNF is distinct from BNF in the entities and operations it allows. Instead of strings, MBNF builds arrangements of symbols that we call math-text. Sometimes "syntax" is defined by interleaving MBNF production rules and…
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Taxonomy
TopicsLogic, programming, and type systems · semigroups and automata theory · Computability, Logic, AI Algorithms
