Metanotation

Metanotation, or meta-notation, is notation used to describe, specify, or manipulate other notations. It functions as a form of meta-language in which the symbols and rules define the syntax of a primary notation rather than its content. The concept is central to the design of formal languages, programming languages, data schemas, and linguistic annotation schemes, providing a precise vocabulary for structure and rules.

In formal language theory, metanotation includes the conventions used to define grammars, such as Backus–Naur Form (BNF) and its variants (EBNF, ABNF). These systems employ meta-symbols to describe the syntax of the language they define. For example, productions may be written as <expression> ::= <term> | <expression> + <term>, where angle-bracketed items denote nonterminals and the right-hand side specifies permissible forms.

In linguistics and computational linguistics, metanotation describes annotation schemes, tree structures, and glossing conventions. Bracketed representations encode hierarchical structure, parts of speech, or relational features, enabling consistent encoding of data independent of a particular utterance or language.

Applications include compiler design, parser construction, data format specifications, and standards documentation. Metanotation supports precision, interoperability, and automated tooling, but it can become opaque or inconsistent if the meta-language itself is underspecified or if multiple systems are used without clear mappings.

See also: meta-language, grammar, syntax, Backus–Naur Form, Extended Backus–Naur Form, metaprogramming.