notationsform

Notationsform is a term used in the study of notational systems to describe the particular arrangement and representation of symbols used to express objects, operations, or relations within a domain. A notationsform encompasses the symbol set (the alphabet of signs), the formation rules that specify how symbols may be combined, and the typographic or graphical conventions that affect appearance and interpretation. It also covers the spatial layout, such as whether notation is linear or graphical, and how that layout influences readability and parsing.

Key components typically associated with a notationsform include the syntax or grammar that governs valid expressions, the semantics or intended meaning of expressions, and the conventions for precedence, associativity, grouping, and scope. These elements determine how an expression is constructed and how it is interpreted by readers or machines. Notationsforms can be linear, as in most textual mathematical expressions, or graphical and symbolic, as in music notation or certain diagrammatic representations. They may be static, with fixed symbols and rules, or dynamic, adapting to context or user interaction.

The concept is used to compare different notational traditions, to analyze how changes in form affect comprehension and computation, and to guide the design of new notations in mathematics, computer science, and related fields. Notationsform is distinct from the broader notion of a notation system; it focuses on the concrete arrangement and appearance of symbols, while a notation system also encompasses intended meanings and usage guidelines. Examples include infix mathematical notation, prefix notation in programming, and various graphical notations in science.