formulaan

Formulaan is a term used in discussions of formal notation to denote a parameterized template of a mathematical formula together with explicit conditions on its applicability. It is not a single expression but a compound object that combines three elements: a syntactic template F(x1,...,xn), a domain description for the variables and parameters, and a validity condition V that specifies when the template yields a meaningful object.

Example: a formulaan for the family of linear functions with nonzero slope can be described by the template F(a,b,x)=a x + b, with domain a,b∈R and constraint a≠0. The formulaan represents the set { f(x)=a x + b | a,b∈R, a≠0 }.

Usage and status: in theoretical discussions, formulaan helps compare parametric representations and reason about families across contexts; in teaching, they illustrate how schemas relate to concrete instances. Formulaan is not a standard term in mainstream mathematics; the concept is often described using alternative terms such as "formula schema" or "parameterized expression with side conditions."