Formulo

Formulo is a hypothetical mathematical formalism intended to express formulas and their evaluation steps in a machine-readable structure. It provides a typed, tree-based syntax designed to support symbolic manipulation, formal verification, and automatic code or document generation.

Origin and naming: The term Formulo combines ideas from "formula" with a suffix chosen to convey structural syntax. The concept has appeared in theoretical discussions and educational demonstrations since the mid-2010s within mathematical informatics circles as a tool for exploring formula representation. It is not an established standard and remains largely speculative.

Grammar and semantics: Formulo represents expressions as nodes in a syntax tree. The primary elements are terms, operators (unary, binary, and higher-arity), function symbols, variables, and literals. Expressions are typed, with explicit operator signatures, and evaluation rules define how trees reduce to values within a given context. The system supports macros and parameterized expressions for reuse and instantiation.

Implementation and usage: In speculative workflows, Formulo can be serialized to JSON or XML, imported into theorem provers, or exported to LaTeX or MathML for display. A reference interpreter demonstrates evaluation order and type checking, while libraries in various languages illustrate integration with existing tooling.

Examples: The quadratic formula can be encoded as root = (-b + sqrt(b*b - 4*a*c)) / (2*a). A derivative example might express differentiation as diff(f(x), x) with rules showing how standard derivatives are computed within the Formulo framework.

Reception and challenges: Formulo has not gained broad adoption; it faces barriers such as competing notations, learning curve, and interoperability demands. Proponents argue it clarifies structural information for automation, while critics point to redundancy with established standards. Related topics include LaTeX, MathML, OpenMath, and symbolic computation libraries such as SymPy.