In mathematical logic, propositional logic and predicate logic, a **well-formed formula**, abbreviated **WFF** or **wff**, often simply **formula**, is a finite sequence of symbols from a given alphabet that is part of a formal language.^{[1]} A formal language can be identified with the set of formulas in the language.

A formula is a syntactic object that can be given a semantic meaning by means of an interpretation. Two key uses of formulas are in propositional logic and predicate logic.

- G
Several authors simply say formula.

^{}[5]^{[6]}^{[7]}^{[8]}Modern usages (especially in the context of computer science with mathematical software such as model checkers, automated theorem provers, interactive theorem provers) tend to retain of the notion of formula only the algebraic concept and to leave the question of well-formedness, i.e. of the concrete string representation of formulas (using this or that symbol for connectives and quantifiers, using this or that parenthesizing convention, using Polish or infix notation, etc.) as a mere notational problem.While the expression

*well-formed formula*is still in use,^{[9]}^{[10]}^{[11]}these authors do not necessarily^{[weasel words]}use it in contradistinction to the old sense of*formula*, which is no longer common in mathematical logic.^{[citation needed]}The expression "well-formed formulas" (WFF) also crept into popular culture.

*WFF*is part of an esoteric pun used in the name of the academic game "WFF 'N PROOF: The Game of Modern Logic," by Layman Allen,^{[12]}developed while he was at Yale Law School (he was later a professor at the University of Michigan). The suite of games is designed to teach the principles of symbolic logic to children (in Polish notation).^{[13]}Its name is an echo of*whiffenpoof*, a nonsense word used as a cheer at Yale University made popular in*The Whiffenpoof Song*and The Whiffenpoofs.^{[14]}