Editing Well-formed formula (section)

==Usage of the terminology==
In earlier works on mathematical logic (e.g. by [[Alonzo Church|Church]]<ref>Alonzo Church, [1996] (1944), Introduction to mathematical logic, page 49</ref>), formulas referred to any strings of symbols and among these strings, well-formed formulas were the strings that followed the formation rules of (correct) formulas.

Several authors simply say formula.<ref>[[David Hilbert|Hilbert, David]]; [[Wilhelm Ackermann|Ackermann, Wilhelm]] (1950) [1937], Principles of Mathematical Logic, New York: Chelsea</ref><ref>Hodges, Wilfrid (1997), A shorter model theory, Cambridge University Press, {{isbn|978-0-521-58713-6}}</ref><ref>[[Jon Barwise|Barwise, Jon]], ed. (1982), Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland, {{isbn|978-0-444-86388-1}}</ref><ref>Cori, Rene; Lascar, Daniel (2000), Mathematical Logic: A Course with Exercises, Oxford University Press, {{isbn|978-0-19-850048-3}}</ref> Modern usages (especially in the context of computer science with mathematical software such as [[List of model checking tools|model checkers]], [[automated theorem prover]]s, [[Interactive theorem proving|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 [[order of operations|parenthesizing convention]], using [[Polish notation|Polish]] or [[infix notation|infix]] notation, etc.) as a mere notational problem.

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,<ref>Ehrenburg 2002</ref> 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]]).<ref>More technically, [[Propositional calculus|propositional logic]] using the [[Fitch-style calculus]].</ref> Its name is an echo of ''[[whiffenpoof]]'', a [[nonsense word]] used as a [[Cheering|cheer]] at [[Yale University]] made popular in ''The Whiffenpoof Song'' and [[The Whiffenpoofs]].<ref>Allen (1965) acknowledges the pun.</ref>