[1] A generative grammar can be seen as a recursive definition in string theory.
Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a free monoid.
In 1956 Alonzo Church wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method".
[2] Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by Hans Hermes and one by Alfred Tarski.
[4] As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of Peirce's type-token distinction.