It is interesting to note that the very first papers related to isomorphism of types were written before the notion itself appeared. Their subjects were the study of equality of terms defined on numbers, the isomorphism of objects in certain categories and the invertibility of $\lambda$-terms, but not the isomorphism of types ‘as such’. One may cite the so-called ‘Tarsky High School Algebra Problem’: whether all identities between terms built from $+, x, \uparrow$, variables and constants are derivable from basic ‘high school equalities’, like $(xy)^z=x^zy^z$. The earliest publications related to this problem date from the 1940s, cf. Birkhoff (1940) – an extensive bibliography may be found in Burris and Yeats (2002).