The types of Section C.5 of Transducers (Definition C.5.1) are the expressions built from the unit type $\mathbb{1}$, which has the unique element $1$, by the product $A \times B$, the co-product $A + B$ and the list type $A^*$. Every element of a type has a string representation over a fixed alphabet with eight letters

defined by induction on the type: the unique element of $\mathbb{1}$ is $1$, an element of $A + B$ is $L\,a$ or $R\,b$, a pair is $(a, b)$, and a list is $[a_1, \ldots, a_n]$. Through this representation, type-to-type functions can be computed by string-to-string transducers (Definition C.5.2).