Arity

Example: In the context of Abstract syntax tree (AST)s, if an operator $o$ has an arity $(s_1, \dots, s_n)s$ for $s, s_1, \dots, s_n \in \mathcal{S}$, then $o(a_1, \dots, a_n)$ is of sort $s$ if $a_i$ is of sort $s_i$.

Example: In the context of Abstract binding tree (ABT)s, if an operator $o$ has an arity $(v_1, \dots, v_n)s$, where $s \in \mathcal{S}$ and $v_i$ is$s_1, \dots, s_k.s$, then $o(\vec{x}_1.a_1, \dots, \vec{x}_n.a_n)$ is of sort $s$ if $\vec{x}_i.a_i$ has the corresponding Valence $v_i$.