What does $\sigma(t_0, \ldots, t_{n-1}) \in \mathcal{T}_{\Sigma}^{0}$ in this paper mean? The paper is &quot;Mappings and Grammars on Trees&quot; by William C. Rounds. There was a definition of ranked alphabet in page 3 and I can't understand the second part of the definition.

Definition. A ranked alphabet is a pair $(\Sigma, r)$ where $\Sigma$ is finite, and $r: \Sigma \rightarrow \mathbb{N}$.
We set $\Sigma_n = r^{-1}\{n\}$
Let $(\Sigma, r)$ be a ranked alphabet. The set $\mathcal{T}_{\Sigma}^{0}$ (the constant $\Sigma$-terms) is the smallest set of strings such that:
$\ldots$
(b) if $t_0, \ldots, t_{n-1} \in T_{\Sigma}^{0}$, and $\sigma \in \Sigma_{n}$, then $\sigma(t_0, \ldots, t_{n-1}) \in \mathcal{T}_{\Sigma}^{0}$

The $\sigma$ should be set of the alphabet which is ranked $n$, how can a set of alphabet become a function?
Thank you.
You're over-thinking it. It just says that, if $t_0$, ..., $t_{n-1}$ are in $T^0_\Sigma$ and $\sigma$ is a symbol in the alphabet $\Sigma_n$, then the string consisting of $\sigma$, followed by $($, followed by... is in $T^0_\Sigma$