I'm trying to formally describe a production rule $$x \rightarrow \text{foo}$$ in a context-free grammar, but I don't know the value of the right-hand side (only that there is a production rule of the form $x \rightarrow \text{foo}$).
This notation appears within an algorithm, where the algorithm searches for the rule of the form $x \rightarrow \text{foo}$ and changes the $\text{foo}$-value by appending a string. So the notation $x \rightarrow \alpha$ seems unsuitable since $\alpha$ changes over as the algorithm proceeds.
Question: How would one ordinarily formally write a production rule $x \rightarrow \text{foo}$ where I don't know what $\text{foo}$ is, and the value of $\text{foo}$ will change over time?
I'm new to this topic, so I'm interested in what notation is used for $\text{foo}$ ordinarily. Surely someone has dealt with this notation before and knows the best way to deal with it.
Algorithm 3.40 on p.117 of Elements of Compiler Design By Alexander Meduna has notation for selecting and modifying rules, treating the rule set as a mutable set. You could represent $\text{foo}$ using an uppercase variable like $X$ or $X_{\text{foo}}$ and modify it as needed.