Let me define the following "grammar":
$$A_0 \leftarrow 1$$
$$A_{i+1} \leftarrow A_i \mid A_i \ K_{i+1} \mid A_i \ K_{i+1} \ A_i$$
where $1$ and $K_i$ are terminals (infinite amount of them: $K_1, K_2, \dots$ ), $A_0, A_1, \dots$ are non-terminals, $\mid$ means alternative, $\leftarrow$ defines a non-terminal, $i$ is an integer such that $i \geq 0$.
That is, it looks like a grammar composed of an infinite number of rules and terminals.
My questions are:
- can I call such a construction a "grammar"?
- in which grammar category can I include it?
- have such structures been studied before, can anyone give links or bibliographic references?
Thanks a lot.