name of this notation for defining a set/type: e.g. $\mathbb N = 0 | \sigma \mathbb N$, or e.g. $S = 0 | 1 | SS$?

Question

This is a notation that I've often seen used to define sets: To define the natural numbers: $$\mathbb N = 0 | \sigma \mathbb N,$$ which gives us $0,\sigma 0, \sigma\sigma 0, ...$

$$S = 0 | 1 | SS,$$ which gives us $0,1,00,01,10,11,000,001...$

What is the name of this notation for recursively defining sets?

Answer 1

These are production rules of a context-free grammar.