Extension to CFG, what is it?

Question

Consider the following extension to context-free grammars that permits rules to have in the left-hand side, one (or more) terminal on the right side of the non-terminal. Tha

Answer 1

To answer my question with respect to Prolog's DCG formalism, this extension is now called a semicontext. See N253 DIN Draft for DCGs 2014-04-08 - ISO/IEC WDTR 13211-3:2014-04-08

Given

a1, [b] --> ... .

a2, [b,b] --> ... .

The terminal-sequence [b] is now a semicontext, as well as the terminal-sequence [b,b].

Would the same terminal sequence now appear at the end of the rule, we would have a context:

a3, [b,b] --> ..., [b,b].

So "semi" means here "half" - similar to a semigroup where half of the algebraic properties of a group hold.