Earlier quoted context omitted.
Indeed. Type 0 Grammars are the most powerful grammars we have. https://en.wikipedia.org/wiki/Chomsky_hierarchy#Type-0_gramm... In this type of grammar Godel's incompleteness theorem is equivalent to the Halting problem.
And which programming language did you have in mind?
"Type-0 grammars include all formal grammars. They generate exactly all languages that can be recognized by a Turing machine."