We programmed a program to program new programs (2011)

Speaking aside, can LLM agentic coding be seen as a kind of second-order Futamura projection, ? That we instructed a human language interpreter, and using some rules and template generation, internal pattern matchings by LLMs, turned that into code, and then compiled, hence indirectly completing the Futamura loop.

I would still define first-order Futamura projection as the original definition that you have direct encoding and code-to-code expansion and transformation between so.