> why would we use anything but actual natural language?
Because natural language is not a good tool to describe computational processes.
Which one would you rather write:
(a) p(x) = x^2 + 5x + 4
(b) Let us consider the object in the ring of univariate polynomials with complex coefficients defined by the square of the variable, plus five times the variable plus four.
Every scientific discipline moves away from natural language as soon as possible. Low-code, no-code and the likes have been a dismal failure precisely for this reason. Why would I move back to natural language if I can effectively express my problem in a formal language that I can manipulate at-will?
I am not convinced by the utility in this case. I'm well aware of low code and no code problems, but I am less convinced that the same principles apply to LLM code generation.
By all means use some formal language to describe LLM capabilities and so forth, but the most fantastic thing about using LLMs is that you can convey the why along with the what and get better results and the "why" does not lend itself to expression in formalized notation.
Mathematics is not the only formal languages. Every profession soon invents its own jargon because natural language are too ambiguous. For some that’s enough. But science require more formalism.
Boole’s Laws of Thought or Church’s The Calculi of Lambda-Conversion are mostly describing how to be so precise that the description of the problem equates its solution. But formal languages have their own issues.
Because natural language is not a good tool to describe computational processes.
Which one would you rather write:
(a) p(x) = x^2 + 5x + 4
(b) Let us consider the object in the ring of univariate polynomials with complex coefficients defined by the square of the variable, plus five times the variable plus four.
Every scientific discipline moves away from natural language as soon as possible. Low-code, no-code and the likes have been a dismal failure precisely for this reason. Why would I move back to natural language if I can effectively express my problem in a formal language that I can manipulate at-will?