I would make one small change to the author's analogies of imperative versus declarative and one small change to their description of LLMs for declarative progr

I would make one small change to the author's analogies of imperative versus declarative and one small change to their description of LLMs for declarative programming. First, on imperative versus declarative. I would describe imperative as "giving a list of instructions to follow". The words "instruction" and "direction" are largely synonyms in my mind and the difference may be subtler than the original words they are trying to describe. Instead, I would say that declarative programming gives "a goal and a set of constraints". We describe what we want, not how to get it. A large part of describing what we want is by describing what we don't want or can't do. On using LLMs for declarative programming, I assert that we already do this. Prompt engineering is all about defining a set of constraints on the LLMs response. The goal is often within the system prompt: answer the user's question given the context. The user's request is just one of many constraints on the answer. This declaration in the form of constraints is a direct result of the fact that LLMs operate on conditional probabilities. An LLM chooses each token by taking the list of all possible tokens and their a priori probabilities and conditioning those on the tokens that preceded it. By prefacing the generated output with a list of tokens describing constraints, we condition the LLMs generation to fit those constraints. The generated text is the result of applying the constraints to the space of all possible outcomes. As we know, this isn't perfect. Most declarative languages and their engines use strict logic to limit the generated solutions, whereas LLMs are probabilistic. The constraints aren't specified in concrete terms but as a set of arbitrary tokens whose influence on the generated output is based on frequency of occurrence within a corpus of text rather than any logical rules. Still, the fact that the generated output is the result of conditioning based on a set of tokens provided by the user means that it uses constraints to determine an outcome that fits those constraints, which is exactly how we solve a problem based on a declarative description.