Even if you could state it in a precise formal language the LLM under the agent doesn’t have the capability to understand what the invariant is for and why it’s important. You’ll still get oddly generated code. You might get an LLM that can associate certain tokens with those in the formal language specification which can hold invariants and perhaps even write the proofs… but you’ll still get a whole bunch of other code generated from the informal parts of the prompt.
I agree that simply adding constraints and prompts to you skills and specs isn’t going to prevent these things. Worse, that even if you could invent a better mouse trap the creature will still escape.
The problem is… “elongation:” the addition of code for the sake of the prompt/task/etc. Often less is better. This takes a human with the ability to anticipate what other humans would want/expect. When you need a generator, they’re great but it’s a firehouse that whose use should be restrained a little more.