Meta Prompting for AI Systems

We introduce Meta Prompting (MP), a framework that emphasizes the formal structure of a task rather than content-specific worked examples. We give a categorical formalization in which a functor maps typed task transformations to typed prompt transformations. Functoriality encodes preservation of identities and composition, but it does not by itself guarantee semantic correctness. We extend MP to Recursive Meta Prompting (RMP), in which a proposer model generates candidate prompt edits, a validator enforces the edit schema, and an executor model uses the resulting prompt. We model the accumulation of valid edit scripts with the Writer monad and their application by a monoid action on prompts. This construction makes accumulated edits independent of parenthesization; it does not guarantee convergence or improved task accuracy. Empirically, a Qwen-72B base model guided by example-free meta-prompts attains 46.3% pass@1 on MATH and 83.5% accuracy on GSM8K. Separately, an MP-CR agent synthesizes a tool-executed Game of 24 solver; the original experiment reports 100% success on 1,362 instances, subject to exact re-verification from the corresponding input and per-instance outputs. The batch amortizes one LLM response across all puzzles, so its token accounting is not protocol-matched to per-instance few-shot or search-based methods.