XML Prompting as Grammar-Constrained Interaction: Fixed-Point Semantics, Convergence Guarantees, and Human-AI Protocols

Structured prompting with XML tags has emerged as an effective way to steer large language models (LLMs) toward parseable, schema - adherent outputs in real - world systems. We develop a logic - first treatment of XML prompting that unifies (i) grammar - constrained decoding, (ii) fixed - point semantics over lattices of hierarchical prompts, and (iii) convergent human - AI interaction loops. We formalize a complete lattice of XML trees under a refinement order and prove that monotone prompt - to - prompt operators admit least fixed points (Knaster - Tarski) that characterize steady - state protocols; under a task - aware contraction metric on trees, we further prove Banach - style convergence of iterative guidance. We instantiate these results with context - free grammars (CFGs) for XML schemas and show how constrained decoding guarantees well - formedness while preserving task performance. A set of multi - layer human - AI interaction recipes demonstrates practical deployment patterns, including multi - pass "plan verify revise" routines and agentic tool use. We provide mathematically complete proofs and tie our framework to recent advances in grammar - aligned decoding, chain - of - verification, and programmatic prompting. Keywords: XML prompting; grammar - constrained decoding; fixed - point theorems; Banach contraction; Knaster - Tarski; modal µ - calculus; structured outputs; human - AI interaction; arXiv cs.AI; arXiv cs.CL