Reachability Across the NL/PL Boundary: A Taxonomy-Driven Dataflow Model for LLM-Integrated Applications

LLM API calls have become a standard programming primitive, but they create a program boundary that disrupts traditional dataflow analysis. A runtime value may be inserted into a natural-language prompt through a template placeholder, transformed opaquely by the LLM, and returned as code, JSON, or text consumed by downstream logic. Existing analyses such as taint analysis and program slicing require a dataflow summary that describes how a callee maps inputs to outputs; an LLM call provides no such summary, breaking analysis at what we call the NL/PL boundary. We introduce PRISM, the first reachability model for this boundary. PRISM abstracts the missing dataflow summary of an LLM call as placeholder-to-output reachability. Because the LLM's internal transformation is opaque, the only observable signal is the input-output relationship, which spans an unbounded range of behaviors. PRISM therefore uses a finite taxonomy grounded in quantitative information flow theory. It classifies placeholder-output behavior into 25 labels along two dimensions: information preservation and output modality. Each label yields a reachability predicate for a placeholder. The model is sound with respect to its labeling, with residual error bounded empirically. PRISM is dependable and effective. Independent models and human annotators assign its labels consistently (Fleiss' kappa >= 0.72), and the labels cover 8,119 real-world pairs, leaving no pair unclassifiable; the Good-Turing discovery probability is 0.09%. For taint analysis, PRISM nearly doubles the conservative baseline and outperforms a direct LLM baseline, achieving F1 = 81.7%. Across six real OpenClaw CVEs, it detects every vulnerable flow and confirms every patch (F1 = 100%). In backward slicing, it removes about a quarter of irrelevant code without discarding any true dependency.